1,1,94,0,0.417762," ","integrate(x^m*(B*x+A)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{{\left({\left(B c m^{2} + 5 \, B c m + 6 \, B c\right)} x^{4} + {\left({\left(B b + A c\right)} m^{2} + 8 \, B b + 8 \, A c + 6 \, {\left(B b + A c\right)} m\right)} x^{3} + {\left(A b m^{2} + 7 \, A b m + 12 \, A b\right)} x^{2}\right)} x^{m}}{m^{3} + 9 \, m^{2} + 26 \, m + 24}"," ",0,"((B*c*m^2 + 5*B*c*m + 6*B*c)*x^4 + ((B*b + A*c)*m^2 + 8*B*b + 8*A*c + 6*(B*b + A*c)*m)*x^3 + (A*b*m^2 + 7*A*b*m + 12*A*b)*x^2)*x^m/(m^3 + 9*m^2 + 26*m + 24)","B",0
2,1,29,0,0.355438," ","integrate(x^3*(B*x+A)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{7} x^{7} c B + \frac{1}{6} x^{6} b B + \frac{1}{6} x^{6} c A + \frac{1}{5} x^{5} b A"," ",0,"1/7*x^7*c*B + 1/6*x^6*b*B + 1/6*x^6*c*A + 1/5*x^5*b*A","A",0
3,1,29,0,0.352941," ","integrate(x^2*(B*x+A)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{6} x^{6} c B + \frac{1}{5} x^{5} b B + \frac{1}{5} x^{5} c A + \frac{1}{4} x^{4} b A"," ",0,"1/6*x^6*c*B + 1/5*x^5*b*B + 1/5*x^5*c*A + 1/4*x^4*b*A","A",0
4,1,29,0,0.334910," ","integrate(x*(B*x+A)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{5} x^{5} c B + \frac{1}{4} x^{4} b B + \frac{1}{4} x^{4} c A + \frac{1}{3} x^{3} b A"," ",0,"1/5*x^5*c*B + 1/4*x^4*b*B + 1/4*x^4*c*A + 1/3*x^3*b*A","A",0
5,1,29,0,0.347889," ","integrate((B*x+A)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} b B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} b A"," ",0,"1/4*x^4*c*B + 1/3*x^3*b*B + 1/3*x^3*c*A + 1/2*x^2*b*A","A",0
6,1,24,0,0.389481," ","integrate((B*x+A)*(c*x^2+b*x)/x,x, algorithm=""fricas"")","\frac{1}{3} \, B c x^{3} + A b x + \frac{1}{2} \, {\left(B b + A c\right)} x^{2}"," ",0,"1/3*B*c*x^3 + A*b*x + 1/2*(B*b + A*c)*x^2","A",0
7,1,22,0,0.393650," ","integrate((B*x+A)*(c*x^2+b*x)/x^2,x, algorithm=""fricas"")","\frac{1}{2} \, B c x^{2} + A b \log\left(x\right) + {\left(B b + A c\right)} x"," ",0,"1/2*B*c*x^2 + A*b*log(x) + (B*b + A*c)*x","A",0
8,1,26,0,0.394736," ","integrate((B*x+A)*(c*x^2+b*x)/x^3,x, algorithm=""fricas"")","\frac{B c x^{2} + {\left(B b + A c\right)} x \log\left(x\right) - A b}{x}"," ",0,"(B*c*x^2 + (B*b + A*c)*x*log(x) - A*b)/x","A",0
9,1,29,0,0.398304," ","integrate((B*x+A)*(c*x^2+b*x)/x^4,x, algorithm=""fricas"")","\frac{2 \, B c x^{2} \log\left(x\right) - A b - 2 \, {\left(B b + A c\right)} x}{2 \, x^{2}}"," ",0,"1/2*(2*B*c*x^2*log(x) - A*b - 2*(B*b + A*c)*x)/x^2","A",0
10,1,27,0,0.388598," ","integrate((B*x+A)*(c*x^2+b*x)/x^5,x, algorithm=""fricas"")","-\frac{6 \, B c x^{2} + 2 \, A b + 3 \, {\left(B b + A c\right)} x}{6 \, x^{3}}"," ",0,"-1/6*(6*B*c*x^2 + 2*A*b + 3*(B*b + A*c)*x)/x^3","A",0
11,1,27,0,0.387389," ","integrate((B*x+A)*(c*x^2+b*x)/x^6,x, algorithm=""fricas"")","-\frac{6 \, B c x^{2} + 3 \, A b + 4 \, {\left(B b + A c\right)} x}{12 \, x^{4}}"," ",0,"-1/12*(6*B*c*x^2 + 3*A*b + 4*(B*b + A*c)*x)/x^4","A",0
12,1,27,0,0.387640," ","integrate((B*x+A)*(c*x^2+b*x)/x^7,x, algorithm=""fricas"")","-\frac{20 \, B c x^{2} + 12 \, A b + 15 \, {\left(B b + A c\right)} x}{60 \, x^{5}}"," ",0,"-1/60*(20*B*c*x^2 + 12*A*b + 15*(B*b + A*c)*x)/x^5","A",0
13,1,27,0,0.373558," ","integrate((B*x+A)*(c*x^2+b*x)/x^8,x, algorithm=""fricas"")","-\frac{15 \, B c x^{2} + 10 \, A b + 12 \, {\left(B b + A c\right)} x}{60 \, x^{6}}"," ",0,"-1/60*(15*B*c*x^2 + 10*A*b + 12*(B*b + A*c)*x)/x^6","A",0
14,1,217,0,0.419980," ","integrate(x^m*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{{\left({\left(B c^{2} m^{3} + 12 \, B c^{2} m^{2} + 47 \, B c^{2} m + 60 \, B c^{2}\right)} x^{6} + {\left({\left(2 \, B b c + A c^{2}\right)} m^{3} + 144 \, B b c + 72 \, A c^{2} + 13 \, {\left(2 \, B b c + A c^{2}\right)} m^{2} + 54 \, {\left(2 \, B b c + A c^{2}\right)} m\right)} x^{5} + {\left({\left(B b^{2} + 2 \, A b c\right)} m^{3} + 90 \, B b^{2} + 180 \, A b c + 14 \, {\left(B b^{2} + 2 \, A b c\right)} m^{2} + 63 \, {\left(B b^{2} + 2 \, A b c\right)} m\right)} x^{4} + {\left(A b^{2} m^{3} + 15 \, A b^{2} m^{2} + 74 \, A b^{2} m + 120 \, A b^{2}\right)} x^{3}\right)} x^{m}}{m^{4} + 18 \, m^{3} + 119 \, m^{2} + 342 \, m + 360}"," ",0,"((B*c^2*m^3 + 12*B*c^2*m^2 + 47*B*c^2*m + 60*B*c^2)*x^6 + ((2*B*b*c + A*c^2)*m^3 + 144*B*b*c + 72*A*c^2 + 13*(2*B*b*c + A*c^2)*m^2 + 54*(2*B*b*c + A*c^2)*m)*x^5 + ((B*b^2 + 2*A*b*c)*m^3 + 90*B*b^2 + 180*A*b*c + 14*(B*b^2 + 2*A*b*c)*m^2 + 63*(B*b^2 + 2*A*b*c)*m)*x^4 + (A*b^2*m^3 + 15*A*b^2*m^2 + 74*A*b^2*m + 120*A*b^2)*x^3)*x^m/(m^4 + 18*m^3 + 119*m^2 + 342*m + 360)","B",0
15,1,53,0,0.362121," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{2} B + \frac{1}{4} x^{8} c b B + \frac{1}{8} x^{8} c^{2} A + \frac{1}{7} x^{7} b^{2} B + \frac{2}{7} x^{7} c b A + \frac{1}{6} x^{6} b^{2} A"," ",0,"1/9*x^9*c^2*B + 1/4*x^8*c*b*B + 1/8*x^8*c^2*A + 1/7*x^7*b^2*B + 2/7*x^7*c*b*A + 1/6*x^6*b^2*A","A",0
16,1,53,0,0.349306," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{2} B + \frac{2}{7} x^{7} c b B + \frac{1}{7} x^{7} c^{2} A + \frac{1}{6} x^{6} b^{2} B + \frac{1}{3} x^{6} c b A + \frac{1}{5} x^{5} b^{2} A"," ",0,"1/8*x^8*c^2*B + 2/7*x^7*c*b*B + 1/7*x^7*c^2*A + 1/6*x^6*b^2*B + 1/3*x^6*c*b*A + 1/5*x^5*b^2*A","A",0
17,1,53,0,0.344236," ","integrate(x*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} c^{2} B + \frac{1}{3} x^{6} c b B + \frac{1}{6} x^{6} c^{2} A + \frac{1}{5} x^{5} b^{2} B + \frac{2}{5} x^{5} c b A + \frac{1}{4} x^{4} b^{2} A"," ",0,"1/7*x^7*c^2*B + 1/3*x^6*c*b*B + 1/6*x^6*c^2*A + 1/5*x^5*b^2*B + 2/5*x^5*c*b*A + 1/4*x^4*b^2*A","A",0
18,1,53,0,0.337924," ","integrate((B*x+A)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} c^{2} B + \frac{2}{5} x^{5} c b B + \frac{1}{5} x^{5} c^{2} A + \frac{1}{4} x^{4} b^{2} B + \frac{1}{2} x^{4} c b A + \frac{1}{3} x^{3} b^{2} A"," ",0,"1/6*x^6*c^2*B + 2/5*x^5*c*b*B + 1/5*x^5*c^2*A + 1/4*x^4*b^2*B + 1/2*x^4*c*b*A + 1/3*x^3*b^2*A","A",0
19,1,51,0,0.387817," ","integrate((B*x+A)*(c*x^2+b*x)^2/x,x, algorithm=""fricas"")","\frac{1}{5} \, B c^{2} x^{5} + \frac{1}{2} \, A b^{2} x^{2} + \frac{1}{4} \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + \frac{1}{3} \, {\left(B b^{2} + 2 \, A b c\right)} x^{3}"," ",0,"1/5*B*c^2*x^5 + 1/2*A*b^2*x^2 + 1/4*(2*B*b*c + A*c^2)*x^4 + 1/3*(B*b^2 + 2*A*b*c)*x^3","A",0
20,1,48,0,0.390759," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^2,x, algorithm=""fricas"")","\frac{1}{4} \, B c^{2} x^{4} + A b^{2} x + \frac{1}{3} \, {\left(2 \, B b c + A c^{2}\right)} x^{3} + \frac{1}{2} \, {\left(B b^{2} + 2 \, A b c\right)} x^{2}"," ",0,"1/4*B*c^2*x^4 + A*b^2*x + 1/3*(2*B*b*c + A*c^2)*x^3 + 1/2*(B*b^2 + 2*A*b*c)*x^2","A",0
21,1,46,0,0.389218," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^3,x, algorithm=""fricas"")","\frac{1}{3} \, B c^{2} x^{3} + A b^{2} \log\left(x\right) + \frac{1}{2} \, {\left(2 \, B b c + A c^{2}\right)} x^{2} + {\left(B b^{2} + 2 \, A b c\right)} x"," ",0,"1/3*B*c^2*x^3 + A*b^2*log(x) + 1/2*(2*B*b*c + A*c^2)*x^2 + (B*b^2 + 2*A*b*c)*x","A",0
22,1,52,0,0.403048," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^4,x, algorithm=""fricas"")","\frac{B c^{2} x^{3} - 2 \, A b^{2} + 2 \, {\left(2 \, B b c + A c^{2}\right)} x^{2} + 2 \, {\left(B b^{2} + 2 \, A b c\right)} x \log\left(x\right)}{2 \, x}"," ",0,"1/2*(B*c^2*x^3 - 2*A*b^2 + 2*(2*B*b*c + A*c^2)*x^2 + 2*(B*b^2 + 2*A*b*c)*x*log(x))/x","A",0
23,1,53,0,0.408039," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^5,x, algorithm=""fricas"")","\frac{2 \, B c^{2} x^{3} + 2 \, {\left(2 \, B b c + A c^{2}\right)} x^{2} \log\left(x\right) - A b^{2} - 2 \, {\left(B b^{2} + 2 \, A b c\right)} x}{2 \, x^{2}}"," ",0,"1/2*(2*B*c^2*x^3 + 2*(2*B*b*c + A*c^2)*x^2*log(x) - A*b^2 - 2*(B*b^2 + 2*A*b*c)*x)/x^2","A",0
24,1,53,0,0.394554," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^6,x, algorithm=""fricas"")","\frac{6 \, B c^{2} x^{3} \log\left(x\right) - 2 \, A b^{2} - 6 \, {\left(2 \, B b c + A c^{2}\right)} x^{2} - 3 \, {\left(B b^{2} + 2 \, A b c\right)} x}{6 \, x^{3}}"," ",0,"1/6*(6*B*c^2*x^3*log(x) - 2*A*b^2 - 6*(2*B*b*c + A*c^2)*x^2 - 3*(B*b^2 + 2*A*b*c)*x)/x^3","A",0
25,1,51,0,0.392213," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^7,x, algorithm=""fricas"")","-\frac{12 \, B c^{2} x^{3} + 3 \, A b^{2} + 6 \, {\left(2 \, B b c + A c^{2}\right)} x^{2} + 4 \, {\left(B b^{2} + 2 \, A b c\right)} x}{12 \, x^{4}}"," ",0,"-1/12*(12*B*c^2*x^3 + 3*A*b^2 + 6*(2*B*b*c + A*c^2)*x^2 + 4*(B*b^2 + 2*A*b*c)*x)/x^4","A",0
26,1,51,0,0.388499," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^8,x, algorithm=""fricas"")","-\frac{30 \, B c^{2} x^{3} + 12 \, A b^{2} + 20 \, {\left(2 \, B b c + A c^{2}\right)} x^{2} + 15 \, {\left(B b^{2} + 2 \, A b c\right)} x}{60 \, x^{5}}"," ",0,"-1/60*(30*B*c^2*x^3 + 12*A*b^2 + 20*(2*B*b*c + A*c^2)*x^2 + 15*(B*b^2 + 2*A*b*c)*x)/x^5","A",0
27,1,381,0,0.420698," ","integrate(x^m*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{{\left({\left(B c^{3} m^{4} + 22 \, B c^{3} m^{3} + 179 \, B c^{3} m^{2} + 638 \, B c^{3} m + 840 \, B c^{3}\right)} x^{8} + {\left({\left(3 \, B b c^{2} + A c^{3}\right)} m^{4} + 2880 \, B b c^{2} + 960 \, A c^{3} + 23 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m^{3} + 194 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m^{2} + 712 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m\right)} x^{7} + 3 \, {\left({\left(B b^{2} c + A b c^{2}\right)} m^{4} + 1120 \, B b^{2} c + 1120 \, A b c^{2} + 24 \, {\left(B b^{2} c + A b c^{2}\right)} m^{3} + 211 \, {\left(B b^{2} c + A b c^{2}\right)} m^{2} + 804 \, {\left(B b^{2} c + A b c^{2}\right)} m\right)} x^{6} + {\left({\left(B b^{3} + 3 \, A b^{2} c\right)} m^{4} + 1344 \, B b^{3} + 4032 \, A b^{2} c + 25 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} m^{3} + 230 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} m^{2} + 920 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} m\right)} x^{5} + {\left(A b^{3} m^{4} + 26 \, A b^{3} m^{3} + 251 \, A b^{3} m^{2} + 1066 \, A b^{3} m + 1680 \, A b^{3}\right)} x^{4}\right)} x^{m}}{m^{5} + 30 \, m^{4} + 355 \, m^{3} + 2070 \, m^{2} + 5944 \, m + 6720}"," ",0,"((B*c^3*m^4 + 22*B*c^3*m^3 + 179*B*c^3*m^2 + 638*B*c^3*m + 840*B*c^3)*x^8 + ((3*B*b*c^2 + A*c^3)*m^4 + 2880*B*b*c^2 + 960*A*c^3 + 23*(3*B*b*c^2 + A*c^3)*m^3 + 194*(3*B*b*c^2 + A*c^3)*m^2 + 712*(3*B*b*c^2 + A*c^3)*m)*x^7 + 3*((B*b^2*c + A*b*c^2)*m^4 + 1120*B*b^2*c + 1120*A*b*c^2 + 24*(B*b^2*c + A*b*c^2)*m^3 + 211*(B*b^2*c + A*b*c^2)*m^2 + 804*(B*b^2*c + A*b*c^2)*m)*x^6 + ((B*b^3 + 3*A*b^2*c)*m^4 + 1344*B*b^3 + 4032*A*b^2*c + 25*(B*b^3 + 3*A*b^2*c)*m^3 + 230*(B*b^3 + 3*A*b^2*c)*m^2 + 920*(B*b^3 + 3*A*b^2*c)*m)*x^5 + (A*b^3*m^4 + 26*A*b^3*m^3 + 251*A*b^3*m^2 + 1066*A*b^3*m + 1680*A*b^3)*x^4)*x^m/(m^5 + 30*m^4 + 355*m^3 + 2070*m^2 + 5944*m + 6720)","B",0
28,1,77,0,0.354874," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} c^{3} B + \frac{3}{10} x^{10} c^{2} b B + \frac{1}{10} x^{10} c^{3} A + \frac{1}{3} x^{9} c b^{2} B + \frac{1}{3} x^{9} c^{2} b A + \frac{1}{8} x^{8} b^{3} B + \frac{3}{8} x^{8} c b^{2} A + \frac{1}{7} x^{7} b^{3} A"," ",0,"1/11*x^11*c^3*B + 3/10*x^10*c^2*b*B + 1/10*x^10*c^3*A + 1/3*x^9*c*b^2*B + 1/3*x^9*c^2*b*A + 1/8*x^8*b^3*B + 3/8*x^8*c*b^2*A + 1/7*x^7*b^3*A","A",0
29,1,77,0,0.345618," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} c^{3} B + \frac{1}{3} x^{9} c^{2} b B + \frac{1}{9} x^{9} c^{3} A + \frac{3}{8} x^{8} c b^{2} B + \frac{3}{8} x^{8} c^{2} b A + \frac{1}{7} x^{7} b^{3} B + \frac{3}{7} x^{7} c b^{2} A + \frac{1}{6} x^{6} b^{3} A"," ",0,"1/10*x^10*c^3*B + 1/3*x^9*c^2*b*B + 1/9*x^9*c^3*A + 3/8*x^8*c*b^2*B + 3/8*x^8*c^2*b*A + 1/7*x^7*b^3*B + 3/7*x^7*c*b^2*A + 1/6*x^6*b^3*A","A",0
30,1,77,0,0.343042," ","integrate(x*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{3} B + \frac{3}{8} x^{8} c^{2} b B + \frac{1}{8} x^{8} c^{3} A + \frac{3}{7} x^{7} c b^{2} B + \frac{3}{7} x^{7} c^{2} b A + \frac{1}{6} x^{6} b^{3} B + \frac{1}{2} x^{6} c b^{2} A + \frac{1}{5} x^{5} b^{3} A"," ",0,"1/9*x^9*c^3*B + 3/8*x^8*c^2*b*B + 1/8*x^8*c^3*A + 3/7*x^7*c*b^2*B + 3/7*x^7*c^2*b*A + 1/6*x^6*b^3*B + 1/2*x^6*c*b^2*A + 1/5*x^5*b^3*A","A",0
31,1,77,0,0.348755," ","integrate((B*x+A)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{3} B + \frac{3}{7} x^{7} c^{2} b B + \frac{1}{7} x^{7} c^{3} A + \frac{1}{2} x^{6} c b^{2} B + \frac{1}{2} x^{6} c^{2} b A + \frac{1}{5} x^{5} b^{3} B + \frac{3}{5} x^{5} c b^{2} A + \frac{1}{4} x^{4} b^{3} A"," ",0,"1/8*x^8*c^3*B + 3/7*x^7*c^2*b*B + 1/7*x^7*c^3*A + 1/2*x^6*c*b^2*B + 1/2*x^6*c^2*b*A + 1/5*x^5*b^3*B + 3/5*x^5*c*b^2*A + 1/4*x^4*b^3*A","A",0
32,1,73,0,0.383893," ","integrate((B*x+A)*(c*x^2+b*x)^3/x,x, algorithm=""fricas"")","\frac{1}{7} \, B c^{3} x^{7} + \frac{1}{3} \, A b^{3} x^{3} + \frac{1}{6} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + \frac{3}{5} \, {\left(B b^{2} c + A b c^{2}\right)} x^{5} + \frac{1}{4} \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{4}"," ",0,"1/7*B*c^3*x^7 + 1/3*A*b^3*x^3 + 1/6*(3*B*b*c^2 + A*c^3)*x^6 + 3/5*(B*b^2*c + A*b*c^2)*x^5 + 1/4*(B*b^3 + 3*A*b^2*c)*x^4","A",0
33,1,73,0,0.387857," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^2,x, algorithm=""fricas"")","\frac{1}{6} \, B c^{3} x^{6} + \frac{1}{2} \, A b^{3} x^{2} + \frac{1}{5} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{5} + \frac{3}{4} \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} + \frac{1}{3} \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{3}"," ",0,"1/6*B*c^3*x^6 + 1/2*A*b^3*x^2 + 1/5*(3*B*b*c^2 + A*c^3)*x^5 + 3/4*(B*b^2*c + A*b*c^2)*x^4 + 1/3*(B*b^3 + 3*A*b^2*c)*x^3","A",0
34,1,69,0,0.373236," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^3,x, algorithm=""fricas"")","\frac{1}{5} \, B c^{3} x^{5} + A b^{3} x + \frac{1}{4} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{4} + {\left(B b^{2} c + A b c^{2}\right)} x^{3} + \frac{1}{2} \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}"," ",0,"1/5*B*c^3*x^5 + A*b^3*x + 1/4*(3*B*b*c^2 + A*c^3)*x^4 + (B*b^2*c + A*b*c^2)*x^3 + 1/2*(B*b^3 + 3*A*b^2*c)*x^2","B",0
35,1,68,0,0.393449," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^4,x, algorithm=""fricas"")","\frac{1}{4} \, B c^{3} x^{4} + A b^{3} \log\left(x\right) + \frac{1}{3} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} + \frac{3}{2} \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} + {\left(B b^{3} + 3 \, A b^{2} c\right)} x"," ",0,"1/4*B*c^3*x^4 + A*b^3*log(x) + 1/3*(3*B*b*c^2 + A*c^3)*x^3 + 3/2*(B*b^2*c + A*b*c^2)*x^2 + (B*b^3 + 3*A*b^2*c)*x","A",0
36,1,75,0,0.380497," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^5,x, algorithm=""fricas"")","\frac{2 \, B c^{3} x^{4} - 6 \, A b^{3} + 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} + 18 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} + 6 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x \log\left(x\right)}{6 \, x}"," ",0,"1/6*(2*B*c^3*x^4 - 6*A*b^3 + 3*(3*B*b*c^2 + A*c^3)*x^3 + 18*(B*b^2*c + A*b*c^2)*x^2 + 6*(B*b^3 + 3*A*b^2*c)*x*log(x))/x","A",0
37,1,74,0,0.415375," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^6,x, algorithm=""fricas"")","\frac{B c^{3} x^{4} - A b^{3} + 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} + 6 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} \log\left(x\right) - 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x}{2 \, x^{2}}"," ",0,"1/2*(B*c^3*x^4 - A*b^3 + 2*(3*B*b*c^2 + A*c^3)*x^3 + 6*(B*b^2*c + A*b*c^2)*x^2*log(x) - 2*(B*b^3 + 3*A*b^2*c)*x)/x^2","A",0
38,1,75,0,0.397994," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^7,x, algorithm=""fricas"")","\frac{6 \, B c^{3} x^{4} + 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} \log\left(x\right) - 2 \, A b^{3} - 18 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} - 3 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x}{6 \, x^{3}}"," ",0,"1/6*(6*B*c^3*x^4 + 6*(3*B*b*c^2 + A*c^3)*x^3*log(x) - 2*A*b^3 - 18*(B*b^2*c + A*b*c^2)*x^2 - 3*(B*b^3 + 3*A*b^2*c)*x)/x^3","A",0
39,1,75,0,0.400067," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^8,x, algorithm=""fricas"")","\frac{12 \, B c^{3} x^{4} \log\left(x\right) - 3 \, A b^{3} - 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} - 18 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x}{12 \, x^{4}}"," ",0,"1/12*(12*B*c^3*x^4*log(x) - 3*A*b^3 - 12*(3*B*b*c^2 + A*c^3)*x^3 - 18*(B*b^2*c + A*b*c^2)*x^2 - 4*(B*b^3 + 3*A*b^2*c)*x)/x^4","A",0
40,1,73,0,0.385748," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^9,x, algorithm=""fricas"")","-\frac{20 \, B c^{3} x^{4} + 4 \, A b^{3} + 10 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} + 20 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} + 5 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x}{20 \, x^{5}}"," ",0,"-1/20*(20*B*c^3*x^4 + 4*A*b^3 + 10*(3*B*b*c^2 + A*c^3)*x^3 + 20*(B*b^2*c + A*b*c^2)*x^2 + 5*(B*b^3 + 3*A*b^2*c)*x)/x^5","A",0
41,1,73,0,0.386786," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^10,x, algorithm=""fricas"")","-\frac{30 \, B c^{3} x^{4} + 10 \, A b^{3} + 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} + 45 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} + 12 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x}{60 \, x^{6}}"," ",0,"-1/60*(30*B*c^3*x^4 + 10*A*b^3 + 20*(3*B*b*c^2 + A*c^3)*x^3 + 45*(B*b^2*c + A*b*c^2)*x^2 + 12*(B*b^3 + 3*A*b^2*c)*x)/x^6","A",0
42,1,73,0,0.376124," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^11,x, algorithm=""fricas"")","-\frac{140 \, B c^{3} x^{4} + 60 \, A b^{3} + 105 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} + 252 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} + 70 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x}{420 \, x^{7}}"," ",0,"-1/420*(140*B*c^3*x^4 + 60*A*b^3 + 105*(3*B*b*c^2 + A*c^3)*x^3 + 252*(B*b^2*c + A*b*c^2)*x^2 + 70*(B*b^3 + 3*A*b^2*c)*x)/x^7","A",0
43,1,94,0,0.388698," ","integrate(x^4*(e*x+d)/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{3 \, c^{4} e x^{4} + 4 \, {\left(c^{4} d - b c^{3} e\right)} x^{3} - 6 \, {\left(b c^{3} d - b^{2} c^{2} e\right)} x^{2} + 12 \, {\left(b^{2} c^{2} d - b^{3} c e\right)} x - 12 \, {\left(b^{3} c d - b^{4} e\right)} \log\left(c x + b\right)}{12 \, c^{5}}"," ",0,"1/12*(3*c^4*e*x^4 + 4*(c^4*d - b*c^3*e)*x^3 - 6*(b*c^3*d - b^2*c^2*e)*x^2 + 12*(b^2*c^2*d - b^3*c*e)*x - 12*(b^3*c*d - b^4*e)*log(c*x + b))/c^5","A",0
44,1,71,0,0.392253," ","integrate(x^3*(e*x+d)/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, c^{3} e x^{3} + 3 \, {\left(c^{3} d - b c^{2} e\right)} x^{2} - 6 \, {\left(b c^{2} d - b^{2} c e\right)} x + 6 \, {\left(b^{2} c d - b^{3} e\right)} \log\left(c x + b\right)}{6 \, c^{4}}"," ",0,"1/6*(2*c^3*e*x^3 + 3*(c^3*d - b*c^2*e)*x^2 - 6*(b*c^2*d - b^2*c*e)*x + 6*(b^2*c*d - b^3*e)*log(c*x + b))/c^4","A",0
45,1,47,0,0.391343," ","integrate(x^2*(e*x+d)/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{c^{2} e x^{2} + 2 \, {\left(c^{2} d - b c e\right)} x - 2 \, {\left(b c d - b^{2} e\right)} \log\left(c x + b\right)}{2 \, c^{3}}"," ",0,"1/2*(c^2*e*x^2 + 2*(c^2*d - b*c*e)*x - 2*(b*c*d - b^2*e)*log(c*x + b))/c^3","A",0
46,1,24,0,0.377419," ","integrate(x*(e*x+d)/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{c e x + {\left(c d - b e\right)} \log\left(c x + b\right)}{c^{2}}"," ",0,"(c*e*x + (c*d - b*e)*log(c*x + b))/c^2","A",0
47,1,29,0,0.398962," ","integrate((e*x+d)/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{c d \log\left(x\right) - {\left(c d - b e\right)} \log\left(c x + b\right)}{b c}"," ",0,"(c*d*log(x) - (c*d - b*e)*log(c*x + b))/(b*c)","A",0
48,1,41,0,0.397028," ","integrate((e*x+d)/x/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{{\left(c d - b e\right)} x \log\left(c x + b\right) - {\left(c d - b e\right)} x \log\left(x\right) - b d}{b^{2} x}"," ",0,"((c*d - b*e)*x*log(c*x + b) - (c*d - b*e)*x*log(x) - b*d)/(b^2*x)","A",0
49,1,68,0,0.407602," ","integrate((e*x+d)/x^2/(c*x^2+b*x),x, algorithm=""fricas"")","-\frac{2 \, {\left(c^{2} d - b c e\right)} x^{2} \log\left(c x + b\right) - 2 \, {\left(c^{2} d - b c e\right)} x^{2} \log\left(x\right) + b^{2} d - 2 \, {\left(b c d - b^{2} e\right)} x}{2 \, b^{3} x^{2}}"," ",0,"-1/2*(2*(c^2*d - b*c*e)*x^2*log(c*x + b) - 2*(c^2*d - b*c*e)*x^2*log(x) + b^2*d - 2*(b*c*d - b^2*e)*x)/(b^3*x^2)","A",0
50,1,94,0,0.408674," ","integrate((e*x+d)/x^3/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{6 \, {\left(c^{3} d - b c^{2} e\right)} x^{3} \log\left(c x + b\right) - 6 \, {\left(c^{3} d - b c^{2} e\right)} x^{3} \log\left(x\right) - 2 \, b^{3} d - 6 \, {\left(b c^{2} d - b^{2} c e\right)} x^{2} + 3 \, {\left(b^{2} c d - b^{3} e\right)} x}{6 \, b^{4} x^{3}}"," ",0,"1/6*(6*(c^3*d - b*c^2*e)*x^3*log(c*x + b) - 6*(c^3*d - b*c^2*e)*x^3*log(x) - 2*b^3*d - 6*(b*c^2*d - b^2*c*e)*x^2 + 3*(b^2*c*d - b^3*e)*x)/(b^4*x^3)","A",0
51,1,139,0,0.403950," ","integrate(x^5*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2 \, c^{4} e x^{4} + 6 \, b^{3} c d - 6 \, b^{4} e + {\left(3 \, c^{4} d - 4 \, b c^{3} e\right)} x^{3} - 3 \, {\left(3 \, b c^{3} d - 4 \, b^{2} c^{2} e\right)} x^{2} - 6 \, {\left(2 \, b^{2} c^{2} d - 3 \, b^{3} c e\right)} x + 6 \, {\left(3 \, b^{3} c d - 4 \, b^{4} e + {\left(3 \, b^{2} c^{2} d - 4 \, b^{3} c e\right)} x\right)} \log\left(c x + b\right)}{6 \, {\left(c^{6} x + b c^{5}\right)}}"," ",0,"1/6*(2*c^4*e*x^4 + 6*b^3*c*d - 6*b^4*e + (3*c^4*d - 4*b*c^3*e)*x^3 - 3*(3*b*c^3*d - 4*b^2*c^2*e)*x^2 - 6*(2*b^2*c^2*d - 3*b^3*c*e)*x + 6*(3*b^3*c*d - 4*b^4*e + (3*b^2*c^2*d - 4*b^3*c*e)*x)*log(c*x + b))/(c^6*x + b*c^5)","A",0
52,1,111,0,0.391305," ","integrate(x^4*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{c^{3} e x^{3} - 2 \, b^{2} c d + 2 \, b^{3} e + {\left(2 \, c^{3} d - 3 \, b c^{2} e\right)} x^{2} + 2 \, {\left(b c^{2} d - 2 \, b^{2} c e\right)} x - 2 \, {\left(2 \, b^{2} c d - 3 \, b^{3} e + {\left(2 \, b c^{2} d - 3 \, b^{2} c e\right)} x\right)} \log\left(c x + b\right)}{2 \, {\left(c^{5} x + b c^{4}\right)}}"," ",0,"1/2*(c^3*e*x^3 - 2*b^2*c*d + 2*b^3*e + (2*c^3*d - 3*b*c^2*e)*x^2 + 2*(b*c^2*d - 2*b^2*c*e)*x - 2*(2*b^2*c*d - 3*b^3*e + (2*b*c^2*d - 3*b^2*c*e)*x)*log(c*x + b))/(c^5*x + b*c^4)","A",0
53,1,69,0,0.378269," ","integrate(x^3*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{c^{2} e x^{2} + b c e x + b c d - b^{2} e + {\left(b c d - 2 \, b^{2} e + {\left(c^{2} d - 2 \, b c e\right)} x\right)} \log\left(c x + b\right)}{c^{4} x + b c^{3}}"," ",0,"(c^2*e*x^2 + b*c*e*x + b*c*d - b^2*e + (b*c*d - 2*b^2*e + (c^2*d - 2*b*c*e)*x)*log(c*x + b))/(c^4*x + b*c^3)","A",0
54,1,39,0,0.389488," ","integrate(x^2*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{c d - b e - {\left(c e x + b e\right)} \log\left(c x + b\right)}{c^{3} x + b c^{2}}"," ",0,"-(c*d - b*e - (c*e*x + b*e)*log(c*x + b))/(c^3*x + b*c^2)","A",0
55,1,61,0,0.388477," ","integrate(x*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{b c d - b^{2} e - {\left(c^{2} d x + b c d\right)} \log\left(c x + b\right) + {\left(c^{2} d x + b c d\right)} \log\left(x\right)}{b^{2} c^{2} x + b^{3} c}"," ",0,"(b*c*d - b^2*e - (c^2*d*x + b*c*d)*log(c*x + b) + (c^2*d*x + b*c*d)*log(x))/(b^2*c^2*x + b^3*c)","A",0
56,1,111,0,0.403712," ","integrate((e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{b^{2} d + {\left(2 \, b c d - b^{2} e\right)} x - {\left({\left(2 \, c^{2} d - b c e\right)} x^{2} + {\left(2 \, b c d - b^{2} e\right)} x\right)} \log\left(c x + b\right) + {\left({\left(2 \, c^{2} d - b c e\right)} x^{2} + {\left(2 \, b c d - b^{2} e\right)} x\right)} \log\left(x\right)}{b^{3} c x^{2} + b^{4} x}"," ",0,"-(b^2*d + (2*b*c*d - b^2*e)*x - ((2*c^2*d - b*c*e)*x^2 + (2*b*c*d - b^2*e)*x)*log(c*x + b) + ((2*c^2*d - b*c*e)*x^2 + (2*b*c*d - b^2*e)*x)*log(x))/(b^3*c*x^2 + b^4*x)","A",0
57,1,151,0,0.398375," ","integrate((e*x+d)/x/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{b^{3} d - 2 \, {\left(3 \, b c^{2} d - 2 \, b^{2} c e\right)} x^{2} - {\left(3 \, b^{2} c d - 2 \, b^{3} e\right)} x + 2 \, {\left({\left(3 \, c^{3} d - 2 \, b c^{2} e\right)} x^{3} + {\left(3 \, b c^{2} d - 2 \, b^{2} c e\right)} x^{2}\right)} \log\left(c x + b\right) - 2 \, {\left({\left(3 \, c^{3} d - 2 \, b c^{2} e\right)} x^{3} + {\left(3 \, b c^{2} d - 2 \, b^{2} c e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{4} c x^{3} + b^{5} x^{2}\right)}}"," ",0,"-1/2*(b^3*d - 2*(3*b*c^2*d - 2*b^2*c*e)*x^2 - (3*b^2*c*d - 2*b^3*e)*x + 2*((3*c^3*d - 2*b*c^2*e)*x^3 + (3*b*c^2*d - 2*b^2*c*e)*x^2)*log(c*x + b) - 2*((3*c^3*d - 2*b*c^2*e)*x^3 + (3*b*c^2*d - 2*b^2*c*e)*x^2)*log(x))/(b^4*c*x^3 + b^5*x^2)","A",0
58,1,180,0,0.408823," ","integrate((e*x+d)/x^2/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{4} d + 6 \, {\left(4 \, b c^{3} d - 3 \, b^{2} c^{2} e\right)} x^{3} + 3 \, {\left(4 \, b^{2} c^{2} d - 3 \, b^{3} c e\right)} x^{2} - {\left(4 \, b^{3} c d - 3 \, b^{4} e\right)} x - 6 \, {\left({\left(4 \, c^{4} d - 3 \, b c^{3} e\right)} x^{4} + {\left(4 \, b c^{3} d - 3 \, b^{2} c^{2} e\right)} x^{3}\right)} \log\left(c x + b\right) + 6 \, {\left({\left(4 \, c^{4} d - 3 \, b c^{3} e\right)} x^{4} + {\left(4 \, b c^{3} d - 3 \, b^{2} c^{2} e\right)} x^{3}\right)} \log\left(x\right)}{6 \, {\left(b^{5} c x^{4} + b^{6} x^{3}\right)}}"," ",0,"-1/6*(2*b^4*d + 6*(4*b*c^3*d - 3*b^2*c^2*e)*x^3 + 3*(4*b^2*c^2*d - 3*b^3*c*e)*x^2 - (4*b^3*c*d - 3*b^4*e)*x - 6*((4*c^4*d - 3*b*c^3*e)*x^4 + (4*b*c^3*d - 3*b^2*c^2*e)*x^3)*log(c*x + b) + 6*((4*c^4*d - 3*b*c^3*e)*x^4 + (4*b*c^3*d - 3*b^2*c^2*e)*x^3)*log(x))/(b^5*c*x^4 + b^6*x^3)","A",0
59,1,167,0,0.389761," ","integrate(x^6*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{c^{4} e x^{4} - 5 \, b^{3} c d + 7 \, b^{4} e + 2 \, {\left(c^{4} d - 2 \, b c^{3} e\right)} x^{3} + {\left(4 \, b c^{3} d - 11 \, b^{2} c^{2} e\right)} x^{2} - 2 \, {\left(2 \, b^{2} c^{2} d - b^{3} c e\right)} x - 6 \, {\left(b^{3} c d - 2 \, b^{4} e + {\left(b c^{3} d - 2 \, b^{2} c^{2} e\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 2 \, b^{3} c e\right)} x\right)} \log\left(c x + b\right)}{2 \, {\left(c^{7} x^{2} + 2 \, b c^{6} x + b^{2} c^{5}\right)}}"," ",0,"1/2*(c^4*e*x^4 - 5*b^3*c*d + 7*b^4*e + 2*(c^4*d - 2*b*c^3*e)*x^3 + (4*b*c^3*d - 11*b^2*c^2*e)*x^2 - 2*(2*b^2*c^2*d - b^3*c*e)*x - 6*(b^3*c*d - 2*b^4*e + (b*c^3*d - 2*b^2*c^2*e)*x^2 + 2*(b^2*c^2*d - 2*b^3*c*e)*x)*log(c*x + b))/(c^7*x^2 + 2*b*c^6*x + b^2*c^5)","A",0
60,1,131,0,0.392206," ","integrate(x^5*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2 \, c^{3} e x^{3} + 4 \, b c^{2} e x^{2} + 3 \, b^{2} c d - 5 \, b^{3} e + 4 \, {\left(b c^{2} d - b^{2} c e\right)} x + 2 \, {\left(b^{2} c d - 3 \, b^{3} e + {\left(c^{3} d - 3 \, b c^{2} e\right)} x^{2} + 2 \, {\left(b c^{2} d - 3 \, b^{2} c e\right)} x\right)} \log\left(c x + b\right)}{2 \, {\left(c^{6} x^{2} + 2 \, b c^{5} x + b^{2} c^{4}\right)}}"," ",0,"1/2*(2*c^3*e*x^3 + 4*b*c^2*e*x^2 + 3*b^2*c*d - 5*b^3*e + 4*(b*c^2*d - b^2*c*e)*x + 2*(b^2*c*d - 3*b^3*e + (c^3*d - 3*b*c^2*e)*x^2 + 2*(b*c^2*d - 3*b^2*c*e)*x)*log(c*x + b))/(c^6*x^2 + 2*b*c^5*x + b^2*c^4)","A",0
61,1,79,0,0.383957," ","integrate(x^4*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{b c d - 3 \, b^{2} e + 2 \, {\left(c^{2} d - 2 \, b c e\right)} x - 2 \, {\left(c^{2} e x^{2} + 2 \, b c e x + b^{2} e\right)} \log\left(c x + b\right)}{2 \, {\left(c^{5} x^{2} + 2 \, b c^{4} x + b^{2} c^{3}\right)}}"," ",0,"-1/2*(b*c*d - 3*b^2*e + 2*(c^2*d - 2*b*c*e)*x - 2*(c^2*e*x^2 + 2*b*c*e*x + b^2*e)*log(c*x + b))/(c^5*x^2 + 2*b*c^4*x + b^2*c^3)","A",0
62,1,38,0,0.383923," ","integrate(x^3*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{2 \, c e x + c d + b e}{2 \, {\left(c^{4} x^{2} + 2 \, b c^{3} x + b^{2} c^{2}\right)}}"," ",0,"-1/2*(2*c*e*x + c*d + b*e)/(c^4*x^2 + 2*b*c^3*x + b^2*c^2)","A",0
63,1,109,0,0.391706," ","integrate(x^2*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2 \, b c^{2} d x + 3 \, b^{2} c d - b^{3} e - 2 \, {\left(c^{3} d x^{2} + 2 \, b c^{2} d x + b^{2} c d\right)} \log\left(c x + b\right) + 2 \, {\left(c^{3} d x^{2} + 2 \, b c^{2} d x + b^{2} c d\right)} \log\left(x\right)}{2 \, {\left(b^{3} c^{3} x^{2} + 2 \, b^{4} c^{2} x + b^{5} c\right)}}"," ",0,"1/2*(2*b*c^2*d*x + 3*b^2*c*d - b^3*e - 2*(c^3*d*x^2 + 2*b*c^2*d*x + b^2*c*d)*log(c*x + b) + 2*(c^3*d*x^2 + 2*b*c^2*d*x + b^2*c*d)*log(x))/(b^3*c^3*x^2 + 2*b^4*c^2*x + b^5*c)","A",0
64,1,195,0,0.406888," ","integrate(x*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{2 \, b^{3} d + 2 \, {\left(3 \, b c^{2} d - b^{2} c e\right)} x^{2} + 3 \, {\left(3 \, b^{2} c d - b^{3} e\right)} x - 2 \, {\left({\left(3 \, c^{3} d - b c^{2} e\right)} x^{3} + 2 \, {\left(3 \, b c^{2} d - b^{2} c e\right)} x^{2} + {\left(3 \, b^{2} c d - b^{3} e\right)} x\right)} \log\left(c x + b\right) + 2 \, {\left({\left(3 \, c^{3} d - b c^{2} e\right)} x^{3} + 2 \, {\left(3 \, b c^{2} d - b^{2} c e\right)} x^{2} + {\left(3 \, b^{2} c d - b^{3} e\right)} x\right)} \log\left(x\right)}{2 \, {\left(b^{4} c^{2} x^{3} + 2 \, b^{5} c x^{2} + b^{6} x\right)}}"," ",0,"-1/2*(2*b^3*d + 2*(3*b*c^2*d - b^2*c*e)*x^2 + 3*(3*b^2*c*d - b^3*e)*x - 2*((3*c^3*d - b*c^2*e)*x^3 + 2*(3*b*c^2*d - b^2*c*e)*x^2 + (3*b^2*c*d - b^3*e)*x)*log(c*x + b) + 2*((3*c^3*d - b*c^2*e)*x^3 + 2*(3*b*c^2*d - b^2*c*e)*x^2 + (3*b^2*c*d - b^3*e)*x)*log(x))/(b^4*c^2*x^3 + 2*b^5*c*x^2 + b^6*x)","B",0
65,1,234,0,0.408412," ","integrate((e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{b^{4} d - 6 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} x^{3} - 9 \, {\left(2 \, b^{2} c^{2} d - b^{3} c e\right)} x^{2} - 2 \, {\left(2 \, b^{3} c d - b^{4} e\right)} x + 6 \, {\left({\left(2 \, c^{4} d - b c^{3} e\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} x^{3} + {\left(2 \, b^{2} c^{2} d - b^{3} c e\right)} x^{2}\right)} \log\left(c x + b\right) - 6 \, {\left({\left(2 \, c^{4} d - b c^{3} e\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} x^{3} + {\left(2 \, b^{2} c^{2} d - b^{3} c e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}"," ",0,"-1/2*(b^4*d - 6*(2*b*c^3*d - b^2*c^2*e)*x^3 - 9*(2*b^2*c^2*d - b^3*c*e)*x^2 - 2*(2*b^3*c*d - b^4*e)*x + 6*((2*c^4*d - b*c^3*e)*x^4 + 2*(2*b*c^3*d - b^2*c^2*e)*x^3 + (2*b^2*c^2*d - b^3*c*e)*x^2)*log(c*x + b) - 6*((2*c^4*d - b*c^3*e)*x^4 + 2*(2*b*c^3*d - b^2*c^2*e)*x^3 + (2*b^2*c^2*d - b^3*c*e)*x^2)*log(x))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2)","B",0
66,1,263,0,0.410184," ","integrate((e*x+d)/x/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{2 \, b^{5} d + 12 \, {\left(5 \, b c^{4} d - 3 \, b^{2} c^{3} e\right)} x^{4} + 18 \, {\left(5 \, b^{2} c^{3} d - 3 \, b^{3} c^{2} e\right)} x^{3} + 4 \, {\left(5 \, b^{3} c^{2} d - 3 \, b^{4} c e\right)} x^{2} - {\left(5 \, b^{4} c d - 3 \, b^{5} e\right)} x - 12 \, {\left({\left(5 \, c^{5} d - 3 \, b c^{4} e\right)} x^{5} + 2 \, {\left(5 \, b c^{4} d - 3 \, b^{2} c^{3} e\right)} x^{4} + {\left(5 \, b^{2} c^{3} d - 3 \, b^{3} c^{2} e\right)} x^{3}\right)} \log\left(c x + b\right) + 12 \, {\left({\left(5 \, c^{5} d - 3 \, b c^{4} e\right)} x^{5} + 2 \, {\left(5 \, b c^{4} d - 3 \, b^{2} c^{3} e\right)} x^{4} + {\left(5 \, b^{2} c^{3} d - 3 \, b^{3} c^{2} e\right)} x^{3}\right)} \log\left(x\right)}{6 \, {\left(b^{6} c^{2} x^{5} + 2 \, b^{7} c x^{4} + b^{8} x^{3}\right)}}"," ",0,"-1/6*(2*b^5*d + 12*(5*b*c^4*d - 3*b^2*c^3*e)*x^4 + 18*(5*b^2*c^3*d - 3*b^3*c^2*e)*x^3 + 4*(5*b^3*c^2*d - 3*b^4*c*e)*x^2 - (5*b^4*c*d - 3*b^5*e)*x - 12*((5*c^5*d - 3*b*c^4*e)*x^5 + 2*(5*b*c^4*d - 3*b^2*c^3*e)*x^4 + (5*b^2*c^3*d - 3*b^3*c^2*e)*x^3)*log(c*x + b) + 12*((5*c^5*d - 3*b*c^4*e)*x^5 + 2*(5*b*c^4*d - 3*b^2*c^3*e)*x^4 + (5*b^2*c^3*d - 3*b^3*c^2*e)*x^3)*log(x))/(b^6*c^2*x^5 + 2*b^7*c*x^4 + b^8*x^3)","A",0
67,1,349,0,0.434200," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(3 \, B b^{6} - 4 \, A b^{5} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(1280 \, B c^{6} x^{5} + 315 \, B b^{5} c - 420 \, A b^{4} c^{2} + 128 \, {\left(B b c^{5} + 12 \, A c^{6}\right)} x^{4} - 48 \, {\left(3 \, B b^{2} c^{4} - 4 \, A b c^{5}\right)} x^{3} + 56 \, {\left(3 \, B b^{3} c^{3} - 4 \, A b^{2} c^{4}\right)} x^{2} - 70 \, {\left(3 \, B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{15360 \, c^{6}}, \frac{105 \, {\left(3 \, B b^{6} - 4 \, A b^{5} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(1280 \, B c^{6} x^{5} + 315 \, B b^{5} c - 420 \, A b^{4} c^{2} + 128 \, {\left(B b c^{5} + 12 \, A c^{6}\right)} x^{4} - 48 \, {\left(3 \, B b^{2} c^{4} - 4 \, A b c^{5}\right)} x^{3} + 56 \, {\left(3 \, B b^{3} c^{3} - 4 \, A b^{2} c^{4}\right)} x^{2} - 70 \, {\left(3 \, B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{7680 \, c^{6}}\right]"," ",0,"[-1/15360*(105*(3*B*b^6 - 4*A*b^5*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(1280*B*c^6*x^5 + 315*B*b^5*c - 420*A*b^4*c^2 + 128*(B*b*c^5 + 12*A*c^6)*x^4 - 48*(3*B*b^2*c^4 - 4*A*b*c^5)*x^3 + 56*(3*B*b^3*c^3 - 4*A*b^2*c^4)*x^2 - 70*(3*B*b^4*c^2 - 4*A*b^3*c^3)*x)*sqrt(c*x^2 + b*x))/c^6, 1/7680*(105*(3*B*b^6 - 4*A*b^5*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (1280*B*c^6*x^5 + 315*B*b^5*c - 420*A*b^4*c^2 + 128*(B*b*c^5 + 12*A*c^6)*x^4 - 48*(3*B*b^2*c^4 - 4*A*b*c^5)*x^3 + 56*(3*B*b^3*c^3 - 4*A*b^2*c^4)*x^2 - 70*(3*B*b^4*c^2 - 4*A*b^3*c^3)*x)*sqrt(c*x^2 + b*x))/c^6]","A",0
68,1,302,0,0.418972," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{5} - 10 \, A b^{4} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(384 \, B c^{5} x^{4} - 105 \, B b^{4} c + 150 \, A b^{3} c^{2} + 48 \, {\left(B b c^{4} + 10 \, A c^{5}\right)} x^{3} - 8 \, {\left(7 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} x^{2} + 10 \, {\left(7 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, c^{5}}, -\frac{15 \, {\left(7 \, B b^{5} - 10 \, A b^{4} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(384 \, B c^{5} x^{4} - 105 \, B b^{4} c + 150 \, A b^{3} c^{2} + 48 \, {\left(B b c^{4} + 10 \, A c^{5}\right)} x^{3} - 8 \, {\left(7 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} x^{2} + 10 \, {\left(7 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, c^{5}}\right]"," ",0,"[-1/3840*(15*(7*B*b^5 - 10*A*b^4*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(384*B*c^5*x^4 - 105*B*b^4*c + 150*A*b^3*c^2 + 48*(B*b*c^4 + 10*A*c^5)*x^3 - 8*(7*B*b^2*c^3 - 10*A*b*c^4)*x^2 + 10*(7*B*b^3*c^2 - 10*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^5, -1/1920*(15*(7*B*b^5 - 10*A*b^4*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (384*B*c^5*x^4 - 105*B*b^4*c + 150*A*b^3*c^2 + 48*(B*b*c^4 + 10*A*c^5)*x^3 - 8*(7*B*b^2*c^3 - 10*A*b*c^4)*x^2 + 10*(7*B*b^3*c^2 - 10*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
69,1,253,0,0.429873," ","integrate(x*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(48 \, B c^{4} x^{3} + 15 \, B b^{3} c - 24 \, A b^{2} c^{2} + 8 \, {\left(B b c^{3} + 8 \, A c^{4}\right)} x^{2} - 2 \, {\left(5 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, c^{4}}, \frac{3 \, {\left(5 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(48 \, B c^{4} x^{3} + 15 \, B b^{3} c - 24 \, A b^{2} c^{2} + 8 \, {\left(B b c^{3} + 8 \, A c^{4}\right)} x^{2} - 2 \, {\left(5 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, c^{4}}\right]"," ",0,"[-1/384*(3*(5*B*b^4 - 8*A*b^3*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(48*B*c^4*x^3 + 15*B*b^3*c - 24*A*b^2*c^2 + 8*(B*b*c^3 + 8*A*c^4)*x^2 - 2*(5*B*b^2*c^2 - 8*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/c^4, 1/192*(3*(5*B*b^4 - 8*A*b^3*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (48*B*c^4*x^3 + 15*B*b^3*c - 24*A*b^2*c^2 + 8*(B*b*c^3 + 8*A*c^4)*x^2 - 2*(5*B*b^2*c^2 - 8*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
70,1,204,0,0.428984," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{3} x^{2} - 3 \, B b^{2} c + 6 \, A b c^{2} + 2 \, {\left(B b c^{2} + 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c^{3}}, -\frac{3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(8 \, B c^{3} x^{2} - 3 \, B b^{2} c + 6 \, A b c^{2} + 2 \, {\left(B b c^{2} + 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c^{3}}\right]"," ",0,"[-1/48*(3*(B*b^3 - 2*A*b^2*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(8*B*c^3*x^2 - 3*B*b^2*c + 6*A*b*c^2 + 2*(B*b*c^2 + 6*A*c^3)*x)*sqrt(c*x^2 + b*x))/c^3, -1/24*(3*(B*b^3 - 2*A*b^2*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (8*B*c^3*x^2 - 3*B*b^2*c + 6*A*b*c^2 + 2*(B*b*c^2 + 6*A*c^3)*x)*sqrt(c*x^2 + b*x))/c^3]","A",0
71,1,153,0,0.423803," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x,x, algorithm=""fricas"")","\left[-\frac{{\left(B b^{2} - 4 \, A b c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(2 \, B c^{2} x + B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x}}{8 \, c^{2}}, \frac{{\left(B b^{2} - 4 \, A b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(2 \, B c^{2} x + B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x}}{4 \, c^{2}}\right]"," ",0,"[-1/8*((B*b^2 - 4*A*b*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(2*B*c^2*x + B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x))/c^2, 1/4*((B*b^2 - 4*A*b*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (2*B*c^2*x + B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x))/c^2]","A",0
72,1,138,0,0.420862," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(B b + 2 \, A c\right)} \sqrt{c} x \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(B c x - 2 \, A c\right)} \sqrt{c x^{2} + b x}}{2 \, c x}, -\frac{{\left(B b + 2 \, A c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(B c x - 2 \, A c\right)} \sqrt{c x^{2} + b x}}{c x}\right]"," ",0,"[1/2*((B*b + 2*A*c)*sqrt(c)*x*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(B*c*x - 2*A*c)*sqrt(c*x^2 + b*x))/(c*x), -((B*b + 2*A*c)*sqrt(-c)*x*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (B*c*x - 2*A*c)*sqrt(c*x^2 + b*x))/(c*x)]","A",0
73,1,141,0,0.421423," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, B b \sqrt{c} x^{2} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, \sqrt{c x^{2} + b x} {\left(A b + {\left(3 \, B b + A c\right)} x\right)}}{3 \, b x^{2}}, -\frac{2 \, {\left(3 \, B b \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + \sqrt{c x^{2} + b x} {\left(A b + {\left(3 \, B b + A c\right)} x\right)}\right)}}{3 \, b x^{2}}\right]"," ",0,"[1/3*(3*B*b*sqrt(c)*x^2*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*sqrt(c*x^2 + b*x)*(A*b + (3*B*b + A*c)*x))/(b*x^2), -2/3*(3*B*b*sqrt(-c)*x^2*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + sqrt(c*x^2 + b*x)*(A*b + (3*B*b + A*c)*x))/(b*x^2)]","A",0
74,1,55,0,0.404834," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A b^{2} + {\left(5 \, B b c - 2 \, A c^{2}\right)} x^{2} + {\left(5 \, B b^{2} + A b c\right)} x\right)} \sqrt{c x^{2} + b x}}{15 \, b^{2} x^{3}}"," ",0,"-2/15*(3*A*b^2 + (5*B*b*c - 2*A*c^2)*x^2 + (5*B*b^2 + A*b*c)*x)*sqrt(c*x^2 + b*x)/(b^2*x^3)","A",0
75,1,80,0,0.404167," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, A b^{3} - 2 \, {\left(7 \, B b c^{2} - 4 \, A c^{3}\right)} x^{3} + {\left(7 \, B b^{2} c - 4 \, A b c^{2}\right)} x^{2} + 3 \, {\left(7 \, B b^{3} + A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x}}{105 \, b^{3} x^{4}}"," ",0,"-2/105*(15*A*b^3 - 2*(7*B*b*c^2 - 4*A*c^3)*x^3 + (7*B*b^2*c - 4*A*b*c^2)*x^2 + 3*(7*B*b^3 + A*b^2*c)*x)*sqrt(c*x^2 + b*x)/(b^3*x^4)","A",0
76,1,105,0,0.405566," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^6,x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, A b^{4} + 8 \, {\left(3 \, B b c^{3} - 2 \, A c^{4}\right)} x^{4} - 4 \, {\left(3 \, B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{3} + 3 \, {\left(3 \, B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{2} + 5 \, {\left(9 \, B b^{4} + A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x}}{315 \, b^{4} x^{5}}"," ",0,"-2/315*(35*A*b^4 + 8*(3*B*b*c^3 - 2*A*c^4)*x^4 - 4*(3*B*b^2*c^2 - 2*A*b*c^3)*x^3 + 3*(3*B*b^3*c - 2*A*b^2*c^2)*x^2 + 5*(9*B*b^4 + A*b^3*c)*x)*sqrt(c*x^2 + b*x)/(b^4*x^5)","A",0
77,1,129,0,0.407884," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, A b^{5} - 16 \, {\left(11 \, B b c^{4} - 8 \, A c^{5}\right)} x^{5} + 8 \, {\left(11 \, B b^{2} c^{3} - 8 \, A b c^{4}\right)} x^{4} - 6 \, {\left(11 \, B b^{3} c^{2} - 8 \, A b^{2} c^{3}\right)} x^{3} + 5 \, {\left(11 \, B b^{4} c - 8 \, A b^{3} c^{2}\right)} x^{2} + 35 \, {\left(11 \, B b^{5} + A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x}}{3465 \, b^{5} x^{6}}"," ",0,"-2/3465*(315*A*b^5 - 16*(11*B*b*c^4 - 8*A*c^5)*x^5 + 8*(11*B*b^2*c^3 - 8*A*b*c^4)*x^4 - 6*(11*B*b^3*c^2 - 8*A*b^2*c^3)*x^3 + 5*(11*B*b^4*c - 8*A*b^3*c^2)*x^2 + 35*(11*B*b^5 + A*b^4*c)*x)*sqrt(c*x^2 + b*x)/(b^5*x^6)","A",0
78,1,153,0,0.401884," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^8,x, algorithm=""fricas"")","-\frac{2 \, {\left(3465 \, A b^{6} + 128 \, {\left(13 \, B b c^{5} - 10 \, A c^{6}\right)} x^{6} - 64 \, {\left(13 \, B b^{2} c^{4} - 10 \, A b c^{5}\right)} x^{5} + 48 \, {\left(13 \, B b^{3} c^{3} - 10 \, A b^{2} c^{4}\right)} x^{4} - 40 \, {\left(13 \, B b^{4} c^{2} - 10 \, A b^{3} c^{3}\right)} x^{3} + 35 \, {\left(13 \, B b^{5} c - 10 \, A b^{4} c^{2}\right)} x^{2} + 315 \, {\left(13 \, B b^{6} + A b^{5} c\right)} x\right)} \sqrt{c x^{2} + b x}}{45045 \, b^{6} x^{7}}"," ",0,"-2/45045*(3465*A*b^6 + 128*(13*B*b*c^5 - 10*A*c^6)*x^6 - 64*(13*B*b^2*c^4 - 10*A*b*c^5)*x^5 + 48*(13*B*b^3*c^3 - 10*A*b^2*c^4)*x^4 - 40*(13*B*b^4*c^2 - 10*A*b^3*c^3)*x^3 + 35*(13*B*b^5*c - 10*A*b^4*c^2)*x^2 + 315*(13*B*b^6 + A*b^5*c)*x)*sqrt(c*x^2 + b*x)/(b^6*x^7)","A",0
79,1,446,0,0.427203," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(11 \, B b^{8} - 16 \, A b^{7} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(71680 \, B c^{8} x^{7} - 3465 \, B b^{7} c + 5040 \, A b^{6} c^{2} + 5120 \, {\left(17 \, B b c^{7} + 16 \, A c^{8}\right)} x^{6} + 1280 \, {\left(B b^{2} c^{6} + 80 \, A b c^{7}\right)} x^{5} - 128 \, {\left(11 \, B b^{3} c^{5} - 16 \, A b^{2} c^{6}\right)} x^{4} + 144 \, {\left(11 \, B b^{4} c^{4} - 16 \, A b^{3} c^{5}\right)} x^{3} - 168 \, {\left(11 \, B b^{5} c^{3} - 16 \, A b^{4} c^{4}\right)} x^{2} + 210 \, {\left(11 \, B b^{6} c^{2} - 16 \, A b^{5} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{1146880 \, c^{7}}, -\frac{315 \, {\left(11 \, B b^{8} - 16 \, A b^{7} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(71680 \, B c^{8} x^{7} - 3465 \, B b^{7} c + 5040 \, A b^{6} c^{2} + 5120 \, {\left(17 \, B b c^{7} + 16 \, A c^{8}\right)} x^{6} + 1280 \, {\left(B b^{2} c^{6} + 80 \, A b c^{7}\right)} x^{5} - 128 \, {\left(11 \, B b^{3} c^{5} - 16 \, A b^{2} c^{6}\right)} x^{4} + 144 \, {\left(11 \, B b^{4} c^{4} - 16 \, A b^{3} c^{5}\right)} x^{3} - 168 \, {\left(11 \, B b^{5} c^{3} - 16 \, A b^{4} c^{4}\right)} x^{2} + 210 \, {\left(11 \, B b^{6} c^{2} - 16 \, A b^{5} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{573440 \, c^{7}}\right]"," ",0,"[-1/1146880*(315*(11*B*b^8 - 16*A*b^7*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(71680*B*c^8*x^7 - 3465*B*b^7*c + 5040*A*b^6*c^2 + 5120*(17*B*b*c^7 + 16*A*c^8)*x^6 + 1280*(B*b^2*c^6 + 80*A*b*c^7)*x^5 - 128*(11*B*b^3*c^5 - 16*A*b^2*c^6)*x^4 + 144*(11*B*b^4*c^4 - 16*A*b^3*c^5)*x^3 - 168*(11*B*b^5*c^3 - 16*A*b^4*c^4)*x^2 + 210*(11*B*b^6*c^2 - 16*A*b^5*c^3)*x)*sqrt(c*x^2 + b*x))/c^7, -1/573440*(315*(11*B*b^8 - 16*A*b^7*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (71680*B*c^8*x^7 - 3465*B*b^7*c + 5040*A*b^6*c^2 + 5120*(17*B*b*c^7 + 16*A*c^8)*x^6 + 1280*(B*b^2*c^6 + 80*A*b*c^7)*x^5 - 128*(11*B*b^3*c^5 - 16*A*b^2*c^6)*x^4 + 144*(11*B*b^4*c^4 - 16*A*b^3*c^5)*x^3 - 168*(11*B*b^5*c^3 - 16*A*b^4*c^4)*x^2 + 210*(11*B*b^6*c^2 - 16*A*b^5*c^3)*x)*sqrt(c*x^2 + b*x))/c^7]","A",0
80,1,399,0,0.426781," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B b^{7} - 14 \, A b^{6} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(15360 \, B c^{7} x^{6} + 945 \, B b^{6} c - 1470 \, A b^{5} c^{2} + 1280 \, {\left(15 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 128 \, {\left(3 \, B b^{2} c^{5} + 182 \, A b c^{6}\right)} x^{4} - 48 \, {\left(9 \, B b^{3} c^{4} - 14 \, A b^{2} c^{5}\right)} x^{3} + 56 \, {\left(9 \, B b^{4} c^{3} - 14 \, A b^{3} c^{4}\right)} x^{2} - 70 \, {\left(9 \, B b^{5} c^{2} - 14 \, A b^{4} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{215040 \, c^{6}}, \frac{105 \, {\left(9 \, B b^{7} - 14 \, A b^{6} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(15360 \, B c^{7} x^{6} + 945 \, B b^{6} c - 1470 \, A b^{5} c^{2} + 1280 \, {\left(15 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 128 \, {\left(3 \, B b^{2} c^{5} + 182 \, A b c^{6}\right)} x^{4} - 48 \, {\left(9 \, B b^{3} c^{4} - 14 \, A b^{2} c^{5}\right)} x^{3} + 56 \, {\left(9 \, B b^{4} c^{3} - 14 \, A b^{3} c^{4}\right)} x^{2} - 70 \, {\left(9 \, B b^{5} c^{2} - 14 \, A b^{4} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{107520 \, c^{6}}\right]"," ",0,"[-1/215040*(105*(9*B*b^7 - 14*A*b^6*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(15360*B*c^7*x^6 + 945*B*b^6*c - 1470*A*b^5*c^2 + 1280*(15*B*b*c^6 + 14*A*c^7)*x^5 + 128*(3*B*b^2*c^5 + 182*A*b*c^6)*x^4 - 48*(9*B*b^3*c^4 - 14*A*b^2*c^5)*x^3 + 56*(9*B*b^4*c^3 - 14*A*b^3*c^4)*x^2 - 70*(9*B*b^5*c^2 - 14*A*b^4*c^3)*x)*sqrt(c*x^2 + b*x))/c^6, 1/107520*(105*(9*B*b^7 - 14*A*b^6*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (15360*B*c^7*x^6 + 945*B*b^6*c - 1470*A*b^5*c^2 + 1280*(15*B*b*c^6 + 14*A*c^7)*x^5 + 128*(3*B*b^2*c^5 + 182*A*b*c^6)*x^4 - 48*(9*B*b^3*c^4 - 14*A*b^2*c^5)*x^3 + 56*(9*B*b^4*c^3 - 14*A*b^3*c^4)*x^2 - 70*(9*B*b^5*c^2 - 14*A*b^4*c^3)*x)*sqrt(c*x^2 + b*x))/c^6]","A",0
81,1,350,0,0.436662," ","integrate(x*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{6} - 12 \, A b^{5} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(1280 \, B c^{6} x^{5} - 105 \, B b^{5} c + 180 \, A b^{4} c^{2} + 128 \, {\left(13 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 48 \, {\left(B b^{2} c^{4} + 44 \, A b c^{5}\right)} x^{3} - 8 \, {\left(7 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} x^{2} + 10 \, {\left(7 \, B b^{4} c^{2} - 12 \, A b^{3} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{15360 \, c^{5}}, -\frac{15 \, {\left(7 \, B b^{6} - 12 \, A b^{5} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(1280 \, B c^{6} x^{5} - 105 \, B b^{5} c + 180 \, A b^{4} c^{2} + 128 \, {\left(13 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 48 \, {\left(B b^{2} c^{4} + 44 \, A b c^{5}\right)} x^{3} - 8 \, {\left(7 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} x^{2} + 10 \, {\left(7 \, B b^{4} c^{2} - 12 \, A b^{3} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{7680 \, c^{5}}\right]"," ",0,"[-1/15360*(15*(7*B*b^6 - 12*A*b^5*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(1280*B*c^6*x^5 - 105*B*b^5*c + 180*A*b^4*c^2 + 128*(13*B*b*c^5 + 12*A*c^6)*x^4 + 48*(B*b^2*c^4 + 44*A*b*c^5)*x^3 - 8*(7*B*b^3*c^3 - 12*A*b^2*c^4)*x^2 + 10*(7*B*b^4*c^2 - 12*A*b^3*c^3)*x)*sqrt(c*x^2 + b*x))/c^5, -1/7680*(15*(7*B*b^6 - 12*A*b^5*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (1280*B*c^6*x^5 - 105*B*b^5*c + 180*A*b^4*c^2 + 128*(13*B*b*c^5 + 12*A*c^6)*x^4 + 48*(B*b^2*c^4 + 44*A*b*c^5)*x^3 - 8*(7*B*b^3*c^3 - 12*A*b^2*c^4)*x^2 + 10*(7*B*b^4*c^2 - 12*A*b^3*c^3)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
82,1,297,0,0.421258," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B b^{5} - 2 \, A b^{4} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(128 \, B c^{5} x^{4} + 15 \, B b^{4} c - 30 \, A b^{3} c^{2} + 16 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} x^{3} + 8 \, {\left(B b^{2} c^{3} + 30 \, A b c^{4}\right)} x^{2} - 10 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{1280 \, c^{4}}, \frac{15 \, {\left(B b^{5} - 2 \, A b^{4} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(128 \, B c^{5} x^{4} + 15 \, B b^{4} c - 30 \, A b^{3} c^{2} + 16 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} x^{3} + 8 \, {\left(B b^{2} c^{3} + 30 \, A b c^{4}\right)} x^{2} - 10 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{640 \, c^{4}}\right]"," ",0,"[-1/1280*(15*(B*b^5 - 2*A*b^4*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(128*B*c^5*x^4 + 15*B*b^4*c - 30*A*b^3*c^2 + 16*(11*B*b*c^4 + 10*A*c^5)*x^3 + 8*(B*b^2*c^3 + 30*A*b*c^4)*x^2 - 10*(B*b^3*c^2 - 2*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^4, 1/640*(15*(B*b^5 - 2*A*b^4*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (128*B*c^5*x^4 + 15*B*b^4*c - 30*A*b^3*c^2 + 16*(11*B*b*c^4 + 10*A*c^5)*x^3 + 8*(B*b^2*c^3 + 30*A*b*c^4)*x^2 - 10*(B*b^3*c^2 - 2*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
83,1,256,0,0.418757," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(48 \, B c^{4} x^{3} - 9 \, B b^{3} c + 24 \, A b^{2} c^{2} + 8 \, {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} c^{2} + 56 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, c^{3}}, -\frac{3 \, {\left(3 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(48 \, B c^{4} x^{3} - 9 \, B b^{3} c + 24 \, A b^{2} c^{2} + 8 \, {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} c^{2} + 56 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, c^{3}}\right]"," ",0,"[-1/384*(3*(3*B*b^4 - 8*A*b^3*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(48*B*c^4*x^3 - 9*B*b^3*c + 24*A*b^2*c^2 + 8*(9*B*b*c^3 + 8*A*c^4)*x^2 + 2*(3*B*b^2*c^2 + 56*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/c^3, -1/192*(3*(3*B*b^4 - 8*A*b^3*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (48*B*c^4*x^3 - 9*B*b^3*c + 24*A*b^2*c^2 + 8*(9*B*b*c^3 + 8*A*c^4)*x^2 + 2*(3*B*b^2*c^2 + 56*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/c^3]","A",0
84,1,205,0,0.427357," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b^{3} - 6 \, A b^{2} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{3} x^{2} + 3 \, B b^{2} c + 30 \, A b c^{2} + 2 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c^{2}}, \frac{3 \, {\left(B b^{3} - 6 \, A b^{2} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, B c^{3} x^{2} + 3 \, B b^{2} c + 30 \, A b c^{2} + 2 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c^{2}}\right]"," ",0,"[-1/48*(3*(B*b^3 - 6*A*b^2*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(8*B*c^3*x^2 + 3*B*b^2*c + 30*A*b*c^2 + 2*(7*B*b*c^2 + 6*A*c^3)*x)*sqrt(c*x^2 + b*x))/c^2, 1/24*(3*(B*b^3 - 6*A*b^2*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*B*c^3*x^2 + 3*B*b^2*c + 30*A*b*c^2 + 2*(7*B*b*c^2 + 6*A*c^3)*x)*sqrt(c*x^2 + b*x))/c^2]","A",0
85,1,186,0,0.428691," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B b^{2} + 4 \, A b c\right)} \sqrt{c} x \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, B c^{2} x^{2} - 8 \, A b c + {\left(5 \, B b c + 4 \, A c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, c x}, -\frac{3 \, {\left(B b^{2} + 4 \, A b c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, B c^{2} x^{2} - 8 \, A b c + {\left(5 \, B b c + 4 \, A c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, c x}\right]"," ",0,"[1/8*(3*(B*b^2 + 4*A*b*c)*sqrt(c)*x*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*B*c^2*x^2 - 8*A*b*c + (5*B*b*c + 4*A*c^2)*x)*sqrt(c*x^2 + b*x))/(c*x), -1/4*(3*(B*b^2 + 4*A*b*c)*sqrt(-c)*x*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*B*c^2*x^2 - 8*A*b*c + (5*B*b*c + 4*A*c^2)*x)*sqrt(c*x^2 + b*x))/(c*x)]","A",0
86,1,170,0,0.425829," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, B b + 2 \, A c\right)} \sqrt{c} x^{2} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(3 \, B c x^{2} - 2 \, A b - 2 \, {\left(3 \, B b + 4 \, A c\right)} x\right)} \sqrt{c x^{2} + b x}}{6 \, x^{2}}, -\frac{3 \, {\left(3 \, B b + 2 \, A c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(3 \, B c x^{2} - 2 \, A b - 2 \, {\left(3 \, B b + 4 \, A c\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, x^{2}}\right]"," ",0,"[1/6*(3*(3*B*b + 2*A*c)*sqrt(c)*x^2*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(3*B*c*x^2 - 2*A*b - 2*(3*B*b + 4*A*c)*x)*sqrt(c*x^2 + b*x))/x^2, -1/3*(3*(3*B*b + 2*A*c)*sqrt(-c)*x^2*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (3*B*c*x^2 - 2*A*b - 2*(3*B*b + 4*A*c)*x)*sqrt(c*x^2 + b*x))/x^2]","A",0
87,1,188,0,0.425048," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, B b c^{\frac{3}{2}} x^{3} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(3 \, A b^{2} + {\left(20 \, B b c + 3 \, A c^{2}\right)} x^{2} + {\left(5 \, B b^{2} + 6 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x}}{15 \, b x^{3}}, -\frac{2 \, {\left(15 \, B b \sqrt{-c} c x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(3 \, A b^{2} + {\left(20 \, B b c + 3 \, A c^{2}\right)} x^{2} + {\left(5 \, B b^{2} + 6 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x}\right)}}{15 \, b x^{3}}\right]"," ",0,"[1/15*(15*B*b*c^(3/2)*x^3*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(3*A*b^2 + (20*B*b*c + 3*A*c^2)*x^2 + (5*B*b^2 + 6*A*b*c)*x)*sqrt(c*x^2 + b*x))/(b*x^3), -2/15*(15*B*b*sqrt(-c)*c*x^3*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (3*A*b^2 + (20*B*b*c + 3*A*c^2)*x^2 + (5*B*b^2 + 6*A*b*c)*x)*sqrt(c*x^2 + b*x))/(b*x^3)]","A",0
88,1,78,0,0.402087," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^6,x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, A b^{3} + {\left(7 \, B b c^{2} - 2 \, A c^{3}\right)} x^{3} + {\left(14 \, B b^{2} c + A b c^{2}\right)} x^{2} + {\left(7 \, B b^{3} + 8 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x}}{35 \, b^{2} x^{4}}"," ",0,"-2/35*(5*A*b^3 + (7*B*b*c^2 - 2*A*c^3)*x^3 + (14*B*b^2*c + A*b*c^2)*x^2 + (7*B*b^3 + 8*A*b^2*c)*x)*sqrt(c*x^2 + b*x)/(b^2*x^4)","A",0
89,1,104,0,0.401525," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, A b^{4} - 2 \, {\left(9 \, B b c^{3} - 4 \, A c^{4}\right)} x^{4} + {\left(9 \, B b^{2} c^{2} - 4 \, A b c^{3}\right)} x^{3} + 3 \, {\left(24 \, B b^{3} c + A b^{2} c^{2}\right)} x^{2} + 5 \, {\left(9 \, B b^{4} + 10 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x}}{315 \, b^{3} x^{5}}"," ",0,"-2/315*(35*A*b^4 - 2*(9*B*b*c^3 - 4*A*c^4)*x^4 + (9*B*b^2*c^2 - 4*A*b*c^3)*x^3 + 3*(24*B*b^3*c + A*b^2*c^2)*x^2 + 5*(9*B*b^4 + 10*A*b^3*c)*x)*sqrt(c*x^2 + b*x)/(b^3*x^5)","A",0
90,1,130,0,0.406614," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^8,x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, A b^{5} + 8 \, {\left(11 \, B b c^{4} - 6 \, A c^{5}\right)} x^{5} - 4 \, {\left(11 \, B b^{2} c^{3} - 6 \, A b c^{4}\right)} x^{4} + 3 \, {\left(11 \, B b^{3} c^{2} - 6 \, A b^{2} c^{3}\right)} x^{3} + 5 \, {\left(110 \, B b^{4} c + 3 \, A b^{3} c^{2}\right)} x^{2} + 35 \, {\left(11 \, B b^{5} + 12 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x}}{3465 \, b^{4} x^{6}}"," ",0,"-2/3465*(315*A*b^5 + 8*(11*B*b*c^4 - 6*A*c^5)*x^5 - 4*(11*B*b^2*c^3 - 6*A*b*c^4)*x^4 + 3*(11*B*b^3*c^2 - 6*A*b^2*c^3)*x^3 + 5*(110*B*b^4*c + 3*A*b^3*c^2)*x^2 + 35*(11*B*b^5 + 12*A*b^4*c)*x)*sqrt(c*x^2 + b*x)/(b^4*x^6)","A",0
91,1,153,0,0.417417," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^9,x, algorithm=""fricas"")","-\frac{2 \, {\left(1155 \, A b^{6} - 16 \, {\left(13 \, B b c^{5} - 8 \, A c^{6}\right)} x^{6} + 8 \, {\left(13 \, B b^{2} c^{4} - 8 \, A b c^{5}\right)} x^{5} - 6 \, {\left(13 \, B b^{3} c^{3} - 8 \, A b^{2} c^{4}\right)} x^{4} + 5 \, {\left(13 \, B b^{4} c^{2} - 8 \, A b^{3} c^{3}\right)} x^{3} + 35 \, {\left(52 \, B b^{5} c + A b^{4} c^{2}\right)} x^{2} + 105 \, {\left(13 \, B b^{6} + 14 \, A b^{5} c\right)} x\right)} \sqrt{c x^{2} + b x}}{15015 \, b^{5} x^{7}}"," ",0,"-2/15015*(1155*A*b^6 - 16*(13*B*b*c^5 - 8*A*c^6)*x^6 + 8*(13*B*b^2*c^4 - 8*A*b*c^5)*x^5 - 6*(13*B*b^3*c^3 - 8*A*b^2*c^4)*x^4 + 5*(13*B*b^4*c^2 - 8*A*b^3*c^3)*x^3 + 35*(52*B*b^5*c + A*b^4*c^2)*x^2 + 105*(13*B*b^6 + 14*A*b^5*c)*x)*sqrt(c*x^2 + b*x)/(b^5*x^7)","A",0
92,1,177,0,0.401312," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^10,x, algorithm=""fricas"")","-\frac{2 \, {\left(3003 \, A b^{7} + 128 \, {\left(3 \, B b c^{6} - 2 \, A c^{7}\right)} x^{7} - 64 \, {\left(3 \, B b^{2} c^{5} - 2 \, A b c^{6}\right)} x^{6} + 48 \, {\left(3 \, B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} x^{5} - 40 \, {\left(3 \, B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} x^{4} + 35 \, {\left(3 \, B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} x^{3} + 63 \, {\left(70 \, B b^{6} c + A b^{5} c^{2}\right)} x^{2} + 231 \, {\left(15 \, B b^{7} + 16 \, A b^{6} c\right)} x\right)} \sqrt{c x^{2} + b x}}{45045 \, b^{6} x^{8}}"," ",0,"-2/45045*(3003*A*b^7 + 128*(3*B*b*c^6 - 2*A*c^7)*x^7 - 64*(3*B*b^2*c^5 - 2*A*b*c^6)*x^6 + 48*(3*B*b^3*c^4 - 2*A*b^2*c^5)*x^5 - 40*(3*B*b^4*c^3 - 2*A*b^3*c^4)*x^4 + 35*(3*B*b^5*c^2 - 2*A*b^4*c^3)*x^3 + 63*(70*B*b^6*c + A*b^5*c^2)*x^2 + 231*(15*B*b^7 + 16*A*b^6*c)*x)*sqrt(c*x^2 + b*x)/(b^6*x^8)","A",0
93,1,541,0,0.428375," ","integrate(x^3*(B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left(13 \, B b^{10} - 20 \, A b^{9} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(4128768 \, B c^{10} x^{9} + 45045 \, B b^{9} c - 69300 \, A b^{8} c^{2} + 229376 \, {\left(41 \, B b c^{9} + 20 \, A c^{10}\right)} x^{8} + 14336 \, {\left(383 \, B b^{2} c^{8} + 740 \, A b c^{9}\right)} x^{7} + 15360 \, {\left(B b^{3} c^{7} + 412 \, A b^{2} c^{8}\right)} x^{6} - 1280 \, {\left(13 \, B b^{4} c^{6} - 20 \, A b^{3} c^{7}\right)} x^{5} + 1408 \, {\left(13 \, B b^{5} c^{5} - 20 \, A b^{4} c^{6}\right)} x^{4} - 1584 \, {\left(13 \, B b^{6} c^{4} - 20 \, A b^{5} c^{5}\right)} x^{3} + 1848 \, {\left(13 \, B b^{7} c^{3} - 20 \, A b^{6} c^{4}\right)} x^{2} - 2310 \, {\left(13 \, B b^{8} c^{2} - 20 \, A b^{7} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{82575360 \, c^{8}}, \frac{3465 \, {\left(13 \, B b^{10} - 20 \, A b^{9} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(4128768 \, B c^{10} x^{9} + 45045 \, B b^{9} c - 69300 \, A b^{8} c^{2} + 229376 \, {\left(41 \, B b c^{9} + 20 \, A c^{10}\right)} x^{8} + 14336 \, {\left(383 \, B b^{2} c^{8} + 740 \, A b c^{9}\right)} x^{7} + 15360 \, {\left(B b^{3} c^{7} + 412 \, A b^{2} c^{8}\right)} x^{6} - 1280 \, {\left(13 \, B b^{4} c^{6} - 20 \, A b^{3} c^{7}\right)} x^{5} + 1408 \, {\left(13 \, B b^{5} c^{5} - 20 \, A b^{4} c^{6}\right)} x^{4} - 1584 \, {\left(13 \, B b^{6} c^{4} - 20 \, A b^{5} c^{5}\right)} x^{3} + 1848 \, {\left(13 \, B b^{7} c^{3} - 20 \, A b^{6} c^{4}\right)} x^{2} - 2310 \, {\left(13 \, B b^{8} c^{2} - 20 \, A b^{7} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{41287680 \, c^{8}}\right]"," ",0,"[-1/82575360*(3465*(13*B*b^10 - 20*A*b^9*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(4128768*B*c^10*x^9 + 45045*B*b^9*c - 69300*A*b^8*c^2 + 229376*(41*B*b*c^9 + 20*A*c^10)*x^8 + 14336*(383*B*b^2*c^8 + 740*A*b*c^9)*x^7 + 15360*(B*b^3*c^7 + 412*A*b^2*c^8)*x^6 - 1280*(13*B*b^4*c^6 - 20*A*b^3*c^7)*x^5 + 1408*(13*B*b^5*c^5 - 20*A*b^4*c^6)*x^4 - 1584*(13*B*b^6*c^4 - 20*A*b^5*c^5)*x^3 + 1848*(13*B*b^7*c^3 - 20*A*b^6*c^4)*x^2 - 2310*(13*B*b^8*c^2 - 20*A*b^7*c^3)*x)*sqrt(c*x^2 + b*x))/c^8, 1/41287680*(3465*(13*B*b^10 - 20*A*b^9*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (4128768*B*c^10*x^9 + 45045*B*b^9*c - 69300*A*b^8*c^2 + 229376*(41*B*b*c^9 + 20*A*c^10)*x^8 + 14336*(383*B*b^2*c^8 + 740*A*b*c^9)*x^7 + 15360*(B*b^3*c^7 + 412*A*b^2*c^8)*x^6 - 1280*(13*B*b^4*c^6 - 20*A*b^3*c^7)*x^5 + 1408*(13*B*b^5*c^5 - 20*A*b^4*c^6)*x^4 - 1584*(13*B*b^6*c^4 - 20*A*b^5*c^5)*x^3 + 1848*(13*B*b^7*c^3 - 20*A*b^6*c^4)*x^2 - 2310*(13*B*b^8*c^2 - 20*A*b^7*c^3)*x)*sqrt(c*x^2 + b*x))/c^8]","A",0
94,1,496,0,0.425320," ","integrate(x^2*(B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(11 \, B b^{9} - 18 \, A b^{8} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(229376 \, B c^{9} x^{8} - 3465 \, B b^{8} c + 5670 \, A b^{7} c^{2} + 14336 \, {\left(37 \, B b c^{8} + 18 \, A c^{9}\right)} x^{7} + 3072 \, {\left(103 \, B b^{2} c^{7} + 198 \, A b c^{8}\right)} x^{6} + 256 \, {\left(5 \, B b^{3} c^{6} + 1458 \, A b^{2} c^{7}\right)} x^{5} - 128 \, {\left(11 \, B b^{4} c^{5} - 18 \, A b^{3} c^{6}\right)} x^{4} + 144 \, {\left(11 \, B b^{5} c^{4} - 18 \, A b^{4} c^{5}\right)} x^{3} - 168 \, {\left(11 \, B b^{6} c^{3} - 18 \, A b^{5} c^{4}\right)} x^{2} + 210 \, {\left(11 \, B b^{7} c^{2} - 18 \, A b^{6} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{4128768 \, c^{7}}, -\frac{315 \, {\left(11 \, B b^{9} - 18 \, A b^{8} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(229376 \, B c^{9} x^{8} - 3465 \, B b^{8} c + 5670 \, A b^{7} c^{2} + 14336 \, {\left(37 \, B b c^{8} + 18 \, A c^{9}\right)} x^{7} + 3072 \, {\left(103 \, B b^{2} c^{7} + 198 \, A b c^{8}\right)} x^{6} + 256 \, {\left(5 \, B b^{3} c^{6} + 1458 \, A b^{2} c^{7}\right)} x^{5} - 128 \, {\left(11 \, B b^{4} c^{5} - 18 \, A b^{3} c^{6}\right)} x^{4} + 144 \, {\left(11 \, B b^{5} c^{4} - 18 \, A b^{4} c^{5}\right)} x^{3} - 168 \, {\left(11 \, B b^{6} c^{3} - 18 \, A b^{5} c^{4}\right)} x^{2} + 210 \, {\left(11 \, B b^{7} c^{2} - 18 \, A b^{6} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{2064384 \, c^{7}}\right]"," ",0,"[-1/4128768*(315*(11*B*b^9 - 18*A*b^8*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(229376*B*c^9*x^8 - 3465*B*b^8*c + 5670*A*b^7*c^2 + 14336*(37*B*b*c^8 + 18*A*c^9)*x^7 + 3072*(103*B*b^2*c^7 + 198*A*b*c^8)*x^6 + 256*(5*B*b^3*c^6 + 1458*A*b^2*c^7)*x^5 - 128*(11*B*b^4*c^5 - 18*A*b^3*c^6)*x^4 + 144*(11*B*b^5*c^4 - 18*A*b^4*c^5)*x^3 - 168*(11*B*b^6*c^3 - 18*A*b^5*c^4)*x^2 + 210*(11*B*b^7*c^2 - 18*A*b^6*c^3)*x)*sqrt(c*x^2 + b*x))/c^7, -1/2064384*(315*(11*B*b^9 - 18*A*b^8*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (229376*B*c^9*x^8 - 3465*B*b^8*c + 5670*A*b^7*c^2 + 14336*(37*B*b*c^8 + 18*A*c^9)*x^7 + 3072*(103*B*b^2*c^7 + 198*A*b*c^8)*x^6 + 256*(5*B*b^3*c^6 + 1458*A*b^2*c^7)*x^5 - 128*(11*B*b^4*c^5 - 18*A*b^3*c^6)*x^4 + 144*(11*B*b^5*c^4 - 18*A*b^4*c^5)*x^3 - 168*(11*B*b^6*c^3 - 18*A*b^5*c^4)*x^2 + 210*(11*B*b^7*c^2 - 18*A*b^6*c^3)*x)*sqrt(c*x^2 + b*x))/c^7]","A",0
95,1,447,0,0.432653," ","integrate(x*(B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B b^{8} - 16 \, A b^{7} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(43008 \, B c^{8} x^{7} + 945 \, B b^{7} c - 1680 \, A b^{6} c^{2} + 3072 \, {\left(33 \, B b c^{7} + 16 \, A c^{8}\right)} x^{6} + 256 \, {\left(243 \, B b^{2} c^{6} + 464 \, A b c^{7}\right)} x^{5} + 128 \, {\left(3 \, B b^{3} c^{5} + 592 \, A b^{2} c^{6}\right)} x^{4} - 48 \, {\left(9 \, B b^{4} c^{4} - 16 \, A b^{3} c^{5}\right)} x^{3} + 56 \, {\left(9 \, B b^{5} c^{3} - 16 \, A b^{4} c^{4}\right)} x^{2} - 70 \, {\left(9 \, B b^{6} c^{2} - 16 \, A b^{5} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{688128 \, c^{6}}, \frac{105 \, {\left(9 \, B b^{8} - 16 \, A b^{7} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(43008 \, B c^{8} x^{7} + 945 \, B b^{7} c - 1680 \, A b^{6} c^{2} + 3072 \, {\left(33 \, B b c^{7} + 16 \, A c^{8}\right)} x^{6} + 256 \, {\left(243 \, B b^{2} c^{6} + 464 \, A b c^{7}\right)} x^{5} + 128 \, {\left(3 \, B b^{3} c^{5} + 592 \, A b^{2} c^{6}\right)} x^{4} - 48 \, {\left(9 \, B b^{4} c^{4} - 16 \, A b^{3} c^{5}\right)} x^{3} + 56 \, {\left(9 \, B b^{5} c^{3} - 16 \, A b^{4} c^{4}\right)} x^{2} - 70 \, {\left(9 \, B b^{6} c^{2} - 16 \, A b^{5} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{344064 \, c^{6}}\right]"," ",0,"[-1/688128*(105*(9*B*b^8 - 16*A*b^7*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(43008*B*c^8*x^7 + 945*B*b^7*c - 1680*A*b^6*c^2 + 3072*(33*B*b*c^7 + 16*A*c^8)*x^6 + 256*(243*B*b^2*c^6 + 464*A*b*c^7)*x^5 + 128*(3*B*b^3*c^5 + 592*A*b^2*c^6)*x^4 - 48*(9*B*b^4*c^4 - 16*A*b^3*c^5)*x^3 + 56*(9*B*b^5*c^3 - 16*A*b^4*c^4)*x^2 - 70*(9*B*b^6*c^2 - 16*A*b^5*c^3)*x)*sqrt(c*x^2 + b*x))/c^6, 1/344064*(105*(9*B*b^8 - 16*A*b^7*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (43008*B*c^8*x^7 + 945*B*b^7*c - 1680*A*b^6*c^2 + 3072*(33*B*b*c^7 + 16*A*c^8)*x^6 + 256*(243*B*b^2*c^6 + 464*A*b*c^7)*x^5 + 128*(3*B*b^3*c^5 + 592*A*b^2*c^6)*x^4 - 48*(9*B*b^4*c^4 - 16*A*b^3*c^5)*x^3 + 56*(9*B*b^5*c^3 - 16*A*b^4*c^4)*x^2 - 70*(9*B*b^6*c^2 - 16*A*b^5*c^3)*x)*sqrt(c*x^2 + b*x))/c^6]","A",0
96,1,392,0,0.412117," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B b^{7} - 2 \, A b^{6} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(3072 \, B c^{7} x^{6} - 105 \, B b^{6} c + 210 \, A b^{5} c^{2} + 256 \, {\left(29 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 128 \, {\left(37 \, B b^{2} c^{5} + 70 \, A b c^{6}\right)} x^{4} + 48 \, {\left(B b^{3} c^{4} + 126 \, A b^{2} c^{5}\right)} x^{3} - 56 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} x^{2} + 70 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{43008 \, c^{5}}, -\frac{105 \, {\left(B b^{7} - 2 \, A b^{6} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(3072 \, B c^{7} x^{6} - 105 \, B b^{6} c + 210 \, A b^{5} c^{2} + 256 \, {\left(29 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 128 \, {\left(37 \, B b^{2} c^{5} + 70 \, A b c^{6}\right)} x^{4} + 48 \, {\left(B b^{3} c^{4} + 126 \, A b^{2} c^{5}\right)} x^{3} - 56 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} x^{2} + 70 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{21504 \, c^{5}}\right]"," ",0,"[-1/43008*(105*(B*b^7 - 2*A*b^6*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(3072*B*c^7*x^6 - 105*B*b^6*c + 210*A*b^5*c^2 + 256*(29*B*b*c^6 + 14*A*c^7)*x^5 + 128*(37*B*b^2*c^5 + 70*A*b*c^6)*x^4 + 48*(B*b^3*c^4 + 126*A*b^2*c^5)*x^3 - 56*(B*b^4*c^3 - 2*A*b^3*c^4)*x^2 + 70*(B*b^5*c^2 - 2*A*b^4*c^3)*x)*sqrt(c*x^2 + b*x))/c^5, -1/21504*(105*(B*b^7 - 2*A*b^6*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (3072*B*c^7*x^6 - 105*B*b^6*c + 210*A*b^5*c^2 + 256*(29*B*b*c^6 + 14*A*c^7)*x^5 + 128*(37*B*b^2*c^5 + 70*A*b*c^6)*x^4 + 48*(B*b^3*c^4 + 126*A*b^2*c^5)*x^3 - 56*(B*b^4*c^3 - 2*A*b^3*c^4)*x^2 + 70*(B*b^5*c^2 - 2*A*b^4*c^3)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
97,1,351,0,0.448193," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(5 \, B b^{6} - 12 \, A b^{5} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(1280 \, B c^{6} x^{5} + 75 \, B b^{5} c - 180 \, A b^{4} c^{2} + 128 \, {\left(25 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 144 \, {\left(15 \, B b^{2} c^{4} + 28 \, A b c^{5}\right)} x^{3} + 8 \, {\left(5 \, B b^{3} c^{3} + 372 \, A b^{2} c^{4}\right)} x^{2} - 10 \, {\left(5 \, B b^{4} c^{2} - 12 \, A b^{3} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{15360 \, c^{4}}, \frac{15 \, {\left(5 \, B b^{6} - 12 \, A b^{5} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(1280 \, B c^{6} x^{5} + 75 \, B b^{5} c - 180 \, A b^{4} c^{2} + 128 \, {\left(25 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 144 \, {\left(15 \, B b^{2} c^{4} + 28 \, A b c^{5}\right)} x^{3} + 8 \, {\left(5 \, B b^{3} c^{3} + 372 \, A b^{2} c^{4}\right)} x^{2} - 10 \, {\left(5 \, B b^{4} c^{2} - 12 \, A b^{3} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{7680 \, c^{4}}\right]"," ",0,"[-1/15360*(15*(5*B*b^6 - 12*A*b^5*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(1280*B*c^6*x^5 + 75*B*b^5*c - 180*A*b^4*c^2 + 128*(25*B*b*c^5 + 12*A*c^6)*x^4 + 144*(15*B*b^2*c^4 + 28*A*b*c^5)*x^3 + 8*(5*B*b^3*c^3 + 372*A*b^2*c^4)*x^2 - 10*(5*B*b^4*c^2 - 12*A*b^3*c^3)*x)*sqrt(c*x^2 + b*x))/c^4, 1/7680*(15*(5*B*b^6 - 12*A*b^5*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (1280*B*c^6*x^5 + 75*B*b^5*c - 180*A*b^4*c^2 + 128*(25*B*b*c^5 + 12*A*c^6)*x^4 + 144*(15*B*b^2*c^4 + 28*A*b*c^5)*x^3 + 8*(5*B*b^3*c^3 + 372*A*b^2*c^4)*x^2 - 10*(5*B*b^4*c^2 - 12*A*b^3*c^3)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
98,1,304,0,0.423593," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(384 \, B c^{5} x^{4} - 45 \, B b^{4} c + 150 \, A b^{3} c^{2} + 48 \, {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} x^{3} + 8 \, {\left(93 \, B b^{2} c^{3} + 170 \, A b c^{4}\right)} x^{2} + 10 \, {\left(3 \, B b^{3} c^{2} + 118 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, c^{3}}, -\frac{15 \, {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(384 \, B c^{5} x^{4} - 45 \, B b^{4} c + 150 \, A b^{3} c^{2} + 48 \, {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} x^{3} + 8 \, {\left(93 \, B b^{2} c^{3} + 170 \, A b c^{4}\right)} x^{2} + 10 \, {\left(3 \, B b^{3} c^{2} + 118 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, c^{3}}\right]"," ",0,"[-1/3840*(15*(3*B*b^5 - 10*A*b^4*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(384*B*c^5*x^4 - 45*B*b^4*c + 150*A*b^3*c^2 + 48*(21*B*b*c^4 + 10*A*c^5)*x^3 + 8*(93*B*b^2*c^3 + 170*A*b*c^4)*x^2 + 10*(3*B*b^3*c^2 + 118*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^3, -1/1920*(15*(3*B*b^5 - 10*A*b^4*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (384*B*c^5*x^4 - 45*B*b^4*c + 150*A*b^3*c^2 + 48*(21*B*b*c^4 + 10*A*c^5)*x^3 + 8*(93*B*b^2*c^3 + 170*A*b*c^4)*x^2 + 10*(3*B*b^3*c^2 + 118*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^3]","A",0
99,1,253,0,0.428424," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B b^{4} - 8 \, A b^{3} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(48 \, B c^{4} x^{3} + 15 \, B b^{3} c + 264 \, A b^{2} c^{2} + 8 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(59 \, B b^{2} c^{2} + 104 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, c^{2}}, \frac{15 \, {\left(B b^{4} - 8 \, A b^{3} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(48 \, B c^{4} x^{3} + 15 \, B b^{3} c + 264 \, A b^{2} c^{2} + 8 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(59 \, B b^{2} c^{2} + 104 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, c^{2}}\right]"," ",0,"[-1/384*(15*(B*b^4 - 8*A*b^3*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(48*B*c^4*x^3 + 15*B*b^3*c + 264*A*b^2*c^2 + 8*(17*B*b*c^3 + 8*A*c^4)*x^2 + 2*(59*B*b^2*c^2 + 104*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/c^2, 1/192*(15*(B*b^4 - 8*A*b^3*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (48*B*c^4*x^3 + 15*B*b^3*c + 264*A*b^2*c^2 + 8*(17*B*b*c^3 + 8*A*c^4)*x^2 + 2*(59*B*b^2*c^2 + 104*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/c^2]","A",0
100,1,240,0,0.414747," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B b^{3} + 6 \, A b^{2} c\right)} \sqrt{c} x \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(8 \, B c^{3} x^{3} - 48 \, A b^{2} c + 2 \, {\left(13 \, B b c^{2} + 6 \, A c^{3}\right)} x^{2} + 3 \, {\left(11 \, B b^{2} c + 18 \, A b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c x}, -\frac{15 \, {\left(B b^{3} + 6 \, A b^{2} c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(8 \, B c^{3} x^{3} - 48 \, A b^{2} c + 2 \, {\left(13 \, B b c^{2} + 6 \, A c^{3}\right)} x^{2} + 3 \, {\left(11 \, B b^{2} c + 18 \, A b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c x}\right]"," ",0,"[1/48*(15*(B*b^3 + 6*A*b^2*c)*sqrt(c)*x*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(8*B*c^3*x^3 - 48*A*b^2*c + 2*(13*B*b*c^2 + 6*A*c^3)*x^2 + 3*(11*B*b^2*c + 18*A*b*c^2)*x)*sqrt(c*x^2 + b*x))/(c*x), -1/24*(15*(B*b^3 + 6*A*b^2*c)*sqrt(-c)*x*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (8*B*c^3*x^3 - 48*A*b^2*c + 2*(13*B*b*c^2 + 6*A*c^3)*x^2 + 3*(11*B*b^2*c + 18*A*b*c^2)*x)*sqrt(c*x^2 + b*x))/(c*x)]","A",0
101,1,224,0,0.414760," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, B b^{2} + 4 \, A b c\right)} \sqrt{c} x^{2} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(6 \, B c^{2} x^{3} - 8 \, A b^{2} + 3 \, {\left(9 \, B b c + 4 \, A c^{2}\right)} x^{2} - 8 \, {\left(3 \, B b^{2} + 7 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, x^{2}}, -\frac{15 \, {\left(3 \, B b^{2} + 4 \, A b c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(6 \, B c^{2} x^{3} - 8 \, A b^{2} + 3 \, {\left(9 \, B b c + 4 \, A c^{2}\right)} x^{2} - 8 \, {\left(3 \, B b^{2} + 7 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x}}{12 \, x^{2}}\right]"," ",0,"[1/24*(15*(3*B*b^2 + 4*A*b*c)*sqrt(c)*x^2*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(6*B*c^2*x^3 - 8*A*b^2 + 3*(9*B*b*c + 4*A*c^2)*x^2 - 8*(3*B*b^2 + 7*A*b*c)*x)*sqrt(c*x^2 + b*x))/x^2, -1/12*(15*(3*B*b^2 + 4*A*b*c)*sqrt(-c)*x^2*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (6*B*c^2*x^3 - 8*A*b^2 + 3*(9*B*b*c + 4*A*c^2)*x^2 - 8*(3*B*b^2 + 7*A*b*c)*x)*sqrt(c*x^2 + b*x))/x^2]","A",0
102,1,224,0,0.419141," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, B b c + 2 \, A c^{2}\right)} \sqrt{c} x^{3} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(15 \, B c^{2} x^{3} - 6 \, A b^{2} - 2 \, {\left(35 \, B b c + 23 \, A c^{2}\right)} x^{2} - 2 \, {\left(5 \, B b^{2} + 11 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x}}{30 \, x^{3}}, -\frac{15 \, {\left(5 \, B b c + 2 \, A c^{2}\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(15 \, B c^{2} x^{3} - 6 \, A b^{2} - 2 \, {\left(35 \, B b c + 23 \, A c^{2}\right)} x^{2} - 2 \, {\left(5 \, B b^{2} + 11 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x}}{15 \, x^{3}}\right]"," ",0,"[1/30*(15*(5*B*b*c + 2*A*c^2)*sqrt(c)*x^3*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(15*B*c^2*x^3 - 6*A*b^2 - 2*(35*B*b*c + 23*A*c^2)*x^2 - 2*(5*B*b^2 + 11*A*b*c)*x)*sqrt(c*x^2 + b*x))/x^3, -1/15*(15*(5*B*b*c + 2*A*c^2)*sqrt(-c)*x^3*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (15*B*c^2*x^3 - 6*A*b^2 - 2*(35*B*b*c + 23*A*c^2)*x^2 - 2*(5*B*b^2 + 11*A*b*c)*x)*sqrt(c*x^2 + b*x))/x^3]","A",0
103,1,238,0,0.427047," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^7,x, algorithm=""fricas"")","\left[\frac{105 \, B b c^{\frac{5}{2}} x^{4} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(15 \, A b^{3} + {\left(161 \, B b c^{2} + 15 \, A c^{3}\right)} x^{3} + {\left(77 \, B b^{2} c + 45 \, A b c^{2}\right)} x^{2} + 3 \, {\left(7 \, B b^{3} + 15 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x}}{105 \, b x^{4}}, -\frac{2 \, {\left(105 \, B b \sqrt{-c} c^{2} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(15 \, A b^{3} + {\left(161 \, B b c^{2} + 15 \, A c^{3}\right)} x^{3} + {\left(77 \, B b^{2} c + 45 \, A b c^{2}\right)} x^{2} + 3 \, {\left(7 \, B b^{3} + 15 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x}\right)}}{105 \, b x^{4}}\right]"," ",0,"[1/105*(105*B*b*c^(5/2)*x^4*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(15*A*b^3 + (161*B*b*c^2 + 15*A*c^3)*x^3 + (77*B*b^2*c + 45*A*b*c^2)*x^2 + 3*(7*B*b^3 + 15*A*b^2*c)*x)*sqrt(c*x^2 + b*x))/(b*x^4), -2/105*(105*B*b*sqrt(-c)*c^2*x^4*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (15*A*b^3 + (161*B*b*c^2 + 15*A*c^3)*x^3 + (77*B*b^2*c + 45*A*b*c^2)*x^2 + 3*(7*B*b^3 + 15*A*b^2*c)*x)*sqrt(c*x^2 + b*x))/(b*x^4)]","A",0
104,1,102,0,0.404947," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^8,x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, A b^{4} + {\left(9 \, B b c^{3} - 2 \, A c^{4}\right)} x^{4} + {\left(27 \, B b^{2} c^{2} + A b c^{3}\right)} x^{3} + 3 \, {\left(9 \, B b^{3} c + 5 \, A b^{2} c^{2}\right)} x^{2} + {\left(9 \, B b^{4} + 19 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x}}{63 \, b^{2} x^{5}}"," ",0,"-2/63*(7*A*b^4 + (9*B*b*c^3 - 2*A*c^4)*x^4 + (27*B*b^2*c^2 + A*b*c^3)*x^3 + 3*(9*B*b^3*c + 5*A*b^2*c^2)*x^2 + (9*B*b^4 + 19*A*b^3*c)*x)*sqrt(c*x^2 + b*x)/(b^2*x^5)","B",0
105,1,127,0,0.406855," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^9,x, algorithm=""fricas"")","-\frac{2 \, {\left(63 \, A b^{5} - 2 \, {\left(11 \, B b c^{4} - 4 \, A c^{5}\right)} x^{5} + {\left(11 \, B b^{2} c^{3} - 4 \, A b c^{4}\right)} x^{4} + 3 \, {\left(55 \, B b^{3} c^{2} + A b^{2} c^{3}\right)} x^{3} + {\left(209 \, B b^{4} c + 113 \, A b^{3} c^{2}\right)} x^{2} + 7 \, {\left(11 \, B b^{5} + 23 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x}}{693 \, b^{3} x^{6}}"," ",0,"-2/693*(63*A*b^5 - 2*(11*B*b*c^4 - 4*A*c^5)*x^5 + (11*B*b^2*c^3 - 4*A*b*c^4)*x^4 + 3*(55*B*b^3*c^2 + A*b^2*c^3)*x^3 + (209*B*b^4*c + 113*A*b^3*c^2)*x^2 + 7*(11*B*b^5 + 23*A*b^4*c)*x)*sqrt(c*x^2 + b*x)/(b^3*x^6)","A",0
106,1,153,0,0.402597," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^10,x, algorithm=""fricas"")","-\frac{2 \, {\left(693 \, A b^{6} + 8 \, {\left(13 \, B b c^{5} - 6 \, A c^{6}\right)} x^{6} - 4 \, {\left(13 \, B b^{2} c^{4} - 6 \, A b c^{5}\right)} x^{5} + 3 \, {\left(13 \, B b^{3} c^{3} - 6 \, A b^{2} c^{4}\right)} x^{4} + {\left(1469 \, B b^{4} c^{2} + 15 \, A b^{3} c^{3}\right)} x^{3} + 7 \, {\left(299 \, B b^{5} c + 159 \, A b^{4} c^{2}\right)} x^{2} + 63 \, {\left(13 \, B b^{6} + 27 \, A b^{5} c\right)} x\right)} \sqrt{c x^{2} + b x}}{9009 \, b^{4} x^{7}}"," ",0,"-2/9009*(693*A*b^6 + 8*(13*B*b*c^5 - 6*A*c^6)*x^6 - 4*(13*B*b^2*c^4 - 6*A*b*c^5)*x^5 + 3*(13*B*b^3*c^3 - 6*A*b^2*c^4)*x^4 + (1469*B*b^4*c^2 + 15*A*b^3*c^3)*x^3 + 7*(299*B*b^5*c + 159*A*b^4*c^2)*x^2 + 63*(13*B*b^6 + 27*A*b^5*c)*x)*sqrt(c*x^2 + b*x)/(b^4*x^7)","A",0
107,1,177,0,0.399160," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^11,x, algorithm=""fricas"")","-\frac{2 \, {\left(3003 \, A b^{7} - 16 \, {\left(15 \, B b c^{6} - 8 \, A c^{7}\right)} x^{7} + 8 \, {\left(15 \, B b^{2} c^{5} - 8 \, A b c^{6}\right)} x^{6} - 6 \, {\left(15 \, B b^{3} c^{4} - 8 \, A b^{2} c^{5}\right)} x^{5} + 5 \, {\left(15 \, B b^{4} c^{3} - 8 \, A b^{3} c^{4}\right)} x^{4} + 35 \, {\left(159 \, B b^{5} c^{2} + A b^{4} c^{3}\right)} x^{3} + 63 \, {\left(135 \, B b^{6} c + 71 \, A b^{5} c^{2}\right)} x^{2} + 231 \, {\left(15 \, B b^{7} + 31 \, A b^{6} c\right)} x\right)} \sqrt{c x^{2} + b x}}{45045 \, b^{5} x^{8}}"," ",0,"-2/45045*(3003*A*b^7 - 16*(15*B*b*c^6 - 8*A*c^7)*x^7 + 8*(15*B*b^2*c^5 - 8*A*b*c^6)*x^6 - 6*(15*B*b^3*c^4 - 8*A*b^2*c^5)*x^5 + 5*(15*B*b^4*c^3 - 8*A*b^3*c^4)*x^4 + 35*(159*B*b^5*c^2 + A*b^4*c^3)*x^3 + 63*(135*B*b^6*c + 71*A*b^5*c^2)*x^2 + 231*(15*B*b^7 + 31*A*b^6*c)*x)*sqrt(c*x^2 + b*x)/(b^5*x^8)","A",0
108,1,202,0,0.408572," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^12,x, algorithm=""fricas"")","-\frac{2 \, {\left(45045 \, A b^{8} + 128 \, {\left(17 \, B b c^{7} - 10 \, A c^{8}\right)} x^{8} - 64 \, {\left(17 \, B b^{2} c^{6} - 10 \, A b c^{7}\right)} x^{7} + 48 \, {\left(17 \, B b^{3} c^{5} - 10 \, A b^{2} c^{6}\right)} x^{6} - 40 \, {\left(17 \, B b^{4} c^{4} - 10 \, A b^{3} c^{5}\right)} x^{5} + 35 \, {\left(17 \, B b^{5} c^{3} - 10 \, A b^{4} c^{4}\right)} x^{4} + 63 \, {\left(1207 \, B b^{6} c^{2} + 5 \, A b^{5} c^{3}\right)} x^{3} + 231 \, {\left(527 \, B b^{7} c + 275 \, A b^{6} c^{2}\right)} x^{2} + 3003 \, {\left(17 \, B b^{8} + 35 \, A b^{7} c\right)} x\right)} \sqrt{c x^{2} + b x}}{765765 \, b^{6} x^{9}}"," ",0,"-2/765765*(45045*A*b^8 + 128*(17*B*b*c^7 - 10*A*c^8)*x^8 - 64*(17*B*b^2*c^6 - 10*A*b*c^7)*x^7 + 48*(17*B*b^3*c^5 - 10*A*b^2*c^6)*x^6 - 40*(17*B*b^4*c^4 - 10*A*b^3*c^5)*x^5 + 35*(17*B*b^5*c^3 - 10*A*b^4*c^4)*x^4 + 63*(1207*B*b^6*c^2 + 5*A*b^5*c^3)*x^3 + 231*(527*B*b^7*c + 275*A*b^6*c^2)*x^2 + 3003*(17*B*b^8 + 35*A*b^7*c)*x)*sqrt(c*x^2 + b*x)/(b^6*x^9)","A",0
109,1,303,0,0.436447," ","integrate(x^4*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B b^{5} - 10 \, A b^{4} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(384 \, B c^{5} x^{4} + 945 \, B b^{4} c - 1050 \, A b^{3} c^{2} - 48 \, {\left(9 \, B b c^{4} - 10 \, A c^{5}\right)} x^{3} + 56 \, {\left(9 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} x^{2} - 70 \, {\left(9 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, c^{6}}, \frac{105 \, {\left(9 \, B b^{5} - 10 \, A b^{4} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(384 \, B c^{5} x^{4} + 945 \, B b^{4} c - 1050 \, A b^{3} c^{2} - 48 \, {\left(9 \, B b c^{4} - 10 \, A c^{5}\right)} x^{3} + 56 \, {\left(9 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} x^{2} - 70 \, {\left(9 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, c^{6}}\right]"," ",0,"[-1/3840*(105*(9*B*b^5 - 10*A*b^4*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(384*B*c^5*x^4 + 945*B*b^4*c - 1050*A*b^3*c^2 - 48*(9*B*b*c^4 - 10*A*c^5)*x^3 + 56*(9*B*b^2*c^3 - 10*A*b*c^4)*x^2 - 70*(9*B*b^3*c^2 - 10*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^6, 1/1920*(105*(9*B*b^5 - 10*A*b^4*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (384*B*c^5*x^4 + 945*B*b^4*c - 1050*A*b^3*c^2 - 48*(9*B*b*c^4 - 10*A*c^5)*x^3 + 56*(9*B*b^2*c^3 - 10*A*b*c^4)*x^2 - 70*(9*B*b^3*c^2 - 10*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^6]","A",0
110,1,256,0,0.425995," ","integrate(x^3*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(48 \, B c^{4} x^{3} - 105 \, B b^{3} c + 120 \, A b^{2} c^{2} - 8 \, {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} x^{2} + 10 \, {\left(7 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, c^{5}}, -\frac{15 \, {\left(7 \, B b^{4} - 8 \, A b^{3} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(48 \, B c^{4} x^{3} - 105 \, B b^{3} c + 120 \, A b^{2} c^{2} - 8 \, {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} x^{2} + 10 \, {\left(7 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, c^{5}}\right]"," ",0,"[-1/384*(15*(7*B*b^4 - 8*A*b^3*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(48*B*c^4*x^3 - 105*B*b^3*c + 120*A*b^2*c^2 - 8*(7*B*b*c^3 - 8*A*c^4)*x^2 + 10*(7*B*b^2*c^2 - 8*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/c^5, -1/192*(15*(7*B*b^4 - 8*A*b^3*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (48*B*c^4*x^3 - 105*B*b^3*c + 120*A*b^2*c^2 - 8*(7*B*b*c^3 - 8*A*c^4)*x^2 + 10*(7*B*b^2*c^2 - 8*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
111,1,207,0,0.446557," ","integrate(x^2*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b^{3} - 6 \, A b^{2} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{3} x^{2} + 15 \, B b^{2} c - 18 \, A b c^{2} - 2 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c^{4}}, \frac{3 \, {\left(5 \, B b^{3} - 6 \, A b^{2} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, B c^{3} x^{2} + 15 \, B b^{2} c - 18 \, A b c^{2} - 2 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c^{4}}\right]"," ",0,"[-1/48*(3*(5*B*b^3 - 6*A*b^2*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(8*B*c^3*x^2 + 15*B*b^2*c - 18*A*b*c^2 - 2*(5*B*b*c^2 - 6*A*c^3)*x)*sqrt(c*x^2 + b*x))/c^4, 1/24*(3*(5*B*b^3 - 6*A*b^2*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*B*c^3*x^2 + 15*B*b^2*c - 18*A*b*c^2 - 2*(5*B*b*c^2 - 6*A*c^3)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
112,1,158,0,0.429767," ","integrate(x*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B b^{2} - 4 \, A b c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(2 \, B c^{2} x - 3 \, B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x}}{8 \, c^{3}}, -\frac{{\left(3 \, B b^{2} - 4 \, A b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, B c^{2} x - 3 \, B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x}}{4 \, c^{3}}\right]"," ",0,"[-1/8*((3*B*b^2 - 4*A*b*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(2*B*c^2*x - 3*B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x))/c^3, -1/4*((3*B*b^2 - 4*A*b*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*B*c^2*x - 3*B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x))/c^3]","A",0
113,1,115,0,0.411427," ","integrate((B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c x^{2} + b x} B c - {\left(B b - 2 \, A c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right)}{2 \, c^{2}}, \frac{\sqrt{c x^{2} + b x} B c + {\left(B b - 2 \, A c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right)}{c^{2}}\right]"," ",0,"[1/2*(2*sqrt(c*x^2 + b*x)*B*c - (B*b - 2*A*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)))/c^2, (sqrt(c*x^2 + b*x)*B*c + (B*b - 2*A*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)))/c^2]","A",0
114,1,116,0,0.421890," ","integrate((B*x+A)/x/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{B b \sqrt{c} x \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, \sqrt{c x^{2} + b x} A c}{b c x}, -\frac{2 \, {\left(B b \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + \sqrt{c x^{2} + b x} A c\right)}}{b c x}\right]"," ",0,"[(B*b*sqrt(c)*x*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*sqrt(c*x^2 + b*x)*A*c)/(b*c*x), -2*(B*b*sqrt(-c)*x*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + sqrt(c*x^2 + b*x)*A*c)/(b*c*x)]","A",0
115,1,34,0,0.414495," ","integrate((B*x+A)/x^2/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x} {\left(A b + {\left(3 \, B b - 2 \, A c\right)} x\right)}}{3 \, b^{2} x^{2}}"," ",0,"-2/3*sqrt(c*x^2 + b*x)*(A*b + (3*B*b - 2*A*c)*x)/(b^2*x^2)","A",0
116,1,57,0,0.410391," ","integrate((B*x+A)/x^3/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A b^{2} - 2 \, {\left(5 \, B b c - 4 \, A c^{2}\right)} x^{2} + {\left(5 \, B b^{2} - 4 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x}}{15 \, b^{3} x^{3}}"," ",0,"-2/15*(3*A*b^2 - 2*(5*B*b*c - 4*A*c^2)*x^2 + (5*B*b^2 - 4*A*b*c)*x)*sqrt(c*x^2 + b*x)/(b^3*x^3)","A",0
117,1,82,0,0.413415," ","integrate((B*x+A)/x^4/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, A b^{3} + 8 \, {\left(7 \, B b c^{2} - 6 \, A c^{3}\right)} x^{3} - 4 \, {\left(7 \, B b^{2} c - 6 \, A b c^{2}\right)} x^{2} + 3 \, {\left(7 \, B b^{3} - 6 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x}}{105 \, b^{4} x^{4}}"," ",0,"-2/105*(15*A*b^3 + 8*(7*B*b*c^2 - 6*A*c^3)*x^3 - 4*(7*B*b^2*c - 6*A*b*c^2)*x^2 + 3*(7*B*b^3 - 6*A*b^2*c)*x)*sqrt(c*x^2 + b*x)/(b^4*x^4)","A",0
118,1,106,0,0.414130," ","integrate((B*x+A)/x^5/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, A b^{4} - 16 \, {\left(9 \, B b c^{3} - 8 \, A c^{4}\right)} x^{4} + 8 \, {\left(9 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x^{3} - 6 \, {\left(9 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} x^{2} + 5 \, {\left(9 \, B b^{4} - 8 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x}}{315 \, b^{5} x^{5}}"," ",0,"-2/315*(35*A*b^4 - 16*(9*B*b*c^3 - 8*A*c^4)*x^4 + 8*(9*B*b^2*c^2 - 8*A*b*c^3)*x^3 - 6*(9*B*b^3*c - 8*A*b^2*c^2)*x^2 + 5*(9*B*b^4 - 8*A*b^3*c)*x)*sqrt(c*x^2 + b*x)/(b^5*x^5)","A",0
119,1,130,0,0.413378," ","integrate((B*x+A)/x^6/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, A b^{5} + 128 \, {\left(11 \, B b c^{4} - 10 \, A c^{5}\right)} x^{5} - 64 \, {\left(11 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} x^{4} + 48 \, {\left(11 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} x^{3} - 40 \, {\left(11 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} x^{2} + 35 \, {\left(11 \, B b^{5} - 10 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x}}{3465 \, b^{6} x^{6}}"," ",0,"-2/3465*(315*A*b^5 + 128*(11*B*b*c^4 - 10*A*c^5)*x^5 - 64*(11*B*b^2*c^3 - 10*A*b*c^4)*x^4 + 48*(11*B*b^3*c^2 - 10*A*b^2*c^3)*x^3 - 40*(11*B*b^4*c - 10*A*b^3*c^2)*x^2 + 35*(11*B*b^5 - 10*A*b^4*c)*x)*sqrt(c*x^2 + b*x)/(b^6*x^6)","A",0
120,1,313,0,0.420242," ","integrate(x^4*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{4} - 6 \, A b^{3} c + {\left(7 \, B b^{3} c - 6 \, A b^{2} c^{2}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{4} x^{3} + 105 \, B b^{3} c - 90 \, A b^{2} c^{2} - 2 \, {\left(7 \, B b c^{3} - 6 \, A c^{4}\right)} x^{2} + 5 \, {\left(7 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{6} x + b c^{5}\right)}}, \frac{15 \, {\left(7 \, B b^{4} - 6 \, A b^{3} c + {\left(7 \, B b^{3} c - 6 \, A b^{2} c^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, B c^{4} x^{3} + 105 \, B b^{3} c - 90 \, A b^{2} c^{2} - 2 \, {\left(7 \, B b c^{3} - 6 \, A c^{4}\right)} x^{2} + 5 \, {\left(7 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{6} x + b c^{5}\right)}}\right]"," ",0,"[-1/48*(15*(7*B*b^4 - 6*A*b^3*c + (7*B*b^3*c - 6*A*b^2*c^2)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(8*B*c^4*x^3 + 105*B*b^3*c - 90*A*b^2*c^2 - 2*(7*B*b*c^3 - 6*A*c^4)*x^2 + 5*(7*B*b^2*c^2 - 6*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/(c^6*x + b*c^5), 1/24*(15*(7*B*b^4 - 6*A*b^3*c + (7*B*b^3*c - 6*A*b^2*c^2)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*B*c^4*x^3 + 105*B*b^3*c - 90*A*b^2*c^2 - 2*(7*B*b*c^3 - 6*A*c^4)*x^2 + 5*(7*B*b^2*c^2 - 6*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/(c^6*x + b*c^5)]","A",0
121,1,262,0,0.413062," ","integrate(x^3*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b^{3} - 4 \, A b^{2} c + {\left(5 \, B b^{2} c - 4 \, A b c^{2}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(2 \, B c^{3} x^{2} - 15 \, B b^{2} c + 12 \, A b c^{2} - {\left(5 \, B b c^{2} - 4 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{5} x + b c^{4}\right)}}, -\frac{3 \, {\left(5 \, B b^{3} - 4 \, A b^{2} c + {\left(5 \, B b^{2} c - 4 \, A b c^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, B c^{3} x^{2} - 15 \, B b^{2} c + 12 \, A b c^{2} - {\left(5 \, B b c^{2} - 4 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c^{5} x + b c^{4}\right)}}\right]"," ",0,"[-1/8*(3*(5*B*b^3 - 4*A*b^2*c + (5*B*b^2*c - 4*A*b*c^2)*x)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(2*B*c^3*x^2 - 15*B*b^2*c + 12*A*b*c^2 - (5*B*b*c^2 - 4*A*c^3)*x)*sqrt(c*x^2 + b*x))/(c^5*x + b*c^4), -1/4*(3*(5*B*b^3 - 4*A*b^2*c + (5*B*b^2*c - 4*A*b*c^2)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*B*c^3*x^2 - 15*B*b^2*c + 12*A*b*c^2 - (5*B*b*c^2 - 4*A*c^3)*x)*sqrt(c*x^2 + b*x))/(c^5*x + b*c^4)]","A",0
122,1,202,0,0.418200," ","integrate(x^2*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B b^{2} - 2 \, A b c + {\left(3 \, B b c - 2 \, A c^{2}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(B c^{2} x + 3 \, B b c - 2 \, A c^{2}\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(c^{4} x + b c^{3}\right)}}, \frac{{\left(3 \, B b^{2} - 2 \, A b c + {\left(3 \, B b c - 2 \, A c^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(B c^{2} x + 3 \, B b c - 2 \, A c^{2}\right)} \sqrt{c x^{2} + b x}}{c^{4} x + b c^{3}}\right]"," ",0,"[-1/2*((3*B*b^2 - 2*A*b*c + (3*B*b*c - 2*A*c^2)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(B*c^2*x + 3*B*b*c - 2*A*c^2)*sqrt(c*x^2 + b*x))/(c^4*x + b*c^3), ((3*B*b^2 - 2*A*b*c + (3*B*b*c - 2*A*c^2)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (B*c^2*x + 3*B*b*c - 2*A*c^2)*sqrt(c*x^2 + b*x))/(c^4*x + b*c^3)]","A",0
123,1,164,0,0.421089," ","integrate(x*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B b c x + B b^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(B b c - A c^{2}\right)} \sqrt{c x^{2} + b x}}{b c^{3} x + b^{2} c^{2}}, -\frac{2 \, {\left({\left(B b c x + B b^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(B b c - A c^{2}\right)} \sqrt{c x^{2} + b x}\right)}}{b c^{3} x + b^{2} c^{2}}\right]"," ",0,"[((B*b*c*x + B*b^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(B*b*c - A*c^2)*sqrt(c*x^2 + b*x))/(b*c^3*x + b^2*c^2), -2*((B*b*c*x + B*b^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (B*b*c - A*c^2)*sqrt(c*x^2 + b*x))/(b*c^3*x + b^2*c^2)]","A",0
124,1,44,0,0.400143," ","integrate((B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x} {\left(A b - {\left(B b - 2 \, A c\right)} x\right)}}{b^{2} c x^{2} + b^{3} x}"," ",0,"-2*sqrt(c*x^2 + b*x)*(A*b - (B*b - 2*A*c)*x)/(b^2*c*x^2 + b^3*x)","A",0
125,1,68,0,0.399333," ","integrate((B*x+A)/x/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A b^{2} + 2 \, {\left(3 \, B b c - 4 \, A c^{2}\right)} x^{2} + {\left(3 \, B b^{2} - 4 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{3} c x^{3} + b^{4} x^{2}\right)}}"," ",0,"-2/3*(A*b^2 + 2*(3*B*b*c - 4*A*c^2)*x^2 + (3*B*b^2 - 4*A*b*c)*x)*sqrt(c*x^2 + b*x)/(b^3*c*x^3 + b^4*x^2)","A",0
126,1,93,0,0.411843," ","integrate((B*x+A)/x^2/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A b^{3} - 8 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x^{3} - 4 \, {\left(5 \, B b^{2} c - 6 \, A b c^{2}\right)} x^{2} + {\left(5 \, B b^{3} - 6 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x}}{15 \, {\left(b^{4} c x^{4} + b^{5} x^{3}\right)}}"," ",0,"-2/15*(3*A*b^3 - 8*(5*B*b*c^2 - 6*A*c^3)*x^3 - 4*(5*B*b^2*c - 6*A*b*c^2)*x^2 + (5*B*b^3 - 6*A*b^2*c)*x)*sqrt(c*x^2 + b*x)/(b^4*c*x^4 + b^5*x^3)","A",0
127,1,117,0,0.404630," ","integrate((B*x+A)/x^3/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, A b^{4} + 16 \, {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} x^{4} + 8 \, {\left(7 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x^{3} - 2 \, {\left(7 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} x^{2} + {\left(7 \, B b^{4} - 8 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x}}{35 \, {\left(b^{5} c x^{5} + b^{6} x^{4}\right)}}"," ",0,"-2/35*(5*A*b^4 + 16*(7*B*b*c^3 - 8*A*c^4)*x^4 + 8*(7*B*b^2*c^2 - 8*A*b*c^3)*x^3 - 2*(7*B*b^3*c - 8*A*b^2*c^2)*x^2 + (7*B*b^4 - 8*A*b^3*c)*x)*sqrt(c*x^2 + b*x)/(b^5*c*x^5 + b^6*x^4)","A",0
128,1,142,0,0.412798," ","integrate((B*x+A)/x^4/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, A b^{5} - 128 \, {\left(9 \, B b c^{4} - 10 \, A c^{5}\right)} x^{5} - 64 \, {\left(9 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} x^{4} + 16 \, {\left(9 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} x^{3} - 8 \, {\left(9 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} x^{2} + 5 \, {\left(9 \, B b^{5} - 10 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x}}{315 \, {\left(b^{6} c x^{6} + b^{7} x^{5}\right)}}"," ",0,"-2/315*(35*A*b^5 - 128*(9*B*b*c^4 - 10*A*c^5)*x^5 - 64*(9*B*b^2*c^3 - 10*A*b*c^4)*x^4 + 16*(9*B*b^3*c^2 - 10*A*b^2*c^3)*x^3 - 8*(9*B*b^4*c - 10*A*b^3*c^2)*x^2 + 5*(9*B*b^5 - 10*A*b^4*c)*x)*sqrt(c*x^2 + b*x)/(b^6*c*x^6 + b^7*x^5)","A",0
129,1,380,0,0.434385," ","integrate(x^5*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{4} - 4 \, A b^{3} c + {\left(7 \, B b^{2} c^{2} - 4 \, A b c^{3}\right)} x^{2} + 2 \, {\left(7 \, B b^{3} c - 4 \, A b^{2} c^{2}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(6 \, B c^{4} x^{3} - 105 \, B b^{3} c + 60 \, A b^{2} c^{2} - 3 \, {\left(7 \, B b c^{3} - 4 \, A c^{4}\right)} x^{2} - 20 \, {\left(7 \, B b^{2} c^{2} - 4 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{7} x^{2} + 2 \, b c^{6} x + b^{2} c^{5}\right)}}, -\frac{15 \, {\left(7 \, B b^{4} - 4 \, A b^{3} c + {\left(7 \, B b^{2} c^{2} - 4 \, A b c^{3}\right)} x^{2} + 2 \, {\left(7 \, B b^{3} c - 4 \, A b^{2} c^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(6 \, B c^{4} x^{3} - 105 \, B b^{3} c + 60 \, A b^{2} c^{2} - 3 \, {\left(7 \, B b c^{3} - 4 \, A c^{4}\right)} x^{2} - 20 \, {\left(7 \, B b^{2} c^{2} - 4 \, A b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{12 \, {\left(c^{7} x^{2} + 2 \, b c^{6} x + b^{2} c^{5}\right)}}\right]"," ",0,"[-1/24*(15*(7*B*b^4 - 4*A*b^3*c + (7*B*b^2*c^2 - 4*A*b*c^3)*x^2 + 2*(7*B*b^3*c - 4*A*b^2*c^2)*x)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(6*B*c^4*x^3 - 105*B*b^3*c + 60*A*b^2*c^2 - 3*(7*B*b*c^3 - 4*A*c^4)*x^2 - 20*(7*B*b^2*c^2 - 4*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/(c^7*x^2 + 2*b*c^6*x + b^2*c^5), -1/12*(15*(7*B*b^4 - 4*A*b^3*c + (7*B*b^2*c^2 - 4*A*b*c^3)*x^2 + 2*(7*B*b^3*c - 4*A*b^2*c^2)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (6*B*c^4*x^3 - 105*B*b^3*c + 60*A*b^2*c^2 - 3*(7*B*b*c^3 - 4*A*c^4)*x^2 - 20*(7*B*b^2*c^2 - 4*A*b*c^3)*x)*sqrt(c*x^2 + b*x))/(c^7*x^2 + 2*b*c^6*x + b^2*c^5)]","A",0
130,1,321,0,0.426711," ","integrate(x^4*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b^{3} - 2 \, A b^{2} c + {\left(5 \, B b c^{2} - 2 \, A c^{3}\right)} x^{2} + 2 \, {\left(5 \, B b^{2} c - 2 \, A b c^{2}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(3 \, B c^{3} x^{2} + 15 \, B b^{2} c - 6 \, A b c^{2} + 4 \, {\left(5 \, B b c^{2} - 2 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{6 \, {\left(c^{6} x^{2} + 2 \, b c^{5} x + b^{2} c^{4}\right)}}, \frac{3 \, {\left(5 \, B b^{3} - 2 \, A b^{2} c + {\left(5 \, B b c^{2} - 2 \, A c^{3}\right)} x^{2} + 2 \, {\left(5 \, B b^{2} c - 2 \, A b c^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(3 \, B c^{3} x^{2} + 15 \, B b^{2} c - 6 \, A b c^{2} + 4 \, {\left(5 \, B b c^{2} - 2 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(c^{6} x^{2} + 2 \, b c^{5} x + b^{2} c^{4}\right)}}\right]"," ",0,"[-1/6*(3*(5*B*b^3 - 2*A*b^2*c + (5*B*b*c^2 - 2*A*c^3)*x^2 + 2*(5*B*b^2*c - 2*A*b*c^2)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(3*B*c^3*x^2 + 15*B*b^2*c - 6*A*b*c^2 + 4*(5*B*b*c^2 - 2*A*c^3)*x)*sqrt(c*x^2 + b*x))/(c^6*x^2 + 2*b*c^5*x + b^2*c^4), 1/3*(3*(5*B*b^3 - 2*A*b^2*c + (5*B*b*c^2 - 2*A*c^3)*x^2 + 2*(5*B*b^2*c - 2*A*b*c^2)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (3*B*c^3*x^2 + 15*B*b^2*c - 6*A*b*c^2 + 4*(5*B*b*c^2 - 2*A*c^3)*x)*sqrt(c*x^2 + b*x))/(c^6*x^2 + 2*b*c^5*x + b^2*c^4)]","A",0
131,1,239,0,0.433861," ","integrate(x^3*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B b c^{2} x^{2} + 2 \, B b^{2} c x + B b^{3}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(3 \, B b^{2} c + {\left(4 \, B b c^{2} - A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b c^{5} x^{2} + 2 \, b^{2} c^{4} x + b^{3} c^{3}\right)}}, -\frac{2 \, {\left(3 \, {\left(B b c^{2} x^{2} + 2 \, B b^{2} c x + B b^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(3 \, B b^{2} c + {\left(4 \, B b c^{2} - A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}\right)}}{3 \, {\left(b c^{5} x^{2} + 2 \, b^{2} c^{4} x + b^{3} c^{3}\right)}}\right]"," ",0,"[1/3*(3*(B*b*c^2*x^2 + 2*B*b^2*c*x + B*b^3)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(3*B*b^2*c + (4*B*b*c^2 - A*c^3)*x)*sqrt(c*x^2 + b*x))/(b*c^5*x^2 + 2*b^2*c^4*x + b^3*c^3), -2/3*(3*(B*b*c^2*x^2 + 2*B*b^2*c*x + B*b^3)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (3*B*b^2*c + (4*B*b*c^2 - A*c^3)*x)*sqrt(c*x^2 + b*x))/(b*c^5*x^2 + 2*b^2*c^4*x + b^3*c^3)]","A",0
132,1,51,0,0.395952," ","integrate(x^2*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x} {\left(3 \, A b + {\left(B b + 2 \, A c\right)} x\right)}}{3 \, {\left(b^{2} c^{2} x^{2} + 2 \, b^{3} c x + b^{4}\right)}}"," ",0,"2/3*sqrt(c*x^2 + b*x)*(3*A*b + (B*b + 2*A*c)*x)/(b^2*c^2*x^2 + 2*b^3*c*x + b^4)","A",0
133,1,77,0,0.423193," ","integrate(x*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A b^{2} - 2 \, {\left(B b c - 4 \, A c^{2}\right)} x^{2} - 3 \, {\left(B b^{2} - 4 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{3} c^{2} x^{3} + 2 \, b^{4} c x^{2} + b^{5} x\right)}}"," ",0,"-2/3*(3*A*b^2 - 2*(B*b*c - 4*A*c^2)*x^2 - 3*(B*b^2 - 4*A*b*c)*x)*sqrt(c*x^2 + b*x)/(b^3*c^2*x^3 + 2*b^4*c*x^2 + b^5*x)","A",0
134,1,101,0,0.408389," ","integrate((B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A b^{3} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} x^{3} + 12 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} x^{2} + 3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}"," ",0,"-2/3*(A*b^3 + 8*(B*b*c^2 - 2*A*c^3)*x^3 + 12*(B*b^2*c - 2*A*b*c^2)*x^2 + 3*(B*b^3 - 2*A*b^2*c)*x)*sqrt(c*x^2 + b*x)/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)","A",0
135,1,128,0,0.413459," ","integrate((B*x+A)/x/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A b^{4} - 16 \, {\left(5 \, B b c^{3} - 8 \, A c^{4}\right)} x^{4} - 24 \, {\left(5 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} x^{3} - 6 \, {\left(5 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} x^{2} + {\left(5 \, B b^{4} - 8 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x}}{15 \, {\left(b^{5} c^{2} x^{5} + 2 \, b^{6} c x^{4} + b^{7} x^{3}\right)}}"," ",0,"-2/15*(3*A*b^4 - 16*(5*B*b*c^3 - 8*A*c^4)*x^4 - 24*(5*B*b^2*c^2 - 8*A*b*c^3)*x^3 - 6*(5*B*b^3*c - 8*A*b^2*c^2)*x^2 + (5*B*b^4 - 8*A*b^3*c)*x)*sqrt(c*x^2 + b*x)/(b^5*c^2*x^5 + 2*b^6*c*x^4 + b^7*x^3)","A",0
136,1,153,0,0.404397," ","integrate((B*x+A)/x^2/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, A b^{5} + 128 \, {\left(7 \, B b c^{4} - 10 \, A c^{5}\right)} x^{5} + 192 \, {\left(7 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} x^{4} + 48 \, {\left(7 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} x^{3} - 8 \, {\left(7 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} x^{2} + 3 \, {\left(7 \, B b^{5} - 10 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x}}{105 \, {\left(b^{6} c^{2} x^{6} + 2 \, b^{7} c x^{5} + b^{8} x^{4}\right)}}"," ",0,"-2/105*(15*A*b^5 + 128*(7*B*b*c^4 - 10*A*c^5)*x^5 + 192*(7*B*b^2*c^3 - 10*A*b*c^4)*x^4 + 48*(7*B*b^3*c^2 - 10*A*b^2*c^3)*x^3 - 8*(7*B*b^4*c - 10*A*b^3*c^2)*x^2 + 3*(7*B*b^5 - 10*A*b^4*c)*x)*sqrt(c*x^2 + b*x)/(b^6*c^2*x^6 + 2*b^7*c*x^5 + b^8*x^4)","A",0
137,1,177,0,0.412372," ","integrate((B*x+A)/x^3/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, A b^{6} - 256 \, {\left(3 \, B b c^{5} - 4 \, A c^{6}\right)} x^{6} - 384 \, {\left(3 \, B b^{2} c^{4} - 4 \, A b c^{5}\right)} x^{5} - 96 \, {\left(3 \, B b^{3} c^{3} - 4 \, A b^{2} c^{4}\right)} x^{4} + 16 \, {\left(3 \, B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} x^{3} - 6 \, {\left(3 \, B b^{5} c - 4 \, A b^{4} c^{2}\right)} x^{2} + 3 \, {\left(3 \, B b^{6} - 4 \, A b^{5} c\right)} x\right)} \sqrt{c x^{2} + b x}}{63 \, {\left(b^{7} c^{2} x^{7} + 2 \, b^{8} c x^{6} + b^{9} x^{5}\right)}}"," ",0,"-2/63*(7*A*b^6 - 256*(3*B*b*c^5 - 4*A*c^6)*x^6 - 384*(3*B*b^2*c^4 - 4*A*b*c^5)*x^5 - 96*(3*B*b^3*c^3 - 4*A*b^2*c^4)*x^4 + 16*(3*B*b^4*c^2 - 4*A*b^3*c^3)*x^3 - 6*(3*B*b^5*c - 4*A*b^4*c^2)*x^2 + 3*(3*B*b^6 - 4*A*b^5*c)*x)*sqrt(c*x^2 + b*x)/(b^7*c^2*x^7 + 2*b^8*c*x^6 + b^9*x^5)","A",0
138,1,164,0,0.409042," ","integrate((e*x+d)/(c*x^2+b*x)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{5} d + 128 \, {\left(2 \, c^{5} d - b c^{4} e\right)} x^{5} + 320 \, {\left(2 \, b c^{4} d - b^{2} c^{3} e\right)} x^{4} + 240 \, {\left(2 \, b^{2} c^{3} d - b^{3} c^{2} e\right)} x^{3} + 40 \, {\left(2 \, b^{3} c^{2} d - b^{4} c e\right)} x^{2} - 5 \, {\left(2 \, b^{4} c d - b^{5} e\right)} x\right)} \sqrt{c x^{2} + b x}}{15 \, {\left(b^{6} c^{3} x^{6} + 3 \, b^{7} c^{2} x^{5} + 3 \, b^{8} c x^{4} + b^{9} x^{3}\right)}}"," ",0,"-2/15*(3*b^5*d + 128*(2*c^5*d - b*c^4*e)*x^5 + 320*(2*b*c^4*d - b^2*c^3*e)*x^4 + 240*(2*b^2*c^3*d - b^3*c^2*e)*x^3 + 40*(2*b^3*c^2*d - b^4*c*e)*x^2 - 5*(2*b^4*c*d - b^5*e)*x)*sqrt(c*x^2 + b*x)/(b^6*c^3*x^6 + 3*b^7*c^2*x^5 + 3*b^8*c*x^4 + b^9*x^3)","A",0
139,1,223,0,0.422721," ","integrate((e*x+d)/(c*x^2+b*x)^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, b^{7} d - 1024 \, {\left(2 \, c^{7} d - b c^{6} e\right)} x^{7} - 3584 \, {\left(2 \, b c^{6} d - b^{2} c^{5} e\right)} x^{6} - 4480 \, {\left(2 \, b^{2} c^{5} d - b^{3} c^{4} e\right)} x^{5} - 2240 \, {\left(2 \, b^{3} c^{4} d - b^{4} c^{3} e\right)} x^{4} - 280 \, {\left(2 \, b^{4} c^{3} d - b^{5} c^{2} e\right)} x^{3} + 28 \, {\left(2 \, b^{5} c^{2} d - b^{6} c e\right)} x^{2} - 7 \, {\left(2 \, b^{6} c d - b^{7} e\right)} x\right)} \sqrt{c x^{2} + b x}}{35 \, {\left(b^{8} c^{4} x^{8} + 4 \, b^{9} c^{3} x^{7} + 6 \, b^{10} c^{2} x^{6} + 4 \, b^{11} c x^{5} + b^{12} x^{4}\right)}}"," ",0,"-2/35*(5*b^7*d - 1024*(2*c^7*d - b*c^6*e)*x^7 - 3584*(2*b*c^6*d - b^2*c^5*e)*x^6 - 4480*(2*b^2*c^5*d - b^3*c^4*e)*x^5 - 2240*(2*b^3*c^4*d - b^4*c^3*e)*x^4 - 280*(2*b^4*c^3*d - b^5*c^2*e)*x^3 + 28*(2*b^5*c^2*d - b^6*c*e)*x^2 - 7*(2*b^6*c*d - b^7*e)*x)*sqrt(c*x^2 + b*x)/(b^8*c^4*x^8 + 4*b^9*c^3*x^7 + 6*b^10*c^2*x^6 + 4*b^11*c*x^5 + b^12*x^4)","A",0
140,1,32,0,0.393346," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2}{2145} \, {\left(143 \, B c x^{7} + 195 \, A b x^{5} + 165 \, {\left(B b + A c\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/2145*(143*B*c*x^7 + 195*A*b*x^5 + 165*(B*b + A*c)*x^6)*sqrt(x)","A",0
141,1,32,0,0.401320," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2}{1287} \, {\left(99 \, B c x^{6} + 143 \, A b x^{4} + 117 \, {\left(B b + A c\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/1287*(99*B*c*x^6 + 143*A*b*x^4 + 117*(B*b + A*c)*x^5)*sqrt(x)","A",0
142,1,32,0,0.395955," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2}{693} \, {\left(63 \, B c x^{5} + 99 \, A b x^{3} + 77 \, {\left(B b + A c\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/693*(63*B*c*x^5 + 99*A*b*x^3 + 77*(B*b + A*c)*x^4)*sqrt(x)","A",0
143,1,32,0,0.405618," ","integrate((B*x+A)*(c*x^2+b*x)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B c x^{4} + 63 \, A b x^{2} + 45 \, {\left(B b + A c\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/315*(35*B*c*x^4 + 63*A*b*x^2 + 45*(B*b + A*c)*x^3)*sqrt(x)","A",0
144,1,30,0,0.389043," ","integrate((B*x+A)*(c*x^2+b*x)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, B c x^{3} + 35 \, A b x + 21 \, {\left(B b + A c\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/105*(15*B*c*x^3 + 35*A*b*x + 21*(B*b + A*c)*x^2)*sqrt(x)","A",0
145,1,27,0,0.410402," ","integrate((B*x+A)*(c*x^2+b*x)/x^(3/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(3 \, B c x^{2} + 15 \, A b + 5 \, {\left(B b + A c\right)} x\right)} \sqrt{x}"," ",0,"2/15*(3*B*c*x^2 + 15*A*b + 5*(B*b + A*c)*x)*sqrt(x)","A",0
146,1,26,0,0.400929," ","integrate((B*x+A)*(c*x^2+b*x)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c x^{2} - 3 \, A b + 3 \, {\left(B b + A c\right)} x\right)}}{3 \, \sqrt{x}}"," ",0,"2/3*(B*c*x^2 - 3*A*b + 3*(B*b + A*c)*x)/sqrt(x)","A",0
147,1,27,0,0.396925," ","integrate((B*x+A)*(c*x^2+b*x)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c x^{2} - A b - 3 \, {\left(B b + A c\right)} x\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(3*B*c*x^2 - A*b - 3*(B*b + A*c)*x)/x^(3/2)","A",0
148,1,27,0,0.398326," ","integrate((B*x+A)*(c*x^2+b*x)/x^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, B c x^{2} + 3 \, A b + 5 \, {\left(B b + A c\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(15*B*c*x^2 + 3*A*b + 5*(B*b + A*c)*x)/x^(5/2)","A",0
149,1,56,0,0.384250," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2}{62985} \, {\left(3315 \, B c^{2} x^{9} + 4845 \, A b^{2} x^{6} + 3705 \, {\left(2 \, B b c + A c^{2}\right)} x^{8} + 4199 \, {\left(B b^{2} + 2 \, A b c\right)} x^{7}\right)} \sqrt{x}"," ",0,"2/62985*(3315*B*c^2*x^9 + 4845*A*b^2*x^6 + 3705*(2*B*b*c + A*c^2)*x^8 + 4199*(B*b^2 + 2*A*b*c)*x^7)*sqrt(x)","A",0
150,1,56,0,0.386019," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2}{36465} \, {\left(2145 \, B c^{2} x^{8} + 3315 \, A b^{2} x^{5} + 2431 \, {\left(2 \, B b c + A c^{2}\right)} x^{7} + 2805 \, {\left(B b^{2} + 2 \, A b c\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/36465*(2145*B*c^2*x^8 + 3315*A*b^2*x^5 + 2431*(2*B*b*c + A*c^2)*x^7 + 2805*(B*b^2 + 2*A*b*c)*x^6)*sqrt(x)","A",0
151,1,56,0,0.392878," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2}{6435} \, {\left(429 \, B c^{2} x^{7} + 715 \, A b^{2} x^{4} + 495 \, {\left(2 \, B b c + A c^{2}\right)} x^{6} + 585 \, {\left(B b^{2} + 2 \, A b c\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/6435*(429*B*c^2*x^7 + 715*A*b^2*x^4 + 495*(2*B*b*c + A*c^2)*x^6 + 585*(B*b^2 + 2*A*b*c)*x^5)*sqrt(x)","A",0
152,1,56,0,0.390756," ","integrate((B*x+A)*(c*x^2+b*x)^2*x^(1/2),x, algorithm=""fricas"")","\frac{2}{9009} \, {\left(693 \, B c^{2} x^{6} + 1287 \, A b^{2} x^{3} + 819 \, {\left(2 \, B b c + A c^{2}\right)} x^{5} + 1001 \, {\left(B b^{2} + 2 \, A b c\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/9009*(693*B*c^2*x^6 + 1287*A*b^2*x^3 + 819*(2*B*b*c + A*c^2)*x^5 + 1001*(B*b^2 + 2*A*b*c)*x^4)*sqrt(x)","A",0
153,1,56,0,0.390082," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B c^{2} x^{5} + 693 \, A b^{2} x^{2} + 385 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 495 \, {\left(B b^{2} + 2 \, A b c\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/3465*(315*B*c^2*x^5 + 693*A*b^2*x^2 + 385*(2*B*b*c + A*c^2)*x^4 + 495*(B*b^2 + 2*A*b*c)*x^3)*sqrt(x)","A",0
154,1,54,0,0.405049," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(3/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B c^{2} x^{4} + 105 \, A b^{2} x + 45 \, {\left(2 \, B b c + A c^{2}\right)} x^{3} + 63 \, {\left(B b^{2} + 2 \, A b c\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/315*(35*B*c^2*x^4 + 105*A*b^2*x + 45*(2*B*b*c + A*c^2)*x^3 + 63*(B*b^2 + 2*A*b*c)*x^2)*sqrt(x)","A",0
155,1,51,0,0.406994," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(5/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, B c^{2} x^{3} + 105 \, A b^{2} + 21 \, {\left(2 \, B b c + A c^{2}\right)} x^{2} + 35 \, {\left(B b^{2} + 2 \, A b c\right)} x\right)} \sqrt{x}"," ",0,"2/105*(15*B*c^2*x^3 + 105*A*b^2 + 21*(2*B*b*c + A*c^2)*x^2 + 35*(B*b^2 + 2*A*b*c)*x)*sqrt(x)","A",0
156,1,51,0,0.407585," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{2} x^{3} - 15 \, A b^{2} + 5 \, {\left(2 \, B b c + A c^{2}\right)} x^{2} + 15 \, {\left(B b^{2} + 2 \, A b c\right)} x\right)}}{15 \, \sqrt{x}}"," ",0,"2/15*(3*B*c^2*x^3 - 15*A*b^2 + 5*(2*B*b*c + A*c^2)*x^2 + 15*(B*b^2 + 2*A*b*c)*x)/sqrt(x)","A",0
157,1,50,0,0.407174," ","integrate((B*x+A)*(c*x^2+b*x)^2/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c^{2} x^{3} - A b^{2} + 3 \, {\left(2 \, B b c + A c^{2}\right)} x^{2} - 3 \, {\left(B b^{2} + 2 \, A b c\right)} x\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(B*c^2*x^3 - A*b^2 + 3*(2*B*b*c + A*c^2)*x^2 - 3*(B*b^2 + 2*A*b*c)*x)/x^(3/2)","A",0
158,1,78,0,0.401337," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2}{780045} \, {\left(33915 \, B c^{3} x^{11} + 52003 \, A b^{3} x^{7} + 37145 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{10} + 123165 \, {\left(B b^{2} c + A b c^{2}\right)} x^{9} + 45885 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{8}\right)} \sqrt{x}"," ",0,"2/780045*(33915*B*c^3*x^11 + 52003*A*b^3*x^7 + 37145*(3*B*b*c^2 + A*c^3)*x^10 + 123165*(B*b^2*c + A*b*c^2)*x^9 + 45885*(B*b^3 + 3*A*b^2*c)*x^8)*sqrt(x)","A",0
159,1,78,0,0.406299," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2}{440895} \, {\left(20995 \, B c^{3} x^{10} + 33915 \, A b^{3} x^{6} + 23205 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{9} + 77805 \, {\left(B b^{2} c + A b c^{2}\right)} x^{8} + 29393 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{7}\right)} \sqrt{x}"," ",0,"2/440895*(20995*B*c^3*x^10 + 33915*A*b^3*x^6 + 23205*(3*B*b*c^2 + A*c^3)*x^9 + 77805*(B*b^2*c + A*b*c^2)*x^8 + 29393*(B*b^3 + 3*A*b^2*c)*x^7)*sqrt(x)","A",0
160,1,78,0,0.405452," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2}{230945} \, {\left(12155 \, B c^{3} x^{9} + 20995 \, A b^{3} x^{5} + 13585 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{8} + 46189 \, {\left(B b^{2} c + A b c^{2}\right)} x^{7} + 17765 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/230945*(12155*B*c^3*x^9 + 20995*A*b^3*x^5 + 13585*(3*B*b*c^2 + A*c^3)*x^8 + 46189*(B*b^2*c + A*b*c^2)*x^7 + 17765*(B*b^3 + 3*A*b^2*c)*x^6)*sqrt(x)","A",0
161,1,78,0,0.383206," ","integrate((B*x+A)*(c*x^2+b*x)^3*x^(1/2),x, algorithm=""fricas"")","\frac{2}{109395} \, {\left(6435 \, B c^{3} x^{8} + 12155 \, A b^{3} x^{4} + 7293 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{7} + 25245 \, {\left(B b^{2} c + A b c^{2}\right)} x^{6} + 9945 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/109395*(6435*B*c^3*x^8 + 12155*A*b^3*x^4 + 7293*(3*B*b*c^2 + A*c^3)*x^7 + 25245*(B*b^2*c + A*b*c^2)*x^6 + 9945*(B*b^3 + 3*A*b^2*c)*x^5)*sqrt(x)","A",0
162,1,78,0,0.391788," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3003 \, B c^{3} x^{7} + 6435 \, A b^{3} x^{3} + 3465 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 12285 \, {\left(B b^{2} c + A b c^{2}\right)} x^{5} + 5005 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/45045*(3003*B*c^3*x^7 + 6435*A*b^3*x^3 + 3465*(3*B*b*c^2 + A*c^3)*x^6 + 12285*(B*b^2*c + A*b*c^2)*x^5 + 5005*(B*b^3 + 3*A*b^2*c)*x^4)*sqrt(x)","A",0
163,1,78,0,0.409577," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(3/2),x, algorithm=""fricas"")","\frac{2}{15015} \, {\left(1155 \, B c^{3} x^{6} + 3003 \, A b^{3} x^{2} + 1365 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{5} + 5005 \, {\left(B b^{2} c + A b c^{2}\right)} x^{4} + 2145 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/15015*(1155*B*c^3*x^6 + 3003*A*b^3*x^2 + 1365*(3*B*b*c^2 + A*c^3)*x^5 + 5005*(B*b^2*c + A*b*c^2)*x^4 + 2145*(B*b^3 + 3*A*b^2*c)*x^3)*sqrt(x)","A",0
164,1,76,0,0.400402," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(5/2),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B c^{3} x^{5} + 1155 \, A b^{3} x + 385 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{4} + 1485 \, {\left(B b^{2} c + A b c^{2}\right)} x^{3} + 693 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/3465*(315*B*c^3*x^5 + 1155*A*b^3*x + 385*(3*B*b*c^2 + A*c^3)*x^4 + 1485*(B*b^2*c + A*b*c^2)*x^3 + 693*(B*b^3 + 3*A*b^2*c)*x^2)*sqrt(x)","A",0
165,1,73,0,0.399512," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(7/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B c^{3} x^{4} + 315 \, A b^{3} + 45 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} + 189 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} + 105 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x\right)} \sqrt{x}"," ",0,"2/315*(35*B*c^3*x^4 + 315*A*b^3 + 45*(3*B*b*c^2 + A*c^3)*x^3 + 189*(B*b^2*c + A*b*c^2)*x^2 + 105*(B*b^3 + 3*A*b^2*c)*x)*sqrt(x)","A",0
166,1,73,0,0.393235," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B c^{3} x^{4} - 35 \, A b^{3} + 7 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} + 35 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} + 35 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x\right)}}{35 \, \sqrt{x}}"," ",0,"2/35*(5*B*c^3*x^4 - 35*A*b^3 + 7*(3*B*b*c^2 + A*c^3)*x^3 + 35*(B*b^2*c + A*b*c^2)*x^2 + 35*(B*b^3 + 3*A*b^2*c)*x)/sqrt(x)","A",0
167,1,73,0,0.403489," ","integrate((B*x+A)*(c*x^2+b*x)^3/x^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{3} x^{4} - 5 \, A b^{3} + 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{3} + 45 \, {\left(B b^{2} c + A b c^{2}\right)} x^{2} - 15 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} x\right)}}{15 \, x^{\frac{3}{2}}}"," ",0,"2/15*(3*B*c^3*x^4 - 5*A*b^3 + 5*(3*B*b*c^2 + A*c^3)*x^3 + 45*(B*b^2*c + A*b*c^2)*x^2 - 15*(B*b^3 + 3*A*b^2*c)*x)/x^(3/2)","A",0
168,1,229,0,0.422312," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B b^{3} - A b^{2} c\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x - 2 \, c \sqrt{x} \sqrt{-\frac{b}{c}} - b}{c x + b}\right) - 2 \, {\left(15 \, B c^{3} x^{3} - 105 \, B b^{3} + 105 \, A b^{2} c - 21 \, {\left(B b c^{2} - A c^{3}\right)} x^{2} + 35 \, {\left(B b^{2} c - A b c^{2}\right)} x\right)} \sqrt{x}}{105 \, c^{4}}, \frac{2 \, {\left(105 \, {\left(B b^{3} - A b^{2} c\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c \sqrt{x} \sqrt{\frac{b}{c}}}{b}\right) + {\left(15 \, B c^{3} x^{3} - 105 \, B b^{3} + 105 \, A b^{2} c - 21 \, {\left(B b c^{2} - A c^{3}\right)} x^{2} + 35 \, {\left(B b^{2} c - A b c^{2}\right)} x\right)} \sqrt{x}\right)}}{105 \, c^{4}}\right]"," ",0,"[-1/105*(105*(B*b^3 - A*b^2*c)*sqrt(-b/c)*log((c*x - 2*c*sqrt(x)*sqrt(-b/c) - b)/(c*x + b)) - 2*(15*B*c^3*x^3 - 105*B*b^3 + 105*A*b^2*c - 21*(B*b*c^2 - A*c^3)*x^2 + 35*(B*b^2*c - A*b*c^2)*x)*sqrt(x))/c^4, 2/105*(105*(B*b^3 - A*b^2*c)*sqrt(b/c)*arctan(c*sqrt(x)*sqrt(b/c)/b) + (15*B*c^3*x^3 - 105*B*b^3 + 105*A*b^2*c - 21*(B*b*c^2 - A*c^3)*x^2 + 35*(B*b^2*c - A*b*c^2)*x)*sqrt(x))/c^4]","A",0
169,1,180,0,0.407965," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B b^{2} - A b c\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x + 2 \, c \sqrt{x} \sqrt{-\frac{b}{c}} - b}{c x + b}\right) - 2 \, {\left(3 \, B c^{2} x^{2} + 15 \, B b^{2} - 15 \, A b c - 5 \, {\left(B b c - A c^{2}\right)} x\right)} \sqrt{x}}{15 \, c^{3}}, -\frac{2 \, {\left(15 \, {\left(B b^{2} - A b c\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c \sqrt{x} \sqrt{\frac{b}{c}}}{b}\right) - {\left(3 \, B c^{2} x^{2} + 15 \, B b^{2} - 15 \, A b c - 5 \, {\left(B b c - A c^{2}\right)} x\right)} \sqrt{x}\right)}}{15 \, c^{3}}\right]"," ",0,"[-1/15*(15*(B*b^2 - A*b*c)*sqrt(-b/c)*log((c*x + 2*c*sqrt(x)*sqrt(-b/c) - b)/(c*x + b)) - 2*(3*B*c^2*x^2 + 15*B*b^2 - 15*A*b*c - 5*(B*b*c - A*c^2)*x)*sqrt(x))/c^3, -2/15*(15*(B*b^2 - A*b*c)*sqrt(b/c)*arctan(c*sqrt(x)*sqrt(b/c)/b) - (3*B*c^2*x^2 + 15*B*b^2 - 15*A*b*c - 5*(B*b*c - A*c^2)*x)*sqrt(x))/c^3]","A",0
170,1,129,0,0.422803," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b - A c\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x - 2 \, c \sqrt{x} \sqrt{-\frac{b}{c}} - b}{c x + b}\right) - 2 \, {\left(B c x - 3 \, B b + 3 \, A c\right)} \sqrt{x}}{3 \, c^{2}}, \frac{2 \, {\left(3 \, {\left(B b - A c\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c \sqrt{x} \sqrt{\frac{b}{c}}}{b}\right) + {\left(B c x - 3 \, B b + 3 \, A c\right)} \sqrt{x}\right)}}{3 \, c^{2}}\right]"," ",0,"[-1/3*(3*(B*b - A*c)*sqrt(-b/c)*log((c*x - 2*c*sqrt(x)*sqrt(-b/c) - b)/(c*x + b)) - 2*(B*c*x - 3*B*b + 3*A*c)*sqrt(x))/c^2, 2/3*(3*(B*b - A*c)*sqrt(b/c)*arctan(c*sqrt(x)*sqrt(b/c)/b) + (B*c*x - 3*B*b + 3*A*c)*sqrt(x))/c^2]","A",0
171,1,102,0,0.411172," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{2 \, B b c \sqrt{x} + {\left(B b - A c\right)} \sqrt{-b c} \log\left(\frac{c x - b - 2 \, \sqrt{-b c} \sqrt{x}}{c x + b}\right)}{b c^{2}}, \frac{2 \, {\left(B b c \sqrt{x} + {\left(B b - A c\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c}}{c \sqrt{x}}\right)\right)}}{b c^{2}}\right]"," ",0,"[(2*B*b*c*sqrt(x) + (B*b - A*c)*sqrt(-b*c)*log((c*x - b - 2*sqrt(-b*c)*sqrt(x))/(c*x + b)))/(b*c^2), 2*(B*b*c*sqrt(x) + (B*b - A*c)*sqrt(b*c)*arctan(sqrt(b*c)/(c*sqrt(x))))/(b*c^2)]","A",0
172,1,112,0,0.419984," ","integrate((B*x+A)/(c*x^2+b*x)/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, A b c \sqrt{x} - {\left(B b - A c\right)} \sqrt{-b c} x \log\left(\frac{c x - b + 2 \, \sqrt{-b c} \sqrt{x}}{c x + b}\right)}{b^{2} c x}, -\frac{2 \, {\left(A b c \sqrt{x} + {\left(B b - A c\right)} \sqrt{b c} x \arctan\left(\frac{\sqrt{b c}}{c \sqrt{x}}\right)\right)}}{b^{2} c x}\right]"," ",0,"[-(2*A*b*c*sqrt(x) - (B*b - A*c)*sqrt(-b*c)*x*log((c*x - b + 2*sqrt(-b*c)*sqrt(x))/(c*x + b)))/(b^2*c*x), -2*(A*b*c*sqrt(x) + (B*b - A*c)*sqrt(b*c)*x*arctan(sqrt(b*c)/(c*sqrt(x))))/(b^2*c*x)]","A",0
173,1,146,0,0.427148," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b - A c\right)} x^{2} \sqrt{-\frac{c}{b}} \log\left(\frac{c x + 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(A b + 3 \, {\left(B b - A c\right)} x\right)} \sqrt{x}}{3 \, b^{2} x^{2}}, \frac{2 \, {\left(3 \, {\left(B b - A c\right)} x^{2} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) - {\left(A b + 3 \, {\left(B b - A c\right)} x\right)} \sqrt{x}\right)}}{3 \, b^{2} x^{2}}\right]"," ",0,"[-1/3*(3*(B*b - A*c)*x^2*sqrt(-c/b)*log((c*x + 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(A*b + 3*(B*b - A*c)*x)*sqrt(x))/(b^2*x^2), 2/3*(3*(B*b - A*c)*x^2*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) - (A*b + 3*(B*b - A*c)*x)*sqrt(x))/(b^2*x^2)]","A",0
174,1,195,0,0.421689," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B b c - A c^{2}\right)} x^{3} \sqrt{-\frac{c}{b}} \log\left(\frac{c x - 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(3 \, A b^{2} - 15 \, {\left(B b c - A c^{2}\right)} x^{2} + 5 \, {\left(B b^{2} - A b c\right)} x\right)} \sqrt{x}}{15 \, b^{3} x^{3}}, -\frac{2 \, {\left(15 \, {\left(B b c - A c^{2}\right)} x^{3} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) + {\left(3 \, A b^{2} - 15 \, {\left(B b c - A c^{2}\right)} x^{2} + 5 \, {\left(B b^{2} - A b c\right)} x\right)} \sqrt{x}\right)}}{15 \, b^{3} x^{3}}\right]"," ",0,"[-1/15*(15*(B*b*c - A*c^2)*x^3*sqrt(-c/b)*log((c*x - 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(3*A*b^2 - 15*(B*b*c - A*c^2)*x^2 + 5*(B*b^2 - A*b*c)*x)*sqrt(x))/(b^3*x^3), -2/15*(15*(B*b*c - A*c^2)*x^3*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) + (3*A*b^2 - 15*(B*b*c - A*c^2)*x^2 + 5*(B*b^2 - A*b*c)*x)*sqrt(x))/(b^3*x^3)]","A",0
175,1,246,0,0.439489," ","integrate((B*x+A)/x^(7/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B b c^{2} - A c^{3}\right)} x^{4} \sqrt{-\frac{c}{b}} \log\left(\frac{c x + 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(15 \, A b^{3} + 105 \, {\left(B b c^{2} - A c^{3}\right)} x^{3} - 35 \, {\left(B b^{2} c - A b c^{2}\right)} x^{2} + 21 \, {\left(B b^{3} - A b^{2} c\right)} x\right)} \sqrt{x}}{105 \, b^{4} x^{4}}, \frac{2 \, {\left(105 \, {\left(B b c^{2} - A c^{3}\right)} x^{4} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) - {\left(15 \, A b^{3} + 105 \, {\left(B b c^{2} - A c^{3}\right)} x^{3} - 35 \, {\left(B b^{2} c - A b c^{2}\right)} x^{2} + 21 \, {\left(B b^{3} - A b^{2} c\right)} x\right)} \sqrt{x}\right)}}{105 \, b^{4} x^{4}}\right]"," ",0,"[-1/105*(105*(B*b*c^2 - A*c^3)*x^4*sqrt(-c/b)*log((c*x + 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(15*A*b^3 + 105*(B*b*c^2 - A*c^3)*x^3 - 35*(B*b^2*c - A*b*c^2)*x^2 + 21*(B*b^3 - A*b^2*c)*x)*sqrt(x))/(b^4*x^4), 2/105*(105*(B*b*c^2 - A*c^3)*x^4*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) - (15*A*b^3 + 105*(B*b*c^2 - A*c^3)*x^3 - 35*(B*b^2*c - A*b*c^2)*x^2 + 21*(B*b^3 - A*b^2*c)*x)*sqrt(x))/(b^4*x^4)]","A",0
176,1,291,0,0.425314," ","integrate((B*x+A)/x^(9/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(B b c^{3} - A c^{4}\right)} x^{5} \sqrt{-\frac{c}{b}} \log\left(\frac{c x - 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(35 \, A b^{4} - 315 \, {\left(B b c^{3} - A c^{4}\right)} x^{4} + 105 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} x^{3} - 63 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} x^{2} + 45 \, {\left(B b^{4} - A b^{3} c\right)} x\right)} \sqrt{x}}{315 \, b^{5} x^{5}}, -\frac{2 \, {\left(315 \, {\left(B b c^{3} - A c^{4}\right)} x^{5} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) + {\left(35 \, A b^{4} - 315 \, {\left(B b c^{3} - A c^{4}\right)} x^{4} + 105 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} x^{3} - 63 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} x^{2} + 45 \, {\left(B b^{4} - A b^{3} c\right)} x\right)} \sqrt{x}\right)}}{315 \, b^{5} x^{5}}\right]"," ",0,"[-1/315*(315*(B*b*c^3 - A*c^4)*x^5*sqrt(-c/b)*log((c*x - 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(35*A*b^4 - 315*(B*b*c^3 - A*c^4)*x^4 + 105*(B*b^2*c^2 - A*b*c^3)*x^3 - 63*(B*b^3*c - A*b^2*c^2)*x^2 + 45*(B*b^4 - A*b^3*c)*x)*sqrt(x))/(b^5*x^5), -2/315*(315*(B*b*c^3 - A*c^4)*x^5*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) + (35*A*b^4 - 315*(B*b*c^3 - A*c^4)*x^4 + 105*(B*b^2*c^2 - A*b*c^3)*x^3 - 63*(B*b^3*c - A*b^2*c^2)*x^2 + 45*(B*b^4 - A*b^3*c)*x)*sqrt(x))/(b^5*x^5)]","A",0
177,1,290,0,0.421957," ","integrate(x^(9/2)*(B*x+A)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{3} - 5 \, A b^{2} c + {\left(7 \, B b^{2} c - 5 \, A b c^{2}\right)} x\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x + 2 \, c \sqrt{x} \sqrt{-\frac{b}{c}} - b}{c x + b}\right) - 2 \, {\left(6 \, B c^{3} x^{3} + 105 \, B b^{3} - 75 \, A b^{2} c - 2 \, {\left(7 \, B b c^{2} - 5 \, A c^{3}\right)} x^{2} + 10 \, {\left(7 \, B b^{2} c - 5 \, A b c^{2}\right)} x\right)} \sqrt{x}}{30 \, {\left(c^{5} x + b c^{4}\right)}}, -\frac{15 \, {\left(7 \, B b^{3} - 5 \, A b^{2} c + {\left(7 \, B b^{2} c - 5 \, A b c^{2}\right)} x\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c \sqrt{x} \sqrt{\frac{b}{c}}}{b}\right) - {\left(6 \, B c^{3} x^{3} + 105 \, B b^{3} - 75 \, A b^{2} c - 2 \, {\left(7 \, B b c^{2} - 5 \, A c^{3}\right)} x^{2} + 10 \, {\left(7 \, B b^{2} c - 5 \, A b c^{2}\right)} x\right)} \sqrt{x}}{15 \, {\left(c^{5} x + b c^{4}\right)}}\right]"," ",0,"[-1/30*(15*(7*B*b^3 - 5*A*b^2*c + (7*B*b^2*c - 5*A*b*c^2)*x)*sqrt(-b/c)*log((c*x + 2*c*sqrt(x)*sqrt(-b/c) - b)/(c*x + b)) - 2*(6*B*c^3*x^3 + 105*B*b^3 - 75*A*b^2*c - 2*(7*B*b*c^2 - 5*A*c^3)*x^2 + 10*(7*B*b^2*c - 5*A*b*c^2)*x)*sqrt(x))/(c^5*x + b*c^4), -1/15*(15*(7*B*b^3 - 5*A*b^2*c + (7*B*b^2*c - 5*A*b*c^2)*x)*sqrt(b/c)*arctan(c*sqrt(x)*sqrt(b/c)/b) - (6*B*c^3*x^3 + 105*B*b^3 - 75*A*b^2*c - 2*(7*B*b*c^2 - 5*A*c^3)*x^2 + 10*(7*B*b^2*c - 5*A*b*c^2)*x)*sqrt(x))/(c^5*x + b*c^4)]","A",0
178,1,231,0,0.413898," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b^{2} - 3 \, A b c + {\left(5 \, B b c - 3 \, A c^{2}\right)} x\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x - 2 \, c \sqrt{x} \sqrt{-\frac{b}{c}} - b}{c x + b}\right) - 2 \, {\left(2 \, B c^{2} x^{2} - 15 \, B b^{2} + 9 \, A b c - 2 \, {\left(5 \, B b c - 3 \, A c^{2}\right)} x\right)} \sqrt{x}}{6 \, {\left(c^{4} x + b c^{3}\right)}}, \frac{3 \, {\left(5 \, B b^{2} - 3 \, A b c + {\left(5 \, B b c - 3 \, A c^{2}\right)} x\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c \sqrt{x} \sqrt{\frac{b}{c}}}{b}\right) + {\left(2 \, B c^{2} x^{2} - 15 \, B b^{2} + 9 \, A b c - 2 \, {\left(5 \, B b c - 3 \, A c^{2}\right)} x\right)} \sqrt{x}}{3 \, {\left(c^{4} x + b c^{3}\right)}}\right]"," ",0,"[-1/6*(3*(5*B*b^2 - 3*A*b*c + (5*B*b*c - 3*A*c^2)*x)*sqrt(-b/c)*log((c*x - 2*c*sqrt(x)*sqrt(-b/c) - b)/(c*x + b)) - 2*(2*B*c^2*x^2 - 15*B*b^2 + 9*A*b*c - 2*(5*B*b*c - 3*A*c^2)*x)*sqrt(x))/(c^4*x + b*c^3), 1/3*(3*(5*B*b^2 - 3*A*b*c + (5*B*b*c - 3*A*c^2)*x)*sqrt(b/c)*arctan(c*sqrt(x)*sqrt(b/c)/b) + (2*B*c^2*x^2 - 15*B*b^2 + 9*A*b*c - 2*(5*B*b*c - 3*A*c^2)*x)*sqrt(x))/(c^4*x + b*c^3)]","A",0
179,1,198,0,0.421726," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{{\left(3 \, B b^{2} - A b c + {\left(3 \, B b c - A c^{2}\right)} x\right)} \sqrt{-b c} \log\left(\frac{c x - b - 2 \, \sqrt{-b c} \sqrt{x}}{c x + b}\right) + 2 \, {\left(2 \, B b c^{2} x + 3 \, B b^{2} c - A b c^{2}\right)} \sqrt{x}}{2 \, {\left(b c^{4} x + b^{2} c^{3}\right)}}, \frac{{\left(3 \, B b^{2} - A b c + {\left(3 \, B b c - A c^{2}\right)} x\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c}}{c \sqrt{x}}\right) + {\left(2 \, B b c^{2} x + 3 \, B b^{2} c - A b c^{2}\right)} \sqrt{x}}{b c^{4} x + b^{2} c^{3}}\right]"," ",0,"[1/2*((3*B*b^2 - A*b*c + (3*B*b*c - A*c^2)*x)*sqrt(-b*c)*log((c*x - b - 2*sqrt(-b*c)*sqrt(x))/(c*x + b)) + 2*(2*B*b*c^2*x + 3*B*b^2*c - A*b*c^2)*sqrt(x))/(b*c^4*x + b^2*c^3), ((3*B*b^2 - A*b*c + (3*B*b*c - A*c^2)*x)*sqrt(b*c)*arctan(sqrt(b*c)/(c*sqrt(x))) + (2*B*b*c^2*x + 3*B*b^2*c - A*b*c^2)*sqrt(x))/(b*c^4*x + b^2*c^3)]","A",0
180,1,177,0,0.406230," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(B b^{2} + A b c + {\left(B b c + A c^{2}\right)} x\right)} \sqrt{-b c} \log\left(\frac{c x - b - 2 \, \sqrt{-b c} \sqrt{x}}{c x + b}\right) + 2 \, {\left(B b^{2} c - A b c^{2}\right)} \sqrt{x}}{2 \, {\left(b^{2} c^{3} x + b^{3} c^{2}\right)}}, -\frac{{\left(B b^{2} + A b c + {\left(B b c + A c^{2}\right)} x\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c}}{c \sqrt{x}}\right) + {\left(B b^{2} c - A b c^{2}\right)} \sqrt{x}}{b^{2} c^{3} x + b^{3} c^{2}}\right]"," ",0,"[-1/2*((B*b^2 + A*b*c + (B*b*c + A*c^2)*x)*sqrt(-b*c)*log((c*x - b - 2*sqrt(-b*c)*sqrt(x))/(c*x + b)) + 2*(B*b^2*c - A*b*c^2)*sqrt(x))/(b^2*c^3*x + b^3*c^2), -((B*b^2 + A*b*c + (B*b*c + A*c^2)*x)*sqrt(b*c)*arctan(sqrt(b*c)/(c*sqrt(x))) + (B*b^2*c - A*b*c^2)*sqrt(x))/(b^2*c^3*x + b^3*c^2)]","A",0
181,1,215,0,0.427063," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(B b c - 3 \, A c^{2}\right)} x^{2} + {\left(B b^{2} - 3 \, A b c\right)} x\right)} \sqrt{-b c} \log\left(\frac{c x - b + 2 \, \sqrt{-b c} \sqrt{x}}{c x + b}\right) - 2 \, {\left(2 \, A b^{2} c - {\left(B b^{2} c - 3 \, A b c^{2}\right)} x\right)} \sqrt{x}}{2 \, {\left(b^{3} c^{2} x^{2} + b^{4} c x\right)}}, -\frac{{\left({\left(B b c - 3 \, A c^{2}\right)} x^{2} + {\left(B b^{2} - 3 \, A b c\right)} x\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c}}{c \sqrt{x}}\right) + {\left(2 \, A b^{2} c - {\left(B b^{2} c - 3 \, A b c^{2}\right)} x\right)} \sqrt{x}}{b^{3} c^{2} x^{2} + b^{4} c x}\right]"," ",0,"[1/2*(((B*b*c - 3*A*c^2)*x^2 + (B*b^2 - 3*A*b*c)*x)*sqrt(-b*c)*log((c*x - b + 2*sqrt(-b*c)*sqrt(x))/(c*x + b)) - 2*(2*A*b^2*c - (B*b^2*c - 3*A*b*c^2)*x)*sqrt(x))/(b^3*c^2*x^2 + b^4*c*x), -(((B*b*c - 3*A*c^2)*x^2 + (B*b^2 - 3*A*b*c)*x)*sqrt(b*c)*arctan(sqrt(b*c)/(c*sqrt(x))) + (2*A*b^2*c - (B*b^2*c - 3*A*b*c^2)*x)*sqrt(x))/(b^3*c^2*x^2 + b^4*c*x)]","A",0
182,1,262,0,0.424469," ","integrate((B*x+A)/(c*x^2+b*x)^2/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(3 \, B b c - 5 \, A c^{2}\right)} x^{3} + {\left(3 \, B b^{2} - 5 \, A b c\right)} x^{2}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x + 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(2 \, A b^{2} + 3 \, {\left(3 \, B b c - 5 \, A c^{2}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} - 5 \, A b c\right)} x\right)} \sqrt{x}}{6 \, {\left(b^{3} c x^{3} + b^{4} x^{2}\right)}}, \frac{3 \, {\left({\left(3 \, B b c - 5 \, A c^{2}\right)} x^{3} + {\left(3 \, B b^{2} - 5 \, A b c\right)} x^{2}\right)} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) - {\left(2 \, A b^{2} + 3 \, {\left(3 \, B b c - 5 \, A c^{2}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} - 5 \, A b c\right)} x\right)} \sqrt{x}}{3 \, {\left(b^{3} c x^{3} + b^{4} x^{2}\right)}}\right]"," ",0,"[-1/6*(3*((3*B*b*c - 5*A*c^2)*x^3 + (3*B*b^2 - 5*A*b*c)*x^2)*sqrt(-c/b)*log((c*x + 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(2*A*b^2 + 3*(3*B*b*c - 5*A*c^2)*x^2 + 2*(3*B*b^2 - 5*A*b*c)*x)*sqrt(x))/(b^3*c*x^3 + b^4*x^2), 1/3*(3*((3*B*b*c - 5*A*c^2)*x^3 + (3*B*b^2 - 5*A*b*c)*x^2)*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) - (2*A*b^2 + 3*(3*B*b*c - 5*A*c^2)*x^2 + 2*(3*B*b^2 - 5*A*b*c)*x)*sqrt(x))/(b^3*c*x^3 + b^4*x^2)]","A",0
183,1,319,0,0.417319," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(5 \, B b c^{2} - 7 \, A c^{3}\right)} x^{4} + {\left(5 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{3}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x - 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(6 \, A b^{3} - 15 \, {\left(5 \, B b c^{2} - 7 \, A c^{3}\right)} x^{3} - 10 \, {\left(5 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{2} + 2 \, {\left(5 \, B b^{3} - 7 \, A b^{2} c\right)} x\right)} \sqrt{x}}{30 \, {\left(b^{4} c x^{4} + b^{5} x^{3}\right)}}, -\frac{15 \, {\left({\left(5 \, B b c^{2} - 7 \, A c^{3}\right)} x^{4} + {\left(5 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{3}\right)} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) + {\left(6 \, A b^{3} - 15 \, {\left(5 \, B b c^{2} - 7 \, A c^{3}\right)} x^{3} - 10 \, {\left(5 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{2} + 2 \, {\left(5 \, B b^{3} - 7 \, A b^{2} c\right)} x\right)} \sqrt{x}}{15 \, {\left(b^{4} c x^{4} + b^{5} x^{3}\right)}}\right]"," ",0,"[-1/30*(15*((5*B*b*c^2 - 7*A*c^3)*x^4 + (5*B*b^2*c - 7*A*b*c^2)*x^3)*sqrt(-c/b)*log((c*x - 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(6*A*b^3 - 15*(5*B*b*c^2 - 7*A*c^3)*x^3 - 10*(5*B*b^2*c - 7*A*b*c^2)*x^2 + 2*(5*B*b^3 - 7*A*b^2*c)*x)*sqrt(x))/(b^4*c*x^4 + b^5*x^3), -1/15*(15*((5*B*b*c^2 - 7*A*c^3)*x^4 + (5*B*b^2*c - 7*A*b*c^2)*x^3)*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) + (6*A*b^3 - 15*(5*B*b*c^2 - 7*A*c^3)*x^3 - 10*(5*B*b^2*c - 7*A*b*c^2)*x^2 + 2*(5*B*b^3 - 7*A*b^2*c)*x)*sqrt(x))/(b^4*c*x^4 + b^5*x^3)]","A",0
184,1,372,0,0.431583," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(7 \, B b c^{3} - 9 \, A c^{4}\right)} x^{5} + {\left(7 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{4}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x + 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(30 \, A b^{4} + 105 \, {\left(7 \, B b c^{3} - 9 \, A c^{4}\right)} x^{4} + 70 \, {\left(7 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{3} - 14 \, {\left(7 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{2} + 6 \, {\left(7 \, B b^{4} - 9 \, A b^{3} c\right)} x\right)} \sqrt{x}}{210 \, {\left(b^{5} c x^{5} + b^{6} x^{4}\right)}}, \frac{105 \, {\left({\left(7 \, B b c^{3} - 9 \, A c^{4}\right)} x^{5} + {\left(7 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{4}\right)} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) - {\left(30 \, A b^{4} + 105 \, {\left(7 \, B b c^{3} - 9 \, A c^{4}\right)} x^{4} + 70 \, {\left(7 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{3} - 14 \, {\left(7 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{2} + 6 \, {\left(7 \, B b^{4} - 9 \, A b^{3} c\right)} x\right)} \sqrt{x}}{105 \, {\left(b^{5} c x^{5} + b^{6} x^{4}\right)}}\right]"," ",0,"[-1/210*(105*((7*B*b*c^3 - 9*A*c^4)*x^5 + (7*B*b^2*c^2 - 9*A*b*c^3)*x^4)*sqrt(-c/b)*log((c*x + 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(30*A*b^4 + 105*(7*B*b*c^3 - 9*A*c^4)*x^4 + 70*(7*B*b^2*c^2 - 9*A*b*c^3)*x^3 - 14*(7*B*b^3*c - 9*A*b^2*c^2)*x^2 + 6*(7*B*b^4 - 9*A*b^3*c)*x)*sqrt(x))/(b^5*c*x^5 + b^6*x^4), 1/105*(105*((7*B*b*c^3 - 9*A*c^4)*x^5 + (7*B*b^2*c^2 - 9*A*b*c^3)*x^4)*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) - (30*A*b^4 + 105*(7*B*b*c^3 - 9*A*c^4)*x^4 + 70*(7*B*b^2*c^2 - 9*A*b*c^3)*x^3 - 14*(7*B*b^3*c - 9*A*b^2*c^2)*x^2 + 6*(7*B*b^4 - 9*A*b^3*c)*x)*sqrt(x))/(b^5*c*x^5 + b^6*x^4)]","A",0
185,1,408,0,0.415275," ","integrate(x^(13/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B b^{4} - 5 \, A b^{3} c + {\left(9 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{2} + 2 \, {\left(9 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} x\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x + 2 \, c \sqrt{x} \sqrt{-\frac{b}{c}} - b}{c x + b}\right) - 2 \, {\left(24 \, B c^{4} x^{4} + 945 \, B b^{4} - 525 \, A b^{3} c - 8 \, {\left(9 \, B b c^{3} - 5 \, A c^{4}\right)} x^{3} + 56 \, {\left(9 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{2} + 175 \, {\left(9 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} x\right)} \sqrt{x}}{120 \, {\left(c^{7} x^{2} + 2 \, b c^{6} x + b^{2} c^{5}\right)}}, -\frac{105 \, {\left(9 \, B b^{4} - 5 \, A b^{3} c + {\left(9 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{2} + 2 \, {\left(9 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} x\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c \sqrt{x} \sqrt{\frac{b}{c}}}{b}\right) - {\left(24 \, B c^{4} x^{4} + 945 \, B b^{4} - 525 \, A b^{3} c - 8 \, {\left(9 \, B b c^{3} - 5 \, A c^{4}\right)} x^{3} + 56 \, {\left(9 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{2} + 175 \, {\left(9 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} x\right)} \sqrt{x}}{60 \, {\left(c^{7} x^{2} + 2 \, b c^{6} x + b^{2} c^{5}\right)}}\right]"," ",0,"[-1/120*(105*(9*B*b^4 - 5*A*b^3*c + (9*B*b^2*c^2 - 5*A*b*c^3)*x^2 + 2*(9*B*b^3*c - 5*A*b^2*c^2)*x)*sqrt(-b/c)*log((c*x + 2*c*sqrt(x)*sqrt(-b/c) - b)/(c*x + b)) - 2*(24*B*c^4*x^4 + 945*B*b^4 - 525*A*b^3*c - 8*(9*B*b*c^3 - 5*A*c^4)*x^3 + 56*(9*B*b^2*c^2 - 5*A*b*c^3)*x^2 + 175*(9*B*b^3*c - 5*A*b^2*c^2)*x)*sqrt(x))/(c^7*x^2 + 2*b*c^6*x + b^2*c^5), -1/60*(105*(9*B*b^4 - 5*A*b^3*c + (9*B*b^2*c^2 - 5*A*b*c^3)*x^2 + 2*(9*B*b^3*c - 5*A*b^2*c^2)*x)*sqrt(b/c)*arctan(c*sqrt(x)*sqrt(b/c)/b) - (24*B*c^4*x^4 + 945*B*b^4 - 525*A*b^3*c - 8*(9*B*b*c^3 - 5*A*c^4)*x^3 + 56*(9*B*b^2*c^2 - 5*A*b*c^3)*x^2 + 175*(9*B*b^3*c - 5*A*b^2*c^2)*x)*sqrt(x))/(c^7*x^2 + 2*b*c^6*x + b^2*c^5)]","A",0
186,1,349,0,0.434334," ","integrate(x^(11/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{3} - 3 \, A b^{2} c + {\left(7 \, B b c^{2} - 3 \, A c^{3}\right)} x^{2} + 2 \, {\left(7 \, B b^{2} c - 3 \, A b c^{2}\right)} x\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x - 2 \, c \sqrt{x} \sqrt{-\frac{b}{c}} - b}{c x + b}\right) - 2 \, {\left(8 \, B c^{3} x^{3} - 105 \, B b^{3} + 45 \, A b^{2} c - 8 \, {\left(7 \, B b c^{2} - 3 \, A c^{3}\right)} x^{2} - 25 \, {\left(7 \, B b^{2} c - 3 \, A b c^{2}\right)} x\right)} \sqrt{x}}{24 \, {\left(c^{6} x^{2} + 2 \, b c^{5} x + b^{2} c^{4}\right)}}, \frac{15 \, {\left(7 \, B b^{3} - 3 \, A b^{2} c + {\left(7 \, B b c^{2} - 3 \, A c^{3}\right)} x^{2} + 2 \, {\left(7 \, B b^{2} c - 3 \, A b c^{2}\right)} x\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c \sqrt{x} \sqrt{\frac{b}{c}}}{b}\right) + {\left(8 \, B c^{3} x^{3} - 105 \, B b^{3} + 45 \, A b^{2} c - 8 \, {\left(7 \, B b c^{2} - 3 \, A c^{3}\right)} x^{2} - 25 \, {\left(7 \, B b^{2} c - 3 \, A b c^{2}\right)} x\right)} \sqrt{x}}{12 \, {\left(c^{6} x^{2} + 2 \, b c^{5} x + b^{2} c^{4}\right)}}\right]"," ",0,"[-1/24*(15*(7*B*b^3 - 3*A*b^2*c + (7*B*b*c^2 - 3*A*c^3)*x^2 + 2*(7*B*b^2*c - 3*A*b*c^2)*x)*sqrt(-b/c)*log((c*x - 2*c*sqrt(x)*sqrt(-b/c) - b)/(c*x + b)) - 2*(8*B*c^3*x^3 - 105*B*b^3 + 45*A*b^2*c - 8*(7*B*b*c^2 - 3*A*c^3)*x^2 - 25*(7*B*b^2*c - 3*A*b*c^2)*x)*sqrt(x))/(c^6*x^2 + 2*b*c^5*x + b^2*c^4), 1/12*(15*(7*B*b^3 - 3*A*b^2*c + (7*B*b*c^2 - 3*A*c^3)*x^2 + 2*(7*B*b^2*c - 3*A*b*c^2)*x)*sqrt(b/c)*arctan(c*sqrt(x)*sqrt(b/c)/b) + (8*B*c^3*x^3 - 105*B*b^3 + 45*A*b^2*c - 8*(7*B*b*c^2 - 3*A*c^3)*x^2 - 25*(7*B*b^2*c - 3*A*b*c^2)*x)*sqrt(x))/(c^6*x^2 + 2*b*c^5*x + b^2*c^4)]","A",0
187,1,319,0,0.430181," ","integrate(x^(9/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, B b^{3} - A b^{2} c + {\left(5 \, B b c^{2} - A c^{3}\right)} x^{2} + 2 \, {\left(5 \, B b^{2} c - A b c^{2}\right)} x\right)} \sqrt{-b c} \log\left(\frac{c x - b - 2 \, \sqrt{-b c} \sqrt{x}}{c x + b}\right) + 2 \, {\left(8 \, B b c^{3} x^{2} + 15 \, B b^{3} c - 3 \, A b^{2} c^{2} + 5 \, {\left(5 \, B b^{2} c^{2} - A b c^{3}\right)} x\right)} \sqrt{x}}{8 \, {\left(b c^{6} x^{2} + 2 \, b^{2} c^{5} x + b^{3} c^{4}\right)}}, \frac{3 \, {\left(5 \, B b^{3} - A b^{2} c + {\left(5 \, B b c^{2} - A c^{3}\right)} x^{2} + 2 \, {\left(5 \, B b^{2} c - A b c^{2}\right)} x\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c}}{c \sqrt{x}}\right) + {\left(8 \, B b c^{3} x^{2} + 15 \, B b^{3} c - 3 \, A b^{2} c^{2} + 5 \, {\left(5 \, B b^{2} c^{2} - A b c^{3}\right)} x\right)} \sqrt{x}}{4 \, {\left(b c^{6} x^{2} + 2 \, b^{2} c^{5} x + b^{3} c^{4}\right)}}\right]"," ",0,"[1/8*(3*(5*B*b^3 - A*b^2*c + (5*B*b*c^2 - A*c^3)*x^2 + 2*(5*B*b^2*c - A*b*c^2)*x)*sqrt(-b*c)*log((c*x - b - 2*sqrt(-b*c)*sqrt(x))/(c*x + b)) + 2*(8*B*b*c^3*x^2 + 15*B*b^3*c - 3*A*b^2*c^2 + 5*(5*B*b^2*c^2 - A*b*c^3)*x)*sqrt(x))/(b*c^6*x^2 + 2*b^2*c^5*x + b^3*c^4), 1/4*(3*(5*B*b^3 - A*b^2*c + (5*B*b*c^2 - A*c^3)*x^2 + 2*(5*B*b^2*c - A*b*c^2)*x)*sqrt(b*c)*arctan(sqrt(b*c)/(c*sqrt(x))) + (8*B*b*c^3*x^2 + 15*B*b^3*c - 3*A*b^2*c^2 + 5*(5*B*b^2*c^2 - A*b*c^3)*x)*sqrt(x))/(b*c^6*x^2 + 2*b^2*c^5*x + b^3*c^4)]","A",0
188,1,291,0,0.422026," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B b^{3} + A b^{2} c + {\left(3 \, B b c^{2} + A c^{3}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} c + A b c^{2}\right)} x\right)} \sqrt{-b c} \log\left(\frac{c x - b - 2 \, \sqrt{-b c} \sqrt{x}}{c x + b}\right) + 2 \, {\left(3 \, B b^{3} c + A b^{2} c^{2} + {\left(5 \, B b^{2} c^{2} - A b c^{3}\right)} x\right)} \sqrt{x}}{8 \, {\left(b^{2} c^{5} x^{2} + 2 \, b^{3} c^{4} x + b^{4} c^{3}\right)}}, -\frac{{\left(3 \, B b^{3} + A b^{2} c + {\left(3 \, B b c^{2} + A c^{3}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} c + A b c^{2}\right)} x\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c}}{c \sqrt{x}}\right) + {\left(3 \, B b^{3} c + A b^{2} c^{2} + {\left(5 \, B b^{2} c^{2} - A b c^{3}\right)} x\right)} \sqrt{x}}{4 \, {\left(b^{2} c^{5} x^{2} + 2 \, b^{3} c^{4} x + b^{4} c^{3}\right)}}\right]"," ",0,"[-1/8*((3*B*b^3 + A*b^2*c + (3*B*b*c^2 + A*c^3)*x^2 + 2*(3*B*b^2*c + A*b*c^2)*x)*sqrt(-b*c)*log((c*x - b - 2*sqrt(-b*c)*sqrt(x))/(c*x + b)) + 2*(3*B*b^3*c + A*b^2*c^2 + (5*B*b^2*c^2 - A*b*c^3)*x)*sqrt(x))/(b^2*c^5*x^2 + 2*b^3*c^4*x + b^4*c^3), -1/4*((3*B*b^3 + A*b^2*c + (3*B*b*c^2 + A*c^3)*x^2 + 2*(3*B*b^2*c + A*b*c^2)*x)*sqrt(b*c)*arctan(sqrt(b*c)/(c*sqrt(x))) + (3*B*b^3*c + A*b^2*c^2 + (5*B*b^2*c^2 - A*b*c^3)*x)*sqrt(x))/(b^2*c^5*x^2 + 2*b^3*c^4*x + b^4*c^3)]","A",0
189,1,291,0,0.416895," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(B b^{3} + 3 \, A b^{2} c + {\left(B b c^{2} + 3 \, A c^{3}\right)} x^{2} + 2 \, {\left(B b^{2} c + 3 \, A b c^{2}\right)} x\right)} \sqrt{-b c} \log\left(\frac{c x - b - 2 \, \sqrt{-b c} \sqrt{x}}{c x + b}\right) + 2 \, {\left(B b^{3} c - 5 \, A b^{2} c^{2} - {\left(B b^{2} c^{2} + 3 \, A b c^{3}\right)} x\right)} \sqrt{x}}{8 \, {\left(b^{3} c^{4} x^{2} + 2 \, b^{4} c^{3} x + b^{5} c^{2}\right)}}, -\frac{{\left(B b^{3} + 3 \, A b^{2} c + {\left(B b c^{2} + 3 \, A c^{3}\right)} x^{2} + 2 \, {\left(B b^{2} c + 3 \, A b c^{2}\right)} x\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c}}{c \sqrt{x}}\right) + {\left(B b^{3} c - 5 \, A b^{2} c^{2} - {\left(B b^{2} c^{2} + 3 \, A b c^{3}\right)} x\right)} \sqrt{x}}{4 \, {\left(b^{3} c^{4} x^{2} + 2 \, b^{4} c^{3} x + b^{5} c^{2}\right)}}\right]"," ",0,"[-1/8*((B*b^3 + 3*A*b^2*c + (B*b*c^2 + 3*A*c^3)*x^2 + 2*(B*b^2*c + 3*A*b*c^2)*x)*sqrt(-b*c)*log((c*x - b - 2*sqrt(-b*c)*sqrt(x))/(c*x + b)) + 2*(B*b^3*c - 5*A*b^2*c^2 - (B*b^2*c^2 + 3*A*b*c^3)*x)*sqrt(x))/(b^3*c^4*x^2 + 2*b^4*c^3*x + b^5*c^2), -1/4*((B*b^3 + 3*A*b^2*c + (B*b*c^2 + 3*A*c^3)*x^2 + 2*(B*b^2*c + 3*A*b*c^2)*x)*sqrt(b*c)*arctan(sqrt(b*c)/(c*sqrt(x))) + (B*b^3*c - 5*A*b^2*c^2 - (B*b^2*c^2 + 3*A*b*c^3)*x)*sqrt(x))/(b^3*c^4*x^2 + 2*b^4*c^3*x + b^5*c^2)]","A",0
190,1,331,0,0.429729," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(B b c^{2} - 5 \, A c^{3}\right)} x^{3} + 2 \, {\left(B b^{2} c - 5 \, A b c^{2}\right)} x^{2} + {\left(B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{-b c} \log\left(\frac{c x - b + 2 \, \sqrt{-b c} \sqrt{x}}{c x + b}\right) - 2 \, {\left(8 \, A b^{3} c - 3 \, {\left(B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{2} - 5 \, {\left(B b^{3} c - 5 \, A b^{2} c^{2}\right)} x\right)} \sqrt{x}}{8 \, {\left(b^{4} c^{3} x^{3} + 2 \, b^{5} c^{2} x^{2} + b^{6} c x\right)}}, -\frac{3 \, {\left({\left(B b c^{2} - 5 \, A c^{3}\right)} x^{3} + 2 \, {\left(B b^{2} c - 5 \, A b c^{2}\right)} x^{2} + {\left(B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c}}{c \sqrt{x}}\right) + {\left(8 \, A b^{3} c - 3 \, {\left(B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{2} - 5 \, {\left(B b^{3} c - 5 \, A b^{2} c^{2}\right)} x\right)} \sqrt{x}}{4 \, {\left(b^{4} c^{3} x^{3} + 2 \, b^{5} c^{2} x^{2} + b^{6} c x\right)}}\right]"," ",0,"[1/8*(3*((B*b*c^2 - 5*A*c^3)*x^3 + 2*(B*b^2*c - 5*A*b*c^2)*x^2 + (B*b^3 - 5*A*b^2*c)*x)*sqrt(-b*c)*log((c*x - b + 2*sqrt(-b*c)*sqrt(x))/(c*x + b)) - 2*(8*A*b^3*c - 3*(B*b^2*c^2 - 5*A*b*c^3)*x^2 - 5*(B*b^3*c - 5*A*b^2*c^2)*x)*sqrt(x))/(b^4*c^3*x^3 + 2*b^5*c^2*x^2 + b^6*c*x), -1/4*(3*((B*b*c^2 - 5*A*c^3)*x^3 + 2*(B*b^2*c - 5*A*b*c^2)*x^2 + (B*b^3 - 5*A*b^2*c)*x)*sqrt(b*c)*arctan(sqrt(b*c)/(c*sqrt(x))) + (8*A*b^3*c - 3*(B*b^2*c^2 - 5*A*b*c^3)*x^2 - 5*(B*b^3*c - 5*A*b^2*c^2)*x)*sqrt(x))/(b^4*c^3*x^3 + 2*b^5*c^2*x^2 + b^6*c*x)]","A",0
191,1,380,0,0.432110," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(3 \, B b c^{2} - 7 \, A c^{3}\right)} x^{4} + 2 \, {\left(3 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{3} + {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} x^{2}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x + 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(8 \, A b^{3} + 15 \, {\left(3 \, B b c^{2} - 7 \, A c^{3}\right)} x^{3} + 25 \, {\left(3 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{2} + 8 \, {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} x\right)} \sqrt{x}}{24 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}, \frac{15 \, {\left({\left(3 \, B b c^{2} - 7 \, A c^{3}\right)} x^{4} + 2 \, {\left(3 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{3} + {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} x^{2}\right)} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) - {\left(8 \, A b^{3} + 15 \, {\left(3 \, B b c^{2} - 7 \, A c^{3}\right)} x^{3} + 25 \, {\left(3 \, B b^{2} c - 7 \, A b c^{2}\right)} x^{2} + 8 \, {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} x\right)} \sqrt{x}}{12 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}\right]"," ",0,"[-1/24*(15*((3*B*b*c^2 - 7*A*c^3)*x^4 + 2*(3*B*b^2*c - 7*A*b*c^2)*x^3 + (3*B*b^3 - 7*A*b^2*c)*x^2)*sqrt(-c/b)*log((c*x + 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(8*A*b^3 + 15*(3*B*b*c^2 - 7*A*c^3)*x^3 + 25*(3*B*b^2*c - 7*A*b*c^2)*x^2 + 8*(3*B*b^3 - 7*A*b^2*c)*x)*sqrt(x))/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2), 1/12*(15*((3*B*b*c^2 - 7*A*c^3)*x^4 + 2*(3*B*b^2*c - 7*A*b*c^2)*x^3 + (3*B*b^3 - 7*A*b^2*c)*x^2)*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) - (8*A*b^3 + 15*(3*B*b*c^2 - 7*A*c^3)*x^3 + 25*(3*B*b^2*c - 7*A*b*c^2)*x^2 + 8*(3*B*b^3 - 7*A*b^2*c)*x)*sqrt(x))/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)]","A",0
192,1,437,0,0.430572," ","integrate((B*x+A)/(c*x^2+b*x)^3/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(5 \, B b c^{3} - 9 \, A c^{4}\right)} x^{5} + 2 \, {\left(5 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{4} + {\left(5 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{3}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x - 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(24 \, A b^{4} - 105 \, {\left(5 \, B b c^{3} - 9 \, A c^{4}\right)} x^{4} - 175 \, {\left(5 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{3} - 56 \, {\left(5 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{2} + 8 \, {\left(5 \, B b^{4} - 9 \, A b^{3} c\right)} x\right)} \sqrt{x}}{120 \, {\left(b^{5} c^{2} x^{5} + 2 \, b^{6} c x^{4} + b^{7} x^{3}\right)}}, -\frac{105 \, {\left({\left(5 \, B b c^{3} - 9 \, A c^{4}\right)} x^{5} + 2 \, {\left(5 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{4} + {\left(5 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{3}\right)} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) + {\left(24 \, A b^{4} - 105 \, {\left(5 \, B b c^{3} - 9 \, A c^{4}\right)} x^{4} - 175 \, {\left(5 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{3} - 56 \, {\left(5 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x^{2} + 8 \, {\left(5 \, B b^{4} - 9 \, A b^{3} c\right)} x\right)} \sqrt{x}}{60 \, {\left(b^{5} c^{2} x^{5} + 2 \, b^{6} c x^{4} + b^{7} x^{3}\right)}}\right]"," ",0,"[-1/120*(105*((5*B*b*c^3 - 9*A*c^4)*x^5 + 2*(5*B*b^2*c^2 - 9*A*b*c^3)*x^4 + (5*B*b^3*c - 9*A*b^2*c^2)*x^3)*sqrt(-c/b)*log((c*x - 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(24*A*b^4 - 105*(5*B*b*c^3 - 9*A*c^4)*x^4 - 175*(5*B*b^2*c^2 - 9*A*b*c^3)*x^3 - 56*(5*B*b^3*c - 9*A*b^2*c^2)*x^2 + 8*(5*B*b^4 - 9*A*b^3*c)*x)*sqrt(x))/(b^5*c^2*x^5 + 2*b^6*c*x^4 + b^7*x^3), -1/60*(105*((5*B*b*c^3 - 9*A*c^4)*x^5 + 2*(5*B*b^2*c^2 - 9*A*b*c^3)*x^4 + (5*B*b^3*c - 9*A*b^2*c^2)*x^3)*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) + (24*A*b^4 - 105*(5*B*b*c^3 - 9*A*c^4)*x^4 - 175*(5*B*b^2*c^2 - 9*A*b*c^3)*x^3 - 56*(5*B*b^3*c - 9*A*b^2*c^2)*x^2 + 8*(5*B*b^4 - 9*A*b^3*c)*x)*sqrt(x))/(b^5*c^2*x^5 + 2*b^6*c*x^4 + b^7*x^3)]","A",0
193,1,490,0,0.435881," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{315 \, {\left({\left(7 \, B b c^{4} - 11 \, A c^{5}\right)} x^{6} + 2 \, {\left(7 \, B b^{2} c^{3} - 11 \, A b c^{4}\right)} x^{5} + {\left(7 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} x^{4}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x + 2 \, b \sqrt{x} \sqrt{-\frac{c}{b}} - b}{c x + b}\right) + 2 \, {\left(40 \, A b^{5} + 315 \, {\left(7 \, B b c^{4} - 11 \, A c^{5}\right)} x^{5} + 525 \, {\left(7 \, B b^{2} c^{3} - 11 \, A b c^{4}\right)} x^{4} + 168 \, {\left(7 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} x^{3} - 24 \, {\left(7 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} x^{2} + 8 \, {\left(7 \, B b^{5} - 11 \, A b^{4} c\right)} x\right)} \sqrt{x}}{280 \, {\left(b^{6} c^{2} x^{6} + 2 \, b^{7} c x^{5} + b^{8} x^{4}\right)}}, \frac{315 \, {\left({\left(7 \, B b c^{4} - 11 \, A c^{5}\right)} x^{6} + 2 \, {\left(7 \, B b^{2} c^{3} - 11 \, A b c^{4}\right)} x^{5} + {\left(7 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} x^{4}\right)} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c \sqrt{x}}\right) - {\left(40 \, A b^{5} + 315 \, {\left(7 \, B b c^{4} - 11 \, A c^{5}\right)} x^{5} + 525 \, {\left(7 \, B b^{2} c^{3} - 11 \, A b c^{4}\right)} x^{4} + 168 \, {\left(7 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} x^{3} - 24 \, {\left(7 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} x^{2} + 8 \, {\left(7 \, B b^{5} - 11 \, A b^{4} c\right)} x\right)} \sqrt{x}}{140 \, {\left(b^{6} c^{2} x^{6} + 2 \, b^{7} c x^{5} + b^{8} x^{4}\right)}}\right]"," ",0,"[-1/280*(315*((7*B*b*c^4 - 11*A*c^5)*x^6 + 2*(7*B*b^2*c^3 - 11*A*b*c^4)*x^5 + (7*B*b^3*c^2 - 11*A*b^2*c^3)*x^4)*sqrt(-c/b)*log((c*x + 2*b*sqrt(x)*sqrt(-c/b) - b)/(c*x + b)) + 2*(40*A*b^5 + 315*(7*B*b*c^4 - 11*A*c^5)*x^5 + 525*(7*B*b^2*c^3 - 11*A*b*c^4)*x^4 + 168*(7*B*b^3*c^2 - 11*A*b^2*c^3)*x^3 - 24*(7*B*b^4*c - 11*A*b^3*c^2)*x^2 + 8*(7*B*b^5 - 11*A*b^4*c)*x)*sqrt(x))/(b^6*c^2*x^6 + 2*b^7*c*x^5 + b^8*x^4), 1/140*(315*((7*B*b*c^4 - 11*A*c^5)*x^6 + 2*(7*B*b^2*c^3 - 11*A*b*c^4)*x^5 + (7*B*b^3*c^2 - 11*A*b^2*c^3)*x^4)*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*sqrt(x))) - (40*A*b^5 + 315*(7*B*b*c^4 - 11*A*c^5)*x^5 + 525*(7*B*b^2*c^3 - 11*A*b*c^4)*x^4 + 168*(7*B*b^3*c^2 - 11*A*b^2*c^3)*x^3 - 24*(7*B*b^4*c - 11*A*b^3*c^2)*x^2 + 8*(7*B*b^5 - 11*A*b^4*c)*x)*sqrt(x))/(b^6*c^2*x^6 + 2*b^7*c*x^5 + b^8*x^4)]","A",0
194,1,150,0,0.409142," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, B c^{6} x^{6} - 1280 \, B b^{6} + 1664 \, A b^{5} c + 315 \, {\left(B b c^{5} + 13 \, A c^{6}\right)} x^{5} - 35 \, {\left(10 \, B b^{2} c^{4} - 13 \, A b c^{5}\right)} x^{4} + 40 \, {\left(10 \, B b^{3} c^{3} - 13 \, A b^{2} c^{4}\right)} x^{3} - 48 \, {\left(10 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} x^{2} + 64 \, {\left(10 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{45045 \, c^{6} \sqrt{x}}"," ",0,"2/45045*(3465*B*c^6*x^6 - 1280*B*b^6 + 1664*A*b^5*c + 315*(B*b*c^5 + 13*A*c^6)*x^5 - 35*(10*B*b^2*c^4 - 13*A*b*c^5)*x^4 + 40*(10*B*b^3*c^3 - 13*A*b^2*c^4)*x^3 - 48*(10*B*b^4*c^2 - 13*A*b^3*c^3)*x^2 + 64*(10*B*b^5*c - 13*A*b^4*c^2)*x)*sqrt(c*x^2 + b*x)/(c^6*sqrt(x))","A",0
195,1,126,0,0.405405," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B c^{5} x^{5} + 128 \, B b^{5} - 176 \, A b^{4} c + 35 \, {\left(B b c^{4} + 11 \, A c^{5}\right)} x^{4} - 5 \, {\left(8 \, B b^{2} c^{3} - 11 \, A b c^{4}\right)} x^{3} + 6 \, {\left(8 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} x^{2} - 8 \, {\left(8 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{3465 \, c^{5} \sqrt{x}}"," ",0,"2/3465*(315*B*c^5*x^5 + 128*B*b^5 - 176*A*b^4*c + 35*(B*b*c^4 + 11*A*c^5)*x^4 - 5*(8*B*b^2*c^3 - 11*A*b*c^4)*x^3 + 6*(8*B*b^3*c^2 - 11*A*b^2*c^3)*x^2 - 8*(8*B*b^4*c - 11*A*b^3*c^2)*x)*sqrt(c*x^2 + b*x)/(c^5*sqrt(x))","A",0
196,1,102,0,0.411673," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{4} x^{4} - 16 \, B b^{4} + 24 \, A b^{3} c + 5 \, {\left(B b c^{3} + 9 \, A c^{4}\right)} x^{3} - 3 \, {\left(2 \, B b^{2} c^{2} - 3 \, A b c^{3}\right)} x^{2} + 4 \, {\left(2 \, B b^{3} c - 3 \, A b^{2} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{315 \, c^{4} \sqrt{x}}"," ",0,"2/315*(35*B*c^4*x^4 - 16*B*b^4 + 24*A*b^3*c + 5*(B*b*c^3 + 9*A*c^4)*x^3 - 3*(2*B*b^2*c^2 - 3*A*b*c^3)*x^2 + 4*(2*B*b^3*c - 3*A*b^2*c^2)*x)*sqrt(c*x^2 + b*x)/(c^4*sqrt(x))","A",0
197,1,78,0,0.425592," ","integrate((B*x+A)*x^(1/2)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c^{3} x^{3} + 8 \, B b^{3} - 14 \, A b^{2} c + 3 \, {\left(B b c^{2} + 7 \, A c^{3}\right)} x^{2} - {\left(4 \, B b^{2} c - 7 \, A b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{105 \, c^{3} \sqrt{x}}"," ",0,"2/105*(15*B*c^3*x^3 + 8*B*b^3 - 14*A*b^2*c + 3*(B*b*c^2 + 7*A*c^3)*x^2 - (4*B*b^2*c - 7*A*b*c^2)*x)*sqrt(c*x^2 + b*x)/(c^3*sqrt(x))","A",0
198,1,53,0,0.411938," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{2} x^{2} - 2 \, B b^{2} + 5 \, A b c + {\left(B b c + 5 \, A c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{15 \, c^{2} \sqrt{x}}"," ",0,"2/15*(3*B*c^2*x^2 - 2*B*b^2 + 5*A*b*c + (B*b*c + 5*A*c^2)*x)*sqrt(c*x^2 + b*x)/(c^2*sqrt(x))","A",0
199,1,148,0,0.424108," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, A \sqrt{b} c x \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(B c x + B b + 3 \, A c\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3 \, c x}, \frac{2 \, {\left(3 \, A \sqrt{-b} c x \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(B c x + B b + 3 \, A c\right)} \sqrt{c x^{2} + b x} \sqrt{x}\right)}}{3 \, c x}\right]"," ",0,"[1/3*(3*A*sqrt(b)*c*x*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(B*c*x + B*b + 3*A*c)*sqrt(c*x^2 + b*x)*sqrt(x))/(c*x), 2/3*(3*A*sqrt(-b)*c*x*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (B*c*x + B*b + 3*A*c)*sqrt(c*x^2 + b*x)*sqrt(x))/(c*x)]","A",0
200,1,157,0,0.421906," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B b + A c\right)} \sqrt{b} x^{2} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(2 \, B b x - A b\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{2 \, b x^{2}}, \frac{{\left(2 \, B b + A c\right)} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(2 \, B b x - A b\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{b x^{2}}\right]"," ",0,"[1/2*((2*B*b + A*c)*sqrt(b)*x^2*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(2*B*b*x - A*b)*sqrt(c*x^2 + b*x)*sqrt(x))/(b*x^2), ((2*B*b + A*c)*sqrt(-b)*x^2*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (2*B*b*x - A*b)*sqrt(c*x^2 + b*x)*sqrt(x))/(b*x^2)]","A",0
201,1,187,0,0.424949," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(7/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B b c - A c^{2}\right)} \sqrt{b} x^{3} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(2 \, A b^{2} + {\left(4 \, B b^{2} + A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{8 \, b^{2} x^{3}}, \frac{{\left(4 \, B b c - A c^{2}\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(2 \, A b^{2} + {\left(4 \, B b^{2} + A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{4 \, b^{2} x^{3}}\right]"," ",0,"[-1/8*((4*B*b*c - A*c^2)*sqrt(b)*x^3*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(2*A*b^2 + (4*B*b^2 + A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^3), 1/4*((4*B*b*c - A*c^2)*sqrt(-b)*x^3*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (2*A*b^2 + (4*B*b^2 + A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^3)]","A",0
202,1,238,0,0.429255," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/x^(9/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, B b c^{2} - A c^{3}\right)} \sqrt{b} x^{4} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(8 \, A b^{3} + 3 \, {\left(2 \, B b^{2} c - A b c^{2}\right)} x^{2} + 2 \, {\left(6 \, B b^{3} + A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, b^{3} x^{4}}, -\frac{3 \, {\left(2 \, B b c^{2} - A c^{3}\right)} \sqrt{-b} x^{4} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(8 \, A b^{3} + 3 \, {\left(2 \, B b^{2} c - A b c^{2}\right)} x^{2} + 2 \, {\left(6 \, B b^{3} + A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, b^{3} x^{4}}\right]"," ",0,"[-1/48*(3*(2*B*b*c^2 - A*c^3)*sqrt(b)*x^4*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(8*A*b^3 + 3*(2*B*b^2*c - A*b*c^2)*x^2 + 2*(6*B*b^3 + A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^4), -1/24*(3*(2*B*b*c^2 - A*c^3)*sqrt(-b)*x^4*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (8*A*b^3 + 3*(2*B*b^2*c - A*b*c^2)*x^2 + 2*(6*B*b^3 + A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^4)]","A",0
203,1,174,0,0.409658," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B c^{7} x^{7} - 256 \, B b^{7} + 384 \, A b^{6} c + 231 \, {\left(16 \, B b c^{6} + 15 \, A c^{7}\right)} x^{6} + 63 \, {\left(B b^{2} c^{5} + 70 \, A b c^{6}\right)} x^{5} - 35 \, {\left(2 \, B b^{3} c^{4} - 3 \, A b^{2} c^{5}\right)} x^{4} + 40 \, {\left(2 \, B b^{4} c^{3} - 3 \, A b^{3} c^{4}\right)} x^{3} - 48 \, {\left(2 \, B b^{5} c^{2} - 3 \, A b^{4} c^{3}\right)} x^{2} + 64 \, {\left(2 \, B b^{6} c - 3 \, A b^{5} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{45045 \, c^{6} \sqrt{x}}"," ",0,"2/45045*(3003*B*c^7*x^7 - 256*B*b^7 + 384*A*b^6*c + 231*(16*B*b*c^6 + 15*A*c^7)*x^6 + 63*(B*b^2*c^5 + 70*A*b*c^6)*x^5 - 35*(2*B*b^3*c^4 - 3*A*b^2*c^5)*x^4 + 40*(2*B*b^4*c^3 - 3*A*b^3*c^4)*x^3 - 48*(2*B*b^5*c^2 - 3*A*b^4*c^3)*x^2 + 64*(2*B*b^6*c - 3*A*b^5*c^2)*x)*sqrt(c*x^2 + b*x)/(c^6*sqrt(x))","A",0
204,1,150,0,0.410295," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, B c^{6} x^{6} + 128 \, B b^{6} - 208 \, A b^{5} c + 105 \, {\left(14 \, B b c^{5} + 13 \, A c^{6}\right)} x^{5} + 35 \, {\left(B b^{2} c^{4} + 52 \, A b c^{5}\right)} x^{4} - 5 \, {\left(8 \, B b^{3} c^{3} - 13 \, A b^{2} c^{4}\right)} x^{3} + 6 \, {\left(8 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} x^{2} - 8 \, {\left(8 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{15015 \, c^{5} \sqrt{x}}"," ",0,"2/15015*(1155*B*c^6*x^6 + 128*B*b^6 - 208*A*b^5*c + 105*(14*B*b*c^5 + 13*A*c^6)*x^5 + 35*(B*b^2*c^4 + 52*A*b*c^5)*x^4 - 5*(8*B*b^3*c^3 - 13*A*b^2*c^4)*x^3 + 6*(8*B*b^4*c^2 - 13*A*b^3*c^3)*x^2 - 8*(8*B*b^5*c - 13*A*b^4*c^2)*x)*sqrt(c*x^2 + b*x)/(c^5*sqrt(x))","A",0
205,1,127,0,0.408372," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)*x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B c^{5} x^{5} - 48 \, B b^{5} + 88 \, A b^{4} c + 35 \, {\left(12 \, B b c^{4} + 11 \, A c^{5}\right)} x^{4} + 5 \, {\left(3 \, B b^{2} c^{3} + 110 \, A b c^{4}\right)} x^{3} - 3 \, {\left(6 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} x^{2} + 4 \, {\left(6 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{3465 \, c^{4} \sqrt{x}}"," ",0,"2/3465*(315*B*c^5*x^5 - 48*B*b^5 + 88*A*b^4*c + 35*(12*B*b*c^4 + 11*A*c^5)*x^4 + 5*(3*B*b^2*c^3 + 110*A*b*c^4)*x^3 - 3*(6*B*b^3*c^2 - 11*A*b^2*c^3)*x^2 + 4*(6*B*b^4*c - 11*A*b^3*c^2)*x)*sqrt(c*x^2 + b*x)/(c^4*sqrt(x))","A",0
206,1,102,0,0.408088," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{4} x^{4} + 8 \, B b^{4} - 18 \, A b^{3} c + 5 \, {\left(10 \, B b c^{3} + 9 \, A c^{4}\right)} x^{3} + 3 \, {\left(B b^{2} c^{2} + 24 \, A b c^{3}\right)} x^{2} - {\left(4 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{315 \, c^{3} \sqrt{x}}"," ",0,"2/315*(35*B*c^4*x^4 + 8*B*b^4 - 18*A*b^3*c + 5*(10*B*b*c^3 + 9*A*c^4)*x^3 + 3*(B*b^2*c^2 + 24*A*b*c^3)*x^2 - (4*B*b^3*c - 9*A*b^2*c^2)*x)*sqrt(c*x^2 + b*x)/(c^3*sqrt(x))","A",0
207,1,76,0,0.399844," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B c^{3} x^{3} - 2 \, B b^{3} + 7 \, A b^{2} c + {\left(8 \, B b c^{2} + 7 \, A c^{3}\right)} x^{2} + {\left(B b^{2} c + 14 \, A b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{35 \, c^{2} \sqrt{x}}"," ",0,"2/35*(5*B*c^3*x^3 - 2*B*b^3 + 7*A*b^2*c + (8*B*b*c^2 + 7*A*c^3)*x^2 + (B*b^2*c + 14*A*b*c^2)*x)*sqrt(c*x^2 + b*x)/(c^2*sqrt(x))","A",0
208,1,195,0,0.418072," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, A b^{\frac{3}{2}} c x \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(3 \, B c^{2} x^{2} + 3 \, B b^{2} + 20 \, A b c + {\left(6 \, B b c + 5 \, A c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{15 \, c x}, \frac{2 \, {\left(15 \, A \sqrt{-b} b c x \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(3 \, B c^{2} x^{2} + 3 \, B b^{2} + 20 \, A b c + {\left(6 \, B b c + 5 \, A c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}\right)}}{15 \, c x}\right]"," ",0,"[1/15*(15*A*b^(3/2)*c*x*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(3*B*c^2*x^2 + 3*B*b^2 + 20*A*b*c + (6*B*b*c + 5*A*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(c*x), 2/15*(15*A*sqrt(-b)*b*c*x*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (3*B*c^2*x^2 + 3*B*b^2 + 20*A*b*c + (6*B*b*c + 5*A*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(c*x)]","A",0
209,1,184,0,0.419105," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B b + 3 \, A c\right)} \sqrt{b} x^{2} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(2 \, B c x^{2} - 3 \, A b + 2 \, {\left(4 \, B b + 3 \, A c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{6 \, x^{2}}, \frac{3 \, {\left(2 \, B b + 3 \, A c\right)} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(2 \, B c x^{2} - 3 \, A b + 2 \, {\left(4 \, B b + 3 \, A c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3 \, x^{2}}\right]"," ",0,"[1/6*(3*(2*B*b + 3*A*c)*sqrt(b)*x^2*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(2*B*c*x^2 - 3*A*b + 2*(4*B*b + 3*A*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/x^2, 1/3*(3*(2*B*b + 3*A*c)*sqrt(-b)*x^2*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (2*B*c*x^2 - 3*A*b + 2*(4*B*b + 3*A*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/x^2]","A",0
210,1,206,0,0.421785," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(9/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, B b c + A c^{2}\right)} \sqrt{b} x^{3} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(8 \, B b c x^{2} - 2 \, A b^{2} - {\left(4 \, B b^{2} + 5 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{8 \, b x^{3}}, \frac{3 \, {\left(4 \, B b c + A c^{2}\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(8 \, B b c x^{2} - 2 \, A b^{2} - {\left(4 \, B b^{2} + 5 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{4 \, b x^{3}}\right]"," ",0,"[1/8*(3*(4*B*b*c + A*c^2)*sqrt(b)*x^3*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(8*B*b*c*x^2 - 2*A*b^2 - (4*B*b^2 + 5*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b*x^3), 1/4*(3*(4*B*b*c + A*c^2)*sqrt(-b)*x^3*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (8*B*b*c*x^2 - 2*A*b^2 - (4*B*b^2 + 5*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b*x^3)]","A",0
211,1,239,0,0.427881," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(11/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, B b c^{2} - A c^{3}\right)} \sqrt{b} x^{4} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(8 \, A b^{3} + 3 \, {\left(10 \, B b^{2} c + A b c^{2}\right)} x^{2} + 2 \, {\left(6 \, B b^{3} + 7 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, b^{2} x^{4}}, \frac{3 \, {\left(6 \, B b c^{2} - A c^{3}\right)} \sqrt{-b} x^{4} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(8 \, A b^{3} + 3 \, {\left(10 \, B b^{2} c + A b c^{2}\right)} x^{2} + 2 \, {\left(6 \, B b^{3} + 7 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, b^{2} x^{4}}\right]"," ",0,"[-1/48*(3*(6*B*b*c^2 - A*c^3)*sqrt(b)*x^4*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(8*A*b^3 + 3*(10*B*b^2*c + A*b*c^2)*x^2 + 2*(6*B*b^3 + 7*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^4), 1/24*(3*(6*B*b*c^2 - A*c^3)*sqrt(-b)*x^4*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (8*A*b^3 + 3*(10*B*b^2*c + A*b*c^2)*x^2 + 2*(6*B*b^3 + 7*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^4)]","A",0
212,1,288,0,0.423748," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(13/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, B b c^{3} - 3 \, A c^{4}\right)} \sqrt{b} x^{5} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(48 \, A b^{4} + 3 \, {\left(8 \, B b^{2} c^{2} - 3 \, A b c^{3}\right)} x^{3} + 2 \, {\left(56 \, B b^{3} c + 3 \, A b^{2} c^{2}\right)} x^{2} + 8 \, {\left(8 \, B b^{4} + 9 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{384 \, b^{3} x^{5}}, -\frac{3 \, {\left(8 \, B b c^{3} - 3 \, A c^{4}\right)} \sqrt{-b} x^{5} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(48 \, A b^{4} + 3 \, {\left(8 \, B b^{2} c^{2} - 3 \, A b c^{3}\right)} x^{3} + 2 \, {\left(56 \, B b^{3} c + 3 \, A b^{2} c^{2}\right)} x^{2} + 8 \, {\left(8 \, B b^{4} + 9 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{192 \, b^{3} x^{5}}\right]"," ",0,"[-1/384*(3*(8*B*b*c^3 - 3*A*c^4)*sqrt(b)*x^5*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(48*A*b^4 + 3*(8*B*b^2*c^2 - 3*A*b*c^3)*x^3 + 2*(56*B*b^3*c + 3*A*b^2*c^2)*x^2 + 8*(8*B*b^4 + 9*A*b^3*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^5), -1/192*(3*(8*B*b*c^3 - 3*A*c^4)*sqrt(-b)*x^5*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (48*A*b^4 + 3*(8*B*b^2*c^2 - 3*A*b*c^3)*x^3 + 2*(56*B*b^3*c + 3*A*b^2*c^2)*x^2 + 8*(8*B*b^4 + 9*A*b^3*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^5)]","A",0
213,1,335,0,0.425385," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/x^(15/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, B b c^{4} - A c^{5}\right)} \sqrt{b} x^{6} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(128 \, A b^{5} - 15 \, {\left(2 \, B b^{2} c^{3} - A b c^{4}\right)} x^{4} + 10 \, {\left(2 \, B b^{3} c^{2} - A b^{2} c^{3}\right)} x^{3} + 8 \, {\left(30 \, B b^{4} c + A b^{3} c^{2}\right)} x^{2} + 16 \, {\left(10 \, B b^{5} + 11 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{1280 \, b^{4} x^{6}}, \frac{15 \, {\left(2 \, B b c^{4} - A c^{5}\right)} \sqrt{-b} x^{6} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(128 \, A b^{5} - 15 \, {\left(2 \, B b^{2} c^{3} - A b c^{4}\right)} x^{4} + 10 \, {\left(2 \, B b^{3} c^{2} - A b^{2} c^{3}\right)} x^{3} + 8 \, {\left(30 \, B b^{4} c + A b^{3} c^{2}\right)} x^{2} + 16 \, {\left(10 \, B b^{5} + 11 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{640 \, b^{4} x^{6}}\right]"," ",0,"[-1/1280*(15*(2*B*b*c^4 - A*c^5)*sqrt(b)*x^6*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(128*A*b^5 - 15*(2*B*b^2*c^3 - A*b*c^4)*x^4 + 10*(2*B*b^3*c^2 - A*b^2*c^3)*x^3 + 8*(30*B*b^4*c + A*b^3*c^2)*x^2 + 16*(10*B*b^5 + 11*A*b^4*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^6), 1/640*(15*(2*B*b*c^4 - A*c^5)*sqrt(-b)*x^6*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (128*A*b^5 - 15*(2*B*b^2*c^3 - A*b*c^4)*x^4 + 10*(2*B*b^3*c^2 - A*b^2*c^3)*x^3 + 8*(30*B*b^4*c + A*b^3*c^2)*x^2 + 16*(10*B*b^5 + 11*A*b^4*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^6)]","A",0
214,1,199,0,0.402264," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(45045 \, B c^{8} x^{8} - 1280 \, B b^{8} + 2176 \, A b^{7} c + 3003 \, {\left(35 \, B b c^{7} + 17 \, A c^{8}\right)} x^{7} + 231 \, {\left(275 \, B b^{2} c^{6} + 527 \, A b c^{7}\right)} x^{6} + 63 \, {\left(5 \, B b^{3} c^{5} + 1207 \, A b^{2} c^{6}\right)} x^{5} - 35 \, {\left(10 \, B b^{4} c^{4} - 17 \, A b^{3} c^{5}\right)} x^{4} + 40 \, {\left(10 \, B b^{5} c^{3} - 17 \, A b^{4} c^{4}\right)} x^{3} - 48 \, {\left(10 \, B b^{6} c^{2} - 17 \, A b^{5} c^{3}\right)} x^{2} + 64 \, {\left(10 \, B b^{7} c - 17 \, A b^{6} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{765765 \, c^{6} \sqrt{x}}"," ",0,"2/765765*(45045*B*c^8*x^8 - 1280*B*b^8 + 2176*A*b^7*c + 3003*(35*B*b*c^7 + 17*A*c^8)*x^7 + 231*(275*B*b^2*c^6 + 527*A*b*c^7)*x^6 + 63*(5*B*b^3*c^5 + 1207*A*b^2*c^6)*x^5 - 35*(10*B*b^4*c^4 - 17*A*b^3*c^5)*x^4 + 40*(10*B*b^5*c^3 - 17*A*b^4*c^4)*x^3 - 48*(10*B*b^6*c^2 - 17*A*b^5*c^3)*x^2 + 64*(10*B*b^7*c - 17*A*b^6*c^2)*x)*sqrt(c*x^2 + b*x)/(c^6*sqrt(x))","A",0
215,1,174,0,0.404401," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)*x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B c^{7} x^{7} + 128 \, B b^{7} - 240 \, A b^{6} c + 231 \, {\left(31 \, B b c^{6} + 15 \, A c^{7}\right)} x^{6} + 63 \, {\left(71 \, B b^{2} c^{5} + 135 \, A b c^{6}\right)} x^{5} + 35 \, {\left(B b^{3} c^{4} + 159 \, A b^{2} c^{5}\right)} x^{4} - 5 \, {\left(8 \, B b^{4} c^{3} - 15 \, A b^{3} c^{4}\right)} x^{3} + 6 \, {\left(8 \, B b^{5} c^{2} - 15 \, A b^{4} c^{3}\right)} x^{2} - 8 \, {\left(8 \, B b^{6} c - 15 \, A b^{5} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{45045 \, c^{5} \sqrt{x}}"," ",0,"2/45045*(3003*B*c^7*x^7 + 128*B*b^7 - 240*A*b^6*c + 231*(31*B*b*c^6 + 15*A*c^7)*x^6 + 63*(71*B*b^2*c^5 + 135*A*b*c^6)*x^5 + 35*(B*b^3*c^4 + 159*A*b^2*c^5)*x^4 - 5*(8*B*b^4*c^3 - 15*A*b^3*c^4)*x^3 + 6*(8*B*b^5*c^2 - 15*A*b^4*c^3)*x^2 - 8*(8*B*b^6*c - 15*A*b^5*c^2)*x)*sqrt(c*x^2 + b*x)/(c^5*sqrt(x))","A",0
216,1,150,0,0.403761," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, B c^{6} x^{6} - 48 \, B b^{6} + 104 \, A b^{5} c + 63 \, {\left(27 \, B b c^{5} + 13 \, A c^{6}\right)} x^{5} + 7 \, {\left(159 \, B b^{2} c^{4} + 299 \, A b c^{5}\right)} x^{4} + {\left(15 \, B b^{3} c^{3} + 1469 \, A b^{2} c^{4}\right)} x^{3} - 3 \, {\left(6 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} x^{2} + 4 \, {\left(6 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{9009 \, c^{4} \sqrt{x}}"," ",0,"2/9009*(693*B*c^6*x^6 - 48*B*b^6 + 104*A*b^5*c + 63*(27*B*b*c^5 + 13*A*c^6)*x^5 + 7*(159*B*b^2*c^4 + 299*A*b*c^5)*x^4 + (15*B*b^3*c^3 + 1469*A*b^2*c^4)*x^3 - 3*(6*B*b^4*c^2 - 13*A*b^3*c^3)*x^2 + 4*(6*B*b^5*c - 13*A*b^4*c^2)*x)*sqrt(c*x^2 + b*x)/(c^4*sqrt(x))","A",0
217,1,125,0,0.407712," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B c^{5} x^{5} + 8 \, B b^{5} - 22 \, A b^{4} c + 7 \, {\left(23 \, B b c^{4} + 11 \, A c^{5}\right)} x^{4} + {\left(113 \, B b^{2} c^{3} + 209 \, A b c^{4}\right)} x^{3} + 3 \, {\left(B b^{3} c^{2} + 55 \, A b^{2} c^{3}\right)} x^{2} - {\left(4 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{693 \, c^{3} \sqrt{x}}"," ",0,"2/693*(63*B*c^5*x^5 + 8*B*b^5 - 22*A*b^4*c + 7*(23*B*b*c^4 + 11*A*c^5)*x^4 + (113*B*b^2*c^3 + 209*A*b*c^4)*x^3 + 3*(B*b^3*c^2 + 55*A*b^2*c^3)*x^2 - (4*B*b^4*c - 11*A*b^3*c^2)*x)*sqrt(c*x^2 + b*x)/(c^3*sqrt(x))","A",0
218,1,100,0,0.406111," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, B c^{4} x^{4} - 2 \, B b^{4} + 9 \, A b^{3} c + {\left(19 \, B b c^{3} + 9 \, A c^{4}\right)} x^{3} + 3 \, {\left(5 \, B b^{2} c^{2} + 9 \, A b c^{3}\right)} x^{2} + {\left(B b^{3} c + 27 \, A b^{2} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{63 \, c^{2} \sqrt{x}}"," ",0,"2/63*(7*B*c^4*x^4 - 2*B*b^4 + 9*A*b^3*c + (19*B*b*c^3 + 9*A*c^4)*x^3 + 3*(5*B*b^2*c^2 + 9*A*b*c^3)*x^2 + (B*b^3*c + 27*A*b^2*c^2)*x)*sqrt(c*x^2 + b*x)/(c^2*sqrt(x))","B",0
219,1,245,0,0.422124," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{105 \, A b^{\frac{5}{2}} c x \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(15 \, B c^{3} x^{3} + 15 \, B b^{3} + 161 \, A b^{2} c + 3 \, {\left(15 \, B b c^{2} + 7 \, A c^{3}\right)} x^{2} + {\left(45 \, B b^{2} c + 77 \, A b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{105 \, c x}, \frac{2 \, {\left(105 \, A \sqrt{-b} b^{2} c x \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(15 \, B c^{3} x^{3} + 15 \, B b^{3} + 161 \, A b^{2} c + 3 \, {\left(15 \, B b c^{2} + 7 \, A c^{3}\right)} x^{2} + {\left(45 \, B b^{2} c + 77 \, A b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}\right)}}{105 \, c x}\right]"," ",0,"[1/105*(105*A*b^(5/2)*c*x*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(15*B*c^3*x^3 + 15*B*b^3 + 161*A*b^2*c + 3*(15*B*b*c^2 + 7*A*c^3)*x^2 + (45*B*b^2*c + 77*A*b*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(c*x), 2/105*(105*A*sqrt(-b)*b^2*c*x*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (15*B*c^3*x^3 + 15*B*b^3 + 161*A*b^2*c + 3*(15*B*b*c^2 + 7*A*c^3)*x^2 + (45*B*b^2*c + 77*A*b*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(c*x)]","A",0
220,1,238,0,0.426343," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(9/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(2 \, B b^{2} + 5 \, A b c\right)} \sqrt{b} x^{2} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(6 \, B c^{2} x^{3} - 15 \, A b^{2} + 2 \, {\left(11 \, B b c + 5 \, A c^{2}\right)} x^{2} + 2 \, {\left(23 \, B b^{2} + 35 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{30 \, x^{2}}, \frac{15 \, {\left(2 \, B b^{2} + 5 \, A b c\right)} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(6 \, B c^{2} x^{3} - 15 \, A b^{2} + 2 \, {\left(11 \, B b c + 5 \, A c^{2}\right)} x^{2} + 2 \, {\left(23 \, B b^{2} + 35 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{15 \, x^{2}}\right]"," ",0,"[1/30*(15*(2*B*b^2 + 5*A*b*c)*sqrt(b)*x^2*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(6*B*c^2*x^3 - 15*A*b^2 + 2*(11*B*b*c + 5*A*c^2)*x^2 + 2*(23*B*b^2 + 35*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/x^2, 1/15*(15*(2*B*b^2 + 5*A*b*c)*sqrt(-b)*x^2*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (6*B*c^2*x^3 - 15*A*b^2 + 2*(11*B*b*c + 5*A*c^2)*x^2 + 2*(23*B*b^2 + 35*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/x^2]","A",0
221,1,238,0,0.428664," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(11/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, B b c + 3 \, A c^{2}\right)} \sqrt{b} x^{3} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(8 \, B c^{2} x^{3} - 6 \, A b^{2} + 8 \, {\left(7 \, B b c + 3 \, A c^{2}\right)} x^{2} - 3 \, {\left(4 \, B b^{2} + 9 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, x^{3}}, \frac{15 \, {\left(4 \, B b c + 3 \, A c^{2}\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(8 \, B c^{2} x^{3} - 6 \, A b^{2} + 8 \, {\left(7 \, B b c + 3 \, A c^{2}\right)} x^{2} - 3 \, {\left(4 \, B b^{2} + 9 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{12 \, x^{3}}\right]"," ",0,"[1/24*(15*(4*B*b*c + 3*A*c^2)*sqrt(b)*x^3*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(8*B*c^2*x^3 - 6*A*b^2 + 8*(7*B*b*c + 3*A*c^2)*x^2 - 3*(4*B*b^2 + 9*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/x^3, 1/12*(15*(4*B*b*c + 3*A*c^2)*sqrt(-b)*x^3*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (8*B*c^2*x^3 - 6*A*b^2 + 8*(7*B*b*c + 3*A*c^2)*x^2 - 3*(4*B*b^2 + 9*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/x^3]","A",0
222,1,258,0,0.422720," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(13/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(6 \, B b c^{2} + A c^{3}\right)} \sqrt{b} x^{4} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(48 \, B b c^{2} x^{3} - 8 \, A b^{3} - 3 \, {\left(18 \, B b^{2} c + 11 \, A b c^{2}\right)} x^{2} - 2 \, {\left(6 \, B b^{3} + 13 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, b x^{4}}, \frac{15 \, {\left(6 \, B b c^{2} + A c^{3}\right)} \sqrt{-b} x^{4} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(48 \, B b c^{2} x^{3} - 8 \, A b^{3} - 3 \, {\left(18 \, B b^{2} c + 11 \, A b c^{2}\right)} x^{2} - 2 \, {\left(6 \, B b^{3} + 13 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, b x^{4}}\right]"," ",0,"[1/48*(15*(6*B*b*c^2 + A*c^3)*sqrt(b)*x^4*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(48*B*b*c^2*x^3 - 8*A*b^3 - 3*(18*B*b^2*c + 11*A*b*c^2)*x^2 - 2*(6*B*b^3 + 13*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b*x^4), 1/24*(15*(6*B*b*c^2 + A*c^3)*sqrt(-b)*x^4*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (48*B*b*c^2*x^3 - 8*A*b^3 - 3*(18*B*b^2*c + 11*A*b*c^2)*x^2 - 2*(6*B*b^3 + 13*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b*x^4)]","A",0
223,1,289,0,0.431229," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(15/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(8 \, B b c^{3} - A c^{4}\right)} \sqrt{b} x^{5} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(48 \, A b^{4} + 3 \, {\left(88 \, B b^{2} c^{2} + 5 \, A b c^{3}\right)} x^{3} + 2 \, {\left(104 \, B b^{3} c + 59 \, A b^{2} c^{2}\right)} x^{2} + 8 \, {\left(8 \, B b^{4} + 17 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{384 \, b^{2} x^{5}}, \frac{15 \, {\left(8 \, B b c^{3} - A c^{4}\right)} \sqrt{-b} x^{5} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(48 \, A b^{4} + 3 \, {\left(88 \, B b^{2} c^{2} + 5 \, A b c^{3}\right)} x^{3} + 2 \, {\left(104 \, B b^{3} c + 59 \, A b^{2} c^{2}\right)} x^{2} + 8 \, {\left(8 \, B b^{4} + 17 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{192 \, b^{2} x^{5}}\right]"," ",0,"[-1/384*(15*(8*B*b*c^3 - A*c^4)*sqrt(b)*x^5*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(48*A*b^4 + 3*(88*B*b^2*c^2 + 5*A*b*c^3)*x^3 + 2*(104*B*b^3*c + 59*A*b^2*c^2)*x^2 + 8*(8*B*b^4 + 17*A*b^3*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^5), 1/192*(15*(8*B*b*c^3 - A*c^4)*sqrt(-b)*x^5*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (48*A*b^4 + 3*(88*B*b^2*c^2 + 5*A*b*c^3)*x^3 + 2*(104*B*b^3*c + 59*A*b^2*c^2)*x^2 + 8*(8*B*b^4 + 17*A*b^3*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^5)]","A",0
224,1,336,0,0.433620," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/x^(17/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(10 \, B b c^{4} - 3 \, A c^{5}\right)} \sqrt{b} x^{6} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(384 \, A b^{5} + 15 \, {\left(10 \, B b^{2} c^{3} - 3 \, A b c^{4}\right)} x^{4} + 10 \, {\left(118 \, B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} x^{3} + 8 \, {\left(170 \, B b^{4} c + 93 \, A b^{3} c^{2}\right)} x^{2} + 48 \, {\left(10 \, B b^{5} + 21 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3840 \, b^{3} x^{6}}, -\frac{15 \, {\left(10 \, B b c^{4} - 3 \, A c^{5}\right)} \sqrt{-b} x^{6} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(384 \, A b^{5} + 15 \, {\left(10 \, B b^{2} c^{3} - 3 \, A b c^{4}\right)} x^{4} + 10 \, {\left(118 \, B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} x^{3} + 8 \, {\left(170 \, B b^{4} c + 93 \, A b^{3} c^{2}\right)} x^{2} + 48 \, {\left(10 \, B b^{5} + 21 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{1920 \, b^{3} x^{6}}\right]"," ",0,"[-1/3840*(15*(10*B*b*c^4 - 3*A*c^5)*sqrt(b)*x^6*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(384*A*b^5 + 15*(10*B*b^2*c^3 - 3*A*b*c^4)*x^4 + 10*(118*B*b^3*c^2 + 3*A*b^2*c^3)*x^3 + 8*(170*B*b^4*c + 93*A*b^3*c^2)*x^2 + 48*(10*B*b^5 + 21*A*b^4*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^6), -1/1920*(15*(10*B*b*c^4 - 3*A*c^5)*sqrt(-b)*x^6*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (384*A*b^5 + 15*(10*B*b^2*c^3 - 3*A*b*c^4)*x^4 + 10*(118*B*b^3*c^2 + 3*A*b^2*c^3)*x^3 + 8*(170*B*b^4*c + 93*A*b^3*c^2)*x^2 + 48*(10*B*b^5 + 21*A*b^4*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^6)]","A",0
225,1,103,0,0.406024," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{4} x^{4} + 128 \, B b^{4} - 144 \, A b^{3} c - 5 \, {\left(8 \, B b c^{3} - 9 \, A c^{4}\right)} x^{3} + 6 \, {\left(8 \, B b^{2} c^{2} - 9 \, A b c^{3}\right)} x^{2} - 8 \, {\left(8 \, B b^{3} c - 9 \, A b^{2} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{315 \, c^{5} \sqrt{x}}"," ",0,"2/315*(35*B*c^4*x^4 + 128*B*b^4 - 144*A*b^3*c - 5*(8*B*b*c^3 - 9*A*c^4)*x^3 + 6*(8*B*b^2*c^2 - 9*A*b*c^3)*x^2 - 8*(8*B*b^3*c - 9*A*b^2*c^2)*x)*sqrt(c*x^2 + b*x)/(c^5*sqrt(x))","A",0
226,1,79,0,0.409380," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c^{3} x^{3} - 48 \, B b^{3} + 56 \, A b^{2} c - 3 \, {\left(6 \, B b c^{2} - 7 \, A c^{3}\right)} x^{2} + 4 \, {\left(6 \, B b^{2} c - 7 \, A b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{105 \, c^{4} \sqrt{x}}"," ",0,"2/105*(15*B*c^3*x^3 - 48*B*b^3 + 56*A*b^2*c - 3*(6*B*b*c^2 - 7*A*c^3)*x^2 + 4*(6*B*b^2*c - 7*A*b*c^2)*x)*sqrt(c*x^2 + b*x)/(c^4*sqrt(x))","A",0
227,1,55,0,0.400064," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{2} x^{2} + 8 \, B b^{2} - 10 \, A b c - {\left(4 \, B b c - 5 \, A c^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{15 \, c^{3} \sqrt{x}}"," ",0,"2/15*(3*B*c^2*x^2 + 8*B*b^2 - 10*A*b*c - (4*B*b*c - 5*A*c^2)*x)*sqrt(c*x^2 + b*x)/(c^3*sqrt(x))","A",0
228,1,32,0,0.399190," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c x - 2 \, B b + 3 \, A c\right)} \sqrt{c x^{2} + b x}}{3 \, c^{2} \sqrt{x}}"," ",0,"2/3*(B*c*x - 2*B*b + 3*A*c)*sqrt(c*x^2 + b*x)/(c^2*sqrt(x))","A",0
229,1,166,0,0.408846," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b e} A c x \log\left(-\frac{c e x^{2} + 2 \, b e x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b e} \sqrt{e x}}{x^{2}}\right) + 2 \, \sqrt{c x^{2} + b x} \sqrt{e x} B b}{b c e x}, \frac{2 \, {\left(\sqrt{-b e} A c x \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-b e} \sqrt{e x}}{c e x^{2} + b e x}\right) + \sqrt{c x^{2} + b x} \sqrt{e x} B b\right)}}{b c e x}\right]"," ",0,"[(sqrt(b*e)*A*c*x*log(-(c*e*x^2 + 2*b*e*x - 2*sqrt(c*x^2 + b*x)*sqrt(b*e)*sqrt(e*x))/x^2) + 2*sqrt(c*x^2 + b*x)*sqrt(e*x)*B*b)/(b*c*e*x), 2*(sqrt(-b*e)*A*c*x*arctan(sqrt(c*x^2 + b*x)*sqrt(-b*e)*sqrt(e*x)/(c*e*x^2 + b*e*x)) + sqrt(c*x^2 + b*x)*sqrt(e*x)*B*b)/(b*c*e*x)]","A",0
230,1,144,0,0.432140," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B b - A c\right)} \sqrt{b} x^{2} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, \sqrt{c x^{2} + b x} A b \sqrt{x}}{2 \, b^{2} x^{2}}, \frac{{\left(2 \, B b - A c\right)} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - \sqrt{c x^{2} + b x} A b \sqrt{x}}{b^{2} x^{2}}\right]"," ",0,"[-1/2*((2*B*b - A*c)*sqrt(b)*x^2*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*sqrt(c*x^2 + b*x)*A*b*sqrt(x))/(b^2*x^2), ((2*B*b - A*c)*sqrt(-b)*x^2*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - sqrt(c*x^2 + b*x)*A*b*sqrt(x))/(b^2*x^2)]","A",0
231,1,188,0,0.419460," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B b c - 3 \, A c^{2}\right)} \sqrt{b} x^{3} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(2 \, A b^{2} + {\left(4 \, B b^{2} - 3 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{8 \, b^{3} x^{3}}, -\frac{{\left(4 \, B b c - 3 \, A c^{2}\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(2 \, A b^{2} + {\left(4 \, B b^{2} - 3 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{4 \, b^{3} x^{3}}\right]"," ",0,"[-1/8*((4*B*b*c - 3*A*c^2)*sqrt(b)*x^3*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(2*A*b^2 + (4*B*b^2 - 3*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^3), -1/4*((4*B*b*c - 3*A*c^2)*sqrt(-b)*x^3*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (2*A*b^2 + (4*B*b^2 - 3*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^3)]","A",0
232,1,241,0,0.414154," ","integrate((B*x+A)/x^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, B b c^{2} - 5 \, A c^{3}\right)} \sqrt{b} x^{4} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(8 \, A b^{3} - 3 \, {\left(6 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2} + 2 \, {\left(6 \, B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, b^{4} x^{4}}, \frac{3 \, {\left(6 \, B b c^{2} - 5 \, A c^{3}\right)} \sqrt{-b} x^{4} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(8 \, A b^{3} - 3 \, {\left(6 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2} + 2 \, {\left(6 \, B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, b^{4} x^{4}}\right]"," ",0,"[-1/48*(3*(6*B*b*c^2 - 5*A*c^3)*sqrt(b)*x^4*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(8*A*b^3 - 3*(6*B*b^2*c - 5*A*b*c^2)*x^2 + 2*(6*B*b^3 - 5*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^4), 1/24*(3*(6*B*b*c^2 - 5*A*c^3)*sqrt(-b)*x^4*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (8*A*b^3 - 3*(6*B*b^2*c - 5*A*b*c^2)*x^2 + 2*(6*B*b^3 - 5*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^4)]","A",0
233,1,116,0,0.396514," ","integrate(x^(9/2)*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B c^{4} x^{4} - 128 \, B b^{4} + 112 \, A b^{3} c - {\left(8 \, B b c^{3} - 7 \, A c^{4}\right)} x^{3} + 2 \, {\left(8 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{2} - 8 \, {\left(8 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{35 \, {\left(c^{6} x^{2} + b c^{5} x\right)}}"," ",0,"2/35*(5*B*c^4*x^4 - 128*B*b^4 + 112*A*b^3*c - (8*B*b*c^3 - 7*A*c^4)*x^3 + 2*(8*B*b^2*c^2 - 7*A*b*c^3)*x^2 - 8*(8*B*b^3*c - 7*A*b^2*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^6*x^2 + b*c^5*x)","A",0
234,1,92,0,0.388546," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{3} x^{3} + 48 \, B b^{3} - 40 \, A b^{2} c - {\left(6 \, B b c^{2} - 5 \, A c^{3}\right)} x^{2} + 4 \, {\left(6 \, B b^{2} c - 5 \, A b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{15 \, {\left(c^{5} x^{2} + b c^{4} x\right)}}"," ",0,"2/15*(3*B*c^3*x^3 + 48*B*b^3 - 40*A*b^2*c - (6*B*b*c^2 - 5*A*c^3)*x^2 + 4*(6*B*b^2*c - 5*A*b*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^5*x^2 + b*c^4*x)","A",0
235,1,67,0,0.412857," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c^{2} x^{2} - 8 \, B b^{2} + 6 \, A b c - {\left(4 \, B b c - 3 \, A c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3 \, {\left(c^{4} x^{2} + b c^{3} x\right)}}"," ",0,"2/3*(B*c^2*x^2 - 8*B*b^2 + 6*A*b*c - (4*B*b*c - 3*A*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^4*x^2 + b*c^3*x)","A",0
236,1,45,0,0.403178," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c x + 2 \, B b - A c\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{c^{3} x^{2} + b c^{2} x}"," ",0,"2*(B*c*x + 2*B*b - A*c)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^3*x^2 + b*c^2*x)","A",0
237,1,192,0,0.432496," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A c^{2} x^{2} + A b c x\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, {\left(B b^{2} - A b c\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{b^{2} c^{2} x^{2} + b^{3} c x}, \frac{2 \, {\left({\left(A c^{2} x^{2} + A b c x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(B b^{2} - A b c\right)} \sqrt{c x^{2} + b x} \sqrt{x}\right)}}{b^{2} c^{2} x^{2} + b^{3} c x}\right]"," ",0,"[((A*c^2*x^2 + A*b*c*x)*sqrt(b)*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*(B*b^2 - A*b*c)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*c^2*x^2 + b^3*c*x), 2*((A*c^2*x^2 + A*b*c*x)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (B*b^2 - A*b*c)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*c^2*x^2 + b^3*c*x)]","A",0
238,1,248,0,0.413834," ","integrate((B*x+A)/(c*x^2+b*x)^(3/2)/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, B b c - 3 \, A c^{2}\right)} x^{3} + {\left(2 \, B b^{2} - 3 \, A b c\right)} x^{2}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(A b^{2} - {\left(2 \, B b^{2} - 3 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{2 \, {\left(b^{3} c x^{3} + b^{4} x^{2}\right)}}, \frac{{\left({\left(2 \, B b c - 3 \, A c^{2}\right)} x^{3} + {\left(2 \, B b^{2} - 3 \, A b c\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(A b^{2} - {\left(2 \, B b^{2} - 3 \, A b c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{b^{3} c x^{3} + b^{4} x^{2}}\right]"," ",0,"[-1/2*(((2*B*b*c - 3*A*c^2)*x^3 + (2*B*b^2 - 3*A*b*c)*x^2)*sqrt(b)*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(A*b^2 - (2*B*b^2 - 3*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*c*x^3 + b^4*x^2), (((2*B*b*c - 3*A*c^2)*x^3 + (2*B*b^2 - 3*A*b*c)*x^2)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (A*b^2 - (2*B*b^2 - 3*A*b*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*c*x^3 + b^4*x^2)]","A",0
239,1,304,0,0.423304," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(4 \, B b c^{2} - 5 \, A c^{3}\right)} x^{4} + {\left(4 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{3}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(2 \, A b^{3} + 3 \, {\left(4 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2} + {\left(4 \, B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{8 \, {\left(b^{4} c x^{4} + b^{5} x^{3}\right)}}, -\frac{3 \, {\left({\left(4 \, B b c^{2} - 5 \, A c^{3}\right)} x^{4} + {\left(4 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(2 \, A b^{3} + 3 \, {\left(4 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2} + {\left(4 \, B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{4 \, {\left(b^{4} c x^{4} + b^{5} x^{3}\right)}}\right]"," ",0,"[-1/8*(3*((4*B*b*c^2 - 5*A*c^3)*x^4 + (4*B*b^2*c - 5*A*b*c^2)*x^3)*sqrt(b)*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(2*A*b^3 + 3*(4*B*b^2*c - 5*A*b*c^2)*x^2 + (4*B*b^3 - 5*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*c*x^4 + b^5*x^3), -1/4*(3*((4*B*b*c^2 - 5*A*c^3)*x^4 + (4*B*b^2*c - 5*A*b*c^2)*x^3)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (2*A*b^3 + 3*(4*B*b^2*c - 5*A*b*c^2)*x^2 + (4*B*b^3 - 5*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*c*x^4 + b^5*x^3)]","A",0
240,1,359,0,0.422424," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(6 \, B b c^{3} - 7 \, A c^{4}\right)} x^{5} + {\left(6 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{4}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(8 \, A b^{4} - 15 \, {\left(6 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{3} - 5 \, {\left(6 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{2} + 2 \, {\left(6 \, B b^{4} - 7 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, {\left(b^{5} c x^{5} + b^{6} x^{4}\right)}}, \frac{15 \, {\left({\left(6 \, B b c^{3} - 7 \, A c^{4}\right)} x^{5} + {\left(6 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(8 \, A b^{4} - 15 \, {\left(6 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{3} - 5 \, {\left(6 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{2} + 2 \, {\left(6 \, B b^{4} - 7 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, {\left(b^{5} c x^{5} + b^{6} x^{4}\right)}}\right]"," ",0,"[-1/48*(15*((6*B*b*c^3 - 7*A*c^4)*x^5 + (6*B*b^2*c^2 - 7*A*b*c^3)*x^4)*sqrt(b)*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(8*A*b^4 - 15*(6*B*b^2*c^2 - 7*A*b*c^3)*x^3 - 5*(6*B*b^3*c - 7*A*b^2*c^2)*x^2 + 2*(6*B*b^4 - 7*A*b^3*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^5*c*x^5 + b^6*x^4), 1/24*(15*((6*B*b*c^3 - 7*A*c^4)*x^5 + (6*B*b^2*c^2 - 7*A*b*c^3)*x^4)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (8*A*b^4 - 15*(6*B*b^2*c^2 - 7*A*b*c^3)*x^3 - 5*(6*B*b^3*c - 7*A*b^2*c^2)*x^2 + 2*(6*B*b^4 - 7*A*b^3*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^5*c*x^5 + b^6*x^4)]","A",0
241,1,406,0,0.440104," ","integrate((B*x+A)/x^(7/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(8 \, B b c^{4} - 9 \, A c^{5}\right)} x^{6} + {\left(8 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} x^{5}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(48 \, A b^{5} + 105 \, {\left(8 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} x^{4} + 35 \, {\left(8 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} x^{3} - 14 \, {\left(8 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} x^{2} + 8 \, {\left(8 \, B b^{5} - 9 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{384 \, {\left(b^{6} c x^{6} + b^{7} x^{5}\right)}}, -\frac{105 \, {\left({\left(8 \, B b c^{4} - 9 \, A c^{5}\right)} x^{6} + {\left(8 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} x^{5}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(48 \, A b^{5} + 105 \, {\left(8 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} x^{4} + 35 \, {\left(8 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} x^{3} - 14 \, {\left(8 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} x^{2} + 8 \, {\left(8 \, B b^{5} - 9 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{192 \, {\left(b^{6} c x^{6} + b^{7} x^{5}\right)}}\right]"," ",0,"[-1/384*(105*((8*B*b*c^4 - 9*A*c^5)*x^6 + (8*B*b^2*c^3 - 9*A*b*c^4)*x^5)*sqrt(b)*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(48*A*b^5 + 105*(8*B*b^2*c^3 - 9*A*b*c^4)*x^4 + 35*(8*B*b^3*c^2 - 9*A*b^2*c^3)*x^3 - 14*(8*B*b^4*c - 9*A*b^3*c^2)*x^2 + 8*(8*B*b^5 - 9*A*b^4*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^6*c*x^6 + b^7*x^5), -1/192*(105*((8*B*b*c^4 - 9*A*c^5)*x^6 + (8*B*b^2*c^3 - 9*A*b*c^4)*x^5)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (48*A*b^5 + 105*(8*B*b^2*c^3 - 9*A*b*c^4)*x^4 + 35*(8*B*b^3*c^2 - 9*A*b^2*c^3)*x^3 - 14*(8*B*b^4*c - 9*A*b^3*c^2)*x^2 + 8*(8*B*b^5 - 9*A*b^4*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^6*c*x^6 + b^7*x^5)]","A",0
242,1,127,0,0.405387," ","integrate(x^(11/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{4} x^{4} + 128 \, B b^{4} - 80 \, A b^{3} c - {\left(8 \, B b c^{3} - 5 \, A c^{4}\right)} x^{3} + 6 \, {\left(8 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} x^{2} + 24 \, {\left(8 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{15 \, {\left(c^{7} x^{3} + 2 \, b c^{6} x^{2} + b^{2} c^{5} x\right)}}"," ",0,"2/15*(3*B*c^4*x^4 + 128*B*b^4 - 80*A*b^3*c - (8*B*b*c^3 - 5*A*c^4)*x^3 + 6*(8*B*b^2*c^2 - 5*A*b*c^3)*x^2 + 24*(8*B*b^3*c - 5*A*b^2*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^7*x^3 + 2*b*c^6*x^2 + b^2*c^5*x)","A",0
243,1,102,0,0.391595," ","integrate(x^(9/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c^{3} x^{3} - 16 \, B b^{3} + 8 \, A b^{2} c - 3 \, {\left(2 \, B b c^{2} - A c^{3}\right)} x^{2} - 12 \, {\left(2 \, B b^{2} c - A b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3 \, {\left(c^{6} x^{3} + 2 \, b c^{5} x^{2} + b^{2} c^{4} x\right)}}"," ",0,"2/3*(B*c^3*x^3 - 16*B*b^3 + 8*A*b^2*c - 3*(2*B*b*c^2 - A*c^3)*x^2 - 12*(2*B*b^2*c - A*b*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^6*x^3 + 2*b*c^5*x^2 + b^2*c^4*x)","A",0
244,1,79,0,0.394193," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{2} x^{2} + 8 \, B b^{2} - 2 \, A b c + 3 \, {\left(4 \, B b c - A c^{2}\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3 \, {\left(c^{5} x^{3} + 2 \, b c^{4} x^{2} + b^{2} c^{3} x\right)}}"," ",0,"2/3*(3*B*c^2*x^2 + 8*B*b^2 - 2*A*b*c + 3*(4*B*b*c - A*c^2)*x)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^5*x^3 + 2*b*c^4*x^2 + b^2*c^3*x)","A",0
245,1,56,0,0.412676," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, B c x + 2 \, B b + A c\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3 \, {\left(c^{4} x^{3} + 2 \, b c^{3} x^{2} + b^{2} c^{2} x\right)}}"," ",0,"-2/3*(3*B*c*x + 2*B*b + A*c)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^4*x^3 + 2*b*c^3*x^2 + b^2*c^2*x)","A",0
246,1,262,0,0.421274," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A c^{3} x^{3} + 2 \, A b c^{2} x^{2} + A b^{2} c x\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(3 \, A b c^{2} x - B b^{3} + 4 \, A b^{2} c\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3 \, {\left(b^{3} c^{3} x^{3} + 2 \, b^{4} c^{2} x^{2} + b^{5} c x\right)}}, \frac{2 \, {\left(3 \, {\left(A c^{3} x^{3} + 2 \, A b c^{2} x^{2} + A b^{2} c x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(3 \, A b c^{2} x - B b^{3} + 4 \, A b^{2} c\right)} \sqrt{c x^{2} + b x} \sqrt{x}\right)}}{3 \, {\left(b^{3} c^{3} x^{3} + 2 \, b^{4} c^{2} x^{2} + b^{5} c x\right)}}\right]"," ",0,"[1/3*(3*(A*c^3*x^3 + 2*A*b*c^2*x^2 + A*b^2*c*x)*sqrt(b)*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(3*A*b*c^2*x - B*b^3 + 4*A*b^2*c)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*c^3*x^3 + 2*b^4*c^2*x^2 + b^5*c*x), 2/3*(3*(A*c^3*x^3 + 2*A*b*c^2*x^2 + A*b^2*c*x)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (3*A*b*c^2*x - B*b^3 + 4*A*b^2*c)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*c^3*x^3 + 2*b^4*c^2*x^2 + b^5*c*x)]","A",0
247,1,367,0,0.438198," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, B b c^{2} - 5 \, A c^{3}\right)} x^{4} + 2 \, {\left(2 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{3} + {\left(2 \, B b^{3} - 5 \, A b^{2} c\right)} x^{2}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(3 \, A b^{3} - 3 \, {\left(2 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2} - 4 \, {\left(2 \, B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{6 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}, \frac{3 \, {\left({\left(2 \, B b c^{2} - 5 \, A c^{3}\right)} x^{4} + 2 \, {\left(2 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{3} + {\left(2 \, B b^{3} - 5 \, A b^{2} c\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(3 \, A b^{3} - 3 \, {\left(2 \, B b^{2} c - 5 \, A b c^{2}\right)} x^{2} - 4 \, {\left(2 \, B b^{3} - 5 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}\right]"," ",0,"[-1/6*(3*((2*B*b*c^2 - 5*A*c^3)*x^4 + 2*(2*B*b^2*c - 5*A*b*c^2)*x^3 + (2*B*b^3 - 5*A*b^2*c)*x^2)*sqrt(b)*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(3*A*b^3 - 3*(2*B*b^2*c - 5*A*b*c^2)*x^2 - 4*(2*B*b^3 - 5*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2), 1/3*(3*((2*B*b*c^2 - 5*A*c^3)*x^4 + 2*(2*B*b^2*c - 5*A*b*c^2)*x^3 + (2*B*b^3 - 5*A*b^2*c)*x^2)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (3*A*b^3 - 3*(2*B*b^2*c - 5*A*b*c^2)*x^2 - 4*(2*B*b^3 - 5*A*b^2*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)]","A",0
248,1,424,0,0.420610," ","integrate((B*x+A)/(c*x^2+b*x)^(5/2)/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(4 \, B b c^{3} - 7 \, A c^{4}\right)} x^{5} + 2 \, {\left(4 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{4} + {\left(4 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{3}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(6 \, A b^{4} + 15 \, {\left(4 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{3} + 20 \, {\left(4 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{2} + 3 \, {\left(4 \, B b^{4} - 7 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, {\left(b^{5} c^{2} x^{5} + 2 \, b^{6} c x^{4} + b^{7} x^{3}\right)}}, -\frac{15 \, {\left({\left(4 \, B b c^{3} - 7 \, A c^{4}\right)} x^{5} + 2 \, {\left(4 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{4} + {\left(4 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(6 \, A b^{4} + 15 \, {\left(4 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} x^{3} + 20 \, {\left(4 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} x^{2} + 3 \, {\left(4 \, B b^{4} - 7 \, A b^{3} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{12 \, {\left(b^{5} c^{2} x^{5} + 2 \, b^{6} c x^{4} + b^{7} x^{3}\right)}}\right]"," ",0,"[-1/24*(15*((4*B*b*c^3 - 7*A*c^4)*x^5 + 2*(4*B*b^2*c^2 - 7*A*b*c^3)*x^4 + (4*B*b^3*c - 7*A*b^2*c^2)*x^3)*sqrt(b)*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(6*A*b^4 + 15*(4*B*b^2*c^2 - 7*A*b*c^3)*x^3 + 20*(4*B*b^3*c - 7*A*b^2*c^2)*x^2 + 3*(4*B*b^4 - 7*A*b^3*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^5*c^2*x^5 + 2*b^6*c*x^4 + b^7*x^3), -1/12*(15*((4*B*b*c^3 - 7*A*c^4)*x^5 + 2*(4*B*b^2*c^2 - 7*A*b*c^3)*x^4 + (4*B*b^3*c - 7*A*b^2*c^2)*x^3)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (6*A*b^4 + 15*(4*B*b^2*c^2 - 7*A*b*c^3)*x^3 + 20*(4*B*b^3*c - 7*A*b^2*c^2)*x^2 + 3*(4*B*b^4 - 7*A*b^3*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^5*c^2*x^5 + 2*b^6*c*x^4 + b^7*x^3)]","A",0
249,1,477,0,0.446344," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(2 \, B b c^{4} - 3 \, A c^{5}\right)} x^{6} + 2 \, {\left(2 \, B b^{2} c^{3} - 3 \, A b c^{4}\right)} x^{5} + {\left(2 \, B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} x^{4}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(8 \, A b^{5} - 105 \, {\left(2 \, B b^{2} c^{3} - 3 \, A b c^{4}\right)} x^{4} - 140 \, {\left(2 \, B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} x^{3} - 21 \, {\left(2 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} x^{2} + 6 \, {\left(2 \, B b^{5} - 3 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, {\left(b^{6} c^{2} x^{6} + 2 \, b^{7} c x^{5} + b^{8} x^{4}\right)}}, \frac{105 \, {\left({\left(2 \, B b c^{4} - 3 \, A c^{5}\right)} x^{6} + 2 \, {\left(2 \, B b^{2} c^{3} - 3 \, A b c^{4}\right)} x^{5} + {\left(2 \, B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} x^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(8 \, A b^{5} - 105 \, {\left(2 \, B b^{2} c^{3} - 3 \, A b c^{4}\right)} x^{4} - 140 \, {\left(2 \, B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} x^{3} - 21 \, {\left(2 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} x^{2} + 6 \, {\left(2 \, B b^{5} - 3 \, A b^{4} c\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, {\left(b^{6} c^{2} x^{6} + 2 \, b^{7} c x^{5} + b^{8} x^{4}\right)}}\right]"," ",0,"[-1/48*(105*((2*B*b*c^4 - 3*A*c^5)*x^6 + 2*(2*B*b^2*c^3 - 3*A*b*c^4)*x^5 + (2*B*b^3*c^2 - 3*A*b^2*c^3)*x^4)*sqrt(b)*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(8*A*b^5 - 105*(2*B*b^2*c^3 - 3*A*b*c^4)*x^4 - 140*(2*B*b^3*c^2 - 3*A*b^2*c^3)*x^3 - 21*(2*B*b^4*c - 3*A*b^3*c^2)*x^2 + 6*(2*B*b^5 - 3*A*b^4*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^6*c^2*x^6 + 2*b^7*c*x^5 + b^8*x^4), 1/24*(105*((2*B*b*c^4 - 3*A*c^5)*x^6 + 2*(2*B*b^2*c^3 - 3*A*b*c^4)*x^5 + (2*B*b^3*c^2 - 3*A*b^2*c^3)*x^4)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (8*A*b^5 - 105*(2*B*b^2*c^3 - 3*A*b*c^4)*x^4 - 140*(2*B*b^3*c^2 - 3*A*b^2*c^3)*x^3 - 21*(2*B*b^4*c - 3*A*b^3*c^2)*x^2 + 6*(2*B*b^5 - 3*A*b^4*c)*x)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^6*c^2*x^6 + 2*b^7*c*x^5 + b^8*x^4)]","A",0
250,1,31,0,0.417489," ","integrate(x^(1+p)*(3*c*x+2*b)*(c*x^2+b*x)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{2} + b x\right)} {\left(c x^{2} + b x\right)}^{p} x^{p + 1}}{p + 1}"," ",0,"(c*x^2 + b*x)*(c*x^2 + b*x)^p*x^(p + 1)/(p + 1)","A",0
251,1,29,0,0.351351," ","integrate(x^3*(B*x+A)*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} c B + \frac{1}{6} x^{6} c A + \frac{1}{5} x^{5} a B + \frac{1}{4} x^{4} a A"," ",0,"1/7*x^7*c*B + 1/6*x^6*c*A + 1/5*x^5*a*B + 1/4*x^4*a*A","A",0
252,1,29,0,0.346180," ","integrate(x^2*(B*x+A)*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{6} x^{6} c B + \frac{1}{5} x^{5} c A + \frac{1}{4} x^{4} a B + \frac{1}{3} x^{3} a A"," ",0,"1/6*x^6*c*B + 1/5*x^5*c*A + 1/4*x^4*a*B + 1/3*x^3*a*A","A",0
253,1,29,0,0.336134," ","integrate(x*(B*x+A)*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{5} x^{5} c B + \frac{1}{4} x^{4} c A + \frac{1}{3} x^{3} a B + \frac{1}{2} x^{2} a A"," ",0,"1/5*x^5*c*B + 1/4*x^4*c*A + 1/3*x^3*a*B + 1/2*x^2*a*A","A",0
254,1,26,0,0.346750," ","integrate((B*x+A)*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} a B + x a A"," ",0,"1/4*x^4*c*B + 1/3*x^3*c*A + 1/2*x^2*a*B + x*a*A","A",0
255,1,24,0,0.390438," ","integrate((B*x+A)*(c*x^2+a)/x,x, algorithm=""fricas"")","\frac{1}{3} \, B c x^{3} + \frac{1}{2} \, A c x^{2} + B a x + A a \log\left(x\right)"," ",0,"1/3*B*c*x^3 + 1/2*A*c*x^2 + B*a*x + A*a*log(x)","A",0
256,1,30,0,0.375359," ","integrate((B*x+A)*(c*x^2+a)/x^2,x, algorithm=""fricas"")","\frac{B c x^{3} + 2 \, A c x^{2} + 2 \, B a x \log\left(x\right) - 2 \, A a}{2 \, x}"," ",0,"1/2*(B*c*x^3 + 2*A*c*x^2 + 2*B*a*x*log(x) - 2*A*a)/x","A",0
257,1,31,0,0.390536," ","integrate((B*x+A)*(c*x^2+a)/x^3,x, algorithm=""fricas"")","\frac{2 \, B c x^{3} + 2 \, A c x^{2} \log\left(x\right) - 2 \, B a x - A a}{2 \, x^{2}}"," ",0,"1/2*(2*B*c*x^3 + 2*A*c*x^2*log(x) - 2*B*a*x - A*a)/x^2","A",0
258,1,53,0,0.349011," ","integrate(x^3*(B*x+A)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{2} B + \frac{1}{8} x^{8} c^{2} A + \frac{2}{7} x^{7} c a B + \frac{1}{3} x^{6} c a A + \frac{1}{5} x^{5} a^{2} B + \frac{1}{4} x^{4} a^{2} A"," ",0,"1/9*x^9*c^2*B + 1/8*x^8*c^2*A + 2/7*x^7*c*a*B + 1/3*x^6*c*a*A + 1/5*x^5*a^2*B + 1/4*x^4*a^2*A","A",0
259,1,53,0,0.350617," ","integrate(x^2*(B*x+A)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{2} B + \frac{1}{7} x^{7} c^{2} A + \frac{1}{3} x^{6} c a B + \frac{2}{5} x^{5} c a A + \frac{1}{4} x^{4} a^{2} B + \frac{1}{3} x^{3} a^{2} A"," ",0,"1/8*x^8*c^2*B + 1/7*x^7*c^2*A + 1/3*x^6*c*a*B + 2/5*x^5*c*a*A + 1/4*x^4*a^2*B + 1/3*x^3*a^2*A","A",0
260,1,53,0,0.358654," ","integrate(x*(B*x+A)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} c^{2} B + \frac{1}{6} x^{6} c^{2} A + \frac{2}{5} x^{5} c a B + \frac{1}{2} x^{4} c a A + \frac{1}{3} x^{3} a^{2} B + \frac{1}{2} x^{2} a^{2} A"," ",0,"1/7*x^7*c^2*B + 1/6*x^6*c^2*A + 2/5*x^5*c*a*B + 1/2*x^4*c*a*A + 1/3*x^3*a^2*B + 1/2*x^2*a^2*A","A",0
261,1,50,0,0.352450," ","integrate((B*x+A)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} c^{2} B + \frac{1}{5} x^{5} c^{2} A + \frac{1}{2} x^{4} c a B + \frac{2}{3} x^{3} c a A + \frac{1}{2} x^{2} a^{2} B + x a^{2} A"," ",0,"1/6*x^6*c^2*B + 1/5*x^5*c^2*A + 1/2*x^4*c*a*B + 2/3*x^3*c*a*A + 1/2*x^2*a^2*B + x*a^2*A","A",0
262,1,47,0,0.393743," ","integrate((B*x+A)*(c*x^2+a)^2/x,x, algorithm=""fricas"")","\frac{1}{5} \, B c^{2} x^{5} + \frac{1}{4} \, A c^{2} x^{4} + \frac{2}{3} \, B a c x^{3} + A a c x^{2} + B a^{2} x + A a^{2} \log\left(x\right)"," ",0,"1/5*B*c^2*x^5 + 1/4*A*c^2*x^4 + 2/3*B*a*c*x^3 + A*a*c*x^2 + B*a^2*x + A*a^2*log(x)","A",0
263,1,55,0,0.397565," ","integrate((B*x+A)*(c*x^2+a)^2/x^2,x, algorithm=""fricas"")","\frac{3 \, B c^{2} x^{5} + 4 \, A c^{2} x^{4} + 12 \, B a c x^{3} + 24 \, A a c x^{2} + 12 \, B a^{2} x \log\left(x\right) - 12 \, A a^{2}}{12 \, x}"," ",0,"1/12*(3*B*c^2*x^5 + 4*A*c^2*x^4 + 12*B*a*c*x^3 + 24*A*a*c*x^2 + 12*B*a^2*x*log(x) - 12*A*a^2)/x","A",0
264,1,55,0,0.395775," ","integrate((B*x+A)*(c*x^2+a)^2/x^3,x, algorithm=""fricas"")","\frac{2 \, B c^{2} x^{5} + 3 \, A c^{2} x^{4} + 12 \, B a c x^{3} + 12 \, A a c x^{2} \log\left(x\right) - 6 \, B a^{2} x - 3 \, A a^{2}}{6 \, x^{2}}"," ",0,"1/6*(2*B*c^2*x^5 + 3*A*c^2*x^4 + 12*B*a*c*x^3 + 12*A*a*c*x^2*log(x) - 6*B*a^2*x - 3*A*a^2)/x^2","A",0
265,1,77,0,0.346035," ","integrate(x^3*(B*x+A)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} c^{3} B + \frac{1}{10} x^{10} c^{3} A + \frac{1}{3} x^{9} c^{2} a B + \frac{3}{8} x^{8} c^{2} a A + \frac{3}{7} x^{7} c a^{2} B + \frac{1}{2} x^{6} c a^{2} A + \frac{1}{5} x^{5} a^{3} B + \frac{1}{4} x^{4} a^{3} A"," ",0,"1/11*x^11*c^3*B + 1/10*x^10*c^3*A + 1/3*x^9*c^2*a*B + 3/8*x^8*c^2*a*A + 3/7*x^7*c*a^2*B + 1/2*x^6*c*a^2*A + 1/5*x^5*a^3*B + 1/4*x^4*a^3*A","A",0
266,1,77,0,0.346013," ","integrate(x^2*(B*x+A)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} c^{3} B + \frac{1}{9} x^{9} c^{3} A + \frac{3}{8} x^{8} c^{2} a B + \frac{3}{7} x^{7} c^{2} a A + \frac{1}{2} x^{6} c a^{2} B + \frac{3}{5} x^{5} c a^{2} A + \frac{1}{4} x^{4} a^{3} B + \frac{1}{3} x^{3} a^{3} A"," ",0,"1/10*x^10*c^3*B + 1/9*x^9*c^3*A + 3/8*x^8*c^2*a*B + 3/7*x^7*c^2*a*A + 1/2*x^6*c*a^2*B + 3/5*x^5*c*a^2*A + 1/4*x^4*a^3*B + 1/3*x^3*a^3*A","A",0
267,1,77,0,0.342656," ","integrate(x*(B*x+A)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{3} B + \frac{1}{8} x^{8} c^{3} A + \frac{3}{7} x^{7} c^{2} a B + \frac{1}{2} x^{6} c^{2} a A + \frac{3}{5} x^{5} c a^{2} B + \frac{3}{4} x^{4} c a^{2} A + \frac{1}{3} x^{3} a^{3} B + \frac{1}{2} x^{2} a^{3} A"," ",0,"1/9*x^9*c^3*B + 1/8*x^8*c^3*A + 3/7*x^7*c^2*a*B + 1/2*x^6*c^2*a*A + 3/5*x^5*c*a^2*B + 3/4*x^4*c*a^2*A + 1/3*x^3*a^3*B + 1/2*x^2*a^3*A","A",0
268,1,73,0,0.344077," ","integrate((B*x+A)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{3} B + \frac{1}{7} x^{7} c^{3} A + \frac{1}{2} x^{6} c^{2} a B + \frac{3}{5} x^{5} c^{2} a A + \frac{3}{4} x^{4} c a^{2} B + x^{3} c a^{2} A + \frac{1}{2} x^{2} a^{3} B + x a^{3} A"," ",0,"1/8*x^8*c^3*B + 1/7*x^7*c^3*A + 1/2*x^6*c^2*a*B + 3/5*x^5*c^2*a*A + 3/4*x^4*c*a^2*B + x^3*c*a^2*A + 1/2*x^2*a^3*B + x*a^3*A","A",0
269,1,71,0,0.390246," ","integrate((B*x+A)*(c*x^2+a)^3/x,x, algorithm=""fricas"")","\frac{1}{7} \, B c^{3} x^{7} + \frac{1}{6} \, A c^{3} x^{6} + \frac{3}{5} \, B a c^{2} x^{5} + \frac{3}{4} \, A a c^{2} x^{4} + B a^{2} c x^{3} + \frac{3}{2} \, A a^{2} c x^{2} + B a^{3} x + A a^{3} \log\left(x\right)"," ",0,"1/7*B*c^3*x^7 + 1/6*A*c^3*x^6 + 3/5*B*a*c^2*x^5 + 3/4*A*a*c^2*x^4 + B*a^2*c*x^3 + 3/2*A*a^2*c*x^2 + B*a^3*x + A*a^3*log(x)","A",0
270,1,79,0,0.396955," ","integrate((B*x+A)*(c*x^2+a)^3/x^2,x, algorithm=""fricas"")","\frac{10 \, B c^{3} x^{7} + 12 \, A c^{3} x^{6} + 45 \, B a c^{2} x^{5} + 60 \, A a c^{2} x^{4} + 90 \, B a^{2} c x^{3} + 180 \, A a^{2} c x^{2} + 60 \, B a^{3} x \log\left(x\right) - 60 \, A a^{3}}{60 \, x}"," ",0,"1/60*(10*B*c^3*x^7 + 12*A*c^3*x^6 + 45*B*a*c^2*x^5 + 60*A*a*c^2*x^4 + 90*B*a^2*c*x^3 + 180*A*a^2*c*x^2 + 60*B*a^3*x*log(x) - 60*A*a^3)/x","A",0
271,1,79,0,0.387297," ","integrate((B*x+A)*(c*x^2+a)^3/x^3,x, algorithm=""fricas"")","\frac{4 \, B c^{3} x^{7} + 5 \, A c^{3} x^{6} + 20 \, B a c^{2} x^{5} + 30 \, A a c^{2} x^{4} + 60 \, B a^{2} c x^{3} + 60 \, A a^{2} c x^{2} \log\left(x\right) - 20 \, B a^{3} x - 10 \, A a^{3}}{20 \, x^{2}}"," ",0,"1/20*(4*B*c^3*x^7 + 5*A*c^3*x^6 + 20*B*a*c^2*x^5 + 30*A*a*c^2*x^4 + 60*B*a^2*c*x^3 + 60*A*a^2*c*x^2*log(x) - 20*B*a^3*x - 10*A*a^3)/x^2","A",0
272,1,101,0,0.352232," ","integrate(x^3*(B*x+A)*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{13} x^{13} c^{4} B + \frac{1}{12} x^{12} c^{4} A + \frac{4}{11} x^{11} c^{3} a B + \frac{2}{5} x^{10} c^{3} a A + \frac{2}{3} x^{9} c^{2} a^{2} B + \frac{3}{4} x^{8} c^{2} a^{2} A + \frac{4}{7} x^{7} c a^{3} B + \frac{2}{3} x^{6} c a^{3} A + \frac{1}{5} x^{5} a^{4} B + \frac{1}{4} x^{4} a^{4} A"," ",0,"1/13*x^13*c^4*B + 1/12*x^12*c^4*A + 4/11*x^11*c^3*a*B + 2/5*x^10*c^3*a*A + 2/3*x^9*c^2*a^2*B + 3/4*x^8*c^2*a^2*A + 4/7*x^7*c*a^3*B + 2/3*x^6*c*a^3*A + 1/5*x^5*a^4*B + 1/4*x^4*a^4*A","A",0
273,1,101,0,0.353771," ","integrate(x^2*(B*x+A)*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{12} x^{12} c^{4} B + \frac{1}{11} x^{11} c^{4} A + \frac{2}{5} x^{10} c^{3} a B + \frac{4}{9} x^{9} c^{3} a A + \frac{3}{4} x^{8} c^{2} a^{2} B + \frac{6}{7} x^{7} c^{2} a^{2} A + \frac{2}{3} x^{6} c a^{3} B + \frac{4}{5} x^{5} c a^{3} A + \frac{1}{4} x^{4} a^{4} B + \frac{1}{3} x^{3} a^{4} A"," ",0,"1/12*x^12*c^4*B + 1/11*x^11*c^4*A + 2/5*x^10*c^3*a*B + 4/9*x^9*c^3*a*A + 3/4*x^8*c^2*a^2*B + 6/7*x^7*c^2*a^2*A + 2/3*x^6*c*a^3*B + 4/5*x^5*c*a^3*A + 1/4*x^4*a^4*B + 1/3*x^3*a^4*A","A",0
274,1,99,0,0.359840," ","integrate(x*(B*x+A)*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{11} x^{11} c^{4} B + \frac{1}{10} x^{10} c^{4} A + \frac{4}{9} x^{9} c^{3} a B + \frac{1}{2} x^{8} c^{3} a A + \frac{6}{7} x^{7} c^{2} a^{2} B + x^{6} c^{2} a^{2} A + \frac{4}{5} x^{5} c a^{3} B + x^{4} c a^{3} A + \frac{1}{3} x^{3} a^{4} B + \frac{1}{2} x^{2} a^{4} A"," ",0,"1/11*x^11*c^4*B + 1/10*x^10*c^4*A + 4/9*x^9*c^3*a*B + 1/2*x^8*c^3*a*A + 6/7*x^7*c^2*a^2*B + x^6*c^2*a^2*A + 4/5*x^5*c*a^3*B + x^4*c*a^3*A + 1/3*x^3*a^4*B + 1/2*x^2*a^4*A","A",0
275,1,96,0,0.352182," ","integrate((B*x+A)*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{10} x^{10} c^{4} B + \frac{1}{9} x^{9} c^{4} A + \frac{1}{2} x^{8} c^{3} a B + \frac{4}{7} x^{7} c^{3} a A + x^{6} c^{2} a^{2} B + \frac{6}{5} x^{5} c^{2} a^{2} A + x^{4} c a^{3} B + \frac{4}{3} x^{3} c a^{3} A + \frac{1}{2} x^{2} a^{4} B + x a^{4} A"," ",0,"1/10*x^10*c^4*B + 1/9*x^9*c^4*A + 1/2*x^8*c^3*a*B + 4/7*x^7*c^3*a*A + x^6*c^2*a^2*B + 6/5*x^5*c^2*a^2*A + x^4*c*a^3*B + 4/3*x^3*c*a^3*A + 1/2*x^2*a^4*B + x*a^4*A","A",0
276,1,96,0,0.399168," ","integrate((B*x+A)*(c*x^2+a)^4/x,x, algorithm=""fricas"")","\frac{1}{9} \, B c^{4} x^{9} + \frac{1}{8} \, A c^{4} x^{8} + \frac{4}{7} \, B a c^{3} x^{7} + \frac{2}{3} \, A a c^{3} x^{6} + \frac{6}{5} \, B a^{2} c^{2} x^{5} + \frac{3}{2} \, A a^{2} c^{2} x^{4} + \frac{4}{3} \, B a^{3} c x^{3} + 2 \, A a^{3} c x^{2} + B a^{4} x + A a^{4} \log\left(x\right)"," ",0,"1/9*B*c^4*x^9 + 1/8*A*c^4*x^8 + 4/7*B*a*c^3*x^7 + 2/3*A*a*c^3*x^6 + 6/5*B*a^2*c^2*x^5 + 3/2*A*a^2*c^2*x^4 + 4/3*B*a^3*c*x^3 + 2*A*a^3*c*x^2 + B*a^4*x + A*a^4*log(x)","A",0
277,1,103,0,0.395509," ","integrate((B*x+A)*(c*x^2+a)^4/x^2,x, algorithm=""fricas"")","\frac{105 \, B c^{4} x^{9} + 120 \, A c^{4} x^{8} + 560 \, B a c^{3} x^{7} + 672 \, A a c^{3} x^{6} + 1260 \, B a^{2} c^{2} x^{5} + 1680 \, A a^{2} c^{2} x^{4} + 1680 \, B a^{3} c x^{3} + 3360 \, A a^{3} c x^{2} + 840 \, B a^{4} x \log\left(x\right) - 840 \, A a^{4}}{840 \, x}"," ",0,"1/840*(105*B*c^4*x^9 + 120*A*c^4*x^8 + 560*B*a*c^3*x^7 + 672*A*a*c^3*x^6 + 1260*B*a^2*c^2*x^5 + 1680*A*a^2*c^2*x^4 + 1680*B*a^3*c*x^3 + 3360*A*a^3*c*x^2 + 840*B*a^4*x*log(x) - 840*A*a^4)/x","A",0
278,1,103,0,0.394474," ","integrate((B*x+A)*(c*x^2+a)^4/x^3,x, algorithm=""fricas"")","\frac{30 \, B c^{4} x^{9} + 35 \, A c^{4} x^{8} + 168 \, B a c^{3} x^{7} + 210 \, A a c^{3} x^{6} + 420 \, B a^{2} c^{2} x^{5} + 630 \, A a^{2} c^{2} x^{4} + 840 \, B a^{3} c x^{3} + 840 \, A a^{3} c x^{2} \log\left(x\right) - 210 \, B a^{4} x - 105 \, A a^{4}}{210 \, x^{2}}"," ",0,"1/210*(30*B*c^4*x^9 + 35*A*c^4*x^8 + 168*B*a*c^3*x^7 + 210*A*a*c^3*x^6 + 420*B*a^2*c^2*x^5 + 630*A*a^2*c^2*x^4 + 840*B*a^3*c*x^3 + 840*A*a^3*c*x^2*log(x) - 210*B*a^4*x - 105*A*a^4)/x^2","A",0
279,1,176,0,0.403410," ","integrate(x^4*(e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, c^{2} e x^{4} + 4 \, c^{2} d x^{3} - 6 \, a c e x^{2} + 6 \, a c d \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{a}{c}} - a}{c x^{2} + a}\right) - 12 \, a c d x + 6 \, a^{2} e \log\left(c x^{2} + a\right)}{12 \, c^{3}}, \frac{3 \, c^{2} e x^{4} + 4 \, c^{2} d x^{3} - 6 \, a c e x^{2} + 12 \, a c d \sqrt{\frac{a}{c}} \arctan\left(\frac{c x \sqrt{\frac{a}{c}}}{a}\right) - 12 \, a c d x + 6 \, a^{2} e \log\left(c x^{2} + a\right)}{12 \, c^{3}}\right]"," ",0,"[1/12*(3*c^2*e*x^4 + 4*c^2*d*x^3 - 6*a*c*e*x^2 + 6*a*c*d*sqrt(-a/c)*log((c*x^2 + 2*c*x*sqrt(-a/c) - a)/(c*x^2 + a)) - 12*a*c*d*x + 6*a^2*e*log(c*x^2 + a))/c^3, 1/12*(3*c^2*e*x^4 + 4*c^2*d*x^3 - 6*a*c*e*x^2 + 12*a*c*d*sqrt(a/c)*arctan(c*x*sqrt(a/c)/a) - 12*a*c*d*x + 6*a^2*e*log(c*x^2 + a))/c^3]","A",0
280,1,144,0,0.392795," ","integrate(x^3*(e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, c e x^{3} + 3 \, c d x^{2} + 3 \, a e \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{a}{c}} - a}{c x^{2} + a}\right) - 6 \, a e x - 3 \, a d \log\left(c x^{2} + a\right)}{6 \, c^{2}}, \frac{2 \, c e x^{3} + 3 \, c d x^{2} + 6 \, a e \sqrt{\frac{a}{c}} \arctan\left(\frac{c x \sqrt{\frac{a}{c}}}{a}\right) - 6 \, a e x - 3 \, a d \log\left(c x^{2} + a\right)}{6 \, c^{2}}\right]"," ",0,"[1/6*(2*c*e*x^3 + 3*c*d*x^2 + 3*a*e*sqrt(-a/c)*log((c*x^2 + 2*c*x*sqrt(-a/c) - a)/(c*x^2 + a)) - 6*a*e*x - 3*a*d*log(c*x^2 + a))/c^2, 1/6*(2*c*e*x^3 + 3*c*d*x^2 + 6*a*e*sqrt(a/c)*arctan(c*x*sqrt(a/c)/a) - 6*a*e*x - 3*a*d*log(c*x^2 + a))/c^2]","A",0
281,1,127,0,0.411012," ","integrate(x^2*(e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{c e x^{2} + c d \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{a}{c}} - a}{c x^{2} + a}\right) + 2 \, c d x - a e \log\left(c x^{2} + a\right)}{2 \, c^{2}}, \frac{c e x^{2} - 2 \, c d \sqrt{\frac{a}{c}} \arctan\left(\frac{c x \sqrt{\frac{a}{c}}}{a}\right) + 2 \, c d x - a e \log\left(c x^{2} + a\right)}{2 \, c^{2}}\right]"," ",0,"[1/2*(c*e*x^2 + c*d*sqrt(-a/c)*log((c*x^2 - 2*c*x*sqrt(-a/c) - a)/(c*x^2 + a)) + 2*c*d*x - a*e*log(c*x^2 + a))/c^2, 1/2*(c*e*x^2 - 2*c*d*sqrt(a/c)*arctan(c*x*sqrt(a/c)/a) + 2*c*d*x - a*e*log(c*x^2 + a))/c^2]","A",0
282,1,108,0,0.407078," ","integrate(x*(e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{e \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{a}{c}} - a}{c x^{2} + a}\right) + 2 \, e x + d \log\left(c x^{2} + a\right)}{2 \, c}, -\frac{2 \, e \sqrt{\frac{a}{c}} \arctan\left(\frac{c x \sqrt{\frac{a}{c}}}{a}\right) - 2 \, e x - d \log\left(c x^{2} + a\right)}{2 \, c}\right]"," ",0,"[1/2*(e*sqrt(-a/c)*log((c*x^2 - 2*c*x*sqrt(-a/c) - a)/(c*x^2 + a)) + 2*e*x + d*log(c*x^2 + a))/c, -1/2*(2*e*sqrt(a/c)*arctan(c*x*sqrt(a/c)/a) - 2*e*x - d*log(c*x^2 + a))/c]","A",0
283,1,98,0,0.411914," ","integrate((e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{a e \log\left(c x^{2} + a\right) - \sqrt{-a c} d \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{2 \, a c}, \frac{a e \log\left(c x^{2} + a\right) + 2 \, \sqrt{a c} d \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{2 \, a c}\right]"," ",0,"[1/2*(a*e*log(c*x^2 + a) - sqrt(-a*c)*d*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a*c), 1/2*(a*e*log(c*x^2 + a) + 2*sqrt(a*c)*d*arctan(sqrt(a*c)*x/a))/(a*c)]","A",0
284,1,109,0,0.420190," ","integrate((e*x+d)/x/(c*x^2+a),x, algorithm=""fricas"")","\left[-\frac{c d \log\left(c x^{2} + a\right) - 2 \, c d \log\left(x\right) + \sqrt{-a c} e \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{2 \, a c}, -\frac{c d \log\left(c x^{2} + a\right) - 2 \, c d \log\left(x\right) - 2 \, \sqrt{a c} e \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{2 \, a c}\right]"," ",0,"[-1/2*(c*d*log(c*x^2 + a) - 2*c*d*log(x) + sqrt(-a*c)*e*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a*c), -1/2*(c*d*log(c*x^2 + a) - 2*c*d*log(x) - 2*sqrt(a*c)*e*arctan(sqrt(a*c)*x/a))/(a*c)]","A",0
285,1,124,0,0.420229," ","integrate((e*x+d)/x^2/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{d x \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) - e x \log\left(c x^{2} + a\right) + 2 \, e x \log\left(x\right) - 2 \, d}{2 \, a x}, -\frac{2 \, d x \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + e x \log\left(c x^{2} + a\right) - 2 \, e x \log\left(x\right) + 2 \, d}{2 \, a x}\right]"," ",0,"[1/2*(d*x*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) - e*x*log(c*x^2 + a) + 2*e*x*log(x) - 2*d)/(a*x), -1/2*(2*d*x*sqrt(c/a)*arctan(x*sqrt(c/a)) + e*x*log(c*x^2 + a) - 2*e*x*log(x) + 2*d)/(a*x)]","A",0
286,1,153,0,0.419022," ","integrate((e*x+d)/x^3/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{a e x^{2} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + c d x^{2} \log\left(c x^{2} + a\right) - 2 \, c d x^{2} \log\left(x\right) - 2 \, a e x - a d}{2 \, a^{2} x^{2}}, -\frac{2 \, a e x^{2} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) - c d x^{2} \log\left(c x^{2} + a\right) + 2 \, c d x^{2} \log\left(x\right) + 2 \, a e x + a d}{2 \, a^{2} x^{2}}\right]"," ",0,"[1/2*(a*e*x^2*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + c*d*x^2*log(c*x^2 + a) - 2*c*d*x^2*log(x) - 2*a*e*x - a*d)/(a^2*x^2), -1/2*(2*a*e*x^2*sqrt(c/a)*arctan(x*sqrt(c/a)) - c*d*x^2*log(c*x^2 + a) + 2*c*d*x^2*log(x) + 2*a*e*x + a*d)/(a^2*x^2)]","A",0
287,1,170,0,0.411705," ","integrate((e*x+d)/x^4/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, c d x^{3} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} + 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 3 \, c e x^{3} \log\left(c x^{2} + a\right) - 6 \, c e x^{3} \log\left(x\right) + 6 \, c d x^{2} - 3 \, a e x - 2 \, a d}{6 \, a^{2} x^{3}}, \frac{6 \, c d x^{3} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + 3 \, c e x^{3} \log\left(c x^{2} + a\right) - 6 \, c e x^{3} \log\left(x\right) + 6 \, c d x^{2} - 3 \, a e x - 2 \, a d}{6 \, a^{2} x^{3}}\right]"," ",0,"[1/6*(3*c*d*x^3*sqrt(-c/a)*log((c*x^2 + 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 3*c*e*x^3*log(c*x^2 + a) - 6*c*e*x^3*log(x) + 6*c*d*x^2 - 3*a*e*x - 2*a*d)/(a^2*x^3), 1/6*(6*c*d*x^3*sqrt(c/a)*arctan(x*sqrt(c/a)) + 3*c*e*x^3*log(c*x^2 + a) - 6*c*e*x^3*log(x) + 6*c*d*x^2 - 3*a*e*x - 2*a*d)/(a^2*x^3)]","A",0
288,1,102,0,0.417609," ","integrate((e*x+d)/(-c*x^2+a),x, algorithm=""fricas"")","\left[-\frac{a e \log\left(c x^{2} - a\right) - \sqrt{a c} d \log\left(\frac{c x^{2} + 2 \, \sqrt{a c} x + a}{c x^{2} - a}\right)}{2 \, a c}, -\frac{a e \log\left(c x^{2} - a\right) + 2 \, \sqrt{-a c} d \arctan\left(\frac{\sqrt{-a c} x}{a}\right)}{2 \, a c}\right]"," ",0,"[-1/2*(a*e*log(c*x^2 - a) - sqrt(a*c)*d*log((c*x^2 + 2*sqrt(a*c)*x + a)/(c*x^2 - a)))/(a*c), -1/2*(a*e*log(c*x^2 - a) + 2*sqrt(-a*c)*d*arctan(sqrt(-a*c)*x/a))/(a*c)]","A",0
289,1,248,0,0.396336," ","integrate(x^4*(e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, c^{2} e x^{4} + 4 \, c^{2} d x^{3} + 2 \, a c e x^{2} + 6 \, a c d x - 2 \, a^{2} e + 3 \, {\left(c^{2} d x^{2} + a c d\right)} \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{a}{c}} - a}{c x^{2} + a}\right) - 4 \, {\left(a c e x^{2} + a^{2} e\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(c^{4} x^{2} + a c^{3}\right)}}, \frac{c^{2} e x^{4} + 2 \, c^{2} d x^{3} + a c e x^{2} + 3 \, a c d x - a^{2} e - 3 \, {\left(c^{2} d x^{2} + a c d\right)} \sqrt{\frac{a}{c}} \arctan\left(\frac{c x \sqrt{\frac{a}{c}}}{a}\right) - 2 \, {\left(a c e x^{2} + a^{2} e\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{4} x^{2} + a c^{3}\right)}}\right]"," ",0,"[1/4*(2*c^2*e*x^4 + 4*c^2*d*x^3 + 2*a*c*e*x^2 + 6*a*c*d*x - 2*a^2*e + 3*(c^2*d*x^2 + a*c*d)*sqrt(-a/c)*log((c*x^2 - 2*c*x*sqrt(-a/c) - a)/(c*x^2 + a)) - 4*(a*c*e*x^2 + a^2*e)*log(c*x^2 + a))/(c^4*x^2 + a*c^3), 1/2*(c^2*e*x^4 + 2*c^2*d*x^3 + a*c*e*x^2 + 3*a*c*d*x - a^2*e - 3*(c^2*d*x^2 + a*c*d)*sqrt(a/c)*arctan(c*x*sqrt(a/c)/a) - 2*(a*c*e*x^2 + a^2*e)*log(c*x^2 + a))/(c^4*x^2 + a*c^3)]","A",0
290,1,192,0,0.413738," ","integrate(x^3*(e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c e x^{3} + 6 \, a e x + 3 \, {\left(c e x^{2} + a e\right)} \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{a}{c}} - a}{c x^{2} + a}\right) + 2 \, a d + 2 \, {\left(c d x^{2} + a d\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(c^{3} x^{2} + a c^{2}\right)}}, \frac{2 \, c e x^{3} + 3 \, a e x - 3 \, {\left(c e x^{2} + a e\right)} \sqrt{\frac{a}{c}} \arctan\left(\frac{c x \sqrt{\frac{a}{c}}}{a}\right) + a d + {\left(c d x^{2} + a d\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} x^{2} + a c^{2}\right)}}\right]"," ",0,"[1/4*(4*c*e*x^3 + 6*a*e*x + 3*(c*e*x^2 + a*e)*sqrt(-a/c)*log((c*x^2 - 2*c*x*sqrt(-a/c) - a)/(c*x^2 + a)) + 2*a*d + 2*(c*d*x^2 + a*d)*log(c*x^2 + a))/(c^3*x^2 + a*c^2), 1/2*(2*c*e*x^3 + 3*a*e*x - 3*(c*e*x^2 + a*e)*sqrt(a/c)*arctan(c*x*sqrt(a/c)/a) + a*d + (c*d*x^2 + a*d)*log(c*x^2 + a))/(c^3*x^2 + a*c^2)]","A",0
291,1,186,0,0.393212," ","integrate(x^2*(e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a c d x - 2 \, a^{2} e + {\left(c d x^{2} + a d\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(a c e x^{2} + a^{2} e\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}}, -\frac{a c d x - a^{2} e - {\left(c d x^{2} + a d\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(a c e x^{2} + a^{2} e\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}}\right]"," ",0,"[-1/4*(2*a*c*d*x - 2*a^2*e + (c*d*x^2 + a*d)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(a*c*e*x^2 + a^2*e)*log(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2), -1/2*(a*c*d*x - a^2*e - (c*d*x^2 + a*d)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (a*c*e*x^2 + a^2*e)*log(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2)]","A",0
292,1,137,0,0.407326," ","integrate(x*(e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a c e x + 2 \, a c d + {\left(c e x^{2} + a e\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{4 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}}, -\frac{a c e x + a c d - {\left(c e x^{2} + a e\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{2 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}}\right]"," ",0,"[-1/4*(2*a*c*e*x + 2*a*c*d + (c*e*x^2 + a*e)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a*c^3*x^2 + a^2*c^2), -1/2*(a*c*e*x + a*c*d - (c*e*x^2 + a*e)*sqrt(a*c)*arctan(sqrt(a*c)*x/a))/(a*c^3*x^2 + a^2*c^2)]","A",0
293,1,140,0,0.407604," ","integrate((e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a c d x - 2 \, a^{2} e - {\left(c d x^{2} + a d\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{4 \, {\left(a^{2} c^{2} x^{2} + a^{3} c\right)}}, \frac{a c d x - a^{2} e + {\left(c d x^{2} + a d\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{2 \, {\left(a^{2} c^{2} x^{2} + a^{3} c\right)}}\right]"," ",0,"[1/4*(2*a*c*d*x - 2*a^2*e - (c*d*x^2 + a*d)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a^2*c^2*x^2 + a^3*c), 1/2*(a*c*d*x - a^2*e + (c*d*x^2 + a*d)*sqrt(a*c)*arctan(sqrt(a*c)*x/a))/(a^2*c^2*x^2 + a^3*c)]","A",0
294,1,217,0,0.425140," ","integrate((e*x+d)/x/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a c e x + 2 \, a c d - {\left(c e x^{2} + a e\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(c^{2} d x^{2} + a c d\right)} \log\left(c x^{2} + a\right) + 4 \, {\left(c^{2} d x^{2} + a c d\right)} \log\left(x\right)}{4 \, {\left(a^{2} c^{2} x^{2} + a^{3} c\right)}}, \frac{a c e x + a c d + {\left(c e x^{2} + a e\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(c^{2} d x^{2} + a c d\right)} \log\left(c x^{2} + a\right) + 2 \, {\left(c^{2} d x^{2} + a c d\right)} \log\left(x\right)}{2 \, {\left(a^{2} c^{2} x^{2} + a^{3} c\right)}}\right]"," ",0,"[1/4*(2*a*c*e*x + 2*a*c*d - (c*e*x^2 + a*e)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(c^2*d*x^2 + a*c*d)*log(c*x^2 + a) + 4*(c^2*d*x^2 + a*c*d)*log(x))/(a^2*c^2*x^2 + a^3*c), 1/2*(a*c*e*x + a*c*d + (c*e*x^2 + a*e)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (c^2*d*x^2 + a*c*d)*log(c*x^2 + a) + 2*(c^2*d*x^2 + a*c*d)*log(x))/(a^2*c^2*x^2 + a^3*c)]","A",0
295,1,225,0,0.431356," ","integrate((e*x+d)/x^2/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, c d x^{2} - 2 \, a e x - 3 \, {\left(c d x^{3} + a d x\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 4 \, a d + 2 \, {\left(c e x^{3} + a e x\right)} \log\left(c x^{2} + a\right) - 4 \, {\left(c e x^{3} + a e x\right)} \log\left(x\right)}{4 \, {\left(a^{2} c x^{3} + a^{3} x\right)}}, -\frac{3 \, c d x^{2} - a e x + 3 \, {\left(c d x^{3} + a d x\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + 2 \, a d + {\left(c e x^{3} + a e x\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(c e x^{3} + a e x\right)} \log\left(x\right)}{2 \, {\left(a^{2} c x^{3} + a^{3} x\right)}}\right]"," ",0,"[-1/4*(6*c*d*x^2 - 2*a*e*x - 3*(c*d*x^3 + a*d*x)*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 4*a*d + 2*(c*e*x^3 + a*e*x)*log(c*x^2 + a) - 4*(c*e*x^3 + a*e*x)*log(x))/(a^2*c*x^3 + a^3*x), -1/2*(3*c*d*x^2 - a*e*x + 3*(c*d*x^3 + a*d*x)*sqrt(c/a)*arctan(x*sqrt(c/a)) + 2*a*d + (c*e*x^3 + a*e*x)*log(c*x^2 + a) - 2*(c*e*x^3 + a*e*x)*log(x))/(a^2*c*x^3 + a^3*x)]","A",0
296,1,285,0,0.587528," ","integrate((e*x+d)/x^3/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, a c e x^{3} + 4 \, a c d x^{2} + 4 \, a^{2} e x + 2 \, a^{2} d - 3 \, {\left(a c e x^{4} + a^{2} e x^{2}\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) - 4 \, {\left(c^{2} d x^{4} + a c d x^{2}\right)} \log\left(c x^{2} + a\right) + 8 \, {\left(c^{2} d x^{4} + a c d x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{3} c x^{4} + a^{4} x^{2}\right)}}, -\frac{3 \, a c e x^{3} + 2 \, a c d x^{2} + 2 \, a^{2} e x + a^{2} d + 3 \, {\left(a c e x^{4} + a^{2} e x^{2}\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) - 2 \, {\left(c^{2} d x^{4} + a c d x^{2}\right)} \log\left(c x^{2} + a\right) + 4 \, {\left(c^{2} d x^{4} + a c d x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} c x^{4} + a^{4} x^{2}\right)}}\right]"," ",0,"[-1/4*(6*a*c*e*x^3 + 4*a*c*d*x^2 + 4*a^2*e*x + 2*a^2*d - 3*(a*c*e*x^4 + a^2*e*x^2)*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) - 4*(c^2*d*x^4 + a*c*d*x^2)*log(c*x^2 + a) + 8*(c^2*d*x^4 + a*c*d*x^2)*log(x))/(a^3*c*x^4 + a^4*x^2), -1/2*(3*a*c*e*x^3 + 2*a*c*d*x^2 + 2*a^2*e*x + a^2*d + 3*(a*c*e*x^4 + a^2*e*x^2)*sqrt(c/a)*arctan(x*sqrt(c/a)) - 2*(c^2*d*x^4 + a*c*d*x^2)*log(c*x^2 + a) + 4*(c^2*d*x^4 + a*c*d*x^2)*log(x))/(a^3*c*x^4 + a^4*x^2)]","A",0
297,1,89,0,0.535093," ","integrate(x^4*(e*x+d)/(-c^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{3 \, c^{4} e x^{4} + 4 \, c^{4} d x^{3} + 6 \, a^{2} c^{2} e x^{2} + 12 \, a^{2} c^{2} d x - 6 \, {\left(a^{3} c d - a^{4} e\right)} \log\left(c x + a\right) + 6 \, {\left(a^{3} c d + a^{4} e\right)} \log\left(c x - a\right)}{12 \, c^{6}}"," ",0,"-1/12*(3*c^4*e*x^4 + 4*c^4*d*x^3 + 6*a^2*c^2*e*x^2 + 12*a^2*c^2*d*x - 6*(a^3*c*d - a^4*e)*log(c*x + a) + 6*(a^3*c*d + a^4*e)*log(c*x - a))/c^6","A",0
298,1,75,0,0.409290," ","integrate(x^3*(e*x+d)/(-c^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{2 \, c^{3} e x^{3} + 3 \, c^{3} d x^{2} + 6 \, a^{2} c e x + 3 \, {\left(a^{2} c d - a^{3} e\right)} \log\left(c x + a\right) + 3 \, {\left(a^{2} c d + a^{3} e\right)} \log\left(c x - a\right)}{6 \, c^{5}}"," ",0,"-1/6*(2*c^3*e*x^3 + 3*c^3*d*x^2 + 6*a^2*c*e*x + 3*(a^2*c*d - a^3*e)*log(c*x + a) + 3*(a^2*c*d + a^3*e)*log(c*x - a))/c^5","A",0
299,1,59,0,0.413612," ","integrate(x^2*(e*x+d)/(-c^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{c^{2} e x^{2} + 2 \, c^{2} d x - {\left(a c d - a^{2} e\right)} \log\left(c x + a\right) + {\left(a c d + a^{2} e\right)} \log\left(c x - a\right)}{2 \, c^{4}}"," ",0,"-1/2*(c^2*e*x^2 + 2*c^2*d*x - (a*c*d - a^2*e)*log(c*x + a) + (a*c*d + a^2*e)*log(c*x - a))/c^4","A",0
300,1,42,0,0.413366," ","integrate(x*(e*x+d)/(-c^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{2 \, c e x + {\left(c d - a e\right)} \log\left(c x + a\right) + {\left(c d + a e\right)} \log\left(c x - a\right)}{2 \, c^{3}}"," ",0,"-1/2*(2*c*e*x + (c*d - a*e)*log(c*x + a) + (c*d + a*e)*log(c*x - a))/c^3","A",0
301,1,41,0,0.403126," ","integrate((e*x+d)/(-c^2*x^2+a^2),x, algorithm=""fricas"")","\frac{{\left(c d - a e\right)} \log\left(c x + a\right) - {\left(c d + a e\right)} \log\left(c x - a\right)}{2 \, a c^{2}}"," ",0,"1/2*((c*d - a*e)*log(c*x + a) - (c*d + a*e)*log(c*x - a))/(a*c^2)","A",0
302,1,48,0,0.432825," ","integrate((e*x+d)/x/(-c^2*x^2+a^2),x, algorithm=""fricas"")","\frac{2 \, c d \log\left(x\right) - {\left(c d - a e\right)} \log\left(c x + a\right) - {\left(c d + a e\right)} \log\left(c x - a\right)}{2 \, a^{2} c}"," ",0,"1/2*(2*c*d*log(x) - (c*d - a*e)*log(c*x + a) - (c*d + a*e)*log(c*x - a))/(a^2*c)","A",0
303,1,54,0,0.417714," ","integrate((e*x+d)/x^2/(-c^2*x^2+a^2),x, algorithm=""fricas"")","\frac{2 \, a e x \log\left(x\right) + {\left(c d - a e\right)} x \log\left(c x + a\right) - {\left(c d + a e\right)} x \log\left(c x - a\right) - 2 \, a d}{2 \, a^{3} x}"," ",0,"1/2*(2*a*e*x*log(x) + (c*d - a*e)*x*log(c*x + a) - (c*d + a*e)*x*log(c*x - a) - 2*a*d)/(a^3*x)","A",0
304,1,78,0,0.431705," ","integrate((e*x+d)/x^3/(-c^2*x^2+a^2),x, algorithm=""fricas"")","\frac{2 \, c^{2} d x^{2} \log\left(x\right) - 2 \, a^{2} e x - {\left(c^{2} d - a c e\right)} x^{2} \log\left(c x + a\right) - {\left(c^{2} d + a c e\right)} x^{2} \log\left(c x - a\right) - a^{2} d}{2 \, a^{4} x^{2}}"," ",0,"1/2*(2*c^2*d*x^2*log(x) - 2*a^2*e*x - (c^2*d - a*c*e)*x^2*log(c*x + a) - (c^2*d + a*c*e)*x^2*log(c*x - a) - a^2*d)/(a^4*x^2)","A",0
305,1,93,0,0.413880," ","integrate((e*x+d)/x^4/(-c^2*x^2+a^2),x, algorithm=""fricas"")","\frac{6 \, a c^{2} e x^{3} \log\left(x\right) - 6 \, a c^{2} d x^{2} - 3 \, a^{3} e x + 3 \, {\left(c^{3} d - a c^{2} e\right)} x^{3} \log\left(c x + a\right) - 3 \, {\left(c^{3} d + a c^{2} e\right)} x^{3} \log\left(c x - a\right) - 2 \, a^{3} d}{6 \, a^{5} x^{3}}"," ",0,"1/6*(6*a*c^2*e*x^3*log(x) - 6*a*c^2*d*x^2 - 3*a^3*e*x + 3*(c^3*d - a*c^2*e)*x^3*log(c*x + a) - 3*(c^3*d + a*c^2*e)*x^3*log(c*x - a) - 2*a^3*d)/(a^5*x^3)","A",0
306,1,156,0,0.401821," ","integrate(x^4*(e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, c^{4} e x^{4} + 4 \, c^{4} d x^{3} - 2 \, a^{2} c^{2} e x^{2} - 6 \, a^{2} c^{2} d x - 2 \, a^{4} e + {\left(3 \, a^{3} c d - 4 \, a^{4} e - {\left(3 \, a c^{3} d - 4 \, a^{2} c^{2} e\right)} x^{2}\right)} \log\left(c x + a\right) - {\left(3 \, a^{3} c d + 4 \, a^{4} e - {\left(3 \, a c^{3} d + 4 \, a^{2} c^{2} e\right)} x^{2}\right)} \log\left(c x - a\right)}{4 \, {\left(c^{8} x^{2} - a^{2} c^{6}\right)}}"," ",0,"1/4*(2*c^4*e*x^4 + 4*c^4*d*x^3 - 2*a^2*c^2*e*x^2 - 6*a^2*c^2*d*x - 2*a^4*e + (3*a^3*c*d - 4*a^4*e - (3*a*c^3*d - 4*a^2*c^2*e)*x^2)*log(c*x + a) - (3*a^3*c*d + 4*a^4*e - (3*a*c^3*d + 4*a^2*c^2*e)*x^2)*log(c*x - a))/(c^8*x^2 - a^2*c^6)","A",0
307,1,129,0,0.394205," ","integrate(x^3*(e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{4 \, c^{3} e x^{3} - 6 \, a^{2} c e x - 2 \, a^{2} c d - {\left(2 \, a^{2} c d - 3 \, a^{3} e - {\left(2 \, c^{3} d - 3 \, a c^{2} e\right)} x^{2}\right)} \log\left(c x + a\right) - {\left(2 \, a^{2} c d + 3 \, a^{3} e - {\left(2 \, c^{3} d + 3 \, a c^{2} e\right)} x^{2}\right)} \log\left(c x - a\right)}{4 \, {\left(c^{7} x^{2} - a^{2} c^{5}\right)}}"," ",0,"1/4*(4*c^3*e*x^3 - 6*a^2*c*e*x - 2*a^2*c*d - (2*a^2*c*d - 3*a^3*e - (2*c^3*d - 3*a*c^2*e)*x^2)*log(c*x + a) - (2*a^2*c*d + 3*a^3*e - (2*c^3*d + 3*a*c^2*e)*x^2)*log(c*x - a))/(c^7*x^2 - a^2*c^5)","A",0
308,1,115,0,0.391518," ","integrate(x^2*(e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{2 \, a c^{2} d x + 2 \, a^{3} e - {\left(a^{2} c d - 2 \, a^{3} e - {\left(c^{3} d - 2 \, a c^{2} e\right)} x^{2}\right)} \log\left(c x + a\right) + {\left(a^{2} c d + 2 \, a^{3} e - {\left(c^{3} d + 2 \, a c^{2} e\right)} x^{2}\right)} \log\left(c x - a\right)}{4 \, {\left(a c^{6} x^{2} - a^{3} c^{4}\right)}}"," ",0,"-1/4*(2*a*c^2*d*x + 2*a^3*e - (a^2*c*d - 2*a^3*e - (c^3*d - 2*a*c^2*e)*x^2)*log(c*x + a) + (a^2*c*d + 2*a^3*e - (c^3*d + 2*a*c^2*e)*x^2)*log(c*x - a))/(a*c^6*x^2 - a^3*c^4)","A",0
309,1,80,0,0.452254," ","integrate(x*(e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{2 \, a c e x + 2 \, a c d + {\left(c^{2} e x^{2} - a^{2} e\right)} \log\left(c x + a\right) - {\left(c^{2} e x^{2} - a^{2} e\right)} \log\left(c x - a\right)}{4 \, {\left(a c^{5} x^{2} - a^{3} c^{3}\right)}}"," ",0,"-1/4*(2*a*c*e*x + 2*a*c*d + (c^2*e*x^2 - a^2*e)*log(c*x + a) - (c^2*e*x^2 - a^2*e)*log(c*x - a))/(a*c^5*x^2 - a^3*c^3)","A",0
310,1,87,0,0.454848," ","integrate((e*x+d)/(-c^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{2 \, a c^{2} d x + 2 \, a^{3} e - {\left(c^{3} d x^{2} - a^{2} c d\right)} \log\left(c x + a\right) + {\left(c^{3} d x^{2} - a^{2} c d\right)} \log\left(c x - a\right)}{4 \, {\left(a^{3} c^{4} x^{2} - a^{5} c^{2}\right)}}"," ",0,"-1/4*(2*a*c^2*d*x + 2*a^3*e - (c^3*d*x^2 - a^2*c*d)*log(c*x + a) + (c^3*d*x^2 - a^2*c*d)*log(c*x - a))/(a^3*c^4*x^2 - a^5*c^2)","A",0
311,1,139,0,0.433489," ","integrate((e*x+d)/x/(-c^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} c e x + 2 \, a^{2} c d - {\left(2 \, a^{2} c d - a^{3} e - {\left(2 \, c^{3} d - a c^{2} e\right)} x^{2}\right)} \log\left(c x + a\right) - {\left(2 \, a^{2} c d + a^{3} e - {\left(2 \, c^{3} d + a c^{2} e\right)} x^{2}\right)} \log\left(c x - a\right) - 4 \, {\left(c^{3} d x^{2} - a^{2} c d\right)} \log\left(x\right)}{4 \, {\left(a^{4} c^{3} x^{2} - a^{6} c\right)}}"," ",0,"-1/4*(2*a^2*c*e*x + 2*a^2*c*d - (2*a^2*c*d - a^3*e - (2*c^3*d - a*c^2*e)*x^2)*log(c*x + a) - (2*a^2*c*d + a^3*e - (2*c^3*d + a*c^2*e)*x^2)*log(c*x - a) - 4*(c^3*d*x^2 - a^2*c*d)*log(x))/(a^4*c^3*x^2 - a^6*c)","A",0
312,1,155,0,0.491087," ","integrate((e*x+d)/x^2/(-c^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{6 \, a c^{2} d x^{2} + 2 \, a^{3} e x - 4 \, a^{3} d - {\left({\left(3 \, c^{3} d - 2 \, a c^{2} e\right)} x^{3} - {\left(3 \, a^{2} c d - 2 \, a^{3} e\right)} x\right)} \log\left(c x + a\right) + {\left({\left(3 \, c^{3} d + 2 \, a c^{2} e\right)} x^{3} - {\left(3 \, a^{2} c d + 2 \, a^{3} e\right)} x\right)} \log\left(c x - a\right) - 4 \, {\left(a c^{2} e x^{3} - a^{3} e x\right)} \log\left(x\right)}{4 \, {\left(a^{5} c^{2} x^{3} - a^{7} x\right)}}"," ",0,"-1/4*(6*a*c^2*d*x^2 + 2*a^3*e*x - 4*a^3*d - ((3*c^3*d - 2*a*c^2*e)*x^3 - (3*a^2*c*d - 2*a^3*e)*x)*log(c*x + a) + ((3*c^3*d + 2*a*c^2*e)*x^3 - (3*a^2*c*d + 2*a^3*e)*x)*log(c*x - a) - 4*(a*c^2*e*x^3 - a^3*e*x)*log(x))/(a^5*c^2*x^3 - a^7*x)","A",0
313,1,184,0,0.429711," ","integrate((e*x+d)/x^3/(-c^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{6 \, a^{2} c^{2} e x^{3} + 4 \, a^{2} c^{2} d x^{2} - 4 \, a^{4} e x - 2 \, a^{4} d + {\left({\left(4 \, c^{4} d - 3 \, a c^{3} e\right)} x^{4} - {\left(4 \, a^{2} c^{2} d - 3 \, a^{3} c e\right)} x^{2}\right)} \log\left(c x + a\right) + {\left({\left(4 \, c^{4} d + 3 \, a c^{3} e\right)} x^{4} - {\left(4 \, a^{2} c^{2} d + 3 \, a^{3} c e\right)} x^{2}\right)} \log\left(c x - a\right) - 8 \, {\left(c^{4} d x^{4} - a^{2} c^{2} d x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{6} c^{2} x^{4} - a^{8} x^{2}\right)}}"," ",0,"-1/4*(6*a^2*c^2*e*x^3 + 4*a^2*c^2*d*x^2 - 4*a^4*e*x - 2*a^4*d + ((4*c^4*d - 3*a*c^3*e)*x^4 - (4*a^2*c^2*d - 3*a^3*c*e)*x^2)*log(c*x + a) + ((4*c^4*d + 3*a*c^3*e)*x^4 - (4*a^2*c^2*d + 3*a^3*c*e)*x^2)*log(c*x - a) - 8*(c^4*d*x^4 - a^2*c^2*d*x^2)*log(x))/(a^6*c^2*x^4 - a^8*x^2)","A",0
314,1,224,0,0.494726," ","integrate(x^4*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, A a^{3} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(240 \, B c^{3} x^{6} + 280 \, A c^{3} x^{5} + 48 \, B a c^{2} x^{4} + 70 \, A a c^{2} x^{3} - 64 \, B a^{2} c x^{2} - 105 \, A a^{2} c x + 128 \, B a^{3}\right)} \sqrt{c x^{2} + a}}{3360 \, c^{3}}, -\frac{105 \, A a^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(240 \, B c^{3} x^{6} + 280 \, A c^{3} x^{5} + 48 \, B a c^{2} x^{4} + 70 \, A a c^{2} x^{3} - 64 \, B a^{2} c x^{2} - 105 \, A a^{2} c x + 128 \, B a^{3}\right)} \sqrt{c x^{2} + a}}{1680 \, c^{3}}\right]"," ",0,"[1/3360*(105*A*a^3*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(240*B*c^3*x^6 + 280*A*c^3*x^5 + 48*B*a*c^2*x^4 + 70*A*a*c^2*x^3 - 64*B*a^2*c*x^2 - 105*A*a^2*c*x + 128*B*a^3)*sqrt(c*x^2 + a))/c^3, -1/1680*(105*A*a^3*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (240*B*c^3*x^6 + 280*A*c^3*x^5 + 48*B*a*c^2*x^4 + 70*A*a*c^2*x^3 - 64*B*a^2*c*x^2 - 105*A*a^2*c*x + 128*B*a^3)*sqrt(c*x^2 + a))/c^3]","A",0
315,1,206,0,0.485042," ","integrate(x^3*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, B a^{3} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(40 \, B c^{3} x^{5} + 48 \, A c^{3} x^{4} + 10 \, B a c^{2} x^{3} + 16 \, A a c^{2} x^{2} - 15 \, B a^{2} c x - 32 \, A a^{2} c\right)} \sqrt{c x^{2} + a}}{480 \, c^{3}}, -\frac{15 \, B a^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(40 \, B c^{3} x^{5} + 48 \, A c^{3} x^{4} + 10 \, B a c^{2} x^{3} + 16 \, A a c^{2} x^{2} - 15 \, B a^{2} c x - 32 \, A a^{2} c\right)} \sqrt{c x^{2} + a}}{240 \, c^{3}}\right]"," ",0,"[1/480*(15*B*a^3*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(40*B*c^3*x^5 + 48*A*c^3*x^4 + 10*B*a*c^2*x^3 + 16*A*a*c^2*x^2 - 15*B*a^2*c*x - 32*A*a^2*c)*sqrt(c*x^2 + a))/c^3, -1/240*(15*B*a^3*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (40*B*c^3*x^5 + 48*A*c^3*x^4 + 10*B*a*c^2*x^3 + 16*A*a*c^2*x^2 - 15*B*a^2*c*x - 32*A*a^2*c)*sqrt(c*x^2 + a))/c^3]","A",0
316,1,175,0,0.511341," ","integrate(x^2*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, A a^{2} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(24 \, B c^{2} x^{4} + 30 \, A c^{2} x^{3} + 8 \, B a c x^{2} + 15 \, A a c x - 16 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{240 \, c^{2}}, \frac{15 \, A a^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(24 \, B c^{2} x^{4} + 30 \, A c^{2} x^{3} + 8 \, B a c x^{2} + 15 \, A a c x - 16 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{120 \, c^{2}}\right]"," ",0,"[1/240*(15*A*a^2*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(24*B*c^2*x^4 + 30*A*c^2*x^3 + 8*B*a*c*x^2 + 15*A*a*c*x - 16*B*a^2)*sqrt(c*x^2 + a))/c^2, 1/120*(15*A*a^2*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (24*B*c^2*x^4 + 30*A*c^2*x^3 + 8*B*a*c*x^2 + 15*A*a*c*x - 16*B*a^2)*sqrt(c*x^2 + a))/c^2]","A",0
317,1,157,0,0.468307," ","integrate(x*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, B a^{2} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(6 \, B c^{2} x^{3} + 8 \, A c^{2} x^{2} + 3 \, B a c x + 8 \, A a c\right)} \sqrt{c x^{2} + a}}{48 \, c^{2}}, \frac{3 \, B a^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(6 \, B c^{2} x^{3} + 8 \, A c^{2} x^{2} + 3 \, B a c x + 8 \, A a c\right)} \sqrt{c x^{2} + a}}{24 \, c^{2}}\right]"," ",0,"[1/48*(3*B*a^2*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(6*B*c^2*x^3 + 8*A*c^2*x^2 + 3*B*a*c*x + 8*A*a*c)*sqrt(c*x^2 + a))/c^2, 1/24*(3*B*a^2*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (6*B*c^2*x^3 + 8*A*c^2*x^2 + 3*B*a*c*x + 8*A*a*c)*sqrt(c*x^2 + a))/c^2]","A",0
318,1,128,0,0.473848," ","integrate((B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, A a \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(2 \, B c x^{2} + 3 \, A c x + 2 \, B a\right)} \sqrt{c x^{2} + a}}{12 \, c}, -\frac{3 \, A a \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, B c x^{2} + 3 \, A c x + 2 \, B a\right)} \sqrt{c x^{2} + a}}{6 \, c}\right]"," ",0,"[1/12*(3*A*a*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(2*B*c*x^2 + 3*A*c*x + 2*B*a)*sqrt(c*x^2 + a))/c, -1/6*(3*A*a*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*B*c*x^2 + 3*A*c*x + 2*B*a)*sqrt(c*x^2 + a))/c]","A",0
319,1,341,0,0.508652," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{B a \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, A \sqrt{a} c \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(B c x + 2 \, A c\right)} \sqrt{c x^{2} + a}}{4 \, c}, -\frac{B a \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - A \sqrt{a} c \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(B c x + 2 \, A c\right)} \sqrt{c x^{2} + a}}{2 \, c}, \frac{4 \, A \sqrt{-a} c \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + B a \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(B c x + 2 \, A c\right)} \sqrt{c x^{2} + a}}{4 \, c}, -\frac{B a \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 2 \, A \sqrt{-a} c \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(B c x + 2 \, A c\right)} \sqrt{c x^{2} + a}}{2 \, c}\right]"," ",0,"[1/4*(B*a*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*A*sqrt(a)*c*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(B*c*x + 2*A*c)*sqrt(c*x^2 + a))/c, -1/2*(B*a*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - A*sqrt(a)*c*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - (B*c*x + 2*A*c)*sqrt(c*x^2 + a))/c, 1/4*(4*A*sqrt(-a)*c*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + B*a*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(B*c*x + 2*A*c)*sqrt(c*x^2 + a))/c, -1/2*(B*a*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 2*A*sqrt(-a)*c*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (B*c*x + 2*A*c)*sqrt(c*x^2 + a))/c]","A",0
320,1,333,0,0.517980," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{A \sqrt{c} x \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + B \sqrt{a} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, \sqrt{c x^{2} + a} {\left(B x - A\right)}}{2 \, x}, -\frac{2 \, A \sqrt{-c} x \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - B \sqrt{a} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, \sqrt{c x^{2} + a} {\left(B x - A\right)}}{2 \, x}, \frac{2 \, B \sqrt{-a} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + A \sqrt{c} x \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, \sqrt{c x^{2} + a} {\left(B x - A\right)}}{2 \, x}, -\frac{A \sqrt{-c} x \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - B \sqrt{-a} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - \sqrt{c x^{2} + a} {\left(B x - A\right)}}{x}\right]"," ",0,"[1/2*(A*sqrt(c)*x*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + B*sqrt(a)*x*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*sqrt(c*x^2 + a)*(B*x - A))/x, -1/2*(2*A*sqrt(-c)*x*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - B*sqrt(a)*x*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*sqrt(c*x^2 + a)*(B*x - A))/x, 1/2*(2*B*sqrt(-a)*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + A*sqrt(c)*x*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*sqrt(c*x^2 + a)*(B*x - A))/x, -(A*sqrt(-c)*x*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - B*sqrt(-a)*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - sqrt(c*x^2 + a)*(B*x - A))/x]","A",0
321,1,377,0,0.582629," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{2 \, B a \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + A \sqrt{a} c x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(2 \, B a x + A a\right)} \sqrt{c x^{2} + a}}{4 \, a x^{2}}, -\frac{4 \, B a \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - A \sqrt{a} c x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, B a x + A a\right)} \sqrt{c x^{2} + a}}{4 \, a x^{2}}, \frac{A \sqrt{-a} c x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + B a \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - {\left(2 \, B a x + A a\right)} \sqrt{c x^{2} + a}}{2 \, a x^{2}}, -\frac{2 \, B a \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - A \sqrt{-a} c x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, B a x + A a\right)} \sqrt{c x^{2} + a}}{2 \, a x^{2}}\right]"," ",0,"[1/4*(2*B*a*sqrt(c)*x^2*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + A*sqrt(a)*c*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(2*B*a*x + A*a)*sqrt(c*x^2 + a))/(a*x^2), -1/4*(4*B*a*sqrt(-c)*x^2*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - A*sqrt(a)*c*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*B*a*x + A*a)*sqrt(c*x^2 + a))/(a*x^2), 1/2*(A*sqrt(-a)*c*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + B*a*sqrt(c)*x^2*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - (2*B*a*x + A*a)*sqrt(c*x^2 + a))/(a*x^2), -1/2*(2*B*a*sqrt(-c)*x^2*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - A*sqrt(-a)*c*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (2*B*a*x + A*a)*sqrt(c*x^2 + a))/(a*x^2)]","A",0
322,1,142,0,0.468192," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, B \sqrt{a} c x^{3} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(2 \, A c x^{2} + 3 \, B a x + 2 \, A a\right)} \sqrt{c x^{2} + a}}{12 \, a x^{3}}, \frac{3 \, B \sqrt{-a} c x^{3} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, A c x^{2} + 3 \, B a x + 2 \, A a\right)} \sqrt{c x^{2} + a}}{6 \, a x^{3}}\right]"," ",0,"[1/12*(3*B*sqrt(a)*c*x^3*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(2*A*c*x^2 + 3*B*a*x + 2*A*a)*sqrt(c*x^2 + a))/(a*x^3), 1/6*(3*B*sqrt(-a)*c*x^3*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (2*A*c*x^2 + 3*B*a*x + 2*A*a)*sqrt(c*x^2 + a))/(a*x^3)]","A",0
323,1,171,0,0.449074," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, A \sqrt{a} c^{2} x^{4} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(8 \, B a c x^{3} + 3 \, A a c x^{2} + 8 \, B a^{2} x + 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{48 \, a^{2} x^{4}}, -\frac{3 \, A \sqrt{-a} c^{2} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(8 \, B a c x^{3} + 3 \, A a c x^{2} + 8 \, B a^{2} x + 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{24 \, a^{2} x^{4}}\right]"," ",0,"[1/48*(3*A*sqrt(a)*c^2*x^4*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(8*B*a*c*x^3 + 3*A*a*c*x^2 + 8*B*a^2*x + 6*A*a^2)*sqrt(c*x^2 + a))/(a^2*x^4), -1/24*(3*A*sqrt(-a)*c^2*x^4*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (8*B*a*c*x^3 + 3*A*a*c*x^2 + 8*B*a^2*x + 6*A*a^2)*sqrt(c*x^2 + a))/(a^2*x^4)]","A",0
324,1,190,0,0.484291," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, B \sqrt{a} c^{2} x^{5} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(16 \, A c^{2} x^{4} - 15 \, B a c x^{3} - 8 \, A a c x^{2} - 30 \, B a^{2} x - 24 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{240 \, a^{2} x^{5}}, -\frac{15 \, B \sqrt{-a} c^{2} x^{5} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(16 \, A c^{2} x^{4} - 15 \, B a c x^{3} - 8 \, A a c x^{2} - 30 \, B a^{2} x - 24 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{120 \, a^{2} x^{5}}\right]"," ",0,"[1/240*(15*B*sqrt(a)*c^2*x^5*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(16*A*c^2*x^4 - 15*B*a*c*x^3 - 8*A*a*c*x^2 - 30*B*a^2*x - 24*A*a^2)*sqrt(c*x^2 + a))/(a^2*x^5), -1/120*(15*B*sqrt(-a)*c^2*x^5*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (16*A*c^2*x^4 - 15*B*a*c*x^3 - 8*A*a*c*x^2 - 30*B*a^2*x - 24*A*a^2)*sqrt(c*x^2 + a))/(a^2*x^5)]","A",0
325,1,219,0,0.505991," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/x^7,x, algorithm=""fricas"")","\left[\frac{15 \, A \sqrt{a} c^{3} x^{6} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(32 \, B a c^{2} x^{5} + 15 \, A a c^{2} x^{4} - 16 \, B a^{2} c x^{3} - 10 \, A a^{2} c x^{2} - 48 \, B a^{3} x - 40 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{480 \, a^{3} x^{6}}, \frac{15 \, A \sqrt{-a} c^{3} x^{6} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(32 \, B a c^{2} x^{5} + 15 \, A a c^{2} x^{4} - 16 \, B a^{2} c x^{3} - 10 \, A a^{2} c x^{2} - 48 \, B a^{3} x - 40 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{240 \, a^{3} x^{6}}\right]"," ",0,"[1/480*(15*A*sqrt(a)*c^3*x^6*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(32*B*a*c^2*x^5 + 15*A*a*c^2*x^4 - 16*B*a^2*c*x^3 - 10*A*a^2*c*x^2 - 48*B*a^3*x - 40*A*a^3)*sqrt(c*x^2 + a))/(a^3*x^6), 1/240*(15*A*sqrt(-a)*c^3*x^6*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (32*B*a*c^2*x^5 + 15*A*a*c^2*x^4 - 16*B*a^2*c*x^3 - 10*A*a^2*c*x^2 - 48*B*a^3*x - 40*A*a^3)*sqrt(c*x^2 + a))/(a^3*x^6)]","A",0
326,1,272,0,0.521990," ","integrate(x^4*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{945 \, A a^{4} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(4480 \, B c^{4} x^{8} + 5040 \, A c^{4} x^{7} + 6400 \, B a c^{3} x^{6} + 7560 \, A a c^{3} x^{5} + 384 \, B a^{2} c^{2} x^{4} + 630 \, A a^{2} c^{2} x^{3} - 512 \, B a^{3} c x^{2} - 945 \, A a^{3} c x + 1024 \, B a^{4}\right)} \sqrt{c x^{2} + a}}{80640 \, c^{3}}, -\frac{945 \, A a^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(4480 \, B c^{4} x^{8} + 5040 \, A c^{4} x^{7} + 6400 \, B a c^{3} x^{6} + 7560 \, A a c^{3} x^{5} + 384 \, B a^{2} c^{2} x^{4} + 630 \, A a^{2} c^{2} x^{3} - 512 \, B a^{3} c x^{2} - 945 \, A a^{3} c x + 1024 \, B a^{4}\right)} \sqrt{c x^{2} + a}}{40320 \, c^{3}}\right]"," ",0,"[1/80640*(945*A*a^4*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(4480*B*c^4*x^8 + 5040*A*c^4*x^7 + 6400*B*a*c^3*x^6 + 7560*A*a*c^3*x^5 + 384*B*a^2*c^2*x^4 + 630*A*a^2*c^2*x^3 - 512*B*a^3*c*x^2 - 945*A*a^3*c*x + 1024*B*a^4)*sqrt(c*x^2 + a))/c^3, -1/40320*(945*A*a^4*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (4480*B*c^4*x^8 + 5040*A*c^4*x^7 + 6400*B*a*c^3*x^6 + 7560*A*a*c^3*x^5 + 384*B*a^2*c^2*x^4 + 630*A*a^2*c^2*x^3 - 512*B*a^3*c*x^2 - 945*A*a^3*c*x + 1024*B*a^4)*sqrt(c*x^2 + a))/c^3]","A",0
327,1,254,0,0.481873," ","integrate(x^3*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, B a^{4} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(560 \, B c^{4} x^{7} + 640 \, A c^{4} x^{6} + 840 \, B a c^{3} x^{5} + 1024 \, A a c^{3} x^{4} + 70 \, B a^{2} c^{2} x^{3} + 128 \, A a^{2} c^{2} x^{2} - 105 \, B a^{3} c x - 256 \, A a^{3} c\right)} \sqrt{c x^{2} + a}}{8960 \, c^{3}}, -\frac{105 \, B a^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(560 \, B c^{4} x^{7} + 640 \, A c^{4} x^{6} + 840 \, B a c^{3} x^{5} + 1024 \, A a c^{3} x^{4} + 70 \, B a^{2} c^{2} x^{3} + 128 \, A a^{2} c^{2} x^{2} - 105 \, B a^{3} c x - 256 \, A a^{3} c\right)} \sqrt{c x^{2} + a}}{4480 \, c^{3}}\right]"," ",0,"[1/8960*(105*B*a^4*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(560*B*c^4*x^7 + 640*A*c^4*x^6 + 840*B*a*c^3*x^5 + 1024*A*a*c^3*x^4 + 70*B*a^2*c^2*x^3 + 128*A*a^2*c^2*x^2 - 105*B*a^3*c*x - 256*A*a^3*c)*sqrt(c*x^2 + a))/c^3, -1/4480*(105*B*a^4*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (560*B*c^4*x^7 + 640*A*c^4*x^6 + 840*B*a*c^3*x^5 + 1024*A*a*c^3*x^4 + 70*B*a^2*c^2*x^3 + 128*A*a^2*c^2*x^2 - 105*B*a^3*c*x - 256*A*a^3*c)*sqrt(c*x^2 + a))/c^3]","A",0
328,1,223,0,0.454272," ","integrate(x^2*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, A a^{3} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(240 \, B c^{3} x^{6} + 280 \, A c^{3} x^{5} + 384 \, B a c^{2} x^{4} + 490 \, A a c^{2} x^{3} + 48 \, B a^{2} c x^{2} + 105 \, A a^{2} c x - 96 \, B a^{3}\right)} \sqrt{c x^{2} + a}}{3360 \, c^{2}}, \frac{105 \, A a^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(240 \, B c^{3} x^{6} + 280 \, A c^{3} x^{5} + 384 \, B a c^{2} x^{4} + 490 \, A a c^{2} x^{3} + 48 \, B a^{2} c x^{2} + 105 \, A a^{2} c x - 96 \, B a^{3}\right)} \sqrt{c x^{2} + a}}{1680 \, c^{2}}\right]"," ",0,"[1/3360*(105*A*a^3*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(240*B*c^3*x^6 + 280*A*c^3*x^5 + 384*B*a*c^2*x^4 + 490*A*a*c^2*x^3 + 48*B*a^2*c*x^2 + 105*A*a^2*c*x - 96*B*a^3)*sqrt(c*x^2 + a))/c^2, 1/1680*(105*A*a^3*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (240*B*c^3*x^6 + 280*A*c^3*x^5 + 384*B*a*c^2*x^4 + 490*A*a*c^2*x^3 + 48*B*a^2*c*x^2 + 105*A*a^2*c*x - 96*B*a^3)*sqrt(c*x^2 + a))/c^2]","A",0
329,1,205,0,0.455970," ","integrate(x*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, B a^{3} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(40 \, B c^{3} x^{5} + 48 \, A c^{3} x^{4} + 70 \, B a c^{2} x^{3} + 96 \, A a c^{2} x^{2} + 15 \, B a^{2} c x + 48 \, A a^{2} c\right)} \sqrt{c x^{2} + a}}{480 \, c^{2}}, \frac{15 \, B a^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(40 \, B c^{3} x^{5} + 48 \, A c^{3} x^{4} + 70 \, B a c^{2} x^{3} + 96 \, A a c^{2} x^{2} + 15 \, B a^{2} c x + 48 \, A a^{2} c\right)} \sqrt{c x^{2} + a}}{240 \, c^{2}}\right]"," ",0,"[1/480*(15*B*a^3*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(40*B*c^3*x^5 + 48*A*c^3*x^4 + 70*B*a*c^2*x^3 + 96*A*a*c^2*x^2 + 15*B*a^2*c*x + 48*A*a^2*c)*sqrt(c*x^2 + a))/c^2, 1/240*(15*B*a^3*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (40*B*c^3*x^5 + 48*A*c^3*x^4 + 70*B*a*c^2*x^3 + 96*A*a*c^2*x^2 + 15*B*a^2*c*x + 48*A*a^2*c)*sqrt(c*x^2 + a))/c^2]","A",0
330,1,176,0,0.441527," ","integrate((B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, A a^{2} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(8 \, B c^{2} x^{4} + 10 \, A c^{2} x^{3} + 16 \, B a c x^{2} + 25 \, A a c x + 8 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{80 \, c}, -\frac{15 \, A a^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(8 \, B c^{2} x^{4} + 10 \, A c^{2} x^{3} + 16 \, B a c x^{2} + 25 \, A a c x + 8 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{40 \, c}\right]"," ",0,"[1/80*(15*A*a^2*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(8*B*c^2*x^4 + 10*A*c^2*x^3 + 16*B*a*c*x^2 + 25*A*a*c*x + 8*B*a^2)*sqrt(c*x^2 + a))/c, -1/40*(15*A*a^2*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (8*B*c^2*x^4 + 10*A*c^2*x^3 + 16*B*a*c*x^2 + 25*A*a*c*x + 8*B*a^2)*sqrt(c*x^2 + a))/c]","A",0
331,1,439,0,0.490130," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{9 \, B a^{2} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 24 \, A a^{\frac{3}{2}} c \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(6 \, B c^{2} x^{3} + 8 \, A c^{2} x^{2} + 15 \, B a c x + 32 \, A a c\right)} \sqrt{c x^{2} + a}}{48 \, c}, -\frac{9 \, B a^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 12 \, A a^{\frac{3}{2}} c \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(6 \, B c^{2} x^{3} + 8 \, A c^{2} x^{2} + 15 \, B a c x + 32 \, A a c\right)} \sqrt{c x^{2} + a}}{24 \, c}, \frac{48 \, A \sqrt{-a} a c \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 9 \, B a^{2} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(6 \, B c^{2} x^{3} + 8 \, A c^{2} x^{2} + 15 \, B a c x + 32 \, A a c\right)} \sqrt{c x^{2} + a}}{48 \, c}, -\frac{9 \, B a^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 24 \, A \sqrt{-a} a c \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, B c^{2} x^{3} + 8 \, A c^{2} x^{2} + 15 \, B a c x + 32 \, A a c\right)} \sqrt{c x^{2} + a}}{24 \, c}\right]"," ",0,"[1/48*(9*B*a^2*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 24*A*a^(3/2)*c*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(6*B*c^2*x^3 + 8*A*c^2*x^2 + 15*B*a*c*x + 32*A*a*c)*sqrt(c*x^2 + a))/c, -1/24*(9*B*a^2*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 12*A*a^(3/2)*c*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - (6*B*c^2*x^3 + 8*A*c^2*x^2 + 15*B*a*c*x + 32*A*a*c)*sqrt(c*x^2 + a))/c, 1/48*(48*A*sqrt(-a)*a*c*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 9*B*a^2*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(6*B*c^2*x^3 + 8*A*c^2*x^2 + 15*B*a*c*x + 32*A*a*c)*sqrt(c*x^2 + a))/c, -1/24*(9*B*a^2*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 24*A*sqrt(-a)*a*c*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (6*B*c^2*x^3 + 8*A*c^2*x^2 + 15*B*a*c*x + 32*A*a*c)*sqrt(c*x^2 + a))/c]","A",0
332,1,411,0,0.488406," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{9 \, A a \sqrt{c} x \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 6 \, B a^{\frac{3}{2}} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, B c x^{3} + 3 \, A c x^{2} + 8 \, B a x - 6 \, A a\right)} \sqrt{c x^{2} + a}}{12 \, x}, -\frac{9 \, A a \sqrt{-c} x \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 3 \, B a^{\frac{3}{2}} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(2 \, B c x^{3} + 3 \, A c x^{2} + 8 \, B a x - 6 \, A a\right)} \sqrt{c x^{2} + a}}{6 \, x}, \frac{12 \, B \sqrt{-a} a x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 9 \, A a \sqrt{c} x \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(2 \, B c x^{3} + 3 \, A c x^{2} + 8 \, B a x - 6 \, A a\right)} \sqrt{c x^{2} + a}}{12 \, x}, -\frac{9 \, A a \sqrt{-c} x \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 6 \, B \sqrt{-a} a x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, B c x^{3} + 3 \, A c x^{2} + 8 \, B a x - 6 \, A a\right)} \sqrt{c x^{2} + a}}{6 \, x}\right]"," ",0,"[1/12*(9*A*a*sqrt(c)*x*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 6*B*a^(3/2)*x*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*B*c*x^3 + 3*A*c*x^2 + 8*B*a*x - 6*A*a)*sqrt(c*x^2 + a))/x, -1/6*(9*A*a*sqrt(-c)*x*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 3*B*a^(3/2)*x*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - (2*B*c*x^3 + 3*A*c*x^2 + 8*B*a*x - 6*A*a)*sqrt(c*x^2 + a))/x, 1/12*(12*B*sqrt(-a)*a*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 9*A*a*sqrt(c)*x*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(2*B*c*x^3 + 3*A*c*x^2 + 8*B*a*x - 6*A*a)*sqrt(c*x^2 + a))/x, -1/6*(9*A*a*sqrt(-c)*x*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 6*B*sqrt(-a)*a*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (2*B*c*x^3 + 3*A*c*x^2 + 8*B*a*x - 6*A*a)*sqrt(c*x^2 + a))/x]","A",0
333,1,425,0,0.478031," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, B a \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 3 \, A \sqrt{a} c x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(B c x^{3} + 2 \, A c x^{2} - 2 \, B a x - A a\right)} \sqrt{c x^{2} + a}}{4 \, x^{2}}, -\frac{6 \, B a \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 3 \, A \sqrt{a} c x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(B c x^{3} + 2 \, A c x^{2} - 2 \, B a x - A a\right)} \sqrt{c x^{2} + a}}{4 \, x^{2}}, \frac{6 \, A \sqrt{-a} c x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 3 \, B a \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(B c x^{3} + 2 \, A c x^{2} - 2 \, B a x - A a\right)} \sqrt{c x^{2} + a}}{4 \, x^{2}}, -\frac{3 \, B a \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 3 \, A \sqrt{-a} c x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(B c x^{3} + 2 \, A c x^{2} - 2 \, B a x - A a\right)} \sqrt{c x^{2} + a}}{2 \, x^{2}}\right]"," ",0,"[1/4*(3*B*a*sqrt(c)*x^2*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 3*A*sqrt(a)*c*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(B*c*x^3 + 2*A*c*x^2 - 2*B*a*x - A*a)*sqrt(c*x^2 + a))/x^2, -1/4*(6*B*a*sqrt(-c)*x^2*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 3*A*sqrt(a)*c*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(B*c*x^3 + 2*A*c*x^2 - 2*B*a*x - A*a)*sqrt(c*x^2 + a))/x^2, 1/4*(6*A*sqrt(-a)*c*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 3*B*a*sqrt(c)*x^2*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(B*c*x^3 + 2*A*c*x^2 - 2*B*a*x - A*a)*sqrt(c*x^2 + a))/x^2, -1/2*(3*B*a*sqrt(-c)*x^2*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 3*A*sqrt(-a)*c*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (B*c*x^3 + 2*A*c*x^2 - 2*B*a*x - A*a)*sqrt(c*x^2 + a))/x^2]","A",0
334,1,426,0,0.487531," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{6 \, A c^{\frac{3}{2}} x^{3} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 9 \, B \sqrt{a} c x^{3} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(6 \, B c x^{3} - 8 \, A c x^{2} - 3 \, B a x - 2 \, A a\right)} \sqrt{c x^{2} + a}}{12 \, x^{3}}, -\frac{12 \, A \sqrt{-c} c x^{3} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 9 \, B \sqrt{a} c x^{3} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(6 \, B c x^{3} - 8 \, A c x^{2} - 3 \, B a x - 2 \, A a\right)} \sqrt{c x^{2} + a}}{12 \, x^{3}}, \frac{9 \, B \sqrt{-a} c x^{3} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 3 \, A c^{\frac{3}{2}} x^{3} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + {\left(6 \, B c x^{3} - 8 \, A c x^{2} - 3 \, B a x - 2 \, A a\right)} \sqrt{c x^{2} + a}}{6 \, x^{3}}, -\frac{6 \, A \sqrt{-c} c x^{3} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 9 \, B \sqrt{-a} c x^{3} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, B c x^{3} - 8 \, A c x^{2} - 3 \, B a x - 2 \, A a\right)} \sqrt{c x^{2} + a}}{6 \, x^{3}}\right]"," ",0,"[1/12*(6*A*c^(3/2)*x^3*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 9*B*sqrt(a)*c*x^3*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(6*B*c*x^3 - 8*A*c*x^2 - 3*B*a*x - 2*A*a)*sqrt(c*x^2 + a))/x^3, -1/12*(12*A*sqrt(-c)*c*x^3*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 9*B*sqrt(a)*c*x^3*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(6*B*c*x^3 - 8*A*c*x^2 - 3*B*a*x - 2*A*a)*sqrt(c*x^2 + a))/x^3, 1/6*(9*B*sqrt(-a)*c*x^3*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 3*A*c^(3/2)*x^3*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + (6*B*c*x^3 - 8*A*c*x^2 - 3*B*a*x - 2*A*a)*sqrt(c*x^2 + a))/x^3, -1/6*(6*A*sqrt(-c)*c*x^3*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 9*B*sqrt(-a)*c*x^3*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (6*B*c*x^3 - 8*A*c*x^2 - 3*B*a*x - 2*A*a)*sqrt(c*x^2 + a))/x^3]","A",0
335,1,474,0,0.475145," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{24 \, B a c^{\frac{3}{2}} x^{4} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 9 \, A \sqrt{a} c^{2} x^{4} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(32 \, B a c x^{3} + 15 \, A a c x^{2} + 8 \, B a^{2} x + 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{48 \, a x^{4}}, -\frac{48 \, B a \sqrt{-c} c x^{4} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 9 \, A \sqrt{a} c^{2} x^{4} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(32 \, B a c x^{3} + 15 \, A a c x^{2} + 8 \, B a^{2} x + 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{48 \, a x^{4}}, \frac{9 \, A \sqrt{-a} c^{2} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 12 \, B a c^{\frac{3}{2}} x^{4} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - {\left(32 \, B a c x^{3} + 15 \, A a c x^{2} + 8 \, B a^{2} x + 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{24 \, a x^{4}}, -\frac{24 \, B a \sqrt{-c} c x^{4} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 9 \, A \sqrt{-a} c^{2} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(32 \, B a c x^{3} + 15 \, A a c x^{2} + 8 \, B a^{2} x + 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{24 \, a x^{4}}\right]"," ",0,"[1/48*(24*B*a*c^(3/2)*x^4*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 9*A*sqrt(a)*c^2*x^4*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(32*B*a*c*x^3 + 15*A*a*c*x^2 + 8*B*a^2*x + 6*A*a^2)*sqrt(c*x^2 + a))/(a*x^4), -1/48*(48*B*a*sqrt(-c)*c*x^4*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 9*A*sqrt(a)*c^2*x^4*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(32*B*a*c*x^3 + 15*A*a*c*x^2 + 8*B*a^2*x + 6*A*a^2)*sqrt(c*x^2 + a))/(a*x^4), 1/24*(9*A*sqrt(-a)*c^2*x^4*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 12*B*a*c^(3/2)*x^4*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - (32*B*a*c*x^3 + 15*A*a*c*x^2 + 8*B*a^2*x + 6*A*a^2)*sqrt(c*x^2 + a))/(a*x^4), -1/24*(24*B*a*sqrt(-c)*c*x^4*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 9*A*sqrt(-a)*c^2*x^4*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (32*B*a*c*x^3 + 15*A*a*c*x^2 + 8*B*a^2*x + 6*A*a^2)*sqrt(c*x^2 + a))/(a*x^4)]","A",0
336,1,190,0,0.451278," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, B \sqrt{a} c^{2} x^{5} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(8 \, A c^{2} x^{4} + 25 \, B a c x^{3} + 16 \, A a c x^{2} + 10 \, B a^{2} x + 8 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{80 \, a x^{5}}, \frac{15 \, B \sqrt{-a} c^{2} x^{5} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(8 \, A c^{2} x^{4} + 25 \, B a c x^{3} + 16 \, A a c x^{2} + 10 \, B a^{2} x + 8 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{40 \, a x^{5}}\right]"," ",0,"[1/80*(15*B*sqrt(a)*c^2*x^5*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(8*A*c^2*x^4 + 25*B*a*c*x^3 + 16*A*a*c*x^2 + 10*B*a^2*x + 8*A*a^2)*sqrt(c*x^2 + a))/(a*x^5), 1/40*(15*B*sqrt(-a)*c^2*x^5*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (8*A*c^2*x^4 + 25*B*a*c*x^3 + 16*A*a*c*x^2 + 10*B*a^2*x + 8*A*a^2)*sqrt(c*x^2 + a))/(a*x^5)]","A",0
337,1,219,0,0.466957," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{15 \, A \sqrt{a} c^{3} x^{6} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(48 \, B a c^{2} x^{5} + 15 \, A a c^{2} x^{4} + 96 \, B a^{2} c x^{3} + 70 \, A a^{2} c x^{2} + 48 \, B a^{3} x + 40 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{480 \, a^{2} x^{6}}, -\frac{15 \, A \sqrt{-a} c^{3} x^{6} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(48 \, B a c^{2} x^{5} + 15 \, A a c^{2} x^{4} + 96 \, B a^{2} c x^{3} + 70 \, A a^{2} c x^{2} + 48 \, B a^{3} x + 40 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{240 \, a^{2} x^{6}}\right]"," ",0,"[1/480*(15*A*sqrt(a)*c^3*x^6*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(48*B*a*c^2*x^5 + 15*A*a*c^2*x^4 + 96*B*a^2*c*x^3 + 70*A*a^2*c*x^2 + 48*B*a^3*x + 40*A*a^3)*sqrt(c*x^2 + a))/(a^2*x^6), -1/240*(15*A*sqrt(-a)*c^3*x^6*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (48*B*a*c^2*x^5 + 15*A*a*c^2*x^4 + 96*B*a^2*c*x^3 + 70*A*a^2*c*x^2 + 48*B*a^3*x + 40*A*a^3)*sqrt(c*x^2 + a))/(a^2*x^6)]","A",0
338,1,238,0,0.481584," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/x^8,x, algorithm=""fricas"")","\left[\frac{105 \, B \sqrt{a} c^{3} x^{7} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(96 \, A c^{3} x^{6} - 105 \, B a c^{2} x^{5} - 48 \, A a c^{2} x^{4} - 490 \, B a^{2} c x^{3} - 384 \, A a^{2} c x^{2} - 280 \, B a^{3} x - 240 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{3360 \, a^{2} x^{7}}, -\frac{105 \, B \sqrt{-a} c^{3} x^{7} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(96 \, A c^{3} x^{6} - 105 \, B a c^{2} x^{5} - 48 \, A a c^{2} x^{4} - 490 \, B a^{2} c x^{3} - 384 \, A a^{2} c x^{2} - 280 \, B a^{3} x - 240 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{1680 \, a^{2} x^{7}}\right]"," ",0,"[1/3360*(105*B*sqrt(a)*c^3*x^7*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(96*A*c^3*x^6 - 105*B*a*c^2*x^5 - 48*A*a*c^2*x^4 - 490*B*a^2*c*x^3 - 384*A*a^2*c*x^2 - 280*B*a^3*x - 240*A*a^3)*sqrt(c*x^2 + a))/(a^2*x^7), -1/1680*(105*B*sqrt(-a)*c^3*x^7*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (96*A*c^3*x^6 - 105*B*a*c^2*x^5 - 48*A*a*c^2*x^4 - 490*B*a^2*c*x^3 - 384*A*a^2*c*x^2 - 280*B*a^3*x - 240*A*a^3)*sqrt(c*x^2 + a))/(a^2*x^7)]","A",0
339,1,320,0,0.489967," ","integrate(x^4*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{10395 \, A a^{5} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(80640 \, B c^{5} x^{10} + 88704 \, A c^{5} x^{9} + 206080 \, B a c^{4} x^{8} + 232848 \, A a c^{4} x^{7} + 144640 \, B a^{2} c^{3} x^{6} + 171864 \, A a^{2} c^{3} x^{5} + 3840 \, B a^{3} c^{2} x^{4} + 6930 \, A a^{3} c^{2} x^{3} - 5120 \, B a^{4} c x^{2} - 10395 \, A a^{4} c x + 10240 \, B a^{5}\right)} \sqrt{c x^{2} + a}}{1774080 \, c^{3}}, -\frac{10395 \, A a^{5} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(80640 \, B c^{5} x^{10} + 88704 \, A c^{5} x^{9} + 206080 \, B a c^{4} x^{8} + 232848 \, A a c^{4} x^{7} + 144640 \, B a^{2} c^{3} x^{6} + 171864 \, A a^{2} c^{3} x^{5} + 3840 \, B a^{3} c^{2} x^{4} + 6930 \, A a^{3} c^{2} x^{3} - 5120 \, B a^{4} c x^{2} - 10395 \, A a^{4} c x + 10240 \, B a^{5}\right)} \sqrt{c x^{2} + a}}{887040 \, c^{3}}\right]"," ",0,"[1/1774080*(10395*A*a^5*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(80640*B*c^5*x^10 + 88704*A*c^5*x^9 + 206080*B*a*c^4*x^8 + 232848*A*a*c^4*x^7 + 144640*B*a^2*c^3*x^6 + 171864*A*a^2*c^3*x^5 + 3840*B*a^3*c^2*x^4 + 6930*A*a^3*c^2*x^3 - 5120*B*a^4*c*x^2 - 10395*A*a^4*c*x + 10240*B*a^5)*sqrt(c*x^2 + a))/c^3, -1/887040*(10395*A*a^5*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (80640*B*c^5*x^10 + 88704*A*c^5*x^9 + 206080*B*a*c^4*x^8 + 232848*A*a*c^4*x^7 + 144640*B*a^2*c^3*x^6 + 171864*A*a^2*c^3*x^5 + 3840*B*a^3*c^2*x^4 + 6930*A*a^3*c^2*x^3 - 5120*B*a^4*c*x^2 - 10395*A*a^4*c*x + 10240*B*a^5)*sqrt(c*x^2 + a))/c^3]","A",0
340,1,302,0,0.517020," ","integrate(x^3*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{945 \, B a^{5} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(8064 \, B c^{5} x^{9} + 8960 \, A c^{5} x^{8} + 21168 \, B a c^{4} x^{7} + 24320 \, A a c^{4} x^{6} + 15624 \, B a^{2} c^{3} x^{5} + 19200 \, A a^{2} c^{3} x^{4} + 630 \, B a^{3} c^{2} x^{3} + 1280 \, A a^{3} c^{2} x^{2} - 945 \, B a^{4} c x - 2560 \, A a^{4} c\right)} \sqrt{c x^{2} + a}}{161280 \, c^{3}}, -\frac{945 \, B a^{5} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(8064 \, B c^{5} x^{9} + 8960 \, A c^{5} x^{8} + 21168 \, B a c^{4} x^{7} + 24320 \, A a c^{4} x^{6} + 15624 \, B a^{2} c^{3} x^{5} + 19200 \, A a^{2} c^{3} x^{4} + 630 \, B a^{3} c^{2} x^{3} + 1280 \, A a^{3} c^{2} x^{2} - 945 \, B a^{4} c x - 2560 \, A a^{4} c\right)} \sqrt{c x^{2} + a}}{80640 \, c^{3}}\right]"," ",0,"[1/161280*(945*B*a^5*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(8064*B*c^5*x^9 + 8960*A*c^5*x^8 + 21168*B*a*c^4*x^7 + 24320*A*a*c^4*x^6 + 15624*B*a^2*c^3*x^5 + 19200*A*a^2*c^3*x^4 + 630*B*a^3*c^2*x^3 + 1280*A*a^3*c^2*x^2 - 945*B*a^4*c*x - 2560*A*a^4*c)*sqrt(c*x^2 + a))/c^3, -1/80640*(945*B*a^5*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (8064*B*c^5*x^9 + 8960*A*c^5*x^8 + 21168*B*a*c^4*x^7 + 24320*A*a*c^4*x^6 + 15624*B*a^2*c^3*x^5 + 19200*A*a^2*c^3*x^4 + 630*B*a^3*c^2*x^3 + 1280*A*a^3*c^2*x^2 - 945*B*a^4*c*x - 2560*A*a^4*c)*sqrt(c*x^2 + a))/c^3]","A",0
341,1,271,0,0.474597," ","integrate(x^2*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, A a^{4} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(896 \, B c^{4} x^{8} + 1008 \, A c^{4} x^{7} + 2432 \, B a c^{3} x^{6} + 2856 \, A a c^{3} x^{5} + 1920 \, B a^{2} c^{2} x^{4} + 2478 \, A a^{2} c^{2} x^{3} + 128 \, B a^{3} c x^{2} + 315 \, A a^{3} c x - 256 \, B a^{4}\right)} \sqrt{c x^{2} + a}}{16128 \, c^{2}}, \frac{315 \, A a^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(896 \, B c^{4} x^{8} + 1008 \, A c^{4} x^{7} + 2432 \, B a c^{3} x^{6} + 2856 \, A a c^{3} x^{5} + 1920 \, B a^{2} c^{2} x^{4} + 2478 \, A a^{2} c^{2} x^{3} + 128 \, B a^{3} c x^{2} + 315 \, A a^{3} c x - 256 \, B a^{4}\right)} \sqrt{c x^{2} + a}}{8064 \, c^{2}}\right]"," ",0,"[1/16128*(315*A*a^4*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(896*B*c^4*x^8 + 1008*A*c^4*x^7 + 2432*B*a*c^3*x^6 + 2856*A*a*c^3*x^5 + 1920*B*a^2*c^2*x^4 + 2478*A*a^2*c^2*x^3 + 128*B*a^3*c*x^2 + 315*A*a^3*c*x - 256*B*a^4)*sqrt(c*x^2 + a))/c^2, 1/8064*(315*A*a^4*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (896*B*c^4*x^8 + 1008*A*c^4*x^7 + 2432*B*a*c^3*x^6 + 2856*A*a*c^3*x^5 + 1920*B*a^2*c^2*x^4 + 2478*A*a^2*c^2*x^3 + 128*B*a^3*c*x^2 + 315*A*a^3*c*x - 256*B*a^4)*sqrt(c*x^2 + a))/c^2]","A",0
342,1,253,0,0.473371," ","integrate(x*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, B a^{4} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(336 \, B c^{4} x^{7} + 384 \, A c^{4} x^{6} + 952 \, B a c^{3} x^{5} + 1152 \, A a c^{3} x^{4} + 826 \, B a^{2} c^{2} x^{3} + 1152 \, A a^{2} c^{2} x^{2} + 105 \, B a^{3} c x + 384 \, A a^{3} c\right)} \sqrt{c x^{2} + a}}{5376 \, c^{2}}, \frac{105 \, B a^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(336 \, B c^{4} x^{7} + 384 \, A c^{4} x^{6} + 952 \, B a c^{3} x^{5} + 1152 \, A a c^{3} x^{4} + 826 \, B a^{2} c^{2} x^{3} + 1152 \, A a^{2} c^{2} x^{2} + 105 \, B a^{3} c x + 384 \, A a^{3} c\right)} \sqrt{c x^{2} + a}}{2688 \, c^{2}}\right]"," ",0,"[1/5376*(105*B*a^4*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(336*B*c^4*x^7 + 384*A*c^4*x^6 + 952*B*a*c^3*x^5 + 1152*A*a*c^3*x^4 + 826*B*a^2*c^2*x^3 + 1152*A*a^2*c^2*x^2 + 105*B*a^3*c*x + 384*A*a^3*c)*sqrt(c*x^2 + a))/c^2, 1/2688*(105*B*a^4*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (336*B*c^4*x^7 + 384*A*c^4*x^6 + 952*B*a*c^3*x^5 + 1152*A*a*c^3*x^4 + 826*B*a^2*c^2*x^3 + 1152*A*a^2*c^2*x^2 + 105*B*a^3*c*x + 384*A*a^3*c)*sqrt(c*x^2 + a))/c^2]","A",0
343,1,224,0,0.468965," ","integrate((B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, A a^{3} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(48 \, B c^{3} x^{6} + 56 \, A c^{3} x^{5} + 144 \, B a c^{2} x^{4} + 182 \, A a c^{2} x^{3} + 144 \, B a^{2} c x^{2} + 231 \, A a^{2} c x + 48 \, B a^{3}\right)} \sqrt{c x^{2} + a}}{672 \, c}, -\frac{105 \, A a^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(48 \, B c^{3} x^{6} + 56 \, A c^{3} x^{5} + 144 \, B a c^{2} x^{4} + 182 \, A a c^{2} x^{3} + 144 \, B a^{2} c x^{2} + 231 \, A a^{2} c x + 48 \, B a^{3}\right)} \sqrt{c x^{2} + a}}{336 \, c}\right]"," ",0,"[1/672*(105*A*a^3*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(48*B*c^3*x^6 + 56*A*c^3*x^5 + 144*B*a*c^2*x^4 + 182*A*a*c^2*x^3 + 144*B*a^2*c*x^2 + 231*A*a^2*c*x + 48*B*a^3)*sqrt(c*x^2 + a))/c, -1/336*(105*A*a^3*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (48*B*c^3*x^6 + 56*A*c^3*x^5 + 144*B*a*c^2*x^4 + 182*A*a*c^2*x^3 + 144*B*a^2*c*x^2 + 231*A*a^2*c*x + 48*B*a^3)*sqrt(c*x^2 + a))/c]","A",0
344,1,539,0,0.479092," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{75 \, B a^{3} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 240 \, A a^{\frac{5}{2}} c \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(40 \, B c^{3} x^{5} + 48 \, A c^{3} x^{4} + 130 \, B a c^{2} x^{3} + 176 \, A a c^{2} x^{2} + 165 \, B a^{2} c x + 368 \, A a^{2} c\right)} \sqrt{c x^{2} + a}}{480 \, c}, -\frac{75 \, B a^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 120 \, A a^{\frac{5}{2}} c \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(40 \, B c^{3} x^{5} + 48 \, A c^{3} x^{4} + 130 \, B a c^{2} x^{3} + 176 \, A a c^{2} x^{2} + 165 \, B a^{2} c x + 368 \, A a^{2} c\right)} \sqrt{c x^{2} + a}}{240 \, c}, \frac{480 \, A \sqrt{-a} a^{2} c \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 75 \, B a^{3} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(40 \, B c^{3} x^{5} + 48 \, A c^{3} x^{4} + 130 \, B a c^{2} x^{3} + 176 \, A a c^{2} x^{2} + 165 \, B a^{2} c x + 368 \, A a^{2} c\right)} \sqrt{c x^{2} + a}}{480 \, c}, -\frac{75 \, B a^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 240 \, A \sqrt{-a} a^{2} c \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(40 \, B c^{3} x^{5} + 48 \, A c^{3} x^{4} + 130 \, B a c^{2} x^{3} + 176 \, A a c^{2} x^{2} + 165 \, B a^{2} c x + 368 \, A a^{2} c\right)} \sqrt{c x^{2} + a}}{240 \, c}\right]"," ",0,"[1/480*(75*B*a^3*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 240*A*a^(5/2)*c*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(40*B*c^3*x^5 + 48*A*c^3*x^4 + 130*B*a*c^2*x^3 + 176*A*a*c^2*x^2 + 165*B*a^2*c*x + 368*A*a^2*c)*sqrt(c*x^2 + a))/c, -1/240*(75*B*a^3*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 120*A*a^(5/2)*c*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - (40*B*c^3*x^5 + 48*A*c^3*x^4 + 130*B*a*c^2*x^3 + 176*A*a*c^2*x^2 + 165*B*a^2*c*x + 368*A*a^2*c)*sqrt(c*x^2 + a))/c, 1/480*(480*A*sqrt(-a)*a^2*c*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 75*B*a^3*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(40*B*c^3*x^5 + 48*A*c^3*x^4 + 130*B*a*c^2*x^3 + 176*A*a*c^2*x^2 + 165*B*a^2*c*x + 368*A*a^2*c)*sqrt(c*x^2 + a))/c, -1/240*(75*B*a^3*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 240*A*sqrt(-a)*a^2*c*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (40*B*c^3*x^5 + 48*A*c^3*x^4 + 130*B*a*c^2*x^3 + 176*A*a*c^2*x^2 + 165*B*a^2*c*x + 368*A*a^2*c)*sqrt(c*x^2 + a))/c]","A",0
345,1,519,0,0.510214," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^2,x, algorithm=""fricas"")","\left[\frac{225 \, A a^{2} \sqrt{c} x \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 120 \, B a^{\frac{5}{2}} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(24 \, B c^{2} x^{5} + 30 \, A c^{2} x^{4} + 88 \, B a c x^{3} + 135 \, A a c x^{2} + 184 \, B a^{2} x - 120 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{240 \, x}, -\frac{225 \, A a^{2} \sqrt{-c} x \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 60 \, B a^{\frac{5}{2}} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(24 \, B c^{2} x^{5} + 30 \, A c^{2} x^{4} + 88 \, B a c x^{3} + 135 \, A a c x^{2} + 184 \, B a^{2} x - 120 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{120 \, x}, \frac{240 \, B \sqrt{-a} a^{2} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 225 \, A a^{2} \sqrt{c} x \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(24 \, B c^{2} x^{5} + 30 \, A c^{2} x^{4} + 88 \, B a c x^{3} + 135 \, A a c x^{2} + 184 \, B a^{2} x - 120 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{240 \, x}, -\frac{225 \, A a^{2} \sqrt{-c} x \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 120 \, B \sqrt{-a} a^{2} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(24 \, B c^{2} x^{5} + 30 \, A c^{2} x^{4} + 88 \, B a c x^{3} + 135 \, A a c x^{2} + 184 \, B a^{2} x - 120 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{120 \, x}\right]"," ",0,"[1/240*(225*A*a^2*sqrt(c)*x*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 120*B*a^(5/2)*x*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(24*B*c^2*x^5 + 30*A*c^2*x^4 + 88*B*a*c*x^3 + 135*A*a*c*x^2 + 184*B*a^2*x - 120*A*a^2)*sqrt(c*x^2 + a))/x, -1/120*(225*A*a^2*sqrt(-c)*x*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 60*B*a^(5/2)*x*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - (24*B*c^2*x^5 + 30*A*c^2*x^4 + 88*B*a*c*x^3 + 135*A*a*c*x^2 + 184*B*a^2*x - 120*A*a^2)*sqrt(c*x^2 + a))/x, 1/240*(240*B*sqrt(-a)*a^2*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 225*A*a^2*sqrt(c)*x*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(24*B*c^2*x^5 + 30*A*c^2*x^4 + 88*B*a*c*x^3 + 135*A*a*c*x^2 + 184*B*a^2*x - 120*A*a^2)*sqrt(c*x^2 + a))/x, -1/120*(225*A*a^2*sqrt(-c)*x*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 120*B*sqrt(-a)*a^2*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (24*B*c^2*x^5 + 30*A*c^2*x^4 + 88*B*a*c*x^3 + 135*A*a*c*x^2 + 184*B*a^2*x - 120*A*a^2)*sqrt(c*x^2 + a))/x]","A",0
346,1,535,0,0.507334," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^3,x, algorithm=""fricas"")","\left[\frac{45 \, B a^{2} \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 60 \, A a^{\frac{3}{2}} c x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(6 \, B c^{2} x^{5} + 8 \, A c^{2} x^{4} + 27 \, B a c x^{3} + 56 \, A a c x^{2} - 24 \, B a^{2} x - 12 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{48 \, x^{2}}, -\frac{45 \, B a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 30 \, A a^{\frac{3}{2}} c x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(6 \, B c^{2} x^{5} + 8 \, A c^{2} x^{4} + 27 \, B a c x^{3} + 56 \, A a c x^{2} - 24 \, B a^{2} x - 12 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{24 \, x^{2}}, \frac{120 \, A \sqrt{-a} a c x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 45 \, B a^{2} \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(6 \, B c^{2} x^{5} + 8 \, A c^{2} x^{4} + 27 \, B a c x^{3} + 56 \, A a c x^{2} - 24 \, B a^{2} x - 12 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{48 \, x^{2}}, -\frac{45 \, B a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 60 \, A \sqrt{-a} a c x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, B c^{2} x^{5} + 8 \, A c^{2} x^{4} + 27 \, B a c x^{3} + 56 \, A a c x^{2} - 24 \, B a^{2} x - 12 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{24 \, x^{2}}\right]"," ",0,"[1/48*(45*B*a^2*sqrt(c)*x^2*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 60*A*a^(3/2)*c*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(6*B*c^2*x^5 + 8*A*c^2*x^4 + 27*B*a*c*x^3 + 56*A*a*c*x^2 - 24*B*a^2*x - 12*A*a^2)*sqrt(c*x^2 + a))/x^2, -1/24*(45*B*a^2*sqrt(-c)*x^2*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 30*A*a^(3/2)*c*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - (6*B*c^2*x^5 + 8*A*c^2*x^4 + 27*B*a*c*x^3 + 56*A*a*c*x^2 - 24*B*a^2*x - 12*A*a^2)*sqrt(c*x^2 + a))/x^2, 1/48*(120*A*sqrt(-a)*a*c*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 45*B*a^2*sqrt(c)*x^2*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(6*B*c^2*x^5 + 8*A*c^2*x^4 + 27*B*a*c*x^3 + 56*A*a*c*x^2 - 24*B*a^2*x - 12*A*a^2)*sqrt(c*x^2 + a))/x^2, -1/24*(45*B*a^2*sqrt(-c)*x^2*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 60*A*sqrt(-a)*a*c*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (6*B*c^2*x^5 + 8*A*c^2*x^4 + 27*B*a*c*x^3 + 56*A*a*c*x^2 - 24*B*a^2*x - 12*A*a^2)*sqrt(c*x^2 + a))/x^2]","A",0
347,1,529,0,0.525620," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, A a c^{\frac{3}{2}} x^{3} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 15 \, B a^{\frac{3}{2}} c x^{3} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, B c^{2} x^{5} + 3 \, A c^{2} x^{4} + 14 \, B a c x^{3} - 14 \, A a c x^{2} - 3 \, B a^{2} x - 2 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{12 \, x^{3}}, -\frac{30 \, A a \sqrt{-c} c x^{3} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 15 \, B a^{\frac{3}{2}} c x^{3} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(2 \, B c^{2} x^{5} + 3 \, A c^{2} x^{4} + 14 \, B a c x^{3} - 14 \, A a c x^{2} - 3 \, B a^{2} x - 2 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{12 \, x^{3}}, \frac{30 \, B \sqrt{-a} a c x^{3} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 15 \, A a c^{\frac{3}{2}} x^{3} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(2 \, B c^{2} x^{5} + 3 \, A c^{2} x^{4} + 14 \, B a c x^{3} - 14 \, A a c x^{2} - 3 \, B a^{2} x - 2 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{12 \, x^{3}}, -\frac{15 \, A a \sqrt{-c} c x^{3} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 15 \, B \sqrt{-a} a c x^{3} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, B c^{2} x^{5} + 3 \, A c^{2} x^{4} + 14 \, B a c x^{3} - 14 \, A a c x^{2} - 3 \, B a^{2} x - 2 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{6 \, x^{3}}\right]"," ",0,"[1/12*(15*A*a*c^(3/2)*x^3*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 15*B*a^(3/2)*c*x^3*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*B*c^2*x^5 + 3*A*c^2*x^4 + 14*B*a*c*x^3 - 14*A*a*c*x^2 - 3*B*a^2*x - 2*A*a^2)*sqrt(c*x^2 + a))/x^3, -1/12*(30*A*a*sqrt(-c)*c*x^3*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 15*B*a^(3/2)*c*x^3*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(2*B*c^2*x^5 + 3*A*c^2*x^4 + 14*B*a*c*x^3 - 14*A*a*c*x^2 - 3*B*a^2*x - 2*A*a^2)*sqrt(c*x^2 + a))/x^3, 1/12*(30*B*sqrt(-a)*a*c*x^3*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 15*A*a*c^(3/2)*x^3*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(2*B*c^2*x^5 + 3*A*c^2*x^4 + 14*B*a*c*x^3 - 14*A*a*c*x^2 - 3*B*a^2*x - 2*A*a^2)*sqrt(c*x^2 + a))/x^3, -1/6*(15*A*a*sqrt(-c)*c*x^3*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 15*B*sqrt(-a)*a*c*x^3*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (2*B*c^2*x^5 + 3*A*c^2*x^4 + 14*B*a*c*x^3 - 14*A*a*c*x^2 - 3*B*a^2*x - 2*A*a^2)*sqrt(c*x^2 + a))/x^3]","A",0
348,1,534,0,0.538311," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^5,x, algorithm=""fricas"")","\left[\frac{60 \, B a c^{\frac{3}{2}} x^{4} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 45 \, A \sqrt{a} c^{2} x^{4} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(12 \, B c^{2} x^{5} + 24 \, A c^{2} x^{4} - 56 \, B a c x^{3} - 27 \, A a c x^{2} - 8 \, B a^{2} x - 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{48 \, x^{4}}, -\frac{120 \, B a \sqrt{-c} c x^{4} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 45 \, A \sqrt{a} c^{2} x^{4} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(12 \, B c^{2} x^{5} + 24 \, A c^{2} x^{4} - 56 \, B a c x^{3} - 27 \, A a c x^{2} - 8 \, B a^{2} x - 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{48 \, x^{4}}, \frac{45 \, A \sqrt{-a} c^{2} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 30 \, B a c^{\frac{3}{2}} x^{4} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + {\left(12 \, B c^{2} x^{5} + 24 \, A c^{2} x^{4} - 56 \, B a c x^{3} - 27 \, A a c x^{2} - 8 \, B a^{2} x - 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{24 \, x^{4}}, -\frac{60 \, B a \sqrt{-c} c x^{4} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 45 \, A \sqrt{-a} c^{2} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(12 \, B c^{2} x^{5} + 24 \, A c^{2} x^{4} - 56 \, B a c x^{3} - 27 \, A a c x^{2} - 8 \, B a^{2} x - 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{24 \, x^{4}}\right]"," ",0,"[1/48*(60*B*a*c^(3/2)*x^4*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 45*A*sqrt(a)*c^2*x^4*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(12*B*c^2*x^5 + 24*A*c^2*x^4 - 56*B*a*c*x^3 - 27*A*a*c*x^2 - 8*B*a^2*x - 6*A*a^2)*sqrt(c*x^2 + a))/x^4, -1/48*(120*B*a*sqrt(-c)*c*x^4*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 45*A*sqrt(a)*c^2*x^4*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(12*B*c^2*x^5 + 24*A*c^2*x^4 - 56*B*a*c*x^3 - 27*A*a*c*x^2 - 8*B*a^2*x - 6*A*a^2)*sqrt(c*x^2 + a))/x^4, 1/24*(45*A*sqrt(-a)*c^2*x^4*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 30*B*a*c^(3/2)*x^4*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + (12*B*c^2*x^5 + 24*A*c^2*x^4 - 56*B*a*c*x^3 - 27*A*a*c*x^2 - 8*B*a^2*x - 6*A*a^2)*sqrt(c*x^2 + a))/x^4, -1/24*(60*B*a*sqrt(-c)*c*x^4*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 45*A*sqrt(-a)*c^2*x^4*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (12*B*c^2*x^5 + 24*A*c^2*x^4 - 56*B*a*c*x^3 - 27*A*a*c*x^2 - 8*B*a^2*x - 6*A*a^2)*sqrt(c*x^2 + a))/x^4]","A",0
349,1,534,0,0.519297," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^6,x, algorithm=""fricas"")","\left[\frac{120 \, A c^{\frac{5}{2}} x^{5} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 225 \, B \sqrt{a} c^{2} x^{5} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(120 \, B c^{2} x^{5} - 184 \, A c^{2} x^{4} - 135 \, B a c x^{3} - 88 \, A a c x^{2} - 30 \, B a^{2} x - 24 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{240 \, x^{5}}, -\frac{240 \, A \sqrt{-c} c^{2} x^{5} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 225 \, B \sqrt{a} c^{2} x^{5} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(120 \, B c^{2} x^{5} - 184 \, A c^{2} x^{4} - 135 \, B a c x^{3} - 88 \, A a c x^{2} - 30 \, B a^{2} x - 24 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{240 \, x^{5}}, \frac{225 \, B \sqrt{-a} c^{2} x^{5} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 60 \, A c^{\frac{5}{2}} x^{5} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + {\left(120 \, B c^{2} x^{5} - 184 \, A c^{2} x^{4} - 135 \, B a c x^{3} - 88 \, A a c x^{2} - 30 \, B a^{2} x - 24 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{120 \, x^{5}}, -\frac{120 \, A \sqrt{-c} c^{2} x^{5} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 225 \, B \sqrt{-a} c^{2} x^{5} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(120 \, B c^{2} x^{5} - 184 \, A c^{2} x^{4} - 135 \, B a c x^{3} - 88 \, A a c x^{2} - 30 \, B a^{2} x - 24 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{120 \, x^{5}}\right]"," ",0,"[1/240*(120*A*c^(5/2)*x^5*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 225*B*sqrt(a)*c^2*x^5*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(120*B*c^2*x^5 - 184*A*c^2*x^4 - 135*B*a*c*x^3 - 88*A*a*c*x^2 - 30*B*a^2*x - 24*A*a^2)*sqrt(c*x^2 + a))/x^5, -1/240*(240*A*sqrt(-c)*c^2*x^5*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 225*B*sqrt(a)*c^2*x^5*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(120*B*c^2*x^5 - 184*A*c^2*x^4 - 135*B*a*c*x^3 - 88*A*a*c*x^2 - 30*B*a^2*x - 24*A*a^2)*sqrt(c*x^2 + a))/x^5, 1/120*(225*B*sqrt(-a)*c^2*x^5*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 60*A*c^(5/2)*x^5*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + (120*B*c^2*x^5 - 184*A*c^2*x^4 - 135*B*a*c*x^3 - 88*A*a*c*x^2 - 30*B*a^2*x - 24*A*a^2)*sqrt(c*x^2 + a))/x^5, -1/120*(120*A*sqrt(-c)*c^2*x^5*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 225*B*sqrt(-a)*c^2*x^5*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (120*B*c^2*x^5 - 184*A*c^2*x^4 - 135*B*a*c*x^3 - 88*A*a*c*x^2 - 30*B*a^2*x - 24*A*a^2)*sqrt(c*x^2 + a))/x^5]","A",0
350,1,574,0,0.516888," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^7,x, algorithm=""fricas"")","\left[\frac{240 \, B a c^{\frac{5}{2}} x^{6} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 75 \, A \sqrt{a} c^{3} x^{6} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(368 \, B a c^{2} x^{5} + 165 \, A a c^{2} x^{4} + 176 \, B a^{2} c x^{3} + 130 \, A a^{2} c x^{2} + 48 \, B a^{3} x + 40 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{480 \, a x^{6}}, -\frac{480 \, B a \sqrt{-c} c^{2} x^{6} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 75 \, A \sqrt{a} c^{3} x^{6} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(368 \, B a c^{2} x^{5} + 165 \, A a c^{2} x^{4} + 176 \, B a^{2} c x^{3} + 130 \, A a^{2} c x^{2} + 48 \, B a^{3} x + 40 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{480 \, a x^{6}}, \frac{75 \, A \sqrt{-a} c^{3} x^{6} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + 120 \, B a c^{\frac{5}{2}} x^{6} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - {\left(368 \, B a c^{2} x^{5} + 165 \, A a c^{2} x^{4} + 176 \, B a^{2} c x^{3} + 130 \, A a^{2} c x^{2} + 48 \, B a^{3} x + 40 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{240 \, a x^{6}}, -\frac{240 \, B a \sqrt{-c} c^{2} x^{6} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 75 \, A \sqrt{-a} c^{3} x^{6} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(368 \, B a c^{2} x^{5} + 165 \, A a c^{2} x^{4} + 176 \, B a^{2} c x^{3} + 130 \, A a^{2} c x^{2} + 48 \, B a^{3} x + 40 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{240 \, a x^{6}}\right]"," ",0,"[1/480*(240*B*a*c^(5/2)*x^6*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 75*A*sqrt(a)*c^3*x^6*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(368*B*a*c^2*x^5 + 165*A*a*c^2*x^4 + 176*B*a^2*c*x^3 + 130*A*a^2*c*x^2 + 48*B*a^3*x + 40*A*a^3)*sqrt(c*x^2 + a))/(a*x^6), -1/480*(480*B*a*sqrt(-c)*c^2*x^6*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 75*A*sqrt(a)*c^3*x^6*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(368*B*a*c^2*x^5 + 165*A*a*c^2*x^4 + 176*B*a^2*c*x^3 + 130*A*a^2*c*x^2 + 48*B*a^3*x + 40*A*a^3)*sqrt(c*x^2 + a))/(a*x^6), 1/240*(75*A*sqrt(-a)*c^3*x^6*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + 120*B*a*c^(5/2)*x^6*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - (368*B*a*c^2*x^5 + 165*A*a*c^2*x^4 + 176*B*a^2*c*x^3 + 130*A*a^2*c*x^2 + 48*B*a^3*x + 40*A*a^3)*sqrt(c*x^2 + a))/(a*x^6), -1/240*(240*B*a*sqrt(-c)*c^2*x^6*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 75*A*sqrt(-a)*c^3*x^6*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (368*B*a*c^2*x^5 + 165*A*a*c^2*x^4 + 176*B*a^2*c*x^3 + 130*A*a^2*c*x^2 + 48*B*a^3*x + 40*A*a^3)*sqrt(c*x^2 + a))/(a*x^6)]","A",0
351,1,238,0,0.488587," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^8,x, algorithm=""fricas"")","\left[\frac{105 \, B \sqrt{a} c^{3} x^{7} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(48 \, A c^{3} x^{6} + 231 \, B a c^{2} x^{5} + 144 \, A a c^{2} x^{4} + 182 \, B a^{2} c x^{3} + 144 \, A a^{2} c x^{2} + 56 \, B a^{3} x + 48 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{672 \, a x^{7}}, \frac{105 \, B \sqrt{-a} c^{3} x^{7} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(48 \, A c^{3} x^{6} + 231 \, B a c^{2} x^{5} + 144 \, A a c^{2} x^{4} + 182 \, B a^{2} c x^{3} + 144 \, A a^{2} c x^{2} + 56 \, B a^{3} x + 48 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{336 \, a x^{7}}\right]"," ",0,"[1/672*(105*B*sqrt(a)*c^3*x^7*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(48*A*c^3*x^6 + 231*B*a*c^2*x^5 + 144*A*a*c^2*x^4 + 182*B*a^2*c*x^3 + 144*A*a^2*c*x^2 + 56*B*a^3*x + 48*A*a^3)*sqrt(c*x^2 + a))/(a*x^7), 1/336*(105*B*sqrt(-a)*c^3*x^7*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (48*A*c^3*x^6 + 231*B*a*c^2*x^5 + 144*A*a*c^2*x^4 + 182*B*a^2*c*x^3 + 144*A*a^2*c*x^2 + 56*B*a^3*x + 48*A*a^3)*sqrt(c*x^2 + a))/(a*x^7)]","A",0
352,1,267,0,0.525105," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^9,x, algorithm=""fricas"")","\left[\frac{105 \, A \sqrt{a} c^{4} x^{8} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(384 \, B a c^{3} x^{7} + 105 \, A a c^{3} x^{6} + 1152 \, B a^{2} c^{2} x^{5} + 826 \, A a^{2} c^{2} x^{4} + 1152 \, B a^{3} c x^{3} + 952 \, A a^{3} c x^{2} + 384 \, B a^{4} x + 336 \, A a^{4}\right)} \sqrt{c x^{2} + a}}{5376 \, a^{2} x^{8}}, -\frac{105 \, A \sqrt{-a} c^{4} x^{8} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(384 \, B a c^{3} x^{7} + 105 \, A a c^{3} x^{6} + 1152 \, B a^{2} c^{2} x^{5} + 826 \, A a^{2} c^{2} x^{4} + 1152 \, B a^{3} c x^{3} + 952 \, A a^{3} c x^{2} + 384 \, B a^{4} x + 336 \, A a^{4}\right)} \sqrt{c x^{2} + a}}{2688 \, a^{2} x^{8}}\right]"," ",0,"[1/5376*(105*A*sqrt(a)*c^4*x^8*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(384*B*a*c^3*x^7 + 105*A*a*c^3*x^6 + 1152*B*a^2*c^2*x^5 + 826*A*a^2*c^2*x^4 + 1152*B*a^3*c*x^3 + 952*A*a^3*c*x^2 + 384*B*a^4*x + 336*A*a^4)*sqrt(c*x^2 + a))/(a^2*x^8), -1/2688*(105*A*sqrt(-a)*c^4*x^8*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (384*B*a*c^3*x^7 + 105*A*a*c^3*x^6 + 1152*B*a^2*c^2*x^5 + 826*A*a^2*c^2*x^4 + 1152*B*a^3*c*x^3 + 952*A*a^3*c*x^2 + 384*B*a^4*x + 336*A*a^4)*sqrt(c*x^2 + a))/(a^2*x^8)]","A",0
353,1,286,0,0.563536," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/x^10,x, algorithm=""fricas"")","\left[\frac{315 \, B \sqrt{a} c^{4} x^{9} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(256 \, A c^{4} x^{8} - 315 \, B a c^{3} x^{7} - 128 \, A a c^{3} x^{6} - 2478 \, B a^{2} c^{2} x^{5} - 1920 \, A a^{2} c^{2} x^{4} - 2856 \, B a^{3} c x^{3} - 2432 \, A a^{3} c x^{2} - 1008 \, B a^{4} x - 896 \, A a^{4}\right)} \sqrt{c x^{2} + a}}{16128 \, a^{2} x^{9}}, -\frac{315 \, B \sqrt{-a} c^{4} x^{9} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(256 \, A c^{4} x^{8} - 315 \, B a c^{3} x^{7} - 128 \, A a c^{3} x^{6} - 2478 \, B a^{2} c^{2} x^{5} - 1920 \, A a^{2} c^{2} x^{4} - 2856 \, B a^{3} c x^{3} - 2432 \, A a^{3} c x^{2} - 1008 \, B a^{4} x - 896 \, A a^{4}\right)} \sqrt{c x^{2} + a}}{8064 \, a^{2} x^{9}}\right]"," ",0,"[1/16128*(315*B*sqrt(a)*c^4*x^9*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(256*A*c^4*x^8 - 315*B*a*c^3*x^7 - 128*A*a*c^3*x^6 - 2478*B*a^2*c^2*x^5 - 1920*A*a^2*c^2*x^4 - 2856*B*a^3*c*x^3 - 2432*A*a^3*c*x^2 - 1008*B*a^4*x - 896*A*a^4)*sqrt(c*x^2 + a))/(a^2*x^9), -1/8064*(315*B*sqrt(-a)*c^4*x^9*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (256*A*c^4*x^8 - 315*B*a*c^3*x^7 - 128*A*a*c^3*x^6 - 2478*B*a^2*c^2*x^5 - 1920*A*a^2*c^2*x^4 - 2856*B*a^3*c*x^3 - 2432*A*a^3*c*x^2 - 1008*B*a^4*x - 896*A*a^4)*sqrt(c*x^2 + a))/(a^2*x^9)]","A",0
354,1,176,0,0.472233," ","integrate(x^4*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{45 \, A a^{2} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(24 \, B c^{2} x^{4} + 30 \, A c^{2} x^{3} - 32 \, B a c x^{2} - 45 \, A a c x + 64 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{240 \, c^{3}}, -\frac{45 \, A a^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(24 \, B c^{2} x^{4} + 30 \, A c^{2} x^{3} - 32 \, B a c x^{2} - 45 \, A a c x + 64 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{120 \, c^{3}}\right]"," ",0,"[1/240*(45*A*a^2*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(24*B*c^2*x^4 + 30*A*c^2*x^3 - 32*B*a*c*x^2 - 45*A*a*c*x + 64*B*a^2)*sqrt(c*x^2 + a))/c^3, -1/120*(45*A*a^2*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (24*B*c^2*x^4 + 30*A*c^2*x^3 - 32*B*a*c*x^2 - 45*A*a*c*x + 64*B*a^2)*sqrt(c*x^2 + a))/c^3]","A",0
355,1,158,0,0.449949," ","integrate(x^3*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{9 \, B a^{2} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(6 \, B c^{2} x^{3} + 8 \, A c^{2} x^{2} - 9 \, B a c x - 16 \, A a c\right)} \sqrt{c x^{2} + a}}{48 \, c^{3}}, -\frac{9 \, B a^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, B c^{2} x^{3} + 8 \, A c^{2} x^{2} - 9 \, B a c x - 16 \, A a c\right)} \sqrt{c x^{2} + a}}{24 \, c^{3}}\right]"," ",0,"[1/48*(9*B*a^2*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(6*B*c^2*x^3 + 8*A*c^2*x^2 - 9*B*a*c*x - 16*A*a*c)*sqrt(c*x^2 + a))/c^3, -1/24*(9*B*a^2*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (6*B*c^2*x^3 + 8*A*c^2*x^2 - 9*B*a*c*x - 16*A*a*c)*sqrt(c*x^2 + a))/c^3]","A",0
356,1,127,0,0.454535," ","integrate(x^2*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, A a \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(2 \, B c x^{2} + 3 \, A c x - 4 \, B a\right)} \sqrt{c x^{2} + a}}{12 \, c^{2}}, \frac{3 \, A a \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, B c x^{2} + 3 \, A c x - 4 \, B a\right)} \sqrt{c x^{2} + a}}{6 \, c^{2}}\right]"," ",0,"[1/12*(3*A*a*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(2*B*c*x^2 + 3*A*c*x - 4*B*a)*sqrt(c*x^2 + a))/c^2, 1/6*(3*A*a*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (2*B*c*x^2 + 3*A*c*x - 4*B*a)*sqrt(c*x^2 + a))/c^2]","A",0
357,1,109,0,0.489555," ","integrate(x*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B a \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(B c x + 2 \, A c\right)} \sqrt{c x^{2} + a}}{4 \, c^{2}}, \frac{B a \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(B c x + 2 \, A c\right)} \sqrt{c x^{2} + a}}{2 \, c^{2}}\right]"," ",0,"[1/4*(B*a*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(B*c*x + 2*A*c)*sqrt(c*x^2 + a))/c^2, 1/2*(B*a*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (B*c*x + 2*A*c)*sqrt(c*x^2 + a))/c^2]","A",0
358,1,92,0,0.456870," ","integrate((B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, \sqrt{c x^{2} + a} B}{2 \, c}, -\frac{A \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - \sqrt{c x^{2} + a} B}{c}\right]"," ",0,"[1/2*(A*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*sqrt(c*x^2 + a)*B)/c, -(A*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - sqrt(c*x^2 + a)*B)/c]","A",0
359,1,273,0,0.499636," ","integrate((B*x+A)/x/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B a \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + A \sqrt{a} c \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right)}{2 \, a c}, -\frac{2 \, B a \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - A \sqrt{a} c \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right)}{2 \, a c}, \frac{2 \, A \sqrt{-a} c \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + B a \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right)}{2 \, a c}, -\frac{B a \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - A \sqrt{-a} c \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right)}{a c}\right]"," ",0,"[1/2*(B*a*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + A*sqrt(a)*c*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2))/(a*c), -1/2*(2*B*a*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - A*sqrt(a)*c*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2))/(a*c), 1/2*(2*A*sqrt(-a)*c*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + B*a*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a))/(a*c), -(B*a*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - A*sqrt(-a)*c*arctan(sqrt(-a)/sqrt(c*x^2 + a)))/(a*c)]","A",0
360,1,101,0,0.468768," ","integrate((B*x+A)/x^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B \sqrt{a} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, \sqrt{c x^{2} + a} A}{2 \, a x}, \frac{B \sqrt{-a} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - \sqrt{c x^{2} + a} A}{a x}\right]"," ",0,"[1/2*(B*sqrt(a)*x*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*sqrt(c*x^2 + a)*A)/(a*x), (B*sqrt(-a)*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - sqrt(c*x^2 + a)*A)/(a*x)]","A",0
361,1,123,0,0.458550," ","integrate((B*x+A)/x^3/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{a} c x^{2} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(2 \, B a x + A a\right)} \sqrt{c x^{2} + a}}{4 \, a^{2} x^{2}}, -\frac{A \sqrt{-a} c x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, B a x + A a\right)} \sqrt{c x^{2} + a}}{2 \, a^{2} x^{2}}\right]"," ",0,"[1/4*(A*sqrt(a)*c*x^2*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(2*B*a*x + A*a)*sqrt(c*x^2 + a))/(a^2*x^2), -1/2*(A*sqrt(-a)*c*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (2*B*a*x + A*a)*sqrt(c*x^2 + a))/(a^2*x^2)]","A",0
362,1,142,0,0.462175," ","integrate((B*x+A)/x^4/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, B \sqrt{a} c x^{3} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(4 \, A c x^{2} - 3 \, B a x - 2 \, A a\right)} \sqrt{c x^{2} + a}}{12 \, a^{2} x^{3}}, -\frac{3 \, B \sqrt{-a} c x^{3} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(4 \, A c x^{2} - 3 \, B a x - 2 \, A a\right)} \sqrt{c x^{2} + a}}{6 \, a^{2} x^{3}}\right]"," ",0,"[1/12*(3*B*sqrt(a)*c*x^3*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(4*A*c*x^2 - 3*B*a*x - 2*A*a)*sqrt(c*x^2 + a))/(a^2*x^3), -1/6*(3*B*sqrt(-a)*c*x^3*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (4*A*c*x^2 - 3*B*a*x - 2*A*a)*sqrt(c*x^2 + a))/(a^2*x^3)]","A",0
363,1,171,0,0.480315," ","integrate((B*x+A)/x^5/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{9 \, A \sqrt{a} c^{2} x^{4} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(16 \, B a c x^{3} + 9 \, A a c x^{2} - 8 \, B a^{2} x - 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{48 \, a^{3} x^{4}}, \frac{9 \, A \sqrt{-a} c^{2} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(16 \, B a c x^{3} + 9 \, A a c x^{2} - 8 \, B a^{2} x - 6 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{24 \, a^{3} x^{4}}\right]"," ",0,"[1/48*(9*A*sqrt(a)*c^2*x^4*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(16*B*a*c*x^3 + 9*A*a*c*x^2 - 8*B*a^2*x - 6*A*a^2)*sqrt(c*x^2 + a))/(a^3*x^4), 1/24*(9*A*sqrt(-a)*c^2*x^4*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (16*B*a*c*x^3 + 9*A*a*c*x^2 - 8*B*a^2*x - 6*A*a^2)*sqrt(c*x^2 + a))/(a^3*x^4)]","A",0
364,1,190,0,0.467336," ","integrate((B*x+A)/x^6/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{45 \, B \sqrt{a} c^{2} x^{5} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(64 \, A c^{2} x^{4} - 45 \, B a c x^{3} - 32 \, A a c x^{2} + 30 \, B a^{2} x + 24 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{240 \, a^{3} x^{5}}, \frac{45 \, B \sqrt{-a} c^{2} x^{5} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(64 \, A c^{2} x^{4} - 45 \, B a c x^{3} - 32 \, A a c x^{2} + 30 \, B a^{2} x + 24 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{120 \, a^{3} x^{5}}\right]"," ",0,"[1/240*(45*B*sqrt(a)*c^2*x^5*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(64*A*c^2*x^4 - 45*B*a*c*x^3 - 32*A*a*c*x^2 + 30*B*a^2*x + 24*A*a^2)*sqrt(c*x^2 + a))/(a^3*x^5), 1/120*(45*B*sqrt(-a)*c^2*x^5*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (64*A*c^2*x^4 - 45*B*a*c*x^3 - 32*A*a*c*x^2 + 30*B*a^2*x + 24*A*a^2)*sqrt(c*x^2 + a))/(a^3*x^5)]","A",0
365,1,217,0,0.478976," ","integrate(x^4*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{9 \, {\left(A a c x^{2} + A a^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(2 \, B c^{2} x^{4} + 3 \, A c^{2} x^{3} - 8 \, B a c x^{2} + 9 \, A a c x - 16 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{12 \, {\left(c^{4} x^{2} + a c^{3}\right)}}, \frac{9 \, {\left(A a c x^{2} + A a^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, B c^{2} x^{4} + 3 \, A c^{2} x^{3} - 8 \, B a c x^{2} + 9 \, A a c x - 16 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{4} x^{2} + a c^{3}\right)}}\right]"," ",0,"[1/12*(9*(A*a*c*x^2 + A*a^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(2*B*c^2*x^4 + 3*A*c^2*x^3 - 8*B*a*c*x^2 + 9*A*a*c*x - 16*B*a^2)*sqrt(c*x^2 + a))/(c^4*x^2 + a*c^3), 1/6*(9*(A*a*c*x^2 + A*a^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (2*B*c^2*x^4 + 3*A*c^2*x^3 - 8*B*a*c*x^2 + 9*A*a*c*x - 16*B*a^2)*sqrt(c*x^2 + a))/(c^4*x^2 + a*c^3)]","A",0
366,1,197,0,0.479891," ","integrate(x^3*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a c x^{2} + B a^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(B c^{2} x^{3} + 2 \, A c^{2} x^{2} + 3 \, B a c x + 4 \, A a c\right)} \sqrt{c x^{2} + a}}{4 \, {\left(c^{4} x^{2} + a c^{3}\right)}}, \frac{3 \, {\left(B a c x^{2} + B a^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(B c^{2} x^{3} + 2 \, A c^{2} x^{2} + 3 \, B a c x + 4 \, A a c\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{4} x^{2} + a c^{3}\right)}}\right]"," ",0,"[1/4*(3*(B*a*c*x^2 + B*a^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(B*c^2*x^3 + 2*A*c^2*x^2 + 3*B*a*c*x + 4*A*a*c)*sqrt(c*x^2 + a))/(c^4*x^2 + a*c^3), 1/2*(3*(B*a*c*x^2 + B*a^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (B*c^2*x^3 + 2*A*c^2*x^2 + 3*B*a*c*x + 4*A*a*c)*sqrt(c*x^2 + a))/(c^4*x^2 + a*c^3)]","A",0
367,1,164,0,0.458109," ","integrate(x^2*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A c x^{2} + A a\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(B c x^{2} - A c x + 2 \, B a\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} x^{2} + a c^{2}\right)}}, -\frac{{\left(A c x^{2} + A a\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(B c x^{2} - A c x + 2 \, B a\right)} \sqrt{c x^{2} + a}}{c^{3} x^{2} + a c^{2}}\right]"," ",0,"[1/2*((A*c*x^2 + A*a)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(B*c*x^2 - A*c*x + 2*B*a)*sqrt(c*x^2 + a))/(c^3*x^2 + a*c^2), -((A*c*x^2 + A*a)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (B*c*x^2 - A*c*x + 2*B*a)*sqrt(c*x^2 + a))/(c^3*x^2 + a*c^2)]","A",0
368,1,147,0,0.464815," ","integrate(x*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B c x^{2} + B a\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(B c x + A c\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} x^{2} + a c^{2}\right)}}, -\frac{{\left(B c x^{2} + B a\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(B c x + A c\right)} \sqrt{c x^{2} + a}}{c^{3} x^{2} + a c^{2}}\right]"," ",0,"[1/2*((B*c*x^2 + B*a)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(B*c*x + A*c)*sqrt(c*x^2 + a))/(c^3*x^2 + a*c^2), -((B*c*x^2 + B*a)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (B*c*x + A*c)*sqrt(c*x^2 + a))/(c^3*x^2 + a*c^2)]","A",0
369,1,35,0,0.454715," ","integrate((B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(A c x - B a\right)} \sqrt{c x^{2} + a}}{a c^{2} x^{2} + a^{2} c}"," ",0,"(A*c*x - B*a)*sqrt(c*x^2 + a)/(a*c^2*x^2 + a^2*c)","A",0
370,1,146,0,0.475747," ","integrate((B*x+A)/x/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A c x^{2} + A a\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(B a x + A a\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c x^{2} + a^{3}\right)}}, \frac{{\left(A c x^{2} + A a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(B a x + A a\right)} \sqrt{c x^{2} + a}}{a^{2} c x^{2} + a^{3}}\right]"," ",0,"[1/2*((A*c*x^2 + A*a)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(B*a*x + A*a)*sqrt(c*x^2 + a))/(a^2*c*x^2 + a^3), ((A*c*x^2 + A*a)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (B*a*x + A*a)*sqrt(c*x^2 + a))/(a^2*c*x^2 + a^3)]","A",0
371,1,169,0,0.462741," ","integrate((B*x+A)/x^2/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B c x^{3} + B a x\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(2 \, A c x^{2} - B a x + A a\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c x^{3} + a^{3} x\right)}}, \frac{{\left(B c x^{3} + B a x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, A c x^{2} - B a x + A a\right)} \sqrt{c x^{2} + a}}{a^{2} c x^{3} + a^{3} x}\right]"," ",0,"[1/2*((B*c*x^3 + B*a*x)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(2*A*c*x^2 - B*a*x + A*a)*sqrt(c*x^2 + a))/(a^2*c*x^3 + a^3*x), ((B*c*x^3 + B*a*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (2*A*c*x^2 - B*a*x + A*a)*sqrt(c*x^2 + a))/(a^2*c*x^3 + a^3*x)]","A",0
372,1,211,0,0.465287," ","integrate((B*x+A)/x^3/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A c^{2} x^{4} + A a c x^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(4 \, B a c x^{3} + 3 \, A a c x^{2} + 2 \, B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a}}{4 \, {\left(a^{3} c x^{4} + a^{4} x^{2}\right)}}, -\frac{3 \, {\left(A c^{2} x^{4} + A a c x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(4 \, B a c x^{3} + 3 \, A a c x^{2} + 2 \, B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{3} c x^{4} + a^{4} x^{2}\right)}}\right]"," ",0,"[1/4*(3*(A*c^2*x^4 + A*a*c*x^2)*sqrt(a)*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(4*B*a*c*x^3 + 3*A*a*c*x^2 + 2*B*a^2*x + A*a^2)*sqrt(c*x^2 + a))/(a^3*c*x^4 + a^4*x^2), -1/2*(3*(A*c^2*x^4 + A*a*c*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (4*B*a*c*x^3 + 3*A*a*c*x^2 + 2*B*a^2*x + A*a^2)*sqrt(c*x^2 + a))/(a^3*c*x^4 + a^4*x^2)]","A",0
373,1,232,0,0.458670," ","integrate((B*x+A)/x^4/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{9 \, {\left(B c^{2} x^{5} + B a c x^{3}\right)} \sqrt{a} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(16 \, A c^{2} x^{4} - 9 \, B a c x^{3} + 8 \, A a c x^{2} - 3 \, B a^{2} x - 2 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{12 \, {\left(a^{3} c x^{5} + a^{4} x^{3}\right)}}, -\frac{9 \, {\left(B c^{2} x^{5} + B a c x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(16 \, A c^{2} x^{4} - 9 \, B a c x^{3} + 8 \, A a c x^{2} - 3 \, B a^{2} x - 2 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{3} c x^{5} + a^{4} x^{3}\right)}}\right]"," ",0,"[1/12*(9*(B*c^2*x^5 + B*a*c*x^3)*sqrt(a)*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(16*A*c^2*x^4 - 9*B*a*c*x^3 + 8*A*a*c*x^2 - 3*B*a^2*x - 2*A*a^2)*sqrt(c*x^2 + a))/(a^3*c*x^5 + a^4*x^3), -1/6*(9*(B*c^2*x^5 + B*a*c*x^3)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (16*A*c^2*x^4 - 9*B*a*c*x^3 + 8*A*a*c*x^2 - 3*B*a^2*x - 2*A*a^2)*sqrt(c*x^2 + a))/(a^3*c*x^5 + a^4*x^3)]","A",0
374,1,258,0,0.452669," ","integrate(x^4*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A c^{2} x^{4} + 2 \, A a c x^{2} + A a^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(3 \, B c^{2} x^{4} - 4 \, A c^{2} x^{3} + 12 \, B a c x^{2} - 3 \, A a c x + 8 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{5} x^{4} + 2 \, a c^{4} x^{2} + a^{2} c^{3}\right)}}, -\frac{3 \, {\left(A c^{2} x^{4} + 2 \, A a c x^{2} + A a^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(3 \, B c^{2} x^{4} - 4 \, A c^{2} x^{3} + 12 \, B a c x^{2} - 3 \, A a c x + 8 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{3 \, {\left(c^{5} x^{4} + 2 \, a c^{4} x^{2} + a^{2} c^{3}\right)}}\right]"," ",0,"[1/6*(3*(A*c^2*x^4 + 2*A*a*c*x^2 + A*a^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(3*B*c^2*x^4 - 4*A*c^2*x^3 + 12*B*a*c*x^2 - 3*A*a*c*x + 8*B*a^2)*sqrt(c*x^2 + a))/(c^5*x^4 + 2*a*c^4*x^2 + a^2*c^3), -1/3*(3*(A*c^2*x^4 + 2*A*a*c*x^2 + A*a^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (3*B*c^2*x^4 - 4*A*c^2*x^3 + 12*B*a*c*x^2 - 3*A*a*c*x + 8*B*a^2)*sqrt(c*x^2 + a))/(c^5*x^4 + 2*a*c^4*x^2 + a^2*c^3)]","A",0
375,1,239,0,0.460761," ","integrate(x^3*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B c^{2} x^{4} + 2 \, B a c x^{2} + B a^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(4 \, B c^{2} x^{3} + 3 \, A c^{2} x^{2} + 3 \, B a c x + 2 \, A a c\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{5} x^{4} + 2 \, a c^{4} x^{2} + a^{2} c^{3}\right)}}, -\frac{3 \, {\left(B c^{2} x^{4} + 2 \, B a c x^{2} + B a^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(4 \, B c^{2} x^{3} + 3 \, A c^{2} x^{2} + 3 \, B a c x + 2 \, A a c\right)} \sqrt{c x^{2} + a}}{3 \, {\left(c^{5} x^{4} + 2 \, a c^{4} x^{2} + a^{2} c^{3}\right)}}\right]"," ",0,"[1/6*(3*(B*c^2*x^4 + 2*B*a*c*x^2 + B*a^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(4*B*c^2*x^3 + 3*A*c^2*x^2 + 3*B*a*c*x + 2*A*a*c)*sqrt(c*x^2 + a))/(c^5*x^4 + 2*a*c^4*x^2 + a^2*c^3), -1/3*(3*(B*c^2*x^4 + 2*B*a*c*x^2 + B*a^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (4*B*c^2*x^3 + 3*A*c^2*x^2 + 3*B*a*c*x + 2*A*a*c)*sqrt(c*x^2 + a))/(c^5*x^4 + 2*a*c^4*x^2 + a^2*c^3)]","A",0
376,1,63,0,0.429536," ","integrate(x^2*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(A c^{2} x^{3} - 3 \, B a c x^{2} - 2 \, B a^{2}\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a c^{4} x^{4} + 2 \, a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}"," ",0,"1/3*(A*c^2*x^3 - 3*B*a*c*x^2 - 2*B*a^2)*sqrt(c*x^2 + a)/(a*c^4*x^4 + 2*a^2*c^3*x^2 + a^3*c^2)","A",0
377,1,49,0,0.433275," ","integrate(x*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(B c x^{3} - A a\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a c^{3} x^{4} + 2 \, a^{2} c^{2} x^{2} + a^{3} c\right)}}"," ",0,"1/3*(B*c*x^3 - A*a)*sqrt(c*x^2 + a)/(a*c^3*x^4 + 2*a^2*c^2*x^2 + a^3*c)","A",0
378,1,62,0,0.421043," ","integrate((B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, A c^{2} x^{3} + 3 \, A a c x - B a^{2}\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"1/3*(2*A*c^2*x^3 + 3*A*a*c*x - B*a^2)*sqrt(c*x^2 + a)/(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)","A",0
379,1,239,0,0.446958," ","integrate((B*x+A)/x/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A c^{2} x^{4} + 2 \, A a c x^{2} + A a^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, B a c x^{3} + 3 \, A a c x^{2} + 3 \, B a^{2} x + 4 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{3} c^{2} x^{4} + 2 \, a^{4} c x^{2} + a^{5}\right)}}, \frac{3 \, {\left(A c^{2} x^{4} + 2 \, A a c x^{2} + A a^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, B a c x^{3} + 3 \, A a c x^{2} + 3 \, B a^{2} x + 4 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{3} c^{2} x^{4} + 2 \, a^{4} c x^{2} + a^{5}\right)}}\right]"," ",0,"[1/6*(3*(A*c^2*x^4 + 2*A*a*c*x^2 + A*a^2)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*B*a*c*x^3 + 3*A*a*c*x^2 + 3*B*a^2*x + 4*A*a^2)*sqrt(c*x^2 + a))/(a^3*c^2*x^4 + 2*a^4*c*x^2 + a^5), 1/3*(3*(A*c^2*x^4 + 2*A*a*c*x^2 + A*a^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (2*B*a*c*x^3 + 3*A*a*c*x^2 + 3*B*a^2*x + 4*A*a^2)*sqrt(c*x^2 + a))/(a^3*c^2*x^4 + 2*a^4*c*x^2 + a^5)]","A",0
380,1,264,0,0.458527," ","integrate((B*x+A)/x^2/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B c^{2} x^{5} + 2 \, B a c x^{3} + B a^{2} x\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(8 \, A c^{2} x^{4} - 3 \, B a c x^{3} + 12 \, A a c x^{2} - 4 \, B a^{2} x + 3 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{3} c^{2} x^{5} + 2 \, a^{4} c x^{3} + a^{5} x\right)}}, \frac{3 \, {\left(B c^{2} x^{5} + 2 \, B a c x^{3} + B a^{2} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(8 \, A c^{2} x^{4} - 3 \, B a c x^{3} + 12 \, A a c x^{2} - 4 \, B a^{2} x + 3 \, A a^{2}\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{3} c^{2} x^{5} + 2 \, a^{4} c x^{3} + a^{5} x\right)}}\right]"," ",0,"[1/6*(3*(B*c^2*x^5 + 2*B*a*c*x^3 + B*a^2*x)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(8*A*c^2*x^4 - 3*B*a*c*x^3 + 12*A*a*c*x^2 - 4*B*a^2*x + 3*A*a^2)*sqrt(c*x^2 + a))/(a^3*c^2*x^5 + 2*a^4*c*x^3 + a^5*x), 1/3*(3*(B*c^2*x^5 + 2*B*a*c*x^3 + B*a^2*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (8*A*c^2*x^4 - 3*B*a*c*x^3 + 12*A*a*c*x^2 - 4*B*a^2*x + 3*A*a^2)*sqrt(c*x^2 + a))/(a^3*c^2*x^5 + 2*a^4*c*x^3 + a^5*x)]","A",0
381,1,307,0,0.453339," ","integrate((B*x+A)/x^3/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(A c^{3} x^{6} + 2 \, A a c^{2} x^{4} + A a^{2} c x^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(16 \, B a c^{2} x^{5} + 15 \, A a c^{2} x^{4} + 24 \, B a^{2} c x^{3} + 20 \, A a^{2} c x^{2} + 6 \, B a^{3} x + 3 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{12 \, {\left(a^{4} c^{2} x^{6} + 2 \, a^{5} c x^{4} + a^{6} x^{2}\right)}}, -\frac{15 \, {\left(A c^{3} x^{6} + 2 \, A a c^{2} x^{4} + A a^{2} c x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(16 \, B a c^{2} x^{5} + 15 \, A a c^{2} x^{4} + 24 \, B a^{2} c x^{3} + 20 \, A a^{2} c x^{2} + 6 \, B a^{3} x + 3 \, A a^{3}\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{4} c^{2} x^{6} + 2 \, a^{5} c x^{4} + a^{6} x^{2}\right)}}\right]"," ",0,"[1/12*(15*(A*c^3*x^6 + 2*A*a*c^2*x^4 + A*a^2*c*x^2)*sqrt(a)*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(16*B*a*c^2*x^5 + 15*A*a*c^2*x^4 + 24*B*a^2*c*x^3 + 20*A*a^2*c*x^2 + 6*B*a^3*x + 3*A*a^3)*sqrt(c*x^2 + a))/(a^4*c^2*x^6 + 2*a^5*c*x^4 + a^6*x^2), -1/6*(15*(A*c^3*x^6 + 2*A*a*c^2*x^4 + A*a^2*c*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (16*B*a*c^2*x^5 + 15*A*a*c^2*x^4 + 24*B*a^2*c*x^3 + 20*A*a^2*c*x^2 + 6*B*a^3*x + 3*A*a^3)*sqrt(c*x^2 + a))/(a^4*c^2*x^6 + 2*a^5*c*x^4 + a^6*x^2)]","A",0
382,1,85,0,0.428398," ","integrate((e*x+d)/(c*x^2+a)^(7/2),x, algorithm=""fricas"")","\frac{{\left(8 \, c^{3} d x^{5} + 20 \, a c^{2} d x^{3} + 15 \, a^{2} c d x - 3 \, a^{3} e\right)} \sqrt{c x^{2} + a}}{15 \, {\left(a^{3} c^{4} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{5} c^{2} x^{2} + a^{6} c\right)}}"," ",0,"1/15*(8*c^3*d*x^5 + 20*a*c^2*d*x^3 + 15*a^2*c*d*x - 3*a^3*e)*sqrt(c*x^2 + a)/(a^3*c^4*x^6 + 3*a^4*c^3*x^4 + 3*a^5*c^2*x^2 + a^6*c)","A",0
383,1,108,0,0.435649," ","integrate((e*x+d)/(c*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(16 \, c^{4} d x^{7} + 56 \, a c^{3} d x^{5} + 70 \, a^{2} c^{2} d x^{3} + 35 \, a^{3} c d x - 5 \, a^{4} e\right)} \sqrt{c x^{2} + a}}{35 \, {\left(a^{4} c^{5} x^{8} + 4 \, a^{5} c^{4} x^{6} + 6 \, a^{6} c^{3} x^{4} + 4 \, a^{7} c^{2} x^{2} + a^{8} c\right)}}"," ",0,"1/35*(16*c^4*d*x^7 + 56*a*c^3*d*x^5 + 70*a^2*c^2*d*x^3 + 35*a^3*c*d*x - 5*a^4*e)*sqrt(c*x^2 + a)/(a^4*c^5*x^8 + 4*a^5*c^4*x^6 + 6*a^6*c^3*x^4 + 4*a^7*c^2*x^2 + a^8*c)","A",0
384,1,34,0,0.414207," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+a),x, algorithm=""fricas"")","\frac{2}{6435} \, {\left(429 \, B c x^{7} + 495 \, A c x^{6} + 585 \, B a x^{5} + 715 \, A a x^{4}\right)} \sqrt{x}"," ",0,"2/6435*(429*B*c*x^7 + 495*A*c*x^6 + 585*B*a*x^5 + 715*A*a*x^4)*sqrt(x)","A",0
385,1,34,0,0.425321," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+a),x, algorithm=""fricas"")","\frac{2}{9009} \, {\left(693 \, B c x^{6} + 819 \, A c x^{5} + 1001 \, B a x^{4} + 1287 \, A a x^{3}\right)} \sqrt{x}"," ",0,"2/9009*(693*B*c*x^6 + 819*A*c*x^5 + 1001*B*a*x^4 + 1287*A*a*x^3)*sqrt(x)","A",0
386,1,34,0,0.394042," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+a),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B c x^{5} + 385 \, A c x^{4} + 495 \, B a x^{3} + 693 \, A a x^{2}\right)} \sqrt{x}"," ",0,"2/3465*(315*B*c*x^5 + 385*A*c*x^4 + 495*B*a*x^3 + 693*A*a*x^2)*sqrt(x)","A",0
387,1,32,0,0.393319," ","integrate((B*x+A)*(c*x^2+a)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B c x^{4} + 45 \, A c x^{3} + 63 \, B a x^{2} + 105 \, A a x\right)} \sqrt{x}"," ",0,"2/315*(35*B*c*x^4 + 45*A*c*x^3 + 63*B*a*x^2 + 105*A*a*x)*sqrt(x)","A",0
388,1,29,0,0.406808," ","integrate((B*x+A)*(c*x^2+a)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, B c x^{3} + 21 \, A c x^{2} + 35 \, B a x + 105 \, A a\right)} \sqrt{x}"," ",0,"2/105*(15*B*c*x^3 + 21*A*c*x^2 + 35*B*a*x + 105*A*a)*sqrt(x)","A",0
389,1,29,0,0.406093," ","integrate((B*x+A)*(c*x^2+a)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c x^{3} + 5 \, A c x^{2} + 15 \, B a x - 15 \, A a\right)}}{15 \, \sqrt{x}}"," ",0,"2/15*(3*B*c*x^3 + 5*A*c*x^2 + 15*B*a*x - 15*A*a)/sqrt(x)","A",0
390,1,28,0,0.402181," ","integrate((B*x+A)*(c*x^2+a)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c x^{3} + 3 \, A c x^{2} - 3 \, B a x - A a\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(B*c*x^3 + 3*A*c*x^2 - 3*B*a*x - A*a)/x^(3/2)","A",0
391,1,29,0,0.410718," ","integrate((B*x+A)*(c*x^2+a)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c x^{3} - 15 \, A c x^{2} - 5 \, B a x - 3 \, A a\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(15*B*c*x^3 - 15*A*c*x^2 - 5*B*a*x - 3*A*a)/x^(5/2)","A",0
392,1,29,0,0.407545," ","integrate((B*x+A)*(c*x^2+a)/x^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, B c x^{3} + 35 \, A c x^{2} + 21 \, B a x + 15 \, A a\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"-2/105*(105*B*c*x^3 + 35*A*c*x^2 + 21*B*a*x + 15*A*a)/x^(7/2)","A",0
393,1,58,0,0.405294," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{2}{2078505} \, {\left(109395 \, B c^{2} x^{9} + 122265 \, A c^{2} x^{8} + 277134 \, B a c x^{7} + 319770 \, A a c x^{6} + 188955 \, B a^{2} x^{5} + 230945 \, A a^{2} x^{4}\right)} \sqrt{x}"," ",0,"2/2078505*(109395*B*c^2*x^9 + 122265*A*c^2*x^8 + 277134*B*a*c*x^7 + 319770*A*a*c*x^6 + 188955*B*a^2*x^5 + 230945*A*a^2*x^4)*sqrt(x)","A",0
394,1,58,0,0.412645," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{2}{765765} \, {\left(45045 \, B c^{2} x^{8} + 51051 \, A c^{2} x^{7} + 117810 \, B a c x^{6} + 139230 \, A a c x^{5} + 85085 \, B a^{2} x^{4} + 109395 \, A a^{2} x^{3}\right)} \sqrt{x}"," ",0,"2/765765*(45045*B*c^2*x^8 + 51051*A*c^2*x^7 + 117810*B*a*c*x^6 + 139230*A*a*c*x^5 + 85085*B*a^2*x^4 + 109395*A*a^2*x^3)*sqrt(x)","A",0
395,1,58,0,0.403848," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3003 \, B c^{2} x^{7} + 3465 \, A c^{2} x^{6} + 8190 \, B a c x^{5} + 10010 \, A a c x^{4} + 6435 \, B a^{2} x^{3} + 9009 \, A a^{2} x^{2}\right)} \sqrt{x}"," ",0,"2/45045*(3003*B*c^2*x^7 + 3465*A*c^2*x^6 + 8190*B*a*c*x^5 + 10010*A*a*c*x^4 + 6435*B*a^2*x^3 + 9009*A*a^2*x^2)*sqrt(x)","A",0
396,1,56,0,0.395257," ","integrate((B*x+A)*(c*x^2+a)^2*x^(1/2),x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3465 \, B c^{2} x^{6} + 4095 \, A c^{2} x^{5} + 10010 \, B a c x^{4} + 12870 \, A a c x^{3} + 9009 \, B a^{2} x^{2} + 15015 \, A a^{2} x\right)} \sqrt{x}"," ",0,"2/45045*(3465*B*c^2*x^6 + 4095*A*c^2*x^5 + 10010*B*a*c*x^4 + 12870*A*a*c*x^3 + 9009*B*a^2*x^2 + 15015*A*a^2*x)*sqrt(x)","A",0
397,1,53,0,0.421274," ","integrate((B*x+A)*(c*x^2+a)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B c^{2} x^{5} + 385 \, A c^{2} x^{4} + 990 \, B a c x^{3} + 1386 \, A a c x^{2} + 1155 \, B a^{2} x + 3465 \, A a^{2}\right)} \sqrt{x}"," ",0,"2/3465*(315*B*c^2*x^5 + 385*A*c^2*x^4 + 990*B*a*c*x^3 + 1386*A*a*c*x^2 + 1155*B*a^2*x + 3465*A*a^2)*sqrt(x)","A",0
398,1,53,0,0.424604," ","integrate((B*x+A)*(c*x^2+a)^2/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{2} x^{5} + 45 \, A c^{2} x^{4} + 126 \, B a c x^{3} + 210 \, A a c x^{2} + 315 \, B a^{2} x - 315 \, A a^{2}\right)}}{315 \, \sqrt{x}}"," ",0,"2/315*(35*B*c^2*x^5 + 45*A*c^2*x^4 + 126*B*a*c*x^3 + 210*A*a*c*x^2 + 315*B*a^2*x - 315*A*a^2)/sqrt(x)","A",0
399,1,53,0,0.406402," ","integrate((B*x+A)*(c*x^2+a)^2/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c^{2} x^{5} + 21 \, A c^{2} x^{4} + 70 \, B a c x^{3} + 210 \, A a c x^{2} - 105 \, B a^{2} x - 35 \, A a^{2}\right)}}{105 \, x^{\frac{3}{2}}}"," ",0,"2/105*(15*B*c^2*x^5 + 21*A*c^2*x^4 + 70*B*a*c*x^3 + 210*A*a*c*x^2 - 105*B*a^2*x - 35*A*a^2)/x^(3/2)","A",0
400,1,53,0,0.412174," ","integrate((B*x+A)*(c*x^2+a)^2/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{2} x^{5} + 5 \, A c^{2} x^{4} + 30 \, B a c x^{3} - 30 \, A a c x^{2} - 5 \, B a^{2} x - 3 \, A a^{2}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(3*B*c^2*x^5 + 5*A*c^2*x^4 + 30*B*a*c*x^3 - 30*A*a*c*x^2 - 5*B*a^2*x - 3*A*a^2)/x^(5/2)","A",0
401,1,53,0,0.413812," ","integrate((B*x+A)*(c*x^2+a)^2/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{2} x^{5} + 105 \, A c^{2} x^{4} - 210 \, B a c x^{3} - 70 \, A a c x^{2} - 21 \, B a^{2} x - 15 \, A a^{2}\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"2/105*(35*B*c^2*x^5 + 105*A*c^2*x^4 - 210*B*a*c*x^3 - 70*A*a*c*x^2 - 21*B*a^2*x - 15*A*a^2)/x^(7/2)","A",0
402,1,82,0,0.403960," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{2}{334639305} \, {\left(14549535 \, B c^{3} x^{11} + 15935205 \, A c^{3} x^{10} + 52837785 \, B a c^{2} x^{9} + 59053995 \, A a c^{2} x^{8} + 66927861 \, B a^{2} c x^{7} + 77224455 \, A a^{2} c x^{6} + 30421755 \, B a^{3} x^{5} + 37182145 \, A a^{3} x^{4}\right)} \sqrt{x}"," ",0,"2/334639305*(14549535*B*c^3*x^11 + 15935205*A*c^3*x^10 + 52837785*B*a*c^2*x^9 + 59053995*A*a*c^2*x^8 + 66927861*B*a^2*c*x^7 + 77224455*A*a^2*c*x^6 + 30421755*B*a^3*x^5 + 37182145*A*a^3*x^4)*sqrt(x)","A",0
403,1,82,0,0.406929," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{2}{14549535} \, {\left(692835 \, B c^{3} x^{10} + 765765 \, A c^{3} x^{9} + 2567565 \, B a c^{2} x^{8} + 2909907 \, A a c^{2} x^{7} + 3357585 \, B a^{2} c x^{6} + 3968055 \, A a^{2} c x^{5} + 1616615 \, B a^{3} x^{4} + 2078505 \, A a^{3} x^{3}\right)} \sqrt{x}"," ",0,"2/14549535*(692835*B*c^3*x^10 + 765765*A*c^3*x^9 + 2567565*B*a*c^2*x^8 + 2909907*A*a*c^2*x^7 + 3357585*B*a^2*c*x^6 + 3968055*A*a^2*c*x^5 + 1616615*B*a^3*x^4 + 2078505*A*a^3*x^3)*sqrt(x)","A",0
404,1,82,0,0.410362," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{2}{4849845} \, {\left(255255 \, B c^{3} x^{9} + 285285 \, A c^{3} x^{8} + 969969 \, B a c^{2} x^{7} + 1119195 \, A a c^{2} x^{6} + 1322685 \, B a^{2} c x^{5} + 1616615 \, A a^{2} c x^{4} + 692835 \, B a^{3} x^{3} + 969969 \, A a^{3} x^{2}\right)} \sqrt{x}"," ",0,"2/4849845*(255255*B*c^3*x^9 + 285285*A*c^3*x^8 + 969969*B*a*c^2*x^7 + 1119195*A*a*c^2*x^6 + 1322685*B*a^2*c*x^5 + 1616615*A*a^2*c*x^4 + 692835*B*a^3*x^3 + 969969*A*a^3*x^2)*sqrt(x)","A",0
405,1,80,0,0.404404," ","integrate((B*x+A)*(c*x^2+a)^3*x^(1/2),x, algorithm=""fricas"")","\frac{2}{255255} \, {\left(15015 \, B c^{3} x^{8} + 17017 \, A c^{3} x^{7} + 58905 \, B a c^{2} x^{6} + 69615 \, A a c^{2} x^{5} + 85085 \, B a^{2} c x^{4} + 109395 \, A a^{2} c x^{3} + 51051 \, B a^{3} x^{2} + 85085 \, A a^{3} x\right)} \sqrt{x}"," ",0,"2/255255*(15015*B*c^3*x^8 + 17017*A*c^3*x^7 + 58905*B*a*c^2*x^6 + 69615*A*a*c^2*x^5 + 85085*B*a^2*c*x^4 + 109395*A*a^2*c*x^3 + 51051*B*a^3*x^2 + 85085*A*a^3*x)*sqrt(x)","A",0
406,1,77,0,0.405545," ","integrate((B*x+A)*(c*x^2+a)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{15015} \, {\left(1001 \, B c^{3} x^{7} + 1155 \, A c^{3} x^{6} + 4095 \, B a c^{2} x^{5} + 5005 \, A a c^{2} x^{4} + 6435 \, B a^{2} c x^{3} + 9009 \, A a^{2} c x^{2} + 5005 \, B a^{3} x + 15015 \, A a^{3}\right)} \sqrt{x}"," ",0,"2/15015*(1001*B*c^3*x^7 + 1155*A*c^3*x^6 + 4095*B*a*c^2*x^5 + 5005*A*a*c^2*x^4 + 6435*B*a^2*c*x^3 + 9009*A*a^2*c*x^2 + 5005*B*a^3*x + 15015*A*a^3)*sqrt(x)","A",0
407,1,77,0,0.411406," ","integrate((B*x+A)*(c*x^2+a)^3/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, B c^{3} x^{7} + 1365 \, A c^{3} x^{6} + 5005 \, B a c^{2} x^{5} + 6435 \, A a c^{2} x^{4} + 9009 \, B a^{2} c x^{3} + 15015 \, A a^{2} c x^{2} + 15015 \, B a^{3} x - 15015 \, A a^{3}\right)}}{15015 \, \sqrt{x}}"," ",0,"2/15015*(1155*B*c^3*x^7 + 1365*A*c^3*x^6 + 5005*B*a*c^2*x^5 + 6435*A*a*c^2*x^4 + 9009*B*a^2*c*x^3 + 15015*A*a^2*c*x^2 + 15015*B*a^3*x - 15015*A*a^3)/sqrt(x)","A",0
408,1,77,0,0.400984," ","integrate((B*x+A)*(c*x^2+a)^3/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B c^{3} x^{7} + 385 \, A c^{3} x^{6} + 1485 \, B a c^{2} x^{5} + 2079 \, A a c^{2} x^{4} + 3465 \, B a^{2} c x^{3} + 10395 \, A a^{2} c x^{2} - 3465 \, B a^{3} x - 1155 \, A a^{3}\right)}}{3465 \, x^{\frac{3}{2}}}"," ",0,"2/3465*(315*B*c^3*x^7 + 385*A*c^3*x^6 + 1485*B*a*c^2*x^5 + 2079*A*a*c^2*x^4 + 3465*B*a^2*c*x^3 + 10395*A*a^2*c*x^2 - 3465*B*a^3*x - 1155*A*a^3)/x^(3/2)","A",0
409,1,77,0,0.395036," ","integrate((B*x+A)*(c*x^2+a)^3/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{3} x^{7} + 45 \, A c^{3} x^{6} + 189 \, B a c^{2} x^{5} + 315 \, A a c^{2} x^{4} + 945 \, B a^{2} c x^{3} - 945 \, A a^{2} c x^{2} - 105 \, B a^{3} x - 63 \, A a^{3}\right)}}{315 \, x^{\frac{5}{2}}}"," ",0,"2/315*(35*B*c^3*x^7 + 45*A*c^3*x^6 + 189*B*a*c^2*x^5 + 315*A*a*c^2*x^4 + 945*B*a^2*c*x^3 - 945*A*a^2*c*x^2 - 105*B*a^3*x - 63*A*a^3)/x^(5/2)","A",0
410,1,77,0,0.418695," ","integrate((B*x+A)*(c*x^2+a)^3/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B c^{3} x^{7} + 7 \, A c^{3} x^{6} + 35 \, B a c^{2} x^{5} + 105 \, A a c^{2} x^{4} - 105 \, B a^{2} c x^{3} - 35 \, A a^{2} c x^{2} - 7 \, B a^{3} x - 5 \, A a^{3}\right)}}{35 \, x^{\frac{7}{2}}}"," ",0,"2/35*(5*B*c^3*x^7 + 7*A*c^3*x^6 + 35*B*a*c^2*x^5 + 105*A*a*c^2*x^4 - 105*B*a^2*c*x^3 - 35*A*a^2*c*x^2 - 7*B*a^3*x - 5*A*a^3)/x^(7/2)","A",0
411,1,77,0,0.404001," ","integrate((B*x+A)*(c*x^2+a)^3/x^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B c^{3} x^{7} + 105 \, A c^{3} x^{6} + 945 \, B a c^{2} x^{5} - 945 \, A a c^{2} x^{4} - 315 \, B a^{2} c x^{3} - 189 \, A a^{2} c x^{2} - 45 \, B a^{3} x - 35 \, A a^{3}\right)}}{315 \, x^{\frac{9}{2}}}"," ",0,"2/315*(63*B*c^3*x^7 + 105*A*c^3*x^6 + 945*B*a*c^2*x^5 - 945*A*a*c^2*x^4 - 315*B*a^2*c*x^3 - 189*A*a^2*c*x^2 - 45*B*a^3*x - 35*A*a^3)/x^(9/2)","A",0
412,1,862,0,0.462521," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{15 \, c^{2} \sqrt{\frac{c^{4} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} + 2 \, A B a^{2}}{c^{4}}} \log\left(-{\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} \sqrt{x} + {\left(A c^{7} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} + B^{3} a^{3} c^{2} - A^{2} B a^{2} c^{3}\right)} \sqrt{\frac{c^{4} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} + 2 \, A B a^{2}}{c^{4}}}\right) - 15 \, c^{2} \sqrt{\frac{c^{4} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} + 2 \, A B a^{2}}{c^{4}}} \log\left(-{\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} \sqrt{x} - {\left(A c^{7} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} + B^{3} a^{3} c^{2} - A^{2} B a^{2} c^{3}\right)} \sqrt{\frac{c^{4} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} + 2 \, A B a^{2}}{c^{4}}}\right) - 15 \, c^{2} \sqrt{-\frac{c^{4} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} - 2 \, A B a^{2}}{c^{4}}} \log\left(-{\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} \sqrt{x} + {\left(A c^{7} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} - B^{3} a^{3} c^{2} + A^{2} B a^{2} c^{3}\right)} \sqrt{-\frac{c^{4} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} - 2 \, A B a^{2}}{c^{4}}}\right) + 15 \, c^{2} \sqrt{-\frac{c^{4} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} - 2 \, A B a^{2}}{c^{4}}} \log\left(-{\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} \sqrt{x} - {\left(A c^{7} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} - B^{3} a^{3} c^{2} + A^{2} B a^{2} c^{3}\right)} \sqrt{-\frac{c^{4} \sqrt{-\frac{B^{4} a^{5} - 2 \, A^{2} B^{2} a^{4} c + A^{4} a^{3} c^{2}}{c^{9}}} - 2 \, A B a^{2}}{c^{4}}}\right) - 4 \, {\left(3 \, B c x^{2} + 5 \, A c x - 15 \, B a\right)} \sqrt{x}}{30 \, c^{2}}"," ",0,"-1/30*(15*c^2*sqrt((c^4*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) + 2*A*B*a^2)/c^4)*log(-(B^4*a^4 - A^4*a^2*c^2)*sqrt(x) + (A*c^7*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) + B^3*a^3*c^2 - A^2*B*a^2*c^3)*sqrt((c^4*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) + 2*A*B*a^2)/c^4)) - 15*c^2*sqrt((c^4*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) + 2*A*B*a^2)/c^4)*log(-(B^4*a^4 - A^4*a^2*c^2)*sqrt(x) - (A*c^7*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) + B^3*a^3*c^2 - A^2*B*a^2*c^3)*sqrt((c^4*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) + 2*A*B*a^2)/c^4)) - 15*c^2*sqrt(-(c^4*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) - 2*A*B*a^2)/c^4)*log(-(B^4*a^4 - A^4*a^2*c^2)*sqrt(x) + (A*c^7*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) - B^3*a^3*c^2 + A^2*B*a^2*c^3)*sqrt(-(c^4*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) - 2*A*B*a^2)/c^4)) + 15*c^2*sqrt(-(c^4*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) - 2*A*B*a^2)/c^4)*log(-(B^4*a^4 - A^4*a^2*c^2)*sqrt(x) - (A*c^7*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) - B^3*a^3*c^2 + A^2*B*a^2*c^3)*sqrt(-(c^4*sqrt(-(B^4*a^5 - 2*A^2*B^2*a^4*c + A^4*a^3*c^2)/c^9) - 2*A*B*a^2)/c^4)) - 4*(3*B*c*x^2 + 5*A*c*x - 15*B*a)*sqrt(x))/c^2","B",0
413,1,772,0,0.464521," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{3 \, c \sqrt{-\frac{c^{3} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} + 2 \, A B a}{c^{3}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(B c^{5} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} - A B^{2} a c^{2} + A^{3} c^{3}\right)} \sqrt{-\frac{c^{3} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} + 2 \, A B a}{c^{3}}}\right) - 3 \, c \sqrt{-\frac{c^{3} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} + 2 \, A B a}{c^{3}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(B c^{5} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} - A B^{2} a c^{2} + A^{3} c^{3}\right)} \sqrt{-\frac{c^{3} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} + 2 \, A B a}{c^{3}}}\right) - 3 \, c \sqrt{\frac{c^{3} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} - 2 \, A B a}{c^{3}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(B c^{5} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} + A B^{2} a c^{2} - A^{3} c^{3}\right)} \sqrt{\frac{c^{3} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} - 2 \, A B a}{c^{3}}}\right) + 3 \, c \sqrt{\frac{c^{3} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} - 2 \, A B a}{c^{3}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(B c^{5} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} + A B^{2} a c^{2} - A^{3} c^{3}\right)} \sqrt{\frac{c^{3} \sqrt{-\frac{B^{4} a^{3} - 2 \, A^{2} B^{2} a^{2} c + A^{4} a c^{2}}{c^{7}}} - 2 \, A B a}{c^{3}}}\right) - 4 \, {\left(B x + 3 \, A\right)} \sqrt{x}}{6 \, c}"," ",0,"-1/6*(3*c*sqrt(-(c^3*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) + 2*A*B*a)/c^3)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (B*c^5*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) - A*B^2*a*c^2 + A^3*c^3)*sqrt(-(c^3*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) + 2*A*B*a)/c^3)) - 3*c*sqrt(-(c^3*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) + 2*A*B*a)/c^3)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (B*c^5*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) - A*B^2*a*c^2 + A^3*c^3)*sqrt(-(c^3*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) + 2*A*B*a)/c^3)) - 3*c*sqrt((c^3*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) - 2*A*B*a)/c^3)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (B*c^5*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) + A*B^2*a*c^2 - A^3*c^3)*sqrt((c^3*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) - 2*A*B*a)/c^3)) + 3*c*sqrt((c^3*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) - 2*A*B*a)/c^3)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (B*c^5*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) + A*B^2*a*c^2 - A^3*c^3)*sqrt((c^3*sqrt(-(B^4*a^3 - 2*A^2*B^2*a^2*c + A^4*a*c^2)/c^7) - 2*A*B*a)/c^3)) - 4*(B*x + 3*A)*sqrt(x))/c","B",0
414,1,764,0,0.431954," ","integrate(x^(1/2)*(B*x+A)/(c*x^2+a),x, algorithm=""fricas"")","\frac{c \sqrt{\frac{c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} + 2 \, A B}{c^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(A a c^{4} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} + B^{3} a^{2} c - A^{2} B a c^{2}\right)} \sqrt{\frac{c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} + 2 \, A B}{c^{2}}}\right) - c \sqrt{\frac{c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} + 2 \, A B}{c^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(A a c^{4} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} + B^{3} a^{2} c - A^{2} B a c^{2}\right)} \sqrt{\frac{c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} + 2 \, A B}{c^{2}}}\right) - c \sqrt{-\frac{c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} - 2 \, A B}{c^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(A a c^{4} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} - B^{3} a^{2} c + A^{2} B a c^{2}\right)} \sqrt{-\frac{c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} - 2 \, A B}{c^{2}}}\right) + c \sqrt{-\frac{c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} - 2 \, A B}{c^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(A a c^{4} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} - B^{3} a^{2} c + A^{2} B a c^{2}\right)} \sqrt{-\frac{c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a c^{5}}} - 2 \, A B}{c^{2}}}\right) + 4 \, B \sqrt{x}}{2 \, c}"," ",0,"1/2*(c*sqrt((c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) + 2*A*B)/c^2)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (A*a*c^4*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) + B^3*a^2*c - A^2*B*a*c^2)*sqrt((c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) + 2*A*B)/c^2)) - c*sqrt((c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) + 2*A*B)/c^2)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (A*a*c^4*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) + B^3*a^2*c - A^2*B*a*c^2)*sqrt((c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) + 2*A*B)/c^2)) - c*sqrt(-(c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) - 2*A*B)/c^2)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (A*a*c^4*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) - B^3*a^2*c + A^2*B*a*c^2)*sqrt(-(c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) - 2*A*B)/c^2)) + c*sqrt(-(c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) - 2*A*B)/c^2)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (A*a*c^4*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) - B^3*a^2*c + A^2*B*a*c^2)*sqrt(-(c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a*c^5)) - 2*A*B)/c^2)) + 4*B*sqrt(x))/c","B",0
415,1,775,0,0.458263," ","integrate((B*x+A)/x^(1/2)/(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-\frac{a c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 2 \, A B}{a c}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(B a^{3} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - A B^{2} a^{2} c + A^{3} a c^{2}\right)} \sqrt{-\frac{a c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 2 \, A B}{a c}}\right) - \frac{1}{2} \, \sqrt{-\frac{a c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 2 \, A B}{a c}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(B a^{3} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - A B^{2} a^{2} c + A^{3} a c^{2}\right)} \sqrt{-\frac{a c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 2 \, A B}{a c}}\right) - \frac{1}{2} \, \sqrt{\frac{a c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 2 \, A B}{a c}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(B a^{3} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + A B^{2} a^{2} c - A^{3} a c^{2}\right)} \sqrt{\frac{a c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 2 \, A B}{a c}}\right) + \frac{1}{2} \, \sqrt{\frac{a c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 2 \, A B}{a c}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(B a^{3} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + A B^{2} a^{2} c - A^{3} a c^{2}\right)} \sqrt{\frac{a c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 2 \, A B}{a c}}\right)"," ",0,"1/2*sqrt(-(a*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 2*A*B)/(a*c))*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (B*a^3*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - A*B^2*a^2*c + A^3*a*c^2)*sqrt(-(a*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 2*A*B)/(a*c))) - 1/2*sqrt(-(a*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 2*A*B)/(a*c))*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (B*a^3*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - A*B^2*a^2*c + A^3*a*c^2)*sqrt(-(a*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 2*A*B)/(a*c))) - 1/2*sqrt((a*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 2*A*B)/(a*c))*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (B*a^3*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + A*B^2*a^2*c - A^3*a*c^2)*sqrt((a*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 2*A*B)/(a*c))) + 1/2*sqrt((a*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 2*A*B)/(a*c))*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (B*a^3*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + A*B^2*a^2*c - A^3*a*c^2)*sqrt((a*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 2*A*B)/(a*c)))","B",0
416,1,767,0,0.441774," ","integrate((B*x+A)/x^(3/2)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{a x \sqrt{\frac{a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} + 2 \, A B}{a^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(A a^{4} c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} + B^{3} a^{3} - A^{2} B a^{2} c\right)} \sqrt{\frac{a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} + 2 \, A B}{a^{2}}}\right) - a x \sqrt{\frac{a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} + 2 \, A B}{a^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(A a^{4} c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} + B^{3} a^{3} - A^{2} B a^{2} c\right)} \sqrt{\frac{a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} + 2 \, A B}{a^{2}}}\right) - a x \sqrt{-\frac{a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} - 2 \, A B}{a^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(A a^{4} c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} - B^{3} a^{3} + A^{2} B a^{2} c\right)} \sqrt{-\frac{a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} - 2 \, A B}{a^{2}}}\right) + a x \sqrt{-\frac{a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} - 2 \, A B}{a^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(A a^{4} c \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} - B^{3} a^{3} + A^{2} B a^{2} c\right)} \sqrt{-\frac{a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c}} - 2 \, A B}{a^{2}}}\right) + 4 \, A \sqrt{x}}{2 \, a x}"," ",0,"-1/2*(a*x*sqrt((a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) + 2*A*B)/a^2)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (A*a^4*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) + B^3*a^3 - A^2*B*a^2*c)*sqrt((a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) + 2*A*B)/a^2)) - a*x*sqrt((a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) + 2*A*B)/a^2)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (A*a^4*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) + B^3*a^3 - A^2*B*a^2*c)*sqrt((a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) + 2*A*B)/a^2)) - a*x*sqrt(-(a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) - 2*A*B)/a^2)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (A*a^4*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) - B^3*a^3 + A^2*B*a^2*c)*sqrt(-(a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) - 2*A*B)/a^2)) + a*x*sqrt(-(a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) - 2*A*B)/a^2)*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (A*a^4*c*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) - B^3*a^3 + A^2*B*a^2*c)*sqrt(-(a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c)) - 2*A*B)/a^2)) + 4*A*sqrt(x))/(a*x)","B",0
417,1,802,0,0.449709," ","integrate((B*x+A)/x^(5/2)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{3 \, a x^{2} \sqrt{-\frac{a^{3} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} + 2 \, A B c}{a^{3}}} \log\left(-{\left(B^{4} a^{2} c - A^{4} c^{3}\right)} \sqrt{x} + {\left(B a^{6} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} - A B^{2} a^{3} c + A^{3} a^{2} c^{2}\right)} \sqrt{-\frac{a^{3} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} + 2 \, A B c}{a^{3}}}\right) - 3 \, a x^{2} \sqrt{-\frac{a^{3} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} + 2 \, A B c}{a^{3}}} \log\left(-{\left(B^{4} a^{2} c - A^{4} c^{3}\right)} \sqrt{x} - {\left(B a^{6} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} - A B^{2} a^{3} c + A^{3} a^{2} c^{2}\right)} \sqrt{-\frac{a^{3} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} + 2 \, A B c}{a^{3}}}\right) - 3 \, a x^{2} \sqrt{\frac{a^{3} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} - 2 \, A B c}{a^{3}}} \log\left(-{\left(B^{4} a^{2} c - A^{4} c^{3}\right)} \sqrt{x} + {\left(B a^{6} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} + A B^{2} a^{3} c - A^{3} a^{2} c^{2}\right)} \sqrt{\frac{a^{3} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} - 2 \, A B c}{a^{3}}}\right) + 3 \, a x^{2} \sqrt{\frac{a^{3} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} - 2 \, A B c}{a^{3}}} \log\left(-{\left(B^{4} a^{2} c - A^{4} c^{3}\right)} \sqrt{x} - {\left(B a^{6} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} + A B^{2} a^{3} c - A^{3} a^{2} c^{2}\right)} \sqrt{\frac{a^{3} \sqrt{-\frac{B^{4} a^{2} c - 2 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}}{a^{7}}} - 2 \, A B c}{a^{3}}}\right) + 4 \, {\left(3 \, B x + A\right)} \sqrt{x}}{6 \, a x^{2}}"," ",0,"-1/6*(3*a*x^2*sqrt(-(a^3*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) + 2*A*B*c)/a^3)*log(-(B^4*a^2*c - A^4*c^3)*sqrt(x) + (B*a^6*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) - A*B^2*a^3*c + A^3*a^2*c^2)*sqrt(-(a^3*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) + 2*A*B*c)/a^3)) - 3*a*x^2*sqrt(-(a^3*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) + 2*A*B*c)/a^3)*log(-(B^4*a^2*c - A^4*c^3)*sqrt(x) - (B*a^6*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) - A*B^2*a^3*c + A^3*a^2*c^2)*sqrt(-(a^3*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) + 2*A*B*c)/a^3)) - 3*a*x^2*sqrt((a^3*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) - 2*A*B*c)/a^3)*log(-(B^4*a^2*c - A^4*c^3)*sqrt(x) + (B*a^6*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) + A*B^2*a^3*c - A^3*a^2*c^2)*sqrt((a^3*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) - 2*A*B*c)/a^3)) + 3*a*x^2*sqrt((a^3*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) - 2*A*B*c)/a^3)*log(-(B^4*a^2*c - A^4*c^3)*sqrt(x) - (B*a^6*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) + A*B^2*a^3*c - A^3*a^2*c^2)*sqrt((a^3*sqrt(-(B^4*a^2*c - 2*A^2*B^2*a*c^2 + A^4*c^3)/a^7) - 2*A*B*c)/a^3)) + 4*(3*B*x + A)*sqrt(x))/(a*x^2)","B",0
418,1,869,0,0.443620," ","integrate((B*x+A)/x^(7/2)/(c*x^2+a),x, algorithm=""fricas"")","\frac{15 \, a^{2} x^{3} \sqrt{\frac{a^{4} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} + 2 \, A B c^{2}}{a^{4}}} \log\left(-{\left(B^{4} a^{2} c^{2} - A^{4} c^{4}\right)} \sqrt{x} + {\left(A a^{7} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} + B^{3} a^{4} c - A^{2} B a^{3} c^{2}\right)} \sqrt{\frac{a^{4} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} + 2 \, A B c^{2}}{a^{4}}}\right) - 15 \, a^{2} x^{3} \sqrt{\frac{a^{4} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} + 2 \, A B c^{2}}{a^{4}}} \log\left(-{\left(B^{4} a^{2} c^{2} - A^{4} c^{4}\right)} \sqrt{x} - {\left(A a^{7} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} + B^{3} a^{4} c - A^{2} B a^{3} c^{2}\right)} \sqrt{\frac{a^{4} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} + 2 \, A B c^{2}}{a^{4}}}\right) - 15 \, a^{2} x^{3} \sqrt{-\frac{a^{4} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} - 2 \, A B c^{2}}{a^{4}}} \log\left(-{\left(B^{4} a^{2} c^{2} - A^{4} c^{4}\right)} \sqrt{x} + {\left(A a^{7} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} - B^{3} a^{4} c + A^{2} B a^{3} c^{2}\right)} \sqrt{-\frac{a^{4} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} - 2 \, A B c^{2}}{a^{4}}}\right) + 15 \, a^{2} x^{3} \sqrt{-\frac{a^{4} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} - 2 \, A B c^{2}}{a^{4}}} \log\left(-{\left(B^{4} a^{2} c^{2} - A^{4} c^{4}\right)} \sqrt{x} - {\left(A a^{7} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} - B^{3} a^{4} c + A^{2} B a^{3} c^{2}\right)} \sqrt{-\frac{a^{4} \sqrt{-\frac{B^{4} a^{2} c^{3} - 2 \, A^{2} B^{2} a c^{4} + A^{4} c^{5}}{a^{9}}} - 2 \, A B c^{2}}{a^{4}}}\right) + 4 \, {\left(15 \, A c x^{2} - 5 \, B a x - 3 \, A a\right)} \sqrt{x}}{30 \, a^{2} x^{3}}"," ",0,"1/30*(15*a^2*x^3*sqrt((a^4*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) + 2*A*B*c^2)/a^4)*log(-(B^4*a^2*c^2 - A^4*c^4)*sqrt(x) + (A*a^7*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) + B^3*a^4*c - A^2*B*a^3*c^2)*sqrt((a^4*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) + 2*A*B*c^2)/a^4)) - 15*a^2*x^3*sqrt((a^4*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) + 2*A*B*c^2)/a^4)*log(-(B^4*a^2*c^2 - A^4*c^4)*sqrt(x) - (A*a^7*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) + B^3*a^4*c - A^2*B*a^3*c^2)*sqrt((a^4*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) + 2*A*B*c^2)/a^4)) - 15*a^2*x^3*sqrt(-(a^4*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) - 2*A*B*c^2)/a^4)*log(-(B^4*a^2*c^2 - A^4*c^4)*sqrt(x) + (A*a^7*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) - B^3*a^4*c + A^2*B*a^3*c^2)*sqrt(-(a^4*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) - 2*A*B*c^2)/a^4)) + 15*a^2*x^3*sqrt(-(a^4*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) - 2*A*B*c^2)/a^4)*log(-(B^4*a^2*c^2 - A^4*c^4)*sqrt(x) - (A*a^7*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) - B^3*a^4*c + A^2*B*a^3*c^2)*sqrt(-(a^4*sqrt(-(B^4*a^2*c^3 - 2*A^2*B^2*a*c^4 + A^4*c^5)/a^9) - 2*A*B*c^2)/a^4)) + 4*(15*A*c*x^2 - 5*B*a*x - 3*A*a)*sqrt(x))/(a^2*x^3)","B",0
419,1,884,0,0.444379," ","integrate((B*x+A)/x^(9/2)/(c*x^2+a),x, algorithm=""fricas"")","\frac{105 \, a^{2} x^{4} \sqrt{-\frac{a^{5} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} + 2 \, A B c^{3}}{a^{5}}} \log\left(-{\left(B^{4} a^{2} c^{4} - A^{4} c^{6}\right)} \sqrt{x} + {\left(B a^{9} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} - A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} \sqrt{-\frac{a^{5} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} + 2 \, A B c^{3}}{a^{5}}}\right) - 105 \, a^{2} x^{4} \sqrt{-\frac{a^{5} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} + 2 \, A B c^{3}}{a^{5}}} \log\left(-{\left(B^{4} a^{2} c^{4} - A^{4} c^{6}\right)} \sqrt{x} - {\left(B a^{9} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} - A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} \sqrt{-\frac{a^{5} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} + 2 \, A B c^{3}}{a^{5}}}\right) - 105 \, a^{2} x^{4} \sqrt{\frac{a^{5} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} - 2 \, A B c^{3}}{a^{5}}} \log\left(-{\left(B^{4} a^{2} c^{4} - A^{4} c^{6}\right)} \sqrt{x} + {\left(B a^{9} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} + A B^{2} a^{4} c^{3} - A^{3} a^{3} c^{4}\right)} \sqrt{\frac{a^{5} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} - 2 \, A B c^{3}}{a^{5}}}\right) + 105 \, a^{2} x^{4} \sqrt{\frac{a^{5} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} - 2 \, A B c^{3}}{a^{5}}} \log\left(-{\left(B^{4} a^{2} c^{4} - A^{4} c^{6}\right)} \sqrt{x} - {\left(B a^{9} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} + A B^{2} a^{4} c^{3} - A^{3} a^{3} c^{4}\right)} \sqrt{\frac{a^{5} \sqrt{-\frac{B^{4} a^{2} c^{5} - 2 \, A^{2} B^{2} a c^{6} + A^{4} c^{7}}{a^{11}}} - 2 \, A B c^{3}}{a^{5}}}\right) + 4 \, {\left(105 \, B c x^{3} + 35 \, A c x^{2} - 21 \, B a x - 15 \, A a\right)} \sqrt{x}}{210 \, a^{2} x^{4}}"," ",0,"1/210*(105*a^2*x^4*sqrt(-(a^5*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) + 2*A*B*c^3)/a^5)*log(-(B^4*a^2*c^4 - A^4*c^6)*sqrt(x) + (B*a^9*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) - A*B^2*a^4*c^3 + A^3*a^3*c^4)*sqrt(-(a^5*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) + 2*A*B*c^3)/a^5)) - 105*a^2*x^4*sqrt(-(a^5*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) + 2*A*B*c^3)/a^5)*log(-(B^4*a^2*c^4 - A^4*c^6)*sqrt(x) - (B*a^9*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) - A*B^2*a^4*c^3 + A^3*a^3*c^4)*sqrt(-(a^5*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) + 2*A*B*c^3)/a^5)) - 105*a^2*x^4*sqrt((a^5*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) - 2*A*B*c^3)/a^5)*log(-(B^4*a^2*c^4 - A^4*c^6)*sqrt(x) + (B*a^9*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) + A*B^2*a^4*c^3 - A^3*a^3*c^4)*sqrt((a^5*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) - 2*A*B*c^3)/a^5)) + 105*a^2*x^4*sqrt((a^5*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) - 2*A*B*c^3)/a^5)*log(-(B^4*a^2*c^4 - A^4*c^6)*sqrt(x) - (B*a^9*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) + A*B^2*a^4*c^3 - A^3*a^3*c^4)*sqrt((a^5*sqrt(-(B^4*a^2*c^5 - 2*A^2*B^2*a*c^6 + A^4*c^7)/a^11) - 2*A*B*c^3)/a^5)) + 4*(105*B*c*x^3 + 35*A*c*x^2 - 21*B*a*x - 15*A*a)*sqrt(x))/(a^2*x^4)","B",0
420,1,884,0,0.440633," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(c^{3} x^{2} + a c^{2}\right)} \sqrt{\frac{c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} + 30 \, A B}{c^{4}}} \log\left(-{\left(625 \, B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(3 \, A a c^{7} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} + 125 \, B^{3} a^{2} c^{2} - 45 \, A^{2} B a c^{3}\right)} \sqrt{\frac{c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} + 30 \, A B}{c^{4}}}\right) - {\left(c^{3} x^{2} + a c^{2}\right)} \sqrt{\frac{c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} + 30 \, A B}{c^{4}}} \log\left(-{\left(625 \, B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(3 \, A a c^{7} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} + 125 \, B^{3} a^{2} c^{2} - 45 \, A^{2} B a c^{3}\right)} \sqrt{\frac{c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} + 30 \, A B}{c^{4}}}\right) - {\left(c^{3} x^{2} + a c^{2}\right)} \sqrt{-\frac{c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} - 30 \, A B}{c^{4}}} \log\left(-{\left(625 \, B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(3 \, A a c^{7} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} - 125 \, B^{3} a^{2} c^{2} + 45 \, A^{2} B a c^{3}\right)} \sqrt{-\frac{c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} - 30 \, A B}{c^{4}}}\right) + {\left(c^{3} x^{2} + a c^{2}\right)} \sqrt{-\frac{c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} - 30 \, A B}{c^{4}}} \log\left(-{\left(625 \, B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(3 \, A a c^{7} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} - 125 \, B^{3} a^{2} c^{2} + 45 \, A^{2} B a c^{3}\right)} \sqrt{-\frac{c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a c^{9}}} - 30 \, A B}{c^{4}}}\right) + 4 \, {\left(4 \, B c x^{2} - A c x + 5 \, B a\right)} \sqrt{x}}{8 \, {\left(c^{3} x^{2} + a c^{2}\right)}}"," ",0,"1/8*((c^3*x^2 + a*c^2)*sqrt((c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) + 30*A*B)/c^4)*log(-(625*B^4*a^2 - 81*A^4*c^2)*sqrt(x) + (3*A*a*c^7*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) + 125*B^3*a^2*c^2 - 45*A^2*B*a*c^3)*sqrt((c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) + 30*A*B)/c^4)) - (c^3*x^2 + a*c^2)*sqrt((c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) + 30*A*B)/c^4)*log(-(625*B^4*a^2 - 81*A^4*c^2)*sqrt(x) - (3*A*a*c^7*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) + 125*B^3*a^2*c^2 - 45*A^2*B*a*c^3)*sqrt((c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) + 30*A*B)/c^4)) - (c^3*x^2 + a*c^2)*sqrt(-(c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) - 30*A*B)/c^4)*log(-(625*B^4*a^2 - 81*A^4*c^2)*sqrt(x) + (3*A*a*c^7*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) - 125*B^3*a^2*c^2 + 45*A^2*B*a*c^3)*sqrt(-(c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) - 30*A*B)/c^4)) + (c^3*x^2 + a*c^2)*sqrt(-(c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) - 30*A*B)/c^4)*log(-(625*B^4*a^2 - 81*A^4*c^2)*sqrt(x) - (3*A*a*c^7*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) - 125*B^3*a^2*c^2 + 45*A^2*B*a*c^3)*sqrt(-(c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a*c^9)) - 30*A*B)/c^4)) + 4*(4*B*c*x^2 - A*c*x + 5*B*a)*sqrt(x))/(c^3*x^2 + a*c^2)","B",0
421,1,888,0,0.467212," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(c^{2} x^{2} + a c\right)} \sqrt{-\frac{a c^{3} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} + 6 \, A B}{a c^{3}}} \log\left(-{\left(81 \, B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(3 \, B a^{3} c^{5} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} - 9 \, A B^{2} a^{2} c^{2} + A^{3} a c^{3}\right)} \sqrt{-\frac{a c^{3} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} + 6 \, A B}{a c^{3}}}\right) - {\left(c^{2} x^{2} + a c\right)} \sqrt{-\frac{a c^{3} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} + 6 \, A B}{a c^{3}}} \log\left(-{\left(81 \, B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(3 \, B a^{3} c^{5} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} - 9 \, A B^{2} a^{2} c^{2} + A^{3} a c^{3}\right)} \sqrt{-\frac{a c^{3} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} + 6 \, A B}{a c^{3}}}\right) - {\left(c^{2} x^{2} + a c\right)} \sqrt{\frac{a c^{3} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} - 6 \, A B}{a c^{3}}} \log\left(-{\left(81 \, B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(3 \, B a^{3} c^{5} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} + 9 \, A B^{2} a^{2} c^{2} - A^{3} a c^{3}\right)} \sqrt{\frac{a c^{3} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} - 6 \, A B}{a c^{3}}}\right) + {\left(c^{2} x^{2} + a c\right)} \sqrt{\frac{a c^{3} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} - 6 \, A B}{a c^{3}}} \log\left(-{\left(81 \, B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(3 \, B a^{3} c^{5} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} + 9 \, A B^{2} a^{2} c^{2} - A^{3} a c^{3}\right)} \sqrt{\frac{a c^{3} \sqrt{-\frac{81 \, B^{4} a^{2} - 18 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{7}}} - 6 \, A B}{a c^{3}}}\right) - 4 \, {\left(B x + A\right)} \sqrt{x}}{8 \, {\left(c^{2} x^{2} + a c\right)}}"," ",0,"1/8*((c^2*x^2 + a*c)*sqrt(-(a*c^3*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) + 6*A*B)/(a*c^3))*log(-(81*B^4*a^2 - A^4*c^2)*sqrt(x) + (3*B*a^3*c^5*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) - 9*A*B^2*a^2*c^2 + A^3*a*c^3)*sqrt(-(a*c^3*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) + 6*A*B)/(a*c^3))) - (c^2*x^2 + a*c)*sqrt(-(a*c^3*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) + 6*A*B)/(a*c^3))*log(-(81*B^4*a^2 - A^4*c^2)*sqrt(x) - (3*B*a^3*c^5*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) - 9*A*B^2*a^2*c^2 + A^3*a*c^3)*sqrt(-(a*c^3*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) + 6*A*B)/(a*c^3))) - (c^2*x^2 + a*c)*sqrt((a*c^3*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) - 6*A*B)/(a*c^3))*log(-(81*B^4*a^2 - A^4*c^2)*sqrt(x) + (3*B*a^3*c^5*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) + 9*A*B^2*a^2*c^2 - A^3*a*c^3)*sqrt((a*c^3*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) - 6*A*B)/(a*c^3))) + (c^2*x^2 + a*c)*sqrt((a*c^3*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) - 6*A*B)/(a*c^3))*log(-(81*B^4*a^2 - A^4*c^2)*sqrt(x) - (3*B*a^3*c^5*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) + 9*A*B^2*a^2*c^2 - A^3*a*c^3)*sqrt((a*c^3*sqrt(-(81*B^4*a^2 - 18*A^2*B^2*a*c + A^4*c^2)/(a^3*c^7)) - 6*A*B)/(a*c^3))) - 4*(B*x + A)*sqrt(x))/(c^2*x^2 + a*c)","B",0
422,1,901,0,0.454780," ","integrate(x^(1/2)*(B*x+A)/(c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{-\frac{a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} + 2 \, A B}{a^{2} c^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(A a^{4} c^{4} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} + B^{3} a^{3} c - A^{2} B a^{2} c^{2}\right)} \sqrt{-\frac{a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} + 2 \, A B}{a^{2} c^{2}}}\right) - {\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{-\frac{a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} + 2 \, A B}{a^{2} c^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(A a^{4} c^{4} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} + B^{3} a^{3} c - A^{2} B a^{2} c^{2}\right)} \sqrt{-\frac{a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} + 2 \, A B}{a^{2} c^{2}}}\right) - {\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{\frac{a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} - 2 \, A B}{a^{2} c^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + {\left(A a^{4} c^{4} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} - B^{3} a^{3} c + A^{2} B a^{2} c^{2}\right)} \sqrt{\frac{a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} - 2 \, A B}{a^{2} c^{2}}}\right) + {\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{\frac{a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} - 2 \, A B}{a^{2} c^{2}}} \log\left(-{\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - {\left(A a^{4} c^{4} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} - B^{3} a^{3} c + A^{2} B a^{2} c^{2}\right)} \sqrt{\frac{a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{5} c^{5}}} - 2 \, A B}{a^{2} c^{2}}}\right) - 4 \, {\left(A c x - B a\right)} \sqrt{x}}{8 \, {\left(a c^{2} x^{2} + a^{2} c\right)}}"," ",0,"-1/8*((a*c^2*x^2 + a^2*c)*sqrt(-(a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) + 2*A*B)/(a^2*c^2))*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (A*a^4*c^4*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) + B^3*a^3*c - A^2*B*a^2*c^2)*sqrt(-(a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) + 2*A*B)/(a^2*c^2))) - (a*c^2*x^2 + a^2*c)*sqrt(-(a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) + 2*A*B)/(a^2*c^2))*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (A*a^4*c^4*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) + B^3*a^3*c - A^2*B*a^2*c^2)*sqrt(-(a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) + 2*A*B)/(a^2*c^2))) - (a*c^2*x^2 + a^2*c)*sqrt((a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) - 2*A*B)/(a^2*c^2))*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) + (A*a^4*c^4*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) - B^3*a^3*c + A^2*B*a^2*c^2)*sqrt((a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) - 2*A*B)/(a^2*c^2))) + (a*c^2*x^2 + a^2*c)*sqrt((a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) - 2*A*B)/(a^2*c^2))*log(-(B^4*a^2 - A^4*c^2)*sqrt(x) - (A*a^4*c^4*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) - B^3*a^3*c + A^2*B*a^2*c^2)*sqrt((a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^5*c^5)) - 2*A*B)/(a^2*c^2))) - 4*(A*c*x - B*a)*sqrt(x))/(a*c^2*x^2 + a^2*c)","B",0
423,1,877,0,0.457157," ","integrate((B*x+A)/x^(1/2)/(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(a c x^{2} + a^{2}\right)} \sqrt{-\frac{a^{3} c \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} + 6 \, A B}{a^{3} c}} \log\left(-{\left(B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(B a^{6} c^{2} \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} - 3 \, A B^{2} a^{3} c + 27 \, A^{3} a^{2} c^{2}\right)} \sqrt{-\frac{a^{3} c \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} + 6 \, A B}{a^{3} c}}\right) - {\left(a c x^{2} + a^{2}\right)} \sqrt{-\frac{a^{3} c \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} + 6 \, A B}{a^{3} c}} \log\left(-{\left(B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(B a^{6} c^{2} \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} - 3 \, A B^{2} a^{3} c + 27 \, A^{3} a^{2} c^{2}\right)} \sqrt{-\frac{a^{3} c \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} + 6 \, A B}{a^{3} c}}\right) - {\left(a c x^{2} + a^{2}\right)} \sqrt{\frac{a^{3} c \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} - 6 \, A B}{a^{3} c}} \log\left(-{\left(B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(B a^{6} c^{2} \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} + 3 \, A B^{2} a^{3} c - 27 \, A^{3} a^{2} c^{2}\right)} \sqrt{\frac{a^{3} c \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} - 6 \, A B}{a^{3} c}}\right) + {\left(a c x^{2} + a^{2}\right)} \sqrt{\frac{a^{3} c \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} - 6 \, A B}{a^{3} c}} \log\left(-{\left(B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(B a^{6} c^{2} \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} + 3 \, A B^{2} a^{3} c - 27 \, A^{3} a^{2} c^{2}\right)} \sqrt{\frac{a^{3} c \sqrt{-\frac{B^{4} a^{2} - 18 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{7} c^{3}}} - 6 \, A B}{a^{3} c}}\right) + 4 \, {\left(B x + A\right)} \sqrt{x}}{8 \, {\left(a c x^{2} + a^{2}\right)}}"," ",0,"1/8*((a*c*x^2 + a^2)*sqrt(-(a^3*c*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) + 6*A*B)/(a^3*c))*log(-(B^4*a^2 - 81*A^4*c^2)*sqrt(x) + (B*a^6*c^2*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) - 3*A*B^2*a^3*c + 27*A^3*a^2*c^2)*sqrt(-(a^3*c*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) + 6*A*B)/(a^3*c))) - (a*c*x^2 + a^2)*sqrt(-(a^3*c*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) + 6*A*B)/(a^3*c))*log(-(B^4*a^2 - 81*A^4*c^2)*sqrt(x) - (B*a^6*c^2*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) - 3*A*B^2*a^3*c + 27*A^3*a^2*c^2)*sqrt(-(a^3*c*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) + 6*A*B)/(a^3*c))) - (a*c*x^2 + a^2)*sqrt((a^3*c*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) - 6*A*B)/(a^3*c))*log(-(B^4*a^2 - 81*A^4*c^2)*sqrt(x) + (B*a^6*c^2*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) + 3*A*B^2*a^3*c - 27*A^3*a^2*c^2)*sqrt((a^3*c*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) - 6*A*B)/(a^3*c))) + (a*c*x^2 + a^2)*sqrt((a^3*c*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) - 6*A*B)/(a^3*c))*log(-(B^4*a^2 - 81*A^4*c^2)*sqrt(x) - (B*a^6*c^2*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) + 3*A*B^2*a^3*c - 27*A^3*a^2*c^2)*sqrt((a^3*c*sqrt(-(B^4*a^2 - 18*A^2*B^2*a*c + 81*A^4*c^2)/(a^7*c^3)) - 6*A*B)/(a^3*c))) + 4*(B*x + A)*sqrt(x))/(a*c*x^2 + a^2)","B",0
424,1,877,0,0.451211," ","integrate((B*x+A)/x^(3/2)/(c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} c x^{3} + a^{3} x\right)} \sqrt{\frac{a^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} + 30 \, A B}{a^{4}}} \log\left(-{\left(81 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(5 \, A a^{7} c \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} + 27 \, B^{3} a^{4} - 75 \, A^{2} B a^{3} c\right)} \sqrt{\frac{a^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} + 30 \, A B}{a^{4}}}\right) - {\left(a^{2} c x^{3} + a^{3} x\right)} \sqrt{\frac{a^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} + 30 \, A B}{a^{4}}} \log\left(-{\left(81 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(5 \, A a^{7} c \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} + 27 \, B^{3} a^{4} - 75 \, A^{2} B a^{3} c\right)} \sqrt{\frac{a^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} + 30 \, A B}{a^{4}}}\right) - {\left(a^{2} c x^{3} + a^{3} x\right)} \sqrt{-\frac{a^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} - 30 \, A B}{a^{4}}} \log\left(-{\left(81 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(5 \, A a^{7} c \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} - 27 \, B^{3} a^{4} + 75 \, A^{2} B a^{3} c\right)} \sqrt{-\frac{a^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} - 30 \, A B}{a^{4}}}\right) + {\left(a^{2} c x^{3} + a^{3} x\right)} \sqrt{-\frac{a^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} - 30 \, A B}{a^{4}}} \log\left(-{\left(81 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(5 \, A a^{7} c \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} - 27 \, B^{3} a^{4} + 75 \, A^{2} B a^{3} c\right)} \sqrt{-\frac{a^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c}} - 30 \, A B}{a^{4}}}\right) + 4 \, {\left(5 \, A c x^{2} - B a x + 4 \, A a\right)} \sqrt{x}}{8 \, {\left(a^{2} c x^{3} + a^{3} x\right)}}"," ",0,"-1/8*((a^2*c*x^3 + a^3*x)*sqrt((a^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) + 30*A*B)/a^4)*log(-(81*B^4*a^2 - 625*A^4*c^2)*sqrt(x) + (5*A*a^7*c*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) + 27*B^3*a^4 - 75*A^2*B*a^3*c)*sqrt((a^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) + 30*A*B)/a^4)) - (a^2*c*x^3 + a^3*x)*sqrt((a^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) + 30*A*B)/a^4)*log(-(81*B^4*a^2 - 625*A^4*c^2)*sqrt(x) - (5*A*a^7*c*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) + 27*B^3*a^4 - 75*A^2*B*a^3*c)*sqrt((a^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) + 30*A*B)/a^4)) - (a^2*c*x^3 + a^3*x)*sqrt(-(a^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) - 30*A*B)/a^4)*log(-(81*B^4*a^2 - 625*A^4*c^2)*sqrt(x) + (5*A*a^7*c*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) - 27*B^3*a^4 + 75*A^2*B*a^3*c)*sqrt(-(a^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) - 30*A*B)/a^4)) + (a^2*c*x^3 + a^3*x)*sqrt(-(a^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) - 30*A*B)/a^4)*log(-(81*B^4*a^2 - 625*A^4*c^2)*sqrt(x) - (5*A*a^7*c*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) - 27*B^3*a^4 + 75*A^2*B*a^3*c)*sqrt(-(a^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c)) - 30*A*B)/a^4)) + 4*(5*A*c*x^2 - B*a*x + 4*A*a)*sqrt(x))/(a^2*c*x^3 + a^3*x)","B",0
425,1,916,0,0.450416," ","integrate((B*x+A)/x^(5/2)/(c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} c x^{4} + a^{3} x^{2}\right)} \sqrt{-\frac{a^{5} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 70 \, A B c}{a^{5}}} \log\left(-{\left(625 \, B^{4} a^{2} c - 2401 \, A^{4} c^{3}\right)} \sqrt{x} + {\left(5 \, B a^{9} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 175 \, A B^{2} a^{4} c + 343 \, A^{3} a^{3} c^{2}\right)} \sqrt{-\frac{a^{5} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 70 \, A B c}{a^{5}}}\right) - 3 \, {\left(a^{2} c x^{4} + a^{3} x^{2}\right)} \sqrt{-\frac{a^{5} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 70 \, A B c}{a^{5}}} \log\left(-{\left(625 \, B^{4} a^{2} c - 2401 \, A^{4} c^{3}\right)} \sqrt{x} - {\left(5 \, B a^{9} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 175 \, A B^{2} a^{4} c + 343 \, A^{3} a^{3} c^{2}\right)} \sqrt{-\frac{a^{5} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 70 \, A B c}{a^{5}}}\right) - 3 \, {\left(a^{2} c x^{4} + a^{3} x^{2}\right)} \sqrt{\frac{a^{5} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 70 \, A B c}{a^{5}}} \log\left(-{\left(625 \, B^{4} a^{2} c - 2401 \, A^{4} c^{3}\right)} \sqrt{x} + {\left(5 \, B a^{9} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 175 \, A B^{2} a^{4} c - 343 \, A^{3} a^{3} c^{2}\right)} \sqrt{\frac{a^{5} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 70 \, A B c}{a^{5}}}\right) + 3 \, {\left(a^{2} c x^{4} + a^{3} x^{2}\right)} \sqrt{\frac{a^{5} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 70 \, A B c}{a^{5}}} \log\left(-{\left(625 \, B^{4} a^{2} c - 2401 \, A^{4} c^{3}\right)} \sqrt{x} - {\left(5 \, B a^{9} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 175 \, A B^{2} a^{4} c - 343 \, A^{3} a^{3} c^{2}\right)} \sqrt{\frac{a^{5} \sqrt{-\frac{625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 70 \, A B c}{a^{5}}}\right) + 4 \, {\left(15 \, B c x^{3} + 7 \, A c x^{2} + 12 \, B a x + 4 \, A a\right)} \sqrt{x}}{24 \, {\left(a^{2} c x^{4} + a^{3} x^{2}\right)}}"," ",0,"-1/24*(3*(a^2*c*x^4 + a^3*x^2)*sqrt(-(a^5*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) + 70*A*B*c)/a^5)*log(-(625*B^4*a^2*c - 2401*A^4*c^3)*sqrt(x) + (5*B*a^9*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) - 175*A*B^2*a^4*c + 343*A^3*a^3*c^2)*sqrt(-(a^5*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) + 70*A*B*c)/a^5)) - 3*(a^2*c*x^4 + a^3*x^2)*sqrt(-(a^5*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) + 70*A*B*c)/a^5)*log(-(625*B^4*a^2*c - 2401*A^4*c^3)*sqrt(x) - (5*B*a^9*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) - 175*A*B^2*a^4*c + 343*A^3*a^3*c^2)*sqrt(-(a^5*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) + 70*A*B*c)/a^5)) - 3*(a^2*c*x^4 + a^3*x^2)*sqrt((a^5*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) - 70*A*B*c)/a^5)*log(-(625*B^4*a^2*c - 2401*A^4*c^3)*sqrt(x) + (5*B*a^9*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) + 175*A*B^2*a^4*c - 343*A^3*a^3*c^2)*sqrt((a^5*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) - 70*A*B*c)/a^5)) + 3*(a^2*c*x^4 + a^3*x^2)*sqrt((a^5*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) - 70*A*B*c)/a^5)*log(-(625*B^4*a^2*c - 2401*A^4*c^3)*sqrt(x) - (5*B*a^9*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) + 175*A*B^2*a^4*c - 343*A^3*a^3*c^2)*sqrt((a^5*sqrt(-(625*B^4*a^2*c - 2450*A^2*B^2*a*c^2 + 2401*A^4*c^3)/a^11) - 70*A*B*c)/a^5)) + 4*(15*B*c*x^3 + 7*A*c*x^2 + 12*B*a*x + 4*A*a)*sqrt(x))/(a^2*c*x^4 + a^3*x^2)","B",0
426,1,986,0,0.456216," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(c^{4} x^{4} + 2 \, a c^{3} x^{2} + a^{2} c^{2}\right)} \sqrt{-\frac{a c^{5} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} + 210 \, A B}{a c^{5}}} \log\left(-{\left(194481 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(21 \, B a^{3} c^{8} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} - 2205 \, A B^{2} a^{2} c^{3} + 125 \, A^{3} a c^{4}\right)} \sqrt{-\frac{a c^{5} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} + 210 \, A B}{a c^{5}}}\right) - {\left(c^{4} x^{4} + 2 \, a c^{3} x^{2} + a^{2} c^{2}\right)} \sqrt{-\frac{a c^{5} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} + 210 \, A B}{a c^{5}}} \log\left(-{\left(194481 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(21 \, B a^{3} c^{8} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} - 2205 \, A B^{2} a^{2} c^{3} + 125 \, A^{3} a c^{4}\right)} \sqrt{-\frac{a c^{5} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} + 210 \, A B}{a c^{5}}}\right) - {\left(c^{4} x^{4} + 2 \, a c^{3} x^{2} + a^{2} c^{2}\right)} \sqrt{\frac{a c^{5} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} - 210 \, A B}{a c^{5}}} \log\left(-{\left(194481 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(21 \, B a^{3} c^{8} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} + 2205 \, A B^{2} a^{2} c^{3} - 125 \, A^{3} a c^{4}\right)} \sqrt{\frac{a c^{5} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} - 210 \, A B}{a c^{5}}}\right) + {\left(c^{4} x^{4} + 2 \, a c^{3} x^{2} + a^{2} c^{2}\right)} \sqrt{\frac{a c^{5} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} - 210 \, A B}{a c^{5}}} \log\left(-{\left(194481 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(21 \, B a^{3} c^{8} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} + 2205 \, A B^{2} a^{2} c^{3} - 125 \, A^{3} a c^{4}\right)} \sqrt{\frac{a c^{5} \sqrt{-\frac{194481 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{3} c^{11}}} - 210 \, A B}{a c^{5}}}\right) - 4 \, {\left(11 \, B c x^{3} + 9 \, A c x^{2} + 7 \, B a x + 5 \, A a\right)} \sqrt{x}}{64 \, {\left(c^{4} x^{4} + 2 \, a c^{3} x^{2} + a^{2} c^{2}\right)}}"," ",0,"1/64*((c^4*x^4 + 2*a*c^3*x^2 + a^2*c^2)*sqrt(-(a*c^5*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) + 210*A*B)/(a*c^5))*log(-(194481*B^4*a^2 - 625*A^4*c^2)*sqrt(x) + (21*B*a^3*c^8*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) - 2205*A*B^2*a^2*c^3 + 125*A^3*a*c^4)*sqrt(-(a*c^5*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) + 210*A*B)/(a*c^5))) - (c^4*x^4 + 2*a*c^3*x^2 + a^2*c^2)*sqrt(-(a*c^5*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) + 210*A*B)/(a*c^5))*log(-(194481*B^4*a^2 - 625*A^4*c^2)*sqrt(x) - (21*B*a^3*c^8*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) - 2205*A*B^2*a^2*c^3 + 125*A^3*a*c^4)*sqrt(-(a*c^5*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) + 210*A*B)/(a*c^5))) - (c^4*x^4 + 2*a*c^3*x^2 + a^2*c^2)*sqrt((a*c^5*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) - 210*A*B)/(a*c^5))*log(-(194481*B^4*a^2 - 625*A^4*c^2)*sqrt(x) + (21*B*a^3*c^8*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) + 2205*A*B^2*a^2*c^3 - 125*A^3*a*c^4)*sqrt((a*c^5*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) - 210*A*B)/(a*c^5))) + (c^4*x^4 + 2*a*c^3*x^2 + a^2*c^2)*sqrt((a*c^5*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) - 210*A*B)/(a*c^5))*log(-(194481*B^4*a^2 - 625*A^4*c^2)*sqrt(x) - (21*B*a^3*c^8*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) + 2205*A*B^2*a^2*c^3 - 125*A^3*a*c^4)*sqrt((a*c^5*sqrt(-(194481*B^4*a^2 - 22050*A^2*B^2*a*c + 625*A^4*c^2)/(a^3*c^11)) - 210*A*B)/(a*c^5))) - 4*(11*B*c*x^3 + 9*A*c*x^2 + 7*B*a*x + 5*A*a)*sqrt(x))/(c^4*x^4 + 2*a*c^3*x^2 + a^2*c^2)","B",0
427,1,1031,0,0.465932," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","-\frac{{\left(a c^{4} x^{4} + 2 \, a^{2} c^{3} x^{2} + a^{3} c^{2}\right)} \sqrt{-\frac{a^{2} c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} + 30 \, A B}{a^{2} c^{4}}} \log\left(-{\left(625 \, B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(3 \, A a^{4} c^{7} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} + 125 \, B^{3} a^{3} c^{2} - 45 \, A^{2} B a^{2} c^{3}\right)} \sqrt{-\frac{a^{2} c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} + 30 \, A B}{a^{2} c^{4}}}\right) - {\left(a c^{4} x^{4} + 2 \, a^{2} c^{3} x^{2} + a^{3} c^{2}\right)} \sqrt{-\frac{a^{2} c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} + 30 \, A B}{a^{2} c^{4}}} \log\left(-{\left(625 \, B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(3 \, A a^{4} c^{7} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} + 125 \, B^{3} a^{3} c^{2} - 45 \, A^{2} B a^{2} c^{3}\right)} \sqrt{-\frac{a^{2} c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} + 30 \, A B}{a^{2} c^{4}}}\right) - {\left(a c^{4} x^{4} + 2 \, a^{2} c^{3} x^{2} + a^{3} c^{2}\right)} \sqrt{\frac{a^{2} c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} - 30 \, A B}{a^{2} c^{4}}} \log\left(-{\left(625 \, B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(3 \, A a^{4} c^{7} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} - 125 \, B^{3} a^{3} c^{2} + 45 \, A^{2} B a^{2} c^{3}\right)} \sqrt{\frac{a^{2} c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} - 30 \, A B}{a^{2} c^{4}}}\right) + {\left(a c^{4} x^{4} + 2 \, a^{2} c^{3} x^{2} + a^{3} c^{2}\right)} \sqrt{\frac{a^{2} c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} - 30 \, A B}{a^{2} c^{4}}} \log\left(-{\left(625 \, B^{4} a^{2} - 81 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(3 \, A a^{4} c^{7} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} - 125 \, B^{3} a^{3} c^{2} + 45 \, A^{2} B a^{2} c^{3}\right)} \sqrt{\frac{a^{2} c^{4} \sqrt{-\frac{625 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}}{a^{5} c^{9}}} - 30 \, A B}{a^{2} c^{4}}}\right) - 4 \, {\left(3 \, A c^{2} x^{3} - 9 \, B a c x^{2} - A a c x - 5 \, B a^{2}\right)} \sqrt{x}}{64 \, {\left(a c^{4} x^{4} + 2 \, a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}"," ",0,"-1/64*((a*c^4*x^4 + 2*a^2*c^3*x^2 + a^3*c^2)*sqrt(-(a^2*c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) + 30*A*B)/(a^2*c^4))*log(-(625*B^4*a^2 - 81*A^4*c^2)*sqrt(x) + (3*A*a^4*c^7*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) + 125*B^3*a^3*c^2 - 45*A^2*B*a^2*c^3)*sqrt(-(a^2*c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) + 30*A*B)/(a^2*c^4))) - (a*c^4*x^4 + 2*a^2*c^3*x^2 + a^3*c^2)*sqrt(-(a^2*c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) + 30*A*B)/(a^2*c^4))*log(-(625*B^4*a^2 - 81*A^4*c^2)*sqrt(x) - (3*A*a^4*c^7*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) + 125*B^3*a^3*c^2 - 45*A^2*B*a^2*c^3)*sqrt(-(a^2*c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) + 30*A*B)/(a^2*c^4))) - (a*c^4*x^4 + 2*a^2*c^3*x^2 + a^3*c^2)*sqrt((a^2*c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) - 30*A*B)/(a^2*c^4))*log(-(625*B^4*a^2 - 81*A^4*c^2)*sqrt(x) + (3*A*a^4*c^7*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) - 125*B^3*a^3*c^2 + 45*A^2*B*a^2*c^3)*sqrt((a^2*c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) - 30*A*B)/(a^2*c^4))) + (a*c^4*x^4 + 2*a^2*c^3*x^2 + a^3*c^2)*sqrt((a^2*c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) - 30*A*B)/(a^2*c^4))*log(-(625*B^4*a^2 - 81*A^4*c^2)*sqrt(x) - (3*A*a^4*c^7*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) - 125*B^3*a^3*c^2 + 45*A^2*B*a^2*c^3)*sqrt((a^2*c^4*sqrt(-(625*B^4*a^2 - 450*A^2*B^2*a*c + 81*A^4*c^2)/(a^5*c^9)) - 30*A*B)/(a^2*c^4))) - 4*(3*A*c^2*x^3 - 9*B*a*c*x^2 - A*a*c*x - 5*B*a^2)*sqrt(x))/(a*c^4*x^4 + 2*a^2*c^3*x^2 + a^3*c^2)","B",0
428,1,982,0,0.473724," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(a c^{3} x^{4} + 2 \, a^{2} c^{2} x^{2} + a^{3} c\right)} \sqrt{-\frac{a^{3} c^{3} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} + 2 \, A B}{a^{3} c^{3}}} \log\left(-27 \, {\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + 27 \, {\left(B a^{6} c^{5} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} - A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{a^{3} c^{3} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} + 2 \, A B}{a^{3} c^{3}}}\right) - 3 \, {\left(a c^{3} x^{4} + 2 \, a^{2} c^{2} x^{2} + a^{3} c\right)} \sqrt{-\frac{a^{3} c^{3} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} + 2 \, A B}{a^{3} c^{3}}} \log\left(-27 \, {\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - 27 \, {\left(B a^{6} c^{5} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} - A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{a^{3} c^{3} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} + 2 \, A B}{a^{3} c^{3}}}\right) - 3 \, {\left(a c^{3} x^{4} + 2 \, a^{2} c^{2} x^{2} + a^{3} c\right)} \sqrt{\frac{a^{3} c^{3} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} - 2 \, A B}{a^{3} c^{3}}} \log\left(-27 \, {\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} + 27 \, {\left(B a^{6} c^{5} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} + A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{\frac{a^{3} c^{3} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} - 2 \, A B}{a^{3} c^{3}}}\right) + 3 \, {\left(a c^{3} x^{4} + 2 \, a^{2} c^{2} x^{2} + a^{3} c\right)} \sqrt{\frac{a^{3} c^{3} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} - 2 \, A B}{a^{3} c^{3}}} \log\left(-27 \, {\left(B^{4} a^{2} - A^{4} c^{2}\right)} \sqrt{x} - 27 \, {\left(B a^{6} c^{5} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} + A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{\frac{a^{3} c^{3} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{7} c^{7}}} - 2 \, A B}{a^{3} c^{3}}}\right) + 4 \, {\left(3 \, B c x^{3} + A c x^{2} - B a x - 3 \, A a\right)} \sqrt{x}}{64 \, {\left(a c^{3} x^{4} + 2 \, a^{2} c^{2} x^{2} + a^{3} c\right)}}"," ",0,"1/64*(3*(a*c^3*x^4 + 2*a^2*c^2*x^2 + a^3*c)*sqrt(-(a^3*c^3*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) + 2*A*B)/(a^3*c^3))*log(-27*(B^4*a^2 - A^4*c^2)*sqrt(x) + 27*(B*a^6*c^5*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) - A*B^2*a^3*c^2 + A^3*a^2*c^3)*sqrt(-(a^3*c^3*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) + 2*A*B)/(a^3*c^3))) - 3*(a*c^3*x^4 + 2*a^2*c^2*x^2 + a^3*c)*sqrt(-(a^3*c^3*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) + 2*A*B)/(a^3*c^3))*log(-27*(B^4*a^2 - A^4*c^2)*sqrt(x) - 27*(B*a^6*c^5*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) - A*B^2*a^3*c^2 + A^3*a^2*c^3)*sqrt(-(a^3*c^3*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) + 2*A*B)/(a^3*c^3))) - 3*(a*c^3*x^4 + 2*a^2*c^2*x^2 + a^3*c)*sqrt((a^3*c^3*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) - 2*A*B)/(a^3*c^3))*log(-27*(B^4*a^2 - A^4*c^2)*sqrt(x) + 27*(B*a^6*c^5*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) + A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt((a^3*c^3*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) - 2*A*B)/(a^3*c^3))) + 3*(a*c^3*x^4 + 2*a^2*c^2*x^2 + a^3*c)*sqrt((a^3*c^3*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) - 2*A*B)/(a^3*c^3))*log(-27*(B^4*a^2 - A^4*c^2)*sqrt(x) - 27*(B*a^6*c^5*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) + A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt((a^3*c^3*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^7*c^7)) - 2*A*B)/(a^3*c^3))) + 4*(3*B*c*x^3 + A*c*x^2 - B*a*x - 3*A*a)*sqrt(x))/(a*c^3*x^4 + 2*a^2*c^2*x^2 + a^3*c)","B",0
429,1,1022,0,0.459948," ","integrate(x^(1/2)*(B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{a^{4} c^{2} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} + 30 \, A B}{a^{4} c^{2}}} \log\left(-{\left(81 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(5 \, A a^{7} c^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} + 27 \, B^{3} a^{4} c - 75 \, A^{2} B a^{3} c^{2}\right)} \sqrt{-\frac{a^{4} c^{2} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} + 30 \, A B}{a^{4} c^{2}}}\right) - {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{a^{4} c^{2} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} + 30 \, A B}{a^{4} c^{2}}} \log\left(-{\left(81 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(5 \, A a^{7} c^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} + 27 \, B^{3} a^{4} c - 75 \, A^{2} B a^{3} c^{2}\right)} \sqrt{-\frac{a^{4} c^{2} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} + 30 \, A B}{a^{4} c^{2}}}\right) - {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{a^{4} c^{2} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} - 30 \, A B}{a^{4} c^{2}}} \log\left(-{\left(81 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(5 \, A a^{7} c^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} - 27 \, B^{3} a^{4} c + 75 \, A^{2} B a^{3} c^{2}\right)} \sqrt{\frac{a^{4} c^{2} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} - 30 \, A B}{a^{4} c^{2}}}\right) + {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{a^{4} c^{2} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} - 30 \, A B}{a^{4} c^{2}}} \log\left(-{\left(81 \, B^{4} a^{2} - 625 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(5 \, A a^{7} c^{4} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} - 27 \, B^{3} a^{4} c + 75 \, A^{2} B a^{3} c^{2}\right)} \sqrt{\frac{a^{4} c^{2} \sqrt{-\frac{81 \, B^{4} a^{2} - 450 \, A^{2} B^{2} a c + 625 \, A^{4} c^{2}}{a^{9} c^{5}}} - 30 \, A B}{a^{4} c^{2}}}\right) - 4 \, {\left(5 \, A c^{2} x^{3} + B a c x^{2} + 9 \, A a c x - 3 \, B a^{2}\right)} \sqrt{x}}{64 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"-1/64*((a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(a^4*c^2*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) + 30*A*B)/(a^4*c^2))*log(-(81*B^4*a^2 - 625*A^4*c^2)*sqrt(x) + (5*A*a^7*c^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) + 27*B^3*a^4*c - 75*A^2*B*a^3*c^2)*sqrt(-(a^4*c^2*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) + 30*A*B)/(a^4*c^2))) - (a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(a^4*c^2*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) + 30*A*B)/(a^4*c^2))*log(-(81*B^4*a^2 - 625*A^4*c^2)*sqrt(x) - (5*A*a^7*c^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) + 27*B^3*a^4*c - 75*A^2*B*a^3*c^2)*sqrt(-(a^4*c^2*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) + 30*A*B)/(a^4*c^2))) - (a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt((a^4*c^2*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) - 30*A*B)/(a^4*c^2))*log(-(81*B^4*a^2 - 625*A^4*c^2)*sqrt(x) + (5*A*a^7*c^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) - 27*B^3*a^4*c + 75*A^2*B*a^3*c^2)*sqrt((a^4*c^2*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) - 30*A*B)/(a^4*c^2))) + (a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt((a^4*c^2*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) - 30*A*B)/(a^4*c^2))*log(-(81*B^4*a^2 - 625*A^4*c^2)*sqrt(x) - (5*A*a^7*c^4*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) - 27*B^3*a^4*c + 75*A^2*B*a^3*c^2)*sqrt((a^4*c^2*sqrt(-(81*B^4*a^2 - 450*A^2*B^2*a*c + 625*A^4*c^2)/(a^9*c^5)) - 30*A*B)/(a^4*c^2))) - 4*(5*A*c^2*x^3 + B*a*c*x^2 + 9*A*a*c*x - 3*B*a^2)*sqrt(x))/(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)","B",0
430,1,981,0,0.473637," ","integrate((B*x+A)/x^(1/2)/(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(a^{2} c^{2} x^{4} + 2 \, a^{3} c x^{2} + a^{4}\right)} \sqrt{-\frac{a^{5} c \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} + 210 \, A B}{a^{5} c}} \log\left(-{\left(625 \, B^{4} a^{2} - 194481 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(5 \, B a^{9} c^{2} \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} - 525 \, A B^{2} a^{4} c + 9261 \, A^{3} a^{3} c^{2}\right)} \sqrt{-\frac{a^{5} c \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} + 210 \, A B}{a^{5} c}}\right) - {\left(a^{2} c^{2} x^{4} + 2 \, a^{3} c x^{2} + a^{4}\right)} \sqrt{-\frac{a^{5} c \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} + 210 \, A B}{a^{5} c}} \log\left(-{\left(625 \, B^{4} a^{2} - 194481 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(5 \, B a^{9} c^{2} \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} - 525 \, A B^{2} a^{4} c + 9261 \, A^{3} a^{3} c^{2}\right)} \sqrt{-\frac{a^{5} c \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} + 210 \, A B}{a^{5} c}}\right) - {\left(a^{2} c^{2} x^{4} + 2 \, a^{3} c x^{2} + a^{4}\right)} \sqrt{\frac{a^{5} c \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} - 210 \, A B}{a^{5} c}} \log\left(-{\left(625 \, B^{4} a^{2} - 194481 \, A^{4} c^{2}\right)} \sqrt{x} + {\left(5 \, B a^{9} c^{2} \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} + 525 \, A B^{2} a^{4} c - 9261 \, A^{3} a^{3} c^{2}\right)} \sqrt{\frac{a^{5} c \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} - 210 \, A B}{a^{5} c}}\right) + {\left(a^{2} c^{2} x^{4} + 2 \, a^{3} c x^{2} + a^{4}\right)} \sqrt{\frac{a^{5} c \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} - 210 \, A B}{a^{5} c}} \log\left(-{\left(625 \, B^{4} a^{2} - 194481 \, A^{4} c^{2}\right)} \sqrt{x} - {\left(5 \, B a^{9} c^{2} \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} + 525 \, A B^{2} a^{4} c - 9261 \, A^{3} a^{3} c^{2}\right)} \sqrt{\frac{a^{5} c \sqrt{-\frac{625 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 194481 \, A^{4} c^{2}}{a^{11} c^{3}}} - 210 \, A B}{a^{5} c}}\right) + 4 \, {\left(5 \, B c x^{3} + 7 \, A c x^{2} + 9 \, B a x + 11 \, A a\right)} \sqrt{x}}{64 \, {\left(a^{2} c^{2} x^{4} + 2 \, a^{3} c x^{2} + a^{4}\right)}}"," ",0,"1/64*((a^2*c^2*x^4 + 2*a^3*c*x^2 + a^4)*sqrt(-(a^5*c*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) + 210*A*B)/(a^5*c))*log(-(625*B^4*a^2 - 194481*A^4*c^2)*sqrt(x) + (5*B*a^9*c^2*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) - 525*A*B^2*a^4*c + 9261*A^3*a^3*c^2)*sqrt(-(a^5*c*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) + 210*A*B)/(a^5*c))) - (a^2*c^2*x^4 + 2*a^3*c*x^2 + a^4)*sqrt(-(a^5*c*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) + 210*A*B)/(a^5*c))*log(-(625*B^4*a^2 - 194481*A^4*c^2)*sqrt(x) - (5*B*a^9*c^2*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) - 525*A*B^2*a^4*c + 9261*A^3*a^3*c^2)*sqrt(-(a^5*c*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) + 210*A*B)/(a^5*c))) - (a^2*c^2*x^4 + 2*a^3*c*x^2 + a^4)*sqrt((a^5*c*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) - 210*A*B)/(a^5*c))*log(-(625*B^4*a^2 - 194481*A^4*c^2)*sqrt(x) + (5*B*a^9*c^2*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) + 525*A*B^2*a^4*c - 9261*A^3*a^3*c^2)*sqrt((a^5*c*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) - 210*A*B)/(a^5*c))) + (a^2*c^2*x^4 + 2*a^3*c*x^2 + a^4)*sqrt((a^5*c*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) - 210*A*B)/(a^5*c))*log(-(625*B^4*a^2 - 194481*A^4*c^2)*sqrt(x) - (5*B*a^9*c^2*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) + 525*A*B^2*a^4*c - 9261*A^3*a^3*c^2)*sqrt((a^5*c*sqrt(-(625*B^4*a^2 - 22050*A^2*B^2*a*c + 194481*A^4*c^2)/(a^11*c^3)) - 210*A*B)/(a^5*c))) + 4*(5*B*c*x^3 + 7*A*c*x^2 + 9*B*a*x + 11*A*a)*sqrt(x))/(a^2*c^2*x^4 + 2*a^3*c*x^2 + a^4)","B",0
431,1,958,0,0.450633," ","integrate((B*x+A)/x^(3/2)/(c*x^2+a)^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{3} c^{2} x^{5} + 2 \, a^{4} c x^{3} + a^{5} x\right)} \sqrt{\frac{a^{6} \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} + 210 \, A B}{a^{6}}} \log\left(-9 \, {\left(2401 \, B^{4} a^{2} - 50625 \, A^{4} c^{2}\right)} \sqrt{x} + 9 \, {\left(15 \, A a^{10} c \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} + 343 \, B^{3} a^{5} - 1575 \, A^{2} B a^{4} c\right)} \sqrt{\frac{a^{6} \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} + 210 \, A B}{a^{6}}}\right) - 3 \, {\left(a^{3} c^{2} x^{5} + 2 \, a^{4} c x^{3} + a^{5} x\right)} \sqrt{\frac{a^{6} \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} + 210 \, A B}{a^{6}}} \log\left(-9 \, {\left(2401 \, B^{4} a^{2} - 50625 \, A^{4} c^{2}\right)} \sqrt{x} - 9 \, {\left(15 \, A a^{10} c \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} + 343 \, B^{3} a^{5} - 1575 \, A^{2} B a^{4} c\right)} \sqrt{\frac{a^{6} \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} + 210 \, A B}{a^{6}}}\right) - 3 \, {\left(a^{3} c^{2} x^{5} + 2 \, a^{4} c x^{3} + a^{5} x\right)} \sqrt{-\frac{a^{6} \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} - 210 \, A B}{a^{6}}} \log\left(-9 \, {\left(2401 \, B^{4} a^{2} - 50625 \, A^{4} c^{2}\right)} \sqrt{x} + 9 \, {\left(15 \, A a^{10} c \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} - 343 \, B^{3} a^{5} + 1575 \, A^{2} B a^{4} c\right)} \sqrt{-\frac{a^{6} \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} - 210 \, A B}{a^{6}}}\right) + 3 \, {\left(a^{3} c^{2} x^{5} + 2 \, a^{4} c x^{3} + a^{5} x\right)} \sqrt{-\frac{a^{6} \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} - 210 \, A B}{a^{6}}} \log\left(-9 \, {\left(2401 \, B^{4} a^{2} - 50625 \, A^{4} c^{2}\right)} \sqrt{x} - 9 \, {\left(15 \, A a^{10} c \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} - 343 \, B^{3} a^{5} + 1575 \, A^{2} B a^{4} c\right)} \sqrt{-\frac{a^{6} \sqrt{-\frac{2401 \, B^{4} a^{2} - 22050 \, A^{2} B^{2} a c + 50625 \, A^{4} c^{2}}{a^{13} c}} - 210 \, A B}{a^{6}}}\right) + 4 \, {\left(45 \, A c^{2} x^{4} - 7 \, B a c x^{3} + 81 \, A a c x^{2} - 11 \, B a^{2} x + 32 \, A a^{2}\right)} \sqrt{x}}{64 \, {\left(a^{3} c^{2} x^{5} + 2 \, a^{4} c x^{3} + a^{5} x\right)}}"," ",0,"-1/64*(3*(a^3*c^2*x^5 + 2*a^4*c*x^3 + a^5*x)*sqrt((a^6*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) + 210*A*B)/a^6)*log(-9*(2401*B^4*a^2 - 50625*A^4*c^2)*sqrt(x) + 9*(15*A*a^10*c*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) + 343*B^3*a^5 - 1575*A^2*B*a^4*c)*sqrt((a^6*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) + 210*A*B)/a^6)) - 3*(a^3*c^2*x^5 + 2*a^4*c*x^3 + a^5*x)*sqrt((a^6*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) + 210*A*B)/a^6)*log(-9*(2401*B^4*a^2 - 50625*A^4*c^2)*sqrt(x) - 9*(15*A*a^10*c*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) + 343*B^3*a^5 - 1575*A^2*B*a^4*c)*sqrt((a^6*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) + 210*A*B)/a^6)) - 3*(a^3*c^2*x^5 + 2*a^4*c*x^3 + a^5*x)*sqrt(-(a^6*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) - 210*A*B)/a^6)*log(-9*(2401*B^4*a^2 - 50625*A^4*c^2)*sqrt(x) + 9*(15*A*a^10*c*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) - 343*B^3*a^5 + 1575*A^2*B*a^4*c)*sqrt(-(a^6*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) - 210*A*B)/a^6)) + 3*(a^3*c^2*x^5 + 2*a^4*c*x^3 + a^5*x)*sqrt(-(a^6*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) - 210*A*B)/a^6)*log(-9*(2401*B^4*a^2 - 50625*A^4*c^2)*sqrt(x) - 9*(15*A*a^10*c*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) - 343*B^3*a^5 + 1575*A^2*B*a^4*c)*sqrt(-(a^6*sqrt(-(2401*B^4*a^2 - 22050*A^2*B^2*a*c + 50625*A^4*c^2)/(a^13*c)) - 210*A*B)/a^6)) + 4*(45*A*c^2*x^4 - 7*B*a*c*x^3 + 81*A*a*c*x^2 - 11*B*a^2*x + 32*A*a^2)*sqrt(x))/(a^3*c^2*x^5 + 2*a^4*c*x^3 + a^5*x)","B",0
432,1,33,0,0.426247," ","integrate((1-x)/(x^2+1)/x^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{2 \, \sqrt{2} {\left(x + 1\right)} \sqrt{x} + x^{2} + 4 \, x + 1}{x^{2} + 1}\right)"," ",0,"1/2*sqrt(2)*log((2*sqrt(2)*(x + 1)*sqrt(x) + x^2 + 4*x + 1)/(x^2 + 1))","A",0
433,0,0,0,0.436548," ","integrate((e*x)^(7/2)*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B e^{3} x^{4} + A e^{3} x^{3}\right)} \sqrt{c x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*e^3*x^4 + A*e^3*x^3)*sqrt(c*x^2 + a)*sqrt(e*x), x)","F",0
434,0,0,0,0.435868," ","integrate((e*x)^(5/2)*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B e^{2} x^{3} + A e^{2} x^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*e^2*x^3 + A*e^2*x^2)*sqrt(c*x^2 + a)*sqrt(e*x), x)","F",0
435,0,0,0,0.428901," ","integrate((e*x)^(3/2)*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B e x^{2} + A e x\right)} \sqrt{c x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*e*x^2 + A*e*x)*sqrt(c*x^2 + a)*sqrt(e*x), x)","F",0
436,0,0,0,0.437710," ","integrate((e*x)^(1/2)*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x), x)","F",0
437,0,0,0,0.429249," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{e x}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(e*x), x)","F",0
438,0,0,0,0.445002," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(e^2*x^2), x)","F",0
439,0,0,0,0.451054," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{e^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(e^3*x^3), x)","F",0
440,0,0,0,0.432264," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(e^4*x^4), x)","F",0
441,0,0,0,0.437970," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{e^{5} x^{5}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(e^5*x^5), x)","F",0
442,0,0,0,0.448057," ","integrate((e*x)^(5/2)*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c e^{2} x^{5} + A c e^{2} x^{4} + B a e^{2} x^{3} + A a e^{2} x^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*c*e^2*x^5 + A*c*e^2*x^4 + B*a*e^2*x^3 + A*a*e^2*x^2)*sqrt(c*x^2 + a)*sqrt(e*x), x)","F",0
443,0,0,0,0.440624," ","integrate((e*x)^(3/2)*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c e x^{4} + A c e x^{3} + B a e x^{2} + A a e x\right)} \sqrt{c x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*c*e*x^4 + A*c*e*x^3 + B*a*e*x^2 + A*a*e*x)*sqrt(c*x^2 + a)*sqrt(e*x), x)","F",0
444,0,0,0,0.436150," ","integrate((e*x)^(1/2)*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*sqrt(e*x), x)","F",0
445,0,0,0,0.446531," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e x}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*sqrt(e*x)/(e*x), x)","F",0
446,0,0,0,0.444909," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*sqrt(e*x)/(e^2*x^2), x)","F",0
447,0,0,0,0.449265," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e^{3} x^{3}}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*sqrt(e*x)/(e^3*x^3), x)","F",0
448,0,0,0,0.445284," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*sqrt(e*x)/(e^4*x^4), x)","F",0
449,0,0,0,0.443562," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e^{5} x^{5}}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*sqrt(e*x)/(e^5*x^5), x)","F",0
450,0,0,0,0.482510," ","integrate((e*x)^(3/2)*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c^{2} e x^{6} + A c^{2} e x^{5} + 2 \, B a c e x^{4} + 2 \, A a c e x^{3} + B a^{2} e x^{2} + A a^{2} e x\right)} \sqrt{c x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*c^2*e*x^6 + A*c^2*e*x^5 + 2*B*a*c*e*x^4 + 2*A*a*c*e*x^3 + B*a^2*e*x^2 + A*a^2*e*x)*sqrt(c*x^2 + a)*sqrt(e*x), x)","F",0
451,0,0,0,0.464081," ","integrate((e*x)^(1/2)*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c^{2} x^{5} + A c^{2} x^{4} + 2 \, B a c x^{3} + 2 \, A a c x^{2} + B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*c^2*x^5 + A*c^2*x^4 + 2*B*a*c*x^3 + 2*A*a*c*x^2 + B*a^2*x + A*a^2)*sqrt(c*x^2 + a)*sqrt(e*x), x)","F",0
452,0,0,0,0.460625," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c^{2} x^{5} + A c^{2} x^{4} + 2 \, B a c x^{3} + 2 \, A a c x^{2} + B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e x}, x\right)"," ",0,"integral((B*c^2*x^5 + A*c^2*x^4 + 2*B*a*c*x^3 + 2*A*a*c*x^2 + B*a^2*x + A*a^2)*sqrt(c*x^2 + a)*sqrt(e*x)/(e*x), x)","F",0
453,0,0,0,0.451098," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c^{2} x^{5} + A c^{2} x^{4} + 2 \, B a c x^{3} + 2 \, A a c x^{2} + B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral((B*c^2*x^5 + A*c^2*x^4 + 2*B*a*c*x^3 + 2*A*a*c*x^2 + B*a^2*x + A*a^2)*sqrt(c*x^2 + a)*sqrt(e*x)/(e^2*x^2), x)","F",0
454,0,0,0,0.454444," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c^{2} x^{5} + A c^{2} x^{4} + 2 \, B a c x^{3} + 2 \, A a c x^{2} + B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e^{3} x^{3}}, x\right)"," ",0,"integral((B*c^2*x^5 + A*c^2*x^4 + 2*B*a*c*x^3 + 2*A*a*c*x^2 + B*a^2*x + A*a^2)*sqrt(c*x^2 + a)*sqrt(e*x)/(e^3*x^3), x)","F",0
455,0,0,0,0.477080," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c^{2} x^{5} + A c^{2} x^{4} + 2 \, B a c x^{3} + 2 \, A a c x^{2} + B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral((B*c^2*x^5 + A*c^2*x^4 + 2*B*a*c*x^3 + 2*A*a*c*x^2 + B*a^2*x + A*a^2)*sqrt(c*x^2 + a)*sqrt(e*x)/(e^4*x^4), x)","F",0
456,0,0,0,0.469036," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c^{2} x^{5} + A c^{2} x^{4} + 2 \, B a c x^{3} + 2 \, A a c x^{2} + B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e^{5} x^{5}}, x\right)"," ",0,"integral((B*c^2*x^5 + A*c^2*x^4 + 2*B*a*c*x^3 + 2*A*a*c*x^2 + B*a^2*x + A*a^2)*sqrt(c*x^2 + a)*sqrt(e*x)/(e^5*x^5), x)","F",0
457,0,0,0,0.495298," ","integrate((B*x+A)*(c*x^2+a)^(5/2)/(e*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c^{2} x^{5} + A c^{2} x^{4} + 2 \, B a c x^{3} + 2 \, A a c x^{2} + B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{e^{6} x^{6}}, x\right)"," ",0,"integral((B*c^2*x^5 + A*c^2*x^4 + 2*B*a*c*x^3 + 2*A*a*c*x^2 + B*a^2*x + A*a^2)*sqrt(c*x^2 + a)*sqrt(e*x)/(e^6*x^6), x)","F",0
458,0,0,0,0.468915," ","integrate((e*x)^(7/2)*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{3} x^{4} + A e^{3} x^{3}\right)} \sqrt{e x}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((B*e^3*x^4 + A*e^3*x^3)*sqrt(e*x)/sqrt(c*x^2 + a), x)","F",0
459,0,0,0,0.443203," ","integrate((e*x)^(5/2)*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{3} + A e^{2} x^{2}\right)} \sqrt{e x}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((B*e^2*x^3 + A*e^2*x^2)*sqrt(e*x)/sqrt(c*x^2 + a), x)","F",0
460,0,0,0,0.474452," ","integrate((e*x)^(3/2)*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A e x\right)} \sqrt{e x}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((B*e*x^2 + A*e*x)*sqrt(e*x)/sqrt(c*x^2 + a), x)","F",0
461,0,0,0,0.463404," ","integrate((e*x)^(1/2)*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \sqrt{e x}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((B*x + A)*sqrt(e*x)/sqrt(c*x^2 + a), x)","F",0
462,0,0,0,0.463536," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c e x^{3} + a e x}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c*e*x^3 + a*e*x), x)","F",0
463,0,0,0,0.439202," ","integrate((B*x+A)/(e*x)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c e^{2} x^{4} + a e^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c*e^2*x^4 + a*e^2*x^2), x)","F",0
464,0,0,0,0.448774," ","integrate((B*x+A)/(e*x)^(5/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c e^{3} x^{5} + a e^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c*e^3*x^5 + a*e^3*x^3), x)","F",0
465,0,0,0,0.470392," ","integrate((B*x+A)/(e*x)^(7/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c e^{4} x^{6} + a e^{4} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c*e^4*x^6 + a*e^4*x^4), x)","F",0
466,0,0,0,0.553111," ","integrate((e*x)^(7/2)*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{3} x^{4} + A e^{3} x^{3}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e^3*x^4 + A*e^3*x^3)*sqrt(c*x^2 + a)*sqrt(e*x)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
467,0,0,0,0.530005," ","integrate((e*x)^(5/2)*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{3} + A e^{2} x^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e^2*x^3 + A*e^2*x^2)*sqrt(c*x^2 + a)*sqrt(e*x)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
468,0,0,0,0.475471," ","integrate((e*x)^(3/2)*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A e x\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e*x^2 + A*e*x)*sqrt(c*x^2 + a)*sqrt(e*x)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
469,0,0,0,0.455492," ","integrate((e*x)^(1/2)*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
470,0,0,0,0.451234," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{2} e x^{5} + 2 \, a c e x^{3} + a^{2} e x}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^2*e*x^5 + 2*a*c*e*x^3 + a^2*e*x), x)","F",0
471,0,0,0,0.463522," ","integrate((B*x+A)/(e*x)^(3/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{2} e^{2} x^{6} + 2 \, a c e^{2} x^{4} + a^{2} e^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^2*e^2*x^6 + 2*a*c*e^2*x^4 + a^2*e^2*x^2), x)","F",0
472,0,0,0,0.448982," ","integrate((B*x+A)/(e*x)^(5/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{2} e^{3} x^{7} + 2 \, a c e^{3} x^{5} + a^{2} e^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^2*e^3*x^7 + 2*a*c*e^3*x^5 + a^2*e^3*x^3), x)","F",0
473,0,0,0,0.441078," ","integrate((B*x+A)/(e*x)^(7/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{2} e^{4} x^{8} + 2 \, a c e^{4} x^{6} + a^{2} e^{4} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^2*e^4*x^8 + 2*a*c*e^4*x^6 + a^2*e^4*x^4), x)","F",0
474,0,0,0,0.497541," ","integrate((e*x)^(13/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{6} x^{7} + A e^{6} x^{6}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((B*e^6*x^7 + A*e^6*x^6)*sqrt(c*x^2 + a)*sqrt(e*x)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
475,0,0,0,0.500665," ","integrate((e*x)^(11/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{5} x^{6} + A e^{5} x^{5}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((B*e^5*x^6 + A*e^5*x^5)*sqrt(c*x^2 + a)*sqrt(e*x)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
476,0,0,0,0.461937," ","integrate((e*x)^(9/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{4} x^{5} + A e^{4} x^{4}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((B*e^4*x^5 + A*e^4*x^4)*sqrt(c*x^2 + a)*sqrt(e*x)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
477,0,0,0,0.566446," ","integrate((e*x)^(7/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{3} x^{4} + A e^{3} x^{3}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((B*e^3*x^4 + A*e^3*x^3)*sqrt(c*x^2 + a)*sqrt(e*x)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
478,0,0,0,0.453933," ","integrate((e*x)^(5/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{3} + A e^{2} x^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((B*e^2*x^3 + A*e^2*x^2)*sqrt(c*x^2 + a)*sqrt(e*x)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
479,0,0,0,0.448832," ","integrate((e*x)^(3/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A e x\right)} \sqrt{c x^{2} + a} \sqrt{e x}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((B*e*x^2 + A*e*x)*sqrt(c*x^2 + a)*sqrt(e*x)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
480,0,0,0,0.454981," ","integrate((e*x)^(1/2)*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
481,0,0,0,0.452869," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{3} e x^{7} + 3 \, a c^{2} e x^{5} + 3 \, a^{2} c e x^{3} + a^{3} e x}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^3*e*x^7 + 3*a*c^2*e*x^5 + 3*a^2*c*e*x^3 + a^3*e*x), x)","F",0
482,0,0,0,0.440855," ","integrate((B*x+A)/(e*x)^(3/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{3} e^{2} x^{8} + 3 \, a c^{2} e^{2} x^{6} + 3 \, a^{2} c e^{2} x^{4} + a^{3} e^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^3*e^2*x^8 + 3*a*c^2*e^2*x^6 + 3*a^2*c*e^2*x^4 + a^3*e^2*x^2), x)","F",0
483,0,0,0,0.450309," ","integrate((B*x+A)/(e*x)^(5/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{3} e^{3} x^{9} + 3 \, a c^{2} e^{3} x^{7} + 3 \, a^{2} c e^{3} x^{5} + a^{3} e^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^3*e^3*x^9 + 3*a*c^2*e^3*x^7 + 3*a^2*c*e^3*x^5 + a^3*e^3*x^3), x)","F",0
484,0,0,0,0.443843," ","integrate((B*x+A)/(e*x)^(7/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x}}{c^{3} e^{4} x^{10} + 3 \, a c^{2} e^{4} x^{8} + 3 \, a^{2} c e^{4} x^{6} + a^{3} e^{4} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x)/(c^3*e^4*x^10 + 3*a*c^2*e^4*x^8 + 3*a^2*c*e^4*x^6 + a^3*e^4*x^4), x)","F",0
485,1,1051,0,0.554895," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{{\left({\left(B c^{4} m^{9} + 45 \, B c^{4} m^{8} + 870 \, B c^{4} m^{7} + 9450 \, B c^{4} m^{6} + 63273 \, B c^{4} m^{5} + 269325 \, B c^{4} m^{4} + 723680 \, B c^{4} m^{3} + 1172700 \, B c^{4} m^{2} + 1026576 \, B c^{4} m + 362880 \, B c^{4}\right)} x^{10} + {\left(A c^{4} m^{9} + 46 \, A c^{4} m^{8} + 906 \, A c^{4} m^{7} + 9996 \, A c^{4} m^{6} + 67809 \, A c^{4} m^{5} + 291774 \, A c^{4} m^{4} + 790964 \, A c^{4} m^{3} + 1290824 \, A c^{4} m^{2} + 1136160 \, A c^{4} m + 403200 \, A c^{4}\right)} x^{9} + 4 \, {\left(B a c^{3} m^{9} + 47 \, B a c^{3} m^{8} + 944 \, B a c^{3} m^{7} + 10598 \, B a c^{3} m^{6} + 72989 \, B a c^{3} m^{5} + 318143 \, B a c^{3} m^{4} + 871786 \, B a c^{3} m^{3} + 1435212 \, B a c^{3} m^{2} + 1271880 \, B a c^{3} m + 453600 \, B a c^{3}\right)} x^{8} + 4 \, {\left(A a c^{3} m^{9} + 48 \, A a c^{3} m^{8} + 984 \, A a c^{3} m^{7} + 11262 \, A a c^{3} m^{6} + 78939 \, A a c^{3} m^{5} + 349482 \, A a c^{3} m^{4} + 970556 \, A a c^{3} m^{3} + 1615608 \, A a c^{3} m^{2} + 1444320 \, A a c^{3} m + 518400 \, A a c^{3}\right)} x^{7} + 6 \, {\left(B a^{2} c^{2} m^{9} + 49 \, B a^{2} c^{2} m^{8} + 1026 \, B a^{2} c^{2} m^{7} + 11994 \, B a^{2} c^{2} m^{6} + 85809 \, B a^{2} c^{2} m^{5} + 387201 \, B a^{2} c^{2} m^{4} + 1093724 \, B a^{2} c^{2} m^{3} + 1847156 \, B a^{2} c^{2} m^{2} + 1670640 \, B a^{2} c^{2} m + 604800 \, B a^{2} c^{2}\right)} x^{6} + 6 \, {\left(A a^{2} c^{2} m^{9} + 50 \, A a^{2} c^{2} m^{8} + 1070 \, A a^{2} c^{2} m^{7} + 12800 \, A a^{2} c^{2} m^{6} + 93773 \, A a^{2} c^{2} m^{5} + 433190 \, A a^{2} c^{2} m^{4} + 1250980 \, A a^{2} c^{2} m^{3} + 2154600 \, A a^{2} c^{2} m^{2} + 1980576 \, A a^{2} c^{2} m + 725760 \, A a^{2} c^{2}\right)} x^{5} + 4 \, {\left(B a^{3} c m^{9} + 51 \, B a^{3} c m^{8} + 1116 \, B a^{3} c m^{7} + 13686 \, B a^{3} c m^{6} + 103029 \, B a^{3} c m^{5} + 489939 \, B a^{3} c m^{4} + 1457174 \, B a^{3} c m^{3} + 2580804 \, B a^{3} c m^{2} + 2430360 \, B a^{3} c m + 907200 \, B a^{3} c\right)} x^{4} + 4 \, {\left(A a^{3} c m^{9} + 52 \, A a^{3} c m^{8} + 1164 \, A a^{3} c m^{7} + 14658 \, A a^{3} c m^{6} + 113799 \, A a^{3} c m^{5} + 560658 \, A a^{3} c m^{4} + 1734956 \, A a^{3} c m^{3} + 3204632 \, A a^{3} c m^{2} + 3139680 \, A a^{3} c m + 1209600 \, A a^{3} c\right)} x^{3} + {\left(B a^{4} m^{9} + 53 \, B a^{4} m^{8} + 1214 \, B a^{4} m^{7} + 15722 \, B a^{4} m^{6} + 126329 \, B a^{4} m^{5} + 649397 \, B a^{4} m^{4} + 2118136 \, B a^{4} m^{3} + 4173228 \, B a^{4} m^{2} + 4407120 \, B a^{4} m + 1814400 \, B a^{4}\right)} x^{2} + {\left(A a^{4} m^{9} + 54 \, A a^{4} m^{8} + 1266 \, A a^{4} m^{7} + 16884 \, A a^{4} m^{6} + 140889 \, A a^{4} m^{5} + 761166 \, A a^{4} m^{4} + 2655764 \, A a^{4} m^{3} + 5753736 \, A a^{4} m^{2} + 6999840 \, A a^{4} m + 3628800 \, A a^{4}\right)} x\right)} \left(e x\right)^{m}}{m^{10} + 55 \, m^{9} + 1320 \, m^{8} + 18150 \, m^{7} + 157773 \, m^{6} + 902055 \, m^{5} + 3416930 \, m^{4} + 8409500 \, m^{3} + 12753576 \, m^{2} + 10628640 \, m + 3628800}"," ",0,"((B*c^4*m^9 + 45*B*c^4*m^8 + 870*B*c^4*m^7 + 9450*B*c^4*m^6 + 63273*B*c^4*m^5 + 269325*B*c^4*m^4 + 723680*B*c^4*m^3 + 1172700*B*c^4*m^2 + 1026576*B*c^4*m + 362880*B*c^4)*x^10 + (A*c^4*m^9 + 46*A*c^4*m^8 + 906*A*c^4*m^7 + 9996*A*c^4*m^6 + 67809*A*c^4*m^5 + 291774*A*c^4*m^4 + 790964*A*c^4*m^3 + 1290824*A*c^4*m^2 + 1136160*A*c^4*m + 403200*A*c^4)*x^9 + 4*(B*a*c^3*m^9 + 47*B*a*c^3*m^8 + 944*B*a*c^3*m^7 + 10598*B*a*c^3*m^6 + 72989*B*a*c^3*m^5 + 318143*B*a*c^3*m^4 + 871786*B*a*c^3*m^3 + 1435212*B*a*c^3*m^2 + 1271880*B*a*c^3*m + 453600*B*a*c^3)*x^8 + 4*(A*a*c^3*m^9 + 48*A*a*c^3*m^8 + 984*A*a*c^3*m^7 + 11262*A*a*c^3*m^6 + 78939*A*a*c^3*m^5 + 349482*A*a*c^3*m^4 + 970556*A*a*c^3*m^3 + 1615608*A*a*c^3*m^2 + 1444320*A*a*c^3*m + 518400*A*a*c^3)*x^7 + 6*(B*a^2*c^2*m^9 + 49*B*a^2*c^2*m^8 + 1026*B*a^2*c^2*m^7 + 11994*B*a^2*c^2*m^6 + 85809*B*a^2*c^2*m^5 + 387201*B*a^2*c^2*m^4 + 1093724*B*a^2*c^2*m^3 + 1847156*B*a^2*c^2*m^2 + 1670640*B*a^2*c^2*m + 604800*B*a^2*c^2)*x^6 + 6*(A*a^2*c^2*m^9 + 50*A*a^2*c^2*m^8 + 1070*A*a^2*c^2*m^7 + 12800*A*a^2*c^2*m^6 + 93773*A*a^2*c^2*m^5 + 433190*A*a^2*c^2*m^4 + 1250980*A*a^2*c^2*m^3 + 2154600*A*a^2*c^2*m^2 + 1980576*A*a^2*c^2*m + 725760*A*a^2*c^2)*x^5 + 4*(B*a^3*c*m^9 + 51*B*a^3*c*m^8 + 1116*B*a^3*c*m^7 + 13686*B*a^3*c*m^6 + 103029*B*a^3*c*m^5 + 489939*B*a^3*c*m^4 + 1457174*B*a^3*c*m^3 + 2580804*B*a^3*c*m^2 + 2430360*B*a^3*c*m + 907200*B*a^3*c)*x^4 + 4*(A*a^3*c*m^9 + 52*A*a^3*c*m^8 + 1164*A*a^3*c*m^7 + 14658*A*a^3*c*m^6 + 113799*A*a^3*c*m^5 + 560658*A*a^3*c*m^4 + 1734956*A*a^3*c*m^3 + 3204632*A*a^3*c*m^2 + 3139680*A*a^3*c*m + 1209600*A*a^3*c)*x^3 + (B*a^4*m^9 + 53*B*a^4*m^8 + 1214*B*a^4*m^7 + 15722*B*a^4*m^6 + 126329*B*a^4*m^5 + 649397*B*a^4*m^4 + 2118136*B*a^4*m^3 + 4173228*B*a^4*m^2 + 4407120*B*a^4*m + 1814400*B*a^4)*x^2 + (A*a^4*m^9 + 54*A*a^4*m^8 + 1266*A*a^4*m^7 + 16884*A*a^4*m^6 + 140889*A*a^4*m^5 + 761166*A*a^4*m^4 + 2655764*A*a^4*m^3 + 5753736*A*a^4*m^2 + 6999840*A*a^4*m + 3628800*A*a^4)*x)*(e*x)^m/(m^10 + 55*m^9 + 1320*m^8 + 18150*m^7 + 157773*m^6 + 902055*m^5 + 3416930*m^4 + 8409500*m^3 + 12753576*m^2 + 10628640*m + 3628800)","B",0
486,1,649,0,0.447589," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left({\left(B c^{3} m^{7} + 28 \, B c^{3} m^{6} + 322 \, B c^{3} m^{5} + 1960 \, B c^{3} m^{4} + 6769 \, B c^{3} m^{3} + 13132 \, B c^{3} m^{2} + 13068 \, B c^{3} m + 5040 \, B c^{3}\right)} x^{8} + {\left(A c^{3} m^{7} + 29 \, A c^{3} m^{6} + 343 \, A c^{3} m^{5} + 2135 \, A c^{3} m^{4} + 7504 \, A c^{3} m^{3} + 14756 \, A c^{3} m^{2} + 14832 \, A c^{3} m + 5760 \, A c^{3}\right)} x^{7} + 3 \, {\left(B a c^{2} m^{7} + 30 \, B a c^{2} m^{6} + 366 \, B a c^{2} m^{5} + 2340 \, B a c^{2} m^{4} + 8409 \, B a c^{2} m^{3} + 16830 \, B a c^{2} m^{2} + 17144 \, B a c^{2} m + 6720 \, B a c^{2}\right)} x^{6} + 3 \, {\left(A a c^{2} m^{7} + 31 \, A a c^{2} m^{6} + 391 \, A a c^{2} m^{5} + 2581 \, A a c^{2} m^{4} + 9544 \, A a c^{2} m^{3} + 19564 \, A a c^{2} m^{2} + 20304 \, A a c^{2} m + 8064 \, A a c^{2}\right)} x^{5} + 3 \, {\left(B a^{2} c m^{7} + 32 \, B a^{2} c m^{6} + 418 \, B a^{2} c m^{5} + 2864 \, B a^{2} c m^{4} + 10993 \, B a^{2} c m^{3} + 23312 \, B a^{2} c m^{2} + 24876 \, B a^{2} c m + 10080 \, B a^{2} c\right)} x^{4} + 3 \, {\left(A a^{2} c m^{7} + 33 \, A a^{2} c m^{6} + 447 \, A a^{2} c m^{5} + 3195 \, A a^{2} c m^{4} + 12864 \, A a^{2} c m^{3} + 28692 \, A a^{2} c m^{2} + 32048 \, A a^{2} c m + 13440 \, A a^{2} c\right)} x^{3} + {\left(B a^{3} m^{7} + 34 \, B a^{3} m^{6} + 478 \, B a^{3} m^{5} + 3580 \, B a^{3} m^{4} + 15289 \, B a^{3} m^{3} + 36706 \, B a^{3} m^{2} + 44712 \, B a^{3} m + 20160 \, B a^{3}\right)} x^{2} + {\left(A a^{3} m^{7} + 35 \, A a^{3} m^{6} + 511 \, A a^{3} m^{5} + 4025 \, A a^{3} m^{4} + 18424 \, A a^{3} m^{3} + 48860 \, A a^{3} m^{2} + 69264 \, A a^{3} m + 40320 \, A a^{3}\right)} x\right)} \left(e x\right)^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320}"," ",0,"((B*c^3*m^7 + 28*B*c^3*m^6 + 322*B*c^3*m^5 + 1960*B*c^3*m^4 + 6769*B*c^3*m^3 + 13132*B*c^3*m^2 + 13068*B*c^3*m + 5040*B*c^3)*x^8 + (A*c^3*m^7 + 29*A*c^3*m^6 + 343*A*c^3*m^5 + 2135*A*c^3*m^4 + 7504*A*c^3*m^3 + 14756*A*c^3*m^2 + 14832*A*c^3*m + 5760*A*c^3)*x^7 + 3*(B*a*c^2*m^7 + 30*B*a*c^2*m^6 + 366*B*a*c^2*m^5 + 2340*B*a*c^2*m^4 + 8409*B*a*c^2*m^3 + 16830*B*a*c^2*m^2 + 17144*B*a*c^2*m + 6720*B*a*c^2)*x^6 + 3*(A*a*c^2*m^7 + 31*A*a*c^2*m^6 + 391*A*a*c^2*m^5 + 2581*A*a*c^2*m^4 + 9544*A*a*c^2*m^3 + 19564*A*a*c^2*m^2 + 20304*A*a*c^2*m + 8064*A*a*c^2)*x^5 + 3*(B*a^2*c*m^7 + 32*B*a^2*c*m^6 + 418*B*a^2*c*m^5 + 2864*B*a^2*c*m^4 + 10993*B*a^2*c*m^3 + 23312*B*a^2*c*m^2 + 24876*B*a^2*c*m + 10080*B*a^2*c)*x^4 + 3*(A*a^2*c*m^7 + 33*A*a^2*c*m^6 + 447*A*a^2*c*m^5 + 3195*A*a^2*c*m^4 + 12864*A*a^2*c*m^3 + 28692*A*a^2*c*m^2 + 32048*A*a^2*c*m + 13440*A*a^2*c)*x^3 + (B*a^3*m^7 + 34*B*a^3*m^6 + 478*B*a^3*m^5 + 3580*B*a^3*m^4 + 15289*B*a^3*m^3 + 36706*B*a^3*m^2 + 44712*B*a^3*m + 20160*B*a^3)*x^2 + (A*a^3*m^7 + 35*A*a^3*m^6 + 511*A*a^3*m^5 + 4025*A*a^3*m^4 + 18424*A*a^3*m^3 + 48860*A*a^3*m^2 + 69264*A*a^3*m + 40320*A*a^3)*x)*(e*x)^m/(m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)","B",0
487,1,343,0,0.429814," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(B c^{2} m^{5} + 15 \, B c^{2} m^{4} + 85 \, B c^{2} m^{3} + 225 \, B c^{2} m^{2} + 274 \, B c^{2} m + 120 \, B c^{2}\right)} x^{6} + {\left(A c^{2} m^{5} + 16 \, A c^{2} m^{4} + 95 \, A c^{2} m^{3} + 260 \, A c^{2} m^{2} + 324 \, A c^{2} m + 144 \, A c^{2}\right)} x^{5} + 2 \, {\left(B a c m^{5} + 17 \, B a c m^{4} + 107 \, B a c m^{3} + 307 \, B a c m^{2} + 396 \, B a c m + 180 \, B a c\right)} x^{4} + 2 \, {\left(A a c m^{5} + 18 \, A a c m^{4} + 121 \, A a c m^{3} + 372 \, A a c m^{2} + 508 \, A a c m + 240 \, A a c\right)} x^{3} + {\left(B a^{2} m^{5} + 19 \, B a^{2} m^{4} + 137 \, B a^{2} m^{3} + 461 \, B a^{2} m^{2} + 702 \, B a^{2} m + 360 \, B a^{2}\right)} x^{2} + {\left(A a^{2} m^{5} + 20 \, A a^{2} m^{4} + 155 \, A a^{2} m^{3} + 580 \, A a^{2} m^{2} + 1044 \, A a^{2} m + 720 \, A a^{2}\right)} x\right)} \left(e x\right)^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"((B*c^2*m^5 + 15*B*c^2*m^4 + 85*B*c^2*m^3 + 225*B*c^2*m^2 + 274*B*c^2*m + 120*B*c^2)*x^6 + (A*c^2*m^5 + 16*A*c^2*m^4 + 95*A*c^2*m^3 + 260*A*c^2*m^2 + 324*A*c^2*m + 144*A*c^2)*x^5 + 2*(B*a*c*m^5 + 17*B*a*c*m^4 + 107*B*a*c*m^3 + 307*B*a*c*m^2 + 396*B*a*c*m + 180*B*a*c)*x^4 + 2*(A*a*c*m^5 + 18*A*a*c*m^4 + 121*A*a*c*m^3 + 372*A*a*c*m^2 + 508*A*a*c*m + 240*A*a*c)*x^3 + (B*a^2*m^5 + 19*B*a^2*m^4 + 137*B*a^2*m^3 + 461*B*a^2*m^2 + 702*B*a^2*m + 360*B*a^2)*x^2 + (A*a^2*m^5 + 20*A*a^2*m^4 + 155*A*a^2*m^3 + 580*A*a^2*m^2 + 1044*A*a^2*m + 720*A*a^2)*x)*(e*x)^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
488,1,133,0,0.434449," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a),x, algorithm=""fricas"")","\frac{{\left({\left(B c m^{3} + 6 \, B c m^{2} + 11 \, B c m + 6 \, B c\right)} x^{4} + {\left(A c m^{3} + 7 \, A c m^{2} + 14 \, A c m + 8 \, A c\right)} x^{3} + {\left(B a m^{3} + 8 \, B a m^{2} + 19 \, B a m + 12 \, B a\right)} x^{2} + {\left(A a m^{3} + 9 \, A a m^{2} + 26 \, A a m + 24 \, A a\right)} x\right)} \left(e x\right)^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"((B*c*m^3 + 6*B*c*m^2 + 11*B*c*m + 6*B*c)*x^4 + (A*c*m^3 + 7*A*c*m^2 + 14*A*c*m + 8*A*c)*x^3 + (B*a*m^3 + 8*B*a*m^2 + 19*B*a*m + 12*B*a)*x^2 + (A*a*m^3 + 9*A*a*m^2 + 26*A*a*m + 24*A*a)*x)*(e*x)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","A",0
489,0,0,0,0.446322," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \left(e x\right)^{m}}{c x^{2} + a}, x\right)"," ",0,"integral((B*x + A)*(e*x)^m/(c*x^2 + a), x)","F",0
490,0,0,0,0.441713," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \left(e x\right)^{m}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((B*x + A)*(e*x)^m/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
491,0,0,0,0.506115," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \left(e x\right)^{m}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((B*x + A)*(e*x)^m/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
492,0,0,0,0.494856," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c^{2} x^{5} + A c^{2} x^{4} + 2 \, B a c x^{3} + 2 \, A a c x^{2} + B a^{2} x + A a^{2}\right)} \sqrt{c x^{2} + a} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*c^2*x^5 + A*c^2*x^4 + 2*B*a*c*x^3 + 2*A*a*c*x^2 + B*a^2*x + A*a^2)*sqrt(c*x^2 + a)*(e*x)^m, x)","F",0
493,0,0,0,0.438974," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*(e*x)^m, x)","F",0
494,0,0,0,0.428415," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + a} {\left(B x + A\right)} \left(e x\right)^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*(e*x)^m, x)","F",0
495,0,0,0,0.433072," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \left(e x\right)^{m}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((B*x + A)*(e*x)^m/sqrt(c*x^2 + a), x)","F",0
496,0,0,0,0.428239," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \left(e x\right)^{m}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*(e*x)^m/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
497,0,0,0,0.440786," ","integrate((e*x)^m*(B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \left(e x\right)^{m}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*(e*x)^m/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
498,0,0,0,0.443968," ","integrate(x^m*(a*x+1)/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{a^{3} x^{3} - a^{2} x^{2} - a x + 1}, x\right)"," ",0,"integral(x^m/(a^3*x^3 - a^2*x^2 - a*x + 1), x)","F",0
499,0,0,0,0.443599," ","integrate(x^m/(-a*x+1)^2/(a*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{a^{3} x^{3} - a^{2} x^{2} - a x + 1}, x\right)"," ",0,"integral(x^m/(a^3*x^3 - a^2*x^2 - a*x + 1), x)","F",0
500,0,0,0,0.451374," ","integrate(x^m/(-a^2*x^2+1)^2+a*x^(1+m)/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{m + 1} + x^{m}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral((a*x^(m + 1) + x^m)/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
501,0,0,0,0.463201," ","integrate(x^m/(-a*x+1)/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{a^{3} x^{3} - a^{2} x^{2} - a x + 1}, x\right)"," ",0,"integral(x^m/(a^3*x^3 - a^2*x^2 - a*x + 1), x)","F",0
502,0,0,0,0.439585," ","integrate((e*x)^m*(B*x+A)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(c x^{2} + a\right)}^{p} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*x + A)*(c*x^2 + a)^p*(e*x)^m, x)","F",0
503,0,0,0,0.443929," ","integrate(x^3*(e*x+d)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{4} + d x^{3}\right)} {\left(c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^4 + d*x^3)*(c*x^2 + a)^p, x)","F",0
504,0,0,0,0.517996," ","integrate(x^2*(e*x+d)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{3} + d x^{2}\right)} {\left(c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^3 + d*x^2)*(c*x^2 + a)^p, x)","F",0
505,0,0,0,0.491398," ","integrate(x*(e*x+d)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{2} + d x\right)} {\left(c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^2 + d*x)*(c*x^2 + a)^p, x)","F",0
506,0,0,0,0.457953," ","integrate((e*x+d)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x + d)*(c*x^2 + a)^p, x)","F",0
507,0,0,0,0.441037," ","integrate((e*x+d)*(c*x^2+a)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}}{x}, x\right)"," ",0,"integral((e*x + d)*(c*x^2 + a)^p/x, x)","F",0
508,0,0,0,0.433807," ","integrate((e*x+d)*(c*x^2+a)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((e*x + d)*(c*x^2 + a)^p/x^2, x)","F",0
509,0,0,0,0.426785," ","integrate((e*x+d)*(c*x^2+a)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((e*x + d)*(c*x^2 + a)^p/x^3, x)","F",0
510,1,53,0,0.391070," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{2} B + \frac{2}{7} x^{7} b a B + \frac{1}{7} x^{7} b^{2} A + \frac{1}{6} x^{6} a^{2} B + \frac{1}{3} x^{6} b a A + \frac{1}{5} x^{5} a^{2} A"," ",0,"1/8*x^8*b^2*B + 2/7*x^7*b*a*B + 1/7*x^7*b^2*A + 1/6*x^6*a^2*B + 1/3*x^6*b*a*A + 1/5*x^5*a^2*A","A",0
511,1,53,0,0.368685," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b^{2} B + \frac{1}{3} x^{6} b a B + \frac{1}{6} x^{6} b^{2} A + \frac{1}{5} x^{5} a^{2} B + \frac{2}{5} x^{5} b a A + \frac{1}{4} x^{4} a^{2} A"," ",0,"1/7*x^7*b^2*B + 1/3*x^6*b*a*B + 1/6*x^6*b^2*A + 1/5*x^5*a^2*B + 2/5*x^5*b*a*A + 1/4*x^4*a^2*A","A",0
512,1,53,0,0.356922," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} b^{2} B + \frac{2}{5} x^{5} b a B + \frac{1}{5} x^{5} b^{2} A + \frac{1}{4} x^{4} a^{2} B + \frac{1}{2} x^{4} b a A + \frac{1}{3} x^{3} a^{2} A"," ",0,"1/6*x^6*b^2*B + 2/5*x^5*b*a*B + 1/5*x^5*b^2*A + 1/4*x^4*a^2*B + 1/2*x^4*b*a*A + 1/3*x^3*a^2*A","A",0
513,1,53,0,0.359922," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{5} x^{5} b^{2} B + \frac{1}{2} x^{4} b a B + \frac{1}{4} x^{4} b^{2} A + \frac{1}{3} x^{3} a^{2} B + \frac{2}{3} x^{3} b a A + \frac{1}{2} x^{2} a^{2} A"," ",0,"1/5*x^5*b^2*B + 1/2*x^4*b*a*B + 1/4*x^4*b^2*A + 1/3*x^3*a^2*B + 2/3*x^3*b*a*A + 1/2*x^2*a^2*A","A",0
514,1,49,0,0.355637," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{4} x^{4} b^{2} B + \frac{2}{3} x^{3} b a B + \frac{1}{3} x^{3} b^{2} A + \frac{1}{2} x^{2} a^{2} B + x^{2} b a A + x a^{2} A"," ",0,"1/4*x^4*b^2*B + 2/3*x^3*b*a*B + 1/3*x^3*b^2*A + 1/2*x^2*a^2*B + x^2*b*a*A + x*a^2*A","A",0
515,1,46,0,0.406291," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x,x, algorithm=""fricas"")","\frac{1}{3} \, B b^{2} x^{3} + A a^{2} \log\left(x\right) + \frac{1}{2} \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + {\left(B a^{2} + 2 \, A a b\right)} x"," ",0,"1/3*B*b^2*x^3 + A*a^2*log(x) + 1/2*(2*B*a*b + A*b^2)*x^2 + (B*a^2 + 2*A*a*b)*x","A",0
516,1,52,0,0.431740," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^2,x, algorithm=""fricas"")","\frac{B b^{2} x^{3} - 2 \, A a^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} x \log\left(x\right)}{2 \, x}"," ",0,"1/2*(B*b^2*x^3 - 2*A*a^2 + 2*(2*B*a*b + A*b^2)*x^2 + 2*(B*a^2 + 2*A*a*b)*x*log(x))/x","A",0
517,1,53,0,0.431145," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^3,x, algorithm=""fricas"")","\frac{2 \, B b^{2} x^{3} + 2 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} \log\left(x\right) - A a^{2} - 2 \, {\left(B a^{2} + 2 \, A a b\right)} x}{2 \, x^{2}}"," ",0,"1/2*(2*B*b^2*x^3 + 2*(2*B*a*b + A*b^2)*x^2*log(x) - A*a^2 - 2*(B*a^2 + 2*A*a*b)*x)/x^2","A",0
518,1,53,0,0.413208," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^4,x, algorithm=""fricas"")","\frac{6 \, B b^{2} x^{3} \log\left(x\right) - 2 \, A a^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} x}{6 \, x^{3}}"," ",0,"1/6*(6*B*b^2*x^3*log(x) - 2*A*a^2 - 6*(2*B*a*b + A*b^2)*x^2 - 3*(B*a^2 + 2*A*a*b)*x)/x^3","A",0
519,1,51,0,0.390457," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^5,x, algorithm=""fricas"")","-\frac{12 \, B b^{2} x^{3} + 3 \, A a^{2} + 6 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 4 \, {\left(B a^{2} + 2 \, A a b\right)} x}{12 \, x^{4}}"," ",0,"-1/12*(12*B*b^2*x^3 + 3*A*a^2 + 6*(2*B*a*b + A*b^2)*x^2 + 4*(B*a^2 + 2*A*a*b)*x)/x^4","A",0
520,1,51,0,0.404705," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^6,x, algorithm=""fricas"")","-\frac{30 \, B b^{2} x^{3} + 12 \, A a^{2} + 20 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} x}{60 \, x^{5}}"," ",0,"-1/60*(30*B*b^2*x^3 + 12*A*a^2 + 20*(2*B*a*b + A*b^2)*x^2 + 15*(B*a^2 + 2*A*a*b)*x)/x^5","A",0
521,1,51,0,0.391502," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^7,x, algorithm=""fricas"")","-\frac{20 \, B b^{2} x^{3} + 10 \, A a^{2} + 15 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 12 \, {\left(B a^{2} + 2 \, A a b\right)} x}{60 \, x^{6}}"," ",0,"-1/60*(20*B*b^2*x^3 + 10*A*a^2 + 15*(2*B*a*b + A*b^2)*x^2 + 12*(B*a^2 + 2*A*a*b)*x)/x^6","A",0
522,1,51,0,0.391369," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^8,x, algorithm=""fricas"")","-\frac{105 \, B b^{2} x^{3} + 60 \, A a^{2} + 84 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 70 \, {\left(B a^{2} + 2 \, A a b\right)} x}{420 \, x^{7}}"," ",0,"-1/420*(105*B*b^2*x^3 + 60*A*a^2 + 84*(2*B*a*b + A*b^2)*x^2 + 70*(B*a^2 + 2*A*a*b)*x)/x^7","A",0
523,1,101,0,0.349293," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} b^{4} B + \frac{4}{9} x^{9} b^{3} a B + \frac{1}{9} x^{9} b^{4} A + \frac{3}{4} x^{8} b^{2} a^{2} B + \frac{1}{2} x^{8} b^{3} a A + \frac{4}{7} x^{7} b a^{3} B + \frac{6}{7} x^{7} b^{2} a^{2} A + \frac{1}{6} x^{6} a^{4} B + \frac{2}{3} x^{6} b a^{3} A + \frac{1}{5} x^{5} a^{4} A"," ",0,"1/10*x^10*b^4*B + 4/9*x^9*b^3*a*B + 1/9*x^9*b^4*A + 3/4*x^8*b^2*a^2*B + 1/2*x^8*b^3*a*A + 4/7*x^7*b*a^3*B + 6/7*x^7*b^2*a^2*A + 1/6*x^6*a^4*B + 2/3*x^6*b*a^3*A + 1/5*x^5*a^4*A","A",0
524,1,100,0,0.361453," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} b^{4} B + \frac{1}{2} x^{8} b^{3} a B + \frac{1}{8} x^{8} b^{4} A + \frac{6}{7} x^{7} b^{2} a^{2} B + \frac{4}{7} x^{7} b^{3} a A + \frac{2}{3} x^{6} b a^{3} B + x^{6} b^{2} a^{2} A + \frac{1}{5} x^{5} a^{4} B + \frac{4}{5} x^{5} b a^{3} A + \frac{1}{4} x^{4} a^{4} A"," ",0,"1/9*x^9*b^4*B + 1/2*x^8*b^3*a*B + 1/8*x^8*b^4*A + 6/7*x^7*b^2*a^2*B + 4/7*x^7*b^3*a*A + 2/3*x^6*b*a^3*B + x^6*b^2*a^2*A + 1/5*x^5*a^4*B + 4/5*x^5*b*a^3*A + 1/4*x^4*a^4*A","A",0
525,1,99,0,0.363523," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{4} B + \frac{4}{7} x^{7} b^{3} a B + \frac{1}{7} x^{7} b^{4} A + x^{6} b^{2} a^{2} B + \frac{2}{3} x^{6} b^{3} a A + \frac{4}{5} x^{5} b a^{3} B + \frac{6}{5} x^{5} b^{2} a^{2} A + \frac{1}{4} x^{4} a^{4} B + x^{4} b a^{3} A + \frac{1}{3} x^{3} a^{4} A"," ",0,"1/8*x^8*b^4*B + 4/7*x^7*b^3*a*B + 1/7*x^7*b^4*A + x^6*b^2*a^2*B + 2/3*x^6*b^3*a*A + 4/5*x^5*b*a^3*B + 6/5*x^5*b^2*a^2*A + 1/4*x^4*a^4*B + x^4*b*a^3*A + 1/3*x^3*a^4*A","A",0
526,1,100,0,0.367821," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} b^{4} B + \frac{2}{3} x^{6} b^{3} a B + \frac{1}{6} x^{6} b^{4} A + \frac{6}{5} x^{5} b^{2} a^{2} B + \frac{4}{5} x^{5} b^{3} a A + x^{4} b a^{3} B + \frac{3}{2} x^{4} b^{2} a^{2} A + \frac{1}{3} x^{3} a^{4} B + \frac{4}{3} x^{3} b a^{3} A + \frac{1}{2} x^{2} a^{4} A"," ",0,"1/7*x^7*b^4*B + 2/3*x^6*b^3*a*B + 1/6*x^6*b^4*A + 6/5*x^5*b^2*a^2*B + 4/5*x^5*b^3*a*A + x^4*b*a^3*B + 3/2*x^4*b^2*a^2*A + 1/3*x^3*a^4*B + 4/3*x^3*b*a^3*A + 1/2*x^2*a^4*A","A",0
527,1,97,0,0.364583," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} b^{4} B + \frac{4}{5} x^{5} b^{3} a B + \frac{1}{5} x^{5} b^{4} A + \frac{3}{2} x^{4} b^{2} a^{2} B + x^{4} b^{3} a A + \frac{4}{3} x^{3} b a^{3} B + 2 x^{3} b^{2} a^{2} A + \frac{1}{2} x^{2} a^{4} B + 2 x^{2} b a^{3} A + x a^{4} A"," ",0,"1/6*x^6*b^4*B + 4/5*x^5*b^3*a*B + 1/5*x^5*b^4*A + 3/2*x^4*b^2*a^2*B + x^4*b^3*a*A + 4/3*x^3*b*a^3*B + 2*x^3*b^2*a^2*A + 1/2*x^2*a^4*B + 2*x^2*b*a^3*A + x*a^4*A","B",0
528,1,93,0,0.399475," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x,x, algorithm=""fricas"")","\frac{1}{5} \, B b^{4} x^{5} + A a^{4} \log\left(x\right) + \frac{1}{4} \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + \frac{2}{3} \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} x"," ",0,"1/5*B*b^4*x^5 + A*a^4*log(x) + 1/4*(4*B*a*b^3 + A*b^4)*x^4 + 2/3*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + (2*B*a^3*b + 3*A*a^2*b^2)*x^2 + (B*a^4 + 4*A*a^3*b)*x","A",0
529,1,101,0,0.396479," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^2,x, algorithm=""fricas"")","\frac{3 \, B b^{4} x^{5} - 12 \, A a^{4} + 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 12 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 24 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 12 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x \log\left(x\right)}{12 \, x}"," ",0,"1/12*(3*B*b^4*x^5 - 12*A*a^4 + 4*(4*B*a*b^3 + A*b^4)*x^4 + 12*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 24*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 + 12*(B*a^4 + 4*A*a^3*b)*x*log(x))/x","A",0
530,1,101,0,0.395617," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^3,x, algorithm=""fricas"")","\frac{2 \, B b^{4} x^{5} - 3 \, A a^{4} + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 12 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 12 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} \log\left(x\right) - 6 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{6 \, x^{2}}"," ",0,"1/6*(2*B*b^4*x^5 - 3*A*a^4 + 3*(4*B*a*b^3 + A*b^4)*x^4 + 12*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 12*(2*B*a^3*b + 3*A*a^2*b^2)*x^2*log(x) - 6*(B*a^4 + 4*A*a^3*b)*x)/x^2","A",0
531,1,101,0,0.394216," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^4,x, algorithm=""fricas"")","\frac{3 \, B b^{4} x^{5} - 2 \, A a^{4} + 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 12 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} \log\left(x\right) - 12 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} - 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{6 \, x^{3}}"," ",0,"1/6*(3*B*b^4*x^5 - 2*A*a^4 + 6*(4*B*a*b^3 + A*b^4)*x^4 + 12*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3*log(x) - 12*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 - 3*(B*a^4 + 4*A*a^3*b)*x)/x^3","A",0
532,1,101,0,0.406237," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^5,x, algorithm=""fricas"")","\frac{12 \, B b^{4} x^{5} + 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} \log\left(x\right) - 3 \, A a^{4} - 24 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} - 12 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} - 4 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{12 \, x^{4}}"," ",0,"1/12*(12*B*b^4*x^5 + 12*(4*B*a*b^3 + A*b^4)*x^4*log(x) - 3*A*a^4 - 24*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 - 12*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 - 4*(B*a^4 + 4*A*a^3*b)*x)/x^4","A",0
533,1,101,0,0.406218," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^6,x, algorithm=""fricas"")","\frac{60 \, B b^{4} x^{5} \log\left(x\right) - 12 \, A a^{4} - 60 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} - 60 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} - 40 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} - 15 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{60 \, x^{5}}"," ",0,"1/60*(60*B*b^4*x^5*log(x) - 12*A*a^4 - 60*(4*B*a*b^3 + A*b^4)*x^4 - 60*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 - 40*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 - 15*(B*a^4 + 4*A*a^3*b)*x)/x^5","A",0
534,1,99,0,0.396312," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^7,x, algorithm=""fricas"")","-\frac{30 \, B b^{4} x^{5} + 5 \, A a^{4} + 15 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 20 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 15 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 6 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{30 \, x^{6}}"," ",0,"-1/30*(30*B*b^4*x^5 + 5*A*a^4 + 15*(4*B*a*b^3 + A*b^4)*x^4 + 20*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 15*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 + 6*(B*a^4 + 4*A*a^3*b)*x)/x^6","B",0
535,1,99,0,0.392816," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^8,x, algorithm=""fricas"")","-\frac{105 \, B b^{4} x^{5} + 30 \, A a^{4} + 70 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 105 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 84 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 35 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{210 \, x^{7}}"," ",0,"-1/210*(105*B*b^4*x^5 + 30*A*a^4 + 70*(4*B*a*b^3 + A*b^4)*x^4 + 105*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 84*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 + 35*(B*a^4 + 4*A*a^3*b)*x)/x^7","A",0
536,1,99,0,0.390942," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^9,x, algorithm=""fricas"")","-\frac{280 \, B b^{4} x^{5} + 105 \, A a^{4} + 210 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 336 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 280 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 120 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{840 \, x^{8}}"," ",0,"-1/840*(280*B*b^4*x^5 + 105*A*a^4 + 210*(4*B*a*b^3 + A*b^4)*x^4 + 336*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 280*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 + 120*(B*a^4 + 4*A*a^3*b)*x)/x^8","A",0
537,1,99,0,0.394250," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^10,x, algorithm=""fricas"")","-\frac{630 \, B b^{4} x^{5} + 280 \, A a^{4} + 504 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 840 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 720 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 315 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{2520 \, x^{9}}"," ",0,"-1/2520*(630*B*b^4*x^5 + 280*A*a^4 + 504*(4*B*a*b^3 + A*b^4)*x^4 + 840*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 720*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 + 315*(B*a^4 + 4*A*a^3*b)*x)/x^9","A",0
538,1,99,0,0.394523," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^11,x, algorithm=""fricas"")","-\frac{252 \, B b^{4} x^{5} + 126 \, A a^{4} + 210 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 360 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 315 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 140 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x}{1260 \, x^{10}}"," ",0,"-1/1260*(252*B*b^4*x^5 + 126*A*a^4 + 210*(4*B*a*b^3 + A*b^4)*x^4 + 360*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 315*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 + 140*(B*a^4 + 4*A*a^3*b)*x)/x^10","A",0
539,1,149,0,0.349762," ","integrate(x^5*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} b^{6} B + \frac{1}{2} x^{12} b^{5} a B + \frac{1}{12} x^{12} b^{6} A + \frac{15}{11} x^{11} b^{4} a^{2} B + \frac{6}{11} x^{11} b^{5} a A + 2 x^{10} b^{3} a^{3} B + \frac{3}{2} x^{10} b^{4} a^{2} A + \frac{5}{3} x^{9} b^{2} a^{4} B + \frac{20}{9} x^{9} b^{3} a^{3} A + \frac{3}{4} x^{8} b a^{5} B + \frac{15}{8} x^{8} b^{2} a^{4} A + \frac{1}{7} x^{7} a^{6} B + \frac{6}{7} x^{7} b a^{5} A + \frac{1}{6} x^{6} a^{6} A"," ",0,"1/13*x^13*b^6*B + 1/2*x^12*b^5*a*B + 1/12*x^12*b^6*A + 15/11*x^11*b^4*a^2*B + 6/11*x^11*b^5*a*A + 2*x^10*b^3*a^3*B + 3/2*x^10*b^4*a^2*A + 5/3*x^9*b^2*a^4*B + 20/9*x^9*b^3*a^3*A + 3/4*x^8*b*a^5*B + 15/8*x^8*b^2*a^4*A + 1/7*x^7*a^6*B + 6/7*x^7*b*a^5*A + 1/6*x^6*a^6*A","A",0
540,1,148,0,0.355345," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{12} x^{12} b^{6} B + \frac{6}{11} x^{11} b^{5} a B + \frac{1}{11} x^{11} b^{6} A + \frac{3}{2} x^{10} b^{4} a^{2} B + \frac{3}{5} x^{10} b^{5} a A + \frac{20}{9} x^{9} b^{3} a^{3} B + \frac{5}{3} x^{9} b^{4} a^{2} A + \frac{15}{8} x^{8} b^{2} a^{4} B + \frac{5}{2} x^{8} b^{3} a^{3} A + \frac{6}{7} x^{7} b a^{5} B + \frac{15}{7} x^{7} b^{2} a^{4} A + \frac{1}{6} x^{6} a^{6} B + x^{6} b a^{5} A + \frac{1}{5} x^{5} a^{6} A"," ",0,"1/12*x^12*b^6*B + 6/11*x^11*b^5*a*B + 1/11*x^11*b^6*A + 3/2*x^10*b^4*a^2*B + 3/5*x^10*b^5*a*A + 20/9*x^9*b^3*a^3*B + 5/3*x^9*b^4*a^2*A + 15/8*x^8*b^2*a^4*B + 5/2*x^8*b^3*a^3*A + 6/7*x^7*b*a^5*B + 15/7*x^7*b^2*a^4*A + 1/6*x^6*a^6*B + x^6*b*a^5*A + 1/5*x^5*a^6*A","A",0
541,1,148,0,0.407764," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} b^{6} B + \frac{3}{5} x^{10} b^{5} a B + \frac{1}{10} x^{10} b^{6} A + \frac{5}{3} x^{9} b^{4} a^{2} B + \frac{2}{3} x^{9} b^{5} a A + \frac{5}{2} x^{8} b^{3} a^{3} B + \frac{15}{8} x^{8} b^{4} a^{2} A + \frac{15}{7} x^{7} b^{2} a^{4} B + \frac{20}{7} x^{7} b^{3} a^{3} A + x^{6} b a^{5} B + \frac{5}{2} x^{6} b^{2} a^{4} A + \frac{1}{5} x^{5} a^{6} B + \frac{6}{5} x^{5} b a^{5} A + \frac{1}{4} x^{4} a^{6} A"," ",0,"1/11*x^11*b^6*B + 3/5*x^10*b^5*a*B + 1/10*x^10*b^6*A + 5/3*x^9*b^4*a^2*B + 2/3*x^9*b^5*a*A + 5/2*x^8*b^3*a^3*B + 15/8*x^8*b^4*a^2*A + 15/7*x^7*b^2*a^4*B + 20/7*x^7*b^3*a^3*A + x^6*b*a^5*B + 5/2*x^6*b^2*a^4*A + 1/5*x^5*a^6*B + 6/5*x^5*b*a^5*A + 1/4*x^4*a^6*A","A",0
542,1,149,0,0.376510," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} b^{6} B + \frac{2}{3} x^{9} b^{5} a B + \frac{1}{9} x^{9} b^{6} A + \frac{15}{8} x^{8} b^{4} a^{2} B + \frac{3}{4} x^{8} b^{5} a A + \frac{20}{7} x^{7} b^{3} a^{3} B + \frac{15}{7} x^{7} b^{4} a^{2} A + \frac{5}{2} x^{6} b^{2} a^{4} B + \frac{10}{3} x^{6} b^{3} a^{3} A + \frac{6}{5} x^{5} b a^{5} B + 3 x^{5} b^{2} a^{4} A + \frac{1}{4} x^{4} a^{6} B + \frac{3}{2} x^{4} b a^{5} A + \frac{1}{3} x^{3} a^{6} A"," ",0,"1/10*x^10*b^6*B + 2/3*x^9*b^5*a*B + 1/9*x^9*b^6*A + 15/8*x^8*b^4*a^2*B + 3/4*x^8*b^5*a*A + 20/7*x^7*b^3*a^3*B + 15/7*x^7*b^4*a^2*A + 5/2*x^6*b^2*a^4*B + 10/3*x^6*b^3*a^3*A + 6/5*x^5*b*a^5*B + 3*x^5*b^2*a^4*A + 1/4*x^4*a^6*B + 3/2*x^4*b*a^5*A + 1/3*x^3*a^6*A","A",0
543,1,149,0,0.352411," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} b^{6} B + \frac{3}{4} x^{8} b^{5} a B + \frac{1}{8} x^{8} b^{6} A + \frac{15}{7} x^{7} b^{4} a^{2} B + \frac{6}{7} x^{7} b^{5} a A + \frac{10}{3} x^{6} b^{3} a^{3} B + \frac{5}{2} x^{6} b^{4} a^{2} A + 3 x^{5} b^{2} a^{4} B + 4 x^{5} b^{3} a^{3} A + \frac{3}{2} x^{4} b a^{5} B + \frac{15}{4} x^{4} b^{2} a^{4} A + \frac{1}{3} x^{3} a^{6} B + 2 x^{3} b a^{5} A + \frac{1}{2} x^{2} a^{6} A"," ",0,"1/9*x^9*b^6*B + 3/4*x^8*b^5*a*B + 1/8*x^8*b^6*A + 15/7*x^7*b^4*a^2*B + 6/7*x^7*b^5*a*A + 10/3*x^6*b^3*a^3*B + 5/2*x^6*b^4*a^2*A + 3*x^5*b^2*a^4*B + 4*x^5*b^3*a^3*A + 3/2*x^4*b*a^5*B + 15/4*x^4*b^2*a^4*A + 1/3*x^3*a^6*B + 2*x^3*b*a^5*A + 1/2*x^2*a^6*A","B",0
544,1,145,0,0.354900," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{6} B + \frac{6}{7} x^{7} b^{5} a B + \frac{1}{7} x^{7} b^{6} A + \frac{5}{2} x^{6} b^{4} a^{2} B + x^{6} b^{5} a A + 4 x^{5} b^{3} a^{3} B + 3 x^{5} b^{4} a^{2} A + \frac{15}{4} x^{4} b^{2} a^{4} B + 5 x^{4} b^{3} a^{3} A + 2 x^{3} b a^{5} B + 5 x^{3} b^{2} a^{4} A + \frac{1}{2} x^{2} a^{6} B + 3 x^{2} b a^{5} A + x a^{6} A"," ",0,"1/8*x^8*b^6*B + 6/7*x^7*b^5*a*B + 1/7*x^7*b^6*A + 5/2*x^6*b^4*a^2*B + x^6*b^5*a*A + 4*x^5*b^3*a^3*B + 3*x^5*b^4*a^2*A + 15/4*x^4*b^2*a^4*B + 5*x^4*b^3*a^3*A + 2*x^3*b*a^5*B + 5*x^3*b^2*a^4*A + 1/2*x^2*a^6*B + 3*x^2*b*a^5*A + x*a^6*A","B",0
545,1,142,0,0.486115," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x,x, algorithm=""fricas"")","\frac{1}{7} \, B b^{6} x^{7} + A a^{6} \log\left(x\right) + \frac{1}{6} \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + \frac{3}{5} \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + \frac{5}{4} \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + \frac{5}{3} \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + \frac{3}{2} \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + {\left(B a^{6} + 6 \, A a^{5} b\right)} x"," ",0,"1/7*B*b^6*x^7 + A*a^6*log(x) + 1/6*(6*B*a*b^5 + A*b^6)*x^6 + 3/5*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 5/4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 5/3*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 3/2*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + (B*a^6 + 6*A*a^5*b)*x","A",0
546,1,149,0,0.419487," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^2,x, algorithm=""fricas"")","\frac{10 \, B b^{6} x^{7} - 60 \, A a^{6} + 12 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 45 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 100 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 150 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 180 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 60 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x \log\left(x\right)}{60 \, x}"," ",0,"1/60*(10*B*b^6*x^7 - 60*A*a^6 + 12*(6*B*a*b^5 + A*b^6)*x^6 + 45*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 100*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 150*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 180*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 60*(B*a^6 + 6*A*a^5*b)*x*log(x))/x","A",0
547,1,149,0,0.421150," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^3,x, algorithm=""fricas"")","\frac{4 \, B b^{6} x^{7} - 10 \, A a^{6} + 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 20 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 50 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 100 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 60 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} \log\left(x\right) - 20 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{20 \, x^{2}}"," ",0,"1/20*(4*B*b^6*x^7 - 10*A*a^6 + 5*(6*B*a*b^5 + A*b^6)*x^6 + 20*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 50*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 100*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 60*(2*B*a^5*b + 5*A*a^4*b^2)*x^2*log(x) - 20*(B*a^6 + 6*A*a^5*b)*x)/x^2","A",0
548,1,149,0,0.405077," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^4,x, algorithm=""fricas"")","\frac{3 \, B b^{6} x^{7} - 4 \, A a^{6} + 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 18 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 60 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 60 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} \log\left(x\right) - 36 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} - 6 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{12 \, x^{3}}"," ",0,"1/12*(3*B*b^6*x^7 - 4*A*a^6 + 4*(6*B*a*b^5 + A*b^6)*x^6 + 18*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 60*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 60*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3*log(x) - 36*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 - 6*(B*a^6 + 6*A*a^5*b)*x)/x^3","A",0
549,1,149,0,0.418632," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^5,x, algorithm=""fricas"")","\frac{4 \, B b^{6} x^{7} - 3 \, A a^{6} + 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 36 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 60 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} \log\left(x\right) - 60 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} - 18 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} - 4 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{12 \, x^{4}}"," ",0,"1/12*(4*B*b^6*x^7 - 3*A*a^6 + 6*(6*B*a*b^5 + A*b^6)*x^6 + 36*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 60*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4*log(x) - 60*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 - 18*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 - 4*(B*a^6 + 6*A*a^5*b)*x)/x^4","A",0
550,1,149,0,0.405094," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^6,x, algorithm=""fricas"")","\frac{10 \, B b^{6} x^{7} - 4 \, A a^{6} + 20 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 60 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} \log\left(x\right) - 100 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} - 50 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} - 20 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} - 5 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{20 \, x^{5}}"," ",0,"1/20*(10*B*b^6*x^7 - 4*A*a^6 + 20*(6*B*a*b^5 + A*b^6)*x^6 + 60*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5*log(x) - 100*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 - 50*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 - 20*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 - 5*(B*a^6 + 6*A*a^5*b)*x)/x^5","A",0
551,1,149,0,0.493125," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^7,x, algorithm=""fricas"")","\frac{60 \, B b^{6} x^{7} + 60 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} \log\left(x\right) - 10 \, A a^{6} - 180 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} - 150 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} - 100 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} - 45 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} - 12 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{60 \, x^{6}}"," ",0,"1/60*(60*B*b^6*x^7 + 60*(6*B*a*b^5 + A*b^6)*x^6*log(x) - 10*A*a^6 - 180*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 - 150*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 - 100*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 - 45*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 - 12*(B*a^6 + 6*A*a^5*b)*x)/x^6","A",0
552,1,149,0,0.415526," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^8,x, algorithm=""fricas"")","\frac{420 \, B b^{6} x^{7} \log\left(x\right) - 60 \, A a^{6} - 420 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} - 630 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} - 700 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} - 525 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} - 252 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} - 70 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{420 \, x^{7}}"," ",0,"1/420*(420*B*b^6*x^7*log(x) - 60*A*a^6 - 420*(6*B*a*b^5 + A*b^6)*x^6 - 630*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 - 700*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 - 525*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 - 252*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 - 70*(B*a^6 + 6*A*a^5*b)*x)/x^7","A",0
553,1,147,0,0.388692," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^9,x, algorithm=""fricas"")","-\frac{56 \, B b^{6} x^{7} + 7 \, A a^{6} + 28 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 56 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 70 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 56 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 28 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 8 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{56 \, x^{8}}"," ",0,"-1/56*(56*B*b^6*x^7 + 7*A*a^6 + 28*(6*B*a*b^5 + A*b^6)*x^6 + 56*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 70*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 56*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 28*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 8*(B*a^6 + 6*A*a^5*b)*x)/x^8","B",0
554,1,147,0,0.389730," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^10,x, algorithm=""fricas"")","-\frac{252 \, B b^{6} x^{7} + 56 \, A a^{6} + 168 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 378 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 504 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 420 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 216 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 63 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{504 \, x^{9}}"," ",0,"-1/504*(252*B*b^6*x^7 + 56*A*a^6 + 168*(6*B*a*b^5 + A*b^6)*x^6 + 378*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 504*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 420*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 216*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 63*(B*a^6 + 6*A*a^5*b)*x)/x^9","B",0
555,1,147,0,0.392035," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^11,x, algorithm=""fricas"")","-\frac{840 \, B b^{6} x^{7} + 252 \, A a^{6} + 630 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 1512 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 2100 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 1800 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 945 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 280 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{2520 \, x^{10}}"," ",0,"-1/2520*(840*B*b^6*x^7 + 252*A*a^6 + 630*(6*B*a*b^5 + A*b^6)*x^6 + 1512*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 2100*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 1800*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 945*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 280*(B*a^6 + 6*A*a^5*b)*x)/x^10","A",0
556,1,147,0,0.394950," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^12,x, algorithm=""fricas"")","-\frac{2310 \, B b^{6} x^{7} + 840 \, A a^{6} + 1848 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 4620 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 6600 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 5775 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 3080 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 924 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{9240 \, x^{11}}"," ",0,"-1/9240*(2310*B*b^6*x^7 + 840*A*a^6 + 1848*(6*B*a*b^5 + A*b^6)*x^6 + 4620*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 6600*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 5775*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 3080*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 924*(B*a^6 + 6*A*a^5*b)*x)/x^11","A",0
557,1,147,0,0.407235," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^13,x, algorithm=""fricas"")","-\frac{5544 \, B b^{6} x^{7} + 2310 \, A a^{6} + 4620 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 11880 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 17325 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 15400 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 8316 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 2520 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{27720 \, x^{12}}"," ",0,"-1/27720*(5544*B*b^6*x^7 + 2310*A*a^6 + 4620*(6*B*a*b^5 + A*b^6)*x^6 + 11880*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 17325*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 15400*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 8316*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 2520*(B*a^6 + 6*A*a^5*b)*x)/x^12","A",0
558,1,147,0,0.421928," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^14,x, algorithm=""fricas"")","-\frac{12012 \, B b^{6} x^{7} + 5544 \, A a^{6} + 10296 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 27027 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 40040 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 36036 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 19656 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 6006 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x}{72072 \, x^{13}}"," ",0,"-1/72072*(12012*B*b^6*x^7 + 5544*A*a^6 + 10296*(6*B*a*b^5 + A*b^6)*x^6 + 27027*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 40040*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 36036*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 19656*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 6006*(B*a^6 + 6*A*a^5*b)*x)/x^13","A",0
559,1,132,0,0.368249," ","integrate(x^7*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{19} x^{19} e + \frac{5}{9} x^{18} e + \frac{1}{18} x^{18} d + \frac{45}{17} x^{17} e + \frac{10}{17} x^{17} d + \frac{15}{2} x^{16} e + \frac{45}{16} x^{16} d + 14 x^{15} e + 8 x^{15} d + 18 x^{14} e + 15 x^{14} d + \frac{210}{13} x^{13} e + \frac{252}{13} x^{13} d + 10 x^{12} e + \frac{35}{2} x^{12} d + \frac{45}{11} x^{11} e + \frac{120}{11} x^{11} d + x^{10} e + \frac{9}{2} x^{10} d + \frac{1}{9} x^{9} e + \frac{10}{9} x^{9} d + \frac{1}{8} x^{8} d"," ",0,"1/19*x^19*e + 5/9*x^18*e + 1/18*x^18*d + 45/17*x^17*e + 10/17*x^17*d + 15/2*x^16*e + 45/16*x^16*d + 14*x^15*e + 8*x^15*d + 18*x^14*e + 15*x^14*d + 210/13*x^13*e + 252/13*x^13*d + 10*x^12*e + 35/2*x^12*d + 45/11*x^11*e + 120/11*x^11*d + x^10*e + 9/2*x^10*d + 1/9*x^9*e + 10/9*x^9*d + 1/8*x^8*d","A",0
560,1,133,0,0.347180," ","integrate(x^6*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{18} x^{18} e + \frac{10}{17} x^{17} e + \frac{1}{17} x^{17} d + \frac{45}{16} x^{16} e + \frac{5}{8} x^{16} d + 8 x^{15} e + 3 x^{15} d + 15 x^{14} e + \frac{60}{7} x^{14} d + \frac{252}{13} x^{13} e + \frac{210}{13} x^{13} d + \frac{35}{2} x^{12} e + 21 x^{12} d + \frac{120}{11} x^{11} e + \frac{210}{11} x^{11} d + \frac{9}{2} x^{10} e + 12 x^{10} d + \frac{10}{9} x^{9} e + 5 x^{9} d + \frac{1}{8} x^{8} e + \frac{5}{4} x^{8} d + \frac{1}{7} x^{7} d"," ",0,"1/18*x^18*e + 10/17*x^17*e + 1/17*x^17*d + 45/16*x^16*e + 5/8*x^16*d + 8*x^15*e + 3*x^15*d + 15*x^14*e + 60/7*x^14*d + 252/13*x^13*e + 210/13*x^13*d + 35/2*x^12*e + 21*x^12*d + 120/11*x^11*e + 210/11*x^11*d + 9/2*x^10*e + 12*x^10*d + 10/9*x^9*e + 5*x^9*d + 1/8*x^8*e + 5/4*x^8*d + 1/7*x^7*d","A",0
561,1,133,0,0.420326," ","integrate(x^5*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{17} x^{17} e + \frac{5}{8} x^{16} e + \frac{1}{16} x^{16} d + 3 x^{15} e + \frac{2}{3} x^{15} d + \frac{60}{7} x^{14} e + \frac{45}{14} x^{14} d + \frac{210}{13} x^{13} e + \frac{120}{13} x^{13} d + 21 x^{12} e + \frac{35}{2} x^{12} d + \frac{210}{11} x^{11} e + \frac{252}{11} x^{11} d + 12 x^{10} e + 21 x^{10} d + 5 x^{9} e + \frac{40}{3} x^{9} d + \frac{5}{4} x^{8} e + \frac{45}{8} x^{8} d + \frac{1}{7} x^{7} e + \frac{10}{7} x^{7} d + \frac{1}{6} x^{6} d"," ",0,"1/17*x^17*e + 5/8*x^16*e + 1/16*x^16*d + 3*x^15*e + 2/3*x^15*d + 60/7*x^14*e + 45/14*x^14*d + 210/13*x^13*e + 120/13*x^13*d + 21*x^12*e + 35/2*x^12*d + 210/11*x^11*e + 252/11*x^11*d + 12*x^10*e + 21*x^10*d + 5*x^9*e + 40/3*x^9*d + 5/4*x^8*e + 45/8*x^8*d + 1/7*x^7*e + 10/7*x^7*d + 1/6*x^6*d","A",0
562,1,133,0,0.384401," ","integrate(x^4*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{16} x^{16} e + \frac{2}{3} x^{15} e + \frac{1}{15} x^{15} d + \frac{45}{14} x^{14} e + \frac{5}{7} x^{14} d + \frac{120}{13} x^{13} e + \frac{45}{13} x^{13} d + \frac{35}{2} x^{12} e + 10 x^{12} d + \frac{252}{11} x^{11} e + \frac{210}{11} x^{11} d + 21 x^{10} e + \frac{126}{5} x^{10} d + \frac{40}{3} x^{9} e + \frac{70}{3} x^{9} d + \frac{45}{8} x^{8} e + 15 x^{8} d + \frac{10}{7} x^{7} e + \frac{45}{7} x^{7} d + \frac{1}{6} x^{6} e + \frac{5}{3} x^{6} d + \frac{1}{5} x^{5} d"," ",0,"1/16*x^16*e + 2/3*x^15*e + 1/15*x^15*d + 45/14*x^14*e + 5/7*x^14*d + 120/13*x^13*e + 45/13*x^13*d + 35/2*x^12*e + 10*x^12*d + 252/11*x^11*e + 210/11*x^11*d + 21*x^10*e + 126/5*x^10*d + 40/3*x^9*e + 70/3*x^9*d + 45/8*x^8*e + 15*x^8*d + 10/7*x^7*e + 45/7*x^7*d + 1/6*x^6*e + 5/3*x^6*d + 1/5*x^5*d","A",0
563,1,133,0,0.358267," ","integrate(x^3*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{15} x^{15} e + \frac{5}{7} x^{14} e + \frac{1}{14} x^{14} d + \frac{45}{13} x^{13} e + \frac{10}{13} x^{13} d + 10 x^{12} e + \frac{15}{4} x^{12} d + \frac{210}{11} x^{11} e + \frac{120}{11} x^{11} d + \frac{126}{5} x^{10} e + 21 x^{10} d + \frac{70}{3} x^{9} e + 28 x^{9} d + 15 x^{8} e + \frac{105}{4} x^{8} d + \frac{45}{7} x^{7} e + \frac{120}{7} x^{7} d + \frac{5}{3} x^{6} e + \frac{15}{2} x^{6} d + \frac{1}{5} x^{5} e + 2 x^{5} d + \frac{1}{4} x^{4} d"," ",0,"1/15*x^15*e + 5/7*x^14*e + 1/14*x^14*d + 45/13*x^13*e + 10/13*x^13*d + 10*x^12*e + 15/4*x^12*d + 210/11*x^11*e + 120/11*x^11*d + 126/5*x^10*e + 21*x^10*d + 70/3*x^9*e + 28*x^9*d + 15*x^8*e + 105/4*x^8*d + 45/7*x^7*e + 120/7*x^7*d + 5/3*x^6*e + 15/2*x^6*d + 1/5*x^5*e + 2*x^5*d + 1/4*x^4*d","B",0
564,1,133,0,0.374603," ","integrate(x^2*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{14} x^{14} e + \frac{10}{13} x^{13} e + \frac{1}{13} x^{13} d + \frac{15}{4} x^{12} e + \frac{5}{6} x^{12} d + \frac{120}{11} x^{11} e + \frac{45}{11} x^{11} d + 21 x^{10} e + 12 x^{10} d + 28 x^{9} e + \frac{70}{3} x^{9} d + \frac{105}{4} x^{8} e + \frac{63}{2} x^{8} d + \frac{120}{7} x^{7} e + 30 x^{7} d + \frac{15}{2} x^{6} e + 20 x^{6} d + 2 x^{5} e + 9 x^{5} d + \frac{1}{4} x^{4} e + \frac{5}{2} x^{4} d + \frac{1}{3} x^{3} d"," ",0,"1/14*x^14*e + 10/13*x^13*e + 1/13*x^13*d + 15/4*x^12*e + 5/6*x^12*d + 120/11*x^11*e + 45/11*x^11*d + 21*x^10*e + 12*x^10*d + 28*x^9*e + 70/3*x^9*d + 105/4*x^8*e + 63/2*x^8*d + 120/7*x^7*e + 30*x^7*d + 15/2*x^6*e + 20*x^6*d + 2*x^5*e + 9*x^5*d + 1/4*x^4*e + 5/2*x^4*d + 1/3*x^3*d","B",0
565,1,133,0,0.361353," ","integrate(x*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e + \frac{5}{6} x^{12} e + \frac{1}{12} x^{12} d + \frac{45}{11} x^{11} e + \frac{10}{11} x^{11} d + 12 x^{10} e + \frac{9}{2} x^{10} d + \frac{70}{3} x^{9} e + \frac{40}{3} x^{9} d + \frac{63}{2} x^{8} e + \frac{105}{4} x^{8} d + 30 x^{7} e + 36 x^{7} d + 20 x^{6} e + 35 x^{6} d + 9 x^{5} e + 24 x^{5} d + \frac{5}{2} x^{4} e + \frac{45}{4} x^{4} d + \frac{1}{3} x^{3} e + \frac{10}{3} x^{3} d + \frac{1}{2} x^{2} d"," ",0,"1/13*x^13*e + 5/6*x^12*e + 1/12*x^12*d + 45/11*x^11*e + 10/11*x^11*d + 12*x^10*e + 9/2*x^10*d + 70/3*x^9*e + 40/3*x^9*d + 63/2*x^8*e + 105/4*x^8*d + 30*x^7*e + 36*x^7*d + 20*x^6*e + 35*x^6*d + 9*x^5*e + 24*x^5*d + 5/2*x^4*e + 45/4*x^4*d + 1/3*x^3*e + 10/3*x^3*d + 1/2*x^2*d","B",0
566,1,129,0,0.353429," ","integrate((e*x+d)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e + \frac{10}{11} x^{11} e + \frac{1}{11} x^{11} d + \frac{9}{2} x^{10} e + x^{10} d + \frac{40}{3} x^{9} e + 5 x^{9} d + \frac{105}{4} x^{8} e + 15 x^{8} d + 36 x^{7} e + 30 x^{7} d + 35 x^{6} e + 42 x^{6} d + 24 x^{5} e + 42 x^{5} d + \frac{45}{4} x^{4} e + 30 x^{4} d + \frac{10}{3} x^{3} e + 15 x^{3} d + \frac{1}{2} x^{2} e + 5 x^{2} d + x d"," ",0,"1/12*x^12*e + 10/11*x^11*e + 1/11*x^11*d + 9/2*x^10*e + x^10*d + 40/3*x^9*e + 5*x^9*d + 105/4*x^8*e + 15*x^8*d + 36*x^7*e + 30*x^7*d + 35*x^6*e + 42*x^6*d + 24*x^5*e + 42*x^5*d + 45/4*x^4*e + 30*x^4*d + 10/3*x^3*e + 15*x^3*d + 1/2*x^2*e + 5*x^2*d + x*d","B",0
567,1,124,0,0.401379," ","integrate((e*x+d)*(x^2+2*x+1)^5/x,x, algorithm=""fricas"")","\frac{1}{11} \, e x^{11} + \frac{1}{10} \, {\left(d + 10 \, e\right)} x^{10} + \frac{5}{9} \, {\left(2 \, d + 9 \, e\right)} x^{9} + \frac{15}{8} \, {\left(3 \, d + 8 \, e\right)} x^{8} + \frac{30}{7} \, {\left(4 \, d + 7 \, e\right)} x^{7} + 7 \, {\left(5 \, d + 6 \, e\right)} x^{6} + \frac{42}{5} \, {\left(6 \, d + 5 \, e\right)} x^{5} + \frac{15}{2} \, {\left(7 \, d + 4 \, e\right)} x^{4} + 5 \, {\left(8 \, d + 3 \, e\right)} x^{3} + \frac{5}{2} \, {\left(9 \, d + 2 \, e\right)} x^{2} + {\left(10 \, d + e\right)} x + d \log\left(x\right)"," ",0,"1/11*e*x^11 + 1/10*(d + 10*e)*x^10 + 5/9*(2*d + 9*e)*x^9 + 15/8*(3*d + 8*e)*x^8 + 30/7*(4*d + 7*e)*x^7 + 7*(5*d + 6*e)*x^6 + 42/5*(6*d + 5*e)*x^5 + 15/2*(7*d + 4*e)*x^4 + 5*(8*d + 3*e)*x^3 + 5/2*(9*d + 2*e)*x^2 + (10*d + e)*x + d*log(x)","A",0
568,1,131,0,0.420991," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^2,x, algorithm=""fricas"")","\frac{252 \, e x^{11} + 280 \, {\left(d + 10 \, e\right)} x^{10} + 1575 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 5400 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 12600 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 21168 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 26460 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 25200 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 18900 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 12600 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 2520 \, {\left(10 \, d + e\right)} x \log\left(x\right) - 2520 \, d}{2520 \, x}"," ",0,"1/2520*(252*e*x^11 + 280*(d + 10*e)*x^10 + 1575*(2*d + 9*e)*x^9 + 5400*(3*d + 8*e)*x^8 + 12600*(4*d + 7*e)*x^7 + 21168*(5*d + 6*e)*x^6 + 26460*(6*d + 5*e)*x^5 + 25200*(7*d + 4*e)*x^4 + 18900*(8*d + 3*e)*x^3 + 12600*(9*d + 2*e)*x^2 + 2520*(10*d + e)*x*log(x) - 2520*d)/x","A",0
569,1,131,0,0.399161," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^3,x, algorithm=""fricas"")","\frac{56 \, e x^{11} + 63 \, {\left(d + 10 \, e\right)} x^{10} + 360 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 1260 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 3024 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 5292 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 7056 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 7560 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 7560 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 2520 \, {\left(9 \, d + 2 \, e\right)} x^{2} \log\left(x\right) - 504 \, {\left(10 \, d + e\right)} x - 252 \, d}{504 \, x^{2}}"," ",0,"1/504*(56*e*x^11 + 63*(d + 10*e)*x^10 + 360*(2*d + 9*e)*x^9 + 1260*(3*d + 8*e)*x^8 + 3024*(4*d + 7*e)*x^7 + 5292*(5*d + 6*e)*x^6 + 7056*(6*d + 5*e)*x^5 + 7560*(7*d + 4*e)*x^4 + 7560*(8*d + 3*e)*x^3 + 2520*(9*d + 2*e)*x^2*log(x) - 504*(10*d + e)*x - 252*d)/x^2","A",0
570,1,131,0,0.422343," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^4,x, algorithm=""fricas"")","\frac{21 \, e x^{11} + 24 \, {\left(d + 10 \, e\right)} x^{10} + 140 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 504 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 1260 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 2352 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 3528 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 5040 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 2520 \, {\left(8 \, d + 3 \, e\right)} x^{3} \log\left(x\right) - 840 \, {\left(9 \, d + 2 \, e\right)} x^{2} - 84 \, {\left(10 \, d + e\right)} x - 56 \, d}{168 \, x^{3}}"," ",0,"1/168*(21*e*x^11 + 24*(d + 10*e)*x^10 + 140*(2*d + 9*e)*x^9 + 504*(3*d + 8*e)*x^8 + 1260*(4*d + 7*e)*x^7 + 2352*(5*d + 6*e)*x^6 + 3528*(6*d + 5*e)*x^5 + 5040*(7*d + 4*e)*x^4 + 2520*(8*d + 3*e)*x^3*log(x) - 840*(9*d + 2*e)*x^2 - 84*(10*d + e)*x - 56*d)/x^3","A",0
571,1,131,0,0.403346," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^5,x, algorithm=""fricas"")","\frac{12 \, e x^{11} + 14 \, {\left(d + 10 \, e\right)} x^{10} + 84 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 315 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 840 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 1764 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 3528 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 2520 \, {\left(7 \, d + 4 \, e\right)} x^{4} \log\left(x\right) - 1260 \, {\left(8 \, d + 3 \, e\right)} x^{3} - 210 \, {\left(9 \, d + 2 \, e\right)} x^{2} - 28 \, {\left(10 \, d + e\right)} x - 21 \, d}{84 \, x^{4}}"," ",0,"1/84*(12*e*x^11 + 14*(d + 10*e)*x^10 + 84*(2*d + 9*e)*x^9 + 315*(3*d + 8*e)*x^8 + 840*(4*d + 7*e)*x^7 + 1764*(5*d + 6*e)*x^6 + 3528*(6*d + 5*e)*x^5 + 2520*(7*d + 4*e)*x^4*log(x) - 1260*(8*d + 3*e)*x^3 - 210*(9*d + 2*e)*x^2 - 28*(10*d + e)*x - 21*d)/x^4","A",0
572,1,131,0,0.407534," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^6,x, algorithm=""fricas"")","\frac{10 \, e x^{11} + 12 \, {\left(d + 10 \, e\right)} x^{10} + 75 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 300 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 900 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 2520 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 2520 \, {\left(6 \, d + 5 \, e\right)} x^{5} \log\left(x\right) - 1800 \, {\left(7 \, d + 4 \, e\right)} x^{4} - 450 \, {\left(8 \, d + 3 \, e\right)} x^{3} - 100 \, {\left(9 \, d + 2 \, e\right)} x^{2} - 15 \, {\left(10 \, d + e\right)} x - 12 \, d}{60 \, x^{5}}"," ",0,"1/60*(10*e*x^11 + 12*(d + 10*e)*x^10 + 75*(2*d + 9*e)*x^9 + 300*(3*d + 8*e)*x^8 + 900*(4*d + 7*e)*x^7 + 2520*(5*d + 6*e)*x^6 + 2520*(6*d + 5*e)*x^5*log(x) - 1800*(7*d + 4*e)*x^4 - 450*(8*d + 3*e)*x^3 - 100*(9*d + 2*e)*x^2 - 15*(10*d + e)*x - 12*d)/x^5","A",0
573,1,131,0,0.401085," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^7,x, algorithm=""fricas"")","\frac{12 \, e x^{11} + 15 \, {\left(d + 10 \, e\right)} x^{10} + 100 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 450 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 1800 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 2520 \, {\left(5 \, d + 6 \, e\right)} x^{6} \log\left(x\right) - 2520 \, {\left(6 \, d + 5 \, e\right)} x^{5} - 900 \, {\left(7 \, d + 4 \, e\right)} x^{4} - 300 \, {\left(8 \, d + 3 \, e\right)} x^{3} - 75 \, {\left(9 \, d + 2 \, e\right)} x^{2} - 12 \, {\left(10 \, d + e\right)} x - 10 \, d}{60 \, x^{6}}"," ",0,"1/60*(12*e*x^11 + 15*(d + 10*e)*x^10 + 100*(2*d + 9*e)*x^9 + 450*(3*d + 8*e)*x^8 + 1800*(4*d + 7*e)*x^7 + 2520*(5*d + 6*e)*x^6*log(x) - 2520*(6*d + 5*e)*x^5 - 900*(7*d + 4*e)*x^4 - 300*(8*d + 3*e)*x^3 - 75*(9*d + 2*e)*x^2 - 12*(10*d + e)*x - 10*d)/x^6","A",0
574,1,131,0,0.396114," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^8,x, algorithm=""fricas"")","\frac{21 \, e x^{11} + 28 \, {\left(d + 10 \, e\right)} x^{10} + 210 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 1260 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 2520 \, {\left(4 \, d + 7 \, e\right)} x^{7} \log\left(x\right) - 3528 \, {\left(5 \, d + 6 \, e\right)} x^{6} - 1764 \, {\left(6 \, d + 5 \, e\right)} x^{5} - 840 \, {\left(7 \, d + 4 \, e\right)} x^{4} - 315 \, {\left(8 \, d + 3 \, e\right)} x^{3} - 84 \, {\left(9 \, d + 2 \, e\right)} x^{2} - 14 \, {\left(10 \, d + e\right)} x - 12 \, d}{84 \, x^{7}}"," ",0,"1/84*(21*e*x^11 + 28*(d + 10*e)*x^10 + 210*(2*d + 9*e)*x^9 + 1260*(3*d + 8*e)*x^8 + 2520*(4*d + 7*e)*x^7*log(x) - 3528*(5*d + 6*e)*x^6 - 1764*(6*d + 5*e)*x^5 - 840*(7*d + 4*e)*x^4 - 315*(8*d + 3*e)*x^3 - 84*(9*d + 2*e)*x^2 - 14*(10*d + e)*x - 12*d)/x^7","A",0
575,1,131,0,0.423022," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^9,x, algorithm=""fricas"")","\frac{56 \, e x^{11} + 84 \, {\left(d + 10 \, e\right)} x^{10} + 840 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 2520 \, {\left(3 \, d + 8 \, e\right)} x^{8} \log\left(x\right) - 5040 \, {\left(4 \, d + 7 \, e\right)} x^{7} - 3528 \, {\left(5 \, d + 6 \, e\right)} x^{6} - 2352 \, {\left(6 \, d + 5 \, e\right)} x^{5} - 1260 \, {\left(7 \, d + 4 \, e\right)} x^{4} - 504 \, {\left(8 \, d + 3 \, e\right)} x^{3} - 140 \, {\left(9 \, d + 2 \, e\right)} x^{2} - 24 \, {\left(10 \, d + e\right)} x - 21 \, d}{168 \, x^{8}}"," ",0,"1/168*(56*e*x^11 + 84*(d + 10*e)*x^10 + 840*(2*d + 9*e)*x^9 + 2520*(3*d + 8*e)*x^8*log(x) - 5040*(4*d + 7*e)*x^7 - 3528*(5*d + 6*e)*x^6 - 2352*(6*d + 5*e)*x^5 - 1260*(7*d + 4*e)*x^4 - 504*(8*d + 3*e)*x^3 - 140*(9*d + 2*e)*x^2 - 24*(10*d + e)*x - 21*d)/x^8","A",0
576,1,131,0,0.424982," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^10,x, algorithm=""fricas"")","\frac{252 \, e x^{11} + 504 \, {\left(d + 10 \, e\right)} x^{10} + 2520 \, {\left(2 \, d + 9 \, e\right)} x^{9} \log\left(x\right) - 7560 \, {\left(3 \, d + 8 \, e\right)} x^{8} - 7560 \, {\left(4 \, d + 7 \, e\right)} x^{7} - 7056 \, {\left(5 \, d + 6 \, e\right)} x^{6} - 5292 \, {\left(6 \, d + 5 \, e\right)} x^{5} - 3024 \, {\left(7 \, d + 4 \, e\right)} x^{4} - 1260 \, {\left(8 \, d + 3 \, e\right)} x^{3} - 360 \, {\left(9 \, d + 2 \, e\right)} x^{2} - 63 \, {\left(10 \, d + e\right)} x - 56 \, d}{504 \, x^{9}}"," ",0,"1/504*(252*e*x^11 + 504*(d + 10*e)*x^10 + 2520*(2*d + 9*e)*x^9*log(x) - 7560*(3*d + 8*e)*x^8 - 7560*(4*d + 7*e)*x^7 - 7056*(5*d + 6*e)*x^6 - 5292*(6*d + 5*e)*x^5 - 3024*(7*d + 4*e)*x^4 - 1260*(8*d + 3*e)*x^3 - 360*(9*d + 2*e)*x^2 - 63*(10*d + e)*x - 56*d)/x^9","A",0
577,1,131,0,0.420721," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^11,x, algorithm=""fricas"")","\frac{2520 \, e x^{11} + 2520 \, {\left(d + 10 \, e\right)} x^{10} \log\left(x\right) - 12600 \, {\left(2 \, d + 9 \, e\right)} x^{9} - 18900 \, {\left(3 \, d + 8 \, e\right)} x^{8} - 25200 \, {\left(4 \, d + 7 \, e\right)} x^{7} - 26460 \, {\left(5 \, d + 6 \, e\right)} x^{6} - 21168 \, {\left(6 \, d + 5 \, e\right)} x^{5} - 12600 \, {\left(7 \, d + 4 \, e\right)} x^{4} - 5400 \, {\left(8 \, d + 3 \, e\right)} x^{3} - 1575 \, {\left(9 \, d + 2 \, e\right)} x^{2} - 280 \, {\left(10 \, d + e\right)} x - 252 \, d}{2520 \, x^{10}}"," ",0,"1/2520*(2520*e*x^11 + 2520*(d + 10*e)*x^10*log(x) - 12600*(2*d + 9*e)*x^9 - 18900*(3*d + 8*e)*x^8 - 25200*(4*d + 7*e)*x^7 - 26460*(5*d + 6*e)*x^6 - 21168*(6*d + 5*e)*x^5 - 12600*(7*d + 4*e)*x^4 - 5400*(8*d + 3*e)*x^3 - 1575*(9*d + 2*e)*x^2 - 280*(10*d + e)*x - 252*d)/x^10","A",0
578,1,131,0,0.402207," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^12,x, algorithm=""fricas"")","\frac{27720 \, e x^{11} \log\left(x\right) - 27720 \, {\left(d + 10 \, e\right)} x^{10} - 69300 \, {\left(2 \, d + 9 \, e\right)} x^{9} - 138600 \, {\left(3 \, d + 8 \, e\right)} x^{8} - 207900 \, {\left(4 \, d + 7 \, e\right)} x^{7} - 232848 \, {\left(5 \, d + 6 \, e\right)} x^{6} - 194040 \, {\left(6 \, d + 5 \, e\right)} x^{5} - 118800 \, {\left(7 \, d + 4 \, e\right)} x^{4} - 51975 \, {\left(8 \, d + 3 \, e\right)} x^{3} - 15400 \, {\left(9 \, d + 2 \, e\right)} x^{2} - 2772 \, {\left(10 \, d + e\right)} x - 2520 \, d}{27720 \, x^{11}}"," ",0,"1/27720*(27720*e*x^11*log(x) - 27720*(d + 10*e)*x^10 - 69300*(2*d + 9*e)*x^9 - 138600*(3*d + 8*e)*x^8 - 207900*(4*d + 7*e)*x^7 - 232848*(5*d + 6*e)*x^6 - 194040*(6*d + 5*e)*x^5 - 118800*(7*d + 4*e)*x^4 - 51975*(8*d + 3*e)*x^3 - 15400*(9*d + 2*e)*x^2 - 2772*(10*d + e)*x - 2520*d)/x^11","A",0
579,1,129,0,0.389979," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^13,x, algorithm=""fricas"")","-\frac{132 \, e x^{11} + 66 \, {\left(d + 10 \, e\right)} x^{10} + 220 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 495 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 792 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 924 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 792 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 495 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 220 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 66 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 12 \, {\left(10 \, d + e\right)} x + 11 \, d}{132 \, x^{12}}"," ",0,"-1/132*(132*e*x^11 + 66*(d + 10*e)*x^10 + 220*(2*d + 9*e)*x^9 + 495*(3*d + 8*e)*x^8 + 792*(4*d + 7*e)*x^7 + 924*(5*d + 6*e)*x^6 + 792*(6*d + 5*e)*x^5 + 495*(7*d + 4*e)*x^4 + 220*(8*d + 3*e)*x^3 + 66*(9*d + 2*e)*x^2 + 12*(10*d + e)*x + 11*d)/x^12","B",0
580,1,129,0,0.397889," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^14,x, algorithm=""fricas"")","-\frac{858 \, e x^{11} + 572 \, {\left(d + 10 \, e\right)} x^{10} + 2145 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 5148 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 8580 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 10296 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 9009 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 5720 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 2574 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 780 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 143 \, {\left(10 \, d + e\right)} x + 132 \, d}{1716 \, x^{13}}"," ",0,"-1/1716*(858*e*x^11 + 572*(d + 10*e)*x^10 + 2145*(2*d + 9*e)*x^9 + 5148*(3*d + 8*e)*x^8 + 8580*(4*d + 7*e)*x^7 + 10296*(5*d + 6*e)*x^6 + 9009*(6*d + 5*e)*x^5 + 5720*(7*d + 4*e)*x^4 + 2574*(8*d + 3*e)*x^3 + 780*(9*d + 2*e)*x^2 + 143*(10*d + e)*x + 132*d)/x^13","B",0
581,1,129,0,0.402708," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^15,x, algorithm=""fricas"")","-\frac{4004 \, e x^{11} + 3003 \, {\left(d + 10 \, e\right)} x^{10} + 12012 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 30030 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 51480 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 63063 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 56056 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 36036 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 16380 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 5005 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 924 \, {\left(10 \, d + e\right)} x + 858 \, d}{12012 \, x^{14}}"," ",0,"-1/12012*(4004*e*x^11 + 3003*(d + 10*e)*x^10 + 12012*(2*d + 9*e)*x^9 + 30030*(3*d + 8*e)*x^8 + 51480*(4*d + 7*e)*x^7 + 63063*(5*d + 6*e)*x^6 + 56056*(6*d + 5*e)*x^5 + 36036*(7*d + 4*e)*x^4 + 16380*(8*d + 3*e)*x^3 + 5005*(9*d + 2*e)*x^2 + 924*(10*d + e)*x + 858*d)/x^14","B",0
582,1,129,0,0.413535," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^16,x, algorithm=""fricas"")","-\frac{15015 \, e x^{11} + 12012 \, {\left(d + 10 \, e\right)} x^{10} + 50050 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 128700 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 225225 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 280280 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 252252 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 163800 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 75075 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 23100 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 4290 \, {\left(10 \, d + e\right)} x + 4004 \, d}{60060 \, x^{15}}"," ",0,"-1/60060*(15015*e*x^11 + 12012*(d + 10*e)*x^10 + 50050*(2*d + 9*e)*x^9 + 128700*(3*d + 8*e)*x^8 + 225225*(4*d + 7*e)*x^7 + 280280*(5*d + 6*e)*x^6 + 252252*(6*d + 5*e)*x^5 + 163800*(7*d + 4*e)*x^4 + 75075*(8*d + 3*e)*x^3 + 23100*(9*d + 2*e)*x^2 + 4290*(10*d + e)*x + 4004*d)/x^15","A",0
583,1,129,0,0.433598," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^17,x, algorithm=""fricas"")","-\frac{48048 \, e x^{11} + 40040 \, {\left(d + 10 \, e\right)} x^{10} + 171600 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 450450 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 800800 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 1009008 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 917280 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 600600 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 277200 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 85800 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 16016 \, {\left(10 \, d + e\right)} x + 15015 \, d}{240240 \, x^{16}}"," ",0,"-1/240240*(48048*e*x^11 + 40040*(d + 10*e)*x^10 + 171600*(2*d + 9*e)*x^9 + 450450*(3*d + 8*e)*x^8 + 800800*(4*d + 7*e)*x^7 + 1009008*(5*d + 6*e)*x^6 + 917280*(6*d + 5*e)*x^5 + 600600*(7*d + 4*e)*x^4 + 277200*(8*d + 3*e)*x^3 + 85800*(9*d + 2*e)*x^2 + 16016*(10*d + e)*x + 15015*d)/x^16","A",0
584,1,129,0,0.399121," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^18,x, algorithm=""fricas"")","-\frac{136136 \, e x^{11} + 116688 \, {\left(d + 10 \, e\right)} x^{10} + 510510 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 1361360 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 2450448 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 3118752 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 2858856 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 1884960 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 875160 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 272272 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 51051 \, {\left(10 \, d + e\right)} x + 48048 \, d}{816816 \, x^{17}}"," ",0,"-1/816816*(136136*e*x^11 + 116688*(d + 10*e)*x^10 + 510510*(2*d + 9*e)*x^9 + 1361360*(3*d + 8*e)*x^8 + 2450448*(4*d + 7*e)*x^7 + 3118752*(5*d + 6*e)*x^6 + 2858856*(6*d + 5*e)*x^5 + 1884960*(7*d + 4*e)*x^4 + 875160*(8*d + 3*e)*x^3 + 272272*(9*d + 2*e)*x^2 + 51051*(10*d + e)*x + 48048*d)/x^17","A",0
585,1,129,0,0.377847," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^19,x, algorithm=""fricas"")","-\frac{350064 \, e x^{11} + 306306 \, {\left(d + 10 \, e\right)} x^{10} + 1361360 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 3675672 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 6683040 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 8576568 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 7916832 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 5250960 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 2450448 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 765765 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 144144 \, {\left(10 \, d + e\right)} x + 136136 \, d}{2450448 \, x^{18}}"," ",0,"-1/2450448*(350064*e*x^11 + 306306*(d + 10*e)*x^10 + 1361360*(2*d + 9*e)*x^9 + 3675672*(3*d + 8*e)*x^8 + 6683040*(4*d + 7*e)*x^7 + 8576568*(5*d + 6*e)*x^6 + 7916832*(6*d + 5*e)*x^5 + 5250960*(7*d + 4*e)*x^4 + 2450448*(8*d + 3*e)*x^3 + 765765*(9*d + 2*e)*x^2 + 144144*(10*d + e)*x + 136136*d)/x^18","A",0
586,1,129,0,0.389397," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^20,x, algorithm=""fricas"")","-\frac{831402 \, e x^{11} + 739024 \, {\left(d + 10 \, e\right)} x^{10} + 3325608 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 9069840 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 16628040 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 21488544 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 19953648 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 13302432 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 6235515 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 1956240 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 369512 \, {\left(10 \, d + e\right)} x + 350064 \, d}{6651216 \, x^{19}}"," ",0,"-1/6651216*(831402*e*x^11 + 739024*(d + 10*e)*x^10 + 3325608*(2*d + 9*e)*x^9 + 9069840*(3*d + 8*e)*x^8 + 16628040*(4*d + 7*e)*x^7 + 21488544*(5*d + 6*e)*x^6 + 19953648*(6*d + 5*e)*x^5 + 13302432*(7*d + 4*e)*x^4 + 6235515*(8*d + 3*e)*x^3 + 1956240*(9*d + 2*e)*x^2 + 369512*(10*d + e)*x + 350064*d)/x^19","A",0
587,1,129,0,0.394728," ","integrate((e*x+d)*(x^2+2*x+1)^5/x^21,x, algorithm=""fricas"")","-\frac{1847560 \, e x^{11} + 1662804 \, {\left(d + 10 \, e\right)} x^{10} + 7558200 \, {\left(2 \, d + 9 \, e\right)} x^{9} + 20785050 \, {\left(3 \, d + 8 \, e\right)} x^{8} + 38372400 \, {\left(4 \, d + 7 \, e\right)} x^{7} + 49884120 \, {\left(5 \, d + 6 \, e\right)} x^{6} + 46558512 \, {\left(6 \, d + 5 \, e\right)} x^{5} + 31177575 \, {\left(7 \, d + 4 \, e\right)} x^{4} + 14671800 \, {\left(8 \, d + 3 \, e\right)} x^{3} + 4618900 \, {\left(9 \, d + 2 \, e\right)} x^{2} + 875160 \, {\left(10 \, d + e\right)} x + 831402 \, d}{16628040 \, x^{20}}"," ",0,"-1/16628040*(1847560*e*x^11 + 1662804*(d + 10*e)*x^10 + 7558200*(2*d + 9*e)*x^9 + 20785050*(3*d + 8*e)*x^8 + 38372400*(4*d + 7*e)*x^7 + 49884120*(5*d + 6*e)*x^6 + 46558512*(6*d + 5*e)*x^5 + 31177575*(7*d + 4*e)*x^4 + 14671800*(8*d + 3*e)*x^3 + 4618900*(9*d + 2*e)*x^2 + 875160*(10*d + e)*x + 831402*d)/x^20","A",0
588,1,61,0,0.355688," ","integrate(x^11*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{23} x^{23} + \frac{1}{2} x^{22} + \frac{55}{21} x^{21} + \frac{33}{4} x^{20} + \frac{330}{19} x^{19} + \frac{77}{3} x^{18} + \frac{462}{17} x^{17} + \frac{165}{8} x^{16} + 11 x^{15} + \frac{55}{14} x^{14} + \frac{11}{13} x^{13} + \frac{1}{12} x^{12}"," ",0,"1/23*x^23 + 1/2*x^22 + 55/21*x^21 + 33/4*x^20 + 330/19*x^19 + 77/3*x^18 + 462/17*x^17 + 165/8*x^16 + 11*x^15 + 55/14*x^14 + 11/13*x^13 + 1/12*x^12","A",0
589,1,61,0,0.356867," ","integrate(x^10*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{22} x^{22} + \frac{11}{21} x^{21} + \frac{11}{4} x^{20} + \frac{165}{19} x^{19} + \frac{55}{3} x^{18} + \frac{462}{17} x^{17} + \frac{231}{8} x^{16} + 22 x^{15} + \frac{165}{14} x^{14} + \frac{55}{13} x^{13} + \frac{11}{12} x^{12} + \frac{1}{11} x^{11}"," ",0,"1/22*x^22 + 11/21*x^21 + 11/4*x^20 + 165/19*x^19 + 55/3*x^18 + 462/17*x^17 + 231/8*x^16 + 22*x^15 + 165/14*x^14 + 55/13*x^13 + 11/12*x^12 + 1/11*x^11","A",0
590,1,59,0,0.358097," ","integrate(x^9*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{21} x^{21} + \frac{11}{20} x^{20} + \frac{55}{19} x^{19} + \frac{55}{6} x^{18} + \frac{330}{17} x^{17} + \frac{231}{8} x^{16} + \frac{154}{5} x^{15} + \frac{165}{7} x^{14} + \frac{165}{13} x^{13} + \frac{55}{12} x^{12} + x^{11} + \frac{1}{10} x^{10}"," ",0,"1/21*x^21 + 11/20*x^20 + 55/19*x^19 + 55/6*x^18 + 330/17*x^17 + 231/8*x^16 + 154/5*x^15 + 165/7*x^14 + 165/13*x^13 + 55/12*x^12 + x^11 + 1/10*x^10","A",0
591,1,61,0,0.350420," ","integrate(x^8*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{20} x^{20} + \frac{11}{19} x^{19} + \frac{55}{18} x^{18} + \frac{165}{17} x^{17} + \frac{165}{8} x^{16} + \frac{154}{5} x^{15} + 33 x^{14} + \frac{330}{13} x^{13} + \frac{55}{4} x^{12} + 5 x^{11} + \frac{11}{10} x^{10} + \frac{1}{9} x^{9}"," ",0,"1/20*x^20 + 11/19*x^19 + 55/18*x^18 + 165/17*x^17 + 165/8*x^16 + 154/5*x^15 + 33*x^14 + 330/13*x^13 + 55/4*x^12 + 5*x^11 + 11/10*x^10 + 1/9*x^9","A",0
592,1,61,0,0.351200," ","integrate(x^7*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{19} x^{19} + \frac{11}{18} x^{18} + \frac{55}{17} x^{17} + \frac{165}{16} x^{16} + 22 x^{15} + 33 x^{14} + \frac{462}{13} x^{13} + \frac{55}{2} x^{12} + 15 x^{11} + \frac{11}{2} x^{10} + \frac{11}{9} x^{9} + \frac{1}{8} x^{8}"," ",0,"1/19*x^19 + 11/18*x^18 + 55/17*x^17 + 165/16*x^16 + 22*x^15 + 33*x^14 + 462/13*x^13 + 55/2*x^12 + 15*x^11 + 11/2*x^10 + 11/9*x^9 + 1/8*x^8","A",0
593,1,61,0,0.351703," ","integrate(x^6*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{18} x^{18} + \frac{11}{17} x^{17} + \frac{55}{16} x^{16} + 11 x^{15} + \frac{165}{7} x^{14} + \frac{462}{13} x^{13} + \frac{77}{2} x^{12} + 30 x^{11} + \frac{33}{2} x^{10} + \frac{55}{9} x^{9} + \frac{11}{8} x^{8} + \frac{1}{7} x^{7}"," ",0,"1/18*x^18 + 11/17*x^17 + 55/16*x^16 + 11*x^15 + 165/7*x^14 + 462/13*x^13 + 77/2*x^12 + 30*x^11 + 33/2*x^10 + 55/9*x^9 + 11/8*x^8 + 1/7*x^7","A",0
594,1,61,0,0.355225," ","integrate(x^5*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{17} x^{17} + \frac{11}{16} x^{16} + \frac{11}{3} x^{15} + \frac{165}{14} x^{14} + \frac{330}{13} x^{13} + \frac{77}{2} x^{12} + 42 x^{11} + 33 x^{10} + \frac{55}{3} x^{9} + \frac{55}{8} x^{8} + \frac{11}{7} x^{7} + \frac{1}{6} x^{6}"," ",0,"1/17*x^17 + 11/16*x^16 + 11/3*x^15 + 165/14*x^14 + 330/13*x^13 + 77/2*x^12 + 42*x^11 + 33*x^10 + 55/3*x^9 + 55/8*x^8 + 11/7*x^7 + 1/6*x^6","A",0
595,1,61,0,0.352133," ","integrate(x^4*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{16} x^{16} + \frac{11}{15} x^{15} + \frac{55}{14} x^{14} + \frac{165}{13} x^{13} + \frac{55}{2} x^{12} + 42 x^{11} + \frac{231}{5} x^{10} + \frac{110}{3} x^{9} + \frac{165}{8} x^{8} + \frac{55}{7} x^{7} + \frac{11}{6} x^{6} + \frac{1}{5} x^{5}"," ",0,"1/16*x^16 + 11/15*x^15 + 55/14*x^14 + 165/13*x^13 + 55/2*x^12 + 42*x^11 + 231/5*x^10 + 110/3*x^9 + 165/8*x^8 + 55/7*x^7 + 11/6*x^6 + 1/5*x^5","A",0
596,1,61,0,0.345218," ","integrate(x^3*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{15} x^{15} + \frac{11}{14} x^{14} + \frac{55}{13} x^{13} + \frac{55}{4} x^{12} + 30 x^{11} + \frac{231}{5} x^{10} + \frac{154}{3} x^{9} + \frac{165}{4} x^{8} + \frac{165}{7} x^{7} + \frac{55}{6} x^{6} + \frac{11}{5} x^{5} + \frac{1}{4} x^{4}"," ",0,"1/15*x^15 + 11/14*x^14 + 55/13*x^13 + 55/4*x^12 + 30*x^11 + 231/5*x^10 + 154/3*x^9 + 165/4*x^8 + 165/7*x^7 + 55/6*x^6 + 11/5*x^5 + 1/4*x^4","B",0
597,1,61,0,0.338263," ","integrate(x^2*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{14} x^{14} + \frac{11}{13} x^{13} + \frac{55}{12} x^{12} + 15 x^{11} + 33 x^{10} + \frac{154}{3} x^{9} + \frac{231}{4} x^{8} + \frac{330}{7} x^{7} + \frac{55}{2} x^{6} + 11 x^{5} + \frac{11}{4} x^{4} + \frac{1}{3} x^{3}"," ",0,"1/14*x^14 + 11/13*x^13 + 55/12*x^12 + 15*x^11 + 33*x^10 + 154/3*x^9 + 231/4*x^8 + 330/7*x^7 + 55/2*x^6 + 11*x^5 + 11/4*x^4 + 1/3*x^3","B",0
598,1,61,0,0.360697," ","integrate(x*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{13} x^{13} + \frac{11}{12} x^{12} + 5 x^{11} + \frac{33}{2} x^{10} + \frac{110}{3} x^{9} + \frac{231}{4} x^{8} + 66 x^{7} + 55 x^{6} + 33 x^{5} + \frac{55}{4} x^{4} + \frac{11}{3} x^{3} + \frac{1}{2} x^{2}"," ",0,"1/13*x^13 + 11/12*x^12 + 5*x^11 + 33/2*x^10 + 110/3*x^9 + 231/4*x^8 + 66*x^7 + 55*x^6 + 33*x^5 + 55/4*x^4 + 11/3*x^3 + 1/2*x^2","B",0
599,1,55,0,0.360976," ","integrate((1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{1}{12} x^{12} + x^{11} + \frac{11}{2} x^{10} + \frac{55}{3} x^{9} + \frac{165}{4} x^{8} + 66 x^{7} + 77 x^{6} + 66 x^{5} + \frac{165}{4} x^{4} + \frac{55}{3} x^{3} + \frac{11}{2} x^{2} + x"," ",0,"1/12*x^12 + x^11 + 11/2*x^10 + 55/3*x^9 + 165/4*x^8 + 66*x^7 + 77*x^6 + 66*x^5 + 165/4*x^4 + 55/3*x^3 + 11/2*x^2 + x","B",0
600,1,56,0,0.392654," ","integrate((1+x)*(x^2+2*x+1)^5/x,x, algorithm=""fricas"")","\frac{1}{11} \, x^{11} + \frac{11}{10} \, x^{10} + \frac{55}{9} \, x^{9} + \frac{165}{8} \, x^{8} + \frac{330}{7} \, x^{7} + 77 \, x^{6} + \frac{462}{5} \, x^{5} + \frac{165}{2} \, x^{4} + 55 \, x^{3} + \frac{55}{2} \, x^{2} + 11 \, x + \log\left(x\right)"," ",0,"1/11*x^11 + 11/10*x^10 + 55/9*x^9 + 165/8*x^8 + 330/7*x^7 + 77*x^6 + 462/5*x^5 + 165/2*x^4 + 55*x^3 + 55/2*x^2 + 11*x + log(x)","A",0
601,1,62,0,0.401575," ","integrate((1+x)*(x^2+2*x+1)^5/x^2,x, algorithm=""fricas"")","\frac{252 \, x^{11} + 3080 \, x^{10} + 17325 \, x^{9} + 59400 \, x^{8} + 138600 \, x^{7} + 232848 \, x^{6} + 291060 \, x^{5} + 277200 \, x^{4} + 207900 \, x^{3} + 138600 \, x^{2} + 27720 \, x \log\left(x\right) - 2520}{2520 \, x}"," ",0,"1/2520*(252*x^11 + 3080*x^10 + 17325*x^9 + 59400*x^8 + 138600*x^7 + 232848*x^6 + 291060*x^5 + 277200*x^4 + 207900*x^3 + 138600*x^2 + 27720*x*log(x) - 2520)/x","A",0
602,1,62,0,0.387708," ","integrate((1+x)*(x^2+2*x+1)^5/x^3,x, algorithm=""fricas"")","\frac{56 \, x^{11} + 693 \, x^{10} + 3960 \, x^{9} + 13860 \, x^{8} + 33264 \, x^{7} + 58212 \, x^{6} + 77616 \, x^{5} + 83160 \, x^{4} + 83160 \, x^{3} + 27720 \, x^{2} \log\left(x\right) - 5544 \, x - 252}{504 \, x^{2}}"," ",0,"1/504*(56*x^11 + 693*x^10 + 3960*x^9 + 13860*x^8 + 33264*x^7 + 58212*x^6 + 77616*x^5 + 83160*x^4 + 83160*x^3 + 27720*x^2*log(x) - 5544*x - 252)/x^2","A",0
603,1,62,0,0.415998," ","integrate((1+x)*(x^2+2*x+1)^5/x^4,x, algorithm=""fricas"")","\frac{21 \, x^{11} + 264 \, x^{10} + 1540 \, x^{9} + 5544 \, x^{8} + 13860 \, x^{7} + 25872 \, x^{6} + 38808 \, x^{5} + 55440 \, x^{4} + 27720 \, x^{3} \log\left(x\right) - 9240 \, x^{2} - 924 \, x - 56}{168 \, x^{3}}"," ",0,"1/168*(21*x^11 + 264*x^10 + 1540*x^9 + 5544*x^8 + 13860*x^7 + 25872*x^6 + 38808*x^5 + 55440*x^4 + 27720*x^3*log(x) - 9240*x^2 - 924*x - 56)/x^3","A",0
604,1,62,0,0.389420," ","integrate((1+x)*(x^2+2*x+1)^5/x^5,x, algorithm=""fricas"")","\frac{12 \, x^{11} + 154 \, x^{10} + 924 \, x^{9} + 3465 \, x^{8} + 9240 \, x^{7} + 19404 \, x^{6} + 38808 \, x^{5} + 27720 \, x^{4} \log\left(x\right) - 13860 \, x^{3} - 2310 \, x^{2} - 308 \, x - 21}{84 \, x^{4}}"," ",0,"1/84*(12*x^11 + 154*x^10 + 924*x^9 + 3465*x^8 + 9240*x^7 + 19404*x^6 + 38808*x^5 + 27720*x^4*log(x) - 13860*x^3 - 2310*x^2 - 308*x - 21)/x^4","A",0
605,1,62,0,0.395418," ","integrate((1+x)*(x^2+2*x+1)^5/x^6,x, algorithm=""fricas"")","\frac{10 \, x^{11} + 132 \, x^{10} + 825 \, x^{9} + 3300 \, x^{8} + 9900 \, x^{7} + 27720 \, x^{6} + 27720 \, x^{5} \log\left(x\right) - 19800 \, x^{4} - 4950 \, x^{3} - 1100 \, x^{2} - 165 \, x - 12}{60 \, x^{5}}"," ",0,"1/60*(10*x^11 + 132*x^10 + 825*x^9 + 3300*x^8 + 9900*x^7 + 27720*x^6 + 27720*x^5*log(x) - 19800*x^4 - 4950*x^3 - 1100*x^2 - 165*x - 12)/x^5","A",0
606,1,62,0,0.396593," ","integrate((1+x)*(x^2+2*x+1)^5/x^7,x, algorithm=""fricas"")","\frac{12 \, x^{11} + 165 \, x^{10} + 1100 \, x^{9} + 4950 \, x^{8} + 19800 \, x^{7} + 27720 \, x^{6} \log\left(x\right) - 27720 \, x^{5} - 9900 \, x^{4} - 3300 \, x^{3} - 825 \, x^{2} - 132 \, x - 10}{60 \, x^{6}}"," ",0,"1/60*(12*x^11 + 165*x^10 + 1100*x^9 + 4950*x^8 + 19800*x^7 + 27720*x^6*log(x) - 27720*x^5 - 9900*x^4 - 3300*x^3 - 825*x^2 - 132*x - 10)/x^6","A",0
607,1,62,0,0.402902," ","integrate((1+x)*(x^2+2*x+1)^5/x^8,x, algorithm=""fricas"")","\frac{21 \, x^{11} + 308 \, x^{10} + 2310 \, x^{9} + 13860 \, x^{8} + 27720 \, x^{7} \log\left(x\right) - 38808 \, x^{6} - 19404 \, x^{5} - 9240 \, x^{4} - 3465 \, x^{3} - 924 \, x^{2} - 154 \, x - 12}{84 \, x^{7}}"," ",0,"1/84*(21*x^11 + 308*x^10 + 2310*x^9 + 13860*x^8 + 27720*x^7*log(x) - 38808*x^6 - 19404*x^5 - 9240*x^4 - 3465*x^3 - 924*x^2 - 154*x - 12)/x^7","A",0
608,1,62,0,0.393749," ","integrate((1+x)*(x^2+2*x+1)^5/x^9,x, algorithm=""fricas"")","\frac{56 \, x^{11} + 924 \, x^{10} + 9240 \, x^{9} + 27720 \, x^{8} \log\left(x\right) - 55440 \, x^{7} - 38808 \, x^{6} - 25872 \, x^{5} - 13860 \, x^{4} - 5544 \, x^{3} - 1540 \, x^{2} - 264 \, x - 21}{168 \, x^{8}}"," ",0,"1/168*(56*x^11 + 924*x^10 + 9240*x^9 + 27720*x^8*log(x) - 55440*x^7 - 38808*x^6 - 25872*x^5 - 13860*x^4 - 5544*x^3 - 1540*x^2 - 264*x - 21)/x^8","A",0
609,1,62,0,0.408597," ","integrate((1+x)*(x^2+2*x+1)^5/x^10,x, algorithm=""fricas"")","\frac{252 \, x^{11} + 5544 \, x^{10} + 27720 \, x^{9} \log\left(x\right) - 83160 \, x^{8} - 83160 \, x^{7} - 77616 \, x^{6} - 58212 \, x^{5} - 33264 \, x^{4} - 13860 \, x^{3} - 3960 \, x^{2} - 693 \, x - 56}{504 \, x^{9}}"," ",0,"1/504*(252*x^11 + 5544*x^10 + 27720*x^9*log(x) - 83160*x^8 - 83160*x^7 - 77616*x^6 - 58212*x^5 - 33264*x^4 - 13860*x^3 - 3960*x^2 - 693*x - 56)/x^9","A",0
610,1,62,0,0.399334," ","integrate((1+x)*(x^2+2*x+1)^5/x^11,x, algorithm=""fricas"")","\frac{2520 \, x^{11} + 27720 \, x^{10} \log\left(x\right) - 138600 \, x^{9} - 207900 \, x^{8} - 277200 \, x^{7} - 291060 \, x^{6} - 232848 \, x^{5} - 138600 \, x^{4} - 59400 \, x^{3} - 17325 \, x^{2} - 3080 \, x - 252}{2520 \, x^{10}}"," ",0,"1/2520*(2520*x^11 + 27720*x^10*log(x) - 138600*x^9 - 207900*x^8 - 277200*x^7 - 291060*x^6 - 232848*x^5 - 138600*x^4 - 59400*x^3 - 17325*x^2 - 3080*x - 252)/x^10","A",0
611,1,62,0,0.385257," ","integrate((1+x)*(x^2+2*x+1)^5/x^12,x, algorithm=""fricas"")","\frac{27720 \, x^{11} \log\left(x\right) - 304920 \, x^{10} - 762300 \, x^{9} - 1524600 \, x^{8} - 2286900 \, x^{7} - 2561328 \, x^{6} - 2134440 \, x^{5} - 1306800 \, x^{4} - 571725 \, x^{3} - 169400 \, x^{2} - 30492 \, x - 2520}{27720 \, x^{11}}"," ",0,"1/27720*(27720*x^11*log(x) - 304920*x^10 - 762300*x^9 - 1524600*x^8 - 2286900*x^7 - 2561328*x^6 - 2134440*x^5 - 1306800*x^4 - 571725*x^3 - 169400*x^2 - 30492*x - 2520)/x^11","A",0
612,1,60,0,0.384866," ","integrate((1+x)*(x^2+2*x+1)^5/x^13,x, algorithm=""fricas"")","-\frac{12 \, x^{11} + 66 \, x^{10} + 220 \, x^{9} + 495 \, x^{8} + 792 \, x^{7} + 924 \, x^{6} + 792 \, x^{5} + 495 \, x^{4} + 220 \, x^{3} + 66 \, x^{2} + 12 \, x + 1}{12 \, x^{12}}"," ",0,"-1/12*(12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1)/x^12","B",0
613,1,60,0,0.376894," ","integrate((1+x)*(x^2+2*x+1)^5/x^14,x, algorithm=""fricas"")","-\frac{78 \, x^{11} + 572 \, x^{10} + 2145 \, x^{9} + 5148 \, x^{8} + 8580 \, x^{7} + 10296 \, x^{6} + 9009 \, x^{5} + 5720 \, x^{4} + 2574 \, x^{3} + 780 \, x^{2} + 143 \, x + 12}{156 \, x^{13}}"," ",0,"-1/156*(78*x^11 + 572*x^10 + 2145*x^9 + 5148*x^8 + 8580*x^7 + 10296*x^6 + 9009*x^5 + 5720*x^4 + 2574*x^3 + 780*x^2 + 143*x + 12)/x^13","B",0
614,1,60,0,0.392410," ","integrate((1+x)*(x^2+2*x+1)^5/x^15,x, algorithm=""fricas"")","-\frac{364 \, x^{11} + 3003 \, x^{10} + 12012 \, x^{9} + 30030 \, x^{8} + 51480 \, x^{7} + 63063 \, x^{6} + 56056 \, x^{5} + 36036 \, x^{4} + 16380 \, x^{3} + 5005 \, x^{2} + 924 \, x + 78}{1092 \, x^{14}}"," ",0,"-1/1092*(364*x^11 + 3003*x^10 + 12012*x^9 + 30030*x^8 + 51480*x^7 + 63063*x^6 + 56056*x^5 + 36036*x^4 + 16380*x^3 + 5005*x^2 + 924*x + 78)/x^14","A",0
615,1,60,0,0.389493," ","integrate((1+x)*(x^2+2*x+1)^5/x^16,x, algorithm=""fricas"")","-\frac{1365 \, x^{11} + 12012 \, x^{10} + 50050 \, x^{9} + 128700 \, x^{8} + 225225 \, x^{7} + 280280 \, x^{6} + 252252 \, x^{5} + 163800 \, x^{4} + 75075 \, x^{3} + 23100 \, x^{2} + 4290 \, x + 364}{5460 \, x^{15}}"," ",0,"-1/5460*(1365*x^11 + 12012*x^10 + 50050*x^9 + 128700*x^8 + 225225*x^7 + 280280*x^6 + 252252*x^5 + 163800*x^4 + 75075*x^3 + 23100*x^2 + 4290*x + 364)/x^15","A",0
616,1,60,0,0.397023," ","integrate((1+x)*(x^2+2*x+1)^5/x^17,x, algorithm=""fricas"")","-\frac{4368 \, x^{11} + 40040 \, x^{10} + 171600 \, x^{9} + 450450 \, x^{8} + 800800 \, x^{7} + 1009008 \, x^{6} + 917280 \, x^{5} + 600600 \, x^{4} + 277200 \, x^{3} + 85800 \, x^{2} + 16016 \, x + 1365}{21840 \, x^{16}}"," ",0,"-1/21840*(4368*x^11 + 40040*x^10 + 171600*x^9 + 450450*x^8 + 800800*x^7 + 1009008*x^6 + 917280*x^5 + 600600*x^4 + 277200*x^3 + 85800*x^2 + 16016*x + 1365)/x^16","A",0
617,1,60,0,0.392900," ","integrate((1+x)*(x^2+2*x+1)^5/x^18,x, algorithm=""fricas"")","-\frac{12376 \, x^{11} + 116688 \, x^{10} + 510510 \, x^{9} + 1361360 \, x^{8} + 2450448 \, x^{7} + 3118752 \, x^{6} + 2858856 \, x^{5} + 1884960 \, x^{4} + 875160 \, x^{3} + 272272 \, x^{2} + 51051 \, x + 4368}{74256 \, x^{17}}"," ",0,"-1/74256*(12376*x^11 + 116688*x^10 + 510510*x^9 + 1361360*x^8 + 2450448*x^7 + 3118752*x^6 + 2858856*x^5 + 1884960*x^4 + 875160*x^3 + 272272*x^2 + 51051*x + 4368)/x^17","A",0
618,1,60,0,0.394158," ","integrate((1+x)*(x^2+2*x+1)^5/x^19,x, algorithm=""fricas"")","-\frac{31824 \, x^{11} + 306306 \, x^{10} + 1361360 \, x^{9} + 3675672 \, x^{8} + 6683040 \, x^{7} + 8576568 \, x^{6} + 7916832 \, x^{5} + 5250960 \, x^{4} + 2450448 \, x^{3} + 765765 \, x^{2} + 144144 \, x + 12376}{222768 \, x^{18}}"," ",0,"-1/222768*(31824*x^11 + 306306*x^10 + 1361360*x^9 + 3675672*x^8 + 6683040*x^7 + 8576568*x^6 + 7916832*x^5 + 5250960*x^4 + 2450448*x^3 + 765765*x^2 + 144144*x + 12376)/x^18","A",0
619,1,60,0,0.394316," ","integrate((1+x)*(x^2+2*x+1)^5/x^20,x, algorithm=""fricas"")","-\frac{75582 \, x^{11} + 739024 \, x^{10} + 3325608 \, x^{9} + 9069840 \, x^{8} + 16628040 \, x^{7} + 21488544 \, x^{6} + 19953648 \, x^{5} + 13302432 \, x^{4} + 6235515 \, x^{3} + 1956240 \, x^{2} + 369512 \, x + 31824}{604656 \, x^{19}}"," ",0,"-1/604656*(75582*x^11 + 739024*x^10 + 3325608*x^9 + 9069840*x^8 + 16628040*x^7 + 21488544*x^6 + 19953648*x^5 + 13302432*x^4 + 6235515*x^3 + 1956240*x^2 + 369512*x + 31824)/x^19","A",0
620,1,60,0,0.390897," ","integrate((1+x)*(x^2+2*x+1)^5/x^21,x, algorithm=""fricas"")","-\frac{167960 \, x^{11} + 1662804 \, x^{10} + 7558200 \, x^{9} + 20785050 \, x^{8} + 38372400 \, x^{7} + 49884120 \, x^{6} + 46558512 \, x^{5} + 31177575 \, x^{4} + 14671800 \, x^{3} + 4618900 \, x^{2} + 875160 \, x + 75582}{1511640 \, x^{20}}"," ",0,"-1/1511640*(167960*x^11 + 1662804*x^10 + 7558200*x^9 + 20785050*x^8 + 38372400*x^7 + 49884120*x^6 + 46558512*x^5 + 31177575*x^4 + 14671800*x^3 + 4618900*x^2 + 875160*x + 75582)/x^20","A",0
621,1,60,0,0.388041," ","integrate((1+x)*(x^2+2*x+1)^5/x^22,x, algorithm=""fricas"")","-\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}}"," ",0,"-1/3527160*(352716*x^11 + 3527160*x^10 + 16166150*x^9 + 44767800*x^8 + 83140200*x^7 + 108636528*x^6 + 101846745*x^5 + 68468400*x^4 + 32332300*x^3 + 10210200*x^2 + 1939938*x + 167960)/x^21","A",0
622,1,188,0,0.403684," ","integrate(x^5*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{12 \, B b^{6} x^{6} - 60 \, B a^{6} + 60 \, A a^{5} b - 3 \, {\left(6 \, B a b^{5} - 5 \, A b^{6}\right)} x^{5} + 5 \, {\left(6 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} x^{4} - 10 \, {\left(6 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} x^{3} + 30 \, {\left(6 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} x^{2} + 60 \, {\left(5 \, B a^{5} b - 4 \, A a^{4} b^{2}\right)} x - 60 \, {\left(6 \, B a^{6} - 5 \, A a^{5} b + {\left(6 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} x\right)} \log\left(b x + a\right)}{60 \, {\left(b^{8} x + a b^{7}\right)}}"," ",0,"1/60*(12*B*b^6*x^6 - 60*B*a^6 + 60*A*a^5*b - 3*(6*B*a*b^5 - 5*A*b^6)*x^5 + 5*(6*B*a^2*b^4 - 5*A*a*b^5)*x^4 - 10*(6*B*a^3*b^3 - 5*A*a^2*b^4)*x^3 + 30*(6*B*a^4*b^2 - 5*A*a^3*b^3)*x^2 + 60*(5*B*a^5*b - 4*A*a^4*b^2)*x - 60*(6*B*a^6 - 5*A*a^5*b + (6*B*a^5*b - 5*A*a^4*b^2)*x)*log(b*x + a))/(b^8*x + a*b^7)","A",0
623,1,164,0,0.404161," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{3 \, B b^{5} x^{5} + 12 \, B a^{5} - 12 \, A a^{4} b - {\left(5 \, B a b^{4} - 4 \, A b^{5}\right)} x^{4} + 2 \, {\left(5 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} x^{3} - 6 \, {\left(5 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} x^{2} - 12 \, {\left(4 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x + 12 \, {\left(5 \, B a^{5} - 4 \, A a^{4} b + {\left(5 \, B a^{4} b - 4 \, A a^{3} b^{2}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{7} x + a b^{6}\right)}}"," ",0,"1/12*(3*B*b^5*x^5 + 12*B*a^5 - 12*A*a^4*b - (5*B*a*b^4 - 4*A*b^5)*x^4 + 2*(5*B*a^2*b^3 - 4*A*a*b^4)*x^3 - 6*(5*B*a^3*b^2 - 4*A*a^2*b^3)*x^2 - 12*(4*B*a^4*b - 3*A*a^3*b^2)*x + 12*(5*B*a^5 - 4*A*a^4*b + (5*B*a^4*b - 4*A*a^3*b^2)*x)*log(b*x + a))/(b^7*x + a*b^6)","A",0
624,1,140,0,0.406854," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, B b^{4} x^{4} - 6 \, B a^{4} + 6 \, A a^{3} b - {\left(4 \, B a b^{3} - 3 \, A b^{4}\right)} x^{3} + 3 \, {\left(4 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{2} + 6 \, {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} x - 6 \, {\left(4 \, B a^{4} - 3 \, A a^{3} b + {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"1/6*(2*B*b^4*x^4 - 6*B*a^4 + 6*A*a^3*b - (4*B*a*b^3 - 3*A*b^4)*x^3 + 3*(4*B*a^2*b^2 - 3*A*a*b^3)*x^2 + 6*(3*B*a^3*b - 2*A*a^2*b^2)*x - 6*(4*B*a^4 - 3*A*a^3*b + (4*B*a^3*b - 3*A*a^2*b^2)*x)*log(b*x + a))/(b^6*x + a*b^5)","A",0
625,1,113,0,0.415743," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{B b^{3} x^{3} + 2 \, B a^{3} - 2 \, A a^{2} b - {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} x^{2} - 2 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x + 2 \, {\left(3 \, B a^{3} - 2 \, A a^{2} b + {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(B*b^3*x^3 + 2*B*a^3 - 2*A*a^2*b - (3*B*a*b^2 - 2*A*b^3)*x^2 - 2*(2*B*a^2*b - A*a*b^2)*x + 2*(3*B*a^3 - 2*A*a^2*b + (3*B*a^2*b - 2*A*a*b^2)*x)*log(b*x + a))/(b^5*x + a*b^4)","A",0
626,1,72,0,0.405596," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{B b^{2} x^{2} + B a b x - B a^{2} + A a b - {\left(2 \, B a^{2} - A a b + {\left(2 \, B a b - A b^{2}\right)} x\right)} \log\left(b x + a\right)}{b^{4} x + a b^{3}}"," ",0,"(B*b^2*x^2 + B*a*b*x - B*a^2 + A*a*b - (2*B*a^2 - A*a*b + (2*B*a*b - A*b^2)*x)*log(b*x + a))/(b^4*x + a*b^3)","A",0
627,1,37,0,0.401998," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{B a - A b + {\left(B b x + B a\right)} \log\left(b x + a\right)}{b^{3} x + a b^{2}}"," ",0,"(B*a - A*b + (B*b*x + B*a)*log(b*x + a))/(b^3*x + a*b^2)","A",0
628,1,62,0,0.423498," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{B a^{2} - A a b + {\left(A b^{2} x + A a b\right)} \log\left(b x + a\right) - {\left(A b^{2} x + A a b\right)} \log\left(x\right)}{a^{2} b^{2} x + a^{3} b}"," ",0,"-(B*a^2 - A*a*b + (A*b^2*x + A*a*b)*log(b*x + a) - (A*b^2*x + A*a*b)*log(x))/(a^2*b^2*x + a^3*b)","A",0
629,1,107,0,0.404975," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{A a^{2} - {\left(B a^{2} - 2 \, A a b\right)} x + {\left({\left(B a b - 2 \, A b^{2}\right)} x^{2} + {\left(B a^{2} - 2 \, A a b\right)} x\right)} \log\left(b x + a\right) - {\left({\left(B a b - 2 \, A b^{2}\right)} x^{2} + {\left(B a^{2} - 2 \, A a b\right)} x\right)} \log\left(x\right)}{a^{3} b x^{2} + a^{4} x}"," ",0,"-(A*a^2 - (B*a^2 - 2*A*a*b)*x + ((B*a*b - 2*A*b^2)*x^2 + (B*a^2 - 2*A*a*b)*x)*log(b*x + a) - ((B*a*b - 2*A*b^2)*x^2 + (B*a^2 - 2*A*a*b)*x)*log(x))/(a^3*b*x^2 + a^4*x)","A",0
630,1,150,0,0.409678," ","integrate((B*x+A)/x^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{A a^{3} + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{2} + {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} x - 2 \, {\left({\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} x^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{2}\right)} \log\left(b x + a\right) + 2 \, {\left({\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} x^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}"," ",0,"-1/2*(A*a^3 + 2*(2*B*a^2*b - 3*A*a*b^2)*x^2 + (2*B*a^3 - 3*A*a^2*b)*x - 2*((2*B*a*b^2 - 3*A*b^3)*x^3 + (2*B*a^2*b - 3*A*a*b^2)*x^2)*log(b*x + a) + 2*((2*B*a*b^2 - 3*A*b^3)*x^3 + (2*B*a^2*b - 3*A*a*b^2)*x^2)*log(x))/(a^4*b*x^3 + a^5*x^2)","A",0
631,1,179,0,0.414973," ","integrate((B*x+A)/x^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{2 \, A a^{4} - 6 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} - 3 \, {\left(3 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} x^{2} + {\left(3 \, B a^{4} - 4 \, A a^{3} b\right)} x + 6 \, {\left({\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} x^{4} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3}\right)} \log\left(b x + a\right) - 6 \, {\left({\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} x^{4} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{5} b x^{4} + a^{6} x^{3}\right)}}"," ",0,"-1/6*(2*A*a^4 - 6*(3*B*a^2*b^2 - 4*A*a*b^3)*x^3 - 3*(3*B*a^3*b - 4*A*a^2*b^2)*x^2 + (3*B*a^4 - 4*A*a^3*b)*x + 6*((3*B*a*b^3 - 4*A*b^4)*x^4 + (3*B*a^2*b^2 - 4*A*a*b^3)*x^3)*log(b*x + a) - 6*((3*B*a*b^3 - 4*A*b^4)*x^4 + (3*B*a^2*b^2 - 4*A*a*b^3)*x^3)*log(x))/(a^5*b*x^4 + a^6*x^3)","A",0
632,1,203,0,0.400434," ","integrate((B*x+A)/x^5/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{3 \, A a^{5} + 12 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} + 6 \, {\left(4 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3} - 2 \, {\left(4 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} x^{2} + {\left(4 \, B a^{5} - 5 \, A a^{4} b\right)} x - 12 \, {\left({\left(4 \, B a b^{4} - 5 \, A b^{5}\right)} x^{5} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4}\right)} \log\left(b x + a\right) + 12 \, {\left({\left(4 \, B a b^{4} - 5 \, A b^{5}\right)} x^{5} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4}\right)} \log\left(x\right)}{12 \, {\left(a^{6} b x^{5} + a^{7} x^{4}\right)}}"," ",0,"-1/12*(3*A*a^5 + 12*(4*B*a^2*b^3 - 5*A*a*b^4)*x^4 + 6*(4*B*a^3*b^2 - 5*A*a^2*b^3)*x^3 - 2*(4*B*a^4*b - 5*A*a^3*b^2)*x^2 + (4*B*a^5 - 5*A*a^4*b)*x - 12*((4*B*a*b^4 - 5*A*b^5)*x^5 + (4*B*a^2*b^3 - 5*A*a*b^4)*x^4)*log(b*x + a) + 12*((4*B*a*b^4 - 5*A*b^5)*x^5 + (4*B*a^2*b^3 - 5*A*a*b^4)*x^4)*log(x))/(a^6*b*x^5 + a^7*x^4)","A",0
633,1,257,0,0.403591," ","integrate(x^5*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, B b^{6} x^{6} - 74 \, B a^{6} + 47 \, A a^{5} b - 3 \, {\left(2 \, B a b^{5} - A b^{6}\right)} x^{5} + 15 \, {\left(2 \, B a^{2} b^{4} - A a b^{5}\right)} x^{4} + {\left(146 \, B a^{3} b^{3} - 63 \, A a^{2} b^{4}\right)} x^{3} + 3 \, {\left(26 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} x^{2} - 3 \, {\left(34 \, B a^{5} b - 27 \, A a^{4} b^{2}\right)} x - 60 \, {\left(2 \, B a^{6} - A a^{5} b + {\left(2 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} x^{3} + 3 \, {\left(2 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} x^{2} + 3 \, {\left(2 \, B a^{5} b - A a^{4} b^{2}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{10} x^{3} + 3 \, a b^{9} x^{2} + 3 \, a^{2} b^{8} x + a^{3} b^{7}\right)}}"," ",0,"1/6*(2*B*b^6*x^6 - 74*B*a^6 + 47*A*a^5*b - 3*(2*B*a*b^5 - A*b^6)*x^5 + 15*(2*B*a^2*b^4 - A*a*b^5)*x^4 + (146*B*a^3*b^3 - 63*A*a^2*b^4)*x^3 + 3*(26*B*a^4*b^2 - 3*A*a^3*b^3)*x^2 - 3*(34*B*a^5*b - 27*A*a^4*b^2)*x - 60*(2*B*a^6 - A*a^5*b + (2*B*a^3*b^3 - A*a^2*b^4)*x^3 + 3*(2*B*a^4*b^2 - A*a^3*b^3)*x^2 + 3*(2*B*a^5*b - A*a^4*b^2)*x)*log(b*x + a))/(b^10*x^3 + 3*a*b^9*x^2 + 3*a^2*b^8*x + a^3*b^7)","A",0
634,1,231,0,0.408080," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{3 \, B b^{5} x^{5} + 47 \, B a^{5} - 26 \, A a^{4} b - 3 \, {\left(5 \, B a b^{4} - 2 \, A b^{5}\right)} x^{4} - 9 \, {\left(7 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} x^{3} - 9 \, {\left(B a^{3} b^{2} + 2 \, A a^{2} b^{3}\right)} x^{2} + 27 \, {\left(3 \, B a^{4} b - 2 \, A a^{3} b^{2}\right)} x + 12 \, {\left(5 \, B a^{5} - 2 \, A a^{4} b + {\left(5 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} x^{3} + 3 \, {\left(5 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} x^{2} + 3 \, {\left(5 \, B a^{4} b - 2 \, A a^{3} b^{2}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{9} x^{3} + 3 \, a b^{8} x^{2} + 3 \, a^{2} b^{7} x + a^{3} b^{6}\right)}}"," ",0,"1/6*(3*B*b^5*x^5 + 47*B*a^5 - 26*A*a^4*b - 3*(5*B*a*b^4 - 2*A*b^5)*x^4 - 9*(7*B*a^2*b^3 - 2*A*a*b^4)*x^3 - 9*(B*a^3*b^2 + 2*A*a^2*b^3)*x^2 + 27*(3*B*a^4*b - 2*A*a^3*b^2)*x + 12*(5*B*a^5 - 2*A*a^4*b + (5*B*a^2*b^3 - 2*A*a*b^4)*x^3 + 3*(5*B*a^3*b^2 - 2*A*a^2*b^3)*x^2 + 3*(5*B*a^4*b - 2*A*a^3*b^2)*x)*log(b*x + a))/(b^9*x^3 + 3*a*b^8*x^2 + 3*a^2*b^7*x + a^3*b^6)","A",0
635,1,193,0,0.401248," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{6 \, B b^{4} x^{4} + 18 \, B a b^{3} x^{3} - 26 \, B a^{4} + 11 \, A a^{3} b - 18 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 27 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} x - 6 \, {\left(4 \, B a^{4} - A a^{3} b + {\left(4 \, B a b^{3} - A b^{4}\right)} x^{3} + 3 \, {\left(4 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} + 3 \, {\left(4 \, B a^{3} b - A a^{2} b^{2}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}"," ",0,"1/6*(6*B*b^4*x^4 + 18*B*a*b^3*x^3 - 26*B*a^4 + 11*A*a^3*b - 18*(B*a^2*b^2 - A*a*b^3)*x^2 - 27*(2*B*a^3*b - A*a^2*b^2)*x - 6*(4*B*a^4 - A*a^3*b + (4*B*a*b^3 - A*b^4)*x^3 + 3*(4*B*a^2*b^2 - A*a*b^3)*x^2 + 3*(4*B*a^3*b - A*a^2*b^2)*x)*log(b*x + a))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5)","B",0
636,1,128,0,0.401729," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{11 \, B a^{3} - 2 \, A a^{2} b + 6 \, {\left(3 \, B a b^{2} - A b^{3}\right)} x^{2} + 3 \, {\left(9 \, B a^{2} b - 2 \, A a b^{2}\right)} x + 6 \, {\left(B b^{3} x^{3} + 3 \, B a b^{2} x^{2} + 3 \, B a^{2} b x + B a^{3}\right)} \log\left(b x + a\right)}{6 \, {\left(b^{7} x^{3} + 3 \, a b^{6} x^{2} + 3 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}"," ",0,"1/6*(11*B*a^3 - 2*A*a^2*b + 6*(3*B*a*b^2 - A*b^3)*x^2 + 3*(9*B*a^2*b - 2*A*a*b^2)*x + 6*(B*b^3*x^3 + 3*B*a*b^2*x^2 + 3*B*a^2*b*x + B*a^3)*log(b*x + a))/(b^7*x^3 + 3*a*b^6*x^2 + 3*a^2*b^5*x + a^3*b^4)","A",0
637,1,71,0,0.399896," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{6 \, B b^{2} x^{2} + 2 \, B a^{2} + A a b + 3 \, {\left(2 \, B a b + A b^{2}\right)} x}{6 \, {\left(b^{6} x^{3} + 3 \, a b^{5} x^{2} + 3 \, a^{2} b^{4} x + a^{3} b^{3}\right)}}"," ",0,"-1/6*(6*B*b^2*x^2 + 2*B*a^2 + A*a*b + 3*(2*B*a*b + A*b^2)*x)/(b^6*x^3 + 3*a*b^5*x^2 + 3*a^2*b^4*x + a^3*b^3)","A",0
638,1,50,0,0.416826," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{3 \, B b x + B a + 2 \, A b}{6 \, {\left(b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x + a^{3} b^{2}\right)}}"," ",0,"-1/6*(3*B*b*x + B*a + 2*A*b)/(b^5*x^3 + 3*a*b^4*x^2 + 3*a^2*b^3*x + a^3*b^2)","A",0
639,1,156,0,0.440686," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{6 \, A a b^{3} x^{2} + 15 \, A a^{2} b^{2} x - 2 \, B a^{4} + 11 \, A a^{3} b - 6 \, {\left(A b^{4} x^{3} + 3 \, A a b^{3} x^{2} + 3 \, A a^{2} b^{2} x + A a^{3} b\right)} \log\left(b x + a\right) + 6 \, {\left(A b^{4} x^{3} + 3 \, A a b^{3} x^{2} + 3 \, A a^{2} b^{2} x + A a^{3} b\right)} \log\left(x\right)}{6 \, {\left(a^{4} b^{4} x^{3} + 3 \, a^{5} b^{3} x^{2} + 3 \, a^{6} b^{2} x + a^{7} b\right)}}"," ",0,"1/6*(6*A*a*b^3*x^2 + 15*A*a^2*b^2*x - 2*B*a^4 + 11*A*a^3*b - 6*(A*b^4*x^3 + 3*A*a*b^3*x^2 + 3*A*a^2*b^2*x + A*a^3*b)*log(b*x + a) + 6*(A*b^4*x^3 + 3*A*a*b^3*x^2 + 3*A*a^2*b^2*x + A*a^3*b)*log(x))/(a^4*b^4*x^3 + 3*a^5*b^3*x^2 + 3*a^6*b^2*x + a^7*b)","B",0
640,1,267,0,0.408097," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{6 \, A a^{4} - 6 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} - 15 \, {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} x^{2} - 11 \, {\left(B a^{4} - 4 \, A a^{3} b\right)} x + 6 \, {\left({\left(B a b^{3} - 4 \, A b^{4}\right)} x^{4} + 3 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} + 3 \, {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} x^{2} + {\left(B a^{4} - 4 \, A a^{3} b\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left({\left(B a b^{3} - 4 \, A b^{4}\right)} x^{4} + 3 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} + 3 \, {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} x^{2} + {\left(B a^{4} - 4 \, A a^{3} b\right)} x\right)} \log\left(x\right)}{6 \, {\left(a^{5} b^{3} x^{4} + 3 \, a^{6} b^{2} x^{3} + 3 \, a^{7} b x^{2} + a^{8} x\right)}}"," ",0,"-1/6*(6*A*a^4 - 6*(B*a^2*b^2 - 4*A*a*b^3)*x^3 - 15*(B*a^3*b - 4*A*a^2*b^2)*x^2 - 11*(B*a^4 - 4*A*a^3*b)*x + 6*((B*a*b^3 - 4*A*b^4)*x^4 + 3*(B*a^2*b^2 - 4*A*a*b^3)*x^3 + 3*(B*a^3*b - 4*A*a^2*b^2)*x^2 + (B*a^4 - 4*A*a^3*b)*x)*log(b*x + a) - 6*((B*a*b^3 - 4*A*b^4)*x^4 + 3*(B*a^2*b^2 - 4*A*a*b^3)*x^3 + 3*(B*a^3*b - 4*A*a^2*b^2)*x^2 + (B*a^4 - 4*A*a^3*b)*x)*log(x))/(a^5*b^3*x^4 + 3*a^6*b^2*x^3 + 3*a^7*b*x^2 + a^8*x)","B",0
641,1,318,0,0.420516," ","integrate((B*x+A)/x^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{3 \, A a^{5} + 12 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} + 30 \, {\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3} + 22 \, {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} x^{2} + 3 \, {\left(2 \, B a^{5} - 5 \, A a^{4} b\right)} x - 12 \, {\left({\left(2 \, B a b^{4} - 5 \, A b^{5}\right)} x^{5} + 3 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} + 3 \, {\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3} + {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} x^{2}\right)} \log\left(b x + a\right) + 12 \, {\left({\left(2 \, B a b^{4} - 5 \, A b^{5}\right)} x^{5} + 3 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} + 3 \, {\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3} + {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} x^{2}\right)} \log\left(x\right)}{6 \, {\left(a^{6} b^{3} x^{5} + 3 \, a^{7} b^{2} x^{4} + 3 \, a^{8} b x^{3} + a^{9} x^{2}\right)}}"," ",0,"-1/6*(3*A*a^5 + 12*(2*B*a^2*b^3 - 5*A*a*b^4)*x^4 + 30*(2*B*a^3*b^2 - 5*A*a^2*b^3)*x^3 + 22*(2*B*a^4*b - 5*A*a^3*b^2)*x^2 + 3*(2*B*a^5 - 5*A*a^4*b)*x - 12*((2*B*a*b^4 - 5*A*b^5)*x^5 + 3*(2*B*a^2*b^3 - 5*A*a*b^4)*x^4 + 3*(2*B*a^3*b^2 - 5*A*a^2*b^3)*x^3 + (2*B*a^4*b - 5*A*a^3*b^2)*x^2)*log(b*x + a) + 12*((2*B*a*b^4 - 5*A*b^5)*x^5 + 3*(2*B*a^2*b^3 - 5*A*a*b^4)*x^4 + 3*(2*B*a^3*b^2 - 5*A*a^2*b^3)*x^3 + (2*B*a^4*b - 5*A*a^3*b^2)*x^2)*log(x))/(a^6*b^3*x^5 + 3*a^7*b^2*x^4 + 3*a^8*b*x^3 + a^9*x^2)","B",0
642,1,333,0,0.412665," ","integrate((B*x+A)/x^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{2 \, A a^{6} - 60 \, {\left(B a^{2} b^{4} - 2 \, A a b^{5}\right)} x^{5} - 150 \, {\left(B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} x^{4} - 110 \, {\left(B a^{4} b^{2} - 2 \, A a^{3} b^{3}\right)} x^{3} - 15 \, {\left(B a^{5} b - 2 \, A a^{4} b^{2}\right)} x^{2} + 3 \, {\left(B a^{6} - 2 \, A a^{5} b\right)} x + 60 \, {\left({\left(B a b^{5} - 2 \, A b^{6}\right)} x^{6} + 3 \, {\left(B a^{2} b^{4} - 2 \, A a b^{5}\right)} x^{5} + 3 \, {\left(B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} x^{4} + {\left(B a^{4} b^{2} - 2 \, A a^{3} b^{3}\right)} x^{3}\right)} \log\left(b x + a\right) - 60 \, {\left({\left(B a b^{5} - 2 \, A b^{6}\right)} x^{6} + 3 \, {\left(B a^{2} b^{4} - 2 \, A a b^{5}\right)} x^{5} + 3 \, {\left(B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} x^{4} + {\left(B a^{4} b^{2} - 2 \, A a^{3} b^{3}\right)} x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{7} b^{3} x^{6} + 3 \, a^{8} b^{2} x^{5} + 3 \, a^{9} b x^{4} + a^{10} x^{3}\right)}}"," ",0,"-1/6*(2*A*a^6 - 60*(B*a^2*b^4 - 2*A*a*b^5)*x^5 - 150*(B*a^3*b^3 - 2*A*a^2*b^4)*x^4 - 110*(B*a^4*b^2 - 2*A*a^3*b^3)*x^3 - 15*(B*a^5*b - 2*A*a^4*b^2)*x^2 + 3*(B*a^6 - 2*A*a^5*b)*x + 60*((B*a*b^5 - 2*A*b^6)*x^6 + 3*(B*a^2*b^4 - 2*A*a*b^5)*x^5 + 3*(B*a^3*b^3 - 2*A*a^2*b^4)*x^4 + (B*a^4*b^2 - 2*A*a^3*b^3)*x^3)*log(b*x + a) - 60*((B*a*b^5 - 2*A*b^6)*x^6 + 3*(B*a^2*b^4 - 2*A*a*b^5)*x^5 + 3*(B*a^3*b^3 - 2*A*a^2*b^4)*x^4 + (B*a^4*b^2 - 2*A*a^3*b^3)*x^3)*log(x))/(a^7*b^3*x^6 + 3*a^8*b^2*x^5 + 3*a^9*b*x^4 + a^10*x^3)","B",0
643,1,349,0,0.395901," ","integrate(x^6*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{10 \, B b^{7} x^{7} + 459 \, B a^{7} - 174 \, A a^{6} b - 10 \, {\left(7 \, B a b^{6} - 2 \, A b^{7}\right)} x^{6} - 100 \, {\left(5 \, B a^{2} b^{5} - A a b^{6}\right)} x^{5} - 100 \, {\left(4 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} x^{4} + 100 \, {\left(13 \, B a^{4} b^{3} - 8 \, A a^{3} b^{4}\right)} x^{3} + 300 \, {\left(9 \, B a^{5} b^{2} - 4 \, A a^{4} b^{3}\right)} x^{2} + 375 \, {\left(5 \, B a^{6} b - 2 \, A a^{5} b^{2}\right)} x + 60 \, {\left(7 \, B a^{7} - 2 \, A a^{6} b + {\left(7 \, B a^{2} b^{5} - 2 \, A a b^{6}\right)} x^{5} + 5 \, {\left(7 \, B a^{3} b^{4} - 2 \, A a^{2} b^{5}\right)} x^{4} + 10 \, {\left(7 \, B a^{4} b^{3} - 2 \, A a^{3} b^{4}\right)} x^{3} + 10 \, {\left(7 \, B a^{5} b^{2} - 2 \, A a^{4} b^{3}\right)} x^{2} + 5 \, {\left(7 \, B a^{6} b - 2 \, A a^{5} b^{2}\right)} x\right)} \log\left(b x + a\right)}{20 \, {\left(b^{13} x^{5} + 5 \, a b^{12} x^{4} + 10 \, a^{2} b^{11} x^{3} + 10 \, a^{3} b^{10} x^{2} + 5 \, a^{4} b^{9} x + a^{5} b^{8}\right)}}"," ",0,"1/20*(10*B*b^7*x^7 + 459*B*a^7 - 174*A*a^6*b - 10*(7*B*a*b^6 - 2*A*b^7)*x^6 - 100*(5*B*a^2*b^5 - A*a*b^6)*x^5 - 100*(4*B*a^3*b^4 + A*a^2*b^5)*x^4 + 100*(13*B*a^4*b^3 - 8*A*a^3*b^4)*x^3 + 300*(9*B*a^5*b^2 - 4*A*a^4*b^3)*x^2 + 375*(5*B*a^6*b - 2*A*a^5*b^2)*x + 60*(7*B*a^7 - 2*A*a^6*b + (7*B*a^2*b^5 - 2*A*a*b^6)*x^5 + 5*(7*B*a^3*b^4 - 2*A*a^2*b^5)*x^4 + 10*(7*B*a^4*b^3 - 2*A*a^3*b^4)*x^3 + 10*(7*B*a^5*b^2 - 2*A*a^4*b^3)*x^2 + 5*(7*B*a^6*b - 2*A*a^5*b^2)*x)*log(b*x + a))/(b^13*x^5 + 5*a*b^12*x^4 + 10*a^2*b^11*x^3 + 10*a^3*b^10*x^2 + 5*a^4*b^9*x + a^5*b^8)","B",0
644,1,311,0,0.403198," ","integrate(x^5*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{60 \, B b^{6} x^{6} + 300 \, B a b^{5} x^{5} - 522 \, B a^{6} + 137 \, A a^{5} b - 300 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} x^{4} - 300 \, {\left(8 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} x^{3} - 100 \, {\left(36 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} x^{2} - 125 \, {\left(18 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} x - 60 \, {\left(6 \, B a^{6} - A a^{5} b + {\left(6 \, B a b^{5} - A b^{6}\right)} x^{5} + 5 \, {\left(6 \, B a^{2} b^{4} - A a b^{5}\right)} x^{4} + 10 \, {\left(6 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(6 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(6 \, B a^{5} b - A a^{4} b^{2}\right)} x\right)} \log\left(b x + a\right)}{60 \, {\left(b^{12} x^{5} + 5 \, a b^{11} x^{4} + 10 \, a^{2} b^{10} x^{3} + 10 \, a^{3} b^{9} x^{2} + 5 \, a^{4} b^{8} x + a^{5} b^{7}\right)}}"," ",0,"1/60*(60*B*b^6*x^6 + 300*B*a*b^5*x^5 - 522*B*a^6 + 137*A*a^5*b - 300*(B*a^2*b^4 - A*a*b^5)*x^4 - 300*(8*B*a^3*b^3 - 3*A*a^2*b^4)*x^3 - 100*(36*B*a^4*b^2 - 11*A*a^3*b^3)*x^2 - 125*(18*B*a^5*b - 5*A*a^4*b^2)*x - 60*(6*B*a^6 - A*a^5*b + (6*B*a*b^5 - A*b^6)*x^5 + 5*(6*B*a^2*b^4 - A*a*b^5)*x^4 + 10*(6*B*a^3*b^3 - A*a^2*b^4)*x^3 + 10*(6*B*a^4*b^2 - A*a^3*b^3)*x^2 + 5*(6*B*a^5*b - A*a^4*b^2)*x)*log(b*x + a))/(b^12*x^5 + 5*a*b^11*x^4 + 10*a^2*b^10*x^3 + 10*a^3*b^9*x^2 + 5*a^4*b^8*x + a^5*b^7)","B",0
645,1,222,0,0.406146," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{137 \, B a^{5} - 12 \, A a^{4} b + 60 \, {\left(5 \, B a b^{4} - A b^{5}\right)} x^{4} + 60 \, {\left(15 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} x^{3} + 20 \, {\left(55 \, B a^{3} b^{2} - 6 \, A a^{2} b^{3}\right)} x^{2} + 5 \, {\left(125 \, B a^{4} b - 12 \, A a^{3} b^{2}\right)} x + 60 \, {\left(B b^{5} x^{5} + 5 \, B a b^{4} x^{4} + 10 \, B a^{2} b^{3} x^{3} + 10 \, B a^{3} b^{2} x^{2} + 5 \, B a^{4} b x + B a^{5}\right)} \log\left(b x + a\right)}{60 \, {\left(b^{11} x^{5} + 5 \, a b^{10} x^{4} + 10 \, a^{2} b^{9} x^{3} + 10 \, a^{3} b^{8} x^{2} + 5 \, a^{4} b^{7} x + a^{5} b^{6}\right)}}"," ",0,"1/60*(137*B*a^5 - 12*A*a^4*b + 60*(5*B*a*b^4 - A*b^5)*x^4 + 60*(15*B*a^2*b^3 - 2*A*a*b^4)*x^3 + 20*(55*B*a^3*b^2 - 6*A*a^2*b^3)*x^2 + 5*(125*B*a^4*b - 12*A*a^3*b^2)*x + 60*(B*b^5*x^5 + 5*B*a*b^4*x^4 + 10*B*a^2*b^3*x^3 + 10*B*a^3*b^2*x^2 + 5*B*a^4*b*x + B*a^5)*log(b*x + a))/(b^11*x^5 + 5*a*b^10*x^4 + 10*a^2*b^9*x^3 + 10*a^3*b^8*x^2 + 5*a^4*b^7*x + a^5*b^6)","B",0
646,1,139,0,0.385313," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{20 \, B b^{4} x^{4} + 4 \, B a^{4} + A a^{3} b + 10 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{3} + 10 \, {\left(4 \, B a^{2} b^{2} + A a b^{3}\right)} x^{2} + 5 \, {\left(4 \, B a^{3} b + A a^{2} b^{2}\right)} x}{20 \, {\left(b^{10} x^{5} + 5 \, a b^{9} x^{4} + 10 \, a^{2} b^{8} x^{3} + 10 \, a^{3} b^{7} x^{2} + 5 \, a^{4} b^{6} x + a^{5} b^{5}\right)}}"," ",0,"-1/20*(20*B*b^4*x^4 + 4*B*a^4 + A*a^3*b + 10*(4*B*a*b^3 + A*b^4)*x^3 + 10*(4*B*a^2*b^2 + A*a*b^3)*x^2 + 5*(4*B*a^3*b + A*a^2*b^2)*x)/(b^10*x^5 + 5*a*b^9*x^4 + 10*a^2*b^8*x^3 + 10*a^3*b^7*x^2 + 5*a^4*b^6*x + a^5*b^5)","B",0
647,1,119,0,0.385736," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{30 \, B b^{3} x^{3} + 3 \, B a^{3} + 2 \, A a^{2} b + 10 \, {\left(3 \, B a b^{2} + 2 \, A b^{3}\right)} x^{2} + 5 \, {\left(3 \, B a^{2} b + 2 \, A a b^{2}\right)} x}{60 \, {\left(b^{9} x^{5} + 5 \, a b^{8} x^{4} + 10 \, a^{2} b^{7} x^{3} + 10 \, a^{3} b^{6} x^{2} + 5 \, a^{4} b^{5} x + a^{5} b^{4}\right)}}"," ",0,"-1/60*(30*B*b^3*x^3 + 3*B*a^3 + 2*A*a^2*b + 10*(3*B*a*b^2 + 2*A*b^3)*x^2 + 5*(3*B*a^2*b + 2*A*a*b^2)*x)/(b^9*x^5 + 5*a*b^8*x^4 + 10*a^2*b^7*x^3 + 10*a^3*b^6*x^2 + 5*a^4*b^5*x + a^5*b^4)","A",0
648,1,95,0,0.401632," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{20 \, B b^{2} x^{2} + 2 \, B a^{2} + 3 \, A a b + 5 \, {\left(2 \, B a b + 3 \, A b^{2}\right)} x}{60 \, {\left(b^{8} x^{5} + 5 \, a b^{7} x^{4} + 10 \, a^{2} b^{6} x^{3} + 10 \, a^{3} b^{5} x^{2} + 5 \, a^{4} b^{4} x + a^{5} b^{3}\right)}}"," ",0,"-1/60*(20*B*b^2*x^2 + 2*B*a^2 + 3*A*a*b + 5*(2*B*a*b + 3*A*b^2)*x)/(b^8*x^5 + 5*a*b^7*x^4 + 10*a^2*b^6*x^3 + 10*a^3*b^5*x^2 + 5*a^4*b^4*x + a^5*b^3)","A",0
649,1,72,0,0.403175," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{5 \, B b x + B a + 4 \, A b}{20 \, {\left(b^{7} x^{5} + 5 \, a b^{6} x^{4} + 10 \, a^{2} b^{5} x^{3} + 10 \, a^{3} b^{4} x^{2} + 5 \, a^{4} b^{3} x + a^{5} b^{2}\right)}}"," ",0,"-1/20*(5*B*b*x + B*a + 4*A*b)/(b^7*x^5 + 5*a*b^6*x^4 + 10*a^2*b^5*x^3 + 10*a^3*b^4*x^2 + 5*a^4*b^3*x + a^5*b^2)","B",0
650,1,250,0,0.419033," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{60 \, A a b^{5} x^{4} + 270 \, A a^{2} b^{4} x^{3} + 470 \, A a^{3} b^{3} x^{2} + 385 \, A a^{4} b^{2} x - 12 \, B a^{6} + 137 \, A a^{5} b - 60 \, {\left(A b^{6} x^{5} + 5 \, A a b^{5} x^{4} + 10 \, A a^{2} b^{4} x^{3} + 10 \, A a^{3} b^{3} x^{2} + 5 \, A a^{4} b^{2} x + A a^{5} b\right)} \log\left(b x + a\right) + 60 \, {\left(A b^{6} x^{5} + 5 \, A a b^{5} x^{4} + 10 \, A a^{2} b^{4} x^{3} + 10 \, A a^{3} b^{3} x^{2} + 5 \, A a^{4} b^{2} x + A a^{5} b\right)} \log\left(x\right)}{60 \, {\left(a^{6} b^{6} x^{5} + 5 \, a^{7} b^{5} x^{4} + 10 \, a^{8} b^{4} x^{3} + 10 \, a^{9} b^{3} x^{2} + 5 \, a^{10} b^{2} x + a^{11} b\right)}}"," ",0,"1/60*(60*A*a*b^5*x^4 + 270*A*a^2*b^4*x^3 + 470*A*a^3*b^3*x^2 + 385*A*a^4*b^2*x - 12*B*a^6 + 137*A*a^5*b - 60*(A*b^6*x^5 + 5*A*a*b^5*x^4 + 10*A*a^2*b^4*x^3 + 10*A*a^3*b^3*x^2 + 5*A*a^4*b^2*x + A*a^5*b)*log(b*x + a) + 60*(A*b^6*x^5 + 5*A*a*b^5*x^4 + 10*A*a^2*b^4*x^3 + 10*A*a^3*b^3*x^2 + 5*A*a^4*b^2*x + A*a^5*b)*log(x))/(a^6*b^6*x^5 + 5*a^7*b^5*x^4 + 10*a^8*b^4*x^3 + 10*a^9*b^3*x^2 + 5*a^10*b^2*x + a^11*b)","B",0
651,1,427,0,0.431702," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{60 \, A a^{6} - 60 \, {\left(B a^{2} b^{4} - 6 \, A a b^{5}\right)} x^{5} - 270 \, {\left(B a^{3} b^{3} - 6 \, A a^{2} b^{4}\right)} x^{4} - 470 \, {\left(B a^{4} b^{2} - 6 \, A a^{3} b^{3}\right)} x^{3} - 385 \, {\left(B a^{5} b - 6 \, A a^{4} b^{2}\right)} x^{2} - 137 \, {\left(B a^{6} - 6 \, A a^{5} b\right)} x + 60 \, {\left({\left(B a b^{5} - 6 \, A b^{6}\right)} x^{6} + 5 \, {\left(B a^{2} b^{4} - 6 \, A a b^{5}\right)} x^{5} + 10 \, {\left(B a^{3} b^{3} - 6 \, A a^{2} b^{4}\right)} x^{4} + 10 \, {\left(B a^{4} b^{2} - 6 \, A a^{3} b^{3}\right)} x^{3} + 5 \, {\left(B a^{5} b - 6 \, A a^{4} b^{2}\right)} x^{2} + {\left(B a^{6} - 6 \, A a^{5} b\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left({\left(B a b^{5} - 6 \, A b^{6}\right)} x^{6} + 5 \, {\left(B a^{2} b^{4} - 6 \, A a b^{5}\right)} x^{5} + 10 \, {\left(B a^{3} b^{3} - 6 \, A a^{2} b^{4}\right)} x^{4} + 10 \, {\left(B a^{4} b^{2} - 6 \, A a^{3} b^{3}\right)} x^{3} + 5 \, {\left(B a^{5} b - 6 \, A a^{4} b^{2}\right)} x^{2} + {\left(B a^{6} - 6 \, A a^{5} b\right)} x\right)} \log\left(x\right)}{60 \, {\left(a^{7} b^{5} x^{6} + 5 \, a^{8} b^{4} x^{5} + 10 \, a^{9} b^{3} x^{4} + 10 \, a^{10} b^{2} x^{3} + 5 \, a^{11} b x^{2} + a^{12} x\right)}}"," ",0,"-1/60*(60*A*a^6 - 60*(B*a^2*b^4 - 6*A*a*b^5)*x^5 - 270*(B*a^3*b^3 - 6*A*a^2*b^4)*x^4 - 470*(B*a^4*b^2 - 6*A*a^3*b^3)*x^3 - 385*(B*a^5*b - 6*A*a^4*b^2)*x^2 - 137*(B*a^6 - 6*A*a^5*b)*x + 60*((B*a*b^5 - 6*A*b^6)*x^6 + 5*(B*a^2*b^4 - 6*A*a*b^5)*x^5 + 10*(B*a^3*b^3 - 6*A*a^2*b^4)*x^4 + 10*(B*a^4*b^2 - 6*A*a^3*b^3)*x^3 + 5*(B*a^5*b - 6*A*a^4*b^2)*x^2 + (B*a^6 - 6*A*a^5*b)*x)*log(b*x + a) - 60*((B*a*b^5 - 6*A*b^6)*x^6 + 5*(B*a^2*b^4 - 6*A*a*b^5)*x^5 + 10*(B*a^3*b^3 - 6*A*a^2*b^4)*x^4 + 10*(B*a^4*b^2 - 6*A*a^3*b^3)*x^3 + 5*(B*a^5*b - 6*A*a^4*b^2)*x^2 + (B*a^6 - 6*A*a^5*b)*x)*log(x))/(a^7*b^5*x^6 + 5*a^8*b^4*x^5 + 10*a^9*b^3*x^4 + 10*a^10*b^2*x^3 + 5*a^11*b*x^2 + a^12*x)","B",0
652,1,484,0,0.440822," ","integrate((B*x+A)/x^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{10 \, A a^{7} + 60 \, {\left(2 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} x^{6} + 270 \, {\left(2 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5}\right)} x^{5} + 470 \, {\left(2 \, B a^{4} b^{3} - 7 \, A a^{3} b^{4}\right)} x^{4} + 385 \, {\left(2 \, B a^{5} b^{2} - 7 \, A a^{4} b^{3}\right)} x^{3} + 137 \, {\left(2 \, B a^{6} b - 7 \, A a^{5} b^{2}\right)} x^{2} + 10 \, {\left(2 \, B a^{7} - 7 \, A a^{6} b\right)} x - 60 \, {\left({\left(2 \, B a b^{6} - 7 \, A b^{7}\right)} x^{7} + 5 \, {\left(2 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} x^{6} + 10 \, {\left(2 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5}\right)} x^{5} + 10 \, {\left(2 \, B a^{4} b^{3} - 7 \, A a^{3} b^{4}\right)} x^{4} + 5 \, {\left(2 \, B a^{5} b^{2} - 7 \, A a^{4} b^{3}\right)} x^{3} + {\left(2 \, B a^{6} b - 7 \, A a^{5} b^{2}\right)} x^{2}\right)} \log\left(b x + a\right) + 60 \, {\left({\left(2 \, B a b^{6} - 7 \, A b^{7}\right)} x^{7} + 5 \, {\left(2 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} x^{6} + 10 \, {\left(2 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5}\right)} x^{5} + 10 \, {\left(2 \, B a^{4} b^{3} - 7 \, A a^{3} b^{4}\right)} x^{4} + 5 \, {\left(2 \, B a^{5} b^{2} - 7 \, A a^{4} b^{3}\right)} x^{3} + {\left(2 \, B a^{6} b - 7 \, A a^{5} b^{2}\right)} x^{2}\right)} \log\left(x\right)}{20 \, {\left(a^{8} b^{5} x^{7} + 5 \, a^{9} b^{4} x^{6} + 10 \, a^{10} b^{3} x^{5} + 10 \, a^{11} b^{2} x^{4} + 5 \, a^{12} b x^{3} + a^{13} x^{2}\right)}}"," ",0,"-1/20*(10*A*a^7 + 60*(2*B*a^2*b^5 - 7*A*a*b^6)*x^6 + 270*(2*B*a^3*b^4 - 7*A*a^2*b^5)*x^5 + 470*(2*B*a^4*b^3 - 7*A*a^3*b^4)*x^4 + 385*(2*B*a^5*b^2 - 7*A*a^4*b^3)*x^3 + 137*(2*B*a^6*b - 7*A*a^5*b^2)*x^2 + 10*(2*B*a^7 - 7*A*a^6*b)*x - 60*((2*B*a*b^6 - 7*A*b^7)*x^7 + 5*(2*B*a^2*b^5 - 7*A*a*b^6)*x^6 + 10*(2*B*a^3*b^4 - 7*A*a^2*b^5)*x^5 + 10*(2*B*a^4*b^3 - 7*A*a^3*b^4)*x^4 + 5*(2*B*a^5*b^2 - 7*A*a^4*b^3)*x^3 + (2*B*a^6*b - 7*A*a^5*b^2)*x^2)*log(b*x + a) + 60*((2*B*a*b^6 - 7*A*b^7)*x^7 + 5*(2*B*a^2*b^5 - 7*A*a*b^6)*x^6 + 10*(2*B*a^3*b^4 - 7*A*a^2*b^5)*x^5 + 10*(2*B*a^4*b^3 - 7*A*a^3*b^4)*x^4 + 5*(2*B*a^5*b^2 - 7*A*a^4*b^3)*x^3 + (2*B*a^6*b - 7*A*a^5*b^2)*x^2)*log(x))/(a^8*b^5*x^7 + 5*a^9*b^4*x^6 + 10*a^10*b^3*x^5 + 10*a^11*b^2*x^4 + 5*a^12*b*x^3 + a^13*x^2)","B",0
653,1,27,0,0.442365," ","integrate(x^4*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{7} \, B b x^{7} + \frac{1}{5} \, A a x^{5} + \frac{1}{6} \, {\left(B a + A b\right)} x^{6}"," ",0,"1/7*B*b*x^7 + 1/5*A*a*x^5 + 1/6*(B*a + A*b)*x^6","A",0
654,1,27,0,0.432078," ","integrate(x^3*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, B b x^{6} + \frac{1}{4} \, A a x^{4} + \frac{1}{5} \, {\left(B a + A b\right)} x^{5}"," ",0,"1/6*B*b*x^6 + 1/4*A*a*x^4 + 1/5*(B*a + A*b)*x^5","A",0
655,1,27,0,0.407515," ","integrate(x^2*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, B b x^{5} + \frac{1}{3} \, A a x^{3} + \frac{1}{4} \, {\left(B a + A b\right)} x^{4}"," ",0,"1/5*B*b*x^5 + 1/3*A*a*x^3 + 1/4*(B*a + A*b)*x^4","A",0
656,1,27,0,0.413716," ","integrate(x*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, B b x^{4} + \frac{1}{2} \, A a x^{2} + \frac{1}{3} \, {\left(B a + A b\right)} x^{3}"," ",0,"1/4*B*b*x^4 + 1/2*A*a*x^2 + 1/3*(B*a + A*b)*x^3","A",0
657,1,24,0,0.393143," ","integrate((B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, B b x^{3} + A a x + \frac{1}{2} \, {\left(B a + A b\right)} x^{2}"," ",0,"1/3*B*b*x^3 + A*a*x + 1/2*(B*a + A*b)*x^2","A",0
658,1,22,0,0.394629," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{2} \, B b x^{2} + A a \log\left(x\right) + {\left(B a + A b\right)} x"," ",0,"1/2*B*b*x^2 + A*a*log(x) + (B*a + A*b)*x","A",0
659,1,26,0,0.407394," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{B b x^{2} + {\left(B a + A b\right)} x \log\left(x\right) - A a}{x}"," ",0,"(B*b*x^2 + (B*a + A*b)*x*log(x) - A*a)/x","A",0
660,1,29,0,0.406193," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, B b x^{2} \log\left(x\right) - A a - 2 \, {\left(B a + A b\right)} x}{2 \, x^{2}}"," ",0,"1/2*(2*B*b*x^2*log(x) - A*a - 2*(B*a + A*b)*x)/x^2","A",0
661,1,27,0,0.407768," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{6 \, B b x^{2} + 2 \, A a + 3 \, {\left(B a + A b\right)} x}{6 \, x^{3}}"," ",0,"-1/6*(6*B*b*x^2 + 2*A*a + 3*(B*a + A*b)*x)/x^3","A",0
662,1,27,0,0.397736," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{6 \, B b x^{2} + 3 \, A a + 4 \, {\left(B a + A b\right)} x}{12 \, x^{4}}"," ",0,"-1/12*(6*B*b*x^2 + 3*A*a + 4*(B*a + A*b)*x)/x^4","A",0
663,1,27,0,0.396105," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^6,x, algorithm=""fricas"")","-\frac{20 \, B b x^{2} + 12 \, A a + 15 \, {\left(B a + A b\right)} x}{60 \, x^{5}}"," ",0,"-1/60*(20*B*b*x^2 + 12*A*a + 15*(B*a + A*b)*x)/x^5","A",0
664,1,27,0,0.401213," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^7,x, algorithm=""fricas"")","-\frac{15 \, B b x^{2} + 10 \, A a + 12 \, {\left(B a + A b\right)} x}{60 \, x^{6}}"," ",0,"-1/60*(15*B*b*x^2 + 10*A*a + 12*(B*a + A*b)*x)/x^6","A",0
665,1,73,0,0.423085," ","integrate(x^5*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{10} \, B b^{3} x^{10} + \frac{1}{6} \, A a^{3} x^{6} + \frac{1}{9} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{9} + \frac{3}{8} \, {\left(B a^{2} b + A a b^{2}\right)} x^{8} + \frac{1}{7} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{7}"," ",0,"1/10*B*b^3*x^10 + 1/6*A*a^3*x^6 + 1/9*(3*B*a*b^2 + A*b^3)*x^9 + 3/8*(B*a^2*b + A*a*b^2)*x^8 + 1/7*(B*a^3 + 3*A*a^2*b)*x^7","A",0
666,1,73,0,0.387737," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{9} \, B b^{3} x^{9} + \frac{1}{5} \, A a^{3} x^{5} + \frac{1}{8} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{8} + \frac{3}{7} \, {\left(B a^{2} b + A a b^{2}\right)} x^{7} + \frac{1}{6} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{6}"," ",0,"1/9*B*b^3*x^9 + 1/5*A*a^3*x^5 + 1/8*(3*B*a*b^2 + A*b^3)*x^8 + 3/7*(B*a^2*b + A*a*b^2)*x^7 + 1/6*(B*a^3 + 3*A*a^2*b)*x^6","A",0
667,1,73,0,0.411755," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{8} \, B b^{3} x^{8} + \frac{1}{4} \, A a^{3} x^{4} + \frac{1}{7} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{7} + \frac{1}{2} \, {\left(B a^{2} b + A a b^{2}\right)} x^{6} + \frac{1}{5} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{5}"," ",0,"1/8*B*b^3*x^8 + 1/4*A*a^3*x^4 + 1/7*(3*B*a*b^2 + A*b^3)*x^7 + 1/2*(B*a^2*b + A*a*b^2)*x^6 + 1/5*(B*a^3 + 3*A*a^2*b)*x^5","A",0
668,1,73,0,0.410923," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{7} \, B b^{3} x^{7} + \frac{1}{3} \, A a^{3} x^{3} + \frac{1}{6} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + \frac{3}{5} \, {\left(B a^{2} b + A a b^{2}\right)} x^{5} + \frac{1}{4} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{4}"," ",0,"1/7*B*b^3*x^7 + 1/3*A*a^3*x^3 + 1/6*(3*B*a*b^2 + A*b^3)*x^6 + 3/5*(B*a^2*b + A*a*b^2)*x^5 + 1/4*(B*a^3 + 3*A*a^2*b)*x^4","A",0
669,1,73,0,0.421403," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{6} \, B b^{3} x^{6} + \frac{1}{2} \, A a^{3} x^{2} + \frac{1}{5} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{5} + \frac{3}{4} \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} + \frac{1}{3} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{3}"," ",0,"1/6*B*b^3*x^6 + 1/2*A*a^3*x^2 + 1/5*(3*B*a*b^2 + A*b^3)*x^5 + 3/4*(B*a^2*b + A*a*b^2)*x^4 + 1/3*(B*a^3 + 3*A*a^2*b)*x^3","A",0
670,1,69,0,0.411071," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{5} \, B b^{3} x^{5} + A a^{3} x + \frac{1}{4} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{4} + {\left(B a^{2} b + A a b^{2}\right)} x^{3} + \frac{1}{2} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}"," ",0,"1/5*B*b^3*x^5 + A*a^3*x + 1/4*(3*B*a*b^2 + A*b^3)*x^4 + (B*a^2*b + A*a*b^2)*x^3 + 1/2*(B*a^3 + 3*A*a^2*b)*x^2","A",0
671,1,68,0,0.418814," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x,x, algorithm=""fricas"")","\frac{1}{4} \, B b^{3} x^{4} + A a^{3} \log\left(x\right) + \frac{1}{3} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + \frac{3}{2} \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} x"," ",0,"1/4*B*b^3*x^4 + A*a^3*log(x) + 1/3*(3*B*a*b^2 + A*b^3)*x^3 + 3/2*(B*a^2*b + A*a*b^2)*x^2 + (B*a^3 + 3*A*a^2*b)*x","A",0
672,1,75,0,0.420105," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{2 \, B b^{3} x^{4} - 6 \, A a^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 18 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x \log\left(x\right)}{6 \, x}"," ",0,"1/6*(2*B*b^3*x^4 - 6*A*a^3 + 3*(3*B*a*b^2 + A*b^3)*x^3 + 18*(B*a^2*b + A*a*b^2)*x^2 + 6*(B*a^3 + 3*A*a^2*b)*x*log(x))/x","A",0
673,1,74,0,0.407977," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{B b^{3} x^{4} - A a^{3} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} \log\left(x\right) - 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{2 \, x^{2}}"," ",0,"1/2*(B*b^3*x^4 - A*a^3 + 2*(3*B*a*b^2 + A*b^3)*x^3 + 6*(B*a^2*b + A*a*b^2)*x^2*log(x) - 2*(B*a^3 + 3*A*a^2*b)*x)/x^2","A",0
674,1,75,0,0.412889," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{6 \, B b^{3} x^{4} + 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} \log\left(x\right) - 2 \, A a^{3} - 18 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} - 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{6 \, x^{3}}"," ",0,"1/6*(6*B*b^3*x^4 + 6*(3*B*a*b^2 + A*b^3)*x^3*log(x) - 2*A*a^3 - 18*(B*a^2*b + A*a*b^2)*x^2 - 3*(B*a^3 + 3*A*a^2*b)*x)/x^3","A",0
675,1,75,0,0.400155," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^5,x, algorithm=""fricas"")","\frac{12 \, B b^{3} x^{4} \log\left(x\right) - 3 \, A a^{3} - 12 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} - 18 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} - 4 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{12 \, x^{4}}"," ",0,"1/12*(12*B*b^3*x^4*log(x) - 3*A*a^3 - 12*(3*B*a*b^2 + A*b^3)*x^3 - 18*(B*a^2*b + A*a*b^2)*x^2 - 4*(B*a^3 + 3*A*a^2*b)*x)/x^4","A",0
676,1,73,0,0.419376," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^6,x, algorithm=""fricas"")","-\frac{20 \, B b^{3} x^{4} + 4 \, A a^{3} + 10 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 20 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{20 \, x^{5}}"," ",0,"-1/20*(20*B*b^3*x^4 + 4*A*a^3 + 10*(3*B*a*b^2 + A*b^3)*x^3 + 20*(B*a^2*b + A*a*b^2)*x^2 + 5*(B*a^3 + 3*A*a^2*b)*x)/x^5","A",0
677,1,73,0,0.416573," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^7,x, algorithm=""fricas"")","-\frac{30 \, B b^{3} x^{4} + 10 \, A a^{3} + 20 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 45 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 12 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{60 \, x^{6}}"," ",0,"-1/60*(30*B*b^3*x^4 + 10*A*a^3 + 20*(3*B*a*b^2 + A*b^3)*x^3 + 45*(B*a^2*b + A*a*b^2)*x^2 + 12*(B*a^3 + 3*A*a^2*b)*x)/x^6","A",0
678,1,73,0,0.410459," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^8,x, algorithm=""fricas"")","-\frac{140 \, B b^{3} x^{4} + 60 \, A a^{3} + 105 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 252 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 70 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{420 \, x^{7}}"," ",0,"-1/420*(140*B*b^3*x^4 + 60*A*a^3 + 105*(3*B*a*b^2 + A*b^3)*x^3 + 252*(B*a^2*b + A*a*b^2)*x^2 + 70*(B*a^3 + 3*A*a^2*b)*x)/x^7","A",0
679,1,73,0,0.422148," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^9,x, algorithm=""fricas"")","-\frac{70 \, B b^{3} x^{4} + 35 \, A a^{3} + 56 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 140 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 40 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{280 \, x^{8}}"," ",0,"-1/280*(70*B*b^3*x^4 + 35*A*a^3 + 56*(3*B*a*b^2 + A*b^3)*x^3 + 140*(B*a^2*b + A*a*b^2)*x^2 + 40*(B*a^3 + 3*A*a^2*b)*x)/x^8","A",0
680,1,73,0,0.416487," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^10,x, algorithm=""fricas"")","-\frac{504 \, B b^{3} x^{4} + 280 \, A a^{3} + 420 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 1080 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 315 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{2520 \, x^{9}}"," ",0,"-1/2520*(504*B*b^3*x^4 + 280*A*a^3 + 420*(3*B*a*b^2 + A*b^3)*x^3 + 1080*(B*a^2*b + A*a*b^2)*x^2 + 315*(B*a^3 + 3*A*a^2*b)*x)/x^9","A",0
681,1,73,0,0.418841," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^11,x, algorithm=""fricas"")","-\frac{420 \, B b^{3} x^{4} + 252 \, A a^{3} + 360 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 945 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 280 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{2520 \, x^{10}}"," ",0,"-1/2520*(420*B*b^3*x^4 + 252*A*a^3 + 360*(3*B*a*b^2 + A*b^3)*x^3 + 945*(B*a^2*b + A*a*b^2)*x^2 + 280*(B*a^3 + 3*A*a^2*b)*x)/x^10","A",0
682,1,73,0,0.407796," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^12,x, algorithm=""fricas"")","-\frac{1320 \, B b^{3} x^{4} + 840 \, A a^{3} + 1155 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 3080 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 924 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{9240 \, x^{11}}"," ",0,"-1/9240*(1320*B*b^3*x^4 + 840*A*a^3 + 1155*(3*B*a*b^2 + A*b^3)*x^3 + 3080*(B*a^2*b + A*a*b^2)*x^2 + 924*(B*a^3 + 3*A*a^2*b)*x)/x^11","A",0
683,1,118,0,0.406049," ","integrate(x^6*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{13} \, B b^{5} x^{13} + \frac{1}{7} \, A a^{5} x^{7} + \frac{1}{12} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{12} + \frac{5}{11} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{11} + {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{10} + \frac{5}{9} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{9} + \frac{1}{8} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{8}"," ",0,"1/13*B*b^5*x^13 + 1/7*A*a^5*x^7 + 1/12*(5*B*a*b^4 + A*b^5)*x^12 + 5/11*(2*B*a^2*b^3 + A*a*b^4)*x^11 + (B*a^3*b^2 + A*a^2*b^3)*x^10 + 5/9*(B*a^4*b + 2*A*a^3*b^2)*x^9 + 1/8*(B*a^5 + 5*A*a^4*b)*x^8","A",0
684,1,119,0,0.437932," ","integrate(x^5*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{12} \, B b^{5} x^{12} + \frac{1}{6} \, A a^{5} x^{6} + \frac{1}{11} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{11} + \frac{1}{2} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{10} + \frac{10}{9} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + \frac{5}{8} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{8} + \frac{1}{7} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{7}"," ",0,"1/12*B*b^5*x^12 + 1/6*A*a^5*x^6 + 1/11*(5*B*a*b^4 + A*b^5)*x^11 + 1/2*(2*B*a^2*b^3 + A*a*b^4)*x^10 + 10/9*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 5/8*(B*a^4*b + 2*A*a^3*b^2)*x^8 + 1/7*(B*a^5 + 5*A*a^4*b)*x^7","A",0
685,1,119,0,0.419447," ","integrate(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{11} \, B b^{5} x^{11} + \frac{1}{5} \, A a^{5} x^{5} + \frac{1}{10} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + \frac{5}{9} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{9} + \frac{5}{4} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{8} + \frac{5}{7} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{7} + \frac{1}{6} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{6}"," ",0,"1/11*B*b^5*x^11 + 1/5*A*a^5*x^5 + 1/10*(5*B*a*b^4 + A*b^5)*x^10 + 5/9*(2*B*a^2*b^3 + A*a*b^4)*x^9 + 5/4*(B*a^3*b^2 + A*a^2*b^3)*x^8 + 5/7*(B*a^4*b + 2*A*a^3*b^2)*x^7 + 1/6*(B*a^5 + 5*A*a^4*b)*x^6","A",0
686,1,119,0,0.415935," ","integrate(x^3*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{10} \, B b^{5} x^{10} + \frac{1}{4} \, A a^{5} x^{4} + \frac{1}{9} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{9} + \frac{5}{8} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + \frac{10}{7} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{7} + \frac{5}{6} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} + \frac{1}{5} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{5}"," ",0,"1/10*B*b^5*x^10 + 1/4*A*a^5*x^4 + 1/9*(5*B*a*b^4 + A*b^5)*x^9 + 5/8*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 10/7*(B*a^3*b^2 + A*a^2*b^3)*x^7 + 5/6*(B*a^4*b + 2*A*a^3*b^2)*x^6 + 1/5*(B*a^5 + 5*A*a^4*b)*x^5","A",0
687,1,118,0,0.410724," ","integrate(x^2*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{9} \, B b^{5} x^{9} + \frac{1}{3} \, A a^{5} x^{3} + \frac{1}{8} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{8} + \frac{5}{7} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{7} + \frac{5}{3} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{5} + \frac{1}{4} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{4}"," ",0,"1/9*B*b^5*x^9 + 1/3*A*a^5*x^3 + 1/8*(5*B*a*b^4 + A*b^5)*x^8 + 5/7*(2*B*a^2*b^3 + A*a*b^4)*x^7 + 5/3*(B*a^3*b^2 + A*a^2*b^3)*x^6 + (B*a^4*b + 2*A*a^3*b^2)*x^5 + 1/4*(B*a^5 + 5*A*a^4*b)*x^4","A",0
688,1,119,0,0.406296," ","integrate(x*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{8} \, B b^{5} x^{8} + \frac{1}{2} \, A a^{5} x^{2} + \frac{1}{7} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{7} + \frac{5}{6} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{6} + 2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{5} + \frac{5}{4} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + \frac{1}{3} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}"," ",0,"1/8*B*b^5*x^8 + 1/2*A*a^5*x^2 + 1/7*(5*B*a*b^4 + A*b^5)*x^7 + 5/6*(2*B*a^2*b^3 + A*a*b^4)*x^6 + 2*(B*a^3*b^2 + A*a^2*b^3)*x^5 + 5/4*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 1/3*(B*a^5 + 5*A*a^4*b)*x^3","A",0
689,1,115,0,0.487283," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{7} \, B b^{5} x^{7} + A a^{5} x + \frac{1}{6} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{6} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{5} + \frac{5}{2} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{4} + \frac{5}{3} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{3} + \frac{1}{2} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}"," ",0,"1/7*B*b^5*x^7 + A*a^5*x + 1/6*(5*B*a*b^4 + A*b^5)*x^6 + (2*B*a^2*b^3 + A*a*b^4)*x^5 + 5/2*(B*a^3*b^2 + A*a^2*b^3)*x^4 + 5/3*(B*a^4*b + 2*A*a^3*b^2)*x^3 + 1/2*(B*a^5 + 5*A*a^4*b)*x^2","A",0
690,1,114,0,0.425075," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x,x, algorithm=""fricas"")","\frac{1}{6} \, B b^{5} x^{6} + A a^{5} \log\left(x\right) + \frac{1}{5} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + \frac{5}{4} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + \frac{10}{3} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + \frac{5}{2} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + {\left(B a^{5} + 5 \, A a^{4} b\right)} x"," ",0,"1/6*B*b^5*x^6 + A*a^5*log(x) + 1/5*(5*B*a*b^4 + A*b^5)*x^5 + 5/4*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 10/3*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 5/2*(B*a^4*b + 2*A*a^3*b^2)*x^2 + (B*a^5 + 5*A*a^4*b)*x","A",0
691,1,121,0,0.414841," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^2,x, algorithm=""fricas"")","\frac{12 \, B b^{5} x^{6} - 60 \, A a^{5} + 15 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 100 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 300 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 60 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x \log\left(x\right)}{60 \, x}"," ",0,"1/60*(12*B*b^5*x^6 - 60*A*a^5 + 15*(5*B*a*b^4 + A*b^5)*x^5 + 100*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 300*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 300*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 60*(B*a^5 + 5*A*a^4*b)*x*log(x))/x","A",0
692,1,121,0,0.408763," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{3 \, B b^{5} x^{6} - 6 \, A a^{5} + 4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 60 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} \log\left(x\right) - 12 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{12 \, x^{2}}"," ",0,"1/12*(3*B*b^5*x^6 - 6*A*a^5 + 4*(5*B*a*b^4 + A*b^5)*x^5 + 30*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 120*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 60*(B*a^4*b + 2*A*a^3*b^2)*x^2*log(x) - 12*(B*a^5 + 5*A*a^4*b)*x)/x^2","A",0
693,1,121,0,0.414449," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^4,x, algorithm=""fricas"")","\frac{2 \, B b^{5} x^{6} - 2 \, A a^{5} + 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 60 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} \log\left(x\right) - 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{6 \, x^{3}}"," ",0,"1/6*(2*B*b^5*x^6 - 2*A*a^5 + 3*(5*B*a*b^4 + A*b^5)*x^5 + 30*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 60*(B*a^3*b^2 + A*a^2*b^3)*x^3*log(x) - 30*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 3*(B*a^5 + 5*A*a^4*b)*x)/x^3","A",0
694,1,121,0,0.423266," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^5,x, algorithm=""fricas"")","\frac{6 \, B b^{5} x^{6} - 3 \, A a^{5} + 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 60 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} \log\left(x\right) - 120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} - 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 4 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{12 \, x^{4}}"," ",0,"1/12*(6*B*b^5*x^6 - 3*A*a^5 + 12*(5*B*a*b^4 + A*b^5)*x^5 + 60*(2*B*a^2*b^3 + A*a*b^4)*x^4*log(x) - 120*(B*a^3*b^2 + A*a^2*b^3)*x^3 - 30*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 4*(B*a^5 + 5*A*a^4*b)*x)/x^4","A",0
695,1,121,0,0.413725," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^6,x, algorithm=""fricas"")","\frac{60 \, B b^{5} x^{6} + 60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} \log\left(x\right) - 12 \, A a^{5} - 300 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} - 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} - 100 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 15 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{60 \, x^{5}}"," ",0,"1/60*(60*B*b^5*x^6 + 60*(5*B*a*b^4 + A*b^5)*x^5*log(x) - 12*A*a^5 - 300*(2*B*a^2*b^3 + A*a*b^4)*x^4 - 300*(B*a^3*b^2 + A*a^2*b^3)*x^3 - 100*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 15*(B*a^5 + 5*A*a^4*b)*x)/x^5","A",0
696,1,121,0,0.408937," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^7,x, algorithm=""fricas"")","\frac{60 \, B b^{5} x^{6} \log\left(x\right) - 10 \, A a^{5} - 60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} - 150 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} - 200 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} - 75 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 12 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{60 \, x^{6}}"," ",0,"1/60*(60*B*b^5*x^6*log(x) - 10*A*a^5 - 60*(5*B*a*b^4 + A*b^5)*x^5 - 150*(2*B*a^2*b^3 + A*a*b^4)*x^4 - 200*(B*a^3*b^2 + A*a^2*b^3)*x^3 - 75*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 12*(B*a^5 + 5*A*a^4*b)*x)/x^6","A",0
697,1,119,0,0.402426," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^8,x, algorithm=""fricas"")","-\frac{42 \, B b^{5} x^{6} + 6 \, A a^{5} + 21 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 70 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 42 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 7 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{42 \, x^{7}}"," ",0,"-1/42*(42*B*b^5*x^6 + 6*A*a^5 + 21*(5*B*a*b^4 + A*b^5)*x^5 + 70*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 105*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 42*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 7*(B*a^5 + 5*A*a^4*b)*x)/x^7","A",0
698,1,119,0,0.438666," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^9,x, algorithm=""fricas"")","-\frac{84 \, B b^{5} x^{6} + 21 \, A a^{5} + 56 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 210 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 336 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 140 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 24 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{168 \, x^{8}}"," ",0,"-1/168*(84*B*b^5*x^6 + 21*A*a^5 + 56*(5*B*a*b^4 + A*b^5)*x^5 + 210*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 336*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 140*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 24*(B*a^5 + 5*A*a^4*b)*x)/x^8","A",0
699,1,119,0,0.406149," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^10,x, algorithm=""fricas"")","-\frac{168 \, B b^{5} x^{6} + 56 \, A a^{5} + 126 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 504 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 840 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 360 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 63 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{504 \, x^{9}}"," ",0,"-1/504*(168*B*b^5*x^6 + 56*A*a^5 + 126*(5*B*a*b^4 + A*b^5)*x^5 + 504*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 840*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 360*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 63*(B*a^5 + 5*A*a^4*b)*x)/x^9","A",0
700,1,119,0,0.413149," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^11,x, algorithm=""fricas"")","-\frac{630 \, B b^{5} x^{6} + 252 \, A a^{5} + 504 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 2100 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 3600 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 1575 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 280 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{2520 \, x^{10}}"," ",0,"-1/2520*(630*B*b^5*x^6 + 252*A*a^5 + 504*(5*B*a*b^4 + A*b^5)*x^5 + 2100*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 3600*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 1575*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 280*(B*a^5 + 5*A*a^4*b)*x)/x^10","A",0
701,1,119,0,0.412096," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^12,x, algorithm=""fricas"")","-\frac{2772 \, B b^{5} x^{6} + 1260 \, A a^{5} + 2310 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 9900 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 17325 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 7700 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 1386 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{13860 \, x^{11}}"," ",0,"-1/13860*(2772*B*b^5*x^6 + 1260*A*a^5 + 2310*(5*B*a*b^4 + A*b^5)*x^5 + 9900*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 17325*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 7700*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 1386*(B*a^5 + 5*A*a^4*b)*x)/x^11","A",0
702,1,119,0,0.409362," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^13,x, algorithm=""fricas"")","-\frac{924 \, B b^{5} x^{6} + 462 \, A a^{5} + 792 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 3465 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 6160 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 2772 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 504 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{5544 \, x^{12}}"," ",0,"-1/5544*(924*B*b^5*x^6 + 462*A*a^5 + 792*(5*B*a*b^4 + A*b^5)*x^5 + 3465*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 6160*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 2772*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 504*(B*a^5 + 5*A*a^4*b)*x)/x^12","A",0
703,1,119,0,0.392385," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^14,x, algorithm=""fricas"")","-\frac{10296 \, B b^{5} x^{6} + 5544 \, A a^{5} + 9009 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 40040 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 72072 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 32760 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 6006 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{72072 \, x^{13}}"," ",0,"-1/72072*(10296*B*b^5*x^6 + 5544*A*a^5 + 9009*(5*B*a*b^4 + A*b^5)*x^5 + 40040*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 72072*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 32760*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 6006*(B*a^5 + 5*A*a^4*b)*x)/x^13","A",0
704,1,117,0,0.407364," ","integrate(x^4*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{12 \, B b^{5} x^{5} - 15 \, {\left(B a b^{4} - A b^{5}\right)} x^{4} + 20 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} x^{3} - 30 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{2} + 60 \, {\left(B a^{4} b - A a^{3} b^{2}\right)} x - 60 \, {\left(B a^{5} - A a^{4} b\right)} \log\left(b x + a\right)}{60 \, b^{6}}"," ",0,"1/60*(12*B*b^5*x^5 - 15*(B*a*b^4 - A*b^5)*x^4 + 20*(B*a^2*b^3 - A*a*b^4)*x^3 - 30*(B*a^3*b^2 - A*a^2*b^3)*x^2 + 60*(B*a^4*b - A*a^3*b^2)*x - 60*(B*a^5 - A*a^4*b)*log(b*x + a))/b^6","A",0
705,1,94,0,0.405075," ","integrate(x^3*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{3 \, B b^{4} x^{4} - 4 \, {\left(B a b^{3} - A b^{4}\right)} x^{3} + 6 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 12 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x + 12 \, {\left(B a^{4} - A a^{3} b\right)} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*B*b^4*x^4 - 4*(B*a*b^3 - A*b^4)*x^3 + 6*(B*a^2*b^2 - A*a*b^3)*x^2 - 12*(B*a^3*b - A*a^2*b^2)*x + 12*(B*a^4 - A*a^3*b)*log(b*x + a))/b^5","A",0
706,1,71,0,0.412214," ","integrate(x^2*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, B b^{3} x^{3} - 3 \, {\left(B a b^{2} - A b^{3}\right)} x^{2} + 6 \, {\left(B a^{2} b - A a b^{2}\right)} x - 6 \, {\left(B a^{3} - A a^{2} b\right)} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*B*b^3*x^3 - 3*(B*a*b^2 - A*b^3)*x^2 + 6*(B*a^2*b - A*a*b^2)*x - 6*(B*a^3 - A*a^2*b)*log(b*x + a))/b^4","A",0
707,1,47,0,0.394145," ","integrate(x*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{B b^{2} x^{2} - 2 \, {\left(B a b - A b^{2}\right)} x + 2 \, {\left(B a^{2} - A a b\right)} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(B*b^2*x^2 - 2*(B*a*b - A*b^2)*x + 2*(B*a^2 - A*a*b)*log(b*x + a))/b^3","A",0
708,1,25,0,0.409765," ","integrate((B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{B b x - {\left(B a - A b\right)} \log\left(b x + a\right)}{b^{2}}"," ",0,"(B*b*x - (B*a - A*b)*log(b*x + a))/b^2","A",0
709,1,28,0,0.424955," ","integrate((B*x+A)/x/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{A b \log\left(x\right) + {\left(B a - A b\right)} \log\left(b x + a\right)}{a b}"," ",0,"(A*b*log(x) + (B*a - A*b)*log(b*x + a))/(a*b)","A",0
710,1,41,0,0.432381," ","integrate((B*x+A)/x^2/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(B a - A b\right)} x \log\left(b x + a\right) - {\left(B a - A b\right)} x \log\left(x\right) + A a}{a^{2} x}"," ",0,"-((B*a - A*b)*x*log(b*x + a) - (B*a - A*b)*x*log(x) + A*a)/(a^2*x)","A",0
711,1,69,0,0.495089," ","integrate((B*x+A)/x^3/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B a b - A b^{2}\right)} x^{2} \log\left(b x + a\right) - 2 \, {\left(B a b - A b^{2}\right)} x^{2} \log\left(x\right) - A a^{2} - 2 \, {\left(B a^{2} - A a b\right)} x}{2 \, a^{3} x^{2}}"," ",0,"1/2*(2*(B*a*b - A*b^2)*x^2*log(b*x + a) - 2*(B*a*b - A*b^2)*x^2*log(x) - A*a^2 - 2*(B*a^2 - A*a*b)*x)/(a^3*x^2)","A",0
712,1,94,0,0.426675," ","integrate((B*x+A)/x^4/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, {\left(B a b^{2} - A b^{3}\right)} x^{3} \log\left(b x + a\right) - 6 \, {\left(B a b^{2} - A b^{3}\right)} x^{3} \log\left(x\right) + 2 \, A a^{3} - 6 \, {\left(B a^{2} b - A a b^{2}\right)} x^{2} + 3 \, {\left(B a^{3} - A a^{2} b\right)} x}{6 \, a^{4} x^{3}}"," ",0,"-1/6*(6*(B*a*b^2 - A*b^3)*x^3*log(b*x + a) - 6*(B*a*b^2 - A*b^3)*x^3*log(x) + 2*A*a^3 - 6*(B*a^2*b - A*a*b^2)*x^2 + 3*(B*a^3 - A*a^2*b)*x)/(a^4*x^3)","A",0
713,1,117,0,0.421263," ","integrate((B*x+A)/x^5/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{12 \, {\left(B a b^{3} - A b^{4}\right)} x^{4} \log\left(b x + a\right) - 12 \, {\left(B a b^{3} - A b^{4}\right)} x^{4} \log\left(x\right) - 3 \, A a^{4} - 12 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{3} + 6 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x^{2} - 4 \, {\left(B a^{4} - A a^{3} b\right)} x}{12 \, a^{5} x^{4}}"," ",0,"1/12*(12*(B*a*b^3 - A*b^4)*x^4*log(b*x + a) - 12*(B*a*b^3 - A*b^4)*x^4*log(x) - 3*A*a^4 - 12*(B*a^2*b^2 - A*a*b^3)*x^3 + 6*(B*a^3*b - A*a^2*b^2)*x^2 - 4*(B*a^4 - A*a^3*b)*x)/(a^5*x^4)","A",0
714,1,197,0,0.424127," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, B b^{5} x^{5} - 27 \, B a^{5} + 21 \, A a^{4} b - {\left(5 \, B a b^{4} - 3 \, A b^{5}\right)} x^{4} + 4 \, {\left(5 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{3} + 3 \, {\left(21 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{2} + 6 \, {\left(B a^{4} b + A a^{3} b^{2}\right)} x - 12 \, {\left(5 \, B a^{5} - 3 \, A a^{4} b + {\left(5 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{2} + 2 \, {\left(5 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{8} x^{2} + 2 \, a b^{7} x + a^{2} b^{6}\right)}}"," ",0,"1/6*(2*B*b^5*x^5 - 27*B*a^5 + 21*A*a^4*b - (5*B*a*b^4 - 3*A*b^5)*x^4 + 4*(5*B*a^2*b^3 - 3*A*a*b^4)*x^3 + 3*(21*B*a^3*b^2 - 11*A*a^2*b^3)*x^2 + 6*(B*a^4*b + A*a^3*b^2)*x - 12*(5*B*a^5 - 3*A*a^4*b + (5*B*a^3*b^2 - 3*A*a^2*b^3)*x^2 + 2*(5*B*a^4*b - 3*A*a^3*b^2)*x)*log(b*x + a))/(b^8*x^2 + 2*a*b^7*x + a^2*b^6)","A",0
715,1,171,0,0.410112," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{B b^{4} x^{4} + 7 \, B a^{4} - 5 \, A a^{3} b - 2 \, {\left(2 \, B a b^{3} - A b^{4}\right)} x^{3} - {\left(11 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{2} + 2 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x + 6 \, {\left(2 \, B a^{4} - A a^{3} b + {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} + 2 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/2*(B*b^4*x^4 + 7*B*a^4 - 5*A*a^3*b - 2*(2*B*a*b^3 - A*b^4)*x^3 - (11*B*a^2*b^2 - 4*A*a*b^3)*x^2 + 2*(B*a^3*b - 2*A*a^2*b^2)*x + 6*(2*B*a^4 - A*a^3*b + (2*B*a^2*b^2 - A*a*b^3)*x^2 + 2*(2*B*a^3*b - A*a^2*b^2)*x)*log(b*x + a))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","A",0
716,1,134,0,0.407106," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, B b^{3} x^{3} + 4 \, B a b^{2} x^{2} - 5 \, B a^{3} + 3 \, A a^{2} b - 4 \, {\left(B a^{2} b - A a b^{2}\right)} x - 2 \, {\left(3 \, B a^{3} - A a^{2} b + {\left(3 \, B a b^{2} - A b^{3}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b - A a b^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*B*b^3*x^3 + 4*B*a*b^2*x^2 - 5*B*a^3 + 3*A*a^2*b - 4*(B*a^2*b - A*a*b^2)*x - 2*(3*B*a^3 - A*a^2*b + (3*B*a*b^2 - A*b^3)*x^2 + 2*(3*B*a^2*b - A*a*b^2)*x)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","A",0
717,1,81,0,0.426282," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{3 \, B a^{2} - A a b + 2 \, {\left(2 \, B a b - A b^{2}\right)} x + 2 \, {\left(B b^{2} x^{2} + 2 \, B a b x + B a^{2}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"1/2*(3*B*a^2 - A*a*b + 2*(2*B*a*b - A*b^2)*x + 2*(B*b^2*x^2 + 2*B*a*b*x + B*a^2)*log(b*x + a))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
718,1,38,0,0.414045," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, B b x + B a + A b}{2 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*B*b*x + B*a + A*b)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
719,1,109,0,0.430471," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, A a b^{2} x - B a^{3} + 3 \, A a^{2} b - 2 \, {\left(A b^{3} x^{2} + 2 \, A a b^{2} x + A a^{2} b\right)} \log\left(b x + a\right) + 2 \, {\left(A b^{3} x^{2} + 2 \, A a b^{2} x + A a^{2} b\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{3} x^{2} + 2 \, a^{4} b^{2} x + a^{5} b\right)}}"," ",0,"1/2*(2*A*a*b^2*x - B*a^3 + 3*A*a^2*b - 2*(A*b^3*x^2 + 2*A*a*b^2*x + A*a^2*b)*log(b*x + a) + 2*(A*b^3*x^2 + 2*A*a*b^2*x + A*a^2*b)*log(x))/(a^3*b^3*x^2 + 2*a^4*b^2*x + a^5*b)","A",0
720,1,187,0,0.437384," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, A a^{3} - 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{2} - 3 \, {\left(B a^{3} - 3 \, A a^{2} b\right)} x + 2 \, {\left({\left(B a b^{2} - 3 \, A b^{3}\right)} x^{3} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left({\left(B a b^{2} - 3 \, A b^{3}\right)} x^{3} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} x\right)} \log\left(x\right)}{2 \, {\left(a^{4} b^{2} x^{3} + 2 \, a^{5} b x^{2} + a^{6} x\right)}}"," ",0,"-1/2*(2*A*a^3 - 2*(B*a^2*b - 3*A*a*b^2)*x^2 - 3*(B*a^3 - 3*A*a^2*b)*x + 2*((B*a*b^2 - 3*A*b^3)*x^3 + 2*(B*a^2*b - 3*A*a*b^2)*x^2 + (B*a^3 - 3*A*a^2*b)*x)*log(b*x + a) - 2*((B*a*b^2 - 3*A*b^3)*x^3 + 2*(B*a^2*b - 3*A*a*b^2)*x^2 + (B*a^3 - 3*A*a^2*b)*x)*log(x))/(a^4*b^2*x^3 + 2*a^5*b*x^2 + a^6*x)","A",0
721,1,225,0,0.424983," ","integrate((B*x+A)/x^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{A a^{4} + 6 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3} + 9 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{2} + 2 \, {\left(B a^{4} - 2 \, A a^{3} b\right)} x - 6 \, {\left({\left(B a b^{3} - 2 \, A b^{4}\right)} x^{4} + 2 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{2}\right)} \log\left(b x + a\right) + 6 \, {\left({\left(B a b^{3} - 2 \, A b^{4}\right)} x^{4} + 2 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}"," ",0,"-1/2*(A*a^4 + 6*(B*a^2*b^2 - 2*A*a*b^3)*x^3 + 9*(B*a^3*b - 2*A*a^2*b^2)*x^2 + 2*(B*a^4 - 2*A*a^3*b)*x - 6*((B*a*b^3 - 2*A*b^4)*x^4 + 2*(B*a^2*b^2 - 2*A*a*b^3)*x^3 + (B*a^3*b - 2*A*a^2*b^2)*x^2)*log(b*x + a) + 6*((B*a*b^3 - 2*A*b^4)*x^4 + 2*(B*a^2*b^2 - 2*A*a*b^3)*x^3 + (B*a^3*b - 2*A*a^2*b^2)*x^2)*log(x))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2)","A",0
722,1,252,0,0.418522," ","integrate(x^4*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, B b^{5} x^{5} + 48 \, B a b^{4} x^{4} - 77 \, B a^{5} + 25 \, A a^{4} b - 48 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} x^{3} - 36 \, {\left(7 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{2} - 8 \, {\left(31 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x - 12 \, {\left(5 \, B a^{5} - A a^{4} b + {\left(5 \, B a b^{4} - A b^{5}\right)} x^{4} + 4 \, {\left(5 \, B a^{2} b^{3} - A a b^{4}\right)} x^{3} + 6 \, {\left(5 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(5 \, B a^{4} b - A a^{3} b^{2}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}"," ",0,"1/12*(12*B*b^5*x^5 + 48*B*a*b^4*x^4 - 77*B*a^5 + 25*A*a^4*b - 48*(B*a^2*b^3 - A*a*b^4)*x^3 - 36*(7*B*a^3*b^2 - 3*A*a^2*b^3)*x^2 - 8*(31*B*a^4*b - 11*A*a^3*b^2)*x - 12*(5*B*a^5 - A*a^4*b + (5*B*a*b^4 - A*b^5)*x^4 + 4*(5*B*a^2*b^3 - A*a*b^4)*x^3 + 6*(5*B*a^3*b^2 - A*a^2*b^3)*x^2 + 4*(5*B*a^4*b - A*a^3*b^2)*x)*log(b*x + a))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6)","A",0
723,1,175,0,0.428320," ","integrate(x^3*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{25 \, B a^{4} - 3 \, A a^{3} b + 12 \, {\left(4 \, B a b^{3} - A b^{4}\right)} x^{3} + 18 \, {\left(6 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} + 4 \, {\left(22 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} x + 12 \, {\left(B b^{4} x^{4} + 4 \, B a b^{3} x^{3} + 6 \, B a^{2} b^{2} x^{2} + 4 \, B a^{3} b x + B a^{4}\right)} \log\left(b x + a\right)}{12 \, {\left(b^{9} x^{4} + 4 \, a b^{8} x^{3} + 6 \, a^{2} b^{7} x^{2} + 4 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}"," ",0,"1/12*(25*B*a^4 - 3*A*a^3*b + 12*(4*B*a*b^3 - A*b^4)*x^3 + 18*(6*B*a^2*b^2 - A*a*b^3)*x^2 + 4*(22*B*a^3*b - 3*A*a^2*b^2)*x + 12*(B*b^4*x^4 + 4*B*a*b^3*x^3 + 6*B*a^2*b^2*x^2 + 4*B*a^3*b*x + B*a^4)*log(b*x + a))/(b^9*x^4 + 4*a*b^8*x^3 + 6*a^2*b^7*x^2 + 4*a^3*b^6*x + a^4*b^5)","A",0
724,1,105,0,0.439077," ","integrate(x^2*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{12 \, B b^{3} x^{3} + 3 \, B a^{3} + A a^{2} b + 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{2} + 4 \, {\left(3 \, B a^{2} b + A a b^{2}\right)} x}{12 \, {\left(b^{8} x^{4} + 4 \, a b^{7} x^{3} + 6 \, a^{2} b^{6} x^{2} + 4 \, a^{3} b^{5} x + a^{4} b^{4}\right)}}"," ",0,"-1/12*(12*B*b^3*x^3 + 3*B*a^3 + A*a^2*b + 6*(3*B*a*b^2 + A*b^3)*x^2 + 4*(3*B*a^2*b + A*a*b^2)*x)/(b^8*x^4 + 4*a*b^7*x^3 + 6*a^2*b^6*x^2 + 4*a^3*b^5*x + a^4*b^4)","A",0
725,1,80,0,0.435523," ","integrate(x*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{6 \, B b^{2} x^{2} + B a^{2} + A a b + 4 \, {\left(B a b + A b^{2}\right)} x}{12 \, {\left(b^{7} x^{4} + 4 \, a b^{6} x^{3} + 6 \, a^{2} b^{5} x^{2} + 4 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}"," ",0,"-1/12*(6*B*b^2*x^2 + B*a^2 + A*a*b + 4*(B*a*b + A*b^2)*x)/(b^7*x^4 + 4*a*b^6*x^3 + 6*a^2*b^5*x^2 + 4*a^3*b^4*x + a^4*b^3)","A",0
726,1,61,0,0.415865," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, B b x + B a + 3 \, A b}{12 \, {\left(b^{6} x^{4} + 4 \, a b^{5} x^{3} + 6 \, a^{2} b^{4} x^{2} + 4 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}"," ",0,"-1/12*(4*B*b*x + B*a + 3*A*b)/(b^6*x^4 + 4*a*b^5*x^3 + 6*a^2*b^4*x^2 + 4*a^3*b^3*x + a^4*b^2)","A",0
727,1,203,0,0.409793," ","integrate((B*x+A)/x/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, A a b^{4} x^{3} + 42 \, A a^{2} b^{3} x^{2} + 52 \, A a^{3} b^{2} x - 3 \, B a^{5} + 25 \, A a^{4} b - 12 \, {\left(A b^{5} x^{4} + 4 \, A a b^{4} x^{3} + 6 \, A a^{2} b^{3} x^{2} + 4 \, A a^{3} b^{2} x + A a^{4} b\right)} \log\left(b x + a\right) + 12 \, {\left(A b^{5} x^{4} + 4 \, A a b^{4} x^{3} + 6 \, A a^{2} b^{3} x^{2} + 4 \, A a^{3} b^{2} x + A a^{4} b\right)} \log\left(x\right)}{12 \, {\left(a^{5} b^{5} x^{4} + 4 \, a^{6} b^{4} x^{3} + 6 \, a^{7} b^{3} x^{2} + 4 \, a^{8} b^{2} x + a^{9} b\right)}}"," ",0,"1/12*(12*A*a*b^4*x^3 + 42*A*a^2*b^3*x^2 + 52*A*a^3*b^2*x - 3*B*a^5 + 25*A*a^4*b - 12*(A*b^5*x^4 + 4*A*a*b^4*x^3 + 6*A*a^2*b^3*x^2 + 4*A*a^3*b^2*x + A*a^4*b)*log(b*x + a) + 12*(A*b^5*x^4 + 4*A*a*b^4*x^3 + 6*A*a^2*b^3*x^2 + 4*A*a^3*b^2*x + A*a^4*b)*log(x))/(a^5*b^5*x^4 + 4*a^6*b^4*x^3 + 6*a^7*b^3*x^2 + 4*a^8*b^2*x + a^9*b)","A",0
728,1,347,0,0.445333," ","integrate((B*x+A)/x^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{12 \, A a^{5} - 12 \, {\left(B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} - 42 \, {\left(B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3} - 52 \, {\left(B a^{4} b - 5 \, A a^{3} b^{2}\right)} x^{2} - 25 \, {\left(B a^{5} - 5 \, A a^{4} b\right)} x + 12 \, {\left({\left(B a b^{4} - 5 \, A b^{5}\right)} x^{5} + 4 \, {\left(B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} + 6 \, {\left(B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3} + 4 \, {\left(B a^{4} b - 5 \, A a^{3} b^{2}\right)} x^{2} + {\left(B a^{5} - 5 \, A a^{4} b\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left({\left(B a b^{4} - 5 \, A b^{5}\right)} x^{5} + 4 \, {\left(B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} + 6 \, {\left(B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3} + 4 \, {\left(B a^{4} b - 5 \, A a^{3} b^{2}\right)} x^{2} + {\left(B a^{5} - 5 \, A a^{4} b\right)} x\right)} \log\left(x\right)}{12 \, {\left(a^{6} b^{4} x^{5} + 4 \, a^{7} b^{3} x^{4} + 6 \, a^{8} b^{2} x^{3} + 4 \, a^{9} b x^{2} + a^{10} x\right)}}"," ",0,"-1/12*(12*A*a^5 - 12*(B*a^2*b^3 - 5*A*a*b^4)*x^4 - 42*(B*a^3*b^2 - 5*A*a^2*b^3)*x^3 - 52*(B*a^4*b - 5*A*a^3*b^2)*x^2 - 25*(B*a^5 - 5*A*a^4*b)*x + 12*((B*a*b^4 - 5*A*b^5)*x^5 + 4*(B*a^2*b^3 - 5*A*a*b^4)*x^4 + 6*(B*a^3*b^2 - 5*A*a^2*b^3)*x^3 + 4*(B*a^4*b - 5*A*a^3*b^2)*x^2 + (B*a^5 - 5*A*a^4*b)*x)*log(b*x + a) - 12*((B*a*b^4 - 5*A*b^5)*x^5 + 4*(B*a^2*b^3 - 5*A*a*b^4)*x^4 + 6*(B*a^3*b^2 - 5*A*a^2*b^3)*x^3 + 4*(B*a^4*b - 5*A*a^3*b^2)*x^2 + (B*a^5 - 5*A*a^4*b)*x)*log(x))/(a^6*b^4*x^5 + 4*a^7*b^3*x^4 + 6*a^8*b^2*x^3 + 4*a^9*b*x^2 + a^10*x)","A",0
729,1,56,0,0.420442," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2}{6435} \, {\left(429 \, B b^{2} x^{7} + 715 \, A a^{2} x^{4} + 495 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 585 \, {\left(B a^{2} + 2 \, A a b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/6435*(429*B*b^2*x^7 + 715*A*a^2*x^4 + 495*(2*B*a*b + A*b^2)*x^6 + 585*(B*a^2 + 2*A*a*b)*x^5)*sqrt(x)","A",0
730,1,56,0,0.418056," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2}{9009} \, {\left(693 \, B b^{2} x^{6} + 1287 \, A a^{2} x^{3} + 819 \, {\left(2 \, B a b + A b^{2}\right)} x^{5} + 1001 \, {\left(B a^{2} + 2 \, A a b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/9009*(693*B*b^2*x^6 + 1287*A*a^2*x^3 + 819*(2*B*a*b + A*b^2)*x^5 + 1001*(B*a^2 + 2*A*a*b)*x^4)*sqrt(x)","A",0
731,1,56,0,0.400851," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B b^{2} x^{5} + 693 \, A a^{2} x^{2} + 385 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 495 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/3465*(315*B*b^2*x^5 + 693*A*a^2*x^2 + 385*(2*B*a*b + A*b^2)*x^4 + 495*(B*a^2 + 2*A*a*b)*x^3)*sqrt(x)","A",0
732,1,54,0,0.398665," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B b^{2} x^{4} + 105 \, A a^{2} x + 45 \, {\left(2 \, B a b + A b^{2}\right)} x^{3} + 63 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/315*(35*B*b^2*x^4 + 105*A*a^2*x + 45*(2*B*a*b + A*b^2)*x^3 + 63*(B*a^2 + 2*A*a*b)*x^2)*sqrt(x)","A",0
733,1,51,0,0.423507," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, B b^{2} x^{3} + 105 \, A a^{2} + 21 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 35 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)} \sqrt{x}"," ",0,"2/105*(15*B*b^2*x^3 + 105*A*a^2 + 21*(2*B*a*b + A*b^2)*x^2 + 35*(B*a^2 + 2*A*a*b)*x)*sqrt(x)","A",0
734,1,51,0,0.410538," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} x^{3} - 15 \, A a^{2} + 5 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{15 \, \sqrt{x}}"," ",0,"2/15*(3*B*b^2*x^3 - 15*A*a^2 + 5*(2*B*a*b + A*b^2)*x^2 + 15*(B*a^2 + 2*A*a*b)*x)/sqrt(x)","A",0
735,1,50,0,0.429217," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{2} x^{3} - A a^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(B*b^2*x^3 - A*a^2 + 3*(2*B*a*b + A*b^2)*x^2 - 3*(B*a^2 + 2*A*a*b)*x)/x^(3/2)","A",0
736,1,51,0,0.420702," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{2} x^{3} - 3 \, A a^{2} - 15 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} - 5 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(15*B*b^2*x^3 - 3*A*a^2 - 15*(2*B*a*b + A*b^2)*x^2 - 5*(B*a^2 + 2*A*a*b)*x)/x^(5/2)","A",0
737,1,51,0,0.406625," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, B b^{2} x^{3} + 15 \, A a^{2} + 35 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 21 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"-2/105*(105*B*b^2*x^3 + 15*A*a^2 + 35*(2*B*a*b + A*b^2)*x^2 + 21*(B*a^2 + 2*A*a*b)*x)/x^(7/2)","A",0
738,1,104,0,0.428861," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2}{2078505} \, {\left(109395 \, B b^{4} x^{9} + 230945 \, A a^{4} x^{4} + 122265 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{8} + 277134 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{7} + 319770 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{6} + 188955 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/2078505*(109395*B*b^4*x^9 + 230945*A*a^4*x^4 + 122265*(4*B*a*b^3 + A*b^4)*x^8 + 277134*(3*B*a^2*b^2 + 2*A*a*b^3)*x^7 + 319770*(2*B*a^3*b + 3*A*a^2*b^2)*x^6 + 188955*(B*a^4 + 4*A*a^3*b)*x^5)*sqrt(x)","A",0
739,1,104,0,0.411836," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2}{765765} \, {\left(45045 \, B b^{4} x^{8} + 109395 \, A a^{4} x^{3} + 51051 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{7} + 117810 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{6} + 139230 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{5} + 85085 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/765765*(45045*B*b^4*x^8 + 109395*A*a^4*x^3 + 51051*(4*B*a*b^3 + A*b^4)*x^7 + 117810*(3*B*a^2*b^2 + 2*A*a*b^3)*x^6 + 139230*(2*B*a^3*b + 3*A*a^2*b^2)*x^5 + 85085*(B*a^4 + 4*A*a^3*b)*x^4)*sqrt(x)","A",0
740,1,104,0,0.412487," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3003 \, B b^{4} x^{7} + 9009 \, A a^{4} x^{2} + 3465 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{6} + 8190 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{5} + 10010 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{4} + 6435 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/45045*(3003*B*b^4*x^7 + 9009*A*a^4*x^2 + 3465*(4*B*a*b^3 + A*b^4)*x^6 + 8190*(3*B*a^2*b^2 + 2*A*a*b^3)*x^5 + 10010*(2*B*a^3*b + 3*A*a^2*b^2)*x^4 + 6435*(B*a^4 + 4*A*a^3*b)*x^3)*sqrt(x)","A",0
741,1,102,0,0.422959," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2*x^(1/2),x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3465 \, B b^{4} x^{6} + 15015 \, A a^{4} x + 4095 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{5} + 10010 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{4} + 12870 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{3} + 9009 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/45045*(3465*B*b^4*x^6 + 15015*A*a^4*x + 4095*(4*B*a*b^3 + A*b^4)*x^5 + 10010*(3*B*a^2*b^2 + 2*A*a*b^3)*x^4 + 12870*(2*B*a^3*b + 3*A*a^2*b^2)*x^3 + 9009*(B*a^4 + 4*A*a^3*b)*x^2)*sqrt(x)","A",0
742,1,99,0,0.425775," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B b^{4} x^{5} + 3465 \, A a^{4} + 385 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 990 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 1386 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 1155 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x\right)} \sqrt{x}"," ",0,"2/3465*(315*B*b^4*x^5 + 3465*A*a^4 + 385*(4*B*a*b^3 + A*b^4)*x^4 + 990*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 1386*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 + 1155*(B*a^4 + 4*A*a^3*b)*x)*sqrt(x)","A",0
743,1,99,0,0.410332," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{4} x^{5} - 315 \, A a^{4} + 45 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 126 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 210 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 315 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x\right)}}{315 \, \sqrt{x}}"," ",0,"2/315*(35*B*b^4*x^5 - 315*A*a^4 + 45*(4*B*a*b^3 + A*b^4)*x^4 + 126*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 210*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 + 315*(B*a^4 + 4*A*a^3*b)*x)/sqrt(x)","A",0
744,1,99,0,0.424062," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{4} x^{5} - 35 \, A a^{4} + 21 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 70 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} + 210 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} - 105 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x\right)}}{105 \, x^{\frac{3}{2}}}"," ",0,"2/105*(15*B*b^4*x^5 - 35*A*a^4 + 21*(4*B*a*b^3 + A*b^4)*x^4 + 70*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 + 210*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 - 105*(B*a^4 + 4*A*a^3*b)*x)/x^(3/2)","A",0
745,1,99,0,0.405386," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{4} x^{5} - 3 \, A a^{4} + 5 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} + 30 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} - 30 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} - 5 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(3*B*b^4*x^5 - 3*A*a^4 + 5*(4*B*a*b^3 + A*b^4)*x^4 + 30*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 - 30*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 - 5*(B*a^4 + 4*A*a^3*b)*x)/x^(5/2)","A",0
746,1,99,0,0.420259," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{4} x^{5} - 15 \, A a^{4} + 105 \, {\left(4 \, B a b^{3} + A b^{4}\right)} x^{4} - 210 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3} - 70 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} - 21 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} x\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"2/105*(35*B*b^4*x^5 - 15*A*a^4 + 105*(4*B*a*b^3 + A*b^4)*x^4 - 210*(3*B*a^2*b^2 + 2*A*a*b^3)*x^3 - 70*(2*B*a^3*b + 3*A*a^2*b^2)*x^2 - 21*(B*a^4 + 4*A*a^3*b)*x)/x^(7/2)","A",0
747,1,152,0,0.408205," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2}{66927861} \, {\left(2909907 \, B b^{6} x^{11} + 7436429 \, A a^{6} x^{4} + 3187041 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{10} + 10567557 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{9} + 19684665 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{8} + 22309287 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{7} + 15444891 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{6} + 6084351 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/66927861*(2909907*B*b^6*x^11 + 7436429*A*a^6*x^4 + 3187041*(6*B*a*b^5 + A*b^6)*x^10 + 10567557*(5*B*a^2*b^4 + 2*A*a*b^5)*x^9 + 19684665*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^8 + 22309287*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^7 + 15444891*(2*B*a^5*b + 5*A*a^4*b^2)*x^6 + 6084351*(B*a^6 + 6*A*a^5*b)*x^5)*sqrt(x)","A",0
748,1,152,0,0.410008," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2}{2909907} \, {\left(138567 \, B b^{6} x^{10} + 415701 \, A a^{6} x^{3} + 153153 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{9} + 513513 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{8} + 969969 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{7} + 1119195 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{6} + 793611 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{5} + 323323 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/2909907*(138567*B*b^6*x^10 + 415701*A*a^6*x^3 + 153153*(6*B*a*b^5 + A*b^6)*x^9 + 513513*(5*B*a^2*b^4 + 2*A*a*b^5)*x^8 + 969969*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^7 + 1119195*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^6 + 793611*(2*B*a^5*b + 5*A*a^4*b^2)*x^5 + 323323*(B*a^6 + 6*A*a^5*b)*x^4)*sqrt(x)","A",0
749,1,152,0,0.415338," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2}{4849845} \, {\left(255255 \, B b^{6} x^{9} + 969969 \, A a^{6} x^{2} + 285285 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{8} + 969969 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{7} + 1865325 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{6} + 2204475 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{5} + 1616615 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{4} + 692835 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/4849845*(255255*B*b^6*x^9 + 969969*A*a^6*x^2 + 285285*(6*B*a*b^5 + A*b^6)*x^8 + 969969*(5*B*a^2*b^4 + 2*A*a*b^5)*x^7 + 1865325*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^6 + 2204475*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^5 + 1616615*(2*B*a^5*b + 5*A*a^4*b^2)*x^4 + 692835*(B*a^6 + 6*A*a^5*b)*x^3)*sqrt(x)","A",0
750,1,150,0,0.423313," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3*x^(1/2),x, algorithm=""fricas"")","\frac{2}{765765} \, {\left(45045 \, B b^{6} x^{8} + 255255 \, A a^{6} x + 51051 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{7} + 176715 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{6} + 348075 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{5} + 425425 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{4} + 328185 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{3} + 153153 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/765765*(45045*B*b^6*x^8 + 255255*A*a^6*x + 51051*(6*B*a*b^5 + A*b^6)*x^7 + 176715*(5*B*a^2*b^4 + 2*A*a*b^5)*x^6 + 348075*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^5 + 425425*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^4 + 328185*(2*B*a^5*b + 5*A*a^4*b^2)*x^3 + 153153*(B*a^6 + 6*A*a^5*b)*x^2)*sqrt(x)","A",0
751,1,147,0,0.404536," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3003 \, B b^{6} x^{7} + 45045 \, A a^{6} + 3465 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 12285 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 25025 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 32175 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 27027 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 15015 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x\right)} \sqrt{x}"," ",0,"2/45045*(3003*B*b^6*x^7 + 45045*A*a^6 + 3465*(6*B*a*b^5 + A*b^6)*x^6 + 12285*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 25025*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 32175*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 27027*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 15015*(B*a^6 + 6*A*a^5*b)*x)*sqrt(x)","A",0
752,1,147,0,0.402143," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, B b^{6} x^{7} - 3003 \, A a^{6} + 273 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 1001 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 2145 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 3003 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 3003 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} + 3003 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x\right)}}{3003 \, \sqrt{x}}"," ",0,"2/3003*(231*B*b^6*x^7 - 3003*A*a^6 + 273*(6*B*a*b^5 + A*b^6)*x^6 + 1001*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 2145*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 3003*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 3003*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 + 3003*(B*a^6 + 6*A*a^5*b)*x)/sqrt(x)","A",0
753,1,147,0,0.395005," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B b^{6} x^{7} - 231 \, A a^{6} + 77 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 297 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 693 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 1155 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} + 2079 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} - 693 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x\right)}}{693 \, x^{\frac{3}{2}}}"," ",0,"2/693*(63*B*b^6*x^7 - 231*A*a^6 + 77*(6*B*a*b^5 + A*b^6)*x^6 + 297*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 693*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 1155*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 + 2079*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 - 693*(B*a^6 + 6*A*a^5*b)*x)/x^(3/2)","A",0
754,1,147,0,0.411279," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{6} x^{7} - 63 \, A a^{6} + 45 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 189 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 525 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} + 1575 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} - 945 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} - 105 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x\right)}}{315 \, x^{\frac{5}{2}}}"," ",0,"2/315*(35*B*b^6*x^7 - 63*A*a^6 + 45*(6*B*a*b^5 + A*b^6)*x^6 + 189*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 525*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 + 1575*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 - 945*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 - 105*(B*a^6 + 6*A*a^5*b)*x)/x^(5/2)","A",0
755,1,147,0,0.417254," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{6} x^{7} - 5 \, A a^{6} + 7 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 35 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} + 175 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} - 175 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} - 35 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} - 7 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x\right)}}{35 \, x^{\frac{7}{2}}}"," ",0,"2/35*(5*B*b^6*x^7 - 5*A*a^6 + 7*(6*B*a*b^5 + A*b^6)*x^6 + 35*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 + 175*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 - 175*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 - 35*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 - 7*(B*a^6 + 6*A*a^5*b)*x)/x^(7/2)","A",0
756,1,147,0,0.419751," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B b^{6} x^{7} - 35 \, A a^{6} + 105 \, {\left(6 \, B a b^{5} + A b^{6}\right)} x^{6} + 945 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} x^{5} - 1575 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{4} - 525 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} x^{3} - 189 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} x^{2} - 45 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} x\right)}}{315 \, x^{\frac{9}{2}}}"," ",0,"2/315*(63*B*b^6*x^7 - 35*A*a^6 + 105*(6*B*a*b^5 + A*b^6)*x^6 + 945*(5*B*a^2*b^4 + 2*A*a*b^5)*x^5 - 1575*(4*B*a^3*b^3 + 3*A*a^2*b^4)*x^4 - 525*(3*B*a^4*b^2 + 4*A*a^3*b^3)*x^3 - 189*(2*B*a^5*b + 5*A*a^4*b^2)*x^2 - 45*(B*a^6 + 6*A*a^5*b)*x)/x^(9/2)","A",0
757,1,341,0,0.433132," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b + {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(30 \, B b^{4} x^{4} - 945 \, B a^{4} + 735 \, A a^{3} b - 6 \, {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} x^{3} + 14 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{2} - 70 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{210 \, {\left(b^{6} x + a b^{5}\right)}}, \frac{105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b + {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(30 \, B b^{4} x^{4} - 945 \, B a^{4} + 735 \, A a^{3} b - 6 \, {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} x^{3} + 14 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{2} - 70 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{105 \, {\left(b^{6} x + a b^{5}\right)}}\right]"," ",0,"[-1/210*(105*(9*B*a^4 - 7*A*a^3*b + (9*B*a^3*b - 7*A*a^2*b^2)*x)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(30*B*b^4*x^4 - 945*B*a^4 + 735*A*a^3*b - 6*(9*B*a*b^3 - 7*A*b^4)*x^3 + 14*(9*B*a^2*b^2 - 7*A*a*b^3)*x^2 - 70*(9*B*a^3*b - 7*A*a^2*b^2)*x)*sqrt(x))/(b^6*x + a*b^5), 1/105*(105*(9*B*a^4 - 7*A*a^3*b + (9*B*a^3*b - 7*A*a^2*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (30*B*b^4*x^4 - 945*B*a^4 + 735*A*a^3*b - 6*(9*B*a*b^3 - 7*A*b^4)*x^3 + 14*(9*B*a^2*b^2 - 7*A*a*b^3)*x^2 - 70*(9*B*a^3*b - 7*A*a^2*b^2)*x)*sqrt(x))/(b^6*x + a*b^5)]","A",0
758,1,290,0,0.428117," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(6 \, B b^{3} x^{3} + 105 \, B a^{3} - 75 \, A a^{2} b - 2 \, {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} x^{2} + 10 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x\right)} \sqrt{x}}{30 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(6 \, B b^{3} x^{3} + 105 \, B a^{3} - 75 \, A a^{2} b - 2 \, {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} x^{2} + 10 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x\right)} \sqrt{x}}{15 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[-1/30*(15*(7*B*a^3 - 5*A*a^2*b + (7*B*a^2*b - 5*A*a*b^2)*x)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(6*B*b^3*x^3 + 105*B*a^3 - 75*A*a^2*b - 2*(7*B*a*b^2 - 5*A*b^3)*x^2 + 10*(7*B*a^2*b - 5*A*a*b^2)*x)*sqrt(x))/(b^5*x + a*b^4), -1/15*(15*(7*B*a^3 - 5*A*a^2*b + (7*B*a^2*b - 5*A*a*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (6*B*b^3*x^3 + 105*B*a^3 - 75*A*a^2*b - 2*(7*B*a*b^2 - 5*A*b^3)*x^2 + 10*(7*B*a^2*b - 5*A*a*b^2)*x)*sqrt(x))/(b^5*x + a*b^4)]","A",0
759,1,231,0,0.435002," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{2} - 3 \, A a b + {\left(5 \, B a b - 3 \, A b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(2 \, B b^{2} x^{2} - 15 \, B a^{2} + 9 \, A a b - 2 \, {\left(5 \, B a b - 3 \, A b^{2}\right)} x\right)} \sqrt{x}}{6 \, {\left(b^{4} x + a b^{3}\right)}}, \frac{3 \, {\left(5 \, B a^{2} - 3 \, A a b + {\left(5 \, B a b - 3 \, A b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(2 \, B b^{2} x^{2} - 15 \, B a^{2} + 9 \, A a b - 2 \, {\left(5 \, B a b - 3 \, A b^{2}\right)} x\right)} \sqrt{x}}{3 \, {\left(b^{4} x + a b^{3}\right)}}\right]"," ",0,"[-1/6*(3*(5*B*a^2 - 3*A*a*b + (5*B*a*b - 3*A*b^2)*x)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(2*B*b^2*x^2 - 15*B*a^2 + 9*A*a*b - 2*(5*B*a*b - 3*A*b^2)*x)*sqrt(x))/(b^4*x + a*b^3), 1/3*(3*(5*B*a^2 - 3*A*a*b + (5*B*a*b - 3*A*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (2*B*b^2*x^2 - 15*B*a^2 + 9*A*a*b - 2*(5*B*a*b - 3*A*b^2)*x)*sqrt(x))/(b^4*x + a*b^3)]","A",0
760,1,198,0,0.441259," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, B a^{2} - A a b + {\left(3 \, B a b - A b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(2 \, B a b^{2} x + 3 \, B a^{2} b - A a b^{2}\right)} \sqrt{x}}{2 \, {\left(a b^{4} x + a^{2} b^{3}\right)}}, \frac{{\left(3 \, B a^{2} - A a b + {\left(3 \, B a b - A b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(2 \, B a b^{2} x + 3 \, B a^{2} b - A a b^{2}\right)} \sqrt{x}}{a b^{4} x + a^{2} b^{3}}\right]"," ",0,"[1/2*((3*B*a^2 - A*a*b + (3*B*a*b - A*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(2*B*a*b^2*x + 3*B*a^2*b - A*a*b^2)*sqrt(x))/(a*b^4*x + a^2*b^3), ((3*B*a^2 - A*a*b + (3*B*a*b - A*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (2*B*a*b^2*x + 3*B*a^2*b - A*a*b^2)*sqrt(x))/(a*b^4*x + a^2*b^3)]","A",0
761,1,177,0,0.432349," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{2} + A a b + {\left(B a b + A b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(B a^{2} b - A a b^{2}\right)} \sqrt{x}}{2 \, {\left(a^{2} b^{3} x + a^{3} b^{2}\right)}}, -\frac{{\left(B a^{2} + A a b + {\left(B a b + A b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(B a^{2} b - A a b^{2}\right)} \sqrt{x}}{a^{2} b^{3} x + a^{3} b^{2}}\right]"," ",0,"[-1/2*((B*a^2 + A*a*b + (B*a*b + A*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(B*a^2*b - A*a*b^2)*sqrt(x))/(a^2*b^3*x + a^3*b^2), -((B*a^2 + A*a*b + (B*a*b + A*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (B*a^2*b - A*a*b^2)*sqrt(x))/(a^2*b^3*x + a^3*b^2)]","A",0
762,1,215,0,0.435219," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(B a b - 3 \, A b^{2}\right)} x^{2} + {\left(B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a + 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) - 2 \, {\left(2 \, A a^{2} b - {\left(B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{x}}{2 \, {\left(a^{3} b^{2} x^{2} + a^{4} b x\right)}}, -\frac{{\left({\left(B a b - 3 \, A b^{2}\right)} x^{2} + {\left(B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(2 \, A a^{2} b - {\left(B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{x}}{a^{3} b^{2} x^{2} + a^{4} b x}\right]"," ",0,"[1/2*(((B*a*b - 3*A*b^2)*x^2 + (B*a^2 - 3*A*a*b)*x)*sqrt(-a*b)*log((b*x - a + 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) - 2*(2*A*a^2*b - (B*a^2*b - 3*A*a*b^2)*x)*sqrt(x))/(a^3*b^2*x^2 + a^4*b*x), -(((B*a*b - 3*A*b^2)*x^2 + (B*a^2 - 3*A*a*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (2*A*a^2*b - (B*a^2*b - 3*A*a*b^2)*x)*sqrt(x))/(a^3*b^2*x^2 + a^4*b*x)]","A",0
763,1,262,0,0.436818," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(3 \, B a b - 5 \, A b^{2}\right)} x^{3} + {\left(3 \, B a^{2} - 5 \, A a b\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(2 \, A a^{2} + 3 \, {\left(3 \, B a b - 5 \, A b^{2}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} x\right)} \sqrt{x}}{6 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}, \frac{3 \, {\left({\left(3 \, B a b - 5 \, A b^{2}\right)} x^{3} + {\left(3 \, B a^{2} - 5 \, A a b\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(2 \, A a^{2} + 3 \, {\left(3 \, B a b - 5 \, A b^{2}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} x\right)} \sqrt{x}}{3 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}\right]"," ",0,"[-1/6*(3*((3*B*a*b - 5*A*b^2)*x^3 + (3*B*a^2 - 5*A*a*b)*x^2)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(2*A*a^2 + 3*(3*B*a*b - 5*A*b^2)*x^2 + 2*(3*B*a^2 - 5*A*a*b)*x)*sqrt(x))/(a^3*b*x^3 + a^4*x^2), 1/3*(3*((3*B*a*b - 5*A*b^2)*x^3 + (3*B*a^2 - 5*A*a*b)*x^2)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (2*A*a^2 + 3*(3*B*a*b - 5*A*b^2)*x^2 + 2*(3*B*a^2 - 5*A*a*b)*x)*sqrt(x))/(a^3*b*x^3 + a^4*x^2)]","A",0
764,1,319,0,0.430151," ","integrate((B*x+A)/x^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{4} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(6 \, A a^{3} - 15 \, {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{3} - 10 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2} + 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} x\right)} \sqrt{x}}{30 \, {\left(a^{4} b x^{4} + a^{5} x^{3}\right)}}, -\frac{15 \, {\left({\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{4} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) + {\left(6 \, A a^{3} - 15 \, {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{3} - 10 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2} + 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} x\right)} \sqrt{x}}{15 \, {\left(a^{4} b x^{4} + a^{5} x^{3}\right)}}\right]"," ",0,"[-1/30*(15*((5*B*a*b^2 - 7*A*b^3)*x^4 + (5*B*a^2*b - 7*A*a*b^2)*x^3)*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(6*A*a^3 - 15*(5*B*a*b^2 - 7*A*b^3)*x^3 - 10*(5*B*a^2*b - 7*A*a*b^2)*x^2 + 2*(5*B*a^3 - 7*A*a^2*b)*x)*sqrt(x))/(a^4*b*x^4 + a^5*x^3), -1/15*(15*((5*B*a*b^2 - 7*A*b^3)*x^4 + (5*B*a^2*b - 7*A*a*b^2)*x^3)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) + (6*A*a^3 - 15*(5*B*a*b^2 - 7*A*b^3)*x^3 - 10*(5*B*a^2*b - 7*A*a*b^2)*x^2 + 2*(5*B*a^3 - 7*A*a^2*b)*x)*sqrt(x))/(a^4*b*x^4 + a^5*x^3)]","A",0
765,1,372,0,0.421738," ","integrate((B*x+A)/x^(9/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(7 \, B a b^{3} - 9 \, A b^{4}\right)} x^{5} + {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(30 \, A a^{4} + 105 \, {\left(7 \, B a b^{3} - 9 \, A b^{4}\right)} x^{4} + 70 \, {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{3} - 14 \, {\left(7 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{2} + 6 \, {\left(7 \, B a^{4} - 9 \, A a^{3} b\right)} x\right)} \sqrt{x}}{210 \, {\left(a^{5} b x^{5} + a^{6} x^{4}\right)}}, \frac{105 \, {\left({\left(7 \, B a b^{3} - 9 \, A b^{4}\right)} x^{5} + {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(30 \, A a^{4} + 105 \, {\left(7 \, B a b^{3} - 9 \, A b^{4}\right)} x^{4} + 70 \, {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{3} - 14 \, {\left(7 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{2} + 6 \, {\left(7 \, B a^{4} - 9 \, A a^{3} b\right)} x\right)} \sqrt{x}}{105 \, {\left(a^{5} b x^{5} + a^{6} x^{4}\right)}}\right]"," ",0,"[-1/210*(105*((7*B*a*b^3 - 9*A*b^4)*x^5 + (7*B*a^2*b^2 - 9*A*a*b^3)*x^4)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(30*A*a^4 + 105*(7*B*a*b^3 - 9*A*b^4)*x^4 + 70*(7*B*a^2*b^2 - 9*A*a*b^3)*x^3 - 14*(7*B*a^3*b - 9*A*a^2*b^2)*x^2 + 6*(7*B*a^4 - 9*A*a^3*b)*x)*sqrt(x))/(a^5*b*x^5 + a^6*x^4), 1/105*(105*((7*B*a*b^3 - 9*A*b^4)*x^5 + (7*B*a^2*b^2 - 9*A*a*b^3)*x^4)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (30*A*a^4 + 105*(7*B*a*b^3 - 9*A*b^4)*x^4 + 70*(7*B*a^2*b^2 - 9*A*a*b^3)*x^3 - 14*(7*B*a^3*b - 9*A*a^2*b^2)*x^2 + 6*(7*B*a^4 - 9*A*a^3*b)*x)*sqrt(x))/(a^5*b*x^5 + a^6*x^4)]","A",0
766,1,467,0,0.435110," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(3 \, B a^{4} - A a^{3} b + {\left(3 \, B a b^{3} - A b^{4}\right)} x^{3} + 3 \, {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} + 3 \, {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(16 \, B b^{4} x^{4} - 315 \, B a^{4} + 105 \, A a^{3} b - 48 \, {\left(3 \, B a b^{3} - A b^{4}\right)} x^{3} - 231 \, {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 280 \, {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{48 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}, \frac{105 \, {\left(3 \, B a^{4} - A a^{3} b + {\left(3 \, B a b^{3} - A b^{4}\right)} x^{3} + 3 \, {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} + 3 \, {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(16 \, B b^{4} x^{4} - 315 \, B a^{4} + 105 \, A a^{3} b - 48 \, {\left(3 \, B a b^{3} - A b^{4}\right)} x^{3} - 231 \, {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 280 \, {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{24 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}\right]"," ",0,"[-1/48*(105*(3*B*a^4 - A*a^3*b + (3*B*a*b^3 - A*b^4)*x^3 + 3*(3*B*a^2*b^2 - A*a*b^3)*x^2 + 3*(3*B*a^3*b - A*a^2*b^2)*x)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(16*B*b^4*x^4 - 315*B*a^4 + 105*A*a^3*b - 48*(3*B*a*b^3 - A*b^4)*x^3 - 231*(3*B*a^2*b^2 - A*a*b^3)*x^2 - 280*(3*B*a^3*b - A*a^2*b^2)*x)*sqrt(x))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5), 1/24*(105*(3*B*a^4 - A*a^3*b + (3*B*a*b^3 - A*b^4)*x^3 + 3*(3*B*a^2*b^2 - A*a*b^3)*x^2 + 3*(3*B*a^3*b - A*a^2*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (16*B*b^4*x^4 - 315*B*a^4 + 105*A*a^3*b - 48*(3*B*a*b^3 - A*b^4)*x^3 - 231*(3*B*a^2*b^2 - A*a*b^3)*x^2 - 280*(3*B*a^3*b - A*a^2*b^2)*x)*sqrt(x))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5)]","A",0
767,1,437,0,0.443586," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, B a^{4} - A a^{3} b + {\left(7 \, B a b^{3} - A b^{4}\right)} x^{3} + 3 \, {\left(7 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} + 3 \, {\left(7 \, B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(48 \, B a b^{4} x^{3} + 105 \, B a^{4} b - 15 \, A a^{3} b^{2} + 33 \, {\left(7 \, B a^{2} b^{3} - A a b^{4}\right)} x^{2} + 40 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x\right)} \sqrt{x}}{48 \, {\left(a b^{8} x^{3} + 3 \, a^{2} b^{7} x^{2} + 3 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}, \frac{15 \, {\left(7 \, B a^{4} - A a^{3} b + {\left(7 \, B a b^{3} - A b^{4}\right)} x^{3} + 3 \, {\left(7 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} + 3 \, {\left(7 \, B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(48 \, B a b^{4} x^{3} + 105 \, B a^{4} b - 15 \, A a^{3} b^{2} + 33 \, {\left(7 \, B a^{2} b^{3} - A a b^{4}\right)} x^{2} + 40 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x\right)} \sqrt{x}}{24 \, {\left(a b^{8} x^{3} + 3 \, a^{2} b^{7} x^{2} + 3 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}\right]"," ",0,"[1/48*(15*(7*B*a^4 - A*a^3*b + (7*B*a*b^3 - A*b^4)*x^3 + 3*(7*B*a^2*b^2 - A*a*b^3)*x^2 + 3*(7*B*a^3*b - A*a^2*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(48*B*a*b^4*x^3 + 105*B*a^4*b - 15*A*a^3*b^2 + 33*(7*B*a^2*b^3 - A*a*b^4)*x^2 + 40*(7*B*a^3*b^2 - A*a^2*b^3)*x)*sqrt(x))/(a*b^8*x^3 + 3*a^2*b^7*x^2 + 3*a^3*b^6*x + a^4*b^5), 1/24*(15*(7*B*a^4 - A*a^3*b + (7*B*a*b^3 - A*b^4)*x^3 + 3*(7*B*a^2*b^2 - A*a*b^3)*x^2 + 3*(7*B*a^3*b - A*a^2*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (48*B*a*b^4*x^3 + 105*B*a^4*b - 15*A*a^3*b^2 + 33*(7*B*a^2*b^3 - A*a*b^4)*x^2 + 40*(7*B*a^3*b^2 - A*a^2*b^3)*x)*sqrt(x))/(a*b^8*x^3 + 3*a^2*b^7*x^2 + 3*a^3*b^6*x + a^4*b^5)]","A",0
768,1,411,0,0.461648," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{4} + A a^{3} b + {\left(5 \, B a b^{3} + A b^{4}\right)} x^{3} + 3 \, {\left(5 \, B a^{2} b^{2} + A a b^{3}\right)} x^{2} + 3 \, {\left(5 \, B a^{3} b + A a^{2} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(15 \, B a^{4} b + 3 \, A a^{3} b^{2} + 3 \, {\left(11 \, B a^{2} b^{3} - A a b^{4}\right)} x^{2} + 8 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x\right)} \sqrt{x}}{48 \, {\left(a^{2} b^{7} x^{3} + 3 \, a^{3} b^{6} x^{2} + 3 \, a^{4} b^{5} x + a^{5} b^{4}\right)}}, -\frac{3 \, {\left(5 \, B a^{4} + A a^{3} b + {\left(5 \, B a b^{3} + A b^{4}\right)} x^{3} + 3 \, {\left(5 \, B a^{2} b^{2} + A a b^{3}\right)} x^{2} + 3 \, {\left(5 \, B a^{3} b + A a^{2} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(15 \, B a^{4} b + 3 \, A a^{3} b^{2} + 3 \, {\left(11 \, B a^{2} b^{3} - A a b^{4}\right)} x^{2} + 8 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x\right)} \sqrt{x}}{24 \, {\left(a^{2} b^{7} x^{3} + 3 \, a^{3} b^{6} x^{2} + 3 \, a^{4} b^{5} x + a^{5} b^{4}\right)}}\right]"," ",0,"[-1/48*(3*(5*B*a^4 + A*a^3*b + (5*B*a*b^3 + A*b^4)*x^3 + 3*(5*B*a^2*b^2 + A*a*b^3)*x^2 + 3*(5*B*a^3*b + A*a^2*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(15*B*a^4*b + 3*A*a^3*b^2 + 3*(11*B*a^2*b^3 - A*a*b^4)*x^2 + 8*(5*B*a^3*b^2 + A*a^2*b^3)*x)*sqrt(x))/(a^2*b^7*x^3 + 3*a^3*b^6*x^2 + 3*a^4*b^5*x + a^5*b^4), -1/24*(3*(5*B*a^4 + A*a^3*b + (5*B*a*b^3 + A*b^4)*x^3 + 3*(5*B*a^2*b^2 + A*a*b^3)*x^2 + 3*(5*B*a^3*b + A*a^2*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (15*B*a^4*b + 3*A*a^3*b^2 + 3*(11*B*a^2*b^3 - A*a*b^4)*x^2 + 8*(5*B*a^3*b^2 + A*a^2*b^3)*x)*sqrt(x))/(a^2*b^7*x^3 + 3*a^3*b^6*x^2 + 3*a^4*b^5*x + a^5*b^4)]","A",0
769,1,399,0,0.443912," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{4} + A a^{3} b + {\left(B a b^{3} + A b^{4}\right)} x^{3} + 3 \, {\left(B a^{2} b^{2} + A a b^{3}\right)} x^{2} + 3 \, {\left(B a^{3} b + A a^{2} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(3 \, B a^{4} b + 3 \, A a^{3} b^{2} - 3 \, {\left(B a^{2} b^{3} + A a b^{4}\right)} x^{2} + 8 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} x\right)} \sqrt{x}}{48 \, {\left(a^{3} b^{6} x^{3} + 3 \, a^{4} b^{5} x^{2} + 3 \, a^{5} b^{4} x + a^{6} b^{3}\right)}}, -\frac{3 \, {\left(B a^{4} + A a^{3} b + {\left(B a b^{3} + A b^{4}\right)} x^{3} + 3 \, {\left(B a^{2} b^{2} + A a b^{3}\right)} x^{2} + 3 \, {\left(B a^{3} b + A a^{2} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(3 \, B a^{4} b + 3 \, A a^{3} b^{2} - 3 \, {\left(B a^{2} b^{3} + A a b^{4}\right)} x^{2} + 8 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} x\right)} \sqrt{x}}{24 \, {\left(a^{3} b^{6} x^{3} + 3 \, a^{4} b^{5} x^{2} + 3 \, a^{5} b^{4} x + a^{6} b^{3}\right)}}\right]"," ",0,"[-1/48*(3*(B*a^4 + A*a^3*b + (B*a*b^3 + A*b^4)*x^3 + 3*(B*a^2*b^2 + A*a*b^3)*x^2 + 3*(B*a^3*b + A*a^2*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(3*B*a^4*b + 3*A*a^3*b^2 - 3*(B*a^2*b^3 + A*a*b^4)*x^2 + 8*(B*a^3*b^2 - A*a^2*b^3)*x)*sqrt(x))/(a^3*b^6*x^3 + 3*a^4*b^5*x^2 + 3*a^5*b^4*x + a^6*b^3), -1/24*(3*(B*a^4 + A*a^3*b + (B*a*b^3 + A*b^4)*x^3 + 3*(B*a^2*b^2 + A*a*b^3)*x^2 + 3*(B*a^3*b + A*a^2*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (3*B*a^4*b + 3*A*a^3*b^2 - 3*(B*a^2*b^3 + A*a*b^4)*x^2 + 8*(B*a^3*b^2 - A*a^2*b^3)*x)*sqrt(x))/(a^3*b^6*x^3 + 3*a^4*b^5*x^2 + 3*a^5*b^4*x + a^6*b^3)]","A",0
770,1,409,0,0.444176," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{4} + 5 \, A a^{3} b + {\left(B a b^{3} + 5 \, A b^{4}\right)} x^{3} + 3 \, {\left(B a^{2} b^{2} + 5 \, A a b^{3}\right)} x^{2} + 3 \, {\left(B a^{3} b + 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(3 \, B a^{4} b - 33 \, A a^{3} b^{2} - 3 \, {\left(B a^{2} b^{3} + 5 \, A a b^{4}\right)} x^{2} - 8 \, {\left(B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} x\right)} \sqrt{x}}{48 \, {\left(a^{4} b^{5} x^{3} + 3 \, a^{5} b^{4} x^{2} + 3 \, a^{6} b^{3} x + a^{7} b^{2}\right)}}, -\frac{3 \, {\left(B a^{4} + 5 \, A a^{3} b + {\left(B a b^{3} + 5 \, A b^{4}\right)} x^{3} + 3 \, {\left(B a^{2} b^{2} + 5 \, A a b^{3}\right)} x^{2} + 3 \, {\left(B a^{3} b + 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(3 \, B a^{4} b - 33 \, A a^{3} b^{2} - 3 \, {\left(B a^{2} b^{3} + 5 \, A a b^{4}\right)} x^{2} - 8 \, {\left(B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} x\right)} \sqrt{x}}{24 \, {\left(a^{4} b^{5} x^{3} + 3 \, a^{5} b^{4} x^{2} + 3 \, a^{6} b^{3} x + a^{7} b^{2}\right)}}\right]"," ",0,"[-1/48*(3*(B*a^4 + 5*A*a^3*b + (B*a*b^3 + 5*A*b^4)*x^3 + 3*(B*a^2*b^2 + 5*A*a*b^3)*x^2 + 3*(B*a^3*b + 5*A*a^2*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(3*B*a^4*b - 33*A*a^3*b^2 - 3*(B*a^2*b^3 + 5*A*a*b^4)*x^2 - 8*(B*a^3*b^2 + 5*A*a^2*b^3)*x)*sqrt(x))/(a^4*b^5*x^3 + 3*a^5*b^4*x^2 + 3*a^6*b^3*x + a^7*b^2), -1/24*(3*(B*a^4 + 5*A*a^3*b + (B*a*b^3 + 5*A*b^4)*x^3 + 3*(B*a^2*b^2 + 5*A*a*b^3)*x^2 + 3*(B*a^3*b + 5*A*a^2*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (3*B*a^4*b - 33*A*a^3*b^2 - 3*(B*a^2*b^3 + 5*A*a*b^4)*x^2 - 8*(B*a^3*b^2 + 5*A*a^2*b^3)*x)*sqrt(x))/(a^4*b^5*x^3 + 3*a^5*b^4*x^2 + 3*a^6*b^3*x + a^7*b^2)]","A",0
771,1,445,0,0.448407," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(B a b^{3} - 7 \, A b^{4}\right)} x^{4} + 3 \, {\left(B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} + 3 \, {\left(B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2} + {\left(B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a + 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) - 2 \, {\left(48 \, A a^{4} b - 15 \, {\left(B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{3} - 40 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{2} - 33 \, {\left(B a^{4} b - 7 \, A a^{3} b^{2}\right)} x\right)} \sqrt{x}}{48 \, {\left(a^{5} b^{4} x^{4} + 3 \, a^{6} b^{3} x^{3} + 3 \, a^{7} b^{2} x^{2} + a^{8} b x\right)}}, -\frac{15 \, {\left({\left(B a b^{3} - 7 \, A b^{4}\right)} x^{4} + 3 \, {\left(B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} + 3 \, {\left(B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2} + {\left(B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(48 \, A a^{4} b - 15 \, {\left(B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{3} - 40 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{2} - 33 \, {\left(B a^{4} b - 7 \, A a^{3} b^{2}\right)} x\right)} \sqrt{x}}{24 \, {\left(a^{5} b^{4} x^{4} + 3 \, a^{6} b^{3} x^{3} + 3 \, a^{7} b^{2} x^{2} + a^{8} b x\right)}}\right]"," ",0,"[1/48*(15*((B*a*b^3 - 7*A*b^4)*x^4 + 3*(B*a^2*b^2 - 7*A*a*b^3)*x^3 + 3*(B*a^3*b - 7*A*a^2*b^2)*x^2 + (B*a^4 - 7*A*a^3*b)*x)*sqrt(-a*b)*log((b*x - a + 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) - 2*(48*A*a^4*b - 15*(B*a^2*b^3 - 7*A*a*b^4)*x^3 - 40*(B*a^3*b^2 - 7*A*a^2*b^3)*x^2 - 33*(B*a^4*b - 7*A*a^3*b^2)*x)*sqrt(x))/(a^5*b^4*x^4 + 3*a^6*b^3*x^3 + 3*a^7*b^2*x^2 + a^8*b*x), -1/24*(15*((B*a*b^3 - 7*A*b^4)*x^4 + 3*(B*a^2*b^2 - 7*A*a*b^3)*x^3 + 3*(B*a^3*b - 7*A*a^2*b^2)*x^2 + (B*a^4 - 7*A*a^3*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (48*A*a^4*b - 15*(B*a^2*b^3 - 7*A*a*b^4)*x^3 - 40*(B*a^3*b^2 - 7*A*a^2*b^3)*x^2 - 33*(B*a^4*b - 7*A*a^3*b^2)*x)*sqrt(x))/(a^5*b^4*x^4 + 3*a^6*b^3*x^3 + 3*a^7*b^2*x^2 + a^8*b*x)]","A",0
772,1,482,0,0.451964," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(B a b^{3} - 3 \, A b^{4}\right)} x^{5} + 3 \, {\left(B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} + 3 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{3} + {\left(B a^{4} - 3 \, A a^{3} b\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(16 \, A a^{4} + 105 \, {\left(B a b^{3} - 3 \, A b^{4}\right)} x^{4} + 280 \, {\left(B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{3} + 231 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2} + 48 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} x\right)} \sqrt{x}}{48 \, {\left(a^{5} b^{3} x^{5} + 3 \, a^{6} b^{2} x^{4} + 3 \, a^{7} b x^{3} + a^{8} x^{2}\right)}}, \frac{105 \, {\left({\left(B a b^{3} - 3 \, A b^{4}\right)} x^{5} + 3 \, {\left(B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} + 3 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{3} + {\left(B a^{4} - 3 \, A a^{3} b\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(16 \, A a^{4} + 105 \, {\left(B a b^{3} - 3 \, A b^{4}\right)} x^{4} + 280 \, {\left(B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{3} + 231 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2} + 48 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} x\right)} \sqrt{x}}{24 \, {\left(a^{5} b^{3} x^{5} + 3 \, a^{6} b^{2} x^{4} + 3 \, a^{7} b x^{3} + a^{8} x^{2}\right)}}\right]"," ",0,"[-1/48*(105*((B*a*b^3 - 3*A*b^4)*x^5 + 3*(B*a^2*b^2 - 3*A*a*b^3)*x^4 + 3*(B*a^3*b - 3*A*a^2*b^2)*x^3 + (B*a^4 - 3*A*a^3*b)*x^2)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(16*A*a^4 + 105*(B*a*b^3 - 3*A*b^4)*x^4 + 280*(B*a^2*b^2 - 3*A*a*b^3)*x^3 + 231*(B*a^3*b - 3*A*a^2*b^2)*x^2 + 48*(B*a^4 - 3*A*a^3*b)*x)*sqrt(x))/(a^5*b^3*x^5 + 3*a^6*b^2*x^4 + 3*a^7*b*x^3 + a^8*x^2), 1/24*(105*((B*a*b^3 - 3*A*b^4)*x^5 + 3*(B*a^2*b^2 - 3*A*a*b^3)*x^4 + 3*(B*a^3*b - 3*A*a^2*b^2)*x^3 + (B*a^4 - 3*A*a^3*b)*x^2)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (16*A*a^4 + 105*(B*a*b^3 - 3*A*b^4)*x^4 + 280*(B*a^2*b^2 - 3*A*a*b^3)*x^3 + 231*(B*a^3*b - 3*A*a^2*b^2)*x^2 + 48*(B*a^4 - 3*A*a^3*b)*x)*sqrt(x))/(a^5*b^3*x^5 + 3*a^6*b^2*x^4 + 3*a^7*b*x^3 + a^8*x^2)]","A",0
773,1,703,0,0.474432," ","integrate(x^(11/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left(13 \, B a^{6} - 3 \, A a^{5} b + {\left(13 \, B a b^{5} - 3 \, A b^{6}\right)} x^{5} + 5 \, {\left(13 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} x^{4} + 10 \, {\left(13 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(13 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(13 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(1280 \, B b^{6} x^{6} - 45045 \, B a^{6} + 10395 \, A a^{5} b - 1280 \, {\left(13 \, B a b^{5} - 3 \, A b^{6}\right)} x^{5} - 10615 \, {\left(13 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} x^{4} - 26070 \, {\left(13 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} x^{3} - 29568 \, {\left(13 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} x^{2} - 16170 \, {\left(13 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} x\right)} \sqrt{x}}{3840 \, {\left(b^{12} x^{5} + 5 \, a b^{11} x^{4} + 10 \, a^{2} b^{10} x^{3} + 10 \, a^{3} b^{9} x^{2} + 5 \, a^{4} b^{8} x + a^{5} b^{7}\right)}}, \frac{3465 \, {\left(13 \, B a^{6} - 3 \, A a^{5} b + {\left(13 \, B a b^{5} - 3 \, A b^{6}\right)} x^{5} + 5 \, {\left(13 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} x^{4} + 10 \, {\left(13 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(13 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(13 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(1280 \, B b^{6} x^{6} - 45045 \, B a^{6} + 10395 \, A a^{5} b - 1280 \, {\left(13 \, B a b^{5} - 3 \, A b^{6}\right)} x^{5} - 10615 \, {\left(13 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} x^{4} - 26070 \, {\left(13 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} x^{3} - 29568 \, {\left(13 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} x^{2} - 16170 \, {\left(13 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} x\right)} \sqrt{x}}{1920 \, {\left(b^{12} x^{5} + 5 \, a b^{11} x^{4} + 10 \, a^{2} b^{10} x^{3} + 10 \, a^{3} b^{9} x^{2} + 5 \, a^{4} b^{8} x + a^{5} b^{7}\right)}}\right]"," ",0,"[-1/3840*(3465*(13*B*a^6 - 3*A*a^5*b + (13*B*a*b^5 - 3*A*b^6)*x^5 + 5*(13*B*a^2*b^4 - 3*A*a*b^5)*x^4 + 10*(13*B*a^3*b^3 - 3*A*a^2*b^4)*x^3 + 10*(13*B*a^4*b^2 - 3*A*a^3*b^3)*x^2 + 5*(13*B*a^5*b - 3*A*a^4*b^2)*x)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(1280*B*b^6*x^6 - 45045*B*a^6 + 10395*A*a^5*b - 1280*(13*B*a*b^5 - 3*A*b^6)*x^5 - 10615*(13*B*a^2*b^4 - 3*A*a*b^5)*x^4 - 26070*(13*B*a^3*b^3 - 3*A*a^2*b^4)*x^3 - 29568*(13*B*a^4*b^2 - 3*A*a^3*b^3)*x^2 - 16170*(13*B*a^5*b - 3*A*a^4*b^2)*x)*sqrt(x))/(b^12*x^5 + 5*a*b^11*x^4 + 10*a^2*b^10*x^3 + 10*a^3*b^9*x^2 + 5*a^4*b^8*x + a^5*b^7), 1/1920*(3465*(13*B*a^6 - 3*A*a^5*b + (13*B*a*b^5 - 3*A*b^6)*x^5 + 5*(13*B*a^2*b^4 - 3*A*a*b^5)*x^4 + 10*(13*B*a^3*b^3 - 3*A*a^2*b^4)*x^3 + 10*(13*B*a^4*b^2 - 3*A*a^3*b^3)*x^2 + 5*(13*B*a^5*b - 3*A*a^4*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (1280*B*b^6*x^6 - 45045*B*a^6 + 10395*A*a^5*b - 1280*(13*B*a*b^5 - 3*A*b^6)*x^5 - 10615*(13*B*a^2*b^4 - 3*A*a*b^5)*x^4 - 26070*(13*B*a^3*b^3 - 3*A*a^2*b^4)*x^3 - 29568*(13*B*a^4*b^2 - 3*A*a^3*b^3)*x^2 - 16170*(13*B*a^5*b - 3*A*a^4*b^2)*x)*sqrt(x))/(b^12*x^5 + 5*a*b^11*x^4 + 10*a^2*b^10*x^3 + 10*a^3*b^9*x^2 + 5*a^4*b^8*x + a^5*b^7)]","A",0
774,1,673,0,0.452311," ","integrate(x^(9/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(11 \, B a^{6} - A a^{5} b + {\left(11 \, B a b^{5} - A b^{6}\right)} x^{5} + 5 \, {\left(11 \, B a^{2} b^{4} - A a b^{5}\right)} x^{4} + 10 \, {\left(11 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(11 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(11 \, B a^{5} b - A a^{4} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(1280 \, B a b^{6} x^{5} + 3465 \, B a^{6} b - 315 \, A a^{5} b^{2} + 965 \, {\left(11 \, B a^{2} b^{5} - A a b^{6}\right)} x^{4} + 2370 \, {\left(11 \, B a^{3} b^{4} - A a^{2} b^{5}\right)} x^{3} + 2688 \, {\left(11 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} x^{2} + 1470 \, {\left(11 \, B a^{5} b^{2} - A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{1280 \, {\left(a b^{12} x^{5} + 5 \, a^{2} b^{11} x^{4} + 10 \, a^{3} b^{10} x^{3} + 10 \, a^{4} b^{9} x^{2} + 5 \, a^{5} b^{8} x + a^{6} b^{7}\right)}}, \frac{315 \, {\left(11 \, B a^{6} - A a^{5} b + {\left(11 \, B a b^{5} - A b^{6}\right)} x^{5} + 5 \, {\left(11 \, B a^{2} b^{4} - A a b^{5}\right)} x^{4} + 10 \, {\left(11 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(11 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(11 \, B a^{5} b - A a^{4} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(1280 \, B a b^{6} x^{5} + 3465 \, B a^{6} b - 315 \, A a^{5} b^{2} + 965 \, {\left(11 \, B a^{2} b^{5} - A a b^{6}\right)} x^{4} + 2370 \, {\left(11 \, B a^{3} b^{4} - A a^{2} b^{5}\right)} x^{3} + 2688 \, {\left(11 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} x^{2} + 1470 \, {\left(11 \, B a^{5} b^{2} - A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{640 \, {\left(a b^{12} x^{5} + 5 \, a^{2} b^{11} x^{4} + 10 \, a^{3} b^{10} x^{3} + 10 \, a^{4} b^{9} x^{2} + 5 \, a^{5} b^{8} x + a^{6} b^{7}\right)}}\right]"," ",0,"[1/1280*(315*(11*B*a^6 - A*a^5*b + (11*B*a*b^5 - A*b^6)*x^5 + 5*(11*B*a^2*b^4 - A*a*b^5)*x^4 + 10*(11*B*a^3*b^3 - A*a^2*b^4)*x^3 + 10*(11*B*a^4*b^2 - A*a^3*b^3)*x^2 + 5*(11*B*a^5*b - A*a^4*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(1280*B*a*b^6*x^5 + 3465*B*a^6*b - 315*A*a^5*b^2 + 965*(11*B*a^2*b^5 - A*a*b^6)*x^4 + 2370*(11*B*a^3*b^4 - A*a^2*b^5)*x^3 + 2688*(11*B*a^4*b^3 - A*a^3*b^4)*x^2 + 1470*(11*B*a^5*b^2 - A*a^4*b^3)*x)*sqrt(x))/(a*b^12*x^5 + 5*a^2*b^11*x^4 + 10*a^3*b^10*x^3 + 10*a^4*b^9*x^2 + 5*a^5*b^8*x + a^6*b^7), 1/640*(315*(11*B*a^6 - A*a^5*b + (11*B*a*b^5 - A*b^6)*x^5 + 5*(11*B*a^2*b^4 - A*a*b^5)*x^4 + 10*(11*B*a^3*b^3 - A*a^2*b^4)*x^3 + 10*(11*B*a^4*b^2 - A*a^3*b^3)*x^2 + 5*(11*B*a^5*b - A*a^4*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (1280*B*a*b^6*x^5 + 3465*B*a^6*b - 315*A*a^5*b^2 + 965*(11*B*a^2*b^5 - A*a*b^6)*x^4 + 2370*(11*B*a^3*b^4 - A*a^2*b^5)*x^3 + 2688*(11*B*a^4*b^3 - A*a^3*b^4)*x^2 + 1470*(11*B*a^5*b^2 - A*a^4*b^3)*x)*sqrt(x))/(a*b^12*x^5 + 5*a^2*b^11*x^4 + 10*a^3*b^10*x^3 + 10*a^4*b^9*x^2 + 5*a^5*b^8*x + a^6*b^7)]","A",0
775,1,639,0,0.453395," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B a^{6} + A a^{5} b + {\left(9 \, B a b^{5} + A b^{6}\right)} x^{5} + 5 \, {\left(9 \, B a^{2} b^{4} + A a b^{5}\right)} x^{4} + 10 \, {\left(9 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(9 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(9 \, B a^{5} b + A a^{4} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(945 \, B a^{6} b + 105 \, A a^{5} b^{2} + 15 \, {\left(193 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} x^{4} + 790 \, {\left(9 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} x^{3} + 896 \, {\left(9 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} x^{2} + 490 \, {\left(9 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{3840 \, {\left(a^{2} b^{11} x^{5} + 5 \, a^{3} b^{10} x^{4} + 10 \, a^{4} b^{9} x^{3} + 10 \, a^{5} b^{8} x^{2} + 5 \, a^{6} b^{7} x + a^{7} b^{6}\right)}}, -\frac{105 \, {\left(9 \, B a^{6} + A a^{5} b + {\left(9 \, B a b^{5} + A b^{6}\right)} x^{5} + 5 \, {\left(9 \, B a^{2} b^{4} + A a b^{5}\right)} x^{4} + 10 \, {\left(9 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(9 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(9 \, B a^{5} b + A a^{4} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(945 \, B a^{6} b + 105 \, A a^{5} b^{2} + 15 \, {\left(193 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} x^{4} + 790 \, {\left(9 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} x^{3} + 896 \, {\left(9 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} x^{2} + 490 \, {\left(9 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{1920 \, {\left(a^{2} b^{11} x^{5} + 5 \, a^{3} b^{10} x^{4} + 10 \, a^{4} b^{9} x^{3} + 10 \, a^{5} b^{8} x^{2} + 5 \, a^{6} b^{7} x + a^{7} b^{6}\right)}}\right]"," ",0,"[-1/3840*(105*(9*B*a^6 + A*a^5*b + (9*B*a*b^5 + A*b^6)*x^5 + 5*(9*B*a^2*b^4 + A*a*b^5)*x^4 + 10*(9*B*a^3*b^3 + A*a^2*b^4)*x^3 + 10*(9*B*a^4*b^2 + A*a^3*b^3)*x^2 + 5*(9*B*a^5*b + A*a^4*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(945*B*a^6*b + 105*A*a^5*b^2 + 15*(193*B*a^2*b^5 - 7*A*a*b^6)*x^4 + 790*(9*B*a^3*b^4 + A*a^2*b^5)*x^3 + 896*(9*B*a^4*b^3 + A*a^3*b^4)*x^2 + 490*(9*B*a^5*b^2 + A*a^4*b^3)*x)*sqrt(x))/(a^2*b^11*x^5 + 5*a^3*b^10*x^4 + 10*a^4*b^9*x^3 + 10*a^5*b^8*x^2 + 5*a^6*b^7*x + a^7*b^6), -1/1920*(105*(9*B*a^6 + A*a^5*b + (9*B*a*b^5 + A*b^6)*x^5 + 5*(9*B*a^2*b^4 + A*a*b^5)*x^4 + 10*(9*B*a^3*b^3 + A*a^2*b^4)*x^3 + 10*(9*B*a^4*b^2 + A*a^3*b^3)*x^2 + 5*(9*B*a^5*b + A*a^4*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (945*B*a^6*b + 105*A*a^5*b^2 + 15*(193*B*a^2*b^5 - 7*A*a*b^6)*x^4 + 790*(9*B*a^3*b^4 + A*a^2*b^5)*x^3 + 896*(9*B*a^4*b^3 + A*a^3*b^4)*x^2 + 490*(9*B*a^5*b^2 + A*a^4*b^3)*x)*sqrt(x))/(a^2*b^11*x^5 + 5*a^3*b^10*x^4 + 10*a^4*b^9*x^3 + 10*a^5*b^8*x^2 + 5*a^6*b^7*x + a^7*b^6)]","A",0
776,1,657,0,0.457851," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{6} + 3 \, A a^{5} b + {\left(7 \, B a b^{5} + 3 \, A b^{6}\right)} x^{5} + 5 \, {\left(7 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} x^{4} + 10 \, {\left(7 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(7 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(7 \, B a^{5} b + 3 \, A a^{4} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(105 \, B a^{6} b + 45 \, A a^{5} b^{2} - 15 \, {\left(7 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} x^{4} + 10 \, {\left(79 \, B a^{3} b^{4} - 21 \, A a^{2} b^{5}\right)} x^{3} + 128 \, {\left(7 \, B a^{4} b^{3} + 3 \, A a^{3} b^{4}\right)} x^{2} + 70 \, {\left(7 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{3840 \, {\left(a^{3} b^{10} x^{5} + 5 \, a^{4} b^{9} x^{4} + 10 \, a^{5} b^{8} x^{3} + 10 \, a^{6} b^{7} x^{2} + 5 \, a^{7} b^{6} x + a^{8} b^{5}\right)}}, -\frac{15 \, {\left(7 \, B a^{6} + 3 \, A a^{5} b + {\left(7 \, B a b^{5} + 3 \, A b^{6}\right)} x^{5} + 5 \, {\left(7 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} x^{4} + 10 \, {\left(7 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(7 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(7 \, B a^{5} b + 3 \, A a^{4} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(105 \, B a^{6} b + 45 \, A a^{5} b^{2} - 15 \, {\left(7 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} x^{4} + 10 \, {\left(79 \, B a^{3} b^{4} - 21 \, A a^{2} b^{5}\right)} x^{3} + 128 \, {\left(7 \, B a^{4} b^{3} + 3 \, A a^{3} b^{4}\right)} x^{2} + 70 \, {\left(7 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{1920 \, {\left(a^{3} b^{10} x^{5} + 5 \, a^{4} b^{9} x^{4} + 10 \, a^{5} b^{8} x^{3} + 10 \, a^{6} b^{7} x^{2} + 5 \, a^{7} b^{6} x + a^{8} b^{5}\right)}}\right]"," ",0,"[-1/3840*(15*(7*B*a^6 + 3*A*a^5*b + (7*B*a*b^5 + 3*A*b^6)*x^5 + 5*(7*B*a^2*b^4 + 3*A*a*b^5)*x^4 + 10*(7*B*a^3*b^3 + 3*A*a^2*b^4)*x^3 + 10*(7*B*a^4*b^2 + 3*A*a^3*b^3)*x^2 + 5*(7*B*a^5*b + 3*A*a^4*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(105*B*a^6*b + 45*A*a^5*b^2 - 15*(7*B*a^2*b^5 + 3*A*a*b^6)*x^4 + 10*(79*B*a^3*b^4 - 21*A*a^2*b^5)*x^3 + 128*(7*B*a^4*b^3 + 3*A*a^3*b^4)*x^2 + 70*(7*B*a^5*b^2 + 3*A*a^4*b^3)*x)*sqrt(x))/(a^3*b^10*x^5 + 5*a^4*b^9*x^4 + 10*a^5*b^8*x^3 + 10*a^6*b^7*x^2 + 5*a^7*b^6*x + a^8*b^5), -1/1920*(15*(7*B*a^6 + 3*A*a^5*b + (7*B*a*b^5 + 3*A*b^6)*x^5 + 5*(7*B*a^2*b^4 + 3*A*a*b^5)*x^4 + 10*(7*B*a^3*b^3 + 3*A*a^2*b^4)*x^3 + 10*(7*B*a^4*b^2 + 3*A*a^3*b^3)*x^2 + 5*(7*B*a^5*b + 3*A*a^4*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (105*B*a^6*b + 45*A*a^5*b^2 - 15*(7*B*a^2*b^5 + 3*A*a*b^6)*x^4 + 10*(79*B*a^3*b^4 - 21*A*a^2*b^5)*x^3 + 128*(7*B*a^4*b^3 + 3*A*a^3*b^4)*x^2 + 70*(7*B*a^5*b^2 + 3*A*a^4*b^3)*x)*sqrt(x))/(a^3*b^10*x^5 + 5*a^4*b^9*x^4 + 10*a^5*b^8*x^3 + 10*a^6*b^7*x^2 + 5*a^7*b^6*x + a^8*b^5)]","A",0
777,1,619,0,0.459016," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a^{6} + A a^{5} b + {\left(B a b^{5} + A b^{6}\right)} x^{5} + 5 \, {\left(B a^{2} b^{4} + A a b^{5}\right)} x^{4} + 10 \, {\left(B a^{3} b^{3} + A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(B a^{4} b^{2} + A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(B a^{5} b + A a^{4} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(15 \, B a^{6} b + 15 \, A a^{5} b^{2} - 15 \, {\left(B a^{2} b^{5} + A a b^{6}\right)} x^{4} - 70 \, {\left(B a^{3} b^{4} + A a^{2} b^{5}\right)} x^{3} + 128 \, {\left(B a^{4} b^{3} - A a^{3} b^{4}\right)} x^{2} + 70 \, {\left(B a^{5} b^{2} + A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{1280 \, {\left(a^{4} b^{9} x^{5} + 5 \, a^{5} b^{8} x^{4} + 10 \, a^{6} b^{7} x^{3} + 10 \, a^{7} b^{6} x^{2} + 5 \, a^{8} b^{5} x + a^{9} b^{4}\right)}}, -\frac{15 \, {\left(B a^{6} + A a^{5} b + {\left(B a b^{5} + A b^{6}\right)} x^{5} + 5 \, {\left(B a^{2} b^{4} + A a b^{5}\right)} x^{4} + 10 \, {\left(B a^{3} b^{3} + A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(B a^{4} b^{2} + A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(B a^{5} b + A a^{4} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(15 \, B a^{6} b + 15 \, A a^{5} b^{2} - 15 \, {\left(B a^{2} b^{5} + A a b^{6}\right)} x^{4} - 70 \, {\left(B a^{3} b^{4} + A a^{2} b^{5}\right)} x^{3} + 128 \, {\left(B a^{4} b^{3} - A a^{3} b^{4}\right)} x^{2} + 70 \, {\left(B a^{5} b^{2} + A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{640 \, {\left(a^{4} b^{9} x^{5} + 5 \, a^{5} b^{8} x^{4} + 10 \, a^{6} b^{7} x^{3} + 10 \, a^{7} b^{6} x^{2} + 5 \, a^{8} b^{5} x + a^{9} b^{4}\right)}}\right]"," ",0,"[-1/1280*(15*(B*a^6 + A*a^5*b + (B*a*b^5 + A*b^6)*x^5 + 5*(B*a^2*b^4 + A*a*b^5)*x^4 + 10*(B*a^3*b^3 + A*a^2*b^4)*x^3 + 10*(B*a^4*b^2 + A*a^3*b^3)*x^2 + 5*(B*a^5*b + A*a^4*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(15*B*a^6*b + 15*A*a^5*b^2 - 15*(B*a^2*b^5 + A*a*b^6)*x^4 - 70*(B*a^3*b^4 + A*a^2*b^5)*x^3 + 128*(B*a^4*b^3 - A*a^3*b^4)*x^2 + 70*(B*a^5*b^2 + A*a^4*b^3)*x)*sqrt(x))/(a^4*b^9*x^5 + 5*a^5*b^8*x^4 + 10*a^6*b^7*x^3 + 10*a^7*b^6*x^2 + 5*a^8*b^5*x + a^9*b^4), -1/640*(15*(B*a^6 + A*a^5*b + (B*a*b^5 + A*b^6)*x^5 + 5*(B*a^2*b^4 + A*a*b^5)*x^4 + 10*(B*a^3*b^3 + A*a^2*b^4)*x^3 + 10*(B*a^4*b^2 + A*a^3*b^3)*x^2 + 5*(B*a^5*b + A*a^4*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (15*B*a^6*b + 15*A*a^5*b^2 - 15*(B*a^2*b^5 + A*a*b^6)*x^4 - 70*(B*a^3*b^4 + A*a^2*b^5)*x^3 + 128*(B*a^4*b^3 - A*a^3*b^4)*x^2 + 70*(B*a^5*b^2 + A*a^4*b^3)*x)*sqrt(x))/(a^4*b^9*x^5 + 5*a^5*b^8*x^4 + 10*a^6*b^7*x^3 + 10*a^7*b^6*x^2 + 5*a^8*b^5*x + a^9*b^4)]","A",0
778,1,657,0,0.465068," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, B a^{6} + 7 \, A a^{5} b + {\left(3 \, B a b^{5} + 7 \, A b^{6}\right)} x^{5} + 5 \, {\left(3 \, B a^{2} b^{4} + 7 \, A a b^{5}\right)} x^{4} + 10 \, {\left(3 \, B a^{3} b^{3} + 7 \, A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(3 \, B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(3 \, B a^{5} b + 7 \, A a^{4} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(45 \, B a^{6} b + 105 \, A a^{5} b^{2} - 15 \, {\left(3 \, B a^{2} b^{5} + 7 \, A a b^{6}\right)} x^{4} - 70 \, {\left(3 \, B a^{3} b^{4} + 7 \, A a^{2} b^{5}\right)} x^{3} - 128 \, {\left(3 \, B a^{4} b^{3} + 7 \, A a^{3} b^{4}\right)} x^{2} + 10 \, {\left(21 \, B a^{5} b^{2} - 79 \, A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{3840 \, {\left(a^{5} b^{8} x^{5} + 5 \, a^{6} b^{7} x^{4} + 10 \, a^{7} b^{6} x^{3} + 10 \, a^{8} b^{5} x^{2} + 5 \, a^{9} b^{4} x + a^{10} b^{3}\right)}}, -\frac{15 \, {\left(3 \, B a^{6} + 7 \, A a^{5} b + {\left(3 \, B a b^{5} + 7 \, A b^{6}\right)} x^{5} + 5 \, {\left(3 \, B a^{2} b^{4} + 7 \, A a b^{5}\right)} x^{4} + 10 \, {\left(3 \, B a^{3} b^{3} + 7 \, A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(3 \, B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(3 \, B a^{5} b + 7 \, A a^{4} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(45 \, B a^{6} b + 105 \, A a^{5} b^{2} - 15 \, {\left(3 \, B a^{2} b^{5} + 7 \, A a b^{6}\right)} x^{4} - 70 \, {\left(3 \, B a^{3} b^{4} + 7 \, A a^{2} b^{5}\right)} x^{3} - 128 \, {\left(3 \, B a^{4} b^{3} + 7 \, A a^{3} b^{4}\right)} x^{2} + 10 \, {\left(21 \, B a^{5} b^{2} - 79 \, A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{1920 \, {\left(a^{5} b^{8} x^{5} + 5 \, a^{6} b^{7} x^{4} + 10 \, a^{7} b^{6} x^{3} + 10 \, a^{8} b^{5} x^{2} + 5 \, a^{9} b^{4} x + a^{10} b^{3}\right)}}\right]"," ",0,"[-1/3840*(15*(3*B*a^6 + 7*A*a^5*b + (3*B*a*b^5 + 7*A*b^6)*x^5 + 5*(3*B*a^2*b^4 + 7*A*a*b^5)*x^4 + 10*(3*B*a^3*b^3 + 7*A*a^2*b^4)*x^3 + 10*(3*B*a^4*b^2 + 7*A*a^3*b^3)*x^2 + 5*(3*B*a^5*b + 7*A*a^4*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(45*B*a^6*b + 105*A*a^5*b^2 - 15*(3*B*a^2*b^5 + 7*A*a*b^6)*x^4 - 70*(3*B*a^3*b^4 + 7*A*a^2*b^5)*x^3 - 128*(3*B*a^4*b^3 + 7*A*a^3*b^4)*x^2 + 10*(21*B*a^5*b^2 - 79*A*a^4*b^3)*x)*sqrt(x))/(a^5*b^8*x^5 + 5*a^6*b^7*x^4 + 10*a^7*b^6*x^3 + 10*a^8*b^5*x^2 + 5*a^9*b^4*x + a^10*b^3), -1/1920*(15*(3*B*a^6 + 7*A*a^5*b + (3*B*a*b^5 + 7*A*b^6)*x^5 + 5*(3*B*a^2*b^4 + 7*A*a*b^5)*x^4 + 10*(3*B*a^3*b^3 + 7*A*a^2*b^4)*x^3 + 10*(3*B*a^4*b^2 + 7*A*a^3*b^3)*x^2 + 5*(3*B*a^5*b + 7*A*a^4*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (45*B*a^6*b + 105*A*a^5*b^2 - 15*(3*B*a^2*b^5 + 7*A*a*b^6)*x^4 - 70*(3*B*a^3*b^4 + 7*A*a^2*b^5)*x^3 - 128*(3*B*a^4*b^3 + 7*A*a^3*b^4)*x^2 + 10*(21*B*a^5*b^2 - 79*A*a^4*b^3)*x)*sqrt(x))/(a^5*b^8*x^5 + 5*a^6*b^7*x^4 + 10*a^7*b^6*x^3 + 10*a^8*b^5*x^2 + 5*a^9*b^4*x + a^10*b^3)]","A",0
779,1,637,0,0.451016," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B a^{6} + 9 \, A a^{5} b + {\left(B a b^{5} + 9 \, A b^{6}\right)} x^{5} + 5 \, {\left(B a^{2} b^{4} + 9 \, A a b^{5}\right)} x^{4} + 10 \, {\left(B a^{3} b^{3} + 9 \, A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(B a^{4} b^{2} + 9 \, A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(B a^{5} b + 9 \, A a^{4} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(105 \, B a^{6} b - 2895 \, A a^{5} b^{2} - 105 \, {\left(B a^{2} b^{5} + 9 \, A a b^{6}\right)} x^{4} - 490 \, {\left(B a^{3} b^{4} + 9 \, A a^{2} b^{5}\right)} x^{3} - 896 \, {\left(B a^{4} b^{3} + 9 \, A a^{3} b^{4}\right)} x^{2} - 790 \, {\left(B a^{5} b^{2} + 9 \, A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{3840 \, {\left(a^{6} b^{7} x^{5} + 5 \, a^{7} b^{6} x^{4} + 10 \, a^{8} b^{5} x^{3} + 10 \, a^{9} b^{4} x^{2} + 5 \, a^{10} b^{3} x + a^{11} b^{2}\right)}}, -\frac{105 \, {\left(B a^{6} + 9 \, A a^{5} b + {\left(B a b^{5} + 9 \, A b^{6}\right)} x^{5} + 5 \, {\left(B a^{2} b^{4} + 9 \, A a b^{5}\right)} x^{4} + 10 \, {\left(B a^{3} b^{3} + 9 \, A a^{2} b^{4}\right)} x^{3} + 10 \, {\left(B a^{4} b^{2} + 9 \, A a^{3} b^{3}\right)} x^{2} + 5 \, {\left(B a^{5} b + 9 \, A a^{4} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(105 \, B a^{6} b - 2895 \, A a^{5} b^{2} - 105 \, {\left(B a^{2} b^{5} + 9 \, A a b^{6}\right)} x^{4} - 490 \, {\left(B a^{3} b^{4} + 9 \, A a^{2} b^{5}\right)} x^{3} - 896 \, {\left(B a^{4} b^{3} + 9 \, A a^{3} b^{4}\right)} x^{2} - 790 \, {\left(B a^{5} b^{2} + 9 \, A a^{4} b^{3}\right)} x\right)} \sqrt{x}}{1920 \, {\left(a^{6} b^{7} x^{5} + 5 \, a^{7} b^{6} x^{4} + 10 \, a^{8} b^{5} x^{3} + 10 \, a^{9} b^{4} x^{2} + 5 \, a^{10} b^{3} x + a^{11} b^{2}\right)}}\right]"," ",0,"[-1/3840*(105*(B*a^6 + 9*A*a^5*b + (B*a*b^5 + 9*A*b^6)*x^5 + 5*(B*a^2*b^4 + 9*A*a*b^5)*x^4 + 10*(B*a^3*b^3 + 9*A*a^2*b^4)*x^3 + 10*(B*a^4*b^2 + 9*A*a^3*b^3)*x^2 + 5*(B*a^5*b + 9*A*a^4*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(105*B*a^6*b - 2895*A*a^5*b^2 - 105*(B*a^2*b^5 + 9*A*a*b^6)*x^4 - 490*(B*a^3*b^4 + 9*A*a^2*b^5)*x^3 - 896*(B*a^4*b^3 + 9*A*a^3*b^4)*x^2 - 790*(B*a^5*b^2 + 9*A*a^4*b^3)*x)*sqrt(x))/(a^6*b^7*x^5 + 5*a^7*b^6*x^4 + 10*a^8*b^5*x^3 + 10*a^9*b^4*x^2 + 5*a^10*b^3*x + a^11*b^2), -1/1920*(105*(B*a^6 + 9*A*a^5*b + (B*a*b^5 + 9*A*b^6)*x^5 + 5*(B*a^2*b^4 + 9*A*a*b^5)*x^4 + 10*(B*a^3*b^3 + 9*A*a^2*b^4)*x^3 + 10*(B*a^4*b^2 + 9*A*a^3*b^3)*x^2 + 5*(B*a^5*b + 9*A*a^4*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (105*B*a^6*b - 2895*A*a^5*b^2 - 105*(B*a^2*b^5 + 9*A*a*b^6)*x^4 - 490*(B*a^3*b^4 + 9*A*a^2*b^5)*x^3 - 896*(B*a^4*b^3 + 9*A*a^3*b^4)*x^2 - 790*(B*a^5*b^2 + 9*A*a^4*b^3)*x)*sqrt(x))/(a^6*b^7*x^5 + 5*a^7*b^6*x^4 + 10*a^8*b^5*x^3 + 10*a^9*b^4*x^2 + 5*a^10*b^3*x + a^11*b^2)]","A",0
780,1,673,0,0.477859," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left({\left(B a b^{5} - 11 \, A b^{6}\right)} x^{6} + 5 \, {\left(B a^{2} b^{4} - 11 \, A a b^{5}\right)} x^{5} + 10 \, {\left(B a^{3} b^{3} - 11 \, A a^{2} b^{4}\right)} x^{4} + 10 \, {\left(B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} x^{3} + 5 \, {\left(B a^{5} b - 11 \, A a^{4} b^{2}\right)} x^{2} + {\left(B a^{6} - 11 \, A a^{5} b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a + 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) - 2 \, {\left(1280 \, A a^{6} b - 315 \, {\left(B a^{2} b^{5} - 11 \, A a b^{6}\right)} x^{5} - 1470 \, {\left(B a^{3} b^{4} - 11 \, A a^{2} b^{5}\right)} x^{4} - 2688 \, {\left(B a^{4} b^{3} - 11 \, A a^{3} b^{4}\right)} x^{3} - 2370 \, {\left(B a^{5} b^{2} - 11 \, A a^{4} b^{3}\right)} x^{2} - 965 \, {\left(B a^{6} b - 11 \, A a^{5} b^{2}\right)} x\right)} \sqrt{x}}{1280 \, {\left(a^{7} b^{6} x^{6} + 5 \, a^{8} b^{5} x^{5} + 10 \, a^{9} b^{4} x^{4} + 10 \, a^{10} b^{3} x^{3} + 5 \, a^{11} b^{2} x^{2} + a^{12} b x\right)}}, -\frac{315 \, {\left({\left(B a b^{5} - 11 \, A b^{6}\right)} x^{6} + 5 \, {\left(B a^{2} b^{4} - 11 \, A a b^{5}\right)} x^{5} + 10 \, {\left(B a^{3} b^{3} - 11 \, A a^{2} b^{4}\right)} x^{4} + 10 \, {\left(B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} x^{3} + 5 \, {\left(B a^{5} b - 11 \, A a^{4} b^{2}\right)} x^{2} + {\left(B a^{6} - 11 \, A a^{5} b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(1280 \, A a^{6} b - 315 \, {\left(B a^{2} b^{5} - 11 \, A a b^{6}\right)} x^{5} - 1470 \, {\left(B a^{3} b^{4} - 11 \, A a^{2} b^{5}\right)} x^{4} - 2688 \, {\left(B a^{4} b^{3} - 11 \, A a^{3} b^{4}\right)} x^{3} - 2370 \, {\left(B a^{5} b^{2} - 11 \, A a^{4} b^{3}\right)} x^{2} - 965 \, {\left(B a^{6} b - 11 \, A a^{5} b^{2}\right)} x\right)} \sqrt{x}}{640 \, {\left(a^{7} b^{6} x^{6} + 5 \, a^{8} b^{5} x^{5} + 10 \, a^{9} b^{4} x^{4} + 10 \, a^{10} b^{3} x^{3} + 5 \, a^{11} b^{2} x^{2} + a^{12} b x\right)}}\right]"," ",0,"[1/1280*(315*((B*a*b^5 - 11*A*b^6)*x^6 + 5*(B*a^2*b^4 - 11*A*a*b^5)*x^5 + 10*(B*a^3*b^3 - 11*A*a^2*b^4)*x^4 + 10*(B*a^4*b^2 - 11*A*a^3*b^3)*x^3 + 5*(B*a^5*b - 11*A*a^4*b^2)*x^2 + (B*a^6 - 11*A*a^5*b)*x)*sqrt(-a*b)*log((b*x - a + 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) - 2*(1280*A*a^6*b - 315*(B*a^2*b^5 - 11*A*a*b^6)*x^5 - 1470*(B*a^3*b^4 - 11*A*a^2*b^5)*x^4 - 2688*(B*a^4*b^3 - 11*A*a^3*b^4)*x^3 - 2370*(B*a^5*b^2 - 11*A*a^4*b^3)*x^2 - 965*(B*a^6*b - 11*A*a^5*b^2)*x)*sqrt(x))/(a^7*b^6*x^6 + 5*a^8*b^5*x^5 + 10*a^9*b^4*x^4 + 10*a^10*b^3*x^3 + 5*a^11*b^2*x^2 + a^12*b*x), -1/640*(315*((B*a*b^5 - 11*A*b^6)*x^6 + 5*(B*a^2*b^4 - 11*A*a*b^5)*x^5 + 10*(B*a^3*b^3 - 11*A*a^2*b^4)*x^4 + 10*(B*a^4*b^2 - 11*A*a^3*b^3)*x^3 + 5*(B*a^5*b - 11*A*a^4*b^2)*x^2 + (B*a^6 - 11*A*a^5*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (1280*A*a^6*b - 315*(B*a^2*b^5 - 11*A*a*b^6)*x^5 - 1470*(B*a^3*b^4 - 11*A*a^2*b^5)*x^4 - 2688*(B*a^4*b^3 - 11*A*a^3*b^4)*x^3 - 2370*(B*a^5*b^2 - 11*A*a^4*b^3)*x^2 - 965*(B*a^6*b - 11*A*a^5*b^2)*x)*sqrt(x))/(a^7*b^6*x^6 + 5*a^8*b^5*x^5 + 10*a^9*b^4*x^4 + 10*a^10*b^3*x^3 + 5*a^11*b^2*x^2 + a^12*b*x)]","A",0
781,1,734,0,0.457127," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left({\left(3 \, B a b^{5} - 13 \, A b^{6}\right)} x^{7} + 5 \, {\left(3 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} x^{6} + 10 \, {\left(3 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{5} + 10 \, {\left(3 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{4} + 5 \, {\left(3 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x^{3} + {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(1280 \, A a^{6} + 3465 \, {\left(3 \, B a b^{5} - 13 \, A b^{6}\right)} x^{6} + 16170 \, {\left(3 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} x^{5} + 29568 \, {\left(3 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{4} + 26070 \, {\left(3 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{3} + 10615 \, {\left(3 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x^{2} + 1280 \, {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} x\right)} \sqrt{x}}{3840 \, {\left(a^{7} b^{5} x^{7} + 5 \, a^{8} b^{4} x^{6} + 10 \, a^{9} b^{3} x^{5} + 10 \, a^{10} b^{2} x^{4} + 5 \, a^{11} b x^{3} + a^{12} x^{2}\right)}}, \frac{3465 \, {\left({\left(3 \, B a b^{5} - 13 \, A b^{6}\right)} x^{7} + 5 \, {\left(3 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} x^{6} + 10 \, {\left(3 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{5} + 10 \, {\left(3 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{4} + 5 \, {\left(3 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x^{3} + {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(1280 \, A a^{6} + 3465 \, {\left(3 \, B a b^{5} - 13 \, A b^{6}\right)} x^{6} + 16170 \, {\left(3 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} x^{5} + 29568 \, {\left(3 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{4} + 26070 \, {\left(3 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{3} + 10615 \, {\left(3 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x^{2} + 1280 \, {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} x\right)} \sqrt{x}}{1920 \, {\left(a^{7} b^{5} x^{7} + 5 \, a^{8} b^{4} x^{6} + 10 \, a^{9} b^{3} x^{5} + 10 \, a^{10} b^{2} x^{4} + 5 \, a^{11} b x^{3} + a^{12} x^{2}\right)}}\right]"," ",0,"[-1/3840*(3465*((3*B*a*b^5 - 13*A*b^6)*x^7 + 5*(3*B*a^2*b^4 - 13*A*a*b^5)*x^6 + 10*(3*B*a^3*b^3 - 13*A*a^2*b^4)*x^5 + 10*(3*B*a^4*b^2 - 13*A*a^3*b^3)*x^4 + 5*(3*B*a^5*b - 13*A*a^4*b^2)*x^3 + (3*B*a^6 - 13*A*a^5*b)*x^2)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(1280*A*a^6 + 3465*(3*B*a*b^5 - 13*A*b^6)*x^6 + 16170*(3*B*a^2*b^4 - 13*A*a*b^5)*x^5 + 29568*(3*B*a^3*b^3 - 13*A*a^2*b^4)*x^4 + 26070*(3*B*a^4*b^2 - 13*A*a^3*b^3)*x^3 + 10615*(3*B*a^5*b - 13*A*a^4*b^2)*x^2 + 1280*(3*B*a^6 - 13*A*a^5*b)*x)*sqrt(x))/(a^7*b^5*x^7 + 5*a^8*b^4*x^6 + 10*a^9*b^3*x^5 + 10*a^10*b^2*x^4 + 5*a^11*b*x^3 + a^12*x^2), 1/1920*(3465*((3*B*a*b^5 - 13*A*b^6)*x^7 + 5*(3*B*a^2*b^4 - 13*A*a*b^5)*x^6 + 10*(3*B*a^3*b^3 - 13*A*a^2*b^4)*x^5 + 10*(3*B*a^4*b^2 - 13*A*a^3*b^3)*x^4 + 5*(3*B*a^5*b - 13*A*a^4*b^2)*x^3 + (3*B*a^6 - 13*A*a^5*b)*x^2)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (1280*A*a^6 + 3465*(3*B*a*b^5 - 13*A*b^6)*x^6 + 16170*(3*B*a^2*b^4 - 13*A*a*b^5)*x^5 + 29568*(3*B*a^3*b^3 - 13*A*a^2*b^4)*x^4 + 26070*(3*B*a^4*b^2 - 13*A*a^3*b^3)*x^3 + 10615*(3*B*a^5*b - 13*A*a^4*b^2)*x^2 + 1280*(3*B*a^6 - 13*A*a^5*b)*x)*sqrt(x))/(a^7*b^5*x^7 + 5*a^8*b^4*x^6 + 10*a^9*b^3*x^5 + 10*a^10*b^2*x^4 + 5*a^11*b*x^3 + a^12*x^2)]","A",0
782,1,32,0,0.418889," ","integrate(x^(7/2)*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2}{1287} \, {\left(99 \, B b x^{6} + 143 \, A a x^{4} + 117 \, {\left(B a + A b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/1287*(99*B*b*x^6 + 143*A*a*x^4 + 117*(B*a + A*b)*x^5)*sqrt(x)","A",0
783,1,32,0,0.404816," ","integrate(x^(5/2)*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2}{693} \, {\left(63 \, B b x^{5} + 99 \, A a x^{3} + 77 \, {\left(B a + A b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/693*(63*B*b*x^5 + 99*A*a*x^3 + 77*(B*a + A*b)*x^4)*sqrt(x)","A",0
784,1,32,0,0.413656," ","integrate(x^(3/2)*(B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B b x^{4} + 63 \, A a x^{2} + 45 \, {\left(B a + A b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/315*(35*B*b*x^4 + 63*A*a*x^2 + 45*(B*a + A*b)*x^3)*sqrt(x)","A",0
785,1,30,0,0.405674," ","integrate((B*x+A)*x^(1/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, B b x^{3} + 35 \, A a x + 21 \, {\left(B a + A b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/105*(15*B*b*x^3 + 35*A*a*x + 21*(B*a + A*b)*x^2)*sqrt(x)","A",0
786,1,27,0,0.409241," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(3 \, B b x^{2} + 15 \, A a + 5 \, {\left(B a + A b\right)} x\right)} \sqrt{x}"," ",0,"2/15*(3*B*b*x^2 + 15*A*a + 5*(B*a + A*b)*x)*sqrt(x)","A",0
787,1,26,0,0.420635," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b x^{2} - 3 \, A a + 3 \, {\left(B a + A b\right)} x\right)}}{3 \, \sqrt{x}}"," ",0,"2/3*(B*b*x^2 - 3*A*a + 3*(B*a + A*b)*x)/sqrt(x)","A",0
788,1,27,0,0.420956," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b x^{2} - A a - 3 \, {\left(B a + A b\right)} x\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(3*B*b*x^2 - A*a - 3*(B*a + A*b)*x)/x^(3/2)","A",0
789,1,27,0,0.403730," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, B b x^{2} + 3 \, A a + 5 \, {\left(B a + A b\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(15*B*b*x^2 + 3*A*a + 5*(B*a + A*b)*x)/x^(5/2)","A",0
790,1,27,0,0.418104," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/x^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, B b x^{2} + 15 \, A a + 21 \, {\left(B a + A b\right)} x\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"-2/105*(35*B*b*x^2 + 15*A*a + 21*(B*a + A*b)*x)/x^(7/2)","A",0
791,1,78,0,0.417660," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2}{109395} \, {\left(6435 \, B b^{3} x^{8} + 12155 \, A a^{3} x^{4} + 7293 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{7} + 25245 \, {\left(B a^{2} b + A a b^{2}\right)} x^{6} + 9945 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/109395*(6435*B*b^3*x^8 + 12155*A*a^3*x^4 + 7293*(3*B*a*b^2 + A*b^3)*x^7 + 25245*(B*a^2*b + A*a*b^2)*x^6 + 9945*(B*a^3 + 3*A*a^2*b)*x^5)*sqrt(x)","A",0
792,1,78,0,0.420918," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3003 \, B b^{3} x^{7} + 6435 \, A a^{3} x^{3} + 3465 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 12285 \, {\left(B a^{2} b + A a b^{2}\right)} x^{5} + 5005 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/45045*(3003*B*b^3*x^7 + 6435*A*a^3*x^3 + 3465*(3*B*a*b^2 + A*b^3)*x^6 + 12285*(B*a^2*b + A*a*b^2)*x^5 + 5005*(B*a^3 + 3*A*a^2*b)*x^4)*sqrt(x)","A",0
793,1,78,0,0.428335," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2}{15015} \, {\left(1155 \, B b^{3} x^{6} + 3003 \, A a^{3} x^{2} + 1365 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{5} + 5005 \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} + 2145 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/15015*(1155*B*b^3*x^6 + 3003*A*a^3*x^2 + 1365*(3*B*a*b^2 + A*b^3)*x^5 + 5005*(B*a^2*b + A*a*b^2)*x^4 + 2145*(B*a^3 + 3*A*a^2*b)*x^3)*sqrt(x)","A",0
794,1,76,0,0.412756," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B b^{3} x^{5} + 1155 \, A a^{3} x + 385 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{4} + 1485 \, {\left(B a^{2} b + A a b^{2}\right)} x^{3} + 693 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/3465*(315*B*b^3*x^5 + 1155*A*a^3*x + 385*(3*B*a*b^2 + A*b^3)*x^4 + 1485*(B*a^2*b + A*a*b^2)*x^3 + 693*(B*a^3 + 3*A*a^2*b)*x^2)*sqrt(x)","A",0
795,1,73,0,0.413884," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B b^{3} x^{4} + 315 \, A a^{3} + 45 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 189 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)} \sqrt{x}"," ",0,"2/315*(35*B*b^3*x^4 + 315*A*a^3 + 45*(3*B*a*b^2 + A*b^3)*x^3 + 189*(B*a^2*b + A*a*b^2)*x^2 + 105*(B*a^3 + 3*A*a^2*b)*x)*sqrt(x)","A",0
796,1,73,0,0.431509," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} x^{4} - 35 \, A a^{3} + 7 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 35 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{35 \, \sqrt{x}}"," ",0,"2/35*(5*B*b^3*x^4 - 35*A*a^3 + 7*(3*B*a*b^2 + A*b^3)*x^3 + 35*(B*a^2*b + A*a*b^2)*x^2 + 35*(B*a^3 + 3*A*a^2*b)*x)/sqrt(x)","A",0
797,1,73,0,0.421368," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{3} x^{4} - 5 \, A a^{3} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 45 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} - 15 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{15 \, x^{\frac{3}{2}}}"," ",0,"2/15*(3*B*b^3*x^4 - 5*A*a^3 + 5*(3*B*a*b^2 + A*b^3)*x^3 + 45*(B*a^2*b + A*a*b^2)*x^2 - 15*(B*a^3 + 3*A*a^2*b)*x)/x^(3/2)","A",0
798,1,73,0,0.414600," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} x^{4} - 3 \, A a^{3} + 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} - 45 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} - 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(5*B*b^3*x^4 - 3*A*a^3 + 15*(3*B*a*b^2 + A*b^3)*x^3 - 45*(B*a^2*b + A*a*b^2)*x^2 - 5*(B*a^3 + 3*A*a^2*b)*x)/x^(5/2)","A",0
799,1,73,0,0.412770," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{3} x^{4} - 5 \, A a^{3} - 35 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} - 35 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} - 7 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{35 \, x^{\frac{7}{2}}}"," ",0,"2/35*(35*B*b^3*x^4 - 5*A*a^3 - 35*(3*B*a*b^2 + A*b^3)*x^3 - 35*(B*a^2*b + A*a*b^2)*x^2 - 7*(B*a^3 + 3*A*a^2*b)*x)/x^(7/2)","A",0
800,1,124,0,0.429040," ","integrate(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2}{2909907} \, {\left(138567 \, B b^{5} x^{10} + 323323 \, A a^{5} x^{4} + 153153 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{9} + 855855 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 1939938 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{7} + 1119195 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} + 264537 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/2909907*(138567*B*b^5*x^10 + 323323*A*a^5*x^4 + 153153*(5*B*a*b^4 + A*b^5)*x^9 + 855855*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 1939938*(B*a^3*b^2 + A*a^2*b^3)*x^7 + 1119195*(B*a^4*b + 2*A*a^3*b^2)*x^6 + 264537*(B*a^5 + 5*A*a^4*b)*x^5)*sqrt(x)","A",0
801,1,124,0,0.429685," ","integrate(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2}{2909907} \, {\left(153153 \, B b^{5} x^{9} + 415701 \, A a^{5} x^{3} + 171171 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{8} + 969969 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{7} + 2238390 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 1322685 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{5} + 323323 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/2909907*(153153*B*b^5*x^9 + 415701*A*a^5*x^3 + 171171*(5*B*a*b^4 + A*b^5)*x^8 + 969969*(2*B*a^2*b^3 + A*a*b^4)*x^7 + 2238390*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 1322685*(B*a^4*b + 2*A*a^3*b^2)*x^5 + 323323*(B*a^5 + 5*A*a^4*b)*x^4)*sqrt(x)","A",0
802,1,124,0,0.439496," ","integrate(x^(3/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2}{765765} \, {\left(45045 \, B b^{5} x^{8} + 153153 \, A a^{5} x^{2} + 51051 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{7} + 294525 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{6} + 696150 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{5} + 425425 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 109395 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/765765*(45045*B*b^5*x^8 + 153153*A*a^5*x^2 + 51051*(5*B*a*b^4 + A*b^5)*x^7 + 294525*(2*B*a^2*b^3 + A*a*b^4)*x^6 + 696150*(B*a^3*b^2 + A*a^2*b^3)*x^5 + 425425*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 109395*(B*a^5 + 5*A*a^4*b)*x^3)*sqrt(x)","A",0
803,1,122,0,0.429079," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3003 \, B b^{5} x^{7} + 15015 \, A a^{5} x + 3465 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{6} + 20475 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{5} + 50050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{4} + 32175 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{3} + 9009 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/45045*(3003*B*b^5*x^7 + 15015*A*a^5*x + 3465*(5*B*a*b^4 + A*b^5)*x^6 + 20475*(2*B*a^2*b^3 + A*a*b^4)*x^5 + 50050*(B*a^3*b^2 + A*a^2*b^3)*x^4 + 32175*(B*a^4*b + 2*A*a^3*b^2)*x^3 + 9009*(B*a^5 + 5*A*a^4*b)*x^2)*sqrt(x)","A",0
804,1,119,0,0.416001," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{9009} \, {\left(693 \, B b^{5} x^{6} + 9009 \, A a^{5} + 819 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 5005 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 12870 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 9009 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 3003 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x\right)} \sqrt{x}"," ",0,"2/9009*(693*B*b^5*x^6 + 9009*A*a^5 + 819*(5*B*a*b^4 + A*b^5)*x^5 + 5005*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 12870*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 9009*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 3003*(B*a^5 + 5*A*a^4*b)*x)*sqrt(x)","A",0
805,1,119,0,0.466149," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B b^{5} x^{6} - 693 \, A a^{5} + 77 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 495 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 1386 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 1155 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 693 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x\right)}}{693 \, \sqrt{x}}"," ",0,"2/693*(63*B*b^5*x^6 - 693*A*a^5 + 77*(5*B*a*b^4 + A*b^5)*x^5 + 495*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 1386*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 1155*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 693*(B*a^5 + 5*A*a^4*b)*x)/sqrt(x)","A",0
806,1,119,0,0.604880," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, B b^{5} x^{6} - 21 \, A a^{5} + 9 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 63 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 210 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 315 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 63 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x\right)}}{63 \, x^{\frac{3}{2}}}"," ",0,"2/63*(7*B*b^5*x^6 - 21*A*a^5 + 9*(5*B*a*b^4 + A*b^5)*x^5 + 63*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 210*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 315*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 63*(B*a^5 + 5*A*a^4*b)*x)/x^(3/2)","A",0
807,1,119,0,0.556818," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{5} x^{6} - 21 \, A a^{5} + 21 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 175 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 1050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} - 525 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 35 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x\right)}}{105 \, x^{\frac{5}{2}}}"," ",0,"2/105*(15*B*b^5*x^6 - 21*A*a^5 + 21*(5*B*a*b^4 + A*b^5)*x^5 + 175*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 1050*(B*a^3*b^2 + A*a^2*b^3)*x^3 - 525*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 35*(B*a^5 + 5*A*a^4*b)*x)/x^(5/2)","A",0
808,1,119,0,0.437675," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(21 \, B b^{5} x^{6} - 15 \, A a^{5} + 35 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 525 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} - 1050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} - 175 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 21 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"2/105*(21*B*b^5*x^6 - 15*A*a^5 + 35*(5*B*a*b^4 + A*b^5)*x^5 + 525*(2*B*a^2*b^3 + A*a*b^4)*x^4 - 1050*(B*a^3*b^2 + A*a^2*b^3)*x^3 - 175*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 21*(B*a^5 + 5*A*a^4*b)*x)/x^(7/2)","A",0
809,1,276,0,0.466677," ","integrate(x^(7/2)*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(B a^{4} - A a^{3} b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(35 \, B b^{4} x^{4} + 315 \, B a^{4} - 315 \, A a^{3} b - 45 \, {\left(B a b^{3} - A b^{4}\right)} x^{3} + 63 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 105 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{315 \, b^{5}}, -\frac{2 \, {\left(315 \, {\left(B a^{4} - A a^{3} b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(35 \, B b^{4} x^{4} + 315 \, B a^{4} - 315 \, A a^{3} b - 45 \, {\left(B a b^{3} - A b^{4}\right)} x^{3} + 63 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 105 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{x}\right)}}{315 \, b^{5}}\right]"," ",0,"[-1/315*(315*(B*a^4 - A*a^3*b)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(35*B*b^4*x^4 + 315*B*a^4 - 315*A*a^3*b - 45*(B*a*b^3 - A*b^4)*x^3 + 63*(B*a^2*b^2 - A*a*b^3)*x^2 - 105*(B*a^3*b - A*a^2*b^2)*x)*sqrt(x))/b^5, -2/315*(315*(B*a^4 - A*a^3*b)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (35*B*b^4*x^4 + 315*B*a^4 - 315*A*a^3*b - 45*(B*a*b^3 - A*b^4)*x^3 + 63*(B*a^2*b^2 - A*a*b^3)*x^2 - 105*(B*a^3*b - A*a^2*b^2)*x)*sqrt(x))/b^5]","A",0
810,1,229,0,0.465360," ","integrate(x^(5/2)*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(15 \, B b^{3} x^{3} - 105 \, B a^{3} + 105 \, A a^{2} b - 21 \, {\left(B a b^{2} - A b^{3}\right)} x^{2} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{x}}{105 \, b^{4}}, \frac{2 \, {\left(105 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(15 \, B b^{3} x^{3} - 105 \, B a^{3} + 105 \, A a^{2} b - 21 \, {\left(B a b^{2} - A b^{3}\right)} x^{2} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{x}\right)}}{105 \, b^{4}}\right]"," ",0,"[-1/105*(105*(B*a^3 - A*a^2*b)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(15*B*b^3*x^3 - 105*B*a^3 + 105*A*a^2*b - 21*(B*a*b^2 - A*b^3)*x^2 + 35*(B*a^2*b - A*a*b^2)*x)*sqrt(x))/b^4, 2/105*(105*(B*a^3 - A*a^2*b)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (15*B*b^3*x^3 - 105*B*a^3 + 105*A*a^2*b - 21*(B*a*b^2 - A*b^3)*x^2 + 35*(B*a^2*b - A*a*b^2)*x)*sqrt(x))/b^4]","A",0
811,1,180,0,0.451794," ","integrate(x^(3/2)*(B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a^{2} - A a b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(3 \, B b^{2} x^{2} + 15 \, B a^{2} - 15 \, A a b - 5 \, {\left(B a b - A b^{2}\right)} x\right)} \sqrt{x}}{15 \, b^{3}}, -\frac{2 \, {\left(15 \, {\left(B a^{2} - A a b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(3 \, B b^{2} x^{2} + 15 \, B a^{2} - 15 \, A a b - 5 \, {\left(B a b - A b^{2}\right)} x\right)} \sqrt{x}\right)}}{15 \, b^{3}}\right]"," ",0,"[-1/15*(15*(B*a^2 - A*a*b)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(3*B*b^2*x^2 + 15*B*a^2 - 15*A*a*b - 5*(B*a*b - A*b^2)*x)*sqrt(x))/b^3, -2/15*(15*(B*a^2 - A*a*b)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (3*B*b^2*x^2 + 15*B*a^2 - 15*A*a*b - 5*(B*a*b - A*b^2)*x)*sqrt(x))/b^3]","A",0
812,1,129,0,0.430353," ","integrate((B*x+A)*x^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a - A b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(B b x - 3 \, B a + 3 \, A b\right)} \sqrt{x}}{3 \, b^{2}}, \frac{2 \, {\left(3 \, {\left(B a - A b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(B b x - 3 \, B a + 3 \, A b\right)} \sqrt{x}\right)}}{3 \, b^{2}}\right]"," ",0,"[-1/3*(3*(B*a - A*b)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(B*b*x - 3*B*a + 3*A*b)*sqrt(x))/b^2, 2/3*(3*(B*a - A*b)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (B*b*x - 3*B*a + 3*A*b)*sqrt(x))/b^2]","A",0
813,1,102,0,0.447294," ","integrate((B*x+A)/x^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, B a b \sqrt{x} + {\left(B a - A b\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right)}{a b^{2}}, \frac{2 \, {\left(B a b \sqrt{x} + {\left(B a - A b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right)\right)}}{a b^{2}}\right]"," ",0,"[(2*B*a*b*sqrt(x) + (B*a - A*b)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)))/(a*b^2), 2*(B*a*b*sqrt(x) + (B*a - A*b)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))))/(a*b^2)]","A",0
814,1,112,0,0.459285," ","integrate((B*x+A)/x^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, A a b \sqrt{x} - {\left(B a - A b\right)} \sqrt{-a b} x \log\left(\frac{b x - a + 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right)}{a^{2} b x}, -\frac{2 \, {\left(A a b \sqrt{x} + {\left(B a - A b\right)} \sqrt{a b} x \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right)\right)}}{a^{2} b x}\right]"," ",0,"[-(2*A*a*b*sqrt(x) - (B*a - A*b)*sqrt(-a*b)*x*log((b*x - a + 2*sqrt(-a*b)*sqrt(x))/(b*x + a)))/(a^2*b*x), -2*(A*a*b*sqrt(x) + (B*a - A*b)*sqrt(a*b)*x*arctan(sqrt(a*b)/(b*sqrt(x))))/(a^2*b*x)]","A",0
815,1,146,0,0.454010," ","integrate((B*x+A)/x^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a - A b\right)} x^{2} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(A a + 3 \, {\left(B a - A b\right)} x\right)} \sqrt{x}}{3 \, a^{2} x^{2}}, \frac{2 \, {\left(3 \, {\left(B a - A b\right)} x^{2} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(A a + 3 \, {\left(B a - A b\right)} x\right)} \sqrt{x}\right)}}{3 \, a^{2} x^{2}}\right]"," ",0,"[-1/3*(3*(B*a - A*b)*x^2*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(A*a + 3*(B*a - A*b)*x)*sqrt(x))/(a^2*x^2), 2/3*(3*(B*a - A*b)*x^2*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (A*a + 3*(B*a - A*b)*x)*sqrt(x))/(a^2*x^2)]","A",0
816,1,195,0,0.554632," ","integrate((B*x+A)/x^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a b - A b^{2}\right)} x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(3 \, A a^{2} - 15 \, {\left(B a b - A b^{2}\right)} x^{2} + 5 \, {\left(B a^{2} - A a b\right)} x\right)} \sqrt{x}}{15 \, a^{3} x^{3}}, -\frac{2 \, {\left(15 \, {\left(B a b - A b^{2}\right)} x^{3} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) + {\left(3 \, A a^{2} - 15 \, {\left(B a b - A b^{2}\right)} x^{2} + 5 \, {\left(B a^{2} - A a b\right)} x\right)} \sqrt{x}\right)}}{15 \, a^{3} x^{3}}\right]"," ",0,"[-1/15*(15*(B*a*b - A*b^2)*x^3*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(3*A*a^2 - 15*(B*a*b - A*b^2)*x^2 + 5*(B*a^2 - A*a*b)*x)*sqrt(x))/(a^3*x^3), -2/15*(15*(B*a*b - A*b^2)*x^3*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) + (3*A*a^2 - 15*(B*a*b - A*b^2)*x^2 + 5*(B*a^2 - A*a*b)*x)*sqrt(x))/(a^3*x^3)]","A",0
817,1,246,0,0.656454," ","integrate((B*x+A)/x^(9/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B a b^{2} - A b^{3}\right)} x^{4} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(15 \, A a^{3} + 105 \, {\left(B a b^{2} - A b^{3}\right)} x^{3} - 35 \, {\left(B a^{2} b - A a b^{2}\right)} x^{2} + 21 \, {\left(B a^{3} - A a^{2} b\right)} x\right)} \sqrt{x}}{105 \, a^{4} x^{4}}, \frac{2 \, {\left(105 \, {\left(B a b^{2} - A b^{3}\right)} x^{4} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(15 \, A a^{3} + 105 \, {\left(B a b^{2} - A b^{3}\right)} x^{3} - 35 \, {\left(B a^{2} b - A a b^{2}\right)} x^{2} + 21 \, {\left(B a^{3} - A a^{2} b\right)} x\right)} \sqrt{x}\right)}}{105 \, a^{4} x^{4}}\right]"," ",0,"[-1/105*(105*(B*a*b^2 - A*b^3)*x^4*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(15*A*a^3 + 105*(B*a*b^2 - A*b^3)*x^3 - 35*(B*a^2*b - A*a*b^2)*x^2 + 21*(B*a^3 - A*a^2*b)*x)*sqrt(x))/(a^4*x^4), 2/105*(105*(B*a*b^2 - A*b^3)*x^4*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (15*A*a^3 + 105*(B*a*b^2 - A*b^3)*x^3 - 35*(B*a^2*b - A*a*b^2)*x^2 + 21*(B*a^3 - A*a^2*b)*x)*sqrt(x))/(a^4*x^4)]","A",0
818,1,408,0,0.474934," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} + 2 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(24 \, B b^{4} x^{4} + 945 \, B a^{4} - 525 \, A a^{3} b - 8 \, {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} x^{3} + 56 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} + 175 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{120 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} + 2 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(24 \, B b^{4} x^{4} + 945 \, B a^{4} - 525 \, A a^{3} b - 8 \, {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} x^{3} + 56 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} + 175 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{60 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[-1/120*(105*(9*B*a^4 - 5*A*a^3*b + (9*B*a^2*b^2 - 5*A*a*b^3)*x^2 + 2*(9*B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(24*B*b^4*x^4 + 945*B*a^4 - 525*A*a^3*b - 8*(9*B*a*b^3 - 5*A*b^4)*x^3 + 56*(9*B*a^2*b^2 - 5*A*a*b^3)*x^2 + 175*(9*B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/60*(105*(9*B*a^4 - 5*A*a^3*b + (9*B*a^2*b^2 - 5*A*a*b^3)*x^2 + 2*(9*B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (24*B*b^4*x^4 + 945*B*a^4 - 525*A*a^3*b - 8*(9*B*a*b^3 - 5*A*b^4)*x^3 + 56*(9*B*a^2*b^2 - 5*A*a*b^3)*x^2 + 175*(9*B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","A",0
819,1,349,0,0.428456," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b + {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{2} + 2 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(8 \, B b^{3} x^{3} - 105 \, B a^{3} + 45 \, A a^{2} b - 8 \, {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{2} - 25 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{x}}{24 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, \frac{15 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b + {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{2} + 2 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(8 \, B b^{3} x^{3} - 105 \, B a^{3} + 45 \, A a^{2} b - 8 \, {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{2} - 25 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{x}}{12 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[-1/24*(15*(7*B*a^3 - 3*A*a^2*b + (7*B*a*b^2 - 3*A*b^3)*x^2 + 2*(7*B*a^2*b - 3*A*a*b^2)*x)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(8*B*b^3*x^3 - 105*B*a^3 + 45*A*a^2*b - 8*(7*B*a*b^2 - 3*A*b^3)*x^2 - 25*(7*B*a^2*b - 3*A*a*b^2)*x)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), 1/12*(15*(7*B*a^3 - 3*A*a^2*b + (7*B*a*b^2 - 3*A*b^3)*x^2 + 2*(7*B*a^2*b - 3*A*a*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (8*B*b^3*x^3 - 105*B*a^3 + 45*A*a^2*b - 8*(7*B*a*b^2 - 3*A*b^3)*x^2 - 25*(7*B*a^2*b - 3*A*a*b^2)*x)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
820,1,319,0,0.440599," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, B a^{3} - A a^{2} b + {\left(5 \, B a b^{2} - A b^{3}\right)} x^{2} + 2 \, {\left(5 \, B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(8 \, B a b^{3} x^{2} + 15 \, B a^{3} b - 3 \, A a^{2} b^{2} + 5 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x\right)} \sqrt{x}}{8 \, {\left(a b^{6} x^{2} + 2 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}, \frac{3 \, {\left(5 \, B a^{3} - A a^{2} b + {\left(5 \, B a b^{2} - A b^{3}\right)} x^{2} + 2 \, {\left(5 \, B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(8 \, B a b^{3} x^{2} + 15 \, B a^{3} b - 3 \, A a^{2} b^{2} + 5 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x\right)} \sqrt{x}}{4 \, {\left(a b^{6} x^{2} + 2 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}\right]"," ",0,"[1/8*(3*(5*B*a^3 - A*a^2*b + (5*B*a*b^2 - A*b^3)*x^2 + 2*(5*B*a^2*b - A*a*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(8*B*a*b^3*x^2 + 15*B*a^3*b - 3*A*a^2*b^2 + 5*(5*B*a^2*b^2 - A*a*b^3)*x)*sqrt(x))/(a*b^6*x^2 + 2*a^2*b^5*x + a^3*b^4), 1/4*(3*(5*B*a^3 - A*a^2*b + (5*B*a*b^2 - A*b^3)*x^2 + 2*(5*B*a^2*b - A*a*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (8*B*a*b^3*x^2 + 15*B*a^3*b - 3*A*a^2*b^2 + 5*(5*B*a^2*b^2 - A*a*b^3)*x)*sqrt(x))/(a*b^6*x^2 + 2*a^2*b^5*x + a^3*b^4)]","A",0
821,1,291,0,0.448906," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B a^{3} + A a^{2} b + {\left(3 \, B a b^{2} + A b^{3}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b + A a b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(3 \, B a^{3} b + A a^{2} b^{2} + {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{2} b^{5} x^{2} + 2 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}, -\frac{{\left(3 \, B a^{3} + A a^{2} b + {\left(3 \, B a b^{2} + A b^{3}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b + A a b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(3 \, B a^{3} b + A a^{2} b^{2} + {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x\right)} \sqrt{x}}{4 \, {\left(a^{2} b^{5} x^{2} + 2 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}\right]"," ",0,"[-1/8*((3*B*a^3 + A*a^2*b + (3*B*a*b^2 + A*b^3)*x^2 + 2*(3*B*a^2*b + A*a*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(3*B*a^3*b + A*a^2*b^2 + (5*B*a^2*b^2 - A*a*b^3)*x)*sqrt(x))/(a^2*b^5*x^2 + 2*a^3*b^4*x + a^4*b^3), -1/4*((3*B*a^3 + A*a^2*b + (3*B*a*b^2 + A*b^3)*x^2 + 2*(3*B*a^2*b + A*a*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (3*B*a^3*b + A*a^2*b^2 + (5*B*a^2*b^2 - A*a*b^3)*x)*sqrt(x))/(a^2*b^5*x^2 + 2*a^3*b^4*x + a^4*b^3)]","A",0
822,1,291,0,0.450467," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2)/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{3} + 3 \, A a^{2} b + {\left(B a b^{2} + 3 \, A b^{3}\right)} x^{2} + 2 \, {\left(B a^{2} b + 3 \, A a b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2} - {\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{3} b^{4} x^{2} + 2 \, a^{4} b^{3} x + a^{5} b^{2}\right)}}, -\frac{{\left(B a^{3} + 3 \, A a^{2} b + {\left(B a b^{2} + 3 \, A b^{3}\right)} x^{2} + 2 \, {\left(B a^{2} b + 3 \, A a b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(B a^{3} b - 5 \, A a^{2} b^{2} - {\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} x\right)} \sqrt{x}}{4 \, {\left(a^{3} b^{4} x^{2} + 2 \, a^{4} b^{3} x + a^{5} b^{2}\right)}}\right]"," ",0,"[-1/8*((B*a^3 + 3*A*a^2*b + (B*a*b^2 + 3*A*b^3)*x^2 + 2*(B*a^2*b + 3*A*a*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(B*a^3*b - 5*A*a^2*b^2 - (B*a^2*b^2 + 3*A*a*b^3)*x)*sqrt(x))/(a^3*b^4*x^2 + 2*a^4*b^3*x + a^5*b^2), -1/4*((B*a^3 + 3*A*a^2*b + (B*a*b^2 + 3*A*b^3)*x^2 + 2*(B*a^2*b + 3*A*a*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (B*a^3*b - 5*A*a^2*b^2 - (B*a^2*b^2 + 3*A*a*b^3)*x)*sqrt(x))/(a^3*b^4*x^2 + 2*a^4*b^3*x + a^5*b^2)]","A",0
823,1,331,0,0.426176," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(B a b^{2} - 5 \, A b^{3}\right)} x^{3} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + {\left(B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a + 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) - 2 \, {\left(8 \, A a^{3} b - 3 \, {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} - 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{4} b^{3} x^{3} + 2 \, a^{5} b^{2} x^{2} + a^{6} b x\right)}}, -\frac{3 \, {\left({\left(B a b^{2} - 5 \, A b^{3}\right)} x^{3} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + {\left(B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(8 \, A a^{3} b - 3 \, {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} - 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{4 \, {\left(a^{4} b^{3} x^{3} + 2 \, a^{5} b^{2} x^{2} + a^{6} b x\right)}}\right]"," ",0,"[1/8*(3*((B*a*b^2 - 5*A*b^3)*x^3 + 2*(B*a^2*b - 5*A*a*b^2)*x^2 + (B*a^3 - 5*A*a^2*b)*x)*sqrt(-a*b)*log((b*x - a + 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) - 2*(8*A*a^3*b - 3*(B*a^2*b^2 - 5*A*a*b^3)*x^2 - 5*(B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(a^4*b^3*x^3 + 2*a^5*b^2*x^2 + a^6*b*x), -1/4*(3*((B*a*b^2 - 5*A*b^3)*x^3 + 2*(B*a^2*b - 5*A*a*b^2)*x^2 + (B*a^3 - 5*A*a^2*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (8*A*a^3*b - 3*(B*a^2*b^2 - 5*A*a*b^3)*x^2 - 5*(B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(a^4*b^3*x^3 + 2*a^5*b^2*x^2 + a^6*b*x)]","A",0
824,1,380,0,0.446513," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{4} + 2 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(8 \, A a^{3} + 15 \, {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{3} + 25 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x\right)} \sqrt{x}}{24 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}, \frac{15 \, {\left({\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{4} + 2 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(8 \, A a^{3} + 15 \, {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{3} + 25 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x\right)} \sqrt{x}}{12 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}\right]"," ",0,"[-1/24*(15*((3*B*a*b^2 - 7*A*b^3)*x^4 + 2*(3*B*a^2*b - 7*A*a*b^2)*x^3 + (3*B*a^3 - 7*A*a^2*b)*x^2)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(8*A*a^3 + 15*(3*B*a*b^2 - 7*A*b^3)*x^3 + 25*(3*B*a^2*b - 7*A*a*b^2)*x^2 + 8*(3*B*a^3 - 7*A*a^2*b)*x)*sqrt(x))/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2), 1/12*(15*((3*B*a*b^2 - 7*A*b^3)*x^4 + 2*(3*B*a^2*b - 7*A*a*b^2)*x^3 + (3*B*a^3 - 7*A*a^2*b)*x^2)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (8*A*a^3 + 15*(3*B*a*b^2 - 7*A*b^3)*x^3 + 25*(3*B*a^2*b - 7*A*a*b^2)*x^2 + 8*(3*B*a^3 - 7*A*a^2*b)*x)*sqrt(x))/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2)]","A",0
825,1,437,0,0.462281," ","integrate((B*x+A)/x^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{5} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{4} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(24 \, A a^{4} - 105 \, {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{4} - 175 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{3} - 56 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} x\right)} \sqrt{x}}{120 \, {\left(a^{5} b^{2} x^{5} + 2 \, a^{6} b x^{4} + a^{7} x^{3}\right)}}, -\frac{105 \, {\left({\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{5} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{4} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) + {\left(24 \, A a^{4} - 105 \, {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{4} - 175 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{3} - 56 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} x\right)} \sqrt{x}}{60 \, {\left(a^{5} b^{2} x^{5} + 2 \, a^{6} b x^{4} + a^{7} x^{3}\right)}}\right]"," ",0,"[-1/120*(105*((5*B*a*b^3 - 9*A*b^4)*x^5 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*x^4 + (5*B*a^3*b - 9*A*a^2*b^2)*x^3)*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(24*A*a^4 - 105*(5*B*a*b^3 - 9*A*b^4)*x^4 - 175*(5*B*a^2*b^2 - 9*A*a*b^3)*x^3 - 56*(5*B*a^3*b - 9*A*a^2*b^2)*x^2 + 8*(5*B*a^4 - 9*A*a^3*b)*x)*sqrt(x))/(a^5*b^2*x^5 + 2*a^6*b*x^4 + a^7*x^3), -1/60*(105*((5*B*a*b^3 - 9*A*b^4)*x^5 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*x^4 + (5*B*a^3*b - 9*A*a^2*b^2)*x^3)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) + (24*A*a^4 - 105*(5*B*a*b^3 - 9*A*b^4)*x^4 - 175*(5*B*a^2*b^2 - 9*A*a*b^3)*x^3 - 56*(5*B*a^3*b - 9*A*a^2*b^2)*x^2 + 8*(5*B*a^4 - 9*A*a^3*b)*x)*sqrt(x))/(a^5*b^2*x^5 + 2*a^6*b*x^4 + a^7*x^3)]","A",0
826,1,644,0,0.454367," ","integrate(x^(11/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left(13 \, B a^{6} - 5 \, A a^{5} b + {\left(13 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} x^{4} + 4 \, {\left(13 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} x^{3} + 6 \, {\left(13 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} x^{2} + 4 \, {\left(13 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(384 \, B b^{6} x^{6} + 45045 \, B a^{6} - 17325 \, A a^{5} b - 128 \, {\left(13 \, B a b^{5} - 5 \, A b^{6}\right)} x^{5} + 1408 \, {\left(13 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} x^{4} + 9207 \, {\left(13 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} x^{3} + 16863 \, {\left(13 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} x^{2} + 12705 \, {\left(13 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} x\right)} \sqrt{x}}{1920 \, {\left(b^{11} x^{4} + 4 \, a b^{10} x^{3} + 6 \, a^{2} b^{9} x^{2} + 4 \, a^{3} b^{8} x + a^{4} b^{7}\right)}}, -\frac{3465 \, {\left(13 \, B a^{6} - 5 \, A a^{5} b + {\left(13 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} x^{4} + 4 \, {\left(13 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} x^{3} + 6 \, {\left(13 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} x^{2} + 4 \, {\left(13 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(384 \, B b^{6} x^{6} + 45045 \, B a^{6} - 17325 \, A a^{5} b - 128 \, {\left(13 \, B a b^{5} - 5 \, A b^{6}\right)} x^{5} + 1408 \, {\left(13 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} x^{4} + 9207 \, {\left(13 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} x^{3} + 16863 \, {\left(13 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} x^{2} + 12705 \, {\left(13 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} x\right)} \sqrt{x}}{960 \, {\left(b^{11} x^{4} + 4 \, a b^{10} x^{3} + 6 \, a^{2} b^{9} x^{2} + 4 \, a^{3} b^{8} x + a^{4} b^{7}\right)}}\right]"," ",0,"[-1/1920*(3465*(13*B*a^6 - 5*A*a^5*b + (13*B*a^2*b^4 - 5*A*a*b^5)*x^4 + 4*(13*B*a^3*b^3 - 5*A*a^2*b^4)*x^3 + 6*(13*B*a^4*b^2 - 5*A*a^3*b^3)*x^2 + 4*(13*B*a^5*b - 5*A*a^4*b^2)*x)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(384*B*b^6*x^6 + 45045*B*a^6 - 17325*A*a^5*b - 128*(13*B*a*b^5 - 5*A*b^6)*x^5 + 1408*(13*B*a^2*b^4 - 5*A*a*b^5)*x^4 + 9207*(13*B*a^3*b^3 - 5*A*a^2*b^4)*x^3 + 16863*(13*B*a^4*b^2 - 5*A*a^3*b^3)*x^2 + 12705*(13*B*a^5*b - 5*A*a^4*b^2)*x)*sqrt(x))/(b^11*x^4 + 4*a*b^10*x^3 + 6*a^2*b^9*x^2 + 4*a^3*b^8*x + a^4*b^7), -1/960*(3465*(13*B*a^6 - 5*A*a^5*b + (13*B*a^2*b^4 - 5*A*a*b^5)*x^4 + 4*(13*B*a^3*b^3 - 5*A*a^2*b^4)*x^3 + 6*(13*B*a^4*b^2 - 5*A*a^3*b^3)*x^2 + 4*(13*B*a^5*b - 5*A*a^4*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (384*B*b^6*x^6 + 45045*B*a^6 - 17325*A*a^5*b - 128*(13*B*a*b^5 - 5*A*b^6)*x^5 + 1408*(13*B*a^2*b^4 - 5*A*a*b^5)*x^4 + 9207*(13*B*a^3*b^3 - 5*A*a^2*b^4)*x^3 + 16863*(13*B*a^4*b^2 - 5*A*a^3*b^3)*x^2 + 12705*(13*B*a^5*b - 5*A*a^4*b^2)*x)*sqrt(x))/(b^11*x^4 + 4*a*b^10*x^3 + 6*a^2*b^9*x^2 + 4*a^3*b^8*x + a^4*b^7)]","A",0
827,1,585,0,0.558546," ","integrate(x^(9/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(11 \, B a^{5} - 3 \, A a^{4} b + {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} x^{4} + 4 \, {\left(11 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{3} + 6 \, {\left(11 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(11 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(128 \, B b^{5} x^{5} - 3465 \, B a^{5} + 945 \, A a^{4} b - 128 \, {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} x^{4} - 837 \, {\left(11 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{3} - 1533 \, {\left(11 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{2} - 1155 \, {\left(11 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x\right)} \sqrt{x}}{384 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}, \frac{315 \, {\left(11 \, B a^{5} - 3 \, A a^{4} b + {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} x^{4} + 4 \, {\left(11 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{3} + 6 \, {\left(11 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(11 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(128 \, B b^{5} x^{5} - 3465 \, B a^{5} + 945 \, A a^{4} b - 128 \, {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} x^{4} - 837 \, {\left(11 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{3} - 1533 \, {\left(11 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{2} - 1155 \, {\left(11 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x\right)} \sqrt{x}}{192 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}\right]"," ",0,"[-1/384*(315*(11*B*a^5 - 3*A*a^4*b + (11*B*a*b^4 - 3*A*b^5)*x^4 + 4*(11*B*a^2*b^3 - 3*A*a*b^4)*x^3 + 6*(11*B*a^3*b^2 - 3*A*a^2*b^3)*x^2 + 4*(11*B*a^4*b - 3*A*a^3*b^2)*x)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(128*B*b^5*x^5 - 3465*B*a^5 + 945*A*a^4*b - 128*(11*B*a*b^4 - 3*A*b^5)*x^4 - 837*(11*B*a^2*b^3 - 3*A*a*b^4)*x^3 - 1533*(11*B*a^3*b^2 - 3*A*a^2*b^3)*x^2 - 1155*(11*B*a^4*b - 3*A*a^3*b^2)*x)*sqrt(x))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6), 1/192*(315*(11*B*a^5 - 3*A*a^4*b + (11*B*a*b^4 - 3*A*b^5)*x^4 + 4*(11*B*a^2*b^3 - 3*A*a*b^4)*x^3 + 6*(11*B*a^3*b^2 - 3*A*a^2*b^3)*x^2 + 4*(11*B*a^4*b - 3*A*a^3*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (128*B*b^5*x^5 - 3465*B*a^5 + 945*A*a^4*b - 128*(11*B*a*b^4 - 3*A*b^5)*x^4 - 837*(11*B*a^2*b^3 - 3*A*a*b^4)*x^3 - 1533*(11*B*a^3*b^2 - 3*A*a^2*b^3)*x^2 - 1155*(11*B*a^4*b - 3*A*a^3*b^2)*x)*sqrt(x))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6)]","A",0
828,1,555,0,0.465971," ","integrate(x^(7/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(9 \, B a^{5} - A a^{4} b + {\left(9 \, B a b^{4} - A b^{5}\right)} x^{4} + 4 \, {\left(9 \, B a^{2} b^{3} - A a b^{4}\right)} x^{3} + 6 \, {\left(9 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(9 \, B a^{4} b - A a^{3} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(384 \, B a b^{5} x^{4} + 945 \, B a^{5} b - 105 \, A a^{4} b^{2} + 279 \, {\left(9 \, B a^{2} b^{4} - A a b^{5}\right)} x^{3} + 511 \, {\left(9 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} x^{2} + 385 \, {\left(9 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{384 \, {\left(a b^{10} x^{4} + 4 \, a^{2} b^{9} x^{3} + 6 \, a^{3} b^{8} x^{2} + 4 \, a^{4} b^{7} x + a^{5} b^{6}\right)}}, \frac{105 \, {\left(9 \, B a^{5} - A a^{4} b + {\left(9 \, B a b^{4} - A b^{5}\right)} x^{4} + 4 \, {\left(9 \, B a^{2} b^{3} - A a b^{4}\right)} x^{3} + 6 \, {\left(9 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(9 \, B a^{4} b - A a^{3} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(384 \, B a b^{5} x^{4} + 945 \, B a^{5} b - 105 \, A a^{4} b^{2} + 279 \, {\left(9 \, B a^{2} b^{4} - A a b^{5}\right)} x^{3} + 511 \, {\left(9 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} x^{2} + 385 \, {\left(9 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{192 \, {\left(a b^{10} x^{4} + 4 \, a^{2} b^{9} x^{3} + 6 \, a^{3} b^{8} x^{2} + 4 \, a^{4} b^{7} x + a^{5} b^{6}\right)}}\right]"," ",0,"[1/384*(105*(9*B*a^5 - A*a^4*b + (9*B*a*b^4 - A*b^5)*x^4 + 4*(9*B*a^2*b^3 - A*a*b^4)*x^3 + 6*(9*B*a^3*b^2 - A*a^2*b^3)*x^2 + 4*(9*B*a^4*b - A*a^3*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(384*B*a*b^5*x^4 + 945*B*a^5*b - 105*A*a^4*b^2 + 279*(9*B*a^2*b^4 - A*a*b^5)*x^3 + 511*(9*B*a^3*b^3 - A*a^2*b^4)*x^2 + 385*(9*B*a^4*b^2 - A*a^3*b^3)*x)*sqrt(x))/(a*b^10*x^4 + 4*a^2*b^9*x^3 + 6*a^3*b^8*x^2 + 4*a^4*b^7*x + a^5*b^6), 1/192*(105*(9*B*a^5 - A*a^4*b + (9*B*a*b^4 - A*b^5)*x^4 + 4*(9*B*a^2*b^3 - A*a*b^4)*x^3 + 6*(9*B*a^3*b^2 - A*a^2*b^3)*x^2 + 4*(9*B*a^4*b - A*a^3*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (384*B*a*b^5*x^4 + 945*B*a^5*b - 105*A*a^4*b^2 + 279*(9*B*a^2*b^4 - A*a*b^5)*x^3 + 511*(9*B*a^3*b^3 - A*a^2*b^4)*x^2 + 385*(9*B*a^4*b^2 - A*a^3*b^3)*x)*sqrt(x))/(a*b^10*x^4 + 4*a^2*b^9*x^3 + 6*a^3*b^8*x^2 + 4*a^4*b^7*x + a^5*b^6)]","A",0
829,1,525,0,0.468836," ","integrate(x^(5/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{5} + A a^{4} b + {\left(7 \, B a b^{4} + A b^{5}\right)} x^{4} + 4 \, {\left(7 \, B a^{2} b^{3} + A a b^{4}\right)} x^{3} + 6 \, {\left(7 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(7 \, B a^{4} b + A a^{3} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(105 \, B a^{5} b + 15 \, A a^{4} b^{2} + 3 \, {\left(93 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} x^{3} + 73 \, {\left(7 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} x^{2} + 55 \, {\left(7 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{384 \, {\left(a^{2} b^{9} x^{4} + 4 \, a^{3} b^{8} x^{3} + 6 \, a^{4} b^{7} x^{2} + 4 \, a^{5} b^{6} x + a^{6} b^{5}\right)}}, -\frac{15 \, {\left(7 \, B a^{5} + A a^{4} b + {\left(7 \, B a b^{4} + A b^{5}\right)} x^{4} + 4 \, {\left(7 \, B a^{2} b^{3} + A a b^{4}\right)} x^{3} + 6 \, {\left(7 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(7 \, B a^{4} b + A a^{3} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(105 \, B a^{5} b + 15 \, A a^{4} b^{2} + 3 \, {\left(93 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} x^{3} + 73 \, {\left(7 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} x^{2} + 55 \, {\left(7 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{192 \, {\left(a^{2} b^{9} x^{4} + 4 \, a^{3} b^{8} x^{3} + 6 \, a^{4} b^{7} x^{2} + 4 \, a^{5} b^{6} x + a^{6} b^{5}\right)}}\right]"," ",0,"[-1/384*(15*(7*B*a^5 + A*a^4*b + (7*B*a*b^4 + A*b^5)*x^4 + 4*(7*B*a^2*b^3 + A*a*b^4)*x^3 + 6*(7*B*a^3*b^2 + A*a^2*b^3)*x^2 + 4*(7*B*a^4*b + A*a^3*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(105*B*a^5*b + 15*A*a^4*b^2 + 3*(93*B*a^2*b^4 - 5*A*a*b^5)*x^3 + 73*(7*B*a^3*b^3 + A*a^2*b^4)*x^2 + 55*(7*B*a^4*b^2 + A*a^3*b^3)*x)*sqrt(x))/(a^2*b^9*x^4 + 4*a^3*b^8*x^3 + 6*a^4*b^7*x^2 + 4*a^5*b^6*x + a^6*b^5), -1/192*(15*(7*B*a^5 + A*a^4*b + (7*B*a*b^4 + A*b^5)*x^4 + 4*(7*B*a^2*b^3 + A*a*b^4)*x^3 + 6*(7*B*a^3*b^2 + A*a^2*b^3)*x^2 + 4*(7*B*a^4*b + A*a^3*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (105*B*a^5*b + 15*A*a^4*b^2 + 3*(93*B*a^2*b^4 - 5*A*a*b^5)*x^3 + 73*(7*B*a^3*b^3 + A*a^2*b^4)*x^2 + 55*(7*B*a^4*b^2 + A*a^3*b^3)*x)*sqrt(x))/(a^2*b^9*x^4 + 4*a^3*b^8*x^3 + 6*a^4*b^7*x^2 + 4*a^5*b^6*x + a^6*b^5)]","A",0
830,1,537,0,0.447448," ","integrate(x^(3/2)*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{5} + 3 \, A a^{4} b + {\left(5 \, B a b^{4} + 3 \, A b^{5}\right)} x^{4} + 4 \, {\left(5 \, B a^{2} b^{3} + 3 \, A a b^{4}\right)} x^{3} + 6 \, {\left(5 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(5 \, B a^{4} b + 3 \, A a^{3} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(15 \, B a^{5} b + 9 \, A a^{4} b^{2} - 3 \, {\left(5 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} x^{3} + {\left(73 \, B a^{3} b^{3} - 33 \, A a^{2} b^{4}\right)} x^{2} + 11 \, {\left(5 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{384 \, {\left(a^{3} b^{8} x^{4} + 4 \, a^{4} b^{7} x^{3} + 6 \, a^{5} b^{6} x^{2} + 4 \, a^{6} b^{5} x + a^{7} b^{4}\right)}}, -\frac{3 \, {\left(5 \, B a^{5} + 3 \, A a^{4} b + {\left(5 \, B a b^{4} + 3 \, A b^{5}\right)} x^{4} + 4 \, {\left(5 \, B a^{2} b^{3} + 3 \, A a b^{4}\right)} x^{3} + 6 \, {\left(5 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(5 \, B a^{4} b + 3 \, A a^{3} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(15 \, B a^{5} b + 9 \, A a^{4} b^{2} - 3 \, {\left(5 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} x^{3} + {\left(73 \, B a^{3} b^{3} - 33 \, A a^{2} b^{4}\right)} x^{2} + 11 \, {\left(5 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{192 \, {\left(a^{3} b^{8} x^{4} + 4 \, a^{4} b^{7} x^{3} + 6 \, a^{5} b^{6} x^{2} + 4 \, a^{6} b^{5} x + a^{7} b^{4}\right)}}\right]"," ",0,"[-1/384*(3*(5*B*a^5 + 3*A*a^4*b + (5*B*a*b^4 + 3*A*b^5)*x^4 + 4*(5*B*a^2*b^3 + 3*A*a*b^4)*x^3 + 6*(5*B*a^3*b^2 + 3*A*a^2*b^3)*x^2 + 4*(5*B*a^4*b + 3*A*a^3*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(15*B*a^5*b + 9*A*a^4*b^2 - 3*(5*B*a^2*b^4 + 3*A*a*b^5)*x^3 + (73*B*a^3*b^3 - 33*A*a^2*b^4)*x^2 + 11*(5*B*a^4*b^2 + 3*A*a^3*b^3)*x)*sqrt(x))/(a^3*b^8*x^4 + 4*a^4*b^7*x^3 + 6*a^5*b^6*x^2 + 4*a^6*b^5*x + a^7*b^4), -1/192*(3*(5*B*a^5 + 3*A*a^4*b + (5*B*a*b^4 + 3*A*b^5)*x^4 + 4*(5*B*a^2*b^3 + 3*A*a*b^4)*x^3 + 6*(5*B*a^3*b^2 + 3*A*a^2*b^3)*x^2 + 4*(5*B*a^4*b + 3*A*a^3*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (15*B*a^5*b + 9*A*a^4*b^2 - 3*(5*B*a^2*b^4 + 3*A*a*b^5)*x^3 + (73*B*a^3*b^3 - 33*A*a^2*b^4)*x^2 + 11*(5*B*a^4*b^2 + 3*A*a^3*b^3)*x)*sqrt(x))/(a^3*b^8*x^4 + 4*a^4*b^7*x^3 + 6*a^5*b^6*x^2 + 4*a^6*b^5*x + a^7*b^4)]","A",0
831,1,537,0,0.470025," ","integrate((B*x+A)*x^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, B a^{5} + 5 \, A a^{4} b + {\left(3 \, B a b^{4} + 5 \, A b^{5}\right)} x^{4} + 4 \, {\left(3 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} x^{3} + 6 \, {\left(3 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(3 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(9 \, B a^{5} b + 15 \, A a^{4} b^{2} - 3 \, {\left(3 \, B a^{2} b^{4} + 5 \, A a b^{5}\right)} x^{3} - 11 \, {\left(3 \, B a^{3} b^{3} + 5 \, A a^{2} b^{4}\right)} x^{2} + {\left(33 \, B a^{4} b^{2} - 73 \, A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{384 \, {\left(a^{4} b^{7} x^{4} + 4 \, a^{5} b^{6} x^{3} + 6 \, a^{6} b^{5} x^{2} + 4 \, a^{7} b^{4} x + a^{8} b^{3}\right)}}, -\frac{3 \, {\left(3 \, B a^{5} + 5 \, A a^{4} b + {\left(3 \, B a b^{4} + 5 \, A b^{5}\right)} x^{4} + 4 \, {\left(3 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} x^{3} + 6 \, {\left(3 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(3 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(9 \, B a^{5} b + 15 \, A a^{4} b^{2} - 3 \, {\left(3 \, B a^{2} b^{4} + 5 \, A a b^{5}\right)} x^{3} - 11 \, {\left(3 \, B a^{3} b^{3} + 5 \, A a^{2} b^{4}\right)} x^{2} + {\left(33 \, B a^{4} b^{2} - 73 \, A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{192 \, {\left(a^{4} b^{7} x^{4} + 4 \, a^{5} b^{6} x^{3} + 6 \, a^{6} b^{5} x^{2} + 4 \, a^{7} b^{4} x + a^{8} b^{3}\right)}}\right]"," ",0,"[-1/384*(3*(3*B*a^5 + 5*A*a^4*b + (3*B*a*b^4 + 5*A*b^5)*x^4 + 4*(3*B*a^2*b^3 + 5*A*a*b^4)*x^3 + 6*(3*B*a^3*b^2 + 5*A*a^2*b^3)*x^2 + 4*(3*B*a^4*b + 5*A*a^3*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(9*B*a^5*b + 15*A*a^4*b^2 - 3*(3*B*a^2*b^4 + 5*A*a*b^5)*x^3 - 11*(3*B*a^3*b^3 + 5*A*a^2*b^4)*x^2 + (33*B*a^4*b^2 - 73*A*a^3*b^3)*x)*sqrt(x))/(a^4*b^7*x^4 + 4*a^5*b^6*x^3 + 6*a^6*b^5*x^2 + 4*a^7*b^4*x + a^8*b^3), -1/192*(3*(3*B*a^5 + 5*A*a^4*b + (3*B*a*b^4 + 5*A*b^5)*x^4 + 4*(3*B*a^2*b^3 + 5*A*a*b^4)*x^3 + 6*(3*B*a^3*b^2 + 5*A*a^2*b^3)*x^2 + 4*(3*B*a^4*b + 5*A*a^3*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (9*B*a^5*b + 15*A*a^4*b^2 - 3*(3*B*a^2*b^4 + 5*A*a*b^5)*x^3 - 11*(3*B*a^3*b^3 + 5*A*a^2*b^4)*x^2 + (33*B*a^4*b^2 - 73*A*a^3*b^3)*x)*sqrt(x))/(a^4*b^7*x^4 + 4*a^5*b^6*x^3 + 6*a^6*b^5*x^2 + 4*a^7*b^4*x + a^8*b^3)]","A",0
832,1,523,0,0.428586," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2)/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a^{5} + 7 \, A a^{4} b + {\left(B a b^{4} + 7 \, A b^{5}\right)} x^{4} + 4 \, {\left(B a^{2} b^{3} + 7 \, A a b^{4}\right)} x^{3} + 6 \, {\left(B a^{3} b^{2} + 7 \, A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(B a^{4} b + 7 \, A a^{3} b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(15 \, B a^{5} b - 279 \, A a^{4} b^{2} - 15 \, {\left(B a^{2} b^{4} + 7 \, A a b^{5}\right)} x^{3} - 55 \, {\left(B a^{3} b^{3} + 7 \, A a^{2} b^{4}\right)} x^{2} - 73 \, {\left(B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{384 \, {\left(a^{5} b^{6} x^{4} + 4 \, a^{6} b^{5} x^{3} + 6 \, a^{7} b^{4} x^{2} + 4 \, a^{8} b^{3} x + a^{9} b^{2}\right)}}, -\frac{15 \, {\left(B a^{5} + 7 \, A a^{4} b + {\left(B a b^{4} + 7 \, A b^{5}\right)} x^{4} + 4 \, {\left(B a^{2} b^{3} + 7 \, A a b^{4}\right)} x^{3} + 6 \, {\left(B a^{3} b^{2} + 7 \, A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(B a^{4} b + 7 \, A a^{3} b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(15 \, B a^{5} b - 279 \, A a^{4} b^{2} - 15 \, {\left(B a^{2} b^{4} + 7 \, A a b^{5}\right)} x^{3} - 55 \, {\left(B a^{3} b^{3} + 7 \, A a^{2} b^{4}\right)} x^{2} - 73 \, {\left(B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} x\right)} \sqrt{x}}{192 \, {\left(a^{5} b^{6} x^{4} + 4 \, a^{6} b^{5} x^{3} + 6 \, a^{7} b^{4} x^{2} + 4 \, a^{8} b^{3} x + a^{9} b^{2}\right)}}\right]"," ",0,"[-1/384*(15*(B*a^5 + 7*A*a^4*b + (B*a*b^4 + 7*A*b^5)*x^4 + 4*(B*a^2*b^3 + 7*A*a*b^4)*x^3 + 6*(B*a^3*b^2 + 7*A*a^2*b^3)*x^2 + 4*(B*a^4*b + 7*A*a^3*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(15*B*a^5*b - 279*A*a^4*b^2 - 15*(B*a^2*b^4 + 7*A*a*b^5)*x^3 - 55*(B*a^3*b^3 + 7*A*a^2*b^4)*x^2 - 73*(B*a^4*b^2 + 7*A*a^3*b^3)*x)*sqrt(x))/(a^5*b^6*x^4 + 4*a^6*b^5*x^3 + 6*a^7*b^4*x^2 + 4*a^8*b^3*x + a^9*b^2), -1/192*(15*(B*a^5 + 7*A*a^4*b + (B*a*b^4 + 7*A*b^5)*x^4 + 4*(B*a^2*b^3 + 7*A*a*b^4)*x^3 + 6*(B*a^3*b^2 + 7*A*a^2*b^3)*x^2 + 4*(B*a^4*b + 7*A*a^3*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (15*B*a^5*b - 279*A*a^4*b^2 - 15*(B*a^2*b^4 + 7*A*a*b^5)*x^3 - 55*(B*a^3*b^3 + 7*A*a^2*b^4)*x^2 - 73*(B*a^4*b^2 + 7*A*a^3*b^3)*x)*sqrt(x))/(a^5*b^6*x^4 + 4*a^6*b^5*x^3 + 6*a^7*b^4*x^2 + 4*a^8*b^3*x + a^9*b^2)]","A",0
833,1,559,0,0.438064," ","integrate((B*x+A)/x^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(B a b^{4} - 9 \, A b^{5}\right)} x^{5} + 4 \, {\left(B a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{4} + 6 \, {\left(B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{3} + 4 \, {\left(B a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{2} + {\left(B a^{5} - 9 \, A a^{4} b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a + 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) - 2 \, {\left(384 \, A a^{5} b - 105 \, {\left(B a^{2} b^{4} - 9 \, A a b^{5}\right)} x^{4} - 385 \, {\left(B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} x^{3} - 511 \, {\left(B a^{4} b^{2} - 9 \, A a^{3} b^{3}\right)} x^{2} - 279 \, {\left(B a^{5} b - 9 \, A a^{4} b^{2}\right)} x\right)} \sqrt{x}}{384 \, {\left(a^{6} b^{5} x^{5} + 4 \, a^{7} b^{4} x^{4} + 6 \, a^{8} b^{3} x^{3} + 4 \, a^{9} b^{2} x^{2} + a^{10} b x\right)}}, -\frac{105 \, {\left({\left(B a b^{4} - 9 \, A b^{5}\right)} x^{5} + 4 \, {\left(B a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{4} + 6 \, {\left(B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{3} + 4 \, {\left(B a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{2} + {\left(B a^{5} - 9 \, A a^{4} b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(384 \, A a^{5} b - 105 \, {\left(B a^{2} b^{4} - 9 \, A a b^{5}\right)} x^{4} - 385 \, {\left(B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} x^{3} - 511 \, {\left(B a^{4} b^{2} - 9 \, A a^{3} b^{3}\right)} x^{2} - 279 \, {\left(B a^{5} b - 9 \, A a^{4} b^{2}\right)} x\right)} \sqrt{x}}{192 \, {\left(a^{6} b^{5} x^{5} + 4 \, a^{7} b^{4} x^{4} + 6 \, a^{8} b^{3} x^{3} + 4 \, a^{9} b^{2} x^{2} + a^{10} b x\right)}}\right]"," ",0,"[1/384*(105*((B*a*b^4 - 9*A*b^5)*x^5 + 4*(B*a^2*b^3 - 9*A*a*b^4)*x^4 + 6*(B*a^3*b^2 - 9*A*a^2*b^3)*x^3 + 4*(B*a^4*b - 9*A*a^3*b^2)*x^2 + (B*a^5 - 9*A*a^4*b)*x)*sqrt(-a*b)*log((b*x - a + 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) - 2*(384*A*a^5*b - 105*(B*a^2*b^4 - 9*A*a*b^5)*x^4 - 385*(B*a^3*b^3 - 9*A*a^2*b^4)*x^3 - 511*(B*a^4*b^2 - 9*A*a^3*b^3)*x^2 - 279*(B*a^5*b - 9*A*a^4*b^2)*x)*sqrt(x))/(a^6*b^5*x^5 + 4*a^7*b^4*x^4 + 6*a^8*b^3*x^3 + 4*a^9*b^2*x^2 + a^10*b*x), -1/192*(105*((B*a*b^4 - 9*A*b^5)*x^5 + 4*(B*a^2*b^3 - 9*A*a*b^4)*x^4 + 6*(B*a^3*b^2 - 9*A*a^2*b^3)*x^3 + 4*(B*a^4*b - 9*A*a^3*b^2)*x^2 + (B*a^5 - 9*A*a^4*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (384*A*a^5*b - 105*(B*a^2*b^4 - 9*A*a*b^5)*x^4 - 385*(B*a^3*b^3 - 9*A*a^2*b^4)*x^3 - 511*(B*a^4*b^2 - 9*A*a^3*b^3)*x^2 - 279*(B*a^5*b - 9*A*a^4*b^2)*x)*sqrt(x))/(a^6*b^5*x^5 + 4*a^7*b^4*x^4 + 6*a^8*b^3*x^3 + 4*a^9*b^2*x^2 + a^10*b*x)]","A",0
834,1,616,0,0.438731," ","integrate((B*x+A)/x^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left({\left(3 \, B a b^{4} - 11 \, A b^{5}\right)} x^{6} + 4 \, {\left(3 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} x^{5} + 6 \, {\left(3 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{4} + 4 \, {\left(3 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x^{3} + {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(128 \, A a^{5} + 315 \, {\left(3 \, B a b^{4} - 11 \, A b^{5}\right)} x^{5} + 1155 \, {\left(3 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} x^{4} + 1533 \, {\left(3 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{3} + 837 \, {\left(3 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x^{2} + 128 \, {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} x\right)} \sqrt{x}}{384 \, {\left(a^{6} b^{4} x^{6} + 4 \, a^{7} b^{3} x^{5} + 6 \, a^{8} b^{2} x^{4} + 4 \, a^{9} b x^{3} + a^{10} x^{2}\right)}}, \frac{315 \, {\left({\left(3 \, B a b^{4} - 11 \, A b^{5}\right)} x^{6} + 4 \, {\left(3 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} x^{5} + 6 \, {\left(3 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{4} + 4 \, {\left(3 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x^{3} + {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(128 \, A a^{5} + 315 \, {\left(3 \, B a b^{4} - 11 \, A b^{5}\right)} x^{5} + 1155 \, {\left(3 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} x^{4} + 1533 \, {\left(3 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{3} + 837 \, {\left(3 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x^{2} + 128 \, {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} x\right)} \sqrt{x}}{192 \, {\left(a^{6} b^{4} x^{6} + 4 \, a^{7} b^{3} x^{5} + 6 \, a^{8} b^{2} x^{4} + 4 \, a^{9} b x^{3} + a^{10} x^{2}\right)}}\right]"," ",0,"[-1/384*(315*((3*B*a*b^4 - 11*A*b^5)*x^6 + 4*(3*B*a^2*b^3 - 11*A*a*b^4)*x^5 + 6*(3*B*a^3*b^2 - 11*A*a^2*b^3)*x^4 + 4*(3*B*a^4*b - 11*A*a^3*b^2)*x^3 + (3*B*a^5 - 11*A*a^4*b)*x^2)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(128*A*a^5 + 315*(3*B*a*b^4 - 11*A*b^5)*x^5 + 1155*(3*B*a^2*b^3 - 11*A*a*b^4)*x^4 + 1533*(3*B*a^3*b^2 - 11*A*a^2*b^3)*x^3 + 837*(3*B*a^4*b - 11*A*a^3*b^2)*x^2 + 128*(3*B*a^5 - 11*A*a^4*b)*x)*sqrt(x))/(a^6*b^4*x^6 + 4*a^7*b^3*x^5 + 6*a^8*b^2*x^4 + 4*a^9*b*x^3 + a^10*x^2), 1/192*(315*((3*B*a*b^4 - 11*A*b^5)*x^6 + 4*(3*B*a^2*b^3 - 11*A*a*b^4)*x^5 + 6*(3*B*a^3*b^2 - 11*A*a^2*b^3)*x^4 + 4*(3*B*a^4*b - 11*A*a^3*b^2)*x^3 + (3*B*a^5 - 11*A*a^4*b)*x^2)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (128*A*a^5 + 315*(3*B*a*b^4 - 11*A*b^5)*x^5 + 1155*(3*B*a^2*b^3 - 11*A*a*b^4)*x^4 + 1533*(3*B*a^3*b^2 - 11*A*a^2*b^3)*x^3 + 837*(3*B*a^4*b - 11*A*a^3*b^2)*x^2 + 128*(3*B*a^5 - 11*A*a^4*b)*x)*sqrt(x))/(a^6*b^4*x^6 + 4*a^7*b^3*x^5 + 6*a^8*b^2*x^4 + 4*a^9*b*x^3 + a^10*x^2)]","A",0
835,1,673,0,0.461215," ","integrate((B*x+A)/x^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left({\left(5 \, B a b^{5} - 13 \, A b^{6}\right)} x^{7} + 4 \, {\left(5 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} x^{6} + 6 \, {\left(5 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{5} + 4 \, {\left(5 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{4} + {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(384 \, A a^{6} - 3465 \, {\left(5 \, B a b^{5} - 13 \, A b^{6}\right)} x^{6} - 12705 \, {\left(5 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} x^{5} - 16863 \, {\left(5 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{4} - 9207 \, {\left(5 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{3} - 1408 \, {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x^{2} + 128 \, {\left(5 \, B a^{6} - 13 \, A a^{5} b\right)} x\right)} \sqrt{x}}{1920 \, {\left(a^{7} b^{4} x^{7} + 4 \, a^{8} b^{3} x^{6} + 6 \, a^{9} b^{2} x^{5} + 4 \, a^{10} b x^{4} + a^{11} x^{3}\right)}}, -\frac{3465 \, {\left({\left(5 \, B a b^{5} - 13 \, A b^{6}\right)} x^{7} + 4 \, {\left(5 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} x^{6} + 6 \, {\left(5 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{5} + 4 \, {\left(5 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{4} + {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) + {\left(384 \, A a^{6} - 3465 \, {\left(5 \, B a b^{5} - 13 \, A b^{6}\right)} x^{6} - 12705 \, {\left(5 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} x^{5} - 16863 \, {\left(5 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{4} - 9207 \, {\left(5 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{3} - 1408 \, {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x^{2} + 128 \, {\left(5 \, B a^{6} - 13 \, A a^{5} b\right)} x\right)} \sqrt{x}}{960 \, {\left(a^{7} b^{4} x^{7} + 4 \, a^{8} b^{3} x^{6} + 6 \, a^{9} b^{2} x^{5} + 4 \, a^{10} b x^{4} + a^{11} x^{3}\right)}}\right]"," ",0,"[-1/1920*(3465*((5*B*a*b^5 - 13*A*b^6)*x^7 + 4*(5*B*a^2*b^4 - 13*A*a*b^5)*x^6 + 6*(5*B*a^3*b^3 - 13*A*a^2*b^4)*x^5 + 4*(5*B*a^4*b^2 - 13*A*a^3*b^3)*x^4 + (5*B*a^5*b - 13*A*a^4*b^2)*x^3)*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(384*A*a^6 - 3465*(5*B*a*b^5 - 13*A*b^6)*x^6 - 12705*(5*B*a^2*b^4 - 13*A*a*b^5)*x^5 - 16863*(5*B*a^3*b^3 - 13*A*a^2*b^4)*x^4 - 9207*(5*B*a^4*b^2 - 13*A*a^3*b^3)*x^3 - 1408*(5*B*a^5*b - 13*A*a^4*b^2)*x^2 + 128*(5*B*a^6 - 13*A*a^5*b)*x)*sqrt(x))/(a^7*b^4*x^7 + 4*a^8*b^3*x^6 + 6*a^9*b^2*x^5 + 4*a^10*b*x^4 + a^11*x^3), -1/960*(3465*((5*B*a*b^5 - 13*A*b^6)*x^7 + 4*(5*B*a^2*b^4 - 13*A*a*b^5)*x^6 + 6*(5*B*a^3*b^3 - 13*A*a^2*b^4)*x^5 + 4*(5*B*a^4*b^2 - 13*A*a^3*b^3)*x^4 + (5*B*a^5*b - 13*A*a^4*b^2)*x^3)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) + (384*A*a^6 - 3465*(5*B*a*b^5 - 13*A*b^6)*x^6 - 12705*(5*B*a^2*b^4 - 13*A*a*b^5)*x^5 - 16863*(5*B*a^3*b^3 - 13*A*a^2*b^4)*x^4 - 9207*(5*B*a^4*b^2 - 13*A*a^3*b^3)*x^3 - 1408*(5*B*a^5*b - 13*A*a^4*b^2)*x^2 + 128*(5*B*a^6 - 13*A*a^5*b)*x)*sqrt(x))/(a^7*b^4*x^7 + 4*a^8*b^3*x^6 + 6*a^9*b^2*x^5 + 4*a^10*b*x^4 + a^11*x^3)]","A",0
836,1,1191,0,0.450618," ","integrate(x^m*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{{\left({\left(B b^{6} m^{7} + 28 \, B b^{6} m^{6} + 322 \, B b^{6} m^{5} + 1960 \, B b^{6} m^{4} + 6769 \, B b^{6} m^{3} + 13132 \, B b^{6} m^{2} + 13068 \, B b^{6} m + 5040 \, B b^{6}\right)} x^{8} + {\left({\left(6 \, B a b^{5} + A b^{6}\right)} m^{7} + 34560 \, B a b^{5} + 5760 \, A b^{6} + 29 \, {\left(6 \, B a b^{5} + A b^{6}\right)} m^{6} + 343 \, {\left(6 \, B a b^{5} + A b^{6}\right)} m^{5} + 2135 \, {\left(6 \, B a b^{5} + A b^{6}\right)} m^{4} + 7504 \, {\left(6 \, B a b^{5} + A b^{6}\right)} m^{3} + 14756 \, {\left(6 \, B a b^{5} + A b^{6}\right)} m^{2} + 14832 \, {\left(6 \, B a b^{5} + A b^{6}\right)} m\right)} x^{7} + 3 \, {\left({\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} m^{7} + 33600 \, B a^{2} b^{4} + 13440 \, A a b^{5} + 30 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} m^{6} + 366 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} m^{5} + 2340 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} m^{4} + 8409 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} m^{3} + 16830 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} m^{2} + 17144 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} m\right)} x^{6} + 5 \, {\left({\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} m^{7} + 32256 \, B a^{3} b^{3} + 24192 \, A a^{2} b^{4} + 31 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} m^{6} + 391 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} m^{5} + 2581 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} m^{4} + 9544 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} m^{3} + 19564 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} m^{2} + 20304 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} m\right)} x^{5} + 5 \, {\left({\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} m^{7} + 30240 \, B a^{4} b^{2} + 40320 \, A a^{3} b^{3} + 32 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} m^{6} + 418 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} m^{5} + 2864 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} m^{4} + 10993 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} m^{3} + 23312 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} m^{2} + 24876 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} m\right)} x^{4} + 3 \, {\left({\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} m^{7} + 26880 \, B a^{5} b + 67200 \, A a^{4} b^{2} + 33 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} m^{6} + 447 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} m^{5} + 3195 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} m^{4} + 12864 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} m^{3} + 28692 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} m^{2} + 32048 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} m\right)} x^{3} + {\left({\left(B a^{6} + 6 \, A a^{5} b\right)} m^{7} + 20160 \, B a^{6} + 120960 \, A a^{5} b + 34 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} m^{6} + 478 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} m^{5} + 3580 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} m^{4} + 15289 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} m^{3} + 36706 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} m^{2} + 44712 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} m\right)} x^{2} + {\left(A a^{6} m^{7} + 35 \, A a^{6} m^{6} + 511 \, A a^{6} m^{5} + 4025 \, A a^{6} m^{4} + 18424 \, A a^{6} m^{3} + 48860 \, A a^{6} m^{2} + 69264 \, A a^{6} m + 40320 \, A a^{6}\right)} x\right)} x^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320}"," ",0,"((B*b^6*m^7 + 28*B*b^6*m^6 + 322*B*b^6*m^5 + 1960*B*b^6*m^4 + 6769*B*b^6*m^3 + 13132*B*b^6*m^2 + 13068*B*b^6*m + 5040*B*b^6)*x^8 + ((6*B*a*b^5 + A*b^6)*m^7 + 34560*B*a*b^5 + 5760*A*b^6 + 29*(6*B*a*b^5 + A*b^6)*m^6 + 343*(6*B*a*b^5 + A*b^6)*m^5 + 2135*(6*B*a*b^5 + A*b^6)*m^4 + 7504*(6*B*a*b^5 + A*b^6)*m^3 + 14756*(6*B*a*b^5 + A*b^6)*m^2 + 14832*(6*B*a*b^5 + A*b^6)*m)*x^7 + 3*((5*B*a^2*b^4 + 2*A*a*b^5)*m^7 + 33600*B*a^2*b^4 + 13440*A*a*b^5 + 30*(5*B*a^2*b^4 + 2*A*a*b^5)*m^6 + 366*(5*B*a^2*b^4 + 2*A*a*b^5)*m^5 + 2340*(5*B*a^2*b^4 + 2*A*a*b^5)*m^4 + 8409*(5*B*a^2*b^4 + 2*A*a*b^5)*m^3 + 16830*(5*B*a^2*b^4 + 2*A*a*b^5)*m^2 + 17144*(5*B*a^2*b^4 + 2*A*a*b^5)*m)*x^6 + 5*((4*B*a^3*b^3 + 3*A*a^2*b^4)*m^7 + 32256*B*a^3*b^3 + 24192*A*a^2*b^4 + 31*(4*B*a^3*b^3 + 3*A*a^2*b^4)*m^6 + 391*(4*B*a^3*b^3 + 3*A*a^2*b^4)*m^5 + 2581*(4*B*a^3*b^3 + 3*A*a^2*b^4)*m^4 + 9544*(4*B*a^3*b^3 + 3*A*a^2*b^4)*m^3 + 19564*(4*B*a^3*b^3 + 3*A*a^2*b^4)*m^2 + 20304*(4*B*a^3*b^3 + 3*A*a^2*b^4)*m)*x^5 + 5*((3*B*a^4*b^2 + 4*A*a^3*b^3)*m^7 + 30240*B*a^4*b^2 + 40320*A*a^3*b^3 + 32*(3*B*a^4*b^2 + 4*A*a^3*b^3)*m^6 + 418*(3*B*a^4*b^2 + 4*A*a^3*b^3)*m^5 + 2864*(3*B*a^4*b^2 + 4*A*a^3*b^3)*m^4 + 10993*(3*B*a^4*b^2 + 4*A*a^3*b^3)*m^3 + 23312*(3*B*a^4*b^2 + 4*A*a^3*b^3)*m^2 + 24876*(3*B*a^4*b^2 + 4*A*a^3*b^3)*m)*x^4 + 3*((2*B*a^5*b + 5*A*a^4*b^2)*m^7 + 26880*B*a^5*b + 67200*A*a^4*b^2 + 33*(2*B*a^5*b + 5*A*a^4*b^2)*m^6 + 447*(2*B*a^5*b + 5*A*a^4*b^2)*m^5 + 3195*(2*B*a^5*b + 5*A*a^4*b^2)*m^4 + 12864*(2*B*a^5*b + 5*A*a^4*b^2)*m^3 + 28692*(2*B*a^5*b + 5*A*a^4*b^2)*m^2 + 32048*(2*B*a^5*b + 5*A*a^4*b^2)*m)*x^3 + ((B*a^6 + 6*A*a^5*b)*m^7 + 20160*B*a^6 + 120960*A*a^5*b + 34*(B*a^6 + 6*A*a^5*b)*m^6 + 478*(B*a^6 + 6*A*a^5*b)*m^5 + 3580*(B*a^6 + 6*A*a^5*b)*m^4 + 15289*(B*a^6 + 6*A*a^5*b)*m^3 + 36706*(B*a^6 + 6*A*a^5*b)*m^2 + 44712*(B*a^6 + 6*A*a^5*b)*m)*x^2 + (A*a^6*m^7 + 35*A*a^6*m^6 + 511*A*a^6*m^5 + 4025*A*a^6*m^4 + 18424*A*a^6*m^3 + 48860*A*a^6*m^2 + 69264*A*a^6*m + 40320*A*a^6)*x)*x^m/(m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)","B",0
837,1,607,0,0.445670," ","integrate(x^m*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{{\left({\left(B b^{4} m^{5} + 15 \, B b^{4} m^{4} + 85 \, B b^{4} m^{3} + 225 \, B b^{4} m^{2} + 274 \, B b^{4} m + 120 \, B b^{4}\right)} x^{6} + {\left({\left(4 \, B a b^{3} + A b^{4}\right)} m^{5} + 576 \, B a b^{3} + 144 \, A b^{4} + 16 \, {\left(4 \, B a b^{3} + A b^{4}\right)} m^{4} + 95 \, {\left(4 \, B a b^{3} + A b^{4}\right)} m^{3} + 260 \, {\left(4 \, B a b^{3} + A b^{4}\right)} m^{2} + 324 \, {\left(4 \, B a b^{3} + A b^{4}\right)} m\right)} x^{5} + 2 \, {\left({\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m^{5} + 540 \, B a^{2} b^{2} + 360 \, A a b^{3} + 17 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m^{4} + 107 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m^{3} + 307 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m^{2} + 396 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m\right)} x^{4} + 2 \, {\left({\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m^{5} + 480 \, B a^{3} b + 720 \, A a^{2} b^{2} + 18 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m^{4} + 121 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m^{3} + 372 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m^{2} + 508 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m\right)} x^{3} + {\left({\left(B a^{4} + 4 \, A a^{3} b\right)} m^{5} + 360 \, B a^{4} + 1440 \, A a^{3} b + 19 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} m^{4} + 137 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} m^{3} + 461 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} m^{2} + 702 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} m\right)} x^{2} + {\left(A a^{4} m^{5} + 20 \, A a^{4} m^{4} + 155 \, A a^{4} m^{3} + 580 \, A a^{4} m^{2} + 1044 \, A a^{4} m + 720 \, A a^{4}\right)} x\right)} x^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"((B*b^4*m^5 + 15*B*b^4*m^4 + 85*B*b^4*m^3 + 225*B*b^4*m^2 + 274*B*b^4*m + 120*B*b^4)*x^6 + ((4*B*a*b^3 + A*b^4)*m^5 + 576*B*a*b^3 + 144*A*b^4 + 16*(4*B*a*b^3 + A*b^4)*m^4 + 95*(4*B*a*b^3 + A*b^4)*m^3 + 260*(4*B*a*b^3 + A*b^4)*m^2 + 324*(4*B*a*b^3 + A*b^4)*m)*x^5 + 2*((3*B*a^2*b^2 + 2*A*a*b^3)*m^5 + 540*B*a^2*b^2 + 360*A*a*b^3 + 17*(3*B*a^2*b^2 + 2*A*a*b^3)*m^4 + 107*(3*B*a^2*b^2 + 2*A*a*b^3)*m^3 + 307*(3*B*a^2*b^2 + 2*A*a*b^3)*m^2 + 396*(3*B*a^2*b^2 + 2*A*a*b^3)*m)*x^4 + 2*((2*B*a^3*b + 3*A*a^2*b^2)*m^5 + 480*B*a^3*b + 720*A*a^2*b^2 + 18*(2*B*a^3*b + 3*A*a^2*b^2)*m^4 + 121*(2*B*a^3*b + 3*A*a^2*b^2)*m^3 + 372*(2*B*a^3*b + 3*A*a^2*b^2)*m^2 + 508*(2*B*a^3*b + 3*A*a^2*b^2)*m)*x^3 + ((B*a^4 + 4*A*a^3*b)*m^5 + 360*B*a^4 + 1440*A*a^3*b + 19*(B*a^4 + 4*A*a^3*b)*m^4 + 137*(B*a^4 + 4*A*a^3*b)*m^3 + 461*(B*a^4 + 4*A*a^3*b)*m^2 + 702*(B*a^4 + 4*A*a^3*b)*m)*x^2 + (A*a^4*m^5 + 20*A*a^4*m^4 + 155*A*a^4*m^3 + 580*A*a^4*m^2 + 1044*A*a^4*m + 720*A*a^4)*x)*x^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
838,1,215,0,0.430948," ","integrate(x^m*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{2} m^{3} + 6 \, B b^{2} m^{2} + 11 \, B b^{2} m + 6 \, B b^{2}\right)} x^{4} + {\left({\left(2 \, B a b + A b^{2}\right)} m^{3} + 16 \, B a b + 8 \, A b^{2} + 7 \, {\left(2 \, B a b + A b^{2}\right)} m^{2} + 14 \, {\left(2 \, B a b + A b^{2}\right)} m\right)} x^{3} + {\left({\left(B a^{2} + 2 \, A a b\right)} m^{3} + 12 \, B a^{2} + 24 \, A a b + 8 \, {\left(B a^{2} + 2 \, A a b\right)} m^{2} + 19 \, {\left(B a^{2} + 2 \, A a b\right)} m\right)} x^{2} + {\left(A a^{2} m^{3} + 9 \, A a^{2} m^{2} + 26 \, A a^{2} m + 24 \, A a^{2}\right)} x\right)} x^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"((B*b^2*m^3 + 6*B*b^2*m^2 + 11*B*b^2*m + 6*B*b^2)*x^4 + ((2*B*a*b + A*b^2)*m^3 + 16*B*a*b + 8*A*b^2 + 7*(2*B*a*b + A*b^2)*m^2 + 14*(2*B*a*b + A*b^2)*m)*x^3 + ((B*a^2 + 2*A*a*b)*m^3 + 12*B*a^2 + 24*A*a*b + 8*(B*a^2 + 2*A*a*b)*m^2 + 19*(B*a^2 + 2*A*a*b)*m)*x^2 + (A*a^2*m^3 + 9*A*a^2*m^2 + 26*A*a^2*m + 24*A*a^2)*x)*x^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
839,0,0,0,0.447534," ","integrate(x^m*(B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} x^{m}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right)"," ",0,"integral((B*x + A)*x^m/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
840,0,0,0,0.431858," ","integrate(x^m*(B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} x^{m}}{b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}}, x\right)"," ",0,"integral((B*x + A)*x^m/(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4), x)","F",0
841,1,757,0,0.434124," ","integrate(x^m*(1+x)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{{\left({\left(m^{11} + 66 \, m^{10} + 1925 \, m^{9} + 32670 \, m^{8} + 357423 \, m^{7} + 2637558 \, m^{6} + 13339535 \, m^{5} + 45995730 \, m^{4} + 105258076 \, m^{3} + 150917976 \, m^{2} + 120543840 \, m + 39916800\right)} x^{12} + 11 \, {\left(m^{11} + 67 \, m^{10} + 1980 \, m^{9} + 33990 \, m^{8} + 375573 \, m^{7} + 2795331 \, m^{6} + 14241590 \, m^{5} + 49412660 \, m^{4} + 113667576 \, m^{3} + 163671552 \, m^{2} + 131172480 \, m + 43545600\right)} x^{11} + 55 \, {\left(m^{11} + 68 \, m^{10} + 2037 \, m^{9} + 35400 \, m^{8} + 395463 \, m^{7} + 2972004 \, m^{6} + 15270191 \, m^{5} + 53368240 \, m^{4} + 123524436 \, m^{3} + 178770528 \, m^{2} + 143854272 \, m + 47900160\right)} x^{10} + 165 \, {\left(m^{11} + 69 \, m^{10} + 2096 \, m^{9} + 36906 \, m^{8} + 417309 \, m^{7} + 3170853 \, m^{6} + 16452554 \, m^{5} + 57997164 \, m^{4} + 135232360 \, m^{3} + 196923648 \, m^{2} + 159246720 \, m + 53222400\right)} x^{9} + 330 \, {\left(m^{11} + 70 \, m^{10} + 2157 \, m^{9} + 38514 \, m^{8} + 441351 \, m^{7} + 3395826 \, m^{6} + 17823623 \, m^{5} + 63481166 \, m^{4} + 149357508 \, m^{3} + 219154824 \, m^{2} + 178320960 \, m + 59875200\right)} x^{8} + 462 \, {\left(m^{11} + 71 \, m^{10} + 2220 \, m^{9} + 40230 \, m^{8} + 467853 \, m^{7} + 3651663 \, m^{6} + 19428590 \, m^{5} + 70070020 \, m^{4} + 166716696 \, m^{3} + 246998016 \, m^{2} + 202573440 \, m + 68428800\right)} x^{7} + 462 \, {\left(m^{11} + 72 \, m^{10} + 2285 \, m^{9} + 42060 \, m^{8} + 497103 \, m^{7} + 3944016 \, m^{6} + 21326135 \, m^{5} + 78113340 \, m^{4} + 188526796 \, m^{3} + 282854112 \, m^{2} + 234434880 \, m + 79833600\right)} x^{6} + 330 \, {\left(m^{11} + 73 \, m^{10} + 2352 \, m^{9} + 44010 \, m^{8} + 529413 \, m^{7} + 4279569 \, m^{6} + 23592386 \, m^{5} + 88108220 \, m^{4} + 216665736 \, m^{3} + 330686208 \, m^{2} + 278128512 \, m + 95800320\right)} x^{5} + 165 \, {\left(m^{11} + 74 \, m^{10} + 2421 \, m^{9} + 46086 \, m^{8} + 565119 \, m^{7} + 4666158 \, m^{6} + 26325599 \, m^{5} + 100767754 \, m^{4} + 254135820 \, m^{3} + 397471608 \, m^{2} + 341673120 \, m + 119750400\right)} x^{4} + 55 \, {\left(m^{11} + 75 \, m^{10} + 2492 \, m^{9} + 48294 \, m^{8} + 604581 \, m^{7} + 5112891 \, m^{6} + 29651558 \, m^{5} + 117115476 \, m^{4} + 305860408 \, m^{3} + 496433664 \, m^{2} + 442258560 \, m + 159667200\right)} x^{3} + 11 \, {\left(m^{11} + 76 \, m^{10} + 2565 \, m^{9} + 50640 \, m^{8} + 648183 \, m^{7} + 5630268 \, m^{6} + 33729695 \, m^{5} + 138610760 \, m^{4} + 379985316 \, m^{3} + 654044256 \, m^{2} + 623471040 \, m + 239500800\right)} x^{2} + {\left(m^{11} + 77 \, m^{10} + 2640 \, m^{9} + 53130 \, m^{8} + 696333 \, m^{7} + 6230301 \, m^{6} + 38759930 \, m^{5} + 167310220 \, m^{4} + 489896616 \, m^{3} + 924118272 \, m^{2} + 1007441280 \, m + 479001600\right)} x\right)} x^{m}}{m^{12} + 78 \, m^{11} + 2717 \, m^{10} + 55770 \, m^{9} + 749463 \, m^{8} + 6926634 \, m^{7} + 44990231 \, m^{6} + 206070150 \, m^{5} + 657206836 \, m^{4} + 1414014888 \, m^{3} + 1931559552 \, m^{2} + 1486442880 \, m + 479001600}"," ",0,"((m^11 + 66*m^10 + 1925*m^9 + 32670*m^8 + 357423*m^7 + 2637558*m^6 + 13339535*m^5 + 45995730*m^4 + 105258076*m^3 + 150917976*m^2 + 120543840*m + 39916800)*x^12 + 11*(m^11 + 67*m^10 + 1980*m^9 + 33990*m^8 + 375573*m^7 + 2795331*m^6 + 14241590*m^5 + 49412660*m^4 + 113667576*m^3 + 163671552*m^2 + 131172480*m + 43545600)*x^11 + 55*(m^11 + 68*m^10 + 2037*m^9 + 35400*m^8 + 395463*m^7 + 2972004*m^6 + 15270191*m^5 + 53368240*m^4 + 123524436*m^3 + 178770528*m^2 + 143854272*m + 47900160)*x^10 + 165*(m^11 + 69*m^10 + 2096*m^9 + 36906*m^8 + 417309*m^7 + 3170853*m^6 + 16452554*m^5 + 57997164*m^4 + 135232360*m^3 + 196923648*m^2 + 159246720*m + 53222400)*x^9 + 330*(m^11 + 70*m^10 + 2157*m^9 + 38514*m^8 + 441351*m^7 + 3395826*m^6 + 17823623*m^5 + 63481166*m^4 + 149357508*m^3 + 219154824*m^2 + 178320960*m + 59875200)*x^8 + 462*(m^11 + 71*m^10 + 2220*m^9 + 40230*m^8 + 467853*m^7 + 3651663*m^6 + 19428590*m^5 + 70070020*m^4 + 166716696*m^3 + 246998016*m^2 + 202573440*m + 68428800)*x^7 + 462*(m^11 + 72*m^10 + 2285*m^9 + 42060*m^8 + 497103*m^7 + 3944016*m^6 + 21326135*m^5 + 78113340*m^4 + 188526796*m^3 + 282854112*m^2 + 234434880*m + 79833600)*x^6 + 330*(m^11 + 73*m^10 + 2352*m^9 + 44010*m^8 + 529413*m^7 + 4279569*m^6 + 23592386*m^5 + 88108220*m^4 + 216665736*m^3 + 330686208*m^2 + 278128512*m + 95800320)*x^5 + 165*(m^11 + 74*m^10 + 2421*m^9 + 46086*m^8 + 565119*m^7 + 4666158*m^6 + 26325599*m^5 + 100767754*m^4 + 254135820*m^3 + 397471608*m^2 + 341673120*m + 119750400)*x^4 + 55*(m^11 + 75*m^10 + 2492*m^9 + 48294*m^8 + 604581*m^7 + 5112891*m^6 + 29651558*m^5 + 117115476*m^4 + 305860408*m^3 + 496433664*m^2 + 442258560*m + 159667200)*x^3 + 11*(m^11 + 76*m^10 + 2565*m^9 + 50640*m^8 + 648183*m^7 + 5630268*m^6 + 33729695*m^5 + 138610760*m^4 + 379985316*m^3 + 654044256*m^2 + 623471040*m + 239500800)*x^2 + (m^11 + 77*m^10 + 2640*m^9 + 53130*m^8 + 696333*m^7 + 6230301*m^6 + 38759930*m^5 + 167310220*m^4 + 489896616*m^3 + 924118272*m^2 + 1007441280*m + 479001600)*x)*x^m/(m^12 + 78*m^11 + 2717*m^10 + 55770*m^9 + 749463*m^8 + 6926634*m^7 + 44990231*m^6 + 206070150*m^5 + 657206836*m^4 + 1414014888*m^3 + 1931559552*m^2 + 1486442880*m + 479001600)","B",0
842,1,1569,0,0.455071," ","integrate(x^m*(e*x+d)*(x^2+2*x+1)^5,x, algorithm=""fricas"")","\frac{{\left({\left(e m^{11} + 66 \, e m^{10} + 1925 \, e m^{9} + 32670 \, e m^{8} + 357423 \, e m^{7} + 2637558 \, e m^{6} + 13339535 \, e m^{5} + 45995730 \, e m^{4} + 105258076 \, e m^{3} + 150917976 \, e m^{2} + 120543840 \, e m + 39916800 \, e\right)} x^{12} + {\left({\left(d + 10 \, e\right)} m^{11} + 67 \, {\left(d + 10 \, e\right)} m^{10} + 1980 \, {\left(d + 10 \, e\right)} m^{9} + 33990 \, {\left(d + 10 \, e\right)} m^{8} + 375573 \, {\left(d + 10 \, e\right)} m^{7} + 2795331 \, {\left(d + 10 \, e\right)} m^{6} + 14241590 \, {\left(d + 10 \, e\right)} m^{5} + 49412660 \, {\left(d + 10 \, e\right)} m^{4} + 113667576 \, {\left(d + 10 \, e\right)} m^{3} + 163671552 \, {\left(d + 10 \, e\right)} m^{2} + 131172480 \, {\left(d + 10 \, e\right)} m + 43545600 \, d + 435456000 \, e\right)} x^{11} + 5 \, {\left({\left(2 \, d + 9 \, e\right)} m^{11} + 68 \, {\left(2 \, d + 9 \, e\right)} m^{10} + 2037 \, {\left(2 \, d + 9 \, e\right)} m^{9} + 35400 \, {\left(2 \, d + 9 \, e\right)} m^{8} + 395463 \, {\left(2 \, d + 9 \, e\right)} m^{7} + 2972004 \, {\left(2 \, d + 9 \, e\right)} m^{6} + 15270191 \, {\left(2 \, d + 9 \, e\right)} m^{5} + 53368240 \, {\left(2 \, d + 9 \, e\right)} m^{4} + 123524436 \, {\left(2 \, d + 9 \, e\right)} m^{3} + 178770528 \, {\left(2 \, d + 9 \, e\right)} m^{2} + 143854272 \, {\left(2 \, d + 9 \, e\right)} m + 95800320 \, d + 431101440 \, e\right)} x^{10} + 15 \, {\left({\left(3 \, d + 8 \, e\right)} m^{11} + 69 \, {\left(3 \, d + 8 \, e\right)} m^{10} + 2096 \, {\left(3 \, d + 8 \, e\right)} m^{9} + 36906 \, {\left(3 \, d + 8 \, e\right)} m^{8} + 417309 \, {\left(3 \, d + 8 \, e\right)} m^{7} + 3170853 \, {\left(3 \, d + 8 \, e\right)} m^{6} + 16452554 \, {\left(3 \, d + 8 \, e\right)} m^{5} + 57997164 \, {\left(3 \, d + 8 \, e\right)} m^{4} + 135232360 \, {\left(3 \, d + 8 \, e\right)} m^{3} + 196923648 \, {\left(3 \, d + 8 \, e\right)} m^{2} + 159246720 \, {\left(3 \, d + 8 \, e\right)} m + 159667200 \, d + 425779200 \, e\right)} x^{9} + 30 \, {\left({\left(4 \, d + 7 \, e\right)} m^{11} + 70 \, {\left(4 \, d + 7 \, e\right)} m^{10} + 2157 \, {\left(4 \, d + 7 \, e\right)} m^{9} + 38514 \, {\left(4 \, d + 7 \, e\right)} m^{8} + 441351 \, {\left(4 \, d + 7 \, e\right)} m^{7} + 3395826 \, {\left(4 \, d + 7 \, e\right)} m^{6} + 17823623 \, {\left(4 \, d + 7 \, e\right)} m^{5} + 63481166 \, {\left(4 \, d + 7 \, e\right)} m^{4} + 149357508 \, {\left(4 \, d + 7 \, e\right)} m^{3} + 219154824 \, {\left(4 \, d + 7 \, e\right)} m^{2} + 178320960 \, {\left(4 \, d + 7 \, e\right)} m + 239500800 \, d + 419126400 \, e\right)} x^{8} + 42 \, {\left({\left(5 \, d + 6 \, e\right)} m^{11} + 71 \, {\left(5 \, d + 6 \, e\right)} m^{10} + 2220 \, {\left(5 \, d + 6 \, e\right)} m^{9} + 40230 \, {\left(5 \, d + 6 \, e\right)} m^{8} + 467853 \, {\left(5 \, d + 6 \, e\right)} m^{7} + 3651663 \, {\left(5 \, d + 6 \, e\right)} m^{6} + 19428590 \, {\left(5 \, d + 6 \, e\right)} m^{5} + 70070020 \, {\left(5 \, d + 6 \, e\right)} m^{4} + 166716696 \, {\left(5 \, d + 6 \, e\right)} m^{3} + 246998016 \, {\left(5 \, d + 6 \, e\right)} m^{2} + 202573440 \, {\left(5 \, d + 6 \, e\right)} m + 342144000 \, d + 410572800 \, e\right)} x^{7} + 42 \, {\left({\left(6 \, d + 5 \, e\right)} m^{11} + 72 \, {\left(6 \, d + 5 \, e\right)} m^{10} + 2285 \, {\left(6 \, d + 5 \, e\right)} m^{9} + 42060 \, {\left(6 \, d + 5 \, e\right)} m^{8} + 497103 \, {\left(6 \, d + 5 \, e\right)} m^{7} + 3944016 \, {\left(6 \, d + 5 \, e\right)} m^{6} + 21326135 \, {\left(6 \, d + 5 \, e\right)} m^{5} + 78113340 \, {\left(6 \, d + 5 \, e\right)} m^{4} + 188526796 \, {\left(6 \, d + 5 \, e\right)} m^{3} + 282854112 \, {\left(6 \, d + 5 \, e\right)} m^{2} + 234434880 \, {\left(6 \, d + 5 \, e\right)} m + 479001600 \, d + 399168000 \, e\right)} x^{6} + 30 \, {\left({\left(7 \, d + 4 \, e\right)} m^{11} + 73 \, {\left(7 \, d + 4 \, e\right)} m^{10} + 2352 \, {\left(7 \, d + 4 \, e\right)} m^{9} + 44010 \, {\left(7 \, d + 4 \, e\right)} m^{8} + 529413 \, {\left(7 \, d + 4 \, e\right)} m^{7} + 4279569 \, {\left(7 \, d + 4 \, e\right)} m^{6} + 23592386 \, {\left(7 \, d + 4 \, e\right)} m^{5} + 88108220 \, {\left(7 \, d + 4 \, e\right)} m^{4} + 216665736 \, {\left(7 \, d + 4 \, e\right)} m^{3} + 330686208 \, {\left(7 \, d + 4 \, e\right)} m^{2} + 278128512 \, {\left(7 \, d + 4 \, e\right)} m + 670602240 \, d + 383201280 \, e\right)} x^{5} + 15 \, {\left({\left(8 \, d + 3 \, e\right)} m^{11} + 74 \, {\left(8 \, d + 3 \, e\right)} m^{10} + 2421 \, {\left(8 \, d + 3 \, e\right)} m^{9} + 46086 \, {\left(8 \, d + 3 \, e\right)} m^{8} + 565119 \, {\left(8 \, d + 3 \, e\right)} m^{7} + 4666158 \, {\left(8 \, d + 3 \, e\right)} m^{6} + 26325599 \, {\left(8 \, d + 3 \, e\right)} m^{5} + 100767754 \, {\left(8 \, d + 3 \, e\right)} m^{4} + 254135820 \, {\left(8 \, d + 3 \, e\right)} m^{3} + 397471608 \, {\left(8 \, d + 3 \, e\right)} m^{2} + 341673120 \, {\left(8 \, d + 3 \, e\right)} m + 958003200 \, d + 359251200 \, e\right)} x^{4} + 5 \, {\left({\left(9 \, d + 2 \, e\right)} m^{11} + 75 \, {\left(9 \, d + 2 \, e\right)} m^{10} + 2492 \, {\left(9 \, d + 2 \, e\right)} m^{9} + 48294 \, {\left(9 \, d + 2 \, e\right)} m^{8} + 604581 \, {\left(9 \, d + 2 \, e\right)} m^{7} + 5112891 \, {\left(9 \, d + 2 \, e\right)} m^{6} + 29651558 \, {\left(9 \, d + 2 \, e\right)} m^{5} + 117115476 \, {\left(9 \, d + 2 \, e\right)} m^{4} + 305860408 \, {\left(9 \, d + 2 \, e\right)} m^{3} + 496433664 \, {\left(9 \, d + 2 \, e\right)} m^{2} + 442258560 \, {\left(9 \, d + 2 \, e\right)} m + 1437004800 \, d + 319334400 \, e\right)} x^{3} + {\left({\left(10 \, d + e\right)} m^{11} + 76 \, {\left(10 \, d + e\right)} m^{10} + 2565 \, {\left(10 \, d + e\right)} m^{9} + 50640 \, {\left(10 \, d + e\right)} m^{8} + 648183 \, {\left(10 \, d + e\right)} m^{7} + 5630268 \, {\left(10 \, d + e\right)} m^{6} + 33729695 \, {\left(10 \, d + e\right)} m^{5} + 138610760 \, {\left(10 \, d + e\right)} m^{4} + 379985316 \, {\left(10 \, d + e\right)} m^{3} + 654044256 \, {\left(10 \, d + e\right)} m^{2} + 623471040 \, {\left(10 \, d + e\right)} m + 2395008000 \, d + 239500800 \, e\right)} x^{2} + {\left(d m^{11} + 77 \, d m^{10} + 2640 \, d m^{9} + 53130 \, d m^{8} + 696333 \, d m^{7} + 6230301 \, d m^{6} + 38759930 \, d m^{5} + 167310220 \, d m^{4} + 489896616 \, d m^{3} + 924118272 \, d m^{2} + 1007441280 \, d m + 479001600 \, d\right)} x\right)} x^{m}}{m^{12} + 78 \, m^{11} + 2717 \, m^{10} + 55770 \, m^{9} + 749463 \, m^{8} + 6926634 \, m^{7} + 44990231 \, m^{6} + 206070150 \, m^{5} + 657206836 \, m^{4} + 1414014888 \, m^{3} + 1931559552 \, m^{2} + 1486442880 \, m + 479001600}"," ",0,"((e*m^11 + 66*e*m^10 + 1925*e*m^9 + 32670*e*m^8 + 357423*e*m^7 + 2637558*e*m^6 + 13339535*e*m^5 + 45995730*e*m^4 + 105258076*e*m^3 + 150917976*e*m^2 + 120543840*e*m + 39916800*e)*x^12 + ((d + 10*e)*m^11 + 67*(d + 10*e)*m^10 + 1980*(d + 10*e)*m^9 + 33990*(d + 10*e)*m^8 + 375573*(d + 10*e)*m^7 + 2795331*(d + 10*e)*m^6 + 14241590*(d + 10*e)*m^5 + 49412660*(d + 10*e)*m^4 + 113667576*(d + 10*e)*m^3 + 163671552*(d + 10*e)*m^2 + 131172480*(d + 10*e)*m + 43545600*d + 435456000*e)*x^11 + 5*((2*d + 9*e)*m^11 + 68*(2*d + 9*e)*m^10 + 2037*(2*d + 9*e)*m^9 + 35400*(2*d + 9*e)*m^8 + 395463*(2*d + 9*e)*m^7 + 2972004*(2*d + 9*e)*m^6 + 15270191*(2*d + 9*e)*m^5 + 53368240*(2*d + 9*e)*m^4 + 123524436*(2*d + 9*e)*m^3 + 178770528*(2*d + 9*e)*m^2 + 143854272*(2*d + 9*e)*m + 95800320*d + 431101440*e)*x^10 + 15*((3*d + 8*e)*m^11 + 69*(3*d + 8*e)*m^10 + 2096*(3*d + 8*e)*m^9 + 36906*(3*d + 8*e)*m^8 + 417309*(3*d + 8*e)*m^7 + 3170853*(3*d + 8*e)*m^6 + 16452554*(3*d + 8*e)*m^5 + 57997164*(3*d + 8*e)*m^4 + 135232360*(3*d + 8*e)*m^3 + 196923648*(3*d + 8*e)*m^2 + 159246720*(3*d + 8*e)*m + 159667200*d + 425779200*e)*x^9 + 30*((4*d + 7*e)*m^11 + 70*(4*d + 7*e)*m^10 + 2157*(4*d + 7*e)*m^9 + 38514*(4*d + 7*e)*m^8 + 441351*(4*d + 7*e)*m^7 + 3395826*(4*d + 7*e)*m^6 + 17823623*(4*d + 7*e)*m^5 + 63481166*(4*d + 7*e)*m^4 + 149357508*(4*d + 7*e)*m^3 + 219154824*(4*d + 7*e)*m^2 + 178320960*(4*d + 7*e)*m + 239500800*d + 419126400*e)*x^8 + 42*((5*d + 6*e)*m^11 + 71*(5*d + 6*e)*m^10 + 2220*(5*d + 6*e)*m^9 + 40230*(5*d + 6*e)*m^8 + 467853*(5*d + 6*e)*m^7 + 3651663*(5*d + 6*e)*m^6 + 19428590*(5*d + 6*e)*m^5 + 70070020*(5*d + 6*e)*m^4 + 166716696*(5*d + 6*e)*m^3 + 246998016*(5*d + 6*e)*m^2 + 202573440*(5*d + 6*e)*m + 342144000*d + 410572800*e)*x^7 + 42*((6*d + 5*e)*m^11 + 72*(6*d + 5*e)*m^10 + 2285*(6*d + 5*e)*m^9 + 42060*(6*d + 5*e)*m^8 + 497103*(6*d + 5*e)*m^7 + 3944016*(6*d + 5*e)*m^6 + 21326135*(6*d + 5*e)*m^5 + 78113340*(6*d + 5*e)*m^4 + 188526796*(6*d + 5*e)*m^3 + 282854112*(6*d + 5*e)*m^2 + 234434880*(6*d + 5*e)*m + 479001600*d + 399168000*e)*x^6 + 30*((7*d + 4*e)*m^11 + 73*(7*d + 4*e)*m^10 + 2352*(7*d + 4*e)*m^9 + 44010*(7*d + 4*e)*m^8 + 529413*(7*d + 4*e)*m^7 + 4279569*(7*d + 4*e)*m^6 + 23592386*(7*d + 4*e)*m^5 + 88108220*(7*d + 4*e)*m^4 + 216665736*(7*d + 4*e)*m^3 + 330686208*(7*d + 4*e)*m^2 + 278128512*(7*d + 4*e)*m + 670602240*d + 383201280*e)*x^5 + 15*((8*d + 3*e)*m^11 + 74*(8*d + 3*e)*m^10 + 2421*(8*d + 3*e)*m^9 + 46086*(8*d + 3*e)*m^8 + 565119*(8*d + 3*e)*m^7 + 4666158*(8*d + 3*e)*m^6 + 26325599*(8*d + 3*e)*m^5 + 100767754*(8*d + 3*e)*m^4 + 254135820*(8*d + 3*e)*m^3 + 397471608*(8*d + 3*e)*m^2 + 341673120*(8*d + 3*e)*m + 958003200*d + 359251200*e)*x^4 + 5*((9*d + 2*e)*m^11 + 75*(9*d + 2*e)*m^10 + 2492*(9*d + 2*e)*m^9 + 48294*(9*d + 2*e)*m^8 + 604581*(9*d + 2*e)*m^7 + 5112891*(9*d + 2*e)*m^6 + 29651558*(9*d + 2*e)*m^5 + 117115476*(9*d + 2*e)*m^4 + 305860408*(9*d + 2*e)*m^3 + 496433664*(9*d + 2*e)*m^2 + 442258560*(9*d + 2*e)*m + 1437004800*d + 319334400*e)*x^3 + ((10*d + e)*m^11 + 76*(10*d + e)*m^10 + 2565*(10*d + e)*m^9 + 50640*(10*d + e)*m^8 + 648183*(10*d + e)*m^7 + 5630268*(10*d + e)*m^6 + 33729695*(10*d + e)*m^5 + 138610760*(10*d + e)*m^4 + 379985316*(10*d + e)*m^3 + 654044256*(10*d + e)*m^2 + 623471040*(10*d + e)*m + 2395008000*d + 239500800*e)*x^2 + (d*m^11 + 77*d*m^10 + 2640*d*m^9 + 53130*d*m^8 + 696333*d*m^7 + 6230301*d*m^6 + 38759930*d*m^5 + 167310220*d*m^4 + 489896616*d*m^3 + 924118272*d*m^2 + 1007441280*d*m + 479001600*d)*x)*x^m/(m^12 + 78*m^11 + 2717*m^10 + 55770*m^9 + 749463*m^8 + 6926634*m^7 + 44990231*m^6 + 206070150*m^5 + 657206836*m^4 + 1414014888*m^3 + 1931559552*m^2 + 1486442880*m + 479001600)","B",0
843,1,43,0,0.343216," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} c B + \frac{1}{6} x^{6} b B + \frac{1}{6} x^{6} c A + \frac{1}{5} x^{5} a B + \frac{1}{5} x^{5} b A + \frac{1}{4} x^{4} a A"," ",0,"1/7*x^7*c*B + 1/6*x^6*b*B + 1/6*x^6*c*A + 1/5*x^5*a*B + 1/5*x^5*b*A + 1/4*x^4*a*A","A",0
844,1,43,0,0.359004," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{6} x^{6} c B + \frac{1}{5} x^{5} b B + \frac{1}{5} x^{5} c A + \frac{1}{4} x^{4} a B + \frac{1}{4} x^{4} b A + \frac{1}{3} x^{3} a A"," ",0,"1/6*x^6*c*B + 1/5*x^5*b*B + 1/5*x^5*c*A + 1/4*x^4*a*B + 1/4*x^4*b*A + 1/3*x^3*a*A","A",0
845,1,43,0,0.349832," ","integrate(x*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{5} x^{5} c B + \frac{1}{4} x^{4} b B + \frac{1}{4} x^{4} c A + \frac{1}{3} x^{3} a B + \frac{1}{3} x^{3} b A + \frac{1}{2} x^{2} a A"," ",0,"1/5*x^5*c*B + 1/4*x^4*b*B + 1/4*x^4*c*A + 1/3*x^3*a*B + 1/3*x^3*b*A + 1/2*x^2*a*A","A",0
846,1,40,0,0.345022," ","integrate((B*x+A)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} b B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} a B + \frac{1}{2} x^{2} b A + x a A"," ",0,"1/4*x^4*c*B + 1/3*x^3*b*B + 1/3*x^3*c*A + 1/2*x^2*a*B + 1/2*x^2*b*A + x*a*A","A",0
847,1,34,0,0.396083," ","integrate((B*x+A)*(c*x^2+b*x+a)/x,x, algorithm=""fricas"")","\frac{1}{3} \, B c x^{3} + \frac{1}{2} \, {\left(B b + A c\right)} x^{2} + A a \log\left(x\right) + {\left(B a + A b\right)} x"," ",0,"1/3*B*c*x^3 + 1/2*(B*b + A*c)*x^2 + A*a*log(x) + (B*a + A*b)*x","A",0
848,1,40,0,0.391860," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^2,x, algorithm=""fricas"")","\frac{B c x^{3} + 2 \, {\left(B b + A c\right)} x^{2} + 2 \, {\left(B a + A b\right)} x \log\left(x\right) - 2 \, A a}{2 \, x}"," ",0,"1/2*(B*c*x^3 + 2*(B*b + A*c)*x^2 + 2*(B*a + A*b)*x*log(x) - 2*A*a)/x","A",0
849,1,41,0,0.398704," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^3,x, algorithm=""fricas"")","\frac{2 \, B c x^{3} + 2 \, {\left(B b + A c\right)} x^{2} \log\left(x\right) - A a - 2 \, {\left(B a + A b\right)} x}{2 \, x^{2}}"," ",0,"1/2*(2*B*c*x^3 + 2*(B*b + A*c)*x^2*log(x) - A*a - 2*(B*a + A*b)*x)/x^2","A",0
850,1,41,0,0.394928," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^4,x, algorithm=""fricas"")","\frac{6 \, B c x^{3} \log\left(x\right) - 6 \, {\left(B b + A c\right)} x^{2} - 2 \, A a - 3 \, {\left(B a + A b\right)} x}{6 \, x^{3}}"," ",0,"1/6*(6*B*c*x^3*log(x) - 6*(B*b + A*c)*x^2 - 2*A*a - 3*(B*a + A*b)*x)/x^3","A",0
851,1,39,0,0.391000," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^5,x, algorithm=""fricas"")","-\frac{12 \, B c x^{3} + 6 \, {\left(B b + A c\right)} x^{2} + 3 \, A a + 4 \, {\left(B a + A b\right)} x}{12 \, x^{4}}"," ",0,"-1/12*(12*B*c*x^3 + 6*(B*b + A*c)*x^2 + 3*A*a + 4*(B*a + A*b)*x)/x^4","A",0
852,1,39,0,0.387811," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^6,x, algorithm=""fricas"")","-\frac{30 \, B c x^{3} + 20 \, {\left(B b + A c\right)} x^{2} + 12 \, A a + 15 \, {\left(B a + A b\right)} x}{60 \, x^{5}}"," ",0,"-1/60*(30*B*c*x^3 + 20*(B*b + A*c)*x^2 + 12*A*a + 15*(B*a + A*b)*x)/x^5","A",0
853,1,39,0,0.382277," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^7,x, algorithm=""fricas"")","-\frac{20 \, B c x^{3} + 15 \, {\left(B b + A c\right)} x^{2} + 10 \, A a + 12 \, {\left(B a + A b\right)} x}{60 \, x^{6}}"," ",0,"-1/60*(20*B*c*x^3 + 15*(B*b + A*c)*x^2 + 10*A*a + 12*(B*a + A*b)*x)/x^6","A",0
854,1,39,0,0.383373," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^8,x, algorithm=""fricas"")","-\frac{105 \, B c x^{3} + 84 \, {\left(B b + A c\right)} x^{2} + 60 \, A a + 70 \, {\left(B a + A b\right)} x}{420 \, x^{7}}"," ",0,"-1/420*(105*B*c*x^3 + 84*(B*b + A*c)*x^2 + 60*A*a + 70*(B*a + A*b)*x)/x^7","A",0
855,1,103,0,0.367898," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{2} B + \frac{2}{7} x^{7} c b B + \frac{1}{7} x^{7} c^{2} A + \frac{1}{6} x^{6} b^{2} B + \frac{1}{3} x^{6} c a B + \frac{1}{3} x^{6} c b A + \frac{2}{5} x^{5} b a B + \frac{1}{5} x^{5} b^{2} A + \frac{2}{5} x^{5} c a A + \frac{1}{4} x^{4} a^{2} B + \frac{1}{2} x^{4} b a A + \frac{1}{3} x^{3} a^{2} A"," ",0,"1/8*x^8*c^2*B + 2/7*x^7*c*b*B + 1/7*x^7*c^2*A + 1/6*x^6*b^2*B + 1/3*x^6*c*a*B + 1/3*x^6*c*b*A + 2/5*x^5*b*a*B + 1/5*x^5*b^2*A + 2/5*x^5*c*a*A + 1/4*x^4*a^2*B + 1/2*x^4*b*a*A + 1/3*x^3*a^2*A","A",0
856,1,103,0,0.358170," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} c^{2} B + \frac{1}{3} x^{6} c b B + \frac{1}{6} x^{6} c^{2} A + \frac{1}{5} x^{5} b^{2} B + \frac{2}{5} x^{5} c a B + \frac{2}{5} x^{5} c b A + \frac{1}{2} x^{4} b a B + \frac{1}{4} x^{4} b^{2} A + \frac{1}{2} x^{4} c a A + \frac{1}{3} x^{3} a^{2} B + \frac{2}{3} x^{3} b a A + \frac{1}{2} x^{2} a^{2} A"," ",0,"1/7*x^7*c^2*B + 1/3*x^6*c*b*B + 1/6*x^6*c^2*A + 1/5*x^5*b^2*B + 2/5*x^5*c*a*B + 2/5*x^5*c*b*A + 1/2*x^4*b*a*B + 1/4*x^4*b^2*A + 1/2*x^4*c*a*A + 1/3*x^3*a^2*B + 2/3*x^3*b*a*A + 1/2*x^2*a^2*A","A",0
857,1,99,0,0.366691," ","integrate((B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} c^{2} B + \frac{2}{5} x^{5} c b B + \frac{1}{5} x^{5} c^{2} A + \frac{1}{4} x^{4} b^{2} B + \frac{1}{2} x^{4} c a B + \frac{1}{2} x^{4} c b A + \frac{2}{3} x^{3} b a B + \frac{1}{3} x^{3} b^{2} A + \frac{2}{3} x^{3} c a A + \frac{1}{2} x^{2} a^{2} B + x^{2} b a A + x a^{2} A"," ",0,"1/6*x^6*c^2*B + 2/5*x^5*c*b*B + 1/5*x^5*c^2*A + 1/4*x^4*b^2*B + 1/2*x^4*c*a*B + 1/2*x^4*c*b*A + 2/3*x^3*b*a*B + 1/3*x^3*b^2*A + 2/3*x^3*c*a*A + 1/2*x^2*a^2*B + x^2*b*a*A + x*a^2*A","A",0
858,1,88,0,0.421337," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x,x, algorithm=""fricas"")","\frac{1}{5} \, B c^{2} x^{5} + \frac{1}{4} \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + \frac{1}{3} \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} + A a^{2} \log\left(x\right) + \frac{1}{2} \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} + {\left(B a^{2} + 2 \, A a b\right)} x"," ",0,"1/5*B*c^2*x^5 + 1/4*(2*B*b*c + A*c^2)*x^4 + 1/3*(B*b^2 + 2*(B*a + A*b)*c)*x^3 + A*a^2*log(x) + 1/2*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 + (B*a^2 + 2*A*a*b)*x","A",0
859,1,95,0,0.395467," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^2,x, algorithm=""fricas"")","\frac{3 \, B c^{2} x^{5} + 4 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 6 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} - 12 \, A a^{2} + 12 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} + 12 \, {\left(B a^{2} + 2 \, A a b\right)} x \log\left(x\right)}{12 \, x}"," ",0,"1/12*(3*B*c^2*x^5 + 4*(2*B*b*c + A*c^2)*x^4 + 6*(B*b^2 + 2*(B*a + A*b)*c)*x^3 - 12*A*a^2 + 12*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 + 12*(B*a^2 + 2*A*a*b)*x*log(x))/x","A",0
860,1,95,0,0.417192," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^3,x, algorithm=""fricas"")","\frac{2 \, B c^{2} x^{5} + 3 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 6 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} + 6 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} \log\left(x\right) - 3 \, A a^{2} - 6 \, {\left(B a^{2} + 2 \, A a b\right)} x}{6 \, x^{2}}"," ",0,"1/6*(2*B*c^2*x^5 + 3*(2*B*b*c + A*c^2)*x^4 + 6*(B*b^2 + 2*(B*a + A*b)*c)*x^3 + 6*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2*log(x) - 3*A*a^2 - 6*(B*a^2 + 2*A*a*b)*x)/x^2","A",0
861,1,95,0,0.396162," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^4,x, algorithm=""fricas"")","\frac{3 \, B c^{2} x^{5} + 6 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 6 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} \log\left(x\right) - 2 \, A a^{2} - 6 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} x}{6 \, x^{3}}"," ",0,"1/6*(3*B*c^2*x^5 + 6*(2*B*b*c + A*c^2)*x^4 + 6*(B*b^2 + 2*(B*a + A*b)*c)*x^3*log(x) - 2*A*a^2 - 6*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 - 3*(B*a^2 + 2*A*a*b)*x)/x^3","A",0
862,1,95,0,0.408594," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^5,x, algorithm=""fricas"")","\frac{12 \, B c^{2} x^{5} + 12 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} \log\left(x\right) - 12 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} - 3 \, A a^{2} - 6 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} - 4 \, {\left(B a^{2} + 2 \, A a b\right)} x}{12 \, x^{4}}"," ",0,"1/12*(12*B*c^2*x^5 + 12*(2*B*b*c + A*c^2)*x^4*log(x) - 12*(B*b^2 + 2*(B*a + A*b)*c)*x^3 - 3*A*a^2 - 6*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 - 4*(B*a^2 + 2*A*a*b)*x)/x^4","A",0
863,1,95,0,0.400200," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^6,x, algorithm=""fricas"")","\frac{60 \, B c^{2} x^{5} \log\left(x\right) - 60 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} - 30 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} - 12 \, A a^{2} - 20 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} - 15 \, {\left(B a^{2} + 2 \, A a b\right)} x}{60 \, x^{5}}"," ",0,"1/60*(60*B*c^2*x^5*log(x) - 60*(2*B*b*c + A*c^2)*x^4 - 30*(B*b^2 + 2*(B*a + A*b)*c)*x^3 - 12*A*a^2 - 20*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 - 15*(B*a^2 + 2*A*a*b)*x)/x^5","A",0
864,1,93,0,0.398248," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^7,x, algorithm=""fricas"")","-\frac{60 \, B c^{2} x^{5} + 30 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 20 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} + 10 \, A a^{2} + 15 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} + 12 \, {\left(B a^{2} + 2 \, A a b\right)} x}{60 \, x^{6}}"," ",0,"-1/60*(60*B*c^2*x^5 + 30*(2*B*b*c + A*c^2)*x^4 + 20*(B*b^2 + 2*(B*a + A*b)*c)*x^3 + 10*A*a^2 + 15*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 + 12*(B*a^2 + 2*A*a*b)*x)/x^6","A",0
865,1,93,0,0.398886," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^8,x, algorithm=""fricas"")","-\frac{210 \, B c^{2} x^{5} + 140 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 105 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} + 60 \, A a^{2} + 84 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} + 70 \, {\left(B a^{2} + 2 \, A a b\right)} x}{420 \, x^{7}}"," ",0,"-1/420*(210*B*c^2*x^5 + 140*(2*B*b*c + A*c^2)*x^4 + 105*(B*b^2 + 2*(B*a + A*b)*c)*x^3 + 60*A*a^2 + 84*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 + 70*(B*a^2 + 2*A*a*b)*x)/x^7","A",0
866,1,93,0,0.391544," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^9,x, algorithm=""fricas"")","-\frac{280 \, B c^{2} x^{5} + 210 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 168 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} + 105 \, A a^{2} + 140 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} + 120 \, {\left(B a^{2} + 2 \, A a b\right)} x}{840 \, x^{8}}"," ",0,"-1/840*(280*B*c^2*x^5 + 210*(2*B*b*c + A*c^2)*x^4 + 168*(B*b^2 + 2*(B*a + A*b)*c)*x^3 + 105*A*a^2 + 140*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 + 120*(B*a^2 + 2*A*a*b)*x)/x^8","A",0
867,1,192,0,0.359845," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} c^{3} B + \frac{1}{3} x^{9} c^{2} b B + \frac{1}{9} x^{9} c^{3} A + \frac{3}{8} x^{8} c b^{2} B + \frac{3}{8} x^{8} c^{2} a B + \frac{3}{8} x^{8} c^{2} b A + \frac{1}{7} x^{7} b^{3} B + \frac{6}{7} x^{7} c b a B + \frac{3}{7} x^{7} c b^{2} A + \frac{3}{7} x^{7} c^{2} a A + \frac{1}{2} x^{6} b^{2} a B + \frac{1}{2} x^{6} c a^{2} B + \frac{1}{6} x^{6} b^{3} A + x^{6} c b a A + \frac{3}{5} x^{5} b a^{2} B + \frac{3}{5} x^{5} b^{2} a A + \frac{3}{5} x^{5} c a^{2} A + \frac{1}{4} x^{4} a^{3} B + \frac{3}{4} x^{4} b a^{2} A + \frac{1}{3} x^{3} a^{3} A"," ",0,"1/10*x^10*c^3*B + 1/3*x^9*c^2*b*B + 1/9*x^9*c^3*A + 3/8*x^8*c*b^2*B + 3/8*x^8*c^2*a*B + 3/8*x^8*c^2*b*A + 1/7*x^7*b^3*B + 6/7*x^7*c*b*a*B + 3/7*x^7*c*b^2*A + 3/7*x^7*c^2*a*A + 1/2*x^6*b^2*a*B + 1/2*x^6*c*a^2*B + 1/6*x^6*b^3*A + x^6*c*b*a*A + 3/5*x^5*b*a^2*B + 3/5*x^5*b^2*a*A + 3/5*x^5*c*a^2*A + 1/4*x^4*a^3*B + 3/4*x^4*b*a^2*A + 1/3*x^3*a^3*A","A",0
868,1,191,0,0.363511," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{3} B + \frac{3}{8} x^{8} c^{2} b B + \frac{1}{8} x^{8} c^{3} A + \frac{3}{7} x^{7} c b^{2} B + \frac{3}{7} x^{7} c^{2} a B + \frac{3}{7} x^{7} c^{2} b A + \frac{1}{6} x^{6} b^{3} B + x^{6} c b a B + \frac{1}{2} x^{6} c b^{2} A + \frac{1}{2} x^{6} c^{2} a A + \frac{3}{5} x^{5} b^{2} a B + \frac{3}{5} x^{5} c a^{2} B + \frac{1}{5} x^{5} b^{3} A + \frac{6}{5} x^{5} c b a A + \frac{3}{4} x^{4} b a^{2} B + \frac{3}{4} x^{4} b^{2} a A + \frac{3}{4} x^{4} c a^{2} A + \frac{1}{3} x^{3} a^{3} B + x^{3} b a^{2} A + \frac{1}{2} x^{2} a^{3} A"," ",0,"1/9*x^9*c^3*B + 3/8*x^8*c^2*b*B + 1/8*x^8*c^3*A + 3/7*x^7*c*b^2*B + 3/7*x^7*c^2*a*B + 3/7*x^7*c^2*b*A + 1/6*x^6*b^3*B + x^6*c*b*a*B + 1/2*x^6*c*b^2*A + 1/2*x^6*c^2*a*A + 3/5*x^5*b^2*a*B + 3/5*x^5*c*a^2*B + 1/5*x^5*b^3*A + 6/5*x^5*c*b*a*A + 3/4*x^4*b*a^2*B + 3/4*x^4*b^2*a*A + 3/4*x^4*c*a^2*A + 1/3*x^3*a^3*B + x^3*b*a^2*A + 1/2*x^2*a^3*A","A",0
869,1,187,0,0.346250," ","integrate((B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{3} B + \frac{3}{7} x^{7} c^{2} b B + \frac{1}{7} x^{7} c^{3} A + \frac{1}{2} x^{6} c b^{2} B + \frac{1}{2} x^{6} c^{2} a B + \frac{1}{2} x^{6} c^{2} b A + \frac{1}{5} x^{5} b^{3} B + \frac{6}{5} x^{5} c b a B + \frac{3}{5} x^{5} c b^{2} A + \frac{3}{5} x^{5} c^{2} a A + \frac{3}{4} x^{4} b^{2} a B + \frac{3}{4} x^{4} c a^{2} B + \frac{1}{4} x^{4} b^{3} A + \frac{3}{2} x^{4} c b a A + x^{3} b a^{2} B + x^{3} b^{2} a A + x^{3} c a^{2} A + \frac{1}{2} x^{2} a^{3} B + \frac{3}{2} x^{2} b a^{2} A + x a^{3} A"," ",0,"1/8*x^8*c^3*B + 3/7*x^7*c^2*b*B + 1/7*x^7*c^3*A + 1/2*x^6*c*b^2*B + 1/2*x^6*c^2*a*B + 1/2*x^6*c^2*b*A + 1/5*x^5*b^3*B + 6/5*x^5*c*b*a*B + 3/5*x^5*c*b^2*A + 3/5*x^5*c^2*a*A + 3/4*x^4*b^2*a*B + 3/4*x^4*c*a^2*B + 1/4*x^4*b^3*A + 3/2*x^4*c*b*a*A + x^3*b*a^2*B + x^3*b^2*a*A + x^3*c*a^2*A + 1/2*x^2*a^3*B + 3/2*x^2*b*a^2*A + x*a^3*A","A",0
870,1,161,0,0.389198," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x,x, algorithm=""fricas"")","\frac{1}{7} \, B c^{3} x^{7} + \frac{1}{6} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + \frac{3}{5} \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + \frac{1}{4} \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} + A a^{3} \log\left(x\right) + \frac{1}{3} \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} + \frac{3}{2} \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} x"," ",0,"1/7*B*c^3*x^7 + 1/6*(3*B*b*c^2 + A*c^3)*x^6 + 3/5*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 1/4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 + A*a^3*log(x) + 1/3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 + 3/2*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 + (B*a^3 + 3*A*a^2*b)*x","A",0
871,1,168,0,0.401063," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^2,x, algorithm=""fricas"")","\frac{10 \, B c^{3} x^{7} + 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 45 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 20 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 60 \, A a^{3} + 30 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} + 180 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} + 60 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x \log\left(x\right)}{60 \, x}"," ",0,"1/60*(10*B*c^3*x^7 + 12*(3*B*b*c^2 + A*c^3)*x^6 + 45*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 20*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 60*A*a^3 + 30*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 + 180*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 + 60*(B*a^3 + 3*A*a^2*b)*x*log(x))/x","A",0
872,1,168,0,0.409757," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^3,x, algorithm=""fricas"")","\frac{4 \, B c^{3} x^{7} + 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 20 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 10 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 10 \, A a^{3} + 20 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} + 60 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} \log\left(x\right) - 20 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{20 \, x^{2}}"," ",0,"1/20*(4*B*c^3*x^7 + 5*(3*B*b*c^2 + A*c^3)*x^6 + 20*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 10*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 10*A*a^3 + 20*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 + 60*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2*log(x) - 20*(B*a^3 + 3*A*a^2*b)*x)/x^2","A",0
873,1,168,0,0.417821," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^4,x, algorithm=""fricas"")","\frac{3 \, B c^{3} x^{7} + 4 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 18 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 12 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} + 12 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} \log\left(x\right) - 4 \, A a^{3} - 36 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} - 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{12 \, x^{3}}"," ",0,"1/12*(3*B*c^3*x^7 + 4*(3*B*b*c^2 + A*c^3)*x^6 + 18*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 12*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 + 12*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3*log(x) - 4*A*a^3 - 36*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 - 6*(B*a^3 + 3*A*a^2*b)*x)/x^3","A",0
874,1,168,0,0.410719," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^5,x, algorithm=""fricas"")","\frac{4 \, B c^{3} x^{7} + 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 36 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 12 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} \log\left(x\right) - 3 \, A a^{3} - 12 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} - 18 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} - 4 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{12 \, x^{4}}"," ",0,"1/12*(4*B*c^3*x^7 + 6*(3*B*b*c^2 + A*c^3)*x^6 + 36*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 12*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4*log(x) - 3*A*a^3 - 12*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 - 18*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 - 4*(B*a^3 + 3*A*a^2*b)*x)/x^4","A",0
875,1,168,0,0.401150," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^6,x, algorithm=""fricas"")","\frac{10 \, B c^{3} x^{7} + 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 60 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} \log\left(x\right) - 20 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 4 \, A a^{3} - 10 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} - 20 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} - 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{20 \, x^{5}}"," ",0,"1/20*(10*B*c^3*x^7 + 20*(3*B*b*c^2 + A*c^3)*x^6 + 60*(B*b^2*c + (B*a + A*b)*c^2)*x^5*log(x) - 20*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 4*A*a^3 - 10*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 - 20*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 - 5*(B*a^3 + 3*A*a^2*b)*x)/x^5","A",0
876,1,168,0,0.397654," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^7,x, algorithm=""fricas"")","\frac{60 \, B c^{3} x^{7} + 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} \log\left(x\right) - 180 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} - 30 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 10 \, A a^{3} - 20 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} - 45 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} - 12 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{60 \, x^{6}}"," ",0,"1/60*(60*B*c^3*x^7 + 60*(3*B*b*c^2 + A*c^3)*x^6*log(x) - 180*(B*b^2*c + (B*a + A*b)*c^2)*x^5 - 30*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 10*A*a^3 - 20*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 - 45*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 - 12*(B*a^3 + 3*A*a^2*b)*x)/x^6","A",0
877,1,168,0,0.391668," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^8,x, algorithm=""fricas"")","\frac{420 \, B c^{3} x^{7} \log\left(x\right) - 420 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} - 630 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} - 140 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 60 \, A a^{3} - 105 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} - 252 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} - 70 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{420 \, x^{7}}"," ",0,"1/420*(420*B*c^3*x^7*log(x) - 420*(3*B*b*c^2 + A*c^3)*x^6 - 630*(B*b^2*c + (B*a + A*b)*c^2)*x^5 - 140*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 60*A*a^3 - 105*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 - 252*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 - 70*(B*a^3 + 3*A*a^2*b)*x)/x^7","A",0
878,1,166,0,0.405153," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^9,x, algorithm=""fricas"")","-\frac{280 \, B c^{3} x^{7} + 140 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 280 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 70 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} + 35 \, A a^{3} + 56 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} + 140 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} + 40 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{280 \, x^{8}}"," ",0,"-1/280*(280*B*c^3*x^7 + 140*(3*B*b*c^2 + A*c^3)*x^6 + 280*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 70*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 + 35*A*a^3 + 56*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 + 140*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 + 40*(B*a^3 + 3*A*a^2*b)*x)/x^8","A",0
879,1,166,0,0.412107," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^10,x, algorithm=""fricas"")","-\frac{1260 \, B c^{3} x^{7} + 840 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 1890 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 504 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} + 280 \, A a^{3} + 420 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} + 1080 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} + 315 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{2520 \, x^{9}}"," ",0,"-1/2520*(1260*B*c^3*x^7 + 840*(3*B*b*c^2 + A*c^3)*x^6 + 1890*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 504*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 + 280*A*a^3 + 420*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 + 1080*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 + 315*(B*a^3 + 3*A*a^2*b)*x)/x^9","A",0
880,1,166,0,0.402144," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^11,x, algorithm=""fricas"")","-\frac{840 \, B c^{3} x^{7} + 630 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 1512 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 420 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} + 252 \, A a^{3} + 360 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} + 945 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} + 280 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{2520 \, x^{10}}"," ",0,"-1/2520*(840*B*c^3*x^7 + 630*(3*B*b*c^2 + A*c^3)*x^6 + 1512*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 420*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 + 252*A*a^3 + 360*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 + 945*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 + 280*(B*a^3 + 3*A*a^2*b)*x)/x^10","A",0
881,1,730,0,0.449986," ","integrate(x^4*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e x^{4} + 4 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} x^{3} - 6 \, {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e\right)} x^{2} - 6 \, \sqrt{b^{2} - 4 \, a c} {\left({\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 12 \, {\left({\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} e\right)} x - 6 \, {\left({\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{12 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)}}, \frac{3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e x^{4} + 4 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} x^{3} - 6 \, {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e\right)} x^{2} - 12 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 12 \, {\left({\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} e\right)} x - 6 \, {\left({\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{12 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)}}\right]"," ",0,"[1/12*(3*(b^2*c^4 - 4*a*c^5)*e*x^4 + 4*((b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*x^3 - 6*((b^3*c^3 - 4*a*b*c^4)*d - (b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*e)*x^2 - 6*sqrt(b^2 - 4*a*c)*((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 12*((b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*e)*x - 6*((b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*d - (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*e)*log(c*x^2 + b*x + a))/(b^2*c^5 - 4*a*c^6), 1/12*(3*(b^2*c^4 - 4*a*c^5)*e*x^4 + 4*((b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*x^3 - 6*((b^3*c^3 - 4*a*b*c^4)*d - (b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*e)*x^2 - 12*sqrt(-b^2 + 4*a*c)*((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 12*((b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*e)*x - 6*((b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*d - (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*e)*log(c*x^2 + b*x + a))/(b^2*c^5 - 4*a*c^6)]","A",0
882,1,563,0,0.446965," ","integrate(x^3*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e x^{3} + 3 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} x^{2} - 3 \, \sqrt{b^{2} - 4 \, a c} {\left({\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 6 \, {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e\right)} x + 3 \, {\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}, \frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e x^{3} + 3 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} x^{2} + 6 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 6 \, {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e\right)} x + 3 \, {\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}\right]"," ",0,"[1/6*(2*(b^2*c^3 - 4*a*c^4)*e*x^3 + 3*((b^2*c^3 - 4*a*c^4)*d - (b^3*c^2 - 4*a*b*c^3)*e)*x^2 - 3*sqrt(b^2 - 4*a*c)*((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 6*((b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e)*x + 3*((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*e)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5), 1/6*(2*(b^2*c^3 - 4*a*c^4)*e*x^3 + 3*((b^2*c^3 - 4*a*c^4)*d - (b^3*c^2 - 4*a*b*c^3)*e)*x^2 + 6*sqrt(-b^2 + 4*a*c)*((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 6*((b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e)*x + 3*((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*e)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5)]","A",0
883,1,414,0,0.444480," ","integrate(x^2*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e x^{2} + \sqrt{b^{2} - 4 \, a c} {\left({\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(b^{3} c - 4 \, a b c^{2}\right)} e\right)} x - {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}, \frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e x^{2} - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(b^{3} c - 4 \, a b c^{2}\right)} e\right)} x - {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}\right]"," ",0,"[1/2*((b^2*c^2 - 4*a*c^3)*e*x^2 + sqrt(b^2 - 4*a*c)*((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*((b^2*c^2 - 4*a*c^3)*d - (b^3*c - 4*a*b*c^2)*e)*x - ((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4), 1/2*((b^2*c^2 - 4*a*c^3)*e*x^2 - 2*sqrt(-b^2 + 4*a*c)*((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*((b^2*c^2 - 4*a*c^3)*d - (b^3*c - 4*a*b*c^2)*e)*x - ((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4)]","A",0
884,1,289,0,0.430082," ","integrate(x*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e x + {\left(b c d - {\left(b^{2} - 2 \, a c\right)} e\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e x + 2 \, {\left(b c d - {\left(b^{2} - 2 \, a c\right)} e\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/2*(2*(b^2*c - 4*a*c^2)*e*x + (b*c*d - (b^2 - 2*a*c)*e)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3), 1/2*(2*(b^2*c - 4*a*c^2)*e*x + 2*(b*c*d - (b^2 - 2*a*c)*e)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3)]","A",0
885,1,204,0,0.442168," ","integrate((e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{2} + b x + a\right) - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c d - b e\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{2} + b x + a\right) - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(2 \, c d - b e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[1/2*((b^2 - 4*a*c)*e*log(c*x^2 + b*x + a) - sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(b^2*c - 4*a*c^2), 1/2*((b^2 - 4*a*c)*e*log(c*x^2 + b*x + a) - 2*sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(b^2*c - 4*a*c^2)]","A",0
886,1,228,0,0.525014," ","integrate((e*x+d)/x/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(c x^{2} + b x + a\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(x\right) + \sqrt{b^{2} - 4 \, a c} {\left(b d - 2 \, a e\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}, -\frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(c x^{2} + b x + a\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(x\right) - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(b d - 2 \, a e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}\right]"," ",0,"[-1/2*((b^2 - 4*a*c)*d*log(c*x^2 + b*x + a) - 2*(b^2 - 4*a*c)*d*log(x) + sqrt(b^2 - 4*a*c)*(b*d - 2*a*e)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(a*b^2 - 4*a^2*c), -1/2*((b^2 - 4*a*c)*d*log(c*x^2 + b*x + a) - 2*(b^2 - 4*a*c)*d*log(x) - 2*sqrt(-b^2 + 4*a*c)*(b*d - 2*a*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(a*b^2 - 4*a^2*c)]","A",0
887,1,361,0,0.681189," ","integrate((e*x+d)/x^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{{\left(a b e - {\left(b^{2} - 2 \, a c\right)} d\right)} \sqrt{b^{2} - 4 \, a c} x \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} x \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} x \log\left(x\right) - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x}, \frac{2 \, {\left(a b e - {\left(b^{2} - 2 \, a c\right)} d\right)} \sqrt{-b^{2} + 4 \, a c} x \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} x \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} x \log\left(x\right) - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x}\right]"," ",0,"[1/2*((a*b*e - (b^2 - 2*a*c)*d)*sqrt(b^2 - 4*a*c)*x*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + ((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*x*log(c*x^2 + b*x + a) - 2*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*x*log(x) - 2*(a*b^2 - 4*a^2*c)*d)/((a^2*b^2 - 4*a^3*c)*x), 1/2*(2*(a*b*e - (b^2 - 2*a*c)*d)*sqrt(-b^2 + 4*a*c)*x*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + ((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*x*log(c*x^2 + b*x + a) - 2*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*x*log(x) - 2*(a*b^2 - 4*a^2*c)*d)/((a^2*b^2 - 4*a^3*c)*x)]","A",0
888,1,517,0,0.826467," ","integrate((e*x+d)/x^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} {\left({\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e\right)} x^{2} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 4 \, a^{2} b c\right)} e\right)} x^{2} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 4 \, a^{2} b c\right)} e\right)} x^{2} \log\left(x\right) - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d + 2 \, {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e\right)} x}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e\right)} x^{2} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 4 \, a^{2} b c\right)} e\right)} x^{2} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 4 \, a^{2} b c\right)} e\right)} x^{2} \log\left(x\right) - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d + 2 \, {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e\right)} x}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2}}\right]"," ",0,"[1/2*(sqrt(b^2 - 4*a*c)*((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e)*x^2*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - ((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d - (a*b^3 - 4*a^2*b*c)*e)*x^2*log(c*x^2 + b*x + a) + 2*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d - (a*b^3 - 4*a^2*b*c)*e)*x^2*log(x) - (a^2*b^2 - 4*a^3*c)*d + 2*((a*b^3 - 4*a^2*b*c)*d - (a^2*b^2 - 4*a^3*c)*e)*x)/((a^3*b^2 - 4*a^4*c)*x^2), 1/2*(2*sqrt(-b^2 + 4*a*c)*((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e)*x^2*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - ((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d - (a*b^3 - 4*a^2*b*c)*e)*x^2*log(c*x^2 + b*x + a) + 2*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d - (a*b^3 - 4*a^2*b*c)*e)*x^2*log(x) - (a^2*b^2 - 4*a^3*c)*d + 2*((a*b^3 - 4*a^2*b*c)*d - (a^2*b^2 - 4*a^3*c)*e)*x)/((a^3*b^2 - 4*a^4*c)*x^2)]","A",0
889,1,687,0,1.539419," ","integrate((e*x+d)/x^4/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b^{2} - 4 \, a c} {\left({\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e\right)} x^{3} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 3 \, {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e\right)} x^{3} \log\left(c x^{2} + b x + a\right) - 6 \, {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e\right)} x^{3} \log\left(x\right) - 6 \, {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e\right)} x^{2} - 2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d + 3 \, {\left({\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e\right)} x}{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}}, -\frac{6 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e\right)} x^{3} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 3 \, {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e\right)} x^{3} \log\left(c x^{2} + b x + a\right) + 6 \, {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e\right)} x^{3} \log\left(x\right) + 6 \, {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e\right)} x^{2} + 2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d - 3 \, {\left({\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e\right)} x}{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}}\right]"," ",0,"[1/6*(3*sqrt(b^2 - 4*a*c)*((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e)*x^3*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 3*((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e)*x^3*log(c*x^2 + b*x + a) - 6*((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e)*x^3*log(x) - 6*((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d - (a^2*b^3 - 4*a^3*b*c)*e)*x^2 - 2*(a^3*b^2 - 4*a^4*c)*d + 3*((a^2*b^3 - 4*a^3*b*c)*d - (a^3*b^2 - 4*a^4*c)*e)*x)/((a^4*b^2 - 4*a^5*c)*x^3), -1/6*(6*sqrt(-b^2 + 4*a*c)*((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e)*x^3*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 3*((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e)*x^3*log(c*x^2 + b*x + a) + 6*((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e)*x^3*log(x) + 6*((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d - (a^2*b^3 - 4*a^3*b*c)*e)*x^2 + 2*(a^3*b^2 - 4*a^4*c)*d - 3*((a^2*b^3 - 4*a^3*b*c)*d - (a^3*b^2 - 4*a^4*c)*e)*x)/((a^4*b^2 - 4*a^5*c)*x^3)]","A",0
890,1,1696,0,0.480815," ","integrate(x^4*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e x^{4} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d - 3 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e\right)} x^{3} + {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d - {\left(4 \, b^{6} c - 33 \, a b^{4} c^{2} + 72 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} e\right)} x^{2} + {\left({\left(2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d - {\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} e\right)} x^{2} + 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 6 \, a^{3} c^{3}\right)} d - {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} e + {\left(2 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} d - {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(a b^{5} c - 7 \, a^{2} b^{3} c^{2} + 12 \, a^{3} b c^{3}\right)} d + 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} e - 2 \, {\left({\left(b^{6} c - 9 \, a b^{4} c^{2} + 26 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 11 \, a b^{5} c + 41 \, a^{2} b^{3} c^{2} - 52 \, a^{3} b c^{3}\right)} e\right)} x - {\left({\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d - {\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} e\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d - {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} e + {\left(2 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d - {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} e\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{2} + {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x\right)}}, \frac{{\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e x^{4} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d - 3 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e\right)} x^{3} + {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d - {\left(4 \, b^{6} c - 33 \, a b^{4} c^{2} + 72 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} e\right)} x^{2} - 2 \, {\left({\left(2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d - {\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} e\right)} x^{2} + 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 6 \, a^{3} c^{3}\right)} d - {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} e + {\left(2 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} d - {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(a b^{5} c - 7 \, a^{2} b^{3} c^{2} + 12 \, a^{3} b c^{3}\right)} d + 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} e - 2 \, {\left({\left(b^{6} c - 9 \, a b^{4} c^{2} + 26 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 11 \, a b^{5} c + 41 \, a^{2} b^{3} c^{2} - 52 \, a^{3} b c^{3}\right)} e\right)} x - {\left({\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d - {\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} e\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d - {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} e + {\left(2 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d - {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} e\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{2} + {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x\right)}}\right]"," ",0,"[1/2*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*e*x^4 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d - 3*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e)*x^3 + (2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d - (4*b^6*c - 33*a*b^4*c^2 + 72*a^2*b^2*c^3 - 16*a^3*c^4)*e)*x^2 + ((2*(b^4*c^2 - 6*a*b^2*c^3 + 6*a^2*c^4)*d - (3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*e)*x^2 + 2*(a*b^4*c - 6*a^2*b^2*c^2 + 6*a^3*c^3)*d - (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*e + (2*(b^5*c - 6*a*b^3*c^2 + 6*a^2*b*c^3)*d - (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(a*b^5*c - 7*a^2*b^3*c^2 + 12*a^3*b*c^3)*d + 2*(a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*e - 2*((b^6*c - 9*a*b^4*c^2 + 26*a^2*b^2*c^3 - 24*a^3*c^4)*d - (b^7 - 11*a*b^5*c + 41*a^2*b^3*c^2 - 52*a^3*b*c^3)*e)*x - ((2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d - (3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*e)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d - (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*e + (2*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d - (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*e)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^2 + (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x), 1/2*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*e*x^4 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d - 3*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e)*x^3 + (2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d - (4*b^6*c - 33*a*b^4*c^2 + 72*a^2*b^2*c^3 - 16*a^3*c^4)*e)*x^2 - 2*((2*(b^4*c^2 - 6*a*b^2*c^3 + 6*a^2*c^4)*d - (3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*e)*x^2 + 2*(a*b^4*c - 6*a^2*b^2*c^2 + 6*a^3*c^3)*d - (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*e + (2*(b^5*c - 6*a*b^3*c^2 + 6*a^2*b*c^3)*d - (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(a*b^5*c - 7*a^2*b^3*c^2 + 12*a^3*b*c^3)*d + 2*(a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*e - 2*((b^6*c - 9*a*b^4*c^2 + 26*a^2*b^2*c^3 - 24*a^3*c^4)*d - (b^7 - 11*a*b^5*c + 41*a^2*b^3*c^2 - 52*a^3*b*c^3)*e)*x - ((2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d - (3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*e)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d - (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*e + (2*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d - (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*e)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^2 + (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x)]","B",0
891,1,1283,0,0.458394," ","integrate(x^3*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e x^{3} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e x^{2} + {\left({\left({\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} d - 2 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e\right)} x^{2} + {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} e + {\left({\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} d - 2 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d - 2 \, {\left(a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} e + 2 \, {\left({\left(b^{5} c - 7 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} e\right)} x + {\left({\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e\right)} x^{2} + {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d - 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e + {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d - 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x\right)}}, \frac{2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e x^{3} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e x^{2} + 2 \, {\left({\left({\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} d - 2 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e\right)} x^{2} + {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} e + {\left({\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} d - 2 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d - 2 \, {\left(a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} e + 2 \, {\left({\left(b^{5} c - 7 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} e\right)} x + {\left({\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e\right)} x^{2} + {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d - 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e + {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d - 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e*x^3 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e*x^2 + (((b^3*c^2 - 6*a*b*c^3)*d - 2*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e)*x^2 + (a*b^3*c - 6*a^2*b*c^2)*d - 2*(a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*e + ((b^4*c - 6*a*b^2*c^2)*d - 2*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(a*b^4*c - 6*a^2*b^2*c^2 + 8*a^3*c^3)*d - 2*(a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2)*e + 2*((b^5*c - 7*a*b^3*c^2 + 12*a^2*b*c^3)*d - (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*e)*x + (((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d - 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e)*x^2 + (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d - 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e + ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d - 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x), 1/2*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e*x^3 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e*x^2 + 2*(((b^3*c^2 - 6*a*b*c^3)*d - 2*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e)*x^2 + (a*b^3*c - 6*a^2*b*c^2)*d - 2*(a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*e + ((b^4*c - 6*a*b^2*c^2)*d - 2*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(a*b^4*c - 6*a^2*b^2*c^2 + 8*a^3*c^3)*d - 2*(a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2)*e + 2*((b^5*c - 7*a*b^3*c^2 + 12*a^2*b*c^3)*d - (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*e)*x + (((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d - 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e)*x^2 + (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d - 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e + ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d - 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x)]","B",0
892,1,813,0,0.462379," ","integrate(x^2*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(4 \, a^{2} c^{2} d + {\left(4 \, a c^{3} d + {\left(b^{3} c - 6 \, a b c^{2}\right)} e\right)} x^{2} + {\left(a b^{3} - 6 \, a^{2} b c\right)} e + {\left(4 \, a b c^{2} d + {\left(b^{4} - 6 \, a b^{2} c\right)} e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e - 2 \, {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} e\right)} x + {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}, \frac{2 \, {\left(4 \, a^{2} c^{2} d + {\left(4 \, a c^{3} d + {\left(b^{3} c - 6 \, a b c^{2}\right)} e\right)} x^{2} + {\left(a b^{3} - 6 \, a^{2} b c\right)} e + {\left(4 \, a b c^{2} d + {\left(b^{4} - 6 \, a b^{2} c\right)} e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e - 2 \, {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} e\right)} x + {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}\right]"," ",0,"[1/2*((4*a^2*c^2*d + (4*a*c^3*d + (b^3*c - 6*a*b*c^2)*e)*x^2 + (a*b^3 - 6*a^2*b*c)*e + (4*a*b*c^2*d + (b^4 - 6*a*b^2*c)*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(a*b^3*c - 4*a^2*b*c^2)*d + 2*(a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e - 2*((b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d - (b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*e)*x + ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e)*log(c*x^2 + b*x + a))/(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x), 1/2*(2*(4*a^2*c^2*d + (4*a*c^3*d + (b^3*c - 6*a*b*c^2)*e)*x^2 + (a*b^3 - 6*a^2*b*c)*e + (4*a*b*c^2*d + (b^4 - 6*a*b^2*c)*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(a*b^3*c - 4*a^2*b*c^2)*d + 2*(a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e - 2*((b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d - (b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*e)*x + ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e)*log(c*x^2 + b*x + a))/(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x)]","B",0
893,1,521,0,0.431133," ","integrate(x*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(a b c d - 2 \, a^{2} c e + {\left(b c^{2} d - 2 \, a c^{2} e\right)} x^{2} + {\left(b^{2} c d - 2 \, a b c e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 4 \, a^{2} b c\right)} e + {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} e\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}, -\frac{2 \, {\left(a b c d - 2 \, a^{2} c e + {\left(b c^{2} d - 2 \, a c^{2} e\right)} x^{2} + {\left(b^{2} c d - 2 \, a b c e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d + {\left(a b^{3} - 4 \, a^{2} b c\right)} e - {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} e\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}\right]"," ",0,"[((a*b*c*d - 2*a^2*c*e + (b*c^2*d - 2*a*c^2*e)*x^2 + (b^2*c*d - 2*a*b*c*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(a*b^2*c - 4*a^2*c^2)*d - (a*b^3 - 4*a^2*b*c)*e + ((b^3*c - 4*a*b*c^2)*d - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*e)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x), -(2*(a*b*c*d - 2*a^2*c*e + (b*c^2*d - 2*a*c^2*e)*x^2 + (b^2*c*d - 2*a*b*c*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(a*b^2*c - 4*a^2*c^2)*d + (a*b^3 - 4*a^2*b*c)*e - ((b^3*c - 4*a*b*c^2)*d - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*e)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x)]","B",0
894,1,459,0,0.468144," ","integrate((e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a c d - a b e + {\left(2 \, c^{2} d - b c e\right)} x^{2} + {\left(2 \, b c d - b^{2} e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(b^{3} - 4 \, a b c\right)} d + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e - {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}, \frac{2 \, {\left(2 \, a c d - a b e + {\left(2 \, c^{2} d - b c e\right)} x^{2} + {\left(2 \, b c d - b^{2} e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} d + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e - {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}\right]"," ",0,"[((2*a*c*d - a*b*e + (2*c^2*d - b*c*e)*x^2 + (2*b*c*d - b^2*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (b^3 - 4*a*b*c)*d + 2*(a*b^2 - 4*a^2*c)*e - (2*(b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x), (2*(2*a*c*d - a*b*e + (2*c^2*d - b*c*e)*x^2 + (2*b*c*d - b^2*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*d + 2*(a*b^2 - 4*a^2*c)*e - (2*(b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)]","B",0
895,1,955,0,0.845300," ","integrate((e*x+d)/x/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, a^{3} c e + {\left(4 \, a^{2} c^{2} e + {\left(b^{3} c - 6 \, a b c^{2}\right)} d\right)} x^{2} + {\left(a b^{3} - 6 \, a^{2} b c\right)} d + {\left(4 \, a^{2} b c e + {\left(b^{4} - 6 \, a b^{2} c\right)} d\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} d + 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e - 2 \, {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} x + {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{2} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)}}, \frac{2 \, {\left(4 \, a^{3} c e + {\left(4 \, a^{2} c^{2} e + {\left(b^{3} c - 6 \, a b c^{2}\right)} d\right)} x^{2} + {\left(a b^{3} - 6 \, a^{2} b c\right)} d + {\left(4 \, a^{2} b c e + {\left(b^{4} - 6 \, a b^{2} c\right)} d\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} d - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e + 2 \, {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} x - {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{2} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)}}\right]"," ",0,"[-1/2*((4*a^3*c*e + (4*a^2*c^2*e + (b^3*c - 6*a*b*c^2)*d)*x^2 + (a*b^3 - 6*a^2*b*c)*d + (4*a^2*b*c*e + (b^4 - 6*a*b^2*c)*d)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*d + 2*(a^2*b^3 - 4*a^3*b*c)*e - 2*((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*x + ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*d)*log(c*x^2 + b*x + a) - 2*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*d)*log(x))/(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*x^2 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x), 1/2*(2*(4*a^3*c*e + (4*a^2*c^2*e + (b^3*c - 6*a*b*c^2)*d)*x^2 + (a*b^3 - 6*a^2*b*c)*d + (4*a^2*b*c*e + (b^4 - 6*a*b^2*c)*d)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*d - 2*(a^2*b^3 - 4*a^3*b*c)*e + 2*((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*x - ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*d)*log(c*x^2 + b*x + a) + 2*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*d)*log(x))/(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*x^2 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x)]","B",0
896,1,1615,0,2.034379," ","integrate((e*x+d)/x^2/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d - {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} e\right)} x^{2} + {\left({\left(2 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d - {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} e\right)} x^{3} + {\left(2 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 6 \, a^{2} b^{2} c\right)} e\right)} x^{2} + {\left(2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 6 \, a^{3} b c\right)} e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d + 2 \, {\left({\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} e\right)} x - {\left({\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d - {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} e\right)} x^{3} + {\left(2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e\right)} x^{2} + {\left(2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d - {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} e\right)} x^{3} + {\left(2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e\right)} x^{2} + {\left(2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e\right)} x\right)} \log\left(x\right)}{2 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x\right)}}, -\frac{2 \, {\left(2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d - {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} e\right)} x^{2} + 2 \, {\left({\left(2 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d - {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} e\right)} x^{3} + {\left(2 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 6 \, a^{2} b^{2} c\right)} e\right)} x^{2} + {\left(2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 6 \, a^{3} b c\right)} e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d + 2 \, {\left({\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} e\right)} x - {\left({\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d - {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} e\right)} x^{3} + {\left(2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e\right)} x^{2} + {\left(2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d - {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} e\right)} x^{3} + {\left(2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e\right)} x^{2} + {\left(2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e\right)} x\right)} \log\left(x\right)}{2 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d - (a^2*b^3*c - 4*a^3*b*c^2)*e)*x^2 + ((2*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d - (a*b^3*c - 6*a^2*b*c^2)*e)*x^3 + (2*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d - (a*b^4 - 6*a^2*b^2*c)*e)*x^2 + (2*(a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d - (a^2*b^3 - 6*a^3*b*c)*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*d + 2*((2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d - (a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*e)*x - ((2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d - (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*e)*x^3 + (2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e)*x^2 + (2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d - (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e)*x)*log(c*x^2 + b*x + a) + 2*((2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d - (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*e)*x^3 + (2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e)*x^2 + (2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d - (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e)*x)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x), -1/2*(2*(2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d - (a^2*b^3*c - 4*a^3*b*c^2)*e)*x^2 + 2*((2*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d - (a*b^3*c - 6*a^2*b*c^2)*e)*x^3 + (2*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d - (a*b^4 - 6*a^2*b^2*c)*e)*x^2 + (2*(a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d - (a^2*b^3 - 6*a^3*b*c)*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*d + 2*((2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d - (a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*e)*x - ((2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d - (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*e)*x^3 + (2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e)*x^2 + (2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d - (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e)*x)*log(c*x^2 + b*x + a) + 2*((2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d - (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*e)*x^3 + (2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e)*x^2 + (2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d - (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e)*x)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x)]","B",0
897,1,2003,0,4.078416," ","integrate((e*x+d)/x^3/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(3 \, a b^{5} c - 23 \, a^{2} b^{3} c^{2} + 44 \, a^{3} b c^{3}\right)} d - 2 \, {\left(a^{2} b^{4} c - 7 \, a^{3} b^{2} c^{2} + 12 \, a^{4} c^{3}\right)} e\right)} x^{3} + {\left({\left(6 \, a b^{6} - 49 \, a^{2} b^{4} c + 108 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d - 2 \, {\left(2 \, a^{2} b^{5} - 15 \, a^{3} b^{3} c + 28 \, a^{4} b c^{2}\right)} e\right)} x^{2} + {\left({\left({\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} d - 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 6 \, a^{3} c^{3}\right)} e\right)} x^{4} + {\left({\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} d - 2 \, {\left(a b^{5} - 6 \, a^{2} b^{3} c + 6 \, a^{3} b c^{2}\right)} e\right)} x^{3} + {\left({\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} e\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} d + {\left(3 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} e\right)} x - {\left({\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} e\right)} x^{4} + {\left({\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} d - 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e\right)} x^{3} + {\left({\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e\right)} x^{2}\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} e\right)} x^{4} + {\left({\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} d - 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e\right)} x^{3} + {\left({\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} x^{4} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x^{2}\right)}}, \frac{2 \, {\left({\left(3 \, a b^{5} c - 23 \, a^{2} b^{3} c^{2} + 44 \, a^{3} b c^{3}\right)} d - 2 \, {\left(a^{2} b^{4} c - 7 \, a^{3} b^{2} c^{2} + 12 \, a^{4} c^{3}\right)} e\right)} x^{3} + {\left({\left(6 \, a b^{6} - 49 \, a^{2} b^{4} c + 108 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d - 2 \, {\left(2 \, a^{2} b^{5} - 15 \, a^{3} b^{3} c + 28 \, a^{4} b c^{2}\right)} e\right)} x^{2} + 2 \, {\left({\left({\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} d - 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 6 \, a^{3} c^{3}\right)} e\right)} x^{4} + {\left({\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} d - 2 \, {\left(a b^{5} - 6 \, a^{2} b^{3} c + 6 \, a^{3} b c^{2}\right)} e\right)} x^{3} + {\left({\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} e\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} d + {\left(3 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} e\right)} x - {\left({\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} e\right)} x^{4} + {\left({\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} d - 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e\right)} x^{3} + {\left({\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e\right)} x^{2}\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} e\right)} x^{4} + {\left({\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} d - 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e\right)} x^{3} + {\left({\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} x^{4} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/2*(2*((3*a*b^5*c - 23*a^2*b^3*c^2 + 44*a^3*b*c^3)*d - 2*(a^2*b^4*c - 7*a^3*b^2*c^2 + 12*a^4*c^3)*e)*x^3 + ((6*a*b^6 - 49*a^2*b^4*c + 108*a^3*b^2*c^2 - 32*a^4*c^3)*d - 2*(2*a^2*b^5 - 15*a^3*b^3*c + 28*a^4*b*c^2)*e)*x^2 + (((3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*d - 2*(a*b^4*c - 6*a^2*b^2*c^2 + 6*a^3*c^3)*e)*x^4 + ((3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*d - 2*(a*b^5 - 6*a^2*b^3*c + 6*a^3*b*c^2)*e)*x^3 + ((3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*d - 2*(a^2*b^4 - 6*a^3*b^2*c + 6*a^4*c^2)*e)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*d + (3*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d - 2*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*e)*x - (((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*d - 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*e)*x^4 + ((3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*d - 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e)*x^3 + ((3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*d - 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e)*x^2)*log(c*x^2 + b*x + a) + 2*(((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*d - 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*e)*x^4 + ((3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*d - 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e)*x^3 + ((3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*d - 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e)*x^2)*log(x))/((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*x^4 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x^2), 1/2*(2*((3*a*b^5*c - 23*a^2*b^3*c^2 + 44*a^3*b*c^3)*d - 2*(a^2*b^4*c - 7*a^3*b^2*c^2 + 12*a^4*c^3)*e)*x^3 + ((6*a*b^6 - 49*a^2*b^4*c + 108*a^3*b^2*c^2 - 32*a^4*c^3)*d - 2*(2*a^2*b^5 - 15*a^3*b^3*c + 28*a^4*b*c^2)*e)*x^2 + 2*(((3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*d - 2*(a*b^4*c - 6*a^2*b^2*c^2 + 6*a^3*c^3)*e)*x^4 + ((3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*d - 2*(a*b^5 - 6*a^2*b^3*c + 6*a^3*b*c^2)*e)*x^3 + ((3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*d - 2*(a^2*b^4 - 6*a^3*b^2*c + 6*a^4*c^2)*e)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*d + (3*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d - 2*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*e)*x - (((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*d - 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*e)*x^4 + ((3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*d - 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e)*x^3 + ((3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*d - 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e)*x^2)*log(c*x^2 + b*x + a) + 2*(((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*d - 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*e)*x^4 + ((3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*d - 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e)*x^3 + ((3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*d - 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e)*x^2)*log(x))/((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*x^4 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x^2)]","B",0
898,1,9,0,0.380313," ","integrate((5+2*x)/(x^2+5*x+4),x, algorithm=""fricas"")","\log\left(x^{2} + 5 \, x + 4\right)"," ",0,"log(x^2 + 5*x + 4)","A",0
899,1,13,0,0.387335," ","integrate((7+3*x)/(x^2+6*x+8),x, algorithm=""fricas"")","\frac{5}{2} \, \log\left(x + 4\right) + \frac{1}{2} \, \log\left(x + 2\right)"," ",0,"5/2*log(x + 4) + 1/2*log(x + 2)","A",0
900,1,14,0,0.411334," ","integrate((5+2*x)/(x^2+4*x+5),x, algorithm=""fricas"")","\arctan\left(x + 2\right) + \log\left(x^{2} + 4 \, x + 5\right)"," ",0,"arctan(x + 2) + log(x^2 + 4*x + 5)","A",0
901,1,26,0,0.397290," ","integrate((-2+7*x)/(2*x^2-16*x+42),x, algorithm=""fricas"")","\frac{13}{5} \, \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} {\left(x - 4\right)}\right) + \frac{7}{4} \, \log\left(x^{2} - 8 \, x + 21\right)"," ",0,"13/5*sqrt(5)*arctan(1/5*sqrt(5)*(x - 4)) + 7/4*log(x^2 - 8*x + 21)","A",0
902,1,49,0,0.414045," ","integrate((3+x)/(x^2+3*x+1),x, algorithm=""fricas"")","\frac{3}{10} \, \sqrt{5} \log\left(\frac{2 \, x^{2} - \sqrt{5} {\left(2 \, x + 3\right)} + 6 \, x + 7}{x^{2} + 3 \, x + 1}\right) + \frac{1}{2} \, \log\left(x^{2} + 3 \, x + 1\right)"," ",0,"3/10*sqrt(5)*log((2*x^2 - sqrt(5)*(2*x + 3) + 6*x + 7)/(x^2 + 3*x + 1)) + 1/2*log(x^2 + 3*x + 1)","A",0
903,1,51,0,0.440165," ","integrate((-1+2*x)/(4*x^2+8*x+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{3} \log\left(\frac{4 \, x^{2} + 4 \, \sqrt{3} {\left(x + 1\right)} + 8 \, x + 7}{4 \, x^{2} + 8 \, x + 1}\right) + \frac{1}{4} \, \log\left(4 \, x^{2} + 8 \, x + 1\right)"," ",0,"1/4*sqrt(3)*log((4*x^2 + 4*sqrt(3)*(x + 1) + 8*x + 7)/(4*x^2 + 8*x + 1)) + 1/4*log(4*x^2 + 8*x + 1)","A",0
904,1,14,0,0.435867," ","integrate((3+2*x)/(4*x^2+12*x+13)^2,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(4 \, x^{2} + 12 \, x + 13\right)}}"," ",0,"-1/4/(4*x^2 + 12*x + 13)","A",0
905,1,31,0,0.431637," ","integrate((4+x)/(x^2+4*x+5)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} + 4 \, x + 5\right)} \arctan\left(x + 2\right) + 2 \, x + 3}{2 \, {\left(x^{2} + 4 \, x + 5\right)}}"," ",0,"1/2*(2*(x^2 + 4*x + 5)*arctan(x + 2) + 2*x + 3)/(x^2 + 4*x + 5)","A",0
906,1,37,0,0.422144," ","integrate((-1+3*x)/(x^2+x+1)^2,x, algorithm=""fricas"")","-\frac{10 \, \sqrt{3} {\left(x^{2} + x + 1\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + 15 \, x + 21}{9 \, {\left(x^{2} + x + 1\right)}}"," ",0,"-1/9*(10*sqrt(3)*(x^2 + x + 1)*arctan(1/3*sqrt(3)*(2*x + 1)) + 15*x + 21)/(x^2 + x + 1)","A",0
907,1,71,0,0.445140," ","integrate((1+x)/(x^2-x+1)^3,x, algorithm=""fricas"")","\frac{6 \, x^{3} + 4 \, \sqrt{3} {\left(x^{4} - 2 \, x^{3} + 3 \, x^{2} - 2 \, x + 1\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 9 \, x^{2} + 12 \, x - 6}{6 \, {\left(x^{4} - 2 \, x^{3} + 3 \, x^{2} - 2 \, x + 1\right)}}"," ",0,"1/6*(6*x^3 + 4*sqrt(3)*(x^4 - 2*x^3 + 3*x^2 - 2*x + 1)*arctan(1/3*sqrt(3)*(2*x - 1)) - 9*x^2 + 12*x - 6)/(x^4 - 2*x^3 + 3*x^2 - 2*x + 1)","A",0
908,1,10,0,0.414920," ","integrate(1/(B*x+A),x, algorithm=""fricas"")","\frac{\log\left(B x + A\right)}{B}"," ",0,"log(B*x + A)/B","A",0
909,1,10,0,0.466719," ","integrate((B*x+A)/(B^2*x^2+2*A*B*x+A^2),x, algorithm=""fricas"")","\frac{\log\left(B x + A\right)}{B}"," ",0,"log(B*x + A)/B","A",0
910,1,843,0,0.562533," ","integrate(x^4*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(33 \, B b^{7} + 128 \, A a^{3} c^{4} - 160 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{3} + 280 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} c^{2} - 42 \, {\left(6 \, B a b^{5} + A b^{6}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(15360 \, B c^{7} x^{6} - 3465 \, B b^{6} c + 1280 \, {\left(B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 32 \, {\left(256 \, B a^{3} + 791 \, A a^{2} b\right)} c^{4} - 128 \, {\left(11 \, B b^{2} c^{5} - 2 \, {\left(12 \, B a + 7 \, A b\right)} c^{6}\right)} x^{4} - 336 \, {\left(103 \, B a^{2} b^{2} + 70 \, A a b^{3}\right)} c^{3} + 16 \, {\left(99 \, B b^{3} c^{4} + 280 \, A a c^{6} - 2 \, {\left(158 \, B a b + 63 \, A b^{2}\right)} c^{5}\right)} x^{3} + 210 \, {\left(104 \, B a b^{4} + 21 \, A b^{5}\right)} c^{2} - 8 \, {\left(231 \, B b^{4} c^{3} + 8 \, {\left(64 \, B a^{2} + 119 \, A a b\right)} c^{5} - 6 \, {\left(162 \, B a b^{2} + 49 \, A b^{3}\right)} c^{4}\right)} x^{2} + 2 \, {\left(1155 \, B b^{5} c^{2} - 3360 \, A a^{2} c^{5} + 16 \, {\left(397 \, B a^{2} b + 392 \, A a b^{2}\right)} c^{4} - 42 \, {\left(144 \, B a b^{3} + 35 \, A b^{4}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{430080 \, c^{7}}, -\frac{105 \, {\left(33 \, B b^{7} + 128 \, A a^{3} c^{4} - 160 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{3} + 280 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} c^{2} - 42 \, {\left(6 \, B a b^{5} + A b^{6}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(15360 \, B c^{7} x^{6} - 3465 \, B b^{6} c + 1280 \, {\left(B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 32 \, {\left(256 \, B a^{3} + 791 \, A a^{2} b\right)} c^{4} - 128 \, {\left(11 \, B b^{2} c^{5} - 2 \, {\left(12 \, B a + 7 \, A b\right)} c^{6}\right)} x^{4} - 336 \, {\left(103 \, B a^{2} b^{2} + 70 \, A a b^{3}\right)} c^{3} + 16 \, {\left(99 \, B b^{3} c^{4} + 280 \, A a c^{6} - 2 \, {\left(158 \, B a b + 63 \, A b^{2}\right)} c^{5}\right)} x^{3} + 210 \, {\left(104 \, B a b^{4} + 21 \, A b^{5}\right)} c^{2} - 8 \, {\left(231 \, B b^{4} c^{3} + 8 \, {\left(64 \, B a^{2} + 119 \, A a b\right)} c^{5} - 6 \, {\left(162 \, B a b^{2} + 49 \, A b^{3}\right)} c^{4}\right)} x^{2} + 2 \, {\left(1155 \, B b^{5} c^{2} - 3360 \, A a^{2} c^{5} + 16 \, {\left(397 \, B a^{2} b + 392 \, A a b^{2}\right)} c^{4} - 42 \, {\left(144 \, B a b^{3} + 35 \, A b^{4}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{215040 \, c^{7}}\right]"," ",0,"[1/430080*(105*(33*B*b^7 + 128*A*a^3*c^4 - 160*(2*B*a^3*b + 3*A*a^2*b^2)*c^3 + 280*(2*B*a^2*b^3 + A*a*b^4)*c^2 - 42*(6*B*a*b^5 + A*b^6)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(15360*B*c^7*x^6 - 3465*B*b^6*c + 1280*(B*b*c^6 + 14*A*c^7)*x^5 + 32*(256*B*a^3 + 791*A*a^2*b)*c^4 - 128*(11*B*b^2*c^5 - 2*(12*B*a + 7*A*b)*c^6)*x^4 - 336*(103*B*a^2*b^2 + 70*A*a*b^3)*c^3 + 16*(99*B*b^3*c^4 + 280*A*a*c^6 - 2*(158*B*a*b + 63*A*b^2)*c^5)*x^3 + 210*(104*B*a*b^4 + 21*A*b^5)*c^2 - 8*(231*B*b^4*c^3 + 8*(64*B*a^2 + 119*A*a*b)*c^5 - 6*(162*B*a*b^2 + 49*A*b^3)*c^4)*x^2 + 2*(1155*B*b^5*c^2 - 3360*A*a^2*c^5 + 16*(397*B*a^2*b + 392*A*a*b^2)*c^4 - 42*(144*B*a*b^3 + 35*A*b^4)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^7, -1/215040*(105*(33*B*b^7 + 128*A*a^3*c^4 - 160*(2*B*a^3*b + 3*A*a^2*b^2)*c^3 + 280*(2*B*a^2*b^3 + A*a*b^4)*c^2 - 42*(6*B*a*b^5 + A*b^6)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(15360*B*c^7*x^6 - 3465*B*b^6*c + 1280*(B*b*c^6 + 14*A*c^7)*x^5 + 32*(256*B*a^3 + 791*A*a^2*b)*c^4 - 128*(11*B*b^2*c^5 - 2*(12*B*a + 7*A*b)*c^6)*x^4 - 336*(103*B*a^2*b^2 + 70*A*a*b^3)*c^3 + 16*(99*B*b^3*c^4 + 280*A*a*c^6 - 2*(158*B*a*b + 63*A*b^2)*c^5)*x^3 + 210*(104*B*a*b^4 + 21*A*b^5)*c^2 - 8*(231*B*b^4*c^3 + 8*(64*B*a^2 + 119*A*a*b)*c^5 - 6*(162*B*a*b^2 + 49*A*b^3)*c^4)*x^2 + 2*(1155*B*b^5*c^2 - 3360*A*a^2*c^5 + 16*(397*B*a^2*b + 392*A*a*b^2)*c^4 - 42*(144*B*a*b^3 + 35*A*b^4)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^7]","A",0
911,1,667,0,0.529763," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(21 \, B b^{6} - 64 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3} + 80 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2} - 28 \, {\left(5 \, B a b^{4} + A b^{5}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1280 \, B c^{6} x^{5} + 315 \, B b^{5} c - 1024 \, A a^{2} c^{4} + 128 \, {\left(B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 16 \, {\left(113 \, B a^{2} b + 115 \, A a b^{2}\right)} c^{3} - 16 \, {\left(9 \, B b^{2} c^{4} - 4 \, {\left(5 \, B a + 3 \, A b\right)} c^{5}\right)} x^{3} - 420 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c^{2} + 8 \, {\left(21 \, B b^{3} c^{3} + 64 \, A a c^{5} - 4 \, {\left(17 \, B a b + 7 \, A b^{2}\right)} c^{4}\right)} x^{2} - 2 \, {\left(105 \, B b^{4} c^{2} + 16 \, {\left(15 \, B a^{2} + 29 \, A a b\right)} c^{4} - 28 \, {\left(16 \, B a b^{2} + 5 \, A b^{3}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{6}}, \frac{15 \, {\left(21 \, B b^{6} - 64 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3} + 80 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2} - 28 \, {\left(5 \, B a b^{4} + A b^{5}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(1280 \, B c^{6} x^{5} + 315 \, B b^{5} c - 1024 \, A a^{2} c^{4} + 128 \, {\left(B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 16 \, {\left(113 \, B a^{2} b + 115 \, A a b^{2}\right)} c^{3} - 16 \, {\left(9 \, B b^{2} c^{4} - 4 \, {\left(5 \, B a + 3 \, A b\right)} c^{5}\right)} x^{3} - 420 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c^{2} + 8 \, {\left(21 \, B b^{3} c^{3} + 64 \, A a c^{5} - 4 \, {\left(17 \, B a b + 7 \, A b^{2}\right)} c^{4}\right)} x^{2} - 2 \, {\left(105 \, B b^{4} c^{2} + 16 \, {\left(15 \, B a^{2} + 29 \, A a b\right)} c^{4} - 28 \, {\left(16 \, B a b^{2} + 5 \, A b^{3}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{6}}\right]"," ",0,"[-1/30720*(15*(21*B*b^6 - 64*(B*a^3 + 3*A*a^2*b)*c^3 + 80*(3*B*a^2*b^2 + 2*A*a*b^3)*c^2 - 28*(5*B*a*b^4 + A*b^5)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(1280*B*c^6*x^5 + 315*B*b^5*c - 1024*A*a^2*c^4 + 128*(B*b*c^5 + 12*A*c^6)*x^4 + 16*(113*B*a^2*b + 115*A*a*b^2)*c^3 - 16*(9*B*b^2*c^4 - 4*(5*B*a + 3*A*b)*c^5)*x^3 - 420*(4*B*a*b^3 + A*b^4)*c^2 + 8*(21*B*b^3*c^3 + 64*A*a*c^5 - 4*(17*B*a*b + 7*A*b^2)*c^4)*x^2 - 2*(105*B*b^4*c^2 + 16*(15*B*a^2 + 29*A*a*b)*c^4 - 28*(16*B*a*b^2 + 5*A*b^3)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/15360*(15*(21*B*b^6 - 64*(B*a^3 + 3*A*a^2*b)*c^3 + 80*(3*B*a^2*b^2 + 2*A*a*b^3)*c^2 - 28*(5*B*a*b^4 + A*b^5)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(1280*B*c^6*x^5 + 315*B*b^5*c - 1024*A*a^2*c^4 + 128*(B*b*c^5 + 12*A*c^6)*x^4 + 16*(113*B*a^2*b + 115*A*a*b^2)*c^3 - 16*(9*B*b^2*c^4 - 4*(5*B*a + 3*A*b)*c^5)*x^3 - 420*(4*B*a*b^3 + A*b^4)*c^2 + 8*(21*B*b^3*c^3 + 64*A*a*c^5 - 4*(17*B*a*b + 7*A*b^2)*c^4)*x^2 - 2*(105*B*b^4*c^2 + 16*(15*B*a^2 + 29*A*a*b)*c^4 - 28*(16*B*a*b^2 + 5*A*b^3)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6]","A",0
912,1,517,0,0.499713," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{5} - 32 \, A a^{2} c^{3} + 48 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 10 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(384 \, B c^{5} x^{4} - 105 \, B b^{4} c - 8 \, {\left(32 \, B a^{2} + 65 \, A a b\right)} c^{3} + 48 \, {\left(B b c^{4} + 10 \, A c^{5}\right)} x^{3} + 10 \, {\left(46 \, B a b^{2} + 15 \, A b^{3}\right)} c^{2} - 8 \, {\left(7 \, B b^{2} c^{3} - 2 \, {\left(8 \, B a + 5 \, A b\right)} c^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{3} c^{2} + 120 \, A a c^{4} - 2 \, {\left(58 \, B a b + 25 \, A b^{2}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{5}}, -\frac{15 \, {\left(7 \, B b^{5} - 32 \, A a^{2} c^{3} + 48 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 10 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(384 \, B c^{5} x^{4} - 105 \, B b^{4} c - 8 \, {\left(32 \, B a^{2} + 65 \, A a b\right)} c^{3} + 48 \, {\left(B b c^{4} + 10 \, A c^{5}\right)} x^{3} + 10 \, {\left(46 \, B a b^{2} + 15 \, A b^{3}\right)} c^{2} - 8 \, {\left(7 \, B b^{2} c^{3} - 2 \, {\left(8 \, B a + 5 \, A b\right)} c^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{3} c^{2} + 120 \, A a c^{4} - 2 \, {\left(58 \, B a b + 25 \, A b^{2}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, c^{5}}\right]"," ",0,"[-1/7680*(15*(7*B*b^5 - 32*A*a^2*c^3 + 48*(B*a^2*b + A*a*b^2)*c^2 - 10*(4*B*a*b^3 + A*b^4)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(384*B*c^5*x^4 - 105*B*b^4*c - 8*(32*B*a^2 + 65*A*a*b)*c^3 + 48*(B*b*c^4 + 10*A*c^5)*x^3 + 10*(46*B*a*b^2 + 15*A*b^3)*c^2 - 8*(7*B*b^2*c^3 - 2*(8*B*a + 5*A*b)*c^4)*x^2 + 2*(35*B*b^3*c^2 + 120*A*a*c^4 - 2*(58*B*a*b + 25*A*b^2)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/3840*(15*(7*B*b^5 - 32*A*a^2*c^3 + 48*(B*a^2*b + A*a*b^2)*c^2 - 10*(4*B*a*b^3 + A*b^4)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(384*B*c^5*x^4 - 105*B*b^4*c - 8*(32*B*a^2 + 65*A*a*b)*c^3 + 48*(B*b*c^4 + 10*A*c^5)*x^3 + 10*(46*B*a*b^2 + 15*A*b^3)*c^2 - 8*(7*B*b^2*c^3 - 2*(8*B*a + 5*A*b)*c^4)*x^2 + 2*(35*B*b^3*c^2 + 120*A*a*c^4 - 2*(58*B*a*b + 25*A*b^2)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
913,1,393,0,0.482678," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, B b^{4} + 16 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, B c^{4} x^{3} + 15 \, B b^{3} c + 64 \, A a c^{3} - 4 \, {\left(13 \, B a b + 6 \, A b^{2}\right)} c^{2} + 8 \, {\left(B b c^{3} + 8 \, A c^{4}\right)} x^{2} - 2 \, {\left(5 \, B b^{2} c^{2} - 4 \, {\left(3 \, B a + 2 \, A b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{4}}, \frac{3 \, {\left(5 \, B b^{4} + 16 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(48 \, B c^{4} x^{3} + 15 \, B b^{3} c + 64 \, A a c^{3} - 4 \, {\left(13 \, B a b + 6 \, A b^{2}\right)} c^{2} + 8 \, {\left(B b c^{3} + 8 \, A c^{4}\right)} x^{2} - 2 \, {\left(5 \, B b^{2} c^{2} - 4 \, {\left(3 \, B a + 2 \, A b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{4}}\right]"," ",0,"[1/768*(3*(5*B*b^4 + 16*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(48*B*c^4*x^3 + 15*B*b^3*c + 64*A*a*c^3 - 4*(13*B*a*b + 6*A*b^2)*c^2 + 8*(B*b*c^3 + 8*A*c^4)*x^2 - 2*(5*B*b^2*c^2 - 4*(3*B*a + 2*A*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/384*(3*(5*B*b^4 + 16*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(48*B*c^4*x^3 + 15*B*b^3*c + 64*A*a*c^3 - 4*(13*B*a*b + 6*A*b^2)*c^2 + 8*(B*b*c^3 + 8*A*c^4)*x^2 - 2*(5*B*b^2*c^2 - 4*(3*B*a + 2*A*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
914,1,291,0,0.478625," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B b^{3} + 8 \, A a c^{2} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, B c^{3} x^{2} - 3 \, B b^{2} c + 2 \, {\left(4 \, B a + 3 \, A b\right)} c^{2} + 2 \, {\left(B b c^{2} + 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{3}}, -\frac{3 \, {\left(B b^{3} + 8 \, A a c^{2} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(8 \, B c^{3} x^{2} - 3 \, B b^{2} c + 2 \, {\left(4 \, B a + 3 \, A b\right)} c^{2} + 2 \, {\left(B b c^{2} + 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{3}}\right]"," ",0,"[1/96*(3*(B*b^3 + 8*A*a*c^2 - 2*(2*B*a*b + A*b^2)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*B*c^3*x^2 - 3*B*b^2*c + 2*(4*B*a + 3*A*b)*c^2 + 2*(B*b*c^2 + 6*A*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^3, -1/48*(3*(B*b^3 + 8*A*a*c^2 - 2*(2*B*a*b + A*b^2)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(8*B*c^3*x^2 - 3*B*b^2*c + 2*(4*B*a + 3*A*b)*c^2 + 2*(B*b*c^2 + 6*A*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
915,1,651,0,1.412271," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{8 \, A \sqrt{a} c^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - {\left(B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, B c^{2} x + B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x + a}}{16 \, c^{2}}, \frac{4 \, A \sqrt{a} c^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + {\left(B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(2 \, B c^{2} x + B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{2}}, \frac{16 \, A \sqrt{-a} c^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - {\left(B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, B c^{2} x + B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x + a}}{16 \, c^{2}}, \frac{8 \, A \sqrt{-a} c^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + {\left(B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(2 \, B c^{2} x + B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{2}}\right]"," ",0,"[1/16*(8*A*sqrt(a)*c^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - (B*b^2 - 4*(B*a + A*b)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(2*B*c^2*x + B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x + a))/c^2, 1/8*(4*A*sqrt(a)*c^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + (B*b^2 - 4*(B*a + A*b)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(2*B*c^2*x + B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x + a))/c^2, 1/16*(16*A*sqrt(-a)*c^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - (B*b^2 - 4*(B*a + A*b)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(2*B*c^2*x + B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x + a))/c^2, 1/8*(8*A*sqrt(-a)*c^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + (B*b^2 - 4*(B*a + A*b)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(2*B*c^2*x + B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x + a))/c^2]","A",0
916,1,648,0,0.906669," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a + A b\right)} \sqrt{a} c x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + {\left(B a b + 2 \, A a c\right)} \sqrt{c} x \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(B a c x - A a c\right)} \sqrt{c x^{2} + b x + a}}{4 \, a c x}, \frac{{\left(2 \, B a + A b\right)} \sqrt{a} c x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 2 \, {\left(B a b + 2 \, A a c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 4 \, {\left(B a c x - A a c\right)} \sqrt{c x^{2} + b x + a}}{4 \, a c x}, \frac{2 \, {\left(2 \, B a + A b\right)} \sqrt{-a} c x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + {\left(B a b + 2 \, A a c\right)} \sqrt{c} x \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(B a c x - A a c\right)} \sqrt{c x^{2} + b x + a}}{4 \, a c x}, \frac{{\left(2 \, B a + A b\right)} \sqrt{-a} c x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - {\left(B a b + 2 \, A a c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(B a c x - A a c\right)} \sqrt{c x^{2} + b x + a}}{2 \, a c x}\right]"," ",0,"[1/4*((2*B*a + A*b)*sqrt(a)*c*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + (B*a*b + 2*A*a*c)*sqrt(c)*x*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(B*a*c*x - A*a*c)*sqrt(c*x^2 + b*x + a))/(a*c*x), 1/4*((2*B*a + A*b)*sqrt(a)*c*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 2*(B*a*b + 2*A*a*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 4*(B*a*c*x - A*a*c)*sqrt(c*x^2 + b*x + a))/(a*c*x), 1/4*(2*(2*B*a + A*b)*sqrt(-a)*c*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + (B*a*b + 2*A*a*c)*sqrt(c)*x*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(B*a*c*x - A*a*c)*sqrt(c*x^2 + b*x + a))/(a*c*x), 1/2*((2*B*a + A*b)*sqrt(-a)*c*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - (B*a*b + 2*A*a*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(B*a*c*x - A*a*c)*sqrt(c*x^2 + b*x + a))/(a*c*x)]","A",0
917,1,699,0,0.955001," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{8 \, B a^{2} \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + {\left(4 \, B a b - A b^{2} + 4 \, A a c\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} + A a b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, a^{2} x^{2}}, -\frac{16 \, B a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - {\left(4 \, B a b - A b^{2} + 4 \, A a c\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} + A a b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, a^{2} x^{2}}, \frac{4 \, B a^{2} \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + {\left(4 \, B a b - A b^{2} + 4 \, A a c\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} + A a b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, a^{2} x^{2}}, -\frac{8 \, B a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - {\left(4 \, B a b - A b^{2} + 4 \, A a c\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} + A a b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, a^{2} x^{2}}\right]"," ",0,"[1/16*(8*B*a^2*sqrt(c)*x^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + (4*B*a*b - A*b^2 + 4*A*a*c)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(2*A*a^2 + (4*B*a^2 + A*a*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^2), -1/16*(16*B*a^2*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - (4*B*a*b - A*b^2 + 4*A*a*c)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(2*A*a^2 + (4*B*a^2 + A*a*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^2), 1/8*(4*B*a^2*sqrt(c)*x^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + (4*B*a*b - A*b^2 + 4*A*a*c)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(2*A*a^2 + (4*B*a^2 + A*a*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^2), -1/8*(8*B*a^2*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - (4*B*a*b - A*b^2 + 4*A*a*c)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(2*A*a^2 + (4*B*a^2 + A*a*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^2)]","A",0
918,1,317,0,0.700713," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a b^{2} - A b^{3} - 4 \, {\left(2 \, B a^{2} - A a b\right)} c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(8 \, A a^{3} + {\left(6 \, B a^{2} b - 3 \, A a b^{2} + 8 \, A a^{2} c\right)} x^{2} + 2 \, {\left(6 \, B a^{3} + A a^{2} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, a^{3} x^{3}}, -\frac{3 \, {\left(2 \, B a b^{2} - A b^{3} - 4 \, {\left(2 \, B a^{2} - A a b\right)} c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(8 \, A a^{3} + {\left(6 \, B a^{2} b - 3 \, A a b^{2} + 8 \, A a^{2} c\right)} x^{2} + 2 \, {\left(6 \, B a^{3} + A a^{2} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, a^{3} x^{3}}\right]"," ",0,"[1/96*(3*(2*B*a*b^2 - A*b^3 - 4*(2*B*a^2 - A*a*b)*c)*sqrt(a)*x^3*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(8*A*a^3 + (6*B*a^2*b - 3*A*a*b^2 + 8*A*a^2*c)*x^2 + 2*(6*B*a^3 + A*a^2*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^3), -1/48*(3*(2*B*a*b^2 - A*b^3 - 4*(2*B*a^2 - A*a*b)*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(8*A*a^3 + (6*B*a^2*b - 3*A*a*b^2 + 8*A*a^2*c)*x^2 + 2*(6*B*a^3 + A*a^2*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^3)]","A",0
919,1,425,0,1.024827," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, B a b^{3} - 5 \, A b^{4} - 16 \, A a^{2} c^{2} - 8 \, {\left(4 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(48 \, A a^{4} - {\left(24 \, B a^{2} b^{2} - 15 \, A a b^{3} - 4 \, {\left(16 \, B a^{3} - 13 \, A a^{2} b\right)} c\right)} x^{3} + 2 \, {\left(8 \, B a^{3} b - 5 \, A a^{2} b^{2} + 12 \, A a^{3} c\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, a^{4} x^{4}}, \frac{3 \, {\left(8 \, B a b^{3} - 5 \, A b^{4} - 16 \, A a^{2} c^{2} - 8 \, {\left(4 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(48 \, A a^{4} - {\left(24 \, B a^{2} b^{2} - 15 \, A a b^{3} - 4 \, {\left(16 \, B a^{3} - 13 \, A a^{2} b\right)} c\right)} x^{3} + 2 \, {\left(8 \, B a^{3} b - 5 \, A a^{2} b^{2} + 12 \, A a^{3} c\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, a^{4} x^{4}}\right]"," ",0,"[-1/768*(3*(8*B*a*b^3 - 5*A*b^4 - 16*A*a^2*c^2 - 8*(4*B*a^2*b - 3*A*a*b^2)*c)*sqrt(a)*x^4*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(48*A*a^4 - (24*B*a^2*b^2 - 15*A*a*b^3 - 4*(16*B*a^3 - 13*A*a^2*b)*c)*x^3 + 2*(8*B*a^3*b - 5*A*a^2*b^2 + 12*A*a^3*c)*x^2 + 8*(8*B*a^4 + A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^4), 1/384*(3*(8*B*a*b^3 - 5*A*b^4 - 16*A*a^2*c^2 - 8*(4*B*a^2*b - 3*A*a*b^2)*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(48*A*a^4 - (24*B*a^2*b^2 - 15*A*a*b^3 - 4*(16*B*a^3 - 13*A*a^2*b)*c)*x^3 + 2*(8*B*a^3*b - 5*A*a^2*b^2 + 12*A*a^3*c)*x^2 + 8*(8*B*a^4 + A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^4)]","A",0
920,1,553,0,1.949564," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(10 \, B a b^{4} - 7 \, A b^{5} + 16 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{2} - 8 \, {\left(6 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} \sqrt{a} x^{5} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(384 \, A a^{5} + {\left(150 \, B a^{2} b^{3} - 105 \, A a b^{4} - 256 \, A a^{3} c^{2} - 20 \, {\left(26 \, B a^{3} b - 23 \, A a^{2} b^{2}\right)} c\right)} x^{4} - 2 \, {\left(50 \, B a^{3} b^{2} - 35 \, A a^{2} b^{3} - 4 \, {\left(30 \, B a^{4} - 29 \, A a^{3} b\right)} c\right)} x^{3} + 8 \, {\left(10 \, B a^{4} b - 7 \, A a^{3} b^{2} + 16 \, A a^{4} c\right)} x^{2} + 48 \, {\left(10 \, B a^{5} + A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, a^{5} x^{5}}, -\frac{15 \, {\left(10 \, B a b^{4} - 7 \, A b^{5} + 16 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{2} - 8 \, {\left(6 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(384 \, A a^{5} + {\left(150 \, B a^{2} b^{3} - 105 \, A a b^{4} - 256 \, A a^{3} c^{2} - 20 \, {\left(26 \, B a^{3} b - 23 \, A a^{2} b^{2}\right)} c\right)} x^{4} - 2 \, {\left(50 \, B a^{3} b^{2} - 35 \, A a^{2} b^{3} - 4 \, {\left(30 \, B a^{4} - 29 \, A a^{3} b\right)} c\right)} x^{3} + 8 \, {\left(10 \, B a^{4} b - 7 \, A a^{3} b^{2} + 16 \, A a^{4} c\right)} x^{2} + 48 \, {\left(10 \, B a^{5} + A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, a^{5} x^{5}}\right]"," ",0,"[-1/7680*(15*(10*B*a*b^4 - 7*A*b^5 + 16*(2*B*a^3 - 3*A*a^2*b)*c^2 - 8*(6*B*a^2*b^2 - 5*A*a*b^3)*c)*sqrt(a)*x^5*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(384*A*a^5 + (150*B*a^2*b^3 - 105*A*a*b^4 - 256*A*a^3*c^2 - 20*(26*B*a^3*b - 23*A*a^2*b^2)*c)*x^4 - 2*(50*B*a^3*b^2 - 35*A*a^2*b^3 - 4*(30*B*a^4 - 29*A*a^3*b)*c)*x^3 + 8*(10*B*a^4*b - 7*A*a^3*b^2 + 16*A*a^4*c)*x^2 + 48*(10*B*a^5 + A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^5), -1/3840*(15*(10*B*a*b^4 - 7*A*b^5 + 16*(2*B*a^3 - 3*A*a^2*b)*c^2 - 8*(6*B*a^2*b^2 - 5*A*a*b^3)*c)*sqrt(-a)*x^5*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(384*A*a^5 + (150*B*a^2*b^3 - 105*A*a*b^4 - 256*A*a^3*c^2 - 20*(26*B*a^3*b - 23*A*a^2*b^2)*c)*x^4 - 2*(50*B*a^3*b^2 - 35*A*a^2*b^3 - 4*(30*B*a^4 - 29*A*a^3*b)*c)*x^3 + 8*(10*B*a^4*b - 7*A*a^3*b^2 + 16*A*a^4*c)*x^2 + 48*(10*B*a^5 + A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^5)]","A",0
921,1,709,0,3.395386," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^7,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(28 \, B a b^{5} - 21 \, A b^{6} + 64 \, A a^{3} c^{3} + 48 \, {\left(4 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{2} - 20 \, {\left(8 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} c\right)} \sqrt{a} x^{6} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(1280 \, A a^{6} - {\left(420 \, B a^{2} b^{4} - 315 \, A a b^{5} + 16 \, {\left(64 \, B a^{4} - 113 \, A a^{3} b\right)} c^{2} - 80 \, {\left(23 \, B a^{3} b^{2} - 21 \, A a^{2} b^{3}\right)} c\right)} x^{5} + 2 \, {\left(140 \, B a^{3} b^{3} - 105 \, A a^{2} b^{4} - 240 \, A a^{4} c^{2} - 16 \, {\left(29 \, B a^{4} b - 28 \, A a^{3} b^{2}\right)} c\right)} x^{4} - 8 \, {\left(28 \, B a^{4} b^{2} - 21 \, A a^{3} b^{3} - 4 \, {\left(16 \, B a^{5} - 17 \, A a^{4} b\right)} c\right)} x^{3} + 16 \, {\left(12 \, B a^{5} b - 9 \, A a^{4} b^{2} + 20 \, A a^{5} c\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + A a^{5} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, a^{6} x^{6}}, \frac{15 \, {\left(28 \, B a b^{5} - 21 \, A b^{6} + 64 \, A a^{3} c^{3} + 48 \, {\left(4 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{2} - 20 \, {\left(8 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} c\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(1280 \, A a^{6} - {\left(420 \, B a^{2} b^{4} - 315 \, A a b^{5} + 16 \, {\left(64 \, B a^{4} - 113 \, A a^{3} b\right)} c^{2} - 80 \, {\left(23 \, B a^{3} b^{2} - 21 \, A a^{2} b^{3}\right)} c\right)} x^{5} + 2 \, {\left(140 \, B a^{3} b^{3} - 105 \, A a^{2} b^{4} - 240 \, A a^{4} c^{2} - 16 \, {\left(29 \, B a^{4} b - 28 \, A a^{3} b^{2}\right)} c\right)} x^{4} - 8 \, {\left(28 \, B a^{4} b^{2} - 21 \, A a^{3} b^{3} - 4 \, {\left(16 \, B a^{5} - 17 \, A a^{4} b\right)} c\right)} x^{3} + 16 \, {\left(12 \, B a^{5} b - 9 \, A a^{4} b^{2} + 20 \, A a^{5} c\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + A a^{5} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, a^{6} x^{6}}\right]"," ",0,"[1/30720*(15*(28*B*a*b^5 - 21*A*b^6 + 64*A*a^3*c^3 + 48*(4*B*a^3*b - 5*A*a^2*b^2)*c^2 - 20*(8*B*a^2*b^3 - 7*A*a*b^4)*c)*sqrt(a)*x^6*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(1280*A*a^6 - (420*B*a^2*b^4 - 315*A*a*b^5 + 16*(64*B*a^4 - 113*A*a^3*b)*c^2 - 80*(23*B*a^3*b^2 - 21*A*a^2*b^3)*c)*x^5 + 2*(140*B*a^3*b^3 - 105*A*a^2*b^4 - 240*A*a^4*c^2 - 16*(29*B*a^4*b - 28*A*a^3*b^2)*c)*x^4 - 8*(28*B*a^4*b^2 - 21*A*a^3*b^3 - 4*(16*B*a^5 - 17*A*a^4*b)*c)*x^3 + 16*(12*B*a^5*b - 9*A*a^4*b^2 + 20*A*a^5*c)*x^2 + 128*(12*B*a^6 + A*a^5*b)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^6), 1/15360*(15*(28*B*a*b^5 - 21*A*b^6 + 64*A*a^3*c^3 + 48*(4*B*a^3*b - 5*A*a^2*b^2)*c^2 - 20*(8*B*a^2*b^3 - 7*A*a*b^4)*c)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(1280*A*a^6 - (420*B*a^2*b^4 - 315*A*a*b^5 + 16*(64*B*a^4 - 113*A*a^3*b)*c^2 - 80*(23*B*a^3*b^2 - 21*A*a^2*b^3)*c)*x^5 + 2*(140*B*a^3*b^3 - 105*A*a^2*b^4 - 240*A*a^4*c^2 - 16*(29*B*a^4*b - 28*A*a^3*b^2)*c)*x^4 - 8*(28*B*a^4*b^2 - 21*A*a^3*b^3 - 4*(16*B*a^5 - 17*A*a^4*b)*c)*x^3 + 16*(12*B*a^5*b - 9*A*a^4*b^2 + 20*A*a^5*c)*x^2 + 128*(12*B*a^6 + A*a^5*b)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^6)]","A",0
922,1,1263,0,0.718528," ","integrate(x^4*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(143 \, B b^{9} - 1536 \, A a^{4} c^{5} + 3840 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} c^{4} - 2240 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} c^{3} + 2016 \, {\left(3 \, B a^{2} b^{5} + A a b^{6}\right)} c^{2} - 198 \, {\left(8 \, B a b^{7} + A b^{8}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1146880 \, B c^{9} x^{8} + 45045 \, B b^{8} c + 71680 \, {\left(19 \, B b c^{8} + 18 \, A c^{9}\right)} x^{7} + 5120 \, {\left(3 \, B b^{2} c^{7} + 2 \, {\left(160 \, B a + 153 \, A b\right)} c^{8}\right)} x^{6} + 128 \, {\left(2048 \, B a^{4} + 8271 \, A a^{3} b\right)} c^{5} - 1280 \, {\left(13 \, B b^{3} c^{6} - 1512 \, A a c^{8} - 6 \, {\left(10 \, B a b + 3 \, A b^{2}\right)} c^{7}\right)} x^{5} - 2592 \, {\left(566 \, B a^{3} b^{2} + 567 \, A a^{2} b^{3}\right)} c^{4} + 128 \, {\left(143 \, B b^{4} c^{5} + 24 \, {\left(32 \, B a^{2} + 39 \, A a b\right)} c^{7} - 6 \, {\left(134 \, B a b^{2} + 33 \, A b^{3}\right)} c^{6}\right)} x^{4} + 504 \, {\left(2746 \, B a^{2} b^{4} + 1095 \, A a b^{5}\right)} c^{3} - 16 \, {\left(1287 \, B b^{5} c^{4} - 10080 \, A a^{2} c^{7} + 48 \, {\left(269 \, B a^{2} b + 213 \, A a b^{2}\right)} c^{6} - 22 \, {\left(388 \, B a b^{3} + 81 \, A b^{4}\right)} c^{5}\right)} x^{3} - 2310 \, {\left(190 \, B a b^{6} + 27 \, A b^{7}\right)} c^{2} + 8 \, {\left(3003 \, B b^{6} c^{3} - 32 \, {\left(512 \, B a^{3} + 1359 \, A a^{2} b\right)} c^{6} + 240 \, {\left(197 \, B a^{2} b^{2} + 117 \, A a b^{3}\right)} c^{5} - 198 \, {\left(116 \, B a b^{4} + 21 \, A b^{5}\right)} c^{4}\right)} x^{2} - 2 \, {\left(15015 \, B b^{7} c^{2} + 120960 \, A a^{3} c^{6} - 32 \, {\left(7402 \, B a^{3} b + 10629 \, A a^{2} b^{2}\right)} c^{5} + 72 \, {\left(4706 \, B a^{2} b^{3} + 2247 \, A a b^{4}\right)} c^{4} - 1386 \, {\left(94 \, B a b^{5} + 15 \, A b^{6}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{41287680 \, c^{8}}, \frac{315 \, {\left(143 \, B b^{9} - 1536 \, A a^{4} c^{5} + 3840 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} c^{4} - 2240 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} c^{3} + 2016 \, {\left(3 \, B a^{2} b^{5} + A a b^{6}\right)} c^{2} - 198 \, {\left(8 \, B a b^{7} + A b^{8}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(1146880 \, B c^{9} x^{8} + 45045 \, B b^{8} c + 71680 \, {\left(19 \, B b c^{8} + 18 \, A c^{9}\right)} x^{7} + 5120 \, {\left(3 \, B b^{2} c^{7} + 2 \, {\left(160 \, B a + 153 \, A b\right)} c^{8}\right)} x^{6} + 128 \, {\left(2048 \, B a^{4} + 8271 \, A a^{3} b\right)} c^{5} - 1280 \, {\left(13 \, B b^{3} c^{6} - 1512 \, A a c^{8} - 6 \, {\left(10 \, B a b + 3 \, A b^{2}\right)} c^{7}\right)} x^{5} - 2592 \, {\left(566 \, B a^{3} b^{2} + 567 \, A a^{2} b^{3}\right)} c^{4} + 128 \, {\left(143 \, B b^{4} c^{5} + 24 \, {\left(32 \, B a^{2} + 39 \, A a b\right)} c^{7} - 6 \, {\left(134 \, B a b^{2} + 33 \, A b^{3}\right)} c^{6}\right)} x^{4} + 504 \, {\left(2746 \, B a^{2} b^{4} + 1095 \, A a b^{5}\right)} c^{3} - 16 \, {\left(1287 \, B b^{5} c^{4} - 10080 \, A a^{2} c^{7} + 48 \, {\left(269 \, B a^{2} b + 213 \, A a b^{2}\right)} c^{6} - 22 \, {\left(388 \, B a b^{3} + 81 \, A b^{4}\right)} c^{5}\right)} x^{3} - 2310 \, {\left(190 \, B a b^{6} + 27 \, A b^{7}\right)} c^{2} + 8 \, {\left(3003 \, B b^{6} c^{3} - 32 \, {\left(512 \, B a^{3} + 1359 \, A a^{2} b\right)} c^{6} + 240 \, {\left(197 \, B a^{2} b^{2} + 117 \, A a b^{3}\right)} c^{5} - 198 \, {\left(116 \, B a b^{4} + 21 \, A b^{5}\right)} c^{4}\right)} x^{2} - 2 \, {\left(15015 \, B b^{7} c^{2} + 120960 \, A a^{3} c^{6} - 32 \, {\left(7402 \, B a^{3} b + 10629 \, A a^{2} b^{2}\right)} c^{5} + 72 \, {\left(4706 \, B a^{2} b^{3} + 2247 \, A a b^{4}\right)} c^{4} - 1386 \, {\left(94 \, B a b^{5} + 15 \, A b^{6}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{20643840 \, c^{8}}\right]"," ",0,"[-1/41287680*(315*(143*B*b^9 - 1536*A*a^4*c^5 + 3840*(B*a^4*b + 2*A*a^3*b^2)*c^4 - 2240*(4*B*a^3*b^3 + 3*A*a^2*b^4)*c^3 + 2016*(3*B*a^2*b^5 + A*a*b^6)*c^2 - 198*(8*B*a*b^7 + A*b^8)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(1146880*B*c^9*x^8 + 45045*B*b^8*c + 71680*(19*B*b*c^8 + 18*A*c^9)*x^7 + 5120*(3*B*b^2*c^7 + 2*(160*B*a + 153*A*b)*c^8)*x^6 + 128*(2048*B*a^4 + 8271*A*a^3*b)*c^5 - 1280*(13*B*b^3*c^6 - 1512*A*a*c^8 - 6*(10*B*a*b + 3*A*b^2)*c^7)*x^5 - 2592*(566*B*a^3*b^2 + 567*A*a^2*b^3)*c^4 + 128*(143*B*b^4*c^5 + 24*(32*B*a^2 + 39*A*a*b)*c^7 - 6*(134*B*a*b^2 + 33*A*b^3)*c^6)*x^4 + 504*(2746*B*a^2*b^4 + 1095*A*a*b^5)*c^3 - 16*(1287*B*b^5*c^4 - 10080*A*a^2*c^7 + 48*(269*B*a^2*b + 213*A*a*b^2)*c^6 - 22*(388*B*a*b^3 + 81*A*b^4)*c^5)*x^3 - 2310*(190*B*a*b^6 + 27*A*b^7)*c^2 + 8*(3003*B*b^6*c^3 - 32*(512*B*a^3 + 1359*A*a^2*b)*c^6 + 240*(197*B*a^2*b^2 + 117*A*a*b^3)*c^5 - 198*(116*B*a*b^4 + 21*A*b^5)*c^4)*x^2 - 2*(15015*B*b^7*c^2 + 120960*A*a^3*c^6 - 32*(7402*B*a^3*b + 10629*A*a^2*b^2)*c^5 + 72*(4706*B*a^2*b^3 + 2247*A*a*b^4)*c^4 - 1386*(94*B*a*b^5 + 15*A*b^6)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^8, 1/20643840*(315*(143*B*b^9 - 1536*A*a^4*c^5 + 3840*(B*a^4*b + 2*A*a^3*b^2)*c^4 - 2240*(4*B*a^3*b^3 + 3*A*a^2*b^4)*c^3 + 2016*(3*B*a^2*b^5 + A*a*b^6)*c^2 - 198*(8*B*a*b^7 + A*b^8)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(1146880*B*c^9*x^8 + 45045*B*b^8*c + 71680*(19*B*b*c^8 + 18*A*c^9)*x^7 + 5120*(3*B*b^2*c^7 + 2*(160*B*a + 153*A*b)*c^8)*x^6 + 128*(2048*B*a^4 + 8271*A*a^3*b)*c^5 - 1280*(13*B*b^3*c^6 - 1512*A*a*c^8 - 6*(10*B*a*b + 3*A*b^2)*c^7)*x^5 - 2592*(566*B*a^3*b^2 + 567*A*a^2*b^3)*c^4 + 128*(143*B*b^4*c^5 + 24*(32*B*a^2 + 39*A*a*b)*c^7 - 6*(134*B*a*b^2 + 33*A*b^3)*c^6)*x^4 + 504*(2746*B*a^2*b^4 + 1095*A*a*b^5)*c^3 - 16*(1287*B*b^5*c^4 - 10080*A*a^2*c^7 + 48*(269*B*a^2*b + 213*A*a*b^2)*c^6 - 22*(388*B*a*b^3 + 81*A*b^4)*c^5)*x^3 - 2310*(190*B*a*b^6 + 27*A*b^7)*c^2 + 8*(3003*B*b^6*c^3 - 32*(512*B*a^3 + 1359*A*a^2*b)*c^6 + 240*(197*B*a^2*b^2 + 117*A*a*b^3)*c^5 - 198*(116*B*a*b^4 + 21*A*b^5)*c^4)*x^2 - 2*(15015*B*b^7*c^2 + 120960*A*a^3*c^6 - 32*(7402*B*a^3*b + 10629*A*a^2*b^2)*c^5 + 72*(4706*B*a^2*b^3 + 2247*A*a*b^4)*c^4 - 1386*(94*B*a*b^5 + 15*A*b^6)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^8]","A",0
923,1,1037,0,0.618430," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(33 \, B b^{8} + 256 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} c^{4} - 1280 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{3} + 224 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} c^{2} - 48 \, {\left(7 \, B a b^{6} + A b^{7}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(71680 \, B c^{8} x^{7} - 3465 \, B b^{7} c - 32768 \, A a^{3} c^{5} + 5120 \, {\left(17 \, B b c^{7} + 16 \, A c^{8}\right)} x^{6} + 1280 \, {\left(B b^{2} c^{6} + 4 \, {\left(21 \, B a + 20 \, A b\right)} c^{7}\right)} x^{5} + 64 \, {\left(919 \, B a^{3} b + 1372 \, A a^{2} b^{2}\right)} c^{4} - 128 \, {\left(11 \, B b^{3} c^{5} - 1024 \, A a c^{7} - 4 \, {\left(13 \, B a b + 4 \, A b^{2}\right)} c^{6}\right)} x^{4} - 1008 \, {\left(81 \, B a^{2} b^{3} + 40 \, A a b^{4}\right)} c^{3} + 16 \, {\left(99 \, B b^{4} c^{4} + 16 \, {\left(35 \, B a^{2} + 44 \, A a b\right)} c^{6} - 8 \, {\left(71 \, B a b^{2} + 18 \, A b^{3}\right)} c^{5}\right)} x^{3} + 420 \, {\left(73 \, B a b^{5} + 12 \, A b^{6}\right)} c^{2} - 8 \, {\left(231 \, B b^{5} c^{3} - 2048 \, A a^{2} c^{6} + 16 \, {\left(151 \, B a^{2} b + 124 \, A a b^{2}\right)} c^{5} - 24 \, {\left(65 \, B a b^{3} + 14 \, A b^{4}\right)} c^{4}\right)} x^{2} + 2 \, {\left(1155 \, B b^{6} c^{2} - 64 \, {\left(105 \, B a^{3} + 292 \, A a^{2} b\right)} c^{5} + 16 \, {\left(1181 \, B a^{2} b^{2} + 728 \, A a b^{3}\right)} c^{4} - 84 \, {\left(107 \, B a b^{4} + 20 \, A b^{5}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2293760 \, c^{7}}, -\frac{105 \, {\left(33 \, B b^{8} + 256 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} c^{4} - 1280 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{3} + 224 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} c^{2} - 48 \, {\left(7 \, B a b^{6} + A b^{7}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(71680 \, B c^{8} x^{7} - 3465 \, B b^{7} c - 32768 \, A a^{3} c^{5} + 5120 \, {\left(17 \, B b c^{7} + 16 \, A c^{8}\right)} x^{6} + 1280 \, {\left(B b^{2} c^{6} + 4 \, {\left(21 \, B a + 20 \, A b\right)} c^{7}\right)} x^{5} + 64 \, {\left(919 \, B a^{3} b + 1372 \, A a^{2} b^{2}\right)} c^{4} - 128 \, {\left(11 \, B b^{3} c^{5} - 1024 \, A a c^{7} - 4 \, {\left(13 \, B a b + 4 \, A b^{2}\right)} c^{6}\right)} x^{4} - 1008 \, {\left(81 \, B a^{2} b^{3} + 40 \, A a b^{4}\right)} c^{3} + 16 \, {\left(99 \, B b^{4} c^{4} + 16 \, {\left(35 \, B a^{2} + 44 \, A a b\right)} c^{6} - 8 \, {\left(71 \, B a b^{2} + 18 \, A b^{3}\right)} c^{5}\right)} x^{3} + 420 \, {\left(73 \, B a b^{5} + 12 \, A b^{6}\right)} c^{2} - 8 \, {\left(231 \, B b^{5} c^{3} - 2048 \, A a^{2} c^{6} + 16 \, {\left(151 \, B a^{2} b + 124 \, A a b^{2}\right)} c^{5} - 24 \, {\left(65 \, B a b^{3} + 14 \, A b^{4}\right)} c^{4}\right)} x^{2} + 2 \, {\left(1155 \, B b^{6} c^{2} - 64 \, {\left(105 \, B a^{3} + 292 \, A a^{2} b\right)} c^{5} + 16 \, {\left(1181 \, B a^{2} b^{2} + 728 \, A a b^{3}\right)} c^{4} - 84 \, {\left(107 \, B a b^{4} + 20 \, A b^{5}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1146880 \, c^{7}}\right]"," ",0,"[1/2293760*(105*(33*B*b^8 + 256*(B*a^4 + 4*A*a^3*b)*c^4 - 1280*(B*a^3*b^2 + A*a^2*b^3)*c^3 + 224*(5*B*a^2*b^4 + 2*A*a*b^5)*c^2 - 48*(7*B*a*b^6 + A*b^7)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(71680*B*c^8*x^7 - 3465*B*b^7*c - 32768*A*a^3*c^5 + 5120*(17*B*b*c^7 + 16*A*c^8)*x^6 + 1280*(B*b^2*c^6 + 4*(21*B*a + 20*A*b)*c^7)*x^5 + 64*(919*B*a^3*b + 1372*A*a^2*b^2)*c^4 - 128*(11*B*b^3*c^5 - 1024*A*a*c^7 - 4*(13*B*a*b + 4*A*b^2)*c^6)*x^4 - 1008*(81*B*a^2*b^3 + 40*A*a*b^4)*c^3 + 16*(99*B*b^4*c^4 + 16*(35*B*a^2 + 44*A*a*b)*c^6 - 8*(71*B*a*b^2 + 18*A*b^3)*c^5)*x^3 + 420*(73*B*a*b^5 + 12*A*b^6)*c^2 - 8*(231*B*b^5*c^3 - 2048*A*a^2*c^6 + 16*(151*B*a^2*b + 124*A*a*b^2)*c^5 - 24*(65*B*a*b^3 + 14*A*b^4)*c^4)*x^2 + 2*(1155*B*b^6*c^2 - 64*(105*B*a^3 + 292*A*a^2*b)*c^5 + 16*(1181*B*a^2*b^2 + 728*A*a*b^3)*c^4 - 84*(107*B*a*b^4 + 20*A*b^5)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^7, -1/1146880*(105*(33*B*b^8 + 256*(B*a^4 + 4*A*a^3*b)*c^4 - 1280*(B*a^3*b^2 + A*a^2*b^3)*c^3 + 224*(5*B*a^2*b^4 + 2*A*a*b^5)*c^2 - 48*(7*B*a*b^6 + A*b^7)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(71680*B*c^8*x^7 - 3465*B*b^7*c - 32768*A*a^3*c^5 + 5120*(17*B*b*c^7 + 16*A*c^8)*x^6 + 1280*(B*b^2*c^6 + 4*(21*B*a + 20*A*b)*c^7)*x^5 + 64*(919*B*a^3*b + 1372*A*a^2*b^2)*c^4 - 128*(11*B*b^3*c^5 - 1024*A*a*c^7 - 4*(13*B*a*b + 4*A*b^2)*c^6)*x^4 - 1008*(81*B*a^2*b^3 + 40*A*a*b^4)*c^3 + 16*(99*B*b^4*c^4 + 16*(35*B*a^2 + 44*A*a*b)*c^6 - 8*(71*B*a*b^2 + 18*A*b^3)*c^5)*x^3 + 420*(73*B*a*b^5 + 12*A*b^6)*c^2 - 8*(231*B*b^5*c^3 - 2048*A*a^2*c^6 + 16*(151*B*a^2*b + 124*A*a*b^2)*c^5 - 24*(65*B*a*b^3 + 14*A*b^4)*c^4)*x^2 + 2*(1155*B*b^6*c^2 - 64*(105*B*a^3 + 292*A*a^2*b)*c^5 + 16*(1181*B*a^2*b^2 + 728*A*a*b^3)*c^4 - 84*(107*B*a*b^4 + 20*A*b^5)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^7]","A",0
924,1,845,0,0.590424," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(9 \, B b^{7} + 128 \, A a^{3} c^{4} - 96 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{3} + 120 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} c^{2} - 14 \, {\left(6 \, B a b^{5} + A b^{6}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(15360 \, B c^{7} x^{6} + 945 \, B b^{6} c + 1280 \, {\left(15 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} - 96 \, {\left(64 \, B a^{3} + 189 \, A a^{2} b\right)} c^{4} + 128 \, {\left(3 \, B b^{2} c^{5} + 2 \, {\left(96 \, B a + 91 \, A b\right)} c^{6}\right)} x^{4} + 112 \, {\left(147 \, B a^{2} b^{2} + 95 \, A a b^{3}\right)} c^{3} - 16 \, {\left(27 \, B b^{3} c^{4} - 1960 \, A a c^{6} - 6 \, {\left(22 \, B a b + 7 \, A b^{2}\right)} c^{5}\right)} x^{3} - 210 \, {\left(36 \, B a b^{4} + 7 \, A b^{5}\right)} c^{2} + 8 \, {\left(63 \, B b^{4} c^{3} + 24 \, {\left(16 \, B a^{2} + 21 \, A a b\right)} c^{5} - 2 \, {\left(186 \, B a b^{2} + 49 \, A b^{3}\right)} c^{4}\right)} x^{2} - 2 \, {\left(315 \, B b^{5} c^{2} - 3360 \, A a^{2} c^{5} + 48 \, {\left(73 \, B a^{2} b + 63 \, A a b^{2}\right)} c^{4} - 14 \, {\left(156 \, B a b^{3} + 35 \, A b^{4}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{430080 \, c^{6}}, \frac{105 \, {\left(9 \, B b^{7} + 128 \, A a^{3} c^{4} - 96 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{3} + 120 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} c^{2} - 14 \, {\left(6 \, B a b^{5} + A b^{6}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(15360 \, B c^{7} x^{6} + 945 \, B b^{6} c + 1280 \, {\left(15 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} - 96 \, {\left(64 \, B a^{3} + 189 \, A a^{2} b\right)} c^{4} + 128 \, {\left(3 \, B b^{2} c^{5} + 2 \, {\left(96 \, B a + 91 \, A b\right)} c^{6}\right)} x^{4} + 112 \, {\left(147 \, B a^{2} b^{2} + 95 \, A a b^{3}\right)} c^{3} - 16 \, {\left(27 \, B b^{3} c^{4} - 1960 \, A a c^{6} - 6 \, {\left(22 \, B a b + 7 \, A b^{2}\right)} c^{5}\right)} x^{3} - 210 \, {\left(36 \, B a b^{4} + 7 \, A b^{5}\right)} c^{2} + 8 \, {\left(63 \, B b^{4} c^{3} + 24 \, {\left(16 \, B a^{2} + 21 \, A a b\right)} c^{5} - 2 \, {\left(186 \, B a b^{2} + 49 \, A b^{3}\right)} c^{4}\right)} x^{2} - 2 \, {\left(315 \, B b^{5} c^{2} - 3360 \, A a^{2} c^{5} + 48 \, {\left(73 \, B a^{2} b + 63 \, A a b^{2}\right)} c^{4} - 14 \, {\left(156 \, B a b^{3} + 35 \, A b^{4}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{215040 \, c^{6}}\right]"," ",0,"[1/430080*(105*(9*B*b^7 + 128*A*a^3*c^4 - 96*(2*B*a^3*b + 3*A*a^2*b^2)*c^3 + 120*(2*B*a^2*b^3 + A*a*b^4)*c^2 - 14*(6*B*a*b^5 + A*b^6)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(15360*B*c^7*x^6 + 945*B*b^6*c + 1280*(15*B*b*c^6 + 14*A*c^7)*x^5 - 96*(64*B*a^3 + 189*A*a^2*b)*c^4 + 128*(3*B*b^2*c^5 + 2*(96*B*a + 91*A*b)*c^6)*x^4 + 112*(147*B*a^2*b^2 + 95*A*a*b^3)*c^3 - 16*(27*B*b^3*c^4 - 1960*A*a*c^6 - 6*(22*B*a*b + 7*A*b^2)*c^5)*x^3 - 210*(36*B*a*b^4 + 7*A*b^5)*c^2 + 8*(63*B*b^4*c^3 + 24*(16*B*a^2 + 21*A*a*b)*c^5 - 2*(186*B*a*b^2 + 49*A*b^3)*c^4)*x^2 - 2*(315*B*b^5*c^2 - 3360*A*a^2*c^5 + 48*(73*B*a^2*b + 63*A*a*b^2)*c^4 - 14*(156*B*a*b^3 + 35*A*b^4)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/215040*(105*(9*B*b^7 + 128*A*a^3*c^4 - 96*(2*B*a^3*b + 3*A*a^2*b^2)*c^3 + 120*(2*B*a^2*b^3 + A*a*b^4)*c^2 - 14*(6*B*a*b^5 + A*b^6)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(15360*B*c^7*x^6 + 945*B*b^6*c + 1280*(15*B*b*c^6 + 14*A*c^7)*x^5 - 96*(64*B*a^3 + 189*A*a^2*b)*c^4 + 128*(3*B*b^2*c^5 + 2*(96*B*a + 91*A*b)*c^6)*x^4 + 112*(147*B*a^2*b^2 + 95*A*a*b^3)*c^3 - 16*(27*B*b^3*c^4 - 1960*A*a*c^6 - 6*(22*B*a*b + 7*A*b^2)*c^5)*x^3 - 210*(36*B*a*b^4 + 7*A*b^5)*c^2 + 8*(63*B*b^4*c^3 + 24*(16*B*a^2 + 21*A*a*b)*c^5 - 2*(186*B*a*b^2 + 49*A*b^3)*c^4)*x^2 - 2*(315*B*b^5*c^2 - 3360*A*a^2*c^5 + 48*(73*B*a^2*b + 63*A*a*b^2)*c^4 - 14*(156*B*a*b^3 + 35*A*b^4)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6]","A",0
925,1,669,0,0.529572," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{6} - 64 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3} + 48 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2} - 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1280 \, B c^{6} x^{5} - 105 \, B b^{5} c + 1536 \, A a^{2} c^{4} + 128 \, {\left(13 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} - 48 \, {\left(27 \, B a^{2} b + 25 \, A a b^{2}\right)} c^{3} + 16 \, {\left(3 \, B b^{2} c^{4} + 4 \, {\left(35 \, B a + 33 \, A b\right)} c^{5}\right)} x^{3} + 20 \, {\left(38 \, B a b^{3} + 9 \, A b^{4}\right)} c^{2} - 8 \, {\left(7 \, B b^{3} c^{3} - 384 \, A a c^{5} - 12 \, {\left(3 \, B a b + A b^{2}\right)} c^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{4} c^{2} + 48 \, {\left(5 \, B a^{2} + 7 \, A a b\right)} c^{4} - 12 \, {\left(18 \, B a b^{2} + 5 \, A b^{3}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{5}}, -\frac{15 \, {\left(7 \, B b^{6} - 64 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3} + 48 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2} - 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(1280 \, B c^{6} x^{5} - 105 \, B b^{5} c + 1536 \, A a^{2} c^{4} + 128 \, {\left(13 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} - 48 \, {\left(27 \, B a^{2} b + 25 \, A a b^{2}\right)} c^{3} + 16 \, {\left(3 \, B b^{2} c^{4} + 4 \, {\left(35 \, B a + 33 \, A b\right)} c^{5}\right)} x^{3} + 20 \, {\left(38 \, B a b^{3} + 9 \, A b^{4}\right)} c^{2} - 8 \, {\left(7 \, B b^{3} c^{3} - 384 \, A a c^{5} - 12 \, {\left(3 \, B a b + A b^{2}\right)} c^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{4} c^{2} + 48 \, {\left(5 \, B a^{2} + 7 \, A a b\right)} c^{4} - 12 \, {\left(18 \, B a b^{2} + 5 \, A b^{3}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{5}}\right]"," ",0,"[-1/30720*(15*(7*B*b^6 - 64*(B*a^3 + 3*A*a^2*b)*c^3 + 48*(3*B*a^2*b^2 + 2*A*a*b^3)*c^2 - 12*(5*B*a*b^4 + A*b^5)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(1280*B*c^6*x^5 - 105*B*b^5*c + 1536*A*a^2*c^4 + 128*(13*B*b*c^5 + 12*A*c^6)*x^4 - 48*(27*B*a^2*b + 25*A*a*b^2)*c^3 + 16*(3*B*b^2*c^4 + 4*(35*B*a + 33*A*b)*c^5)*x^3 + 20*(38*B*a*b^3 + 9*A*b^4)*c^2 - 8*(7*B*b^3*c^3 - 384*A*a*c^5 - 12*(3*B*a*b + A*b^2)*c^4)*x^2 + 2*(35*B*b^4*c^2 + 48*(5*B*a^2 + 7*A*a*b)*c^4 - 12*(18*B*a*b^2 + 5*A*b^3)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/15360*(15*(7*B*b^6 - 64*(B*a^3 + 3*A*a^2*b)*c^3 + 48*(3*B*a^2*b^2 + 2*A*a*b^3)*c^2 - 12*(5*B*a*b^4 + A*b^5)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(1280*B*c^6*x^5 - 105*B*b^5*c + 1536*A*a^2*c^4 + 128*(13*B*b*c^5 + 12*A*c^6)*x^4 - 48*(27*B*a^2*b + 25*A*a*b^2)*c^3 + 16*(3*B*b^2*c^4 + 4*(35*B*a + 33*A*b)*c^5)*x^3 + 20*(38*B*a*b^3 + 9*A*b^4)*c^2 - 8*(7*B*b^3*c^3 - 384*A*a*c^5 - 12*(3*B*a*b + A*b^2)*c^4)*x^2 + 2*(35*B*b^4*c^2 + 48*(5*B*a^2 + 7*A*a*b)*c^4 - 12*(18*B*a*b^2 + 5*A*b^3)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
926,1,515,0,0.473478," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B b^{5} - 32 \, A a^{2} c^{3} + 16 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(128 \, B c^{5} x^{4} + 15 \, B b^{4} c + 8 \, {\left(16 \, B a^{2} + 25 \, A a b\right)} c^{3} + 16 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} x^{3} - 10 \, {\left(10 \, B a b^{2} + 3 \, A b^{3}\right)} c^{2} + 8 \, {\left(B b^{2} c^{3} + 2 \, {\left(16 \, B a + 15 \, A b\right)} c^{4}\right)} x^{2} - 2 \, {\left(5 \, B b^{3} c^{2} - 200 \, A a c^{4} - 2 \, {\left(14 \, B a b + 5 \, A b^{2}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2560 \, c^{4}}, \frac{15 \, {\left(B b^{5} - 32 \, A a^{2} c^{3} + 16 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(128 \, B c^{5} x^{4} + 15 \, B b^{4} c + 8 \, {\left(16 \, B a^{2} + 25 \, A a b\right)} c^{3} + 16 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} x^{3} - 10 \, {\left(10 \, B a b^{2} + 3 \, A b^{3}\right)} c^{2} + 8 \, {\left(B b^{2} c^{3} + 2 \, {\left(16 \, B a + 15 \, A b\right)} c^{4}\right)} x^{2} - 2 \, {\left(5 \, B b^{3} c^{2} - 200 \, A a c^{4} - 2 \, {\left(14 \, B a b + 5 \, A b^{2}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1280 \, c^{4}}\right]"," ",0,"[1/2560*(15*(B*b^5 - 32*A*a^2*c^3 + 16*(B*a^2*b + A*a*b^2)*c^2 - 2*(4*B*a*b^3 + A*b^4)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(128*B*c^5*x^4 + 15*B*b^4*c + 8*(16*B*a^2 + 25*A*a*b)*c^3 + 16*(11*B*b*c^4 + 10*A*c^5)*x^3 - 10*(10*B*a*b^2 + 3*A*b^3)*c^2 + 8*(B*b^2*c^3 + 2*(16*B*a + 15*A*b)*c^4)*x^2 - 2*(5*B*b^3*c^2 - 200*A*a*c^4 - 2*(14*B*a*b + 5*A*b^2)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/1280*(15*(B*b^5 - 32*A*a^2*c^3 + 16*(B*a^2*b + A*a*b^2)*c^2 - 2*(4*B*a*b^3 + A*b^4)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(128*B*c^5*x^4 + 15*B*b^4*c + 8*(16*B*a^2 + 25*A*a*b)*c^3 + 16*(11*B*b*c^4 + 10*A*c^5)*x^3 - 10*(10*B*a*b^2 + 3*A*b^3)*c^2 + 8*(B*b^2*c^3 + 2*(16*B*a + 15*A*b)*c^4)*x^2 - 2*(5*B*b^3*c^2 - 200*A*a*c^4 - 2*(14*B*a*b + 5*A*b^2)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
927,1,1023,0,5.167590," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{384 \, A a^{\frac{3}{2}} c^{3} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 3 \, {\left(3 \, B b^{4} + 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, B c^{4} x^{3} - 9 \, B b^{3} c + 256 \, A a c^{3} + 12 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} c^{2} + 8 \, {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} c^{2} + 4 \, {\left(15 \, B a + 14 \, A b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{3}}, \frac{192 \, A a^{\frac{3}{2}} c^{3} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 3 \, {\left(3 \, B b^{4} + 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(48 \, B c^{4} x^{3} - 9 \, B b^{3} c + 256 \, A a c^{3} + 12 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} c^{2} + 8 \, {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} c^{2} + 4 \, {\left(15 \, B a + 14 \, A b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{3}}, \frac{768 \, A \sqrt{-a} a c^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 3 \, {\left(3 \, B b^{4} + 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, B c^{4} x^{3} - 9 \, B b^{3} c + 256 \, A a c^{3} + 12 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} c^{2} + 8 \, {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} c^{2} + 4 \, {\left(15 \, B a + 14 \, A b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{3}}, \frac{384 \, A \sqrt{-a} a c^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 3 \, {\left(3 \, B b^{4} + 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(48 \, B c^{4} x^{3} - 9 \, B b^{3} c + 256 \, A a c^{3} + 12 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} c^{2} + 8 \, {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} c^{2} + 4 \, {\left(15 \, B a + 14 \, A b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{3}}\right]"," ",0,"[1/768*(384*A*a^(3/2)*c^3*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 3*(3*B*b^4 + 48*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(48*B*c^4*x^3 - 9*B*b^3*c + 256*A*a*c^3 + 12*(5*B*a*b + 2*A*b^2)*c^2 + 8*(9*B*b*c^3 + 8*A*c^4)*x^2 + 2*(3*B*b^2*c^2 + 4*(15*B*a + 14*A*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^3, 1/384*(192*A*a^(3/2)*c^3*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 3*(3*B*b^4 + 48*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(48*B*c^4*x^3 - 9*B*b^3*c + 256*A*a*c^3 + 12*(5*B*a*b + 2*A*b^2)*c^2 + 8*(9*B*b*c^3 + 8*A*c^4)*x^2 + 2*(3*B*b^2*c^2 + 4*(15*B*a + 14*A*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^3, 1/768*(768*A*sqrt(-a)*a*c^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 3*(3*B*b^4 + 48*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(48*B*c^4*x^3 - 9*B*b^3*c + 256*A*a*c^3 + 12*(5*B*a*b + 2*A*b^2)*c^2 + 8*(9*B*b*c^3 + 8*A*c^4)*x^2 + 2*(3*B*b^2*c^2 + 4*(15*B*a + 14*A*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^3, 1/384*(384*A*sqrt(-a)*a*c^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 3*(3*B*b^4 + 48*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(48*B*c^4*x^3 - 9*B*b^3*c + 256*A*a*c^3 + 12*(5*B*a*b + 2*A*b^2)*c^2 + 8*(9*B*b*c^3 + 8*A*c^4)*x^2 + 2*(3*B*b^2*c^2 + 4*(15*B*a + 14*A*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
928,1,917,0,2.344907," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{24 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{a} c^{2} x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 3 \, {\left(B b^{3} - 24 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{c} x \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, B c^{3} x^{3} - 24 \, A a c^{2} + 2 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} x^{2} + {\left(3 \, B b^{2} c + 2 \, {\left(16 \, B a + 15 \, A b\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{2} x}, \frac{12 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{a} c^{2} x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 3 \, {\left(B b^{3} - 24 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(8 \, B c^{3} x^{3} - 24 \, A a c^{2} + 2 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} x^{2} + {\left(3 \, B b^{2} c + 2 \, {\left(16 \, B a + 15 \, A b\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{2} x}, \frac{48 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{-a} c^{2} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 3 \, {\left(B b^{3} - 24 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{c} x \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, B c^{3} x^{3} - 24 \, A a c^{2} + 2 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} x^{2} + {\left(3 \, B b^{2} c + 2 \, {\left(16 \, B a + 15 \, A b\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{2} x}, \frac{24 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{-a} c^{2} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 3 \, {\left(B b^{3} - 24 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(8 \, B c^{3} x^{3} - 24 \, A a c^{2} + 2 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} x^{2} + {\left(3 \, B b^{2} c + 2 \, {\left(16 \, B a + 15 \, A b\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{2} x}\right]"," ",0,"[1/96*(24*(2*B*a + 3*A*b)*sqrt(a)*c^2*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 3*(B*b^3 - 24*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*sqrt(c)*x*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*B*c^3*x^3 - 24*A*a*c^2 + 2*(7*B*b*c^2 + 6*A*c^3)*x^2 + (3*B*b^2*c + 2*(16*B*a + 15*A*b)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^2*x), 1/48*(12*(2*B*a + 3*A*b)*sqrt(a)*c^2*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 3*(B*b^3 - 24*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(8*B*c^3*x^3 - 24*A*a*c^2 + 2*(7*B*b*c^2 + 6*A*c^3)*x^2 + (3*B*b^2*c + 2*(16*B*a + 15*A*b)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^2*x), 1/96*(48*(2*B*a + 3*A*b)*sqrt(-a)*c^2*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 3*(B*b^3 - 24*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*sqrt(c)*x*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*B*c^3*x^3 - 24*A*a*c^2 + 2*(7*B*b*c^2 + 6*A*c^3)*x^2 + (3*B*b^2*c + 2*(16*B*a + 15*A*b)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^2*x), 1/48*(24*(2*B*a + 3*A*b)*sqrt(-a)*c^2*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 3*(B*b^3 - 24*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(8*B*c^3*x^3 - 24*A*a*c^2 + 2*(7*B*b*c^2 + 6*A*c^3)*x^2 + (3*B*b^2*c + 2*(16*B*a + 15*A*b)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^2*x)]","A",0
929,1,921,0,1.902779," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a b^{2} + 4 \, {\left(B a^{2} + A a b\right)} c\right)} \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 3 \, {\left(4 \, A a c^{2} + {\left(4 \, B a b + A b^{2}\right)} c\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(2 \, B a c^{2} x^{3} - 2 \, A a^{2} c - {\left(4 \, B a^{2} + 5 \, A a b\right)} c x + {\left(5 \, B a b c + 4 \, A a c^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{16 \, a c x^{2}}, -\frac{6 \, {\left(B a b^{2} + 4 \, {\left(B a^{2} + A a b\right)} c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 3 \, {\left(4 \, A a c^{2} + {\left(4 \, B a b + A b^{2}\right)} c\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(2 \, B a c^{2} x^{3} - 2 \, A a^{2} c - {\left(4 \, B a^{2} + 5 \, A a b\right)} c x + {\left(5 \, B a b c + 4 \, A a c^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{16 \, a c x^{2}}, \frac{6 \, {\left(4 \, A a c^{2} + {\left(4 \, B a b + A b^{2}\right)} c\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 3 \, {\left(B a b^{2} + 4 \, {\left(B a^{2} + A a b\right)} c\right)} \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, B a c^{2} x^{3} - 2 \, A a^{2} c - {\left(4 \, B a^{2} + 5 \, A a b\right)} c x + {\left(5 \, B a b c + 4 \, A a c^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{16 \, a c x^{2}}, \frac{3 \, {\left(4 \, A a c^{2} + {\left(4 \, B a b + A b^{2}\right)} c\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 3 \, {\left(B a b^{2} + 4 \, {\left(B a^{2} + A a b\right)} c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(2 \, B a c^{2} x^{3} - 2 \, A a^{2} c - {\left(4 \, B a^{2} + 5 \, A a b\right)} c x + {\left(5 \, B a b c + 4 \, A a c^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{8 \, a c x^{2}}\right]"," ",0,"[1/16*(3*(B*a*b^2 + 4*(B*a^2 + A*a*b)*c)*sqrt(c)*x^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 3*(4*A*a*c^2 + (4*B*a*b + A*b^2)*c)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(2*B*a*c^2*x^3 - 2*A*a^2*c - (4*B*a^2 + 5*A*a*b)*c*x + (5*B*a*b*c + 4*A*a*c^2)*x^2)*sqrt(c*x^2 + b*x + a))/(a*c*x^2), -1/16*(6*(B*a*b^2 + 4*(B*a^2 + A*a*b)*c)*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 3*(4*A*a*c^2 + (4*B*a*b + A*b^2)*c)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(2*B*a*c^2*x^3 - 2*A*a^2*c - (4*B*a^2 + 5*A*a*b)*c*x + (5*B*a*b*c + 4*A*a*c^2)*x^2)*sqrt(c*x^2 + b*x + a))/(a*c*x^2), 1/16*(6*(4*A*a*c^2 + (4*B*a*b + A*b^2)*c)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 3*(B*a*b^2 + 4*(B*a^2 + A*a*b)*c)*sqrt(c)*x^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(2*B*a*c^2*x^3 - 2*A*a^2*c - (4*B*a^2 + 5*A*a*b)*c*x + (5*B*a*b*c + 4*A*a*c^2)*x^2)*sqrt(c*x^2 + b*x + a))/(a*c*x^2), 1/8*(3*(4*A*a*c^2 + (4*B*a*b + A*b^2)*c)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 3*(B*a*b^2 + 4*(B*a^2 + A*a*b)*c)*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(2*B*a*c^2*x^3 - 2*A*a^2*c - (4*B*a^2 + 5*A*a*b)*c*x + (5*B*a*b*c + 4*A*a*c^2)*x^2)*sqrt(c*x^2 + b*x + a))/(a*c*x^2)]","A",0
930,1,953,0,2.013666," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{24 \, {\left(3 \, B a^{2} b + 2 \, A a^{2} c\right)} \sqrt{c} x^{3} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 3 \, {\left(6 \, B a b^{2} - A b^{3} + 12 \, {\left(2 \, B a^{2} + A a b\right)} c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(24 \, B a^{2} c x^{3} - 8 \, A a^{3} - {\left(30 \, B a^{2} b + 3 \, A a b^{2} + 32 \, A a^{2} c\right)} x^{2} - 2 \, {\left(6 \, B a^{3} + 7 \, A a^{2} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, a^{2} x^{3}}, -\frac{48 \, {\left(3 \, B a^{2} b + 2 \, A a^{2} c\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 3 \, {\left(6 \, B a b^{2} - A b^{3} + 12 \, {\left(2 \, B a^{2} + A a b\right)} c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(24 \, B a^{2} c x^{3} - 8 \, A a^{3} - {\left(30 \, B a^{2} b + 3 \, A a b^{2} + 32 \, A a^{2} c\right)} x^{2} - 2 \, {\left(6 \, B a^{3} + 7 \, A a^{2} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, a^{2} x^{3}}, \frac{3 \, {\left(6 \, B a b^{2} - A b^{3} + 12 \, {\left(2 \, B a^{2} + A a b\right)} c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 12 \, {\left(3 \, B a^{2} b + 2 \, A a^{2} c\right)} \sqrt{c} x^{3} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, {\left(24 \, B a^{2} c x^{3} - 8 \, A a^{3} - {\left(30 \, B a^{2} b + 3 \, A a b^{2} + 32 \, A a^{2} c\right)} x^{2} - 2 \, {\left(6 \, B a^{3} + 7 \, A a^{2} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, a^{2} x^{3}}, \frac{3 \, {\left(6 \, B a b^{2} - A b^{3} + 12 \, {\left(2 \, B a^{2} + A a b\right)} c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 24 \, {\left(3 \, B a^{2} b + 2 \, A a^{2} c\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(24 \, B a^{2} c x^{3} - 8 \, A a^{3} - {\left(30 \, B a^{2} b + 3 \, A a b^{2} + 32 \, A a^{2} c\right)} x^{2} - 2 \, {\left(6 \, B a^{3} + 7 \, A a^{2} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, a^{2} x^{3}}\right]"," ",0,"[1/96*(24*(3*B*a^2*b + 2*A*a^2*c)*sqrt(c)*x^3*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 3*(6*B*a*b^2 - A*b^3 + 12*(2*B*a^2 + A*a*b)*c)*sqrt(a)*x^3*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(24*B*a^2*c*x^3 - 8*A*a^3 - (30*B*a^2*b + 3*A*a*b^2 + 32*A*a^2*c)*x^2 - 2*(6*B*a^3 + 7*A*a^2*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^3), -1/96*(48*(3*B*a^2*b + 2*A*a^2*c)*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 3*(6*B*a*b^2 - A*b^3 + 12*(2*B*a^2 + A*a*b)*c)*sqrt(a)*x^3*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(24*B*a^2*c*x^3 - 8*A*a^3 - (30*B*a^2*b + 3*A*a*b^2 + 32*A*a^2*c)*x^2 - 2*(6*B*a^3 + 7*A*a^2*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^3), 1/48*(3*(6*B*a*b^2 - A*b^3 + 12*(2*B*a^2 + A*a*b)*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 12*(3*B*a^2*b + 2*A*a^2*c)*sqrt(c)*x^3*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 2*(24*B*a^2*c*x^3 - 8*A*a^3 - (30*B*a^2*b + 3*A*a*b^2 + 32*A*a^2*c)*x^2 - 2*(6*B*a^3 + 7*A*a^2*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^3), 1/48*(3*(6*B*a*b^2 - A*b^3 + 12*(2*B*a^2 + A*a*b)*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 24*(3*B*a^2*b + 2*A*a^2*c)*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(24*B*a^2*c*x^3 - 8*A*a^3 - (30*B*a^2*b + 3*A*a*b^2 + 32*A*a^2*c)*x^2 - 2*(6*B*a^3 + 7*A*a^2*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^3)]","A",0
931,1,1083,0,2.571547," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{384 \, B a^{3} c^{\frac{3}{2}} x^{4} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 3 \, {\left(8 \, B a b^{3} - 3 \, A b^{4} - 48 \, A a^{2} c^{2} - 24 \, {\left(4 \, B a^{2} b - A a b^{2}\right)} c\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(48 \, A a^{4} + {\left(24 \, B a^{2} b^{2} - 9 \, A a b^{3} + 4 \, {\left(64 \, B a^{3} + 15 \, A a^{2} b\right)} c\right)} x^{3} + 2 \, {\left(56 \, B a^{3} b + 3 \, A a^{2} b^{2} + 60 \, A a^{3} c\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + 9 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, a^{3} x^{4}}, -\frac{768 \, B a^{3} \sqrt{-c} c x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 3 \, {\left(8 \, B a b^{3} - 3 \, A b^{4} - 48 \, A a^{2} c^{2} - 24 \, {\left(4 \, B a^{2} b - A a b^{2}\right)} c\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(48 \, A a^{4} + {\left(24 \, B a^{2} b^{2} - 9 \, A a b^{3} + 4 \, {\left(64 \, B a^{3} + 15 \, A a^{2} b\right)} c\right)} x^{3} + 2 \, {\left(56 \, B a^{3} b + 3 \, A a^{2} b^{2} + 60 \, A a^{3} c\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + 9 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, a^{3} x^{4}}, \frac{192 \, B a^{3} c^{\frac{3}{2}} x^{4} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 3 \, {\left(8 \, B a b^{3} - 3 \, A b^{4} - 48 \, A a^{2} c^{2} - 24 \, {\left(4 \, B a^{2} b - A a b^{2}\right)} c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(48 \, A a^{4} + {\left(24 \, B a^{2} b^{2} - 9 \, A a b^{3} + 4 \, {\left(64 \, B a^{3} + 15 \, A a^{2} b\right)} c\right)} x^{3} + 2 \, {\left(56 \, B a^{3} b + 3 \, A a^{2} b^{2} + 60 \, A a^{3} c\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + 9 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, a^{3} x^{4}}, -\frac{384 \, B a^{3} \sqrt{-c} c x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 3 \, {\left(8 \, B a b^{3} - 3 \, A b^{4} - 48 \, A a^{2} c^{2} - 24 \, {\left(4 \, B a^{2} b - A a b^{2}\right)} c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(48 \, A a^{4} + {\left(24 \, B a^{2} b^{2} - 9 \, A a b^{3} + 4 \, {\left(64 \, B a^{3} + 15 \, A a^{2} b\right)} c\right)} x^{3} + 2 \, {\left(56 \, B a^{3} b + 3 \, A a^{2} b^{2} + 60 \, A a^{3} c\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + 9 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, a^{3} x^{4}}\right]"," ",0,"[1/768*(384*B*a^3*c^(3/2)*x^4*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 3*(8*B*a*b^3 - 3*A*b^4 - 48*A*a^2*c^2 - 24*(4*B*a^2*b - A*a*b^2)*c)*sqrt(a)*x^4*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(48*A*a^4 + (24*B*a^2*b^2 - 9*A*a*b^3 + 4*(64*B*a^3 + 15*A*a^2*b)*c)*x^3 + 2*(56*B*a^3*b + 3*A*a^2*b^2 + 60*A*a^3*c)*x^2 + 8*(8*B*a^4 + 9*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^4), -1/768*(768*B*a^3*sqrt(-c)*c*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 3*(8*B*a*b^3 - 3*A*b^4 - 48*A*a^2*c^2 - 24*(4*B*a^2*b - A*a*b^2)*c)*sqrt(a)*x^4*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(48*A*a^4 + (24*B*a^2*b^2 - 9*A*a*b^3 + 4*(64*B*a^3 + 15*A*a^2*b)*c)*x^3 + 2*(56*B*a^3*b + 3*A*a^2*b^2 + 60*A*a^3*c)*x^2 + 8*(8*B*a^4 + 9*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^4), 1/384*(192*B*a^3*c^(3/2)*x^4*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 3*(8*B*a*b^3 - 3*A*b^4 - 48*A*a^2*c^2 - 24*(4*B*a^2*b - A*a*b^2)*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(48*A*a^4 + (24*B*a^2*b^2 - 9*A*a*b^3 + 4*(64*B*a^3 + 15*A*a^2*b)*c)*x^3 + 2*(56*B*a^3*b + 3*A*a^2*b^2 + 60*A*a^3*c)*x^2 + 8*(8*B*a^4 + 9*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^4), -1/384*(384*B*a^3*sqrt(-c)*c*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 3*(8*B*a*b^3 - 3*A*b^4 - 48*A*a^2*c^2 - 24*(4*B*a^2*b - A*a*b^2)*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(48*A*a^4 + (24*B*a^2*b^2 - 9*A*a*b^3 + 4*(64*B*a^3 + 15*A*a^2*b)*c)*x^3 + 2*(56*B*a^3*b + 3*A*a^2*b^2 + 60*A*a^3*c)*x^2 + 8*(8*B*a^4 + 9*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^4)]","A",0
932,1,555,0,1.930430," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(2 \, B a b^{4} - A b^{5} + 16 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - 8 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{a} x^{5} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(128 \, A a^{5} - {\left(30 \, B a^{2} b^{3} - 15 \, A a b^{4} - 128 \, A a^{3} c^{2} - 100 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} x^{4} + 2 \, {\left(10 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3} + 4 \, {\left(50 \, B a^{4} + 7 \, A a^{3} b\right)} c\right)} x^{3} + 8 \, {\left(30 \, B a^{4} b + A a^{3} b^{2} + 32 \, A a^{4} c\right)} x^{2} + 16 \, {\left(10 \, B a^{5} + 11 \, A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2560 \, a^{4} x^{5}}, \frac{15 \, {\left(2 \, B a b^{4} - A b^{5} + 16 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - 8 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(128 \, A a^{5} - {\left(30 \, B a^{2} b^{3} - 15 \, A a b^{4} - 128 \, A a^{3} c^{2} - 100 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} x^{4} + 2 \, {\left(10 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3} + 4 \, {\left(50 \, B a^{4} + 7 \, A a^{3} b\right)} c\right)} x^{3} + 8 \, {\left(30 \, B a^{4} b + A a^{3} b^{2} + 32 \, A a^{4} c\right)} x^{2} + 16 \, {\left(10 \, B a^{5} + 11 \, A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1280 \, a^{4} x^{5}}\right]"," ",0,"[1/2560*(15*(2*B*a*b^4 - A*b^5 + 16*(2*B*a^3 - A*a^2*b)*c^2 - 8*(2*B*a^2*b^2 - A*a*b^3)*c)*sqrt(a)*x^5*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(128*A*a^5 - (30*B*a^2*b^3 - 15*A*a*b^4 - 128*A*a^3*c^2 - 100*(2*B*a^3*b - A*a^2*b^2)*c)*x^4 + 2*(10*B*a^3*b^2 - 5*A*a^2*b^3 + 4*(50*B*a^4 + 7*A*a^3*b)*c)*x^3 + 8*(30*B*a^4*b + A*a^3*b^2 + 32*A*a^4*c)*x^2 + 16*(10*B*a^5 + 11*A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^5), 1/1280*(15*(2*B*a*b^4 - A*b^5 + 16*(2*B*a^3 - A*a^2*b)*c^2 - 8*(2*B*a^2*b^2 - A*a*b^3)*c)*sqrt(-a)*x^5*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(128*A*a^5 - (30*B*a^2*b^3 - 15*A*a*b^4 - 128*A*a^3*c^2 - 100*(2*B*a^3*b - A*a^2*b^2)*c)*x^4 + 2*(10*B*a^3*b^2 - 5*A*a^2*b^3 + 4*(50*B*a^4 + 7*A*a^3*b)*c)*x^3 + 8*(30*B*a^4*b + A*a^3*b^2 + 32*A*a^4*c)*x^2 + 16*(10*B*a^5 + 11*A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^5)]","A",0
933,1,709,0,3.578410," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(12 \, B a b^{5} - 7 \, A b^{6} + 64 \, A a^{3} c^{3} + 48 \, {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c^{2} - 12 \, {\left(8 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c\right)} \sqrt{a} x^{6} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(1280 \, A a^{6} + {\left(180 \, B a^{2} b^{4} - 105 \, A a b^{5} + 48 \, {\left(32 \, B a^{4} - 27 \, A a^{3} b\right)} c^{2} - 40 \, {\left(30 \, B a^{3} b^{2} - 19 \, A a^{2} b^{3}\right)} c\right)} x^{5} - 2 \, {\left(60 \, B a^{3} b^{3} - 35 \, A a^{2} b^{4} - 240 \, A a^{4} c^{2} - 24 \, {\left(14 \, B a^{4} b - 9 \, A a^{3} b^{2}\right)} c\right)} x^{4} + 8 \, {\left(12 \, B a^{4} b^{2} - 7 \, A a^{3} b^{3} + 12 \, {\left(32 \, B a^{5} + 3 \, A a^{4} b\right)} c\right)} x^{3} + 16 \, {\left(132 \, B a^{5} b + 3 \, A a^{4} b^{2} + 140 \, A a^{5} c\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 13 \, A a^{5} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, a^{5} x^{6}}, -\frac{15 \, {\left(12 \, B a b^{5} - 7 \, A b^{6} + 64 \, A a^{3} c^{3} + 48 \, {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c^{2} - 12 \, {\left(8 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(1280 \, A a^{6} + {\left(180 \, B a^{2} b^{4} - 105 \, A a b^{5} + 48 \, {\left(32 \, B a^{4} - 27 \, A a^{3} b\right)} c^{2} - 40 \, {\left(30 \, B a^{3} b^{2} - 19 \, A a^{2} b^{3}\right)} c\right)} x^{5} - 2 \, {\left(60 \, B a^{3} b^{3} - 35 \, A a^{2} b^{4} - 240 \, A a^{4} c^{2} - 24 \, {\left(14 \, B a^{4} b - 9 \, A a^{3} b^{2}\right)} c\right)} x^{4} + 8 \, {\left(12 \, B a^{4} b^{2} - 7 \, A a^{3} b^{3} + 12 \, {\left(32 \, B a^{5} + 3 \, A a^{4} b\right)} c\right)} x^{3} + 16 \, {\left(132 \, B a^{5} b + 3 \, A a^{4} b^{2} + 140 \, A a^{5} c\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 13 \, A a^{5} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, a^{5} x^{6}}\right]"," ",0,"[1/30720*(15*(12*B*a*b^5 - 7*A*b^6 + 64*A*a^3*c^3 + 48*(4*B*a^3*b - 3*A*a^2*b^2)*c^2 - 12*(8*B*a^2*b^3 - 5*A*a*b^4)*c)*sqrt(a)*x^6*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(1280*A*a^6 + (180*B*a^2*b^4 - 105*A*a*b^5 + 48*(32*B*a^4 - 27*A*a^3*b)*c^2 - 40*(30*B*a^3*b^2 - 19*A*a^2*b^3)*c)*x^5 - 2*(60*B*a^3*b^3 - 35*A*a^2*b^4 - 240*A*a^4*c^2 - 24*(14*B*a^4*b - 9*A*a^3*b^2)*c)*x^4 + 8*(12*B*a^4*b^2 - 7*A*a^3*b^3 + 12*(32*B*a^5 + 3*A*a^4*b)*c)*x^3 + 16*(132*B*a^5*b + 3*A*a^4*b^2 + 140*A*a^5*c)*x^2 + 128*(12*B*a^6 + 13*A*a^5*b)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^6), -1/15360*(15*(12*B*a*b^5 - 7*A*b^6 + 64*A*a^3*c^3 + 48*(4*B*a^3*b - 3*A*a^2*b^2)*c^2 - 12*(8*B*a^2*b^3 - 5*A*a*b^4)*c)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(1280*A*a^6 + (180*B*a^2*b^4 - 105*A*a*b^5 + 48*(32*B*a^4 - 27*A*a^3*b)*c^2 - 40*(30*B*a^3*b^2 - 19*A*a^2*b^3)*c)*x^5 - 2*(60*B*a^3*b^3 - 35*A*a^2*b^4 - 240*A*a^4*c^2 - 24*(14*B*a^4*b - 9*A*a^3*b^2)*c)*x^4 + 8*(12*B*a^4*b^2 - 7*A*a^3*b^3 + 12*(32*B*a^5 + 3*A*a^4*b)*c)*x^3 + 16*(132*B*a^5*b + 3*A*a^4*b^2 + 140*A*a^5*c)*x^2 + 128*(12*B*a^6 + 13*A*a^5*b)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^6)]","A",0
934,1,889,0,4.543503," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/x^8,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(14 \, B a b^{6} - 9 \, A b^{7} - 64 \, {\left(2 \, B a^{4} - 3 \, A a^{3} b\right)} c^{3} + 48 \, {\left(6 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2} - 12 \, {\left(10 \, B a^{2} b^{4} - 7 \, A a b^{5}\right)} c\right)} \sqrt{a} x^{7} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(15360 \, A a^{7} - {\left(1470 \, B a^{2} b^{5} - 945 \, A a b^{6} + 6144 \, A a^{4} c^{3} + 336 \, {\left(54 \, B a^{4} b - 49 \, A a^{3} b^{2}\right)} c^{2} - 280 \, {\left(38 \, B a^{3} b^{3} - 27 \, A a^{2} b^{4}\right)} c\right)} x^{6} + 2 \, {\left(490 \, B a^{3} b^{4} - 315 \, A a^{2} b^{5} + 48 \, {\left(70 \, B a^{5} - 73 \, A a^{4} b\right)} c^{2} - 168 \, {\left(18 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} c\right)} x^{5} - 8 \, {\left(98 \, B a^{4} b^{3} - 63 \, A a^{3} b^{4} - 384 \, A a^{5} c^{2} - 12 \, {\left(42 \, B a^{5} b - 31 \, A a^{4} b^{2}\right)} c\right)} x^{4} + 16 \, {\left(42 \, B a^{5} b^{2} - 27 \, A a^{4} b^{3} + 4 \, {\left(490 \, B a^{6} + 33 \, A a^{5} b\right)} c\right)} x^{3} + 128 \, {\left(182 \, B a^{6} b + 3 \, A a^{5} b^{2} + 192 \, A a^{6} c\right)} x^{2} + 1280 \, {\left(14 \, B a^{7} + 15 \, A a^{6} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{430080 \, a^{6} x^{7}}, \frac{105 \, {\left(14 \, B a b^{6} - 9 \, A b^{7} - 64 \, {\left(2 \, B a^{4} - 3 \, A a^{3} b\right)} c^{3} + 48 \, {\left(6 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2} - 12 \, {\left(10 \, B a^{2} b^{4} - 7 \, A a b^{5}\right)} c\right)} \sqrt{-a} x^{7} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(15360 \, A a^{7} - {\left(1470 \, B a^{2} b^{5} - 945 \, A a b^{6} + 6144 \, A a^{4} c^{3} + 336 \, {\left(54 \, B a^{4} b - 49 \, A a^{3} b^{2}\right)} c^{2} - 280 \, {\left(38 \, B a^{3} b^{3} - 27 \, A a^{2} b^{4}\right)} c\right)} x^{6} + 2 \, {\left(490 \, B a^{3} b^{4} - 315 \, A a^{2} b^{5} + 48 \, {\left(70 \, B a^{5} - 73 \, A a^{4} b\right)} c^{2} - 168 \, {\left(18 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} c\right)} x^{5} - 8 \, {\left(98 \, B a^{4} b^{3} - 63 \, A a^{3} b^{4} - 384 \, A a^{5} c^{2} - 12 \, {\left(42 \, B a^{5} b - 31 \, A a^{4} b^{2}\right)} c\right)} x^{4} + 16 \, {\left(42 \, B a^{5} b^{2} - 27 \, A a^{4} b^{3} + 4 \, {\left(490 \, B a^{6} + 33 \, A a^{5} b\right)} c\right)} x^{3} + 128 \, {\left(182 \, B a^{6} b + 3 \, A a^{5} b^{2} + 192 \, A a^{6} c\right)} x^{2} + 1280 \, {\left(14 \, B a^{7} + 15 \, A a^{6} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{215040 \, a^{6} x^{7}}\right]"," ",0,"[1/430080*(105*(14*B*a*b^6 - 9*A*b^7 - 64*(2*B*a^4 - 3*A*a^3*b)*c^3 + 48*(6*B*a^3*b^2 - 5*A*a^2*b^3)*c^2 - 12*(10*B*a^2*b^4 - 7*A*a*b^5)*c)*sqrt(a)*x^7*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(15360*A*a^7 - (1470*B*a^2*b^5 - 945*A*a*b^6 + 6144*A*a^4*c^3 + 336*(54*B*a^4*b - 49*A*a^3*b^2)*c^2 - 280*(38*B*a^3*b^3 - 27*A*a^2*b^4)*c)*x^6 + 2*(490*B*a^3*b^4 - 315*A*a^2*b^5 + 48*(70*B*a^5 - 73*A*a^4*b)*c^2 - 168*(18*B*a^4*b^2 - 13*A*a^3*b^3)*c)*x^5 - 8*(98*B*a^4*b^3 - 63*A*a^3*b^4 - 384*A*a^5*c^2 - 12*(42*B*a^5*b - 31*A*a^4*b^2)*c)*x^4 + 16*(42*B*a^5*b^2 - 27*A*a^4*b^3 + 4*(490*B*a^6 + 33*A*a^5*b)*c)*x^3 + 128*(182*B*a^6*b + 3*A*a^5*b^2 + 192*A*a^6*c)*x^2 + 1280*(14*B*a^7 + 15*A*a^6*b)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^7), 1/215040*(105*(14*B*a*b^6 - 9*A*b^7 - 64*(2*B*a^4 - 3*A*a^3*b)*c^3 + 48*(6*B*a^3*b^2 - 5*A*a^2*b^3)*c^2 - 12*(10*B*a^2*b^4 - 7*A*a*b^5)*c)*sqrt(-a)*x^7*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(15360*A*a^7 - (1470*B*a^2*b^5 - 945*A*a*b^6 + 6144*A*a^4*c^3 + 336*(54*B*a^4*b - 49*A*a^3*b^2)*c^2 - 280*(38*B*a^3*b^3 - 27*A*a^2*b^4)*c)*x^6 + 2*(490*B*a^3*b^4 - 315*A*a^2*b^5 + 48*(70*B*a^5 - 73*A*a^4*b)*c^2 - 168*(18*B*a^4*b^2 - 13*A*a^3*b^3)*c)*x^5 - 8*(98*B*a^4*b^3 - 63*A*a^3*b^4 - 384*A*a^5*c^2 - 12*(42*B*a^5*b - 31*A*a^4*b^2)*c)*x^4 + 16*(42*B*a^5*b^2 - 27*A*a^4*b^3 + 4*(490*B*a^6 + 33*A*a^5*b)*c)*x^3 + 128*(182*B*a^6*b + 3*A*a^5*b^2 + 192*A*a^6*c)*x^2 + 1280*(14*B*a^7 + 15*A*a^6*b)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^7)]","A",0
935,1,1775,0,0.848621," ","integrate(x^4*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(195 \, B b^{11} + 6144 \, A a^{5} c^{6} - 7680 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} c^{5} + 44800 \, {\left(B a^{4} b^{3} + A a^{3} b^{4}\right)} c^{4} - 20160 \, {\left(2 \, B a^{3} b^{5} + A a^{2} b^{6}\right)} c^{3} + 3960 \, {\left(4 \, B a^{2} b^{7} + A a b^{8}\right)} c^{2} - 286 \, {\left(10 \, B a b^{9} + A b^{10}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(82575360 \, B c^{11} x^{10} - 675675 \, B b^{10} c + 4128768 \, {\left(45 \, B b c^{10} + 22 \, A c^{11}\right)} x^{9} + 229376 \, {\left(465 \, B b^{2} c^{9} + 2 \, {\left(460 \, B a + 451 \, A b\right)} c^{10}\right)} x^{8} + 14336 \, {\left(15 \, B b^{3} c^{8} + 16632 \, A a c^{10} + 2 \, {\left(8650 \, B a b + 4213 \, A b^{2}\right)} c^{9}\right)} x^{7} + 2560 \, {\left(4096 \, B a^{5} + 20449 \, A a^{4} b\right)} c^{6} - 1024 \, {\left(225 \, B b^{4} c^{7} - 8 \, {\left(18080 \, B a^{2} + 34991 \, A a b\right)} c^{9} - 30 \, {\left(54 \, B a b^{2} + 11 \, A b^{3}\right)} c^{8}\right)} x^{6} - 42240 \, {\left(1733 \, B a^{4} b^{2} + 2295 \, A a^{3} b^{3}\right)} c^{5} + 256 \, {\left(975 \, B b^{5} c^{6} + 687456 \, A a^{2} c^{9} + 240 \, {\left(71 \, B a^{2} b + 44 \, A a b^{2}\right)} c^{8} - 10 \, {\left(800 \, B a b^{3} + 143 \, A b^{4}\right)} c^{7}\right)} x^{5} + 12672 \, {\left(7265 \, B a^{3} b^{4} + 4319 \, A a^{2} b^{5}\right)} c^{4} - 128 \, {\left(2145 \, B b^{6} c^{5} - 480 \, {\left(64 \, B a^{3} + 121 \, A a^{2} b\right)} c^{8} + 240 \, {\left(221 \, B a^{2} b^{2} + 110 \, A a b^{3}\right)} c^{7} - 26 \, {\left(760 \, B a b^{4} + 121 \, A b^{5}\right)} c^{6}\right)} x^{4} - 18480 \, {\left(2372 \, B a^{2} b^{6} + 671 \, A a b^{7}\right)} c^{3} + 16 \, {\left(19305 \, B b^{7} c^{4} + 443520 \, A a^{3} c^{8} - 480 \, {\left(1286 \, B a^{3} b + 1529 \, A a^{2} b^{2}\right)} c^{7} + 40 \, {\left(15934 \, B a^{2} b^{3} + 6655 \, A a b^{4}\right)} c^{6} - 858 \, {\left(230 \, B a b^{5} + 33 \, A b^{6}\right)} c^{5}\right)} x^{3} + 90090 \, {\left(100 \, B a b^{8} + 11 \, A b^{9}\right)} c^{2} - 8 \, {\left(45045 \, B b^{8} c^{3} + 640 \, {\left(1024 \, B a^{4} + 3553 \, A a^{3} b\right)} c^{7} - 480 \, {\left(5358 \, B a^{3} b^{2} + 4741 \, A a^{2} b^{3}\right)} c^{6} + 792 \, {\left(2410 \, B a^{2} b^{4} + 869 \, A a b^{5}\right)} c^{5} - 858 \, {\left(590 \, B a b^{6} + 77 \, A b^{7}\right)} c^{4}\right)} x^{2} + 2 \, {\left(225225 \, B b^{9} c^{2} - 5322240 \, A a^{4} c^{7} + 1280 \, {\left(8347 \, B a^{4} b + 15763 \, A a^{3} b^{2}\right)} c^{6} - 21120 \, {\left(971 \, B a^{3} b^{3} + 690 \, A a^{2} b^{4}\right)} c^{5} + 1584 \, {\left(7520 \, B a^{2} b^{5} + 2387 \, A a b^{6}\right)} c^{4} - 30030 \, {\left(92 \, B a b^{7} + 11 \, A b^{8}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3633315840 \, c^{9}}, -\frac{3465 \, {\left(195 \, B b^{11} + 6144 \, A a^{5} c^{6} - 7680 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} c^{5} + 44800 \, {\left(B a^{4} b^{3} + A a^{3} b^{4}\right)} c^{4} - 20160 \, {\left(2 \, B a^{3} b^{5} + A a^{2} b^{6}\right)} c^{3} + 3960 \, {\left(4 \, B a^{2} b^{7} + A a b^{8}\right)} c^{2} - 286 \, {\left(10 \, B a b^{9} + A b^{10}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(82575360 \, B c^{11} x^{10} - 675675 \, B b^{10} c + 4128768 \, {\left(45 \, B b c^{10} + 22 \, A c^{11}\right)} x^{9} + 229376 \, {\left(465 \, B b^{2} c^{9} + 2 \, {\left(460 \, B a + 451 \, A b\right)} c^{10}\right)} x^{8} + 14336 \, {\left(15 \, B b^{3} c^{8} + 16632 \, A a c^{10} + 2 \, {\left(8650 \, B a b + 4213 \, A b^{2}\right)} c^{9}\right)} x^{7} + 2560 \, {\left(4096 \, B a^{5} + 20449 \, A a^{4} b\right)} c^{6} - 1024 \, {\left(225 \, B b^{4} c^{7} - 8 \, {\left(18080 \, B a^{2} + 34991 \, A a b\right)} c^{9} - 30 \, {\left(54 \, B a b^{2} + 11 \, A b^{3}\right)} c^{8}\right)} x^{6} - 42240 \, {\left(1733 \, B a^{4} b^{2} + 2295 \, A a^{3} b^{3}\right)} c^{5} + 256 \, {\left(975 \, B b^{5} c^{6} + 687456 \, A a^{2} c^{9} + 240 \, {\left(71 \, B a^{2} b + 44 \, A a b^{2}\right)} c^{8} - 10 \, {\left(800 \, B a b^{3} + 143 \, A b^{4}\right)} c^{7}\right)} x^{5} + 12672 \, {\left(7265 \, B a^{3} b^{4} + 4319 \, A a^{2} b^{5}\right)} c^{4} - 128 \, {\left(2145 \, B b^{6} c^{5} - 480 \, {\left(64 \, B a^{3} + 121 \, A a^{2} b\right)} c^{8} + 240 \, {\left(221 \, B a^{2} b^{2} + 110 \, A a b^{3}\right)} c^{7} - 26 \, {\left(760 \, B a b^{4} + 121 \, A b^{5}\right)} c^{6}\right)} x^{4} - 18480 \, {\left(2372 \, B a^{2} b^{6} + 671 \, A a b^{7}\right)} c^{3} + 16 \, {\left(19305 \, B b^{7} c^{4} + 443520 \, A a^{3} c^{8} - 480 \, {\left(1286 \, B a^{3} b + 1529 \, A a^{2} b^{2}\right)} c^{7} + 40 \, {\left(15934 \, B a^{2} b^{3} + 6655 \, A a b^{4}\right)} c^{6} - 858 \, {\left(230 \, B a b^{5} + 33 \, A b^{6}\right)} c^{5}\right)} x^{3} + 90090 \, {\left(100 \, B a b^{8} + 11 \, A b^{9}\right)} c^{2} - 8 \, {\left(45045 \, B b^{8} c^{3} + 640 \, {\left(1024 \, B a^{4} + 3553 \, A a^{3} b\right)} c^{7} - 480 \, {\left(5358 \, B a^{3} b^{2} + 4741 \, A a^{2} b^{3}\right)} c^{6} + 792 \, {\left(2410 \, B a^{2} b^{4} + 869 \, A a b^{5}\right)} c^{5} - 858 \, {\left(590 \, B a b^{6} + 77 \, A b^{7}\right)} c^{4}\right)} x^{2} + 2 \, {\left(225225 \, B b^{9} c^{2} - 5322240 \, A a^{4} c^{7} + 1280 \, {\left(8347 \, B a^{4} b + 15763 \, A a^{3} b^{2}\right)} c^{6} - 21120 \, {\left(971 \, B a^{3} b^{3} + 690 \, A a^{2} b^{4}\right)} c^{5} + 1584 \, {\left(7520 \, B a^{2} b^{5} + 2387 \, A a b^{6}\right)} c^{4} - 30030 \, {\left(92 \, B a b^{7} + 11 \, A b^{8}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1816657920 \, c^{9}}\right]"," ",0,"[1/3633315840*(3465*(195*B*b^11 + 6144*A*a^5*c^6 - 7680*(2*B*a^5*b + 5*A*a^4*b^2)*c^5 + 44800*(B*a^4*b^3 + A*a^3*b^4)*c^4 - 20160*(2*B*a^3*b^5 + A*a^2*b^6)*c^3 + 3960*(4*B*a^2*b^7 + A*a*b^8)*c^2 - 286*(10*B*a*b^9 + A*b^10)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(82575360*B*c^11*x^10 - 675675*B*b^10*c + 4128768*(45*B*b*c^10 + 22*A*c^11)*x^9 + 229376*(465*B*b^2*c^9 + 2*(460*B*a + 451*A*b)*c^10)*x^8 + 14336*(15*B*b^3*c^8 + 16632*A*a*c^10 + 2*(8650*B*a*b + 4213*A*b^2)*c^9)*x^7 + 2560*(4096*B*a^5 + 20449*A*a^4*b)*c^6 - 1024*(225*B*b^4*c^7 - 8*(18080*B*a^2 + 34991*A*a*b)*c^9 - 30*(54*B*a*b^2 + 11*A*b^3)*c^8)*x^6 - 42240*(1733*B*a^4*b^2 + 2295*A*a^3*b^3)*c^5 + 256*(975*B*b^5*c^6 + 687456*A*a^2*c^9 + 240*(71*B*a^2*b + 44*A*a*b^2)*c^8 - 10*(800*B*a*b^3 + 143*A*b^4)*c^7)*x^5 + 12672*(7265*B*a^3*b^4 + 4319*A*a^2*b^5)*c^4 - 128*(2145*B*b^6*c^5 - 480*(64*B*a^3 + 121*A*a^2*b)*c^8 + 240*(221*B*a^2*b^2 + 110*A*a*b^3)*c^7 - 26*(760*B*a*b^4 + 121*A*b^5)*c^6)*x^4 - 18480*(2372*B*a^2*b^6 + 671*A*a*b^7)*c^3 + 16*(19305*B*b^7*c^4 + 443520*A*a^3*c^8 - 480*(1286*B*a^3*b + 1529*A*a^2*b^2)*c^7 + 40*(15934*B*a^2*b^3 + 6655*A*a*b^4)*c^6 - 858*(230*B*a*b^5 + 33*A*b^6)*c^5)*x^3 + 90090*(100*B*a*b^8 + 11*A*b^9)*c^2 - 8*(45045*B*b^8*c^3 + 640*(1024*B*a^4 + 3553*A*a^3*b)*c^7 - 480*(5358*B*a^3*b^2 + 4741*A*a^2*b^3)*c^6 + 792*(2410*B*a^2*b^4 + 869*A*a*b^5)*c^5 - 858*(590*B*a*b^6 + 77*A*b^7)*c^4)*x^2 + 2*(225225*B*b^9*c^2 - 5322240*A*a^4*c^7 + 1280*(8347*B*a^4*b + 15763*A*a^3*b^2)*c^6 - 21120*(971*B*a^3*b^3 + 690*A*a^2*b^4)*c^5 + 1584*(7520*B*a^2*b^5 + 2387*A*a*b^6)*c^4 - 30030*(92*B*a*b^7 + 11*A*b^8)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^9, -1/1816657920*(3465*(195*B*b^11 + 6144*A*a^5*c^6 - 7680*(2*B*a^5*b + 5*A*a^4*b^2)*c^5 + 44800*(B*a^4*b^3 + A*a^3*b^4)*c^4 - 20160*(2*B*a^3*b^5 + A*a^2*b^6)*c^3 + 3960*(4*B*a^2*b^7 + A*a*b^8)*c^2 - 286*(10*B*a*b^9 + A*b^10)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(82575360*B*c^11*x^10 - 675675*B*b^10*c + 4128768*(45*B*b*c^10 + 22*A*c^11)*x^9 + 229376*(465*B*b^2*c^9 + 2*(460*B*a + 451*A*b)*c^10)*x^8 + 14336*(15*B*b^3*c^8 + 16632*A*a*c^10 + 2*(8650*B*a*b + 4213*A*b^2)*c^9)*x^7 + 2560*(4096*B*a^5 + 20449*A*a^4*b)*c^6 - 1024*(225*B*b^4*c^7 - 8*(18080*B*a^2 + 34991*A*a*b)*c^9 - 30*(54*B*a*b^2 + 11*A*b^3)*c^8)*x^6 - 42240*(1733*B*a^4*b^2 + 2295*A*a^3*b^3)*c^5 + 256*(975*B*b^5*c^6 + 687456*A*a^2*c^9 + 240*(71*B*a^2*b + 44*A*a*b^2)*c^8 - 10*(800*B*a*b^3 + 143*A*b^4)*c^7)*x^5 + 12672*(7265*B*a^3*b^4 + 4319*A*a^2*b^5)*c^4 - 128*(2145*B*b^6*c^5 - 480*(64*B*a^3 + 121*A*a^2*b)*c^8 + 240*(221*B*a^2*b^2 + 110*A*a*b^3)*c^7 - 26*(760*B*a*b^4 + 121*A*b^5)*c^6)*x^4 - 18480*(2372*B*a^2*b^6 + 671*A*a*b^7)*c^3 + 16*(19305*B*b^7*c^4 + 443520*A*a^3*c^8 - 480*(1286*B*a^3*b + 1529*A*a^2*b^2)*c^7 + 40*(15934*B*a^2*b^3 + 6655*A*a*b^4)*c^6 - 858*(230*B*a*b^5 + 33*A*b^6)*c^5)*x^3 + 90090*(100*B*a*b^8 + 11*A*b^9)*c^2 - 8*(45045*B*b^8*c^3 + 640*(1024*B*a^4 + 3553*A*a^3*b)*c^7 - 480*(5358*B*a^3*b^2 + 4741*A*a^2*b^3)*c^6 + 792*(2410*B*a^2*b^4 + 869*A*a*b^5)*c^5 - 858*(590*B*a*b^6 + 77*A*b^7)*c^4)*x^2 + 2*(225225*B*b^9*c^2 - 5322240*A*a^4*c^7 + 1280*(8347*B*a^4*b + 15763*A*a^3*b^2)*c^6 - 21120*(971*B*a^3*b^3 + 690*A*a^2*b^4)*c^5 + 1584*(7520*B*a^2*b^5 + 2387*A*a*b^6)*c^4 - 30030*(92*B*a*b^7 + 11*A*b^8)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^9]","A",0
936,1,1511,0,0.764088," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(143 \, B b^{10} - 3072 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} c^{5} + 6400 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} c^{4} - 4480 \, {\left(5 \, B a^{3} b^{4} + 3 \, A a^{2} b^{5}\right)} c^{3} + 1440 \, {\left(7 \, B a^{2} b^{6} + 2 \, A a b^{7}\right)} c^{2} - 220 \, {\left(9 \, B a b^{8} + A b^{9}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(4128768 \, B c^{10} x^{9} + 45045 \, B b^{9} c - 1310720 \, A a^{4} c^{6} + 229376 \, {\left(41 \, B b c^{9} + 20 \, A c^{10}\right)} x^{8} + 14336 \, {\left(383 \, B b^{2} c^{8} + 4 \, {\left(189 \, B a + 185 \, A b\right)} c^{9}\right)} x^{7} + 1024 \, {\left(15 \, B b^{3} c^{7} + 12160 \, A a c^{9} + 4 \, {\left(3181 \, B a b + 1545 \, A b^{2}\right)} c^{8}\right)} x^{6} + 14080 \, {\left(169 \, B a^{4} b + 333 \, A a^{3} b^{2}\right)} c^{5} - 256 \, {\left(65 \, B b^{4} c^{6} - 48 \, {\left(651 \, B a^{2} + 1255 \, A a b\right)} c^{8} - 20 \, {\left(24 \, B a b^{2} + 5 \, A b^{3}\right)} c^{7}\right)} x^{5} - 2880 \, {\left(1530 \, B a^{3} b^{3} + 1127 \, A a^{2} b^{4}\right)} c^{4} + 128 \, {\left(143 \, B b^{5} c^{5} + 76800 \, A a^{2} c^{8} + 240 \, {\left(11 \, B a^{2} b + 7 \, A a b^{2}\right)} c^{7} - 20 \, {\left(60 \, B a b^{3} + 11 \, A b^{4}\right)} c^{6}\right)} x^{4} + 336 \, {\left(7404 \, B a^{2} b^{5} + 2425 \, A a b^{6}\right)} c^{3} - 16 \, {\left(1287 \, B b^{6} c^{4} - 960 \, {\left(21 \, B a^{3} + 41 \, A a^{2} b\right)} c^{7} + 80 \, {\left(417 \, B a^{2} b^{2} + 214 \, A a b^{3}\right)} c^{6} - 220 \, {\left(55 \, B a b^{4} + 9 \, A b^{5}\right)} c^{5}\right)} x^{3} - 4620 \, {\left(122 \, B a b^{7} + 15 \, A b^{8}\right)} c^{2} + 8 \, {\left(3003 \, B b^{7} c^{3} + 81920 \, A a^{3} c^{7} - 6080 \, {\left(17 \, B a^{3} b + 21 \, A a^{2} b^{2}\right)} c^{6} + 240 \, {\left(431 \, B a^{2} b^{3} + 186 \, A a b^{4}\right)} c^{5} - 132 \, {\left(237 \, B a b^{5} + 35 \, A b^{6}\right)} c^{4}\right)} x^{2} - 2 \, {\left(15015 \, B b^{8} c^{2} + 1280 \, {\left(189 \, B a^{4} + 689 \, A a^{3} b\right)} c^{6} - 320 \, {\left(2866 \, B a^{3} b^{2} + 2637 \, A a^{2} b^{3}\right)} c^{5} + 720 \, {\left(920 \, B a^{2} b^{4} + 343 \, A a b^{5}\right)} c^{4} - 924 \, {\left(186 \, B a b^{6} + 25 \, A b^{7}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{165150720 \, c^{8}}, \frac{315 \, {\left(143 \, B b^{10} - 3072 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} c^{5} + 6400 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} c^{4} - 4480 \, {\left(5 \, B a^{3} b^{4} + 3 \, A a^{2} b^{5}\right)} c^{3} + 1440 \, {\left(7 \, B a^{2} b^{6} + 2 \, A a b^{7}\right)} c^{2} - 220 \, {\left(9 \, B a b^{8} + A b^{9}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(4128768 \, B c^{10} x^{9} + 45045 \, B b^{9} c - 1310720 \, A a^{4} c^{6} + 229376 \, {\left(41 \, B b c^{9} + 20 \, A c^{10}\right)} x^{8} + 14336 \, {\left(383 \, B b^{2} c^{8} + 4 \, {\left(189 \, B a + 185 \, A b\right)} c^{9}\right)} x^{7} + 1024 \, {\left(15 \, B b^{3} c^{7} + 12160 \, A a c^{9} + 4 \, {\left(3181 \, B a b + 1545 \, A b^{2}\right)} c^{8}\right)} x^{6} + 14080 \, {\left(169 \, B a^{4} b + 333 \, A a^{3} b^{2}\right)} c^{5} - 256 \, {\left(65 \, B b^{4} c^{6} - 48 \, {\left(651 \, B a^{2} + 1255 \, A a b\right)} c^{8} - 20 \, {\left(24 \, B a b^{2} + 5 \, A b^{3}\right)} c^{7}\right)} x^{5} - 2880 \, {\left(1530 \, B a^{3} b^{3} + 1127 \, A a^{2} b^{4}\right)} c^{4} + 128 \, {\left(143 \, B b^{5} c^{5} + 76800 \, A a^{2} c^{8} + 240 \, {\left(11 \, B a^{2} b + 7 \, A a b^{2}\right)} c^{7} - 20 \, {\left(60 \, B a b^{3} + 11 \, A b^{4}\right)} c^{6}\right)} x^{4} + 336 \, {\left(7404 \, B a^{2} b^{5} + 2425 \, A a b^{6}\right)} c^{3} - 16 \, {\left(1287 \, B b^{6} c^{4} - 960 \, {\left(21 \, B a^{3} + 41 \, A a^{2} b\right)} c^{7} + 80 \, {\left(417 \, B a^{2} b^{2} + 214 \, A a b^{3}\right)} c^{6} - 220 \, {\left(55 \, B a b^{4} + 9 \, A b^{5}\right)} c^{5}\right)} x^{3} - 4620 \, {\left(122 \, B a b^{7} + 15 \, A b^{8}\right)} c^{2} + 8 \, {\left(3003 \, B b^{7} c^{3} + 81920 \, A a^{3} c^{7} - 6080 \, {\left(17 \, B a^{3} b + 21 \, A a^{2} b^{2}\right)} c^{6} + 240 \, {\left(431 \, B a^{2} b^{3} + 186 \, A a b^{4}\right)} c^{5} - 132 \, {\left(237 \, B a b^{5} + 35 \, A b^{6}\right)} c^{4}\right)} x^{2} - 2 \, {\left(15015 \, B b^{8} c^{2} + 1280 \, {\left(189 \, B a^{4} + 689 \, A a^{3} b\right)} c^{6} - 320 \, {\left(2866 \, B a^{3} b^{2} + 2637 \, A a^{2} b^{3}\right)} c^{5} + 720 \, {\left(920 \, B a^{2} b^{4} + 343 \, A a b^{5}\right)} c^{4} - 924 \, {\left(186 \, B a b^{6} + 25 \, A b^{7}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{82575360 \, c^{8}}\right]"," ",0,"[-1/165150720*(315*(143*B*b^10 - 3072*(B*a^5 + 5*A*a^4*b)*c^5 + 6400*(3*B*a^4*b^2 + 4*A*a^3*b^3)*c^4 - 4480*(5*B*a^3*b^4 + 3*A*a^2*b^5)*c^3 + 1440*(7*B*a^2*b^6 + 2*A*a*b^7)*c^2 - 220*(9*B*a*b^8 + A*b^9)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(4128768*B*c^10*x^9 + 45045*B*b^9*c - 1310720*A*a^4*c^6 + 229376*(41*B*b*c^9 + 20*A*c^10)*x^8 + 14336*(383*B*b^2*c^8 + 4*(189*B*a + 185*A*b)*c^9)*x^7 + 1024*(15*B*b^3*c^7 + 12160*A*a*c^9 + 4*(3181*B*a*b + 1545*A*b^2)*c^8)*x^6 + 14080*(169*B*a^4*b + 333*A*a^3*b^2)*c^5 - 256*(65*B*b^4*c^6 - 48*(651*B*a^2 + 1255*A*a*b)*c^8 - 20*(24*B*a*b^2 + 5*A*b^3)*c^7)*x^5 - 2880*(1530*B*a^3*b^3 + 1127*A*a^2*b^4)*c^4 + 128*(143*B*b^5*c^5 + 76800*A*a^2*c^8 + 240*(11*B*a^2*b + 7*A*a*b^2)*c^7 - 20*(60*B*a*b^3 + 11*A*b^4)*c^6)*x^4 + 336*(7404*B*a^2*b^5 + 2425*A*a*b^6)*c^3 - 16*(1287*B*b^6*c^4 - 960*(21*B*a^3 + 41*A*a^2*b)*c^7 + 80*(417*B*a^2*b^2 + 214*A*a*b^3)*c^6 - 220*(55*B*a*b^4 + 9*A*b^5)*c^5)*x^3 - 4620*(122*B*a*b^7 + 15*A*b^8)*c^2 + 8*(3003*B*b^7*c^3 + 81920*A*a^3*c^7 - 6080*(17*B*a^3*b + 21*A*a^2*b^2)*c^6 + 240*(431*B*a^2*b^3 + 186*A*a*b^4)*c^5 - 132*(237*B*a*b^5 + 35*A*b^6)*c^4)*x^2 - 2*(15015*B*b^8*c^2 + 1280*(189*B*a^4 + 689*A*a^3*b)*c^6 - 320*(2866*B*a^3*b^2 + 2637*A*a^2*b^3)*c^5 + 720*(920*B*a^2*b^4 + 343*A*a*b^5)*c^4 - 924*(186*B*a*b^6 + 25*A*b^7)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^8, 1/82575360*(315*(143*B*b^10 - 3072*(B*a^5 + 5*A*a^4*b)*c^5 + 6400*(3*B*a^4*b^2 + 4*A*a^3*b^3)*c^4 - 4480*(5*B*a^3*b^4 + 3*A*a^2*b^5)*c^3 + 1440*(7*B*a^2*b^6 + 2*A*a*b^7)*c^2 - 220*(9*B*a*b^8 + A*b^9)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(4128768*B*c^10*x^9 + 45045*B*b^9*c - 1310720*A*a^4*c^6 + 229376*(41*B*b*c^9 + 20*A*c^10)*x^8 + 14336*(383*B*b^2*c^8 + 4*(189*B*a + 185*A*b)*c^9)*x^7 + 1024*(15*B*b^3*c^7 + 12160*A*a*c^9 + 4*(3181*B*a*b + 1545*A*b^2)*c^8)*x^6 + 14080*(169*B*a^4*b + 333*A*a^3*b^2)*c^5 - 256*(65*B*b^4*c^6 - 48*(651*B*a^2 + 1255*A*a*b)*c^8 - 20*(24*B*a*b^2 + 5*A*b^3)*c^7)*x^5 - 2880*(1530*B*a^3*b^3 + 1127*A*a^2*b^4)*c^4 + 128*(143*B*b^5*c^5 + 76800*A*a^2*c^8 + 240*(11*B*a^2*b + 7*A*a*b^2)*c^7 - 20*(60*B*a*b^3 + 11*A*b^4)*c^6)*x^4 + 336*(7404*B*a^2*b^5 + 2425*A*a*b^6)*c^3 - 16*(1287*B*b^6*c^4 - 960*(21*B*a^3 + 41*A*a^2*b)*c^7 + 80*(417*B*a^2*b^2 + 214*A*a*b^3)*c^6 - 220*(55*B*a*b^4 + 9*A*b^5)*c^5)*x^3 - 4620*(122*B*a*b^7 + 15*A*b^8)*c^2 + 8*(3003*B*b^7*c^3 + 81920*A*a^3*c^7 - 6080*(17*B*a^3*b + 21*A*a^2*b^2)*c^6 + 240*(431*B*a^2*b^3 + 186*A*a*b^4)*c^5 - 132*(237*B*a*b^5 + 35*A*b^6)*c^4)*x^2 - 2*(15015*B*b^8*c^2 + 1280*(189*B*a^4 + 689*A*a^3*b)*c^6 - 320*(2866*B*a^3*b^2 + 2637*A*a^2*b^3)*c^5 + 720*(920*B*a^2*b^4 + 343*A*a*b^5)*c^4 - 924*(186*B*a*b^6 + 25*A*b^7)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^8]","A",0
937,1,1263,0,0.659962," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(11 \, B b^{9} - 512 \, A a^{4} c^{5} + 768 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} c^{4} - 320 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} c^{3} + 224 \, {\left(3 \, B a^{2} b^{5} + A a b^{6}\right)} c^{2} - 18 \, {\left(8 \, B a b^{7} + A b^{8}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(229376 \, B c^{9} x^{8} - 3465 \, B b^{8} c + 14336 \, {\left(37 \, B b c^{8} + 18 \, A c^{9}\right)} x^{7} + 1024 \, {\left(309 \, B b^{2} c^{7} + 2 \, {\left(304 \, B a + 297 \, A b\right)} c^{8}\right)} x^{6} - 128 \, {\left(512 \, B a^{4} + 1989 \, A a^{3} b\right)} c^{5} + 256 \, {\left(5 \, B b^{3} c^{6} + 2856 \, A a c^{8} + 6 \, {\left(502 \, B a b + 243 \, A b^{2}\right)} c^{7}\right)} x^{5} + 96 \, {\left(2442 \, B a^{3} b^{2} + 2359 \, A a^{2} b^{3}\right)} c^{4} - 128 \, {\left(11 \, B b^{4} c^{5} - 24 \, {\left(160 \, B a^{2} + 307 \, A a b\right)} c^{7} - 6 \, {\left(14 \, B a b^{2} + 3 \, A b^{3}\right)} c^{6}\right)} x^{4} - 504 \, {\left(322 \, B a^{2} b^{4} + 125 \, A a b^{5}\right)} c^{3} + 16 \, {\left(99 \, B b^{5} c^{4} + 39648 \, A a^{2} c^{7} + 48 \, {\left(41 \, B a^{2} b + 27 \, A a b^{2}\right)} c^{6} - 2 \, {\left(428 \, B a b^{3} + 81 \, A b^{4}\right)} c^{5}\right)} x^{3} + 210 \, {\left(194 \, B a b^{6} + 27 \, A b^{7}\right)} c^{2} - 8 \, {\left(231 \, B b^{6} c^{3} - 32 \, {\left(128 \, B a^{3} + 261 \, A a^{2} b\right)} c^{6} + 48 \, {\left(133 \, B a^{2} b^{2} + 71 \, A a b^{3}\right)} c^{5} - 18 \, {\left(124 \, B a b^{4} + 21 \, A b^{5}\right)} c^{4}\right)} x^{2} + 2 \, {\left(1155 \, B b^{7} c^{2} + 40320 \, A a^{3} c^{6} - 32 \, {\left(1378 \, B a^{3} b + 1791 \, A a^{2} b^{2}\right)} c^{5} + 24 \, {\left(1758 \, B a^{2} b^{3} + 791 \, A a b^{4}\right)} c^{4} - 126 \, {\left(98 \, B a b^{5} + 15 \, A b^{6}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8257536 \, c^{7}}, -\frac{315 \, {\left(11 \, B b^{9} - 512 \, A a^{4} c^{5} + 768 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} c^{4} - 320 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} c^{3} + 224 \, {\left(3 \, B a^{2} b^{5} + A a b^{6}\right)} c^{2} - 18 \, {\left(8 \, B a b^{7} + A b^{8}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(229376 \, B c^{9} x^{8} - 3465 \, B b^{8} c + 14336 \, {\left(37 \, B b c^{8} + 18 \, A c^{9}\right)} x^{7} + 1024 \, {\left(309 \, B b^{2} c^{7} + 2 \, {\left(304 \, B a + 297 \, A b\right)} c^{8}\right)} x^{6} - 128 \, {\left(512 \, B a^{4} + 1989 \, A a^{3} b\right)} c^{5} + 256 \, {\left(5 \, B b^{3} c^{6} + 2856 \, A a c^{8} + 6 \, {\left(502 \, B a b + 243 \, A b^{2}\right)} c^{7}\right)} x^{5} + 96 \, {\left(2442 \, B a^{3} b^{2} + 2359 \, A a^{2} b^{3}\right)} c^{4} - 128 \, {\left(11 \, B b^{4} c^{5} - 24 \, {\left(160 \, B a^{2} + 307 \, A a b\right)} c^{7} - 6 \, {\left(14 \, B a b^{2} + 3 \, A b^{3}\right)} c^{6}\right)} x^{4} - 504 \, {\left(322 \, B a^{2} b^{4} + 125 \, A a b^{5}\right)} c^{3} + 16 \, {\left(99 \, B b^{5} c^{4} + 39648 \, A a^{2} c^{7} + 48 \, {\left(41 \, B a^{2} b + 27 \, A a b^{2}\right)} c^{6} - 2 \, {\left(428 \, B a b^{3} + 81 \, A b^{4}\right)} c^{5}\right)} x^{3} + 210 \, {\left(194 \, B a b^{6} + 27 \, A b^{7}\right)} c^{2} - 8 \, {\left(231 \, B b^{6} c^{3} - 32 \, {\left(128 \, B a^{3} + 261 \, A a^{2} b\right)} c^{6} + 48 \, {\left(133 \, B a^{2} b^{2} + 71 \, A a b^{3}\right)} c^{5} - 18 \, {\left(124 \, B a b^{4} + 21 \, A b^{5}\right)} c^{4}\right)} x^{2} + 2 \, {\left(1155 \, B b^{7} c^{2} + 40320 \, A a^{3} c^{6} - 32 \, {\left(1378 \, B a^{3} b + 1791 \, A a^{2} b^{2}\right)} c^{5} + 24 \, {\left(1758 \, B a^{2} b^{3} + 791 \, A a b^{4}\right)} c^{4} - 126 \, {\left(98 \, B a b^{5} + 15 \, A b^{6}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4128768 \, c^{7}}\right]"," ",0,"[1/8257536*(315*(11*B*b^9 - 512*A*a^4*c^5 + 768*(B*a^4*b + 2*A*a^3*b^2)*c^4 - 320*(4*B*a^3*b^3 + 3*A*a^2*b^4)*c^3 + 224*(3*B*a^2*b^5 + A*a*b^6)*c^2 - 18*(8*B*a*b^7 + A*b^8)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(229376*B*c^9*x^8 - 3465*B*b^8*c + 14336*(37*B*b*c^8 + 18*A*c^9)*x^7 + 1024*(309*B*b^2*c^7 + 2*(304*B*a + 297*A*b)*c^8)*x^6 - 128*(512*B*a^4 + 1989*A*a^3*b)*c^5 + 256*(5*B*b^3*c^6 + 2856*A*a*c^8 + 6*(502*B*a*b + 243*A*b^2)*c^7)*x^5 + 96*(2442*B*a^3*b^2 + 2359*A*a^2*b^3)*c^4 - 128*(11*B*b^4*c^5 - 24*(160*B*a^2 + 307*A*a*b)*c^7 - 6*(14*B*a*b^2 + 3*A*b^3)*c^6)*x^4 - 504*(322*B*a^2*b^4 + 125*A*a*b^5)*c^3 + 16*(99*B*b^5*c^4 + 39648*A*a^2*c^7 + 48*(41*B*a^2*b + 27*A*a*b^2)*c^6 - 2*(428*B*a*b^3 + 81*A*b^4)*c^5)*x^3 + 210*(194*B*a*b^6 + 27*A*b^7)*c^2 - 8*(231*B*b^6*c^3 - 32*(128*B*a^3 + 261*A*a^2*b)*c^6 + 48*(133*B*a^2*b^2 + 71*A*a*b^3)*c^5 - 18*(124*B*a*b^4 + 21*A*b^5)*c^4)*x^2 + 2*(1155*B*b^7*c^2 + 40320*A*a^3*c^6 - 32*(1378*B*a^3*b + 1791*A*a^2*b^2)*c^5 + 24*(1758*B*a^2*b^3 + 791*A*a*b^4)*c^4 - 126*(98*B*a*b^5 + 15*A*b^6)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^7, -1/4128768*(315*(11*B*b^9 - 512*A*a^4*c^5 + 768*(B*a^4*b + 2*A*a^3*b^2)*c^4 - 320*(4*B*a^3*b^3 + 3*A*a^2*b^4)*c^3 + 224*(3*B*a^2*b^5 + A*a*b^6)*c^2 - 18*(8*B*a*b^7 + A*b^8)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(229376*B*c^9*x^8 - 3465*B*b^8*c + 14336*(37*B*b*c^8 + 18*A*c^9)*x^7 + 1024*(309*B*b^2*c^7 + 2*(304*B*a + 297*A*b)*c^8)*x^6 - 128*(512*B*a^4 + 1989*A*a^3*b)*c^5 + 256*(5*B*b^3*c^6 + 2856*A*a*c^8 + 6*(502*B*a*b + 243*A*b^2)*c^7)*x^5 + 96*(2442*B*a^3*b^2 + 2359*A*a^2*b^3)*c^4 - 128*(11*B*b^4*c^5 - 24*(160*B*a^2 + 307*A*a*b)*c^7 - 6*(14*B*a*b^2 + 3*A*b^3)*c^6)*x^4 - 504*(322*B*a^2*b^4 + 125*A*a*b^5)*c^3 + 16*(99*B*b^5*c^4 + 39648*A*a^2*c^7 + 48*(41*B*a^2*b + 27*A*a*b^2)*c^6 - 2*(428*B*a*b^3 + 81*A*b^4)*c^5)*x^3 + 210*(194*B*a*b^6 + 27*A*b^7)*c^2 - 8*(231*B*b^6*c^3 - 32*(128*B*a^3 + 261*A*a^2*b)*c^6 + 48*(133*B*a^2*b^2 + 71*A*a*b^3)*c^5 - 18*(124*B*a*b^4 + 21*A*b^5)*c^4)*x^2 + 2*(1155*B*b^7*c^2 + 40320*A*a^3*c^6 - 32*(1378*B*a^3*b + 1791*A*a^2*b^2)*c^5 + 24*(1758*B*a^2*b^3 + 791*A*a*b^4)*c^4 - 126*(98*B*a*b^5 + 15*A*b^6)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^7]","B",0
938,1,1039,0,0.587182," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(9 \, B b^{8} + 256 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} c^{4} - 768 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{3} + 96 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} c^{2} - 16 \, {\left(7 \, B a b^{6} + A b^{7}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(43008 \, B c^{8} x^{7} + 945 \, B b^{7} c + 49152 \, A a^{3} c^{5} + 3072 \, {\left(33 \, B b c^{7} + 16 \, A c^{8}\right)} x^{6} + 256 \, {\left(243 \, B b^{2} c^{6} + 4 \, {\left(119 \, B a + 116 \, A b\right)} c^{7}\right)} x^{5} - 192 \, {\left(221 \, B a^{3} b + 308 \, A a^{2} b^{2}\right)} c^{4} + 128 \, {\left(3 \, B b^{3} c^{5} + 1152 \, A a c^{7} + 4 \, {\left(307 \, B a b + 148 \, A b^{2}\right)} c^{6}\right)} x^{4} + 112 \, {\left(337 \, B a^{2} b^{3} + 160 \, A a b^{4}\right)} c^{3} - 16 \, {\left(27 \, B b^{4} c^{4} - 16 \, {\left(413 \, B a^{2} + 788 \, A a b\right)} c^{6} - 24 \, {\left(9 \, B a b^{2} + 2 \, A b^{3}\right)} c^{5}\right)} x^{3} - 420 \, {\left(25 \, B a b^{5} + 4 \, A b^{6}\right)} c^{2} + 8 \, {\left(63 \, B b^{5} c^{3} + 18432 \, A a^{2} c^{6} + 48 \, {\left(29 \, B a^{2} b + 20 \, A a b^{2}\right)} c^{5} - 8 \, {\left(71 \, B a b^{3} + 14 \, A b^{4}\right)} c^{4}\right)} x^{2} - 2 \, {\left(315 \, B b^{6} c^{2} - 192 \, {\left(35 \, B a^{3} + 76 \, A a^{2} b\right)} c^{5} + 48 \, {\left(199 \, B a^{2} b^{2} + 112 \, A a b^{3}\right)} c^{4} - 28 \, {\left(113 \, B a b^{4} + 20 \, A b^{5}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1376256 \, c^{6}}, \frac{105 \, {\left(9 \, B b^{8} + 256 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} c^{4} - 768 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{3} + 96 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} c^{2} - 16 \, {\left(7 \, B a b^{6} + A b^{7}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(43008 \, B c^{8} x^{7} + 945 \, B b^{7} c + 49152 \, A a^{3} c^{5} + 3072 \, {\left(33 \, B b c^{7} + 16 \, A c^{8}\right)} x^{6} + 256 \, {\left(243 \, B b^{2} c^{6} + 4 \, {\left(119 \, B a + 116 \, A b\right)} c^{7}\right)} x^{5} - 192 \, {\left(221 \, B a^{3} b + 308 \, A a^{2} b^{2}\right)} c^{4} + 128 \, {\left(3 \, B b^{3} c^{5} + 1152 \, A a c^{7} + 4 \, {\left(307 \, B a b + 148 \, A b^{2}\right)} c^{6}\right)} x^{4} + 112 \, {\left(337 \, B a^{2} b^{3} + 160 \, A a b^{4}\right)} c^{3} - 16 \, {\left(27 \, B b^{4} c^{4} - 16 \, {\left(413 \, B a^{2} + 788 \, A a b\right)} c^{6} - 24 \, {\left(9 \, B a b^{2} + 2 \, A b^{3}\right)} c^{5}\right)} x^{3} - 420 \, {\left(25 \, B a b^{5} + 4 \, A b^{6}\right)} c^{2} + 8 \, {\left(63 \, B b^{5} c^{3} + 18432 \, A a^{2} c^{6} + 48 \, {\left(29 \, B a^{2} b + 20 \, A a b^{2}\right)} c^{5} - 8 \, {\left(71 \, B a b^{3} + 14 \, A b^{4}\right)} c^{4}\right)} x^{2} - 2 \, {\left(315 \, B b^{6} c^{2} - 192 \, {\left(35 \, B a^{3} + 76 \, A a^{2} b\right)} c^{5} + 48 \, {\left(199 \, B a^{2} b^{2} + 112 \, A a b^{3}\right)} c^{4} - 28 \, {\left(113 \, B a b^{4} + 20 \, A b^{5}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{688128 \, c^{6}}\right]"," ",0,"[1/1376256*(105*(9*B*b^8 + 256*(B*a^4 + 4*A*a^3*b)*c^4 - 768*(B*a^3*b^2 + A*a^2*b^3)*c^3 + 96*(5*B*a^2*b^4 + 2*A*a*b^5)*c^2 - 16*(7*B*a*b^6 + A*b^7)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(43008*B*c^8*x^7 + 945*B*b^7*c + 49152*A*a^3*c^5 + 3072*(33*B*b*c^7 + 16*A*c^8)*x^6 + 256*(243*B*b^2*c^6 + 4*(119*B*a + 116*A*b)*c^7)*x^5 - 192*(221*B*a^3*b + 308*A*a^2*b^2)*c^4 + 128*(3*B*b^3*c^5 + 1152*A*a*c^7 + 4*(307*B*a*b + 148*A*b^2)*c^6)*x^4 + 112*(337*B*a^2*b^3 + 160*A*a*b^4)*c^3 - 16*(27*B*b^4*c^4 - 16*(413*B*a^2 + 788*A*a*b)*c^6 - 24*(9*B*a*b^2 + 2*A*b^3)*c^5)*x^3 - 420*(25*B*a*b^5 + 4*A*b^6)*c^2 + 8*(63*B*b^5*c^3 + 18432*A*a^2*c^6 + 48*(29*B*a^2*b + 20*A*a*b^2)*c^5 - 8*(71*B*a*b^3 + 14*A*b^4)*c^4)*x^2 - 2*(315*B*b^6*c^2 - 192*(35*B*a^3 + 76*A*a^2*b)*c^5 + 48*(199*B*a^2*b^2 + 112*A*a*b^3)*c^4 - 28*(113*B*a*b^4 + 20*A*b^5)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/688128*(105*(9*B*b^8 + 256*(B*a^4 + 4*A*a^3*b)*c^4 - 768*(B*a^3*b^2 + A*a^2*b^3)*c^3 + 96*(5*B*a^2*b^4 + 2*A*a*b^5)*c^2 - 16*(7*B*a*b^6 + A*b^7)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(43008*B*c^8*x^7 + 945*B*b^7*c + 49152*A*a^3*c^5 + 3072*(33*B*b*c^7 + 16*A*c^8)*x^6 + 256*(243*B*b^2*c^6 + 4*(119*B*a + 116*A*b)*c^7)*x^5 - 192*(221*B*a^3*b + 308*A*a^2*b^2)*c^4 + 128*(3*B*b^3*c^5 + 1152*A*a*c^7 + 4*(307*B*a*b + 148*A*b^2)*c^6)*x^4 + 112*(337*B*a^2*b^3 + 160*A*a*b^4)*c^3 - 16*(27*B*b^4*c^4 - 16*(413*B*a^2 + 788*A*a*b)*c^6 - 24*(9*B*a*b^2 + 2*A*b^3)*c^5)*x^3 - 420*(25*B*a*b^5 + 4*A*b^6)*c^2 + 8*(63*B*b^5*c^3 + 18432*A*a^2*c^6 + 48*(29*B*a^2*b + 20*A*a*b^2)*c^5 - 8*(71*B*a*b^3 + 14*A*b^4)*c^4)*x^2 - 2*(315*B*b^6*c^2 - 192*(35*B*a^3 + 76*A*a^2*b)*c^5 + 48*(199*B*a^2*b^2 + 112*A*a*b^3)*c^4 - 28*(113*B*a*b^4 + 20*A*b^5)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6]","B",0
939,1,843,0,0.522842," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B b^{7} + 128 \, A a^{3} c^{4} - 32 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{3} + 24 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} c^{2} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(3072 \, B c^{7} x^{6} - 105 \, B b^{6} c + 256 \, {\left(29 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 96 \, {\left(32 \, B a^{3} + 77 \, A a^{2} b\right)} c^{4} + 128 \, {\left(37 \, B b^{2} c^{5} + 2 \, {\left(36 \, B a + 35 \, A b\right)} c^{6}\right)} x^{4} - 112 \, {\left(33 \, B a^{2} b^{2} + 20 \, A a b^{3}\right)} c^{3} + 16 \, {\left(3 \, B b^{3} c^{4} + 728 \, A a c^{6} + 2 \, {\left(394 \, B a b + 189 \, A b^{2}\right)} c^{5}\right)} x^{3} + 70 \, {\left(16 \, B a b^{4} + 3 \, A b^{5}\right)} c^{2} - 8 \, {\left(7 \, B b^{4} c^{3} - 24 \, {\left(48 \, B a^{2} + 91 \, A a b\right)} c^{5} - 2 \, {\left(30 \, B a b^{2} + 7 \, A b^{3}\right)} c^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{5} c^{2} + 7392 \, A a^{2} c^{5} + 48 \, {\left(19 \, B a^{2} b + 14 \, A a b^{2}\right)} c^{4} - 14 \, {\left(24 \, B a b^{3} + 5 \, A b^{4}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{86016 \, c^{5}}, -\frac{105 \, {\left(B b^{7} + 128 \, A a^{3} c^{4} - 32 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{3} + 24 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} c^{2} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(3072 \, B c^{7} x^{6} - 105 \, B b^{6} c + 256 \, {\left(29 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 96 \, {\left(32 \, B a^{3} + 77 \, A a^{2} b\right)} c^{4} + 128 \, {\left(37 \, B b^{2} c^{5} + 2 \, {\left(36 \, B a + 35 \, A b\right)} c^{6}\right)} x^{4} - 112 \, {\left(33 \, B a^{2} b^{2} + 20 \, A a b^{3}\right)} c^{3} + 16 \, {\left(3 \, B b^{3} c^{4} + 728 \, A a c^{6} + 2 \, {\left(394 \, B a b + 189 \, A b^{2}\right)} c^{5}\right)} x^{3} + 70 \, {\left(16 \, B a b^{4} + 3 \, A b^{5}\right)} c^{2} - 8 \, {\left(7 \, B b^{4} c^{3} - 24 \, {\left(48 \, B a^{2} + 91 \, A a b\right)} c^{5} - 2 \, {\left(30 \, B a b^{2} + 7 \, A b^{3}\right)} c^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{5} c^{2} + 7392 \, A a^{2} c^{5} + 48 \, {\left(19 \, B a^{2} b + 14 \, A a b^{2}\right)} c^{4} - 14 \, {\left(24 \, B a b^{3} + 5 \, A b^{4}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{43008 \, c^{5}}\right]"," ",0,"[-1/86016*(105*(B*b^7 + 128*A*a^3*c^4 - 32*(2*B*a^3*b + 3*A*a^2*b^2)*c^3 + 24*(2*B*a^2*b^3 + A*a*b^4)*c^2 - 2*(6*B*a*b^5 + A*b^6)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(3072*B*c^7*x^6 - 105*B*b^6*c + 256*(29*B*b*c^6 + 14*A*c^7)*x^5 + 96*(32*B*a^3 + 77*A*a^2*b)*c^4 + 128*(37*B*b^2*c^5 + 2*(36*B*a + 35*A*b)*c^6)*x^4 - 112*(33*B*a^2*b^2 + 20*A*a*b^3)*c^3 + 16*(3*B*b^3*c^4 + 728*A*a*c^6 + 2*(394*B*a*b + 189*A*b^2)*c^5)*x^3 + 70*(16*B*a*b^4 + 3*A*b^5)*c^2 - 8*(7*B*b^4*c^3 - 24*(48*B*a^2 + 91*A*a*b)*c^5 - 2*(30*B*a*b^2 + 7*A*b^3)*c^4)*x^2 + 2*(35*B*b^5*c^2 + 7392*A*a^2*c^5 + 48*(19*B*a^2*b + 14*A*a*b^2)*c^4 - 14*(24*B*a*b^3 + 5*A*b^4)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/43008*(105*(B*b^7 + 128*A*a^3*c^4 - 32*(2*B*a^3*b + 3*A*a^2*b^2)*c^3 + 24*(2*B*a^2*b^3 + A*a*b^4)*c^2 - 2*(6*B*a*b^5 + A*b^6)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(3072*B*c^7*x^6 - 105*B*b^6*c + 256*(29*B*b*c^6 + 14*A*c^7)*x^5 + 96*(32*B*a^3 + 77*A*a^2*b)*c^4 + 128*(37*B*b^2*c^5 + 2*(36*B*a + 35*A*b)*c^6)*x^4 - 112*(33*B*a^2*b^2 + 20*A*a*b^3)*c^3 + 16*(3*B*b^3*c^4 + 728*A*a*c^6 + 2*(394*B*a*b + 189*A*b^2)*c^5)*x^3 + 70*(16*B*a*b^4 + 3*A*b^5)*c^2 - 8*(7*B*b^4*c^3 - 24*(48*B*a^2 + 91*A*a*b)*c^5 - 2*(30*B*a*b^2 + 7*A*b^3)*c^4)*x^2 + 2*(35*B*b^5*c^2 + 7392*A*a^2*c^5 + 48*(19*B*a^2*b + 14*A*a*b^2)*c^4 - 14*(24*B*a*b^3 + 5*A*b^4)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^5]","B",0
940,1,1575,0,16.450901," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{15360 \, A a^{\frac{5}{2}} c^{4} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 15 \, {\left(5 \, B b^{6} - 320 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3} + 80 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2} - 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(1280 \, B c^{6} x^{5} + 75 \, B b^{5} c + 11776 \, A a^{2} c^{4} + 128 \, {\left(25 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 240 \, {\left(11 \, B a^{2} b + 9 \, A a b^{2}\right)} c^{3} + 16 \, {\left(135 \, B b^{2} c^{4} + 4 \, {\left(65 \, B a + 63 \, A b\right)} c^{5}\right)} x^{3} - 20 \, {\left(40 \, B a b^{3} + 9 \, A b^{4}\right)} c^{2} + 8 \, {\left(5 \, B b^{3} c^{3} + 704 \, A a c^{5} + 12 \, {\left(65 \, B a b + 31 \, A b^{2}\right)} c^{4}\right)} x^{2} - 2 \, {\left(25 \, B b^{4} c^{2} - 16 \, {\left(165 \, B a^{2} + 311 \, A a b\right)} c^{4} - 60 \, {\left(4 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{4}}, \frac{7680 \, A a^{\frac{5}{2}} c^{4} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 15 \, {\left(5 \, B b^{6} - 320 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3} + 80 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2} - 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(1280 \, B c^{6} x^{5} + 75 \, B b^{5} c + 11776 \, A a^{2} c^{4} + 128 \, {\left(25 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 240 \, {\left(11 \, B a^{2} b + 9 \, A a b^{2}\right)} c^{3} + 16 \, {\left(135 \, B b^{2} c^{4} + 4 \, {\left(65 \, B a + 63 \, A b\right)} c^{5}\right)} x^{3} - 20 \, {\left(40 \, B a b^{3} + 9 \, A b^{4}\right)} c^{2} + 8 \, {\left(5 \, B b^{3} c^{3} + 704 \, A a c^{5} + 12 \, {\left(65 \, B a b + 31 \, A b^{2}\right)} c^{4}\right)} x^{2} - 2 \, {\left(25 \, B b^{4} c^{2} - 16 \, {\left(165 \, B a^{2} + 311 \, A a b\right)} c^{4} - 60 \, {\left(4 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{4}}, \frac{30720 \, A \sqrt{-a} a^{2} c^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 15 \, {\left(5 \, B b^{6} - 320 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3} + 80 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2} - 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(1280 \, B c^{6} x^{5} + 75 \, B b^{5} c + 11776 \, A a^{2} c^{4} + 128 \, {\left(25 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 240 \, {\left(11 \, B a^{2} b + 9 \, A a b^{2}\right)} c^{3} + 16 \, {\left(135 \, B b^{2} c^{4} + 4 \, {\left(65 \, B a + 63 \, A b\right)} c^{5}\right)} x^{3} - 20 \, {\left(40 \, B a b^{3} + 9 \, A b^{4}\right)} c^{2} + 8 \, {\left(5 \, B b^{3} c^{3} + 704 \, A a c^{5} + 12 \, {\left(65 \, B a b + 31 \, A b^{2}\right)} c^{4}\right)} x^{2} - 2 \, {\left(25 \, B b^{4} c^{2} - 16 \, {\left(165 \, B a^{2} + 311 \, A a b\right)} c^{4} - 60 \, {\left(4 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{4}}, \frac{15360 \, A \sqrt{-a} a^{2} c^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 15 \, {\left(5 \, B b^{6} - 320 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{3} + 80 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2} - 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(1280 \, B c^{6} x^{5} + 75 \, B b^{5} c + 11776 \, A a^{2} c^{4} + 128 \, {\left(25 \, B b c^{5} + 12 \, A c^{6}\right)} x^{4} + 240 \, {\left(11 \, B a^{2} b + 9 \, A a b^{2}\right)} c^{3} + 16 \, {\left(135 \, B b^{2} c^{4} + 4 \, {\left(65 \, B a + 63 \, A b\right)} c^{5}\right)} x^{3} - 20 \, {\left(40 \, B a b^{3} + 9 \, A b^{4}\right)} c^{2} + 8 \, {\left(5 \, B b^{3} c^{3} + 704 \, A a c^{5} + 12 \, {\left(65 \, B a b + 31 \, A b^{2}\right)} c^{4}\right)} x^{2} - 2 \, {\left(25 \, B b^{4} c^{2} - 16 \, {\left(165 \, B a^{2} + 311 \, A a b\right)} c^{4} - 60 \, {\left(4 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{4}}\right]"," ",0,"[1/30720*(15360*A*a^(5/2)*c^4*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 15*(5*B*b^6 - 320*(B*a^3 + 3*A*a^2*b)*c^3 + 80*(3*B*a^2*b^2 + 2*A*a*b^3)*c^2 - 12*(5*B*a*b^4 + A*b^5)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(1280*B*c^6*x^5 + 75*B*b^5*c + 11776*A*a^2*c^4 + 128*(25*B*b*c^5 + 12*A*c^6)*x^4 + 240*(11*B*a^2*b + 9*A*a*b^2)*c^3 + 16*(135*B*b^2*c^4 + 4*(65*B*a + 63*A*b)*c^5)*x^3 - 20*(40*B*a*b^3 + 9*A*b^4)*c^2 + 8*(5*B*b^3*c^3 + 704*A*a*c^5 + 12*(65*B*a*b + 31*A*b^2)*c^4)*x^2 - 2*(25*B*b^4*c^2 - 16*(165*B*a^2 + 311*A*a*b)*c^4 - 60*(4*B*a*b^2 + A*b^3)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/15360*(7680*A*a^(5/2)*c^4*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 15*(5*B*b^6 - 320*(B*a^3 + 3*A*a^2*b)*c^3 + 80*(3*B*a^2*b^2 + 2*A*a*b^3)*c^2 - 12*(5*B*a*b^4 + A*b^5)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(1280*B*c^6*x^5 + 75*B*b^5*c + 11776*A*a^2*c^4 + 128*(25*B*b*c^5 + 12*A*c^6)*x^4 + 240*(11*B*a^2*b + 9*A*a*b^2)*c^3 + 16*(135*B*b^2*c^4 + 4*(65*B*a + 63*A*b)*c^5)*x^3 - 20*(40*B*a*b^3 + 9*A*b^4)*c^2 + 8*(5*B*b^3*c^3 + 704*A*a*c^5 + 12*(65*B*a*b + 31*A*b^2)*c^4)*x^2 - 2*(25*B*b^4*c^2 - 16*(165*B*a^2 + 311*A*a*b)*c^4 - 60*(4*B*a*b^2 + A*b^3)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/30720*(30720*A*sqrt(-a)*a^2*c^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 15*(5*B*b^6 - 320*(B*a^3 + 3*A*a^2*b)*c^3 + 80*(3*B*a^2*b^2 + 2*A*a*b^3)*c^2 - 12*(5*B*a*b^4 + A*b^5)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(1280*B*c^6*x^5 + 75*B*b^5*c + 11776*A*a^2*c^4 + 128*(25*B*b*c^5 + 12*A*c^6)*x^4 + 240*(11*B*a^2*b + 9*A*a*b^2)*c^3 + 16*(135*B*b^2*c^4 + 4*(65*B*a + 63*A*b)*c^5)*x^3 - 20*(40*B*a*b^3 + 9*A*b^4)*c^2 + 8*(5*B*b^3*c^3 + 704*A*a*c^5 + 12*(65*B*a*b + 31*A*b^2)*c^4)*x^2 - 2*(25*B*b^4*c^2 - 16*(165*B*a^2 + 311*A*a*b)*c^4 - 60*(4*B*a*b^2 + A*b^3)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/15360*(15360*A*sqrt(-a)*a^2*c^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 15*(5*B*b^6 - 320*(B*a^3 + 3*A*a^2*b)*c^3 + 80*(3*B*a^2*b^2 + 2*A*a*b^3)*c^2 - 12*(5*B*a*b^4 + A*b^5)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(1280*B*c^6*x^5 + 75*B*b^5*c + 11776*A*a^2*c^4 + 128*(25*B*b*c^5 + 12*A*c^6)*x^4 + 240*(11*B*a^2*b + 9*A*a*b^2)*c^3 + 16*(135*B*b^2*c^4 + 4*(65*B*a + 63*A*b)*c^5)*x^3 - 20*(40*B*a*b^3 + 9*A*b^4)*c^2 + 8*(5*B*b^3*c^3 + 704*A*a*c^5 + 12*(65*B*a*b + 31*A*b^2)*c^4)*x^2 - 2*(25*B*b^4*c^2 - 16*(165*B*a^2 + 311*A*a*b)*c^4 - 60*(4*B*a*b^2 + A*b^3)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
941,1,1393,0,8.464666," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^2,x, algorithm=""fricas"")","\left[\frac{1920 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} \sqrt{a} c^{3} x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 15 \, {\left(3 \, B b^{5} + 480 \, A a^{2} c^{3} + 240 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 10 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{c} x \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(384 \, B c^{5} x^{5} - 1920 \, A a^{2} c^{3} + 48 \, {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} x^{4} + 8 \, {\left(93 \, B b^{2} c^{3} + 2 \, {\left(88 \, B a + 85 \, A b\right)} c^{4}\right)} x^{3} + 2 \, {\left(15 \, B b^{3} c^{2} + 1080 \, A a c^{4} + 2 \, {\left(622 \, B a b + 295 \, A b^{2}\right)} c^{3}\right)} x^{2} - {\left(45 \, B b^{4} c - 8 \, {\left(368 \, B a^{2} + 695 \, A a b\right)} c^{3} - 30 \, {\left(18 \, B a b^{2} + 5 \, A b^{3}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{3} x}, \frac{960 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} \sqrt{a} c^{3} x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 15 \, {\left(3 \, B b^{5} + 480 \, A a^{2} c^{3} + 240 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 10 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(384 \, B c^{5} x^{5} - 1920 \, A a^{2} c^{3} + 48 \, {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} x^{4} + 8 \, {\left(93 \, B b^{2} c^{3} + 2 \, {\left(88 \, B a + 85 \, A b\right)} c^{4}\right)} x^{3} + 2 \, {\left(15 \, B b^{3} c^{2} + 1080 \, A a c^{4} + 2 \, {\left(622 \, B a b + 295 \, A b^{2}\right)} c^{3}\right)} x^{2} - {\left(45 \, B b^{4} c - 8 \, {\left(368 \, B a^{2} + 695 \, A a b\right)} c^{3} - 30 \, {\left(18 \, B a b^{2} + 5 \, A b^{3}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, c^{3} x}, \frac{3840 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} \sqrt{-a} c^{3} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 15 \, {\left(3 \, B b^{5} + 480 \, A a^{2} c^{3} + 240 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 10 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{c} x \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(384 \, B c^{5} x^{5} - 1920 \, A a^{2} c^{3} + 48 \, {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} x^{4} + 8 \, {\left(93 \, B b^{2} c^{3} + 2 \, {\left(88 \, B a + 85 \, A b\right)} c^{4}\right)} x^{3} + 2 \, {\left(15 \, B b^{3} c^{2} + 1080 \, A a c^{4} + 2 \, {\left(622 \, B a b + 295 \, A b^{2}\right)} c^{3}\right)} x^{2} - {\left(45 \, B b^{4} c - 8 \, {\left(368 \, B a^{2} + 695 \, A a b\right)} c^{3} - 30 \, {\left(18 \, B a b^{2} + 5 \, A b^{3}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{3} x}, \frac{1920 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} \sqrt{-a} c^{3} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 15 \, {\left(3 \, B b^{5} + 480 \, A a^{2} c^{3} + 240 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 10 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(384 \, B c^{5} x^{5} - 1920 \, A a^{2} c^{3} + 48 \, {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} x^{4} + 8 \, {\left(93 \, B b^{2} c^{3} + 2 \, {\left(88 \, B a + 85 \, A b\right)} c^{4}\right)} x^{3} + 2 \, {\left(15 \, B b^{3} c^{2} + 1080 \, A a c^{4} + 2 \, {\left(622 \, B a b + 295 \, A b^{2}\right)} c^{3}\right)} x^{2} - {\left(45 \, B b^{4} c - 8 \, {\left(368 \, B a^{2} + 695 \, A a b\right)} c^{3} - 30 \, {\left(18 \, B a b^{2} + 5 \, A b^{3}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, c^{3} x}\right]"," ",0,"[1/7680*(1920*(2*B*a^2 + 5*A*a*b)*sqrt(a)*c^3*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 15*(3*B*b^5 + 480*A*a^2*c^3 + 240*(B*a^2*b + A*a*b^2)*c^2 - 10*(4*B*a*b^3 + A*b^4)*c)*sqrt(c)*x*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(384*B*c^5*x^5 - 1920*A*a^2*c^3 + 48*(21*B*b*c^4 + 10*A*c^5)*x^4 + 8*(93*B*b^2*c^3 + 2*(88*B*a + 85*A*b)*c^4)*x^3 + 2*(15*B*b^3*c^2 + 1080*A*a*c^4 + 2*(622*B*a*b + 295*A*b^2)*c^3)*x^2 - (45*B*b^4*c - 8*(368*B*a^2 + 695*A*a*b)*c^3 - 30*(18*B*a*b^2 + 5*A*b^3)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^3*x), 1/3840*(960*(2*B*a^2 + 5*A*a*b)*sqrt(a)*c^3*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 15*(3*B*b^5 + 480*A*a^2*c^3 + 240*(B*a^2*b + A*a*b^2)*c^2 - 10*(4*B*a*b^3 + A*b^4)*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(384*B*c^5*x^5 - 1920*A*a^2*c^3 + 48*(21*B*b*c^4 + 10*A*c^5)*x^4 + 8*(93*B*b^2*c^3 + 2*(88*B*a + 85*A*b)*c^4)*x^3 + 2*(15*B*b^3*c^2 + 1080*A*a*c^4 + 2*(622*B*a*b + 295*A*b^2)*c^3)*x^2 - (45*B*b^4*c - 8*(368*B*a^2 + 695*A*a*b)*c^3 - 30*(18*B*a*b^2 + 5*A*b^3)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^3*x), 1/7680*(3840*(2*B*a^2 + 5*A*a*b)*sqrt(-a)*c^3*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 15*(3*B*b^5 + 480*A*a^2*c^3 + 240*(B*a^2*b + A*a*b^2)*c^2 - 10*(4*B*a*b^3 + A*b^4)*c)*sqrt(c)*x*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(384*B*c^5*x^5 - 1920*A*a^2*c^3 + 48*(21*B*b*c^4 + 10*A*c^5)*x^4 + 8*(93*B*b^2*c^3 + 2*(88*B*a + 85*A*b)*c^4)*x^3 + 2*(15*B*b^3*c^2 + 1080*A*a*c^4 + 2*(622*B*a*b + 295*A*b^2)*c^3)*x^2 - (45*B*b^4*c - 8*(368*B*a^2 + 695*A*a*b)*c^3 - 30*(18*B*a*b^2 + 5*A*b^3)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^3*x), 1/3840*(1920*(2*B*a^2 + 5*A*a*b)*sqrt(-a)*c^3*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 15*(3*B*b^5 + 480*A*a^2*c^3 + 240*(B*a^2*b + A*a*b^2)*c^2 - 10*(4*B*a*b^3 + A*b^4)*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(384*B*c^5*x^5 - 1920*A*a^2*c^3 + 48*(21*B*b*c^4 + 10*A*c^5)*x^4 + 8*(93*B*b^2*c^3 + 2*(88*B*a + 85*A*b)*c^4)*x^3 + 2*(15*B*b^3*c^2 + 1080*A*a*c^4 + 2*(622*B*a*b + 295*A*b^2)*c^3)*x^2 - (45*B*b^4*c - 8*(368*B*a^2 + 695*A*a*b)*c^3 - 30*(18*B*a*b^2 + 5*A*b^3)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^3*x)]","A",0
942,1,1269,0,5.677041," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B b^{4} - 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 240 \, {\left(4 \, A a c^{3} + {\left(4 \, B a b + 3 \, A b^{2}\right)} c^{2}\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(48 \, B c^{4} x^{5} - 96 \, A a^{2} c^{2} + 8 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} x^{4} - 48 \, {\left(4 \, B a^{2} + 9 \, A a b\right)} c^{2} x + 2 \, {\left(59 \, B b^{2} c^{2} + 4 \, {\left(27 \, B a + 26 \, A b\right)} c^{3}\right)} x^{3} + {\left(15 \, B b^{3} c + 448 \, A a c^{3} + 4 \, {\left(139 \, B a b + 66 \, A b^{2}\right)} c^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{2} x^{2}}, \frac{15 \, {\left(B b^{4} - 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 120 \, {\left(4 \, A a c^{3} + {\left(4 \, B a b + 3 \, A b^{2}\right)} c^{2}\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 2 \, {\left(48 \, B c^{4} x^{5} - 96 \, A a^{2} c^{2} + 8 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} x^{4} - 48 \, {\left(4 \, B a^{2} + 9 \, A a b\right)} c^{2} x + 2 \, {\left(59 \, B b^{2} c^{2} + 4 \, {\left(27 \, B a + 26 \, A b\right)} c^{3}\right)} x^{3} + {\left(15 \, B b^{3} c + 448 \, A a c^{3} + 4 \, {\left(139 \, B a b + 66 \, A b^{2}\right)} c^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{2} x^{2}}, \frac{480 \, {\left(4 \, A a c^{3} + {\left(4 \, B a b + 3 \, A b^{2}\right)} c^{2}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 15 \, {\left(B b^{4} - 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, B c^{4} x^{5} - 96 \, A a^{2} c^{2} + 8 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} x^{4} - 48 \, {\left(4 \, B a^{2} + 9 \, A a b\right)} c^{2} x + 2 \, {\left(59 \, B b^{2} c^{2} + 4 \, {\left(27 \, B a + 26 \, A b\right)} c^{3}\right)} x^{3} + {\left(15 \, B b^{3} c + 448 \, A a c^{3} + 4 \, {\left(139 \, B a b + 66 \, A b^{2}\right)} c^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{2} x^{2}}, \frac{240 \, {\left(4 \, A a c^{3} + {\left(4 \, B a b + 3 \, A b^{2}\right)} c^{2}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 15 \, {\left(B b^{4} - 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(48 \, B c^{4} x^{5} - 96 \, A a^{2} c^{2} + 8 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} x^{4} - 48 \, {\left(4 \, B a^{2} + 9 \, A a b\right)} c^{2} x + 2 \, {\left(59 \, B b^{2} c^{2} + 4 \, {\left(27 \, B a + 26 \, A b\right)} c^{3}\right)} x^{3} + {\left(15 \, B b^{3} c + 448 \, A a c^{3} + 4 \, {\left(139 \, B a b + 66 \, A b^{2}\right)} c^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{2} x^{2}}\right]"," ",0,"[-1/768*(15*(B*b^4 - 48*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(c)*x^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 240*(4*A*a*c^3 + (4*B*a*b + 3*A*b^2)*c^2)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(48*B*c^4*x^5 - 96*A*a^2*c^2 + 8*(17*B*b*c^3 + 8*A*c^4)*x^4 - 48*(4*B*a^2 + 9*A*a*b)*c^2*x + 2*(59*B*b^2*c^2 + 4*(27*B*a + 26*A*b)*c^3)*x^3 + (15*B*b^3*c + 448*A*a*c^3 + 4*(139*B*a*b + 66*A*b^2)*c^2)*x^2)*sqrt(c*x^2 + b*x + a))/(c^2*x^2), 1/384*(15*(B*b^4 - 48*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 120*(4*A*a*c^3 + (4*B*a*b + 3*A*b^2)*c^2)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 2*(48*B*c^4*x^5 - 96*A*a^2*c^2 + 8*(17*B*b*c^3 + 8*A*c^4)*x^4 - 48*(4*B*a^2 + 9*A*a*b)*c^2*x + 2*(59*B*b^2*c^2 + 4*(27*B*a + 26*A*b)*c^3)*x^3 + (15*B*b^3*c + 448*A*a*c^3 + 4*(139*B*a*b + 66*A*b^2)*c^2)*x^2)*sqrt(c*x^2 + b*x + a))/(c^2*x^2), 1/768*(480*(4*A*a*c^3 + (4*B*a*b + 3*A*b^2)*c^2)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 15*(B*b^4 - 48*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(c)*x^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(48*B*c^4*x^5 - 96*A*a^2*c^2 + 8*(17*B*b*c^3 + 8*A*c^4)*x^4 - 48*(4*B*a^2 + 9*A*a*b)*c^2*x + 2*(59*B*b^2*c^2 + 4*(27*B*a + 26*A*b)*c^3)*x^3 + (15*B*b^3*c + 448*A*a*c^3 + 4*(139*B*a*b + 66*A*b^2)*c^2)*x^2)*sqrt(c*x^2 + b*x + a))/(c^2*x^2), 1/384*(240*(4*A*a*c^3 + (4*B*a*b + 3*A*b^2)*c^2)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 15*(B*b^4 - 48*(B*a^2 + 2*A*a*b)*c^2 - 8*(3*B*a*b^2 + A*b^3)*c)*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(48*B*c^4*x^5 - 96*A*a^2*c^2 + 8*(17*B*b*c^3 + 8*A*c^4)*x^4 - 48*(4*B*a^2 + 9*A*a*b)*c^2*x + 2*(59*B*b^2*c^2 + 4*(27*B*a + 26*A*b)*c^3)*x^3 + (15*B*b^3*c + 448*A*a*c^3 + 4*(139*B*a*b + 66*A*b^2)*c^2)*x^2)*sqrt(c*x^2 + b*x + a))/(c^2*x^2)]","A",0
943,1,1293,0,3.270834," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B a b^{3} + 8 \, A a^{2} c^{2} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c\right)} \sqrt{c} x^{3} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 15 \, {\left(4 \, {\left(2 \, B a^{2} + 3 \, A a b\right)} c^{2} + {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(8 \, B a c^{3} x^{5} - 8 \, A a^{3} c + 2 \, {\left(13 \, B a b c^{2} + 6 \, A a c^{3}\right)} x^{4} + {\left(33 \, B a b^{2} c + 2 \, {\left(28 \, B a^{2} + 27 \, A a b\right)} c^{2}\right)} x^{3} - 2 \, {\left(6 \, B a^{3} + 13 \, A a^{2} b\right)} c x - {\left(56 \, A a^{2} c^{2} + 3 \, {\left(18 \, B a^{2} b + 11 \, A a b^{2}\right)} c\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{96 \, a c x^{3}}, -\frac{30 \, {\left(B a b^{3} + 8 \, A a^{2} c^{2} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 15 \, {\left(4 \, {\left(2 \, B a^{2} + 3 \, A a b\right)} c^{2} + {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(8 \, B a c^{3} x^{5} - 8 \, A a^{3} c + 2 \, {\left(13 \, B a b c^{2} + 6 \, A a c^{3}\right)} x^{4} + {\left(33 \, B a b^{2} c + 2 \, {\left(28 \, B a^{2} + 27 \, A a b\right)} c^{2}\right)} x^{3} - 2 \, {\left(6 \, B a^{3} + 13 \, A a^{2} b\right)} c x - {\left(56 \, A a^{2} c^{2} + 3 \, {\left(18 \, B a^{2} b + 11 \, A a b^{2}\right)} c\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{96 \, a c x^{3}}, \frac{30 \, {\left(4 \, {\left(2 \, B a^{2} + 3 \, A a b\right)} c^{2} + {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 15 \, {\left(B a b^{3} + 8 \, A a^{2} c^{2} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c\right)} \sqrt{c} x^{3} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, B a c^{3} x^{5} - 8 \, A a^{3} c + 2 \, {\left(13 \, B a b c^{2} + 6 \, A a c^{3}\right)} x^{4} + {\left(33 \, B a b^{2} c + 2 \, {\left(28 \, B a^{2} + 27 \, A a b\right)} c^{2}\right)} x^{3} - 2 \, {\left(6 \, B a^{3} + 13 \, A a^{2} b\right)} c x - {\left(56 \, A a^{2} c^{2} + 3 \, {\left(18 \, B a^{2} b + 11 \, A a b^{2}\right)} c\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{96 \, a c x^{3}}, \frac{15 \, {\left(4 \, {\left(2 \, B a^{2} + 3 \, A a b\right)} c^{2} + {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 15 \, {\left(B a b^{3} + 8 \, A a^{2} c^{2} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(8 \, B a c^{3} x^{5} - 8 \, A a^{3} c + 2 \, {\left(13 \, B a b c^{2} + 6 \, A a c^{3}\right)} x^{4} + {\left(33 \, B a b^{2} c + 2 \, {\left(28 \, B a^{2} + 27 \, A a b\right)} c^{2}\right)} x^{3} - 2 \, {\left(6 \, B a^{3} + 13 \, A a^{2} b\right)} c x - {\left(56 \, A a^{2} c^{2} + 3 \, {\left(18 \, B a^{2} b + 11 \, A a b^{2}\right)} c\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{48 \, a c x^{3}}\right]"," ",0,"[1/96*(15*(B*a*b^3 + 8*A*a^2*c^2 + 6*(2*B*a^2*b + A*a*b^2)*c)*sqrt(c)*x^3*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 15*(4*(2*B*a^2 + 3*A*a*b)*c^2 + (6*B*a*b^2 + A*b^3)*c)*sqrt(a)*x^3*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(8*B*a*c^3*x^5 - 8*A*a^3*c + 2*(13*B*a*b*c^2 + 6*A*a*c^3)*x^4 + (33*B*a*b^2*c + 2*(28*B*a^2 + 27*A*a*b)*c^2)*x^3 - 2*(6*B*a^3 + 13*A*a^2*b)*c*x - (56*A*a^2*c^2 + 3*(18*B*a^2*b + 11*A*a*b^2)*c)*x^2)*sqrt(c*x^2 + b*x + a))/(a*c*x^3), -1/96*(30*(B*a*b^3 + 8*A*a^2*c^2 + 6*(2*B*a^2*b + A*a*b^2)*c)*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 15*(4*(2*B*a^2 + 3*A*a*b)*c^2 + (6*B*a*b^2 + A*b^3)*c)*sqrt(a)*x^3*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(8*B*a*c^3*x^5 - 8*A*a^3*c + 2*(13*B*a*b*c^2 + 6*A*a*c^3)*x^4 + (33*B*a*b^2*c + 2*(28*B*a^2 + 27*A*a*b)*c^2)*x^3 - 2*(6*B*a^3 + 13*A*a^2*b)*c*x - (56*A*a^2*c^2 + 3*(18*B*a^2*b + 11*A*a*b^2)*c)*x^2)*sqrt(c*x^2 + b*x + a))/(a*c*x^3), 1/96*(30*(4*(2*B*a^2 + 3*A*a*b)*c^2 + (6*B*a*b^2 + A*b^3)*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 15*(B*a*b^3 + 8*A*a^2*c^2 + 6*(2*B*a^2*b + A*a*b^2)*c)*sqrt(c)*x^3*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*B*a*c^3*x^5 - 8*A*a^3*c + 2*(13*B*a*b*c^2 + 6*A*a*c^3)*x^4 + (33*B*a*b^2*c + 2*(28*B*a^2 + 27*A*a*b)*c^2)*x^3 - 2*(6*B*a^3 + 13*A*a^2*b)*c*x - (56*A*a^2*c^2 + 3*(18*B*a^2*b + 11*A*a*b^2)*c)*x^2)*sqrt(c*x^2 + b*x + a))/(a*c*x^3), 1/48*(15*(4*(2*B*a^2 + 3*A*a*b)*c^2 + (6*B*a*b^2 + A*b^3)*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 15*(B*a*b^3 + 8*A*a^2*c^2 + 6*(2*B*a^2*b + A*a*b^2)*c)*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(8*B*a*c^3*x^5 - 8*A*a^3*c + 2*(13*B*a*b*c^2 + 6*A*a*c^3)*x^4 + (33*B*a*b^2*c + 2*(28*B*a^2 + 27*A*a*b)*c^2)*x^3 - 2*(6*B*a^3 + 13*A*a^2*b)*c*x - (56*A*a^2*c^2 + 3*(18*B*a^2*b + 11*A*a*b^2)*c)*x^2)*sqrt(c*x^2 + b*x + a))/(a*c*x^3)]","A",0
944,1,1305,0,4.508454," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^5,x, algorithm=""fricas"")","\left[\frac{240 \, {\left(3 \, B a^{2} b^{2} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c\right)} \sqrt{c} x^{4} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 15 \, {\left(8 \, B a b^{3} - A b^{4} + 48 \, A a^{2} c^{2} + 24 \, {\left(4 \, B a^{2} b + A a b^{2}\right)} c\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(96 \, B a^{2} c^{2} x^{5} - 48 \, A a^{4} + 48 \, {\left(9 \, B a^{2} b c + 4 \, A a^{2} c^{2}\right)} x^{4} - {\left(264 \, B a^{2} b^{2} + 15 \, A a b^{3} + 4 \, {\left(112 \, B a^{3} + 139 \, A a^{2} b\right)} c\right)} x^{3} - 2 \, {\left(104 \, B a^{3} b + 59 \, A a^{2} b^{2} + 108 \, A a^{3} c\right)} x^{2} - 8 \, {\left(8 \, B a^{4} + 17 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, a^{2} x^{4}}, -\frac{480 \, {\left(3 \, B a^{2} b^{2} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 15 \, {\left(8 \, B a b^{3} - A b^{4} + 48 \, A a^{2} c^{2} + 24 \, {\left(4 \, B a^{2} b + A a b^{2}\right)} c\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(96 \, B a^{2} c^{2} x^{5} - 48 \, A a^{4} + 48 \, {\left(9 \, B a^{2} b c + 4 \, A a^{2} c^{2}\right)} x^{4} - {\left(264 \, B a^{2} b^{2} + 15 \, A a b^{3} + 4 \, {\left(112 \, B a^{3} + 139 \, A a^{2} b\right)} c\right)} x^{3} - 2 \, {\left(104 \, B a^{3} b + 59 \, A a^{2} b^{2} + 108 \, A a^{3} c\right)} x^{2} - 8 \, {\left(8 \, B a^{4} + 17 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, a^{2} x^{4}}, \frac{15 \, {\left(8 \, B a b^{3} - A b^{4} + 48 \, A a^{2} c^{2} + 24 \, {\left(4 \, B a^{2} b + A a b^{2}\right)} c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 120 \, {\left(3 \, B a^{2} b^{2} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c\right)} \sqrt{c} x^{4} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, {\left(96 \, B a^{2} c^{2} x^{5} - 48 \, A a^{4} + 48 \, {\left(9 \, B a^{2} b c + 4 \, A a^{2} c^{2}\right)} x^{4} - {\left(264 \, B a^{2} b^{2} + 15 \, A a b^{3} + 4 \, {\left(112 \, B a^{3} + 139 \, A a^{2} b\right)} c\right)} x^{3} - 2 \, {\left(104 \, B a^{3} b + 59 \, A a^{2} b^{2} + 108 \, A a^{3} c\right)} x^{2} - 8 \, {\left(8 \, B a^{4} + 17 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, a^{2} x^{4}}, \frac{15 \, {\left(8 \, B a b^{3} - A b^{4} + 48 \, A a^{2} c^{2} + 24 \, {\left(4 \, B a^{2} b + A a b^{2}\right)} c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 240 \, {\left(3 \, B a^{2} b^{2} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(96 \, B a^{2} c^{2} x^{5} - 48 \, A a^{4} + 48 \, {\left(9 \, B a^{2} b c + 4 \, A a^{2} c^{2}\right)} x^{4} - {\left(264 \, B a^{2} b^{2} + 15 \, A a b^{3} + 4 \, {\left(112 \, B a^{3} + 139 \, A a^{2} b\right)} c\right)} x^{3} - 2 \, {\left(104 \, B a^{3} b + 59 \, A a^{2} b^{2} + 108 \, A a^{3} c\right)} x^{2} - 8 \, {\left(8 \, B a^{4} + 17 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, a^{2} x^{4}}\right]"," ",0,"[1/768*(240*(3*B*a^2*b^2 + 4*(B*a^3 + A*a^2*b)*c)*sqrt(c)*x^4*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 15*(8*B*a*b^3 - A*b^4 + 48*A*a^2*c^2 + 24*(4*B*a^2*b + A*a*b^2)*c)*sqrt(a)*x^4*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(96*B*a^2*c^2*x^5 - 48*A*a^4 + 48*(9*B*a^2*b*c + 4*A*a^2*c^2)*x^4 - (264*B*a^2*b^2 + 15*A*a*b^3 + 4*(112*B*a^3 + 139*A*a^2*b)*c)*x^3 - 2*(104*B*a^3*b + 59*A*a^2*b^2 + 108*A*a^3*c)*x^2 - 8*(8*B*a^4 + 17*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^4), -1/768*(480*(3*B*a^2*b^2 + 4*(B*a^3 + A*a^2*b)*c)*sqrt(-c)*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 15*(8*B*a*b^3 - A*b^4 + 48*A*a^2*c^2 + 24*(4*B*a^2*b + A*a*b^2)*c)*sqrt(a)*x^4*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(96*B*a^2*c^2*x^5 - 48*A*a^4 + 48*(9*B*a^2*b*c + 4*A*a^2*c^2)*x^4 - (264*B*a^2*b^2 + 15*A*a*b^3 + 4*(112*B*a^3 + 139*A*a^2*b)*c)*x^3 - 2*(104*B*a^3*b + 59*A*a^2*b^2 + 108*A*a^3*c)*x^2 - 8*(8*B*a^4 + 17*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^4), 1/384*(15*(8*B*a*b^3 - A*b^4 + 48*A*a^2*c^2 + 24*(4*B*a^2*b + A*a*b^2)*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 120*(3*B*a^2*b^2 + 4*(B*a^3 + A*a^2*b)*c)*sqrt(c)*x^4*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 2*(96*B*a^2*c^2*x^5 - 48*A*a^4 + 48*(9*B*a^2*b*c + 4*A*a^2*c^2)*x^4 - (264*B*a^2*b^2 + 15*A*a*b^3 + 4*(112*B*a^3 + 139*A*a^2*b)*c)*x^3 - 2*(104*B*a^3*b + 59*A*a^2*b^2 + 108*A*a^3*c)*x^2 - 8*(8*B*a^4 + 17*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^4), 1/384*(15*(8*B*a*b^3 - A*b^4 + 48*A*a^2*c^2 + 24*(4*B*a^2*b + A*a*b^2)*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 240*(3*B*a^2*b^2 + 4*(B*a^3 + A*a^2*b)*c)*sqrt(-c)*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(96*B*a^2*c^2*x^5 - 48*A*a^4 + 48*(9*B*a^2*b*c + 4*A*a^2*c^2)*x^4 - (264*B*a^2*b^2 + 15*A*a*b^3 + 4*(112*B*a^3 + 139*A*a^2*b)*c)*x^3 - 2*(104*B*a^3*b + 59*A*a^2*b^2 + 108*A*a^3*c)*x^2 - 8*(8*B*a^4 + 17*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^2*x^4)]","A",0
945,1,1445,0,6.848028," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^6,x, algorithm=""fricas"")","\left[\frac{1920 \, {\left(5 \, B a^{3} b c + 2 \, A a^{3} c^{2}\right)} \sqrt{c} x^{5} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 15 \, {\left(10 \, B a b^{4} - 3 \, A b^{5} - 240 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} - 40 \, {\left(6 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{a} x^{5} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(1920 \, B a^{3} c^{2} x^{5} - 384 \, A a^{5} - {\left(150 \, B a^{2} b^{3} - 45 \, A a b^{4} + 2944 \, A a^{3} c^{2} + 20 \, {\left(278 \, B a^{3} b + 27 \, A a^{2} b^{2}\right)} c\right)} x^{4} - 2 \, {\left(590 \, B a^{3} b^{2} + 15 \, A a^{2} b^{3} + 4 \, {\left(270 \, B a^{4} + 311 \, A a^{3} b\right)} c\right)} x^{3} - 8 \, {\left(170 \, B a^{4} b + 93 \, A a^{3} b^{2} + 176 \, A a^{4} c\right)} x^{2} - 48 \, {\left(10 \, B a^{5} + 21 \, A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, a^{3} x^{5}}, -\frac{3840 \, {\left(5 \, B a^{3} b c + 2 \, A a^{3} c^{2}\right)} \sqrt{-c} x^{5} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 15 \, {\left(10 \, B a b^{4} - 3 \, A b^{5} - 240 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} - 40 \, {\left(6 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{a} x^{5} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(1920 \, B a^{3} c^{2} x^{5} - 384 \, A a^{5} - {\left(150 \, B a^{2} b^{3} - 45 \, A a b^{4} + 2944 \, A a^{3} c^{2} + 20 \, {\left(278 \, B a^{3} b + 27 \, A a^{2} b^{2}\right)} c\right)} x^{4} - 2 \, {\left(590 \, B a^{3} b^{2} + 15 \, A a^{2} b^{3} + 4 \, {\left(270 \, B a^{4} + 311 \, A a^{3} b\right)} c\right)} x^{3} - 8 \, {\left(170 \, B a^{4} b + 93 \, A a^{3} b^{2} + 176 \, A a^{4} c\right)} x^{2} - 48 \, {\left(10 \, B a^{5} + 21 \, A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, a^{3} x^{5}}, -\frac{15 \, {\left(10 \, B a b^{4} - 3 \, A b^{5} - 240 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} - 40 \, {\left(6 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 960 \, {\left(5 \, B a^{3} b c + 2 \, A a^{3} c^{2}\right)} \sqrt{c} x^{5} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 2 \, {\left(1920 \, B a^{3} c^{2} x^{5} - 384 \, A a^{5} - {\left(150 \, B a^{2} b^{3} - 45 \, A a b^{4} + 2944 \, A a^{3} c^{2} + 20 \, {\left(278 \, B a^{3} b + 27 \, A a^{2} b^{2}\right)} c\right)} x^{4} - 2 \, {\left(590 \, B a^{3} b^{2} + 15 \, A a^{2} b^{3} + 4 \, {\left(270 \, B a^{4} + 311 \, A a^{3} b\right)} c\right)} x^{3} - 8 \, {\left(170 \, B a^{4} b + 93 \, A a^{3} b^{2} + 176 \, A a^{4} c\right)} x^{2} - 48 \, {\left(10 \, B a^{5} + 21 \, A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, a^{3} x^{5}}, -\frac{15 \, {\left(10 \, B a b^{4} - 3 \, A b^{5} - 240 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} - 40 \, {\left(6 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 1920 \, {\left(5 \, B a^{3} b c + 2 \, A a^{3} c^{2}\right)} \sqrt{-c} x^{5} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(1920 \, B a^{3} c^{2} x^{5} - 384 \, A a^{5} - {\left(150 \, B a^{2} b^{3} - 45 \, A a b^{4} + 2944 \, A a^{3} c^{2} + 20 \, {\left(278 \, B a^{3} b + 27 \, A a^{2} b^{2}\right)} c\right)} x^{4} - 2 \, {\left(590 \, B a^{3} b^{2} + 15 \, A a^{2} b^{3} + 4 \, {\left(270 \, B a^{4} + 311 \, A a^{3} b\right)} c\right)} x^{3} - 8 \, {\left(170 \, B a^{4} b + 93 \, A a^{3} b^{2} + 176 \, A a^{4} c\right)} x^{2} - 48 \, {\left(10 \, B a^{5} + 21 \, A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, a^{3} x^{5}}\right]"," ",0,"[1/7680*(1920*(5*B*a^3*b*c + 2*A*a^3*c^2)*sqrt(c)*x^5*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 15*(10*B*a*b^4 - 3*A*b^5 - 240*(2*B*a^3 + A*a^2*b)*c^2 - 40*(6*B*a^2*b^2 - A*a*b^3)*c)*sqrt(a)*x^5*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(1920*B*a^3*c^2*x^5 - 384*A*a^5 - (150*B*a^2*b^3 - 45*A*a*b^4 + 2944*A*a^3*c^2 + 20*(278*B*a^3*b + 27*A*a^2*b^2)*c)*x^4 - 2*(590*B*a^3*b^2 + 15*A*a^2*b^3 + 4*(270*B*a^4 + 311*A*a^3*b)*c)*x^3 - 8*(170*B*a^4*b + 93*A*a^3*b^2 + 176*A*a^4*c)*x^2 - 48*(10*B*a^5 + 21*A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^5), -1/7680*(3840*(5*B*a^3*b*c + 2*A*a^3*c^2)*sqrt(-c)*x^5*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 15*(10*B*a*b^4 - 3*A*b^5 - 240*(2*B*a^3 + A*a^2*b)*c^2 - 40*(6*B*a^2*b^2 - A*a*b^3)*c)*sqrt(a)*x^5*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(1920*B*a^3*c^2*x^5 - 384*A*a^5 - (150*B*a^2*b^3 - 45*A*a*b^4 + 2944*A*a^3*c^2 + 20*(278*B*a^3*b + 27*A*a^2*b^2)*c)*x^4 - 2*(590*B*a^3*b^2 + 15*A*a^2*b^3 + 4*(270*B*a^4 + 311*A*a^3*b)*c)*x^3 - 8*(170*B*a^4*b + 93*A*a^3*b^2 + 176*A*a^4*c)*x^2 - 48*(10*B*a^5 + 21*A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^5), -1/3840*(15*(10*B*a*b^4 - 3*A*b^5 - 240*(2*B*a^3 + A*a^2*b)*c^2 - 40*(6*B*a^2*b^2 - A*a*b^3)*c)*sqrt(-a)*x^5*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 960*(5*B*a^3*b*c + 2*A*a^3*c^2)*sqrt(c)*x^5*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 2*(1920*B*a^3*c^2*x^5 - 384*A*a^5 - (150*B*a^2*b^3 - 45*A*a*b^4 + 2944*A*a^3*c^2 + 20*(278*B*a^3*b + 27*A*a^2*b^2)*c)*x^4 - 2*(590*B*a^3*b^2 + 15*A*a^2*b^3 + 4*(270*B*a^4 + 311*A*a^3*b)*c)*x^3 - 8*(170*B*a^4*b + 93*A*a^3*b^2 + 176*A*a^4*c)*x^2 - 48*(10*B*a^5 + 21*A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^5), -1/3840*(15*(10*B*a*b^4 - 3*A*b^5 - 240*(2*B*a^3 + A*a^2*b)*c^2 - 40*(6*B*a^2*b^2 - A*a*b^3)*c)*sqrt(-a)*x^5*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 1920*(5*B*a^3*b*c + 2*A*a^3*c^2)*sqrt(-c)*x^5*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(1920*B*a^3*c^2*x^5 - 384*A*a^5 - (150*B*a^2*b^3 - 45*A*a*b^4 + 2944*A*a^3*c^2 + 20*(278*B*a^3*b + 27*A*a^2*b^2)*c)*x^4 - 2*(590*B*a^3*b^2 + 15*A*a^2*b^3 + 4*(270*B*a^4 + 311*A*a^3*b)*c)*x^3 - 8*(170*B*a^4*b + 93*A*a^3*b^2 + 176*A*a^4*c)*x^2 - 48*(10*B*a^5 + 21*A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^5)]","A",0
946,1,1659,0,8.717601," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^7,x, algorithm=""fricas"")","\left[\frac{15360 \, B a^{4} c^{\frac{5}{2}} x^{6} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 15 \, {\left(12 \, B a b^{5} - 5 \, A b^{6} + 320 \, A a^{3} c^{3} + 240 \, {\left(4 \, B a^{3} b - A a^{2} b^{2}\right)} c^{2} - 20 \, {\left(8 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} c\right)} \sqrt{a} x^{6} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(1280 \, A a^{6} - {\left(180 \, B a^{2} b^{4} - 75 \, A a b^{5} - 16 \, {\left(736 \, B a^{4} + 165 \, A a^{3} b\right)} c^{2} - 80 \, {\left(27 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} c\right)} x^{5} + 2 \, {\left(60 \, B a^{3} b^{3} - 25 \, A a^{2} b^{4} + 2640 \, A a^{4} c^{2} + 16 \, {\left(311 \, B a^{4} b + 15 \, A a^{3} b^{2}\right)} c\right)} x^{4} + 8 \, {\left(372 \, B a^{4} b^{2} + 5 \, A a^{3} b^{3} + 4 \, {\left(176 \, B a^{5} + 195 \, A a^{4} b\right)} c\right)} x^{3} + 16 \, {\left(252 \, B a^{5} b + 135 \, A a^{4} b^{2} + 260 \, A a^{5} c\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 25 \, A a^{5} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, a^{4} x^{6}}, -\frac{30720 \, B a^{4} \sqrt{-c} c^{2} x^{6} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 15 \, {\left(12 \, B a b^{5} - 5 \, A b^{6} + 320 \, A a^{3} c^{3} + 240 \, {\left(4 \, B a^{3} b - A a^{2} b^{2}\right)} c^{2} - 20 \, {\left(8 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} c\right)} \sqrt{a} x^{6} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(1280 \, A a^{6} - {\left(180 \, B a^{2} b^{4} - 75 \, A a b^{5} - 16 \, {\left(736 \, B a^{4} + 165 \, A a^{3} b\right)} c^{2} - 80 \, {\left(27 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} c\right)} x^{5} + 2 \, {\left(60 \, B a^{3} b^{3} - 25 \, A a^{2} b^{4} + 2640 \, A a^{4} c^{2} + 16 \, {\left(311 \, B a^{4} b + 15 \, A a^{3} b^{2}\right)} c\right)} x^{4} + 8 \, {\left(372 \, B a^{4} b^{2} + 5 \, A a^{3} b^{3} + 4 \, {\left(176 \, B a^{5} + 195 \, A a^{4} b\right)} c\right)} x^{3} + 16 \, {\left(252 \, B a^{5} b + 135 \, A a^{4} b^{2} + 260 \, A a^{5} c\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 25 \, A a^{5} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, a^{4} x^{6}}, \frac{7680 \, B a^{4} c^{\frac{5}{2}} x^{6} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 15 \, {\left(12 \, B a b^{5} - 5 \, A b^{6} + 320 \, A a^{3} c^{3} + 240 \, {\left(4 \, B a^{3} b - A a^{2} b^{2}\right)} c^{2} - 20 \, {\left(8 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} c\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(1280 \, A a^{6} - {\left(180 \, B a^{2} b^{4} - 75 \, A a b^{5} - 16 \, {\left(736 \, B a^{4} + 165 \, A a^{3} b\right)} c^{2} - 80 \, {\left(27 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} c\right)} x^{5} + 2 \, {\left(60 \, B a^{3} b^{3} - 25 \, A a^{2} b^{4} + 2640 \, A a^{4} c^{2} + 16 \, {\left(311 \, B a^{4} b + 15 \, A a^{3} b^{2}\right)} c\right)} x^{4} + 8 \, {\left(372 \, B a^{4} b^{2} + 5 \, A a^{3} b^{3} + 4 \, {\left(176 \, B a^{5} + 195 \, A a^{4} b\right)} c\right)} x^{3} + 16 \, {\left(252 \, B a^{5} b + 135 \, A a^{4} b^{2} + 260 \, A a^{5} c\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 25 \, A a^{5} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, a^{4} x^{6}}, -\frac{15360 \, B a^{4} \sqrt{-c} c^{2} x^{6} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 15 \, {\left(12 \, B a b^{5} - 5 \, A b^{6} + 320 \, A a^{3} c^{3} + 240 \, {\left(4 \, B a^{3} b - A a^{2} b^{2}\right)} c^{2} - 20 \, {\left(8 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} c\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(1280 \, A a^{6} - {\left(180 \, B a^{2} b^{4} - 75 \, A a b^{5} - 16 \, {\left(736 \, B a^{4} + 165 \, A a^{3} b\right)} c^{2} - 80 \, {\left(27 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} c\right)} x^{5} + 2 \, {\left(60 \, B a^{3} b^{3} - 25 \, A a^{2} b^{4} + 2640 \, A a^{4} c^{2} + 16 \, {\left(311 \, B a^{4} b + 15 \, A a^{3} b^{2}\right)} c\right)} x^{4} + 8 \, {\left(372 \, B a^{4} b^{2} + 5 \, A a^{3} b^{3} + 4 \, {\left(176 \, B a^{5} + 195 \, A a^{4} b\right)} c\right)} x^{3} + 16 \, {\left(252 \, B a^{5} b + 135 \, A a^{4} b^{2} + 260 \, A a^{5} c\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 25 \, A a^{5} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, a^{4} x^{6}}\right]"," ",0,"[1/30720*(15360*B*a^4*c^(5/2)*x^6*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 15*(12*B*a*b^5 - 5*A*b^6 + 320*A*a^3*c^3 + 240*(4*B*a^3*b - A*a^2*b^2)*c^2 - 20*(8*B*a^2*b^3 - 3*A*a*b^4)*c)*sqrt(a)*x^6*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(1280*A*a^6 - (180*B*a^2*b^4 - 75*A*a*b^5 - 16*(736*B*a^4 + 165*A*a^3*b)*c^2 - 80*(27*B*a^3*b^2 - 10*A*a^2*b^3)*c)*x^5 + 2*(60*B*a^3*b^3 - 25*A*a^2*b^4 + 2640*A*a^4*c^2 + 16*(311*B*a^4*b + 15*A*a^3*b^2)*c)*x^4 + 8*(372*B*a^4*b^2 + 5*A*a^3*b^3 + 4*(176*B*a^5 + 195*A*a^4*b)*c)*x^3 + 16*(252*B*a^5*b + 135*A*a^4*b^2 + 260*A*a^5*c)*x^2 + 128*(12*B*a^6 + 25*A*a^5*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^6), -1/30720*(30720*B*a^4*sqrt(-c)*c^2*x^6*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 15*(12*B*a*b^5 - 5*A*b^6 + 320*A*a^3*c^3 + 240*(4*B*a^3*b - A*a^2*b^2)*c^2 - 20*(8*B*a^2*b^3 - 3*A*a*b^4)*c)*sqrt(a)*x^6*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(1280*A*a^6 - (180*B*a^2*b^4 - 75*A*a*b^5 - 16*(736*B*a^4 + 165*A*a^3*b)*c^2 - 80*(27*B*a^3*b^2 - 10*A*a^2*b^3)*c)*x^5 + 2*(60*B*a^3*b^3 - 25*A*a^2*b^4 + 2640*A*a^4*c^2 + 16*(311*B*a^4*b + 15*A*a^3*b^2)*c)*x^4 + 8*(372*B*a^4*b^2 + 5*A*a^3*b^3 + 4*(176*B*a^5 + 195*A*a^4*b)*c)*x^3 + 16*(252*B*a^5*b + 135*A*a^4*b^2 + 260*A*a^5*c)*x^2 + 128*(12*B*a^6 + 25*A*a^5*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^6), 1/15360*(7680*B*a^4*c^(5/2)*x^6*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 15*(12*B*a*b^5 - 5*A*b^6 + 320*A*a^3*c^3 + 240*(4*B*a^3*b - A*a^2*b^2)*c^2 - 20*(8*B*a^2*b^3 - 3*A*a*b^4)*c)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(1280*A*a^6 - (180*B*a^2*b^4 - 75*A*a*b^5 - 16*(736*B*a^4 + 165*A*a^3*b)*c^2 - 80*(27*B*a^3*b^2 - 10*A*a^2*b^3)*c)*x^5 + 2*(60*B*a^3*b^3 - 25*A*a^2*b^4 + 2640*A*a^4*c^2 + 16*(311*B*a^4*b + 15*A*a^3*b^2)*c)*x^4 + 8*(372*B*a^4*b^2 + 5*A*a^3*b^3 + 4*(176*B*a^5 + 195*A*a^4*b)*c)*x^3 + 16*(252*B*a^5*b + 135*A*a^4*b^2 + 260*A*a^5*c)*x^2 + 128*(12*B*a^6 + 25*A*a^5*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^6), -1/15360*(15360*B*a^4*sqrt(-c)*c^2*x^6*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 15*(12*B*a*b^5 - 5*A*b^6 + 320*A*a^3*c^3 + 240*(4*B*a^3*b - A*a^2*b^2)*c^2 - 20*(8*B*a^2*b^3 - 3*A*a*b^4)*c)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(1280*A*a^6 - (180*B*a^2*b^4 - 75*A*a*b^5 - 16*(736*B*a^4 + 165*A*a^3*b)*c^2 - 80*(27*B*a^3*b^2 - 10*A*a^2*b^3)*c)*x^5 + 2*(60*B*a^3*b^3 - 25*A*a^2*b^4 + 2640*A*a^4*c^2 + 16*(311*B*a^4*b + 15*A*a^3*b^2)*c)*x^4 + 8*(372*B*a^4*b^2 + 5*A*a^3*b^3 + 4*(176*B*a^5 + 195*A*a^4*b)*c)*x^3 + 16*(252*B*a^5*b + 135*A*a^4*b^2 + 260*A*a^5*c)*x^2 + 128*(12*B*a^6 + 25*A*a^5*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^6)]","A",0
947,1,887,0,4.401297," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^8,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(2 \, B a b^{6} - A b^{7} - 64 \, {\left(2 \, B a^{4} - A a^{3} b\right)} c^{3} + 48 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{2} - 12 \, {\left(2 \, B a^{2} b^{4} - A a b^{5}\right)} c\right)} \sqrt{a} x^{7} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(3072 \, A a^{7} + {\left(210 \, B a^{2} b^{5} - 105 \, A a b^{6} + 3072 \, A a^{4} c^{3} + 3696 \, {\left(2 \, B a^{4} b - A a^{3} b^{2}\right)} c^{2} - 1120 \, {\left(2 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} c\right)} x^{6} - 2 \, {\left(70 \, B a^{3} b^{4} - 35 \, A a^{2} b^{5} - 48 \, {\left(154 \, B a^{5} + 19 \, A a^{4} b\right)} c^{2} - 336 \, {\left(2 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} c\right)} x^{5} + 8 \, {\left(14 \, B a^{4} b^{3} - 7 \, A a^{3} b^{4} + 1152 \, A a^{5} c^{2} + 12 \, {\left(182 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} c\right)} x^{4} + 16 \, {\left(378 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3} + 4 \, {\left(182 \, B a^{6} + 197 \, A a^{5} b\right)} c\right)} x^{3} + 128 \, {\left(70 \, B a^{6} b + 37 \, A a^{5} b^{2} + 72 \, A a^{6} c\right)} x^{2} + 256 \, {\left(14 \, B a^{7} + 29 \, A a^{6} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{86016 \, a^{5} x^{7}}, -\frac{105 \, {\left(2 \, B a b^{6} - A b^{7} - 64 \, {\left(2 \, B a^{4} - A a^{3} b\right)} c^{3} + 48 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{2} - 12 \, {\left(2 \, B a^{2} b^{4} - A a b^{5}\right)} c\right)} \sqrt{-a} x^{7} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(3072 \, A a^{7} + {\left(210 \, B a^{2} b^{5} - 105 \, A a b^{6} + 3072 \, A a^{4} c^{3} + 3696 \, {\left(2 \, B a^{4} b - A a^{3} b^{2}\right)} c^{2} - 1120 \, {\left(2 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} c\right)} x^{6} - 2 \, {\left(70 \, B a^{3} b^{4} - 35 \, A a^{2} b^{5} - 48 \, {\left(154 \, B a^{5} + 19 \, A a^{4} b\right)} c^{2} - 336 \, {\left(2 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} c\right)} x^{5} + 8 \, {\left(14 \, B a^{4} b^{3} - 7 \, A a^{3} b^{4} + 1152 \, A a^{5} c^{2} + 12 \, {\left(182 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} c\right)} x^{4} + 16 \, {\left(378 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3} + 4 \, {\left(182 \, B a^{6} + 197 \, A a^{5} b\right)} c\right)} x^{3} + 128 \, {\left(70 \, B a^{6} b + 37 \, A a^{5} b^{2} + 72 \, A a^{6} c\right)} x^{2} + 256 \, {\left(14 \, B a^{7} + 29 \, A a^{6} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{43008 \, a^{5} x^{7}}\right]"," ",0,"[-1/86016*(105*(2*B*a*b^6 - A*b^7 - 64*(2*B*a^4 - A*a^3*b)*c^3 + 48*(2*B*a^3*b^2 - A*a^2*b^3)*c^2 - 12*(2*B*a^2*b^4 - A*a*b^5)*c)*sqrt(a)*x^7*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(3072*A*a^7 + (210*B*a^2*b^5 - 105*A*a*b^6 + 3072*A*a^4*c^3 + 3696*(2*B*a^4*b - A*a^3*b^2)*c^2 - 1120*(2*B*a^3*b^3 - A*a^2*b^4)*c)*x^6 - 2*(70*B*a^3*b^4 - 35*A*a^2*b^5 - 48*(154*B*a^5 + 19*A*a^4*b)*c^2 - 336*(2*B*a^4*b^2 - A*a^3*b^3)*c)*x^5 + 8*(14*B*a^4*b^3 - 7*A*a^3*b^4 + 1152*A*a^5*c^2 + 12*(182*B*a^5*b + 5*A*a^4*b^2)*c)*x^4 + 16*(378*B*a^5*b^2 + 3*A*a^4*b^3 + 4*(182*B*a^6 + 197*A*a^5*b)*c)*x^3 + 128*(70*B*a^6*b + 37*A*a^5*b^2 + 72*A*a^6*c)*x^2 + 256*(14*B*a^7 + 29*A*a^6*b)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^7), -1/43008*(105*(2*B*a*b^6 - A*b^7 - 64*(2*B*a^4 - A*a^3*b)*c^3 + 48*(2*B*a^3*b^2 - A*a^2*b^3)*c^2 - 12*(2*B*a^2*b^4 - A*a*b^5)*c)*sqrt(-a)*x^7*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(3072*A*a^7 + (210*B*a^2*b^5 - 105*A*a*b^6 + 3072*A*a^4*c^3 + 3696*(2*B*a^4*b - A*a^3*b^2)*c^2 - 1120*(2*B*a^3*b^3 - A*a^2*b^4)*c)*x^6 - 2*(70*B*a^3*b^4 - 35*A*a^2*b^5 - 48*(154*B*a^5 + 19*A*a^4*b)*c^2 - 336*(2*B*a^4*b^2 - A*a^3*b^3)*c)*x^5 + 8*(14*B*a^4*b^3 - 7*A*a^3*b^4 + 1152*A*a^5*c^2 + 12*(182*B*a^5*b + 5*A*a^4*b^2)*c)*x^4 + 16*(378*B*a^5*b^2 + 3*A*a^4*b^3 + 4*(182*B*a^6 + 197*A*a^5*b)*c)*x^3 + 128*(70*B*a^6*b + 37*A*a^5*b^2 + 72*A*a^6*c)*x^2 + 256*(14*B*a^7 + 29*A*a^6*b)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^7)]","B",0
948,1,1091,0,8.074116," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^9,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(16 \, B a b^{7} - 9 \, A b^{8} - 256 \, A a^{4} c^{4} - 256 \, {\left(4 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} c^{3} + 96 \, {\left(8 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c^{2} - 16 \, {\left(12 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} c\right)} \sqrt{a} x^{8} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(43008 \, A a^{8} - {\left(1680 \, B a^{2} b^{6} - 945 \, A a b^{7} - 192 \, {\left(256 \, B a^{5} - 221 \, A a^{4} b\right)} c^{3} + 112 \, {\left(528 \, B a^{4} b^{2} - 337 \, A a^{3} b^{3}\right)} c^{2} - 140 \, {\left(128 \, B a^{3} b^{4} - 75 \, A a^{2} b^{5}\right)} c\right)} x^{7} + 2 \, {\left(560 \, B a^{3} b^{5} - 315 \, A a^{2} b^{6} + 6720 \, A a^{5} c^{3} + 48 \, {\left(304 \, B a^{5} b - 199 \, A a^{4} b^{2}\right)} c^{2} - 28 \, {\left(192 \, B a^{4} b^{3} - 113 \, A a^{3} b^{4}\right)} c\right)} x^{6} - 8 \, {\left(112 \, B a^{4} b^{4} - 63 \, A a^{3} b^{5} - 48 \, {\left(384 \, B a^{6} + 29 \, A a^{5} b\right)} c^{2} - 8 \, {\left(120 \, B a^{5} b^{2} - 71 \, A a^{4} b^{3}\right)} c\right)} x^{5} + 16 \, {\left(48 \, B a^{5} b^{3} - 27 \, A a^{4} b^{4} + 6608 \, A a^{6} c^{2} + 8 \, {\left(1576 \, B a^{6} b + 27 \, A a^{5} b^{2}\right)} c\right)} x^{4} + 128 \, {\left(592 \, B a^{6} b^{2} + 3 \, A a^{5} b^{3} + 4 \, {\left(288 \, B a^{7} + 307 \, A a^{6} b\right)} c\right)} x^{3} + 256 \, {\left(464 \, B a^{7} b + 243 \, A a^{6} b^{2} + 476 \, A a^{7} c\right)} x^{2} + 3072 \, {\left(16 \, B a^{8} + 33 \, A a^{7} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1376256 \, a^{6} x^{8}}, \frac{105 \, {\left(16 \, B a b^{7} - 9 \, A b^{8} - 256 \, A a^{4} c^{4} - 256 \, {\left(4 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} c^{3} + 96 \, {\left(8 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c^{2} - 16 \, {\left(12 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} c\right)} \sqrt{-a} x^{8} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(43008 \, A a^{8} - {\left(1680 \, B a^{2} b^{6} - 945 \, A a b^{7} - 192 \, {\left(256 \, B a^{5} - 221 \, A a^{4} b\right)} c^{3} + 112 \, {\left(528 \, B a^{4} b^{2} - 337 \, A a^{3} b^{3}\right)} c^{2} - 140 \, {\left(128 \, B a^{3} b^{4} - 75 \, A a^{2} b^{5}\right)} c\right)} x^{7} + 2 \, {\left(560 \, B a^{3} b^{5} - 315 \, A a^{2} b^{6} + 6720 \, A a^{5} c^{3} + 48 \, {\left(304 \, B a^{5} b - 199 \, A a^{4} b^{2}\right)} c^{2} - 28 \, {\left(192 \, B a^{4} b^{3} - 113 \, A a^{3} b^{4}\right)} c\right)} x^{6} - 8 \, {\left(112 \, B a^{4} b^{4} - 63 \, A a^{3} b^{5} - 48 \, {\left(384 \, B a^{6} + 29 \, A a^{5} b\right)} c^{2} - 8 \, {\left(120 \, B a^{5} b^{2} - 71 \, A a^{4} b^{3}\right)} c\right)} x^{5} + 16 \, {\left(48 \, B a^{5} b^{3} - 27 \, A a^{4} b^{4} + 6608 \, A a^{6} c^{2} + 8 \, {\left(1576 \, B a^{6} b + 27 \, A a^{5} b^{2}\right)} c\right)} x^{4} + 128 \, {\left(592 \, B a^{6} b^{2} + 3 \, A a^{5} b^{3} + 4 \, {\left(288 \, B a^{7} + 307 \, A a^{6} b\right)} c\right)} x^{3} + 256 \, {\left(464 \, B a^{7} b + 243 \, A a^{6} b^{2} + 476 \, A a^{7} c\right)} x^{2} + 3072 \, {\left(16 \, B a^{8} + 33 \, A a^{7} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{688128 \, a^{6} x^{8}}\right]"," ",0,"[-1/1376256*(105*(16*B*a*b^7 - 9*A*b^8 - 256*A*a^4*c^4 - 256*(4*B*a^4*b - 3*A*a^3*b^2)*c^3 + 96*(8*B*a^3*b^3 - 5*A*a^2*b^4)*c^2 - 16*(12*B*a^2*b^5 - 7*A*a*b^6)*c)*sqrt(a)*x^8*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(43008*A*a^8 - (1680*B*a^2*b^6 - 945*A*a*b^7 - 192*(256*B*a^5 - 221*A*a^4*b)*c^3 + 112*(528*B*a^4*b^2 - 337*A*a^3*b^3)*c^2 - 140*(128*B*a^3*b^4 - 75*A*a^2*b^5)*c)*x^7 + 2*(560*B*a^3*b^5 - 315*A*a^2*b^6 + 6720*A*a^5*c^3 + 48*(304*B*a^5*b - 199*A*a^4*b^2)*c^2 - 28*(192*B*a^4*b^3 - 113*A*a^3*b^4)*c)*x^6 - 8*(112*B*a^4*b^4 - 63*A*a^3*b^5 - 48*(384*B*a^6 + 29*A*a^5*b)*c^2 - 8*(120*B*a^5*b^2 - 71*A*a^4*b^3)*c)*x^5 + 16*(48*B*a^5*b^3 - 27*A*a^4*b^4 + 6608*A*a^6*c^2 + 8*(1576*B*a^6*b + 27*A*a^5*b^2)*c)*x^4 + 128*(592*B*a^6*b^2 + 3*A*a^5*b^3 + 4*(288*B*a^7 + 307*A*a^6*b)*c)*x^3 + 256*(464*B*a^7*b + 243*A*a^6*b^2 + 476*A*a^7*c)*x^2 + 3072*(16*B*a^8 + 33*A*a^7*b)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^8), 1/688128*(105*(16*B*a*b^7 - 9*A*b^8 - 256*A*a^4*c^4 - 256*(4*B*a^4*b - 3*A*a^3*b^2)*c^3 + 96*(8*B*a^3*b^3 - 5*A*a^2*b^4)*c^2 - 16*(12*B*a^2*b^5 - 7*A*a*b^6)*c)*sqrt(-a)*x^8*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(43008*A*a^8 - (1680*B*a^2*b^6 - 945*A*a*b^7 - 192*(256*B*a^5 - 221*A*a^4*b)*c^3 + 112*(528*B*a^4*b^2 - 337*A*a^3*b^3)*c^2 - 140*(128*B*a^3*b^4 - 75*A*a^2*b^5)*c)*x^7 + 2*(560*B*a^3*b^5 - 315*A*a^2*b^6 + 6720*A*a^5*c^3 + 48*(304*B*a^5*b - 199*A*a^4*b^2)*c^2 - 28*(192*B*a^4*b^3 - 113*A*a^3*b^4)*c)*x^6 - 8*(112*B*a^4*b^4 - 63*A*a^3*b^5 - 48*(384*B*a^6 + 29*A*a^5*b)*c^2 - 8*(120*B*a^5*b^2 - 71*A*a^4*b^3)*c)*x^5 + 16*(48*B*a^5*b^3 - 27*A*a^4*b^4 + 6608*A*a^6*c^2 + 8*(1576*B*a^6*b + 27*A*a^5*b^2)*c)*x^4 + 128*(592*B*a^6*b^2 + 3*A*a^5*b^3 + 4*(288*B*a^7 + 307*A*a^6*b)*c)*x^3 + 256*(464*B*a^7*b + 243*A*a^6*b^2 + 476*A*a^7*c)*x^2 + 3072*(16*B*a^8 + 33*A*a^7*b)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^8)]","B",0
949,1,1315,0,9.921541," ","integrate((B*x+A)*(c*x^2+b*x+a)^(5/2)/x^10,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(18 \, B a b^{8} - 11 \, A b^{9} + 256 \, {\left(2 \, B a^{5} - 3 \, A a^{4} b\right)} c^{4} - 256 \, {\left(6 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} c^{3} + 96 \, {\left(10 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5}\right)} c^{2} - 16 \, {\left(14 \, B a^{2} b^{6} - 9 \, A a b^{7}\right)} c\right)} \sqrt{a} x^{9} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(229376 \, A a^{9} + {\left(5670 \, B a^{2} b^{7} - 3465 \, A a b^{8} - 65536 \, A a^{5} c^{4} - 576 \, {\left(442 \, B a^{5} b - 407 \, A a^{4} b^{2}\right)} c^{3} + 336 \, {\left(674 \, B a^{4} b^{3} - 483 \, A a^{3} b^{4}\right)} c^{2} - 420 \, {\left(150 \, B a^{3} b^{5} - 97 \, A a^{2} b^{6}\right)} c\right)} x^{8} - 2 \, {\left(1890 \, B a^{3} b^{6} - 1155 \, A a^{2} b^{7} - 64 \, {\left(630 \, B a^{6} - 689 \, A a^{5} b\right)} c^{3} + 144 \, {\left(398 \, B a^{5} b^{2} - 293 \, A a^{4} b^{3}\right)} c^{2} - 84 \, {\left(226 \, B a^{4} b^{4} - 147 \, A a^{3} b^{5}\right)} c\right)} x^{7} + 8 \, {\left(378 \, B a^{4} b^{5} - 231 \, A a^{3} b^{6} + 4096 \, A a^{6} c^{3} + 48 \, {\left(174 \, B a^{6} b - 133 \, A a^{5} b^{2}\right)} c^{2} - 24 \, {\left(142 \, B a^{5} b^{3} - 93 \, A a^{4} b^{4}\right)} c\right)} x^{6} - 16 \, {\left(162 \, B a^{5} b^{4} - 99 \, A a^{4} b^{5} - 48 \, {\left(826 \, B a^{7} + 41 \, A a^{6} b\right)} c^{2} - 8 \, {\left(162 \, B a^{6} b^{2} - 107 \, A a^{5} b^{3}\right)} c\right)} x^{5} + 128 \, {\left(18 \, B a^{6} b^{3} - 11 \, A a^{5} b^{4} + 3840 \, A a^{7} c^{2} + 12 \, {\left(614 \, B a^{7} b + 7 \, A a^{6} b^{2}\right)} c\right)} x^{4} + 256 \, {\left(1458 \, B a^{7} b^{2} + 5 \, A a^{6} b^{3} + 12 \, {\left(238 \, B a^{8} + 251 \, A a^{7} b\right)} c\right)} x^{3} + 1024 \, {\left(594 \, B a^{8} b + 309 \, A a^{7} b^{2} + 608 \, A a^{8} c\right)} x^{2} + 14336 \, {\left(18 \, B a^{9} + 37 \, A a^{8} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8257536 \, a^{7} x^{9}}, -\frac{315 \, {\left(18 \, B a b^{8} - 11 \, A b^{9} + 256 \, {\left(2 \, B a^{5} - 3 \, A a^{4} b\right)} c^{4} - 256 \, {\left(6 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} c^{3} + 96 \, {\left(10 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5}\right)} c^{2} - 16 \, {\left(14 \, B a^{2} b^{6} - 9 \, A a b^{7}\right)} c\right)} \sqrt{-a} x^{9} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(229376 \, A a^{9} + {\left(5670 \, B a^{2} b^{7} - 3465 \, A a b^{8} - 65536 \, A a^{5} c^{4} - 576 \, {\left(442 \, B a^{5} b - 407 \, A a^{4} b^{2}\right)} c^{3} + 336 \, {\left(674 \, B a^{4} b^{3} - 483 \, A a^{3} b^{4}\right)} c^{2} - 420 \, {\left(150 \, B a^{3} b^{5} - 97 \, A a^{2} b^{6}\right)} c\right)} x^{8} - 2 \, {\left(1890 \, B a^{3} b^{6} - 1155 \, A a^{2} b^{7} - 64 \, {\left(630 \, B a^{6} - 689 \, A a^{5} b\right)} c^{3} + 144 \, {\left(398 \, B a^{5} b^{2} - 293 \, A a^{4} b^{3}\right)} c^{2} - 84 \, {\left(226 \, B a^{4} b^{4} - 147 \, A a^{3} b^{5}\right)} c\right)} x^{7} + 8 \, {\left(378 \, B a^{4} b^{5} - 231 \, A a^{3} b^{6} + 4096 \, A a^{6} c^{3} + 48 \, {\left(174 \, B a^{6} b - 133 \, A a^{5} b^{2}\right)} c^{2} - 24 \, {\left(142 \, B a^{5} b^{3} - 93 \, A a^{4} b^{4}\right)} c\right)} x^{6} - 16 \, {\left(162 \, B a^{5} b^{4} - 99 \, A a^{4} b^{5} - 48 \, {\left(826 \, B a^{7} + 41 \, A a^{6} b\right)} c^{2} - 8 \, {\left(162 \, B a^{6} b^{2} - 107 \, A a^{5} b^{3}\right)} c\right)} x^{5} + 128 \, {\left(18 \, B a^{6} b^{3} - 11 \, A a^{5} b^{4} + 3840 \, A a^{7} c^{2} + 12 \, {\left(614 \, B a^{7} b + 7 \, A a^{6} b^{2}\right)} c\right)} x^{4} + 256 \, {\left(1458 \, B a^{7} b^{2} + 5 \, A a^{6} b^{3} + 12 \, {\left(238 \, B a^{8} + 251 \, A a^{7} b\right)} c\right)} x^{3} + 1024 \, {\left(594 \, B a^{8} b + 309 \, A a^{7} b^{2} + 608 \, A a^{8} c\right)} x^{2} + 14336 \, {\left(18 \, B a^{9} + 37 \, A a^{8} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4128768 \, a^{7} x^{9}}\right]"," ",0,"[1/8257536*(315*(18*B*a*b^8 - 11*A*b^9 + 256*(2*B*a^5 - 3*A*a^4*b)*c^4 - 256*(6*B*a^4*b^2 - 5*A*a^3*b^3)*c^3 + 96*(10*B*a^3*b^4 - 7*A*a^2*b^5)*c^2 - 16*(14*B*a^2*b^6 - 9*A*a*b^7)*c)*sqrt(a)*x^9*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(229376*A*a^9 + (5670*B*a^2*b^7 - 3465*A*a*b^8 - 65536*A*a^5*c^4 - 576*(442*B*a^5*b - 407*A*a^4*b^2)*c^3 + 336*(674*B*a^4*b^3 - 483*A*a^3*b^4)*c^2 - 420*(150*B*a^3*b^5 - 97*A*a^2*b^6)*c)*x^8 - 2*(1890*B*a^3*b^6 - 1155*A*a^2*b^7 - 64*(630*B*a^6 - 689*A*a^5*b)*c^3 + 144*(398*B*a^5*b^2 - 293*A*a^4*b^3)*c^2 - 84*(226*B*a^4*b^4 - 147*A*a^3*b^5)*c)*x^7 + 8*(378*B*a^4*b^5 - 231*A*a^3*b^6 + 4096*A*a^6*c^3 + 48*(174*B*a^6*b - 133*A*a^5*b^2)*c^2 - 24*(142*B*a^5*b^3 - 93*A*a^4*b^4)*c)*x^6 - 16*(162*B*a^5*b^4 - 99*A*a^4*b^5 - 48*(826*B*a^7 + 41*A*a^6*b)*c^2 - 8*(162*B*a^6*b^2 - 107*A*a^5*b^3)*c)*x^5 + 128*(18*B*a^6*b^3 - 11*A*a^5*b^4 + 3840*A*a^7*c^2 + 12*(614*B*a^7*b + 7*A*a^6*b^2)*c)*x^4 + 256*(1458*B*a^7*b^2 + 5*A*a^6*b^3 + 12*(238*B*a^8 + 251*A*a^7*b)*c)*x^3 + 1024*(594*B*a^8*b + 309*A*a^7*b^2 + 608*A*a^8*c)*x^2 + 14336*(18*B*a^9 + 37*A*a^8*b)*x)*sqrt(c*x^2 + b*x + a))/(a^7*x^9), -1/4128768*(315*(18*B*a*b^8 - 11*A*b^9 + 256*(2*B*a^5 - 3*A*a^4*b)*c^4 - 256*(6*B*a^4*b^2 - 5*A*a^3*b^3)*c^3 + 96*(10*B*a^3*b^4 - 7*A*a^2*b^5)*c^2 - 16*(14*B*a^2*b^6 - 9*A*a*b^7)*c)*sqrt(-a)*x^9*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(229376*A*a^9 + (5670*B*a^2*b^7 - 3465*A*a*b^8 - 65536*A*a^5*c^4 - 576*(442*B*a^5*b - 407*A*a^4*b^2)*c^3 + 336*(674*B*a^4*b^3 - 483*A*a^3*b^4)*c^2 - 420*(150*B*a^3*b^5 - 97*A*a^2*b^6)*c)*x^8 - 2*(1890*B*a^3*b^6 - 1155*A*a^2*b^7 - 64*(630*B*a^6 - 689*A*a^5*b)*c^3 + 144*(398*B*a^5*b^2 - 293*A*a^4*b^3)*c^2 - 84*(226*B*a^4*b^4 - 147*A*a^3*b^5)*c)*x^7 + 8*(378*B*a^4*b^5 - 231*A*a^3*b^6 + 4096*A*a^6*c^3 + 48*(174*B*a^6*b - 133*A*a^5*b^2)*c^2 - 24*(142*B*a^5*b^3 - 93*A*a^4*b^4)*c)*x^6 - 16*(162*B*a^5*b^4 - 99*A*a^4*b^5 - 48*(826*B*a^7 + 41*A*a^6*b)*c^2 - 8*(162*B*a^6*b^2 - 107*A*a^5*b^3)*c)*x^5 + 128*(18*B*a^6*b^3 - 11*A*a^5*b^4 + 3840*A*a^7*c^2 + 12*(614*B*a^7*b + 7*A*a^6*b^2)*c)*x^4 + 256*(1458*B*a^7*b^2 + 5*A*a^6*b^3 + 12*(238*B*a^8 + 251*A*a^7*b)*c)*x^3 + 1024*(594*B*a^8*b + 309*A*a^7*b^2 + 608*A*a^8*c)*x^2 + 14336*(18*B*a^9 + 37*A*a^8*b)*x)*sqrt(c*x^2 + b*x + a))/(a^7*x^9)]","A",0
950,1,519,0,0.524683," ","integrate(x^4*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(63 \, B b^{5} - 96 \, A a^{2} c^{3} + 240 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 70 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(384 \, B c^{5} x^{4} + 945 \, B b^{4} c + 8 \, {\left(128 \, B a^{2} + 275 \, A a b\right)} c^{3} - 48 \, {\left(9 \, B b c^{4} - 10 \, A c^{5}\right)} x^{3} - 210 \, {\left(14 \, B a b^{2} + 5 \, A b^{3}\right)} c^{2} + 8 \, {\left(63 \, B b^{2} c^{3} - 2 \, {\left(32 \, B a + 35 \, A b\right)} c^{4}\right)} x^{2} - 2 \, {\left(315 \, B b^{3} c^{2} + 360 \, A a c^{4} - 14 \, {\left(46 \, B a b + 25 \, A b^{2}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{6}}, \frac{15 \, {\left(63 \, B b^{5} - 96 \, A a^{2} c^{3} + 240 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 70 \, {\left(4 \, B a b^{3} + A b^{4}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(384 \, B c^{5} x^{4} + 945 \, B b^{4} c + 8 \, {\left(128 \, B a^{2} + 275 \, A a b\right)} c^{3} - 48 \, {\left(9 \, B b c^{4} - 10 \, A c^{5}\right)} x^{3} - 210 \, {\left(14 \, B a b^{2} + 5 \, A b^{3}\right)} c^{2} + 8 \, {\left(63 \, B b^{2} c^{3} - 2 \, {\left(32 \, B a + 35 \, A b\right)} c^{4}\right)} x^{2} - 2 \, {\left(315 \, B b^{3} c^{2} + 360 \, A a c^{4} - 14 \, {\left(46 \, B a b + 25 \, A b^{2}\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, c^{6}}\right]"," ",0,"[-1/7680*(15*(63*B*b^5 - 96*A*a^2*c^3 + 240*(B*a^2*b + A*a*b^2)*c^2 - 70*(4*B*a*b^3 + A*b^4)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(384*B*c^5*x^4 + 945*B*b^4*c + 8*(128*B*a^2 + 275*A*a*b)*c^3 - 48*(9*B*b*c^4 - 10*A*c^5)*x^3 - 210*(14*B*a*b^2 + 5*A*b^3)*c^2 + 8*(63*B*b^2*c^3 - 2*(32*B*a + 35*A*b)*c^4)*x^2 - 2*(315*B*b^3*c^2 + 360*A*a*c^4 - 14*(46*B*a*b + 25*A*b^2)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/3840*(15*(63*B*b^5 - 96*A*a^2*c^3 + 240*(B*a^2*b + A*a*b^2)*c^2 - 70*(4*B*a*b^3 + A*b^4)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(384*B*c^5*x^4 + 945*B*b^4*c + 8*(128*B*a^2 + 275*A*a*b)*c^3 - 48*(9*B*b*c^4 - 10*A*c^5)*x^3 - 210*(14*B*a*b^2 + 5*A*b^3)*c^2 + 8*(63*B*b^2*c^3 - 2*(32*B*a + 35*A*b)*c^4)*x^2 - 2*(315*B*b^3*c^2 + 360*A*a*c^4 - 14*(46*B*a*b + 25*A*b^2)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6]","A",0
951,1,395,0,0.516025," ","integrate(x^3*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, B b^{4} + 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 40 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, B c^{4} x^{3} - 105 \, B b^{3} c - 128 \, A a c^{3} + 20 \, {\left(11 \, B a b + 6 \, A b^{2}\right)} c^{2} - 8 \, {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{2} c^{2} - 4 \, {\left(9 \, B a + 10 \, A b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{5}}, -\frac{3 \, {\left(35 \, B b^{4} + 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 40 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(48 \, B c^{4} x^{3} - 105 \, B b^{3} c - 128 \, A a c^{3} + 20 \, {\left(11 \, B a b + 6 \, A b^{2}\right)} c^{2} - 8 \, {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{2} c^{2} - 4 \, {\left(9 \, B a + 10 \, A b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{5}}\right]"," ",0,"[1/768*(3*(35*B*b^4 + 48*(B*a^2 + 2*A*a*b)*c^2 - 40*(3*B*a*b^2 + A*b^3)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(48*B*c^4*x^3 - 105*B*b^3*c - 128*A*a*c^3 + 20*(11*B*a*b + 6*A*b^2)*c^2 - 8*(7*B*b*c^3 - 8*A*c^4)*x^2 + 2*(35*B*b^2*c^2 - 4*(9*B*a + 10*A*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/384*(3*(35*B*b^4 + 48*(B*a^2 + 2*A*a*b)*c^2 - 40*(3*B*a*b^2 + A*b^3)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(48*B*c^4*x^3 - 105*B*b^3*c - 128*A*a*c^3 + 20*(11*B*a*b + 6*A*b^2)*c^2 - 8*(7*B*b*c^3 - 8*A*c^4)*x^2 + 2*(35*B*b^2*c^2 - 4*(9*B*a + 10*A*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
952,1,295,0,0.456711," ","integrate(x^2*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, B b^{3} + 8 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, B c^{3} x^{2} + 15 \, B b^{2} c - 2 \, {\left(8 \, B a + 9 \, A b\right)} c^{2} - 2 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{4}}, \frac{3 \, {\left(5 \, B b^{3} + 8 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(8 \, B c^{3} x^{2} + 15 \, B b^{2} c - 2 \, {\left(8 \, B a + 9 \, A b\right)} c^{2} - 2 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{4}}\right]"," ",0,"[1/96*(3*(5*B*b^3 + 8*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*B*c^3*x^2 + 15*B*b^2*c - 2*(8*B*a + 9*A*b)*c^2 - 2*(5*B*b*c^2 - 6*A*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/48*(3*(5*B*b^3 + 8*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(8*B*c^3*x^2 + 15*B*b^2*c - 2*(8*B*a + 9*A*b)*c^2 - 2*(5*B*b*c^2 - 6*A*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
953,1,213,0,0.473986," ","integrate(x*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, B c^{2} x - 3 \, B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x + a}}{16 \, c^{3}}, -\frac{{\left(3 \, B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2 \, B c^{2} x - 3 \, B b c + 4 \, A c^{2}\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{3}}\right]"," ",0,"[-1/16*((3*B*b^2 - 4*(B*a + A*b)*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(2*B*c^2*x - 3*B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x + a))/c^3, -1/8*((3*B*b^2 - 4*(B*a + A*b)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2*B*c^2*x - 3*B*b*c + 4*A*c^2)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
954,1,162,0,0.454228," ","integrate((B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c x^{2} + b x + a} B c - {\left(B b - 2 \, A c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, c^{2}}, \frac{2 \, \sqrt{c x^{2} + b x + a} B c + {\left(B b - 2 \, A c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{2 \, c^{2}}\right]"," ",0,"[1/4*(4*sqrt(c*x^2 + b*x + a)*B*c - (B*b - 2*A*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c))/c^2, 1/2*(2*sqrt(c*x^2 + b*x + a)*B*c + (B*b - 2*A*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)))/c^2]","A",0
955,1,468,0,0.575400," ","integrate((B*x+A)/x/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B a \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + A \sqrt{a} c \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right)}{2 \, a c}, -\frac{2 \, B a \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - A \sqrt{a} c \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right)}{2 \, a c}, \frac{2 \, A \sqrt{-a} c \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + B a \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{2 \, a c}, \frac{A \sqrt{-a} c \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - B a \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{a c}\right]"," ",0,"[1/2*(B*a*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + A*sqrt(a)*c*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2))/(a*c), -1/2*(2*B*a*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - A*sqrt(a)*c*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2))/(a*c), 1/2*(2*A*sqrt(-a)*c*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + B*a*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c))/(a*c), (A*sqrt(-a)*c*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - B*a*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)))/(a*c)]","A",0
956,1,177,0,0.531485," ","integrate((B*x+A)/x^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a - A b\right)} \sqrt{a} x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, \sqrt{c x^{2} + b x + a} A a}{4 \, a^{2} x}, \frac{{\left(2 \, B a - A b\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, \sqrt{c x^{2} + b x + a} A a}{2 \, a^{2} x}\right]"," ",0,"[-1/4*((2*B*a - A*b)*sqrt(a)*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*sqrt(c*x^2 + b*x + a)*A*a)/(a^2*x), 1/2*((2*B*a - A*b)*sqrt(-a)*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*sqrt(c*x^2 + b*x + a)*A*a)/(a^2*x)]","A",0
957,1,235,0,0.617860," ","integrate((B*x+A)/x^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, a^{3} x^{2}}, -\frac{{\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, a^{3} x^{2}}\right]"," ",0,"[1/16*((4*B*a*b - 3*A*b^2 + 4*A*a*c)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(2*A*a^2 + (4*B*a^2 - 3*A*a*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^2), -1/8*((4*B*a*b - 3*A*b^2 + 4*A*a*c)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(2*A*a^2 + (4*B*a^2 - 3*A*a*b)*x)*sqrt(c*x^2 + b*x + a))/(a^3*x^2)]","A",0
958,1,321,0,0.729938," ","integrate((B*x+A)/x^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(8 \, A a^{3} - {\left(18 \, B a^{2} b - 15 \, A a b^{2} + 16 \, A a^{2} c\right)} x^{2} + 2 \, {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, a^{4} x^{3}}, \frac{3 \, {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(8 \, A a^{3} - {\left(18 \, B a^{2} b - 15 \, A a b^{2} + 16 \, A a^{2} c\right)} x^{2} + 2 \, {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, a^{4} x^{3}}\right]"," ",0,"[1/96*(3*(6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*sqrt(a)*x^3*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(8*A*a^3 - (18*B*a^2*b - 15*A*a*b^2 + 16*A*a^2*c)*x^2 + 2*(6*B*a^3 - 5*A*a^2*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^3), 1/48*(3*(6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(8*A*a^3 - (18*B*a^2*b - 15*A*a*b^2 + 16*A*a^2*c)*x^2 + 2*(6*B*a^3 - 5*A*a^2*b)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^3)]","A",0
959,1,425,0,0.996423," ","integrate((B*x+A)/x^5/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(40 \, B a b^{3} - 35 \, A b^{4} - 48 \, A a^{2} c^{2} - 24 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} c\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(48 \, A a^{4} + {\left(120 \, B a^{2} b^{2} - 105 \, A a b^{3} - 4 \, {\left(32 \, B a^{3} - 55 \, A a^{2} b\right)} c\right)} x^{3} - 2 \, {\left(40 \, B a^{3} b - 35 \, A a^{2} b^{2} + 36 \, A a^{3} c\right)} x^{2} + 8 \, {\left(8 \, B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, a^{5} x^{4}}, -\frac{3 \, {\left(40 \, B a b^{3} - 35 \, A b^{4} - 48 \, A a^{2} c^{2} - 24 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(48 \, A a^{4} + {\left(120 \, B a^{2} b^{2} - 105 \, A a b^{3} - 4 \, {\left(32 \, B a^{3} - 55 \, A a^{2} b\right)} c\right)} x^{3} - 2 \, {\left(40 \, B a^{3} b - 35 \, A a^{2} b^{2} + 36 \, A a^{3} c\right)} x^{2} + 8 \, {\left(8 \, B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, a^{5} x^{4}}\right]"," ",0,"[-1/768*(3*(40*B*a*b^3 - 35*A*b^4 - 48*A*a^2*c^2 - 24*(4*B*a^2*b - 5*A*a*b^2)*c)*sqrt(a)*x^4*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(48*A*a^4 + (120*B*a^2*b^2 - 105*A*a*b^3 - 4*(32*B*a^3 - 55*A*a^2*b)*c)*x^3 - 2*(40*B*a^3*b - 35*A*a^2*b^2 + 36*A*a^3*c)*x^2 + 8*(8*B*a^4 - 7*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^4), -1/384*(3*(40*B*a*b^3 - 35*A*b^4 - 48*A*a^2*c^2 - 24*(4*B*a^2*b - 5*A*a*b^2)*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(48*A*a^4 + (120*B*a^2*b^2 - 105*A*a*b^3 - 4*(32*B*a^3 - 55*A*a^2*b)*c)*x^3 - 2*(40*B*a^3*b - 35*A*a^2*b^2 + 36*A*a^3*c)*x^2 + 8*(8*B*a^4 - 7*A*a^3*b)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^4)]","A",0
960,1,557,0,1.935596," ","integrate((B*x+A)/x^6/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(70 \, B a b^{4} - 63 \, A b^{5} + 48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} - 40 \, {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} c\right)} \sqrt{a} x^{5} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(384 \, A a^{5} - {\left(1050 \, B a^{2} b^{3} - 945 \, A a b^{4} - 1024 \, A a^{3} c^{2} - 20 \, {\left(110 \, B a^{3} b - 147 \, A a^{2} b^{2}\right)} c\right)} x^{4} + 2 \, {\left(350 \, B a^{3} b^{2} - 315 \, A a^{2} b^{3} - 4 \, {\left(90 \, B a^{4} - 161 \, A a^{3} b\right)} c\right)} x^{3} - 8 \, {\left(70 \, B a^{4} b - 63 \, A a^{3} b^{2} + 64 \, A a^{4} c\right)} x^{2} + 48 \, {\left(10 \, B a^{5} - 9 \, A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, a^{6} x^{5}}, \frac{15 \, {\left(70 \, B a b^{4} - 63 \, A b^{5} + 48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} - 40 \, {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} c\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(384 \, A a^{5} - {\left(1050 \, B a^{2} b^{3} - 945 \, A a b^{4} - 1024 \, A a^{3} c^{2} - 20 \, {\left(110 \, B a^{3} b - 147 \, A a^{2} b^{2}\right)} c\right)} x^{4} + 2 \, {\left(350 \, B a^{3} b^{2} - 315 \, A a^{2} b^{3} - 4 \, {\left(90 \, B a^{4} - 161 \, A a^{3} b\right)} c\right)} x^{3} - 8 \, {\left(70 \, B a^{4} b - 63 \, A a^{3} b^{2} + 64 \, A a^{4} c\right)} x^{2} + 48 \, {\left(10 \, B a^{5} - 9 \, A a^{4} b\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, a^{6} x^{5}}\right]"," ",0,"[-1/7680*(15*(70*B*a*b^4 - 63*A*b^5 + 48*(2*B*a^3 - 5*A*a^2*b)*c^2 - 40*(6*B*a^2*b^2 - 7*A*a*b^3)*c)*sqrt(a)*x^5*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(384*A*a^5 - (1050*B*a^2*b^3 - 945*A*a*b^4 - 1024*A*a^3*c^2 - 20*(110*B*a^3*b - 147*A*a^2*b^2)*c)*x^4 + 2*(350*B*a^3*b^2 - 315*A*a^2*b^3 - 4*(90*B*a^4 - 161*A*a^3*b)*c)*x^3 - 8*(70*B*a^4*b - 63*A*a^3*b^2 + 64*A*a^4*c)*x^2 + 48*(10*B*a^5 - 9*A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^5), 1/3840*(15*(70*B*a*b^4 - 63*A*b^5 + 48*(2*B*a^3 - 5*A*a^2*b)*c^2 - 40*(6*B*a^2*b^2 - 7*A*a*b^3)*c)*sqrt(-a)*x^5*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(384*A*a^5 - (1050*B*a^2*b^3 - 945*A*a*b^4 - 1024*A*a^3*c^2 - 20*(110*B*a^3*b - 147*A*a^2*b^2)*c)*x^4 + 2*(350*B*a^3*b^2 - 315*A*a^2*b^3 - 4*(90*B*a^4 - 161*A*a^3*b)*c)*x^3 - 8*(70*B*a^4*b - 63*A*a^3*b^2 + 64*A*a^4*c)*x^2 + 48*(10*B*a^5 - 9*A*a^4*b)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^5)]","A",0
961,1,1035,0,0.809587," ","integrate(x^4*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, B a b^{5} - 96 \, A a^{3} c^{3} + 48 \, {\left(5 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{2} + {\left(35 \, B b^{5} c - 96 \, A a^{2} c^{4} + 48 \, {\left(5 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{3} - 10 \, {\left(20 \, B a b^{3} + 3 \, A b^{4}\right)} c^{2}\right)} x^{2} - 10 \, {\left(20 \, B a^{2} b^{3} + 3 \, A a b^{4}\right)} c + {\left(35 \, B b^{6} - 96 \, A a^{2} b c^{3} + 48 \, {\left(5 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} c^{2} - 10 \, {\left(20 \, B a b^{4} + 3 \, A b^{5}\right)} c\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(105 \, B a b^{4} c + 8 \, {\left(B b^{2} c^{4} - 4 \, B a c^{5}\right)} x^{4} + 8 \, {\left(32 \, B a^{3} + 39 \, A a^{2} b\right)} c^{3} - 2 \, {\left(7 \, B b^{3} c^{3} + 24 \, A a c^{5} - 2 \, {\left(14 \, B a b + 3 \, A b^{2}\right)} c^{4}\right)} x^{3} - 10 \, {\left(46 \, B a^{2} b^{2} + 9 \, A a b^{3}\right)} c^{2} + {\left(35 \, B b^{4} c^{2} + 8 \, {\left(16 \, B a^{2} + 15 \, A a b\right)} c^{4} - 2 \, {\left(86 \, B a b^{2} + 15 \, A b^{3}\right)} c^{3}\right)} x^{2} + {\left(105 \, B b^{5} c - 144 \, A a^{2} c^{4} + 4 \, {\left(122 \, B a^{2} b + 93 \, A a b^{2}\right)} c^{3} - 10 \, {\left(53 \, B a b^{3} + 9 \, A b^{4}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6} + {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} x^{2} + {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} x\right)}}, \frac{3 \, {\left(35 \, B a b^{5} - 96 \, A a^{3} c^{3} + 48 \, {\left(5 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{2} + {\left(35 \, B b^{5} c - 96 \, A a^{2} c^{4} + 48 \, {\left(5 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{3} - 10 \, {\left(20 \, B a b^{3} + 3 \, A b^{4}\right)} c^{2}\right)} x^{2} - 10 \, {\left(20 \, B a^{2} b^{3} + 3 \, A a b^{4}\right)} c + {\left(35 \, B b^{6} - 96 \, A a^{2} b c^{3} + 48 \, {\left(5 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} c^{2} - 10 \, {\left(20 \, B a b^{4} + 3 \, A b^{5}\right)} c\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(105 \, B a b^{4} c + 8 \, {\left(B b^{2} c^{4} - 4 \, B a c^{5}\right)} x^{4} + 8 \, {\left(32 \, B a^{3} + 39 \, A a^{2} b\right)} c^{3} - 2 \, {\left(7 \, B b^{3} c^{3} + 24 \, A a c^{5} - 2 \, {\left(14 \, B a b + 3 \, A b^{2}\right)} c^{4}\right)} x^{3} - 10 \, {\left(46 \, B a^{2} b^{2} + 9 \, A a b^{3}\right)} c^{2} + {\left(35 \, B b^{4} c^{2} + 8 \, {\left(16 \, B a^{2} + 15 \, A a b\right)} c^{4} - 2 \, {\left(86 \, B a b^{2} + 15 \, A b^{3}\right)} c^{3}\right)} x^{2} + {\left(105 \, B b^{5} c - 144 \, A a^{2} c^{4} + 4 \, {\left(122 \, B a^{2} b + 93 \, A a b^{2}\right)} c^{3} - 10 \, {\left(53 \, B a b^{3} + 9 \, A b^{4}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6} + {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} x^{2} + {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} x\right)}}\right]"," ",0,"[1/96*(3*(35*B*a*b^5 - 96*A*a^3*c^3 + 48*(5*B*a^3*b + 3*A*a^2*b^2)*c^2 + (35*B*b^5*c - 96*A*a^2*c^4 + 48*(5*B*a^2*b + 3*A*a*b^2)*c^3 - 10*(20*B*a*b^3 + 3*A*b^4)*c^2)*x^2 - 10*(20*B*a^2*b^3 + 3*A*a*b^4)*c + (35*B*b^6 - 96*A*a^2*b*c^3 + 48*(5*B*a^2*b^2 + 3*A*a*b^3)*c^2 - 10*(20*B*a*b^4 + 3*A*b^5)*c)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(105*B*a*b^4*c + 8*(B*b^2*c^4 - 4*B*a*c^5)*x^4 + 8*(32*B*a^3 + 39*A*a^2*b)*c^3 - 2*(7*B*b^3*c^3 + 24*A*a*c^5 - 2*(14*B*a*b + 3*A*b^2)*c^4)*x^3 - 10*(46*B*a^2*b^2 + 9*A*a*b^3)*c^2 + (35*B*b^4*c^2 + 8*(16*B*a^2 + 15*A*a*b)*c^4 - 2*(86*B*a*b^2 + 15*A*b^3)*c^3)*x^2 + (105*B*b^5*c - 144*A*a^2*c^4 + 4*(122*B*a^2*b + 93*A*a*b^2)*c^3 - 10*(53*B*a*b^3 + 9*A*b^4)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^5 - 4*a^2*c^6 + (b^2*c^6 - 4*a*c^7)*x^2 + (b^3*c^5 - 4*a*b*c^6)*x), 1/48*(3*(35*B*a*b^5 - 96*A*a^3*c^3 + 48*(5*B*a^3*b + 3*A*a^2*b^2)*c^2 + (35*B*b^5*c - 96*A*a^2*c^4 + 48*(5*B*a^2*b + 3*A*a*b^2)*c^3 - 10*(20*B*a*b^3 + 3*A*b^4)*c^2)*x^2 - 10*(20*B*a^2*b^3 + 3*A*a*b^4)*c + (35*B*b^6 - 96*A*a^2*b*c^3 + 48*(5*B*a^2*b^2 + 3*A*a*b^3)*c^2 - 10*(20*B*a*b^4 + 3*A*b^5)*c)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(105*B*a*b^4*c + 8*(B*b^2*c^4 - 4*B*a*c^5)*x^4 + 8*(32*B*a^3 + 39*A*a^2*b)*c^3 - 2*(7*B*b^3*c^3 + 24*A*a*c^5 - 2*(14*B*a*b + 3*A*b^2)*c^4)*x^3 - 10*(46*B*a^2*b^2 + 9*A*a*b^3)*c^2 + (35*B*b^4*c^2 + 8*(16*B*a^2 + 15*A*a*b)*c^4 - 2*(86*B*a*b^2 + 15*A*b^3)*c^3)*x^2 + (105*B*b^5*c - 144*A*a^2*c^4 + 4*(122*B*a^2*b + 93*A*a*b^2)*c^3 - 10*(53*B*a*b^3 + 9*A*b^4)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^5 - 4*a^2*c^6 + (b^2*c^6 - 4*a*c^7)*x^2 + (b^3*c^5 - 4*a*b*c^6)*x)]","A",0
962,1,793,0,0.714701," ","integrate(x^3*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a b^{4} + 16 \, {\left(B a^{3} + A a^{2} b\right)} c^{2} + {\left(5 \, B b^{4} c + 16 \, {\left(B a^{2} + A a b\right)} c^{3} - 4 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} x^{2} - 4 \, {\left(6 \, B a^{2} b^{2} + A a b^{3}\right)} c + {\left(5 \, B b^{5} + 16 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 4 \, {\left(6 \, B a b^{3} + A b^{4}\right)} c\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(15 \, B a b^{3} c + 32 \, A a^{2} c^{3} - 2 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} x^{3} - 4 \, {\left(13 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} + {\left(5 \, B b^{3} c^{2} + 16 \, A a c^{4} - 4 \, {\left(5 \, B a b + A b^{2}\right)} c^{3}\right)} x^{2} + {\left(15 \, B b^{4} c + 8 \, {\left(3 \, B a^{2} + 5 \, A a b\right)} c^{3} - 2 \, {\left(31 \, B a b^{2} + 6 \, A b^{3}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}, -\frac{3 \, {\left(5 \, B a b^{4} + 16 \, {\left(B a^{3} + A a^{2} b\right)} c^{2} + {\left(5 \, B b^{4} c + 16 \, {\left(B a^{2} + A a b\right)} c^{3} - 4 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} x^{2} - 4 \, {\left(6 \, B a^{2} b^{2} + A a b^{3}\right)} c + {\left(5 \, B b^{5} + 16 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 4 \, {\left(6 \, B a b^{3} + A b^{4}\right)} c\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(15 \, B a b^{3} c + 32 \, A a^{2} c^{3} - 2 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} x^{3} - 4 \, {\left(13 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} + {\left(5 \, B b^{3} c^{2} + 16 \, A a c^{4} - 4 \, {\left(5 \, B a b + A b^{2}\right)} c^{3}\right)} x^{2} + {\left(15 \, B b^{4} c + 8 \, {\left(3 \, B a^{2} + 5 \, A a b\right)} c^{3} - 2 \, {\left(31 \, B a b^{2} + 6 \, A b^{3}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}\right]"," ",0,"[-1/16*(3*(5*B*a*b^4 + 16*(B*a^3 + A*a^2*b)*c^2 + (5*B*b^4*c + 16*(B*a^2 + A*a*b)*c^3 - 4*(6*B*a*b^2 + A*b^3)*c^2)*x^2 - 4*(6*B*a^2*b^2 + A*a*b^3)*c + (5*B*b^5 + 16*(B*a^2*b + A*a*b^2)*c^2 - 4*(6*B*a*b^3 + A*b^4)*c)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(15*B*a*b^3*c + 32*A*a^2*c^3 - 2*(B*b^2*c^3 - 4*B*a*c^4)*x^3 - 4*(13*B*a^2*b + 3*A*a*b^2)*c^2 + (5*B*b^3*c^2 + 16*A*a*c^4 - 4*(5*B*a*b + A*b^2)*c^3)*x^2 + (15*B*b^4*c + 8*(3*B*a^2 + 5*A*a*b)*c^3 - 2*(31*B*a*b^2 + 6*A*b^3)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x), -1/8*(3*(5*B*a*b^4 + 16*(B*a^3 + A*a^2*b)*c^2 + (5*B*b^4*c + 16*(B*a^2 + A*a*b)*c^3 - 4*(6*B*a*b^2 + A*b^3)*c^2)*x^2 - 4*(6*B*a^2*b^2 + A*a*b^3)*c + (5*B*b^5 + 16*(B*a^2*b + A*a*b^2)*c^2 - 4*(6*B*a*b^3 + A*b^4)*c)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(15*B*a*b^3*c + 32*A*a^2*c^3 - 2*(B*b^2*c^3 - 4*B*a*c^4)*x^3 - 4*(13*B*a^2*b + 3*A*a*b^2)*c^2 + (5*B*b^3*c^2 + 16*A*a*c^4 - 4*(5*B*a*b + A*b^2)*c^3)*x^2 + (15*B*b^4*c + 8*(3*B*a^2 + 5*A*a*b)*c^3 - 2*(31*B*a*b^2 + 6*A*b^3)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x)]","B",0
963,1,603,0,0.635063," ","integrate(x^2*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B a b^{3} + 8 \, A a^{2} c^{2} + {\left(3 \, B b^{3} c + 8 \, A a c^{3} - 2 \, {\left(6 \, B a b + A b^{2}\right)} c^{2}\right)} x^{2} - 2 \, {\left(6 \, B a^{2} b + A a b^{2}\right)} c + {\left(3 \, B b^{4} + 8 \, A a b c^{2} - 2 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(3 \, B a b^{2} c - 2 \, {\left(4 \, B a^{2} + A a b\right)} c^{2} + {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} x^{2} + {\left(3 \, B b^{3} c + 4 \, A a c^{3} - 2 \, {\left(5 \, B a b + A b^{2}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x\right)}}, \frac{{\left(3 \, B a b^{3} + 8 \, A a^{2} c^{2} + {\left(3 \, B b^{3} c + 8 \, A a c^{3} - 2 \, {\left(6 \, B a b + A b^{2}\right)} c^{2}\right)} x^{2} - 2 \, {\left(6 \, B a^{2} b + A a b^{2}\right)} c + {\left(3 \, B b^{4} + 8 \, A a b c^{2} - 2 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(3 \, B a b^{2} c - 2 \, {\left(4 \, B a^{2} + A a b\right)} c^{2} + {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} x^{2} + {\left(3 \, B b^{3} c + 4 \, A a c^{3} - 2 \, {\left(5 \, B a b + A b^{2}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/4*((3*B*a*b^3 + 8*A*a^2*c^2 + (3*B*b^3*c + 8*A*a*c^3 - 2*(6*B*a*b + A*b^2)*c^2)*x^2 - 2*(6*B*a^2*b + A*a*b^2)*c + (3*B*b^4 + 8*A*a*b*c^2 - 2*(6*B*a*b^2 + A*b^3)*c)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(3*B*a*b^2*c - 2*(4*B*a^2 + A*a*b)*c^2 + (B*b^2*c^2 - 4*B*a*c^3)*x^2 + (3*B*b^3*c + 4*A*a*c^3 - 2*(5*B*a*b + A*b^2)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x), 1/2*((3*B*a*b^3 + 8*A*a^2*c^2 + (3*B*b^3*c + 8*A*a*c^3 - 2*(6*B*a*b + A*b^2)*c^2)*x^2 - 2*(6*B*a^2*b + A*a*b^2)*c + (3*B*b^4 + 8*A*a*b*c^2 - 2*(6*B*a*b^2 + A*b^3)*c)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(3*B*a*b^2*c - 2*(4*B*a^2 + A*a*b)*c^2 + (B*b^2*c^2 - 4*B*a*c^3)*x^2 + (3*B*b^3*c + 4*A*a*c^3 - 2*(5*B*a*b + A*b^2)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x)]","B",0
964,1,405,0,0.594525," ","integrate(x*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B a b^{2} - 4 \, B a^{2} c + {\left(B b^{2} c - 4 \, B a c^{2}\right)} x^{2} + {\left(B b^{3} - 4 \, B a b c\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(B a b c - 2 \, A a c^{2} + {\left(B b^{2} c - {\left(2 \, B a + A b\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}, -\frac{{\left(B a b^{2} - 4 \, B a^{2} c + {\left(B b^{2} c - 4 \, B a c^{2}\right)} x^{2} + {\left(B b^{3} - 4 \, B a b c\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(B a b c - 2 \, A a c^{2} + {\left(B b^{2} c - {\left(2 \, B a + A b\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x}\right]"," ",0,"[1/2*((B*a*b^2 - 4*B*a^2*c + (B*b^2*c - 4*B*a*c^2)*x^2 + (B*b^3 - 4*B*a*b*c)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(B*a*b*c - 2*A*a*c^2 + (B*b^2*c - (2*B*a + A*b)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x), -((B*a*b^2 - 4*B*a^2*c + (B*b^2*c - 4*B*a*c^2)*x^2 + (B*b^3 - 4*B*a*b*c)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(B*a*b*c - 2*A*a*c^2 + (B*b^2*c - (2*B*a + A*b)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)]","B",0
965,1,74,0,0.526120," ","integrate((B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x + a} {\left(2 \, B a - A b + {\left(B b - 2 \, A c\right)} x\right)}}{a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x}"," ",0,"2*sqrt(c*x^2 + b*x + a)*(2*B*a - A*b + (B*b - 2*A*c)*x)/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)","A",0
966,1,412,0,0.660758," ","integrate((B*x+A)/x/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A a b^{2} - 4 \, A a^{2} c + {\left(A b^{2} c - 4 \, A a c^{2}\right)} x^{2} + {\left(A b^{3} - 4 \, A a b c\right)} x\right)} \sqrt{a} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(B a^{2} b - A a b^{2} + 2 \, A a^{2} c + {\left(2 \, B a^{2} - A a b\right)} c x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{2} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x\right)}}, \frac{{\left(A a b^{2} - 4 \, A a^{2} c + {\left(A b^{2} c - 4 \, A a c^{2}\right)} x^{2} + {\left(A b^{3} - 4 \, A a b c\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(B a^{2} b - A a b^{2} + 2 \, A a^{2} c + {\left(2 \, B a^{2} - A a b\right)} c x\right)} \sqrt{c x^{2} + b x + a}}{a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{2} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x}\right]"," ",0,"[1/2*((A*a*b^2 - 4*A*a^2*c + (A*b^2*c - 4*A*a*c^2)*x^2 + (A*b^3 - 4*A*a*b*c)*x)*sqrt(a)*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(B*a^2*b - A*a*b^2 + 2*A*a^2*c + (2*B*a^2 - A*a*b)*c*x)*sqrt(c*x^2 + b*x + a))/(a^3*b^2 - 4*a^4*c + (a^2*b^2*c - 4*a^3*c^2)*x^2 + (a^2*b^3 - 4*a^3*b*c)*x), ((A*a*b^2 - 4*A*a^2*c + (A*b^2*c - 4*A*a*c^2)*x^2 + (A*b^3 - 4*A*a*b*c)*x)*sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(B*a^2*b - A*a*b^2 + 2*A*a^2*c + (2*B*a^2 - A*a*b)*c*x)*sqrt(c*x^2 + b*x + a))/(a^3*b^2 - 4*a^4*c + (a^2*b^2*c - 4*a^3*c^2)*x^2 + (a^2*b^3 - 4*a^3*b*c)*x)]","B",0
967,1,657,0,0.856185," ","integrate((B*x+A)/x^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2} - {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} x^{3} - {\left(2 \, B a b^{3} - 3 \, A b^{4} - 4 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} x^{2} - {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 4 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} x\right)} \sqrt{a} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(A a^{2} b^{2} - 4 \, A a^{3} c - {\left(8 \, A a^{2} c^{2} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} x^{2} - {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 2 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{3} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x\right)}}, -\frac{{\left({\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2} - {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} x^{3} - {\left(2 \, B a b^{3} - 3 \, A b^{4} - 4 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} x^{2} - {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 4 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(A a^{2} b^{2} - 4 \, A a^{3} c - {\left(8 \, A a^{2} c^{2} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} x^{2} - {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 2 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{3} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x\right)}}\right]"," ",0,"[1/4*(((4*(2*B*a^2 - 3*A*a*b)*c^2 - (2*B*a*b^2 - 3*A*b^3)*c)*x^3 - (2*B*a*b^3 - 3*A*b^4 - 4*(2*B*a^2*b - 3*A*a*b^2)*c)*x^2 - (2*B*a^2*b^2 - 3*A*a*b^3 - 4*(2*B*a^3 - 3*A*a^2*b)*c)*x)*sqrt(a)*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(A*a^2*b^2 - 4*A*a^3*c - (8*A*a^2*c^2 + (2*B*a^2*b - 3*A*a*b^2)*c)*x^2 - (2*B*a^2*b^2 - 3*A*a*b^3 - 2*(2*B*a^3 - 5*A*a^2*b)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^3*b^2*c - 4*a^4*c^2)*x^3 + (a^3*b^3 - 4*a^4*b*c)*x^2 + (a^4*b^2 - 4*a^5*c)*x), -1/2*(((4*(2*B*a^2 - 3*A*a*b)*c^2 - (2*B*a*b^2 - 3*A*b^3)*c)*x^3 - (2*B*a*b^3 - 3*A*b^4 - 4*(2*B*a^2*b - 3*A*a*b^2)*c)*x^2 - (2*B*a^2*b^2 - 3*A*a*b^3 - 4*(2*B*a^3 - 3*A*a^2*b)*c)*x)*sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(A*a^2*b^2 - 4*A*a^3*c - (8*A*a^2*c^2 + (2*B*a^2*b - 3*A*a*b^2)*c)*x^2 - (2*B*a^2*b^2 - 3*A*a*b^3 - 2*(2*B*a^3 - 5*A*a^2*b)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^3*b^2*c - 4*a^4*c^2)*x^3 + (a^3*b^3 - 4*a^4*b*c)*x^2 + (a^4*b^2 - 4*a^5*c)*x)]","B",0
968,1,869,0,1.124401," ","integrate((B*x+A)/x^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(16 \, A a^{2} c^{3} + 8 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c^{2} - {\left(4 \, B a b^{3} - 5 \, A b^{4}\right)} c\right)} x^{4} - {\left(4 \, B a b^{4} - 5 \, A b^{5} - 16 \, A a^{2} b c^{2} - 8 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} c\right)} x^{3} - {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4} - 16 \, A a^{3} c^{2} - 8 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(2 \, A a^{3} b^{2} - 8 \, A a^{4} c - {\left(4 \, {\left(8 \, B a^{3} - 13 \, A a^{2} b\right)} c^{2} - 3 \, {\left(4 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} x^{3} + {\left(12 \, B a^{2} b^{3} - 15 \, A a b^{4} - 24 \, A a^{3} c^{2} - 2 \, {\left(20 \, B a^{3} b - 31 \, A a^{2} b^{2}\right)} c\right)} x^{2} + {\left(4 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3} - 4 \, {\left(4 \, B a^{4} - 5 \, A a^{3} b\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left({\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{4} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(16 \, A a^{2} c^{3} + 8 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c^{2} - {\left(4 \, B a b^{3} - 5 \, A b^{4}\right)} c\right)} x^{4} - {\left(4 \, B a b^{4} - 5 \, A b^{5} - 16 \, A a^{2} b c^{2} - 8 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} c\right)} x^{3} - {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4} - 16 \, A a^{3} c^{2} - 8 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(2 \, A a^{3} b^{2} - 8 \, A a^{4} c - {\left(4 \, {\left(8 \, B a^{3} - 13 \, A a^{2} b\right)} c^{2} - 3 \, {\left(4 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} x^{3} + {\left(12 \, B a^{2} b^{3} - 15 \, A a b^{4} - 24 \, A a^{3} c^{2} - 2 \, {\left(20 \, B a^{3} b - 31 \, A a^{2} b^{2}\right)} c\right)} x^{2} + {\left(4 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3} - 4 \, {\left(4 \, B a^{4} - 5 \, A a^{3} b\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left({\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{4} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(3*((16*A*a^2*c^3 + 8*(2*B*a^2*b - 3*A*a*b^2)*c^2 - (4*B*a*b^3 - 5*A*b^4)*c)*x^4 - (4*B*a*b^4 - 5*A*b^5 - 16*A*a^2*b*c^2 - 8*(2*B*a^2*b^2 - 3*A*a*b^3)*c)*x^3 - (4*B*a^2*b^3 - 5*A*a*b^4 - 16*A*a^3*c^2 - 8*(2*B*a^3*b - 3*A*a^2*b^2)*c)*x^2)*sqrt(a)*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(2*A*a^3*b^2 - 8*A*a^4*c - (4*(8*B*a^3 - 13*A*a^2*b)*c^2 - 3*(4*B*a^2*b^2 - 5*A*a*b^3)*c)*x^3 + (12*B*a^2*b^3 - 15*A*a*b^4 - 24*A*a^3*c^2 - 2*(20*B*a^3*b - 31*A*a^2*b^2)*c)*x^2 + (4*B*a^3*b^2 - 5*A*a^2*b^3 - 4*(4*B*a^4 - 5*A*a^3*b)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^4*b^2*c - 4*a^5*c^2)*x^4 + (a^4*b^3 - 4*a^5*b*c)*x^3 + (a^5*b^2 - 4*a^6*c)*x^2), 1/8*(3*((16*A*a^2*c^3 + 8*(2*B*a^2*b - 3*A*a*b^2)*c^2 - (4*B*a*b^3 - 5*A*b^4)*c)*x^4 - (4*B*a*b^4 - 5*A*b^5 - 16*A*a^2*b*c^2 - 8*(2*B*a^2*b^2 - 3*A*a*b^3)*c)*x^3 - (4*B*a^2*b^3 - 5*A*a*b^4 - 16*A*a^3*c^2 - 8*(2*B*a^3*b - 3*A*a^2*b^2)*c)*x^2)*sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(2*A*a^3*b^2 - 8*A*a^4*c - (4*(8*B*a^3 - 13*A*a^2*b)*c^2 - 3*(4*B*a^2*b^2 - 5*A*a*b^3)*c)*x^3 + (12*B*a^2*b^3 - 15*A*a*b^4 - 24*A*a^3*c^2 - 2*(20*B*a^3*b - 31*A*a^2*b^2)*c)*x^2 + (4*B*a^3*b^2 - 5*A*a^2*b^3 - 4*(4*B*a^4 - 5*A*a^3*b)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^4*b^2*c - 4*a^5*c^2)*x^4 + (a^4*b^3 - 4*a^5*b*c)*x^3 + (a^5*b^2 - 4*a^6*c)*x^2)]","B",0
969,1,1093,0,2.056064," ","integrate((B*x+A)/x^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{3} - 8 \, {\left(18 \, B a^{2} b^{2} - 25 \, A a b^{3}\right)} c^{2} + 5 \, {\left(6 \, B a b^{4} - 7 \, A b^{5}\right)} c\right)} x^{5} + {\left(30 \, B a b^{5} - 35 \, A b^{6} + 48 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{2} - 8 \, {\left(18 \, B a^{2} b^{3} - 25 \, A a b^{4}\right)} c\right)} x^{4} + {\left(30 \, B a^{2} b^{4} - 35 \, A a b^{5} + 48 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{2} - 8 \, {\left(18 \, B a^{3} b^{2} - 25 \, A a^{2} b^{3}\right)} c\right)} x^{3}\right)} \sqrt{a} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(8 \, A a^{4} b^{2} - 32 \, A a^{5} c + {\left(256 \, A a^{3} c^{3} + 4 \, {\left(78 \, B a^{3} b - 115 \, A a^{2} b^{2}\right)} c^{2} - 15 \, {\left(6 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} c\right)} x^{4} - {\left(90 \, B a^{2} b^{4} - 105 \, A a b^{5} + 8 \, {\left(18 \, B a^{4} - 61 \, A a^{3} b\right)} c^{2} - 2 \, {\left(186 \, B a^{3} b^{2} - 265 \, A a^{2} b^{3}\right)} c\right)} x^{3} - {\left(30 \, B a^{3} b^{3} - 35 \, A a^{2} b^{4} - 128 \, A a^{4} c^{2} - 4 \, {\left(30 \, B a^{4} b - 43 \, A a^{3} b^{2}\right)} c\right)} x^{2} + 2 \, {\left(6 \, B a^{4} b^{2} - 7 \, A a^{3} b^{3} - 4 \, {\left(6 \, B a^{5} - 7 \, A a^{4} b\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left({\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} x^{5} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{4} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} x^{3}\right)}}, \frac{3 \, {\left({\left(48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{3} - 8 \, {\left(18 \, B a^{2} b^{2} - 25 \, A a b^{3}\right)} c^{2} + 5 \, {\left(6 \, B a b^{4} - 7 \, A b^{5}\right)} c\right)} x^{5} + {\left(30 \, B a b^{5} - 35 \, A b^{6} + 48 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{2} - 8 \, {\left(18 \, B a^{2} b^{3} - 25 \, A a b^{4}\right)} c\right)} x^{4} + {\left(30 \, B a^{2} b^{4} - 35 \, A a b^{5} + 48 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{2} - 8 \, {\left(18 \, B a^{3} b^{2} - 25 \, A a^{2} b^{3}\right)} c\right)} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(8 \, A a^{4} b^{2} - 32 \, A a^{5} c + {\left(256 \, A a^{3} c^{3} + 4 \, {\left(78 \, B a^{3} b - 115 \, A a^{2} b^{2}\right)} c^{2} - 15 \, {\left(6 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} c\right)} x^{4} - {\left(90 \, B a^{2} b^{4} - 105 \, A a b^{5} + 8 \, {\left(18 \, B a^{4} - 61 \, A a^{3} b\right)} c^{2} - 2 \, {\left(186 \, B a^{3} b^{2} - 265 \, A a^{2} b^{3}\right)} c\right)} x^{3} - {\left(30 \, B a^{3} b^{3} - 35 \, A a^{2} b^{4} - 128 \, A a^{4} c^{2} - 4 \, {\left(30 \, B a^{4} b - 43 \, A a^{3} b^{2}\right)} c\right)} x^{2} + 2 \, {\left(6 \, B a^{4} b^{2} - 7 \, A a^{3} b^{3} - 4 \, {\left(6 \, B a^{5} - 7 \, A a^{4} b\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left({\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} x^{5} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{4} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} x^{3}\right)}}\right]"," ",0,"[1/96*(3*((48*(2*B*a^3 - 5*A*a^2*b)*c^3 - 8*(18*B*a^2*b^2 - 25*A*a*b^3)*c^2 + 5*(6*B*a*b^4 - 7*A*b^5)*c)*x^5 + (30*B*a*b^5 - 35*A*b^6 + 48*(2*B*a^3*b - 5*A*a^2*b^2)*c^2 - 8*(18*B*a^2*b^3 - 25*A*a*b^4)*c)*x^4 + (30*B*a^2*b^4 - 35*A*a*b^5 + 48*(2*B*a^4 - 5*A*a^3*b)*c^2 - 8*(18*B*a^3*b^2 - 25*A*a^2*b^3)*c)*x^3)*sqrt(a)*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(8*A*a^4*b^2 - 32*A*a^5*c + (256*A*a^3*c^3 + 4*(78*B*a^3*b - 115*A*a^2*b^2)*c^2 - 15*(6*B*a^2*b^3 - 7*A*a*b^4)*c)*x^4 - (90*B*a^2*b^4 - 105*A*a*b^5 + 8*(18*B*a^4 - 61*A*a^3*b)*c^2 - 2*(186*B*a^3*b^2 - 265*A*a^2*b^3)*c)*x^3 - (30*B*a^3*b^3 - 35*A*a^2*b^4 - 128*A*a^4*c^2 - 4*(30*B*a^4*b - 43*A*a^3*b^2)*c)*x^2 + 2*(6*B*a^4*b^2 - 7*A*a^3*b^3 - 4*(6*B*a^5 - 7*A*a^4*b)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^5*b^2*c - 4*a^6*c^2)*x^5 + (a^5*b^3 - 4*a^6*b*c)*x^4 + (a^6*b^2 - 4*a^7*c)*x^3), 1/48*(3*((48*(2*B*a^3 - 5*A*a^2*b)*c^3 - 8*(18*B*a^2*b^2 - 25*A*a*b^3)*c^2 + 5*(6*B*a*b^4 - 7*A*b^5)*c)*x^5 + (30*B*a*b^5 - 35*A*b^6 + 48*(2*B*a^3*b - 5*A*a^2*b^2)*c^2 - 8*(18*B*a^2*b^3 - 25*A*a*b^4)*c)*x^4 + (30*B*a^2*b^4 - 35*A*a*b^5 + 48*(2*B*a^4 - 5*A*a^3*b)*c^2 - 8*(18*B*a^3*b^2 - 25*A*a^2*b^3)*c)*x^3)*sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(8*A*a^4*b^2 - 32*A*a^5*c + (256*A*a^3*c^3 + 4*(78*B*a^3*b - 115*A*a^2*b^2)*c^2 - 15*(6*B*a^2*b^3 - 7*A*a*b^4)*c)*x^4 - (90*B*a^2*b^4 - 105*A*a*b^5 + 8*(18*B*a^4 - 61*A*a^3*b)*c^2 - 2*(186*B*a^3*b^2 - 265*A*a^2*b^3)*c)*x^3 - (30*B*a^3*b^3 - 35*A*a^2*b^4 - 128*A*a^4*c^2 - 4*(30*B*a^4*b - 43*A*a^3*b^2)*c)*x^2 + 2*(6*B*a^4*b^2 - 7*A*a^3*b^3 - 4*(6*B*a^5 - 7*A*a^4*b)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^5*b^2*c - 4*a^6*c^2)*x^5 + (a^5*b^3 - 4*a^6*b*c)*x^4 + (a^6*b^2 - 4*a^7*c)*x^3)]","A",0
970,1,1601,0,1.476492," ","integrate(x^4*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{2} b^{5} - 32 \, A a^{4} c^{3} + {\left(5 \, B b^{5} c^{2} - 32 \, A a^{2} c^{5} + 16 \, {\left(5 \, B a^{2} b + A a b^{2}\right)} c^{4} - 2 \, {\left(20 \, B a b^{3} + A b^{4}\right)} c^{3}\right)} x^{4} + 2 \, {\left(5 \, B b^{6} c - 32 \, A a^{2} b c^{4} + 16 \, {\left(5 \, B a^{2} b^{2} + A a b^{3}\right)} c^{3} - 2 \, {\left(20 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} x^{3} + 16 \, {\left(5 \, B a^{4} b + A a^{3} b^{2}\right)} c^{2} + {\left(5 \, B b^{7} + 12 \, A a b^{4} c^{2} + 160 \, B a^{3} b c^{3} - 64 \, A a^{3} c^{4} - 2 \, {\left(15 \, B a b^{5} + A b^{6}\right)} c\right)} x^{2} - 2 \, {\left(20 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c + 2 \, {\left(5 \, B a b^{6} - 32 \, A a^{3} b c^{3} + 16 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{2} - 2 \, {\left(20 \, B a^{2} b^{4} + A a b^{5}\right)} c\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(15 \, B a^{2} b^{4} c + 3 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} x^{4} + 8 \, {\left(16 \, B a^{4} + 5 \, A a^{3} b\right)} c^{3} + 4 \, {\left(5 \, B b^{5} c^{2} - 16 \, A a^{2} c^{5} + 2 \, {\left(32 \, B a^{2} b + 7 \, A a b^{2}\right)} c^{4} - {\left(37 \, B a b^{3} + 2 \, A b^{4}\right)} c^{3}\right)} x^{3} - 2 \, {\left(50 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} c^{2} + 3 \, {\left(5 \, B b^{6} c + 64 \, B a^{3} c^{4} + 4 \, {\left(4 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} c^{3} - 2 \, {\left(15 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} x^{2} + 6 \, {\left(5 \, B a b^{5} c - 8 \, A a^{3} c^{4} + 2 \, {\left(26 \, B a^{3} b + 7 \, A a^{2} b^{2}\right)} c^{3} - {\left(35 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6} + {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} x^{4} + 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} x^{3} + {\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} x^{2} + 2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x\right)}}, \frac{3 \, {\left(5 \, B a^{2} b^{5} - 32 \, A a^{4} c^{3} + {\left(5 \, B b^{5} c^{2} - 32 \, A a^{2} c^{5} + 16 \, {\left(5 \, B a^{2} b + A a b^{2}\right)} c^{4} - 2 \, {\left(20 \, B a b^{3} + A b^{4}\right)} c^{3}\right)} x^{4} + 2 \, {\left(5 \, B b^{6} c - 32 \, A a^{2} b c^{4} + 16 \, {\left(5 \, B a^{2} b^{2} + A a b^{3}\right)} c^{3} - 2 \, {\left(20 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} x^{3} + 16 \, {\left(5 \, B a^{4} b + A a^{3} b^{2}\right)} c^{2} + {\left(5 \, B b^{7} + 12 \, A a b^{4} c^{2} + 160 \, B a^{3} b c^{3} - 64 \, A a^{3} c^{4} - 2 \, {\left(15 \, B a b^{5} + A b^{6}\right)} c\right)} x^{2} - 2 \, {\left(20 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c + 2 \, {\left(5 \, B a b^{6} - 32 \, A a^{3} b c^{3} + 16 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{2} - 2 \, {\left(20 \, B a^{2} b^{4} + A a b^{5}\right)} c\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(15 \, B a^{2} b^{4} c + 3 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} x^{4} + 8 \, {\left(16 \, B a^{4} + 5 \, A a^{3} b\right)} c^{3} + 4 \, {\left(5 \, B b^{5} c^{2} - 16 \, A a^{2} c^{5} + 2 \, {\left(32 \, B a^{2} b + 7 \, A a b^{2}\right)} c^{4} - {\left(37 \, B a b^{3} + 2 \, A b^{4}\right)} c^{3}\right)} x^{3} - 2 \, {\left(50 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} c^{2} + 3 \, {\left(5 \, B b^{6} c + 64 \, B a^{3} c^{4} + 4 \, {\left(4 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} c^{3} - 2 \, {\left(15 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} x^{2} + 6 \, {\left(5 \, B a b^{5} c - 8 \, A a^{3} c^{4} + 2 \, {\left(26 \, B a^{3} b + 7 \, A a^{2} b^{2}\right)} c^{3} - {\left(35 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6} + {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} x^{4} + 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} x^{3} + {\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} x^{2} + 2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x\right)}}\right]"," ",0,"[-1/12*(3*(5*B*a^2*b^5 - 32*A*a^4*c^3 + (5*B*b^5*c^2 - 32*A*a^2*c^5 + 16*(5*B*a^2*b + A*a*b^2)*c^4 - 2*(20*B*a*b^3 + A*b^4)*c^3)*x^4 + 2*(5*B*b^6*c - 32*A*a^2*b*c^4 + 16*(5*B*a^2*b^2 + A*a*b^3)*c^3 - 2*(20*B*a*b^4 + A*b^5)*c^2)*x^3 + 16*(5*B*a^4*b + A*a^3*b^2)*c^2 + (5*B*b^7 + 12*A*a*b^4*c^2 + 160*B*a^3*b*c^3 - 64*A*a^3*c^4 - 2*(15*B*a*b^5 + A*b^6)*c)*x^2 - 2*(20*B*a^3*b^3 + A*a^2*b^4)*c + 2*(5*B*a*b^6 - 32*A*a^3*b*c^3 + 16*(5*B*a^3*b^2 + A*a^2*b^3)*c^2 - 2*(20*B*a^2*b^4 + A*a*b^5)*c)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(15*B*a^2*b^4*c + 3*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*x^4 + 8*(16*B*a^4 + 5*A*a^3*b)*c^3 + 4*(5*B*b^5*c^2 - 16*A*a^2*c^5 + 2*(32*B*a^2*b + 7*A*a*b^2)*c^4 - (37*B*a*b^3 + 2*A*b^4)*c^3)*x^3 - 2*(50*B*a^3*b^2 + 3*A*a^2*b^3)*c^2 + 3*(5*B*b^6*c + 64*B*a^3*c^4 + 4*(4*B*a^2*b^2 + 3*A*a*b^3)*c^3 - 2*(15*B*a*b^4 + A*b^5)*c^2)*x^2 + 6*(5*B*a*b^5*c - 8*A*a^3*c^4 + 2*(26*B*a^3*b + 7*A*a^2*b^2)*c^3 - (35*B*a^2*b^3 + 2*A*a*b^4)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6 + (b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*x^4 + 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*x^3 + (b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*x^2 + 2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x), 1/6*(3*(5*B*a^2*b^5 - 32*A*a^4*c^3 + (5*B*b^5*c^2 - 32*A*a^2*c^5 + 16*(5*B*a^2*b + A*a*b^2)*c^4 - 2*(20*B*a*b^3 + A*b^4)*c^3)*x^4 + 2*(5*B*b^6*c - 32*A*a^2*b*c^4 + 16*(5*B*a^2*b^2 + A*a*b^3)*c^3 - 2*(20*B*a*b^4 + A*b^5)*c^2)*x^3 + 16*(5*B*a^4*b + A*a^3*b^2)*c^2 + (5*B*b^7 + 12*A*a*b^4*c^2 + 160*B*a^3*b*c^3 - 64*A*a^3*c^4 - 2*(15*B*a*b^5 + A*b^6)*c)*x^2 - 2*(20*B*a^3*b^3 + A*a^2*b^4)*c + 2*(5*B*a*b^6 - 32*A*a^3*b*c^3 + 16*(5*B*a^3*b^2 + A*a^2*b^3)*c^2 - 2*(20*B*a^2*b^4 + A*a*b^5)*c)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(15*B*a^2*b^4*c + 3*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*x^4 + 8*(16*B*a^4 + 5*A*a^3*b)*c^3 + 4*(5*B*b^5*c^2 - 16*A*a^2*c^5 + 2*(32*B*a^2*b + 7*A*a*b^2)*c^4 - (37*B*a*b^3 + 2*A*b^4)*c^3)*x^3 - 2*(50*B*a^3*b^2 + 3*A*a^2*b^3)*c^2 + 3*(5*B*b^6*c + 64*B*a^3*c^4 + 4*(4*B*a^2*b^2 + 3*A*a*b^3)*c^3 - 2*(15*B*a*b^4 + A*b^5)*c^2)*x^2 + 6*(5*B*a*b^5*c - 8*A*a^3*c^4 + 2*(26*B*a^3*b + 7*A*a^2*b^2)*c^3 - (35*B*a^2*b^3 + 2*A*a*b^4)*c^2)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6 + (b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*x^4 + 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*x^3 + (b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*x^2 + 2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x)]","B",0
971,1,1061,0,1.486049," ","integrate(x^3*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{2} b^{4} - 8 \, B a^{3} b^{2} c + 16 \, B a^{4} c^{2} + {\left(B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right)} x^{4} + 2 \, {\left(B b^{5} c - 8 \, B a b^{3} c^{2} + 16 \, B a^{2} b c^{3}\right)} x^{3} + {\left(B b^{6} - 6 \, B a b^{4} c + 32 \, B a^{3} c^{3}\right)} x^{2} + 2 \, {\left(B a b^{5} - 8 \, B a^{2} b^{3} c + 16 \, B a^{3} b c^{2}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(3 \, B a^{2} b^{3} c - 20 \, B a^{3} b c^{2} + 16 \, A a^{3} c^{3} + {\left(4 \, B b^{4} c^{2} + 4 \, {\left(8 \, B a^{2} + 3 \, A a b\right)} c^{4} - {\left(28 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} x^{3} + 3 \, {\left(B b^{5} c - 6 \, B a b^{3} c^{2} + 2 \, A a b^{2} c^{3} + 8 \, A a^{2} c^{4}\right)} x^{2} + 6 \, {\left(B a b^{4} c - 7 \, B a^{2} b^{2} c^{2} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}, -\frac{3 \, {\left(B a^{2} b^{4} - 8 \, B a^{3} b^{2} c + 16 \, B a^{4} c^{2} + {\left(B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right)} x^{4} + 2 \, {\left(B b^{5} c - 8 \, B a b^{3} c^{2} + 16 \, B a^{2} b c^{3}\right)} x^{3} + {\left(B b^{6} - 6 \, B a b^{4} c + 32 \, B a^{3} c^{3}\right)} x^{2} + 2 \, {\left(B a b^{5} - 8 \, B a^{2} b^{3} c + 16 \, B a^{3} b c^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(3 \, B a^{2} b^{3} c - 20 \, B a^{3} b c^{2} + 16 \, A a^{3} c^{3} + {\left(4 \, B b^{4} c^{2} + 4 \, {\left(8 \, B a^{2} + 3 \, A a b\right)} c^{4} - {\left(28 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} x^{3} + 3 \, {\left(B b^{5} c - 6 \, B a b^{3} c^{2} + 2 \, A a b^{2} c^{3} + 8 \, A a^{2} c^{4}\right)} x^{2} + 6 \, {\left(B a b^{4} c - 7 \, B a^{2} b^{2} c^{2} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(B*a^2*b^4 - 8*B*a^3*b^2*c + 16*B*a^4*c^2 + (B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*x^4 + 2*(B*b^5*c - 8*B*a*b^3*c^2 + 16*B*a^2*b*c^3)*x^3 + (B*b^6 - 6*B*a*b^4*c + 32*B*a^3*c^3)*x^2 + 2*(B*a*b^5 - 8*B*a^2*b^3*c + 16*B*a^3*b*c^2)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(3*B*a^2*b^3*c - 20*B*a^3*b*c^2 + 16*A*a^3*c^3 + (4*B*b^4*c^2 + 4*(8*B*a^2 + 3*A*a*b)*c^4 - (28*B*a*b^2 + A*b^3)*c^3)*x^3 + 3*(B*b^5*c - 6*B*a*b^3*c^2 + 2*A*a*b^2*c^3 + 8*A*a^2*c^4)*x^2 + 6*(B*a*b^4*c - 7*B*a^2*b^2*c^2 + 4*(B*a^3 + A*a^2*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x), -1/3*(3*(B*a^2*b^4 - 8*B*a^3*b^2*c + 16*B*a^4*c^2 + (B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*x^4 + 2*(B*b^5*c - 8*B*a*b^3*c^2 + 16*B*a^2*b*c^3)*x^3 + (B*b^6 - 6*B*a*b^4*c + 32*B*a^3*c^3)*x^2 + 2*(B*a*b^5 - 8*B*a^2*b^3*c + 16*B*a^3*b*c^2)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(3*B*a^2*b^3*c - 20*B*a^3*b*c^2 + 16*A*a^3*c^3 + (4*B*b^4*c^2 + 4*(8*B*a^2 + 3*A*a*b)*c^4 - (28*B*a*b^2 + A*b^3)*c^3)*x^3 + 3*(B*b^5*c - 6*B*a*b^3*c^2 + 2*A*a*b^2*c^3 + 8*A*a^2*c^4)*x^2 + 6*(B*a*b^4*c - 7*B*a^2*b^2*c^2 + 4*(B*a^3 + A*a^2*b)*c^3)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x)]","B",0
972,1,248,0,1.157208," ","integrate(x^2*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(16 \, B a^{3} - 8 \, A a^{2} b - {\left(B b^{3} + 8 \, A a c^{2} - 2 \, {\left(6 \, B a b - A b^{2}\right)} c\right)} x^{3} + 3 \, {\left(2 \, B a b^{2} - A b^{3} + 4 \, {\left(2 \, B a^{2} - A a b\right)} c\right)} x^{2} + 12 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"-2/3*(16*B*a^3 - 8*A*a^2*b - (B*b^3 + 8*A*a*c^2 - 2*(6*B*a*b - A*b^2)*c)*x^3 + 3*(2*B*a*b^2 - A*b^3 + 4*(2*B*a^2 - A*a*b)*c)*x^2 + 12*(2*B*a^2*b - A*a*b^2)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
973,1,244,0,1.197465," ","integrate(x*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, B a^{2} b - 2 \, A a b^{2} - 8 \, A a^{2} c + 2 \, {\left(B b^{2} c + 4 \, {\left(B a - A b\right)} c^{2}\right)} x^{3} + 3 \, {\left(B b^{3} + 4 \, {\left(B a b - A b^{2}\right)} c\right)} x^{2} + 3 \, {\left(4 \, B a b^{2} - A b^{3} - 4 \, A a b c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"2/3*(8*B*a^2*b - 2*A*a*b^2 - 8*A*a^2*c + 2*(B*b^2*c + 4*(B*a - A*b)*c^2)*x^3 + 3*(B*b^3 + 4*(B*a*b - A*b^2)*c)*x^2 + 3*(4*B*a*b^2 - A*b^3 - 4*A*a*b*c)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
974,1,245,0,1.140462," ","integrate((B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, B a b^{2} + A b^{3} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} x^{3} + 12 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} x^{2} + 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c + 3 \, {\left(B b^{3} - 8 \, A a c^{2} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"-2/3*(2*B*a*b^2 + A*b^3 + 8*(B*b*c^2 - 2*A*c^3)*x^3 + 12*(B*b^2*c - 2*A*b*c^2)*x^2 + 4*(2*B*a^2 - 3*A*a*b)*c + 3*(B*b^3 - 8*A*a*c^2 + 2*(2*B*a*b - A*b^2)*c)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
975,1,1077,0,2.370524," ","integrate((B*x+A)/x/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A a^{2} b^{4} - 8 \, A a^{3} b^{2} c + 16 \, A a^{4} c^{2} + {\left(A b^{4} c^{2} - 8 \, A a b^{2} c^{3} + 16 \, A a^{2} c^{4}\right)} x^{4} + 2 \, {\left(A b^{5} c - 8 \, A a b^{3} c^{2} + 16 \, A a^{2} b c^{3}\right)} x^{3} + {\left(A b^{6} - 6 \, A a b^{4} c + 32 \, A a^{3} c^{3}\right)} x^{2} + 2 \, {\left(A a b^{5} - 8 \, A a^{2} b^{3} c + 16 \, A a^{3} b c^{2}\right)} x\right)} \sqrt{a} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(B a^{3} b^{3} - 4 \, A a^{2} b^{4} - 32 \, A a^{4} c^{2} - {\left(3 \, A a b^{3} c^{2} + 4 \, {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} c^{3}\right)} x^{3} - 6 \, {\left(A a b^{4} c + 4 \, A a^{3} c^{3} + {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} c^{2}\right)} x^{2} - 4 \, {\left(3 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} c - 3 \, {\left(A a b^{5} + 8 \, B a^{4} c^{2} + 2 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{3} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x\right)}}, \frac{3 \, {\left(A a^{2} b^{4} - 8 \, A a^{3} b^{2} c + 16 \, A a^{4} c^{2} + {\left(A b^{4} c^{2} - 8 \, A a b^{2} c^{3} + 16 \, A a^{2} c^{4}\right)} x^{4} + 2 \, {\left(A b^{5} c - 8 \, A a b^{3} c^{2} + 16 \, A a^{2} b c^{3}\right)} x^{3} + {\left(A b^{6} - 6 \, A a b^{4} c + 32 \, A a^{3} c^{3}\right)} x^{2} + 2 \, {\left(A a b^{5} - 8 \, A a^{2} b^{3} c + 16 \, A a^{3} b c^{2}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(B a^{3} b^{3} - 4 \, A a^{2} b^{4} - 32 \, A a^{4} c^{2} - {\left(3 \, A a b^{3} c^{2} + 4 \, {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} c^{3}\right)} x^{3} - 6 \, {\left(A a b^{4} c + 4 \, A a^{3} c^{3} + {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} c^{2}\right)} x^{2} - 4 \, {\left(3 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} c - 3 \, {\left(A a b^{5} + 8 \, B a^{4} c^{2} + 2 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{3} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(A*a^2*b^4 - 8*A*a^3*b^2*c + 16*A*a^4*c^2 + (A*b^4*c^2 - 8*A*a*b^2*c^3 + 16*A*a^2*c^4)*x^4 + 2*(A*b^5*c - 8*A*a*b^3*c^2 + 16*A*a^2*b*c^3)*x^3 + (A*b^6 - 6*A*a*b^4*c + 32*A*a^3*c^3)*x^2 + 2*(A*a*b^5 - 8*A*a^2*b^3*c + 16*A*a^3*b*c^2)*x)*sqrt(a)*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(B*a^3*b^3 - 4*A*a^2*b^4 - 32*A*a^4*c^2 - (3*A*a*b^3*c^2 + 4*(4*B*a^3 - 5*A*a^2*b)*c^3)*x^3 - 6*(A*a*b^4*c + 4*A*a^3*c^3 + (4*B*a^3*b - 7*A*a^2*b^2)*c^2)*x^2 - 4*(3*B*a^4*b - 7*A*a^3*b^2)*c - 3*(A*a*b^5 + 8*B*a^4*c^2 + 2*(B*a^3*b^2 - 3*A*a^2*b^3)*c)*x)*sqrt(c*x^2 + b*x + a))/(a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + (a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^4 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^3 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^2 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x), 1/3*(3*(A*a^2*b^4 - 8*A*a^3*b^2*c + 16*A*a^4*c^2 + (A*b^4*c^2 - 8*A*a*b^2*c^3 + 16*A*a^2*c^4)*x^4 + 2*(A*b^5*c - 8*A*a*b^3*c^2 + 16*A*a^2*b*c^3)*x^3 + (A*b^6 - 6*A*a*b^4*c + 32*A*a^3*c^3)*x^2 + 2*(A*a*b^5 - 8*A*a^2*b^3*c + 16*A*a^3*b*c^2)*x)*sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(B*a^3*b^3 - 4*A*a^2*b^4 - 32*A*a^4*c^2 - (3*A*a*b^3*c^2 + 4*(4*B*a^3 - 5*A*a^2*b)*c^3)*x^3 - 6*(A*a*b^4*c + 4*A*a^3*c^3 + (4*B*a^3*b - 7*A*a^2*b^2)*c^2)*x^2 - 4*(3*B*a^4*b - 7*A*a^3*b^2)*c - 3*(A*a*b^5 + 8*B*a^4*c^2 + 2*(B*a^3*b^2 - 3*A*a^2*b^3)*c)*x)*sqrt(c*x^2 + b*x + a))/(a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + (a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^4 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^3 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^2 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x)]","B",0
976,1,1655,0,3.322665," ","integrate((B*x+A)/x^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(16 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{4} - 8 \, {\left(2 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{3} + {\left(2 \, B a b^{4} - 5 \, A b^{5}\right)} c^{2}\right)} x^{5} + 2 \, {\left(16 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3} - 8 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2} + {\left(2 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} x^{4} + {\left(2 \, B a b^{6} - 5 \, A b^{7} + 32 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{3} - 6 \, {\left(2 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} x^{3} + 2 \, {\left(2 \, B a^{2} b^{5} - 5 \, A a b^{6} + 16 \, {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} c^{2} - 8 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} x^{2} + {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(2 \, B a^{5} - 5 \, A a^{4} b\right)} c^{2} - 8 \, {\left(2 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} c\right)} x\right)} \sqrt{a} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(3 \, A a^{3} b^{4} - 24 \, A a^{4} b^{2} c + 48 \, A a^{5} c^{2} + {\left(128 \, A a^{3} c^{4} + 20 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3} - 3 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2}\right)} x^{4} - 6 \, {\left(4 \, {\left(2 \, B a^{4} - 13 \, A a^{3} b\right)} c^{3} - 7 \, {\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2} + {\left(2 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} x^{3} - 3 \, {\left(2 \, B a^{2} b^{5} - 5 \, A a b^{6} - 16 \, A a^{3} b^{2} c^{2} - 64 \, A a^{4} c^{3} - 6 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} x^{2} - 4 \, {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(B a^{5} - 4 \, A a^{4} b\right)} c^{2} - {\left(14 \, B a^{4} b^{2} - 37 \, A a^{3} b^{3}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left({\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)} x^{5} + 2 \, {\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)} x^{4} + {\left(a^{4} b^{6} - 6 \, a^{5} b^{4} c + 32 \, a^{7} c^{3}\right)} x^{3} + 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} x^{2} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} x\right)}}, \frac{3 \, {\left({\left(16 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{4} - 8 \, {\left(2 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{3} + {\left(2 \, B a b^{4} - 5 \, A b^{5}\right)} c^{2}\right)} x^{5} + 2 \, {\left(16 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3} - 8 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2} + {\left(2 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} x^{4} + {\left(2 \, B a b^{6} - 5 \, A b^{7} + 32 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{3} - 6 \, {\left(2 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} x^{3} + 2 \, {\left(2 \, B a^{2} b^{5} - 5 \, A a b^{6} + 16 \, {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} c^{2} - 8 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} x^{2} + {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(2 \, B a^{5} - 5 \, A a^{4} b\right)} c^{2} - 8 \, {\left(2 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} c\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(3 \, A a^{3} b^{4} - 24 \, A a^{4} b^{2} c + 48 \, A a^{5} c^{2} + {\left(128 \, A a^{3} c^{4} + 20 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3} - 3 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2}\right)} x^{4} - 6 \, {\left(4 \, {\left(2 \, B a^{4} - 13 \, A a^{3} b\right)} c^{3} - 7 \, {\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2} + {\left(2 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} x^{3} - 3 \, {\left(2 \, B a^{2} b^{5} - 5 \, A a b^{6} - 16 \, A a^{3} b^{2} c^{2} - 64 \, A a^{4} c^{3} - 6 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} x^{2} - 4 \, {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(B a^{5} - 4 \, A a^{4} b\right)} c^{2} - {\left(14 \, B a^{4} b^{2} - 37 \, A a^{3} b^{3}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left({\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)} x^{5} + 2 \, {\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)} x^{4} + {\left(a^{4} b^{6} - 6 \, a^{5} b^{4} c + 32 \, a^{7} c^{3}\right)} x^{3} + 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} x^{2} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} x\right)}}\right]"," ",0,"[-1/12*(3*((16*(2*B*a^3 - 5*A*a^2*b)*c^4 - 8*(2*B*a^2*b^2 - 5*A*a*b^3)*c^3 + (2*B*a*b^4 - 5*A*b^5)*c^2)*x^5 + 2*(16*(2*B*a^3*b - 5*A*a^2*b^2)*c^3 - 8*(2*B*a^2*b^3 - 5*A*a*b^4)*c^2 + (2*B*a*b^5 - 5*A*b^6)*c)*x^4 + (2*B*a*b^6 - 5*A*b^7 + 32*(2*B*a^4 - 5*A*a^3*b)*c^3 - 6*(2*B*a^2*b^4 - 5*A*a*b^5)*c)*x^3 + 2*(2*B*a^2*b^5 - 5*A*a*b^6 + 16*(2*B*a^4*b - 5*A*a^3*b^2)*c^2 - 8*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c)*x^2 + (2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(2*B*a^5 - 5*A*a^4*b)*c^2 - 8*(2*B*a^4*b^2 - 5*A*a^3*b^3)*c)*x)*sqrt(a)*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(3*A*a^3*b^4 - 24*A*a^4*b^2*c + 48*A*a^5*c^2 + (128*A*a^3*c^4 + 20*(2*B*a^3*b - 5*A*a^2*b^2)*c^3 - 3*(2*B*a^2*b^3 - 5*A*a*b^4)*c^2)*x^4 - 6*(4*(2*B*a^4 - 13*A*a^3*b)*c^3 - 7*(2*B*a^3*b^2 - 5*A*a^2*b^3)*c^2 + (2*B*a^2*b^4 - 5*A*a*b^5)*c)*x^3 - 3*(2*B*a^2*b^5 - 5*A*a*b^6 - 16*A*a^3*b^2*c^2 - 64*A*a^4*c^3 - 6*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c)*x^2 - 4*(2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(B*a^5 - 4*A*a^4*b)*c^2 - (14*B*a^4*b^2 - 37*A*a^3*b^3)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)*x^5 + 2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)*x^4 + (a^4*b^6 - 6*a^5*b^4*c + 32*a^7*c^3)*x^3 + 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*x^2 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*x), 1/6*(3*((16*(2*B*a^3 - 5*A*a^2*b)*c^4 - 8*(2*B*a^2*b^2 - 5*A*a*b^3)*c^3 + (2*B*a*b^4 - 5*A*b^5)*c^2)*x^5 + 2*(16*(2*B*a^3*b - 5*A*a^2*b^2)*c^3 - 8*(2*B*a^2*b^3 - 5*A*a*b^4)*c^2 + (2*B*a*b^5 - 5*A*b^6)*c)*x^4 + (2*B*a*b^6 - 5*A*b^7 + 32*(2*B*a^4 - 5*A*a^3*b)*c^3 - 6*(2*B*a^2*b^4 - 5*A*a*b^5)*c)*x^3 + 2*(2*B*a^2*b^5 - 5*A*a*b^6 + 16*(2*B*a^4*b - 5*A*a^3*b^2)*c^2 - 8*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c)*x^2 + (2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(2*B*a^5 - 5*A*a^4*b)*c^2 - 8*(2*B*a^4*b^2 - 5*A*a^3*b^3)*c)*x)*sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(3*A*a^3*b^4 - 24*A*a^4*b^2*c + 48*A*a^5*c^2 + (128*A*a^3*c^4 + 20*(2*B*a^3*b - 5*A*a^2*b^2)*c^3 - 3*(2*B*a^2*b^3 - 5*A*a*b^4)*c^2)*x^4 - 6*(4*(2*B*a^4 - 13*A*a^3*b)*c^3 - 7*(2*B*a^3*b^2 - 5*A*a^2*b^3)*c^2 + (2*B*a^2*b^4 - 5*A*a*b^5)*c)*x^3 - 3*(2*B*a^2*b^5 - 5*A*a*b^6 - 16*A*a^3*b^2*c^2 - 64*A*a^4*c^3 - 6*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c)*x^2 - 4*(2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(B*a^5 - 4*A*a^4*b)*c^2 - (14*B*a^4*b^2 - 37*A*a^3*b^3)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)*x^5 + 2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)*x^4 + (a^4*b^6 - 6*a^5*b^4*c + 32*a^7*c^3)*x^3 + 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*x^2 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*x)]","B",0
977,1,2057,0,8.991135," ","integrate((B*x+A)/x^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(64 \, A a^{3} c^{5} + 16 \, {\left(4 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} c^{4} - 4 \, {\left(8 \, B a^{2} b^{3} - 15 \, A a b^{4}\right)} c^{3} + {\left(4 \, B a b^{5} - 7 \, A b^{6}\right)} c^{2}\right)} x^{6} + 2 \, {\left(64 \, A a^{3} b c^{4} + 16 \, {\left(4 \, B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} c^{3} - 4 \, {\left(8 \, B a^{2} b^{4} - 15 \, A a b^{5}\right)} c^{2} + {\left(4 \, B a b^{6} - 7 \, A b^{7}\right)} c\right)} x^{5} + {\left(4 \, B a b^{7} - 7 \, A b^{8} - 24 \, A a^{2} b^{4} c^{2} + 128 \, A a^{4} c^{4} + 32 \, {\left(4 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} c^{3} - 2 \, {\left(12 \, B a^{2} b^{5} - 23 \, A a b^{6}\right)} c\right)} x^{4} + 2 \, {\left(4 \, B a^{2} b^{6} - 7 \, A a b^{7} + 64 \, A a^{4} b c^{3} + 16 \, {\left(4 \, B a^{4} b^{2} - 9 \, A a^{3} b^{3}\right)} c^{2} - 4 \, {\left(8 \, B a^{3} b^{4} - 15 \, A a^{2} b^{5}\right)} c\right)} x^{3} + {\left(4 \, B a^{3} b^{5} - 7 \, A a^{2} b^{6} + 64 \, A a^{5} c^{3} + 16 \, {\left(4 \, B a^{5} b - 9 \, A a^{4} b^{2}\right)} c^{2} - 4 \, {\left(8 \, B a^{4} b^{3} - 15 \, A a^{3} b^{4}\right)} c\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(6 \, A a^{4} b^{4} - 48 \, A a^{5} b^{2} c + 96 \, A a^{6} c^{2} + {\left(16 \, {\left(32 \, B a^{4} - 81 \, A a^{3} b\right)} c^{4} - 40 \, {\left(10 \, B a^{3} b^{2} - 19 \, A a^{2} b^{3}\right)} c^{3} + 15 \, {\left(4 \, B a^{2} b^{4} - 7 \, A a b^{5}\right)} c^{2}\right)} x^{5} + 6 \, {\left(80 \, A a^{4} c^{4} + 8 \, {\left(26 \, B a^{4} b - 63 \, A a^{3} b^{2}\right)} c^{3} - 5 \, {\left(28 \, B a^{3} b^{3} - 53 \, A a^{2} b^{4}\right)} c^{2} + 5 \, {\left(4 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} c\right)} x^{4} + 3 \, {\left(20 \, B a^{2} b^{6} - 35 \, A a b^{7} + 64 \, {\left(4 \, B a^{5} - 7 \, A a^{4} b\right)} c^{3} + 8 \, {\left(8 \, B a^{4} b^{2} - 29 \, A a^{3} b^{3}\right)} c^{2} - 10 \, {\left(12 \, B a^{3} b^{4} - 23 \, A a^{2} b^{5}\right)} c\right)} x^{3} + 4 \, {\left(20 \, B a^{3} b^{5} - 35 \, A a^{2} b^{6} + 160 \, A a^{5} c^{3} + 4 \, {\left(64 \, B a^{5} b - 147 \, A a^{4} b^{2}\right)} c^{2} - {\left(148 \, B a^{4} b^{3} - 279 \, A a^{3} b^{4}\right)} c\right)} x^{2} + 3 \, {\left(4 \, B a^{4} b^{4} - 7 \, A a^{3} b^{5} + 16 \, {\left(4 \, B a^{6} - 7 \, A a^{5} b\right)} c^{2} - 8 \, {\left(4 \, B a^{5} b^{2} - 7 \, A a^{4} b^{3}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left({\left(a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} x^{6} + 2 \, {\left(a^{5} b^{5} c - 8 \, a^{6} b^{3} c^{2} + 16 \, a^{7} b c^{3}\right)} x^{5} + {\left(a^{5} b^{6} - 6 \, a^{6} b^{4} c + 32 \, a^{8} c^{3}\right)} x^{4} + 2 \, {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} x^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} x^{2}\right)}}, -\frac{15 \, {\left({\left(64 \, A a^{3} c^{5} + 16 \, {\left(4 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} c^{4} - 4 \, {\left(8 \, B a^{2} b^{3} - 15 \, A a b^{4}\right)} c^{3} + {\left(4 \, B a b^{5} - 7 \, A b^{6}\right)} c^{2}\right)} x^{6} + 2 \, {\left(64 \, A a^{3} b c^{4} + 16 \, {\left(4 \, B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} c^{3} - 4 \, {\left(8 \, B a^{2} b^{4} - 15 \, A a b^{5}\right)} c^{2} + {\left(4 \, B a b^{6} - 7 \, A b^{7}\right)} c\right)} x^{5} + {\left(4 \, B a b^{7} - 7 \, A b^{8} - 24 \, A a^{2} b^{4} c^{2} + 128 \, A a^{4} c^{4} + 32 \, {\left(4 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} c^{3} - 2 \, {\left(12 \, B a^{2} b^{5} - 23 \, A a b^{6}\right)} c\right)} x^{4} + 2 \, {\left(4 \, B a^{2} b^{6} - 7 \, A a b^{7} + 64 \, A a^{4} b c^{3} + 16 \, {\left(4 \, B a^{4} b^{2} - 9 \, A a^{3} b^{3}\right)} c^{2} - 4 \, {\left(8 \, B a^{3} b^{4} - 15 \, A a^{2} b^{5}\right)} c\right)} x^{3} + {\left(4 \, B a^{3} b^{5} - 7 \, A a^{2} b^{6} + 64 \, A a^{5} c^{3} + 16 \, {\left(4 \, B a^{5} b - 9 \, A a^{4} b^{2}\right)} c^{2} - 4 \, {\left(8 \, B a^{4} b^{3} - 15 \, A a^{3} b^{4}\right)} c\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(6 \, A a^{4} b^{4} - 48 \, A a^{5} b^{2} c + 96 \, A a^{6} c^{2} + {\left(16 \, {\left(32 \, B a^{4} - 81 \, A a^{3} b\right)} c^{4} - 40 \, {\left(10 \, B a^{3} b^{2} - 19 \, A a^{2} b^{3}\right)} c^{3} + 15 \, {\left(4 \, B a^{2} b^{4} - 7 \, A a b^{5}\right)} c^{2}\right)} x^{5} + 6 \, {\left(80 \, A a^{4} c^{4} + 8 \, {\left(26 \, B a^{4} b - 63 \, A a^{3} b^{2}\right)} c^{3} - 5 \, {\left(28 \, B a^{3} b^{3} - 53 \, A a^{2} b^{4}\right)} c^{2} + 5 \, {\left(4 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} c\right)} x^{4} + 3 \, {\left(20 \, B a^{2} b^{6} - 35 \, A a b^{7} + 64 \, {\left(4 \, B a^{5} - 7 \, A a^{4} b\right)} c^{3} + 8 \, {\left(8 \, B a^{4} b^{2} - 29 \, A a^{3} b^{3}\right)} c^{2} - 10 \, {\left(12 \, B a^{3} b^{4} - 23 \, A a^{2} b^{5}\right)} c\right)} x^{3} + 4 \, {\left(20 \, B a^{3} b^{5} - 35 \, A a^{2} b^{6} + 160 \, A a^{5} c^{3} + 4 \, {\left(64 \, B a^{5} b - 147 \, A a^{4} b^{2}\right)} c^{2} - {\left(148 \, B a^{4} b^{3} - 279 \, A a^{3} b^{4}\right)} c\right)} x^{2} + 3 \, {\left(4 \, B a^{4} b^{4} - 7 \, A a^{3} b^{5} + 16 \, {\left(4 \, B a^{6} - 7 \, A a^{5} b\right)} c^{2} - 8 \, {\left(4 \, B a^{5} b^{2} - 7 \, A a^{4} b^{3}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{24 \, {\left({\left(a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} x^{6} + 2 \, {\left(a^{5} b^{5} c - 8 \, a^{6} b^{3} c^{2} + 16 \, a^{7} b c^{3}\right)} x^{5} + {\left(a^{5} b^{6} - 6 \, a^{6} b^{4} c + 32 \, a^{8} c^{3}\right)} x^{4} + 2 \, {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} x^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/48*(15*((64*A*a^3*c^5 + 16*(4*B*a^3*b - 9*A*a^2*b^2)*c^4 - 4*(8*B*a^2*b^3 - 15*A*a*b^4)*c^3 + (4*B*a*b^5 - 7*A*b^6)*c^2)*x^6 + 2*(64*A*a^3*b*c^4 + 16*(4*B*a^3*b^2 - 9*A*a^2*b^3)*c^3 - 4*(8*B*a^2*b^4 - 15*A*a*b^5)*c^2 + (4*B*a*b^6 - 7*A*b^7)*c)*x^5 + (4*B*a*b^7 - 7*A*b^8 - 24*A*a^2*b^4*c^2 + 128*A*a^4*c^4 + 32*(4*B*a^4*b - 7*A*a^3*b^2)*c^3 - 2*(12*B*a^2*b^5 - 23*A*a*b^6)*c)*x^4 + 2*(4*B*a^2*b^6 - 7*A*a*b^7 + 64*A*a^4*b*c^3 + 16*(4*B*a^4*b^2 - 9*A*a^3*b^3)*c^2 - 4*(8*B*a^3*b^4 - 15*A*a^2*b^5)*c)*x^3 + (4*B*a^3*b^5 - 7*A*a^2*b^6 + 64*A*a^5*c^3 + 16*(4*B*a^5*b - 9*A*a^4*b^2)*c^2 - 4*(8*B*a^4*b^3 - 15*A*a^3*b^4)*c)*x^2)*sqrt(a)*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(6*A*a^4*b^4 - 48*A*a^5*b^2*c + 96*A*a^6*c^2 + (16*(32*B*a^4 - 81*A*a^3*b)*c^4 - 40*(10*B*a^3*b^2 - 19*A*a^2*b^3)*c^3 + 15*(4*B*a^2*b^4 - 7*A*a*b^5)*c^2)*x^5 + 6*(80*A*a^4*c^4 + 8*(26*B*a^4*b - 63*A*a^3*b^2)*c^3 - 5*(28*B*a^3*b^3 - 53*A*a^2*b^4)*c^2 + 5*(4*B*a^2*b^5 - 7*A*a*b^6)*c)*x^4 + 3*(20*B*a^2*b^6 - 35*A*a*b^7 + 64*(4*B*a^5 - 7*A*a^4*b)*c^3 + 8*(8*B*a^4*b^2 - 29*A*a^3*b^3)*c^2 - 10*(12*B*a^3*b^4 - 23*A*a^2*b^5)*c)*x^3 + 4*(20*B*a^3*b^5 - 35*A*a^2*b^6 + 160*A*a^5*c^3 + 4*(64*B*a^5*b - 147*A*a^4*b^2)*c^2 - (148*B*a^4*b^3 - 279*A*a^3*b^4)*c)*x^2 + 3*(4*B*a^4*b^4 - 7*A*a^3*b^5 + 16*(4*B*a^6 - 7*A*a^5*b)*c^2 - 8*(4*B*a^5*b^2 - 7*A*a^4*b^3)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^5*b^4*c^2 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*x^6 + 2*(a^5*b^5*c - 8*a^6*b^3*c^2 + 16*a^7*b*c^3)*x^5 + (a^5*b^6 - 6*a^6*b^4*c + 32*a^8*c^3)*x^4 + 2*(a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*x^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*x^2), -1/24*(15*((64*A*a^3*c^5 + 16*(4*B*a^3*b - 9*A*a^2*b^2)*c^4 - 4*(8*B*a^2*b^3 - 15*A*a*b^4)*c^3 + (4*B*a*b^5 - 7*A*b^6)*c^2)*x^6 + 2*(64*A*a^3*b*c^4 + 16*(4*B*a^3*b^2 - 9*A*a^2*b^3)*c^3 - 4*(8*B*a^2*b^4 - 15*A*a*b^5)*c^2 + (4*B*a*b^6 - 7*A*b^7)*c)*x^5 + (4*B*a*b^7 - 7*A*b^8 - 24*A*a^2*b^4*c^2 + 128*A*a^4*c^4 + 32*(4*B*a^4*b - 7*A*a^3*b^2)*c^3 - 2*(12*B*a^2*b^5 - 23*A*a*b^6)*c)*x^4 + 2*(4*B*a^2*b^6 - 7*A*a*b^7 + 64*A*a^4*b*c^3 + 16*(4*B*a^4*b^2 - 9*A*a^3*b^3)*c^2 - 4*(8*B*a^3*b^4 - 15*A*a^2*b^5)*c)*x^3 + (4*B*a^3*b^5 - 7*A*a^2*b^6 + 64*A*a^5*c^3 + 16*(4*B*a^5*b - 9*A*a^4*b^2)*c^2 - 4*(8*B*a^4*b^3 - 15*A*a^3*b^4)*c)*x^2)*sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(6*A*a^4*b^4 - 48*A*a^5*b^2*c + 96*A*a^6*c^2 + (16*(32*B*a^4 - 81*A*a^3*b)*c^4 - 40*(10*B*a^3*b^2 - 19*A*a^2*b^3)*c^3 + 15*(4*B*a^2*b^4 - 7*A*a*b^5)*c^2)*x^5 + 6*(80*A*a^4*c^4 + 8*(26*B*a^4*b - 63*A*a^3*b^2)*c^3 - 5*(28*B*a^3*b^3 - 53*A*a^2*b^4)*c^2 + 5*(4*B*a^2*b^5 - 7*A*a*b^6)*c)*x^4 + 3*(20*B*a^2*b^6 - 35*A*a*b^7 + 64*(4*B*a^5 - 7*A*a^4*b)*c^3 + 8*(8*B*a^4*b^2 - 29*A*a^3*b^3)*c^2 - 10*(12*B*a^3*b^4 - 23*A*a^2*b^5)*c)*x^3 + 4*(20*B*a^3*b^5 - 35*A*a^2*b^6 + 160*A*a^5*c^3 + 4*(64*B*a^5*b - 147*A*a^4*b^2)*c^2 - (148*B*a^4*b^3 - 279*A*a^3*b^4)*c)*x^2 + 3*(4*B*a^4*b^4 - 7*A*a^3*b^5 + 16*(4*B*a^6 - 7*A*a^5*b)*c^2 - 8*(4*B*a^5*b^2 - 7*A*a^4*b^3)*c)*x)*sqrt(c*x^2 + b*x + a))/((a^5*b^4*c^2 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*x^6 + 2*(a^5*b^5*c - 8*a^6*b^3*c^2 + 16*a^7*b*c^3)*x^5 + (a^5*b^6 - 6*a^6*b^4*c + 32*a^8*c^3)*x^4 + 2*(a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*x^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*x^2)]","B",0
978,1,550,0,5.312436," ","integrate((e*x+d)/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, {\left(2 \, c^{5} d - b c^{4} e\right)} x^{5} + 320 \, {\left(2 \, b c^{4} d - b^{2} c^{3} e\right)} x^{4} + 80 \, {\left(2 \, {\left(3 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d - {\left(3 \, b^{3} c^{2} + 4 \, a b c^{3}\right)} e\right)} x^{3} + 40 \, {\left(2 \, {\left(b^{3} c^{2} + 12 \, a b c^{3}\right)} d - {\left(b^{4} c + 12 \, a b^{2} c^{2}\right)} e\right)} x^{2} + {\left(3 \, b^{5} - 40 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} d + 2 \, {\left(a b^{4} - 24 \, a^{2} b^{2} c - 48 \, a^{3} c^{2}\right)} e - 5 \, {\left(2 \, {\left(b^{4} c - 24 \, a b^{2} c^{2} - 48 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 24 \, a b^{3} c - 48 \, a^{2} b c^{2}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{6} + 3 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(b^{8} c - 11 \, a b^{6} c^{2} + 36 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} x^{4} + {\left(b^{9} - 6 \, a b^{7} c - 24 \, a^{2} b^{5} c^{2} + 224 \, a^{3} b^{3} c^{3} - 384 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a b^{8} - 11 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} - 16 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)}}"," ",0,"-2/15*(128*(2*c^5*d - b*c^4*e)*x^5 + 320*(2*b*c^4*d - b^2*c^3*e)*x^4 + 80*(2*(3*b^2*c^3 + 4*a*c^4)*d - (3*b^3*c^2 + 4*a*b*c^3)*e)*x^3 + 40*(2*(b^3*c^2 + 12*a*b*c^3)*d - (b^4*c + 12*a*b^2*c^2)*e)*x^2 + (3*b^5 - 40*a*b^3*c + 240*a^2*b*c^2)*d + 2*(a*b^4 - 24*a^2*b^2*c - 48*a^3*c^2)*e - 5*(2*(b^4*c - 24*a*b^2*c^2 - 48*a^2*c^3)*d - (b^5 - 24*a*b^3*c - 48*a^2*b*c^2)*e)*x)*sqrt(c*x^2 + b*x + a)/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^6 + 3*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 3*(b^8*c - 11*a*b^6*c^2 + 36*a^2*b^4*c^3 - 16*a^3*b^2*c^4 - 64*a^4*c^5)*x^4 + (b^9 - 6*a*b^7*c - 24*a^2*b^5*c^2 + 224*a^3*b^3*c^3 - 384*a^4*b*c^4)*x^3 + 3*(a*b^8 - 11*a^2*b^6*c + 36*a^3*b^4*c^2 - 16*a^4*b^2*c^3 - 64*a^5*c^4)*x^2 + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)","B",0
979,1,941,0,26.442143," ","integrate((e*x+d)/(c*x^2+b*x+a)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1024 \, {\left(2 \, c^{7} d - b c^{6} e\right)} x^{7} + 3584 \, {\left(2 \, b c^{6} d - b^{2} c^{5} e\right)} x^{6} + 896 \, {\left(2 \, {\left(5 \, b^{2} c^{5} + 4 \, a c^{6}\right)} d - {\left(5 \, b^{3} c^{4} + 4 \, a b c^{5}\right)} e\right)} x^{5} + 2240 \, {\left(2 \, {\left(b^{3} c^{4} + 4 \, a b c^{5}\right)} d - {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4}\right)} e\right)} x^{4} + 280 \, {\left(2 \, {\left(b^{4} c^{3} + 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d - {\left(b^{5} c^{2} + 24 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e\right)} x^{3} - 28 \, {\left(2 \, {\left(b^{5} c^{2} - 40 \, a b^{3} c^{3} - 240 \, a^{2} b c^{4}\right)} d - {\left(b^{6} c - 40 \, a b^{4} c^{2} - 240 \, a^{2} b^{2} c^{3}\right)} e\right)} x^{2} - {\left(5 \, b^{7} - 84 \, a b^{5} c + 560 \, a^{2} b^{3} c^{2} - 2240 \, a^{3} b c^{3}\right)} d - 2 \, {\left(a b^{6} - 20 \, a^{2} b^{4} c + 240 \, a^{3} b^{2} c^{2} + 320 \, a^{4} c^{3}\right)} e + 7 \, {\left(2 \, {\left(b^{6} c - 20 \, a b^{4} c^{2} + 240 \, a^{2} b^{2} c^{3} + 320 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 20 \, a b^{5} c + 240 \, a^{2} b^{3} c^{2} + 320 \, a^{3} b c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{35 \, {\left(a^{4} b^{8} - 16 \, a^{5} b^{6} c + 96 \, a^{6} b^{4} c^{2} - 256 \, a^{7} b^{2} c^{3} + 256 \, a^{8} c^{4} + {\left(b^{8} c^{4} - 16 \, a b^{6} c^{5} + 96 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} + 256 \, a^{4} c^{8}\right)} x^{8} + 4 \, {\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{7} + 2 \, {\left(3 \, b^{10} c^{2} - 46 \, a b^{8} c^{3} + 256 \, a^{2} b^{6} c^{4} - 576 \, a^{3} b^{4} c^{5} + 256 \, a^{4} b^{2} c^{6} + 512 \, a^{5} c^{7}\right)} x^{6} + 4 \, {\left(b^{11} c - 13 \, a b^{9} c^{2} + 48 \, a^{2} b^{7} c^{3} + 32 \, a^{3} b^{5} c^{4} - 512 \, a^{4} b^{3} c^{5} + 768 \, a^{5} b c^{6}\right)} x^{5} + {\left(b^{12} - 4 \, a b^{10} c - 90 \, a^{2} b^{8} c^{2} + 800 \, a^{3} b^{6} c^{3} - 2240 \, a^{4} b^{4} c^{4} + 1536 \, a^{5} b^{2} c^{5} + 1536 \, a^{6} c^{6}\right)} x^{4} + 4 \, {\left(a b^{11} - 13 \, a^{2} b^{9} c + 48 \, a^{3} b^{7} c^{2} + 32 \, a^{4} b^{5} c^{3} - 512 \, a^{5} b^{3} c^{4} + 768 \, a^{6} b c^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{10} - 46 \, a^{3} b^{8} c + 256 \, a^{4} b^{6} c^{2} - 576 \, a^{5} b^{4} c^{3} + 256 \, a^{6} b^{2} c^{4} + 512 \, a^{7} c^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{9} - 16 \, a^{4} b^{7} c + 96 \, a^{5} b^{5} c^{2} - 256 \, a^{6} b^{3} c^{3} + 256 \, a^{7} b c^{4}\right)} x\right)}}"," ",0,"2/35*(1024*(2*c^7*d - b*c^6*e)*x^7 + 3584*(2*b*c^6*d - b^2*c^5*e)*x^6 + 896*(2*(5*b^2*c^5 + 4*a*c^6)*d - (5*b^3*c^4 + 4*a*b*c^5)*e)*x^5 + 2240*(2*(b^3*c^4 + 4*a*b*c^5)*d - (b^4*c^3 + 4*a*b^2*c^4)*e)*x^4 + 280*(2*(b^4*c^3 + 24*a*b^2*c^4 + 16*a^2*c^5)*d - (b^5*c^2 + 24*a*b^3*c^3 + 16*a^2*b*c^4)*e)*x^3 - 28*(2*(b^5*c^2 - 40*a*b^3*c^3 - 240*a^2*b*c^4)*d - (b^6*c - 40*a*b^4*c^2 - 240*a^2*b^2*c^3)*e)*x^2 - (5*b^7 - 84*a*b^5*c + 560*a^2*b^3*c^2 - 2240*a^3*b*c^3)*d - 2*(a*b^6 - 20*a^2*b^4*c + 240*a^3*b^2*c^2 + 320*a^4*c^3)*e + 7*(2*(b^6*c - 20*a*b^4*c^2 + 240*a^2*b^2*c^3 + 320*a^3*c^4)*d - (b^7 - 20*a*b^5*c + 240*a^2*b^3*c^2 + 320*a^3*b*c^3)*e)*x)*sqrt(c*x^2 + b*x + a)/(a^4*b^8 - 16*a^5*b^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3 + 256*a^8*c^4 + (b^8*c^4 - 16*a*b^6*c^5 + 96*a^2*b^4*c^6 - 256*a^3*b^2*c^7 + 256*a^4*c^8)*x^8 + 4*(b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^7 + 2*(3*b^10*c^2 - 46*a*b^8*c^3 + 256*a^2*b^6*c^4 - 576*a^3*b^4*c^5 + 256*a^4*b^2*c^6 + 512*a^5*c^7)*x^6 + 4*(b^11*c - 13*a*b^9*c^2 + 48*a^2*b^7*c^3 + 32*a^3*b^5*c^4 - 512*a^4*b^3*c^5 + 768*a^5*b*c^6)*x^5 + (b^12 - 4*a*b^10*c - 90*a^2*b^8*c^2 + 800*a^3*b^6*c^3 - 2240*a^4*b^4*c^4 + 1536*a^5*b^2*c^5 + 1536*a^6*c^6)*x^4 + 4*(a*b^11 - 13*a^2*b^9*c + 48*a^3*b^7*c^2 + 32*a^4*b^5*c^3 - 512*a^5*b^3*c^4 + 768*a^6*b*c^5)*x^3 + 2*(3*a^2*b^10 - 46*a^3*b^8*c + 256*a^4*b^6*c^2 - 576*a^5*b^4*c^3 + 256*a^6*b^2*c^4 + 512*a^7*c^5)*x^2 + 4*(a^3*b^9 - 16*a^4*b^7*c + 96*a^5*b^5*c^2 - 256*a^6*b^3*c^3 + 256*a^7*b*c^4)*x)","B",0
980,1,47,0,0.422211," ","integrate((1-x)/x/(x^2+3*x+1)^(1/2),x, algorithm=""fricas"")","\log\left(4 \, x^{2} - \sqrt{x^{2} + 3 \, x + 1} {\left(4 \, x + 5\right)} + 11 \, x + 5\right) - \log\left(-x + \sqrt{x^{2} + 3 \, x + 1} + 1\right)"," ",0,"log(4*x^2 - sqrt(x^2 + 3*x + 1)*(4*x + 5) + 11*x + 5) - log(-x + sqrt(x^2 + 3*x + 1) + 1)","B",0
981,1,44,0,0.421288," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{2}{6435} \, {\left(429 \, B c x^{7} + 495 \, {\left(B b + A c\right)} x^{6} + 715 \, A a x^{4} + 585 \, {\left(B a + A b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/6435*(429*B*c*x^7 + 495*(B*b + A*c)*x^6 + 715*A*a*x^4 + 585*(B*a + A*b)*x^5)*sqrt(x)","A",0
982,1,44,0,0.411421," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{2}{9009} \, {\left(693 \, B c x^{6} + 819 \, {\left(B b + A c\right)} x^{5} + 1287 \, A a x^{3} + 1001 \, {\left(B a + A b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/9009*(693*B*c*x^6 + 819*(B*b + A*c)*x^5 + 1287*A*a*x^3 + 1001*(B*a + A*b)*x^4)*sqrt(x)","A",0
983,1,44,0,0.419891," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B c x^{5} + 385 \, {\left(B b + A c\right)} x^{4} + 693 \, A a x^{2} + 495 \, {\left(B a + A b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/3465*(315*B*c*x^5 + 385*(B*b + A*c)*x^4 + 693*A*a*x^2 + 495*(B*a + A*b)*x^3)*sqrt(x)","A",0
984,1,42,0,0.409071," ","integrate((B*x+A)*(c*x^2+b*x+a)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B c x^{4} + 45 \, {\left(B b + A c\right)} x^{3} + 105 \, A a x + 63 \, {\left(B a + A b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/315*(35*B*c*x^4 + 45*(B*b + A*c)*x^3 + 105*A*a*x + 63*(B*a + A*b)*x^2)*sqrt(x)","A",0
985,1,39,0,0.421782," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, B c x^{3} + 21 \, {\left(B b + A c\right)} x^{2} + 105 \, A a + 35 \, {\left(B a + A b\right)} x\right)} \sqrt{x}"," ",0,"2/105*(15*B*c*x^3 + 21*(B*b + A*c)*x^2 + 105*A*a + 35*(B*a + A*b)*x)*sqrt(x)","A",0
986,1,39,0,0.414718," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c x^{3} + 5 \, {\left(B b + A c\right)} x^{2} - 15 \, A a + 15 \, {\left(B a + A b\right)} x\right)}}{15 \, \sqrt{x}}"," ",0,"2/15*(3*B*c*x^3 + 5*(B*b + A*c)*x^2 - 15*A*a + 15*(B*a + A*b)*x)/sqrt(x)","A",0
987,1,38,0,0.423497," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c x^{3} + 3 \, {\left(B b + A c\right)} x^{2} - A a - 3 \, {\left(B a + A b\right)} x\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(B*c*x^3 + 3*(B*b + A*c)*x^2 - A*a - 3*(B*a + A*b)*x)/x^(3/2)","A",0
988,1,39,0,0.414212," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c x^{3} - 15 \, {\left(B b + A c\right)} x^{2} - 3 \, A a - 5 \, {\left(B a + A b\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(15*B*c*x^3 - 15*(B*b + A*c)*x^2 - 3*A*a - 5*(B*a + A*b)*x)/x^(5/2)","A",0
989,1,39,0,0.418362," ","integrate((B*x+A)*(c*x^2+b*x+a)/x^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, B c x^{3} + 35 \, {\left(B b + A c\right)} x^{2} + 15 \, A a + 21 \, {\left(B a + A b\right)} x\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"-2/105*(105*B*c*x^3 + 35*(B*b + A*c)*x^2 + 15*A*a + 21*(B*a + A*b)*x)/x^(7/2)","A",0
990,1,98,0,0.424853," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{2}{2078505} \, {\left(109395 \, B c^{2} x^{9} + 122265 \, {\left(2 \, B b c + A c^{2}\right)} x^{8} + 138567 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{7} + 230945 \, A a^{2} x^{4} + 159885 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{6} + 188955 \, {\left(B a^{2} + 2 \, A a b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/2078505*(109395*B*c^2*x^9 + 122265*(2*B*b*c + A*c^2)*x^8 + 138567*(B*b^2 + 2*(B*a + A*b)*c)*x^7 + 230945*A*a^2*x^4 + 159885*(2*B*a*b + A*b^2 + 2*A*a*c)*x^6 + 188955*(B*a^2 + 2*A*a*b)*x^5)*sqrt(x)","A",0
991,1,98,0,0.408112," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{2}{765765} \, {\left(45045 \, B c^{2} x^{8} + 51051 \, {\left(2 \, B b c + A c^{2}\right)} x^{7} + 58905 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{6} + 109395 \, A a^{2} x^{3} + 69615 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{5} + 85085 \, {\left(B a^{2} + 2 \, A a b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/765765*(45045*B*c^2*x^8 + 51051*(2*B*b*c + A*c^2)*x^7 + 58905*(B*b^2 + 2*(B*a + A*b)*c)*x^6 + 109395*A*a^2*x^3 + 69615*(2*B*a*b + A*b^2 + 2*A*a*c)*x^5 + 85085*(B*a^2 + 2*A*a*b)*x^4)*sqrt(x)","A",0
992,1,98,0,0.412755," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3003 \, B c^{2} x^{7} + 3465 \, {\left(2 \, B b c + A c^{2}\right)} x^{6} + 4095 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{5} + 9009 \, A a^{2} x^{2} + 5005 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{4} + 6435 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/45045*(3003*B*c^2*x^7 + 3465*(2*B*b*c + A*c^2)*x^6 + 4095*(B*b^2 + 2*(B*a + A*b)*c)*x^5 + 9009*A*a^2*x^2 + 5005*(2*B*a*b + A*b^2 + 2*A*a*c)*x^4 + 6435*(B*a^2 + 2*A*a*b)*x^3)*sqrt(x)","A",0
993,1,96,0,0.416184," ","integrate((B*x+A)*(c*x^2+b*x+a)^2*x^(1/2),x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3465 \, B c^{2} x^{6} + 4095 \, {\left(2 \, B b c + A c^{2}\right)} x^{5} + 5005 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{4} + 15015 \, A a^{2} x + 6435 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{3} + 9009 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/45045*(3465*B*c^2*x^6 + 4095*(2*B*b*c + A*c^2)*x^5 + 5005*(B*b^2 + 2*(B*a + A*b)*c)*x^4 + 15015*A*a^2*x + 6435*(2*B*a*b + A*b^2 + 2*A*a*c)*x^3 + 9009*(B*a^2 + 2*A*a*b)*x^2)*sqrt(x)","A",0
994,1,93,0,0.414918," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B c^{2} x^{5} + 385 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 495 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} + 3465 \, A a^{2} + 693 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} + 1155 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)} \sqrt{x}"," ",0,"2/3465*(315*B*c^2*x^5 + 385*(2*B*b*c + A*c^2)*x^4 + 495*(B*b^2 + 2*(B*a + A*b)*c)*x^3 + 3465*A*a^2 + 693*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 + 1155*(B*a^2 + 2*A*a*b)*x)*sqrt(x)","A",0
995,1,93,0,0.436203," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{2} x^{5} + 45 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 63 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} - 315 \, A a^{2} + 105 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} + 315 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{315 \, \sqrt{x}}"," ",0,"2/315*(35*B*c^2*x^5 + 45*(2*B*b*c + A*c^2)*x^4 + 63*(B*b^2 + 2*(B*a + A*b)*c)*x^3 - 315*A*a^2 + 105*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 + 315*(B*a^2 + 2*A*a*b)*x)/sqrt(x)","A",0
996,1,93,0,0.422353," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c^{2} x^{5} + 21 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 35 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} - 35 \, A a^{2} + 105 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} - 105 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{105 \, x^{\frac{3}{2}}}"," ",0,"2/105*(15*B*c^2*x^5 + 21*(2*B*b*c + A*c^2)*x^4 + 35*(B*b^2 + 2*(B*a + A*b)*c)*x^3 - 35*A*a^2 + 105*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 - 105*(B*a^2 + 2*A*a*b)*x)/x^(3/2)","A",0
997,1,93,0,0.425703," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{2} x^{5} + 5 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} + 15 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} - 3 \, A a^{2} - 15 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} - 5 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(3*B*c^2*x^5 + 5*(2*B*b*c + A*c^2)*x^4 + 15*(B*b^2 + 2*(B*a + A*b)*c)*x^3 - 3*A*a^2 - 15*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 - 5*(B*a^2 + 2*A*a*b)*x)/x^(5/2)","A",0
998,1,93,0,0.412002," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{2} x^{5} + 105 \, {\left(2 \, B b c + A c^{2}\right)} x^{4} - 105 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} - 15 \, A a^{2} - 35 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} - 21 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"2/105*(35*B*c^2*x^5 + 105*(2*B*b*c + A*c^2)*x^4 - 105*(B*b^2 + 2*(B*a + A*b)*c)*x^3 - 15*A*a^2 - 35*(2*B*a*b + A*b^2 + 2*A*a*c)*x^2 - 21*(B*a^2 + 2*A*a*b)*x)/x^(7/2)","A",0
999,1,171,0,0.418395," ","integrate(x^(7/2)*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2}{334639305} \, {\left(14549535 \, B c^{3} x^{11} + 15935205 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{10} + 52837785 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{9} + 19684665 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{8} + 37182145 \, A a^{3} x^{4} + 22309287 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{7} + 77224455 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{6} + 30421755 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/334639305*(14549535*B*c^3*x^11 + 15935205*(3*B*b*c^2 + A*c^3)*x^10 + 52837785*(B*b^2*c + (B*a + A*b)*c^2)*x^9 + 19684665*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^8 + 37182145*A*a^3*x^4 + 22309287*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^7 + 77224455*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^6 + 30421755*(B*a^3 + 3*A*a^2*b)*x^5)*sqrt(x)","A",0
1000,1,171,0,0.416268," ","integrate(x^(5/2)*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2}{14549535} \, {\left(692835 \, B c^{3} x^{10} + 765765 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{9} + 2567565 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{8} + 969969 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{7} + 2078505 \, A a^{3} x^{3} + 1119195 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{6} + 3968055 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{5} + 1616615 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/14549535*(692835*B*c^3*x^10 + 765765*(3*B*b*c^2 + A*c^3)*x^9 + 2567565*(B*b^2*c + (B*a + A*b)*c^2)*x^8 + 969969*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^7 + 2078505*A*a^3*x^3 + 1119195*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^6 + 3968055*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^5 + 1616615*(B*a^3 + 3*A*a^2*b)*x^4)*sqrt(x)","A",0
1001,1,171,0,0.437084," ","integrate(x^(3/2)*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2}{4849845} \, {\left(255255 \, B c^{3} x^{9} + 285285 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{8} + 969969 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{7} + 373065 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{6} + 969969 \, A a^{3} x^{2} + 440895 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{5} + 1616615 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{4} + 692835 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/4849845*(255255*B*c^3*x^9 + 285285*(3*B*b*c^2 + A*c^3)*x^8 + 969969*(B*b^2*c + (B*a + A*b)*c^2)*x^7 + 373065*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^6 + 969969*A*a^3*x^2 + 440895*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^5 + 1616615*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^4 + 692835*(B*a^3 + 3*A*a^2*b)*x^3)*sqrt(x)","A",0
1002,1,169,0,0.427760," ","integrate((B*x+A)*(c*x^2+b*x+a)^3*x^(1/2),x, algorithm=""fricas"")","\frac{2}{765765} \, {\left(45045 \, B c^{3} x^{8} + 51051 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{7} + 176715 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{6} + 69615 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{5} + 255255 \, A a^{3} x + 85085 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{4} + 328185 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{3} + 153153 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/765765*(45045*B*c^3*x^8 + 51051*(3*B*b*c^2 + A*c^3)*x^7 + 176715*(B*b^2*c + (B*a + A*b)*c^2)*x^6 + 69615*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^5 + 255255*A*a^3*x + 85085*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^4 + 328185*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^3 + 153153*(B*a^3 + 3*A*a^2*b)*x^2)*sqrt(x)","A",0
1003,1,166,0,0.435660," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3003 \, B c^{3} x^{7} + 3465 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 12285 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 5005 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} + 45045 \, A a^{3} + 6435 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} + 27027 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} + 15015 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)} \sqrt{x}"," ",0,"2/45045*(3003*B*c^3*x^7 + 3465*(3*B*b*c^2 + A*c^3)*x^6 + 12285*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 5005*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 + 45045*A*a^3 + 6435*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 + 27027*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 + 15015*(B*a^3 + 3*A*a^2*b)*x)*sqrt(x)","A",0
1004,1,166,0,0.432937," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, B c^{3} x^{7} + 1365 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 5005 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 2145 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 15015 \, A a^{3} + 3003 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} + 15015 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} + 15015 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{15015 \, \sqrt{x}}"," ",0,"2/15015*(1155*B*c^3*x^7 + 1365*(3*B*b*c^2 + A*c^3)*x^6 + 5005*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 2145*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 15015*A*a^3 + 3003*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 + 15015*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 + 15015*(B*a^3 + 3*A*a^2*b)*x)/sqrt(x)","A",0
1005,1,166,0,0.425333," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B c^{3} x^{7} + 385 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 1485 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 693 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 1155 \, A a^{3} + 1155 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} + 10395 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} - 3465 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{3465 \, x^{\frac{3}{2}}}"," ",0,"2/3465*(315*B*c^3*x^7 + 385*(3*B*b*c^2 + A*c^3)*x^6 + 1485*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 693*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 1155*A*a^3 + 1155*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 + 10395*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 - 3465*(B*a^3 + 3*A*a^2*b)*x)/x^(3/2)","A",0
1006,1,166,0,0.413670," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{3} x^{7} + 45 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 189 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 105 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 63 \, A a^{3} + 315 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} - 945 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} - 105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{315 \, x^{\frac{5}{2}}}"," ",0,"2/315*(35*B*c^3*x^7 + 45*(3*B*b*c^2 + A*c^3)*x^6 + 189*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 105*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 63*A*a^3 + 315*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 - 945*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 - 105*(B*a^3 + 3*A*a^2*b)*x)/x^(5/2)","A",0
1007,1,166,0,0.430948," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B c^{3} x^{7} + 7 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 35 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} + 35 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 5 \, A a^{3} - 35 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} - 35 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} - 7 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{35 \, x^{\frac{7}{2}}}"," ",0,"2/35*(5*B*c^3*x^7 + 7*(3*B*b*c^2 + A*c^3)*x^6 + 35*(B*b^2*c + (B*a + A*b)*c^2)*x^5 + 35*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 5*A*a^3 - 35*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 - 35*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 - 7*(B*a^3 + 3*A*a^2*b)*x)/x^(7/2)","A",0
1008,1,166,0,0.428818," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/x^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B c^{3} x^{7} + 105 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{6} + 945 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{5} - 315 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{4} - 35 \, A a^{3} - 105 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{3} - 189 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{2} - 45 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{315 \, x^{\frac{9}{2}}}"," ",0,"2/315*(63*B*c^3*x^7 + 105*(3*B*b*c^2 + A*c^3)*x^6 + 945*(B*b^2*c + (B*a + A*b)*c^2)*x^5 - 315*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^4 - 35*A*a^3 - 105*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^3 - 189*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^2 - 45*(B*a^3 + 3*A*a^2*b)*x)/x^(9/2)","A",0
1009,1,7707,0,8.655476," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} c^{3} \sqrt{-\frac{B^{2} b^{7} + {\left(4 \, A B a^{3} + 5 \, A^{2} a^{2} b\right)} c^{4} - {\left(7 \, B^{2} a^{3} b + 18 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{2} b^{3} + 12 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(\sqrt{2} {\left(B^{3} b^{10} + 4 \, {\left(A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - {\left(4 \, B^{3} a^{5} + 28 \, A B^{2} a^{4} b + 41 \, A^{2} B a^{3} b^{2} + 13 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(29 \, B^{3} a^{4} b^{2} + 87 \, A B^{2} a^{3} b^{3} + 58 \, A^{2} B a^{2} b^{4} + 7 \, A^{3} a b^{5}\right)} c^{4} - {\left(51 \, B^{3} a^{3} b^{4} + 80 \, A B^{2} a^{2} b^{5} + 24 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + {\left(35 \, B^{3} a^{2} b^{6} + 27 \, A B^{2} a b^{7} + 3 \, A^{2} B b^{8}\right)} c^{2} - {\left(10 \, B^{3} a b^{8} + 3 \, A B^{2} b^{9}\right)} c - {\left(B b^{5} c^{7} - 8 \, A a^{2} c^{10} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c^{9} - {\left(7 \, B a b^{3} + A b^{4}\right)} c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{-\frac{B^{2} b^{7} + {\left(4 \, A B a^{3} + 5 \, A^{2} a^{2} b\right)} c^{4} - {\left(7 \, B^{2} a^{3} b + 18 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{2} b^{3} + 12 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left(B^{4} a^{3} b^{6} - A B^{3} a^{2} b^{7} + A^{4} a^{4} c^{5} - {\left(7 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{4} - {\left(B^{4} a^{6} + 5 \, A B^{3} a^{5} b - 9 \, A^{2} B^{2} a^{4} b^{2} - 11 \, A^{3} B a^{3} b^{3} - A^{4} a^{2} b^{4}\right)} c^{3} + {\left(6 \, B^{4} a^{5} b^{2} + 2 \, A B^{3} a^{4} b^{3} - 12 \, A^{2} B^{2} a^{3} b^{4} - 3 \, A^{3} B a^{2} b^{5}\right)} c^{2} - {\left(5 \, B^{4} a^{4} b^{4} - 3 \, A B^{3} a^{3} b^{5} - 3 \, A^{2} B^{2} a^{2} b^{6}\right)} c\right)} \sqrt{x}\right) - 15 \, \sqrt{2} c^{3} \sqrt{-\frac{B^{2} b^{7} + {\left(4 \, A B a^{3} + 5 \, A^{2} a^{2} b\right)} c^{4} - {\left(7 \, B^{2} a^{3} b + 18 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{2} b^{3} + 12 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(-\sqrt{2} {\left(B^{3} b^{10} + 4 \, {\left(A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - {\left(4 \, B^{3} a^{5} + 28 \, A B^{2} a^{4} b + 41 \, A^{2} B a^{3} b^{2} + 13 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(29 \, B^{3} a^{4} b^{2} + 87 \, A B^{2} a^{3} b^{3} + 58 \, A^{2} B a^{2} b^{4} + 7 \, A^{3} a b^{5}\right)} c^{4} - {\left(51 \, B^{3} a^{3} b^{4} + 80 \, A B^{2} a^{2} b^{5} + 24 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + {\left(35 \, B^{3} a^{2} b^{6} + 27 \, A B^{2} a b^{7} + 3 \, A^{2} B b^{8}\right)} c^{2} - {\left(10 \, B^{3} a b^{8} + 3 \, A B^{2} b^{9}\right)} c - {\left(B b^{5} c^{7} - 8 \, A a^{2} c^{10} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c^{9} - {\left(7 \, B a b^{3} + A b^{4}\right)} c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{-\frac{B^{2} b^{7} + {\left(4 \, A B a^{3} + 5 \, A^{2} a^{2} b\right)} c^{4} - {\left(7 \, B^{2} a^{3} b + 18 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{2} b^{3} + 12 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left(B^{4} a^{3} b^{6} - A B^{3} a^{2} b^{7} + A^{4} a^{4} c^{5} - {\left(7 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{4} - {\left(B^{4} a^{6} + 5 \, A B^{3} a^{5} b - 9 \, A^{2} B^{2} a^{4} b^{2} - 11 \, A^{3} B a^{3} b^{3} - A^{4} a^{2} b^{4}\right)} c^{3} + {\left(6 \, B^{4} a^{5} b^{2} + 2 \, A B^{3} a^{4} b^{3} - 12 \, A^{2} B^{2} a^{3} b^{4} - 3 \, A^{3} B a^{2} b^{5}\right)} c^{2} - {\left(5 \, B^{4} a^{4} b^{4} - 3 \, A B^{3} a^{3} b^{5} - 3 \, A^{2} B^{2} a^{2} b^{6}\right)} c\right)} \sqrt{x}\right) + 15 \, \sqrt{2} c^{3} \sqrt{-\frac{B^{2} b^{7} + {\left(4 \, A B a^{3} + 5 \, A^{2} a^{2} b\right)} c^{4} - {\left(7 \, B^{2} a^{3} b + 18 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{2} b^{3} + 12 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(\sqrt{2} {\left(B^{3} b^{10} + 4 \, {\left(A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - {\left(4 \, B^{3} a^{5} + 28 \, A B^{2} a^{4} b + 41 \, A^{2} B a^{3} b^{2} + 13 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(29 \, B^{3} a^{4} b^{2} + 87 \, A B^{2} a^{3} b^{3} + 58 \, A^{2} B a^{2} b^{4} + 7 \, A^{3} a b^{5}\right)} c^{4} - {\left(51 \, B^{3} a^{3} b^{4} + 80 \, A B^{2} a^{2} b^{5} + 24 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + {\left(35 \, B^{3} a^{2} b^{6} + 27 \, A B^{2} a b^{7} + 3 \, A^{2} B b^{8}\right)} c^{2} - {\left(10 \, B^{3} a b^{8} + 3 \, A B^{2} b^{9}\right)} c + {\left(B b^{5} c^{7} - 8 \, A a^{2} c^{10} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c^{9} - {\left(7 \, B a b^{3} + A b^{4}\right)} c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{-\frac{B^{2} b^{7} + {\left(4 \, A B a^{3} + 5 \, A^{2} a^{2} b\right)} c^{4} - {\left(7 \, B^{2} a^{3} b + 18 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{2} b^{3} + 12 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left(B^{4} a^{3} b^{6} - A B^{3} a^{2} b^{7} + A^{4} a^{4} c^{5} - {\left(7 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{4} - {\left(B^{4} a^{6} + 5 \, A B^{3} a^{5} b - 9 \, A^{2} B^{2} a^{4} b^{2} - 11 \, A^{3} B a^{3} b^{3} - A^{4} a^{2} b^{4}\right)} c^{3} + {\left(6 \, B^{4} a^{5} b^{2} + 2 \, A B^{3} a^{4} b^{3} - 12 \, A^{2} B^{2} a^{3} b^{4} - 3 \, A^{3} B a^{2} b^{5}\right)} c^{2} - {\left(5 \, B^{4} a^{4} b^{4} - 3 \, A B^{3} a^{3} b^{5} - 3 \, A^{2} B^{2} a^{2} b^{6}\right)} c\right)} \sqrt{x}\right) - 15 \, \sqrt{2} c^{3} \sqrt{-\frac{B^{2} b^{7} + {\left(4 \, A B a^{3} + 5 \, A^{2} a^{2} b\right)} c^{4} - {\left(7 \, B^{2} a^{3} b + 18 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{2} b^{3} + 12 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(-\sqrt{2} {\left(B^{3} b^{10} + 4 \, {\left(A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - {\left(4 \, B^{3} a^{5} + 28 \, A B^{2} a^{4} b + 41 \, A^{2} B a^{3} b^{2} + 13 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(29 \, B^{3} a^{4} b^{2} + 87 \, A B^{2} a^{3} b^{3} + 58 \, A^{2} B a^{2} b^{4} + 7 \, A^{3} a b^{5}\right)} c^{4} - {\left(51 \, B^{3} a^{3} b^{4} + 80 \, A B^{2} a^{2} b^{5} + 24 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + {\left(35 \, B^{3} a^{2} b^{6} + 27 \, A B^{2} a b^{7} + 3 \, A^{2} B b^{8}\right)} c^{2} - {\left(10 \, B^{3} a b^{8} + 3 \, A B^{2} b^{9}\right)} c + {\left(B b^{5} c^{7} - 8 \, A a^{2} c^{10} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c^{9} - {\left(7 \, B a b^{3} + A b^{4}\right)} c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{-\frac{B^{2} b^{7} + {\left(4 \, A B a^{3} + 5 \, A^{2} a^{2} b\right)} c^{4} - {\left(7 \, B^{2} a^{3} b + 18 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{2} b^{3} + 12 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{B^{4} b^{12} + A^{4} a^{4} c^{8} - 2 \, {\left(A^{2} B^{2} a^{5} + 6 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{7} + {\left(B^{4} a^{6} + 12 \, A B^{3} a^{5} b + 54 \, A^{2} B^{2} a^{4} b^{2} + 52 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{5} b^{2} + 44 \, A B^{3} a^{4} b^{3} + 72 \, A^{2} B^{2} a^{3} b^{4} + 32 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{4} b^{4} + 160 \, A B^{3} a^{3} b^{5} + 132 \, A^{2} B^{2} a^{2} b^{6} + 28 \, A^{3} B a b^{7} + A^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{3} b^{6} + 58 \, A B^{3} a^{2} b^{7} + 24 \, A^{2} B^{2} a b^{8} + 2 \, A^{3} B b^{9}\right)} c^{3} + {\left(37 \, B^{4} a^{2} b^{8} + 36 \, A B^{3} a b^{9} + 6 \, A^{2} B^{2} b^{10}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a b^{10} + 2 \, A B^{3} b^{11}\right)} c}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left(B^{4} a^{3} b^{6} - A B^{3} a^{2} b^{7} + A^{4} a^{4} c^{5} - {\left(7 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{4} - {\left(B^{4} a^{6} + 5 \, A B^{3} a^{5} b - 9 \, A^{2} B^{2} a^{4} b^{2} - 11 \, A^{3} B a^{3} b^{3} - A^{4} a^{2} b^{4}\right)} c^{3} + {\left(6 \, B^{4} a^{5} b^{2} + 2 \, A B^{3} a^{4} b^{3} - 12 \, A^{2} B^{2} a^{3} b^{4} - 3 \, A^{3} B a^{2} b^{5}\right)} c^{2} - {\left(5 \, B^{4} a^{4} b^{4} - 3 \, A B^{3} a^{3} b^{5} - 3 \, A^{2} B^{2} a^{2} b^{6}\right)} c\right)} \sqrt{x}\right) + 4 \, {\left(3 \, B c^{2} x^{2} + 15 \, B b^{2} - 15 \, {\left(B a + A b\right)} c - 5 \, {\left(B b c - A c^{2}\right)} x\right)} \sqrt{x}}{30 \, c^{3}}"," ",0,"1/30*(15*sqrt(2)*c^3*sqrt(-(B^2*b^7 + (4*A*B*a^3 + 5*A^2*a^2*b)*c^4 - (7*B^2*a^3*b + 18*A*B*a^2*b^2 + 5*A^2*a*b^3)*c^3 + (14*B^2*a^2*b^3 + 12*A*B*a*b^4 + A^2*b^5)*c^2 - (7*B^2*a*b^5 + 2*A*B*b^6)*c + (b^2*c^7 - 4*a*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(sqrt(2)*(B^3*b^10 + 4*(A^2*B*a^4 + A^3*a^3*b)*c^6 - (4*B^3*a^5 + 28*A*B^2*a^4*b + 41*A^2*B*a^3*b^2 + 13*A^3*a^2*b^3)*c^5 + (29*B^3*a^4*b^2 + 87*A*B^2*a^3*b^3 + 58*A^2*B*a^2*b^4 + 7*A^3*a*b^5)*c^4 - (51*B^3*a^3*b^4 + 80*A*B^2*a^2*b^5 + 24*A^2*B*a*b^6 + A^3*b^7)*c^3 + (35*B^3*a^2*b^6 + 27*A*B^2*a*b^7 + 3*A^2*B*b^8)*c^2 - (10*B^3*a*b^8 + 3*A*B^2*b^9)*c - (B*b^5*c^7 - 8*A*a^2*c^10 + 6*(2*B*a^2*b + A*a*b^2)*c^9 - (7*B*a*b^3 + A*b^4)*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))*sqrt(-(B^2*b^7 + (4*A*B*a^3 + 5*A^2*a^2*b)*c^4 - (7*B^2*a^3*b + 18*A*B*a^2*b^2 + 5*A^2*a*b^3)*c^3 + (14*B^2*a^2*b^3 + 12*A*B*a*b^4 + A^2*b^5)*c^2 - (7*B^2*a*b^5 + 2*A*B*b^6)*c + (b^2*c^7 - 4*a*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*(B^4*a^3*b^6 - A*B^3*a^2*b^7 + A^4*a^4*c^5 - (7*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^4 - (B^4*a^6 + 5*A*B^3*a^5*b - 9*A^2*B^2*a^4*b^2 - 11*A^3*B*a^3*b^3 - A^4*a^2*b^4)*c^3 + (6*B^4*a^5*b^2 + 2*A*B^3*a^4*b^3 - 12*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5)*c^2 - (5*B^4*a^4*b^4 - 3*A*B^3*a^3*b^5 - 3*A^2*B^2*a^2*b^6)*c)*sqrt(x)) - 15*sqrt(2)*c^3*sqrt(-(B^2*b^7 + (4*A*B*a^3 + 5*A^2*a^2*b)*c^4 - (7*B^2*a^3*b + 18*A*B*a^2*b^2 + 5*A^2*a*b^3)*c^3 + (14*B^2*a^2*b^3 + 12*A*B*a*b^4 + A^2*b^5)*c^2 - (7*B^2*a*b^5 + 2*A*B*b^6)*c + (b^2*c^7 - 4*a*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(-sqrt(2)*(B^3*b^10 + 4*(A^2*B*a^4 + A^3*a^3*b)*c^6 - (4*B^3*a^5 + 28*A*B^2*a^4*b + 41*A^2*B*a^3*b^2 + 13*A^3*a^2*b^3)*c^5 + (29*B^3*a^4*b^2 + 87*A*B^2*a^3*b^3 + 58*A^2*B*a^2*b^4 + 7*A^3*a*b^5)*c^4 - (51*B^3*a^3*b^4 + 80*A*B^2*a^2*b^5 + 24*A^2*B*a*b^6 + A^3*b^7)*c^3 + (35*B^3*a^2*b^6 + 27*A*B^2*a*b^7 + 3*A^2*B*b^8)*c^2 - (10*B^3*a*b^8 + 3*A*B^2*b^9)*c - (B*b^5*c^7 - 8*A*a^2*c^10 + 6*(2*B*a^2*b + A*a*b^2)*c^9 - (7*B*a*b^3 + A*b^4)*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))*sqrt(-(B^2*b^7 + (4*A*B*a^3 + 5*A^2*a^2*b)*c^4 - (7*B^2*a^3*b + 18*A*B*a^2*b^2 + 5*A^2*a*b^3)*c^3 + (14*B^2*a^2*b^3 + 12*A*B*a*b^4 + A^2*b^5)*c^2 - (7*B^2*a*b^5 + 2*A*B*b^6)*c + (b^2*c^7 - 4*a*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*(B^4*a^3*b^6 - A*B^3*a^2*b^7 + A^4*a^4*c^5 - (7*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^4 - (B^4*a^6 + 5*A*B^3*a^5*b - 9*A^2*B^2*a^4*b^2 - 11*A^3*B*a^3*b^3 - A^4*a^2*b^4)*c^3 + (6*B^4*a^5*b^2 + 2*A*B^3*a^4*b^3 - 12*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5)*c^2 - (5*B^4*a^4*b^4 - 3*A*B^3*a^3*b^5 - 3*A^2*B^2*a^2*b^6)*c)*sqrt(x)) + 15*sqrt(2)*c^3*sqrt(-(B^2*b^7 + (4*A*B*a^3 + 5*A^2*a^2*b)*c^4 - (7*B^2*a^3*b + 18*A*B*a^2*b^2 + 5*A^2*a*b^3)*c^3 + (14*B^2*a^2*b^3 + 12*A*B*a*b^4 + A^2*b^5)*c^2 - (7*B^2*a*b^5 + 2*A*B*b^6)*c - (b^2*c^7 - 4*a*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(sqrt(2)*(B^3*b^10 + 4*(A^2*B*a^4 + A^3*a^3*b)*c^6 - (4*B^3*a^5 + 28*A*B^2*a^4*b + 41*A^2*B*a^3*b^2 + 13*A^3*a^2*b^3)*c^5 + (29*B^3*a^4*b^2 + 87*A*B^2*a^3*b^3 + 58*A^2*B*a^2*b^4 + 7*A^3*a*b^5)*c^4 - (51*B^3*a^3*b^4 + 80*A*B^2*a^2*b^5 + 24*A^2*B*a*b^6 + A^3*b^7)*c^3 + (35*B^3*a^2*b^6 + 27*A*B^2*a*b^7 + 3*A^2*B*b^8)*c^2 - (10*B^3*a*b^8 + 3*A*B^2*b^9)*c + (B*b^5*c^7 - 8*A*a^2*c^10 + 6*(2*B*a^2*b + A*a*b^2)*c^9 - (7*B*a*b^3 + A*b^4)*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))*sqrt(-(B^2*b^7 + (4*A*B*a^3 + 5*A^2*a^2*b)*c^4 - (7*B^2*a^3*b + 18*A*B*a^2*b^2 + 5*A^2*a*b^3)*c^3 + (14*B^2*a^2*b^3 + 12*A*B*a*b^4 + A^2*b^5)*c^2 - (7*B^2*a*b^5 + 2*A*B*b^6)*c - (b^2*c^7 - 4*a*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*(B^4*a^3*b^6 - A*B^3*a^2*b^7 + A^4*a^4*c^5 - (7*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^4 - (B^4*a^6 + 5*A*B^3*a^5*b - 9*A^2*B^2*a^4*b^2 - 11*A^3*B*a^3*b^3 - A^4*a^2*b^4)*c^3 + (6*B^4*a^5*b^2 + 2*A*B^3*a^4*b^3 - 12*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5)*c^2 - (5*B^4*a^4*b^4 - 3*A*B^3*a^3*b^5 - 3*A^2*B^2*a^2*b^6)*c)*sqrt(x)) - 15*sqrt(2)*c^3*sqrt(-(B^2*b^7 + (4*A*B*a^3 + 5*A^2*a^2*b)*c^4 - (7*B^2*a^3*b + 18*A*B*a^2*b^2 + 5*A^2*a*b^3)*c^3 + (14*B^2*a^2*b^3 + 12*A*B*a*b^4 + A^2*b^5)*c^2 - (7*B^2*a*b^5 + 2*A*B*b^6)*c - (b^2*c^7 - 4*a*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(-sqrt(2)*(B^3*b^10 + 4*(A^2*B*a^4 + A^3*a^3*b)*c^6 - (4*B^3*a^5 + 28*A*B^2*a^4*b + 41*A^2*B*a^3*b^2 + 13*A^3*a^2*b^3)*c^5 + (29*B^3*a^4*b^2 + 87*A*B^2*a^3*b^3 + 58*A^2*B*a^2*b^4 + 7*A^3*a*b^5)*c^4 - (51*B^3*a^3*b^4 + 80*A*B^2*a^2*b^5 + 24*A^2*B*a*b^6 + A^3*b^7)*c^3 + (35*B^3*a^2*b^6 + 27*A*B^2*a*b^7 + 3*A^2*B*b^8)*c^2 - (10*B^3*a*b^8 + 3*A*B^2*b^9)*c + (B*b^5*c^7 - 8*A*a^2*c^10 + 6*(2*B*a^2*b + A*a*b^2)*c^9 - (7*B*a*b^3 + A*b^4)*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))*sqrt(-(B^2*b^7 + (4*A*B*a^3 + 5*A^2*a^2*b)*c^4 - (7*B^2*a^3*b + 18*A*B*a^2*b^2 + 5*A^2*a*b^3)*c^3 + (14*B^2*a^2*b^3 + 12*A*B*a*b^4 + A^2*b^5)*c^2 - (7*B^2*a*b^5 + 2*A*B*b^6)*c - (b^2*c^7 - 4*a*c^8)*sqrt((B^4*b^12 + A^4*a^4*c^8 - 2*(A^2*B^2*a^5 + 6*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^7 + (B^4*a^6 + 12*A*B^3*a^5*b + 54*A^2*B^2*a^4*b^2 + 52*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^6 - 2*(6*B^4*a^5*b^2 + 44*A*B^3*a^4*b^3 + 72*A^2*B^2*a^3*b^4 + 32*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c^5 + (46*B^4*a^4*b^4 + 160*A*B^3*a^3*b^5 + 132*A^2*B^2*a^2*b^6 + 28*A^3*B*a*b^7 + A^4*b^8)*c^4 - 2*(31*B^4*a^3*b^6 + 58*A*B^3*a^2*b^7 + 24*A^2*B^2*a*b^8 + 2*A^3*B*b^9)*c^3 + (37*B^4*a^2*b^8 + 36*A*B^3*a*b^9 + 6*A^2*B^2*b^10)*c^2 - 2*(5*B^4*a*b^10 + 2*A*B^3*b^11)*c)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*(B^4*a^3*b^6 - A*B^3*a^2*b^7 + A^4*a^4*c^5 - (7*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^4 - (B^4*a^6 + 5*A*B^3*a^5*b - 9*A^2*B^2*a^4*b^2 - 11*A^3*B*a^3*b^3 - A^4*a^2*b^4)*c^3 + (6*B^4*a^5*b^2 + 2*A*B^3*a^4*b^3 - 12*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5)*c^2 - (5*B^4*a^4*b^4 - 3*A*B^3*a^3*b^5 - 3*A^2*B^2*a^2*b^6)*c)*sqrt(x)) + 4*(3*B*c^2*x^2 + 15*B*b^2 - 15*(B*a + A*b)*c - 5*(B*b*c - A*c^2)*x)*sqrt(x))/c^3","B",0
1010,1,5148,0,3.214761," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} c^{2} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(\sqrt{2} {\left(B^{3} b^{7} - 4 \, A^{3} a^{2} c^{5} + {\left(4 \, A B^{2} a^{3} + 20 \, A^{2} B a^{2} b + 5 \, A^{3} a b^{2}\right)} c^{4} - {\left(4 \, B^{3} a^{3} b + 29 \, A B^{2} a^{2} b^{2} + 17 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(13 \, B^{3} a^{2} b^{3} + 19 \, A B^{2} a b^{4} + 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(7 \, B^{3} a b^{5} + 3 \, A B^{2} b^{6}\right)} c - {\left(B b^{4} c^{5} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{7} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left(B^{4} a^{2} b^{4} - A B^{3} a b^{5} - A^{4} a^{2} c^{4} + {\left(5 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} + {\left(B^{4} a^{4} + 3 \, A B^{3} a^{3} b - 6 \, A^{2} B^{2} a^{2} b^{2} - 3 \, A^{3} B a b^{3}\right)} c^{2} - {\left(3 \, B^{4} a^{3} b^{2} - A B^{3} a^{2} b^{3} - 3 \, A^{2} B^{2} a b^{4}\right)} c\right)} \sqrt{x}\right) - 3 \, \sqrt{2} c^{2} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\sqrt{2} {\left(B^{3} b^{7} - 4 \, A^{3} a^{2} c^{5} + {\left(4 \, A B^{2} a^{3} + 20 \, A^{2} B a^{2} b + 5 \, A^{3} a b^{2}\right)} c^{4} - {\left(4 \, B^{3} a^{3} b + 29 \, A B^{2} a^{2} b^{2} + 17 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(13 \, B^{3} a^{2} b^{3} + 19 \, A B^{2} a b^{4} + 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(7 \, B^{3} a b^{5} + 3 \, A B^{2} b^{6}\right)} c - {\left(B b^{4} c^{5} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{7} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left(B^{4} a^{2} b^{4} - A B^{3} a b^{5} - A^{4} a^{2} c^{4} + {\left(5 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} + {\left(B^{4} a^{4} + 3 \, A B^{3} a^{3} b - 6 \, A^{2} B^{2} a^{2} b^{2} - 3 \, A^{3} B a b^{3}\right)} c^{2} - {\left(3 \, B^{4} a^{3} b^{2} - A B^{3} a^{2} b^{3} - 3 \, A^{2} B^{2} a b^{4}\right)} c\right)} \sqrt{x}\right) + 3 \, \sqrt{2} c^{2} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(\sqrt{2} {\left(B^{3} b^{7} - 4 \, A^{3} a^{2} c^{5} + {\left(4 \, A B^{2} a^{3} + 20 \, A^{2} B a^{2} b + 5 \, A^{3} a b^{2}\right)} c^{4} - {\left(4 \, B^{3} a^{3} b + 29 \, A B^{2} a^{2} b^{2} + 17 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(13 \, B^{3} a^{2} b^{3} + 19 \, A B^{2} a b^{4} + 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(7 \, B^{3} a b^{5} + 3 \, A B^{2} b^{6}\right)} c + {\left(B b^{4} c^{5} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{7} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left(B^{4} a^{2} b^{4} - A B^{3} a b^{5} - A^{4} a^{2} c^{4} + {\left(5 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} + {\left(B^{4} a^{4} + 3 \, A B^{3} a^{3} b - 6 \, A^{2} B^{2} a^{2} b^{2} - 3 \, A^{3} B a b^{3}\right)} c^{2} - {\left(3 \, B^{4} a^{3} b^{2} - A B^{3} a^{2} b^{3} - 3 \, A^{2} B^{2} a b^{4}\right)} c\right)} \sqrt{x}\right) - 3 \, \sqrt{2} c^{2} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\sqrt{2} {\left(B^{3} b^{7} - 4 \, A^{3} a^{2} c^{5} + {\left(4 \, A B^{2} a^{3} + 20 \, A^{2} B a^{2} b + 5 \, A^{3} a b^{2}\right)} c^{4} - {\left(4 \, B^{3} a^{3} b + 29 \, A B^{2} a^{2} b^{2} + 17 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(13 \, B^{3} a^{2} b^{3} + 19 \, A B^{2} a b^{4} + 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(7 \, B^{3} a b^{5} + 3 \, A B^{2} b^{6}\right)} c + {\left(B b^{4} c^{5} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{7} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left(B^{4} a^{2} b^{4} - A B^{3} a b^{5} - A^{4} a^{2} c^{4} + {\left(5 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} + {\left(B^{4} a^{4} + 3 \, A B^{3} a^{3} b - 6 \, A^{2} B^{2} a^{2} b^{2} - 3 \, A^{3} B a b^{3}\right)} c^{2} - {\left(3 \, B^{4} a^{3} b^{2} - A B^{3} a^{2} b^{3} - 3 \, A^{2} B^{2} a b^{4}\right)} c\right)} \sqrt{x}\right) + 4 \, {\left(B c x - 3 \, B b + 3 \, A c\right)} \sqrt{x}}{6 \, c^{2}}"," ",0,"1/6*(3*sqrt(2)*c^2*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(sqrt(2)*(B^3*b^7 - 4*A^3*a^2*c^5 + (4*A*B^2*a^3 + 20*A^2*B*a^2*b + 5*A^3*a*b^2)*c^4 - (4*B^3*a^3*b + 29*A*B^2*a^2*b^2 + 17*A^2*B*a*b^3 + A^3*b^4)*c^3 + (13*B^3*a^2*b^3 + 19*A*B^2*a*b^4 + 3*A^2*B*b^5)*c^2 - (7*B^3*a*b^5 + 3*A*B^2*b^6)*c - (B*b^4*c^5 + 4*(2*B*a^2 + A*a*b)*c^7 - (6*B*a*b^2 + A*b^3)*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*(B^4*a^2*b^4 - A*B^3*a*b^5 - A^4*a^2*c^4 + (5*A^3*B*a^2*b + A^4*a*b^2)*c^3 + (B^4*a^4 + 3*A*B^3*a^3*b - 6*A^2*B^2*a^2*b^2 - 3*A^3*B*a*b^3)*c^2 - (3*B^4*a^3*b^2 - A*B^3*a^2*b^3 - 3*A^2*B^2*a*b^4)*c)*sqrt(x)) - 3*sqrt(2)*c^2*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-sqrt(2)*(B^3*b^7 - 4*A^3*a^2*c^5 + (4*A*B^2*a^3 + 20*A^2*B*a^2*b + 5*A^3*a*b^2)*c^4 - (4*B^3*a^3*b + 29*A*B^2*a^2*b^2 + 17*A^2*B*a*b^3 + A^3*b^4)*c^3 + (13*B^3*a^2*b^3 + 19*A*B^2*a*b^4 + 3*A^2*B*b^5)*c^2 - (7*B^3*a*b^5 + 3*A*B^2*b^6)*c - (B*b^4*c^5 + 4*(2*B*a^2 + A*a*b)*c^7 - (6*B*a*b^2 + A*b^3)*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*(B^4*a^2*b^4 - A*B^3*a*b^5 - A^4*a^2*c^4 + (5*A^3*B*a^2*b + A^4*a*b^2)*c^3 + (B^4*a^4 + 3*A*B^3*a^3*b - 6*A^2*B^2*a^2*b^2 - 3*A^3*B*a*b^3)*c^2 - (3*B^4*a^3*b^2 - A*B^3*a^2*b^3 - 3*A^2*B^2*a*b^4)*c)*sqrt(x)) + 3*sqrt(2)*c^2*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(sqrt(2)*(B^3*b^7 - 4*A^3*a^2*c^5 + (4*A*B^2*a^3 + 20*A^2*B*a^2*b + 5*A^3*a*b^2)*c^4 - (4*B^3*a^3*b + 29*A*B^2*a^2*b^2 + 17*A^2*B*a*b^3 + A^3*b^4)*c^3 + (13*B^3*a^2*b^3 + 19*A*B^2*a*b^4 + 3*A^2*B*b^5)*c^2 - (7*B^3*a*b^5 + 3*A*B^2*b^6)*c + (B*b^4*c^5 + 4*(2*B*a^2 + A*a*b)*c^7 - (6*B*a*b^2 + A*b^3)*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*(B^4*a^2*b^4 - A*B^3*a*b^5 - A^4*a^2*c^4 + (5*A^3*B*a^2*b + A^4*a*b^2)*c^3 + (B^4*a^4 + 3*A*B^3*a^3*b - 6*A^2*B^2*a^2*b^2 - 3*A^3*B*a*b^3)*c^2 - (3*B^4*a^3*b^2 - A*B^3*a^2*b^3 - 3*A^2*B^2*a*b^4)*c)*sqrt(x)) - 3*sqrt(2)*c^2*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-sqrt(2)*(B^3*b^7 - 4*A^3*a^2*c^5 + (4*A*B^2*a^3 + 20*A^2*B*a^2*b + 5*A^3*a*b^2)*c^4 - (4*B^3*a^3*b + 29*A*B^2*a^2*b^2 + 17*A^2*B*a*b^3 + A^3*b^4)*c^3 + (13*B^3*a^2*b^3 + 19*A*B^2*a*b^4 + 3*A^2*B*b^5)*c^2 - (7*B^3*a*b^5 + 3*A*B^2*b^6)*c + (B*b^4*c^5 + 4*(2*B*a^2 + A*a*b)*c^7 - (6*B*a*b^2 + A*b^3)*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*(B^4*a^2*b^4 - A*B^3*a*b^5 - A^4*a^2*c^4 + (5*A^3*B*a^2*b + A^4*a*b^2)*c^3 + (B^4*a^4 + 3*A*B^3*a^3*b - 6*A^2*B^2*a^2*b^2 - 3*A^3*B*a*b^3)*c^2 - (3*B^4*a^3*b^2 - A*B^3*a^2*b^3 - 3*A^2*B^2*a*b^4)*c)*sqrt(x)) + 4*(B*c*x - 3*B*b + 3*A*c)*sqrt(x))/c^2","B",0
1011,1,2642,0,0.958804," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{2} c \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\sqrt{2} {\left(B^{3} b^{4} - 4 \, A^{2} B a c^{3} + {\left(4 \, B^{3} a^{2} + 8 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(5 \, B^{3} a b^{2} + 2 \, A B^{2} b^{3}\right)} c - {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + 4 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 3 \, A^{3} B b c^{2} + A^{4} c^{3} - {\left(B^{4} a^{2} + A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} \sqrt{x}\right) - \sqrt{2} c \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-\sqrt{2} {\left(B^{3} b^{4} - 4 \, A^{2} B a c^{3} + {\left(4 \, B^{3} a^{2} + 8 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(5 \, B^{3} a b^{2} + 2 \, A B^{2} b^{3}\right)} c - {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + 4 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 3 \, A^{3} B b c^{2} + A^{4} c^{3} - {\left(B^{4} a^{2} + A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} \sqrt{x}\right) + \sqrt{2} c \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\sqrt{2} {\left(B^{3} b^{4} - 4 \, A^{2} B a c^{3} + {\left(4 \, B^{3} a^{2} + 8 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(5 \, B^{3} a b^{2} + 2 \, A B^{2} b^{3}\right)} c + {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + 4 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 3 \, A^{3} B b c^{2} + A^{4} c^{3} - {\left(B^{4} a^{2} + A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} \sqrt{x}\right) - \sqrt{2} c \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-\sqrt{2} {\left(B^{3} b^{4} - 4 \, A^{2} B a c^{3} + {\left(4 \, B^{3} a^{2} + 8 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(5 \, B^{3} a b^{2} + 2 \, A B^{2} b^{3}\right)} c + {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + 4 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 3 \, A^{3} B b c^{2} + A^{4} c^{3} - {\left(B^{4} a^{2} + A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} \sqrt{x}\right) + 4 \, B \sqrt{x}}{2 \, c}"," ",0,"1/2*(sqrt(2)*c*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(sqrt(2)*(B^3*b^4 - 4*A^2*B*a*c^3 + (4*B^3*a^2 + 8*A*B^2*a*b + A^2*B*b^2)*c^2 - (5*B^3*a*b^2 + 2*A*B^2*b^3)*c - (B*b^3*c^3 + 8*A*a*c^5 - 2*(2*B*a*b + A*b^2)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + 4*(B^4*a*b^2 - A*B^3*b^3 - 3*A^3*B*b*c^2 + A^4*c^3 - (B^4*a^2 + A*B^3*a*b - 3*A^2*B^2*b^2)*c)*sqrt(x)) - sqrt(2)*c*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-sqrt(2)*(B^3*b^4 - 4*A^2*B*a*c^3 + (4*B^3*a^2 + 8*A*B^2*a*b + A^2*B*b^2)*c^2 - (5*B^3*a*b^2 + 2*A*B^2*b^3)*c - (B*b^3*c^3 + 8*A*a*c^5 - 2*(2*B*a*b + A*b^2)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + 4*(B^4*a*b^2 - A*B^3*b^3 - 3*A^3*B*b*c^2 + A^4*c^3 - (B^4*a^2 + A*B^3*a*b - 3*A^2*B^2*b^2)*c)*sqrt(x)) + sqrt(2)*c*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(sqrt(2)*(B^3*b^4 - 4*A^2*B*a*c^3 + (4*B^3*a^2 + 8*A*B^2*a*b + A^2*B*b^2)*c^2 - (5*B^3*a*b^2 + 2*A*B^2*b^3)*c + (B*b^3*c^3 + 8*A*a*c^5 - 2*(2*B*a*b + A*b^2)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + 4*(B^4*a*b^2 - A*B^3*b^3 - 3*A^3*B*b*c^2 + A^4*c^3 - (B^4*a^2 + A*B^3*a*b - 3*A^2*B^2*b^2)*c)*sqrt(x)) - sqrt(2)*c*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-sqrt(2)*(B^3*b^4 - 4*A^2*B*a*c^3 + (4*B^3*a^2 + 8*A*B^2*a*b + A^2*B*b^2)*c^2 - (5*B^3*a*b^2 + 2*A*B^2*b^3)*c + (B*b^3*c^3 + 8*A*a*c^5 - 2*(2*B*a*b + A*b^2)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + 4*(B^4*a*b^2 - A*B^3*b^3 - 3*A^3*B*b*c^2 + A^4*c^3 - (B^4*a^2 + A*B^3*a*b - 3*A^2*B^2*b^2)*c)*sqrt(x)) + 4*B*sqrt(x))/c","B",0
1012,1,1577,0,0.676996," ","integrate((B*x+A)/(c*x^2+b*x+a)/x^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(\sqrt{2} {\left(A B^{2} a b^{2} + 4 \, A^{3} a c^{2} - {\left(4 \, A B^{2} a^{2} + A^{3} b^{2}\right)} c + {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} - 4 \, {\left(B^{4} a^{2} - A B^{3} a b + A^{3} B b c - A^{4} c^{2}\right)} \sqrt{x}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-\sqrt{2} {\left(A B^{2} a b^{2} + 4 \, A^{3} a c^{2} - {\left(4 \, A B^{2} a^{2} + A^{3} b^{2}\right)} c + {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} - 4 \, {\left(B^{4} a^{2} - A B^{3} a b + A^{3} B b c - A^{4} c^{2}\right)} \sqrt{x}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(\sqrt{2} {\left(A B^{2} a b^{2} + 4 \, A^{3} a c^{2} - {\left(4 \, A B^{2} a^{2} + A^{3} b^{2}\right)} c - {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} - 4 \, {\left(B^{4} a^{2} - A B^{3} a b + A^{3} B b c - A^{4} c^{2}\right)} \sqrt{x}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-\sqrt{2} {\left(A B^{2} a b^{2} + 4 \, A^{3} a c^{2} - {\left(4 \, A B^{2} a^{2} + A^{3} b^{2}\right)} c - {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} - 4 \, {\left(B^{4} a^{2} - A B^{3} a b + A^{3} B b c - A^{4} c^{2}\right)} \sqrt{x}\right)"," ",0,"1/2*sqrt(2)*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c + (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(sqrt(2)*(A*B^2*a*b^2 + 4*A^3*a*c^2 - (4*A*B^2*a^2 + A^3*b^2)*c + (4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c + (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2)) - 4*(B^4*a^2 - A*B^3*a*b + A^3*B*b*c - A^4*c^2)*sqrt(x)) - 1/2*sqrt(2)*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c + (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-sqrt(2)*(A*B^2*a*b^2 + 4*A^3*a*c^2 - (4*A*B^2*a^2 + A^3*b^2)*c + (4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c + (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2)) - 4*(B^4*a^2 - A*B^3*a*b + A^3*B*b*c - A^4*c^2)*sqrt(x)) + 1/2*sqrt(2)*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c - (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(sqrt(2)*(A*B^2*a*b^2 + 4*A^3*a*c^2 - (4*A*B^2*a^2 + A^3*b^2)*c - (4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c - (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2)) - 4*(B^4*a^2 - A*B^3*a*b + A^3*B*b*c - A^4*c^2)*sqrt(x)) - 1/2*sqrt(2)*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c - (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-sqrt(2)*(A*B^2*a*b^2 + 4*A^3*a*c^2 - (4*A*B^2*a^2 + A^3*b^2)*c - (4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c - (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2)) - 4*(B^4*a^2 - A*B^3*a*b + A^3*B*b*c - A^4*c^2)*sqrt(x))","B",0
1013,1,2925,0,0.940346," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{2} a x \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\sqrt{2} {\left(B^{3} a^{3} b^{2} - 3 \, A B^{2} a^{2} b^{3} + 3 \, A^{2} B a b^{4} - A^{3} b^{5} + 4 \, {\left(A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{2} - {\left(4 \, B^{3} a^{4} - 12 \, A B^{2} a^{3} b + 13 \, A^{2} B a^{2} b^{2} - 5 \, A^{3} a b^{3}\right)} c - {\left(B a^{4} b^{3} - A a^{3} b^{4} - 8 \, A a^{5} c^{2} - 2 \, {\left(2 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} + 4 \, {\left(A^{4} a c^{3} + {\left(A^{3} B a b - A^{4} b^{2}\right)} c^{2} - {\left(B^{4} a^{3} - 3 \, A B^{3} a^{2} b + 3 \, A^{2} B^{2} a b^{2} - A^{3} B b^{3}\right)} c\right)} \sqrt{x}\right) - \sqrt{2} a x \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-\sqrt{2} {\left(B^{3} a^{3} b^{2} - 3 \, A B^{2} a^{2} b^{3} + 3 \, A^{2} B a b^{4} - A^{3} b^{5} + 4 \, {\left(A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{2} - {\left(4 \, B^{3} a^{4} - 12 \, A B^{2} a^{3} b + 13 \, A^{2} B a^{2} b^{2} - 5 \, A^{3} a b^{3}\right)} c - {\left(B a^{4} b^{3} - A a^{3} b^{4} - 8 \, A a^{5} c^{2} - 2 \, {\left(2 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} + 4 \, {\left(A^{4} a c^{3} + {\left(A^{3} B a b - A^{4} b^{2}\right)} c^{2} - {\left(B^{4} a^{3} - 3 \, A B^{3} a^{2} b + 3 \, A^{2} B^{2} a b^{2} - A^{3} B b^{3}\right)} c\right)} \sqrt{x}\right) + \sqrt{2} a x \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\sqrt{2} {\left(B^{3} a^{3} b^{2} - 3 \, A B^{2} a^{2} b^{3} + 3 \, A^{2} B a b^{4} - A^{3} b^{5} + 4 \, {\left(A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{2} - {\left(4 \, B^{3} a^{4} - 12 \, A B^{2} a^{3} b + 13 \, A^{2} B a^{2} b^{2} - 5 \, A^{3} a b^{3}\right)} c + {\left(B a^{4} b^{3} - A a^{3} b^{4} - 8 \, A a^{5} c^{2} - 2 \, {\left(2 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} + 4 \, {\left(A^{4} a c^{3} + {\left(A^{3} B a b - A^{4} b^{2}\right)} c^{2} - {\left(B^{4} a^{3} - 3 \, A B^{3} a^{2} b + 3 \, A^{2} B^{2} a b^{2} - A^{3} B b^{3}\right)} c\right)} \sqrt{x}\right) - \sqrt{2} a x \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-\sqrt{2} {\left(B^{3} a^{3} b^{2} - 3 \, A B^{2} a^{2} b^{3} + 3 \, A^{2} B a b^{4} - A^{3} b^{5} + 4 \, {\left(A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{2} - {\left(4 \, B^{3} a^{4} - 12 \, A B^{2} a^{3} b + 13 \, A^{2} B a^{2} b^{2} - 5 \, A^{3} a b^{3}\right)} c + {\left(B a^{4} b^{3} - A a^{3} b^{4} - 8 \, A a^{5} c^{2} - 2 \, {\left(2 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} + 4 \, {\left(A^{4} a c^{3} + {\left(A^{3} B a b - A^{4} b^{2}\right)} c^{2} - {\left(B^{4} a^{3} - 3 \, A B^{3} a^{2} b + 3 \, A^{2} B^{2} a b^{2} - A^{3} B b^{3}\right)} c\right)} \sqrt{x}\right) - 4 \, A \sqrt{x}}{2 \, a x}"," ",0,"1/2*(sqrt(2)*a*x*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(sqrt(2)*(B^3*a^3*b^2 - 3*A*B^2*a^2*b^3 + 3*A^2*B*a*b^4 - A^3*b^5 + 4*(A^2*B*a^3 - A^3*a^2*b)*c^2 - (4*B^3*a^4 - 12*A*B^2*a^3*b + 13*A^2*B*a^2*b^2 - 5*A^3*a*b^3)*c - (B*a^4*b^3 - A*a^3*b^4 - 8*A*a^5*c^2 - 2*(2*B*a^5*b - 3*A*a^4*b^2)*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)) + 4*(A^4*a*c^3 + (A^3*B*a*b - A^4*b^2)*c^2 - (B^4*a^3 - 3*A*B^3*a^2*b + 3*A^2*B^2*a*b^2 - A^3*B*b^3)*c)*sqrt(x)) - sqrt(2)*a*x*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-sqrt(2)*(B^3*a^3*b^2 - 3*A*B^2*a^2*b^3 + 3*A^2*B*a*b^4 - A^3*b^5 + 4*(A^2*B*a^3 - A^3*a^2*b)*c^2 - (4*B^3*a^4 - 12*A*B^2*a^3*b + 13*A^2*B*a^2*b^2 - 5*A^3*a*b^3)*c - (B*a^4*b^3 - A*a^3*b^4 - 8*A*a^5*c^2 - 2*(2*B*a^5*b - 3*A*a^4*b^2)*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)) + 4*(A^4*a*c^3 + (A^3*B*a*b - A^4*b^2)*c^2 - (B^4*a^3 - 3*A*B^3*a^2*b + 3*A^2*B^2*a*b^2 - A^3*B*b^3)*c)*sqrt(x)) + sqrt(2)*a*x*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(sqrt(2)*(B^3*a^3*b^2 - 3*A*B^2*a^2*b^3 + 3*A^2*B*a*b^4 - A^3*b^5 + 4*(A^2*B*a^3 - A^3*a^2*b)*c^2 - (4*B^3*a^4 - 12*A*B^2*a^3*b + 13*A^2*B*a^2*b^2 - 5*A^3*a*b^3)*c + (B*a^4*b^3 - A*a^3*b^4 - 8*A*a^5*c^2 - 2*(2*B*a^5*b - 3*A*a^4*b^2)*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)) + 4*(A^4*a*c^3 + (A^3*B*a*b - A^4*b^2)*c^2 - (B^4*a^3 - 3*A*B^3*a^2*b + 3*A^2*B^2*a*b^2 - A^3*B*b^3)*c)*sqrt(x)) - sqrt(2)*a*x*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-sqrt(2)*(B^3*a^3*b^2 - 3*A*B^2*a^2*b^3 + 3*A^2*B*a*b^4 - A^3*b^5 + 4*(A^2*B*a^3 - A^3*a^2*b)*c^2 - (4*B^3*a^4 - 12*A*B^2*a^3*b + 13*A^2*B*a^2*b^2 - 5*A^3*a*b^3)*c + (B*a^4*b^3 - A*a^3*b^4 - 8*A*a^5*c^2 - 2*(2*B*a^5*b - 3*A*a^4*b^2)*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)) + 4*(A^4*a*c^3 + (A^3*B*a*b - A^4*b^2)*c^2 - (B^4*a^3 - 3*A*B^3*a^2*b + 3*A^2*B^2*a*b^2 - A^3*B*b^3)*c)*sqrt(x)) - 4*A*sqrt(x))/(a*x)","B",0
1014,1,5453,0,1.382099," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} a^{2} x^{2} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(\sqrt{2} {\left(B^{3} a^{3} b^{5} - 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} - A^{3} b^{8} - 4 \, A^{3} a^{4} c^{4} + {\left(4 \, A B^{2} a^{5} - 20 \, A^{2} B a^{4} b + 17 \, A^{3} a^{3} b^{2}\right)} c^{3} + {\left(4 \, B^{3} a^{5} b - 25 \, A B^{2} a^{4} b^{2} + 41 \, A^{2} B a^{3} b^{3} - 20 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(5 \, B^{3} a^{4} b^{3} - 18 \, A B^{2} a^{3} b^{4} + 21 \, A^{2} B a^{2} b^{5} - 8 \, A^{3} a b^{6}\right)} c - {\left(B a^{6} b^{4} - A a^{5} b^{5} + 4 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{2} - {\left(6 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} + 4 \, {\left(A^{4} a^{2} c^{5} + 3 \, {\left(A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{4} - {\left(B^{4} a^{4} - 5 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - A^{3} B a b^{3} - A^{4} b^{4}\right)} c^{3} + {\left(B^{4} a^{3} b^{2} - 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} - A^{3} B b^{5}\right)} c^{2}\right)} \sqrt{x}\right) - 3 \, \sqrt{2} a^{2} x^{2} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(-\sqrt{2} {\left(B^{3} a^{3} b^{5} - 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} - A^{3} b^{8} - 4 \, A^{3} a^{4} c^{4} + {\left(4 \, A B^{2} a^{5} - 20 \, A^{2} B a^{4} b + 17 \, A^{3} a^{3} b^{2}\right)} c^{3} + {\left(4 \, B^{3} a^{5} b - 25 \, A B^{2} a^{4} b^{2} + 41 \, A^{2} B a^{3} b^{3} - 20 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(5 \, B^{3} a^{4} b^{3} - 18 \, A B^{2} a^{3} b^{4} + 21 \, A^{2} B a^{2} b^{5} - 8 \, A^{3} a b^{6}\right)} c - {\left(B a^{6} b^{4} - A a^{5} b^{5} + 4 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{2} - {\left(6 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} + 4 \, {\left(A^{4} a^{2} c^{5} + 3 \, {\left(A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{4} - {\left(B^{4} a^{4} - 5 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - A^{3} B a b^{3} - A^{4} b^{4}\right)} c^{3} + {\left(B^{4} a^{3} b^{2} - 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} - A^{3} B b^{5}\right)} c^{2}\right)} \sqrt{x}\right) + 3 \, \sqrt{2} a^{2} x^{2} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(\sqrt{2} {\left(B^{3} a^{3} b^{5} - 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} - A^{3} b^{8} - 4 \, A^{3} a^{4} c^{4} + {\left(4 \, A B^{2} a^{5} - 20 \, A^{2} B a^{4} b + 17 \, A^{3} a^{3} b^{2}\right)} c^{3} + {\left(4 \, B^{3} a^{5} b - 25 \, A B^{2} a^{4} b^{2} + 41 \, A^{2} B a^{3} b^{3} - 20 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(5 \, B^{3} a^{4} b^{3} - 18 \, A B^{2} a^{3} b^{4} + 21 \, A^{2} B a^{2} b^{5} - 8 \, A^{3} a b^{6}\right)} c + {\left(B a^{6} b^{4} - A a^{5} b^{5} + 4 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{2} - {\left(6 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} + 4 \, {\left(A^{4} a^{2} c^{5} + 3 \, {\left(A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{4} - {\left(B^{4} a^{4} - 5 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - A^{3} B a b^{3} - A^{4} b^{4}\right)} c^{3} + {\left(B^{4} a^{3} b^{2} - 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} - A^{3} B b^{5}\right)} c^{2}\right)} \sqrt{x}\right) - 3 \, \sqrt{2} a^{2} x^{2} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(-\sqrt{2} {\left(B^{3} a^{3} b^{5} - 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} - A^{3} b^{8} - 4 \, A^{3} a^{4} c^{4} + {\left(4 \, A B^{2} a^{5} - 20 \, A^{2} B a^{4} b + 17 \, A^{3} a^{3} b^{2}\right)} c^{3} + {\left(4 \, B^{3} a^{5} b - 25 \, A B^{2} a^{4} b^{2} + 41 \, A^{2} B a^{3} b^{3} - 20 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(5 \, B^{3} a^{4} b^{3} - 18 \, A B^{2} a^{3} b^{4} + 21 \, A^{2} B a^{2} b^{5} - 8 \, A^{3} a b^{6}\right)} c + {\left(B a^{6} b^{4} - A a^{5} b^{5} + 4 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{2} - {\left(6 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} + 4 \, {\left(A^{4} a^{2} c^{5} + 3 \, {\left(A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{4} - {\left(B^{4} a^{4} - 5 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - A^{3} B a b^{3} - A^{4} b^{4}\right)} c^{3} + {\left(B^{4} a^{3} b^{2} - 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} - A^{3} B b^{5}\right)} c^{2}\right)} \sqrt{x}\right) - 4 \, {\left(A a + 3 \, {\left(B a - A b\right)} x\right)} \sqrt{x}}{6 \, a^{2} x^{2}}"," ",0,"1/6*(3*sqrt(2)*a^2*x^2*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c + (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(sqrt(2)*(B^3*a^3*b^5 - 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 - A^3*b^8 - 4*A^3*a^4*c^4 + (4*A*B^2*a^5 - 20*A^2*B*a^4*b + 17*A^3*a^3*b^2)*c^3 + (4*B^3*a^5*b - 25*A*B^2*a^4*b^2 + 41*A^2*B*a^3*b^3 - 20*A^3*a^2*b^4)*c^2 - (5*B^3*a^4*b^3 - 18*A*B^2*a^3*b^4 + 21*A^2*B*a^2*b^5 - 8*A^3*a*b^6)*c - (B*a^6*b^4 - A*a^5*b^5 + 4*(2*B*a^8 - 3*A*a^7*b)*c^2 - (6*B*a^7*b^2 - 7*A*a^6*b^3)*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c + (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)) + 4*(A^4*a^2*c^5 + 3*(A^3*B*a^2*b - A^4*a*b^2)*c^4 - (B^4*a^4 - 5*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - A^3*B*a*b^3 - A^4*b^4)*c^3 + (B^4*a^3*b^2 - 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 - A^3*B*b^5)*c^2)*sqrt(x)) - 3*sqrt(2)*a^2*x^2*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c + (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(-sqrt(2)*(B^3*a^3*b^5 - 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 - A^3*b^8 - 4*A^3*a^4*c^4 + (4*A*B^2*a^5 - 20*A^2*B*a^4*b + 17*A^3*a^3*b^2)*c^3 + (4*B^3*a^5*b - 25*A*B^2*a^4*b^2 + 41*A^2*B*a^3*b^3 - 20*A^3*a^2*b^4)*c^2 - (5*B^3*a^4*b^3 - 18*A*B^2*a^3*b^4 + 21*A^2*B*a^2*b^5 - 8*A^3*a*b^6)*c - (B*a^6*b^4 - A*a^5*b^5 + 4*(2*B*a^8 - 3*A*a^7*b)*c^2 - (6*B*a^7*b^2 - 7*A*a^6*b^3)*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c + (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)) + 4*(A^4*a^2*c^5 + 3*(A^3*B*a^2*b - A^4*a*b^2)*c^4 - (B^4*a^4 - 5*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - A^3*B*a*b^3 - A^4*b^4)*c^3 + (B^4*a^3*b^2 - 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 - A^3*B*b^5)*c^2)*sqrt(x)) + 3*sqrt(2)*a^2*x^2*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c - (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(sqrt(2)*(B^3*a^3*b^5 - 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 - A^3*b^8 - 4*A^3*a^4*c^4 + (4*A*B^2*a^5 - 20*A^2*B*a^4*b + 17*A^3*a^3*b^2)*c^3 + (4*B^3*a^5*b - 25*A*B^2*a^4*b^2 + 41*A^2*B*a^3*b^3 - 20*A^3*a^2*b^4)*c^2 - (5*B^3*a^4*b^3 - 18*A*B^2*a^3*b^4 + 21*A^2*B*a^2*b^5 - 8*A^3*a*b^6)*c + (B*a^6*b^4 - A*a^5*b^5 + 4*(2*B*a^8 - 3*A*a^7*b)*c^2 - (6*B*a^7*b^2 - 7*A*a^6*b^3)*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c - (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)) + 4*(A^4*a^2*c^5 + 3*(A^3*B*a^2*b - A^4*a*b^2)*c^4 - (B^4*a^4 - 5*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - A^3*B*a*b^3 - A^4*b^4)*c^3 + (B^4*a^3*b^2 - 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 - A^3*B*b^5)*c^2)*sqrt(x)) - 3*sqrt(2)*a^2*x^2*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c - (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(-sqrt(2)*(B^3*a^3*b^5 - 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 - A^3*b^8 - 4*A^3*a^4*c^4 + (4*A*B^2*a^5 - 20*A^2*B*a^4*b + 17*A^3*a^3*b^2)*c^3 + (4*B^3*a^5*b - 25*A*B^2*a^4*b^2 + 41*A^2*B*a^3*b^3 - 20*A^3*a^2*b^4)*c^2 - (5*B^3*a^4*b^3 - 18*A*B^2*a^3*b^4 + 21*A^2*B*a^2*b^5 - 8*A^3*a*b^6)*c + (B*a^6*b^4 - A*a^5*b^5 + 4*(2*B*a^8 - 3*A*a^7*b)*c^2 - (6*B*a^7*b^2 - 7*A*a^6*b^3)*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c - (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)) + 4*(A^4*a^2*c^5 + 3*(A^3*B*a^2*b - A^4*a*b^2)*c^4 - (B^4*a^4 - 5*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - A^3*B*a*b^3 - A^4*b^4)*c^3 + (B^4*a^3*b^2 - 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 - A^3*B*b^5)*c^2)*sqrt(x)) - 4*(A*a + 3*(B*a - A*b)*x)*sqrt(x))/(a^2*x^2)","B",0
1015,1,7971,0,3.417483," ","integrate((B*x+A)/x^(7/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} a^{3} x^{3} \sqrt{-\frac{B^{2} a^{2} b^{5} - 2 \, A B a b^{6} + A^{2} b^{7} + {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + {\left(5 \, B^{2} a^{4} b - 18 \, A B a^{3} b^{2} + 14 \, A^{2} a^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} + 7 \, A^{2} a b^{5}\right)} c + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} \log\left(\sqrt{2} {\left(B^{3} a^{3} b^{8} - 3 \, A B^{2} a^{2} b^{9} + 3 \, A^{2} B a b^{10} - A^{3} b^{11} - 4 \, {\left(A^{2} B a^{6} - 2 \, A^{3} a^{5} b\right)} c^{5} + {\left(4 \, B^{3} a^{7} - 32 \, A B^{2} a^{6} b + 77 \, A^{2} B a^{5} b^{2} - 54 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(17 \, B^{3} a^{6} b^{2} - 92 \, A B^{2} a^{5} b^{3} + 151 \, A^{2} B a^{4} b^{4} - 77 \, A^{3} a^{3} b^{5}\right)} c^{3} + {\left(20 \, B^{3} a^{5} b^{4} - 81 \, A B^{2} a^{4} b^{5} + 105 \, A^{2} B a^{3} b^{6} - 44 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{6} - 27 \, A B^{2} a^{3} b^{7} + 30 \, A^{2} B a^{2} b^{8} - 11 \, A^{3} a b^{9}\right)} c - {\left(B a^{8} b^{5} - A a^{7} b^{6} + 8 \, A a^{10} c^{3} + 6 \, {\left(2 \, B a^{10} b - 3 \, A a^{9} b^{2}\right)} c^{2} - {\left(7 \, B a^{9} b^{3} - 8 \, A a^{8} b^{4}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 2 \, A B a b^{6} + A^{2} b^{7} + {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + {\left(5 \, B^{2} a^{4} b - 18 \, A B a^{3} b^{2} + 14 \, A^{2} a^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} + 7 \, A^{2} a b^{5}\right)} c + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} + 4 \, {\left(A^{4} a^{3} c^{7} + {\left(5 \, A^{3} B a^{3} b - 6 \, A^{4} a^{2} b^{2}\right)} c^{6} - {\left(B^{4} a^{5} - 7 \, A B^{3} a^{4} b + 9 \, A^{2} B^{2} a^{3} b^{2} + 2 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{5} + {\left(3 \, B^{4} a^{4} b^{2} - 11 \, A B^{3} a^{3} b^{3} + 12 \, A^{2} B^{2} a^{2} b^{4} - 3 \, A^{3} B a b^{5} - A^{4} b^{6}\right)} c^{4} - {\left(B^{4} a^{3} b^{4} - 3 \, A B^{3} a^{2} b^{5} + 3 \, A^{2} B^{2} a b^{6} - A^{3} B b^{7}\right)} c^{3}\right)} \sqrt{x}\right) - 15 \, \sqrt{2} a^{3} x^{3} \sqrt{-\frac{B^{2} a^{2} b^{5} - 2 \, A B a b^{6} + A^{2} b^{7} + {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + {\left(5 \, B^{2} a^{4} b - 18 \, A B a^{3} b^{2} + 14 \, A^{2} a^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} + 7 \, A^{2} a b^{5}\right)} c + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} \log\left(-\sqrt{2} {\left(B^{3} a^{3} b^{8} - 3 \, A B^{2} a^{2} b^{9} + 3 \, A^{2} B a b^{10} - A^{3} b^{11} - 4 \, {\left(A^{2} B a^{6} - 2 \, A^{3} a^{5} b\right)} c^{5} + {\left(4 \, B^{3} a^{7} - 32 \, A B^{2} a^{6} b + 77 \, A^{2} B a^{5} b^{2} - 54 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(17 \, B^{3} a^{6} b^{2} - 92 \, A B^{2} a^{5} b^{3} + 151 \, A^{2} B a^{4} b^{4} - 77 \, A^{3} a^{3} b^{5}\right)} c^{3} + {\left(20 \, B^{3} a^{5} b^{4} - 81 \, A B^{2} a^{4} b^{5} + 105 \, A^{2} B a^{3} b^{6} - 44 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{6} - 27 \, A B^{2} a^{3} b^{7} + 30 \, A^{2} B a^{2} b^{8} - 11 \, A^{3} a b^{9}\right)} c - {\left(B a^{8} b^{5} - A a^{7} b^{6} + 8 \, A a^{10} c^{3} + 6 \, {\left(2 \, B a^{10} b - 3 \, A a^{9} b^{2}\right)} c^{2} - {\left(7 \, B a^{9} b^{3} - 8 \, A a^{8} b^{4}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 2 \, A B a b^{6} + A^{2} b^{7} + {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + {\left(5 \, B^{2} a^{4} b - 18 \, A B a^{3} b^{2} + 14 \, A^{2} a^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} + 7 \, A^{2} a b^{5}\right)} c + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} + 4 \, {\left(A^{4} a^{3} c^{7} + {\left(5 \, A^{3} B a^{3} b - 6 \, A^{4} a^{2} b^{2}\right)} c^{6} - {\left(B^{4} a^{5} - 7 \, A B^{3} a^{4} b + 9 \, A^{2} B^{2} a^{3} b^{2} + 2 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{5} + {\left(3 \, B^{4} a^{4} b^{2} - 11 \, A B^{3} a^{3} b^{3} + 12 \, A^{2} B^{2} a^{2} b^{4} - 3 \, A^{3} B a b^{5} - A^{4} b^{6}\right)} c^{4} - {\left(B^{4} a^{3} b^{4} - 3 \, A B^{3} a^{2} b^{5} + 3 \, A^{2} B^{2} a b^{6} - A^{3} B b^{7}\right)} c^{3}\right)} \sqrt{x}\right) + 15 \, \sqrt{2} a^{3} x^{3} \sqrt{-\frac{B^{2} a^{2} b^{5} - 2 \, A B a b^{6} + A^{2} b^{7} + {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + {\left(5 \, B^{2} a^{4} b - 18 \, A B a^{3} b^{2} + 14 \, A^{2} a^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} + 7 \, A^{2} a b^{5}\right)} c - {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} \log\left(\sqrt{2} {\left(B^{3} a^{3} b^{8} - 3 \, A B^{2} a^{2} b^{9} + 3 \, A^{2} B a b^{10} - A^{3} b^{11} - 4 \, {\left(A^{2} B a^{6} - 2 \, A^{3} a^{5} b\right)} c^{5} + {\left(4 \, B^{3} a^{7} - 32 \, A B^{2} a^{6} b + 77 \, A^{2} B a^{5} b^{2} - 54 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(17 \, B^{3} a^{6} b^{2} - 92 \, A B^{2} a^{5} b^{3} + 151 \, A^{2} B a^{4} b^{4} - 77 \, A^{3} a^{3} b^{5}\right)} c^{3} + {\left(20 \, B^{3} a^{5} b^{4} - 81 \, A B^{2} a^{4} b^{5} + 105 \, A^{2} B a^{3} b^{6} - 44 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{6} - 27 \, A B^{2} a^{3} b^{7} + 30 \, A^{2} B a^{2} b^{8} - 11 \, A^{3} a b^{9}\right)} c + {\left(B a^{8} b^{5} - A a^{7} b^{6} + 8 \, A a^{10} c^{3} + 6 \, {\left(2 \, B a^{10} b - 3 \, A a^{9} b^{2}\right)} c^{2} - {\left(7 \, B a^{9} b^{3} - 8 \, A a^{8} b^{4}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 2 \, A B a b^{6} + A^{2} b^{7} + {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + {\left(5 \, B^{2} a^{4} b - 18 \, A B a^{3} b^{2} + 14 \, A^{2} a^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} + 7 \, A^{2} a b^{5}\right)} c - {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} + 4 \, {\left(A^{4} a^{3} c^{7} + {\left(5 \, A^{3} B a^{3} b - 6 \, A^{4} a^{2} b^{2}\right)} c^{6} - {\left(B^{4} a^{5} - 7 \, A B^{3} a^{4} b + 9 \, A^{2} B^{2} a^{3} b^{2} + 2 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{5} + {\left(3 \, B^{4} a^{4} b^{2} - 11 \, A B^{3} a^{3} b^{3} + 12 \, A^{2} B^{2} a^{2} b^{4} - 3 \, A^{3} B a b^{5} - A^{4} b^{6}\right)} c^{4} - {\left(B^{4} a^{3} b^{4} - 3 \, A B^{3} a^{2} b^{5} + 3 \, A^{2} B^{2} a b^{6} - A^{3} B b^{7}\right)} c^{3}\right)} \sqrt{x}\right) - 15 \, \sqrt{2} a^{3} x^{3} \sqrt{-\frac{B^{2} a^{2} b^{5} - 2 \, A B a b^{6} + A^{2} b^{7} + {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + {\left(5 \, B^{2} a^{4} b - 18 \, A B a^{3} b^{2} + 14 \, A^{2} a^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} + 7 \, A^{2} a b^{5}\right)} c - {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} \log\left(-\sqrt{2} {\left(B^{3} a^{3} b^{8} - 3 \, A B^{2} a^{2} b^{9} + 3 \, A^{2} B a b^{10} - A^{3} b^{11} - 4 \, {\left(A^{2} B a^{6} - 2 \, A^{3} a^{5} b\right)} c^{5} + {\left(4 \, B^{3} a^{7} - 32 \, A B^{2} a^{6} b + 77 \, A^{2} B a^{5} b^{2} - 54 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(17 \, B^{3} a^{6} b^{2} - 92 \, A B^{2} a^{5} b^{3} + 151 \, A^{2} B a^{4} b^{4} - 77 \, A^{3} a^{3} b^{5}\right)} c^{3} + {\left(20 \, B^{3} a^{5} b^{4} - 81 \, A B^{2} a^{4} b^{5} + 105 \, A^{2} B a^{3} b^{6} - 44 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{6} - 27 \, A B^{2} a^{3} b^{7} + 30 \, A^{2} B a^{2} b^{8} - 11 \, A^{3} a b^{9}\right)} c + {\left(B a^{8} b^{5} - A a^{7} b^{6} + 8 \, A a^{10} c^{3} + 6 \, {\left(2 \, B a^{10} b - 3 \, A a^{9} b^{2}\right)} c^{2} - {\left(7 \, B a^{9} b^{3} - 8 \, A a^{8} b^{4}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 2 \, A B a b^{6} + A^{2} b^{7} + {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + {\left(5 \, B^{2} a^{4} b - 18 \, A B a^{3} b^{2} + 14 \, A^{2} a^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} + 7 \, A^{2} a b^{5}\right)} c - {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 4 \, A B^{3} a^{3} b^{9} + 6 \, A^{2} B^{2} a^{2} b^{10} - 4 \, A^{3} B a b^{11} + A^{4} b^{12} + A^{4} a^{6} c^{6} - 2 \, {\left(A^{2} B^{2} a^{7} - 6 \, A^{3} B a^{6} b + 6 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(B^{4} a^{8} - 12 \, A B^{3} a^{7} b + 54 \, A^{2} B^{2} a^{6} b^{2} - 88 \, A^{3} B a^{5} b^{3} + 46 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{7} b^{2} - 26 \, A B^{3} a^{6} b^{3} + 72 \, A^{2} B^{2} a^{5} b^{4} - 80 \, A^{3} B a^{4} b^{5} + 31 \, A^{4} a^{3} b^{6}\right)} c^{3} + {\left(11 \, B^{4} a^{6} b^{4} - 64 \, A B^{3} a^{5} b^{5} + 132 \, A^{2} B^{2} a^{4} b^{6} - 116 \, A^{3} B a^{3} b^{7} + 37 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a^{5} b^{6} - 14 \, A B^{3} a^{4} b^{7} + 24 \, A^{2} B^{2} a^{3} b^{8} - 18 \, A^{3} B a^{2} b^{9} + 5 \, A^{4} a b^{10}\right)} c}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} + 4 \, {\left(A^{4} a^{3} c^{7} + {\left(5 \, A^{3} B a^{3} b - 6 \, A^{4} a^{2} b^{2}\right)} c^{6} - {\left(B^{4} a^{5} - 7 \, A B^{3} a^{4} b + 9 \, A^{2} B^{2} a^{3} b^{2} + 2 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{5} + {\left(3 \, B^{4} a^{4} b^{2} - 11 \, A B^{3} a^{3} b^{3} + 12 \, A^{2} B^{2} a^{2} b^{4} - 3 \, A^{3} B a b^{5} - A^{4} b^{6}\right)} c^{4} - {\left(B^{4} a^{3} b^{4} - 3 \, A B^{3} a^{2} b^{5} + 3 \, A^{2} B^{2} a b^{6} - A^{3} B b^{7}\right)} c^{3}\right)} \sqrt{x}\right) - 4 \, {\left(3 \, A a^{2} - 15 \, {\left(B a b - A b^{2} + A a c\right)} x^{2} + 5 \, {\left(B a^{2} - A a b\right)} x\right)} \sqrt{x}}{30 \, a^{3} x^{3}}"," ",0,"1/30*(15*sqrt(2)*a^3*x^3*sqrt(-(B^2*a^2*b^5 - 2*A*B*a*b^6 + A^2*b^7 + (4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + (5*B^2*a^4*b - 18*A*B*a^3*b^2 + 14*A^2*a^2*b^3)*c^2 - (5*B^2*a^3*b^3 - 12*A*B*a^2*b^4 + 7*A^2*a*b^5)*c + (a^7*b^2 - 4*a^8*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c))*log(sqrt(2)*(B^3*a^3*b^8 - 3*A*B^2*a^2*b^9 + 3*A^2*B*a*b^10 - A^3*b^11 - 4*(A^2*B*a^6 - 2*A^3*a^5*b)*c^5 + (4*B^3*a^7 - 32*A*B^2*a^6*b + 77*A^2*B*a^5*b^2 - 54*A^3*a^4*b^3)*c^4 - (17*B^3*a^6*b^2 - 92*A*B^2*a^5*b^3 + 151*A^2*B*a^4*b^4 - 77*A^3*a^3*b^5)*c^3 + (20*B^3*a^5*b^4 - 81*A*B^2*a^4*b^5 + 105*A^2*B*a^3*b^6 - 44*A^3*a^2*b^7)*c^2 - (8*B^3*a^4*b^6 - 27*A*B^2*a^3*b^7 + 30*A^2*B*a^2*b^8 - 11*A^3*a*b^9)*c - (B*a^8*b^5 - A*a^7*b^6 + 8*A*a^10*c^3 + 6*(2*B*a^10*b - 3*A*a^9*b^2)*c^2 - (7*B*a^9*b^3 - 8*A*a^8*b^4)*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))*sqrt(-(B^2*a^2*b^5 - 2*A*B*a*b^6 + A^2*b^7 + (4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + (5*B^2*a^4*b - 18*A*B*a^3*b^2 + 14*A^2*a^2*b^3)*c^2 - (5*B^2*a^3*b^3 - 12*A*B*a^2*b^4 + 7*A^2*a*b^5)*c + (a^7*b^2 - 4*a^8*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c)) + 4*(A^4*a^3*c^7 + (5*A^3*B*a^3*b - 6*A^4*a^2*b^2)*c^6 - (B^4*a^5 - 7*A*B^3*a^4*b + 9*A^2*B^2*a^3*b^2 + 2*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^5 + (3*B^4*a^4*b^2 - 11*A*B^3*a^3*b^3 + 12*A^2*B^2*a^2*b^4 - 3*A^3*B*a*b^5 - A^4*b^6)*c^4 - (B^4*a^3*b^4 - 3*A*B^3*a^2*b^5 + 3*A^2*B^2*a*b^6 - A^3*B*b^7)*c^3)*sqrt(x)) - 15*sqrt(2)*a^3*x^3*sqrt(-(B^2*a^2*b^5 - 2*A*B*a*b^6 + A^2*b^7 + (4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + (5*B^2*a^4*b - 18*A*B*a^3*b^2 + 14*A^2*a^2*b^3)*c^2 - (5*B^2*a^3*b^3 - 12*A*B*a^2*b^4 + 7*A^2*a*b^5)*c + (a^7*b^2 - 4*a^8*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c))*log(-sqrt(2)*(B^3*a^3*b^8 - 3*A*B^2*a^2*b^9 + 3*A^2*B*a*b^10 - A^3*b^11 - 4*(A^2*B*a^6 - 2*A^3*a^5*b)*c^5 + (4*B^3*a^7 - 32*A*B^2*a^6*b + 77*A^2*B*a^5*b^2 - 54*A^3*a^4*b^3)*c^4 - (17*B^3*a^6*b^2 - 92*A*B^2*a^5*b^3 + 151*A^2*B*a^4*b^4 - 77*A^3*a^3*b^5)*c^3 + (20*B^3*a^5*b^4 - 81*A*B^2*a^4*b^5 + 105*A^2*B*a^3*b^6 - 44*A^3*a^2*b^7)*c^2 - (8*B^3*a^4*b^6 - 27*A*B^2*a^3*b^7 + 30*A^2*B*a^2*b^8 - 11*A^3*a*b^9)*c - (B*a^8*b^5 - A*a^7*b^6 + 8*A*a^10*c^3 + 6*(2*B*a^10*b - 3*A*a^9*b^2)*c^2 - (7*B*a^9*b^3 - 8*A*a^8*b^4)*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))*sqrt(-(B^2*a^2*b^5 - 2*A*B*a*b^6 + A^2*b^7 + (4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + (5*B^2*a^4*b - 18*A*B*a^3*b^2 + 14*A^2*a^2*b^3)*c^2 - (5*B^2*a^3*b^3 - 12*A*B*a^2*b^4 + 7*A^2*a*b^5)*c + (a^7*b^2 - 4*a^8*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c)) + 4*(A^4*a^3*c^7 + (5*A^3*B*a^3*b - 6*A^4*a^2*b^2)*c^6 - (B^4*a^5 - 7*A*B^3*a^4*b + 9*A^2*B^2*a^3*b^2 + 2*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^5 + (3*B^4*a^4*b^2 - 11*A*B^3*a^3*b^3 + 12*A^2*B^2*a^2*b^4 - 3*A^3*B*a*b^5 - A^4*b^6)*c^4 - (B^4*a^3*b^4 - 3*A*B^3*a^2*b^5 + 3*A^2*B^2*a*b^6 - A^3*B*b^7)*c^3)*sqrt(x)) + 15*sqrt(2)*a^3*x^3*sqrt(-(B^2*a^2*b^5 - 2*A*B*a*b^6 + A^2*b^7 + (4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + (5*B^2*a^4*b - 18*A*B*a^3*b^2 + 14*A^2*a^2*b^3)*c^2 - (5*B^2*a^3*b^3 - 12*A*B*a^2*b^4 + 7*A^2*a*b^5)*c - (a^7*b^2 - 4*a^8*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c))*log(sqrt(2)*(B^3*a^3*b^8 - 3*A*B^2*a^2*b^9 + 3*A^2*B*a*b^10 - A^3*b^11 - 4*(A^2*B*a^6 - 2*A^3*a^5*b)*c^5 + (4*B^3*a^7 - 32*A*B^2*a^6*b + 77*A^2*B*a^5*b^2 - 54*A^3*a^4*b^3)*c^4 - (17*B^3*a^6*b^2 - 92*A*B^2*a^5*b^3 + 151*A^2*B*a^4*b^4 - 77*A^3*a^3*b^5)*c^3 + (20*B^3*a^5*b^4 - 81*A*B^2*a^4*b^5 + 105*A^2*B*a^3*b^6 - 44*A^3*a^2*b^7)*c^2 - (8*B^3*a^4*b^6 - 27*A*B^2*a^3*b^7 + 30*A^2*B*a^2*b^8 - 11*A^3*a*b^9)*c + (B*a^8*b^5 - A*a^7*b^6 + 8*A*a^10*c^3 + 6*(2*B*a^10*b - 3*A*a^9*b^2)*c^2 - (7*B*a^9*b^3 - 8*A*a^8*b^4)*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))*sqrt(-(B^2*a^2*b^5 - 2*A*B*a*b^6 + A^2*b^7 + (4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + (5*B^2*a^4*b - 18*A*B*a^3*b^2 + 14*A^2*a^2*b^3)*c^2 - (5*B^2*a^3*b^3 - 12*A*B*a^2*b^4 + 7*A^2*a*b^5)*c - (a^7*b^2 - 4*a^8*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c)) + 4*(A^4*a^3*c^7 + (5*A^3*B*a^3*b - 6*A^4*a^2*b^2)*c^6 - (B^4*a^5 - 7*A*B^3*a^4*b + 9*A^2*B^2*a^3*b^2 + 2*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^5 + (3*B^4*a^4*b^2 - 11*A*B^3*a^3*b^3 + 12*A^2*B^2*a^2*b^4 - 3*A^3*B*a*b^5 - A^4*b^6)*c^4 - (B^4*a^3*b^4 - 3*A*B^3*a^2*b^5 + 3*A^2*B^2*a*b^6 - A^3*B*b^7)*c^3)*sqrt(x)) - 15*sqrt(2)*a^3*x^3*sqrt(-(B^2*a^2*b^5 - 2*A*B*a*b^6 + A^2*b^7 + (4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + (5*B^2*a^4*b - 18*A*B*a^3*b^2 + 14*A^2*a^2*b^3)*c^2 - (5*B^2*a^3*b^3 - 12*A*B*a^2*b^4 + 7*A^2*a*b^5)*c - (a^7*b^2 - 4*a^8*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c))*log(-sqrt(2)*(B^3*a^3*b^8 - 3*A*B^2*a^2*b^9 + 3*A^2*B*a*b^10 - A^3*b^11 - 4*(A^2*B*a^6 - 2*A^3*a^5*b)*c^5 + (4*B^3*a^7 - 32*A*B^2*a^6*b + 77*A^2*B*a^5*b^2 - 54*A^3*a^4*b^3)*c^4 - (17*B^3*a^6*b^2 - 92*A*B^2*a^5*b^3 + 151*A^2*B*a^4*b^4 - 77*A^3*a^3*b^5)*c^3 + (20*B^3*a^5*b^4 - 81*A*B^2*a^4*b^5 + 105*A^2*B*a^3*b^6 - 44*A^3*a^2*b^7)*c^2 - (8*B^3*a^4*b^6 - 27*A*B^2*a^3*b^7 + 30*A^2*B*a^2*b^8 - 11*A^3*a*b^9)*c + (B*a^8*b^5 - A*a^7*b^6 + 8*A*a^10*c^3 + 6*(2*B*a^10*b - 3*A*a^9*b^2)*c^2 - (7*B*a^9*b^3 - 8*A*a^8*b^4)*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))*sqrt(-(B^2*a^2*b^5 - 2*A*B*a*b^6 + A^2*b^7 + (4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + (5*B^2*a^4*b - 18*A*B*a^3*b^2 + 14*A^2*a^2*b^3)*c^2 - (5*B^2*a^3*b^3 - 12*A*B*a^2*b^4 + 7*A^2*a*b^5)*c - (a^7*b^2 - 4*a^8*c)*sqrt((B^4*a^4*b^8 - 4*A*B^3*a^3*b^9 + 6*A^2*B^2*a^2*b^10 - 4*A^3*B*a*b^11 + A^4*b^12 + A^4*a^6*c^6 - 2*(A^2*B^2*a^7 - 6*A^3*B*a^6*b + 6*A^4*a^5*b^2)*c^5 + (B^4*a^8 - 12*A*B^3*a^7*b + 54*A^2*B^2*a^6*b^2 - 88*A^3*B*a^5*b^3 + 46*A^4*a^4*b^4)*c^4 - 2*(3*B^4*a^7*b^2 - 26*A*B^3*a^6*b^3 + 72*A^2*B^2*a^5*b^4 - 80*A^3*B*a^4*b^5 + 31*A^4*a^3*b^6)*c^3 + (11*B^4*a^6*b^4 - 64*A*B^3*a^5*b^5 + 132*A^2*B^2*a^4*b^6 - 116*A^3*B*a^3*b^7 + 37*A^4*a^2*b^8)*c^2 - 2*(3*B^4*a^5*b^6 - 14*A*B^3*a^4*b^7 + 24*A^2*B^2*a^3*b^8 - 18*A^3*B*a^2*b^9 + 5*A^4*a*b^10)*c)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c)) + 4*(A^4*a^3*c^7 + (5*A^3*B*a^3*b - 6*A^4*a^2*b^2)*c^6 - (B^4*a^5 - 7*A*B^3*a^4*b + 9*A^2*B^2*a^3*b^2 + 2*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^5 + (3*B^4*a^4*b^2 - 11*A*B^3*a^3*b^3 + 12*A^2*B^2*a^2*b^4 - 3*A^3*B*a*b^5 - A^4*b^6)*c^4 - (B^4*a^3*b^4 - 3*A*B^3*a^2*b^5 + 3*A^2*B^2*a*b^6 - A^3*B*b^7)*c^3)*sqrt(x)) - 4*(3*A*a^2 - 15*(B*a*b - A*b^2 + A*a*c)*x^2 + 5*(B*a^2 - A*a*b)*x)*sqrt(x))/(a^3*x^3)","B",0
1016,1,10514,0,5.375914," ","integrate((B*x+A)/x^(9/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} a^{4} x^{4} \sqrt{-\frac{B^{2} a^{2} b^{7} - 2 \, A B a b^{8} + A^{2} b^{9} - {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - {\left(7 \, B^{2} a^{5} b - 32 \, A B a^{4} b^{2} + 30 \, A^{2} a^{3} b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{4} b^{3} - 40 \, A B a^{3} b^{4} + 27 \, A^{2} a^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a^{3} b^{5} - 16 \, A B a^{2} b^{6} + 9 \, A^{2} a b^{7}\right)} c + {\left(a^{9} b^{2} - 4 \, a^{10} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}}{a^{9} b^{2} - 4 \, a^{10} c}} \log\left(\sqrt{2} {\left(B^{3} a^{3} b^{11} - 3 \, A B^{2} a^{2} b^{12} + 3 \, A^{2} B a b^{13} - A^{3} b^{14} + 4 \, A^{3} a^{7} c^{7} - {\left(4 \, A B^{2} a^{8} - 40 \, A^{2} B a^{7} b + 53 \, A^{3} a^{6} b^{2}\right)} c^{6} - {\left(8 \, B^{3} a^{8} b - 101 \, A B^{2} a^{7} b^{2} + 270 \, A^{2} B a^{6} b^{3} - 197 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(54 \, B^{3} a^{7} b^{3} - 313 \, A B^{2} a^{6} b^{4} + 545 \, A^{2} B a^{5} b^{5} - 294 \, A^{3} a^{4} b^{6}\right)} c^{4} - {\left(77 \, B^{3} a^{6} b^{5} - 336 \, A B^{2} a^{5} b^{6} + 468 \, A^{2} B a^{4} b^{7} - 210 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(44 \, B^{3} a^{5} b^{7} - 162 \, A B^{2} a^{4} b^{8} + 195 \, A^{2} B a^{3} b^{9} - 77 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(11 \, B^{3} a^{4} b^{9} - 36 \, A B^{2} a^{3} b^{10} + 39 \, A^{2} B a^{2} b^{11} - 14 \, A^{3} a b^{12}\right)} c - {\left(B a^{10} b^{6} - A a^{9} b^{7} - 4 \, {\left(2 \, B a^{13} - 5 \, A a^{12} b\right)} c^{3} + {\left(18 \, B a^{12} b^{2} - 25 \, A a^{11} b^{3}\right)} c^{2} - {\left(8 \, B a^{11} b^{4} - 9 \, A a^{10} b^{5}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} - 2 \, A B a b^{8} + A^{2} b^{9} - {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - {\left(7 \, B^{2} a^{5} b - 32 \, A B a^{4} b^{2} + 30 \, A^{2} a^{3} b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{4} b^{3} - 40 \, A B a^{3} b^{4} + 27 \, A^{2} a^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a^{3} b^{5} - 16 \, A B a^{2} b^{6} + 9 \, A^{2} a b^{7}\right)} c + {\left(a^{9} b^{2} - 4 \, a^{10} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}}{a^{9} b^{2} - 4 \, a^{10} c}} + 4 \, {\left(A^{4} a^{4} c^{9} + {\left(7 \, A^{3} B a^{4} b - 10 \, A^{4} a^{3} b^{2}\right)} c^{8} - {\left(B^{4} a^{6} - 9 \, A B^{3} a^{5} b + 12 \, A^{2} B^{2} a^{4} b^{2} + 10 \, A^{3} B a^{3} b^{3} - 15 \, A^{4} a^{2} b^{4}\right)} c^{7} + {\left(6 \, B^{4} a^{5} b^{2} - 26 \, A B^{3} a^{4} b^{3} + 30 \, A^{2} B^{2} a^{3} b^{4} - 3 \, A^{3} B a^{2} b^{5} - 7 \, A^{4} a b^{6}\right)} c^{6} - {\left(5 \, B^{4} a^{4} b^{4} - 17 \, A B^{3} a^{3} b^{5} + 18 \, A^{2} B^{2} a^{2} b^{6} - 5 \, A^{3} B a b^{7} - A^{4} b^{8}\right)} c^{5} + {\left(B^{4} a^{3} b^{6} - 3 \, A B^{3} a^{2} b^{7} + 3 \, A^{2} B^{2} a b^{8} - A^{3} B b^{9}\right)} c^{4}\right)} \sqrt{x}\right) - 105 \, \sqrt{2} a^{4} x^{4} \sqrt{-\frac{B^{2} a^{2} b^{7} - 2 \, A B a b^{8} + A^{2} b^{9} - {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - {\left(7 \, B^{2} a^{5} b - 32 \, A B a^{4} b^{2} + 30 \, A^{2} a^{3} b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{4} b^{3} - 40 \, A B a^{3} b^{4} + 27 \, A^{2} a^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a^{3} b^{5} - 16 \, A B a^{2} b^{6} + 9 \, A^{2} a b^{7}\right)} c + {\left(a^{9} b^{2} - 4 \, a^{10} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}}{a^{9} b^{2} - 4 \, a^{10} c}} \log\left(-\sqrt{2} {\left(B^{3} a^{3} b^{11} - 3 \, A B^{2} a^{2} b^{12} + 3 \, A^{2} B a b^{13} - A^{3} b^{14} + 4 \, A^{3} a^{7} c^{7} - {\left(4 \, A B^{2} a^{8} - 40 \, A^{2} B a^{7} b + 53 \, A^{3} a^{6} b^{2}\right)} c^{6} - {\left(8 \, B^{3} a^{8} b - 101 \, A B^{2} a^{7} b^{2} + 270 \, A^{2} B a^{6} b^{3} - 197 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(54 \, B^{3} a^{7} b^{3} - 313 \, A B^{2} a^{6} b^{4} + 545 \, A^{2} B a^{5} b^{5} - 294 \, A^{3} a^{4} b^{6}\right)} c^{4} - {\left(77 \, B^{3} a^{6} b^{5} - 336 \, A B^{2} a^{5} b^{6} + 468 \, A^{2} B a^{4} b^{7} - 210 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(44 \, B^{3} a^{5} b^{7} - 162 \, A B^{2} a^{4} b^{8} + 195 \, A^{2} B a^{3} b^{9} - 77 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(11 \, B^{3} a^{4} b^{9} - 36 \, A B^{2} a^{3} b^{10} + 39 \, A^{2} B a^{2} b^{11} - 14 \, A^{3} a b^{12}\right)} c - {\left(B a^{10} b^{6} - A a^{9} b^{7} - 4 \, {\left(2 \, B a^{13} - 5 \, A a^{12} b\right)} c^{3} + {\left(18 \, B a^{12} b^{2} - 25 \, A a^{11} b^{3}\right)} c^{2} - {\left(8 \, B a^{11} b^{4} - 9 \, A a^{10} b^{5}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} - 2 \, A B a b^{8} + A^{2} b^{9} - {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - {\left(7 \, B^{2} a^{5} b - 32 \, A B a^{4} b^{2} + 30 \, A^{2} a^{3} b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{4} b^{3} - 40 \, A B a^{3} b^{4} + 27 \, A^{2} a^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a^{3} b^{5} - 16 \, A B a^{2} b^{6} + 9 \, A^{2} a b^{7}\right)} c + {\left(a^{9} b^{2} - 4 \, a^{10} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}}{a^{9} b^{2} - 4 \, a^{10} c}} + 4 \, {\left(A^{4} a^{4} c^{9} + {\left(7 \, A^{3} B a^{4} b - 10 \, A^{4} a^{3} b^{2}\right)} c^{8} - {\left(B^{4} a^{6} - 9 \, A B^{3} a^{5} b + 12 \, A^{2} B^{2} a^{4} b^{2} + 10 \, A^{3} B a^{3} b^{3} - 15 \, A^{4} a^{2} b^{4}\right)} c^{7} + {\left(6 \, B^{4} a^{5} b^{2} - 26 \, A B^{3} a^{4} b^{3} + 30 \, A^{2} B^{2} a^{3} b^{4} - 3 \, A^{3} B a^{2} b^{5} - 7 \, A^{4} a b^{6}\right)} c^{6} - {\left(5 \, B^{4} a^{4} b^{4} - 17 \, A B^{3} a^{3} b^{5} + 18 \, A^{2} B^{2} a^{2} b^{6} - 5 \, A^{3} B a b^{7} - A^{4} b^{8}\right)} c^{5} + {\left(B^{4} a^{3} b^{6} - 3 \, A B^{3} a^{2} b^{7} + 3 \, A^{2} B^{2} a b^{8} - A^{3} B b^{9}\right)} c^{4}\right)} \sqrt{x}\right) + 105 \, \sqrt{2} a^{4} x^{4} \sqrt{-\frac{B^{2} a^{2} b^{7} - 2 \, A B a b^{8} + A^{2} b^{9} - {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - {\left(7 \, B^{2} a^{5} b - 32 \, A B a^{4} b^{2} + 30 \, A^{2} a^{3} b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{4} b^{3} - 40 \, A B a^{3} b^{4} + 27 \, A^{2} a^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a^{3} b^{5} - 16 \, A B a^{2} b^{6} + 9 \, A^{2} a b^{7}\right)} c - {\left(a^{9} b^{2} - 4 \, a^{10} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}}{a^{9} b^{2} - 4 \, a^{10} c}} \log\left(\sqrt{2} {\left(B^{3} a^{3} b^{11} - 3 \, A B^{2} a^{2} b^{12} + 3 \, A^{2} B a b^{13} - A^{3} b^{14} + 4 \, A^{3} a^{7} c^{7} - {\left(4 \, A B^{2} a^{8} - 40 \, A^{2} B a^{7} b + 53 \, A^{3} a^{6} b^{2}\right)} c^{6} - {\left(8 \, B^{3} a^{8} b - 101 \, A B^{2} a^{7} b^{2} + 270 \, A^{2} B a^{6} b^{3} - 197 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(54 \, B^{3} a^{7} b^{3} - 313 \, A B^{2} a^{6} b^{4} + 545 \, A^{2} B a^{5} b^{5} - 294 \, A^{3} a^{4} b^{6}\right)} c^{4} - {\left(77 \, B^{3} a^{6} b^{5} - 336 \, A B^{2} a^{5} b^{6} + 468 \, A^{2} B a^{4} b^{7} - 210 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(44 \, B^{3} a^{5} b^{7} - 162 \, A B^{2} a^{4} b^{8} + 195 \, A^{2} B a^{3} b^{9} - 77 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(11 \, B^{3} a^{4} b^{9} - 36 \, A B^{2} a^{3} b^{10} + 39 \, A^{2} B a^{2} b^{11} - 14 \, A^{3} a b^{12}\right)} c + {\left(B a^{10} b^{6} - A a^{9} b^{7} - 4 \, {\left(2 \, B a^{13} - 5 \, A a^{12} b\right)} c^{3} + {\left(18 \, B a^{12} b^{2} - 25 \, A a^{11} b^{3}\right)} c^{2} - {\left(8 \, B a^{11} b^{4} - 9 \, A a^{10} b^{5}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} - 2 \, A B a b^{8} + A^{2} b^{9} - {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - {\left(7 \, B^{2} a^{5} b - 32 \, A B a^{4} b^{2} + 30 \, A^{2} a^{3} b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{4} b^{3} - 40 \, A B a^{3} b^{4} + 27 \, A^{2} a^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a^{3} b^{5} - 16 \, A B a^{2} b^{6} + 9 \, A^{2} a b^{7}\right)} c - {\left(a^{9} b^{2} - 4 \, a^{10} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}}{a^{9} b^{2} - 4 \, a^{10} c}} + 4 \, {\left(A^{4} a^{4} c^{9} + {\left(7 \, A^{3} B a^{4} b - 10 \, A^{4} a^{3} b^{2}\right)} c^{8} - {\left(B^{4} a^{6} - 9 \, A B^{3} a^{5} b + 12 \, A^{2} B^{2} a^{4} b^{2} + 10 \, A^{3} B a^{3} b^{3} - 15 \, A^{4} a^{2} b^{4}\right)} c^{7} + {\left(6 \, B^{4} a^{5} b^{2} - 26 \, A B^{3} a^{4} b^{3} + 30 \, A^{2} B^{2} a^{3} b^{4} - 3 \, A^{3} B a^{2} b^{5} - 7 \, A^{4} a b^{6}\right)} c^{6} - {\left(5 \, B^{4} a^{4} b^{4} - 17 \, A B^{3} a^{3} b^{5} + 18 \, A^{2} B^{2} a^{2} b^{6} - 5 \, A^{3} B a b^{7} - A^{4} b^{8}\right)} c^{5} + {\left(B^{4} a^{3} b^{6} - 3 \, A B^{3} a^{2} b^{7} + 3 \, A^{2} B^{2} a b^{8} - A^{3} B b^{9}\right)} c^{4}\right)} \sqrt{x}\right) - 105 \, \sqrt{2} a^{4} x^{4} \sqrt{-\frac{B^{2} a^{2} b^{7} - 2 \, A B a b^{8} + A^{2} b^{9} - {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - {\left(7 \, B^{2} a^{5} b - 32 \, A B a^{4} b^{2} + 30 \, A^{2} a^{3} b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{4} b^{3} - 40 \, A B a^{3} b^{4} + 27 \, A^{2} a^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a^{3} b^{5} - 16 \, A B a^{2} b^{6} + 9 \, A^{2} a b^{7}\right)} c - {\left(a^{9} b^{2} - 4 \, a^{10} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}}{a^{9} b^{2} - 4 \, a^{10} c}} \log\left(-\sqrt{2} {\left(B^{3} a^{3} b^{11} - 3 \, A B^{2} a^{2} b^{12} + 3 \, A^{2} B a b^{13} - A^{3} b^{14} + 4 \, A^{3} a^{7} c^{7} - {\left(4 \, A B^{2} a^{8} - 40 \, A^{2} B a^{7} b + 53 \, A^{3} a^{6} b^{2}\right)} c^{6} - {\left(8 \, B^{3} a^{8} b - 101 \, A B^{2} a^{7} b^{2} + 270 \, A^{2} B a^{6} b^{3} - 197 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(54 \, B^{3} a^{7} b^{3} - 313 \, A B^{2} a^{6} b^{4} + 545 \, A^{2} B a^{5} b^{5} - 294 \, A^{3} a^{4} b^{6}\right)} c^{4} - {\left(77 \, B^{3} a^{6} b^{5} - 336 \, A B^{2} a^{5} b^{6} + 468 \, A^{2} B a^{4} b^{7} - 210 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(44 \, B^{3} a^{5} b^{7} - 162 \, A B^{2} a^{4} b^{8} + 195 \, A^{2} B a^{3} b^{9} - 77 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(11 \, B^{3} a^{4} b^{9} - 36 \, A B^{2} a^{3} b^{10} + 39 \, A^{2} B a^{2} b^{11} - 14 \, A^{3} a b^{12}\right)} c + {\left(B a^{10} b^{6} - A a^{9} b^{7} - 4 \, {\left(2 \, B a^{13} - 5 \, A a^{12} b\right)} c^{3} + {\left(18 \, B a^{12} b^{2} - 25 \, A a^{11} b^{3}\right)} c^{2} - {\left(8 \, B a^{11} b^{4} - 9 \, A a^{10} b^{5}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} - 2 \, A B a b^{8} + A^{2} b^{9} - {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - {\left(7 \, B^{2} a^{5} b - 32 \, A B a^{4} b^{2} + 30 \, A^{2} a^{3} b^{3}\right)} c^{3} + {\left(14 \, B^{2} a^{4} b^{3} - 40 \, A B a^{3} b^{4} + 27 \, A^{2} a^{2} b^{5}\right)} c^{2} - {\left(7 \, B^{2} a^{3} b^{5} - 16 \, A B a^{2} b^{6} + 9 \, A^{2} a b^{7}\right)} c - {\left(a^{9} b^{2} - 4 \, a^{10} c\right)} \sqrt{\frac{B^{4} a^{4} b^{12} - 4 \, A B^{3} a^{3} b^{13} + 6 \, A^{2} B^{2} a^{2} b^{14} - 4 \, A^{3} B a b^{15} + A^{4} b^{16} + A^{4} a^{8} c^{8} - 2 \, {\left(A^{2} B^{2} a^{9} - 8 \, A^{3} B a^{8} b + 10 \, A^{4} a^{7} b^{2}\right)} c^{7} + {\left(B^{4} a^{10} - 16 \, A B^{3} a^{9} b + 96 \, A^{2} B^{2} a^{8} b^{2} - 200 \, A^{3} B a^{7} b^{3} + 130 \, A^{4} a^{6} b^{4}\right)} c^{6} - 2 \, {\left(6 \, B^{4} a^{9} b^{2} - 68 \, A B^{3} a^{8} b^{3} + 240 \, A^{2} B^{2} a^{7} b^{4} - 332 \, A^{3} B a^{6} b^{5} + 157 \, A^{4} a^{5} b^{6}\right)} c^{5} + {\left(46 \, B^{4} a^{8} b^{4} - 344 \, A B^{3} a^{7} b^{5} + 888 \, A^{2} B^{2} a^{6} b^{6} - 956 \, A^{3} B a^{5} b^{7} + 367 \, A^{4} a^{4} b^{8}\right)} c^{4} - 2 \, {\left(31 \, B^{4} a^{7} b^{6} - 182 \, A B^{3} a^{6} b^{7} + 384 \, A^{2} B^{2} a^{5} b^{8} - 348 \, A^{3} B a^{4} b^{9} + 115 \, A^{4} a^{3} b^{10}\right)} c^{3} + {\left(37 \, B^{4} a^{6} b^{8} - 184 \, A B^{3} a^{5} b^{9} + 336 \, A^{2} B^{2} a^{4} b^{10} - 268 \, A^{3} B a^{3} b^{11} + 79 \, A^{4} a^{2} b^{12}\right)} c^{2} - 2 \, {\left(5 \, B^{4} a^{5} b^{10} - 22 \, A B^{3} a^{4} b^{11} + 36 \, A^{2} B^{2} a^{3} b^{12} - 26 \, A^{3} B a^{2} b^{13} + 7 \, A^{4} a b^{14}\right)} c}{a^{18} b^{2} - 4 \, a^{19} c}}}{a^{9} b^{2} - 4 \, a^{10} c}} + 4 \, {\left(A^{4} a^{4} c^{9} + {\left(7 \, A^{3} B a^{4} b - 10 \, A^{4} a^{3} b^{2}\right)} c^{8} - {\left(B^{4} a^{6} - 9 \, A B^{3} a^{5} b + 12 \, A^{2} B^{2} a^{4} b^{2} + 10 \, A^{3} B a^{3} b^{3} - 15 \, A^{4} a^{2} b^{4}\right)} c^{7} + {\left(6 \, B^{4} a^{5} b^{2} - 26 \, A B^{3} a^{4} b^{3} + 30 \, A^{2} B^{2} a^{3} b^{4} - 3 \, A^{3} B a^{2} b^{5} - 7 \, A^{4} a b^{6}\right)} c^{6} - {\left(5 \, B^{4} a^{4} b^{4} - 17 \, A B^{3} a^{3} b^{5} + 18 \, A^{2} B^{2} a^{2} b^{6} - 5 \, A^{3} B a b^{7} - A^{4} b^{8}\right)} c^{5} + {\left(B^{4} a^{3} b^{6} - 3 \, A B^{3} a^{2} b^{7} + 3 \, A^{2} B^{2} a b^{8} - A^{3} B b^{9}\right)} c^{4}\right)} \sqrt{x}\right) - 4 \, {\left(15 \, A a^{3} + 105 \, {\left(B a b^{2} - A b^{3} - {\left(B a^{2} - 2 \, A a b\right)} c\right)} x^{3} - 35 \, {\left(B a^{2} b - A a b^{2} + A a^{2} c\right)} x^{2} + 21 \, {\left(B a^{3} - A a^{2} b\right)} x\right)} \sqrt{x}}{210 \, a^{4} x^{4}}"," ",0,"1/210*(105*sqrt(2)*a^4*x^4*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c + (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c))*log(sqrt(2)*(B^3*a^3*b^11 - 3*A*B^2*a^2*b^12 + 3*A^2*B*a*b^13 - A^3*b^14 + 4*A^3*a^7*c^7 - (4*A*B^2*a^8 - 40*A^2*B*a^7*b + 53*A^3*a^6*b^2)*c^6 - (8*B^3*a^8*b - 101*A*B^2*a^7*b^2 + 270*A^2*B*a^6*b^3 - 197*A^3*a^5*b^4)*c^5 + (54*B^3*a^7*b^3 - 313*A*B^2*a^6*b^4 + 545*A^2*B*a^5*b^5 - 294*A^3*a^4*b^6)*c^4 - (77*B^3*a^6*b^5 - 336*A*B^2*a^5*b^6 + 468*A^2*B*a^4*b^7 - 210*A^3*a^3*b^8)*c^3 + (44*B^3*a^5*b^7 - 162*A*B^2*a^4*b^8 + 195*A^2*B*a^3*b^9 - 77*A^3*a^2*b^10)*c^2 - (11*B^3*a^4*b^9 - 36*A*B^2*a^3*b^10 + 39*A^2*B*a^2*b^11 - 14*A^3*a*b^12)*c - (B*a^10*b^6 - A*a^9*b^7 - 4*(2*B*a^13 - 5*A*a^12*b)*c^3 + (18*B*a^12*b^2 - 25*A*a^11*b^3)*c^2 - (8*B*a^11*b^4 - 9*A*a^10*b^5)*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c + (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c)) + 4*(A^4*a^4*c^9 + (7*A^3*B*a^4*b - 10*A^4*a^3*b^2)*c^8 - (B^4*a^6 - 9*A*B^3*a^5*b + 12*A^2*B^2*a^4*b^2 + 10*A^3*B*a^3*b^3 - 15*A^4*a^2*b^4)*c^7 + (6*B^4*a^5*b^2 - 26*A*B^3*a^4*b^3 + 30*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5 - 7*A^4*a*b^6)*c^6 - (5*B^4*a^4*b^4 - 17*A*B^3*a^3*b^5 + 18*A^2*B^2*a^2*b^6 - 5*A^3*B*a*b^7 - A^4*b^8)*c^5 + (B^4*a^3*b^6 - 3*A*B^3*a^2*b^7 + 3*A^2*B^2*a*b^8 - A^3*B*b^9)*c^4)*sqrt(x)) - 105*sqrt(2)*a^4*x^4*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c + (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c))*log(-sqrt(2)*(B^3*a^3*b^11 - 3*A*B^2*a^2*b^12 + 3*A^2*B*a*b^13 - A^3*b^14 + 4*A^3*a^7*c^7 - (4*A*B^2*a^8 - 40*A^2*B*a^7*b + 53*A^3*a^6*b^2)*c^6 - (8*B^3*a^8*b - 101*A*B^2*a^7*b^2 + 270*A^2*B*a^6*b^3 - 197*A^3*a^5*b^4)*c^5 + (54*B^3*a^7*b^3 - 313*A*B^2*a^6*b^4 + 545*A^2*B*a^5*b^5 - 294*A^3*a^4*b^6)*c^4 - (77*B^3*a^6*b^5 - 336*A*B^2*a^5*b^6 + 468*A^2*B*a^4*b^7 - 210*A^3*a^3*b^8)*c^3 + (44*B^3*a^5*b^7 - 162*A*B^2*a^4*b^8 + 195*A^2*B*a^3*b^9 - 77*A^3*a^2*b^10)*c^2 - (11*B^3*a^4*b^9 - 36*A*B^2*a^3*b^10 + 39*A^2*B*a^2*b^11 - 14*A^3*a*b^12)*c - (B*a^10*b^6 - A*a^9*b^7 - 4*(2*B*a^13 - 5*A*a^12*b)*c^3 + (18*B*a^12*b^2 - 25*A*a^11*b^3)*c^2 - (8*B*a^11*b^4 - 9*A*a^10*b^5)*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c + (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c)) + 4*(A^4*a^4*c^9 + (7*A^3*B*a^4*b - 10*A^4*a^3*b^2)*c^8 - (B^4*a^6 - 9*A*B^3*a^5*b + 12*A^2*B^2*a^4*b^2 + 10*A^3*B*a^3*b^3 - 15*A^4*a^2*b^4)*c^7 + (6*B^4*a^5*b^2 - 26*A*B^3*a^4*b^3 + 30*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5 - 7*A^4*a*b^6)*c^6 - (5*B^4*a^4*b^4 - 17*A*B^3*a^3*b^5 + 18*A^2*B^2*a^2*b^6 - 5*A^3*B*a*b^7 - A^4*b^8)*c^5 + (B^4*a^3*b^6 - 3*A*B^3*a^2*b^7 + 3*A^2*B^2*a*b^8 - A^3*B*b^9)*c^4)*sqrt(x)) + 105*sqrt(2)*a^4*x^4*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c - (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c))*log(sqrt(2)*(B^3*a^3*b^11 - 3*A*B^2*a^2*b^12 + 3*A^2*B*a*b^13 - A^3*b^14 + 4*A^3*a^7*c^7 - (4*A*B^2*a^8 - 40*A^2*B*a^7*b + 53*A^3*a^6*b^2)*c^6 - (8*B^3*a^8*b - 101*A*B^2*a^7*b^2 + 270*A^2*B*a^6*b^3 - 197*A^3*a^5*b^4)*c^5 + (54*B^3*a^7*b^3 - 313*A*B^2*a^6*b^4 + 545*A^2*B*a^5*b^5 - 294*A^3*a^4*b^6)*c^4 - (77*B^3*a^6*b^5 - 336*A*B^2*a^5*b^6 + 468*A^2*B*a^4*b^7 - 210*A^3*a^3*b^8)*c^3 + (44*B^3*a^5*b^7 - 162*A*B^2*a^4*b^8 + 195*A^2*B*a^3*b^9 - 77*A^3*a^2*b^10)*c^2 - (11*B^3*a^4*b^9 - 36*A*B^2*a^3*b^10 + 39*A^2*B*a^2*b^11 - 14*A^3*a*b^12)*c + (B*a^10*b^6 - A*a^9*b^7 - 4*(2*B*a^13 - 5*A*a^12*b)*c^3 + (18*B*a^12*b^2 - 25*A*a^11*b^3)*c^2 - (8*B*a^11*b^4 - 9*A*a^10*b^5)*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c - (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c)) + 4*(A^4*a^4*c^9 + (7*A^3*B*a^4*b - 10*A^4*a^3*b^2)*c^8 - (B^4*a^6 - 9*A*B^3*a^5*b + 12*A^2*B^2*a^4*b^2 + 10*A^3*B*a^3*b^3 - 15*A^4*a^2*b^4)*c^7 + (6*B^4*a^5*b^2 - 26*A*B^3*a^4*b^3 + 30*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5 - 7*A^4*a*b^6)*c^6 - (5*B^4*a^4*b^4 - 17*A*B^3*a^3*b^5 + 18*A^2*B^2*a^2*b^6 - 5*A^3*B*a*b^7 - A^4*b^8)*c^5 + (B^4*a^3*b^6 - 3*A*B^3*a^2*b^7 + 3*A^2*B^2*a*b^8 - A^3*B*b^9)*c^4)*sqrt(x)) - 105*sqrt(2)*a^4*x^4*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c - (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c))*log(-sqrt(2)*(B^3*a^3*b^11 - 3*A*B^2*a^2*b^12 + 3*A^2*B*a*b^13 - A^3*b^14 + 4*A^3*a^7*c^7 - (4*A*B^2*a^8 - 40*A^2*B*a^7*b + 53*A^3*a^6*b^2)*c^6 - (8*B^3*a^8*b - 101*A*B^2*a^7*b^2 + 270*A^2*B*a^6*b^3 - 197*A^3*a^5*b^4)*c^5 + (54*B^3*a^7*b^3 - 313*A*B^2*a^6*b^4 + 545*A^2*B*a^5*b^5 - 294*A^3*a^4*b^6)*c^4 - (77*B^3*a^6*b^5 - 336*A*B^2*a^5*b^6 + 468*A^2*B*a^4*b^7 - 210*A^3*a^3*b^8)*c^3 + (44*B^3*a^5*b^7 - 162*A*B^2*a^4*b^8 + 195*A^2*B*a^3*b^9 - 77*A^3*a^2*b^10)*c^2 - (11*B^3*a^4*b^9 - 36*A*B^2*a^3*b^10 + 39*A^2*B*a^2*b^11 - 14*A^3*a*b^12)*c + (B*a^10*b^6 - A*a^9*b^7 - 4*(2*B*a^13 - 5*A*a^12*b)*c^3 + (18*B*a^12*b^2 - 25*A*a^11*b^3)*c^2 - (8*B*a^11*b^4 - 9*A*a^10*b^5)*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c - (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c)) + 4*(A^4*a^4*c^9 + (7*A^3*B*a^4*b - 10*A^4*a^3*b^2)*c^8 - (B^4*a^6 - 9*A*B^3*a^5*b + 12*A^2*B^2*a^4*b^2 + 10*A^3*B*a^3*b^3 - 15*A^4*a^2*b^4)*c^7 + (6*B^4*a^5*b^2 - 26*A*B^3*a^4*b^3 + 30*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5 - 7*A^4*a*b^6)*c^6 - (5*B^4*a^4*b^4 - 17*A*B^3*a^3*b^5 + 18*A^2*B^2*a^2*b^6 - 5*A^3*B*a*b^7 - A^4*b^8)*c^5 + (B^4*a^3*b^6 - 3*A*B^3*a^2*b^7 + 3*A^2*B^2*a*b^8 - A^3*B*b^9)*c^4)*sqrt(x)) - 4*(15*A*a^3 + 105*(B*a*b^2 - A*b^3 - (B*a^2 - 2*A*a*b)*c)*x^3 - 35*(B*a^2*b - A*a*b^2 + A*a^2*c)*x^2 + 21*(B*a^3 - A*a^2*b)*x)*sqrt(x))/(a^4*x^4)","B",0
1017,1,7251,0,8.894134," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(\sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{10} + 144 \, {\left(10 \, A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - 8 \, {\left(500 \, B^{3} a^{5} + 930 \, A B^{2} a^{4} b + 252 \, A^{2} B a^{3} b^{2} + 11 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(11360 \, B^{3} a^{4} b^{2} + 7608 \, A B^{2} a^{3} b^{3} + 882 \, A^{2} B a^{2} b^{4} + 17 \, A^{3} a b^{5}\right)} c^{4} - {\left(8818 \, B^{3} a^{3} b^{4} + 2841 \, A B^{2} a^{2} b^{5} + 153 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + 9 \, {\left(329 \, B^{3} a^{2} b^{6} + 51 \, A B^{2} a b^{7} + A^{2} B b^{8}\right)} c^{2} - 27 \, {\left(17 \, B^{3} a b^{8} + A B^{2} b^{9}\right)} c - {\left(3 \, B b^{9} c^{5} - 768 \, A a^{4} c^{10} + 128 \, {\left(8 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} c^{9} - 192 \, {\left(5 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{8} + 24 \, {\left(14 \, B a^{2} b^{5} + A a b^{6}\right)} c^{7} - {\left(52 \, B a b^{7} + A b^{8}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} + 2 \, {\left(189 \, B^{4} a^{2} b^{6} - 135 \, A B^{3} a b^{7} + 324 \, A^{4} a^{3} c^{5} - 81 \, {\left(28 \, A^{3} B a^{3} b + A^{4} a^{2} b^{2}\right)} c^{4} - {\left(2500 \, B^{4} a^{5} + 2500 \, A B^{3} a^{4} b - 5016 \, A^{2} B^{2} a^{3} b^{2} - 647 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{3} + 9 \, {\left(625 \, B^{4} a^{4} b^{2} - 303 \, A B^{3} a^{3} b^{3} - 186 \, A^{2} B^{2} a^{2} b^{4} - 5 \, A^{3} B a b^{5}\right)} c^{2} - 27 \, {\left(73 \, B^{4} a^{3} b^{4} - 49 \, A B^{3} a^{2} b^{5} - 5 \, A^{2} B^{2} a b^{6}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(-\sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{10} + 144 \, {\left(10 \, A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - 8 \, {\left(500 \, B^{3} a^{5} + 930 \, A B^{2} a^{4} b + 252 \, A^{2} B a^{3} b^{2} + 11 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(11360 \, B^{3} a^{4} b^{2} + 7608 \, A B^{2} a^{3} b^{3} + 882 \, A^{2} B a^{2} b^{4} + 17 \, A^{3} a b^{5}\right)} c^{4} - {\left(8818 \, B^{3} a^{3} b^{4} + 2841 \, A B^{2} a^{2} b^{5} + 153 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + 9 \, {\left(329 \, B^{3} a^{2} b^{6} + 51 \, A B^{2} a b^{7} + A^{2} B b^{8}\right)} c^{2} - 27 \, {\left(17 \, B^{3} a b^{8} + A B^{2} b^{9}\right)} c - {\left(3 \, B b^{9} c^{5} - 768 \, A a^{4} c^{10} + 128 \, {\left(8 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} c^{9} - 192 \, {\left(5 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{8} + 24 \, {\left(14 \, B a^{2} b^{5} + A a b^{6}\right)} c^{7} - {\left(52 \, B a b^{7} + A b^{8}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} + 2 \, {\left(189 \, B^{4} a^{2} b^{6} - 135 \, A B^{3} a b^{7} + 324 \, A^{4} a^{3} c^{5} - 81 \, {\left(28 \, A^{3} B a^{3} b + A^{4} a^{2} b^{2}\right)} c^{4} - {\left(2500 \, B^{4} a^{5} + 2500 \, A B^{3} a^{4} b - 5016 \, A^{2} B^{2} a^{3} b^{2} - 647 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{3} + 9 \, {\left(625 \, B^{4} a^{4} b^{2} - 303 \, A B^{3} a^{3} b^{3} - 186 \, A^{2} B^{2} a^{2} b^{4} - 5 \, A^{3} B a b^{5}\right)} c^{2} - 27 \, {\left(73 \, B^{4} a^{3} b^{4} - 49 \, A B^{3} a^{2} b^{5} - 5 \, A^{2} B^{2} a b^{6}\right)} c\right)} \sqrt{x}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(\sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{10} + 144 \, {\left(10 \, A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - 8 \, {\left(500 \, B^{3} a^{5} + 930 \, A B^{2} a^{4} b + 252 \, A^{2} B a^{3} b^{2} + 11 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(11360 \, B^{3} a^{4} b^{2} + 7608 \, A B^{2} a^{3} b^{3} + 882 \, A^{2} B a^{2} b^{4} + 17 \, A^{3} a b^{5}\right)} c^{4} - {\left(8818 \, B^{3} a^{3} b^{4} + 2841 \, A B^{2} a^{2} b^{5} + 153 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + 9 \, {\left(329 \, B^{3} a^{2} b^{6} + 51 \, A B^{2} a b^{7} + A^{2} B b^{8}\right)} c^{2} - 27 \, {\left(17 \, B^{3} a b^{8} + A B^{2} b^{9}\right)} c + {\left(3 \, B b^{9} c^{5} - 768 \, A a^{4} c^{10} + 128 \, {\left(8 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} c^{9} - 192 \, {\left(5 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{8} + 24 \, {\left(14 \, B a^{2} b^{5} + A a b^{6}\right)} c^{7} - {\left(52 \, B a b^{7} + A b^{8}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} + 2 \, {\left(189 \, B^{4} a^{2} b^{6} - 135 \, A B^{3} a b^{7} + 324 \, A^{4} a^{3} c^{5} - 81 \, {\left(28 \, A^{3} B a^{3} b + A^{4} a^{2} b^{2}\right)} c^{4} - {\left(2500 \, B^{4} a^{5} + 2500 \, A B^{3} a^{4} b - 5016 \, A^{2} B^{2} a^{3} b^{2} - 647 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{3} + 9 \, {\left(625 \, B^{4} a^{4} b^{2} - 303 \, A B^{3} a^{3} b^{3} - 186 \, A^{2} B^{2} a^{2} b^{4} - 5 \, A^{3} B a b^{5}\right)} c^{2} - 27 \, {\left(73 \, B^{4} a^{3} b^{4} - 49 \, A B^{3} a^{2} b^{5} - 5 \, A^{2} B^{2} a b^{6}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(-\sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{10} + 144 \, {\left(10 \, A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - 8 \, {\left(500 \, B^{3} a^{5} + 930 \, A B^{2} a^{4} b + 252 \, A^{2} B a^{3} b^{2} + 11 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(11360 \, B^{3} a^{4} b^{2} + 7608 \, A B^{2} a^{3} b^{3} + 882 \, A^{2} B a^{2} b^{4} + 17 \, A^{3} a b^{5}\right)} c^{4} - {\left(8818 \, B^{3} a^{3} b^{4} + 2841 \, A B^{2} a^{2} b^{5} + 153 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + 9 \, {\left(329 \, B^{3} a^{2} b^{6} + 51 \, A B^{2} a b^{7} + A^{2} B b^{8}\right)} c^{2} - 27 \, {\left(17 \, B^{3} a b^{8} + A B^{2} b^{9}\right)} c + {\left(3 \, B b^{9} c^{5} - 768 \, A a^{4} c^{10} + 128 \, {\left(8 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} c^{9} - 192 \, {\left(5 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{8} + 24 \, {\left(14 \, B a^{2} b^{5} + A a b^{6}\right)} c^{7} - {\left(52 \, B a b^{7} + A b^{8}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} + 2 \, {\left(189 \, B^{4} a^{2} b^{6} - 135 \, A B^{3} a b^{7} + 324 \, A^{4} a^{3} c^{5} - 81 \, {\left(28 \, A^{3} B a^{3} b + A^{4} a^{2} b^{2}\right)} c^{4} - {\left(2500 \, B^{4} a^{5} + 2500 \, A B^{3} a^{4} b - 5016 \, A^{2} B^{2} a^{3} b^{2} - 647 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{3} + 9 \, {\left(625 \, B^{4} a^{4} b^{2} - 303 \, A B^{3} a^{3} b^{3} - 186 \, A^{2} B^{2} a^{2} b^{4} - 5 \, A^{3} B a b^{5}\right)} c^{2} - 27 \, {\left(73 \, B^{4} a^{3} b^{4} - 49 \, A B^{3} a^{2} b^{5} - 5 \, A^{2} B^{2} a b^{6}\right)} c\right)} \sqrt{x}\right) - 2 \, {\left(3 \, B a b^{2} + 2 \, {\left(B b^{2} c - 4 \, B a c^{2}\right)} x^{2} - {\left(10 \, B a^{2} + A a b\right)} c + {\left(3 \, B b^{3} + 2 \, A a c^{2} - {\left(11 \, B a b + A b^{2}\right)} c\right)} x\right)} \sqrt{x}}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}"," ",0,"-1/2*(sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(sqrt(1/2)*(27*B^3*b^10 + 144*(10*A^2*B*a^4 + A^3*a^3*b)*c^6 - 8*(500*B^3*a^5 + 930*A*B^2*a^4*b + 252*A^2*B*a^3*b^2 + 11*A^3*a^2*b^3)*c^5 + (11360*B^3*a^4*b^2 + 7608*A*B^2*a^3*b^3 + 882*A^2*B*a^2*b^4 + 17*A^3*a*b^5)*c^4 - (8818*B^3*a^3*b^4 + 2841*A*B^2*a^2*b^5 + 153*A^2*B*a*b^6 + A^3*b^7)*c^3 + 9*(329*B^3*a^2*b^6 + 51*A*B^2*a*b^7 + A^2*B*b^8)*c^2 - 27*(17*B^3*a*b^8 + A*B^2*b^9)*c - (3*B*b^9*c^5 - 768*A*a^4*c^10 + 128*(8*B*a^4*b + 5*A*a^3*b^2)*c^9 - 192*(5*B*a^3*b^3 + A*a^2*b^4)*c^8 + 24*(14*B*a^2*b^5 + A*a*b^6)*c^7 - (52*B*a*b^7 + A*b^8)*c^6)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)) + 2*(189*B^4*a^2*b^6 - 135*A*B^3*a*b^7 + 324*A^4*a^3*c^5 - 81*(28*A^3*B*a^3*b + A^4*a^2*b^2)*c^4 - (2500*B^4*a^5 + 2500*A*B^3*a^4*b - 5016*A^2*B^2*a^3*b^2 - 647*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^3 + 9*(625*B^4*a^4*b^2 - 303*A*B^3*a^3*b^3 - 186*A^2*B^2*a^2*b^4 - 5*A^3*B*a*b^5)*c^2 - 27*(73*B^4*a^3*b^4 - 49*A*B^3*a^2*b^5 - 5*A^2*B^2*a*b^6)*c)*sqrt(x)) - sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(-sqrt(1/2)*(27*B^3*b^10 + 144*(10*A^2*B*a^4 + A^3*a^3*b)*c^6 - 8*(500*B^3*a^5 + 930*A*B^2*a^4*b + 252*A^2*B*a^3*b^2 + 11*A^3*a^2*b^3)*c^5 + (11360*B^3*a^4*b^2 + 7608*A*B^2*a^3*b^3 + 882*A^2*B*a^2*b^4 + 17*A^3*a*b^5)*c^4 - (8818*B^3*a^3*b^4 + 2841*A*B^2*a^2*b^5 + 153*A^2*B*a*b^6 + A^3*b^7)*c^3 + 9*(329*B^3*a^2*b^6 + 51*A*B^2*a*b^7 + A^2*B*b^8)*c^2 - 27*(17*B^3*a*b^8 + A*B^2*b^9)*c - (3*B*b^9*c^5 - 768*A*a^4*c^10 + 128*(8*B*a^4*b + 5*A*a^3*b^2)*c^9 - 192*(5*B*a^3*b^3 + A*a^2*b^4)*c^8 + 24*(14*B*a^2*b^5 + A*a*b^6)*c^7 - (52*B*a*b^7 + A*b^8)*c^6)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)) + 2*(189*B^4*a^2*b^6 - 135*A*B^3*a*b^7 + 324*A^4*a^3*c^5 - 81*(28*A^3*B*a^3*b + A^4*a^2*b^2)*c^4 - (2500*B^4*a^5 + 2500*A*B^3*a^4*b - 5016*A^2*B^2*a^3*b^2 - 647*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^3 + 9*(625*B^4*a^4*b^2 - 303*A*B^3*a^3*b^3 - 186*A^2*B^2*a^2*b^4 - 5*A^3*B*a*b^5)*c^2 - 27*(73*B^4*a^3*b^4 - 49*A*B^3*a^2*b^5 - 5*A^2*B^2*a*b^6)*c)*sqrt(x)) + sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(sqrt(1/2)*(27*B^3*b^10 + 144*(10*A^2*B*a^4 + A^3*a^3*b)*c^6 - 8*(500*B^3*a^5 + 930*A*B^2*a^4*b + 252*A^2*B*a^3*b^2 + 11*A^3*a^2*b^3)*c^5 + (11360*B^3*a^4*b^2 + 7608*A*B^2*a^3*b^3 + 882*A^2*B*a^2*b^4 + 17*A^3*a*b^5)*c^4 - (8818*B^3*a^3*b^4 + 2841*A*B^2*a^2*b^5 + 153*A^2*B*a*b^6 + A^3*b^7)*c^3 + 9*(329*B^3*a^2*b^6 + 51*A*B^2*a*b^7 + A^2*B*b^8)*c^2 - 27*(17*B^3*a*b^8 + A*B^2*b^9)*c + (3*B*b^9*c^5 - 768*A*a^4*c^10 + 128*(8*B*a^4*b + 5*A*a^3*b^2)*c^9 - 192*(5*B*a^3*b^3 + A*a^2*b^4)*c^8 + 24*(14*B*a^2*b^5 + A*a*b^6)*c^7 - (52*B*a*b^7 + A*b^8)*c^6)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)) + 2*(189*B^4*a^2*b^6 - 135*A*B^3*a*b^7 + 324*A^4*a^3*c^5 - 81*(28*A^3*B*a^3*b + A^4*a^2*b^2)*c^4 - (2500*B^4*a^5 + 2500*A*B^3*a^4*b - 5016*A^2*B^2*a^3*b^2 - 647*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^3 + 9*(625*B^4*a^4*b^2 - 303*A*B^3*a^3*b^3 - 186*A^2*B^2*a^2*b^4 - 5*A^3*B*a*b^5)*c^2 - 27*(73*B^4*a^3*b^4 - 49*A*B^3*a^2*b^5 - 5*A^2*B^2*a*b^6)*c)*sqrt(x)) - sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(-sqrt(1/2)*(27*B^3*b^10 + 144*(10*A^2*B*a^4 + A^3*a^3*b)*c^6 - 8*(500*B^3*a^5 + 930*A*B^2*a^4*b + 252*A^2*B*a^3*b^2 + 11*A^3*a^2*b^3)*c^5 + (11360*B^3*a^4*b^2 + 7608*A*B^2*a^3*b^3 + 882*A^2*B*a^2*b^4 + 17*A^3*a*b^5)*c^4 - (8818*B^3*a^3*b^4 + 2841*A*B^2*a^2*b^5 + 153*A^2*B*a*b^6 + A^3*b^7)*c^3 + 9*(329*B^3*a^2*b^6 + 51*A*B^2*a*b^7 + A^2*B*b^8)*c^2 - 27*(17*B^3*a*b^8 + A*B^2*b^9)*c + (3*B*b^9*c^5 - 768*A*a^4*c^10 + 128*(8*B*a^4*b + 5*A*a^3*b^2)*c^9 - 192*(5*B*a^3*b^3 + A*a^2*b^4)*c^8 + 24*(14*B*a^2*b^5 + A*a*b^6)*c^7 - (52*B*a*b^7 + A*b^8)*c^6)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)) + 2*(189*B^4*a^2*b^6 - 135*A*B^3*a*b^7 + 324*A^4*a^3*c^5 - 81*(28*A^3*B*a^3*b + A^4*a^2*b^2)*c^4 - (2500*B^4*a^5 + 2500*A*B^3*a^4*b - 5016*A^2*B^2*a^3*b^2 - 647*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^3 + 9*(625*B^4*a^4*b^2 - 303*A*B^3*a^3*b^3 - 186*A^2*B^2*a^2*b^4 - 5*A^3*B*a*b^5)*c^2 - 27*(73*B^4*a^3*b^4 - 49*A*B^3*a^2*b^5 - 5*A^2*B^2*a*b^6)*c)*sqrt(x)) - 2*(3*B*a*b^2 + 2*(B*b^2*c - 4*B*a*c^2)*x^2 - (10*B*a^2 + A*a*b)*c + (3*B*b^3 + 2*A*a*c^2 - (11*B*a*b + A*b^2)*c)*x)*sqrt(x))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)","B",0
1018,1,4653,0,2.840801," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(\sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 17 \, B^{3} a b^{5} c - 32 \, A^{3} a^{2} c^{5} + 16 \, {\left(18 \, A B^{2} a^{3} - 3 \, A^{2} B a^{2} b + A^{3} a b^{2}\right)} c^{4} - 2 \, {\left(72 \, B^{3} a^{3} b + 72 \, A B^{2} a^{2} b^{2} - 12 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(88 \, B^{3} a^{2} b^{3} + 18 \, A B^{2} a b^{4} - 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(B b^{8} c^{3} + 256 \, {\left(3 \, B a^{4} - A a^{3} b\right)} c^{7} - 64 \, {\left(10 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{6} + 48 \, {\left(4 \, B a^{2} b^{4} - A a b^{5}\right)} c^{5} - 4 \, {\left(6 \, B a b^{6} - A b^{7}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} - 2 \, {\left(5 \, B^{4} a b^{4} - 3 \, A B^{3} b^{5} - 4 \, A^{4} a c^{4} + {\left(20 \, A^{3} B a b - 3 \, A^{4} b^{2}\right)} c^{3} + 3 \, {\left(108 \, B^{4} a^{3} - 108 \, A B^{3} a^{2} b + 28 \, A^{2} B^{2} a b^{2} - 3 \, A^{3} B b^{3}\right)} c^{2} - {\left(81 \, B^{4} a^{2} b^{2} - 65 \, A B^{3} a b^{3} + 9 \, A^{2} B^{2} b^{4}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-\sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 17 \, B^{3} a b^{5} c - 32 \, A^{3} a^{2} c^{5} + 16 \, {\left(18 \, A B^{2} a^{3} - 3 \, A^{2} B a^{2} b + A^{3} a b^{2}\right)} c^{4} - 2 \, {\left(72 \, B^{3} a^{3} b + 72 \, A B^{2} a^{2} b^{2} - 12 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(88 \, B^{3} a^{2} b^{3} + 18 \, A B^{2} a b^{4} - 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(B b^{8} c^{3} + 256 \, {\left(3 \, B a^{4} - A a^{3} b\right)} c^{7} - 64 \, {\left(10 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{6} + 48 \, {\left(4 \, B a^{2} b^{4} - A a b^{5}\right)} c^{5} - 4 \, {\left(6 \, B a b^{6} - A b^{7}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} - 2 \, {\left(5 \, B^{4} a b^{4} - 3 \, A B^{3} b^{5} - 4 \, A^{4} a c^{4} + {\left(20 \, A^{3} B a b - 3 \, A^{4} b^{2}\right)} c^{3} + 3 \, {\left(108 \, B^{4} a^{3} - 108 \, A B^{3} a^{2} b + 28 \, A^{2} B^{2} a b^{2} - 3 \, A^{3} B b^{3}\right)} c^{2} - {\left(81 \, B^{4} a^{2} b^{2} - 65 \, A B^{3} a b^{3} + 9 \, A^{2} B^{2} b^{4}\right)} c\right)} \sqrt{x}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(\sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 17 \, B^{3} a b^{5} c - 32 \, A^{3} a^{2} c^{5} + 16 \, {\left(18 \, A B^{2} a^{3} - 3 \, A^{2} B a^{2} b + A^{3} a b^{2}\right)} c^{4} - 2 \, {\left(72 \, B^{3} a^{3} b + 72 \, A B^{2} a^{2} b^{2} - 12 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(88 \, B^{3} a^{2} b^{3} + 18 \, A B^{2} a b^{4} - 3 \, A^{2} B b^{5}\right)} c^{2} + {\left(B b^{8} c^{3} + 256 \, {\left(3 \, B a^{4} - A a^{3} b\right)} c^{7} - 64 \, {\left(10 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{6} + 48 \, {\left(4 \, B a^{2} b^{4} - A a b^{5}\right)} c^{5} - 4 \, {\left(6 \, B a b^{6} - A b^{7}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} - 2 \, {\left(5 \, B^{4} a b^{4} - 3 \, A B^{3} b^{5} - 4 \, A^{4} a c^{4} + {\left(20 \, A^{3} B a b - 3 \, A^{4} b^{2}\right)} c^{3} + 3 \, {\left(108 \, B^{4} a^{3} - 108 \, A B^{3} a^{2} b + 28 \, A^{2} B^{2} a b^{2} - 3 \, A^{3} B b^{3}\right)} c^{2} - {\left(81 \, B^{4} a^{2} b^{2} - 65 \, A B^{3} a b^{3} + 9 \, A^{2} B^{2} b^{4}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-\sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 17 \, B^{3} a b^{5} c - 32 \, A^{3} a^{2} c^{5} + 16 \, {\left(18 \, A B^{2} a^{3} - 3 \, A^{2} B a^{2} b + A^{3} a b^{2}\right)} c^{4} - 2 \, {\left(72 \, B^{3} a^{3} b + 72 \, A B^{2} a^{2} b^{2} - 12 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(88 \, B^{3} a^{2} b^{3} + 18 \, A B^{2} a b^{4} - 3 \, A^{2} B b^{5}\right)} c^{2} + {\left(B b^{8} c^{3} + 256 \, {\left(3 \, B a^{4} - A a^{3} b\right)} c^{7} - 64 \, {\left(10 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{6} + 48 \, {\left(4 \, B a^{2} b^{4} - A a b^{5}\right)} c^{5} - 4 \, {\left(6 \, B a b^{6} - A b^{7}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} - 2 \, {\left(5 \, B^{4} a b^{4} - 3 \, A B^{3} b^{5} - 4 \, A^{4} a c^{4} + {\left(20 \, A^{3} B a b - 3 \, A^{4} b^{2}\right)} c^{3} + 3 \, {\left(108 \, B^{4} a^{3} - 108 \, A B^{3} a^{2} b + 28 \, A^{2} B^{2} a b^{2} - 3 \, A^{3} B b^{3}\right)} c^{2} - {\left(81 \, B^{4} a^{2} b^{2} - 65 \, A B^{3} a b^{3} + 9 \, A^{2} B^{2} b^{4}\right)} c\right)} \sqrt{x}\right) + 2 \, {\left(B a b - 2 \, A a c + {\left(B b^{2} - {\left(2 \, B a + A b\right)} c\right)} x\right)} \sqrt{x}}{2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)}}"," ",0,"-1/2*(sqrt(1/2)*(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(sqrt(1/2)*(B^3*b^7 - 17*B^3*a*b^5*c - 32*A^3*a^2*c^5 + 16*(18*A*B^2*a^3 - 3*A^2*B*a^2*b + A^3*a*b^2)*c^4 - 2*(72*B^3*a^3*b + 72*A*B^2*a^2*b^2 - 12*A^2*B*a*b^3 + A^3*b^4)*c^3 + (88*B^3*a^2*b^3 + 18*A*B^2*a*b^4 - 3*A^2*B*b^5)*c^2 - (B*b^8*c^3 + 256*(3*B*a^4 - A*a^3*b)*c^7 - 64*(10*B*a^3*b^2 - 3*A*a^2*b^3)*c^6 + 48*(4*B*a^2*b^4 - A*a*b^5)*c^5 - 4*(6*B*a*b^6 - A*b^7)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) - 2*(5*B^4*a*b^4 - 3*A*B^3*b^5 - 4*A^4*a*c^4 + (20*A^3*B*a*b - 3*A^4*b^2)*c^3 + 3*(108*B^4*a^3 - 108*A*B^3*a^2*b + 28*A^2*B^2*a*b^2 - 3*A^3*B*b^3)*c^2 - (81*B^4*a^2*b^2 - 65*A*B^3*a*b^3 + 9*A^2*B^2*b^4)*c)*sqrt(x)) - sqrt(1/2)*(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-sqrt(1/2)*(B^3*b^7 - 17*B^3*a*b^5*c - 32*A^3*a^2*c^5 + 16*(18*A*B^2*a^3 - 3*A^2*B*a^2*b + A^3*a*b^2)*c^4 - 2*(72*B^3*a^3*b + 72*A*B^2*a^2*b^2 - 12*A^2*B*a*b^3 + A^3*b^4)*c^3 + (88*B^3*a^2*b^3 + 18*A*B^2*a*b^4 - 3*A^2*B*b^5)*c^2 - (B*b^8*c^3 + 256*(3*B*a^4 - A*a^3*b)*c^7 - 64*(10*B*a^3*b^2 - 3*A*a^2*b^3)*c^6 + 48*(4*B*a^2*b^4 - A*a*b^5)*c^5 - 4*(6*B*a*b^6 - A*b^7)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) - 2*(5*B^4*a*b^4 - 3*A*B^3*b^5 - 4*A^4*a*c^4 + (20*A^3*B*a*b - 3*A^4*b^2)*c^3 + 3*(108*B^4*a^3 - 108*A*B^3*a^2*b + 28*A^2*B^2*a*b^2 - 3*A^3*B*b^3)*c^2 - (81*B^4*a^2*b^2 - 65*A*B^3*a*b^3 + 9*A^2*B^2*b^4)*c)*sqrt(x)) + sqrt(1/2)*(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(sqrt(1/2)*(B^3*b^7 - 17*B^3*a*b^5*c - 32*A^3*a^2*c^5 + 16*(18*A*B^2*a^3 - 3*A^2*B*a^2*b + A^3*a*b^2)*c^4 - 2*(72*B^3*a^3*b + 72*A*B^2*a^2*b^2 - 12*A^2*B*a*b^3 + A^3*b^4)*c^3 + (88*B^3*a^2*b^3 + 18*A*B^2*a*b^4 - 3*A^2*B*b^5)*c^2 + (B*b^8*c^3 + 256*(3*B*a^4 - A*a^3*b)*c^7 - 64*(10*B*a^3*b^2 - 3*A*a^2*b^3)*c^6 + 48*(4*B*a^2*b^4 - A*a*b^5)*c^5 - 4*(6*B*a*b^6 - A*b^7)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) - 2*(5*B^4*a*b^4 - 3*A*B^3*b^5 - 4*A^4*a*c^4 + (20*A^3*B*a*b - 3*A^4*b^2)*c^3 + 3*(108*B^4*a^3 - 108*A*B^3*a^2*b + 28*A^2*B^2*a*b^2 - 3*A^3*B*b^3)*c^2 - (81*B^4*a^2*b^2 - 65*A*B^3*a*b^3 + 9*A^2*B^2*b^4)*c)*sqrt(x)) - sqrt(1/2)*(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-sqrt(1/2)*(B^3*b^7 - 17*B^3*a*b^5*c - 32*A^3*a^2*c^5 + 16*(18*A*B^2*a^3 - 3*A^2*B*a^2*b + A^3*a*b^2)*c^4 - 2*(72*B^3*a^3*b + 72*A*B^2*a^2*b^2 - 12*A^2*B*a*b^3 + A^3*b^4)*c^3 + (88*B^3*a^2*b^3 + 18*A*B^2*a*b^4 - 3*A^2*B*b^5)*c^2 + (B*b^8*c^3 + 256*(3*B*a^4 - A*a^3*b)*c^7 - 64*(10*B*a^3*b^2 - 3*A*a^2*b^3)*c^6 + 48*(4*B*a^2*b^4 - A*a*b^5)*c^5 - 4*(6*B*a*b^6 - A*b^7)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) - 2*(5*B^4*a*b^4 - 3*A*B^3*b^5 - 4*A^4*a*c^4 + (20*A^3*B*a*b - 3*A^4*b^2)*c^3 + 3*(108*B^4*a^3 - 108*A*B^3*a^2*b + 28*A^2*B^2*a*b^2 - 3*A^3*B*b^3)*c^2 - (81*B^4*a^2*b^2 - 65*A*B^3*a*b^3 + 9*A^2*B^2*b^4)*c)*sqrt(x)) + 2*(B*a*b - 2*A*a*c + (B*b^2 - (2*B*a + A*b)*c)*x)*sqrt(x))/(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)","B",0
1019,1,3462,0,1.597605," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c + {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} \log\left(\sqrt{\frac{1}{2}} {\left(2 \, B^{3} a^{2} b^{4} - A B^{2} a b^{5} - 16 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{3} + 8 \, {\left(4 \, B^{3} a^{4} - 2 \, A B^{2} a^{3} b + 2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3}\right)} c^{2} - {\left(16 \, B^{3} a^{3} b^{2} - 8 \, A B^{2} a^{2} b^{3} + 2 \, A^{2} B a b^{4} - A^{3} b^{5}\right)} c + {\left(192 \, B a^{4} b^{3} c^{3} + 256 \, A a^{5} c^{5} - 128 \, {\left(2 \, B a^{5} b + A a^{4} b^{2}\right)} c^{4} - 8 \, {\left(6 \, B a^{3} b^{5} - A a^{2} b^{6}\right)} c^{2} + {\left(4 \, B a^{2} b^{7} - A a b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c + {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} - 2 \, {\left(3 \, B^{4} a^{2} b^{2} - A B^{3} a b^{3} - 4 \, A^{4} a c^{3} + 3 \, {\left(4 \, A^{3} B a b - A^{4} b^{2}\right)} c^{2} + {\left(4 \, B^{4} a^{3} - 12 \, A B^{3} a^{2} b + A^{3} B b^{3}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c + {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} \log\left(-\sqrt{\frac{1}{2}} {\left(2 \, B^{3} a^{2} b^{4} - A B^{2} a b^{5} - 16 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{3} + 8 \, {\left(4 \, B^{3} a^{4} - 2 \, A B^{2} a^{3} b + 2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3}\right)} c^{2} - {\left(16 \, B^{3} a^{3} b^{2} - 8 \, A B^{2} a^{2} b^{3} + 2 \, A^{2} B a b^{4} - A^{3} b^{5}\right)} c + {\left(192 \, B a^{4} b^{3} c^{3} + 256 \, A a^{5} c^{5} - 128 \, {\left(2 \, B a^{5} b + A a^{4} b^{2}\right)} c^{4} - 8 \, {\left(6 \, B a^{3} b^{5} - A a^{2} b^{6}\right)} c^{2} + {\left(4 \, B a^{2} b^{7} - A a b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c + {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} - 2 \, {\left(3 \, B^{4} a^{2} b^{2} - A B^{3} a b^{3} - 4 \, A^{4} a c^{3} + 3 \, {\left(4 \, A^{3} B a b - A^{4} b^{2}\right)} c^{2} + {\left(4 \, B^{4} a^{3} - 12 \, A B^{3} a^{2} b + A^{3} B b^{3}\right)} c\right)} \sqrt{x}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c - {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} \log\left(\sqrt{\frac{1}{2}} {\left(2 \, B^{3} a^{2} b^{4} - A B^{2} a b^{5} - 16 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{3} + 8 \, {\left(4 \, B^{3} a^{4} - 2 \, A B^{2} a^{3} b + 2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3}\right)} c^{2} - {\left(16 \, B^{3} a^{3} b^{2} - 8 \, A B^{2} a^{2} b^{3} + 2 \, A^{2} B a b^{4} - A^{3} b^{5}\right)} c - {\left(192 \, B a^{4} b^{3} c^{3} + 256 \, A a^{5} c^{5} - 128 \, {\left(2 \, B a^{5} b + A a^{4} b^{2}\right)} c^{4} - 8 \, {\left(6 \, B a^{3} b^{5} - A a^{2} b^{6}\right)} c^{2} + {\left(4 \, B a^{2} b^{7} - A a b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c - {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} - 2 \, {\left(3 \, B^{4} a^{2} b^{2} - A B^{3} a b^{3} - 4 \, A^{4} a c^{3} + 3 \, {\left(4 \, A^{3} B a b - A^{4} b^{2}\right)} c^{2} + {\left(4 \, B^{4} a^{3} - 12 \, A B^{3} a^{2} b + A^{3} B b^{3}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c - {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} \log\left(-\sqrt{\frac{1}{2}} {\left(2 \, B^{3} a^{2} b^{4} - A B^{2} a b^{5} - 16 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{3} + 8 \, {\left(4 \, B^{3} a^{4} - 2 \, A B^{2} a^{3} b + 2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3}\right)} c^{2} - {\left(16 \, B^{3} a^{3} b^{2} - 8 \, A B^{2} a^{2} b^{3} + 2 \, A^{2} B a b^{4} - A^{3} b^{5}\right)} c - {\left(192 \, B a^{4} b^{3} c^{3} + 256 \, A a^{5} c^{5} - 128 \, {\left(2 \, B a^{5} b + A a^{4} b^{2}\right)} c^{4} - 8 \, {\left(6 \, B a^{3} b^{5} - A a^{2} b^{6}\right)} c^{2} + {\left(4 \, B a^{2} b^{7} - A a b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c - {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} - 2 \, {\left(3 \, B^{4} a^{2} b^{2} - A B^{3} a b^{3} - 4 \, A^{4} a c^{3} + 3 \, {\left(4 \, A^{3} B a b - A^{4} b^{2}\right)} c^{2} + {\left(4 \, B^{4} a^{3} - 12 \, A B^{3} a^{2} b + A^{3} B b^{3}\right)} c\right)} \sqrt{x}\right) - 2 \, {\left(2 \, B a - A b + {\left(B b - 2 \, A c\right)} x\right)} \sqrt{x}}{2 \, {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)}}"," ",0,"-1/2*(sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c + (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))*log(sqrt(1/2)*(2*B^3*a^2*b^4 - A*B^2*a*b^5 - 16*(2*A^2*B*a^3 - A^3*a^2*b)*c^3 + 8*(4*B^3*a^4 - 2*A*B^2*a^3*b + 2*A^2*B*a^2*b^2 - A^3*a*b^3)*c^2 - (16*B^3*a^3*b^2 - 8*A*B^2*a^2*b^3 + 2*A^2*B*a*b^4 - A^3*b^5)*c + (192*B*a^4*b^3*c^3 + 256*A*a^5*c^5 - 128*(2*B*a^5*b + A*a^4*b^2)*c^4 - 8*(6*B*a^3*b^5 - A*a^2*b^6)*c^2 + (4*B*a^2*b^7 - A*a*b^8)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c + (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)) - 2*(3*B^4*a^2*b^2 - A*B^3*a*b^3 - 4*A^4*a*c^3 + 3*(4*A^3*B*a*b - A^4*b^2)*c^2 + (4*B^4*a^3 - 12*A*B^3*a^2*b + A^3*B*b^3)*c)*sqrt(x)) - sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c + (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))*log(-sqrt(1/2)*(2*B^3*a^2*b^4 - A*B^2*a*b^5 - 16*(2*A^2*B*a^3 - A^3*a^2*b)*c^3 + 8*(4*B^3*a^4 - 2*A*B^2*a^3*b + 2*A^2*B*a^2*b^2 - A^3*a*b^3)*c^2 - (16*B^3*a^3*b^2 - 8*A*B^2*a^2*b^3 + 2*A^2*B*a*b^4 - A^3*b^5)*c + (192*B*a^4*b^3*c^3 + 256*A*a^5*c^5 - 128*(2*B*a^5*b + A*a^4*b^2)*c^4 - 8*(6*B*a^3*b^5 - A*a^2*b^6)*c^2 + (4*B*a^2*b^7 - A*a*b^8)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c + (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)) - 2*(3*B^4*a^2*b^2 - A*B^3*a*b^3 - 4*A^4*a*c^3 + 3*(4*A^3*B*a*b - A^4*b^2)*c^2 + (4*B^4*a^3 - 12*A*B^3*a^2*b + A^3*B*b^3)*c)*sqrt(x)) + sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c - (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))*log(sqrt(1/2)*(2*B^3*a^2*b^4 - A*B^2*a*b^5 - 16*(2*A^2*B*a^3 - A^3*a^2*b)*c^3 + 8*(4*B^3*a^4 - 2*A*B^2*a^3*b + 2*A^2*B*a^2*b^2 - A^3*a*b^3)*c^2 - (16*B^3*a^3*b^2 - 8*A*B^2*a^2*b^3 + 2*A^2*B*a*b^4 - A^3*b^5)*c - (192*B*a^4*b^3*c^3 + 256*A*a^5*c^5 - 128*(2*B*a^5*b + A*a^4*b^2)*c^4 - 8*(6*B*a^3*b^5 - A*a^2*b^6)*c^2 + (4*B*a^2*b^7 - A*a*b^8)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c - (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)) - 2*(3*B^4*a^2*b^2 - A*B^3*a*b^3 - 4*A^4*a*c^3 + 3*(4*A^3*B*a*b - A^4*b^2)*c^2 + (4*B^4*a^3 - 12*A*B^3*a^2*b + A^3*B*b^3)*c)*sqrt(x)) - sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c - (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))*log(-sqrt(1/2)*(2*B^3*a^2*b^4 - A*B^2*a*b^5 - 16*(2*A^2*B*a^3 - A^3*a^2*b)*c^3 + 8*(4*B^3*a^4 - 2*A*B^2*a^3*b + 2*A^2*B*a^2*b^2 - A^3*a*b^3)*c^2 - (16*B^3*a^3*b^2 - 8*A*B^2*a^2*b^3 + 2*A^2*B*a*b^4 - A^3*b^5)*c - (192*B*a^4*b^3*c^3 + 256*A*a^5*c^5 - 128*(2*B*a^5*b + A*a^4*b^2)*c^4 - 8*(6*B*a^3*b^5 - A*a^2*b^6)*c^2 + (4*B*a^2*b^7 - A*a*b^8)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c - (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)) - 2*(3*B^4*a^2*b^2 - A*B^3*a*b^3 - 4*A^4*a*c^3 + 3*(4*A^3*B*a*b - A^4*b^2)*c^2 + (4*B^4*a^3 - 12*A*B^3*a^2*b + A^3*B*b^3)*c)*sqrt(x)) - 2*(2*B*a - A*b + (B*b - 2*A*c)*x)*sqrt(x))/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)","B",0
1020,1,4884,0,3.793001," ","integrate((B*x+A)/(c*x^2+b*x+a)^2/x^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{2} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left(\sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} + 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} + A^{3} b^{8} + 864 \, A^{3} a^{4} c^{4} - 48 \, {\left(2 \, A B^{2} a^{5} + 7 \, A^{2} B a^{4} b + 14 \, A^{3} a^{3} b^{2}\right)} c^{3} + 2 \, {\left(8 \, B^{3} a^{5} b + 48 \, A B^{2} a^{4} b^{2} + 108 \, A^{2} B a^{3} b^{3} + 95 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{3} + 30 \, A B^{2} a^{3} b^{4} + 45 \, A^{2} B a^{2} b^{5} + 23 \, A^{3} a b^{6}\right)} c - {\left(B a^{4} b^{8} + A a^{3} b^{9} + 144 \, A a^{5} b^{5} c^{2} - 256 \, {\left(B a^{8} - 2 \, A a^{7} b\right)} c^{4} + 64 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, B a^{5} b^{6} + 5 \, A a^{4} b^{7}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} + 2 \, {\left(324 \, A^{4} a^{2} c^{4} - 81 \, {\left(4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} - {\left(4 \, B^{4} a^{4} - 20 \, A B^{3} a^{3} b - 84 \, A^{2} B^{2} a^{2} b^{2} - 65 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} - 3 \, {\left(B^{4} a^{3} b^{2} + 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} + A^{3} B b^{5}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{2} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left(-\sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} + 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} + A^{3} b^{8} + 864 \, A^{3} a^{4} c^{4} - 48 \, {\left(2 \, A B^{2} a^{5} + 7 \, A^{2} B a^{4} b + 14 \, A^{3} a^{3} b^{2}\right)} c^{3} + 2 \, {\left(8 \, B^{3} a^{5} b + 48 \, A B^{2} a^{4} b^{2} + 108 \, A^{2} B a^{3} b^{3} + 95 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{3} + 30 \, A B^{2} a^{3} b^{4} + 45 \, A^{2} B a^{2} b^{5} + 23 \, A^{3} a b^{6}\right)} c - {\left(B a^{4} b^{8} + A a^{3} b^{9} + 144 \, A a^{5} b^{5} c^{2} - 256 \, {\left(B a^{8} - 2 \, A a^{7} b\right)} c^{4} + 64 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, B a^{5} b^{6} + 5 \, A a^{4} b^{7}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} + 2 \, {\left(324 \, A^{4} a^{2} c^{4} - 81 \, {\left(4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} - {\left(4 \, B^{4} a^{4} - 20 \, A B^{3} a^{3} b - 84 \, A^{2} B^{2} a^{2} b^{2} - 65 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} - 3 \, {\left(B^{4} a^{3} b^{2} + 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} + A^{3} B b^{5}\right)} c\right)} \sqrt{x}\right) + \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{2} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left(\sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} + 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} + A^{3} b^{8} + 864 \, A^{3} a^{4} c^{4} - 48 \, {\left(2 \, A B^{2} a^{5} + 7 \, A^{2} B a^{4} b + 14 \, A^{3} a^{3} b^{2}\right)} c^{3} + 2 \, {\left(8 \, B^{3} a^{5} b + 48 \, A B^{2} a^{4} b^{2} + 108 \, A^{2} B a^{3} b^{3} + 95 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{3} + 30 \, A B^{2} a^{3} b^{4} + 45 \, A^{2} B a^{2} b^{5} + 23 \, A^{3} a b^{6}\right)} c + {\left(B a^{4} b^{8} + A a^{3} b^{9} + 144 \, A a^{5} b^{5} c^{2} - 256 \, {\left(B a^{8} - 2 \, A a^{7} b\right)} c^{4} + 64 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, B a^{5} b^{6} + 5 \, A a^{4} b^{7}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} + 2 \, {\left(324 \, A^{4} a^{2} c^{4} - 81 \, {\left(4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} - {\left(4 \, B^{4} a^{4} - 20 \, A B^{3} a^{3} b - 84 \, A^{2} B^{2} a^{2} b^{2} - 65 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} - 3 \, {\left(B^{4} a^{3} b^{2} + 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} + A^{3} B b^{5}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{2} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left(-\sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} + 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} + A^{3} b^{8} + 864 \, A^{3} a^{4} c^{4} - 48 \, {\left(2 \, A B^{2} a^{5} + 7 \, A^{2} B a^{4} b + 14 \, A^{3} a^{3} b^{2}\right)} c^{3} + 2 \, {\left(8 \, B^{3} a^{5} b + 48 \, A B^{2} a^{4} b^{2} + 108 \, A^{2} B a^{3} b^{3} + 95 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{3} + 30 \, A B^{2} a^{3} b^{4} + 45 \, A^{2} B a^{2} b^{5} + 23 \, A^{3} a b^{6}\right)} c + {\left(B a^{4} b^{8} + A a^{3} b^{9} + 144 \, A a^{5} b^{5} c^{2} - 256 \, {\left(B a^{8} - 2 \, A a^{7} b\right)} c^{4} + 64 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, B a^{5} b^{6} + 5 \, A a^{4} b^{7}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} + 2 \, {\left(324 \, A^{4} a^{2} c^{4} - 81 \, {\left(4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} - {\left(4 \, B^{4} a^{4} - 20 \, A B^{3} a^{3} b - 84 \, A^{2} B^{2} a^{2} b^{2} - 65 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} - 3 \, {\left(B^{4} a^{3} b^{2} + 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} + A^{3} B b^{5}\right)} c\right)} \sqrt{x}\right) - 2 \, {\left(B a b - A b^{2} + 2 \, A a c + {\left(2 \, B a - A b\right)} c x\right)} \sqrt{x}}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{2} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}"," ",0,"1/2*(sqrt(1/2)*(a^2*b^2 - 4*a^3*c + (a*b^2*c - 4*a^2*c^2)*x^2 + (a*b^3 - 4*a^2*b*c)*x)*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log(sqrt(1/2)*(B^3*a^3*b^5 + 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 + A^3*b^8 + 864*A^3*a^4*c^4 - 48*(2*A*B^2*a^5 + 7*A^2*B*a^4*b + 14*A^3*a^3*b^2)*c^3 + 2*(8*B^3*a^5*b + 48*A*B^2*a^4*b^2 + 108*A^2*B*a^3*b^3 + 95*A^3*a^2*b^4)*c^2 - (8*B^3*a^4*b^3 + 30*A*B^2*a^3*b^4 + 45*A^2*B*a^2*b^5 + 23*A^3*a*b^6)*c - (B*a^4*b^8 + A*a^3*b^9 + 144*A*a^5*b^5*c^2 - 256*(B*a^8 - 2*A*a^7*b)*c^4 + 64*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^3 - 4*(2*B*a^5*b^6 + 5*A*a^4*b^7)*c)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)) + 2*(324*A^4*a^2*c^4 - 81*(4*A^3*B*a^2*b + A^4*a*b^2)*c^3 - (4*B^4*a^4 - 20*A*B^3*a^3*b - 84*A^2*B^2*a^2*b^2 - 65*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 - 3*(B^4*a^3*b^2 + 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 + A^3*B*b^5)*c)*sqrt(x)) - sqrt(1/2)*(a^2*b^2 - 4*a^3*c + (a*b^2*c - 4*a^2*c^2)*x^2 + (a*b^3 - 4*a^2*b*c)*x)*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log(-sqrt(1/2)*(B^3*a^3*b^5 + 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 + A^3*b^8 + 864*A^3*a^4*c^4 - 48*(2*A*B^2*a^5 + 7*A^2*B*a^4*b + 14*A^3*a^3*b^2)*c^3 + 2*(8*B^3*a^5*b + 48*A*B^2*a^4*b^2 + 108*A^2*B*a^3*b^3 + 95*A^3*a^2*b^4)*c^2 - (8*B^3*a^4*b^3 + 30*A*B^2*a^3*b^4 + 45*A^2*B*a^2*b^5 + 23*A^3*a*b^6)*c - (B*a^4*b^8 + A*a^3*b^9 + 144*A*a^5*b^5*c^2 - 256*(B*a^8 - 2*A*a^7*b)*c^4 + 64*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^3 - 4*(2*B*a^5*b^6 + 5*A*a^4*b^7)*c)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)) + 2*(324*A^4*a^2*c^4 - 81*(4*A^3*B*a^2*b + A^4*a*b^2)*c^3 - (4*B^4*a^4 - 20*A*B^3*a^3*b - 84*A^2*B^2*a^2*b^2 - 65*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 - 3*(B^4*a^3*b^2 + 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 + A^3*B*b^5)*c)*sqrt(x)) + sqrt(1/2)*(a^2*b^2 - 4*a^3*c + (a*b^2*c - 4*a^2*c^2)*x^2 + (a*b^3 - 4*a^2*b*c)*x)*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log(sqrt(1/2)*(B^3*a^3*b^5 + 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 + A^3*b^8 + 864*A^3*a^4*c^4 - 48*(2*A*B^2*a^5 + 7*A^2*B*a^4*b + 14*A^3*a^3*b^2)*c^3 + 2*(8*B^3*a^5*b + 48*A*B^2*a^4*b^2 + 108*A^2*B*a^3*b^3 + 95*A^3*a^2*b^4)*c^2 - (8*B^3*a^4*b^3 + 30*A*B^2*a^3*b^4 + 45*A^2*B*a^2*b^5 + 23*A^3*a*b^6)*c + (B*a^4*b^8 + A*a^3*b^9 + 144*A*a^5*b^5*c^2 - 256*(B*a^8 - 2*A*a^7*b)*c^4 + 64*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^3 - 4*(2*B*a^5*b^6 + 5*A*a^4*b^7)*c)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)) + 2*(324*A^4*a^2*c^4 - 81*(4*A^3*B*a^2*b + A^4*a*b^2)*c^3 - (4*B^4*a^4 - 20*A*B^3*a^3*b - 84*A^2*B^2*a^2*b^2 - 65*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 - 3*(B^4*a^3*b^2 + 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 + A^3*B*b^5)*c)*sqrt(x)) - sqrt(1/2)*(a^2*b^2 - 4*a^3*c + (a*b^2*c - 4*a^2*c^2)*x^2 + (a*b^3 - 4*a^2*b*c)*x)*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log(-sqrt(1/2)*(B^3*a^3*b^5 + 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 + A^3*b^8 + 864*A^3*a^4*c^4 - 48*(2*A*B^2*a^5 + 7*A^2*B*a^4*b + 14*A^3*a^3*b^2)*c^3 + 2*(8*B^3*a^5*b + 48*A*B^2*a^4*b^2 + 108*A^2*B*a^3*b^3 + 95*A^3*a^2*b^4)*c^2 - (8*B^3*a^4*b^3 + 30*A*B^2*a^3*b^4 + 45*A^2*B*a^2*b^5 + 23*A^3*a*b^6)*c + (B*a^4*b^8 + A*a^3*b^9 + 144*A*a^5*b^5*c^2 - 256*(B*a^8 - 2*A*a^7*b)*c^4 + 64*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^3 - 4*(2*B*a^5*b^6 + 5*A*a^4*b^7)*c)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)) + 2*(324*A^4*a^2*c^4 - 81*(4*A^3*B*a^2*b + A^4*a*b^2)*c^3 - (4*B^4*a^4 - 20*A*B^3*a^3*b - 84*A^2*B^2*a^2*b^2 - 65*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 - 3*(B^4*a^3*b^2 + 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 + A^3*B*b^5)*c)*sqrt(x)) - 2*(B*a*b - A*b^2 + 2*A*a*c + (2*B*a - A*b)*c*x)*sqrt(x))/(a^2*b^2 - 4*a^3*c + (a*b^2*c - 4*a^2*c^2)*x^2 + (a*b^3 - 4*a^2*b*c)*x)","B",0
1021,1,7597,0,13.288150," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left(\sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{8} - 9 \, A B^{2} a^{2} b^{9} + 27 \, A^{2} B a b^{10} - 27 \, A^{3} b^{11} - 400 \, {\left(6 \, A^{2} B a^{6} - 13 \, A^{3} a^{5} b\right)} c^{5} + 8 \, {\left(108 \, B^{3} a^{7} - 762 \, A B^{2} a^{6} b + 1956 \, A^{2} B a^{5} b^{2} - 1801 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(672 \, B^{3} a^{6} b^{2} - 4968 \, A B^{2} a^{5} b^{3} + 12414 \, A^{2} B a^{4} b^{4} - 10549 \, A^{3} a^{3} b^{5}\right)} c^{3} + 5 \, {\left(38 \, B^{3} a^{5} b^{4} - 297 \, A B^{2} a^{4} b^{5} + 771 \, A^{2} B a^{3} b^{6} - 666 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(23 \, B^{3} a^{4} b^{6} - 192 \, A B^{2} a^{3} b^{7} + 531 \, A^{2} B a^{2} b^{8} - 486 \, A^{3} a b^{9}\right)} c - {\left(B a^{6} b^{9} - 3 \, A a^{5} b^{10} + 1280 \, A a^{10} c^{5} + 128 \, {\left(4 \, B a^{10} b - 17 \, A a^{9} b^{2}\right)} c^{4} - 448 \, {\left(B a^{9} b^{3} - 3 \, A a^{8} b^{4}\right)} c^{3} + 8 \, {\left(18 \, B a^{8} b^{5} - 49 \, A a^{7} b^{6}\right)} c^{2} - 5 \, {\left(4 \, B a^{7} b^{7} - 11 \, A a^{6} b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} + 2 \, {\left(2500 \, A^{4} a^{3} c^{6} + 625 \, {\left(4 \, A^{3} B a^{3} b - 9 \, A^{4} a^{2} b^{2}\right)} c^{5} - 3 \, {\left(108 \, B^{4} a^{5} - 756 \, A B^{3} a^{4} b + 1672 \, A^{2} B^{2} a^{3} b^{2} - 909 \, A^{3} B a^{2} b^{3} - 657 \, A^{4} a b^{4}\right)} c^{4} + {\left(81 \, B^{4} a^{4} b^{2} - 647 \, A B^{3} a^{3} b^{3} + 1674 \, A^{2} B^{2} a^{2} b^{4} - 1323 \, A^{3} B a b^{5} - 189 \, A^{4} b^{6}\right)} c^{3} - 5 \, {\left(B^{4} a^{3} b^{4} - 9 \, A B^{3} a^{2} b^{5} + 27 \, A^{2} B^{2} a b^{6} - 27 \, A^{3} B b^{7}\right)} c^{2}\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left(-\sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{8} - 9 \, A B^{2} a^{2} b^{9} + 27 \, A^{2} B a b^{10} - 27 \, A^{3} b^{11} - 400 \, {\left(6 \, A^{2} B a^{6} - 13 \, A^{3} a^{5} b\right)} c^{5} + 8 \, {\left(108 \, B^{3} a^{7} - 762 \, A B^{2} a^{6} b + 1956 \, A^{2} B a^{5} b^{2} - 1801 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(672 \, B^{3} a^{6} b^{2} - 4968 \, A B^{2} a^{5} b^{3} + 12414 \, A^{2} B a^{4} b^{4} - 10549 \, A^{3} a^{3} b^{5}\right)} c^{3} + 5 \, {\left(38 \, B^{3} a^{5} b^{4} - 297 \, A B^{2} a^{4} b^{5} + 771 \, A^{2} B a^{3} b^{6} - 666 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(23 \, B^{3} a^{4} b^{6} - 192 \, A B^{2} a^{3} b^{7} + 531 \, A^{2} B a^{2} b^{8} - 486 \, A^{3} a b^{9}\right)} c - {\left(B a^{6} b^{9} - 3 \, A a^{5} b^{10} + 1280 \, A a^{10} c^{5} + 128 \, {\left(4 \, B a^{10} b - 17 \, A a^{9} b^{2}\right)} c^{4} - 448 \, {\left(B a^{9} b^{3} - 3 \, A a^{8} b^{4}\right)} c^{3} + 8 \, {\left(18 \, B a^{8} b^{5} - 49 \, A a^{7} b^{6}\right)} c^{2} - 5 \, {\left(4 \, B a^{7} b^{7} - 11 \, A a^{6} b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} + 2 \, {\left(2500 \, A^{4} a^{3} c^{6} + 625 \, {\left(4 \, A^{3} B a^{3} b - 9 \, A^{4} a^{2} b^{2}\right)} c^{5} - 3 \, {\left(108 \, B^{4} a^{5} - 756 \, A B^{3} a^{4} b + 1672 \, A^{2} B^{2} a^{3} b^{2} - 909 \, A^{3} B a^{2} b^{3} - 657 \, A^{4} a b^{4}\right)} c^{4} + {\left(81 \, B^{4} a^{4} b^{2} - 647 \, A B^{3} a^{3} b^{3} + 1674 \, A^{2} B^{2} a^{2} b^{4} - 1323 \, A^{3} B a b^{5} - 189 \, A^{4} b^{6}\right)} c^{3} - 5 \, {\left(B^{4} a^{3} b^{4} - 9 \, A B^{3} a^{2} b^{5} + 27 \, A^{2} B^{2} a b^{6} - 27 \, A^{3} B b^{7}\right)} c^{2}\right)} \sqrt{x}\right) + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left(\sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{8} - 9 \, A B^{2} a^{2} b^{9} + 27 \, A^{2} B a b^{10} - 27 \, A^{3} b^{11} - 400 \, {\left(6 \, A^{2} B a^{6} - 13 \, A^{3} a^{5} b\right)} c^{5} + 8 \, {\left(108 \, B^{3} a^{7} - 762 \, A B^{2} a^{6} b + 1956 \, A^{2} B a^{5} b^{2} - 1801 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(672 \, B^{3} a^{6} b^{2} - 4968 \, A B^{2} a^{5} b^{3} + 12414 \, A^{2} B a^{4} b^{4} - 10549 \, A^{3} a^{3} b^{5}\right)} c^{3} + 5 \, {\left(38 \, B^{3} a^{5} b^{4} - 297 \, A B^{2} a^{4} b^{5} + 771 \, A^{2} B a^{3} b^{6} - 666 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(23 \, B^{3} a^{4} b^{6} - 192 \, A B^{2} a^{3} b^{7} + 531 \, A^{2} B a^{2} b^{8} - 486 \, A^{3} a b^{9}\right)} c + {\left(B a^{6} b^{9} - 3 \, A a^{5} b^{10} + 1280 \, A a^{10} c^{5} + 128 \, {\left(4 \, B a^{10} b - 17 \, A a^{9} b^{2}\right)} c^{4} - 448 \, {\left(B a^{9} b^{3} - 3 \, A a^{8} b^{4}\right)} c^{3} + 8 \, {\left(18 \, B a^{8} b^{5} - 49 \, A a^{7} b^{6}\right)} c^{2} - 5 \, {\left(4 \, B a^{7} b^{7} - 11 \, A a^{6} b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} + 2 \, {\left(2500 \, A^{4} a^{3} c^{6} + 625 \, {\left(4 \, A^{3} B a^{3} b - 9 \, A^{4} a^{2} b^{2}\right)} c^{5} - 3 \, {\left(108 \, B^{4} a^{5} - 756 \, A B^{3} a^{4} b + 1672 \, A^{2} B^{2} a^{3} b^{2} - 909 \, A^{3} B a^{2} b^{3} - 657 \, A^{4} a b^{4}\right)} c^{4} + {\left(81 \, B^{4} a^{4} b^{2} - 647 \, A B^{3} a^{3} b^{3} + 1674 \, A^{2} B^{2} a^{2} b^{4} - 1323 \, A^{3} B a b^{5} - 189 \, A^{4} b^{6}\right)} c^{3} - 5 \, {\left(B^{4} a^{3} b^{4} - 9 \, A B^{3} a^{2} b^{5} + 27 \, A^{2} B^{2} a b^{6} - 27 \, A^{3} B b^{7}\right)} c^{2}\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left(-\sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{8} - 9 \, A B^{2} a^{2} b^{9} + 27 \, A^{2} B a b^{10} - 27 \, A^{3} b^{11} - 400 \, {\left(6 \, A^{2} B a^{6} - 13 \, A^{3} a^{5} b\right)} c^{5} + 8 \, {\left(108 \, B^{3} a^{7} - 762 \, A B^{2} a^{6} b + 1956 \, A^{2} B a^{5} b^{2} - 1801 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(672 \, B^{3} a^{6} b^{2} - 4968 \, A B^{2} a^{5} b^{3} + 12414 \, A^{2} B a^{4} b^{4} - 10549 \, A^{3} a^{3} b^{5}\right)} c^{3} + 5 \, {\left(38 \, B^{3} a^{5} b^{4} - 297 \, A B^{2} a^{4} b^{5} + 771 \, A^{2} B a^{3} b^{6} - 666 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(23 \, B^{3} a^{4} b^{6} - 192 \, A B^{2} a^{3} b^{7} + 531 \, A^{2} B a^{2} b^{8} - 486 \, A^{3} a b^{9}\right)} c + {\left(B a^{6} b^{9} - 3 \, A a^{5} b^{10} + 1280 \, A a^{10} c^{5} + 128 \, {\left(4 \, B a^{10} b - 17 \, A a^{9} b^{2}\right)} c^{4} - 448 \, {\left(B a^{9} b^{3} - 3 \, A a^{8} b^{4}\right)} c^{3} + 8 \, {\left(18 \, B a^{8} b^{5} - 49 \, A a^{7} b^{6}\right)} c^{2} - 5 \, {\left(4 \, B a^{7} b^{7} - 11 \, A a^{6} b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} + 2 \, {\left(2500 \, A^{4} a^{3} c^{6} + 625 \, {\left(4 \, A^{3} B a^{3} b - 9 \, A^{4} a^{2} b^{2}\right)} c^{5} - 3 \, {\left(108 \, B^{4} a^{5} - 756 \, A B^{3} a^{4} b + 1672 \, A^{2} B^{2} a^{3} b^{2} - 909 \, A^{3} B a^{2} b^{3} - 657 \, A^{4} a b^{4}\right)} c^{4} + {\left(81 \, B^{4} a^{4} b^{2} - 647 \, A B^{3} a^{3} b^{3} + 1674 \, A^{2} B^{2} a^{2} b^{4} - 1323 \, A^{3} B a b^{5} - 189 \, A^{4} b^{6}\right)} c^{3} - 5 \, {\left(B^{4} a^{3} b^{4} - 9 \, A B^{3} a^{2} b^{5} + 27 \, A^{2} B^{2} a b^{6} - 27 \, A^{3} B b^{7}\right)} c^{2}\right)} \sqrt{x}\right) + 2 \, {\left(2 \, A a b^{2} - 8 \, A a^{2} c - {\left(10 \, A a c^{2} + {\left(B a b - 3 \, A b^{2}\right)} c\right)} x^{2} - {\left(B a b^{2} - 3 \, A b^{3} - {\left(2 \, B a^{2} - 11 \, A a b\right)} c\right)} x\right)} \sqrt{x}}{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}}"," ",0,"-1/2*(sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^3 + (a^2*b^3 - 4*a^3*b*c)*x^2 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log(sqrt(1/2)*(B^3*a^3*b^8 - 9*A*B^2*a^2*b^9 + 27*A^2*B*a*b^10 - 27*A^3*b^11 - 400*(6*A^2*B*a^6 - 13*A^3*a^5*b)*c^5 + 8*(108*B^3*a^7 - 762*A*B^2*a^6*b + 1956*A^2*B*a^5*b^2 - 1801*A^3*a^4*b^3)*c^4 - (672*B^3*a^6*b^2 - 4968*A*B^2*a^5*b^3 + 12414*A^2*B*a^4*b^4 - 10549*A^3*a^3*b^5)*c^3 + 5*(38*B^3*a^5*b^4 - 297*A*B^2*a^4*b^5 + 771*A^2*B*a^3*b^6 - 666*A^3*a^2*b^7)*c^2 - (23*B^3*a^4*b^6 - 192*A*B^2*a^3*b^7 + 531*A^2*B*a^2*b^8 - 486*A^3*a*b^9)*c - (B*a^6*b^9 - 3*A*a^5*b^10 + 1280*A*a^10*c^5 + 128*(4*B*a^10*b - 17*A*a^9*b^2)*c^4 - 448*(B*a^9*b^3 - 3*A*a^8*b^4)*c^3 + 8*(18*B*a^8*b^5 - 49*A*a^7*b^6)*c^2 - 5*(4*B*a^7*b^7 - 11*A*a^6*b^8)*c)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)) + 2*(2500*A^4*a^3*c^6 + 625*(4*A^3*B*a^3*b - 9*A^4*a^2*b^2)*c^5 - 3*(108*B^4*a^5 - 756*A*B^3*a^4*b + 1672*A^2*B^2*a^3*b^2 - 909*A^3*B*a^2*b^3 - 657*A^4*a*b^4)*c^4 + (81*B^4*a^4*b^2 - 647*A*B^3*a^3*b^3 + 1674*A^2*B^2*a^2*b^4 - 1323*A^3*B*a*b^5 - 189*A^4*b^6)*c^3 - 5*(B^4*a^3*b^4 - 9*A*B^3*a^2*b^5 + 27*A^2*B^2*a*b^6 - 27*A^3*B*b^7)*c^2)*sqrt(x)) - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^3 + (a^2*b^3 - 4*a^3*b*c)*x^2 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log(-sqrt(1/2)*(B^3*a^3*b^8 - 9*A*B^2*a^2*b^9 + 27*A^2*B*a*b^10 - 27*A^3*b^11 - 400*(6*A^2*B*a^6 - 13*A^3*a^5*b)*c^5 + 8*(108*B^3*a^7 - 762*A*B^2*a^6*b + 1956*A^2*B*a^5*b^2 - 1801*A^3*a^4*b^3)*c^4 - (672*B^3*a^6*b^2 - 4968*A*B^2*a^5*b^3 + 12414*A^2*B*a^4*b^4 - 10549*A^3*a^3*b^5)*c^3 + 5*(38*B^3*a^5*b^4 - 297*A*B^2*a^4*b^5 + 771*A^2*B*a^3*b^6 - 666*A^3*a^2*b^7)*c^2 - (23*B^3*a^4*b^6 - 192*A*B^2*a^3*b^7 + 531*A^2*B*a^2*b^8 - 486*A^3*a*b^9)*c - (B*a^6*b^9 - 3*A*a^5*b^10 + 1280*A*a^10*c^5 + 128*(4*B*a^10*b - 17*A*a^9*b^2)*c^4 - 448*(B*a^9*b^3 - 3*A*a^8*b^4)*c^3 + 8*(18*B*a^8*b^5 - 49*A*a^7*b^6)*c^2 - 5*(4*B*a^7*b^7 - 11*A*a^6*b^8)*c)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)) + 2*(2500*A^4*a^3*c^6 + 625*(4*A^3*B*a^3*b - 9*A^4*a^2*b^2)*c^5 - 3*(108*B^4*a^5 - 756*A*B^3*a^4*b + 1672*A^2*B^2*a^3*b^2 - 909*A^3*B*a^2*b^3 - 657*A^4*a*b^4)*c^4 + (81*B^4*a^4*b^2 - 647*A*B^3*a^3*b^3 + 1674*A^2*B^2*a^2*b^4 - 1323*A^3*B*a*b^5 - 189*A^4*b^6)*c^3 - 5*(B^4*a^3*b^4 - 9*A*B^3*a^2*b^5 + 27*A^2*B^2*a*b^6 - 27*A^3*B*b^7)*c^2)*sqrt(x)) + sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^3 + (a^2*b^3 - 4*a^3*b*c)*x^2 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log(sqrt(1/2)*(B^3*a^3*b^8 - 9*A*B^2*a^2*b^9 + 27*A^2*B*a*b^10 - 27*A^3*b^11 - 400*(6*A^2*B*a^6 - 13*A^3*a^5*b)*c^5 + 8*(108*B^3*a^7 - 762*A*B^2*a^6*b + 1956*A^2*B*a^5*b^2 - 1801*A^3*a^4*b^3)*c^4 - (672*B^3*a^6*b^2 - 4968*A*B^2*a^5*b^3 + 12414*A^2*B*a^4*b^4 - 10549*A^3*a^3*b^5)*c^3 + 5*(38*B^3*a^5*b^4 - 297*A*B^2*a^4*b^5 + 771*A^2*B*a^3*b^6 - 666*A^3*a^2*b^7)*c^2 - (23*B^3*a^4*b^6 - 192*A*B^2*a^3*b^7 + 531*A^2*B*a^2*b^8 - 486*A^3*a*b^9)*c + (B*a^6*b^9 - 3*A*a^5*b^10 + 1280*A*a^10*c^5 + 128*(4*B*a^10*b - 17*A*a^9*b^2)*c^4 - 448*(B*a^9*b^3 - 3*A*a^8*b^4)*c^3 + 8*(18*B*a^8*b^5 - 49*A*a^7*b^6)*c^2 - 5*(4*B*a^7*b^7 - 11*A*a^6*b^8)*c)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)) + 2*(2500*A^4*a^3*c^6 + 625*(4*A^3*B*a^3*b - 9*A^4*a^2*b^2)*c^5 - 3*(108*B^4*a^5 - 756*A*B^3*a^4*b + 1672*A^2*B^2*a^3*b^2 - 909*A^3*B*a^2*b^3 - 657*A^4*a*b^4)*c^4 + (81*B^4*a^4*b^2 - 647*A*B^3*a^3*b^3 + 1674*A^2*B^2*a^2*b^4 - 1323*A^3*B*a*b^5 - 189*A^4*b^6)*c^3 - 5*(B^4*a^3*b^4 - 9*A*B^3*a^2*b^5 + 27*A^2*B^2*a*b^6 - 27*A^3*B*b^7)*c^2)*sqrt(x)) - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^3 + (a^2*b^3 - 4*a^3*b*c)*x^2 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log(-sqrt(1/2)*(B^3*a^3*b^8 - 9*A*B^2*a^2*b^9 + 27*A^2*B*a*b^10 - 27*A^3*b^11 - 400*(6*A^2*B*a^6 - 13*A^3*a^5*b)*c^5 + 8*(108*B^3*a^7 - 762*A*B^2*a^6*b + 1956*A^2*B*a^5*b^2 - 1801*A^3*a^4*b^3)*c^4 - (672*B^3*a^6*b^2 - 4968*A*B^2*a^5*b^3 + 12414*A^2*B*a^4*b^4 - 10549*A^3*a^3*b^5)*c^3 + 5*(38*B^3*a^5*b^4 - 297*A*B^2*a^4*b^5 + 771*A^2*B*a^3*b^6 - 666*A^3*a^2*b^7)*c^2 - (23*B^3*a^4*b^6 - 192*A*B^2*a^3*b^7 + 531*A^2*B*a^2*b^8 - 486*A^3*a*b^9)*c + (B*a^6*b^9 - 3*A*a^5*b^10 + 1280*A*a^10*c^5 + 128*(4*B*a^10*b - 17*A*a^9*b^2)*c^4 - 448*(B*a^9*b^3 - 3*A*a^8*b^4)*c^3 + 8*(18*B*a^8*b^5 - 49*A*a^7*b^6)*c^2 - 5*(4*B*a^7*b^7 - 11*A*a^6*b^8)*c)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)) + 2*(2500*A^4*a^3*c^6 + 625*(4*A^3*B*a^3*b - 9*A^4*a^2*b^2)*c^5 - 3*(108*B^4*a^5 - 756*A*B^3*a^4*b + 1672*A^2*B^2*a^3*b^2 - 909*A^3*B*a^2*b^3 - 657*A^4*a*b^4)*c^4 + (81*B^4*a^4*b^2 - 647*A*B^3*a^3*b^3 + 1674*A^2*B^2*a^2*b^4 - 1323*A^3*B*a*b^5 - 189*A^4*b^6)*c^3 - 5*(B^4*a^3*b^4 - 9*A*B^3*a^2*b^5 + 27*A^2*B^2*a*b^6 - 27*A^3*B*b^7)*c^2)*sqrt(x)) + 2*(2*A*a*b^2 - 8*A*a^2*c - (10*A*a*c^2 + (B*a*b - 3*A*b^2)*c)*x^2 - (B*a*b^2 - 3*A*b^3 - (2*B*a^2 - 11*A*a*b)*c)*x)*sqrt(x))/((a^2*b^2*c - 4*a^3*c^2)*x^3 + (a^2*b^3 - 4*a^3*b*c)*x^2 + (a^3*b^2 - 4*a^4*c)*x)","B",0
1022,1,10203,0,29.202826," ","integrate((B*x+A)/x^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left(\sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{11} - 135 \, A B^{2} a^{2} b^{12} + 225 \, A^{2} B a b^{13} - 125 \, A^{3} b^{14} + 10976 \, A^{3} a^{7} c^{7} - 112 \, {\left(50 \, A B^{2} a^{8} - 463 \, A^{2} B a^{7} b + 709 \, A^{3} a^{6} b^{2}\right)} c^{6} - 2 \, {\left(2600 \, B^{3} a^{8} b - 31256 \, A B^{2} a^{7} b^{2} + 96044 \, A^{2} B a^{6} b^{3} - 86495 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(14408 \, B^{3} a^{7} b^{3} - 101006 \, A B^{2} a^{6} b^{4} + 224705 \, A^{2} B a^{5} b^{5} - 160932 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(1507 \, B^{3} a^{6} b^{5} - 8820 \, A B^{2} a^{5} b^{6} + 16991 \, A^{2} B a^{4} b^{7} - 10797 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(3330 \, B^{3} a^{5} b^{7} - 17889 \, A B^{2} a^{4} b^{8} + 31929 \, A^{2} B a^{3} b^{9} - 18940 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(486 \, B^{3} a^{4} b^{9} - 2493 \, A B^{2} a^{3} b^{10} + 4260 \, A^{2} B a^{2} b^{11} - 2425 \, A^{3} a b^{12}\right)} c - {\left(3 \, B a^{8} b^{10} - 5 \, A a^{7} b^{11} - 256 \, {\left(5 \, B a^{13} - 13 \, A a^{12} b\right)} c^{5} + 64 \, {\left(34 \, B a^{12} b^{2} - 73 \, A a^{11} b^{3}\right)} c^{4} - 112 \, {\left(12 \, B a^{11} b^{4} - 23 \, A a^{10} b^{5}\right)} c^{3} + 28 \, {\left(14 \, B a^{10} b^{6} - 25 \, A a^{9} b^{7}\right)} c^{2} - {\left(55 \, B a^{9} b^{8} - 94 \, A a^{8} b^{9}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} + 2 \, {\left(9604 \, A^{4} a^{4} c^{8} + 7203 \, {\left(4 \, A^{3} B a^{4} b - 7 \, A^{4} a^{3} b^{2}\right)} c^{7} - {\left(2500 \, B^{4} a^{6} - 22500 \, A B^{3} a^{5} b + 43524 \, A^{2} B^{2} a^{4} b^{2} + 4343 \, A^{3} B a^{3} b^{3} - 43410 \, A^{4} a^{2} b^{4}\right)} c^{6} + {\left(5625 \, B^{4} a^{5} b^{2} - 31137 \, A B^{3} a^{4} b^{3} + 52821 \, A^{2} B^{2} a^{3} b^{4} - 20190 \, A^{3} B a^{2} b^{5} - 12325 \, A^{4} a b^{6}\right)} c^{5} - 3 \, {\left(657 \, B^{4} a^{4} b^{4} - 3351 \, A B^{3} a^{3} b^{5} + 5560 \, A^{2} B^{2} a^{2} b^{6} - 2775 \, A^{3} B a b^{7} - 375 \, A^{4} b^{8}\right)} c^{4} + 7 \, {\left(27 \, B^{4} a^{3} b^{6} - 135 \, A B^{3} a^{2} b^{7} + 225 \, A^{2} B^{2} a b^{8} - 125 \, A^{3} B b^{9}\right)} c^{3}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left(-\sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{11} - 135 \, A B^{2} a^{2} b^{12} + 225 \, A^{2} B a b^{13} - 125 \, A^{3} b^{14} + 10976 \, A^{3} a^{7} c^{7} - 112 \, {\left(50 \, A B^{2} a^{8} - 463 \, A^{2} B a^{7} b + 709 \, A^{3} a^{6} b^{2}\right)} c^{6} - 2 \, {\left(2600 \, B^{3} a^{8} b - 31256 \, A B^{2} a^{7} b^{2} + 96044 \, A^{2} B a^{6} b^{3} - 86495 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(14408 \, B^{3} a^{7} b^{3} - 101006 \, A B^{2} a^{6} b^{4} + 224705 \, A^{2} B a^{5} b^{5} - 160932 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(1507 \, B^{3} a^{6} b^{5} - 8820 \, A B^{2} a^{5} b^{6} + 16991 \, A^{2} B a^{4} b^{7} - 10797 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(3330 \, B^{3} a^{5} b^{7} - 17889 \, A B^{2} a^{4} b^{8} + 31929 \, A^{2} B a^{3} b^{9} - 18940 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(486 \, B^{3} a^{4} b^{9} - 2493 \, A B^{2} a^{3} b^{10} + 4260 \, A^{2} B a^{2} b^{11} - 2425 \, A^{3} a b^{12}\right)} c - {\left(3 \, B a^{8} b^{10} - 5 \, A a^{7} b^{11} - 256 \, {\left(5 \, B a^{13} - 13 \, A a^{12} b\right)} c^{5} + 64 \, {\left(34 \, B a^{12} b^{2} - 73 \, A a^{11} b^{3}\right)} c^{4} - 112 \, {\left(12 \, B a^{11} b^{4} - 23 \, A a^{10} b^{5}\right)} c^{3} + 28 \, {\left(14 \, B a^{10} b^{6} - 25 \, A a^{9} b^{7}\right)} c^{2} - {\left(55 \, B a^{9} b^{8} - 94 \, A a^{8} b^{9}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} + 2 \, {\left(9604 \, A^{4} a^{4} c^{8} + 7203 \, {\left(4 \, A^{3} B a^{4} b - 7 \, A^{4} a^{3} b^{2}\right)} c^{7} - {\left(2500 \, B^{4} a^{6} - 22500 \, A B^{3} a^{5} b + 43524 \, A^{2} B^{2} a^{4} b^{2} + 4343 \, A^{3} B a^{3} b^{3} - 43410 \, A^{4} a^{2} b^{4}\right)} c^{6} + {\left(5625 \, B^{4} a^{5} b^{2} - 31137 \, A B^{3} a^{4} b^{3} + 52821 \, A^{2} B^{2} a^{3} b^{4} - 20190 \, A^{3} B a^{2} b^{5} - 12325 \, A^{4} a b^{6}\right)} c^{5} - 3 \, {\left(657 \, B^{4} a^{4} b^{4} - 3351 \, A B^{3} a^{3} b^{5} + 5560 \, A^{2} B^{2} a^{2} b^{6} - 2775 \, A^{3} B a b^{7} - 375 \, A^{4} b^{8}\right)} c^{4} + 7 \, {\left(27 \, B^{4} a^{3} b^{6} - 135 \, A B^{3} a^{2} b^{7} + 225 \, A^{2} B^{2} a b^{8} - 125 \, A^{3} B b^{9}\right)} c^{3}\right)} \sqrt{x}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left(\sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{11} - 135 \, A B^{2} a^{2} b^{12} + 225 \, A^{2} B a b^{13} - 125 \, A^{3} b^{14} + 10976 \, A^{3} a^{7} c^{7} - 112 \, {\left(50 \, A B^{2} a^{8} - 463 \, A^{2} B a^{7} b + 709 \, A^{3} a^{6} b^{2}\right)} c^{6} - 2 \, {\left(2600 \, B^{3} a^{8} b - 31256 \, A B^{2} a^{7} b^{2} + 96044 \, A^{2} B a^{6} b^{3} - 86495 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(14408 \, B^{3} a^{7} b^{3} - 101006 \, A B^{2} a^{6} b^{4} + 224705 \, A^{2} B a^{5} b^{5} - 160932 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(1507 \, B^{3} a^{6} b^{5} - 8820 \, A B^{2} a^{5} b^{6} + 16991 \, A^{2} B a^{4} b^{7} - 10797 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(3330 \, B^{3} a^{5} b^{7} - 17889 \, A B^{2} a^{4} b^{8} + 31929 \, A^{2} B a^{3} b^{9} - 18940 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(486 \, B^{3} a^{4} b^{9} - 2493 \, A B^{2} a^{3} b^{10} + 4260 \, A^{2} B a^{2} b^{11} - 2425 \, A^{3} a b^{12}\right)} c + {\left(3 \, B a^{8} b^{10} - 5 \, A a^{7} b^{11} - 256 \, {\left(5 \, B a^{13} - 13 \, A a^{12} b\right)} c^{5} + 64 \, {\left(34 \, B a^{12} b^{2} - 73 \, A a^{11} b^{3}\right)} c^{4} - 112 \, {\left(12 \, B a^{11} b^{4} - 23 \, A a^{10} b^{5}\right)} c^{3} + 28 \, {\left(14 \, B a^{10} b^{6} - 25 \, A a^{9} b^{7}\right)} c^{2} - {\left(55 \, B a^{9} b^{8} - 94 \, A a^{8} b^{9}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} + 2 \, {\left(9604 \, A^{4} a^{4} c^{8} + 7203 \, {\left(4 \, A^{3} B a^{4} b - 7 \, A^{4} a^{3} b^{2}\right)} c^{7} - {\left(2500 \, B^{4} a^{6} - 22500 \, A B^{3} a^{5} b + 43524 \, A^{2} B^{2} a^{4} b^{2} + 4343 \, A^{3} B a^{3} b^{3} - 43410 \, A^{4} a^{2} b^{4}\right)} c^{6} + {\left(5625 \, B^{4} a^{5} b^{2} - 31137 \, A B^{3} a^{4} b^{3} + 52821 \, A^{2} B^{2} a^{3} b^{4} - 20190 \, A^{3} B a^{2} b^{5} - 12325 \, A^{4} a b^{6}\right)} c^{5} - 3 \, {\left(657 \, B^{4} a^{4} b^{4} - 3351 \, A B^{3} a^{3} b^{5} + 5560 \, A^{2} B^{2} a^{2} b^{6} - 2775 \, A^{3} B a b^{7} - 375 \, A^{4} b^{8}\right)} c^{4} + 7 \, {\left(27 \, B^{4} a^{3} b^{6} - 135 \, A B^{3} a^{2} b^{7} + 225 \, A^{2} B^{2} a b^{8} - 125 \, A^{3} B b^{9}\right)} c^{3}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left(-\sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{11} - 135 \, A B^{2} a^{2} b^{12} + 225 \, A^{2} B a b^{13} - 125 \, A^{3} b^{14} + 10976 \, A^{3} a^{7} c^{7} - 112 \, {\left(50 \, A B^{2} a^{8} - 463 \, A^{2} B a^{7} b + 709 \, A^{3} a^{6} b^{2}\right)} c^{6} - 2 \, {\left(2600 \, B^{3} a^{8} b - 31256 \, A B^{2} a^{7} b^{2} + 96044 \, A^{2} B a^{6} b^{3} - 86495 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(14408 \, B^{3} a^{7} b^{3} - 101006 \, A B^{2} a^{6} b^{4} + 224705 \, A^{2} B a^{5} b^{5} - 160932 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(1507 \, B^{3} a^{6} b^{5} - 8820 \, A B^{2} a^{5} b^{6} + 16991 \, A^{2} B a^{4} b^{7} - 10797 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(3330 \, B^{3} a^{5} b^{7} - 17889 \, A B^{2} a^{4} b^{8} + 31929 \, A^{2} B a^{3} b^{9} - 18940 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(486 \, B^{3} a^{4} b^{9} - 2493 \, A B^{2} a^{3} b^{10} + 4260 \, A^{2} B a^{2} b^{11} - 2425 \, A^{3} a b^{12}\right)} c + {\left(3 \, B a^{8} b^{10} - 5 \, A a^{7} b^{11} - 256 \, {\left(5 \, B a^{13} - 13 \, A a^{12} b\right)} c^{5} + 64 \, {\left(34 \, B a^{12} b^{2} - 73 \, A a^{11} b^{3}\right)} c^{4} - 112 \, {\left(12 \, B a^{11} b^{4} - 23 \, A a^{10} b^{5}\right)} c^{3} + 28 \, {\left(14 \, B a^{10} b^{6} - 25 \, A a^{9} b^{7}\right)} c^{2} - {\left(55 \, B a^{9} b^{8} - 94 \, A a^{8} b^{9}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} + 2 \, {\left(9604 \, A^{4} a^{4} c^{8} + 7203 \, {\left(4 \, A^{3} B a^{4} b - 7 \, A^{4} a^{3} b^{2}\right)} c^{7} - {\left(2500 \, B^{4} a^{6} - 22500 \, A B^{3} a^{5} b + 43524 \, A^{2} B^{2} a^{4} b^{2} + 4343 \, A^{3} B a^{3} b^{3} - 43410 \, A^{4} a^{2} b^{4}\right)} c^{6} + {\left(5625 \, B^{4} a^{5} b^{2} - 31137 \, A B^{3} a^{4} b^{3} + 52821 \, A^{2} B^{2} a^{3} b^{4} - 20190 \, A^{3} B a^{2} b^{5} - 12325 \, A^{4} a b^{6}\right)} c^{5} - 3 \, {\left(657 \, B^{4} a^{4} b^{4} - 3351 \, A B^{3} a^{3} b^{5} + 5560 \, A^{2} B^{2} a^{2} b^{6} - 2775 \, A^{3} B a b^{7} - 375 \, A^{4} b^{8}\right)} c^{4} + 7 \, {\left(27 \, B^{4} a^{3} b^{6} - 135 \, A B^{3} a^{2} b^{7} + 225 \, A^{2} B^{2} a b^{8} - 125 \, A^{3} B b^{9}\right)} c^{3}\right)} \sqrt{x}\right) + 2 \, {\left(2 \, A a^{2} b^{2} - 8 \, A a^{3} c - 3 \, {\left({\left(10 \, B a^{2} - 19 \, A a b\right)} c^{2} - {\left(3 \, B a b^{2} - 5 \, A b^{3}\right)} c\right)} x^{3} + {\left(9 \, B a b^{3} - 15 \, A b^{4} - 14 \, A a^{2} c^{2} - {\left(33 \, B a^{2} b - 62 \, A a b^{2}\right)} c\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b^{2} - 5 \, A a b^{3} - 4 \, {\left(3 \, B a^{3} - 5 \, A a^{2} b\right)} c\right)} x\right)} \sqrt{x}}{6 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)}}"," ",0,"-1/6*(3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log(sqrt(1/2)*(27*B^3*a^3*b^11 - 135*A*B^2*a^2*b^12 + 225*A^2*B*a*b^13 - 125*A^3*b^14 + 10976*A^3*a^7*c^7 - 112*(50*A*B^2*a^8 - 463*A^2*B*a^7*b + 709*A^3*a^6*b^2)*c^6 - 2*(2600*B^3*a^8*b - 31256*A*B^2*a^7*b^2 + 96044*A^2*B*a^6*b^3 - 86495*A^3*a^5*b^4)*c^5 + (14408*B^3*a^7*b^3 - 101006*A*B^2*a^6*b^4 + 224705*A^2*B*a^5*b^5 - 160932*A^3*a^4*b^6)*c^4 - 7*(1507*B^3*a^6*b^5 - 8820*A*B^2*a^5*b^6 + 16991*A^2*B*a^4*b^7 - 10797*A^3*a^3*b^8)*c^3 + (3330*B^3*a^5*b^7 - 17889*A*B^2*a^4*b^8 + 31929*A^2*B*a^3*b^9 - 18940*A^3*a^2*b^10)*c^2 - (486*B^3*a^4*b^9 - 2493*A*B^2*a^3*b^10 + 4260*A^2*B*a^2*b^11 - 2425*A^3*a*b^12)*c - (3*B*a^8*b^10 - 5*A*a^7*b^11 - 256*(5*B*a^13 - 13*A*a^12*b)*c^5 + 64*(34*B*a^12*b^2 - 73*A*a^11*b^3)*c^4 - 112*(12*B*a^11*b^4 - 23*A*a^10*b^5)*c^3 + 28*(14*B*a^10*b^6 - 25*A*a^9*b^7)*c^2 - (55*B*a^9*b^8 - 94*A*a^8*b^9)*c)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)) + 2*(9604*A^4*a^4*c^8 + 7203*(4*A^3*B*a^4*b - 7*A^4*a^3*b^2)*c^7 - (2500*B^4*a^6 - 22500*A*B^3*a^5*b + 43524*A^2*B^2*a^4*b^2 + 4343*A^3*B*a^3*b^3 - 43410*A^4*a^2*b^4)*c^6 + (5625*B^4*a^5*b^2 - 31137*A*B^3*a^4*b^3 + 52821*A^2*B^2*a^3*b^4 - 20190*A^3*B*a^2*b^5 - 12325*A^4*a*b^6)*c^5 - 3*(657*B^4*a^4*b^4 - 3351*A*B^3*a^3*b^5 + 5560*A^2*B^2*a^2*b^6 - 2775*A^3*B*a*b^7 - 375*A^4*b^8)*c^4 + 7*(27*B^4*a^3*b^6 - 135*A*B^3*a^2*b^7 + 225*A^2*B^2*a*b^8 - 125*A^3*B*b^9)*c^3)*sqrt(x)) - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log(-sqrt(1/2)*(27*B^3*a^3*b^11 - 135*A*B^2*a^2*b^12 + 225*A^2*B*a*b^13 - 125*A^3*b^14 + 10976*A^3*a^7*c^7 - 112*(50*A*B^2*a^8 - 463*A^2*B*a^7*b + 709*A^3*a^6*b^2)*c^6 - 2*(2600*B^3*a^8*b - 31256*A*B^2*a^7*b^2 + 96044*A^2*B*a^6*b^3 - 86495*A^3*a^5*b^4)*c^5 + (14408*B^3*a^7*b^3 - 101006*A*B^2*a^6*b^4 + 224705*A^2*B*a^5*b^5 - 160932*A^3*a^4*b^6)*c^4 - 7*(1507*B^3*a^6*b^5 - 8820*A*B^2*a^5*b^6 + 16991*A^2*B*a^4*b^7 - 10797*A^3*a^3*b^8)*c^3 + (3330*B^3*a^5*b^7 - 17889*A*B^2*a^4*b^8 + 31929*A^2*B*a^3*b^9 - 18940*A^3*a^2*b^10)*c^2 - (486*B^3*a^4*b^9 - 2493*A*B^2*a^3*b^10 + 4260*A^2*B*a^2*b^11 - 2425*A^3*a*b^12)*c - (3*B*a^8*b^10 - 5*A*a^7*b^11 - 256*(5*B*a^13 - 13*A*a^12*b)*c^5 + 64*(34*B*a^12*b^2 - 73*A*a^11*b^3)*c^4 - 112*(12*B*a^11*b^4 - 23*A*a^10*b^5)*c^3 + 28*(14*B*a^10*b^6 - 25*A*a^9*b^7)*c^2 - (55*B*a^9*b^8 - 94*A*a^8*b^9)*c)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)) + 2*(9604*A^4*a^4*c^8 + 7203*(4*A^3*B*a^4*b - 7*A^4*a^3*b^2)*c^7 - (2500*B^4*a^6 - 22500*A*B^3*a^5*b + 43524*A^2*B^2*a^4*b^2 + 4343*A^3*B*a^3*b^3 - 43410*A^4*a^2*b^4)*c^6 + (5625*B^4*a^5*b^2 - 31137*A*B^3*a^4*b^3 + 52821*A^2*B^2*a^3*b^4 - 20190*A^3*B*a^2*b^5 - 12325*A^4*a*b^6)*c^5 - 3*(657*B^4*a^4*b^4 - 3351*A*B^3*a^3*b^5 + 5560*A^2*B^2*a^2*b^6 - 2775*A^3*B*a*b^7 - 375*A^4*b^8)*c^4 + 7*(27*B^4*a^3*b^6 - 135*A*B^3*a^2*b^7 + 225*A^2*B^2*a*b^8 - 125*A^3*B*b^9)*c^3)*sqrt(x)) + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log(sqrt(1/2)*(27*B^3*a^3*b^11 - 135*A*B^2*a^2*b^12 + 225*A^2*B*a*b^13 - 125*A^3*b^14 + 10976*A^3*a^7*c^7 - 112*(50*A*B^2*a^8 - 463*A^2*B*a^7*b + 709*A^3*a^6*b^2)*c^6 - 2*(2600*B^3*a^8*b - 31256*A*B^2*a^7*b^2 + 96044*A^2*B*a^6*b^3 - 86495*A^3*a^5*b^4)*c^5 + (14408*B^3*a^7*b^3 - 101006*A*B^2*a^6*b^4 + 224705*A^2*B*a^5*b^5 - 160932*A^3*a^4*b^6)*c^4 - 7*(1507*B^3*a^6*b^5 - 8820*A*B^2*a^5*b^6 + 16991*A^2*B*a^4*b^7 - 10797*A^3*a^3*b^8)*c^3 + (3330*B^3*a^5*b^7 - 17889*A*B^2*a^4*b^8 + 31929*A^2*B*a^3*b^9 - 18940*A^3*a^2*b^10)*c^2 - (486*B^3*a^4*b^9 - 2493*A*B^2*a^3*b^10 + 4260*A^2*B*a^2*b^11 - 2425*A^3*a*b^12)*c + (3*B*a^8*b^10 - 5*A*a^7*b^11 - 256*(5*B*a^13 - 13*A*a^12*b)*c^5 + 64*(34*B*a^12*b^2 - 73*A*a^11*b^3)*c^4 - 112*(12*B*a^11*b^4 - 23*A*a^10*b^5)*c^3 + 28*(14*B*a^10*b^6 - 25*A*a^9*b^7)*c^2 - (55*B*a^9*b^8 - 94*A*a^8*b^9)*c)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)) + 2*(9604*A^4*a^4*c^8 + 7203*(4*A^3*B*a^4*b - 7*A^4*a^3*b^2)*c^7 - (2500*B^4*a^6 - 22500*A*B^3*a^5*b + 43524*A^2*B^2*a^4*b^2 + 4343*A^3*B*a^3*b^3 - 43410*A^4*a^2*b^4)*c^6 + (5625*B^4*a^5*b^2 - 31137*A*B^3*a^4*b^3 + 52821*A^2*B^2*a^3*b^4 - 20190*A^3*B*a^2*b^5 - 12325*A^4*a*b^6)*c^5 - 3*(657*B^4*a^4*b^4 - 3351*A*B^3*a^3*b^5 + 5560*A^2*B^2*a^2*b^6 - 2775*A^3*B*a*b^7 - 375*A^4*b^8)*c^4 + 7*(27*B^4*a^3*b^6 - 135*A*B^3*a^2*b^7 + 225*A^2*B^2*a*b^8 - 125*A^3*B*b^9)*c^3)*sqrt(x)) - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log(-sqrt(1/2)*(27*B^3*a^3*b^11 - 135*A*B^2*a^2*b^12 + 225*A^2*B*a*b^13 - 125*A^3*b^14 + 10976*A^3*a^7*c^7 - 112*(50*A*B^2*a^8 - 463*A^2*B*a^7*b + 709*A^3*a^6*b^2)*c^6 - 2*(2600*B^3*a^8*b - 31256*A*B^2*a^7*b^2 + 96044*A^2*B*a^6*b^3 - 86495*A^3*a^5*b^4)*c^5 + (14408*B^3*a^7*b^3 - 101006*A*B^2*a^6*b^4 + 224705*A^2*B*a^5*b^5 - 160932*A^3*a^4*b^6)*c^4 - 7*(1507*B^3*a^6*b^5 - 8820*A*B^2*a^5*b^6 + 16991*A^2*B*a^4*b^7 - 10797*A^3*a^3*b^8)*c^3 + (3330*B^3*a^5*b^7 - 17889*A*B^2*a^4*b^8 + 31929*A^2*B*a^3*b^9 - 18940*A^3*a^2*b^10)*c^2 - (486*B^3*a^4*b^9 - 2493*A*B^2*a^3*b^10 + 4260*A^2*B*a^2*b^11 - 2425*A^3*a*b^12)*c + (3*B*a^8*b^10 - 5*A*a^7*b^11 - 256*(5*B*a^13 - 13*A*a^12*b)*c^5 + 64*(34*B*a^12*b^2 - 73*A*a^11*b^3)*c^4 - 112*(12*B*a^11*b^4 - 23*A*a^10*b^5)*c^3 + 28*(14*B*a^10*b^6 - 25*A*a^9*b^7)*c^2 - (55*B*a^9*b^8 - 94*A*a^8*b^9)*c)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)) + 2*(9604*A^4*a^4*c^8 + 7203*(4*A^3*B*a^4*b - 7*A^4*a^3*b^2)*c^7 - (2500*B^4*a^6 - 22500*A*B^3*a^5*b + 43524*A^2*B^2*a^4*b^2 + 4343*A^3*B*a^3*b^3 - 43410*A^4*a^2*b^4)*c^6 + (5625*B^4*a^5*b^2 - 31137*A*B^3*a^4*b^3 + 52821*A^2*B^2*a^3*b^4 - 20190*A^3*B*a^2*b^5 - 12325*A^4*a*b^6)*c^5 - 3*(657*B^4*a^4*b^4 - 3351*A*B^3*a^3*b^5 + 5560*A^2*B^2*a^2*b^6 - 2775*A^3*B*a*b^7 - 375*A^4*b^8)*c^4 + 7*(27*B^4*a^3*b^6 - 135*A*B^3*a^2*b^7 + 225*A^2*B^2*a*b^8 - 125*A^3*B*b^9)*c^3)*sqrt(x)) + 2*(2*A*a^2*b^2 - 8*A*a^3*c - 3*((10*B*a^2 - 19*A*a*b)*c^2 - (3*B*a*b^2 - 5*A*b^3)*c)*x^3 + (9*B*a*b^3 - 15*A*b^4 - 14*A*a^2*c^2 - (33*B*a^2*b - 62*A*a*b^2)*c)*x^2 + 2*(3*B*a^2*b^2 - 5*A*a*b^3 - 4*(3*B*a^3 - 5*A*a^2*b)*c)*x)*sqrt(x))/((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)","B",0
1023,1,9631,0,21.838980," ","integrate(x^(7/2)*(B*x+A)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{13} + 32000 \, A^{3} a^{5} c^{8} - 640 \, {\left(882 \, A B^{2} a^{6} - 156 \, A^{2} B a^{5} b + 37 \, A^{3} a^{4} b^{2}\right)} c^{7} + 64 \, {\left(10584 \, B^{3} a^{6} b + 5562 \, A B^{2} a^{5} b^{2} - 1083 \, A^{2} B a^{4} b^{3} + 89 \, A^{3} a^{3} b^{4}\right)} c^{6} - 8 \, {\left(93096 \, B^{3} a^{5} b^{3} + 3816 \, A B^{2} a^{4} b^{4} - 1746 \, A^{2} B a^{3} b^{5} + 49 \, A^{3} a^{2} b^{6}\right)} c^{5} + {\left(337392 \, B^{3} a^{4} b^{5} - 24120 \, A B^{2} a^{3} b^{6} - 84 \, A^{2} B a^{2} b^{7} - 17 \, A^{3} a b^{8}\right)} c^{4} - {\left(81324 \, B^{3} a^{3} b^{7} - 6993 \, A B^{2} a^{2} b^{8} + 195 \, A^{2} B a b^{9} - A^{3} b^{10}\right)} c^{3} + 9 \, {\left(1239 \, B^{3} a^{2} b^{9} - 79 \, A B^{2} a b^{10} + A^{2} B b^{11}\right)} c^{2} - 27 \, {\left(31 \, B^{3} a b^{11} - A B^{2} b^{12}\right)} c - {\left(3 \, B b^{14} c^{5} - 4096 \, {\left(42 \, B a^{7} - 13 \, A a^{6} b\right)} c^{12} + 6144 \, {\left(40 \, B a^{6} b^{2} - 11 \, A a^{5} b^{3}\right)} c^{11} - 768 \, {\left(194 \, B a^{5} b^{4} - 45 \, A a^{4} b^{5}\right)} c^{10} + 1280 \, {\left(39 \, B a^{4} b^{6} - 7 \, A a^{3} b^{7}\right)} c^{9} - 240 \, {\left(42 \, B a^{3} b^{8} - 5 \, A a^{2} b^{9}\right)} c^{8} + 24 \, {\left(52 \, B a^{2} b^{10} - 3 \, A a b^{11}\right)} c^{7} - {\left(90 \, B a b^{12} - A b^{13}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} - {\left(1701 \, B^{4} a^{2} b^{8} - 945 \, A B^{3} a b^{9} - 10000 \, A^{4} a^{4} c^{6} + 15000 \, {\left(6 \, A^{3} B a^{4} b - A^{4} a^{3} b^{2}\right)} c^{5} + 3 \, {\left(1037232 \, B^{4} a^{6} - 1037232 \, A B^{3} a^{5} b + 287712 \, A^{2} B^{2} a^{4} b^{2} - 32952 \, A^{3} B a^{3} b^{3} + 497 \, A^{4} a^{2} b^{4}\right)} c^{4} - {\left(1555848 \, B^{4} a^{5} b^{2} - 1298376 \, A B^{3} a^{4} b^{3} + 238464 \, A^{2} B^{2} a^{3} b^{4} - 11277 \, A^{3} B a^{2} b^{5} + 35 \, A^{4} a b^{6}\right)} c^{3} + 9 \, {\left(37701 \, B^{4} a^{4} b^{4} - 26973 \, A B^{3} a^{3} b^{5} + 3066 \, A^{2} B^{2} a^{2} b^{6} - 35 \, A^{3} B a b^{7}\right)} c^{2} - 27 \, {\left(1341 \, B^{4} a^{3} b^{6} - 819 \, A B^{3} a^{2} b^{7} + 35 \, A^{2} B^{2} a b^{8}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{13} + 32000 \, A^{3} a^{5} c^{8} - 640 \, {\left(882 \, A B^{2} a^{6} - 156 \, A^{2} B a^{5} b + 37 \, A^{3} a^{4} b^{2}\right)} c^{7} + 64 \, {\left(10584 \, B^{3} a^{6} b + 5562 \, A B^{2} a^{5} b^{2} - 1083 \, A^{2} B a^{4} b^{3} + 89 \, A^{3} a^{3} b^{4}\right)} c^{6} - 8 \, {\left(93096 \, B^{3} a^{5} b^{3} + 3816 \, A B^{2} a^{4} b^{4} - 1746 \, A^{2} B a^{3} b^{5} + 49 \, A^{3} a^{2} b^{6}\right)} c^{5} + {\left(337392 \, B^{3} a^{4} b^{5} - 24120 \, A B^{2} a^{3} b^{6} - 84 \, A^{2} B a^{2} b^{7} - 17 \, A^{3} a b^{8}\right)} c^{4} - {\left(81324 \, B^{3} a^{3} b^{7} - 6993 \, A B^{2} a^{2} b^{8} + 195 \, A^{2} B a b^{9} - A^{3} b^{10}\right)} c^{3} + 9 \, {\left(1239 \, B^{3} a^{2} b^{9} - 79 \, A B^{2} a b^{10} + A^{2} B b^{11}\right)} c^{2} - 27 \, {\left(31 \, B^{3} a b^{11} - A B^{2} b^{12}\right)} c - {\left(3 \, B b^{14} c^{5} - 4096 \, {\left(42 \, B a^{7} - 13 \, A a^{6} b\right)} c^{12} + 6144 \, {\left(40 \, B a^{6} b^{2} - 11 \, A a^{5} b^{3}\right)} c^{11} - 768 \, {\left(194 \, B a^{5} b^{4} - 45 \, A a^{4} b^{5}\right)} c^{10} + 1280 \, {\left(39 \, B a^{4} b^{6} - 7 \, A a^{3} b^{7}\right)} c^{9} - 240 \, {\left(42 \, B a^{3} b^{8} - 5 \, A a^{2} b^{9}\right)} c^{8} + 24 \, {\left(52 \, B a^{2} b^{10} - 3 \, A a b^{11}\right)} c^{7} - {\left(90 \, B a b^{12} - A b^{13}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} - {\left(1701 \, B^{4} a^{2} b^{8} - 945 \, A B^{3} a b^{9} - 10000 \, A^{4} a^{4} c^{6} + 15000 \, {\left(6 \, A^{3} B a^{4} b - A^{4} a^{3} b^{2}\right)} c^{5} + 3 \, {\left(1037232 \, B^{4} a^{6} - 1037232 \, A B^{3} a^{5} b + 287712 \, A^{2} B^{2} a^{4} b^{2} - 32952 \, A^{3} B a^{3} b^{3} + 497 \, A^{4} a^{2} b^{4}\right)} c^{4} - {\left(1555848 \, B^{4} a^{5} b^{2} - 1298376 \, A B^{3} a^{4} b^{3} + 238464 \, A^{2} B^{2} a^{3} b^{4} - 11277 \, A^{3} B a^{2} b^{5} + 35 \, A^{4} a b^{6}\right)} c^{3} + 9 \, {\left(37701 \, B^{4} a^{4} b^{4} - 26973 \, A B^{3} a^{3} b^{5} + 3066 \, A^{2} B^{2} a^{2} b^{6} - 35 \, A^{3} B a b^{7}\right)} c^{2} - 27 \, {\left(1341 \, B^{4} a^{3} b^{6} - 819 \, A B^{3} a^{2} b^{7} + 35 \, A^{2} B^{2} a b^{8}\right)} c\right)} \sqrt{x}\right) + \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{13} + 32000 \, A^{3} a^{5} c^{8} - 640 \, {\left(882 \, A B^{2} a^{6} - 156 \, A^{2} B a^{5} b + 37 \, A^{3} a^{4} b^{2}\right)} c^{7} + 64 \, {\left(10584 \, B^{3} a^{6} b + 5562 \, A B^{2} a^{5} b^{2} - 1083 \, A^{2} B a^{4} b^{3} + 89 \, A^{3} a^{3} b^{4}\right)} c^{6} - 8 \, {\left(93096 \, B^{3} a^{5} b^{3} + 3816 \, A B^{2} a^{4} b^{4} - 1746 \, A^{2} B a^{3} b^{5} + 49 \, A^{3} a^{2} b^{6}\right)} c^{5} + {\left(337392 \, B^{3} a^{4} b^{5} - 24120 \, A B^{2} a^{3} b^{6} - 84 \, A^{2} B a^{2} b^{7} - 17 \, A^{3} a b^{8}\right)} c^{4} - {\left(81324 \, B^{3} a^{3} b^{7} - 6993 \, A B^{2} a^{2} b^{8} + 195 \, A^{2} B a b^{9} - A^{3} b^{10}\right)} c^{3} + 9 \, {\left(1239 \, B^{3} a^{2} b^{9} - 79 \, A B^{2} a b^{10} + A^{2} B b^{11}\right)} c^{2} - 27 \, {\left(31 \, B^{3} a b^{11} - A B^{2} b^{12}\right)} c + {\left(3 \, B b^{14} c^{5} - 4096 \, {\left(42 \, B a^{7} - 13 \, A a^{6} b\right)} c^{12} + 6144 \, {\left(40 \, B a^{6} b^{2} - 11 \, A a^{5} b^{3}\right)} c^{11} - 768 \, {\left(194 \, B a^{5} b^{4} - 45 \, A a^{4} b^{5}\right)} c^{10} + 1280 \, {\left(39 \, B a^{4} b^{6} - 7 \, A a^{3} b^{7}\right)} c^{9} - 240 \, {\left(42 \, B a^{3} b^{8} - 5 \, A a^{2} b^{9}\right)} c^{8} + 24 \, {\left(52 \, B a^{2} b^{10} - 3 \, A a b^{11}\right)} c^{7} - {\left(90 \, B a b^{12} - A b^{13}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} - {\left(1701 \, B^{4} a^{2} b^{8} - 945 \, A B^{3} a b^{9} - 10000 \, A^{4} a^{4} c^{6} + 15000 \, {\left(6 \, A^{3} B a^{4} b - A^{4} a^{3} b^{2}\right)} c^{5} + 3 \, {\left(1037232 \, B^{4} a^{6} - 1037232 \, A B^{3} a^{5} b + 287712 \, A^{2} B^{2} a^{4} b^{2} - 32952 \, A^{3} B a^{3} b^{3} + 497 \, A^{4} a^{2} b^{4}\right)} c^{4} - {\left(1555848 \, B^{4} a^{5} b^{2} - 1298376 \, A B^{3} a^{4} b^{3} + 238464 \, A^{2} B^{2} a^{3} b^{4} - 11277 \, A^{3} B a^{2} b^{5} + 35 \, A^{4} a b^{6}\right)} c^{3} + 9 \, {\left(37701 \, B^{4} a^{4} b^{4} - 26973 \, A B^{3} a^{3} b^{5} + 3066 \, A^{2} B^{2} a^{2} b^{6} - 35 \, A^{3} B a b^{7}\right)} c^{2} - 27 \, {\left(1341 \, B^{4} a^{3} b^{6} - 819 \, A B^{3} a^{2} b^{7} + 35 \, A^{2} B^{2} a b^{8}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{13} + 32000 \, A^{3} a^{5} c^{8} - 640 \, {\left(882 \, A B^{2} a^{6} - 156 \, A^{2} B a^{5} b + 37 \, A^{3} a^{4} b^{2}\right)} c^{7} + 64 \, {\left(10584 \, B^{3} a^{6} b + 5562 \, A B^{2} a^{5} b^{2} - 1083 \, A^{2} B a^{4} b^{3} + 89 \, A^{3} a^{3} b^{4}\right)} c^{6} - 8 \, {\left(93096 \, B^{3} a^{5} b^{3} + 3816 \, A B^{2} a^{4} b^{4} - 1746 \, A^{2} B a^{3} b^{5} + 49 \, A^{3} a^{2} b^{6}\right)} c^{5} + {\left(337392 \, B^{3} a^{4} b^{5} - 24120 \, A B^{2} a^{3} b^{6} - 84 \, A^{2} B a^{2} b^{7} - 17 \, A^{3} a b^{8}\right)} c^{4} - {\left(81324 \, B^{3} a^{3} b^{7} - 6993 \, A B^{2} a^{2} b^{8} + 195 \, A^{2} B a b^{9} - A^{3} b^{10}\right)} c^{3} + 9 \, {\left(1239 \, B^{3} a^{2} b^{9} - 79 \, A B^{2} a b^{10} + A^{2} B b^{11}\right)} c^{2} - 27 \, {\left(31 \, B^{3} a b^{11} - A B^{2} b^{12}\right)} c + {\left(3 \, B b^{14} c^{5} - 4096 \, {\left(42 \, B a^{7} - 13 \, A a^{6} b\right)} c^{12} + 6144 \, {\left(40 \, B a^{6} b^{2} - 11 \, A a^{5} b^{3}\right)} c^{11} - 768 \, {\left(194 \, B a^{5} b^{4} - 45 \, A a^{4} b^{5}\right)} c^{10} + 1280 \, {\left(39 \, B a^{4} b^{6} - 7 \, A a^{3} b^{7}\right)} c^{9} - 240 \, {\left(42 \, B a^{3} b^{8} - 5 \, A a^{2} b^{9}\right)} c^{8} + 24 \, {\left(52 \, B a^{2} b^{10} - 3 \, A a b^{11}\right)} c^{7} - {\left(90 \, B a b^{12} - A b^{13}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} - {\left(1701 \, B^{4} a^{2} b^{8} - 945 \, A B^{3} a b^{9} - 10000 \, A^{4} a^{4} c^{6} + 15000 \, {\left(6 \, A^{3} B a^{4} b - A^{4} a^{3} b^{2}\right)} c^{5} + 3 \, {\left(1037232 \, B^{4} a^{6} - 1037232 \, A B^{3} a^{5} b + 287712 \, A^{2} B^{2} a^{4} b^{2} - 32952 \, A^{3} B a^{3} b^{3} + 497 \, A^{4} a^{2} b^{4}\right)} c^{4} - {\left(1555848 \, B^{4} a^{5} b^{2} - 1298376 \, A B^{3} a^{4} b^{3} + 238464 \, A^{2} B^{2} a^{3} b^{4} - 11277 \, A^{3} B a^{2} b^{5} + 35 \, A^{4} a b^{6}\right)} c^{3} + 9 \, {\left(37701 \, B^{4} a^{4} b^{4} - 26973 \, A B^{3} a^{3} b^{5} + 3066 \, A^{2} B^{2} a^{2} b^{6} - 35 \, A^{3} B a b^{7}\right)} c^{2} - 27 \, {\left(1341 \, B^{4} a^{3} b^{6} - 819 \, A B^{3} a^{2} b^{7} + 35 \, A^{2} B^{2} a b^{8}\right)} c\right)} \sqrt{x}\right) - 2 \, {\left(3 \, B a^{2} b^{3} + 20 \, A a^{3} c^{2} + {\left(5 \, B b^{4} c + 4 \, {\left(11 \, B a^{2} + 4 \, A a b\right)} c^{3} - {\left(37 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} x^{3} + {\left(3 \, B b^{5} + 36 \, A a^{2} c^{3} - {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} c^{2} - {\left(20 \, B a b^{3} - A b^{4}\right)} c\right)} x^{2} - {\left(24 \, B a^{3} b - A a^{2} b^{2}\right)} c + {\left(6 \, B a b^{4} + 28 \, {\left(B a^{3} + A a^{2} b\right)} c^{2} - {\left(49 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} c\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)}}"," ",0,"1/8*(sqrt(1/2)*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(1/2*sqrt(1/2)*(27*B^3*b^13 + 32000*A^3*a^5*c^8 - 640*(882*A*B^2*a^6 - 156*A^2*B*a^5*b + 37*A^3*a^4*b^2)*c^7 + 64*(10584*B^3*a^6*b + 5562*A*B^2*a^5*b^2 - 1083*A^2*B*a^4*b^3 + 89*A^3*a^3*b^4)*c^6 - 8*(93096*B^3*a^5*b^3 + 3816*A*B^2*a^4*b^4 - 1746*A^2*B*a^3*b^5 + 49*A^3*a^2*b^6)*c^5 + (337392*B^3*a^4*b^5 - 24120*A*B^2*a^3*b^6 - 84*A^2*B*a^2*b^7 - 17*A^3*a*b^8)*c^4 - (81324*B^3*a^3*b^7 - 6993*A*B^2*a^2*b^8 + 195*A^2*B*a*b^9 - A^3*b^10)*c^3 + 9*(1239*B^3*a^2*b^9 - 79*A*B^2*a*b^10 + A^2*B*b^11)*c^2 - 27*(31*B^3*a*b^11 - A*B^2*b^12)*c - (3*B*b^14*c^5 - 4096*(42*B*a^7 - 13*A*a^6*b)*c^12 + 6144*(40*B*a^6*b^2 - 11*A*a^5*b^3)*c^11 - 768*(194*B*a^5*b^4 - 45*A*a^4*b^5)*c^10 + 1280*(39*B*a^4*b^6 - 7*A*a^3*b^7)*c^9 - 240*(42*B*a^3*b^8 - 5*A*a^2*b^9)*c^8 + 24*(52*B*a^2*b^10 - 3*A*a*b^11)*c^7 - (90*B*a*b^12 - A*b^13)*c^6)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)) - (1701*B^4*a^2*b^8 - 945*A*B^3*a*b^9 - 10000*A^4*a^4*c^6 + 15000*(6*A^3*B*a^4*b - A^4*a^3*b^2)*c^5 + 3*(1037232*B^4*a^6 - 1037232*A*B^3*a^5*b + 287712*A^2*B^2*a^4*b^2 - 32952*A^3*B*a^3*b^3 + 497*A^4*a^2*b^4)*c^4 - (1555848*B^4*a^5*b^2 - 1298376*A*B^3*a^4*b^3 + 238464*A^2*B^2*a^3*b^4 - 11277*A^3*B*a^2*b^5 + 35*A^4*a*b^6)*c^3 + 9*(37701*B^4*a^4*b^4 - 26973*A*B^3*a^3*b^5 + 3066*A^2*B^2*a^2*b^6 - 35*A^3*B*a*b^7)*c^2 - 27*(1341*B^4*a^3*b^6 - 819*A*B^3*a^2*b^7 + 35*A^2*B^2*a*b^8)*c)*sqrt(x)) - sqrt(1/2)*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(-1/2*sqrt(1/2)*(27*B^3*b^13 + 32000*A^3*a^5*c^8 - 640*(882*A*B^2*a^6 - 156*A^2*B*a^5*b + 37*A^3*a^4*b^2)*c^7 + 64*(10584*B^3*a^6*b + 5562*A*B^2*a^5*b^2 - 1083*A^2*B*a^4*b^3 + 89*A^3*a^3*b^4)*c^6 - 8*(93096*B^3*a^5*b^3 + 3816*A*B^2*a^4*b^4 - 1746*A^2*B*a^3*b^5 + 49*A^3*a^2*b^6)*c^5 + (337392*B^3*a^4*b^5 - 24120*A*B^2*a^3*b^6 - 84*A^2*B*a^2*b^7 - 17*A^3*a*b^8)*c^4 - (81324*B^3*a^3*b^7 - 6993*A*B^2*a^2*b^8 + 195*A^2*B*a*b^9 - A^3*b^10)*c^3 + 9*(1239*B^3*a^2*b^9 - 79*A*B^2*a*b^10 + A^2*B*b^11)*c^2 - 27*(31*B^3*a*b^11 - A*B^2*b^12)*c - (3*B*b^14*c^5 - 4096*(42*B*a^7 - 13*A*a^6*b)*c^12 + 6144*(40*B*a^6*b^2 - 11*A*a^5*b^3)*c^11 - 768*(194*B*a^5*b^4 - 45*A*a^4*b^5)*c^10 + 1280*(39*B*a^4*b^6 - 7*A*a^3*b^7)*c^9 - 240*(42*B*a^3*b^8 - 5*A*a^2*b^9)*c^8 + 24*(52*B*a^2*b^10 - 3*A*a*b^11)*c^7 - (90*B*a*b^12 - A*b^13)*c^6)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)) - (1701*B^4*a^2*b^8 - 945*A*B^3*a*b^9 - 10000*A^4*a^4*c^6 + 15000*(6*A^3*B*a^4*b - A^4*a^3*b^2)*c^5 + 3*(1037232*B^4*a^6 - 1037232*A*B^3*a^5*b + 287712*A^2*B^2*a^4*b^2 - 32952*A^3*B*a^3*b^3 + 497*A^4*a^2*b^4)*c^4 - (1555848*B^4*a^5*b^2 - 1298376*A*B^3*a^4*b^3 + 238464*A^2*B^2*a^3*b^4 - 11277*A^3*B*a^2*b^5 + 35*A^4*a*b^6)*c^3 + 9*(37701*B^4*a^4*b^4 - 26973*A*B^3*a^3*b^5 + 3066*A^2*B^2*a^2*b^6 - 35*A^3*B*a*b^7)*c^2 - 27*(1341*B^4*a^3*b^6 - 819*A*B^3*a^2*b^7 + 35*A^2*B^2*a*b^8)*c)*sqrt(x)) + sqrt(1/2)*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(1/2*sqrt(1/2)*(27*B^3*b^13 + 32000*A^3*a^5*c^8 - 640*(882*A*B^2*a^6 - 156*A^2*B*a^5*b + 37*A^3*a^4*b^2)*c^7 + 64*(10584*B^3*a^6*b + 5562*A*B^2*a^5*b^2 - 1083*A^2*B*a^4*b^3 + 89*A^3*a^3*b^4)*c^6 - 8*(93096*B^3*a^5*b^3 + 3816*A*B^2*a^4*b^4 - 1746*A^2*B*a^3*b^5 + 49*A^3*a^2*b^6)*c^5 + (337392*B^3*a^4*b^5 - 24120*A*B^2*a^3*b^6 - 84*A^2*B*a^2*b^7 - 17*A^3*a*b^8)*c^4 - (81324*B^3*a^3*b^7 - 6993*A*B^2*a^2*b^8 + 195*A^2*B*a*b^9 - A^3*b^10)*c^3 + 9*(1239*B^3*a^2*b^9 - 79*A*B^2*a*b^10 + A^2*B*b^11)*c^2 - 27*(31*B^3*a*b^11 - A*B^2*b^12)*c + (3*B*b^14*c^5 - 4096*(42*B*a^7 - 13*A*a^6*b)*c^12 + 6144*(40*B*a^6*b^2 - 11*A*a^5*b^3)*c^11 - 768*(194*B*a^5*b^4 - 45*A*a^4*b^5)*c^10 + 1280*(39*B*a^4*b^6 - 7*A*a^3*b^7)*c^9 - 240*(42*B*a^3*b^8 - 5*A*a^2*b^9)*c^8 + 24*(52*B*a^2*b^10 - 3*A*a*b^11)*c^7 - (90*B*a*b^12 - A*b^13)*c^6)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)) - (1701*B^4*a^2*b^8 - 945*A*B^3*a*b^9 - 10000*A^4*a^4*c^6 + 15000*(6*A^3*B*a^4*b - A^4*a^3*b^2)*c^5 + 3*(1037232*B^4*a^6 - 1037232*A*B^3*a^5*b + 287712*A^2*B^2*a^4*b^2 - 32952*A^3*B*a^3*b^3 + 497*A^4*a^2*b^4)*c^4 - (1555848*B^4*a^5*b^2 - 1298376*A*B^3*a^4*b^3 + 238464*A^2*B^2*a^3*b^4 - 11277*A^3*B*a^2*b^5 + 35*A^4*a*b^6)*c^3 + 9*(37701*B^4*a^4*b^4 - 26973*A*B^3*a^3*b^5 + 3066*A^2*B^2*a^2*b^6 - 35*A^3*B*a*b^7)*c^2 - 27*(1341*B^4*a^3*b^6 - 819*A*B^3*a^2*b^7 + 35*A^2*B^2*a*b^8)*c)*sqrt(x)) - sqrt(1/2)*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(-1/2*sqrt(1/2)*(27*B^3*b^13 + 32000*A^3*a^5*c^8 - 640*(882*A*B^2*a^6 - 156*A^2*B*a^5*b + 37*A^3*a^4*b^2)*c^7 + 64*(10584*B^3*a^6*b + 5562*A*B^2*a^5*b^2 - 1083*A^2*B*a^4*b^3 + 89*A^3*a^3*b^4)*c^6 - 8*(93096*B^3*a^5*b^3 + 3816*A*B^2*a^4*b^4 - 1746*A^2*B*a^3*b^5 + 49*A^3*a^2*b^6)*c^5 + (337392*B^3*a^4*b^5 - 24120*A*B^2*a^3*b^6 - 84*A^2*B*a^2*b^7 - 17*A^3*a*b^8)*c^4 - (81324*B^3*a^3*b^7 - 6993*A*B^2*a^2*b^8 + 195*A^2*B*a*b^9 - A^3*b^10)*c^3 + 9*(1239*B^3*a^2*b^9 - 79*A*B^2*a*b^10 + A^2*B*b^11)*c^2 - 27*(31*B^3*a*b^11 - A*B^2*b^12)*c + (3*B*b^14*c^5 - 4096*(42*B*a^7 - 13*A*a^6*b)*c^12 + 6144*(40*B*a^6*b^2 - 11*A*a^5*b^3)*c^11 - 768*(194*B*a^5*b^4 - 45*A*a^4*b^5)*c^10 + 1280*(39*B*a^4*b^6 - 7*A*a^3*b^7)*c^9 - 240*(42*B*a^3*b^8 - 5*A*a^2*b^9)*c^8 + 24*(52*B*a^2*b^10 - 3*A*a*b^11)*c^7 - (90*B*a*b^12 - A*b^13)*c^6)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)) - (1701*B^4*a^2*b^8 - 945*A*B^3*a*b^9 - 10000*A^4*a^4*c^6 + 15000*(6*A^3*B*a^4*b - A^4*a^3*b^2)*c^5 + 3*(1037232*B^4*a^6 - 1037232*A*B^3*a^5*b + 287712*A^2*B^2*a^4*b^2 - 32952*A^3*B*a^3*b^3 + 497*A^4*a^2*b^4)*c^4 - (1555848*B^4*a^5*b^2 - 1298376*A*B^3*a^4*b^3 + 238464*A^2*B^2*a^3*b^4 - 11277*A^3*B*a^2*b^5 + 35*A^4*a*b^6)*c^3 + 9*(37701*B^4*a^4*b^4 - 26973*A*B^3*a^3*b^5 + 3066*A^2*B^2*a^2*b^6 - 35*A^3*B*a*b^7)*c^2 - 27*(1341*B^4*a^3*b^6 - 819*A*B^3*a^2*b^7 + 35*A^2*B^2*a*b^8)*c)*sqrt(x)) - 2*(3*B*a^2*b^3 + 20*A*a^3*c^2 + (5*B*b^4*c + 4*(11*B*a^2 + 4*A*a*b)*c^3 - (37*B*a*b^2 + A*b^3)*c^2)*x^3 + (3*B*b^5 + 36*A*a^2*c^3 - (4*B*a^2*b - 5*A*a*b^2)*c^2 - (20*B*a*b^3 - A*b^4)*c)*x^2 - (24*B*a^3*b - A*a^2*b^2)*c + (6*B*a*b^4 + 28*(B*a^3 + A*a^2*b)*c^2 - (49*B*a^2*b^2 - 2*A*a*b^3)*c)*x)*sqrt(x))/(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)","B",0
1024,1,7056,0,7.254002," ","integrate(x^(5/2)*(B*x+A)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{10} - 2304 \, {\left(5 \, A^{2} B a^{4} - 3 \, A^{3} a^{3} b\right)} c^{6} + 64 \, {\left(500 \, B^{3} a^{5} - 420 \, A B^{2} a^{4} b + 198 \, A^{2} B a^{3} b^{2} - 81 \, A^{3} a^{2} b^{3}\right)} c^{5} - 16 \, {\left(1480 \, B^{3} a^{4} b^{2} - 1284 \, A B^{2} a^{3} b^{3} + 324 \, A^{2} B a^{2} b^{4} - 81 \, A^{3} a b^{5}\right)} c^{4} + 4 \, {\left(1424 \, B^{3} a^{3} b^{4} - 1332 \, A B^{2} a^{2} b^{5} + 234 \, A^{2} B a b^{6} - 27 \, A^{3} b^{7}\right)} c^{3} - {\left(392 \, B^{3} a^{2} b^{6} - 492 \, A B^{2} a b^{7} + 63 \, A^{2} B b^{8}\right)} c^{2} - {\left(17 \, B^{3} a b^{8} + 6 \, A B^{2} b^{9}\right)} c - {\left(B b^{13} c^{3} - 24576 \, A a^{6} c^{10} + 4096 \, {\left(13 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} c^{9} - 1536 \, {\left(44 \, B a^{5} b^{3} - 5 \, A a^{4} b^{4}\right)} c^{8} + 3840 \, {\left(9 \, B a^{4} b^{5} - 2 \, A a^{3} b^{6}\right)} c^{7} - 160 \, {\left(56 \, B a^{3} b^{7} - 15 \, A a^{2} b^{8}\right)} c^{6} + 48 \, {\left(25 \, B a^{2} b^{9} - 7 \, A a b^{10}\right)} c^{5} - 18 \, {\left(4 \, B a b^{11} - A b^{12}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} - {\left(35 \, B^{4} a b^{6} - 15 \, A B^{3} b^{7} - 1296 \, A^{4} a^{2} c^{5} + 648 \, {\left(14 \, A^{3} B a^{2} b - 5 \, A^{4} a b^{2}\right)} c^{4} + {\left(10000 \, B^{4} a^{4} - 30000 \, A B^{3} a^{3} b + 9936 \, A^{2} B^{2} a^{2} b^{2} + 1080 \, A^{3} B a b^{3} - 405 \, A^{4} b^{4}\right)} c^{3} + 3 \, {\left(5000 \, B^{4} a^{3} b^{2} - 3864 \, A B^{3} a^{2} b^{3} + 1080 \, A^{2} B^{2} a b^{4} - 135 \, A^{3} B b^{5}\right)} c^{2} - 3 \, {\left(497 \, B^{4} a^{2} b^{4} - 315 \, A B^{3} a b^{5} + 45 \, A^{2} B^{2} b^{6}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{10} - 2304 \, {\left(5 \, A^{2} B a^{4} - 3 \, A^{3} a^{3} b\right)} c^{6} + 64 \, {\left(500 \, B^{3} a^{5} - 420 \, A B^{2} a^{4} b + 198 \, A^{2} B a^{3} b^{2} - 81 \, A^{3} a^{2} b^{3}\right)} c^{5} - 16 \, {\left(1480 \, B^{3} a^{4} b^{2} - 1284 \, A B^{2} a^{3} b^{3} + 324 \, A^{2} B a^{2} b^{4} - 81 \, A^{3} a b^{5}\right)} c^{4} + 4 \, {\left(1424 \, B^{3} a^{3} b^{4} - 1332 \, A B^{2} a^{2} b^{5} + 234 \, A^{2} B a b^{6} - 27 \, A^{3} b^{7}\right)} c^{3} - {\left(392 \, B^{3} a^{2} b^{6} - 492 \, A B^{2} a b^{7} + 63 \, A^{2} B b^{8}\right)} c^{2} - {\left(17 \, B^{3} a b^{8} + 6 \, A B^{2} b^{9}\right)} c - {\left(B b^{13} c^{3} - 24576 \, A a^{6} c^{10} + 4096 \, {\left(13 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} c^{9} - 1536 \, {\left(44 \, B a^{5} b^{3} - 5 \, A a^{4} b^{4}\right)} c^{8} + 3840 \, {\left(9 \, B a^{4} b^{5} - 2 \, A a^{3} b^{6}\right)} c^{7} - 160 \, {\left(56 \, B a^{3} b^{7} - 15 \, A a^{2} b^{8}\right)} c^{6} + 48 \, {\left(25 \, B a^{2} b^{9} - 7 \, A a b^{10}\right)} c^{5} - 18 \, {\left(4 \, B a b^{11} - A b^{12}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} - {\left(35 \, B^{4} a b^{6} - 15 \, A B^{3} b^{7} - 1296 \, A^{4} a^{2} c^{5} + 648 \, {\left(14 \, A^{3} B a^{2} b - 5 \, A^{4} a b^{2}\right)} c^{4} + {\left(10000 \, B^{4} a^{4} - 30000 \, A B^{3} a^{3} b + 9936 \, A^{2} B^{2} a^{2} b^{2} + 1080 \, A^{3} B a b^{3} - 405 \, A^{4} b^{4}\right)} c^{3} + 3 \, {\left(5000 \, B^{4} a^{3} b^{2} - 3864 \, A B^{3} a^{2} b^{3} + 1080 \, A^{2} B^{2} a b^{4} - 135 \, A^{3} B b^{5}\right)} c^{2} - 3 \, {\left(497 \, B^{4} a^{2} b^{4} - 315 \, A B^{3} a b^{5} + 45 \, A^{2} B^{2} b^{6}\right)} c\right)} \sqrt{x}\right) + \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{10} - 2304 \, {\left(5 \, A^{2} B a^{4} - 3 \, A^{3} a^{3} b\right)} c^{6} + 64 \, {\left(500 \, B^{3} a^{5} - 420 \, A B^{2} a^{4} b + 198 \, A^{2} B a^{3} b^{2} - 81 \, A^{3} a^{2} b^{3}\right)} c^{5} - 16 \, {\left(1480 \, B^{3} a^{4} b^{2} - 1284 \, A B^{2} a^{3} b^{3} + 324 \, A^{2} B a^{2} b^{4} - 81 \, A^{3} a b^{5}\right)} c^{4} + 4 \, {\left(1424 \, B^{3} a^{3} b^{4} - 1332 \, A B^{2} a^{2} b^{5} + 234 \, A^{2} B a b^{6} - 27 \, A^{3} b^{7}\right)} c^{3} - {\left(392 \, B^{3} a^{2} b^{6} - 492 \, A B^{2} a b^{7} + 63 \, A^{2} B b^{8}\right)} c^{2} - {\left(17 \, B^{3} a b^{8} + 6 \, A B^{2} b^{9}\right)} c + {\left(B b^{13} c^{3} - 24576 \, A a^{6} c^{10} + 4096 \, {\left(13 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} c^{9} - 1536 \, {\left(44 \, B a^{5} b^{3} - 5 \, A a^{4} b^{4}\right)} c^{8} + 3840 \, {\left(9 \, B a^{4} b^{5} - 2 \, A a^{3} b^{6}\right)} c^{7} - 160 \, {\left(56 \, B a^{3} b^{7} - 15 \, A a^{2} b^{8}\right)} c^{6} + 48 \, {\left(25 \, B a^{2} b^{9} - 7 \, A a b^{10}\right)} c^{5} - 18 \, {\left(4 \, B a b^{11} - A b^{12}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} - {\left(35 \, B^{4} a b^{6} - 15 \, A B^{3} b^{7} - 1296 \, A^{4} a^{2} c^{5} + 648 \, {\left(14 \, A^{3} B a^{2} b - 5 \, A^{4} a b^{2}\right)} c^{4} + {\left(10000 \, B^{4} a^{4} - 30000 \, A B^{3} a^{3} b + 9936 \, A^{2} B^{2} a^{2} b^{2} + 1080 \, A^{3} B a b^{3} - 405 \, A^{4} b^{4}\right)} c^{3} + 3 \, {\left(5000 \, B^{4} a^{3} b^{2} - 3864 \, A B^{3} a^{2} b^{3} + 1080 \, A^{2} B^{2} a b^{4} - 135 \, A^{3} B b^{5}\right)} c^{2} - 3 \, {\left(497 \, B^{4} a^{2} b^{4} - 315 \, A B^{3} a b^{5} + 45 \, A^{2} B^{2} b^{6}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{10} - 2304 \, {\left(5 \, A^{2} B a^{4} - 3 \, A^{3} a^{3} b\right)} c^{6} + 64 \, {\left(500 \, B^{3} a^{5} - 420 \, A B^{2} a^{4} b + 198 \, A^{2} B a^{3} b^{2} - 81 \, A^{3} a^{2} b^{3}\right)} c^{5} - 16 \, {\left(1480 \, B^{3} a^{4} b^{2} - 1284 \, A B^{2} a^{3} b^{3} + 324 \, A^{2} B a^{2} b^{4} - 81 \, A^{3} a b^{5}\right)} c^{4} + 4 \, {\left(1424 \, B^{3} a^{3} b^{4} - 1332 \, A B^{2} a^{2} b^{5} + 234 \, A^{2} B a b^{6} - 27 \, A^{3} b^{7}\right)} c^{3} - {\left(392 \, B^{3} a^{2} b^{6} - 492 \, A B^{2} a b^{7} + 63 \, A^{2} B b^{8}\right)} c^{2} - {\left(17 \, B^{3} a b^{8} + 6 \, A B^{2} b^{9}\right)} c + {\left(B b^{13} c^{3} - 24576 \, A a^{6} c^{10} + 4096 \, {\left(13 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} c^{9} - 1536 \, {\left(44 \, B a^{5} b^{3} - 5 \, A a^{4} b^{4}\right)} c^{8} + 3840 \, {\left(9 \, B a^{4} b^{5} - 2 \, A a^{3} b^{6}\right)} c^{7} - 160 \, {\left(56 \, B a^{3} b^{7} - 15 \, A a^{2} b^{8}\right)} c^{6} + 48 \, {\left(25 \, B a^{2} b^{9} - 7 \, A a b^{10}\right)} c^{5} - 18 \, {\left(4 \, B a b^{11} - A b^{12}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} - {\left(35 \, B^{4} a b^{6} - 15 \, A B^{3} b^{7} - 1296 \, A^{4} a^{2} c^{5} + 648 \, {\left(14 \, A^{3} B a^{2} b - 5 \, A^{4} a b^{2}\right)} c^{4} + {\left(10000 \, B^{4} a^{4} - 30000 \, A B^{3} a^{3} b + 9936 \, A^{2} B^{2} a^{2} b^{2} + 1080 \, A^{3} B a b^{3} - 405 \, A^{4} b^{4}\right)} c^{3} + 3 \, {\left(5000 \, B^{4} a^{3} b^{2} - 3864 \, A B^{3} a^{2} b^{3} + 1080 \, A^{2} B^{2} a b^{4} - 135 \, A^{3} B b^{5}\right)} c^{2} - 3 \, {\left(497 \, B^{4} a^{2} b^{4} - 315 \, A B^{3} a b^{5} + 45 \, A^{2} B^{2} b^{6}\right)} c\right)} \sqrt{x}\right) + 2 \, {\left(B a^{2} b^{2} - {\left(B b^{3} c + 12 \, A a c^{3} - {\left(16 \, B a b - 3 \, A b^{2}\right)} c^{2}\right)} x^{3} + {\left(B b^{4} + 4 \, {\left(9 \, B a^{2} - 4 \, A a b\right)} c^{2} + 5 \, {\left(B a b^{2} - A b^{3}\right)} c\right)} x^{2} + 4 \, {\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} c + {\left(2 \, B a b^{3} + 4 \, A a^{2} c^{2} + {\left(28 \, B a^{2} b - 19 \, A a b^{2}\right)} c\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)}}"," ",0,"-1/8*(sqrt(1/2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(1/2*sqrt(1/2)*(B^3*b^10 - 2304*(5*A^2*B*a^4 - 3*A^3*a^3*b)*c^6 + 64*(500*B^3*a^5 - 420*A*B^2*a^4*b + 198*A^2*B*a^3*b^2 - 81*A^3*a^2*b^3)*c^5 - 16*(1480*B^3*a^4*b^2 - 1284*A*B^2*a^3*b^3 + 324*A^2*B*a^2*b^4 - 81*A^3*a*b^5)*c^4 + 4*(1424*B^3*a^3*b^4 - 1332*A*B^2*a^2*b^5 + 234*A^2*B*a*b^6 - 27*A^3*b^7)*c^3 - (392*B^3*a^2*b^6 - 492*A*B^2*a*b^7 + 63*A^2*B*b^8)*c^2 - (17*B^3*a*b^8 + 6*A*B^2*b^9)*c - (B*b^13*c^3 - 24576*A*a^6*c^10 + 4096*(13*B*a^6*b + 3*A*a^5*b^2)*c^9 - 1536*(44*B*a^5*b^3 - 5*A*a^4*b^4)*c^8 + 3840*(9*B*a^4*b^5 - 2*A*a^3*b^6)*c^7 - 160*(56*B*a^3*b^7 - 15*A*a^2*b^8)*c^6 + 48*(25*B*a^2*b^9 - 7*A*a*b^10)*c^5 - 18*(4*B*a*b^11 - A*b^12)*c^4)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)) - (35*B^4*a*b^6 - 15*A*B^3*b^7 - 1296*A^4*a^2*c^5 + 648*(14*A^3*B*a^2*b - 5*A^4*a*b^2)*c^4 + (10000*B^4*a^4 - 30000*A*B^3*a^3*b + 9936*A^2*B^2*a^2*b^2 + 1080*A^3*B*a*b^3 - 405*A^4*b^4)*c^3 + 3*(5000*B^4*a^3*b^2 - 3864*A*B^3*a^2*b^3 + 1080*A^2*B^2*a*b^4 - 135*A^3*B*b^5)*c^2 - 3*(497*B^4*a^2*b^4 - 315*A*B^3*a*b^5 + 45*A^2*B^2*b^6)*c)*sqrt(x)) - sqrt(1/2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(-1/2*sqrt(1/2)*(B^3*b^10 - 2304*(5*A^2*B*a^4 - 3*A^3*a^3*b)*c^6 + 64*(500*B^3*a^5 - 420*A*B^2*a^4*b + 198*A^2*B*a^3*b^2 - 81*A^3*a^2*b^3)*c^5 - 16*(1480*B^3*a^4*b^2 - 1284*A*B^2*a^3*b^3 + 324*A^2*B*a^2*b^4 - 81*A^3*a*b^5)*c^4 + 4*(1424*B^3*a^3*b^4 - 1332*A*B^2*a^2*b^5 + 234*A^2*B*a*b^6 - 27*A^3*b^7)*c^3 - (392*B^3*a^2*b^6 - 492*A*B^2*a*b^7 + 63*A^2*B*b^8)*c^2 - (17*B^3*a*b^8 + 6*A*B^2*b^9)*c - (B*b^13*c^3 - 24576*A*a^6*c^10 + 4096*(13*B*a^6*b + 3*A*a^5*b^2)*c^9 - 1536*(44*B*a^5*b^3 - 5*A*a^4*b^4)*c^8 + 3840*(9*B*a^4*b^5 - 2*A*a^3*b^6)*c^7 - 160*(56*B*a^3*b^7 - 15*A*a^2*b^8)*c^6 + 48*(25*B*a^2*b^9 - 7*A*a*b^10)*c^5 - 18*(4*B*a*b^11 - A*b^12)*c^4)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)) - (35*B^4*a*b^6 - 15*A*B^3*b^7 - 1296*A^4*a^2*c^5 + 648*(14*A^3*B*a^2*b - 5*A^4*a*b^2)*c^4 + (10000*B^4*a^4 - 30000*A*B^3*a^3*b + 9936*A^2*B^2*a^2*b^2 + 1080*A^3*B*a*b^3 - 405*A^4*b^4)*c^3 + 3*(5000*B^4*a^3*b^2 - 3864*A*B^3*a^2*b^3 + 1080*A^2*B^2*a*b^4 - 135*A^3*B*b^5)*c^2 - 3*(497*B^4*a^2*b^4 - 315*A*B^3*a*b^5 + 45*A^2*B^2*b^6)*c)*sqrt(x)) + sqrt(1/2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(1/2*sqrt(1/2)*(B^3*b^10 - 2304*(5*A^2*B*a^4 - 3*A^3*a^3*b)*c^6 + 64*(500*B^3*a^5 - 420*A*B^2*a^4*b + 198*A^2*B*a^3*b^2 - 81*A^3*a^2*b^3)*c^5 - 16*(1480*B^3*a^4*b^2 - 1284*A*B^2*a^3*b^3 + 324*A^2*B*a^2*b^4 - 81*A^3*a*b^5)*c^4 + 4*(1424*B^3*a^3*b^4 - 1332*A*B^2*a^2*b^5 + 234*A^2*B*a*b^6 - 27*A^3*b^7)*c^3 - (392*B^3*a^2*b^6 - 492*A*B^2*a*b^7 + 63*A^2*B*b^8)*c^2 - (17*B^3*a*b^8 + 6*A*B^2*b^9)*c + (B*b^13*c^3 - 24576*A*a^6*c^10 + 4096*(13*B*a^6*b + 3*A*a^5*b^2)*c^9 - 1536*(44*B*a^5*b^3 - 5*A*a^4*b^4)*c^8 + 3840*(9*B*a^4*b^5 - 2*A*a^3*b^6)*c^7 - 160*(56*B*a^3*b^7 - 15*A*a^2*b^8)*c^6 + 48*(25*B*a^2*b^9 - 7*A*a*b^10)*c^5 - 18*(4*B*a*b^11 - A*b^12)*c^4)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)) - (35*B^4*a*b^6 - 15*A*B^3*b^7 - 1296*A^4*a^2*c^5 + 648*(14*A^3*B*a^2*b - 5*A^4*a*b^2)*c^4 + (10000*B^4*a^4 - 30000*A*B^3*a^3*b + 9936*A^2*B^2*a^2*b^2 + 1080*A^3*B*a*b^3 - 405*A^4*b^4)*c^3 + 3*(5000*B^4*a^3*b^2 - 3864*A*B^3*a^2*b^3 + 1080*A^2*B^2*a*b^4 - 135*A^3*B*b^5)*c^2 - 3*(497*B^4*a^2*b^4 - 315*A*B^3*a*b^5 + 45*A^2*B^2*b^6)*c)*sqrt(x)) - sqrt(1/2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(-1/2*sqrt(1/2)*(B^3*b^10 - 2304*(5*A^2*B*a^4 - 3*A^3*a^3*b)*c^6 + 64*(500*B^3*a^5 - 420*A*B^2*a^4*b + 198*A^2*B*a^3*b^2 - 81*A^3*a^2*b^3)*c^5 - 16*(1480*B^3*a^4*b^2 - 1284*A*B^2*a^3*b^3 + 324*A^2*B*a^2*b^4 - 81*A^3*a*b^5)*c^4 + 4*(1424*B^3*a^3*b^4 - 1332*A*B^2*a^2*b^5 + 234*A^2*B*a*b^6 - 27*A^3*b^7)*c^3 - (392*B^3*a^2*b^6 - 492*A*B^2*a*b^7 + 63*A^2*B*b^8)*c^2 - (17*B^3*a*b^8 + 6*A*B^2*b^9)*c + (B*b^13*c^3 - 24576*A*a^6*c^10 + 4096*(13*B*a^6*b + 3*A*a^5*b^2)*c^9 - 1536*(44*B*a^5*b^3 - 5*A*a^4*b^4)*c^8 + 3840*(9*B*a^4*b^5 - 2*A*a^3*b^6)*c^7 - 160*(56*B*a^3*b^7 - 15*A*a^2*b^8)*c^6 + 48*(25*B*a^2*b^9 - 7*A*a*b^10)*c^5 - 18*(4*B*a*b^11 - A*b^12)*c^4)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)) - (35*B^4*a*b^6 - 15*A*B^3*b^7 - 1296*A^4*a^2*c^5 + 648*(14*A^3*B*a^2*b - 5*A^4*a*b^2)*c^4 + (10000*B^4*a^4 - 30000*A*B^3*a^3*b + 9936*A^2*B^2*a^2*b^2 + 1080*A^3*B*a*b^3 - 405*A^4*b^4)*c^3 + 3*(5000*B^4*a^3*b^2 - 3864*A*B^3*a^2*b^3 + 1080*A^2*B^2*a*b^4 - 135*A^3*B*b^5)*c^2 - 3*(497*B^4*a^2*b^4 - 315*A*B^3*a*b^5 + 45*A^2*B^2*b^6)*c)*sqrt(x)) + 2*(B*a^2*b^2 - (B*b^3*c + 12*A*a*c^3 - (16*B*a*b - 3*A*b^2)*c^2)*x^3 + (B*b^4 + 4*(9*B*a^2 - 4*A*a*b)*c^2 + 5*(B*a*b^2 - A*b^3)*c)*x^2 + 4*(5*B*a^3 - 3*A*a^2*b)*c + (2*B*a*b^3 + 4*A*a^2*c^2 + (28*B*a^2*b - 19*A*a*b^2)*c)*x)*sqrt(x))/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)","B",0
1025,1,5646,0,4.777884," ","integrate(x^(3/2)*(B*x+A)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c + {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(4 \, B^{3} a^{2} b^{7} - A B^{2} a b^{8} - 256 \, A^{3} a^{4} c^{5} + 128 \, {\left(2 \, A B^{2} a^{5} + 2 \, A^{2} B a^{4} b + A^{3} a^{3} b^{2}\right)} c^{4} - 64 \, {\left(4 \, B^{3} a^{5} b + 2 \, A B^{2} a^{4} b^{2} + 3 \, A^{2} B a^{3} b^{3}\right)} c^{3} + 8 \, {\left(24 \, B^{3} a^{4} b^{3} + 6 \, A^{2} B a^{2} b^{5} - A^{3} a b^{6}\right)} c^{2} - {\left(48 \, B^{3} a^{3} b^{5} - 8 \, A B^{2} a^{2} b^{6} + 4 \, A^{2} B a b^{7} - A^{3} b^{8}\right)} c - {\left(4096 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{7} - 2048 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{6} - 1280 \, {\left(2 \, B a^{6} b^{4} + 5 \, A a^{5} b^{5}\right)} c^{5} + 1280 \, {\left(2 \, B a^{5} b^{6} + A a^{4} b^{7}\right)} c^{4} - 80 \, {\left(10 \, B a^{4} b^{8} + A a^{3} b^{9}\right)} c^{3} + 8 \, {\left(14 \, B a^{3} b^{10} - A a^{2} b^{11}\right)} c^{2} - {\left(6 \, B a^{2} b^{12} - A a b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c + {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} - 27 \, {\left(5 \, B^{4} a^{2} b^{4} - A B^{3} a b^{5} - 16 \, A^{4} a^{2} c^{4} + 40 \, {\left(2 \, A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{3} + {\left(16 \, B^{4} a^{4} - 80 \, A B^{3} a^{3} b + 40 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} + {\left(40 \, B^{4} a^{3} b^{2} - 40 \, A B^{3} a^{2} b^{3} + A^{3} B b^{5}\right)} c\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c + {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(4 \, B^{3} a^{2} b^{7} - A B^{2} a b^{8} - 256 \, A^{3} a^{4} c^{5} + 128 \, {\left(2 \, A B^{2} a^{5} + 2 \, A^{2} B a^{4} b + A^{3} a^{3} b^{2}\right)} c^{4} - 64 \, {\left(4 \, B^{3} a^{5} b + 2 \, A B^{2} a^{4} b^{2} + 3 \, A^{2} B a^{3} b^{3}\right)} c^{3} + 8 \, {\left(24 \, B^{3} a^{4} b^{3} + 6 \, A^{2} B a^{2} b^{5} - A^{3} a b^{6}\right)} c^{2} - {\left(48 \, B^{3} a^{3} b^{5} - 8 \, A B^{2} a^{2} b^{6} + 4 \, A^{2} B a b^{7} - A^{3} b^{8}\right)} c - {\left(4096 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{7} - 2048 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{6} - 1280 \, {\left(2 \, B a^{6} b^{4} + 5 \, A a^{5} b^{5}\right)} c^{5} + 1280 \, {\left(2 \, B a^{5} b^{6} + A a^{4} b^{7}\right)} c^{4} - 80 \, {\left(10 \, B a^{4} b^{8} + A a^{3} b^{9}\right)} c^{3} + 8 \, {\left(14 \, B a^{3} b^{10} - A a^{2} b^{11}\right)} c^{2} - {\left(6 \, B a^{2} b^{12} - A a b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c + {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} - 27 \, {\left(5 \, B^{4} a^{2} b^{4} - A B^{3} a b^{5} - 16 \, A^{4} a^{2} c^{4} + 40 \, {\left(2 \, A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{3} + {\left(16 \, B^{4} a^{4} - 80 \, A B^{3} a^{3} b + 40 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} + {\left(40 \, B^{4} a^{3} b^{2} - 40 \, A B^{3} a^{2} b^{3} + A^{3} B b^{5}\right)} c\right)} \sqrt{x}\right) + 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c - {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(4 \, B^{3} a^{2} b^{7} - A B^{2} a b^{8} - 256 \, A^{3} a^{4} c^{5} + 128 \, {\left(2 \, A B^{2} a^{5} + 2 \, A^{2} B a^{4} b + A^{3} a^{3} b^{2}\right)} c^{4} - 64 \, {\left(4 \, B^{3} a^{5} b + 2 \, A B^{2} a^{4} b^{2} + 3 \, A^{2} B a^{3} b^{3}\right)} c^{3} + 8 \, {\left(24 \, B^{3} a^{4} b^{3} + 6 \, A^{2} B a^{2} b^{5} - A^{3} a b^{6}\right)} c^{2} - {\left(48 \, B^{3} a^{3} b^{5} - 8 \, A B^{2} a^{2} b^{6} + 4 \, A^{2} B a b^{7} - A^{3} b^{8}\right)} c + {\left(4096 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{7} - 2048 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{6} - 1280 \, {\left(2 \, B a^{6} b^{4} + 5 \, A a^{5} b^{5}\right)} c^{5} + 1280 \, {\left(2 \, B a^{5} b^{6} + A a^{4} b^{7}\right)} c^{4} - 80 \, {\left(10 \, B a^{4} b^{8} + A a^{3} b^{9}\right)} c^{3} + 8 \, {\left(14 \, B a^{3} b^{10} - A a^{2} b^{11}\right)} c^{2} - {\left(6 \, B a^{2} b^{12} - A a b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c - {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} - 27 \, {\left(5 \, B^{4} a^{2} b^{4} - A B^{3} a b^{5} - 16 \, A^{4} a^{2} c^{4} + 40 \, {\left(2 \, A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{3} + {\left(16 \, B^{4} a^{4} - 80 \, A B^{3} a^{3} b + 40 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} + {\left(40 \, B^{4} a^{3} b^{2} - 40 \, A B^{3} a^{2} b^{3} + A^{3} B b^{5}\right)} c\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c - {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(4 \, B^{3} a^{2} b^{7} - A B^{2} a b^{8} - 256 \, A^{3} a^{4} c^{5} + 128 \, {\left(2 \, A B^{2} a^{5} + 2 \, A^{2} B a^{4} b + A^{3} a^{3} b^{2}\right)} c^{4} - 64 \, {\left(4 \, B^{3} a^{5} b + 2 \, A B^{2} a^{4} b^{2} + 3 \, A^{2} B a^{3} b^{3}\right)} c^{3} + 8 \, {\left(24 \, B^{3} a^{4} b^{3} + 6 \, A^{2} B a^{2} b^{5} - A^{3} a b^{6}\right)} c^{2} - {\left(48 \, B^{3} a^{3} b^{5} - 8 \, A B^{2} a^{2} b^{6} + 4 \, A^{2} B a b^{7} - A^{3} b^{8}\right)} c + {\left(4096 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{7} - 2048 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{6} - 1280 \, {\left(2 \, B a^{6} b^{4} + 5 \, A a^{5} b^{5}\right)} c^{5} + 1280 \, {\left(2 \, B a^{5} b^{6} + A a^{4} b^{7}\right)} c^{4} - 80 \, {\left(10 \, B a^{4} b^{8} + A a^{3} b^{9}\right)} c^{3} + 8 \, {\left(14 \, B a^{3} b^{10} - A a^{2} b^{11}\right)} c^{2} - {\left(6 \, B a^{2} b^{12} - A a b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c - {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} - 27 \, {\left(5 \, B^{4} a^{2} b^{4} - A B^{3} a b^{5} - 16 \, A^{4} a^{2} c^{4} + 40 \, {\left(2 \, A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{3} + {\left(16 \, B^{4} a^{4} - 80 \, A B^{3} a^{3} b + 40 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} + {\left(40 \, B^{4} a^{3} b^{2} - 40 \, A B^{3} a^{2} b^{3} + A^{3} B b^{5}\right)} c\right)} \sqrt{x}\right) - 2 \, {\left(12 \, B a^{2} b - 3 \, A a b^{2} - 12 \, A a^{2} c + 3 \, {\left(B b^{2} c + 4 \, {\left(B a - A b\right)} c^{2}\right)} x^{3} + {\left(5 \, B b^{3} + 4 \, A a c^{2} + {\left(16 \, B a b - 19 \, A b^{2}\right)} c\right)} x^{2} + {\left(19 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(B a^{2} + 4 \, A a b\right)} c\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"-1/8*(3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c + (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))*log(27/2*sqrt(1/2)*(4*B^3*a^2*b^7 - A*B^2*a*b^8 - 256*A^3*a^4*c^5 + 128*(2*A*B^2*a^5 + 2*A^2*B*a^4*b + A^3*a^3*b^2)*c^4 - 64*(4*B^3*a^5*b + 2*A*B^2*a^4*b^2 + 3*A^2*B*a^3*b^3)*c^3 + 8*(24*B^3*a^4*b^3 + 6*A^2*B*a^2*b^5 - A^3*a*b^6)*c^2 - (48*B^3*a^3*b^5 - 8*A*B^2*a^2*b^6 + 4*A^2*B*a*b^7 - A^3*b^8)*c - (4096*(2*B*a^8 - 3*A*a^7*b)*c^7 - 2048*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^6 - 1280*(2*B*a^6*b^4 + 5*A*a^5*b^5)*c^5 + 1280*(2*B*a^5*b^6 + A*a^4*b^7)*c^4 - 80*(10*B*a^4*b^8 + A*a^3*b^9)*c^3 + 8*(14*B*a^3*b^10 - A*a^2*b^11)*c^2 - (6*B*a^2*b^12 - A*a*b^13)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c + (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)) - 27*(5*B^4*a^2*b^4 - A*B^3*a*b^5 - 16*A^4*a^2*c^4 + 40*(2*A^3*B*a^2*b - A^4*a*b^2)*c^3 + (16*B^4*a^4 - 80*A*B^3*a^3*b + 40*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 + (40*B^4*a^3*b^2 - 40*A*B^3*a^2*b^3 + A^3*B*b^5)*c)*sqrt(x)) - 3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c + (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))*log(-27/2*sqrt(1/2)*(4*B^3*a^2*b^7 - A*B^2*a*b^8 - 256*A^3*a^4*c^5 + 128*(2*A*B^2*a^5 + 2*A^2*B*a^4*b + A^3*a^3*b^2)*c^4 - 64*(4*B^3*a^5*b + 2*A*B^2*a^4*b^2 + 3*A^2*B*a^3*b^3)*c^3 + 8*(24*B^3*a^4*b^3 + 6*A^2*B*a^2*b^5 - A^3*a*b^6)*c^2 - (48*B^3*a^3*b^5 - 8*A*B^2*a^2*b^6 + 4*A^2*B*a*b^7 - A^3*b^8)*c - (4096*(2*B*a^8 - 3*A*a^7*b)*c^7 - 2048*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^6 - 1280*(2*B*a^6*b^4 + 5*A*a^5*b^5)*c^5 + 1280*(2*B*a^5*b^6 + A*a^4*b^7)*c^4 - 80*(10*B*a^4*b^8 + A*a^3*b^9)*c^3 + 8*(14*B*a^3*b^10 - A*a^2*b^11)*c^2 - (6*B*a^2*b^12 - A*a*b^13)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c + (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)) - 27*(5*B^4*a^2*b^4 - A*B^3*a*b^5 - 16*A^4*a^2*c^4 + 40*(2*A^3*B*a^2*b - A^4*a*b^2)*c^3 + (16*B^4*a^4 - 80*A*B^3*a^3*b + 40*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 + (40*B^4*a^3*b^2 - 40*A*B^3*a^2*b^3 + A^3*B*b^5)*c)*sqrt(x)) + 3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c - (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))*log(27/2*sqrt(1/2)*(4*B^3*a^2*b^7 - A*B^2*a*b^8 - 256*A^3*a^4*c^5 + 128*(2*A*B^2*a^5 + 2*A^2*B*a^4*b + A^3*a^3*b^2)*c^4 - 64*(4*B^3*a^5*b + 2*A*B^2*a^4*b^2 + 3*A^2*B*a^3*b^3)*c^3 + 8*(24*B^3*a^4*b^3 + 6*A^2*B*a^2*b^5 - A^3*a*b^6)*c^2 - (48*B^3*a^3*b^5 - 8*A*B^2*a^2*b^6 + 4*A^2*B*a*b^7 - A^3*b^8)*c + (4096*(2*B*a^8 - 3*A*a^7*b)*c^7 - 2048*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^6 - 1280*(2*B*a^6*b^4 + 5*A*a^5*b^5)*c^5 + 1280*(2*B*a^5*b^6 + A*a^4*b^7)*c^4 - 80*(10*B*a^4*b^8 + A*a^3*b^9)*c^3 + 8*(14*B*a^3*b^10 - A*a^2*b^11)*c^2 - (6*B*a^2*b^12 - A*a*b^13)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c - (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)) - 27*(5*B^4*a^2*b^4 - A*B^3*a*b^5 - 16*A^4*a^2*c^4 + 40*(2*A^3*B*a^2*b - A^4*a*b^2)*c^3 + (16*B^4*a^4 - 80*A*B^3*a^3*b + 40*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 + (40*B^4*a^3*b^2 - 40*A*B^3*a^2*b^3 + A^3*B*b^5)*c)*sqrt(x)) - 3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c - (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))*log(-27/2*sqrt(1/2)*(4*B^3*a^2*b^7 - A*B^2*a*b^8 - 256*A^3*a^4*c^5 + 128*(2*A*B^2*a^5 + 2*A^2*B*a^4*b + A^3*a^3*b^2)*c^4 - 64*(4*B^3*a^5*b + 2*A*B^2*a^4*b^2 + 3*A^2*B*a^3*b^3)*c^3 + 8*(24*B^3*a^4*b^3 + 6*A^2*B*a^2*b^5 - A^3*a*b^6)*c^2 - (48*B^3*a^3*b^5 - 8*A*B^2*a^2*b^6 + 4*A^2*B*a*b^7 - A^3*b^8)*c + (4096*(2*B*a^8 - 3*A*a^7*b)*c^7 - 2048*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^6 - 1280*(2*B*a^6*b^4 + 5*A*a^5*b^5)*c^5 + 1280*(2*B*a^5*b^6 + A*a^4*b^7)*c^4 - 80*(10*B*a^4*b^8 + A*a^3*b^9)*c^3 + 8*(14*B*a^3*b^10 - A*a^2*b^11)*c^2 - (6*B*a^2*b^12 - A*a*b^13)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c - (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)) - 27*(5*B^4*a^2*b^4 - A*B^3*a*b^5 - 16*A^4*a^2*c^4 + 40*(2*A^3*B*a^2*b - A^4*a*b^2)*c^3 + (16*B^4*a^4 - 80*A*B^3*a^3*b + 40*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 + (40*B^4*a^3*b^2 - 40*A*B^3*a^2*b^3 + A^3*B*b^5)*c)*sqrt(x)) - 2*(12*B*a^2*b - 3*A*a*b^2 - 12*A*a^2*c + 3*(B*b^2*c + 4*(B*a - A*b)*c^2)*x^3 + (5*B*b^3 + 4*A*a*c^2 + (16*B*a*b - 19*A*b^2)*c)*x^2 + (19*B*a*b^2 - 5*A*b^3 - 4*(B*a^2 + 4*A*a*b)*c)*x)*sqrt(x))/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
1026,1,7267,0,9.404671," ","integrate((B*x+A)*x^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{2} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{8} + 27 \, A B^{2} a^{2} b^{9} + 9 \, A^{2} B a b^{10} + A^{3} b^{11} + 6400 \, {\left(3 \, A^{2} B a^{6} - 4 \, A^{3} a^{5} b\right)} c^{5} - 64 \, {\left(108 \, B^{3} a^{7} - 72 \, A B^{2} a^{6} b + 66 \, A^{2} B a^{5} b^{2} - 341 \, A^{3} a^{4} b^{3}\right)} c^{4} + 16 \, {\left(216 \, B^{3} a^{6} b^{2} - 324 \, A B^{2} a^{5} b^{3} - 288 \, A^{2} B a^{4} b^{4} - 427 \, A^{3} a^{3} b^{5}\right)} c^{3} + 20 \, {\left(108 \, A B^{2} a^{4} b^{5} + 102 \, A^{2} B a^{3} b^{6} + 47 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(216 \, B^{3} a^{4} b^{6} + 396 \, A B^{2} a^{3} b^{7} + 267 \, A^{2} B a^{2} b^{8} + 53 \, A^{3} a b^{9}\right)} c - {\left(3 \, B a^{4} b^{13} + A a^{3} b^{14} + 40960 \, A a^{10} c^{7} - 4096 \, {\left(9 \, B a^{10} b + 8 \, A a^{9} b^{2}\right)} c^{6} + 1536 \, {\left(28 \, B a^{9} b^{3} + A a^{8} b^{4}\right)} c^{5} - 6400 \, {\left(3 \, B a^{8} b^{5} - A a^{7} b^{6}\right)} c^{4} + 160 \, {\left(24 \, B a^{7} b^{7} - 17 \, A a^{6} b^{8}\right)} c^{3} - 240 \, {\left(B a^{6} b^{9} - 2 \, A a^{5} b^{10}\right)} c^{2} - 2 \, {\left(12 \, B a^{5} b^{11} + 19 \, A a^{4} b^{12}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} + {\left(10000 \, A^{4} a^{3} c^{5} - 15000 \, {\left(2 \, A^{3} B a^{3} b - A^{4} a^{2} b^{2}\right)} c^{4} - 3 \, {\left(432 \, B^{4} a^{5} - 3024 \, A B^{3} a^{4} b - 3312 \, A^{2} B^{2} a^{3} b^{2} + 3864 \, A^{3} B a^{2} b^{3} + 497 \, A^{4} a b^{4}\right)} c^{3} - 5 \, {\left(648 \, B^{4} a^{4} b^{2} - 216 \, A B^{3} a^{3} b^{3} - 648 \, A^{2} B^{2} a^{2} b^{4} - 189 \, A^{3} B a b^{5} - 7 \, A^{4} b^{6}\right)} c^{2} - 15 \, {\left(27 \, B^{4} a^{3} b^{4} + 27 \, A B^{3} a^{2} b^{5} + 9 \, A^{2} B^{2} a b^{6} + A^{3} B b^{7}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{2} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{8} + 27 \, A B^{2} a^{2} b^{9} + 9 \, A^{2} B a b^{10} + A^{3} b^{11} + 6400 \, {\left(3 \, A^{2} B a^{6} - 4 \, A^{3} a^{5} b\right)} c^{5} - 64 \, {\left(108 \, B^{3} a^{7} - 72 \, A B^{2} a^{6} b + 66 \, A^{2} B a^{5} b^{2} - 341 \, A^{3} a^{4} b^{3}\right)} c^{4} + 16 \, {\left(216 \, B^{3} a^{6} b^{2} - 324 \, A B^{2} a^{5} b^{3} - 288 \, A^{2} B a^{4} b^{4} - 427 \, A^{3} a^{3} b^{5}\right)} c^{3} + 20 \, {\left(108 \, A B^{2} a^{4} b^{5} + 102 \, A^{2} B a^{3} b^{6} + 47 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(216 \, B^{3} a^{4} b^{6} + 396 \, A B^{2} a^{3} b^{7} + 267 \, A^{2} B a^{2} b^{8} + 53 \, A^{3} a b^{9}\right)} c - {\left(3 \, B a^{4} b^{13} + A a^{3} b^{14} + 40960 \, A a^{10} c^{7} - 4096 \, {\left(9 \, B a^{10} b + 8 \, A a^{9} b^{2}\right)} c^{6} + 1536 \, {\left(28 \, B a^{9} b^{3} + A a^{8} b^{4}\right)} c^{5} - 6400 \, {\left(3 \, B a^{8} b^{5} - A a^{7} b^{6}\right)} c^{4} + 160 \, {\left(24 \, B a^{7} b^{7} - 17 \, A a^{6} b^{8}\right)} c^{3} - 240 \, {\left(B a^{6} b^{9} - 2 \, A a^{5} b^{10}\right)} c^{2} - 2 \, {\left(12 \, B a^{5} b^{11} + 19 \, A a^{4} b^{12}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} + {\left(10000 \, A^{4} a^{3} c^{5} - 15000 \, {\left(2 \, A^{3} B a^{3} b - A^{4} a^{2} b^{2}\right)} c^{4} - 3 \, {\left(432 \, B^{4} a^{5} - 3024 \, A B^{3} a^{4} b - 3312 \, A^{2} B^{2} a^{3} b^{2} + 3864 \, A^{3} B a^{2} b^{3} + 497 \, A^{4} a b^{4}\right)} c^{3} - 5 \, {\left(648 \, B^{4} a^{4} b^{2} - 216 \, A B^{3} a^{3} b^{3} - 648 \, A^{2} B^{2} a^{2} b^{4} - 189 \, A^{3} B a b^{5} - 7 \, A^{4} b^{6}\right)} c^{2} - 15 \, {\left(27 \, B^{4} a^{3} b^{4} + 27 \, A B^{3} a^{2} b^{5} + 9 \, A^{2} B^{2} a b^{6} + A^{3} B b^{7}\right)} c\right)} \sqrt{x}\right) + \sqrt{\frac{1}{2}} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{2} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{8} + 27 \, A B^{2} a^{2} b^{9} + 9 \, A^{2} B a b^{10} + A^{3} b^{11} + 6400 \, {\left(3 \, A^{2} B a^{6} - 4 \, A^{3} a^{5} b\right)} c^{5} - 64 \, {\left(108 \, B^{3} a^{7} - 72 \, A B^{2} a^{6} b + 66 \, A^{2} B a^{5} b^{2} - 341 \, A^{3} a^{4} b^{3}\right)} c^{4} + 16 \, {\left(216 \, B^{3} a^{6} b^{2} - 324 \, A B^{2} a^{5} b^{3} - 288 \, A^{2} B a^{4} b^{4} - 427 \, A^{3} a^{3} b^{5}\right)} c^{3} + 20 \, {\left(108 \, A B^{2} a^{4} b^{5} + 102 \, A^{2} B a^{3} b^{6} + 47 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(216 \, B^{3} a^{4} b^{6} + 396 \, A B^{2} a^{3} b^{7} + 267 \, A^{2} B a^{2} b^{8} + 53 \, A^{3} a b^{9}\right)} c + {\left(3 \, B a^{4} b^{13} + A a^{3} b^{14} + 40960 \, A a^{10} c^{7} - 4096 \, {\left(9 \, B a^{10} b + 8 \, A a^{9} b^{2}\right)} c^{6} + 1536 \, {\left(28 \, B a^{9} b^{3} + A a^{8} b^{4}\right)} c^{5} - 6400 \, {\left(3 \, B a^{8} b^{5} - A a^{7} b^{6}\right)} c^{4} + 160 \, {\left(24 \, B a^{7} b^{7} - 17 \, A a^{6} b^{8}\right)} c^{3} - 240 \, {\left(B a^{6} b^{9} - 2 \, A a^{5} b^{10}\right)} c^{2} - 2 \, {\left(12 \, B a^{5} b^{11} + 19 \, A a^{4} b^{12}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} + {\left(10000 \, A^{4} a^{3} c^{5} - 15000 \, {\left(2 \, A^{3} B a^{3} b - A^{4} a^{2} b^{2}\right)} c^{4} - 3 \, {\left(432 \, B^{4} a^{5} - 3024 \, A B^{3} a^{4} b - 3312 \, A^{2} B^{2} a^{3} b^{2} + 3864 \, A^{3} B a^{2} b^{3} + 497 \, A^{4} a b^{4}\right)} c^{3} - 5 \, {\left(648 \, B^{4} a^{4} b^{2} - 216 \, A B^{3} a^{3} b^{3} - 648 \, A^{2} B^{2} a^{2} b^{4} - 189 \, A^{3} B a b^{5} - 7 \, A^{4} b^{6}\right)} c^{2} - 15 \, {\left(27 \, B^{4} a^{3} b^{4} + 27 \, A B^{3} a^{2} b^{5} + 9 \, A^{2} B^{2} a b^{6} + A^{3} B b^{7}\right)} c\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{2} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{8} + 27 \, A B^{2} a^{2} b^{9} + 9 \, A^{2} B a b^{10} + A^{3} b^{11} + 6400 \, {\left(3 \, A^{2} B a^{6} - 4 \, A^{3} a^{5} b\right)} c^{5} - 64 \, {\left(108 \, B^{3} a^{7} - 72 \, A B^{2} a^{6} b + 66 \, A^{2} B a^{5} b^{2} - 341 \, A^{3} a^{4} b^{3}\right)} c^{4} + 16 \, {\left(216 \, B^{3} a^{6} b^{2} - 324 \, A B^{2} a^{5} b^{3} - 288 \, A^{2} B a^{4} b^{4} - 427 \, A^{3} a^{3} b^{5}\right)} c^{3} + 20 \, {\left(108 \, A B^{2} a^{4} b^{5} + 102 \, A^{2} B a^{3} b^{6} + 47 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(216 \, B^{3} a^{4} b^{6} + 396 \, A B^{2} a^{3} b^{7} + 267 \, A^{2} B a^{2} b^{8} + 53 \, A^{3} a b^{9}\right)} c + {\left(3 \, B a^{4} b^{13} + A a^{3} b^{14} + 40960 \, A a^{10} c^{7} - 4096 \, {\left(9 \, B a^{10} b + 8 \, A a^{9} b^{2}\right)} c^{6} + 1536 \, {\left(28 \, B a^{9} b^{3} + A a^{8} b^{4}\right)} c^{5} - 6400 \, {\left(3 \, B a^{8} b^{5} - A a^{7} b^{6}\right)} c^{4} + 160 \, {\left(24 \, B a^{7} b^{7} - 17 \, A a^{6} b^{8}\right)} c^{3} - 240 \, {\left(B a^{6} b^{9} - 2 \, A a^{5} b^{10}\right)} c^{2} - 2 \, {\left(12 \, B a^{5} b^{11} + 19 \, A a^{4} b^{12}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} + {\left(10000 \, A^{4} a^{3} c^{5} - 15000 \, {\left(2 \, A^{3} B a^{3} b - A^{4} a^{2} b^{2}\right)} c^{4} - 3 \, {\left(432 \, B^{4} a^{5} - 3024 \, A B^{3} a^{4} b - 3312 \, A^{2} B^{2} a^{3} b^{2} + 3864 \, A^{3} B a^{2} b^{3} + 497 \, A^{4} a b^{4}\right)} c^{3} - 5 \, {\left(648 \, B^{4} a^{4} b^{2} - 216 \, A B^{3} a^{3} b^{3} - 648 \, A^{2} B^{2} a^{2} b^{4} - 189 \, A^{3} B a b^{5} - 7 \, A^{4} b^{6}\right)} c^{2} - 15 \, {\left(27 \, B^{4} a^{3} b^{4} + 27 \, A B^{3} a^{2} b^{5} + 9 \, A^{2} B^{2} a b^{6} + A^{3} B b^{7}\right)} c\right)} \sqrt{x}\right) - 2 \, {\left(3 \, B a^{2} b^{2} + A a b^{3} - {\left(20 \, A a c^{3} - {\left(12 \, B a b - A b^{2}\right)} c^{2}\right)} x^{3} - {\left(4 \, {\left(B a^{2} + 7 \, A a b\right)} c^{2} - {\left(19 \, B a b^{2} - 2 \, A b^{3}\right)} c\right)} x^{2} + 4 \, {\left(3 \, B a^{3} - 4 \, A a^{2} b\right)} c + {\left(5 \, B a b^{3} - A b^{4} - 36 \, A a^{2} c^{2} + {\left(16 \, B a^{2} b - 5 \, A a b^{2}\right)} c\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{2} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)}}"," ",0,"1/8*(sqrt(1/2)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^2 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x)*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log(1/2*sqrt(1/2)*(27*B^3*a^3*b^8 + 27*A*B^2*a^2*b^9 + 9*A^2*B*a*b^10 + A^3*b^11 + 6400*(3*A^2*B*a^6 - 4*A^3*a^5*b)*c^5 - 64*(108*B^3*a^7 - 72*A*B^2*a^6*b + 66*A^2*B*a^5*b^2 - 341*A^3*a^4*b^3)*c^4 + 16*(216*B^3*a^6*b^2 - 324*A*B^2*a^5*b^3 - 288*A^2*B*a^4*b^4 - 427*A^3*a^3*b^5)*c^3 + 20*(108*A*B^2*a^4*b^5 + 102*A^2*B*a^3*b^6 + 47*A^3*a^2*b^7)*c^2 - (216*B^3*a^4*b^6 + 396*A*B^2*a^3*b^7 + 267*A^2*B*a^2*b^8 + 53*A^3*a*b^9)*c - (3*B*a^4*b^13 + A*a^3*b^14 + 40960*A*a^10*c^7 - 4096*(9*B*a^10*b + 8*A*a^9*b^2)*c^6 + 1536*(28*B*a^9*b^3 + A*a^8*b^4)*c^5 - 6400*(3*B*a^8*b^5 - A*a^7*b^6)*c^4 + 160*(24*B*a^7*b^7 - 17*A*a^6*b^8)*c^3 - 240*(B*a^6*b^9 - 2*A*a^5*b^10)*c^2 - 2*(12*B*a^5*b^11 + 19*A*a^4*b^12)*c)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)) + (10000*A^4*a^3*c^5 - 15000*(2*A^3*B*a^3*b - A^4*a^2*b^2)*c^4 - 3*(432*B^4*a^5 - 3024*A*B^3*a^4*b - 3312*A^2*B^2*a^3*b^2 + 3864*A^3*B*a^2*b^3 + 497*A^4*a*b^4)*c^3 - 5*(648*B^4*a^4*b^2 - 216*A*B^3*a^3*b^3 - 648*A^2*B^2*a^2*b^4 - 189*A^3*B*a*b^5 - 7*A^4*b^6)*c^2 - 15*(27*B^4*a^3*b^4 + 27*A*B^3*a^2*b^5 + 9*A^2*B^2*a*b^6 + A^3*B*b^7)*c)*sqrt(x)) - sqrt(1/2)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^2 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x)*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log(-1/2*sqrt(1/2)*(27*B^3*a^3*b^8 + 27*A*B^2*a^2*b^9 + 9*A^2*B*a*b^10 + A^3*b^11 + 6400*(3*A^2*B*a^6 - 4*A^3*a^5*b)*c^5 - 64*(108*B^3*a^7 - 72*A*B^2*a^6*b + 66*A^2*B*a^5*b^2 - 341*A^3*a^4*b^3)*c^4 + 16*(216*B^3*a^6*b^2 - 324*A*B^2*a^5*b^3 - 288*A^2*B*a^4*b^4 - 427*A^3*a^3*b^5)*c^3 + 20*(108*A*B^2*a^4*b^5 + 102*A^2*B*a^3*b^6 + 47*A^3*a^2*b^7)*c^2 - (216*B^3*a^4*b^6 + 396*A*B^2*a^3*b^7 + 267*A^2*B*a^2*b^8 + 53*A^3*a*b^9)*c - (3*B*a^4*b^13 + A*a^3*b^14 + 40960*A*a^10*c^7 - 4096*(9*B*a^10*b + 8*A*a^9*b^2)*c^6 + 1536*(28*B*a^9*b^3 + A*a^8*b^4)*c^5 - 6400*(3*B*a^8*b^5 - A*a^7*b^6)*c^4 + 160*(24*B*a^7*b^7 - 17*A*a^6*b^8)*c^3 - 240*(B*a^6*b^9 - 2*A*a^5*b^10)*c^2 - 2*(12*B*a^5*b^11 + 19*A*a^4*b^12)*c)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)) + (10000*A^4*a^3*c^5 - 15000*(2*A^3*B*a^3*b - A^4*a^2*b^2)*c^4 - 3*(432*B^4*a^5 - 3024*A*B^3*a^4*b - 3312*A^2*B^2*a^3*b^2 + 3864*A^3*B*a^2*b^3 + 497*A^4*a*b^4)*c^3 - 5*(648*B^4*a^4*b^2 - 216*A*B^3*a^3*b^3 - 648*A^2*B^2*a^2*b^4 - 189*A^3*B*a*b^5 - 7*A^4*b^6)*c^2 - 15*(27*B^4*a^3*b^4 + 27*A*B^3*a^2*b^5 + 9*A^2*B^2*a*b^6 + A^3*B*b^7)*c)*sqrt(x)) + sqrt(1/2)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^2 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x)*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log(1/2*sqrt(1/2)*(27*B^3*a^3*b^8 + 27*A*B^2*a^2*b^9 + 9*A^2*B*a*b^10 + A^3*b^11 + 6400*(3*A^2*B*a^6 - 4*A^3*a^5*b)*c^5 - 64*(108*B^3*a^7 - 72*A*B^2*a^6*b + 66*A^2*B*a^5*b^2 - 341*A^3*a^4*b^3)*c^4 + 16*(216*B^3*a^6*b^2 - 324*A*B^2*a^5*b^3 - 288*A^2*B*a^4*b^4 - 427*A^3*a^3*b^5)*c^3 + 20*(108*A*B^2*a^4*b^5 + 102*A^2*B*a^3*b^6 + 47*A^3*a^2*b^7)*c^2 - (216*B^3*a^4*b^6 + 396*A*B^2*a^3*b^7 + 267*A^2*B*a^2*b^8 + 53*A^3*a*b^9)*c + (3*B*a^4*b^13 + A*a^3*b^14 + 40960*A*a^10*c^7 - 4096*(9*B*a^10*b + 8*A*a^9*b^2)*c^6 + 1536*(28*B*a^9*b^3 + A*a^8*b^4)*c^5 - 6400*(3*B*a^8*b^5 - A*a^7*b^6)*c^4 + 160*(24*B*a^7*b^7 - 17*A*a^6*b^8)*c^3 - 240*(B*a^6*b^9 - 2*A*a^5*b^10)*c^2 - 2*(12*B*a^5*b^11 + 19*A*a^4*b^12)*c)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)) + (10000*A^4*a^3*c^5 - 15000*(2*A^3*B*a^3*b - A^4*a^2*b^2)*c^4 - 3*(432*B^4*a^5 - 3024*A*B^3*a^4*b - 3312*A^2*B^2*a^3*b^2 + 3864*A^3*B*a^2*b^3 + 497*A^4*a*b^4)*c^3 - 5*(648*B^4*a^4*b^2 - 216*A*B^3*a^3*b^3 - 648*A^2*B^2*a^2*b^4 - 189*A^3*B*a*b^5 - 7*A^4*b^6)*c^2 - 15*(27*B^4*a^3*b^4 + 27*A*B^3*a^2*b^5 + 9*A^2*B^2*a*b^6 + A^3*B*b^7)*c)*sqrt(x)) - sqrt(1/2)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^2 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x)*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log(-1/2*sqrt(1/2)*(27*B^3*a^3*b^8 + 27*A*B^2*a^2*b^9 + 9*A^2*B*a*b^10 + A^3*b^11 + 6400*(3*A^2*B*a^6 - 4*A^3*a^5*b)*c^5 - 64*(108*B^3*a^7 - 72*A*B^2*a^6*b + 66*A^2*B*a^5*b^2 - 341*A^3*a^4*b^3)*c^4 + 16*(216*B^3*a^6*b^2 - 324*A*B^2*a^5*b^3 - 288*A^2*B*a^4*b^4 - 427*A^3*a^3*b^5)*c^3 + 20*(108*A*B^2*a^4*b^5 + 102*A^2*B*a^3*b^6 + 47*A^3*a^2*b^7)*c^2 - (216*B^3*a^4*b^6 + 396*A*B^2*a^3*b^7 + 267*A^2*B*a^2*b^8 + 53*A^3*a*b^9)*c + (3*B*a^4*b^13 + A*a^3*b^14 + 40960*A*a^10*c^7 - 4096*(9*B*a^10*b + 8*A*a^9*b^2)*c^6 + 1536*(28*B*a^9*b^3 + A*a^8*b^4)*c^5 - 6400*(3*B*a^8*b^5 - A*a^7*b^6)*c^4 + 160*(24*B*a^7*b^7 - 17*A*a^6*b^8)*c^3 - 240*(B*a^6*b^9 - 2*A*a^5*b^10)*c^2 - 2*(12*B*a^5*b^11 + 19*A*a^4*b^12)*c)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)) + (10000*A^4*a^3*c^5 - 15000*(2*A^3*B*a^3*b - A^4*a^2*b^2)*c^4 - 3*(432*B^4*a^5 - 3024*A*B^3*a^4*b - 3312*A^2*B^2*a^3*b^2 + 3864*A^3*B*a^2*b^3 + 497*A^4*a*b^4)*c^3 - 5*(648*B^4*a^4*b^2 - 216*A*B^3*a^3*b^3 - 648*A^2*B^2*a^2*b^4 - 189*A^3*B*a*b^5 - 7*A^4*b^6)*c^2 - 15*(27*B^4*a^3*b^4 + 27*A*B^3*a^2*b^5 + 9*A^2*B^2*a*b^6 + A^3*B*b^7)*c)*sqrt(x)) - 2*(3*B*a^2*b^2 + A*a*b^3 - (20*A*a*c^3 - (12*B*a*b - A*b^2)*c^2)*x^3 - (4*(B*a^2 + 7*A*a*b)*c^2 - (19*B*a*b^2 - 2*A*b^3)*c)*x^2 + 4*(3*B*a^3 - 4*A*a^2*b)*c + (5*B*a*b^3 - A*b^4 - 36*A*a^2*c^2 + (16*B*a^2*b - 5*A*a*b^2)*c)*x)*sqrt(x))/(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^2 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x)","B",0
1027,1,9907,0,23.768703," ","integrate((B*x+A)/(c*x^2+b*x+a)^3/x^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{2} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{11} + 9 \, A B^{2} a^{2} b^{12} + 27 \, A^{2} B a b^{13} + 27 \, A^{3} b^{14} - 2370816 \, A^{3} a^{7} c^{7} + 2688 \, {\left(50 \, A B^{2} a^{8} + 384 \, A^{2} B a^{7} b + 1143 \, A^{3} a^{6} b^{2}\right)} c^{6} - 64 \, {\left(400 \, B^{3} a^{8} b + 4062 \, A B^{2} a^{7} b^{2} + 17541 \, A^{2} B a^{6} b^{3} + 26865 \, A^{3} a^{5} b^{4}\right)} c^{5} + 8 \, {\left(2728 \, B^{3} a^{7} b^{3} + 20520 \, A B^{2} a^{6} b^{4} + 62694 \, A^{2} B a^{5} b^{5} + 67797 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(976 \, B^{3} a^{6} b^{5} + 6744 \, A B^{2} a^{5} b^{6} + 16884 \, A^{2} B a^{4} b^{7} + 14985 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(940 \, B^{3} a^{5} b^{7} + 6591 \, A B^{2} a^{4} b^{8} + 15489 \, A^{2} B a^{3} b^{9} + 12528 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(53 \, B^{3} a^{4} b^{9} + 414 \, A B^{2} a^{3} b^{10} + 1053 \, A^{2} B a^{2} b^{11} + 864 \, A^{3} a b^{12}\right)} c - {\left(B a^{6} b^{14} + 3 \, A a^{5} b^{15} + 4096 \, {\left(10 \, B a^{13} - 33 \, A a^{12} b\right)} c^{7} - 2048 \, {\left(16 \, B a^{12} b^{2} - 99 \, A a^{11} b^{3}\right)} c^{6} + 768 \, {\left(2 \, B a^{11} b^{4} - 169 \, A a^{10} b^{5}\right)} c^{5} + 1280 \, {\left(5 \, B a^{10} b^{6} + 36 \, A a^{9} b^{7}\right)} c^{4} - 80 \, {\left(34 \, B a^{9} b^{8} + 123 \, A a^{8} b^{9}\right)} c^{3} + 24 \, {\left(20 \, B a^{8} b^{10} + 53 \, A a^{7} b^{11}\right)} c^{2} - {\left(38 \, B a^{7} b^{12} + 93 \, A a^{6} b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} + {\left(3111696 \, A^{4} a^{4} c^{7} - 1555848 \, {\left(2 \, A^{3} B a^{4} b + A^{4} a^{3} b^{2}\right)} c^{6} - {\left(10000 \, B^{4} a^{6} - 90000 \, A B^{3} a^{5} b - 863136 \, A^{2} B^{2} a^{4} b^{2} - 1298376 \, A^{3} B a^{3} b^{3} - 339309 \, A^{4} a^{2} b^{4}\right)} c^{5} - 3 \, {\left(5000 \, B^{4} a^{5} b^{2} + 32952 \, A B^{3} a^{4} b^{3} + 79488 \, A^{2} B^{2} a^{3} b^{4} + 80919 \, A^{3} B a^{2} b^{5} + 12069 \, A^{4} a b^{6}\right)} c^{4} + 21 \, {\left(71 \, B^{4} a^{4} b^{4} + 537 \, A B^{3} a^{3} b^{5} + 1314 \, A^{2} B^{2} a^{2} b^{6} + 1053 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8}\right)} c^{3} - 35 \, {\left(B^{4} a^{3} b^{6} + 9 \, A B^{3} a^{2} b^{7} + 27 \, A^{2} B^{2} a b^{8} + 27 \, A^{3} B b^{9}\right)} c^{2}\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{2} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{11} + 9 \, A B^{2} a^{2} b^{12} + 27 \, A^{2} B a b^{13} + 27 \, A^{3} b^{14} - 2370816 \, A^{3} a^{7} c^{7} + 2688 \, {\left(50 \, A B^{2} a^{8} + 384 \, A^{2} B a^{7} b + 1143 \, A^{3} a^{6} b^{2}\right)} c^{6} - 64 \, {\left(400 \, B^{3} a^{8} b + 4062 \, A B^{2} a^{7} b^{2} + 17541 \, A^{2} B a^{6} b^{3} + 26865 \, A^{3} a^{5} b^{4}\right)} c^{5} + 8 \, {\left(2728 \, B^{3} a^{7} b^{3} + 20520 \, A B^{2} a^{6} b^{4} + 62694 \, A^{2} B a^{5} b^{5} + 67797 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(976 \, B^{3} a^{6} b^{5} + 6744 \, A B^{2} a^{5} b^{6} + 16884 \, A^{2} B a^{4} b^{7} + 14985 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(940 \, B^{3} a^{5} b^{7} + 6591 \, A B^{2} a^{4} b^{8} + 15489 \, A^{2} B a^{3} b^{9} + 12528 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(53 \, B^{3} a^{4} b^{9} + 414 \, A B^{2} a^{3} b^{10} + 1053 \, A^{2} B a^{2} b^{11} + 864 \, A^{3} a b^{12}\right)} c - {\left(B a^{6} b^{14} + 3 \, A a^{5} b^{15} + 4096 \, {\left(10 \, B a^{13} - 33 \, A a^{12} b\right)} c^{7} - 2048 \, {\left(16 \, B a^{12} b^{2} - 99 \, A a^{11} b^{3}\right)} c^{6} + 768 \, {\left(2 \, B a^{11} b^{4} - 169 \, A a^{10} b^{5}\right)} c^{5} + 1280 \, {\left(5 \, B a^{10} b^{6} + 36 \, A a^{9} b^{7}\right)} c^{4} - 80 \, {\left(34 \, B a^{9} b^{8} + 123 \, A a^{8} b^{9}\right)} c^{3} + 24 \, {\left(20 \, B a^{8} b^{10} + 53 \, A a^{7} b^{11}\right)} c^{2} - {\left(38 \, B a^{7} b^{12} + 93 \, A a^{6} b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} + {\left(3111696 \, A^{4} a^{4} c^{7} - 1555848 \, {\left(2 \, A^{3} B a^{4} b + A^{4} a^{3} b^{2}\right)} c^{6} - {\left(10000 \, B^{4} a^{6} - 90000 \, A B^{3} a^{5} b - 863136 \, A^{2} B^{2} a^{4} b^{2} - 1298376 \, A^{3} B a^{3} b^{3} - 339309 \, A^{4} a^{2} b^{4}\right)} c^{5} - 3 \, {\left(5000 \, B^{4} a^{5} b^{2} + 32952 \, A B^{3} a^{4} b^{3} + 79488 \, A^{2} B^{2} a^{3} b^{4} + 80919 \, A^{3} B a^{2} b^{5} + 12069 \, A^{4} a b^{6}\right)} c^{4} + 21 \, {\left(71 \, B^{4} a^{4} b^{4} + 537 \, A B^{3} a^{3} b^{5} + 1314 \, A^{2} B^{2} a^{2} b^{6} + 1053 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8}\right)} c^{3} - 35 \, {\left(B^{4} a^{3} b^{6} + 9 \, A B^{3} a^{2} b^{7} + 27 \, A^{2} B^{2} a b^{8} + 27 \, A^{3} B b^{9}\right)} c^{2}\right)} \sqrt{x}\right) + \sqrt{\frac{1}{2}} {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{2} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{11} + 9 \, A B^{2} a^{2} b^{12} + 27 \, A^{2} B a b^{13} + 27 \, A^{3} b^{14} - 2370816 \, A^{3} a^{7} c^{7} + 2688 \, {\left(50 \, A B^{2} a^{8} + 384 \, A^{2} B a^{7} b + 1143 \, A^{3} a^{6} b^{2}\right)} c^{6} - 64 \, {\left(400 \, B^{3} a^{8} b + 4062 \, A B^{2} a^{7} b^{2} + 17541 \, A^{2} B a^{6} b^{3} + 26865 \, A^{3} a^{5} b^{4}\right)} c^{5} + 8 \, {\left(2728 \, B^{3} a^{7} b^{3} + 20520 \, A B^{2} a^{6} b^{4} + 62694 \, A^{2} B a^{5} b^{5} + 67797 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(976 \, B^{3} a^{6} b^{5} + 6744 \, A B^{2} a^{5} b^{6} + 16884 \, A^{2} B a^{4} b^{7} + 14985 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(940 \, B^{3} a^{5} b^{7} + 6591 \, A B^{2} a^{4} b^{8} + 15489 \, A^{2} B a^{3} b^{9} + 12528 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(53 \, B^{3} a^{4} b^{9} + 414 \, A B^{2} a^{3} b^{10} + 1053 \, A^{2} B a^{2} b^{11} + 864 \, A^{3} a b^{12}\right)} c + {\left(B a^{6} b^{14} + 3 \, A a^{5} b^{15} + 4096 \, {\left(10 \, B a^{13} - 33 \, A a^{12} b\right)} c^{7} - 2048 \, {\left(16 \, B a^{12} b^{2} - 99 \, A a^{11} b^{3}\right)} c^{6} + 768 \, {\left(2 \, B a^{11} b^{4} - 169 \, A a^{10} b^{5}\right)} c^{5} + 1280 \, {\left(5 \, B a^{10} b^{6} + 36 \, A a^{9} b^{7}\right)} c^{4} - 80 \, {\left(34 \, B a^{9} b^{8} + 123 \, A a^{8} b^{9}\right)} c^{3} + 24 \, {\left(20 \, B a^{8} b^{10} + 53 \, A a^{7} b^{11}\right)} c^{2} - {\left(38 \, B a^{7} b^{12} + 93 \, A a^{6} b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} + {\left(3111696 \, A^{4} a^{4} c^{7} - 1555848 \, {\left(2 \, A^{3} B a^{4} b + A^{4} a^{3} b^{2}\right)} c^{6} - {\left(10000 \, B^{4} a^{6} - 90000 \, A B^{3} a^{5} b - 863136 \, A^{2} B^{2} a^{4} b^{2} - 1298376 \, A^{3} B a^{3} b^{3} - 339309 \, A^{4} a^{2} b^{4}\right)} c^{5} - 3 \, {\left(5000 \, B^{4} a^{5} b^{2} + 32952 \, A B^{3} a^{4} b^{3} + 79488 \, A^{2} B^{2} a^{3} b^{4} + 80919 \, A^{3} B a^{2} b^{5} + 12069 \, A^{4} a b^{6}\right)} c^{4} + 21 \, {\left(71 \, B^{4} a^{4} b^{4} + 537 \, A B^{3} a^{3} b^{5} + 1314 \, A^{2} B^{2} a^{2} b^{6} + 1053 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8}\right)} c^{3} - 35 \, {\left(B^{4} a^{3} b^{6} + 9 \, A B^{3} a^{2} b^{7} + 27 \, A^{2} B^{2} a b^{8} + 27 \, A^{3} B b^{9}\right)} c^{2}\right)} \sqrt{x}\right) - \sqrt{\frac{1}{2}} {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{2} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{11} + 9 \, A B^{2} a^{2} b^{12} + 27 \, A^{2} B a b^{13} + 27 \, A^{3} b^{14} - 2370816 \, A^{3} a^{7} c^{7} + 2688 \, {\left(50 \, A B^{2} a^{8} + 384 \, A^{2} B a^{7} b + 1143 \, A^{3} a^{6} b^{2}\right)} c^{6} - 64 \, {\left(400 \, B^{3} a^{8} b + 4062 \, A B^{2} a^{7} b^{2} + 17541 \, A^{2} B a^{6} b^{3} + 26865 \, A^{3} a^{5} b^{4}\right)} c^{5} + 8 \, {\left(2728 \, B^{3} a^{7} b^{3} + 20520 \, A B^{2} a^{6} b^{4} + 62694 \, A^{2} B a^{5} b^{5} + 67797 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(976 \, B^{3} a^{6} b^{5} + 6744 \, A B^{2} a^{5} b^{6} + 16884 \, A^{2} B a^{4} b^{7} + 14985 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(940 \, B^{3} a^{5} b^{7} + 6591 \, A B^{2} a^{4} b^{8} + 15489 \, A^{2} B a^{3} b^{9} + 12528 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(53 \, B^{3} a^{4} b^{9} + 414 \, A B^{2} a^{3} b^{10} + 1053 \, A^{2} B a^{2} b^{11} + 864 \, A^{3} a b^{12}\right)} c + {\left(B a^{6} b^{14} + 3 \, A a^{5} b^{15} + 4096 \, {\left(10 \, B a^{13} - 33 \, A a^{12} b\right)} c^{7} - 2048 \, {\left(16 \, B a^{12} b^{2} - 99 \, A a^{11} b^{3}\right)} c^{6} + 768 \, {\left(2 \, B a^{11} b^{4} - 169 \, A a^{10} b^{5}\right)} c^{5} + 1280 \, {\left(5 \, B a^{10} b^{6} + 36 \, A a^{9} b^{7}\right)} c^{4} - 80 \, {\left(34 \, B a^{9} b^{8} + 123 \, A a^{8} b^{9}\right)} c^{3} + 24 \, {\left(20 \, B a^{8} b^{10} + 53 \, A a^{7} b^{11}\right)} c^{2} - {\left(38 \, B a^{7} b^{12} + 93 \, A a^{6} b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} + {\left(3111696 \, A^{4} a^{4} c^{7} - 1555848 \, {\left(2 \, A^{3} B a^{4} b + A^{4} a^{3} b^{2}\right)} c^{6} - {\left(10000 \, B^{4} a^{6} - 90000 \, A B^{3} a^{5} b - 863136 \, A^{2} B^{2} a^{4} b^{2} - 1298376 \, A^{3} B a^{3} b^{3} - 339309 \, A^{4} a^{2} b^{4}\right)} c^{5} - 3 \, {\left(5000 \, B^{4} a^{5} b^{2} + 32952 \, A B^{3} a^{4} b^{3} + 79488 \, A^{2} B^{2} a^{3} b^{4} + 80919 \, A^{3} B a^{2} b^{5} + 12069 \, A^{4} a b^{6}\right)} c^{4} + 21 \, {\left(71 \, B^{4} a^{4} b^{4} + 537 \, A B^{3} a^{3} b^{5} + 1314 \, A^{2} B^{2} a^{2} b^{6} + 1053 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8}\right)} c^{3} - 35 \, {\left(B^{4} a^{3} b^{6} + 9 \, A B^{3} a^{2} b^{7} + 27 \, A^{2} B^{2} a b^{8} + 27 \, A^{3} B b^{9}\right)} c^{2}\right)} \sqrt{x}\right) + 2 \, {\left(B a^{2} b^{3} - 5 \, A a b^{4} - 44 \, A a^{3} c^{2} - {\left(4 \, {\left(5 \, B a^{2} - 6 \, A a b\right)} c^{3} + {\left(B a b^{2} + 3 \, A b^{3}\right)} c^{2}\right)} x^{3} - {\left(28 \, A a^{2} c^{3} + 7 \, {\left(4 \, B a^{2} b - 7 \, A a b^{2}\right)} c^{2} + 2 \, {\left(B a b^{3} + 3 \, A b^{4}\right)} c\right)} x^{2} - {\left(16 \, B a^{3} b - 37 \, A a^{2} b^{2}\right)} c - {\left(B a b^{4} + 3 \, A b^{5} + 4 \, {\left(9 \, B a^{3} - A a^{2} b\right)} c^{2} + 5 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} c\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{2} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x\right)}}"," ",0,"-1/8*(sqrt(1/2)*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + (a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^4 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^2 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x)*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log(1/2*sqrt(1/2)*(B^3*a^3*b^11 + 9*A*B^2*a^2*b^12 + 27*A^2*B*a*b^13 + 27*A^3*b^14 - 2370816*A^3*a^7*c^7 + 2688*(50*A*B^2*a^8 + 384*A^2*B*a^7*b + 1143*A^3*a^6*b^2)*c^6 - 64*(400*B^3*a^8*b + 4062*A*B^2*a^7*b^2 + 17541*A^2*B*a^6*b^3 + 26865*A^3*a^5*b^4)*c^5 + 8*(2728*B^3*a^7*b^3 + 20520*A*B^2*a^6*b^4 + 62694*A^2*B*a^5*b^5 + 67797*A^3*a^4*b^6)*c^4 - 7*(976*B^3*a^6*b^5 + 6744*A*B^2*a^5*b^6 + 16884*A^2*B*a^4*b^7 + 14985*A^3*a^3*b^8)*c^3 + (940*B^3*a^5*b^7 + 6591*A*B^2*a^4*b^8 + 15489*A^2*B*a^3*b^9 + 12528*A^3*a^2*b^10)*c^2 - (53*B^3*a^4*b^9 + 414*A*B^2*a^3*b^10 + 1053*A^2*B*a^2*b^11 + 864*A^3*a*b^12)*c - (B*a^6*b^14 + 3*A*a^5*b^15 + 4096*(10*B*a^13 - 33*A*a^12*b)*c^7 - 2048*(16*B*a^12*b^2 - 99*A*a^11*b^3)*c^6 + 768*(2*B*a^11*b^4 - 169*A*a^10*b^5)*c^5 + 1280*(5*B*a^10*b^6 + 36*A*a^9*b^7)*c^4 - 80*(34*B*a^9*b^8 + 123*A*a^8*b^9)*c^3 + 24*(20*B*a^8*b^10 + 53*A*a^7*b^11)*c^2 - (38*B*a^7*b^12 + 93*A*a^6*b^13)*c)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)) + (3111696*A^4*a^4*c^7 - 1555848*(2*A^3*B*a^4*b + A^4*a^3*b^2)*c^6 - (10000*B^4*a^6 - 90000*A*B^3*a^5*b - 863136*A^2*B^2*a^4*b^2 - 1298376*A^3*B*a^3*b^3 - 339309*A^4*a^2*b^4)*c^5 - 3*(5000*B^4*a^5*b^2 + 32952*A*B^3*a^4*b^3 + 79488*A^2*B^2*a^3*b^4 + 80919*A^3*B*a^2*b^5 + 12069*A^4*a*b^6)*c^4 + 21*(71*B^4*a^4*b^4 + 537*A*B^3*a^3*b^5 + 1314*A^2*B^2*a^2*b^6 + 1053*A^3*B*a*b^7 + 81*A^4*b^8)*c^3 - 35*(B^4*a^3*b^6 + 9*A*B^3*a^2*b^7 + 27*A^2*B^2*a*b^8 + 27*A^3*B*b^9)*c^2)*sqrt(x)) - sqrt(1/2)*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + (a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^4 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^2 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x)*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log(-1/2*sqrt(1/2)*(B^3*a^3*b^11 + 9*A*B^2*a^2*b^12 + 27*A^2*B*a*b^13 + 27*A^3*b^14 - 2370816*A^3*a^7*c^7 + 2688*(50*A*B^2*a^8 + 384*A^2*B*a^7*b + 1143*A^3*a^6*b^2)*c^6 - 64*(400*B^3*a^8*b + 4062*A*B^2*a^7*b^2 + 17541*A^2*B*a^6*b^3 + 26865*A^3*a^5*b^4)*c^5 + 8*(2728*B^3*a^7*b^3 + 20520*A*B^2*a^6*b^4 + 62694*A^2*B*a^5*b^5 + 67797*A^3*a^4*b^6)*c^4 - 7*(976*B^3*a^6*b^5 + 6744*A*B^2*a^5*b^6 + 16884*A^2*B*a^4*b^7 + 14985*A^3*a^3*b^8)*c^3 + (940*B^3*a^5*b^7 + 6591*A*B^2*a^4*b^8 + 15489*A^2*B*a^3*b^9 + 12528*A^3*a^2*b^10)*c^2 - (53*B^3*a^4*b^9 + 414*A*B^2*a^3*b^10 + 1053*A^2*B*a^2*b^11 + 864*A^3*a*b^12)*c - (B*a^6*b^14 + 3*A*a^5*b^15 + 4096*(10*B*a^13 - 33*A*a^12*b)*c^7 - 2048*(16*B*a^12*b^2 - 99*A*a^11*b^3)*c^6 + 768*(2*B*a^11*b^4 - 169*A*a^10*b^5)*c^5 + 1280*(5*B*a^10*b^6 + 36*A*a^9*b^7)*c^4 - 80*(34*B*a^9*b^8 + 123*A*a^8*b^9)*c^3 + 24*(20*B*a^8*b^10 + 53*A*a^7*b^11)*c^2 - (38*B*a^7*b^12 + 93*A*a^6*b^13)*c)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)) + (3111696*A^4*a^4*c^7 - 1555848*(2*A^3*B*a^4*b + A^4*a^3*b^2)*c^6 - (10000*B^4*a^6 - 90000*A*B^3*a^5*b - 863136*A^2*B^2*a^4*b^2 - 1298376*A^3*B*a^3*b^3 - 339309*A^4*a^2*b^4)*c^5 - 3*(5000*B^4*a^5*b^2 + 32952*A*B^3*a^4*b^3 + 79488*A^2*B^2*a^3*b^4 + 80919*A^3*B*a^2*b^5 + 12069*A^4*a*b^6)*c^4 + 21*(71*B^4*a^4*b^4 + 537*A*B^3*a^3*b^5 + 1314*A^2*B^2*a^2*b^6 + 1053*A^3*B*a*b^7 + 81*A^4*b^8)*c^3 - 35*(B^4*a^3*b^6 + 9*A*B^3*a^2*b^7 + 27*A^2*B^2*a*b^8 + 27*A^3*B*b^9)*c^2)*sqrt(x)) + sqrt(1/2)*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + (a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^4 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^2 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x)*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log(1/2*sqrt(1/2)*(B^3*a^3*b^11 + 9*A*B^2*a^2*b^12 + 27*A^2*B*a*b^13 + 27*A^3*b^14 - 2370816*A^3*a^7*c^7 + 2688*(50*A*B^2*a^8 + 384*A^2*B*a^7*b + 1143*A^3*a^6*b^2)*c^6 - 64*(400*B^3*a^8*b + 4062*A*B^2*a^7*b^2 + 17541*A^2*B*a^6*b^3 + 26865*A^3*a^5*b^4)*c^5 + 8*(2728*B^3*a^7*b^3 + 20520*A*B^2*a^6*b^4 + 62694*A^2*B*a^5*b^5 + 67797*A^3*a^4*b^6)*c^4 - 7*(976*B^3*a^6*b^5 + 6744*A*B^2*a^5*b^6 + 16884*A^2*B*a^4*b^7 + 14985*A^3*a^3*b^8)*c^3 + (940*B^3*a^5*b^7 + 6591*A*B^2*a^4*b^8 + 15489*A^2*B*a^3*b^9 + 12528*A^3*a^2*b^10)*c^2 - (53*B^3*a^4*b^9 + 414*A*B^2*a^3*b^10 + 1053*A^2*B*a^2*b^11 + 864*A^3*a*b^12)*c + (B*a^6*b^14 + 3*A*a^5*b^15 + 4096*(10*B*a^13 - 33*A*a^12*b)*c^7 - 2048*(16*B*a^12*b^2 - 99*A*a^11*b^3)*c^6 + 768*(2*B*a^11*b^4 - 169*A*a^10*b^5)*c^5 + 1280*(5*B*a^10*b^6 + 36*A*a^9*b^7)*c^4 - 80*(34*B*a^9*b^8 + 123*A*a^8*b^9)*c^3 + 24*(20*B*a^8*b^10 + 53*A*a^7*b^11)*c^2 - (38*B*a^7*b^12 + 93*A*a^6*b^13)*c)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)) + (3111696*A^4*a^4*c^7 - 1555848*(2*A^3*B*a^4*b + A^4*a^3*b^2)*c^6 - (10000*B^4*a^6 - 90000*A*B^3*a^5*b - 863136*A^2*B^2*a^4*b^2 - 1298376*A^3*B*a^3*b^3 - 339309*A^4*a^2*b^4)*c^5 - 3*(5000*B^4*a^5*b^2 + 32952*A*B^3*a^4*b^3 + 79488*A^2*B^2*a^3*b^4 + 80919*A^3*B*a^2*b^5 + 12069*A^4*a*b^6)*c^4 + 21*(71*B^4*a^4*b^4 + 537*A*B^3*a^3*b^5 + 1314*A^2*B^2*a^2*b^6 + 1053*A^3*B*a*b^7 + 81*A^4*b^8)*c^3 - 35*(B^4*a^3*b^6 + 9*A*B^3*a^2*b^7 + 27*A^2*B^2*a*b^8 + 27*A^3*B*b^9)*c^2)*sqrt(x)) - sqrt(1/2)*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + (a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^4 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^2 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x)*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log(-1/2*sqrt(1/2)*(B^3*a^3*b^11 + 9*A*B^2*a^2*b^12 + 27*A^2*B*a*b^13 + 27*A^3*b^14 - 2370816*A^3*a^7*c^7 + 2688*(50*A*B^2*a^8 + 384*A^2*B*a^7*b + 1143*A^3*a^6*b^2)*c^6 - 64*(400*B^3*a^8*b + 4062*A*B^2*a^7*b^2 + 17541*A^2*B*a^6*b^3 + 26865*A^3*a^5*b^4)*c^5 + 8*(2728*B^3*a^7*b^3 + 20520*A*B^2*a^6*b^4 + 62694*A^2*B*a^5*b^5 + 67797*A^3*a^4*b^6)*c^4 - 7*(976*B^3*a^6*b^5 + 6744*A*B^2*a^5*b^6 + 16884*A^2*B*a^4*b^7 + 14985*A^3*a^3*b^8)*c^3 + (940*B^3*a^5*b^7 + 6591*A*B^2*a^4*b^8 + 15489*A^2*B*a^3*b^9 + 12528*A^3*a^2*b^10)*c^2 - (53*B^3*a^4*b^9 + 414*A*B^2*a^3*b^10 + 1053*A^2*B*a^2*b^11 + 864*A^3*a*b^12)*c + (B*a^6*b^14 + 3*A*a^5*b^15 + 4096*(10*B*a^13 - 33*A*a^12*b)*c^7 - 2048*(16*B*a^12*b^2 - 99*A*a^11*b^3)*c^6 + 768*(2*B*a^11*b^4 - 169*A*a^10*b^5)*c^5 + 1280*(5*B*a^10*b^6 + 36*A*a^9*b^7)*c^4 - 80*(34*B*a^9*b^8 + 123*A*a^8*b^9)*c^3 + 24*(20*B*a^8*b^10 + 53*A*a^7*b^11)*c^2 - (38*B*a^7*b^12 + 93*A*a^6*b^13)*c)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)) + (3111696*A^4*a^4*c^7 - 1555848*(2*A^3*B*a^4*b + A^4*a^3*b^2)*c^6 - (10000*B^4*a^6 - 90000*A*B^3*a^5*b - 863136*A^2*B^2*a^4*b^2 - 1298376*A^3*B*a^3*b^3 - 339309*A^4*a^2*b^4)*c^5 - 3*(5000*B^4*a^5*b^2 + 32952*A*B^3*a^4*b^3 + 79488*A^2*B^2*a^3*b^4 + 80919*A^3*B*a^2*b^5 + 12069*A^4*a*b^6)*c^4 + 21*(71*B^4*a^4*b^4 + 537*A*B^3*a^3*b^5 + 1314*A^2*B^2*a^2*b^6 + 1053*A^3*B*a*b^7 + 81*A^4*b^8)*c^3 - 35*(B^4*a^3*b^6 + 9*A*B^3*a^2*b^7 + 27*A^2*B^2*a*b^8 + 27*A^3*B*b^9)*c^2)*sqrt(x)) + 2*(B*a^2*b^3 - 5*A*a*b^4 - 44*A*a^3*c^2 - (4*(5*B*a^2 - 6*A*a*b)*c^3 + (B*a*b^2 + 3*A*b^3)*c^2)*x^3 - (28*A*a^2*c^3 + 7*(4*B*a^2*b - 7*A*a*b^2)*c^2 + 2*(B*a*b^3 + 3*A*b^4)*c)*x^2 - (16*B*a^3*b - 37*A*a^2*b^2)*c - (B*a*b^4 + 3*A*b^5 + 4*(9*B*a^3 - A*a^2*b)*c^2 + 5*(B*a^2*b^2 - 4*A*a*b^3)*c)*x)*sqrt(x))/(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + (a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^4 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^2 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x)","B",0
1028,1,12534,0,71.077613," ","integrate((B*x+A)/x^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{9} - 10 \, A B a b^{10} + 25 \, A^{2} b^{11} + 1680 \, {\left(4 \, A B a^{6} - 11 \, A^{2} a^{5} b\right)} c^{5} + 840 \, {\left(2 \, B^{2} a^{6} b - 16 \, A B a^{5} b^{2} + 33 \, A^{2} a^{4} b^{3}\right)} c^{4} - 105 \, {\left(8 \, B^{2} a^{5} b^{3} - 68 \, A B a^{4} b^{4} + 143 \, A^{2} a^{3} b^{5}\right)} c^{3} + 3 \, {\left(63 \, B^{2} a^{4} b^{5} - 574 \, A B a^{3} b^{6} + 1298 \, A^{2} a^{2} b^{7}\right)} c^{2} - 3 \, {\left(7 \, B^{2} a^{3} b^{7} - 68 \, A B a^{2} b^{8} + 165 \, A^{2} a b^{9}\right)} c + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{14} - 15 \, A B^{2} a^{2} b^{15} + 75 \, A^{2} B a b^{16} - 125 \, A^{3} b^{17} + 57600 \, {\left(7 \, A^{2} B a^{9} - 23 \, A^{3} a^{8} b\right)} c^{8} - 64 \, {\left(1372 \, B^{3} a^{10} - 15204 \, A B^{2} a^{9} b + 61326 \, A^{2} B a^{8} b^{2} - 88823 \, A^{3} a^{7} b^{3}\right)} c^{7} + 16 \, {\left(7112 \, B^{3} a^{9} b^{2} - 83292 \, A B^{2} a^{8} b^{3} + 330300 \, A^{2} B a^{7} b^{4} - 446671 \, A^{3} a^{6} b^{5}\right)} c^{6} - 4 \, {\left(15920 \, B^{3} a^{8} b^{4} - 197004 \, A B^{2} a^{7} b^{5} + 811446 \, A^{2} B a^{6} b^{6} - 1115785 \, A^{3} a^{5} b^{7}\right)} c^{5} + 3 \, {\left(6696 \, B^{3} a^{7} b^{6} - 87308 \, A B^{2} a^{6} b^{7} + 377471 \, A^{2} B a^{5} b^{8} - 541178 \, A^{3} a^{4} b^{9}\right)} c^{4} - 3 \, {\left(1295 \, B^{3} a^{6} b^{8} - 17704 \, A B^{2} a^{5} b^{9} + 80329 \, A^{2} B a^{4} b^{10} - 120911 \, A^{3} a^{3} b^{11}\right)} c^{3} + {\left(464 \, B^{3} a^{5} b^{10} - 6609 \, A B^{2} a^{4} b^{11} + 31317 \, A^{2} B a^{3} b^{12} - 49360 \, A^{3} a^{2} b^{13}\right)} c^{2} - {\left(32 \, B^{3} a^{4} b^{12} - 471 \, A B^{2} a^{3} b^{13} + 2310 \, A^{2} B a^{2} b^{14} - 3775 \, A^{3} a b^{15}\right)} c - {\left(B a^{8} b^{15} - 5 \, A a^{7} b^{16} - 122880 \, A a^{15} c^{8} - 4096 \, {\left(11 \, B a^{15} b - 79 \, A a^{14} b^{2}\right)} c^{7} + 1536 \, {\left(44 \, B a^{14} b^{3} - 223 \, A a^{13} b^{4}\right)} c^{6} - 256 \, {\left(169 \, B a^{13} b^{5} - 770 \, A a^{12} b^{6}\right)} c^{5} + 480 \, {\left(32 \, B a^{12} b^{7} - 143 \, A a^{11} b^{8}\right)} c^{4} - 80 \, {\left(41 \, B a^{11} b^{9} - 187 \, A a^{10} b^{10}\right)} c^{3} + 2 \, {\left(212 \, B a^{10} b^{11} - 1003 \, A a^{9} b^{12}\right)} c^{2} - {\left(31 \, B a^{9} b^{13} - 152 \, A a^{8} b^{14}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{9} - 10 \, A B a b^{10} + 25 \, A^{2} b^{11} + 1680 \, {\left(4 \, A B a^{6} - 11 \, A^{2} a^{5} b\right)} c^{5} + 840 \, {\left(2 \, B^{2} a^{6} b - 16 \, A B a^{5} b^{2} + 33 \, A^{2} a^{4} b^{3}\right)} c^{4} - 105 \, {\left(8 \, B^{2} a^{5} b^{3} - 68 \, A B a^{4} b^{4} + 143 \, A^{2} a^{3} b^{5}\right)} c^{3} + 3 \, {\left(63 \, B^{2} a^{4} b^{5} - 574 \, A B a^{3} b^{6} + 1298 \, A^{2} a^{2} b^{7}\right)} c^{2} - 3 \, {\left(7 \, B^{2} a^{3} b^{7} - 68 \, A B a^{2} b^{8} + 165 \, A^{2} a b^{9}\right)} c + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} + 27 \, {\left(810000 \, A^{4} a^{5} c^{9} + 405000 \, {\left(2 \, A^{3} B a^{5} b - 7 \, A^{4} a^{4} b^{2}\right)} c^{8} - {\left(38416 \, B^{4} a^{7} - 422576 \, A B^{3} a^{6} b + 1439376 \, A^{2} B^{2} a^{5} b^{2} - 1018856 \, A^{3} B a^{4} b^{3} - 1957349 \, A^{4} a^{3} b^{4}\right)} c^{7} + {\left(19208 \, B^{4} a^{6} b^{2} - 239896 \, A B^{3} a^{5} b^{3} + 955704 \, A^{2} B^{2} a^{4} b^{4} - 1067347 \, A^{3} B a^{3} b^{5} - 571030 \, A^{4} a^{2} b^{6}\right)} c^{6} - {\left(4189 \, B^{4} a^{5} b^{4} - 56807 \, A B^{3} a^{4} b^{5} + 251349 \, A^{2} B^{2} a^{3} b^{6} - 344630 \, A^{3} B a^{2} b^{7} - 77825 \, A^{4} a b^{8}\right)} c^{5} + 3 \, {\left(149 \, B^{4} a^{4} b^{6} - 2161 \, A B^{3} a^{3} b^{7} + 10380 \, A^{2} B^{2} a^{2} b^{8} - 16225 \, A^{3} B a b^{9} - 1375 \, A^{4} b^{10}\right)} c^{4} - 21 \, {\left(B^{4} a^{3} b^{8} - 15 \, A B^{3} a^{2} b^{9} + 75 \, A^{2} B^{2} a b^{10} - 125 \, A^{3} B b^{11}\right)} c^{3}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{9} - 10 \, A B a b^{10} + 25 \, A^{2} b^{11} + 1680 \, {\left(4 \, A B a^{6} - 11 \, A^{2} a^{5} b\right)} c^{5} + 840 \, {\left(2 \, B^{2} a^{6} b - 16 \, A B a^{5} b^{2} + 33 \, A^{2} a^{4} b^{3}\right)} c^{4} - 105 \, {\left(8 \, B^{2} a^{5} b^{3} - 68 \, A B a^{4} b^{4} + 143 \, A^{2} a^{3} b^{5}\right)} c^{3} + 3 \, {\left(63 \, B^{2} a^{4} b^{5} - 574 \, A B a^{3} b^{6} + 1298 \, A^{2} a^{2} b^{7}\right)} c^{2} - 3 \, {\left(7 \, B^{2} a^{3} b^{7} - 68 \, A B a^{2} b^{8} + 165 \, A^{2} a b^{9}\right)} c + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{14} - 15 \, A B^{2} a^{2} b^{15} + 75 \, A^{2} B a b^{16} - 125 \, A^{3} b^{17} + 57600 \, {\left(7 \, A^{2} B a^{9} - 23 \, A^{3} a^{8} b\right)} c^{8} - 64 \, {\left(1372 \, B^{3} a^{10} - 15204 \, A B^{2} a^{9} b + 61326 \, A^{2} B a^{8} b^{2} - 88823 \, A^{3} a^{7} b^{3}\right)} c^{7} + 16 \, {\left(7112 \, B^{3} a^{9} b^{2} - 83292 \, A B^{2} a^{8} b^{3} + 330300 \, A^{2} B a^{7} b^{4} - 446671 \, A^{3} a^{6} b^{5}\right)} c^{6} - 4 \, {\left(15920 \, B^{3} a^{8} b^{4} - 197004 \, A B^{2} a^{7} b^{5} + 811446 \, A^{2} B a^{6} b^{6} - 1115785 \, A^{3} a^{5} b^{7}\right)} c^{5} + 3 \, {\left(6696 \, B^{3} a^{7} b^{6} - 87308 \, A B^{2} a^{6} b^{7} + 377471 \, A^{2} B a^{5} b^{8} - 541178 \, A^{3} a^{4} b^{9}\right)} c^{4} - 3 \, {\left(1295 \, B^{3} a^{6} b^{8} - 17704 \, A B^{2} a^{5} b^{9} + 80329 \, A^{2} B a^{4} b^{10} - 120911 \, A^{3} a^{3} b^{11}\right)} c^{3} + {\left(464 \, B^{3} a^{5} b^{10} - 6609 \, A B^{2} a^{4} b^{11} + 31317 \, A^{2} B a^{3} b^{12} - 49360 \, A^{3} a^{2} b^{13}\right)} c^{2} - {\left(32 \, B^{3} a^{4} b^{12} - 471 \, A B^{2} a^{3} b^{13} + 2310 \, A^{2} B a^{2} b^{14} - 3775 \, A^{3} a b^{15}\right)} c - {\left(B a^{8} b^{15} - 5 \, A a^{7} b^{16} - 122880 \, A a^{15} c^{8} - 4096 \, {\left(11 \, B a^{15} b - 79 \, A a^{14} b^{2}\right)} c^{7} + 1536 \, {\left(44 \, B a^{14} b^{3} - 223 \, A a^{13} b^{4}\right)} c^{6} - 256 \, {\left(169 \, B a^{13} b^{5} - 770 \, A a^{12} b^{6}\right)} c^{5} + 480 \, {\left(32 \, B a^{12} b^{7} - 143 \, A a^{11} b^{8}\right)} c^{4} - 80 \, {\left(41 \, B a^{11} b^{9} - 187 \, A a^{10} b^{10}\right)} c^{3} + 2 \, {\left(212 \, B a^{10} b^{11} - 1003 \, A a^{9} b^{12}\right)} c^{2} - {\left(31 \, B a^{9} b^{13} - 152 \, A a^{8} b^{14}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{9} - 10 \, A B a b^{10} + 25 \, A^{2} b^{11} + 1680 \, {\left(4 \, A B a^{6} - 11 \, A^{2} a^{5} b\right)} c^{5} + 840 \, {\left(2 \, B^{2} a^{6} b - 16 \, A B a^{5} b^{2} + 33 \, A^{2} a^{4} b^{3}\right)} c^{4} - 105 \, {\left(8 \, B^{2} a^{5} b^{3} - 68 \, A B a^{4} b^{4} + 143 \, A^{2} a^{3} b^{5}\right)} c^{3} + 3 \, {\left(63 \, B^{2} a^{4} b^{5} - 574 \, A B a^{3} b^{6} + 1298 \, A^{2} a^{2} b^{7}\right)} c^{2} - 3 \, {\left(7 \, B^{2} a^{3} b^{7} - 68 \, A B a^{2} b^{8} + 165 \, A^{2} a b^{9}\right)} c + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} + 27 \, {\left(810000 \, A^{4} a^{5} c^{9} + 405000 \, {\left(2 \, A^{3} B a^{5} b - 7 \, A^{4} a^{4} b^{2}\right)} c^{8} - {\left(38416 \, B^{4} a^{7} - 422576 \, A B^{3} a^{6} b + 1439376 \, A^{2} B^{2} a^{5} b^{2} - 1018856 \, A^{3} B a^{4} b^{3} - 1957349 \, A^{4} a^{3} b^{4}\right)} c^{7} + {\left(19208 \, B^{4} a^{6} b^{2} - 239896 \, A B^{3} a^{5} b^{3} + 955704 \, A^{2} B^{2} a^{4} b^{4} - 1067347 \, A^{3} B a^{3} b^{5} - 571030 \, A^{4} a^{2} b^{6}\right)} c^{6} - {\left(4189 \, B^{4} a^{5} b^{4} - 56807 \, A B^{3} a^{4} b^{5} + 251349 \, A^{2} B^{2} a^{3} b^{6} - 344630 \, A^{3} B a^{2} b^{7} - 77825 \, A^{4} a b^{8}\right)} c^{5} + 3 \, {\left(149 \, B^{4} a^{4} b^{6} - 2161 \, A B^{3} a^{3} b^{7} + 10380 \, A^{2} B^{2} a^{2} b^{8} - 16225 \, A^{3} B a b^{9} - 1375 \, A^{4} b^{10}\right)} c^{4} - 21 \, {\left(B^{4} a^{3} b^{8} - 15 \, A B^{3} a^{2} b^{9} + 75 \, A^{2} B^{2} a b^{10} - 125 \, A^{3} B b^{11}\right)} c^{3}\right)} \sqrt{x}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{9} - 10 \, A B a b^{10} + 25 \, A^{2} b^{11} + 1680 \, {\left(4 \, A B a^{6} - 11 \, A^{2} a^{5} b\right)} c^{5} + 840 \, {\left(2 \, B^{2} a^{6} b - 16 \, A B a^{5} b^{2} + 33 \, A^{2} a^{4} b^{3}\right)} c^{4} - 105 \, {\left(8 \, B^{2} a^{5} b^{3} - 68 \, A B a^{4} b^{4} + 143 \, A^{2} a^{3} b^{5}\right)} c^{3} + 3 \, {\left(63 \, B^{2} a^{4} b^{5} - 574 \, A B a^{3} b^{6} + 1298 \, A^{2} a^{2} b^{7}\right)} c^{2} - 3 \, {\left(7 \, B^{2} a^{3} b^{7} - 68 \, A B a^{2} b^{8} + 165 \, A^{2} a b^{9}\right)} c - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{14} - 15 \, A B^{2} a^{2} b^{15} + 75 \, A^{2} B a b^{16} - 125 \, A^{3} b^{17} + 57600 \, {\left(7 \, A^{2} B a^{9} - 23 \, A^{3} a^{8} b\right)} c^{8} - 64 \, {\left(1372 \, B^{3} a^{10} - 15204 \, A B^{2} a^{9} b + 61326 \, A^{2} B a^{8} b^{2} - 88823 \, A^{3} a^{7} b^{3}\right)} c^{7} + 16 \, {\left(7112 \, B^{3} a^{9} b^{2} - 83292 \, A B^{2} a^{8} b^{3} + 330300 \, A^{2} B a^{7} b^{4} - 446671 \, A^{3} a^{6} b^{5}\right)} c^{6} - 4 \, {\left(15920 \, B^{3} a^{8} b^{4} - 197004 \, A B^{2} a^{7} b^{5} + 811446 \, A^{2} B a^{6} b^{6} - 1115785 \, A^{3} a^{5} b^{7}\right)} c^{5} + 3 \, {\left(6696 \, B^{3} a^{7} b^{6} - 87308 \, A B^{2} a^{6} b^{7} + 377471 \, A^{2} B a^{5} b^{8} - 541178 \, A^{3} a^{4} b^{9}\right)} c^{4} - 3 \, {\left(1295 \, B^{3} a^{6} b^{8} - 17704 \, A B^{2} a^{5} b^{9} + 80329 \, A^{2} B a^{4} b^{10} - 120911 \, A^{3} a^{3} b^{11}\right)} c^{3} + {\left(464 \, B^{3} a^{5} b^{10} - 6609 \, A B^{2} a^{4} b^{11} + 31317 \, A^{2} B a^{3} b^{12} - 49360 \, A^{3} a^{2} b^{13}\right)} c^{2} - {\left(32 \, B^{3} a^{4} b^{12} - 471 \, A B^{2} a^{3} b^{13} + 2310 \, A^{2} B a^{2} b^{14} - 3775 \, A^{3} a b^{15}\right)} c + {\left(B a^{8} b^{15} - 5 \, A a^{7} b^{16} - 122880 \, A a^{15} c^{8} - 4096 \, {\left(11 \, B a^{15} b - 79 \, A a^{14} b^{2}\right)} c^{7} + 1536 \, {\left(44 \, B a^{14} b^{3} - 223 \, A a^{13} b^{4}\right)} c^{6} - 256 \, {\left(169 \, B a^{13} b^{5} - 770 \, A a^{12} b^{6}\right)} c^{5} + 480 \, {\left(32 \, B a^{12} b^{7} - 143 \, A a^{11} b^{8}\right)} c^{4} - 80 \, {\left(41 \, B a^{11} b^{9} - 187 \, A a^{10} b^{10}\right)} c^{3} + 2 \, {\left(212 \, B a^{10} b^{11} - 1003 \, A a^{9} b^{12}\right)} c^{2} - {\left(31 \, B a^{9} b^{13} - 152 \, A a^{8} b^{14}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{9} - 10 \, A B a b^{10} + 25 \, A^{2} b^{11} + 1680 \, {\left(4 \, A B a^{6} - 11 \, A^{2} a^{5} b\right)} c^{5} + 840 \, {\left(2 \, B^{2} a^{6} b - 16 \, A B a^{5} b^{2} + 33 \, A^{2} a^{4} b^{3}\right)} c^{4} - 105 \, {\left(8 \, B^{2} a^{5} b^{3} - 68 \, A B a^{4} b^{4} + 143 \, A^{2} a^{3} b^{5}\right)} c^{3} + 3 \, {\left(63 \, B^{2} a^{4} b^{5} - 574 \, A B a^{3} b^{6} + 1298 \, A^{2} a^{2} b^{7}\right)} c^{2} - 3 \, {\left(7 \, B^{2} a^{3} b^{7} - 68 \, A B a^{2} b^{8} + 165 \, A^{2} a b^{9}\right)} c - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} + 27 \, {\left(810000 \, A^{4} a^{5} c^{9} + 405000 \, {\left(2 \, A^{3} B a^{5} b - 7 \, A^{4} a^{4} b^{2}\right)} c^{8} - {\left(38416 \, B^{4} a^{7} - 422576 \, A B^{3} a^{6} b + 1439376 \, A^{2} B^{2} a^{5} b^{2} - 1018856 \, A^{3} B a^{4} b^{3} - 1957349 \, A^{4} a^{3} b^{4}\right)} c^{7} + {\left(19208 \, B^{4} a^{6} b^{2} - 239896 \, A B^{3} a^{5} b^{3} + 955704 \, A^{2} B^{2} a^{4} b^{4} - 1067347 \, A^{3} B a^{3} b^{5} - 571030 \, A^{4} a^{2} b^{6}\right)} c^{6} - {\left(4189 \, B^{4} a^{5} b^{4} - 56807 \, A B^{3} a^{4} b^{5} + 251349 \, A^{2} B^{2} a^{3} b^{6} - 344630 \, A^{3} B a^{2} b^{7} - 77825 \, A^{4} a b^{8}\right)} c^{5} + 3 \, {\left(149 \, B^{4} a^{4} b^{6} - 2161 \, A B^{3} a^{3} b^{7} + 10380 \, A^{2} B^{2} a^{2} b^{8} - 16225 \, A^{3} B a b^{9} - 1375 \, A^{4} b^{10}\right)} c^{4} - 21 \, {\left(B^{4} a^{3} b^{8} - 15 \, A B^{3} a^{2} b^{9} + 75 \, A^{2} B^{2} a b^{10} - 125 \, A^{3} B b^{11}\right)} c^{3}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{9} - 10 \, A B a b^{10} + 25 \, A^{2} b^{11} + 1680 \, {\left(4 \, A B a^{6} - 11 \, A^{2} a^{5} b\right)} c^{5} + 840 \, {\left(2 \, B^{2} a^{6} b - 16 \, A B a^{5} b^{2} + 33 \, A^{2} a^{4} b^{3}\right)} c^{4} - 105 \, {\left(8 \, B^{2} a^{5} b^{3} - 68 \, A B a^{4} b^{4} + 143 \, A^{2} a^{3} b^{5}\right)} c^{3} + 3 \, {\left(63 \, B^{2} a^{4} b^{5} - 574 \, A B a^{3} b^{6} + 1298 \, A^{2} a^{2} b^{7}\right)} c^{2} - 3 \, {\left(7 \, B^{2} a^{3} b^{7} - 68 \, A B a^{2} b^{8} + 165 \, A^{2} a b^{9}\right)} c - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{14} - 15 \, A B^{2} a^{2} b^{15} + 75 \, A^{2} B a b^{16} - 125 \, A^{3} b^{17} + 57600 \, {\left(7 \, A^{2} B a^{9} - 23 \, A^{3} a^{8} b\right)} c^{8} - 64 \, {\left(1372 \, B^{3} a^{10} - 15204 \, A B^{2} a^{9} b + 61326 \, A^{2} B a^{8} b^{2} - 88823 \, A^{3} a^{7} b^{3}\right)} c^{7} + 16 \, {\left(7112 \, B^{3} a^{9} b^{2} - 83292 \, A B^{2} a^{8} b^{3} + 330300 \, A^{2} B a^{7} b^{4} - 446671 \, A^{3} a^{6} b^{5}\right)} c^{6} - 4 \, {\left(15920 \, B^{3} a^{8} b^{4} - 197004 \, A B^{2} a^{7} b^{5} + 811446 \, A^{2} B a^{6} b^{6} - 1115785 \, A^{3} a^{5} b^{7}\right)} c^{5} + 3 \, {\left(6696 \, B^{3} a^{7} b^{6} - 87308 \, A B^{2} a^{6} b^{7} + 377471 \, A^{2} B a^{5} b^{8} - 541178 \, A^{3} a^{4} b^{9}\right)} c^{4} - 3 \, {\left(1295 \, B^{3} a^{6} b^{8} - 17704 \, A B^{2} a^{5} b^{9} + 80329 \, A^{2} B a^{4} b^{10} - 120911 \, A^{3} a^{3} b^{11}\right)} c^{3} + {\left(464 \, B^{3} a^{5} b^{10} - 6609 \, A B^{2} a^{4} b^{11} + 31317 \, A^{2} B a^{3} b^{12} - 49360 \, A^{3} a^{2} b^{13}\right)} c^{2} - {\left(32 \, B^{3} a^{4} b^{12} - 471 \, A B^{2} a^{3} b^{13} + 2310 \, A^{2} B a^{2} b^{14} - 3775 \, A^{3} a b^{15}\right)} c + {\left(B a^{8} b^{15} - 5 \, A a^{7} b^{16} - 122880 \, A a^{15} c^{8} - 4096 \, {\left(11 \, B a^{15} b - 79 \, A a^{14} b^{2}\right)} c^{7} + 1536 \, {\left(44 \, B a^{14} b^{3} - 223 \, A a^{13} b^{4}\right)} c^{6} - 256 \, {\left(169 \, B a^{13} b^{5} - 770 \, A a^{12} b^{6}\right)} c^{5} + 480 \, {\left(32 \, B a^{12} b^{7} - 143 \, A a^{11} b^{8}\right)} c^{4} - 80 \, {\left(41 \, B a^{11} b^{9} - 187 \, A a^{10} b^{10}\right)} c^{3} + 2 \, {\left(212 \, B a^{10} b^{11} - 1003 \, A a^{9} b^{12}\right)} c^{2} - {\left(31 \, B a^{9} b^{13} - 152 \, A a^{8} b^{14}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{9} - 10 \, A B a b^{10} + 25 \, A^{2} b^{11} + 1680 \, {\left(4 \, A B a^{6} - 11 \, A^{2} a^{5} b\right)} c^{5} + 840 \, {\left(2 \, B^{2} a^{6} b - 16 \, A B a^{5} b^{2} + 33 \, A^{2} a^{4} b^{3}\right)} c^{4} - 105 \, {\left(8 \, B^{2} a^{5} b^{3} - 68 \, A B a^{4} b^{4} + 143 \, A^{2} a^{3} b^{5}\right)} c^{3} + 3 \, {\left(63 \, B^{2} a^{4} b^{5} - 574 \, A B a^{3} b^{6} + 1298 \, A^{2} a^{2} b^{7}\right)} c^{2} - 3 \, {\left(7 \, B^{2} a^{3} b^{7} - 68 \, A B a^{2} b^{8} + 165 \, A^{2} a b^{9}\right)} c - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{8} - 20 \, A B^{3} a^{3} b^{9} + 150 \, A^{2} B^{2} a^{2} b^{10} - 500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 50625 \, A^{4} a^{6} c^{6} - 450 \, {\left(49 \, A^{2} B^{2} a^{7} - 382 \, A^{3} B a^{6} b + 694 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(2401 \, B^{4} a^{8} - 37436 \, A B^{3} a^{7} b + 218886 \, A^{2} B^{2} a^{6} b^{2} - 577016 \, A^{3} B a^{5} b^{3} + 591886 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(539 \, B^{4} a^{7} b^{2} - 9298 \, A B^{3} a^{6} b^{3} + 59592 \, A^{2} B^{2} a^{5} b^{4} - 168016 \, A^{3} B a^{4} b^{5} + 175655 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(73 \, B^{4} a^{6} b^{4} - 1344 \, A B^{3} a^{5} b^{5} + 9228 \, A^{2} B^{2} a^{4} b^{6} - 27980 \, A^{3} B a^{3} b^{7} + 31575 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(11 \, B^{4} a^{5} b^{6} - 214 \, A B^{3} a^{4} b^{7} + 1560 \, A^{2} B^{2} a^{3} b^{8} - 5050 \, A^{3} B a^{2} b^{9} + 6125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} + 27 \, {\left(810000 \, A^{4} a^{5} c^{9} + 405000 \, {\left(2 \, A^{3} B a^{5} b - 7 \, A^{4} a^{4} b^{2}\right)} c^{8} - {\left(38416 \, B^{4} a^{7} - 422576 \, A B^{3} a^{6} b + 1439376 \, A^{2} B^{2} a^{5} b^{2} - 1018856 \, A^{3} B a^{4} b^{3} - 1957349 \, A^{4} a^{3} b^{4}\right)} c^{7} + {\left(19208 \, B^{4} a^{6} b^{2} - 239896 \, A B^{3} a^{5} b^{3} + 955704 \, A^{2} B^{2} a^{4} b^{4} - 1067347 \, A^{3} B a^{3} b^{5} - 571030 \, A^{4} a^{2} b^{6}\right)} c^{6} - {\left(4189 \, B^{4} a^{5} b^{4} - 56807 \, A B^{3} a^{4} b^{5} + 251349 \, A^{2} B^{2} a^{3} b^{6} - 344630 \, A^{3} B a^{2} b^{7} - 77825 \, A^{4} a b^{8}\right)} c^{5} + 3 \, {\left(149 \, B^{4} a^{4} b^{6} - 2161 \, A B^{3} a^{3} b^{7} + 10380 \, A^{2} B^{2} a^{2} b^{8} - 16225 \, A^{3} B a b^{9} - 1375 \, A^{4} b^{10}\right)} c^{4} - 21 \, {\left(B^{4} a^{3} b^{8} - 15 \, A B^{3} a^{2} b^{9} + 75 \, A^{2} B^{2} a b^{10} - 125 \, A^{3} B b^{11}\right)} c^{3}\right)} \sqrt{x}\right) - 2 \, {\left(8 \, A a^{2} b^{4} - 64 \, A a^{3} b^{2} c + 128 \, A a^{4} c^{2} + 3 \, {\left(60 \, A a^{2} c^{4} + {\left(8 \, B a^{2} b - 37 \, A a b^{2}\right)} c^{3} - {\left(B a b^{3} - 5 \, A b^{4}\right)} c^{2}\right)} x^{4} - {\left(28 \, {\left(B a^{3} - 14 \, A a^{2} b\right)} c^{3} - {\left(49 \, B a^{2} b^{2} - 227 \, A a b^{3}\right)} c^{2} + 6 \, {\left(B a b^{4} - 5 \, A b^{5}\right)} c\right)} x^{3} - {\left(3 \, B a b^{5} - 15 \, A b^{6} - 324 \, A a^{3} c^{3} - {\left(4 \, B a^{3} b + 25 \, A a^{2} b^{2}\right)} c^{2} - {\left(20 \, B a^{2} b^{3} - 91 \, A a b^{4}\right)} c\right)} x^{2} - {\left(5 \, B a^{2} b^{4} - 25 \, A a b^{5} + 4 \, {\left(11 \, B a^{4} - 91 \, A a^{3} b\right)} c^{2} - {\left(37 \, B a^{3} b^{2} - 194 \, A a^{2} b^{3}\right)} c\right)} x\right)} \sqrt{x}}{8 \, {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)}}"," ",0,"1/8*(3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)*sqrt(-(B^2*a^2*b^9 - 10*A*B*a*b^10 + 25*A^2*b^11 + 1680*(4*A*B*a^6 - 11*A^2*a^5*b)*c^5 + 840*(2*B^2*a^6*b - 16*A*B*a^5*b^2 + 33*A^2*a^4*b^3)*c^4 - 105*(8*B^2*a^5*b^3 - 68*A*B*a^4*b^4 + 143*A^2*a^3*b^5)*c^3 + 3*(63*B^2*a^4*b^5 - 574*A*B*a^3*b^6 + 1298*A^2*a^2*b^7)*c^2 - 3*(7*B^2*a^3*b^7 - 68*A*B*a^2*b^8 + 165*A^2*a*b^9)*c + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(27/2*sqrt(1/2)*(B^3*a^3*b^14 - 15*A*B^2*a^2*b^15 + 75*A^2*B*a*b^16 - 125*A^3*b^17 + 57600*(7*A^2*B*a^9 - 23*A^3*a^8*b)*c^8 - 64*(1372*B^3*a^10 - 15204*A*B^2*a^9*b + 61326*A^2*B*a^8*b^2 - 88823*A^3*a^7*b^3)*c^7 + 16*(7112*B^3*a^9*b^2 - 83292*A*B^2*a^8*b^3 + 330300*A^2*B*a^7*b^4 - 446671*A^3*a^6*b^5)*c^6 - 4*(15920*B^3*a^8*b^4 - 197004*A*B^2*a^7*b^5 + 811446*A^2*B*a^6*b^6 - 1115785*A^3*a^5*b^7)*c^5 + 3*(6696*B^3*a^7*b^6 - 87308*A*B^2*a^6*b^7 + 377471*A^2*B*a^5*b^8 - 541178*A^3*a^4*b^9)*c^4 - 3*(1295*B^3*a^6*b^8 - 17704*A*B^2*a^5*b^9 + 80329*A^2*B*a^4*b^10 - 120911*A^3*a^3*b^11)*c^3 + (464*B^3*a^5*b^10 - 6609*A*B^2*a^4*b^11 + 31317*A^2*B*a^3*b^12 - 49360*A^3*a^2*b^13)*c^2 - (32*B^3*a^4*b^12 - 471*A*B^2*a^3*b^13 + 2310*A^2*B*a^2*b^14 - 3775*A^3*a*b^15)*c - (B*a^8*b^15 - 5*A*a^7*b^16 - 122880*A*a^15*c^8 - 4096*(11*B*a^15*b - 79*A*a^14*b^2)*c^7 + 1536*(44*B*a^14*b^3 - 223*A*a^13*b^4)*c^6 - 256*(169*B*a^13*b^5 - 770*A*a^12*b^6)*c^5 + 480*(32*B*a^12*b^7 - 143*A*a^11*b^8)*c^4 - 80*(41*B*a^11*b^9 - 187*A*a^10*b^10)*c^3 + 2*(212*B*a^10*b^11 - 1003*A*a^9*b^12)*c^2 - (31*B*a^9*b^13 - 152*A*a^8*b^14)*c)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(B^2*a^2*b^9 - 10*A*B*a*b^10 + 25*A^2*b^11 + 1680*(4*A*B*a^6 - 11*A^2*a^5*b)*c^5 + 840*(2*B^2*a^6*b - 16*A*B*a^5*b^2 + 33*A^2*a^4*b^3)*c^4 - 105*(8*B^2*a^5*b^3 - 68*A*B*a^4*b^4 + 143*A^2*a^3*b^5)*c^3 + 3*(63*B^2*a^4*b^5 - 574*A*B*a^3*b^6 + 1298*A^2*a^2*b^7)*c^2 - 3*(7*B^2*a^3*b^7 - 68*A*B*a^2*b^8 + 165*A^2*a*b^9)*c + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)) + 27*(810000*A^4*a^5*c^9 + 405000*(2*A^3*B*a^5*b - 7*A^4*a^4*b^2)*c^8 - (38416*B^4*a^7 - 422576*A*B^3*a^6*b + 1439376*A^2*B^2*a^5*b^2 - 1018856*A^3*B*a^4*b^3 - 1957349*A^4*a^3*b^4)*c^7 + (19208*B^4*a^6*b^2 - 239896*A*B^3*a^5*b^3 + 955704*A^2*B^2*a^4*b^4 - 1067347*A^3*B*a^3*b^5 - 571030*A^4*a^2*b^6)*c^6 - (4189*B^4*a^5*b^4 - 56807*A*B^3*a^4*b^5 + 251349*A^2*B^2*a^3*b^6 - 344630*A^3*B*a^2*b^7 - 77825*A^4*a*b^8)*c^5 + 3*(149*B^4*a^4*b^6 - 2161*A*B^3*a^3*b^7 + 10380*A^2*B^2*a^2*b^8 - 16225*A^3*B*a*b^9 - 1375*A^4*b^10)*c^4 - 21*(B^4*a^3*b^8 - 15*A*B^3*a^2*b^9 + 75*A^2*B^2*a*b^10 - 125*A^3*B*b^11)*c^3)*sqrt(x)) - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)*sqrt(-(B^2*a^2*b^9 - 10*A*B*a*b^10 + 25*A^2*b^11 + 1680*(4*A*B*a^6 - 11*A^2*a^5*b)*c^5 + 840*(2*B^2*a^6*b - 16*A*B*a^5*b^2 + 33*A^2*a^4*b^3)*c^4 - 105*(8*B^2*a^5*b^3 - 68*A*B*a^4*b^4 + 143*A^2*a^3*b^5)*c^3 + 3*(63*B^2*a^4*b^5 - 574*A*B*a^3*b^6 + 1298*A^2*a^2*b^7)*c^2 - 3*(7*B^2*a^3*b^7 - 68*A*B*a^2*b^8 + 165*A^2*a*b^9)*c + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(-27/2*sqrt(1/2)*(B^3*a^3*b^14 - 15*A*B^2*a^2*b^15 + 75*A^2*B*a*b^16 - 125*A^3*b^17 + 57600*(7*A^2*B*a^9 - 23*A^3*a^8*b)*c^8 - 64*(1372*B^3*a^10 - 15204*A*B^2*a^9*b + 61326*A^2*B*a^8*b^2 - 88823*A^3*a^7*b^3)*c^7 + 16*(7112*B^3*a^9*b^2 - 83292*A*B^2*a^8*b^3 + 330300*A^2*B*a^7*b^4 - 446671*A^3*a^6*b^5)*c^6 - 4*(15920*B^3*a^8*b^4 - 197004*A*B^2*a^7*b^5 + 811446*A^2*B*a^6*b^6 - 1115785*A^3*a^5*b^7)*c^5 + 3*(6696*B^3*a^7*b^6 - 87308*A*B^2*a^6*b^7 + 377471*A^2*B*a^5*b^8 - 541178*A^3*a^4*b^9)*c^4 - 3*(1295*B^3*a^6*b^8 - 17704*A*B^2*a^5*b^9 + 80329*A^2*B*a^4*b^10 - 120911*A^3*a^3*b^11)*c^3 + (464*B^3*a^5*b^10 - 6609*A*B^2*a^4*b^11 + 31317*A^2*B*a^3*b^12 - 49360*A^3*a^2*b^13)*c^2 - (32*B^3*a^4*b^12 - 471*A*B^2*a^3*b^13 + 2310*A^2*B*a^2*b^14 - 3775*A^3*a*b^15)*c - (B*a^8*b^15 - 5*A*a^7*b^16 - 122880*A*a^15*c^8 - 4096*(11*B*a^15*b - 79*A*a^14*b^2)*c^7 + 1536*(44*B*a^14*b^3 - 223*A*a^13*b^4)*c^6 - 256*(169*B*a^13*b^5 - 770*A*a^12*b^6)*c^5 + 480*(32*B*a^12*b^7 - 143*A*a^11*b^8)*c^4 - 80*(41*B*a^11*b^9 - 187*A*a^10*b^10)*c^3 + 2*(212*B*a^10*b^11 - 1003*A*a^9*b^12)*c^2 - (31*B*a^9*b^13 - 152*A*a^8*b^14)*c)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(B^2*a^2*b^9 - 10*A*B*a*b^10 + 25*A^2*b^11 + 1680*(4*A*B*a^6 - 11*A^2*a^5*b)*c^5 + 840*(2*B^2*a^6*b - 16*A*B*a^5*b^2 + 33*A^2*a^4*b^3)*c^4 - 105*(8*B^2*a^5*b^3 - 68*A*B*a^4*b^4 + 143*A^2*a^3*b^5)*c^3 + 3*(63*B^2*a^4*b^5 - 574*A*B*a^3*b^6 + 1298*A^2*a^2*b^7)*c^2 - 3*(7*B^2*a^3*b^7 - 68*A*B*a^2*b^8 + 165*A^2*a*b^9)*c + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)) + 27*(810000*A^4*a^5*c^9 + 405000*(2*A^3*B*a^5*b - 7*A^4*a^4*b^2)*c^8 - (38416*B^4*a^7 - 422576*A*B^3*a^6*b + 1439376*A^2*B^2*a^5*b^2 - 1018856*A^3*B*a^4*b^3 - 1957349*A^4*a^3*b^4)*c^7 + (19208*B^4*a^6*b^2 - 239896*A*B^3*a^5*b^3 + 955704*A^2*B^2*a^4*b^4 - 1067347*A^3*B*a^3*b^5 - 571030*A^4*a^2*b^6)*c^6 - (4189*B^4*a^5*b^4 - 56807*A*B^3*a^4*b^5 + 251349*A^2*B^2*a^3*b^6 - 344630*A^3*B*a^2*b^7 - 77825*A^4*a*b^8)*c^5 + 3*(149*B^4*a^4*b^6 - 2161*A*B^3*a^3*b^7 + 10380*A^2*B^2*a^2*b^8 - 16225*A^3*B*a*b^9 - 1375*A^4*b^10)*c^4 - 21*(B^4*a^3*b^8 - 15*A*B^3*a^2*b^9 + 75*A^2*B^2*a*b^10 - 125*A^3*B*b^11)*c^3)*sqrt(x)) + 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)*sqrt(-(B^2*a^2*b^9 - 10*A*B*a*b^10 + 25*A^2*b^11 + 1680*(4*A*B*a^6 - 11*A^2*a^5*b)*c^5 + 840*(2*B^2*a^6*b - 16*A*B*a^5*b^2 + 33*A^2*a^4*b^3)*c^4 - 105*(8*B^2*a^5*b^3 - 68*A*B*a^4*b^4 + 143*A^2*a^3*b^5)*c^3 + 3*(63*B^2*a^4*b^5 - 574*A*B*a^3*b^6 + 1298*A^2*a^2*b^7)*c^2 - 3*(7*B^2*a^3*b^7 - 68*A*B*a^2*b^8 + 165*A^2*a*b^9)*c - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(27/2*sqrt(1/2)*(B^3*a^3*b^14 - 15*A*B^2*a^2*b^15 + 75*A^2*B*a*b^16 - 125*A^3*b^17 + 57600*(7*A^2*B*a^9 - 23*A^3*a^8*b)*c^8 - 64*(1372*B^3*a^10 - 15204*A*B^2*a^9*b + 61326*A^2*B*a^8*b^2 - 88823*A^3*a^7*b^3)*c^7 + 16*(7112*B^3*a^9*b^2 - 83292*A*B^2*a^8*b^3 + 330300*A^2*B*a^7*b^4 - 446671*A^3*a^6*b^5)*c^6 - 4*(15920*B^3*a^8*b^4 - 197004*A*B^2*a^7*b^5 + 811446*A^2*B*a^6*b^6 - 1115785*A^3*a^5*b^7)*c^5 + 3*(6696*B^3*a^7*b^6 - 87308*A*B^2*a^6*b^7 + 377471*A^2*B*a^5*b^8 - 541178*A^3*a^4*b^9)*c^4 - 3*(1295*B^3*a^6*b^8 - 17704*A*B^2*a^5*b^9 + 80329*A^2*B*a^4*b^10 - 120911*A^3*a^3*b^11)*c^3 + (464*B^3*a^5*b^10 - 6609*A*B^2*a^4*b^11 + 31317*A^2*B*a^3*b^12 - 49360*A^3*a^2*b^13)*c^2 - (32*B^3*a^4*b^12 - 471*A*B^2*a^3*b^13 + 2310*A^2*B*a^2*b^14 - 3775*A^3*a*b^15)*c + (B*a^8*b^15 - 5*A*a^7*b^16 - 122880*A*a^15*c^8 - 4096*(11*B*a^15*b - 79*A*a^14*b^2)*c^7 + 1536*(44*B*a^14*b^3 - 223*A*a^13*b^4)*c^6 - 256*(169*B*a^13*b^5 - 770*A*a^12*b^6)*c^5 + 480*(32*B*a^12*b^7 - 143*A*a^11*b^8)*c^4 - 80*(41*B*a^11*b^9 - 187*A*a^10*b^10)*c^3 + 2*(212*B*a^10*b^11 - 1003*A*a^9*b^12)*c^2 - (31*B*a^9*b^13 - 152*A*a^8*b^14)*c)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(B^2*a^2*b^9 - 10*A*B*a*b^10 + 25*A^2*b^11 + 1680*(4*A*B*a^6 - 11*A^2*a^5*b)*c^5 + 840*(2*B^2*a^6*b - 16*A*B*a^5*b^2 + 33*A^2*a^4*b^3)*c^4 - 105*(8*B^2*a^5*b^3 - 68*A*B*a^4*b^4 + 143*A^2*a^3*b^5)*c^3 + 3*(63*B^2*a^4*b^5 - 574*A*B*a^3*b^6 + 1298*A^2*a^2*b^7)*c^2 - 3*(7*B^2*a^3*b^7 - 68*A*B*a^2*b^8 + 165*A^2*a*b^9)*c - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)) + 27*(810000*A^4*a^5*c^9 + 405000*(2*A^3*B*a^5*b - 7*A^4*a^4*b^2)*c^8 - (38416*B^4*a^7 - 422576*A*B^3*a^6*b + 1439376*A^2*B^2*a^5*b^2 - 1018856*A^3*B*a^4*b^3 - 1957349*A^4*a^3*b^4)*c^7 + (19208*B^4*a^6*b^2 - 239896*A*B^3*a^5*b^3 + 955704*A^2*B^2*a^4*b^4 - 1067347*A^3*B*a^3*b^5 - 571030*A^4*a^2*b^6)*c^6 - (4189*B^4*a^5*b^4 - 56807*A*B^3*a^4*b^5 + 251349*A^2*B^2*a^3*b^6 - 344630*A^3*B*a^2*b^7 - 77825*A^4*a*b^8)*c^5 + 3*(149*B^4*a^4*b^6 - 2161*A*B^3*a^3*b^7 + 10380*A^2*B^2*a^2*b^8 - 16225*A^3*B*a*b^9 - 1375*A^4*b^10)*c^4 - 21*(B^4*a^3*b^8 - 15*A*B^3*a^2*b^9 + 75*A^2*B^2*a*b^10 - 125*A^3*B*b^11)*c^3)*sqrt(x)) - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)*sqrt(-(B^2*a^2*b^9 - 10*A*B*a*b^10 + 25*A^2*b^11 + 1680*(4*A*B*a^6 - 11*A^2*a^5*b)*c^5 + 840*(2*B^2*a^6*b - 16*A*B*a^5*b^2 + 33*A^2*a^4*b^3)*c^4 - 105*(8*B^2*a^5*b^3 - 68*A*B*a^4*b^4 + 143*A^2*a^3*b^5)*c^3 + 3*(63*B^2*a^4*b^5 - 574*A*B*a^3*b^6 + 1298*A^2*a^2*b^7)*c^2 - 3*(7*B^2*a^3*b^7 - 68*A*B*a^2*b^8 + 165*A^2*a*b^9)*c - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(-27/2*sqrt(1/2)*(B^3*a^3*b^14 - 15*A*B^2*a^2*b^15 + 75*A^2*B*a*b^16 - 125*A^3*b^17 + 57600*(7*A^2*B*a^9 - 23*A^3*a^8*b)*c^8 - 64*(1372*B^3*a^10 - 15204*A*B^2*a^9*b + 61326*A^2*B*a^8*b^2 - 88823*A^3*a^7*b^3)*c^7 + 16*(7112*B^3*a^9*b^2 - 83292*A*B^2*a^8*b^3 + 330300*A^2*B*a^7*b^4 - 446671*A^3*a^6*b^5)*c^6 - 4*(15920*B^3*a^8*b^4 - 197004*A*B^2*a^7*b^5 + 811446*A^2*B*a^6*b^6 - 1115785*A^3*a^5*b^7)*c^5 + 3*(6696*B^3*a^7*b^6 - 87308*A*B^2*a^6*b^7 + 377471*A^2*B*a^5*b^8 - 541178*A^3*a^4*b^9)*c^4 - 3*(1295*B^3*a^6*b^8 - 17704*A*B^2*a^5*b^9 + 80329*A^2*B*a^4*b^10 - 120911*A^3*a^3*b^11)*c^3 + (464*B^3*a^5*b^10 - 6609*A*B^2*a^4*b^11 + 31317*A^2*B*a^3*b^12 - 49360*A^3*a^2*b^13)*c^2 - (32*B^3*a^4*b^12 - 471*A*B^2*a^3*b^13 + 2310*A^2*B*a^2*b^14 - 3775*A^3*a*b^15)*c + (B*a^8*b^15 - 5*A*a^7*b^16 - 122880*A*a^15*c^8 - 4096*(11*B*a^15*b - 79*A*a^14*b^2)*c^7 + 1536*(44*B*a^14*b^3 - 223*A*a^13*b^4)*c^6 - 256*(169*B*a^13*b^5 - 770*A*a^12*b^6)*c^5 + 480*(32*B*a^12*b^7 - 143*A*a^11*b^8)*c^4 - 80*(41*B*a^11*b^9 - 187*A*a^10*b^10)*c^3 + 2*(212*B*a^10*b^11 - 1003*A*a^9*b^12)*c^2 - (31*B*a^9*b^13 - 152*A*a^8*b^14)*c)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(B^2*a^2*b^9 - 10*A*B*a*b^10 + 25*A^2*b^11 + 1680*(4*A*B*a^6 - 11*A^2*a^5*b)*c^5 + 840*(2*B^2*a^6*b - 16*A*B*a^5*b^2 + 33*A^2*a^4*b^3)*c^4 - 105*(8*B^2*a^5*b^3 - 68*A*B*a^4*b^4 + 143*A^2*a^3*b^5)*c^3 + 3*(63*B^2*a^4*b^5 - 574*A*B*a^3*b^6 + 1298*A^2*a^2*b^7)*c^2 - 3*(7*B^2*a^3*b^7 - 68*A*B*a^2*b^8 + 165*A^2*a*b^9)*c - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((B^4*a^4*b^8 - 20*A*B^3*a^3*b^9 + 150*A^2*B^2*a^2*b^10 - 500*A^3*B*a*b^11 + 625*A^4*b^12 + 50625*A^4*a^6*c^6 - 450*(49*A^2*B^2*a^7 - 382*A^3*B*a^6*b + 694*A^4*a^5*b^2)*c^5 + (2401*B^4*a^8 - 37436*A*B^3*a^7*b + 218886*A^2*B^2*a^6*b^2 - 577016*A^3*B*a^5*b^3 + 591886*A^4*a^4*b^4)*c^4 - 2*(539*B^4*a^7*b^2 - 9298*A*B^3*a^6*b^3 + 59592*A^2*B^2*a^5*b^4 - 168016*A^3*B*a^4*b^5 + 175655*A^4*a^3*b^6)*c^3 + 3*(73*B^4*a^6*b^4 - 1344*A*B^3*a^5*b^5 + 9228*A^2*B^2*a^4*b^6 - 27980*A^3*B*a^3*b^7 + 31575*A^4*a^2*b^8)*c^2 - 2*(11*B^4*a^5*b^6 - 214*A*B^3*a^4*b^7 + 1560*A^2*B^2*a^3*b^8 - 5050*A^3*B*a^2*b^9 + 6125*A^4*a*b^10)*c)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)) + 27*(810000*A^4*a^5*c^9 + 405000*(2*A^3*B*a^5*b - 7*A^4*a^4*b^2)*c^8 - (38416*B^4*a^7 - 422576*A*B^3*a^6*b + 1439376*A^2*B^2*a^5*b^2 - 1018856*A^3*B*a^4*b^3 - 1957349*A^4*a^3*b^4)*c^7 + (19208*B^4*a^6*b^2 - 239896*A*B^3*a^5*b^3 + 955704*A^2*B^2*a^4*b^4 - 1067347*A^3*B*a^3*b^5 - 571030*A^4*a^2*b^6)*c^6 - (4189*B^4*a^5*b^4 - 56807*A*B^3*a^4*b^5 + 251349*A^2*B^2*a^3*b^6 - 344630*A^3*B*a^2*b^7 - 77825*A^4*a*b^8)*c^5 + 3*(149*B^4*a^4*b^6 - 2161*A*B^3*a^3*b^7 + 10380*A^2*B^2*a^2*b^8 - 16225*A^3*B*a*b^9 - 1375*A^4*b^10)*c^4 - 21*(B^4*a^3*b^8 - 15*A*B^3*a^2*b^9 + 75*A^2*B^2*a*b^10 - 125*A^3*B*b^11)*c^3)*sqrt(x)) - 2*(8*A*a^2*b^4 - 64*A*a^3*b^2*c + 128*A*a^4*c^2 + 3*(60*A*a^2*c^4 + (8*B*a^2*b - 37*A*a*b^2)*c^3 - (B*a*b^3 - 5*A*b^4)*c^2)*x^4 - (28*(B*a^3 - 14*A*a^2*b)*c^3 - (49*B*a^2*b^2 - 227*A*a*b^3)*c^2 + 6*(B*a*b^4 - 5*A*b^5)*c)*x^3 - (3*B*a*b^5 - 15*A*b^6 - 324*A*a^3*c^3 - (4*B*a^3*b + 25*A*a^2*b^2)*c^2 - (20*B*a^2*b^3 - 91*A*a*b^4)*c)*x^2 - (5*B*a^2*b^4 - 25*A*a*b^5 + 4*(11*B*a^4 - 91*A*a^3*b)*c^2 - (37*B*a^3*b^2 - 194*A*a^2*b^3)*c)*x)*sqrt(x))/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)","B",0
1029,0,0,0,0.496666," ","integrate((B*x+A)*x^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \sqrt{x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*sqrt(x), x)","F",0
1030,0,0,0,0.456831," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)}}{\sqrt{x}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)/sqrt(x), x)","F",0
1031,0,0,0,0.474199," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)}}{x^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)/x^(3/2), x)","F",0
1032,0,0,0,0.472490," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)}}{x^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)/x^(5/2), x)","F",0
1033,0,0,0,0.448758," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/x^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)}}{x^{\frac{7}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)/x^(7/2), x)","F",0
1034,0,0,0,0.447958," ","integrate((2-5*x)*x^(7/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(5 \, x^{4} - 2 \, x^{3}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}, x\right)"," ",0,"integral(-(5*x^4 - 2*x^3)*sqrt(3*x^2 + 5*x + 2)*sqrt(x), x)","F",0
1035,0,0,0,0.428430," ","integrate((2-5*x)*x^(5/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(5 \, x^{3} - 2 \, x^{2}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}, x\right)"," ",0,"integral(-(5*x^3 - 2*x^2)*sqrt(3*x^2 + 5*x + 2)*sqrt(x), x)","F",0
1036,0,0,0,0.441716," ","integrate((2-5*x)*x^(3/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(5 \, x^{2} - 2 \, x\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}, x\right)"," ",0,"integral(-(5*x^2 - 2*x)*sqrt(3*x^2 + 5*x + 2)*sqrt(x), x)","F",0
1037,0,0,0,0.448020," ","integrate((2-5*x)*x^(1/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x), x)","F",0
1038,0,0,0,0.441202," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{\sqrt{x}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/sqrt(x), x)","F",0
1039,0,0,0,0.454324," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{3}{2}}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(3/2), x)","F",0
1040,0,0,0,0.436878," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{5}{2}}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(5/2), x)","F",0
1041,0,0,0,0.445219," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{7}{2}}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(7/2), x)","F",0
1042,0,0,0,0.435793," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(9/2), x)","F",0
1043,0,0,0,0.434688," ","integrate((2-5*x)*(3*x^2+5*x+2)^(1/2)/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)}}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)/x^(11/2), x)","F",0
1044,0,0,0,0.459582," ","integrate((2-5*x)*x^(5/2)*(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(15 \, x^{5} + 19 \, x^{4} - 4 \, x^{2}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}, x\right)"," ",0,"integral(-(15*x^5 + 19*x^4 - 4*x^2)*sqrt(3*x^2 + 5*x + 2)*sqrt(x), x)","F",0
1045,0,0,0,0.430933," ","integrate((2-5*x)*x^(3/2)*(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(15 \, x^{4} + 19 \, x^{3} - 4 \, x\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}, x\right)"," ",0,"integral(-(15*x^4 + 19*x^3 - 4*x)*sqrt(3*x^2 + 5*x + 2)*sqrt(x), x)","F",0
1046,0,0,0,0.448459," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(15 \, x^{3} + 19 \, x^{2} - 4\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}, x\right)"," ",0,"integral(-(15*x^3 + 19*x^2 - 4)*sqrt(3*x^2 + 5*x + 2)*sqrt(x), x)","F",0
1047,0,0,0,0.440211," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{3} + 19 \, x^{2} - 4\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{\sqrt{x}}, x\right)"," ",0,"integral(-(15*x^3 + 19*x^2 - 4)*sqrt(3*x^2 + 5*x + 2)/sqrt(x), x)","F",0
1048,0,0,0,0.419154," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{3} + 19 \, x^{2} - 4\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{x^{\frac{3}{2}}}, x\right)"," ",0,"integral(-(15*x^3 + 19*x^2 - 4)*sqrt(3*x^2 + 5*x + 2)/x^(3/2), x)","F",0
1049,0,0,0,0.450272," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{3} + 19 \, x^{2} - 4\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{x^{\frac{5}{2}}}, x\right)"," ",0,"integral(-(15*x^3 + 19*x^2 - 4)*sqrt(3*x^2 + 5*x + 2)/x^(5/2), x)","F",0
1050,0,0,0,0.443843," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{3} + 19 \, x^{2} - 4\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{x^{\frac{7}{2}}}, x\right)"," ",0,"integral(-(15*x^3 + 19*x^2 - 4)*sqrt(3*x^2 + 5*x + 2)/x^(7/2), x)","F",0
1051,0,0,0,0.497475," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{3} + 19 \, x^{2} - 4\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral(-(15*x^3 + 19*x^2 - 4)*sqrt(3*x^2 + 5*x + 2)/x^(9/2), x)","F",0
1052,0,0,0,0.440809," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{3} + 19 \, x^{2} - 4\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral(-(15*x^3 + 19*x^2 - 4)*sqrt(3*x^2 + 5*x + 2)/x^(11/2), x)","F",0
1053,0,0,0,0.433337," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{3} + 19 \, x^{2} - 4\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{x^{\frac{13}{2}}}, x\right)"," ",0,"integral(-(15*x^3 + 19*x^2 - 4)*sqrt(3*x^2 + 5*x + 2)/x^(13/2), x)","F",0
1054,0,0,0,0.429595," ","integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{3} + 19 \, x^{2} - 4\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{x^{\frac{15}{2}}}, x\right)"," ",0,"integral(-(15*x^3 + 19*x^2 - 4)*sqrt(3*x^2 + 5*x + 2)/x^(15/2), x)","F",0
1055,0,0,0,0.483926," ","integrate((B*x+A)/(e*x)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \sqrt{e x}}{c e x^{3} + b e x^{2} + a e x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*sqrt(e*x)/(c*e*x^3 + b*e*x^2 + a*e*x), x)","F",0
1056,0,0,0,0.482759," ","integrate((2-5*x)*x^(7/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{4} - 2 \, x^{3}\right)} \sqrt{x}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}, x\right)"," ",0,"integral(-(5*x^4 - 2*x^3)*sqrt(x)/sqrt(3*x^2 + 5*x + 2), x)","F",0
1057,0,0,0,0.462536," ","integrate((2-5*x)*x^(5/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{3} - 2 \, x^{2}\right)} \sqrt{x}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}, x\right)"," ",0,"integral(-(5*x^3 - 2*x^2)*sqrt(x)/sqrt(3*x^2 + 5*x + 2), x)","F",0
1058,0,0,0,0.539912," ","integrate((2-5*x)*x^(3/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{2} - 2 \, x\right)} \sqrt{x}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}, x\right)"," ",0,"integral(-(5*x^2 - 2*x)*sqrt(x)/sqrt(3*x^2 + 5*x + 2), x)","F",0
1059,0,0,0,0.552694," ","integrate((2-5*x)*x^(1/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x - 2\right)} \sqrt{x}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}, x\right)"," ",0,"integral(-(5*x - 2)*sqrt(x)/sqrt(3*x^2 + 5*x + 2), x)","F",0
1060,0,0,0,0.480546," ","integrate((2-5*x)/x^(1/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{3 \, x^{3} + 5 \, x^{2} + 2 \, x}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(3*x^3 + 5*x^2 + 2*x), x)","F",0
1061,0,0,0,0.447262," ","integrate((2-5*x)/x^(3/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{3 \, x^{4} + 5 \, x^{3} + 2 \, x^{2}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(3*x^4 + 5*x^3 + 2*x^2), x)","F",0
1062,0,0,0,0.425205," ","integrate((2-5*x)/x^(5/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{3 \, x^{5} + 5 \, x^{4} + 2 \, x^{3}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(3*x^5 + 5*x^4 + 2*x^3), x)","F",0
1063,0,0,0,0.440546," ","integrate((2-5*x)/x^(7/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{3 \, x^{6} + 5 \, x^{5} + 2 \, x^{4}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(3*x^6 + 5*x^5 + 2*x^4), x)","F",0
1064,0,0,0,0.421951," ","integrate((2-5*x)*x^(7/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{4} - 2 \, x^{3}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}, x\right)"," ",0,"integral(-(5*x^4 - 2*x^3)*sqrt(3*x^2 + 5*x + 2)*sqrt(x)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4), x)","F",0
1065,0,0,0,0.437731," ","integrate((2-5*x)*x^(5/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{3} - 2 \, x^{2}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}, x\right)"," ",0,"integral(-(5*x^3 - 2*x^2)*sqrt(3*x^2 + 5*x + 2)*sqrt(x)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4), x)","F",0
1066,0,0,0,0.445172," ","integrate((2-5*x)*x^(3/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{2} - 2 \, x\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}, x\right)"," ",0,"integral(-(5*x^2 - 2*x)*sqrt(3*x^2 + 5*x + 2)*sqrt(x)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4), x)","F",0
1067,0,0,0,0.431346," ","integrate((2-5*x)*x^(1/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4), x)","F",0
1068,0,0,0,0.423629," ","integrate((2-5*x)/(3*x^2+5*x+2)^(3/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{9 \, x^{5} + 30 \, x^{4} + 37 \, x^{3} + 20 \, x^{2} + 4 \, x}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(9*x^5 + 30*x^4 + 37*x^3 + 20*x^2 + 4*x), x)","F",0
1069,0,0,0,0.435436," ","integrate((2-5*x)/x^(3/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{9 \, x^{6} + 30 \, x^{5} + 37 \, x^{4} + 20 \, x^{3} + 4 \, x^{2}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(9*x^6 + 30*x^5 + 37*x^4 + 20*x^3 + 4*x^2), x)","F",0
1070,0,0,0,0.449639," ","integrate((2-5*x)/x^(5/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{9 \, x^{7} + 30 \, x^{6} + 37 \, x^{5} + 20 \, x^{4} + 4 \, x^{3}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(9*x^7 + 30*x^6 + 37*x^5 + 20*x^4 + 4*x^3), x)","F",0
1071,0,0,0,0.436771," ","integrate((2-5*x)/x^(7/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{9 \, x^{8} + 30 \, x^{7} + 37 \, x^{6} + 20 \, x^{5} + 4 \, x^{4}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(9*x^8 + 30*x^7 + 37*x^6 + 20*x^5 + 4*x^4), x)","F",0
1072,0,0,0,0.445550," ","integrate((2-5*x)*x^(13/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{7} - 2 \, x^{6}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-(5*x^7 - 2*x^6)*sqrt(3*x^2 + 5*x + 2)*sqrt(x)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
1073,0,0,0,0.437586," ","integrate((2-5*x)*x^(11/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{6} - 2 \, x^{5}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-(5*x^6 - 2*x^5)*sqrt(3*x^2 + 5*x + 2)*sqrt(x)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
1074,0,0,0,0.420655," ","integrate((2-5*x)*x^(9/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{5} - 2 \, x^{4}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-(5*x^5 - 2*x^4)*sqrt(3*x^2 + 5*x + 2)*sqrt(x)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
1075,0,0,0,0.426606," ","integrate((2-5*x)*x^(7/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{4} - 2 \, x^{3}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-(5*x^4 - 2*x^3)*sqrt(3*x^2 + 5*x + 2)*sqrt(x)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
1076,0,0,0,0.415349," ","integrate((2-5*x)*x^(5/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{3} - 2 \, x^{2}\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-(5*x^3 - 2*x^2)*sqrt(3*x^2 + 5*x + 2)*sqrt(x)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
1077,0,0,0,0.415996," ","integrate((2-5*x)*x^(3/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x^{2} - 2 \, x\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{x}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-(5*x^2 - 2*x)*sqrt(3*x^2 + 5*x + 2)*sqrt(x)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
1078,0,0,0,0.436754," ","integrate((2-5*x)*x^(1/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
1079,0,0,0,0.427660," ","integrate((2-5*x)/(3*x^2+5*x+2)^(5/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{27 \, x^{7} + 135 \, x^{6} + 279 \, x^{5} + 305 \, x^{4} + 186 \, x^{3} + 60 \, x^{2} + 8 \, x}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(27*x^7 + 135*x^6 + 279*x^5 + 305*x^4 + 186*x^3 + 60*x^2 + 8*x), x)","F",0
1080,0,0,0,0.438772," ","integrate((2-5*x)/x^(3/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{27 \, x^{8} + 135 \, x^{7} + 279 \, x^{6} + 305 \, x^{5} + 186 \, x^{4} + 60 \, x^{3} + 8 \, x^{2}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(27*x^8 + 135*x^7 + 279*x^6 + 305*x^5 + 186*x^4 + 60*x^3 + 8*x^2), x)","F",0
1081,0,0,0,0.433702," ","integrate((2-5*x)/x^(5/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{27 \, x^{9} + 135 \, x^{8} + 279 \, x^{7} + 305 \, x^{6} + 186 \, x^{5} + 60 \, x^{4} + 8 \, x^{3}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(27*x^9 + 135*x^8 + 279*x^7 + 305*x^6 + 186*x^5 + 60*x^4 + 8*x^3), x)","F",0
1082,0,0,0,0.417168," ","integrate((2-5*x)/x^(7/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x - 2\right)} \sqrt{x}}{27 \, x^{10} + 135 \, x^{9} + 279 \, x^{8} + 305 \, x^{7} + 186 \, x^{6} + 60 \, x^{5} + 8 \, x^{4}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(5*x - 2)*sqrt(x)/(27*x^10 + 135*x^9 + 279*x^8 + 305*x^7 + 186*x^6 + 60*x^5 + 8*x^4), x)","F",0
1083,1,1350,0,0.458047," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left({\left(B c^{3} m^{7} + 28 \, B c^{3} m^{6} + 322 \, B c^{3} m^{5} + 1960 \, B c^{3} m^{4} + 6769 \, B c^{3} m^{3} + 13132 \, B c^{3} m^{2} + 13068 \, B c^{3} m + 5040 \, B c^{3}\right)} x^{8} + {\left({\left(3 \, B b c^{2} + A c^{3}\right)} m^{7} + 29 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m^{6} + 343 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m^{5} + 2135 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m^{4} + 17280 \, B b c^{2} + 5760 \, A c^{3} + 7504 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m^{3} + 14756 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m^{2} + 14832 \, {\left(3 \, B b c^{2} + A c^{3}\right)} m\right)} x^{7} + 3 \, {\left({\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} m^{7} + 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} m^{6} + 366 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} m^{5} + 2340 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} m^{4} + 6720 \, B b^{2} c + 8409 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} m^{3} + 6720 \, {\left(B a + A b\right)} c^{2} + 16830 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} m^{2} + 17144 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} m\right)} x^{6} + {\left({\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} m^{7} + 31 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} m^{6} + 391 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} m^{5} + 2581 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} m^{4} + 8064 \, B b^{3} + 24192 \, A a c^{2} + 9544 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} m^{3} + 19564 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} m^{2} + 24192 \, {\left(2 \, B a b + A b^{2}\right)} c + 20304 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} m\right)} x^{5} + {\left({\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} m^{7} + 32 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} m^{6} + 418 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} m^{5} + 2864 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} m^{4} + 30240 \, B a b^{2} + 10080 \, A b^{3} + 10993 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} m^{3} + 23312 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} m^{2} + 30240 \, {\left(B a^{2} + 2 \, A a b\right)} c + 24876 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} m\right)} x^{4} + 3 \, {\left({\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} m^{7} + 33 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} m^{6} + 447 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} m^{5} + 3195 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} m^{4} + 13440 \, B a^{2} b + 13440 \, A a b^{2} + 13440 \, A a^{2} c + 12864 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} m^{3} + 28692 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} m^{2} + 32048 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} m\right)} x^{3} + {\left({\left(B a^{3} + 3 \, A a^{2} b\right)} m^{7} + 34 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m^{6} + 478 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m^{5} + 3580 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m^{4} + 20160 \, B a^{3} + 60480 \, A a^{2} b + 15289 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m^{3} + 36706 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m^{2} + 44712 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m\right)} x^{2} + {\left(A a^{3} m^{7} + 35 \, A a^{3} m^{6} + 511 \, A a^{3} m^{5} + 4025 \, A a^{3} m^{4} + 18424 \, A a^{3} m^{3} + 48860 \, A a^{3} m^{2} + 69264 \, A a^{3} m + 40320 \, A a^{3}\right)} x\right)} \left(e x\right)^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320}"," ",0,"((B*c^3*m^7 + 28*B*c^3*m^6 + 322*B*c^3*m^5 + 1960*B*c^3*m^4 + 6769*B*c^3*m^3 + 13132*B*c^3*m^2 + 13068*B*c^3*m + 5040*B*c^3)*x^8 + ((3*B*b*c^2 + A*c^3)*m^7 + 29*(3*B*b*c^2 + A*c^3)*m^6 + 343*(3*B*b*c^2 + A*c^3)*m^5 + 2135*(3*B*b*c^2 + A*c^3)*m^4 + 17280*B*b*c^2 + 5760*A*c^3 + 7504*(3*B*b*c^2 + A*c^3)*m^3 + 14756*(3*B*b*c^2 + A*c^3)*m^2 + 14832*(3*B*b*c^2 + A*c^3)*m)*x^7 + 3*((B*b^2*c + (B*a + A*b)*c^2)*m^7 + 30*(B*b^2*c + (B*a + A*b)*c^2)*m^6 + 366*(B*b^2*c + (B*a + A*b)*c^2)*m^5 + 2340*(B*b^2*c + (B*a + A*b)*c^2)*m^4 + 6720*B*b^2*c + 8409*(B*b^2*c + (B*a + A*b)*c^2)*m^3 + 6720*(B*a + A*b)*c^2 + 16830*(B*b^2*c + (B*a + A*b)*c^2)*m^2 + 17144*(B*b^2*c + (B*a + A*b)*c^2)*m)*x^6 + ((B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*m^7 + 31*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*m^6 + 391*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*m^5 + 2581*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*m^4 + 8064*B*b^3 + 24192*A*a*c^2 + 9544*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*m^3 + 19564*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*m^2 + 24192*(2*B*a*b + A*b^2)*c + 20304*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*m)*x^5 + ((3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*m^7 + 32*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*m^6 + 418*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*m^5 + 2864*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*m^4 + 30240*B*a*b^2 + 10080*A*b^3 + 10993*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*m^3 + 23312*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*m^2 + 30240*(B*a^2 + 2*A*a*b)*c + 24876*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*m)*x^4 + 3*((B*a^2*b + A*a*b^2 + A*a^2*c)*m^7 + 33*(B*a^2*b + A*a*b^2 + A*a^2*c)*m^6 + 447*(B*a^2*b + A*a*b^2 + A*a^2*c)*m^5 + 3195*(B*a^2*b + A*a*b^2 + A*a^2*c)*m^4 + 13440*B*a^2*b + 13440*A*a*b^2 + 13440*A*a^2*c + 12864*(B*a^2*b + A*a*b^2 + A*a^2*c)*m^3 + 28692*(B*a^2*b + A*a*b^2 + A*a^2*c)*m^2 + 32048*(B*a^2*b + A*a*b^2 + A*a^2*c)*m)*x^3 + ((B*a^3 + 3*A*a^2*b)*m^7 + 34*(B*a^3 + 3*A*a^2*b)*m^6 + 478*(B*a^3 + 3*A*a^2*b)*m^5 + 3580*(B*a^3 + 3*A*a^2*b)*m^4 + 20160*B*a^3 + 60480*A*a^2*b + 15289*(B*a^3 + 3*A*a^2*b)*m^3 + 36706*(B*a^3 + 3*A*a^2*b)*m^2 + 44712*(B*a^3 + 3*A*a^2*b)*m)*x^2 + (A*a^3*m^7 + 35*A*a^3*m^6 + 511*A*a^3*m^5 + 4025*A*a^3*m^4 + 18424*A*a^3*m^3 + 48860*A*a^3*m^2 + 69264*A*a^3*m + 40320*A*a^3)*x)*(e*x)^m/(m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)","B",0
1084,1,573,0,0.438218," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(B c^{2} m^{5} + 15 \, B c^{2} m^{4} + 85 \, B c^{2} m^{3} + 225 \, B c^{2} m^{2} + 274 \, B c^{2} m + 120 \, B c^{2}\right)} x^{6} + {\left({\left(2 \, B b c + A c^{2}\right)} m^{5} + 16 \, {\left(2 \, B b c + A c^{2}\right)} m^{4} + 95 \, {\left(2 \, B b c + A c^{2}\right)} m^{3} + 288 \, B b c + 144 \, A c^{2} + 260 \, {\left(2 \, B b c + A c^{2}\right)} m^{2} + 324 \, {\left(2 \, B b c + A c^{2}\right)} m\right)} x^{5} + {\left({\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} m^{5} + 17 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} m^{4} + 107 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} m^{3} + 180 \, B b^{2} + 307 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} m^{2} + 360 \, {\left(B a + A b\right)} c + 396 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} m\right)} x^{4} + {\left({\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} m^{5} + 18 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} m^{4} + 121 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} m^{3} + 480 \, B a b + 240 \, A b^{2} + 480 \, A a c + 372 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} m^{2} + 508 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} m\right)} x^{3} + {\left({\left(B a^{2} + 2 \, A a b\right)} m^{5} + 19 \, {\left(B a^{2} + 2 \, A a b\right)} m^{4} + 137 \, {\left(B a^{2} + 2 \, A a b\right)} m^{3} + 360 \, B a^{2} + 720 \, A a b + 461 \, {\left(B a^{2} + 2 \, A a b\right)} m^{2} + 702 \, {\left(B a^{2} + 2 \, A a b\right)} m\right)} x^{2} + {\left(A a^{2} m^{5} + 20 \, A a^{2} m^{4} + 155 \, A a^{2} m^{3} + 580 \, A a^{2} m^{2} + 1044 \, A a^{2} m + 720 \, A a^{2}\right)} x\right)} \left(e x\right)^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"((B*c^2*m^5 + 15*B*c^2*m^4 + 85*B*c^2*m^3 + 225*B*c^2*m^2 + 274*B*c^2*m + 120*B*c^2)*x^6 + ((2*B*b*c + A*c^2)*m^5 + 16*(2*B*b*c + A*c^2)*m^4 + 95*(2*B*b*c + A*c^2)*m^3 + 288*B*b*c + 144*A*c^2 + 260*(2*B*b*c + A*c^2)*m^2 + 324*(2*B*b*c + A*c^2)*m)*x^5 + ((B*b^2 + 2*(B*a + A*b)*c)*m^5 + 17*(B*b^2 + 2*(B*a + A*b)*c)*m^4 + 107*(B*b^2 + 2*(B*a + A*b)*c)*m^3 + 180*B*b^2 + 307*(B*b^2 + 2*(B*a + A*b)*c)*m^2 + 360*(B*a + A*b)*c + 396*(B*b^2 + 2*(B*a + A*b)*c)*m)*x^4 + ((2*B*a*b + A*b^2 + 2*A*a*c)*m^5 + 18*(2*B*a*b + A*b^2 + 2*A*a*c)*m^4 + 121*(2*B*a*b + A*b^2 + 2*A*a*c)*m^3 + 480*B*a*b + 240*A*b^2 + 480*A*a*c + 372*(2*B*a*b + A*b^2 + 2*A*a*c)*m^2 + 508*(2*B*a*b + A*b^2 + 2*A*a*c)*m)*x^3 + ((B*a^2 + 2*A*a*b)*m^5 + 19*(B*a^2 + 2*A*a*b)*m^4 + 137*(B*a^2 + 2*A*a*b)*m^3 + 360*B*a^2 + 720*A*a*b + 461*(B*a^2 + 2*A*a*b)*m^2 + 702*(B*a^2 + 2*A*a*b)*m)*x^2 + (A*a^2*m^5 + 20*A*a^2*m^4 + 155*A*a^2*m^3 + 580*A*a^2*m^2 + 1044*A*a^2*m + 720*A*a^2)*x)*(e*x)^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
1085,1,171,0,0.424790," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left({\left(B c m^{3} + 6 \, B c m^{2} + 11 \, B c m + 6 \, B c\right)} x^{4} + {\left({\left(B b + A c\right)} m^{3} + 7 \, {\left(B b + A c\right)} m^{2} + 8 \, B b + 8 \, A c + 14 \, {\left(B b + A c\right)} m\right)} x^{3} + {\left({\left(B a + A b\right)} m^{3} + 8 \, {\left(B a + A b\right)} m^{2} + 12 \, B a + 12 \, A b + 19 \, {\left(B a + A b\right)} m\right)} x^{2} + {\left(A a m^{3} + 9 \, A a m^{2} + 26 \, A a m + 24 \, A a\right)} x\right)} \left(e x\right)^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"((B*c*m^3 + 6*B*c*m^2 + 11*B*c*m + 6*B*c)*x^4 + ((B*b + A*c)*m^3 + 7*(B*b + A*c)*m^2 + 8*B*b + 8*A*c + 14*(B*b + A*c)*m)*x^3 + ((B*a + A*b)*m^3 + 8*(B*a + A*b)*m^2 + 12*B*a + 12*A*b + 19*(B*a + A*b)*m)*x^2 + (A*a*m^3 + 9*A*a*m^2 + 26*A*a*m + 24*A*a)*x)*(e*x)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
1086,0,0,0,0.437779," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \left(e x\right)^{m}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((B*x + A)*(e*x)^m/(c*x^2 + b*x + a), x)","F",0
1087,0,0,0,0.439960," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \left(e x\right)^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((B*x + A)*(e*x)^m/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1088,0,0,0,0.454886," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c^{2} x^{5} + {\left(2 \, B b c + A c^{2}\right)} x^{4} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} x^{3} + A a^{2} + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} x^{2} + {\left(B a^{2} + 2 \, A a b\right)} x\right)} \sqrt{c x^{2} + b x + a} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*c^2*x^5 + (2*B*b*c + A*c^2)*x^4 + (B*b^2 + 2*(B*a + A*b)*c)*x^3 + A*a^2 + (2*B*a*b + A*b^2 + 2*A*a*c)*x^2 + (B*a^2 + 2*A*a*b)*x)*sqrt(c*x^2 + b*x + a)*(e*x)^m, x)","F",0
1089,0,0,0,0.429908," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B c x^{3} + {\left(B b + A c\right)} x^{2} + A a + {\left(B a + A b\right)} x\right)} \sqrt{c x^{2} + b x + a} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*c*x^3 + (B*b + A*c)*x^2 + A*a + (B*a + A*b)*x)*sqrt(c*x^2 + b*x + a)*(e*x)^m, x)","F",0
1090,0,0,0,0.454159," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \left(e x\right)^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*(e*x)^m, x)","F",0
1091,0,0,0,0.435238," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \left(e x\right)^{m}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((B*x + A)*(e*x)^m/sqrt(c*x^2 + b*x + a), x)","F",0
1092,0,0,0,0.442808," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \left(e x\right)^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*(e*x)^m/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1093,0,0,0,0.429211," ","integrate((e*x)^m*(B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \left(e x\right)^{m}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*(e*x)^m/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1094,0,0,0,0.443907," ","integrate((e*x)^m*(B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*x + A)*(c*x^2 + b*x + a)^p*(e*x)^m, x)","F",0
1095,0,0,0,0.420778," ","integrate(x^3*(B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{4} + A x^{3}\right)} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((B*x^4 + A*x^3)*(c*x^2 + b*x + a)^p, x)","F",0
1096,0,0,0,0.438133," ","integrate(x^2*(B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{3} + A x^{2}\right)} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((B*x^3 + A*x^2)*(c*x^2 + b*x + a)^p, x)","F",0
1097,0,0,0,0.429337," ","integrate(x*(B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{2} + A x\right)} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((B*x^2 + A*x)*(c*x^2 + b*x + a)^p, x)","F",0
1098,0,0,0,0.436329," ","integrate((B*x+A)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((B*x + A)*(c*x^2 + b*x + a)^p, x)","F",0
1099,0,0,0,0.441230," ","integrate((B*x+A)*(c*x^2+b*x+a)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p}}{x}, x\right)"," ",0,"integral((B*x + A)*(c*x^2 + b*x + a)^p/x, x)","F",0
1100,0,0,0,0.439702," ","integrate((B*x+A)*(c*x^2+b*x+a)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((B*x + A)*(c*x^2 + b*x + a)^p/x^2, x)","F",0
1101,0,0,0,0.441090," ","integrate((B*x+A)*(c*x^2+b*x+a)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((B*x + A)*(c*x^2 + b*x + a)^p/x^3, x)","F",0
1102,1,427,0,0.429122," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x),x, algorithm=""fricas"")","-\frac{{\left(A b d^{2} e^{2} m^{2} + 6 \, B c d^{4} + 12 \, A b d^{2} e^{2} - 8 \, {\left(B b + A c\right)} d^{3} e - {\left(B c e^{4} m^{3} + 6 \, B c e^{4} m^{2} + 11 \, B c e^{4} m + 6 \, B c e^{4}\right)} x^{4} - {\left(8 \, {\left(B b + A c\right)} e^{4} + {\left(B c d e^{3} + {\left(B b + A c\right)} e^{4}\right)} m^{3} + {\left(3 \, B c d e^{3} + 7 \, {\left(B b + A c\right)} e^{4}\right)} m^{2} + 2 \, {\left(B c d e^{3} + 7 \, {\left(B b + A c\right)} e^{4}\right)} m\right)} x^{3} - {\left(12 \, A b e^{4} + {\left(A b e^{4} + {\left(B b + A c\right)} d e^{3}\right)} m^{3} - {\left(3 \, B c d^{2} e^{2} - 8 \, A b e^{4} - 5 \, {\left(B b + A c\right)} d e^{3}\right)} m^{2} - {\left(3 \, B c d^{2} e^{2} - 19 \, A b e^{4} - 4 \, {\left(B b + A c\right)} d e^{3}\right)} m\right)} x^{2} + {\left(7 \, A b d^{2} e^{2} - 2 \, {\left(B b + A c\right)} d^{3} e\right)} m - {\left(A b d e^{3} m^{3} + {\left(7 \, A b d e^{3} - 2 \, {\left(B b + A c\right)} d^{2} e^{2}\right)} m^{2} + 2 \, {\left(3 \, B c d^{3} e + 6 \, A b d e^{3} - 4 \, {\left(B b + A c\right)} d^{2} e^{2}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"-(A*b*d^2*e^2*m^2 + 6*B*c*d^4 + 12*A*b*d^2*e^2 - 8*(B*b + A*c)*d^3*e - (B*c*e^4*m^3 + 6*B*c*e^4*m^2 + 11*B*c*e^4*m + 6*B*c*e^4)*x^4 - (8*(B*b + A*c)*e^4 + (B*c*d*e^3 + (B*b + A*c)*e^4)*m^3 + (3*B*c*d*e^3 + 7*(B*b + A*c)*e^4)*m^2 + 2*(B*c*d*e^3 + 7*(B*b + A*c)*e^4)*m)*x^3 - (12*A*b*e^4 + (A*b*e^4 + (B*b + A*c)*d*e^3)*m^3 - (3*B*c*d^2*e^2 - 8*A*b*e^4 - 5*(B*b + A*c)*d*e^3)*m^2 - (3*B*c*d^2*e^2 - 19*A*b*e^4 - 4*(B*b + A*c)*d*e^3)*m)*x^2 + (7*A*b*d^2*e^2 - 2*(B*b + A*c)*d^3*e)*m - (A*b*d*e^3*m^3 + (7*A*b*d*e^3 - 2*(B*b + A*c)*d^2*e^2)*m^2 + 2*(3*B*c*d^3*e + 6*A*b*d*e^3 - 4*(B*b + A*c)*d^2*e^2)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
1103,1,218,0,0.354950," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{4} c B + \frac{4}{7} x^{7} e^{3} d c B + \frac{1}{7} x^{7} e^{4} b B + \frac{1}{7} x^{7} e^{4} c A + x^{6} e^{2} d^{2} c B + \frac{2}{3} x^{6} e^{3} d b B + \frac{2}{3} x^{6} e^{3} d c A + \frac{1}{6} x^{6} e^{4} b A + \frac{4}{5} x^{5} e d^{3} c B + \frac{6}{5} x^{5} e^{2} d^{2} b B + \frac{6}{5} x^{5} e^{2} d^{2} c A + \frac{4}{5} x^{5} e^{3} d b A + \frac{1}{4} x^{4} d^{4} c B + x^{4} e d^{3} b B + x^{4} e d^{3} c A + \frac{3}{2} x^{4} e^{2} d^{2} b A + \frac{1}{3} x^{3} d^{4} b B + \frac{1}{3} x^{3} d^{4} c A + \frac{4}{3} x^{3} e d^{3} b A + \frac{1}{2} x^{2} d^{4} b A"," ",0,"1/8*x^8*e^4*c*B + 4/7*x^7*e^3*d*c*B + 1/7*x^7*e^4*b*B + 1/7*x^7*e^4*c*A + x^6*e^2*d^2*c*B + 2/3*x^6*e^3*d*b*B + 2/3*x^6*e^3*d*c*A + 1/6*x^6*e^4*b*A + 4/5*x^5*e*d^3*c*B + 6/5*x^5*e^2*d^2*b*B + 6/5*x^5*e^2*d^2*c*A + 4/5*x^5*e^3*d*b*A + 1/4*x^4*d^4*c*B + x^4*e*d^3*b*B + x^4*e*d^3*c*A + 3/2*x^4*e^2*d^2*b*A + 1/3*x^3*d^4*b*B + 1/3*x^3*d^4*c*A + 4/3*x^3*e*d^3*b*A + 1/2*x^2*d^4*b*A","A",0
1104,1,168,0,0.352499," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{3} c B + \frac{1}{2} x^{6} e^{2} d c B + \frac{1}{6} x^{6} e^{3} b B + \frac{1}{6} x^{6} e^{3} c A + \frac{3}{5} x^{5} e d^{2} c B + \frac{3}{5} x^{5} e^{2} d b B + \frac{3}{5} x^{5} e^{2} d c A + \frac{1}{5} x^{5} e^{3} b A + \frac{1}{4} x^{4} d^{3} c B + \frac{3}{4} x^{4} e d^{2} b B + \frac{3}{4} x^{4} e d^{2} c A + \frac{3}{4} x^{4} e^{2} d b A + \frac{1}{3} x^{3} d^{3} b B + \frac{1}{3} x^{3} d^{3} c A + x^{3} e d^{2} b A + \frac{1}{2} x^{2} d^{3} b A"," ",0,"1/7*x^7*e^3*c*B + 1/2*x^6*e^2*d*c*B + 1/6*x^6*e^3*b*B + 1/6*x^6*e^3*c*A + 3/5*x^5*e*d^2*c*B + 3/5*x^5*e^2*d*b*B + 3/5*x^5*e^2*d*c*A + 1/5*x^5*e^3*b*A + 1/4*x^4*d^3*c*B + 3/4*x^4*e*d^2*b*B + 3/4*x^4*e*d^2*c*A + 3/4*x^4*e^2*d*b*A + 1/3*x^3*d^3*b*B + 1/3*x^3*d^3*c*A + x^3*e*d^2*b*A + 1/2*x^2*d^3*b*A","A",0
1105,1,117,0,0.357681," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{2} c B + \frac{2}{5} x^{5} e d c B + \frac{1}{5} x^{5} e^{2} b B + \frac{1}{5} x^{5} e^{2} c A + \frac{1}{4} x^{4} d^{2} c B + \frac{1}{2} x^{4} e d b B + \frac{1}{2} x^{4} e d c A + \frac{1}{4} x^{4} e^{2} b A + \frac{1}{3} x^{3} d^{2} b B + \frac{1}{3} x^{3} d^{2} c A + \frac{2}{3} x^{3} e d b A + \frac{1}{2} x^{2} d^{2} b A"," ",0,"1/6*x^6*e^2*c*B + 2/5*x^5*e*d*c*B + 1/5*x^5*e^2*b*B + 1/5*x^5*e^2*c*A + 1/4*x^4*d^2*c*B + 1/2*x^4*e*d*b*B + 1/2*x^4*e*d*c*A + 1/4*x^4*e^2*b*A + 1/3*x^3*d^2*b*B + 1/3*x^3*d^2*c*A + 2/3*x^3*e*d*b*A + 1/2*x^2*d^2*b*A","A",0
1106,1,65,0,0.361256," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e c B + \frac{1}{4} x^{4} d c B + \frac{1}{4} x^{4} e b B + \frac{1}{4} x^{4} e c A + \frac{1}{3} x^{3} d b B + \frac{1}{3} x^{3} d c A + \frac{1}{3} x^{3} e b A + \frac{1}{2} x^{2} d b A"," ",0,"1/5*x^5*e*c*B + 1/4*x^4*d*c*B + 1/4*x^4*e*b*B + 1/4*x^4*e*c*A + 1/3*x^3*d*b*B + 1/3*x^3*d*c*A + 1/3*x^3*e*b*A + 1/2*x^2*d*b*A","A",0
1107,1,29,0,0.358208," ","integrate((B*x+A)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} b B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} b A"," ",0,"1/4*x^4*c*B + 1/3*x^3*b*B + 1/3*x^3*c*A + 1/2*x^2*b*A","A",0
1108,1,106,0,0.399467," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d),x, algorithm=""fricas"")","\frac{2 \, B c e^{3} x^{3} - 3 \, {\left(B c d e^{2} - {\left(B b + A c\right)} e^{3}\right)} x^{2} + 6 \, {\left(B c d^{2} e + A b e^{3} - {\left(B b + A c\right)} d e^{2}\right)} x - 6 \, {\left(B c d^{3} + A b d e^{2} - {\left(B b + A c\right)} d^{2} e\right)} \log\left(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(2*B*c*e^3*x^3 - 3*(B*c*d*e^2 - (B*b + A*c)*e^3)*x^2 + 6*(B*c*d^2*e + A*b*e^3 - (B*b + A*c)*d*e^2)*x - 6*(B*c*d^3 + A*b*d*e^2 - (B*b + A*c)*d^2*e)*log(e*x + d))/e^4","A",0
1109,1,170,0,0.391030," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{B c e^{3} x^{3} + 2 \, B c d^{3} + 2 \, A b d e^{2} - 2 \, {\left(B b + A c\right)} d^{2} e - {\left(3 \, B c d e^{2} - 2 \, {\left(B b + A c\right)} e^{3}\right)} x^{2} - 2 \, {\left(2 \, B c d^{2} e - {\left(B b + A c\right)} d e^{2}\right)} x + 2 \, {\left(3 \, B c d^{3} + A b d e^{2} - 2 \, {\left(B b + A c\right)} d^{2} e + {\left(3 \, B c d^{2} e + A b e^{3} - 2 \, {\left(B b + A c\right)} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(B*c*e^3*x^3 + 2*B*c*d^3 + 2*A*b*d*e^2 - 2*(B*b + A*c)*d^2*e - (3*B*c*d*e^2 - 2*(B*b + A*c)*e^3)*x^2 - 2*(2*B*c*d^2*e - (B*b + A*c)*d*e^2)*x + 2*(3*B*c*d^3 + A*b*d*e^2 - 2*(B*b + A*c)*d^2*e + (3*B*c*d^2*e + A*b*e^3 - 2*(B*b + A*c)*d*e^2)*x)*log(e*x + d))/(e^5*x + d*e^4)","A",0
1110,1,186,0,0.398676," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, B c e^{3} x^{3} + 4 \, B c d e^{2} x^{2} - 5 \, B c d^{3} - A b d e^{2} + 3 \, {\left(B b + A c\right)} d^{2} e - 2 \, {\left(2 \, B c d^{2} e + A b e^{3} - 2 \, {\left(B b + A c\right)} d e^{2}\right)} x - 2 \, {\left(3 \, B c d^{3} - {\left(B b + A c\right)} d^{2} e + {\left(3 \, B c d e^{2} - {\left(B b + A c\right)} e^{3}\right)} x^{2} + 2 \, {\left(3 \, B c d^{2} e - {\left(B b + A c\right)} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(2*B*c*e^3*x^3 + 4*B*c*d*e^2*x^2 - 5*B*c*d^3 - A*b*d*e^2 + 3*(B*b + A*c)*d^2*e - 2*(2*B*c*d^2*e + A*b*e^3 - 2*(B*b + A*c)*d*e^2)*x - 2*(3*B*c*d^3 - (B*b + A*c)*d^2*e + (3*B*c*d*e^2 - (B*b + A*c)*e^3)*x^2 + 2*(3*B*c*d^2*e - (B*b + A*c)*d*e^2)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1111,1,168,0,0.402427," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{11 \, B c d^{3} - A b d e^{2} - 2 \, {\left(B b + A c\right)} d^{2} e + 6 \, {\left(3 \, B c d e^{2} - {\left(B b + A c\right)} e^{3}\right)} x^{2} + 3 \, {\left(9 \, B c d^{2} e - A b e^{3} - 2 \, {\left(B b + A c\right)} d e^{2}\right)} x + 6 \, {\left(B c e^{3} x^{3} + 3 \, B c d e^{2} x^{2} + 3 \, B c d^{2} e x + B c d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(11*B*c*d^3 - A*b*d*e^2 - 2*(B*b + A*c)*d^2*e + 6*(3*B*c*d*e^2 - (B*b + A*c)*e^3)*x^2 + 3*(9*B*c*d^2*e - A*b*e^3 - 2*(B*b + A*c)*d*e^2)*x + 6*(B*c*e^3*x^3 + 3*B*c*d*e^2*x^2 + 3*B*c*d^2*e*x + B*c*d^3)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1112,1,140,0,0.393583," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{12 \, B c e^{3} x^{3} + 3 \, B c d^{3} + A b d e^{2} + {\left(B b + A c\right)} d^{2} e + 6 \, {\left(3 \, B c d e^{2} + {\left(B b + A c\right)} e^{3}\right)} x^{2} + 4 \, {\left(3 \, B c d^{2} e + A b e^{3} + {\left(B b + A c\right)} d e^{2}\right)} x}{12 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-1/12*(12*B*c*e^3*x^3 + 3*B*c*d^3 + A*b*d*e^2 + (B*b + A*c)*d^2*e + 6*(3*B*c*d*e^2 + (B*b + A*c)*e^3)*x^2 + 4*(3*B*c*d^2*e + A*b*e^3 + (B*b + A*c)*d*e^2)*x)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","A",0
1113,1,156,0,0.394919," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{30 \, B c e^{3} x^{3} + 3 \, B c d^{3} + 3 \, A b d e^{2} + 2 \, {\left(B b + A c\right)} d^{2} e + 10 \, {\left(3 \, B c d e^{2} + 2 \, {\left(B b + A c\right)} e^{3}\right)} x^{2} + 5 \, {\left(3 \, B c d^{2} e + 3 \, A b e^{3} + 2 \, {\left(B b + A c\right)} d e^{2}\right)} x}{60 \, {\left(e^{9} x^{5} + 5 \, d e^{8} x^{4} + 10 \, d^{2} e^{7} x^{3} + 10 \, d^{3} e^{6} x^{2} + 5 \, d^{4} e^{5} x + d^{5} e^{4}\right)}}"," ",0,"-1/60*(30*B*c*e^3*x^3 + 3*B*c*d^3 + 3*A*b*d*e^2 + 2*(B*b + A*c)*d^2*e + 10*(3*B*c*d*e^2 + 2*(B*b + A*c)*e^3)*x^2 + 5*(3*B*c*d^2*e + 3*A*b*e^3 + 2*(B*b + A*c)*d*e^2)*x)/(e^9*x^5 + 5*d*e^8*x^4 + 10*d^2*e^7*x^3 + 10*d^3*e^6*x^2 + 5*d^4*e^5*x + d^5*e^4)","A",0
1114,1,1417,0,0.456218," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, A b^{2} d^{3} e^{3} m^{3} - 120 \, B c^{2} d^{6} + 240 \, A b^{2} d^{3} e^{3} + 144 \, {\left(2 \, B b c + A c^{2}\right)} d^{5} e - 180 \, {\left(B b^{2} + 2 \, A b c\right)} d^{4} e^{2} + {\left(B c^{2} e^{6} m^{5} + 15 \, B c^{2} e^{6} m^{4} + 85 \, B c^{2} e^{6} m^{3} + 225 \, B c^{2} e^{6} m^{2} + 274 \, B c^{2} e^{6} m + 120 \, B c^{2} e^{6}\right)} x^{6} + {\left(144 \, {\left(2 \, B b c + A c^{2}\right)} e^{6} + {\left(B c^{2} d e^{5} + {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m^{5} + 2 \, {\left(5 \, B c^{2} d e^{5} + 8 \, {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m^{4} + 5 \, {\left(7 \, B c^{2} d e^{5} + 19 \, {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m^{3} + 10 \, {\left(5 \, B c^{2} d e^{5} + 26 \, {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m^{2} + 12 \, {\left(2 \, B c^{2} d e^{5} + 27 \, {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m\right)} x^{5} + {\left(180 \, {\left(B b^{2} + 2 \, A b c\right)} e^{6} + {\left({\left(2 \, B b c + A c^{2}\right)} d e^{5} + {\left(B b^{2} + 2 \, A b c\right)} e^{6}\right)} m^{5} - {\left(5 \, B c^{2} d^{2} e^{4} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d e^{5} - 17 \, {\left(B b^{2} + 2 \, A b c\right)} e^{6}\right)} m^{4} - {\left(30 \, B c^{2} d^{2} e^{4} - 47 \, {\left(2 \, B b c + A c^{2}\right)} d e^{5} - 107 \, {\left(B b^{2} + 2 \, A b c\right)} e^{6}\right)} m^{3} - {\left(55 \, B c^{2} d^{2} e^{4} - 72 \, {\left(2 \, B b c + A c^{2}\right)} d e^{5} - 307 \, {\left(B b^{2} + 2 \, A b c\right)} e^{6}\right)} m^{2} - 6 \, {\left(5 \, B c^{2} d^{2} e^{4} - 6 \, {\left(2 \, B b c + A c^{2}\right)} d e^{5} - 66 \, {\left(B b^{2} + 2 \, A b c\right)} e^{6}\right)} m\right)} x^{4} + {\left(240 \, A b^{2} e^{6} + {\left(A b^{2} e^{6} + {\left(B b^{2} + 2 \, A b c\right)} d e^{5}\right)} m^{5} + 2 \, {\left(9 \, A b^{2} e^{6} - 2 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{4} + 7 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{5}\right)} m^{4} + {\left(20 \, B c^{2} d^{3} e^{3} + 121 \, A b^{2} e^{6} - 36 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{4} + 65 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{5}\right)} m^{3} + 4 \, {\left(15 \, B c^{2} d^{3} e^{3} + 93 \, A b^{2} e^{6} - 20 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{4} + 28 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{5}\right)} m^{2} + 4 \, {\left(10 \, B c^{2} d^{3} e^{3} + 127 \, A b^{2} e^{6} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{4} + 15 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{5}\right)} m\right)} x^{3} + 6 \, {\left(5 \, A b^{2} d^{3} e^{3} - {\left(B b^{2} + 2 \, A b c\right)} d^{4} e^{2}\right)} m^{2} + {\left(A b^{2} d e^{5} m^{5} + {\left(16 \, A b^{2} d e^{5} - 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{4}\right)} m^{4} + {\left(89 \, A b^{2} d e^{5} + 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{3} - 36 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{4}\right)} m^{3} - {\left(60 \, B c^{2} d^{4} e^{2} - 194 \, A b^{2} d e^{5} - 84 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{3} + 123 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{4}\right)} m^{2} - 6 \, {\left(10 \, B c^{2} d^{4} e^{2} - 20 \, A b^{2} d e^{5} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{3} + 15 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{4}\right)} m\right)} x^{2} + 2 \, {\left(74 \, A b^{2} d^{3} e^{3} + 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{5} e - 33 \, {\left(B b^{2} + 2 \, A b c\right)} d^{4} e^{2}\right)} m - 2 \, {\left(A b^{2} d^{2} e^{4} m^{4} + 3 \, {\left(5 \, A b^{2} d^{2} e^{4} - {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{3}\right)} m^{3} + {\left(74 \, A b^{2} d^{2} e^{4} + 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e^{2} - 33 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{3}\right)} m^{2} - 6 \, {\left(10 \, B c^{2} d^{5} e - 20 \, A b^{2} d^{2} e^{4} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e^{2} + 15 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{6} m^{6} + 21 \, e^{6} m^{5} + 175 \, e^{6} m^{4} + 735 \, e^{6} m^{3} + 1624 \, e^{6} m^{2} + 1764 \, e^{6} m + 720 \, e^{6}}"," ",0,"(2*A*b^2*d^3*e^3*m^3 - 120*B*c^2*d^6 + 240*A*b^2*d^3*e^3 + 144*(2*B*b*c + A*c^2)*d^5*e - 180*(B*b^2 + 2*A*b*c)*d^4*e^2 + (B*c^2*e^6*m^5 + 15*B*c^2*e^6*m^4 + 85*B*c^2*e^6*m^3 + 225*B*c^2*e^6*m^2 + 274*B*c^2*e^6*m + 120*B*c^2*e^6)*x^6 + (144*(2*B*b*c + A*c^2)*e^6 + (B*c^2*d*e^5 + (2*B*b*c + A*c^2)*e^6)*m^5 + 2*(5*B*c^2*d*e^5 + 8*(2*B*b*c + A*c^2)*e^6)*m^4 + 5*(7*B*c^2*d*e^5 + 19*(2*B*b*c + A*c^2)*e^6)*m^3 + 10*(5*B*c^2*d*e^5 + 26*(2*B*b*c + A*c^2)*e^6)*m^2 + 12*(2*B*c^2*d*e^5 + 27*(2*B*b*c + A*c^2)*e^6)*m)*x^5 + (180*(B*b^2 + 2*A*b*c)*e^6 + ((2*B*b*c + A*c^2)*d*e^5 + (B*b^2 + 2*A*b*c)*e^6)*m^5 - (5*B*c^2*d^2*e^4 - 12*(2*B*b*c + A*c^2)*d*e^5 - 17*(B*b^2 + 2*A*b*c)*e^6)*m^4 - (30*B*c^2*d^2*e^4 - 47*(2*B*b*c + A*c^2)*d*e^5 - 107*(B*b^2 + 2*A*b*c)*e^6)*m^3 - (55*B*c^2*d^2*e^4 - 72*(2*B*b*c + A*c^2)*d*e^5 - 307*(B*b^2 + 2*A*b*c)*e^6)*m^2 - 6*(5*B*c^2*d^2*e^4 - 6*(2*B*b*c + A*c^2)*d*e^5 - 66*(B*b^2 + 2*A*b*c)*e^6)*m)*x^4 + (240*A*b^2*e^6 + (A*b^2*e^6 + (B*b^2 + 2*A*b*c)*d*e^5)*m^5 + 2*(9*A*b^2*e^6 - 2*(2*B*b*c + A*c^2)*d^2*e^4 + 7*(B*b^2 + 2*A*b*c)*d*e^5)*m^4 + (20*B*c^2*d^3*e^3 + 121*A*b^2*e^6 - 36*(2*B*b*c + A*c^2)*d^2*e^4 + 65*(B*b^2 + 2*A*b*c)*d*e^5)*m^3 + 4*(15*B*c^2*d^3*e^3 + 93*A*b^2*e^6 - 20*(2*B*b*c + A*c^2)*d^2*e^4 + 28*(B*b^2 + 2*A*b*c)*d*e^5)*m^2 + 4*(10*B*c^2*d^3*e^3 + 127*A*b^2*e^6 - 12*(2*B*b*c + A*c^2)*d^2*e^4 + 15*(B*b^2 + 2*A*b*c)*d*e^5)*m)*x^3 + 6*(5*A*b^2*d^3*e^3 - (B*b^2 + 2*A*b*c)*d^4*e^2)*m^2 + (A*b^2*d*e^5*m^5 + (16*A*b^2*d*e^5 - 3*(B*b^2 + 2*A*b*c)*d^2*e^4)*m^4 + (89*A*b^2*d*e^5 + 12*(2*B*b*c + A*c^2)*d^3*e^3 - 36*(B*b^2 + 2*A*b*c)*d^2*e^4)*m^3 - (60*B*c^2*d^4*e^2 - 194*A*b^2*d*e^5 - 84*(2*B*b*c + A*c^2)*d^3*e^3 + 123*(B*b^2 + 2*A*b*c)*d^2*e^4)*m^2 - 6*(10*B*c^2*d^4*e^2 - 20*A*b^2*d*e^5 - 12*(2*B*b*c + A*c^2)*d^3*e^3 + 15*(B*b^2 + 2*A*b*c)*d^2*e^4)*m)*x^2 + 2*(74*A*b^2*d^3*e^3 + 12*(2*B*b*c + A*c^2)*d^5*e - 33*(B*b^2 + 2*A*b*c)*d^4*e^2)*m - 2*(A*b^2*d^2*e^4*m^4 + 3*(5*A*b^2*d^2*e^4 - (B*b^2 + 2*A*b*c)*d^3*e^3)*m^3 + (74*A*b^2*d^2*e^4 + 12*(2*B*b*c + A*c^2)*d^4*e^2 - 33*(B*b^2 + 2*A*b*c)*d^3*e^3)*m^2 - 6*(10*B*c^2*d^5*e - 20*A*b^2*d^2*e^4 - 12*(2*B*b*c + A*c^2)*d^4*e^2 + 15*(B*b^2 + 2*A*b*c)*d^3*e^3)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)","B",0
1115,1,291,0,0.361192," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{3} c^{2} B + \frac{3}{8} x^{8} e^{2} d c^{2} B + \frac{1}{4} x^{8} e^{3} c b B + \frac{1}{8} x^{8} e^{3} c^{2} A + \frac{3}{7} x^{7} e d^{2} c^{2} B + \frac{6}{7} x^{7} e^{2} d c b B + \frac{1}{7} x^{7} e^{3} b^{2} B + \frac{3}{7} x^{7} e^{2} d c^{2} A + \frac{2}{7} x^{7} e^{3} c b A + \frac{1}{6} x^{6} d^{3} c^{2} B + x^{6} e d^{2} c b B + \frac{1}{2} x^{6} e^{2} d b^{2} B + \frac{1}{2} x^{6} e d^{2} c^{2} A + x^{6} e^{2} d c b A + \frac{1}{6} x^{6} e^{3} b^{2} A + \frac{2}{5} x^{5} d^{3} c b B + \frac{3}{5} x^{5} e d^{2} b^{2} B + \frac{1}{5} x^{5} d^{3} c^{2} A + \frac{6}{5} x^{5} e d^{2} c b A + \frac{3}{5} x^{5} e^{2} d b^{2} A + \frac{1}{4} x^{4} d^{3} b^{2} B + \frac{1}{2} x^{4} d^{3} c b A + \frac{3}{4} x^{4} e d^{2} b^{2} A + \frac{1}{3} x^{3} d^{3} b^{2} A"," ",0,"1/9*x^9*e^3*c^2*B + 3/8*x^8*e^2*d*c^2*B + 1/4*x^8*e^3*c*b*B + 1/8*x^8*e^3*c^2*A + 3/7*x^7*e*d^2*c^2*B + 6/7*x^7*e^2*d*c*b*B + 1/7*x^7*e^3*b^2*B + 3/7*x^7*e^2*d*c^2*A + 2/7*x^7*e^3*c*b*A + 1/6*x^6*d^3*c^2*B + x^6*e*d^2*c*b*B + 1/2*x^6*e^2*d*b^2*B + 1/2*x^6*e*d^2*c^2*A + x^6*e^2*d*c*b*A + 1/6*x^6*e^3*b^2*A + 2/5*x^5*d^3*c*b*B + 3/5*x^5*e*d^2*b^2*B + 1/5*x^5*d^3*c^2*A + 6/5*x^5*e*d^2*c*b*A + 3/5*x^5*e^2*d*b^2*A + 1/4*x^4*d^3*b^2*B + 1/2*x^4*d^3*c*b*A + 3/4*x^4*e*d^2*b^2*A + 1/3*x^3*d^3*b^2*A","A",0
1116,1,205,0,0.348650," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{2} c^{2} B + \frac{2}{7} x^{7} e d c^{2} B + \frac{2}{7} x^{7} e^{2} c b B + \frac{1}{7} x^{7} e^{2} c^{2} A + \frac{1}{6} x^{6} d^{2} c^{2} B + \frac{2}{3} x^{6} e d c b B + \frac{1}{6} x^{6} e^{2} b^{2} B + \frac{1}{3} x^{6} e d c^{2} A + \frac{1}{3} x^{6} e^{2} c b A + \frac{2}{5} x^{5} d^{2} c b B + \frac{2}{5} x^{5} e d b^{2} B + \frac{1}{5} x^{5} d^{2} c^{2} A + \frac{4}{5} x^{5} e d c b A + \frac{1}{5} x^{5} e^{2} b^{2} A + \frac{1}{4} x^{4} d^{2} b^{2} B + \frac{1}{2} x^{4} d^{2} c b A + \frac{1}{2} x^{4} e d b^{2} A + \frac{1}{3} x^{3} d^{2} b^{2} A"," ",0,"1/8*x^8*e^2*c^2*B + 2/7*x^7*e*d*c^2*B + 2/7*x^7*e^2*c*b*B + 1/7*x^7*e^2*c^2*A + 1/6*x^6*d^2*c^2*B + 2/3*x^6*e*d*c*b*B + 1/6*x^6*e^2*b^2*B + 1/3*x^6*e*d*c^2*A + 1/3*x^6*e^2*c*b*A + 2/5*x^5*d^2*c*b*B + 2/5*x^5*e*d*b^2*B + 1/5*x^5*d^2*c^2*A + 4/5*x^5*e*d*c*b*A + 1/5*x^5*e^2*b^2*A + 1/4*x^4*d^2*b^2*B + 1/2*x^4*d^2*c*b*A + 1/2*x^4*e*d*b^2*A + 1/3*x^3*d^2*b^2*A","A",0
1117,1,117,0,0.361131," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e c^{2} B + \frac{1}{6} x^{6} d c^{2} B + \frac{1}{3} x^{6} e c b B + \frac{1}{6} x^{6} e c^{2} A + \frac{2}{5} x^{5} d c b B + \frac{1}{5} x^{5} e b^{2} B + \frac{1}{5} x^{5} d c^{2} A + \frac{2}{5} x^{5} e c b A + \frac{1}{4} x^{4} d b^{2} B + \frac{1}{2} x^{4} d c b A + \frac{1}{4} x^{4} e b^{2} A + \frac{1}{3} x^{3} d b^{2} A"," ",0,"1/7*x^7*e*c^2*B + 1/6*x^6*d*c^2*B + 1/3*x^6*e*c*b*B + 1/6*x^6*e*c^2*A + 2/5*x^5*d*c*b*B + 1/5*x^5*e*b^2*B + 1/5*x^5*d*c^2*A + 2/5*x^5*e*c*b*A + 1/4*x^4*d*b^2*B + 1/2*x^4*d*c*b*A + 1/4*x^4*e*b^2*A + 1/3*x^3*d*b^2*A","A",0
1118,1,53,0,0.352185," ","integrate((B*x+A)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} c^{2} B + \frac{2}{5} x^{5} c b B + \frac{1}{5} x^{5} c^{2} A + \frac{1}{4} x^{4} b^{2} B + \frac{1}{2} x^{4} c b A + \frac{1}{3} x^{3} b^{2} A"," ",0,"1/6*x^6*c^2*B + 2/5*x^5*c*b*B + 1/5*x^5*c^2*A + 1/4*x^4*b^2*B + 1/2*x^4*c*b*A + 1/3*x^3*b^2*A","A",0
1119,1,283,0,0.405671," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d),x, algorithm=""fricas"")","\frac{12 \, B c^{2} e^{5} x^{5} - 15 \, {\left(B c^{2} d e^{4} - {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 20 \, {\left(B c^{2} d^{2} e^{3} - {\left(2 \, B b c + A c^{2}\right)} d e^{4} + {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} - 30 \, {\left(B c^{2} d^{3} e^{2} - A b^{2} e^{5} - {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 60 \, {\left(B c^{2} d^{4} e - A b^{2} d e^{4} - {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x - 60 \, {\left(B c^{2} d^{5} - A b^{2} d^{2} e^{3} - {\left(2 \, B b c + A c^{2}\right)} d^{4} e + {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2}\right)} \log\left(e x + d\right)}{60 \, e^{6}}"," ",0,"1/60*(12*B*c^2*e^5*x^5 - 15*(B*c^2*d*e^4 - (2*B*b*c + A*c^2)*e^5)*x^4 + 20*(B*c^2*d^2*e^3 - (2*B*b*c + A*c^2)*d*e^4 + (B*b^2 + 2*A*b*c)*e^5)*x^3 - 30*(B*c^2*d^3*e^2 - A*b^2*e^5 - (2*B*b*c + A*c^2)*d^2*e^3 + (B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 60*(B*c^2*d^4*e - A*b^2*d*e^4 - (2*B*b*c + A*c^2)*d^3*e^2 + (B*b^2 + 2*A*b*c)*d^2*e^3)*x - 60*(B*c^2*d^5 - A*b^2*d^2*e^3 - (2*B*b*c + A*c^2)*d^4*e + (B*b^2 + 2*A*b*c)*d^3*e^2)*log(e*x + d))/e^6","A",0
1120,1,420,0,0.411030," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{3 \, B c^{2} e^{5} x^{5} + 12 \, B c^{2} d^{5} - 12 \, A b^{2} d^{2} e^{3} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 12 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} - {\left(5 \, B c^{2} d e^{4} - 4 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 2 \, {\left(5 \, B c^{2} d^{2} e^{3} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} - 6 \, {\left(5 \, B c^{2} d^{3} e^{2} - 2 \, A b^{2} e^{5} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} - 12 \, {\left(4 \, B c^{2} d^{4} e - A b^{2} d e^{4} - 3 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 2 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x + 12 \, {\left(5 \, B c^{2} d^{5} - 2 \, A b^{2} d^{2} e^{3} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} + {\left(5 \, B c^{2} d^{4} e - 2 \, A b^{2} d e^{4} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"1/12*(3*B*c^2*e^5*x^5 + 12*B*c^2*d^5 - 12*A*b^2*d^2*e^3 - 12*(2*B*b*c + A*c^2)*d^4*e + 12*(B*b^2 + 2*A*b*c)*d^3*e^2 - (5*B*c^2*d*e^4 - 4*(2*B*b*c + A*c^2)*e^5)*x^4 + 2*(5*B*c^2*d^2*e^3 - 4*(2*B*b*c + A*c^2)*d*e^4 + 3*(B*b^2 + 2*A*b*c)*e^5)*x^3 - 6*(5*B*c^2*d^3*e^2 - 2*A*b^2*e^5 - 4*(2*B*b*c + A*c^2)*d^2*e^3 + 3*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 - 12*(4*B*c^2*d^4*e - A*b^2*d*e^4 - 3*(2*B*b*c + A*c^2)*d^3*e^2 + 2*(B*b^2 + 2*A*b*c)*d^2*e^3)*x + 12*(5*B*c^2*d^5 - 2*A*b^2*d^2*e^3 - 4*(2*B*b*c + A*c^2)*d^4*e + 3*(B*b^2 + 2*A*b*c)*d^3*e^2 + (5*B*c^2*d^4*e - 2*A*b^2*d*e^4 - 4*(2*B*b*c + A*c^2)*d^3*e^2 + 3*(B*b^2 + 2*A*b*c)*d^2*e^3)*x)*log(e*x + d))/(e^7*x + d*e^6)","B",0
1121,1,483,0,0.408480," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, B c^{2} e^{5} x^{5} - 27 \, B c^{2} d^{5} + 9 \, A b^{2} d^{2} e^{3} + 21 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e - 15 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} - {\left(5 \, B c^{2} d e^{4} - 3 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 2 \, {\left(10 \, B c^{2} d^{2} e^{3} - 6 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} + 3 \, {\left(21 \, B c^{2} d^{3} e^{2} - 11 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 4 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 6 \, {\left(B c^{2} d^{4} e + 2 \, A b^{2} d e^{4} + {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} - 2 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x - 6 \, {\left(10 \, B c^{2} d^{5} - A b^{2} d^{2} e^{3} - 6 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} + {\left(10 \, B c^{2} d^{3} e^{2} - A b^{2} e^{5} - 6 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 2 \, {\left(10 \, B c^{2} d^{4} e - A b^{2} d e^{4} - 6 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"1/6*(2*B*c^2*e^5*x^5 - 27*B*c^2*d^5 + 9*A*b^2*d^2*e^3 + 21*(2*B*b*c + A*c^2)*d^4*e - 15*(B*b^2 + 2*A*b*c)*d^3*e^2 - (5*B*c^2*d*e^4 - 3*(2*B*b*c + A*c^2)*e^5)*x^4 + 2*(10*B*c^2*d^2*e^3 - 6*(2*B*b*c + A*c^2)*d*e^4 + 3*(B*b^2 + 2*A*b*c)*e^5)*x^3 + 3*(21*B*c^2*d^3*e^2 - 11*(2*B*b*c + A*c^2)*d^2*e^3 + 4*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 6*(B*c^2*d^4*e + 2*A*b^2*d*e^4 + (2*B*b*c + A*c^2)*d^3*e^2 - 2*(B*b^2 + 2*A*b*c)*d^2*e^3)*x - 6*(10*B*c^2*d^5 - A*b^2*d^2*e^3 - 6*(2*B*b*c + A*c^2)*d^4*e + 3*(B*b^2 + 2*A*b*c)*d^3*e^2 + (10*B*c^2*d^3*e^2 - A*b^2*e^5 - 6*(2*B*b*c + A*c^2)*d^2*e^3 + 3*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 2*(10*B*c^2*d^4*e - A*b^2*d*e^4 - 6*(2*B*b*c + A*c^2)*d^3*e^2 + 3*(B*b^2 + 2*A*b*c)*d^2*e^3)*x)*log(e*x + d))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","B",0
1122,1,505,0,0.394469," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, B c^{2} e^{5} x^{5} + 47 \, B c^{2} d^{5} - 2 \, A b^{2} d^{2} e^{3} - 26 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 11 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} - 3 \, {\left(5 \, B c^{2} d e^{4} - 2 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} - 9 \, {\left(7 \, B c^{2} d^{2} e^{3} - 2 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4}\right)} x^{3} - 3 \, {\left(3 \, B c^{2} d^{3} e^{2} + 2 \, A b^{2} e^{5} + 6 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} - 6 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 3 \, {\left(27 \, B c^{2} d^{4} e - 2 \, A b^{2} d e^{4} - 18 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 9 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x + 6 \, {\left(10 \, B c^{2} d^{5} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} + {\left(10 \, B c^{2} d^{2} e^{3} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} + 3 \, {\left(10 \, B c^{2} d^{3} e^{2} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 3 \, {\left(10 \, B c^{2} d^{4} e - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"1/6*(3*B*c^2*e^5*x^5 + 47*B*c^2*d^5 - 2*A*b^2*d^2*e^3 - 26*(2*B*b*c + A*c^2)*d^4*e + 11*(B*b^2 + 2*A*b*c)*d^3*e^2 - 3*(5*B*c^2*d*e^4 - 2*(2*B*b*c + A*c^2)*e^5)*x^4 - 9*(7*B*c^2*d^2*e^3 - 2*(2*B*b*c + A*c^2)*d*e^4)*x^3 - 3*(3*B*c^2*d^3*e^2 + 2*A*b^2*e^5 + 6*(2*B*b*c + A*c^2)*d^2*e^3 - 6*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 3*(27*B*c^2*d^4*e - 2*A*b^2*d*e^4 - 18*(2*B*b*c + A*c^2)*d^3*e^2 + 9*(B*b^2 + 2*A*b*c)*d^2*e^3)*x + 6*(10*B*c^2*d^5 - 4*(2*B*b*c + A*c^2)*d^4*e + (B*b^2 + 2*A*b*c)*d^3*e^2 + (10*B*c^2*d^2*e^3 - 4*(2*B*b*c + A*c^2)*d*e^4 + (B*b^2 + 2*A*b*c)*e^5)*x^3 + 3*(10*B*c^2*d^3*e^2 - 4*(2*B*b*c + A*c^2)*d^2*e^3 + (B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 3*(10*B*c^2*d^4*e - 4*(2*B*b*c + A*c^2)*d^3*e^2 + (B*b^2 + 2*A*b*c)*d^2*e^3)*x)*log(e*x + d))/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","B",0
1123,1,475,0,0.410143," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{12 \, B c^{2} e^{5} x^{5} + 48 \, B c^{2} d e^{4} x^{4} - 77 \, B c^{2} d^{5} - A b^{2} d^{2} e^{3} + 25 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e - 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} - 12 \, {\left(4 \, B c^{2} d^{2} e^{3} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} - 6 \, {\left(42 \, B c^{2} d^{3} e^{2} + A b^{2} e^{5} - 18 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} - 4 \, {\left(62 \, B c^{2} d^{4} e + A b^{2} d e^{4} - 22 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x - 12 \, {\left(5 \, B c^{2} d^{5} - {\left(2 \, B b c + A c^{2}\right)} d^{4} e + {\left(5 \, B c^{2} d e^{4} - {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 4 \, {\left(5 \, B c^{2} d^{2} e^{3} - {\left(2 \, B b c + A c^{2}\right)} d e^{4}\right)} x^{3} + 6 \, {\left(5 \, B c^{2} d^{3} e^{2} - {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3}\right)} x^{2} + 4 \, {\left(5 \, B c^{2} d^{4} e - {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{10} x^{4} + 4 \, d e^{9} x^{3} + 6 \, d^{2} e^{8} x^{2} + 4 \, d^{3} e^{7} x + d^{4} e^{6}\right)}}"," ",0,"1/12*(12*B*c^2*e^5*x^5 + 48*B*c^2*d*e^4*x^4 - 77*B*c^2*d^5 - A*b^2*d^2*e^3 + 25*(2*B*b*c + A*c^2)*d^4*e - 3*(B*b^2 + 2*A*b*c)*d^3*e^2 - 12*(4*B*c^2*d^2*e^3 - 4*(2*B*b*c + A*c^2)*d*e^4 + (B*b^2 + 2*A*b*c)*e^5)*x^3 - 6*(42*B*c^2*d^3*e^2 + A*b^2*e^5 - 18*(2*B*b*c + A*c^2)*d^2*e^3 + 3*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 - 4*(62*B*c^2*d^4*e + A*b^2*d*e^4 - 22*(2*B*b*c + A*c^2)*d^3*e^2 + 3*(B*b^2 + 2*A*b*c)*d^2*e^3)*x - 12*(5*B*c^2*d^5 - (2*B*b*c + A*c^2)*d^4*e + (5*B*c^2*d*e^4 - (2*B*b*c + A*c^2)*e^5)*x^4 + 4*(5*B*c^2*d^2*e^3 - (2*B*b*c + A*c^2)*d*e^4)*x^3 + 6*(5*B*c^2*d^3*e^2 - (2*B*b*c + A*c^2)*d^2*e^3)*x^2 + 4*(5*B*c^2*d^4*e - (2*B*b*c + A*c^2)*d^3*e^2)*x)*log(e*x + d))/(e^10*x^4 + 4*d*e^9*x^3 + 6*d^2*e^8*x^2 + 4*d^3*e^7*x + d^4*e^6)","B",0
1124,1,407,0,0.409535," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^6,x, algorithm=""fricas"")","\frac{137 \, B c^{2} d^{5} - 2 \, A b^{2} d^{2} e^{3} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e - 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} + 60 \, {\left(5 \, B c^{2} d e^{4} - {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 30 \, {\left(30 \, B c^{2} d^{2} e^{3} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} - {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} + 10 \, {\left(110 \, B c^{2} d^{3} e^{2} - 2 \, A b^{2} e^{5} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} - 3 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 5 \, {\left(125 \, B c^{2} d^{4} e - 2 \, A b^{2} d e^{4} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} - 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x + 60 \, {\left(B c^{2} e^{5} x^{5} + 5 \, B c^{2} d e^{4} x^{4} + 10 \, B c^{2} d^{2} e^{3} x^{3} + 10 \, B c^{2} d^{3} e^{2} x^{2} + 5 \, B c^{2} d^{4} e x + B c^{2} d^{5}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{11} x^{5} + 5 \, d e^{10} x^{4} + 10 \, d^{2} e^{9} x^{3} + 10 \, d^{3} e^{8} x^{2} + 5 \, d^{4} e^{7} x + d^{5} e^{6}\right)}}"," ",0,"1/60*(137*B*c^2*d^5 - 2*A*b^2*d^2*e^3 - 12*(2*B*b*c + A*c^2)*d^4*e - 3*(B*b^2 + 2*A*b*c)*d^3*e^2 + 60*(5*B*c^2*d*e^4 - (2*B*b*c + A*c^2)*e^5)*x^4 + 30*(30*B*c^2*d^2*e^3 - 4*(2*B*b*c + A*c^2)*d*e^4 - (B*b^2 + 2*A*b*c)*e^5)*x^3 + 10*(110*B*c^2*d^3*e^2 - 2*A*b^2*e^5 - 12*(2*B*b*c + A*c^2)*d^2*e^3 - 3*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 5*(125*B*c^2*d^4*e - 2*A*b^2*d*e^4 - 12*(2*B*b*c + A*c^2)*d^3*e^2 - 3*(B*b^2 + 2*A*b*c)*d^2*e^3)*x + 60*(B*c^2*e^5*x^5 + 5*B*c^2*d*e^4*x^4 + 10*B*c^2*d^2*e^3*x^3 + 10*B*c^2*d^3*e^2*x^2 + 5*B*c^2*d^4*e*x + B*c^2*d^5)*log(e*x + d))/(e^11*x^5 + 5*d*e^10*x^4 + 10*d^2*e^9*x^3 + 10*d^3*e^8*x^2 + 5*d^4*e^7*x + d^5*e^6)","A",0
1125,1,340,0,0.397477," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{60 \, B c^{2} e^{5} x^{5} + 10 \, B c^{2} d^{5} + A b^{2} d^{2} e^{3} + 2 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} + 30 \, {\left(5 \, B c^{2} d e^{4} + {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 20 \, {\left(10 \, B c^{2} d^{2} e^{3} + 2 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} + 15 \, {\left(10 \, B c^{2} d^{3} e^{2} + A b^{2} e^{5} + 2 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 6 \, {\left(10 \, B c^{2} d^{4} e + A b^{2} d e^{4} + 2 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x}{60 \, {\left(e^{12} x^{6} + 6 \, d e^{11} x^{5} + 15 \, d^{2} e^{10} x^{4} + 20 \, d^{3} e^{9} x^{3} + 15 \, d^{4} e^{8} x^{2} + 6 \, d^{5} e^{7} x + d^{6} e^{6}\right)}}"," ",0,"-1/60*(60*B*c^2*e^5*x^5 + 10*B*c^2*d^5 + A*b^2*d^2*e^3 + 2*(2*B*b*c + A*c^2)*d^4*e + (B*b^2 + 2*A*b*c)*d^3*e^2 + 30*(5*B*c^2*d*e^4 + (2*B*b*c + A*c^2)*e^5)*x^4 + 20*(10*B*c^2*d^2*e^3 + 2*(2*B*b*c + A*c^2)*d*e^4 + (B*b^2 + 2*A*b*c)*e^5)*x^3 + 15*(10*B*c^2*d^3*e^2 + A*b^2*e^5 + 2*(2*B*b*c + A*c^2)*d^2*e^3 + (B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 6*(10*B*c^2*d^4*e + A*b^2*d*e^4 + 2*(2*B*b*c + A*c^2)*d^3*e^2 + (B*b^2 + 2*A*b*c)*d^2*e^3)*x)/(e^12*x^6 + 6*d*e^11*x^5 + 15*d^2*e^10*x^4 + 20*d^3*e^9*x^3 + 15*d^4*e^8*x^2 + 6*d^5*e^7*x + d^6*e^6)","A",0
1126,1,359,0,0.379781," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{210 \, B c^{2} e^{5} x^{5} + 10 \, B c^{2} d^{5} + 4 \, A b^{2} d^{2} e^{3} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} + 70 \, {\left(5 \, B c^{2} d e^{4} + 2 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 35 \, {\left(10 \, B c^{2} d^{2} e^{3} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} + 21 \, {\left(10 \, B c^{2} d^{3} e^{2} + 4 \, A b^{2} e^{5} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 7 \, {\left(10 \, B c^{2} d^{4} e + 4 \, A b^{2} d e^{4} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x}{420 \, {\left(e^{13} x^{7} + 7 \, d e^{12} x^{6} + 21 \, d^{2} e^{11} x^{5} + 35 \, d^{3} e^{10} x^{4} + 35 \, d^{4} e^{9} x^{3} + 21 \, d^{5} e^{8} x^{2} + 7 \, d^{6} e^{7} x + d^{7} e^{6}\right)}}"," ",0,"-1/420*(210*B*c^2*e^5*x^5 + 10*B*c^2*d^5 + 4*A*b^2*d^2*e^3 + 4*(2*B*b*c + A*c^2)*d^4*e + 3*(B*b^2 + 2*A*b*c)*d^3*e^2 + 70*(5*B*c^2*d*e^4 + 2*(2*B*b*c + A*c^2)*e^5)*x^4 + 35*(10*B*c^2*d^2*e^3 + 4*(2*B*b*c + A*c^2)*d*e^4 + 3*(B*b^2 + 2*A*b*c)*e^5)*x^3 + 21*(10*B*c^2*d^3*e^2 + 4*A*b^2*e^5 + 4*(2*B*b*c + A*c^2)*d^2*e^3 + 3*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 7*(10*B*c^2*d^4*e + 4*A*b^2*d*e^4 + 4*(2*B*b*c + A*c^2)*d^3*e^2 + 3*(B*b^2 + 2*A*b*c)*d^2*e^3)*x)/(e^13*x^7 + 7*d*e^12*x^6 + 21*d^2*e^11*x^5 + 35*d^3*e^10*x^4 + 35*d^4*e^9*x^3 + 21*d^5*e^8*x^2 + 7*d^6*e^7*x + d^7*e^6)","A",0
1127,1,3254,0,0.486530," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{{\left(6 \, A b^{3} d^{4} e^{4} m^{4} + 5040 \, B c^{3} d^{8} + 10080 \, A b^{3} d^{4} e^{4} - 5760 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{7} e + 20160 \, {\left(B b^{2} c + A b c^{2}\right)} d^{6} e^{2} - 8064 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{5} e^{3} - {\left(B c^{3} e^{8} m^{7} + 28 \, B c^{3} e^{8} m^{6} + 322 \, B c^{3} e^{8} m^{5} + 1960 \, B c^{3} e^{8} m^{4} + 6769 \, B c^{3} e^{8} m^{3} + 13132 \, B c^{3} e^{8} m^{2} + 13068 \, B c^{3} e^{8} m + 5040 \, B c^{3} e^{8}\right)} x^{8} - {\left(5760 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8} + {\left(B c^{3} d e^{7} + {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{7} + {\left(21 \, B c^{3} d e^{7} + 29 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{6} + 7 \, {\left(25 \, B c^{3} d e^{7} + 49 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{5} + 35 \, {\left(21 \, B c^{3} d e^{7} + 61 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{4} + 56 \, {\left(29 \, B c^{3} d e^{7} + 134 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{3} + 28 \, {\left(63 \, B c^{3} d e^{7} + 527 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{2} + 144 \, {\left(5 \, B c^{3} d e^{7} + 103 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m\right)} x^{7} - {\left(20160 \, {\left(B b^{2} c + A b c^{2}\right)} e^{8} + {\left({\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} + 3 \, {\left(B b^{2} c + A b c^{2}\right)} e^{8}\right)} m^{7} - {\left(7 \, B c^{3} d^{2} e^{6} - 23 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 90 \, {\left(B b^{2} c + A b c^{2}\right)} e^{8}\right)} m^{6} - {\left(105 \, B c^{3} d^{2} e^{6} - 205 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 1098 \, {\left(B b^{2} c + A b c^{2}\right)} e^{8}\right)} m^{5} - 5 \, {\left(119 \, B c^{3} d^{2} e^{6} - 181 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 1404 \, {\left(B b^{2} c + A b c^{2}\right)} e^{8}\right)} m^{4} - {\left(1575 \, B c^{3} d^{2} e^{6} - 2074 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 25227 \, {\left(B b^{2} c + A b c^{2}\right)} e^{8}\right)} m^{3} - 2 \, {\left(959 \, B c^{3} d^{2} e^{6} - 1156 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 25245 \, {\left(B b^{2} c + A b c^{2}\right)} e^{8}\right)} m^{2} - 24 \, {\left(35 \, B c^{3} d^{2} e^{6} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 2143 \, {\left(B b^{2} c + A b c^{2}\right)} e^{8}\right)} m\right)} x^{6} - {\left(8064 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{8} + {\left(3 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{7} + {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{8}\right)} m^{7} - {\left(6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} - 75 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{7} - 31 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{8}\right)} m^{6} + {\left(42 \, B c^{3} d^{3} e^{5} - 108 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 723 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{7} + 391 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{8}\right)} m^{5} + {\left(420 \, B c^{3} d^{3} e^{5} - 690 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 3405 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{7} + 2581 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{8}\right)} m^{4} + 2 \, {\left(735 \, B c^{3} d^{3} e^{5} - 990 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 4101 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{7} + 4772 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{8}\right)} m^{3} + 4 \, {\left(525 \, B c^{3} d^{3} e^{5} - 636 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 2370 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{7} + 4891 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{8}\right)} m^{2} + 144 \, {\left(7 \, B c^{3} d^{3} e^{5} - 8 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 28 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{7} + 141 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{8}\right)} m\right)} x^{5} - {\left(10080 \, A b^{3} e^{8} + {\left(A b^{3} e^{8} + {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{7}\right)} m^{7} + {\left(32 \, A b^{3} e^{8} - 15 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{6} + 27 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{7}\right)} m^{6} + {\left(418 \, A b^{3} e^{8} + 30 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} - 315 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{6} + 283 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{7}\right)} m^{5} - {\left(210 \, B c^{3} d^{4} e^{4} - 2864 \, A b^{3} e^{8} - 420 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} + 2355 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{6} - 1449 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{7}\right)} m^{4} - {\left(1260 \, B c^{3} d^{4} e^{4} - 10993 \, A b^{3} e^{8} - 1770 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} + 7605 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{6} - 3748 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{7}\right)} m^{3} - 2 \, {\left(1155 \, B c^{3} d^{4} e^{4} - 11656 \, A b^{3} e^{8} - 1410 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} + 5295 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{6} - 2286 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{7}\right)} m^{2} - 36 \, {\left(35 \, B c^{3} d^{4} e^{4} - 691 \, A b^{3} e^{8} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} + 140 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{6} - 56 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{7}\right)} m\right)} x^{4} + 12 \, {\left(13 \, A b^{3} d^{4} e^{4} - 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{5} e^{3}\right)} m^{3} - {\left(A b^{3} d e^{7} m^{7} + {\left(29 \, A b^{3} d e^{7} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{6}\right)} m^{6} + {\left(331 \, A b^{3} d e^{7} + 60 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{5} - 96 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{6}\right)} m^{5} + {\left(1871 \, A b^{3} d e^{7} - 120 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{4} + 1080 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{5} - 844 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{6}\right)} m^{4} + 4 \, {\left(210 \, B c^{3} d^{5} e^{3} + 1345 \, A b^{3} d e^{7} - 330 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{4} + 1545 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{5} - 816 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{6}\right)} m^{3} + 4 \, {\left(630 \, B c^{3} d^{5} e^{3} + 1793 \, A b^{3} d e^{7} - 780 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{4} + 2970 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{5} - 1300 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{6}\right)} m^{2} + 48 \, {\left(35 \, B c^{3} d^{5} e^{3} + 70 \, A b^{3} d e^{7} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{4} + 140 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{5} - 56 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{6}\right)} m\right)} x^{3} + 6 \, {\left(251 \, A b^{3} d^{4} e^{4} + 60 \, {\left(B b^{2} c + A b c^{2}\right)} d^{6} e^{2} - 84 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{5} e^{3}\right)} m^{2} + 3 \, {\left(A b^{3} d^{2} e^{6} m^{6} + {\left(27 \, A b^{3} d^{2} e^{6} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{5}\right)} m^{5} + {\left(277 \, A b^{3} d^{2} e^{6} + 60 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{4} - 88 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{5}\right)} m^{4} + {\left(1317 \, A b^{3} d^{2} e^{6} - 120 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{3} + 960 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{4} - 668 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{5}\right)} m^{3} + 2 \, {\left(420 \, B c^{3} d^{6} e^{2} + 1373 \, A b^{3} d^{2} e^{6} - 540 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{3} + 2130 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{4} - 964 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{5}\right)} m^{2} + 24 \, {\left(35 \, B c^{3} d^{6} e^{2} + 70 \, A b^{3} d^{2} e^{6} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{3} + 140 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{4} - 56 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{5}\right)} m\right)} x^{2} + 12 \, {\left(533 \, A b^{3} d^{4} e^{4} - 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{7} e + 450 \, {\left(B b^{2} c + A b c^{2}\right)} d^{6} e^{2} - 292 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{5} e^{3}\right)} m - 6 \, {\left(A b^{3} d^{3} e^{5} m^{5} + 2 \, {\left(13 \, A b^{3} d^{3} e^{5} - 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{4}\right)} m^{4} + {\left(251 \, A b^{3} d^{3} e^{5} + 60 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{3} - 84 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{4}\right)} m^{3} + 2 \, {\left(533 \, A b^{3} d^{3} e^{5} - 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e^{2} + 450 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{3} - 292 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{4}\right)} m^{2} + 24 \, {\left(35 \, B c^{3} d^{7} e + 70 \, A b^{3} d^{3} e^{5} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e^{2} + 140 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{3} - 56 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{4}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{8} m^{8} + 36 \, e^{8} m^{7} + 546 \, e^{8} m^{6} + 4536 \, e^{8} m^{5} + 22449 \, e^{8} m^{4} + 67284 \, e^{8} m^{3} + 118124 \, e^{8} m^{2} + 109584 \, e^{8} m + 40320 \, e^{8}}"," ",0,"-(6*A*b^3*d^4*e^4*m^4 + 5040*B*c^3*d^8 + 10080*A*b^3*d^4*e^4 - 5760*(3*B*b*c^2 + A*c^3)*d^7*e + 20160*(B*b^2*c + A*b*c^2)*d^6*e^2 - 8064*(B*b^3 + 3*A*b^2*c)*d^5*e^3 - (B*c^3*e^8*m^7 + 28*B*c^3*e^8*m^6 + 322*B*c^3*e^8*m^5 + 1960*B*c^3*e^8*m^4 + 6769*B*c^3*e^8*m^3 + 13132*B*c^3*e^8*m^2 + 13068*B*c^3*e^8*m + 5040*B*c^3*e^8)*x^8 - (5760*(3*B*b*c^2 + A*c^3)*e^8 + (B*c^3*d*e^7 + (3*B*b*c^2 + A*c^3)*e^8)*m^7 + (21*B*c^3*d*e^7 + 29*(3*B*b*c^2 + A*c^3)*e^8)*m^6 + 7*(25*B*c^3*d*e^7 + 49*(3*B*b*c^2 + A*c^3)*e^8)*m^5 + 35*(21*B*c^3*d*e^7 + 61*(3*B*b*c^2 + A*c^3)*e^8)*m^4 + 56*(29*B*c^3*d*e^7 + 134*(3*B*b*c^2 + A*c^3)*e^8)*m^3 + 28*(63*B*c^3*d*e^7 + 527*(3*B*b*c^2 + A*c^3)*e^8)*m^2 + 144*(5*B*c^3*d*e^7 + 103*(3*B*b*c^2 + A*c^3)*e^8)*m)*x^7 - (20160*(B*b^2*c + A*b*c^2)*e^8 + ((3*B*b*c^2 + A*c^3)*d*e^7 + 3*(B*b^2*c + A*b*c^2)*e^8)*m^7 - (7*B*c^3*d^2*e^6 - 23*(3*B*b*c^2 + A*c^3)*d*e^7 - 90*(B*b^2*c + A*b*c^2)*e^8)*m^6 - (105*B*c^3*d^2*e^6 - 205*(3*B*b*c^2 + A*c^3)*d*e^7 - 1098*(B*b^2*c + A*b*c^2)*e^8)*m^5 - 5*(119*B*c^3*d^2*e^6 - 181*(3*B*b*c^2 + A*c^3)*d*e^7 - 1404*(B*b^2*c + A*b*c^2)*e^8)*m^4 - (1575*B*c^3*d^2*e^6 - 2074*(3*B*b*c^2 + A*c^3)*d*e^7 - 25227*(B*b^2*c + A*b*c^2)*e^8)*m^3 - 2*(959*B*c^3*d^2*e^6 - 1156*(3*B*b*c^2 + A*c^3)*d*e^7 - 25245*(B*b^2*c + A*b*c^2)*e^8)*m^2 - 24*(35*B*c^3*d^2*e^6 - 40*(3*B*b*c^2 + A*c^3)*d*e^7 - 2143*(B*b^2*c + A*b*c^2)*e^8)*m)*x^6 - (8064*(B*b^3 + 3*A*b^2*c)*e^8 + (3*(B*b^2*c + A*b*c^2)*d*e^7 + (B*b^3 + 3*A*b^2*c)*e^8)*m^7 - (6*(3*B*b*c^2 + A*c^3)*d^2*e^6 - 75*(B*b^2*c + A*b*c^2)*d*e^7 - 31*(B*b^3 + 3*A*b^2*c)*e^8)*m^6 + (42*B*c^3*d^3*e^5 - 108*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 723*(B*b^2*c + A*b*c^2)*d*e^7 + 391*(B*b^3 + 3*A*b^2*c)*e^8)*m^5 + (420*B*c^3*d^3*e^5 - 690*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 3405*(B*b^2*c + A*b*c^2)*d*e^7 + 2581*(B*b^3 + 3*A*b^2*c)*e^8)*m^4 + 2*(735*B*c^3*d^3*e^5 - 990*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 4101*(B*b^2*c + A*b*c^2)*d*e^7 + 4772*(B*b^3 + 3*A*b^2*c)*e^8)*m^3 + 4*(525*B*c^3*d^3*e^5 - 636*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 2370*(B*b^2*c + A*b*c^2)*d*e^7 + 4891*(B*b^3 + 3*A*b^2*c)*e^8)*m^2 + 144*(7*B*c^3*d^3*e^5 - 8*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 28*(B*b^2*c + A*b*c^2)*d*e^7 + 141*(B*b^3 + 3*A*b^2*c)*e^8)*m)*x^5 - (10080*A*b^3*e^8 + (A*b^3*e^8 + (B*b^3 + 3*A*b^2*c)*d*e^7)*m^7 + (32*A*b^3*e^8 - 15*(B*b^2*c + A*b*c^2)*d^2*e^6 + 27*(B*b^3 + 3*A*b^2*c)*d*e^7)*m^6 + (418*A*b^3*e^8 + 30*(3*B*b*c^2 + A*c^3)*d^3*e^5 - 315*(B*b^2*c + A*b*c^2)*d^2*e^6 + 283*(B*b^3 + 3*A*b^2*c)*d*e^7)*m^5 - (210*B*c^3*d^4*e^4 - 2864*A*b^3*e^8 - 420*(3*B*b*c^2 + A*c^3)*d^3*e^5 + 2355*(B*b^2*c + A*b*c^2)*d^2*e^6 - 1449*(B*b^3 + 3*A*b^2*c)*d*e^7)*m^4 - (1260*B*c^3*d^4*e^4 - 10993*A*b^3*e^8 - 1770*(3*B*b*c^2 + A*c^3)*d^3*e^5 + 7605*(B*b^2*c + A*b*c^2)*d^2*e^6 - 3748*(B*b^3 + 3*A*b^2*c)*d*e^7)*m^3 - 2*(1155*B*c^3*d^4*e^4 - 11656*A*b^3*e^8 - 1410*(3*B*b*c^2 + A*c^3)*d^3*e^5 + 5295*(B*b^2*c + A*b*c^2)*d^2*e^6 - 2286*(B*b^3 + 3*A*b^2*c)*d*e^7)*m^2 - 36*(35*B*c^3*d^4*e^4 - 691*A*b^3*e^8 - 40*(3*B*b*c^2 + A*c^3)*d^3*e^5 + 140*(B*b^2*c + A*b*c^2)*d^2*e^6 - 56*(B*b^3 + 3*A*b^2*c)*d*e^7)*m)*x^4 + 12*(13*A*b^3*d^4*e^4 - 2*(B*b^3 + 3*A*b^2*c)*d^5*e^3)*m^3 - (A*b^3*d*e^7*m^7 + (29*A*b^3*d*e^7 - 4*(B*b^3 + 3*A*b^2*c)*d^2*e^6)*m^6 + (331*A*b^3*d*e^7 + 60*(B*b^2*c + A*b*c^2)*d^3*e^5 - 96*(B*b^3 + 3*A*b^2*c)*d^2*e^6)*m^5 + (1871*A*b^3*d*e^7 - 120*(3*B*b*c^2 + A*c^3)*d^4*e^4 + 1080*(B*b^2*c + A*b*c^2)*d^3*e^5 - 844*(B*b^3 + 3*A*b^2*c)*d^2*e^6)*m^4 + 4*(210*B*c^3*d^5*e^3 + 1345*A*b^3*d*e^7 - 330*(3*B*b*c^2 + A*c^3)*d^4*e^4 + 1545*(B*b^2*c + A*b*c^2)*d^3*e^5 - 816*(B*b^3 + 3*A*b^2*c)*d^2*e^6)*m^3 + 4*(630*B*c^3*d^5*e^3 + 1793*A*b^3*d*e^7 - 780*(3*B*b*c^2 + A*c^3)*d^4*e^4 + 2970*(B*b^2*c + A*b*c^2)*d^3*e^5 - 1300*(B*b^3 + 3*A*b^2*c)*d^2*e^6)*m^2 + 48*(35*B*c^3*d^5*e^3 + 70*A*b^3*d*e^7 - 40*(3*B*b*c^2 + A*c^3)*d^4*e^4 + 140*(B*b^2*c + A*b*c^2)*d^3*e^5 - 56*(B*b^3 + 3*A*b^2*c)*d^2*e^6)*m)*x^3 + 6*(251*A*b^3*d^4*e^4 + 60*(B*b^2*c + A*b*c^2)*d^6*e^2 - 84*(B*b^3 + 3*A*b^2*c)*d^5*e^3)*m^2 + 3*(A*b^3*d^2*e^6*m^6 + (27*A*b^3*d^2*e^6 - 4*(B*b^3 + 3*A*b^2*c)*d^3*e^5)*m^5 + (277*A*b^3*d^2*e^6 + 60*(B*b^2*c + A*b*c^2)*d^4*e^4 - 88*(B*b^3 + 3*A*b^2*c)*d^3*e^5)*m^4 + (1317*A*b^3*d^2*e^6 - 120*(3*B*b*c^2 + A*c^3)*d^5*e^3 + 960*(B*b^2*c + A*b*c^2)*d^4*e^4 - 668*(B*b^3 + 3*A*b^2*c)*d^3*e^5)*m^3 + 2*(420*B*c^3*d^6*e^2 + 1373*A*b^3*d^2*e^6 - 540*(3*B*b*c^2 + A*c^3)*d^5*e^3 + 2130*(B*b^2*c + A*b*c^2)*d^4*e^4 - 964*(B*b^3 + 3*A*b^2*c)*d^3*e^5)*m^2 + 24*(35*B*c^3*d^6*e^2 + 70*A*b^3*d^2*e^6 - 40*(3*B*b*c^2 + A*c^3)*d^5*e^3 + 140*(B*b^2*c + A*b*c^2)*d^4*e^4 - 56*(B*b^3 + 3*A*b^2*c)*d^3*e^5)*m)*x^2 + 12*(533*A*b^3*d^4*e^4 - 60*(3*B*b*c^2 + A*c^3)*d^7*e + 450*(B*b^2*c + A*b*c^2)*d^6*e^2 - 292*(B*b^3 + 3*A*b^2*c)*d^5*e^3)*m - 6*(A*b^3*d^3*e^5*m^5 + 2*(13*A*b^3*d^3*e^5 - 2*(B*b^3 + 3*A*b^2*c)*d^4*e^4)*m^4 + (251*A*b^3*d^3*e^5 + 60*(B*b^2*c + A*b*c^2)*d^5*e^3 - 84*(B*b^3 + 3*A*b^2*c)*d^4*e^4)*m^3 + 2*(533*A*b^3*d^3*e^5 - 60*(3*B*b*c^2 + A*c^3)*d^6*e^2 + 450*(B*b^2*c + A*b*c^2)*d^5*e^3 - 292*(B*b^3 + 3*A*b^2*c)*d^4*e^4)*m^2 + 24*(35*B*c^3*d^7*e + 70*A*b^3*d^3*e^5 - 40*(3*B*b*c^2 + A*c^3)*d^6*e^2 + 140*(B*b^2*c + A*b*c^2)*d^5*e^3 - 56*(B*b^3 + 3*A*b^2*c)*d^4*e^4)*m)*x)*(e*x + d)^m/(e^8*m^8 + 36*e^8*m^7 + 546*e^8*m^6 + 4536*e^8*m^5 + 22449*e^8*m^4 + 67284*e^8*m^3 + 118124*e^8*m^2 + 109584*e^8*m + 40320*e^8)","B",0
1128,1,540,0,0.365409," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{4} c^{3} B + \frac{4}{11} x^{11} e^{3} d c^{3} B + \frac{3}{11} x^{11} e^{4} c^{2} b B + \frac{1}{11} x^{11} e^{4} c^{3} A + \frac{3}{5} x^{10} e^{2} d^{2} c^{3} B + \frac{6}{5} x^{10} e^{3} d c^{2} b B + \frac{3}{10} x^{10} e^{4} c b^{2} B + \frac{2}{5} x^{10} e^{3} d c^{3} A + \frac{3}{10} x^{10} e^{4} c^{2} b A + \frac{4}{9} x^{9} e d^{3} c^{3} B + 2 x^{9} e^{2} d^{2} c^{2} b B + \frac{4}{3} x^{9} e^{3} d c b^{2} B + \frac{1}{9} x^{9} e^{4} b^{3} B + \frac{2}{3} x^{9} e^{2} d^{2} c^{3} A + \frac{4}{3} x^{9} e^{3} d c^{2} b A + \frac{1}{3} x^{9} e^{4} c b^{2} A + \frac{1}{8} x^{8} d^{4} c^{3} B + \frac{3}{2} x^{8} e d^{3} c^{2} b B + \frac{9}{4} x^{8} e^{2} d^{2} c b^{2} B + \frac{1}{2} x^{8} e^{3} d b^{3} B + \frac{1}{2} x^{8} e d^{3} c^{3} A + \frac{9}{4} x^{8} e^{2} d^{2} c^{2} b A + \frac{3}{2} x^{8} e^{3} d c b^{2} A + \frac{1}{8} x^{8} e^{4} b^{3} A + \frac{3}{7} x^{7} d^{4} c^{2} b B + \frac{12}{7} x^{7} e d^{3} c b^{2} B + \frac{6}{7} x^{7} e^{2} d^{2} b^{3} B + \frac{1}{7} x^{7} d^{4} c^{3} A + \frac{12}{7} x^{7} e d^{3} c^{2} b A + \frac{18}{7} x^{7} e^{2} d^{2} c b^{2} A + \frac{4}{7} x^{7} e^{3} d b^{3} A + \frac{1}{2} x^{6} d^{4} c b^{2} B + \frac{2}{3} x^{6} e d^{3} b^{3} B + \frac{1}{2} x^{6} d^{4} c^{2} b A + 2 x^{6} e d^{3} c b^{2} A + x^{6} e^{2} d^{2} b^{3} A + \frac{1}{5} x^{5} d^{4} b^{3} B + \frac{3}{5} x^{5} d^{4} c b^{2} A + \frac{4}{5} x^{5} e d^{3} b^{3} A + \frac{1}{4} x^{4} d^{4} b^{3} A"," ",0,"1/12*x^12*e^4*c^3*B + 4/11*x^11*e^3*d*c^3*B + 3/11*x^11*e^4*c^2*b*B + 1/11*x^11*e^4*c^3*A + 3/5*x^10*e^2*d^2*c^3*B + 6/5*x^10*e^3*d*c^2*b*B + 3/10*x^10*e^4*c*b^2*B + 2/5*x^10*e^3*d*c^3*A + 3/10*x^10*e^4*c^2*b*A + 4/9*x^9*e*d^3*c^3*B + 2*x^9*e^2*d^2*c^2*b*B + 4/3*x^9*e^3*d*c*b^2*B + 1/9*x^9*e^4*b^3*B + 2/3*x^9*e^2*d^2*c^3*A + 4/3*x^9*e^3*d*c^2*b*A + 1/3*x^9*e^4*c*b^2*A + 1/8*x^8*d^4*c^3*B + 3/2*x^8*e*d^3*c^2*b*B + 9/4*x^8*e^2*d^2*c*b^2*B + 1/2*x^8*e^3*d*b^3*B + 1/2*x^8*e*d^3*c^3*A + 9/4*x^8*e^2*d^2*c^2*b*A + 3/2*x^8*e^3*d*c*b^2*A + 1/8*x^8*e^4*b^3*A + 3/7*x^7*d^4*c^2*b*B + 12/7*x^7*e*d^3*c*b^2*B + 6/7*x^7*e^2*d^2*b^3*B + 1/7*x^7*d^4*c^3*A + 12/7*x^7*e*d^3*c^2*b*A + 18/7*x^7*e^2*d^2*c*b^2*A + 4/7*x^7*e^3*d*b^3*A + 1/2*x^6*d^4*c*b^2*B + 2/3*x^6*e*d^3*b^3*B + 1/2*x^6*d^4*c^2*b*A + 2*x^6*e*d^3*c*b^2*A + x^6*e^2*d^2*b^3*A + 1/5*x^5*d^4*b^3*B + 3/5*x^5*d^4*c*b^2*A + 4/5*x^5*e*d^3*b^3*A + 1/4*x^4*d^4*b^3*A","A",0
1129,1,416,0,0.375005," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{3} c^{3} B + \frac{3}{10} x^{10} e^{2} d c^{3} B + \frac{3}{10} x^{10} e^{3} c^{2} b B + \frac{1}{10} x^{10} e^{3} c^{3} A + \frac{1}{3} x^{9} e d^{2} c^{3} B + x^{9} e^{2} d c^{2} b B + \frac{1}{3} x^{9} e^{3} c b^{2} B + \frac{1}{3} x^{9} e^{2} d c^{3} A + \frac{1}{3} x^{9} e^{3} c^{2} b A + \frac{1}{8} x^{8} d^{3} c^{3} B + \frac{9}{8} x^{8} e d^{2} c^{2} b B + \frac{9}{8} x^{8} e^{2} d c b^{2} B + \frac{1}{8} x^{8} e^{3} b^{3} B + \frac{3}{8} x^{8} e d^{2} c^{3} A + \frac{9}{8} x^{8} e^{2} d c^{2} b A + \frac{3}{8} x^{8} e^{3} c b^{2} A + \frac{3}{7} x^{7} d^{3} c^{2} b B + \frac{9}{7} x^{7} e d^{2} c b^{2} B + \frac{3}{7} x^{7} e^{2} d b^{3} B + \frac{1}{7} x^{7} d^{3} c^{3} A + \frac{9}{7} x^{7} e d^{2} c^{2} b A + \frac{9}{7} x^{7} e^{2} d c b^{2} A + \frac{1}{7} x^{7} e^{3} b^{3} A + \frac{1}{2} x^{6} d^{3} c b^{2} B + \frac{1}{2} x^{6} e d^{2} b^{3} B + \frac{1}{2} x^{6} d^{3} c^{2} b A + \frac{3}{2} x^{6} e d^{2} c b^{2} A + \frac{1}{2} x^{6} e^{2} d b^{3} A + \frac{1}{5} x^{5} d^{3} b^{3} B + \frac{3}{5} x^{5} d^{3} c b^{2} A + \frac{3}{5} x^{5} e d^{2} b^{3} A + \frac{1}{4} x^{4} d^{3} b^{3} A"," ",0,"1/11*x^11*e^3*c^3*B + 3/10*x^10*e^2*d*c^3*B + 3/10*x^10*e^3*c^2*b*B + 1/10*x^10*e^3*c^3*A + 1/3*x^9*e*d^2*c^3*B + x^9*e^2*d*c^2*b*B + 1/3*x^9*e^3*c*b^2*B + 1/3*x^9*e^2*d*c^3*A + 1/3*x^9*e^3*c^2*b*A + 1/8*x^8*d^3*c^3*B + 9/8*x^8*e*d^2*c^2*b*B + 9/8*x^8*e^2*d*c*b^2*B + 1/8*x^8*e^3*b^3*B + 3/8*x^8*e*d^2*c^3*A + 9/8*x^8*e^2*d*c^2*b*A + 3/8*x^8*e^3*c*b^2*A + 3/7*x^7*d^3*c^2*b*B + 9/7*x^7*e*d^2*c*b^2*B + 3/7*x^7*e^2*d*b^3*B + 1/7*x^7*d^3*c^3*A + 9/7*x^7*e*d^2*c^2*b*A + 9/7*x^7*e^2*d*c*b^2*A + 1/7*x^7*e^3*b^3*A + 1/2*x^6*d^3*c*b^2*B + 1/2*x^6*e*d^2*b^3*B + 1/2*x^6*d^3*c^2*b*A + 3/2*x^6*e*d^2*c*b^2*A + 1/2*x^6*e^2*d*b^3*A + 1/5*x^5*d^3*b^3*B + 3/5*x^5*d^3*c*b^2*A + 3/5*x^5*e*d^2*b^3*A + 1/4*x^4*d^3*b^3*A","A",0
1130,1,292,0,0.395971," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{2} c^{3} B + \frac{2}{9} x^{9} e d c^{3} B + \frac{1}{3} x^{9} e^{2} c^{2} b B + \frac{1}{9} x^{9} e^{2} c^{3} A + \frac{1}{8} x^{8} d^{2} c^{3} B + \frac{3}{4} x^{8} e d c^{2} b B + \frac{3}{8} x^{8} e^{2} c b^{2} B + \frac{1}{4} x^{8} e d c^{3} A + \frac{3}{8} x^{8} e^{2} c^{2} b A + \frac{3}{7} x^{7} d^{2} c^{2} b B + \frac{6}{7} x^{7} e d c b^{2} B + \frac{1}{7} x^{7} e^{2} b^{3} B + \frac{1}{7} x^{7} d^{2} c^{3} A + \frac{6}{7} x^{7} e d c^{2} b A + \frac{3}{7} x^{7} e^{2} c b^{2} A + \frac{1}{2} x^{6} d^{2} c b^{2} B + \frac{1}{3} x^{6} e d b^{3} B + \frac{1}{2} x^{6} d^{2} c^{2} b A + x^{6} e d c b^{2} A + \frac{1}{6} x^{6} e^{2} b^{3} A + \frac{1}{5} x^{5} d^{2} b^{3} B + \frac{3}{5} x^{5} d^{2} c b^{2} A + \frac{2}{5} x^{5} e d b^{3} A + \frac{1}{4} x^{4} d^{2} b^{3} A"," ",0,"1/10*x^10*e^2*c^3*B + 2/9*x^9*e*d*c^3*B + 1/3*x^9*e^2*c^2*b*B + 1/9*x^9*e^2*c^3*A + 1/8*x^8*d^2*c^3*B + 3/4*x^8*e*d*c^2*b*B + 3/8*x^8*e^2*c*b^2*B + 1/4*x^8*e*d*c^3*A + 3/8*x^8*e^2*c^2*b*A + 3/7*x^7*d^2*c^2*b*B + 6/7*x^7*e*d*c*b^2*B + 1/7*x^7*e^2*b^3*B + 1/7*x^7*d^2*c^3*A + 6/7*x^7*e*d*c^2*b*A + 3/7*x^7*e^2*c*b^2*A + 1/2*x^6*d^2*c*b^2*B + 1/3*x^6*e*d*b^3*B + 1/2*x^6*d^2*c^2*b*A + x^6*e*d*c*b^2*A + 1/6*x^6*e^2*b^3*A + 1/5*x^5*d^2*b^3*B + 3/5*x^5*d^2*c*b^2*A + 2/5*x^5*e*d*b^3*A + 1/4*x^4*d^2*b^3*A","A",0
1131,1,169,0,0.387731," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e c^{3} B + \frac{1}{8} x^{8} d c^{3} B + \frac{3}{8} x^{8} e c^{2} b B + \frac{1}{8} x^{8} e c^{3} A + \frac{3}{7} x^{7} d c^{2} b B + \frac{3}{7} x^{7} e c b^{2} B + \frac{1}{7} x^{7} d c^{3} A + \frac{3}{7} x^{7} e c^{2} b A + \frac{1}{2} x^{6} d c b^{2} B + \frac{1}{6} x^{6} e b^{3} B + \frac{1}{2} x^{6} d c^{2} b A + \frac{1}{2} x^{6} e c b^{2} A + \frac{1}{5} x^{5} d b^{3} B + \frac{3}{5} x^{5} d c b^{2} A + \frac{1}{5} x^{5} e b^{3} A + \frac{1}{4} x^{4} d b^{3} A"," ",0,"1/9*x^9*e*c^3*B + 1/8*x^8*d*c^3*B + 3/8*x^8*e*c^2*b*B + 1/8*x^8*e*c^3*A + 3/7*x^7*d*c^2*b*B + 3/7*x^7*e*c*b^2*B + 1/7*x^7*d*c^3*A + 3/7*x^7*e*c^2*b*A + 1/2*x^6*d*c*b^2*B + 1/6*x^6*e*b^3*B + 1/2*x^6*d*c^2*b*A + 1/2*x^6*e*c*b^2*A + 1/5*x^5*d*b^3*B + 3/5*x^5*d*c*b^2*A + 1/5*x^5*e*b^3*A + 1/4*x^4*d*b^3*A","A",0
1132,1,77,0,0.371721," ","integrate((B*x+A)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{3} B + \frac{3}{7} x^{7} c^{2} b B + \frac{1}{7} x^{7} c^{3} A + \frac{1}{2} x^{6} c b^{2} B + \frac{1}{2} x^{6} c^{2} b A + \frac{1}{5} x^{5} b^{3} B + \frac{3}{5} x^{5} c b^{2} A + \frac{1}{4} x^{4} b^{3} A"," ",0,"1/8*x^8*c^3*B + 3/7*x^7*c^2*b*B + 1/7*x^7*c^3*A + 1/2*x^6*c*b^2*B + 1/2*x^6*c^2*b*A + 1/5*x^5*b^3*B + 3/5*x^5*c*b^2*A + 1/4*x^4*b^3*A","A",0
1133,1,531,0,0.430914," ","integrate((B*x+A)*(c*x^2+b*x)^3/(e*x+d),x, algorithm=""fricas"")","\frac{60 \, B c^{3} e^{7} x^{7} - 70 \, {\left(B c^{3} d e^{6} - {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 84 \, {\left(B c^{3} d^{2} e^{5} - {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 3 \, {\left(B b^{2} c + A b c^{2}\right)} e^{7}\right)} x^{5} - 105 \, {\left(B c^{3} d^{3} e^{4} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 3 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{6} - {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{7}\right)} x^{4} + 140 \, {\left(B c^{3} d^{4} e^{3} + A b^{3} e^{7} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 3 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{5} - {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{6}\right)} x^{3} - 210 \, {\left(B c^{3} d^{5} e^{2} + A b^{3} d e^{6} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 3 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{4} - {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 420 \, {\left(B c^{3} d^{6} e + A b^{3} d^{2} e^{5} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 3 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{3} - {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{4}\right)} x - 420 \, {\left(B c^{3} d^{7} + A b^{3} d^{3} e^{4} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 3 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{2} - {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{3}\right)} \log\left(e x + d\right)}{420 \, e^{8}}"," ",0,"1/420*(60*B*c^3*e^7*x^7 - 70*(B*c^3*d*e^6 - (3*B*b*c^2 + A*c^3)*e^7)*x^6 + 84*(B*c^3*d^2*e^5 - (3*B*b*c^2 + A*c^3)*d*e^6 + 3*(B*b^2*c + A*b*c^2)*e^7)*x^5 - 105*(B*c^3*d^3*e^4 - (3*B*b*c^2 + A*c^3)*d^2*e^5 + 3*(B*b^2*c + A*b*c^2)*d*e^6 - (B*b^3 + 3*A*b^2*c)*e^7)*x^4 + 140*(B*c^3*d^4*e^3 + A*b^3*e^7 - (3*B*b*c^2 + A*c^3)*d^3*e^4 + 3*(B*b^2*c + A*b*c^2)*d^2*e^5 - (B*b^3 + 3*A*b^2*c)*d*e^6)*x^3 - 210*(B*c^3*d^5*e^2 + A*b^3*d*e^6 - (3*B*b*c^2 + A*c^3)*d^4*e^3 + 3*(B*b^2*c + A*b*c^2)*d^3*e^4 - (B*b^3 + 3*A*b^2*c)*d^2*e^5)*x^2 + 420*(B*c^3*d^6*e + A*b^3*d^2*e^5 - (3*B*b*c^2 + A*c^3)*d^5*e^2 + 3*(B*b^2*c + A*b*c^2)*d^4*e^3 - (B*b^3 + 3*A*b^2*c)*d^3*e^4)*x - 420*(B*c^3*d^7 + A*b^3*d^3*e^4 - (3*B*b*c^2 + A*c^3)*d^6*e + 3*(B*b^2*c + A*b*c^2)*d^5*e^2 - (B*b^3 + 3*A*b^2*c)*d^4*e^3)*log(e*x + d))/e^8","B",0
1134,1,722,0,0.422977," ","integrate((B*x+A)*(c*x^2+b*x)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{10 \, B c^{3} e^{7} x^{7} + 60 \, B c^{3} d^{7} + 60 \, A b^{3} d^{3} e^{4} - 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 180 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{2} - 60 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{3} - 2 \, {\left(7 \, B c^{3} d e^{6} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 3 \, {\left(7 \, B c^{3} d^{2} e^{5} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 15 \, {\left(B b^{2} c + A b c^{2}\right)} e^{7}\right)} x^{5} - 5 \, {\left(7 \, B c^{3} d^{3} e^{4} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 15 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{6} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{7}\right)} x^{4} + 10 \, {\left(7 \, B c^{3} d^{4} e^{3} + 3 \, A b^{3} e^{7} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 15 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{5} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{6}\right)} x^{3} - 30 \, {\left(7 \, B c^{3} d^{5} e^{2} + 3 \, A b^{3} d e^{6} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 15 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{4} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} - 60 \, {\left(6 \, B c^{3} d^{6} e + 2 \, A b^{3} d^{2} e^{5} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 12 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{3} - 3 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{4}\right)} x + 60 \, {\left(7 \, B c^{3} d^{7} + 3 \, A b^{3} d^{3} e^{4} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 15 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{2} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{3} + {\left(7 \, B c^{3} d^{6} e + 3 \, A b^{3} d^{2} e^{5} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 15 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{3} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{4}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"1/60*(10*B*c^3*e^7*x^7 + 60*B*c^3*d^7 + 60*A*b^3*d^3*e^4 - 60*(3*B*b*c^2 + A*c^3)*d^6*e + 180*(B*b^2*c + A*b*c^2)*d^5*e^2 - 60*(B*b^3 + 3*A*b^2*c)*d^4*e^3 - 2*(7*B*c^3*d*e^6 - 6*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 3*(7*B*c^3*d^2*e^5 - 6*(3*B*b*c^2 + A*c^3)*d*e^6 + 15*(B*b^2*c + A*b*c^2)*e^7)*x^5 - 5*(7*B*c^3*d^3*e^4 - 6*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 15*(B*b^2*c + A*b*c^2)*d*e^6 - 4*(B*b^3 + 3*A*b^2*c)*e^7)*x^4 + 10*(7*B*c^3*d^4*e^3 + 3*A*b^3*e^7 - 6*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 15*(B*b^2*c + A*b*c^2)*d^2*e^5 - 4*(B*b^3 + 3*A*b^2*c)*d*e^6)*x^3 - 30*(7*B*c^3*d^5*e^2 + 3*A*b^3*d*e^6 - 6*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 15*(B*b^2*c + A*b*c^2)*d^3*e^4 - 4*(B*b^3 + 3*A*b^2*c)*d^2*e^5)*x^2 - 60*(6*B*c^3*d^6*e + 2*A*b^3*d^2*e^5 - 5*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 12*(B*b^2*c + A*b*c^2)*d^4*e^3 - 3*(B*b^3 + 3*A*b^2*c)*d^3*e^4)*x + 60*(7*B*c^3*d^7 + 3*A*b^3*d^3*e^4 - 6*(3*B*b*c^2 + A*c^3)*d^6*e + 15*(B*b^2*c + A*b*c^2)*d^5*e^2 - 4*(B*b^3 + 3*A*b^2*c)*d^4*e^3 + (7*B*c^3*d^6*e + 3*A*b^3*d^2*e^5 - 6*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 15*(B*b^2*c + A*b*c^2)*d^4*e^3 - 4*(B*b^3 + 3*A*b^2*c)*d^3*e^4)*x)*log(e*x + d))/(e^9*x + d*e^8)","B",0
1135,1,819,0,0.425648," ","integrate((B*x+A)*(c*x^2+b*x)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{4 \, B c^{3} e^{7} x^{7} - 130 \, B c^{3} d^{7} - 50 \, A b^{3} d^{3} e^{4} + 110 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e - 270 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{2} + 70 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{3} - {\left(7 \, B c^{3} d e^{6} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 2 \, {\left(7 \, B c^{3} d^{2} e^{5} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 10 \, {\left(B b^{2} c + A b c^{2}\right)} e^{7}\right)} x^{5} - 5 \, {\left(7 \, B c^{3} d^{3} e^{4} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 10 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{6} - 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{7}\right)} x^{4} + 20 \, {\left(7 \, B c^{3} d^{4} e^{3} + A b^{3} e^{7} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 10 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{5} - 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{6}\right)} x^{3} + 10 \, {\left(50 \, B c^{3} d^{5} e^{2} + 4 \, A b^{3} d e^{6} - 34 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 63 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{4} - 11 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 20 \, {\left(8 \, B c^{3} d^{6} e - 2 \, A b^{3} d^{2} e^{5} - 4 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 3 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{3} + {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{4}\right)} x - 60 \, {\left(7 \, B c^{3} d^{7} + A b^{3} d^{3} e^{4} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 10 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{2} - 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{3} + {\left(7 \, B c^{3} d^{5} e^{2} + A b^{3} d e^{6} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 10 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{4} - 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(7 \, B c^{3} d^{6} e + A b^{3} d^{2} e^{5} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 10 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{3} - 2 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{4}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"1/20*(4*B*c^3*e^7*x^7 - 130*B*c^3*d^7 - 50*A*b^3*d^3*e^4 + 110*(3*B*b*c^2 + A*c^3)*d^6*e - 270*(B*b^2*c + A*b*c^2)*d^5*e^2 + 70*(B*b^3 + 3*A*b^2*c)*d^4*e^3 - (7*B*c^3*d*e^6 - 5*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 2*(7*B*c^3*d^2*e^5 - 5*(3*B*b*c^2 + A*c^3)*d*e^6 + 10*(B*b^2*c + A*b*c^2)*e^7)*x^5 - 5*(7*B*c^3*d^3*e^4 - 5*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 10*(B*b^2*c + A*b*c^2)*d*e^6 - 2*(B*b^3 + 3*A*b^2*c)*e^7)*x^4 + 20*(7*B*c^3*d^4*e^3 + A*b^3*e^7 - 5*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 10*(B*b^2*c + A*b*c^2)*d^2*e^5 - 2*(B*b^3 + 3*A*b^2*c)*d*e^6)*x^3 + 10*(50*B*c^3*d^5*e^2 + 4*A*b^3*d*e^6 - 34*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 63*(B*b^2*c + A*b*c^2)*d^3*e^4 - 11*(B*b^3 + 3*A*b^2*c)*d^2*e^5)*x^2 + 20*(8*B*c^3*d^6*e - 2*A*b^3*d^2*e^5 - 4*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 3*(B*b^2*c + A*b*c^2)*d^4*e^3 + (B*b^3 + 3*A*b^2*c)*d^3*e^4)*x - 60*(7*B*c^3*d^7 + A*b^3*d^3*e^4 - 5*(3*B*b*c^2 + A*c^3)*d^6*e + 10*(B*b^2*c + A*b*c^2)*d^5*e^2 - 2*(B*b^3 + 3*A*b^2*c)*d^4*e^3 + (7*B*c^3*d^5*e^2 + A*b^3*d*e^6 - 5*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 10*(B*b^2*c + A*b*c^2)*d^3*e^4 - 2*(B*b^3 + 3*A*b^2*c)*d^2*e^5)*x^2 + 2*(7*B*c^3*d^6*e + A*b^3*d^2*e^5 - 5*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 10*(B*b^2*c + A*b*c^2)*d^4*e^3 - 2*(B*b^3 + 3*A*b^2*c)*d^3*e^4)*x)*log(e*x + d))/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","B",0
1136,1,910,0,0.407051," ","integrate((B*x+A)*(c*x^2+b*x)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, B c^{3} e^{7} x^{7} + 214 \, B c^{3} d^{7} + 22 \, A b^{3} d^{3} e^{4} - 148 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 282 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{2} - 52 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{3} - {\left(7 \, B c^{3} d e^{6} - 4 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 3 \, {\left(7 \, B c^{3} d^{2} e^{5} - 4 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 6 \, {\left(B b^{2} c + A b c^{2}\right)} e^{7}\right)} x^{5} - 3 \, {\left(35 \, B c^{3} d^{3} e^{4} - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 30 \, {\left(B b^{2} c + A b c^{2}\right)} d e^{6} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} e^{7}\right)} x^{4} - 2 \, {\left(278 \, B c^{3} d^{4} e^{3} - 146 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 189 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{5} - 18 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{6}\right)} x^{3} - 6 \, {\left(68 \, B c^{3} d^{5} e^{2} - 6 \, A b^{3} d e^{6} - 26 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 9 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{4} + 6 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 6 \, {\left(37 \, B c^{3} d^{6} e + 9 \, A b^{3} d^{2} e^{5} - 34 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 81 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{3} - 18 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{4}\right)} x + 12 \, {\left(35 \, B c^{3} d^{7} + A b^{3} d^{3} e^{4} - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 30 \, {\left(B b^{2} c + A b c^{2}\right)} d^{5} e^{2} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{4} e^{3} + {\left(35 \, B c^{3} d^{4} e^{3} + A b^{3} e^{7} - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 30 \, {\left(B b^{2} c + A b c^{2}\right)} d^{2} e^{5} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d e^{6}\right)} x^{3} + 3 \, {\left(35 \, B c^{3} d^{5} e^{2} + A b^{3} d e^{6} - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 30 \, {\left(B b^{2} c + A b c^{2}\right)} d^{3} e^{4} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 3 \, {\left(35 \, B c^{3} d^{6} e + A b^{3} d^{2} e^{5} - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 30 \, {\left(B b^{2} c + A b c^{2}\right)} d^{4} e^{3} - 4 \, {\left(B b^{3} + 3 \, A b^{2} c\right)} d^{3} e^{4}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right)}}"," ",0,"1/12*(3*B*c^3*e^7*x^7 + 214*B*c^3*d^7 + 22*A*b^3*d^3*e^4 - 148*(3*B*b*c^2 + A*c^3)*d^6*e + 282*(B*b^2*c + A*b*c^2)*d^5*e^2 - 52*(B*b^3 + 3*A*b^2*c)*d^4*e^3 - (7*B*c^3*d*e^6 - 4*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 3*(7*B*c^3*d^2*e^5 - 4*(3*B*b*c^2 + A*c^3)*d*e^6 + 6*(B*b^2*c + A*b*c^2)*e^7)*x^5 - 3*(35*B*c^3*d^3*e^4 - 20*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 30*(B*b^2*c + A*b*c^2)*d*e^6 - 4*(B*b^3 + 3*A*b^2*c)*e^7)*x^4 - 2*(278*B*c^3*d^4*e^3 - 146*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 189*(B*b^2*c + A*b*c^2)*d^2*e^5 - 18*(B*b^3 + 3*A*b^2*c)*d*e^6)*x^3 - 6*(68*B*c^3*d^5*e^2 - 6*A*b^3*d*e^6 - 26*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 9*(B*b^2*c + A*b*c^2)*d^3*e^4 + 6*(B*b^3 + 3*A*b^2*c)*d^2*e^5)*x^2 + 6*(37*B*c^3*d^6*e + 9*A*b^3*d^2*e^5 - 34*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 81*(B*b^2*c + A*b*c^2)*d^4*e^3 - 18*(B*b^3 + 3*A*b^2*c)*d^3*e^4)*x + 12*(35*B*c^3*d^7 + A*b^3*d^3*e^4 - 20*(3*B*b*c^2 + A*c^3)*d^6*e + 30*(B*b^2*c + A*b*c^2)*d^5*e^2 - 4*(B*b^3 + 3*A*b^2*c)*d^4*e^3 + (35*B*c^3*d^4*e^3 + A*b^3*e^7 - 20*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 30*(B*b^2*c + A*b*c^2)*d^2*e^5 - 4*(B*b^3 + 3*A*b^2*c)*d*e^6)*x^3 + 3*(35*B*c^3*d^5*e^2 + A*b^3*d*e^6 - 20*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 30*(B*b^2*c + A*b*c^2)*d^3*e^4 - 4*(B*b^3 + 3*A*b^2*c)*d^2*e^5)*x^2 + 3*(35*B*c^3*d^6*e + A*b^3*d^2*e^5 - 20*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 30*(B*b^2*c + A*b*c^2)*d^4*e^3 - 4*(B*b^3 + 3*A*b^2*c)*d^3*e^4)*x)*log(e*x + d))/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8)","B",0
1137,1,331,0,0.417058," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{3 \, B b c^{4} e^{4} x^{4} + 12 \, A c^{5} d^{4} \log\left(x\right) + 4 \, {\left(4 \, B b c^{4} d e^{3} - {\left(B b^{2} c^{3} - A b c^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(6 \, B b c^{4} d^{2} e^{2} - 4 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d e^{3} + {\left(B b^{3} c^{2} - A b^{2} c^{3}\right)} e^{4}\right)} x^{2} + 12 \, {\left(4 \, B b c^{4} d^{3} e - 6 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{2} e^{2} + 4 \, {\left(B b^{3} c^{2} - A b^{2} c^{3}\right)} d e^{3} - {\left(B b^{4} c - A b^{3} c^{2}\right)} e^{4}\right)} x + 12 \, {\left({\left(B b c^{4} - A c^{5}\right)} d^{4} - 4 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{3} e + 6 \, {\left(B b^{3} c^{2} - A b^{2} c^{3}\right)} d^{2} e^{2} - 4 \, {\left(B b^{4} c - A b^{3} c^{2}\right)} d e^{3} + {\left(B b^{5} - A b^{4} c\right)} e^{4}\right)} \log\left(c x + b\right)}{12 \, b c^{5}}"," ",0,"1/12*(3*B*b*c^4*e^4*x^4 + 12*A*c^5*d^4*log(x) + 4*(4*B*b*c^4*d*e^3 - (B*b^2*c^3 - A*b*c^4)*e^4)*x^3 + 6*(6*B*b*c^4*d^2*e^2 - 4*(B*b^2*c^3 - A*b*c^4)*d*e^3 + (B*b^3*c^2 - A*b^2*c^3)*e^4)*x^2 + 12*(4*B*b*c^4*d^3*e - 6*(B*b^2*c^3 - A*b*c^4)*d^2*e^2 + 4*(B*b^3*c^2 - A*b^2*c^3)*d*e^3 - (B*b^4*c - A*b^3*c^2)*e^4)*x + 12*((B*b*c^4 - A*c^5)*d^4 - 4*(B*b^2*c^3 - A*b*c^4)*d^3*e + 6*(B*b^3*c^2 - A*b^2*c^3)*d^2*e^2 - 4*(B*b^4*c - A*b^3*c^2)*d*e^3 + (B*b^5 - A*b^4*c)*e^4)*log(c*x + b))/(b*c^5)","A",0
1138,1,216,0,0.411952," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, B b c^{3} e^{3} x^{3} + 6 \, A c^{4} d^{3} \log\left(x\right) + 3 \, {\left(3 \, B b c^{3} d e^{2} - {\left(B b^{2} c^{2} - A b c^{3}\right)} e^{3}\right)} x^{2} + 6 \, {\left(3 \, B b c^{3} d^{2} e - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d e^{2} + {\left(B b^{3} c - A b^{2} c^{2}\right)} e^{3}\right)} x + 6 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{3} - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{2} e + 3 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e^{2} - {\left(B b^{4} - A b^{3} c\right)} e^{3}\right)} \log\left(c x + b\right)}{6 \, b c^{4}}"," ",0,"1/6*(2*B*b*c^3*e^3*x^3 + 6*A*c^4*d^3*log(x) + 3*(3*B*b*c^3*d*e^2 - (B*b^2*c^2 - A*b*c^3)*e^3)*x^2 + 6*(3*B*b*c^3*d^2*e - 3*(B*b^2*c^2 - A*b*c^3)*d*e^2 + (B*b^3*c - A*b^2*c^2)*e^3)*x + 6*((B*b*c^3 - A*c^4)*d^3 - 3*(B*b^2*c^2 - A*b*c^3)*d^2*e + 3*(B*b^3*c - A*b^2*c^2)*d*e^2 - (B*b^4 - A*b^3*c)*e^3)*log(c*x + b))/(b*c^4)","A",0
1139,1,125,0,0.416837," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{B b c^{2} e^{2} x^{2} + 2 \, A c^{3} d^{2} \log\left(x\right) + 2 \, {\left(2 \, B b c^{2} d e - {\left(B b^{2} c - A b c^{2}\right)} e^{2}\right)} x + 2 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{2} - 2 \, {\left(B b^{2} c - A b c^{2}\right)} d e + {\left(B b^{3} - A b^{2} c\right)} e^{2}\right)} \log\left(c x + b\right)}{2 \, b c^{3}}"," ",0,"1/2*(B*b*c^2*e^2*x^2 + 2*A*c^3*d^2*log(x) + 2*(2*B*b*c^2*d*e - (B*b^2*c - A*b*c^2)*e^2)*x + 2*((B*b*c^2 - A*c^3)*d^2 - 2*(B*b^2*c - A*b*c^2)*d*e + (B*b^3 - A*b^2*c)*e^2)*log(c*x + b))/(b*c^3)","A",0
1140,1,57,0,0.416546," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{B b c e x + A c^{2} d \log\left(x\right) + {\left({\left(B b c - A c^{2}\right)} d - {\left(B b^{2} - A b c\right)} e\right)} \log\left(c x + b\right)}{b c^{2}}"," ",0,"(B*b*c*e*x + A*c^2*d*log(x) + ((B*b*c - A*c^2)*d - (B*b^2 - A*b*c)*e)*log(c*x + b))/(b*c^2)","A",0
1141,1,28,0,0.401295," ","integrate((B*x+A)/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{A c \log\left(x\right) + {\left(B b - A c\right)} \log\left(c x + b\right)}{b c}"," ",0,"(A*c*log(x) + (B*b - A*c)*log(c*x + b))/(b*c)","A",0
1142,1,65,0,1.541106," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{{\left(B b - A c\right)} d \log\left(c x + b\right) - {\left(B b d - A b e\right)} \log\left(e x + d\right) + {\left(A c d - A b e\right)} \log\left(x\right)}{b c d^{2} - b^{2} d e}"," ",0,"((B*b - A*c)*d*log(c*x + b) - (B*b*d - A*b*e)*log(e*x + d) + (A*c*d - A*b*e)*log(x))/(b*c*d^2 - b^2*d*e)","A",0
1143,1,260,0,10.347938," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{B b c d^{3} + A b^{2} d e^{2} - {\left(B b^{2} + A b c\right)} d^{2} e + {\left({\left(B b c - A c^{2}\right)} d^{2} e x + {\left(B b c - A c^{2}\right)} d^{3}\right)} \log\left(c x + b\right) - {\left(B b c d^{3} - 2 \, A b c d^{2} e + A b^{2} d e^{2} + {\left(B b c d^{2} e - 2 \, A b c d e^{2} + A b^{2} e^{3}\right)} x\right)} \log\left(e x + d\right) + {\left(A c^{2} d^{3} - 2 \, A b c d^{2} e + A b^{2} d e^{2} + {\left(A c^{2} d^{2} e - 2 \, A b c d e^{2} + A b^{2} e^{3}\right)} x\right)} \log\left(x\right)}{b c^{2} d^{5} - 2 \, b^{2} c d^{4} e + b^{3} d^{3} e^{2} + {\left(b c^{2} d^{4} e - 2 \, b^{2} c d^{3} e^{2} + b^{3} d^{2} e^{3}\right)} x}"," ",0,"(B*b*c*d^3 + A*b^2*d*e^2 - (B*b^2 + A*b*c)*d^2*e + ((B*b*c - A*c^2)*d^2*e*x + (B*b*c - A*c^2)*d^3)*log(c*x + b) - (B*b*c*d^3 - 2*A*b*c*d^2*e + A*b^2*d*e^2 + (B*b*c*d^2*e - 2*A*b*c*d*e^2 + A*b^2*e^3)*x)*log(e*x + d) + (A*c^2*d^3 - 2*A*b*c*d^2*e + A*b^2*d*e^2 + (A*c^2*d^2*e - 2*A*b*c*d*e^2 + A*b^2*e^3)*x)*log(x))/(b*c^2*d^5 - 2*b^2*c*d^4*e + b^3*d^3*e^2 + (b*c^2*d^4*e - 2*b^2*c*d^3*e^2 + b^3*d^2*e^3)*x)","B",0
1144,1,644,0,37.442320," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{3 \, B b c^{2} d^{5} - 3 \, A b^{3} d^{2} e^{3} - {\left(4 \, B b^{2} c + 5 \, A b c^{2}\right)} d^{4} e + {\left(B b^{3} + 8 \, A b^{2} c\right)} d^{3} e^{2} + 2 \, {\left(B b c^{2} d^{4} e + 3 \, A b^{2} c d^{2} e^{3} - A b^{3} d e^{4} - {\left(B b^{2} c + 2 \, A b c^{2}\right)} d^{3} e^{2}\right)} x + 2 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{3} e^{2} x^{2} + 2 \, {\left(B b c^{2} - A c^{3}\right)} d^{4} e x + {\left(B b c^{2} - A c^{3}\right)} d^{5}\right)} \log\left(c x + b\right) - 2 \, {\left(B b c^{2} d^{5} - 3 \, A b c^{2} d^{4} e + 3 \, A b^{2} c d^{3} e^{2} - A b^{3} d^{2} e^{3} + {\left(B b c^{2} d^{3} e^{2} - 3 \, A b c^{2} d^{2} e^{3} + 3 \, A b^{2} c d e^{4} - A b^{3} e^{5}\right)} x^{2} + 2 \, {\left(B b c^{2} d^{4} e - 3 \, A b c^{2} d^{3} e^{2} + 3 \, A b^{2} c d^{2} e^{3} - A b^{3} d e^{4}\right)} x\right)} \log\left(e x + d\right) + 2 \, {\left(A c^{3} d^{5} - 3 \, A b c^{2} d^{4} e + 3 \, A b^{2} c d^{3} e^{2} - A b^{3} d^{2} e^{3} + {\left(A c^{3} d^{3} e^{2} - 3 \, A b c^{2} d^{2} e^{3} + 3 \, A b^{2} c d e^{4} - A b^{3} e^{5}\right)} x^{2} + 2 \, {\left(A c^{3} d^{4} e - 3 \, A b c^{2} d^{3} e^{2} + 3 \, A b^{2} c d^{2} e^{3} - A b^{3} d e^{4}\right)} x\right)} \log\left(x\right)}{2 \, {\left(b c^{3} d^{8} - 3 \, b^{2} c^{2} d^{7} e + 3 \, b^{3} c d^{6} e^{2} - b^{4} d^{5} e^{3} + {\left(b c^{3} d^{6} e^{2} - 3 \, b^{2} c^{2} d^{5} e^{3} + 3 \, b^{3} c d^{4} e^{4} - b^{4} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(b c^{3} d^{7} e - 3 \, b^{2} c^{2} d^{6} e^{2} + 3 \, b^{3} c d^{5} e^{3} - b^{4} d^{4} e^{4}\right)} x\right)}}"," ",0,"1/2*(3*B*b*c^2*d^5 - 3*A*b^3*d^2*e^3 - (4*B*b^2*c + 5*A*b*c^2)*d^4*e + (B*b^3 + 8*A*b^2*c)*d^3*e^2 + 2*(B*b*c^2*d^4*e + 3*A*b^2*c*d^2*e^3 - A*b^3*d*e^4 - (B*b^2*c + 2*A*b*c^2)*d^3*e^2)*x + 2*((B*b*c^2 - A*c^3)*d^3*e^2*x^2 + 2*(B*b*c^2 - A*c^3)*d^4*e*x + (B*b*c^2 - A*c^3)*d^5)*log(c*x + b) - 2*(B*b*c^2*d^5 - 3*A*b*c^2*d^4*e + 3*A*b^2*c*d^3*e^2 - A*b^3*d^2*e^3 + (B*b*c^2*d^3*e^2 - 3*A*b*c^2*d^2*e^3 + 3*A*b^2*c*d*e^4 - A*b^3*e^5)*x^2 + 2*(B*b*c^2*d^4*e - 3*A*b*c^2*d^3*e^2 + 3*A*b^2*c*d^2*e^3 - A*b^3*d*e^4)*x)*log(e*x + d) + 2*(A*c^3*d^5 - 3*A*b*c^2*d^4*e + 3*A*b^2*c*d^3*e^2 - A*b^3*d^2*e^3 + (A*c^3*d^3*e^2 - 3*A*b*c^2*d^2*e^3 + 3*A*b^2*c*d*e^4 - A*b^3*e^5)*x^2 + 2*(A*c^3*d^4*e - 3*A*b*c^2*d^3*e^2 + 3*A*b^2*c*d^2*e^3 - A*b^3*d*e^4)*x)*log(x))/(b*c^3*d^8 - 3*b^2*c^2*d^7*e + 3*b^3*c*d^6*e^2 - b^4*d^5*e^3 + (b*c^3*d^6*e^2 - 3*b^2*c^2*d^5*e^3 + 3*b^3*c*d^4*e^4 - b^4*d^3*e^5)*x^2 + 2*(b*c^3*d^7*e - 3*b^2*c^2*d^6*e^2 + 3*b^3*c*d^5*e^3 - b^4*d^4*e^4)*x)","B",0
1145,1,1133,0,127.906823," ","integrate((B*x+A)/(e*x+d)^4/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{11 \, B b c^{3} d^{7} + 11 \, A b^{4} d^{3} e^{4} - 2 \, {\left(9 \, B b^{2} c^{2} + 13 \, A b c^{3}\right)} d^{6} e + 3 \, {\left(3 \, B b^{3} c + 19 \, A b^{2} c^{2}\right)} d^{5} e^{2} - 2 \, {\left(B b^{4} + 21 \, A b^{3} c\right)} d^{4} e^{3} + 6 \, {\left(B b c^{3} d^{5} e^{2} + 6 \, A b^{2} c^{2} d^{3} e^{4} - 4 \, A b^{3} c d^{2} e^{5} + A b^{4} d e^{6} - {\left(B b^{2} c^{2} + 3 \, A b c^{3}\right)} d^{4} e^{3}\right)} x^{2} + 3 \, {\left(5 \, B b c^{3} d^{6} e - 20 \, A b^{3} c d^{3} e^{4} + 5 \, A b^{4} d^{2} e^{5} - 2 \, {\left(3 \, B b^{2} c^{2} + 7 \, A b c^{3}\right)} d^{5} e^{2} + {\left(B b^{3} c + 29 \, A b^{2} c^{2}\right)} d^{4} e^{3}\right)} x + 6 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{4} e^{3} x^{3} + 3 \, {\left(B b c^{3} - A c^{4}\right)} d^{5} e^{2} x^{2} + 3 \, {\left(B b c^{3} - A c^{4}\right)} d^{6} e x + {\left(B b c^{3} - A c^{4}\right)} d^{7}\right)} \log\left(c x + b\right) - 6 \, {\left(B b c^{3} d^{7} - 4 \, A b c^{3} d^{6} e + 6 \, A b^{2} c^{2} d^{5} e^{2} - 4 \, A b^{3} c d^{4} e^{3} + A b^{4} d^{3} e^{4} + {\left(B b c^{3} d^{4} e^{3} - 4 \, A b c^{3} d^{3} e^{4} + 6 \, A b^{2} c^{2} d^{2} e^{5} - 4 \, A b^{3} c d e^{6} + A b^{4} e^{7}\right)} x^{3} + 3 \, {\left(B b c^{3} d^{5} e^{2} - 4 \, A b c^{3} d^{4} e^{3} + 6 \, A b^{2} c^{2} d^{3} e^{4} - 4 \, A b^{3} c d^{2} e^{5} + A b^{4} d e^{6}\right)} x^{2} + 3 \, {\left(B b c^{3} d^{6} e - 4 \, A b c^{3} d^{5} e^{2} + 6 \, A b^{2} c^{2} d^{4} e^{3} - 4 \, A b^{3} c d^{3} e^{4} + A b^{4} d^{2} e^{5}\right)} x\right)} \log\left(e x + d\right) + 6 \, {\left(A c^{4} d^{7} - 4 \, A b c^{3} d^{6} e + 6 \, A b^{2} c^{2} d^{5} e^{2} - 4 \, A b^{3} c d^{4} e^{3} + A b^{4} d^{3} e^{4} + {\left(A c^{4} d^{4} e^{3} - 4 \, A b c^{3} d^{3} e^{4} + 6 \, A b^{2} c^{2} d^{2} e^{5} - 4 \, A b^{3} c d e^{6} + A b^{4} e^{7}\right)} x^{3} + 3 \, {\left(A c^{4} d^{5} e^{2} - 4 \, A b c^{3} d^{4} e^{3} + 6 \, A b^{2} c^{2} d^{3} e^{4} - 4 \, A b^{3} c d^{2} e^{5} + A b^{4} d e^{6}\right)} x^{2} + 3 \, {\left(A c^{4} d^{6} e - 4 \, A b c^{3} d^{5} e^{2} + 6 \, A b^{2} c^{2} d^{4} e^{3} - 4 \, A b^{3} c d^{3} e^{4} + A b^{4} d^{2} e^{5}\right)} x\right)} \log\left(x\right)}{6 \, {\left(b c^{4} d^{11} - 4 \, b^{2} c^{3} d^{10} e + 6 \, b^{3} c^{2} d^{9} e^{2} - 4 \, b^{4} c d^{8} e^{3} + b^{5} d^{7} e^{4} + {\left(b c^{4} d^{8} e^{3} - 4 \, b^{2} c^{3} d^{7} e^{4} + 6 \, b^{3} c^{2} d^{6} e^{5} - 4 \, b^{4} c d^{5} e^{6} + b^{5} d^{4} e^{7}\right)} x^{3} + 3 \, {\left(b c^{4} d^{9} e^{2} - 4 \, b^{2} c^{3} d^{8} e^{3} + 6 \, b^{3} c^{2} d^{7} e^{4} - 4 \, b^{4} c d^{6} e^{5} + b^{5} d^{5} e^{6}\right)} x^{2} + 3 \, {\left(b c^{4} d^{10} e - 4 \, b^{2} c^{3} d^{9} e^{2} + 6 \, b^{3} c^{2} d^{8} e^{3} - 4 \, b^{4} c d^{7} e^{4} + b^{5} d^{6} e^{5}\right)} x\right)}}"," ",0,"1/6*(11*B*b*c^3*d^7 + 11*A*b^4*d^3*e^4 - 2*(9*B*b^2*c^2 + 13*A*b*c^3)*d^6*e + 3*(3*B*b^3*c + 19*A*b^2*c^2)*d^5*e^2 - 2*(B*b^4 + 21*A*b^3*c)*d^4*e^3 + 6*(B*b*c^3*d^5*e^2 + 6*A*b^2*c^2*d^3*e^4 - 4*A*b^3*c*d^2*e^5 + A*b^4*d*e^6 - (B*b^2*c^2 + 3*A*b*c^3)*d^4*e^3)*x^2 + 3*(5*B*b*c^3*d^6*e - 20*A*b^3*c*d^3*e^4 + 5*A*b^4*d^2*e^5 - 2*(3*B*b^2*c^2 + 7*A*b*c^3)*d^5*e^2 + (B*b^3*c + 29*A*b^2*c^2)*d^4*e^3)*x + 6*((B*b*c^3 - A*c^4)*d^4*e^3*x^3 + 3*(B*b*c^3 - A*c^4)*d^5*e^2*x^2 + 3*(B*b*c^3 - A*c^4)*d^6*e*x + (B*b*c^3 - A*c^4)*d^7)*log(c*x + b) - 6*(B*b*c^3*d^7 - 4*A*b*c^3*d^6*e + 6*A*b^2*c^2*d^5*e^2 - 4*A*b^3*c*d^4*e^3 + A*b^4*d^3*e^4 + (B*b*c^3*d^4*e^3 - 4*A*b*c^3*d^3*e^4 + 6*A*b^2*c^2*d^2*e^5 - 4*A*b^3*c*d*e^6 + A*b^4*e^7)*x^3 + 3*(B*b*c^3*d^5*e^2 - 4*A*b*c^3*d^4*e^3 + 6*A*b^2*c^2*d^3*e^4 - 4*A*b^3*c*d^2*e^5 + A*b^4*d*e^6)*x^2 + 3*(B*b*c^3*d^6*e - 4*A*b*c^3*d^5*e^2 + 6*A*b^2*c^2*d^4*e^3 - 4*A*b^3*c*d^3*e^4 + A*b^4*d^2*e^5)*x)*log(e*x + d) + 6*(A*c^4*d^7 - 4*A*b*c^3*d^6*e + 6*A*b^2*c^2*d^5*e^2 - 4*A*b^3*c*d^4*e^3 + A*b^4*d^3*e^4 + (A*c^4*d^4*e^3 - 4*A*b*c^3*d^3*e^4 + 6*A*b^2*c^2*d^2*e^5 - 4*A*b^3*c*d*e^6 + A*b^4*e^7)*x^3 + 3*(A*c^4*d^5*e^2 - 4*A*b*c^3*d^4*e^3 + 6*A*b^2*c^2*d^3*e^4 - 4*A*b^3*c*d^2*e^5 + A*b^4*d*e^6)*x^2 + 3*(A*c^4*d^6*e - 4*A*b*c^3*d^5*e^2 + 6*A*b^2*c^2*d^4*e^3 - 4*A*b^3*c*d^3*e^4 + A*b^4*d^2*e^5)*x)*log(x))/(b*c^4*d^11 - 4*b^2*c^3*d^10*e + 6*b^3*c^2*d^9*e^2 - 4*b^4*c*d^8*e^3 + b^5*d^7*e^4 + (b*c^4*d^8*e^3 - 4*b^2*c^3*d^7*e^4 + 6*b^3*c^2*d^6*e^5 - 4*b^4*c*d^5*e^6 + b^5*d^4*e^7)*x^3 + 3*(b*c^4*d^9*e^2 - 4*b^2*c^3*d^8*e^3 + 6*b^3*c^2*d^7*e^4 - 4*b^4*c*d^6*e^5 + b^5*d^5*e^6)*x^2 + 3*(b*c^4*d^10*e - 4*b^2*c^3*d^9*e^2 + 6*b^3*c^2*d^8*e^3 - 4*b^4*c*d^7*e^4 + b^5*d^6*e^5)*x)","B",0
1146,1,517,0,0.454939," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{B b^{3} c^{3} e^{4} x^{4} - 2 \, A b^{2} c^{4} d^{4} + {\left(8 \, B b^{3} c^{3} d e^{3} - {\left(3 \, B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} e^{4}\right)} x^{3} + 2 \, {\left(4 \, B b^{4} c^{2} d e^{3} - {\left(2 \, B b^{5} c - A b^{4} c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left({\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} - 4 \, {\left(B b^{3} c^{3} - A b^{2} c^{4}\right)} d^{3} e + 6 \, {\left(B b^{4} c^{2} - A b^{3} c^{3}\right)} d^{2} e^{2} - 4 \, {\left(B b^{5} c - A b^{4} c^{2}\right)} d e^{3} + {\left(B b^{6} - A b^{5} c\right)} e^{4}\right)} x - 2 \, {\left({\left(4 \, A b c^{5} d^{3} e - 6 \, B b^{3} c^{3} d^{2} e^{2} + {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{4} + 4 \, {\left(2 \, B b^{4} c^{2} - A b^{3} c^{3}\right)} d e^{3} - {\left(3 \, B b^{5} c - 2 \, A b^{4} c^{2}\right)} e^{4}\right)} x^{2} + {\left(4 \, A b^{2} c^{4} d^{3} e - 6 \, B b^{4} c^{2} d^{2} e^{2} + {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} + 4 \, {\left(2 \, B b^{5} c - A b^{4} c^{2}\right)} d e^{3} - {\left(3 \, B b^{6} - 2 \, A b^{5} c\right)} e^{4}\right)} x\right)} \log\left(c x + b\right) + 2 \, {\left({\left(4 \, A b c^{5} d^{3} e + {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{4}\right)} x^{2} + {\left(4 \, A b^{2} c^{4} d^{3} e + {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4}\right)} x\right)} \log\left(x\right)}{2 \, {\left(b^{3} c^{5} x^{2} + b^{4} c^{4} x\right)}}"," ",0,"1/2*(B*b^3*c^3*e^4*x^4 - 2*A*b^2*c^4*d^4 + (8*B*b^3*c^3*d*e^3 - (3*B*b^4*c^2 - 2*A*b^3*c^3)*e^4)*x^3 + 2*(4*B*b^4*c^2*d*e^3 - (2*B*b^5*c - A*b^4*c^2)*e^4)*x^2 + 2*((B*b^2*c^4 - 2*A*b*c^5)*d^4 - 4*(B*b^3*c^3 - A*b^2*c^4)*d^3*e + 6*(B*b^4*c^2 - A*b^3*c^3)*d^2*e^2 - 4*(B*b^5*c - A*b^4*c^2)*d*e^3 + (B*b^6 - A*b^5*c)*e^4)*x - 2*((4*A*b*c^5*d^3*e - 6*B*b^3*c^3*d^2*e^2 + (B*b*c^5 - 2*A*c^6)*d^4 + 4*(2*B*b^4*c^2 - A*b^3*c^3)*d*e^3 - (3*B*b^5*c - 2*A*b^4*c^2)*e^4)*x^2 + (4*A*b^2*c^4*d^3*e - 6*B*b^4*c^2*d^2*e^2 + (B*b^2*c^4 - 2*A*b*c^5)*d^4 + 4*(2*B*b^5*c - A*b^4*c^2)*d*e^3 - (3*B*b^6 - 2*A*b^5*c)*e^4)*x)*log(c*x + b) + 2*((4*A*b*c^5*d^3*e + (B*b*c^5 - 2*A*c^6)*d^4)*x^2 + (4*A*b^2*c^4*d^3*e + (B*b^2*c^4 - 2*A*b*c^5)*d^4)*x)*log(x))/(b^3*c^5*x^2 + b^4*c^4*x)","B",0
1147,1,362,0,0.442066," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{B b^{3} c^{2} e^{3} x^{3} + B b^{4} c e^{3} x^{2} - A b^{2} c^{3} d^{3} + {\left({\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 3 \, {\left(B b^{3} c^{2} - A b^{2} c^{3}\right)} d^{2} e + 3 \, {\left(B b^{4} c - A b^{3} c^{2}\right)} d e^{2} - {\left(B b^{5} - A b^{4} c\right)} e^{3}\right)} x - {\left({\left(3 \, A b c^{4} d^{2} e - 3 \, B b^{3} c^{2} d e^{2} + {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} + {\left(2 \, B b^{4} c - A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(3 \, A b^{2} c^{3} d^{2} e - 3 \, B b^{4} c d e^{2} + {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + {\left(2 \, B b^{5} - A b^{4} c\right)} e^{3}\right)} x\right)} \log\left(c x + b\right) + {\left({\left(3 \, A b c^{4} d^{2} e + {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3}\right)} x^{2} + {\left(3 \, A b^{2} c^{3} d^{2} e + {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3}\right)} x\right)} \log\left(x\right)}{b^{3} c^{4} x^{2} + b^{4} c^{3} x}"," ",0,"(B*b^3*c^2*e^3*x^3 + B*b^4*c*e^3*x^2 - A*b^2*c^3*d^3 + ((B*b^2*c^3 - 2*A*b*c^4)*d^3 - 3*(B*b^3*c^2 - A*b^2*c^3)*d^2*e + 3*(B*b^4*c - A*b^3*c^2)*d*e^2 - (B*b^5 - A*b^4*c)*e^3)*x - ((3*A*b*c^4*d^2*e - 3*B*b^3*c^2*d*e^2 + (B*b*c^4 - 2*A*c^5)*d^3 + (2*B*b^4*c - A*b^3*c^2)*e^3)*x^2 + (3*A*b^2*c^3*d^2*e - 3*B*b^4*c*d*e^2 + (B*b^2*c^3 - 2*A*b*c^4)*d^3 + (2*B*b^5 - A*b^4*c)*e^3)*x)*log(c*x + b) + ((3*A*b*c^4*d^2*e + (B*b*c^4 - 2*A*c^5)*d^3)*x^2 + (3*A*b^2*c^3*d^2*e + (B*b^2*c^3 - 2*A*b*c^4)*d^3)*x)*log(x))/(b^3*c^4*x^2 + b^4*c^3*x)","B",0
1148,1,258,0,0.416405," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{A b^{2} c^{2} d^{2} - {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} - 2 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e + {\left(B b^{4} - A b^{3} c\right)} e^{2}\right)} x + {\left({\left(2 \, A b c^{3} d e - B b^{3} c e^{2} + {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2}\right)} x^{2} + {\left(2 \, A b^{2} c^{2} d e - B b^{4} e^{2} + {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2}\right)} x\right)} \log\left(c x + b\right) - {\left({\left(2 \, A b c^{3} d e + {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2}\right)} x^{2} + {\left(2 \, A b^{2} c^{2} d e + {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2}\right)} x\right)} \log\left(x\right)}{b^{3} c^{3} x^{2} + b^{4} c^{2} x}"," ",0,"-(A*b^2*c^2*d^2 - ((B*b^2*c^2 - 2*A*b*c^3)*d^2 - 2*(B*b^3*c - A*b^2*c^2)*d*e + (B*b^4 - A*b^3*c)*e^2)*x + ((2*A*b*c^3*d*e - B*b^3*c*e^2 + (B*b*c^3 - 2*A*c^4)*d^2)*x^2 + (2*A*b^2*c^2*d*e - B*b^4*e^2 + (B*b^2*c^2 - 2*A*b*c^3)*d^2)*x)*log(c*x + b) - ((2*A*b*c^3*d*e + (B*b*c^3 - 2*A*c^4)*d^2)*x^2 + (2*A*b^2*c^2*d*e + (B*b^2*c^2 - 2*A*b*c^3)*d^2)*x)*log(x))/(b^3*c^3*x^2 + b^4*c^2*x)","B",0
1149,1,184,0,0.433994," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{A b^{2} c d - {\left({\left(B b^{2} c - 2 \, A b c^{2}\right)} d - {\left(B b^{3} - A b^{2} c\right)} e\right)} x + {\left({\left(A b c^{2} e + {\left(B b c^{2} - 2 \, A c^{3}\right)} d\right)} x^{2} + {\left(A b^{2} c e + {\left(B b^{2} c - 2 \, A b c^{2}\right)} d\right)} x\right)} \log\left(c x + b\right) - {\left({\left(A b c^{2} e + {\left(B b c^{2} - 2 \, A c^{3}\right)} d\right)} x^{2} + {\left(A b^{2} c e + {\left(B b^{2} c - 2 \, A b c^{2}\right)} d\right)} x\right)} \log\left(x\right)}{b^{3} c^{2} x^{2} + b^{4} c x}"," ",0,"-(A*b^2*c*d - ((B*b^2*c - 2*A*b*c^2)*d - (B*b^3 - A*b^2*c)*e)*x + ((A*b*c^2*e + (B*b*c^2 - 2*A*c^3)*d)*x^2 + (A*b^2*c*e + (B*b^2*c - 2*A*b*c^2)*d)*x)*log(c*x + b) - ((A*b*c^2*e + (B*b*c^2 - 2*A*c^3)*d)*x^2 + (A*b^2*c*e + (B*b^2*c - 2*A*b*c^2)*d)*x)*log(x))/(b^3*c^2*x^2 + b^4*c*x)","B",0
1150,1,107,0,0.401696," ","integrate((B*x+A)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{A b^{2} - {\left(B b^{2} - 2 \, A b c\right)} x + {\left({\left(B b c - 2 \, A c^{2}\right)} x^{2} + {\left(B b^{2} - 2 \, A b c\right)} x\right)} \log\left(c x + b\right) - {\left({\left(B b c - 2 \, A c^{2}\right)} x^{2} + {\left(B b^{2} - 2 \, A b c\right)} x\right)} \log\left(x\right)}{b^{3} c x^{2} + b^{4} x}"," ",0,"-(A*b^2 - (B*b^2 - 2*A*b*c)*x + ((B*b*c - 2*A*c^2)*x^2 + (B*b^2 - 2*A*b*c)*x)*log(c*x + b) - ((B*b*c - 2*A*c^2)*x^2 + (B*b^2 - 2*A*b*c)*x)*log(x))/(b^3*c*x^2 + b^4*x)","A",0
1151,1,450,0,34.689451," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{A b^{2} c^{2} d^{3} - 2 \, A b^{3} c d^{2} e + A b^{4} d e^{2} + {\left(A b^{3} c d e^{2} - {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{3} + {\left(B b^{3} c - 3 \, A b^{2} c^{2}\right)} d^{2} e\right)} x + {\left({\left({\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} - {\left(2 \, B b^{2} c^{2} - 3 \, A b c^{3}\right)} d^{2} e\right)} x^{2} + {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{3} - {\left(2 \, B b^{3} c - 3 \, A b^{2} c^{2}\right)} d^{2} e\right)} x\right)} \log\left(c x + b\right) + {\left({\left(B b^{3} c d e^{2} - A b^{3} c e^{3}\right)} x^{2} + {\left(B b^{4} d e^{2} - A b^{4} e^{3}\right)} x\right)} \log\left(e x + d\right) - {\left({\left(B b^{3} c d e^{2} - A b^{3} c e^{3} + {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} - {\left(2 \, B b^{2} c^{2} - 3 \, A b c^{3}\right)} d^{2} e\right)} x^{2} + {\left(B b^{4} d e^{2} - A b^{4} e^{3} + {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{3} - {\left(2 \, B b^{3} c - 3 \, A b^{2} c^{2}\right)} d^{2} e\right)} x\right)} \log\left(x\right)}{{\left(b^{3} c^{3} d^{4} - 2 \, b^{4} c^{2} d^{3} e + b^{5} c d^{2} e^{2}\right)} x^{2} + {\left(b^{4} c^{2} d^{4} - 2 \, b^{5} c d^{3} e + b^{6} d^{2} e^{2}\right)} x}"," ",0,"-(A*b^2*c^2*d^3 - 2*A*b^3*c*d^2*e + A*b^4*d*e^2 + (A*b^3*c*d*e^2 - (B*b^2*c^2 - 2*A*b*c^3)*d^3 + (B*b^3*c - 3*A*b^2*c^2)*d^2*e)*x + (((B*b*c^3 - 2*A*c^4)*d^3 - (2*B*b^2*c^2 - 3*A*b*c^3)*d^2*e)*x^2 + ((B*b^2*c^2 - 2*A*b*c^3)*d^3 - (2*B*b^3*c - 3*A*b^2*c^2)*d^2*e)*x)*log(c*x + b) + ((B*b^3*c*d*e^2 - A*b^3*c*e^3)*x^2 + (B*b^4*d*e^2 - A*b^4*e^3)*x)*log(e*x + d) - ((B*b^3*c*d*e^2 - A*b^3*c*e^3 + (B*b*c^3 - 2*A*c^4)*d^3 - (2*B*b^2*c^2 - 3*A*b*c^3)*d^2*e)*x^2 + (B*b^4*d*e^2 - A*b^4*e^3 + (B*b^2*c^2 - 2*A*b*c^3)*d^3 - (2*B*b^3*c - 3*A*b^2*c^2)*d^2*e)*x)*log(x))/((b^3*c^3*d^4 - 2*b^4*c^2*d^3*e + b^5*c*d^2*e^2)*x^2 + (b^4*c^2*d^4 - 2*b^5*c*d^3*e + b^6*d^2*e^2)*x)","B",0
1152,1,1034,0,134.900442," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{A b^{2} c^{3} d^{5} - 3 \, A b^{3} c^{2} d^{4} e + 3 \, A b^{4} c d^{3} e^{2} - A b^{5} d^{2} e^{3} - {\left(4 \, A b^{2} c^{3} d^{3} e^{2} + 2 \, A b^{4} c d e^{4} + {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} e - {\left(B b^{4} c + 4 \, A b^{3} c^{2}\right)} d^{2} e^{3}\right)} x^{2} - {\left(B b^{4} c d^{3} e^{2} + 2 \, A b^{5} d e^{4} + {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{5} - {\left(B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} d^{4} e - {\left(B b^{5} + 3 \, A b^{4} c\right)} d^{2} e^{3}\right)} x + {\left({\left({\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} e - {\left(3 \, B b^{2} c^{3} - 4 \, A b c^{4}\right)} d^{3} e^{2}\right)} x^{3} + {\left({\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} - 2 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{4} e - {\left(3 \, B b^{3} c^{2} - 4 \, A b^{2} c^{3}\right)} d^{3} e^{2}\right)} x^{2} + {\left({\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{5} - {\left(3 \, B b^{3} c^{2} - 4 \, A b^{2} c^{3}\right)} d^{4} e\right)} x\right)} \log\left(c x + b\right) + {\left({\left(3 \, B b^{3} c^{2} d^{2} e^{3} + 2 \, A b^{4} c e^{5} - {\left(B b^{4} c + 4 \, A b^{3} c^{2}\right)} d e^{4}\right)} x^{3} + {\left(3 \, B b^{3} c^{2} d^{3} e^{2} + 2 \, A b^{5} e^{5} + 2 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{2} e^{3} - {\left(B b^{5} + 2 \, A b^{4} c\right)} d e^{4}\right)} x^{2} + {\left(3 \, B b^{4} c d^{3} e^{2} + 2 \, A b^{5} d e^{4} - {\left(B b^{5} + 4 \, A b^{4} c\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right) - {\left({\left(3 \, B b^{3} c^{2} d^{2} e^{3} + 2 \, A b^{4} c e^{5} + {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} e - {\left(3 \, B b^{2} c^{3} - 4 \, A b c^{4}\right)} d^{3} e^{2} - {\left(B b^{4} c + 4 \, A b^{3} c^{2}\right)} d e^{4}\right)} x^{3} + {\left(4 \, A b^{2} c^{3} d^{3} e^{2} + 2 \, A b^{5} e^{5} + {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} - 2 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{4} e + 2 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{2} e^{3} - {\left(B b^{5} + 2 \, A b^{4} c\right)} d e^{4}\right)} x^{2} + {\left(3 \, B b^{4} c d^{3} e^{2} + 2 \, A b^{5} d e^{4} + {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{5} - {\left(3 \, B b^{3} c^{2} - 4 \, A b^{2} c^{3}\right)} d^{4} e - {\left(B b^{5} + 4 \, A b^{4} c\right)} d^{2} e^{3}\right)} x\right)} \log\left(x\right)}{{\left(b^{3} c^{4} d^{6} e - 3 \, b^{4} c^{3} d^{5} e^{2} + 3 \, b^{5} c^{2} d^{4} e^{3} - b^{6} c d^{3} e^{4}\right)} x^{3} + {\left(b^{3} c^{4} d^{7} - 2 \, b^{4} c^{3} d^{6} e + 2 \, b^{6} c d^{4} e^{3} - b^{7} d^{3} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{7} - 3 \, b^{5} c^{2} d^{6} e + 3 \, b^{6} c d^{5} e^{2} - b^{7} d^{4} e^{3}\right)} x}"," ",0,"-(A*b^2*c^3*d^5 - 3*A*b^3*c^2*d^4*e + 3*A*b^4*c*d^3*e^2 - A*b^5*d^2*e^3 - (4*A*b^2*c^3*d^3*e^2 + 2*A*b^4*c*d*e^4 + (B*b^2*c^3 - 2*A*b*c^4)*d^4*e - (B*b^4*c + 4*A*b^3*c^2)*d^2*e^3)*x^2 - (B*b^4*c*d^3*e^2 + 2*A*b^5*d*e^4 + (B*b^2*c^3 - 2*A*b*c^4)*d^5 - (B*b^3*c^2 - 3*A*b^2*c^3)*d^4*e - (B*b^5 + 3*A*b^4*c)*d^2*e^3)*x + (((B*b*c^4 - 2*A*c^5)*d^4*e - (3*B*b^2*c^3 - 4*A*b*c^4)*d^3*e^2)*x^3 + ((B*b*c^4 - 2*A*c^5)*d^5 - 2*(B*b^2*c^3 - A*b*c^4)*d^4*e - (3*B*b^3*c^2 - 4*A*b^2*c^3)*d^3*e^2)*x^2 + ((B*b^2*c^3 - 2*A*b*c^4)*d^5 - (3*B*b^3*c^2 - 4*A*b^2*c^3)*d^4*e)*x)*log(c*x + b) + ((3*B*b^3*c^2*d^2*e^3 + 2*A*b^4*c*e^5 - (B*b^4*c + 4*A*b^3*c^2)*d*e^4)*x^3 + (3*B*b^3*c^2*d^3*e^2 + 2*A*b^5*e^5 + 2*(B*b^4*c - 2*A*b^3*c^2)*d^2*e^3 - (B*b^5 + 2*A*b^4*c)*d*e^4)*x^2 + (3*B*b^4*c*d^3*e^2 + 2*A*b^5*d*e^4 - (B*b^5 + 4*A*b^4*c)*d^2*e^3)*x)*log(e*x + d) - ((3*B*b^3*c^2*d^2*e^3 + 2*A*b^4*c*e^5 + (B*b*c^4 - 2*A*c^5)*d^4*e - (3*B*b^2*c^3 - 4*A*b*c^4)*d^3*e^2 - (B*b^4*c + 4*A*b^3*c^2)*d*e^4)*x^3 + (4*A*b^2*c^3*d^3*e^2 + 2*A*b^5*e^5 + (B*b*c^4 - 2*A*c^5)*d^5 - 2*(B*b^2*c^3 - A*b*c^4)*d^4*e + 2*(B*b^4*c - 2*A*b^3*c^2)*d^2*e^3 - (B*b^5 + 2*A*b^4*c)*d*e^4)*x^2 + (3*B*b^4*c*d^3*e^2 + 2*A*b^5*d*e^4 + (B*b^2*c^3 - 2*A*b*c^4)*d^5 - (3*B*b^3*c^2 - 4*A*b^2*c^3)*d^4*e - (B*b^5 + 4*A*b^4*c)*d^2*e^3)*x)*log(x))/((b^3*c^4*d^6*e - 3*b^4*c^3*d^5*e^2 + 3*b^5*c^2*d^4*e^3 - b^6*c*d^3*e^4)*x^3 + (b^3*c^4*d^7 - 2*b^4*c^3*d^6*e + 2*b^6*c*d^4*e^3 - b^7*d^3*e^4)*x^2 + (b^4*c^3*d^7 - 3*b^5*c^2*d^6*e + 3*b^6*c*d^5*e^2 - b^7*d^4*e^3)*x)","B",0
1153,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1154,1,889,0,0.521344," ","integrate((B*x+A)*(e*x+d)^5/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{5} c^{3} e^{5} x^{5} + 4 \, B b^{6} c^{2} e^{5} x^{4} - A b^{4} c^{4} d^{5} + 2 \, {\left(10 \, A b^{3} c^{5} d^{3} e^{2} - 10 \, B b^{5} c^{3} d^{2} e^{3} - 3 \, {\left(B b^{2} c^{6} - 2 \, A b c^{7}\right)} d^{5} + 5 \, {\left(B b^{3} c^{5} - 3 \, A b^{2} c^{6}\right)} d^{4} e + 5 \, {\left(2 \, B b^{6} c^{2} - A b^{5} c^{3}\right)} d e^{4} - 2 \, {\left(B b^{7} c - A b^{6} c^{2}\right)} e^{5}\right)} x^{3} - {\left(9 \, {\left(B b^{3} c^{5} - 2 \, A b^{2} c^{6}\right)} d^{5} - 15 \, {\left(B b^{4} c^{4} - 3 \, A b^{3} c^{5}\right)} d^{4} e + 10 \, {\left(B b^{5} c^{3} - 3 \, A b^{4} c^{4}\right)} d^{3} e^{2} + 10 \, {\left(B b^{6} c^{2} + A b^{5} c^{3}\right)} d^{2} e^{3} - 5 \, {\left(3 \, B b^{7} c - A b^{6} c^{2}\right)} d e^{4} + {\left(5 \, B b^{8} - 3 \, A b^{7} c\right)} e^{5}\right)} x^{2} - 2 \, {\left(5 \, A b^{4} c^{4} d^{4} e + {\left(B b^{4} c^{4} - 2 \, A b^{3} c^{5}\right)} d^{5}\right)} x - 2 \, {\left({\left(10 \, A b^{2} c^{6} d^{3} e^{2} - 5 \, B b^{5} c^{3} d e^{4} - 3 \, {\left(B b c^{7} - 2 \, A c^{8}\right)} d^{5} + 5 \, {\left(B b^{2} c^{6} - 3 \, A b c^{7}\right)} d^{4} e + {\left(3 \, B b^{6} c^{2} - A b^{5} c^{3}\right)} e^{5}\right)} x^{4} + 2 \, {\left(10 \, A b^{3} c^{5} d^{3} e^{2} - 5 \, B b^{6} c^{2} d e^{4} - 3 \, {\left(B b^{2} c^{6} - 2 \, A b c^{7}\right)} d^{5} + 5 \, {\left(B b^{3} c^{5} - 3 \, A b^{2} c^{6}\right)} d^{4} e + {\left(3 \, B b^{7} c - A b^{6} c^{2}\right)} e^{5}\right)} x^{3} + {\left(10 \, A b^{4} c^{4} d^{3} e^{2} - 5 \, B b^{7} c d e^{4} - 3 \, {\left(B b^{3} c^{5} - 2 \, A b^{2} c^{6}\right)} d^{5} + 5 \, {\left(B b^{4} c^{4} - 3 \, A b^{3} c^{5}\right)} d^{4} e + {\left(3 \, B b^{8} - A b^{7} c\right)} e^{5}\right)} x^{2}\right)} \log\left(c x + b\right) + 2 \, {\left({\left(10 \, A b^{2} c^{6} d^{3} e^{2} - 3 \, {\left(B b c^{7} - 2 \, A c^{8}\right)} d^{5} + 5 \, {\left(B b^{2} c^{6} - 3 \, A b c^{7}\right)} d^{4} e\right)} x^{4} + 2 \, {\left(10 \, A b^{3} c^{5} d^{3} e^{2} - 3 \, {\left(B b^{2} c^{6} - 2 \, A b c^{7}\right)} d^{5} + 5 \, {\left(B b^{3} c^{5} - 3 \, A b^{2} c^{6}\right)} d^{4} e\right)} x^{3} + {\left(10 \, A b^{4} c^{4} d^{3} e^{2} - 3 \, {\left(B b^{3} c^{5} - 2 \, A b^{2} c^{6}\right)} d^{5} + 5 \, {\left(B b^{4} c^{4} - 3 \, A b^{3} c^{5}\right)} d^{4} e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{6} x^{4} + 2 \, b^{6} c^{5} x^{3} + b^{7} c^{4} x^{2}\right)}}"," ",0,"1/2*(2*B*b^5*c^3*e^5*x^5 + 4*B*b^6*c^2*e^5*x^4 - A*b^4*c^4*d^5 + 2*(10*A*b^3*c^5*d^3*e^2 - 10*B*b^5*c^3*d^2*e^3 - 3*(B*b^2*c^6 - 2*A*b*c^7)*d^5 + 5*(B*b^3*c^5 - 3*A*b^2*c^6)*d^4*e + 5*(2*B*b^6*c^2 - A*b^5*c^3)*d*e^4 - 2*(B*b^7*c - A*b^6*c^2)*e^5)*x^3 - (9*(B*b^3*c^5 - 2*A*b^2*c^6)*d^5 - 15*(B*b^4*c^4 - 3*A*b^3*c^5)*d^4*e + 10*(B*b^5*c^3 - 3*A*b^4*c^4)*d^3*e^2 + 10*(B*b^6*c^2 + A*b^5*c^3)*d^2*e^3 - 5*(3*B*b^7*c - A*b^6*c^2)*d*e^4 + (5*B*b^8 - 3*A*b^7*c)*e^5)*x^2 - 2*(5*A*b^4*c^4*d^4*e + (B*b^4*c^4 - 2*A*b^3*c^5)*d^5)*x - 2*((10*A*b^2*c^6*d^3*e^2 - 5*B*b^5*c^3*d*e^4 - 3*(B*b*c^7 - 2*A*c^8)*d^5 + 5*(B*b^2*c^6 - 3*A*b*c^7)*d^4*e + (3*B*b^6*c^2 - A*b^5*c^3)*e^5)*x^4 + 2*(10*A*b^3*c^5*d^3*e^2 - 5*B*b^6*c^2*d*e^4 - 3*(B*b^2*c^6 - 2*A*b*c^7)*d^5 + 5*(B*b^3*c^5 - 3*A*b^2*c^6)*d^4*e + (3*B*b^7*c - A*b^6*c^2)*e^5)*x^3 + (10*A*b^4*c^4*d^3*e^2 - 5*B*b^7*c*d*e^4 - 3*(B*b^3*c^5 - 2*A*b^2*c^6)*d^5 + 5*(B*b^4*c^4 - 3*A*b^3*c^5)*d^4*e + (3*B*b^8 - A*b^7*c)*e^5)*x^2)*log(c*x + b) + 2*((10*A*b^2*c^6*d^3*e^2 - 3*(B*b*c^7 - 2*A*c^8)*d^5 + 5*(B*b^2*c^6 - 3*A*b*c^7)*d^4*e)*x^4 + 2*(10*A*b^3*c^5*d^3*e^2 - 3*(B*b^2*c^6 - 2*A*b*c^7)*d^5 + 5*(B*b^3*c^5 - 3*A*b^2*c^6)*d^4*e)*x^3 + (10*A*b^4*c^4*d^3*e^2 - 3*(B*b^3*c^5 - 2*A*b^2*c^6)*d^5 + 5*(B*b^4*c^4 - 3*A*b^3*c^5)*d^4*e)*x^2)*log(x))/(b^5*c^6*x^4 + 2*b^6*c^5*x^3 + b^7*c^4*x^2)","B",0
1155,1,736,0,0.455673," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{A b^{4} c^{3} d^{4} - 2 \, {\left(6 \, A b^{3} c^{4} d^{2} e^{2} - 4 \, B b^{5} c^{2} d e^{3} - 3 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} + 4 \, {\left(B b^{3} c^{4} - 3 \, A b^{2} c^{5}\right)} d^{3} e + {\left(2 \, B b^{6} c - A b^{5} c^{2}\right)} e^{4}\right)} x^{3} + {\left(9 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} - 12 \, {\left(B b^{4} c^{3} - 3 \, A b^{3} c^{4}\right)} d^{3} e + 6 \, {\left(B b^{5} c^{2} - 3 \, A b^{4} c^{3}\right)} d^{2} e^{2} + 4 \, {\left(B b^{6} c + A b^{5} c^{2}\right)} d e^{3} - {\left(3 \, B b^{7} - A b^{6} c\right)} e^{4}\right)} x^{2} + 2 \, {\left(4 \, A b^{4} c^{3} d^{3} e + {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{4}\right)} x + 2 \, {\left({\left(6 \, A b^{2} c^{5} d^{2} e^{2} - B b^{5} c^{2} e^{4} - 3 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} + 4 \, {\left(B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{3} e\right)} x^{4} + 2 \, {\left(6 \, A b^{3} c^{4} d^{2} e^{2} - B b^{6} c e^{4} - 3 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} + 4 \, {\left(B b^{3} c^{4} - 3 \, A b^{2} c^{5}\right)} d^{3} e\right)} x^{3} + {\left(6 \, A b^{4} c^{3} d^{2} e^{2} - B b^{7} e^{4} - 3 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} + 4 \, {\left(B b^{4} c^{3} - 3 \, A b^{3} c^{4}\right)} d^{3} e\right)} x^{2}\right)} \log\left(c x + b\right) - 2 \, {\left({\left(6 \, A b^{2} c^{5} d^{2} e^{2} - 3 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} + 4 \, {\left(B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{3} e\right)} x^{4} + 2 \, {\left(6 \, A b^{3} c^{4} d^{2} e^{2} - 3 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} + 4 \, {\left(B b^{3} c^{4} - 3 \, A b^{2} c^{5}\right)} d^{3} e\right)} x^{3} + {\left(6 \, A b^{4} c^{3} d^{2} e^{2} - 3 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} + 4 \, {\left(B b^{4} c^{3} - 3 \, A b^{3} c^{4}\right)} d^{3} e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{5} x^{4} + 2 \, b^{6} c^{4} x^{3} + b^{7} c^{3} x^{2}\right)}}"," ",0,"-1/2*(A*b^4*c^3*d^4 - 2*(6*A*b^3*c^4*d^2*e^2 - 4*B*b^5*c^2*d*e^3 - 3*(B*b^2*c^5 - 2*A*b*c^6)*d^4 + 4*(B*b^3*c^4 - 3*A*b^2*c^5)*d^3*e + (2*B*b^6*c - A*b^5*c^2)*e^4)*x^3 + (9*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 - 12*(B*b^4*c^3 - 3*A*b^3*c^4)*d^3*e + 6*(B*b^5*c^2 - 3*A*b^4*c^3)*d^2*e^2 + 4*(B*b^6*c + A*b^5*c^2)*d*e^3 - (3*B*b^7 - A*b^6*c)*e^4)*x^2 + 2*(4*A*b^4*c^3*d^3*e + (B*b^4*c^3 - 2*A*b^3*c^4)*d^4)*x + 2*((6*A*b^2*c^5*d^2*e^2 - B*b^5*c^2*e^4 - 3*(B*b*c^6 - 2*A*c^7)*d^4 + 4*(B*b^2*c^5 - 3*A*b*c^6)*d^3*e)*x^4 + 2*(6*A*b^3*c^4*d^2*e^2 - B*b^6*c*e^4 - 3*(B*b^2*c^5 - 2*A*b*c^6)*d^4 + 4*(B*b^3*c^4 - 3*A*b^2*c^5)*d^3*e)*x^3 + (6*A*b^4*c^3*d^2*e^2 - B*b^7*e^4 - 3*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 + 4*(B*b^4*c^3 - 3*A*b^3*c^4)*d^3*e)*x^2)*log(c*x + b) - 2*((6*A*b^2*c^5*d^2*e^2 - 3*(B*b*c^6 - 2*A*c^7)*d^4 + 4*(B*b^2*c^5 - 3*A*b*c^6)*d^3*e)*x^4 + 2*(6*A*b^3*c^4*d^2*e^2 - 3*(B*b^2*c^5 - 2*A*b*c^6)*d^4 + 4*(B*b^3*c^4 - 3*A*b^2*c^5)*d^3*e)*x^3 + (6*A*b^4*c^3*d^2*e^2 - 3*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 + 4*(B*b^4*c^3 - 3*A*b^3*c^4)*d^3*e)*x^2)*log(x))/(b^5*c^5*x^4 + 2*b^6*c^4*x^3 + b^7*c^3*x^2)","B",0
1156,1,627,0,0.458035," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{A b^{4} c^{2} d^{3} - 2 \, {\left(3 \, A b^{3} c^{3} d e^{2} - B b^{5} c e^{3} - 3 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + 3 \, {\left(B b^{3} c^{3} - 3 \, A b^{2} c^{4}\right)} d^{2} e\right)} x^{3} + {\left(9 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 9 \, {\left(B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e + 3 \, {\left(B b^{5} c - 3 \, A b^{4} c^{2}\right)} d e^{2} + {\left(B b^{6} + A b^{5} c\right)} e^{3}\right)} x^{2} + 2 \, {\left(3 \, A b^{4} c^{2} d^{2} e + {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{3}\right)} x + 6 \, {\left({\left(A b^{2} c^{4} d e^{2} - {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} + {\left(B b^{2} c^{4} - 3 \, A b c^{5}\right)} d^{2} e\right)} x^{4} + 2 \, {\left(A b^{3} c^{3} d e^{2} - {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + {\left(B b^{3} c^{3} - 3 \, A b^{2} c^{4}\right)} d^{2} e\right)} x^{3} + {\left(A b^{4} c^{2} d e^{2} - {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} + {\left(B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e\right)} x^{2}\right)} \log\left(c x + b\right) - 6 \, {\left({\left(A b^{2} c^{4} d e^{2} - {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} + {\left(B b^{2} c^{4} - 3 \, A b c^{5}\right)} d^{2} e\right)} x^{4} + 2 \, {\left(A b^{3} c^{3} d e^{2} - {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + {\left(B b^{3} c^{3} - 3 \, A b^{2} c^{4}\right)} d^{2} e\right)} x^{3} + {\left(A b^{4} c^{2} d e^{2} - {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} + {\left(B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}"," ",0,"-1/2*(A*b^4*c^2*d^3 - 2*(3*A*b^3*c^3*d*e^2 - B*b^5*c*e^3 - 3*(B*b^2*c^4 - 2*A*b*c^5)*d^3 + 3*(B*b^3*c^3 - 3*A*b^2*c^4)*d^2*e)*x^3 + (9*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 9*(B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e + 3*(B*b^5*c - 3*A*b^4*c^2)*d*e^2 + (B*b^6 + A*b^5*c)*e^3)*x^2 + 2*(3*A*b^4*c^2*d^2*e + (B*b^4*c^2 - 2*A*b^3*c^3)*d^3)*x + 6*((A*b^2*c^4*d*e^2 - (B*b*c^5 - 2*A*c^6)*d^3 + (B*b^2*c^4 - 3*A*b*c^5)*d^2*e)*x^4 + 2*(A*b^3*c^3*d*e^2 - (B*b^2*c^4 - 2*A*b*c^5)*d^3 + (B*b^3*c^3 - 3*A*b^2*c^4)*d^2*e)*x^3 + (A*b^4*c^2*d*e^2 - (B*b^3*c^3 - 2*A*b^2*c^4)*d^3 + (B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e)*x^2)*log(c*x + b) - 6*((A*b^2*c^4*d*e^2 - (B*b*c^5 - 2*A*c^6)*d^3 + (B*b^2*c^4 - 3*A*b*c^5)*d^2*e)*x^4 + 2*(A*b^3*c^3*d*e^2 - (B*b^2*c^4 - 2*A*b*c^5)*d^3 + (B*b^3*c^3 - 3*A*b^2*c^4)*d^2*e)*x^3 + (A*b^4*c^2*d*e^2 - (B*b^3*c^3 - 2*A*b^2*c^4)*d^3 + (B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e)*x^2)*log(x))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2)","B",0
1157,1,558,0,0.417067," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{A b^{4} c d^{2} - 2 \, {\left(A b^{3} c^{2} e^{2} - 3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} + 2 \, {\left(B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} d e\right)} x^{3} + {\left(9 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - 6 \, {\left(B b^{4} c - 3 \, A b^{3} c^{2}\right)} d e + {\left(B b^{5} - 3 \, A b^{4} c\right)} e^{2}\right)} x^{2} + 2 \, {\left(2 \, A b^{4} c d e + {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{2}\right)} x + 2 \, {\left({\left(A b^{2} c^{3} e^{2} - 3 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} + 2 \, {\left(B b^{2} c^{3} - 3 \, A b c^{4}\right)} d e\right)} x^{4} + 2 \, {\left(A b^{3} c^{2} e^{2} - 3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} + 2 \, {\left(B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} d e\right)} x^{3} + {\left(A b^{4} c e^{2} - 3 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} + 2 \, {\left(B b^{4} c - 3 \, A b^{3} c^{2}\right)} d e\right)} x^{2}\right)} \log\left(c x + b\right) - 2 \, {\left({\left(A b^{2} c^{3} e^{2} - 3 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} + 2 \, {\left(B b^{2} c^{3} - 3 \, A b c^{4}\right)} d e\right)} x^{4} + 2 \, {\left(A b^{3} c^{2} e^{2} - 3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} + 2 \, {\left(B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} d e\right)} x^{3} + {\left(A b^{4} c e^{2} - 3 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} + 2 \, {\left(B b^{4} c - 3 \, A b^{3} c^{2}\right)} d e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}"," ",0,"-1/2*(A*b^4*c*d^2 - 2*(A*b^3*c^2*e^2 - 3*(B*b^2*c^3 - 2*A*b*c^4)*d^2 + 2*(B*b^3*c^2 - 3*A*b^2*c^3)*d*e)*x^3 + (9*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - 6*(B*b^4*c - 3*A*b^3*c^2)*d*e + (B*b^5 - 3*A*b^4*c)*e^2)*x^2 + 2*(2*A*b^4*c*d*e + (B*b^4*c - 2*A*b^3*c^2)*d^2)*x + 2*((A*b^2*c^3*e^2 - 3*(B*b*c^4 - 2*A*c^5)*d^2 + 2*(B*b^2*c^3 - 3*A*b*c^4)*d*e)*x^4 + 2*(A*b^3*c^2*e^2 - 3*(B*b^2*c^3 - 2*A*b*c^4)*d^2 + 2*(B*b^3*c^2 - 3*A*b^2*c^3)*d*e)*x^3 + (A*b^4*c*e^2 - 3*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 + 2*(B*b^4*c - 3*A*b^3*c^2)*d*e)*x^2)*log(c*x + b) - 2*((A*b^2*c^3*e^2 - 3*(B*b*c^4 - 2*A*c^5)*d^2 + 2*(B*b^2*c^3 - 3*A*b*c^4)*d*e)*x^4 + 2*(A*b^3*c^2*e^2 - 3*(B*b^2*c^3 - 2*A*b*c^4)*d^2 + 2*(B*b^3*c^2 - 3*A*b^2*c^3)*d*e)*x^3 + (A*b^4*c*e^2 - 3*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 + 2*(B*b^4*c - 3*A*b^3*c^2)*d*e)*x^2)*log(x))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2)","B",0
1158,1,410,0,0.417292," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{A b^{4} d + 2 \, {\left(3 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d - {\left(B b^{3} c - 3 \, A b^{2} c^{2}\right)} e\right)} x^{3} + 3 \, {\left(3 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d - {\left(B b^{4} - 3 \, A b^{3} c\right)} e\right)} x^{2} + 2 \, {\left(A b^{4} e + {\left(B b^{4} - 2 \, A b^{3} c\right)} d\right)} x - 2 \, {\left({\left(3 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d - {\left(B b^{2} c^{2} - 3 \, A b c^{3}\right)} e\right)} x^{4} + 2 \, {\left(3 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d - {\left(B b^{3} c - 3 \, A b^{2} c^{2}\right)} e\right)} x^{3} + {\left(3 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d - {\left(B b^{4} - 3 \, A b^{3} c\right)} e\right)} x^{2}\right)} \log\left(c x + b\right) + 2 \, {\left({\left(3 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d - {\left(B b^{2} c^{2} - 3 \, A b c^{3}\right)} e\right)} x^{4} + 2 \, {\left(3 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d - {\left(B b^{3} c - 3 \, A b^{2} c^{2}\right)} e\right)} x^{3} + {\left(3 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d - {\left(B b^{4} - 3 \, A b^{3} c\right)} e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}"," ",0,"-1/2*(A*b^4*d + 2*(3*(B*b^2*c^2 - 2*A*b*c^3)*d - (B*b^3*c - 3*A*b^2*c^2)*e)*x^3 + 3*(3*(B*b^3*c - 2*A*b^2*c^2)*d - (B*b^4 - 3*A*b^3*c)*e)*x^2 + 2*(A*b^4*e + (B*b^4 - 2*A*b^3*c)*d)*x - 2*((3*(B*b*c^3 - 2*A*c^4)*d - (B*b^2*c^2 - 3*A*b*c^3)*e)*x^4 + 2*(3*(B*b^2*c^2 - 2*A*b*c^3)*d - (B*b^3*c - 3*A*b^2*c^2)*e)*x^3 + (3*(B*b^3*c - 2*A*b^2*c^2)*d - (B*b^4 - 3*A*b^3*c)*e)*x^2)*log(c*x + b) + 2*((3*(B*b*c^3 - 2*A*c^4)*d - (B*b^2*c^2 - 3*A*b*c^3)*e)*x^4 + 2*(3*(B*b^2*c^2 - 2*A*b*c^3)*d - (B*b^3*c - 3*A*b^2*c^2)*e)*x^3 + (3*(B*b^3*c - 2*A*b^2*c^2)*d - (B*b^4 - 3*A*b^3*c)*e)*x^2)*log(x))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2)","B",0
1159,1,225,0,0.416362," ","integrate((B*x+A)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{A b^{4} + 6 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{3} + 9 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{2} + 2 \, {\left(B b^{4} - 2 \, A b^{3} c\right)} x - 6 \, {\left({\left(B b c^{3} - 2 \, A c^{4}\right)} x^{4} + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{3} + {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{2}\right)} \log\left(c x + b\right) + 6 \, {\left({\left(B b c^{3} - 2 \, A c^{4}\right)} x^{4} + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{3} + {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}"," ",0,"-1/2*(A*b^4 + 6*(B*b^2*c^2 - 2*A*b*c^3)*x^3 + 9*(B*b^3*c - 2*A*b^2*c^2)*x^2 + 2*(B*b^4 - 2*A*b^3*c)*x - 6*((B*b*c^3 - 2*A*c^4)*x^4 + 2*(B*b^2*c^2 - 2*A*b*c^3)*x^3 + (B*b^3*c - 2*A*b^2*c^2)*x^2)*log(c*x + b) + 6*((B*b*c^3 - 2*A*c^4)*x^4 + 2*(B*b^2*c^2 - 2*A*b*c^3)*x^3 + (B*b^3*c - 2*A*b^2*c^2)*x^2)*log(x))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2)","B",0
1160,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1161,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1162,1,1022,0,0.494697," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(64 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 24 \, {\left(5 \, B b^{4} c^{2} - 8 \, A b^{3} c^{3}\right)} d^{2} e + 12 \, {\left(7 \, B b^{5} c - 10 \, A b^{4} c^{2}\right)} d e^{2} - 7 \, {\left(3 \, B b^{6} - 4 \, A b^{5} c\right)} e^{3}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(1280 \, B c^{6} e^{3} x^{5} + 128 \, {\left(36 \, B c^{6} d e^{2} + {\left(B b c^{5} + 12 \, A c^{6}\right)} e^{3}\right)} x^{4} - 960 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + 360 \, {\left(5 \, B b^{3} c^{3} - 8 \, A b^{2} c^{4}\right)} d^{2} e - 180 \, {\left(7 \, B b^{4} c^{2} - 10 \, A b^{3} c^{3}\right)} d e^{2} + 105 \, {\left(3 \, B b^{5} c - 4 \, A b^{4} c^{2}\right)} e^{3} + 48 \, {\left(120 \, B c^{6} d^{2} e + 12 \, {\left(B b c^{5} + 10 \, A c^{6}\right)} d e^{2} - {\left(3 \, B b^{2} c^{4} - 4 \, A b c^{5}\right)} e^{3}\right)} x^{3} + 8 \, {\left(320 \, B c^{6} d^{3} + 120 \, {\left(B b c^{5} + 8 \, A c^{6}\right)} d^{2} e - 12 \, {\left(7 \, B b^{2} c^{4} - 10 \, A b c^{5}\right)} d e^{2} + 7 \, {\left(3 \, B b^{3} c^{3} - 4 \, A b^{2} c^{4}\right)} e^{3}\right)} x^{2} + 10 \, {\left(64 \, {\left(B b c^{5} + 6 \, A c^{6}\right)} d^{3} - 24 \, {\left(5 \, B b^{2} c^{4} - 8 \, A b c^{5}\right)} d^{2} e + 12 \, {\left(7 \, B b^{3} c^{3} - 10 \, A b^{2} c^{4}\right)} d e^{2} - 7 \, {\left(3 \, B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{15360 \, c^{6}}, -\frac{15 \, {\left(64 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 24 \, {\left(5 \, B b^{4} c^{2} - 8 \, A b^{3} c^{3}\right)} d^{2} e + 12 \, {\left(7 \, B b^{5} c - 10 \, A b^{4} c^{2}\right)} d e^{2} - 7 \, {\left(3 \, B b^{6} - 4 \, A b^{5} c\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(1280 \, B c^{6} e^{3} x^{5} + 128 \, {\left(36 \, B c^{6} d e^{2} + {\left(B b c^{5} + 12 \, A c^{6}\right)} e^{3}\right)} x^{4} - 960 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + 360 \, {\left(5 \, B b^{3} c^{3} - 8 \, A b^{2} c^{4}\right)} d^{2} e - 180 \, {\left(7 \, B b^{4} c^{2} - 10 \, A b^{3} c^{3}\right)} d e^{2} + 105 \, {\left(3 \, B b^{5} c - 4 \, A b^{4} c^{2}\right)} e^{3} + 48 \, {\left(120 \, B c^{6} d^{2} e + 12 \, {\left(B b c^{5} + 10 \, A c^{6}\right)} d e^{2} - {\left(3 \, B b^{2} c^{4} - 4 \, A b c^{5}\right)} e^{3}\right)} x^{3} + 8 \, {\left(320 \, B c^{6} d^{3} + 120 \, {\left(B b c^{5} + 8 \, A c^{6}\right)} d^{2} e - 12 \, {\left(7 \, B b^{2} c^{4} - 10 \, A b c^{5}\right)} d e^{2} + 7 \, {\left(3 \, B b^{3} c^{3} - 4 \, A b^{2} c^{4}\right)} e^{3}\right)} x^{2} + 10 \, {\left(64 \, {\left(B b c^{5} + 6 \, A c^{6}\right)} d^{3} - 24 \, {\left(5 \, B b^{2} c^{4} - 8 \, A b c^{5}\right)} d^{2} e + 12 \, {\left(7 \, B b^{3} c^{3} - 10 \, A b^{2} c^{4}\right)} d e^{2} - 7 \, {\left(3 \, B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{7680 \, c^{6}}\right]"," ",0,"[1/15360*(15*(64*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 24*(5*B*b^4*c^2 - 8*A*b^3*c^3)*d^2*e + 12*(7*B*b^5*c - 10*A*b^4*c^2)*d*e^2 - 7*(3*B*b^6 - 4*A*b^5*c)*e^3)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(1280*B*c^6*e^3*x^5 + 128*(36*B*c^6*d*e^2 + (B*b*c^5 + 12*A*c^6)*e^3)*x^4 - 960*(B*b^2*c^4 - 2*A*b*c^5)*d^3 + 360*(5*B*b^3*c^3 - 8*A*b^2*c^4)*d^2*e - 180*(7*B*b^4*c^2 - 10*A*b^3*c^3)*d*e^2 + 105*(3*B*b^5*c - 4*A*b^4*c^2)*e^3 + 48*(120*B*c^6*d^2*e + 12*(B*b*c^5 + 10*A*c^6)*d*e^2 - (3*B*b^2*c^4 - 4*A*b*c^5)*e^3)*x^3 + 8*(320*B*c^6*d^3 + 120*(B*b*c^5 + 8*A*c^6)*d^2*e - 12*(7*B*b^2*c^4 - 10*A*b*c^5)*d*e^2 + 7*(3*B*b^3*c^3 - 4*A*b^2*c^4)*e^3)*x^2 + 10*(64*(B*b*c^5 + 6*A*c^6)*d^3 - 24*(5*B*b^2*c^4 - 8*A*b*c^5)*d^2*e + 12*(7*B*b^3*c^3 - 10*A*b^2*c^4)*d*e^2 - 7*(3*B*b^4*c^2 - 4*A*b^3*c^3)*e^3)*x)*sqrt(c*x^2 + b*x))/c^6, -1/7680*(15*(64*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 24*(5*B*b^4*c^2 - 8*A*b^3*c^3)*d^2*e + 12*(7*B*b^5*c - 10*A*b^4*c^2)*d*e^2 - 7*(3*B*b^6 - 4*A*b^5*c)*e^3)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (1280*B*c^6*e^3*x^5 + 128*(36*B*c^6*d*e^2 + (B*b*c^5 + 12*A*c^6)*e^3)*x^4 - 960*(B*b^2*c^4 - 2*A*b*c^5)*d^3 + 360*(5*B*b^3*c^3 - 8*A*b^2*c^4)*d^2*e - 180*(7*B*b^4*c^2 - 10*A*b^3*c^3)*d*e^2 + 105*(3*B*b^5*c - 4*A*b^4*c^2)*e^3 + 48*(120*B*c^6*d^2*e + 12*(B*b*c^5 + 10*A*c^6)*d*e^2 - (3*B*b^2*c^4 - 4*A*b*c^5)*e^3)*x^3 + 8*(320*B*c^6*d^3 + 120*(B*b*c^5 + 8*A*c^6)*d^2*e - 12*(7*B*b^2*c^4 - 10*A*b*c^5)*d*e^2 + 7*(3*B*b^3*c^3 - 4*A*b^2*c^4)*e^3)*x^2 + 10*(64*(B*b*c^5 + 6*A*c^6)*d^3 - 24*(5*B*b^2*c^4 - 8*A*b*c^5)*d^2*e + 12*(7*B*b^3*c^3 - 10*A*b^2*c^4)*d*e^2 - 7*(3*B*b^4*c^2 - 4*A*b^3*c^3)*e^3)*x)*sqrt(c*x^2 + b*x))/c^6]","A",0
1163,1,684,0,0.474919," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - 4 \, {\left(5 \, B b^{4} c - 8 \, A b^{3} c^{2}\right)} d e + {\left(7 \, B b^{5} - 10 \, A b^{4} c\right)} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(384 \, B c^{5} e^{2} x^{4} + 48 \, {\left(20 \, B c^{5} d e + {\left(B b c^{4} + 10 \, A c^{5}\right)} e^{2}\right)} x^{3} - 240 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} + 60 \, {\left(5 \, B b^{3} c^{2} - 8 \, A b^{2} c^{3}\right)} d e - 15 \, {\left(7 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} e^{2} + 8 \, {\left(80 \, B c^{5} d^{2} + 20 \, {\left(B b c^{4} + 8 \, A c^{5}\right)} d e - {\left(7 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} e^{2}\right)} x^{2} + 10 \, {\left(16 \, {\left(B b c^{4} + 6 \, A c^{5}\right)} d^{2} - 4 \, {\left(5 \, B b^{2} c^{3} - 8 \, A b c^{4}\right)} d e + {\left(7 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, c^{5}}, -\frac{15 \, {\left(16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - 4 \, {\left(5 \, B b^{4} c - 8 \, A b^{3} c^{2}\right)} d e + {\left(7 \, B b^{5} - 10 \, A b^{4} c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(384 \, B c^{5} e^{2} x^{4} + 48 \, {\left(20 \, B c^{5} d e + {\left(B b c^{4} + 10 \, A c^{5}\right)} e^{2}\right)} x^{3} - 240 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} + 60 \, {\left(5 \, B b^{3} c^{2} - 8 \, A b^{2} c^{3}\right)} d e - 15 \, {\left(7 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} e^{2} + 8 \, {\left(80 \, B c^{5} d^{2} + 20 \, {\left(B b c^{4} + 8 \, A c^{5}\right)} d e - {\left(7 \, B b^{2} c^{3} - 10 \, A b c^{4}\right)} e^{2}\right)} x^{2} + 10 \, {\left(16 \, {\left(B b c^{4} + 6 \, A c^{5}\right)} d^{2} - 4 \, {\left(5 \, B b^{2} c^{3} - 8 \, A b c^{4}\right)} d e + {\left(7 \, B b^{3} c^{2} - 10 \, A b^{2} c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, c^{5}}\right]"," ",0,"[-1/3840*(15*(16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - 4*(5*B*b^4*c - 8*A*b^3*c^2)*d*e + (7*B*b^5 - 10*A*b^4*c)*e^2)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(384*B*c^5*e^2*x^4 + 48*(20*B*c^5*d*e + (B*b*c^4 + 10*A*c^5)*e^2)*x^3 - 240*(B*b^2*c^3 - 2*A*b*c^4)*d^2 + 60*(5*B*b^3*c^2 - 8*A*b^2*c^3)*d*e - 15*(7*B*b^4*c - 10*A*b^3*c^2)*e^2 + 8*(80*B*c^5*d^2 + 20*(B*b*c^4 + 8*A*c^5)*d*e - (7*B*b^2*c^3 - 10*A*b*c^4)*e^2)*x^2 + 10*(16*(B*b*c^4 + 6*A*c^5)*d^2 - 4*(5*B*b^2*c^3 - 8*A*b*c^4)*d*e + (7*B*b^3*c^2 - 10*A*b^2*c^3)*e^2)*x)*sqrt(c*x^2 + b*x))/c^5, -1/1920*(15*(16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - 4*(5*B*b^4*c - 8*A*b^3*c^2)*d*e + (7*B*b^5 - 10*A*b^4*c)*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (384*B*c^5*e^2*x^4 + 48*(20*B*c^5*d*e + (B*b*c^4 + 10*A*c^5)*e^2)*x^3 - 240*(B*b^2*c^3 - 2*A*b*c^4)*d^2 + 60*(5*B*b^3*c^2 - 8*A*b^2*c^3)*d*e - 15*(7*B*b^4*c - 10*A*b^3*c^2)*e^2 + 8*(80*B*c^5*d^2 + 20*(B*b*c^4 + 8*A*c^5)*d*e - (7*B*b^2*c^3 - 10*A*b*c^4)*e^2)*x^2 + 10*(16*(B*b*c^4 + 6*A*c^5)*d^2 - 4*(5*B*b^2*c^3 - 8*A*b*c^4)*d*e + (7*B*b^3*c^2 - 10*A*b^2*c^3)*e^2)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
1164,1,408,0,0.441413," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d - {\left(5 \, B b^{4} - 8 \, A b^{3} c\right)} e\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(48 \, B c^{4} e x^{3} + 8 \, {\left(8 \, B c^{4} d + {\left(B b c^{3} + 8 \, A c^{4}\right)} e\right)} x^{2} - 24 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d + 3 \, {\left(5 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} e + 2 \, {\left(8 \, {\left(B b c^{3} + 6 \, A c^{4}\right)} d - {\left(5 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, c^{4}}, -\frac{3 \, {\left(8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d - {\left(5 \, B b^{4} - 8 \, A b^{3} c\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(48 \, B c^{4} e x^{3} + 8 \, {\left(8 \, B c^{4} d + {\left(B b c^{3} + 8 \, A c^{4}\right)} e\right)} x^{2} - 24 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d + 3 \, {\left(5 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} e + 2 \, {\left(8 \, {\left(B b c^{3} + 6 \, A c^{4}\right)} d - {\left(5 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, c^{4}}\right]"," ",0,"[1/384*(3*(8*(B*b^3*c - 2*A*b^2*c^2)*d - (5*B*b^4 - 8*A*b^3*c)*e)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(48*B*c^4*e*x^3 + 8*(8*B*c^4*d + (B*b*c^3 + 8*A*c^4)*e)*x^2 - 24*(B*b^2*c^2 - 2*A*b*c^3)*d + 3*(5*B*b^3*c - 8*A*b^2*c^2)*e + 2*(8*(B*b*c^3 + 6*A*c^4)*d - (5*B*b^2*c^2 - 8*A*b*c^3)*e)*x)*sqrt(c*x^2 + b*x))/c^4, -1/192*(3*(8*(B*b^3*c - 2*A*b^2*c^2)*d - (5*B*b^4 - 8*A*b^3*c)*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (48*B*c^4*e*x^3 + 8*(8*B*c^4*d + (B*b*c^3 + 8*A*c^4)*e)*x^2 - 24*(B*b^2*c^2 - 2*A*b*c^3)*d + 3*(5*B*b^3*c - 8*A*b^2*c^2)*e + 2*(8*(B*b*c^3 + 6*A*c^4)*d - (5*B*b^2*c^2 - 8*A*b*c^3)*e)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
1165,1,204,0,0.452865," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{3} x^{2} - 3 \, B b^{2} c + 6 \, A b c^{2} + 2 \, {\left(B b c^{2} + 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c^{3}}, -\frac{3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(8 \, B c^{3} x^{2} - 3 \, B b^{2} c + 6 \, A b c^{2} + 2 \, {\left(B b c^{2} + 6 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c^{3}}\right]"," ",0,"[-1/48*(3*(B*b^3 - 2*A*b^2*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(8*B*c^3*x^2 - 3*B*b^2*c + 6*A*b*c^2 + 2*(B*b*c^2 + 6*A*c^3)*x)*sqrt(c*x^2 + b*x))/c^3, -1/24*(3*(B*b^3 - 2*A*b^2*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (8*B*c^3*x^2 - 3*B*b^2*c + 6*A*b*c^2 + 2*(B*b*c^2 + 6*A*c^3)*x)*sqrt(c*x^2 + b*x))/c^3]","A",0
1166,1,800,0,1.228707," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, B c^{2} d^{2} - 4 \, {\left(B b c + 2 \, A c^{2}\right)} d e - {\left(B b^{2} - 4 \, A b c\right)} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 8 \, {\left(B c^{2} d - A c^{2} e\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(2 \, B c^{2} e^{2} x - 4 \, B c^{2} d e + {\left(B b c + 4 \, A c^{2}\right)} e^{2}\right)} \sqrt{c x^{2} + b x}}{8 \, c^{2} e^{3}}, -\frac{16 \, {\left(B c^{2} d - A c^{2} e\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(8 \, B c^{2} d^{2} - 4 \, {\left(B b c + 2 \, A c^{2}\right)} d e - {\left(B b^{2} - 4 \, A b c\right)} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(2 \, B c^{2} e^{2} x - 4 \, B c^{2} d e + {\left(B b c + 4 \, A c^{2}\right)} e^{2}\right)} \sqrt{c x^{2} + b x}}{8 \, c^{2} e^{3}}, -\frac{{\left(8 \, B c^{2} d^{2} - 4 \, {\left(B b c + 2 \, A c^{2}\right)} d e - {\left(B b^{2} - 4 \, A b c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 4 \, {\left(B c^{2} d - A c^{2} e\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - {\left(2 \, B c^{2} e^{2} x - 4 \, B c^{2} d e + {\left(B b c + 4 \, A c^{2}\right)} e^{2}\right)} \sqrt{c x^{2} + b x}}{4 \, c^{2} e^{3}}, -\frac{8 \, {\left(B c^{2} d - A c^{2} e\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(8 \, B c^{2} d^{2} - 4 \, {\left(B b c + 2 \, A c^{2}\right)} d e - {\left(B b^{2} - 4 \, A b c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, B c^{2} e^{2} x - 4 \, B c^{2} d e + {\left(B b c + 4 \, A c^{2}\right)} e^{2}\right)} \sqrt{c x^{2} + b x}}{4 \, c^{2} e^{3}}\right]"," ",0,"[1/8*((8*B*c^2*d^2 - 4*(B*b*c + 2*A*c^2)*d*e - (B*b^2 - 4*A*b*c)*e^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 8*(B*c^2*d - A*c^2*e)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(2*B*c^2*e^2*x - 4*B*c^2*d*e + (B*b*c + 4*A*c^2)*e^2)*sqrt(c*x^2 + b*x))/(c^2*e^3), -1/8*(16*(B*c^2*d - A*c^2*e)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (8*B*c^2*d^2 - 4*(B*b*c + 2*A*c^2)*d*e - (B*b^2 - 4*A*b*c)*e^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(2*B*c^2*e^2*x - 4*B*c^2*d*e + (B*b*c + 4*A*c^2)*e^2)*sqrt(c*x^2 + b*x))/(c^2*e^3), -1/4*((8*B*c^2*d^2 - 4*(B*b*c + 2*A*c^2)*d*e - (B*b^2 - 4*A*b*c)*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 4*(B*c^2*d - A*c^2*e)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - (2*B*c^2*e^2*x - 4*B*c^2*d*e + (B*b*c + 4*A*c^2)*e^2)*sqrt(c*x^2 + b*x))/(c^2*e^3), -1/4*(8*(B*c^2*d - A*c^2*e)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (8*B*c^2*d^2 - 4*(B*b*c + 2*A*c^2)*d*e - (B*b^2 - 4*A*b*c)*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*B*c^2*e^2*x - 4*B*c^2*d*e + (B*b*c + 4*A*c^2)*e^2)*sqrt(c*x^2 + b*x))/(c^2*e^3)]","A",0
1167,1,1513,0,0.845164," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B c^{2} d^{4} - {\left(5 \, B b c + 2 \, A c^{2}\right)} d^{3} e + {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{2} + {\left(4 \, B c^{2} d^{3} e - {\left(5 \, B b c + 2 \, A c^{2}\right)} d^{2} e^{2} + {\left(B b^{2} + 2 \, A b c\right)} d e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - {\left(4 \, B c^{2} d^{3} + A b c d e^{2} - {\left(3 \, B b c + 2 \, A c^{2}\right)} d^{2} e + {\left(4 \, B c^{2} d^{2} e + A b c e^{3} - {\left(3 \, B b c + 2 \, A c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(2 \, B c^{2} d^{3} e + A b c d e^{3} - {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{2} + {\left(B c^{2} d^{2} e^{2} - B b c d e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(c^{2} d^{3} e^{3} - b c d^{2} e^{4} + {\left(c^{2} d^{2} e^{4} - b c d e^{5}\right)} x\right)}}, \frac{2 \, {\left(4 \, B c^{2} d^{3} + A b c d e^{2} - {\left(3 \, B b c + 2 \, A c^{2}\right)} d^{2} e + {\left(4 \, B c^{2} d^{2} e + A b c e^{3} - {\left(3 \, B b c + 2 \, A c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(4 \, B c^{2} d^{4} - {\left(5 \, B b c + 2 \, A c^{2}\right)} d^{3} e + {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{2} + {\left(4 \, B c^{2} d^{3} e - {\left(5 \, B b c + 2 \, A c^{2}\right)} d^{2} e^{2} + {\left(B b^{2} + 2 \, A b c\right)} d e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, B c^{2} d^{3} e + A b c d e^{3} - {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{2} + {\left(B c^{2} d^{2} e^{2} - B b c d e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(c^{2} d^{3} e^{3} - b c d^{2} e^{4} + {\left(c^{2} d^{2} e^{4} - b c d e^{5}\right)} x\right)}}, \frac{2 \, {\left(4 \, B c^{2} d^{4} - {\left(5 \, B b c + 2 \, A c^{2}\right)} d^{3} e + {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{2} + {\left(4 \, B c^{2} d^{3} e - {\left(5 \, B b c + 2 \, A c^{2}\right)} d^{2} e^{2} + {\left(B b^{2} + 2 \, A b c\right)} d e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(4 \, B c^{2} d^{3} + A b c d e^{2} - {\left(3 \, B b c + 2 \, A c^{2}\right)} d^{2} e + {\left(4 \, B c^{2} d^{2} e + A b c e^{3} - {\left(3 \, B b c + 2 \, A c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(2 \, B c^{2} d^{3} e + A b c d e^{3} - {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{2} + {\left(B c^{2} d^{2} e^{2} - B b c d e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(c^{2} d^{3} e^{3} - b c d^{2} e^{4} + {\left(c^{2} d^{2} e^{4} - b c d e^{5}\right)} x\right)}}, \frac{{\left(4 \, B c^{2} d^{3} + A b c d e^{2} - {\left(3 \, B b c + 2 \, A c^{2}\right)} d^{2} e + {\left(4 \, B c^{2} d^{2} e + A b c e^{3} - {\left(3 \, B b c + 2 \, A c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(4 \, B c^{2} d^{4} - {\left(5 \, B b c + 2 \, A c^{2}\right)} d^{3} e + {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{2} + {\left(4 \, B c^{2} d^{3} e - {\left(5 \, B b c + 2 \, A c^{2}\right)} d^{2} e^{2} + {\left(B b^{2} + 2 \, A b c\right)} d e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(2 \, B c^{2} d^{3} e + A b c d e^{3} - {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{2} + {\left(B c^{2} d^{2} e^{2} - B b c d e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{c^{2} d^{3} e^{3} - b c d^{2} e^{4} + {\left(c^{2} d^{2} e^{4} - b c d e^{5}\right)} x}\right]"," ",0,"[-1/2*((4*B*c^2*d^4 - (5*B*b*c + 2*A*c^2)*d^3*e + (B*b^2 + 2*A*b*c)*d^2*e^2 + (4*B*c^2*d^3*e - (5*B*b*c + 2*A*c^2)*d^2*e^2 + (B*b^2 + 2*A*b*c)*d*e^3)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - (4*B*c^2*d^3 + A*b*c*d*e^2 - (3*B*b*c + 2*A*c^2)*d^2*e + (4*B*c^2*d^2*e + A*b*c*e^3 - (3*B*b*c + 2*A*c^2)*d*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(2*B*c^2*d^3*e + A*b*c*d*e^3 - (2*B*b*c + A*c^2)*d^2*e^2 + (B*c^2*d^2*e^2 - B*b*c*d*e^3)*x)*sqrt(c*x^2 + b*x))/(c^2*d^3*e^3 - b*c*d^2*e^4 + (c^2*d^2*e^4 - b*c*d*e^5)*x), 1/2*(2*(4*B*c^2*d^3 + A*b*c*d*e^2 - (3*B*b*c + 2*A*c^2)*d^2*e + (4*B*c^2*d^2*e + A*b*c*e^3 - (3*B*b*c + 2*A*c^2)*d*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (4*B*c^2*d^4 - (5*B*b*c + 2*A*c^2)*d^3*e + (B*b^2 + 2*A*b*c)*d^2*e^2 + (4*B*c^2*d^3*e - (5*B*b*c + 2*A*c^2)*d^2*e^2 + (B*b^2 + 2*A*b*c)*d*e^3)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*B*c^2*d^3*e + A*b*c*d*e^3 - (2*B*b*c + A*c^2)*d^2*e^2 + (B*c^2*d^2*e^2 - B*b*c*d*e^3)*x)*sqrt(c*x^2 + b*x))/(c^2*d^3*e^3 - b*c*d^2*e^4 + (c^2*d^2*e^4 - b*c*d*e^5)*x), 1/2*(2*(4*B*c^2*d^4 - (5*B*b*c + 2*A*c^2)*d^3*e + (B*b^2 + 2*A*b*c)*d^2*e^2 + (4*B*c^2*d^3*e - (5*B*b*c + 2*A*c^2)*d^2*e^2 + (B*b^2 + 2*A*b*c)*d*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (4*B*c^2*d^3 + A*b*c*d*e^2 - (3*B*b*c + 2*A*c^2)*d^2*e + (4*B*c^2*d^2*e + A*b*c*e^3 - (3*B*b*c + 2*A*c^2)*d*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(2*B*c^2*d^3*e + A*b*c*d*e^3 - (2*B*b*c + A*c^2)*d^2*e^2 + (B*c^2*d^2*e^2 - B*b*c*d*e^3)*x)*sqrt(c*x^2 + b*x))/(c^2*d^3*e^3 - b*c*d^2*e^4 + (c^2*d^2*e^4 - b*c*d*e^5)*x), ((4*B*c^2*d^3 + A*b*c*d*e^2 - (3*B*b*c + 2*A*c^2)*d^2*e + (4*B*c^2*d^2*e + A*b*c*e^3 - (3*B*b*c + 2*A*c^2)*d*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (4*B*c^2*d^4 - (5*B*b*c + 2*A*c^2)*d^3*e + (B*b^2 + 2*A*b*c)*d^2*e^2 + (4*B*c^2*d^3*e - (5*B*b*c + 2*A*c^2)*d^2*e^2 + (B*b^2 + 2*A*b*c)*d*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (2*B*c^2*d^3*e + A*b*c*d*e^3 - (2*B*b*c + A*c^2)*d^2*e^2 + (B*c^2*d^2*e^2 - B*b*c*d*e^3)*x)*sqrt(c*x^2 + b*x))/(c^2*d^3*e^3 - b*c*d^2*e^4 + (c^2*d^2*e^4 - b*c*d*e^5)*x)]","B",0
1168,1,2234,0,1.947882," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{8 \, {\left(B c^{2} d^{6} - 2 \, B b c d^{5} e + B b^{2} d^{4} e^{2} + {\left(B c^{2} d^{4} e^{2} - 2 \, B b c d^{3} e^{3} + B b^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(B c^{2} d^{5} e - 2 \, B b c d^{4} e^{2} + B b^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - {\left(8 \, B c^{2} d^{5} - 12 \, B b c d^{4} e + 3 \, B b^{2} d^{3} e^{2} + A b^{2} d^{2} e^{3} + {\left(8 \, B c^{2} d^{3} e^{2} - 12 \, B b c d^{2} e^{3} + 3 \, B b^{2} d e^{4} + A b^{2} e^{5}\right)} x^{2} + 2 \, {\left(8 \, B c^{2} d^{4} e - 12 \, B b c d^{3} e^{2} + 3 \, B b^{2} d^{2} e^{3} + A b^{2} d e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(4 \, B c^{2} d^{5} e - 7 \, B b c d^{4} e^{2} + A b^{2} d^{2} e^{4} + {\left(3 \, B b^{2} - A b c\right)} d^{3} e^{3} + {\left(6 \, B c^{2} d^{4} e^{2} - A b^{2} d e^{5} - {\left(11 \, B b c + 2 \, A c^{2}\right)} d^{3} e^{3} + {\left(5 \, B b^{2} + 3 \, A b c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{2} d^{6} e^{3} - 2 \, b c d^{5} e^{4} + b^{2} d^{4} e^{5} + {\left(c^{2} d^{4} e^{5} - 2 \, b c d^{3} e^{6} + b^{2} d^{2} e^{7}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e^{4} - 2 \, b c d^{4} e^{5} + b^{2} d^{3} e^{6}\right)} x\right)}}, -\frac{{\left(8 \, B c^{2} d^{5} - 12 \, B b c d^{4} e + 3 \, B b^{2} d^{3} e^{2} + A b^{2} d^{2} e^{3} + {\left(8 \, B c^{2} d^{3} e^{2} - 12 \, B b c d^{2} e^{3} + 3 \, B b^{2} d e^{4} + A b^{2} e^{5}\right)} x^{2} + 2 \, {\left(8 \, B c^{2} d^{4} e - 12 \, B b c d^{3} e^{2} + 3 \, B b^{2} d^{2} e^{3} + A b^{2} d e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 4 \, {\left(B c^{2} d^{6} - 2 \, B b c d^{5} e + B b^{2} d^{4} e^{2} + {\left(B c^{2} d^{4} e^{2} - 2 \, B b c d^{3} e^{3} + B b^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(B c^{2} d^{5} e - 2 \, B b c d^{4} e^{2} + B b^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + {\left(4 \, B c^{2} d^{5} e - 7 \, B b c d^{4} e^{2} + A b^{2} d^{2} e^{4} + {\left(3 \, B b^{2} - A b c\right)} d^{3} e^{3} + {\left(6 \, B c^{2} d^{4} e^{2} - A b^{2} d e^{5} - {\left(11 \, B b c + 2 \, A c^{2}\right)} d^{3} e^{3} + {\left(5 \, B b^{2} + 3 \, A b c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c^{2} d^{6} e^{3} - 2 \, b c d^{5} e^{4} + b^{2} d^{4} e^{5} + {\left(c^{2} d^{4} e^{5} - 2 \, b c d^{3} e^{6} + b^{2} d^{2} e^{7}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e^{4} - 2 \, b c d^{4} e^{5} + b^{2} d^{3} e^{6}\right)} x\right)}}, -\frac{16 \, {\left(B c^{2} d^{6} - 2 \, B b c d^{5} e + B b^{2} d^{4} e^{2} + {\left(B c^{2} d^{4} e^{2} - 2 \, B b c d^{3} e^{3} + B b^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(B c^{2} d^{5} e - 2 \, B b c d^{4} e^{2} + B b^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, B c^{2} d^{5} - 12 \, B b c d^{4} e + 3 \, B b^{2} d^{3} e^{2} + A b^{2} d^{2} e^{3} + {\left(8 \, B c^{2} d^{3} e^{2} - 12 \, B b c d^{2} e^{3} + 3 \, B b^{2} d e^{4} + A b^{2} e^{5}\right)} x^{2} + 2 \, {\left(8 \, B c^{2} d^{4} e - 12 \, B b c d^{3} e^{2} + 3 \, B b^{2} d^{2} e^{3} + A b^{2} d e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(4 \, B c^{2} d^{5} e - 7 \, B b c d^{4} e^{2} + A b^{2} d^{2} e^{4} + {\left(3 \, B b^{2} - A b c\right)} d^{3} e^{3} + {\left(6 \, B c^{2} d^{4} e^{2} - A b^{2} d e^{5} - {\left(11 \, B b c + 2 \, A c^{2}\right)} d^{3} e^{3} + {\left(5 \, B b^{2} + 3 \, A b c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{2} d^{6} e^{3} - 2 \, b c d^{5} e^{4} + b^{2} d^{4} e^{5} + {\left(c^{2} d^{4} e^{5} - 2 \, b c d^{3} e^{6} + b^{2} d^{2} e^{7}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e^{4} - 2 \, b c d^{4} e^{5} + b^{2} d^{3} e^{6}\right)} x\right)}}, -\frac{{\left(8 \, B c^{2} d^{5} - 12 \, B b c d^{4} e + 3 \, B b^{2} d^{3} e^{2} + A b^{2} d^{2} e^{3} + {\left(8 \, B c^{2} d^{3} e^{2} - 12 \, B b c d^{2} e^{3} + 3 \, B b^{2} d e^{4} + A b^{2} e^{5}\right)} x^{2} + 2 \, {\left(8 \, B c^{2} d^{4} e - 12 \, B b c d^{3} e^{2} + 3 \, B b^{2} d^{2} e^{3} + A b^{2} d e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 8 \, {\left(B c^{2} d^{6} - 2 \, B b c d^{5} e + B b^{2} d^{4} e^{2} + {\left(B c^{2} d^{4} e^{2} - 2 \, B b c d^{3} e^{3} + B b^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(B c^{2} d^{5} e - 2 \, B b c d^{4} e^{2} + B b^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(4 \, B c^{2} d^{5} e - 7 \, B b c d^{4} e^{2} + A b^{2} d^{2} e^{4} + {\left(3 \, B b^{2} - A b c\right)} d^{3} e^{3} + {\left(6 \, B c^{2} d^{4} e^{2} - A b^{2} d e^{5} - {\left(11 \, B b c + 2 \, A c^{2}\right)} d^{3} e^{3} + {\left(5 \, B b^{2} + 3 \, A b c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c^{2} d^{6} e^{3} - 2 \, b c d^{5} e^{4} + b^{2} d^{4} e^{5} + {\left(c^{2} d^{4} e^{5} - 2 \, b c d^{3} e^{6} + b^{2} d^{2} e^{7}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e^{4} - 2 \, b c d^{4} e^{5} + b^{2} d^{3} e^{6}\right)} x\right)}}\right]"," ",0,"[1/8*(8*(B*c^2*d^6 - 2*B*b*c*d^5*e + B*b^2*d^4*e^2 + (B*c^2*d^4*e^2 - 2*B*b*c*d^3*e^3 + B*b^2*d^2*e^4)*x^2 + 2*(B*c^2*d^5*e - 2*B*b*c*d^4*e^2 + B*b^2*d^3*e^3)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - (8*B*c^2*d^5 - 12*B*b*c*d^4*e + 3*B*b^2*d^3*e^2 + A*b^2*d^2*e^3 + (8*B*c^2*d^3*e^2 - 12*B*b*c*d^2*e^3 + 3*B*b^2*d*e^4 + A*b^2*e^5)*x^2 + 2*(8*B*c^2*d^4*e - 12*B*b*c*d^3*e^2 + 3*B*b^2*d^2*e^3 + A*b^2*d*e^4)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(4*B*c^2*d^5*e - 7*B*b*c*d^4*e^2 + A*b^2*d^2*e^4 + (3*B*b^2 - A*b*c)*d^3*e^3 + (6*B*c^2*d^4*e^2 - A*b^2*d*e^5 - (11*B*b*c + 2*A*c^2)*d^3*e^3 + (5*B*b^2 + 3*A*b*c)*d^2*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*d^6*e^3 - 2*b*c*d^5*e^4 + b^2*d^4*e^5 + (c^2*d^4*e^5 - 2*b*c*d^3*e^6 + b^2*d^2*e^7)*x^2 + 2*(c^2*d^5*e^4 - 2*b*c*d^4*e^5 + b^2*d^3*e^6)*x), -1/4*((8*B*c^2*d^5 - 12*B*b*c*d^4*e + 3*B*b^2*d^3*e^2 + A*b^2*d^2*e^3 + (8*B*c^2*d^3*e^2 - 12*B*b*c*d^2*e^3 + 3*B*b^2*d*e^4 + A*b^2*e^5)*x^2 + 2*(8*B*c^2*d^4*e - 12*B*b*c*d^3*e^2 + 3*B*b^2*d^2*e^3 + A*b^2*d*e^4)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 4*(B*c^2*d^6 - 2*B*b*c*d^5*e + B*b^2*d^4*e^2 + (B*c^2*d^4*e^2 - 2*B*b*c*d^3*e^3 + B*b^2*d^2*e^4)*x^2 + 2*(B*c^2*d^5*e - 2*B*b*c*d^4*e^2 + B*b^2*d^3*e^3)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + (4*B*c^2*d^5*e - 7*B*b*c*d^4*e^2 + A*b^2*d^2*e^4 + (3*B*b^2 - A*b*c)*d^3*e^3 + (6*B*c^2*d^4*e^2 - A*b^2*d*e^5 - (11*B*b*c + 2*A*c^2)*d^3*e^3 + (5*B*b^2 + 3*A*b*c)*d^2*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*d^6*e^3 - 2*b*c*d^5*e^4 + b^2*d^4*e^5 + (c^2*d^4*e^5 - 2*b*c*d^3*e^6 + b^2*d^2*e^7)*x^2 + 2*(c^2*d^5*e^4 - 2*b*c*d^4*e^5 + b^2*d^3*e^6)*x), -1/8*(16*(B*c^2*d^6 - 2*B*b*c*d^5*e + B*b^2*d^4*e^2 + (B*c^2*d^4*e^2 - 2*B*b*c*d^3*e^3 + B*b^2*d^2*e^4)*x^2 + 2*(B*c^2*d^5*e - 2*B*b*c*d^4*e^2 + B*b^2*d^3*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*B*c^2*d^5 - 12*B*b*c*d^4*e + 3*B*b^2*d^3*e^2 + A*b^2*d^2*e^3 + (8*B*c^2*d^3*e^2 - 12*B*b*c*d^2*e^3 + 3*B*b^2*d*e^4 + A*b^2*e^5)*x^2 + 2*(8*B*c^2*d^4*e - 12*B*b*c*d^3*e^2 + 3*B*b^2*d^2*e^3 + A*b^2*d*e^4)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(4*B*c^2*d^5*e - 7*B*b*c*d^4*e^2 + A*b^2*d^2*e^4 + (3*B*b^2 - A*b*c)*d^3*e^3 + (6*B*c^2*d^4*e^2 - A*b^2*d*e^5 - (11*B*b*c + 2*A*c^2)*d^3*e^3 + (5*B*b^2 + 3*A*b*c)*d^2*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*d^6*e^3 - 2*b*c*d^5*e^4 + b^2*d^4*e^5 + (c^2*d^4*e^5 - 2*b*c*d^3*e^6 + b^2*d^2*e^7)*x^2 + 2*(c^2*d^5*e^4 - 2*b*c*d^4*e^5 + b^2*d^3*e^6)*x), -1/4*((8*B*c^2*d^5 - 12*B*b*c*d^4*e + 3*B*b^2*d^3*e^2 + A*b^2*d^2*e^3 + (8*B*c^2*d^3*e^2 - 12*B*b*c*d^2*e^3 + 3*B*b^2*d*e^4 + A*b^2*e^5)*x^2 + 2*(8*B*c^2*d^4*e - 12*B*b*c*d^3*e^2 + 3*B*b^2*d^2*e^3 + A*b^2*d*e^4)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 8*(B*c^2*d^6 - 2*B*b*c*d^5*e + B*b^2*d^4*e^2 + (B*c^2*d^4*e^2 - 2*B*b*c*d^3*e^3 + B*b^2*d^2*e^4)*x^2 + 2*(B*c^2*d^5*e - 2*B*b*c*d^4*e^2 + B*b^2*d^3*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (4*B*c^2*d^5*e - 7*B*b*c*d^4*e^2 + A*b^2*d^2*e^4 + (3*B*b^2 - A*b*c)*d^3*e^3 + (6*B*c^2*d^4*e^2 - A*b^2*d*e^5 - (11*B*b*c + 2*A*c^2)*d^3*e^3 + (5*B*b^2 + 3*A*b*c)*d^2*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*d^6*e^3 - 2*b*c*d^5*e^4 + b^2*d^4*e^5 + (c^2*d^4*e^5 - 2*b*c*d^3*e^6 + b^2*d^2*e^7)*x^2 + 2*(c^2*d^5*e^4 - 2*b*c*d^4*e^5 + b^2*d^3*e^6)*x)]","B",0
1169,1,1216,0,0.452708," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A b^{3} d^{3} e + {\left(B b^{3} - 2 \, A b^{2} c\right)} d^{4} + {\left(A b^{3} e^{4} + {\left(B b^{3} - 2 \, A b^{2} c\right)} d e^{3}\right)} x^{3} + 3 \, {\left(A b^{3} d e^{3} + {\left(B b^{3} - 2 \, A b^{2} c\right)} d^{2} e^{2}\right)} x^{2} + 3 \, {\left(A b^{3} d^{2} e^{2} + {\left(B b^{3} - 2 \, A b^{2} c\right)} d^{3} e\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(3 \, A b^{3} d^{3} e^{2} - 3 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{5} + 3 \, {\left(B b^{3} - 3 \, A b^{2} c\right)} d^{4} e + {\left(8 \, B c^{3} d^{5} - 3 \, A b^{3} d e^{4} - 2 \, {\left(11 \, B b c^{2} - 2 \, A c^{3}\right)} d^{4} e + {\left(17 \, B b^{2} c - 8 \, A b c^{2}\right)} d^{3} e^{2} - {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} d^{2} e^{3}\right)} x^{2} - 2 \, {\left(4 \, A b^{3} d^{2} e^{3} - {\left(B b c^{2} + 6 \, A c^{3}\right)} d^{5} + {\left(5 \, B b^{2} c + 13 \, A b c^{2}\right)} d^{4} e - {\left(4 \, B b^{3} + 11 \, A b^{2} c\right)} d^{3} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{3} d^{9} - 3 \, b c^{2} d^{8} e + 3 \, b^{2} c d^{7} e^{2} - b^{3} d^{6} e^{3} + {\left(c^{3} d^{6} e^{3} - 3 \, b c^{2} d^{5} e^{4} + 3 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{2} - 3 \, b c^{2} d^{6} e^{3} + 3 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e - 3 \, b c^{2} d^{7} e^{2} + 3 \, b^{2} c d^{6} e^{3} - b^{3} d^{5} e^{4}\right)} x\right)}}, \frac{3 \, {\left(A b^{3} d^{3} e + {\left(B b^{3} - 2 \, A b^{2} c\right)} d^{4} + {\left(A b^{3} e^{4} + {\left(B b^{3} - 2 \, A b^{2} c\right)} d e^{3}\right)} x^{3} + 3 \, {\left(A b^{3} d e^{3} + {\left(B b^{3} - 2 \, A b^{2} c\right)} d^{2} e^{2}\right)} x^{2} + 3 \, {\left(A b^{3} d^{2} e^{2} + {\left(B b^{3} - 2 \, A b^{2} c\right)} d^{3} e\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(3 \, A b^{3} d^{3} e^{2} - 3 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{5} + 3 \, {\left(B b^{3} - 3 \, A b^{2} c\right)} d^{4} e + {\left(8 \, B c^{3} d^{5} - 3 \, A b^{3} d e^{4} - 2 \, {\left(11 \, B b c^{2} - 2 \, A c^{3}\right)} d^{4} e + {\left(17 \, B b^{2} c - 8 \, A b c^{2}\right)} d^{3} e^{2} - {\left(3 \, B b^{3} - 7 \, A b^{2} c\right)} d^{2} e^{3}\right)} x^{2} - 2 \, {\left(4 \, A b^{3} d^{2} e^{3} - {\left(B b c^{2} + 6 \, A c^{3}\right)} d^{5} + {\left(5 \, B b^{2} c + 13 \, A b c^{2}\right)} d^{4} e - {\left(4 \, B b^{3} + 11 \, A b^{2} c\right)} d^{3} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{3} d^{9} - 3 \, b c^{2} d^{8} e + 3 \, b^{2} c d^{7} e^{2} - b^{3} d^{6} e^{3} + {\left(c^{3} d^{6} e^{3} - 3 \, b c^{2} d^{5} e^{4} + 3 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{2} - 3 \, b c^{2} d^{6} e^{3} + 3 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e - 3 \, b c^{2} d^{7} e^{2} + 3 \, b^{2} c d^{6} e^{3} - b^{3} d^{5} e^{4}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(A*b^3*d^3*e + (B*b^3 - 2*A*b^2*c)*d^4 + (A*b^3*e^4 + (B*b^3 - 2*A*b^2*c)*d*e^3)*x^3 + 3*(A*b^3*d*e^3 + (B*b^3 - 2*A*b^2*c)*d^2*e^2)*x^2 + 3*(A*b^3*d^2*e^2 + (B*b^3 - 2*A*b^2*c)*d^3*e)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(3*A*b^3*d^3*e^2 - 3*(B*b^2*c - 2*A*b*c^2)*d^5 + 3*(B*b^3 - 3*A*b^2*c)*d^4*e + (8*B*c^3*d^5 - 3*A*b^3*d*e^4 - 2*(11*B*b*c^2 - 2*A*c^3)*d^4*e + (17*B*b^2*c - 8*A*b*c^2)*d^3*e^2 - (3*B*b^3 - 7*A*b^2*c)*d^2*e^3)*x^2 - 2*(4*A*b^3*d^2*e^3 - (B*b*c^2 + 6*A*c^3)*d^5 + (5*B*b^2*c + 13*A*b*c^2)*d^4*e - (4*B*b^3 + 11*A*b^2*c)*d^3*e^2)*x)*sqrt(c*x^2 + b*x))/(c^3*d^9 - 3*b*c^2*d^8*e + 3*b^2*c*d^7*e^2 - b^3*d^6*e^3 + (c^3*d^6*e^3 - 3*b*c^2*d^5*e^4 + 3*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x^3 + 3*(c^3*d^7*e^2 - 3*b*c^2*d^6*e^3 + 3*b^2*c*d^5*e^4 - b^3*d^4*e^5)*x^2 + 3*(c^3*d^8*e - 3*b*c^2*d^7*e^2 + 3*b^2*c*d^6*e^3 - b^3*d^5*e^4)*x), 1/24*(3*(A*b^3*d^3*e + (B*b^3 - 2*A*b^2*c)*d^4 + (A*b^3*e^4 + (B*b^3 - 2*A*b^2*c)*d*e^3)*x^3 + 3*(A*b^3*d*e^3 + (B*b^3 - 2*A*b^2*c)*d^2*e^2)*x^2 + 3*(A*b^3*d^2*e^2 + (B*b^3 - 2*A*b^2*c)*d^3*e)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (3*A*b^3*d^3*e^2 - 3*(B*b^2*c - 2*A*b*c^2)*d^5 + 3*(B*b^3 - 3*A*b^2*c)*d^4*e + (8*B*c^3*d^5 - 3*A*b^3*d*e^4 - 2*(11*B*b*c^2 - 2*A*c^3)*d^4*e + (17*B*b^2*c - 8*A*b*c^2)*d^3*e^2 - (3*B*b^3 - 7*A*b^2*c)*d^2*e^3)*x^2 - 2*(4*A*b^3*d^2*e^3 - (B*b*c^2 + 6*A*c^3)*d^5 + (5*B*b^2*c + 13*A*b*c^2)*d^4*e - (4*B*b^3 + 11*A*b^2*c)*d^3*e^2)*x)*sqrt(c*x^2 + b*x))/(c^3*d^9 - 3*b*c^2*d^8*e + 3*b^2*c*d^7*e^2 - b^3*d^6*e^3 + (c^3*d^6*e^3 - 3*b*c^2*d^5*e^4 + 3*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x^3 + 3*(c^3*d^7*e^2 - 3*b*c^2*d^6*e^3 + 3*b^2*c*d^5*e^4 - b^3*d^4*e^5)*x^2 + 3*(c^3*d^8*e - 3*b*c^2*d^7*e^2 + 3*b^2*c*d^6*e^3 - b^3*d^5*e^4)*x)]","B",0
1170,1,2190,0,0.488835," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, A b^{4} d^{4} e^{2} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{6} + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d^{5} e + {\left(5 \, A b^{4} e^{6} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{2} e^{4} + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d e^{5}\right)} x^{4} + 4 \, {\left(5 \, A b^{4} d e^{5} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{3} e^{3} + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d^{2} e^{4}\right)} x^{3} + 6 \, {\left(5 \, A b^{4} d^{2} e^{4} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{4} e^{2} + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d^{3} e^{3}\right)} x^{2} + 4 \, {\left(5 \, A b^{4} d^{3} e^{3} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{5} e + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d^{4} e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(15 \, A b^{4} d^{4} e^{3} + 24 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{7} - 3 \, {\left(11 \, B b^{3} c - 32 \, A b^{2} c^{2}\right)} d^{6} e + 9 \, {\left(B b^{4} - 7 \, A b^{3} c\right)} d^{5} e^{2} - {\left(16 \, B c^{4} d^{6} e + 15 \, A b^{4} d e^{6} - 8 \, {\left(7 \, B b c^{3} - 2 \, A c^{4}\right)} d^{5} e^{2} + 2 \, {\left(29 \, B b^{2} c^{2} - 20 \, A b c^{3}\right)} d^{4} e^{3} - {\left(27 \, B b^{3} c - 62 \, A b^{2} c^{2}\right)} d^{3} e^{4} + {\left(9 \, B b^{4} - 53 \, A b^{3} c\right)} d^{2} e^{5}\right)} x^{3} - {\left(64 \, B c^{4} d^{7} + 55 \, A b^{4} d^{2} e^{5} - 8 \, {\left(29 \, B b c^{3} - 8 \, A c^{4}\right)} d^{6} e + 4 \, {\left(65 \, B b^{2} c^{2} - 42 \, A b c^{3}\right)} d^{5} e^{2} - {\left(125 \, B b^{3} c - 244 \, A b^{2} c^{2}\right)} d^{4} e^{3} + 3 \, {\left(11 \, B b^{4} - 65 \, A b^{3} c\right)} d^{3} e^{4}\right)} x^{2} - {\left(73 \, A b^{4} d^{3} e^{4} + 16 \, {\left(B b c^{3} + 6 \, A c^{4}\right)} d^{7} - 2 \, {\left(55 \, B b^{2} c^{2} + 136 \, A b c^{3}\right)} d^{6} e + {\left(127 \, B b^{3} c + 374 \, A b^{2} c^{2}\right)} d^{5} e^{2} - {\left(33 \, B b^{4} + 271 \, A b^{3} c\right)} d^{4} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{4} d^{12} - 4 \, b c^{3} d^{11} e + 6 \, b^{2} c^{2} d^{10} e^{2} - 4 \, b^{3} c d^{9} e^{3} + b^{4} d^{8} e^{4} + {\left(c^{4} d^{8} e^{4} - 4 \, b c^{3} d^{7} e^{5} + 6 \, b^{2} c^{2} d^{6} e^{6} - 4 \, b^{3} c d^{5} e^{7} + b^{4} d^{4} e^{8}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, b c^{3} d^{8} e^{4} + 6 \, b^{2} c^{2} d^{7} e^{5} - 4 \, b^{3} c d^{6} e^{6} + b^{4} d^{5} e^{7}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, b c^{3} d^{9} e^{3} + 6 \, b^{2} c^{2} d^{8} e^{4} - 4 \, b^{3} c d^{7} e^{5} + b^{4} d^{6} e^{6}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, b c^{3} d^{10} e^{2} + 6 \, b^{2} c^{2} d^{9} e^{3} - 4 \, b^{3} c d^{8} e^{4} + b^{4} d^{7} e^{5}\right)} x\right)}}, -\frac{3 \, {\left(5 \, A b^{4} d^{4} e^{2} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{6} + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d^{5} e + {\left(5 \, A b^{4} e^{6} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{2} e^{4} + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d e^{5}\right)} x^{4} + 4 \, {\left(5 \, A b^{4} d e^{5} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{3} e^{3} + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d^{2} e^{4}\right)} x^{3} + 6 \, {\left(5 \, A b^{4} d^{2} e^{4} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{4} e^{2} + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d^{3} e^{3}\right)} x^{2} + 4 \, {\left(5 \, A b^{4} d^{3} e^{3} - 8 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{5} e + {\left(3 \, B b^{4} - 16 \, A b^{3} c\right)} d^{4} e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(15 \, A b^{4} d^{4} e^{3} + 24 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{7} - 3 \, {\left(11 \, B b^{3} c - 32 \, A b^{2} c^{2}\right)} d^{6} e + 9 \, {\left(B b^{4} - 7 \, A b^{3} c\right)} d^{5} e^{2} - {\left(16 \, B c^{4} d^{6} e + 15 \, A b^{4} d e^{6} - 8 \, {\left(7 \, B b c^{3} - 2 \, A c^{4}\right)} d^{5} e^{2} + 2 \, {\left(29 \, B b^{2} c^{2} - 20 \, A b c^{3}\right)} d^{4} e^{3} - {\left(27 \, B b^{3} c - 62 \, A b^{2} c^{2}\right)} d^{3} e^{4} + {\left(9 \, B b^{4} - 53 \, A b^{3} c\right)} d^{2} e^{5}\right)} x^{3} - {\left(64 \, B c^{4} d^{7} + 55 \, A b^{4} d^{2} e^{5} - 8 \, {\left(29 \, B b c^{3} - 8 \, A c^{4}\right)} d^{6} e + 4 \, {\left(65 \, B b^{2} c^{2} - 42 \, A b c^{3}\right)} d^{5} e^{2} - {\left(125 \, B b^{3} c - 244 \, A b^{2} c^{2}\right)} d^{4} e^{3} + 3 \, {\left(11 \, B b^{4} - 65 \, A b^{3} c\right)} d^{3} e^{4}\right)} x^{2} - {\left(73 \, A b^{4} d^{3} e^{4} + 16 \, {\left(B b c^{3} + 6 \, A c^{4}\right)} d^{7} - 2 \, {\left(55 \, B b^{2} c^{2} + 136 \, A b c^{3}\right)} d^{6} e + {\left(127 \, B b^{3} c + 374 \, A b^{2} c^{2}\right)} d^{5} e^{2} - {\left(33 \, B b^{4} + 271 \, A b^{3} c\right)} d^{4} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{4} d^{12} - 4 \, b c^{3} d^{11} e + 6 \, b^{2} c^{2} d^{10} e^{2} - 4 \, b^{3} c d^{9} e^{3} + b^{4} d^{8} e^{4} + {\left(c^{4} d^{8} e^{4} - 4 \, b c^{3} d^{7} e^{5} + 6 \, b^{2} c^{2} d^{6} e^{6} - 4 \, b^{3} c d^{5} e^{7} + b^{4} d^{4} e^{8}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, b c^{3} d^{8} e^{4} + 6 \, b^{2} c^{2} d^{7} e^{5} - 4 \, b^{3} c d^{6} e^{6} + b^{4} d^{5} e^{7}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, b c^{3} d^{9} e^{3} + 6 \, b^{2} c^{2} d^{8} e^{4} - 4 \, b^{3} c d^{7} e^{5} + b^{4} d^{6} e^{6}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, b c^{3} d^{10} e^{2} + 6 \, b^{2} c^{2} d^{9} e^{3} - 4 \, b^{3} c d^{8} e^{4} + b^{4} d^{7} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/384*(3*(5*A*b^4*d^4*e^2 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^6 + (3*B*b^4 - 16*A*b^3*c)*d^5*e + (5*A*b^4*e^6 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^2*e^4 + (3*B*b^4 - 16*A*b^3*c)*d*e^5)*x^4 + 4*(5*A*b^4*d*e^5 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^3*e^3 + (3*B*b^4 - 16*A*b^3*c)*d^2*e^4)*x^3 + 6*(5*A*b^4*d^2*e^4 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^4*e^2 + (3*B*b^4 - 16*A*b^3*c)*d^3*e^3)*x^2 + 4*(5*A*b^4*d^3*e^3 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^5*e + (3*B*b^4 - 16*A*b^3*c)*d^4*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(15*A*b^4*d^4*e^3 + 24*(B*b^2*c^2 - 2*A*b*c^3)*d^7 - 3*(11*B*b^3*c - 32*A*b^2*c^2)*d^6*e + 9*(B*b^4 - 7*A*b^3*c)*d^5*e^2 - (16*B*c^4*d^6*e + 15*A*b^4*d*e^6 - 8*(7*B*b*c^3 - 2*A*c^4)*d^5*e^2 + 2*(29*B*b^2*c^2 - 20*A*b*c^3)*d^4*e^3 - (27*B*b^3*c - 62*A*b^2*c^2)*d^3*e^4 + (9*B*b^4 - 53*A*b^3*c)*d^2*e^5)*x^3 - (64*B*c^4*d^7 + 55*A*b^4*d^2*e^5 - 8*(29*B*b*c^3 - 8*A*c^4)*d^6*e + 4*(65*B*b^2*c^2 - 42*A*b*c^3)*d^5*e^2 - (125*B*b^3*c - 244*A*b^2*c^2)*d^4*e^3 + 3*(11*B*b^4 - 65*A*b^3*c)*d^3*e^4)*x^2 - (73*A*b^4*d^3*e^4 + 16*(B*b*c^3 + 6*A*c^4)*d^7 - 2*(55*B*b^2*c^2 + 136*A*b*c^3)*d^6*e + (127*B*b^3*c + 374*A*b^2*c^2)*d^5*e^2 - (33*B*b^4 + 271*A*b^3*c)*d^4*e^3)*x)*sqrt(c*x^2 + b*x))/(c^4*d^12 - 4*b*c^3*d^11*e + 6*b^2*c^2*d^10*e^2 - 4*b^3*c*d^9*e^3 + b^4*d^8*e^4 + (c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 + 6*b^2*c^2*d^6*e^6 - 4*b^3*c*d^5*e^7 + b^4*d^4*e^8)*x^4 + 4*(c^4*d^9*e^3 - 4*b*c^3*d^8*e^4 + 6*b^2*c^2*d^7*e^5 - 4*b^3*c*d^6*e^6 + b^4*d^5*e^7)*x^3 + 6*(c^4*d^10*e^2 - 4*b*c^3*d^9*e^3 + 6*b^2*c^2*d^8*e^4 - 4*b^3*c*d^7*e^5 + b^4*d^6*e^6)*x^2 + 4*(c^4*d^11*e - 4*b*c^3*d^10*e^2 + 6*b^2*c^2*d^9*e^3 - 4*b^3*c*d^8*e^4 + b^4*d^7*e^5)*x), -1/192*(3*(5*A*b^4*d^4*e^2 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^6 + (3*B*b^4 - 16*A*b^3*c)*d^5*e + (5*A*b^4*e^6 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^2*e^4 + (3*B*b^4 - 16*A*b^3*c)*d*e^5)*x^4 + 4*(5*A*b^4*d*e^5 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^3*e^3 + (3*B*b^4 - 16*A*b^3*c)*d^2*e^4)*x^3 + 6*(5*A*b^4*d^2*e^4 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^4*e^2 + (3*B*b^4 - 16*A*b^3*c)*d^3*e^3)*x^2 + 4*(5*A*b^4*d^3*e^3 - 8*(B*b^3*c - 2*A*b^2*c^2)*d^5*e + (3*B*b^4 - 16*A*b^3*c)*d^4*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (15*A*b^4*d^4*e^3 + 24*(B*b^2*c^2 - 2*A*b*c^3)*d^7 - 3*(11*B*b^3*c - 32*A*b^2*c^2)*d^6*e + 9*(B*b^4 - 7*A*b^3*c)*d^5*e^2 - (16*B*c^4*d^6*e + 15*A*b^4*d*e^6 - 8*(7*B*b*c^3 - 2*A*c^4)*d^5*e^2 + 2*(29*B*b^2*c^2 - 20*A*b*c^3)*d^4*e^3 - (27*B*b^3*c - 62*A*b^2*c^2)*d^3*e^4 + (9*B*b^4 - 53*A*b^3*c)*d^2*e^5)*x^3 - (64*B*c^4*d^7 + 55*A*b^4*d^2*e^5 - 8*(29*B*b*c^3 - 8*A*c^4)*d^6*e + 4*(65*B*b^2*c^2 - 42*A*b*c^3)*d^5*e^2 - (125*B*b^3*c - 244*A*b^2*c^2)*d^4*e^3 + 3*(11*B*b^4 - 65*A*b^3*c)*d^3*e^4)*x^2 - (73*A*b^4*d^3*e^4 + 16*(B*b*c^3 + 6*A*c^4)*d^7 - 2*(55*B*b^2*c^2 + 136*A*b*c^3)*d^6*e + (127*B*b^3*c + 374*A*b^2*c^2)*d^5*e^2 - (33*B*b^4 + 271*A*b^3*c)*d^4*e^3)*x)*sqrt(c*x^2 + b*x))/(c^4*d^12 - 4*b*c^3*d^11*e + 6*b^2*c^2*d^10*e^2 - 4*b^3*c*d^9*e^3 + b^4*d^8*e^4 + (c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 + 6*b^2*c^2*d^6*e^6 - 4*b^3*c*d^5*e^7 + b^4*d^4*e^8)*x^4 + 4*(c^4*d^9*e^3 - 4*b*c^3*d^8*e^4 + 6*b^2*c^2*d^7*e^5 - 4*b^3*c*d^6*e^6 + b^4*d^5*e^7)*x^3 + 6*(c^4*d^10*e^2 - 4*b*c^3*d^9*e^3 + 6*b^2*c^2*d^8*e^4 - 4*b^3*c*d^7*e^5 + b^4*d^6*e^6)*x^2 + 4*(c^4*d^11*e - 4*b*c^3*d^10*e^2 + 6*b^2*c^2*d^9*e^3 - 4*b^3*c*d^8*e^4 + b^4*d^7*e^5)*x)]","B",0
1171,1,3454,0,0.542665," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, A b^{5} d^{5} e^{3} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{8} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{7} e + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{6} e^{2} + {\left(7 \, A b^{5} e^{8} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} e^{5} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{2} e^{6} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d e^{7}\right)} x^{5} + 5 \, {\left(7 \, A b^{5} d e^{7} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{4} e^{4} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{3} e^{5} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{2} e^{6}\right)} x^{4} + 10 \, {\left(7 \, A b^{5} d^{2} e^{6} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{5} e^{3} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{4} e^{4} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{3} e^{5}\right)} x^{3} + 10 \, {\left(7 \, A b^{5} d^{3} e^{5} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{6} e^{2} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{5} e^{3} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{4} e^{4}\right)} x^{2} + 5 \, {\left(7 \, A b^{5} d^{4} e^{4} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{7} e - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{6} e^{2} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{5} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(105 \, A b^{5} d^{5} e^{4} - 240 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{9} + 60 \, {\left(7 \, B b^{3} c^{2} - 20 \, A b^{2} c^{3}\right)} d^{8} e - 45 \, {\left(5 \, B b^{4} c - 26 \, A b^{3} c^{2}\right)} d^{7} e^{2} + 15 \, {\left(3 \, B b^{5} - 37 \, A b^{4} c\right)} d^{6} e^{3} + {\left(64 \, B c^{5} d^{7} e^{2} - 105 \, A b^{5} d e^{8} - 16 \, {\left(17 \, B b c^{4} - 6 \, A c^{5}\right)} d^{6} e^{3} + 32 \, {\left(11 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d^{5} e^{4} - 2 \, {\left(147 \, B b^{3} c^{2} - 334 \, A b^{2} c^{3}\right)} d^{4} e^{5} + {\left(195 \, B b^{4} c - 856 \, A b^{3} c^{2}\right)} d^{3} e^{6} - 5 \, {\left(9 \, B b^{5} - 97 \, A b^{4} c\right)} d^{2} e^{7}\right)} x^{4} + 2 \, {\left(160 \, B c^{5} d^{8} e - 245 \, A b^{5} d^{2} e^{7} - 24 \, {\left(29 \, B b c^{4} - 10 \, A c^{5}\right)} d^{7} e^{2} + 12 \, {\left(79 \, B b^{2} c^{3} - 62 \, A b c^{4}\right)} d^{6} e^{3} - {\left(763 \, B b^{3} c^{2} - 1622 \, A b^{2} c^{3}\right)} d^{5} e^{4} + 3 \, {\left(152 \, B b^{4} c - 669 \, A b^{3} c^{2}\right)} d^{4} e^{5} - 21 \, {\left(5 \, B b^{5} - 54 \, A b^{4} c\right)} d^{3} e^{6}\right)} x^{3} + 2 \, {\left(320 \, B c^{5} d^{9} - 448 \, A b^{5} d^{3} e^{6} - 480 \, {\left(3 \, B b c^{4} - A c^{5}\right)} d^{8} e + 24 \, {\left(88 \, B b^{2} c^{3} - 65 \, A b c^{4}\right)} d^{7} e^{2} - {\left(1691 \, B b^{3} c^{2} - 3178 \, A b^{2} c^{3}\right)} d^{6} e^{3} + 33 \, {\left(27 \, B b^{4} c - 113 \, A b^{3} c^{2}\right)} d^{5} e^{4} - 3 \, {\left(64 \, B b^{5} - 693 \, A b^{4} c\right)} d^{4} e^{5}\right)} x^{2} - 10 \, {\left(79 \, A b^{5} d^{4} e^{5} - 16 \, {\left(B b c^{4} + 6 \, A c^{5}\right)} d^{9} + 28 \, {\left(5 \, B b^{2} c^{3} + 12 \, A b c^{4}\right)} d^{8} e - {\left(211 \, B b^{3} c^{2} + 642 \, A b^{2} c^{3}\right)} d^{7} e^{2} + {\left(108 \, B b^{4} c + 697 \, A b^{3} c^{2}\right)} d^{6} e^{3} - {\left(21 \, B b^{5} + 374 \, A b^{4} c\right)} d^{5} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, {\left(c^{5} d^{15} - 5 \, b c^{4} d^{14} e + 10 \, b^{2} c^{3} d^{13} e^{2} - 10 \, b^{3} c^{2} d^{12} e^{3} + 5 \, b^{4} c d^{11} e^{4} - b^{5} d^{10} e^{5} + {\left(c^{5} d^{10} e^{5} - 5 \, b c^{4} d^{9} e^{6} + 10 \, b^{2} c^{3} d^{8} e^{7} - 10 \, b^{3} c^{2} d^{7} e^{8} + 5 \, b^{4} c d^{6} e^{9} - b^{5} d^{5} e^{10}\right)} x^{5} + 5 \, {\left(c^{5} d^{11} e^{4} - 5 \, b c^{4} d^{10} e^{5} + 10 \, b^{2} c^{3} d^{9} e^{6} - 10 \, b^{3} c^{2} d^{8} e^{7} + 5 \, b^{4} c d^{7} e^{8} - b^{5} d^{6} e^{9}\right)} x^{4} + 10 \, {\left(c^{5} d^{12} e^{3} - 5 \, b c^{4} d^{11} e^{4} + 10 \, b^{2} c^{3} d^{10} e^{5} - 10 \, b^{3} c^{2} d^{9} e^{6} + 5 \, b^{4} c d^{8} e^{7} - b^{5} d^{7} e^{8}\right)} x^{3} + 10 \, {\left(c^{5} d^{13} e^{2} - 5 \, b c^{4} d^{12} e^{3} + 10 \, b^{2} c^{3} d^{11} e^{4} - 10 \, b^{3} c^{2} d^{10} e^{5} + 5 \, b^{4} c d^{9} e^{6} - b^{5} d^{8} e^{7}\right)} x^{2} + 5 \, {\left(c^{5} d^{14} e - 5 \, b c^{4} d^{13} e^{2} + 10 \, b^{2} c^{3} d^{12} e^{3} - 10 \, b^{3} c^{2} d^{11} e^{4} + 5 \, b^{4} c d^{10} e^{5} - b^{5} d^{9} e^{6}\right)} x\right)}}, \frac{15 \, {\left(7 \, A b^{5} d^{5} e^{3} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{8} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{7} e + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{6} e^{2} + {\left(7 \, A b^{5} e^{8} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} e^{5} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{2} e^{6} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d e^{7}\right)} x^{5} + 5 \, {\left(7 \, A b^{5} d e^{7} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{4} e^{4} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{3} e^{5} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{2} e^{6}\right)} x^{4} + 10 \, {\left(7 \, A b^{5} d^{2} e^{6} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{5} e^{3} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{4} e^{4} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{3} e^{5}\right)} x^{3} + 10 \, {\left(7 \, A b^{5} d^{3} e^{5} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{6} e^{2} - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{5} e^{3} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{4} e^{4}\right)} x^{2} + 5 \, {\left(7 \, A b^{5} d^{4} e^{4} + 16 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{7} e - 12 \, {\left(B b^{4} c - 4 \, A b^{3} c^{2}\right)} d^{6} e^{2} + 3 \, {\left(B b^{5} - 10 \, A b^{4} c\right)} d^{5} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(105 \, A b^{5} d^{5} e^{4} - 240 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{9} + 60 \, {\left(7 \, B b^{3} c^{2} - 20 \, A b^{2} c^{3}\right)} d^{8} e - 45 \, {\left(5 \, B b^{4} c - 26 \, A b^{3} c^{2}\right)} d^{7} e^{2} + 15 \, {\left(3 \, B b^{5} - 37 \, A b^{4} c\right)} d^{6} e^{3} + {\left(64 \, B c^{5} d^{7} e^{2} - 105 \, A b^{5} d e^{8} - 16 \, {\left(17 \, B b c^{4} - 6 \, A c^{5}\right)} d^{6} e^{3} + 32 \, {\left(11 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d^{5} e^{4} - 2 \, {\left(147 \, B b^{3} c^{2} - 334 \, A b^{2} c^{3}\right)} d^{4} e^{5} + {\left(195 \, B b^{4} c - 856 \, A b^{3} c^{2}\right)} d^{3} e^{6} - 5 \, {\left(9 \, B b^{5} - 97 \, A b^{4} c\right)} d^{2} e^{7}\right)} x^{4} + 2 \, {\left(160 \, B c^{5} d^{8} e - 245 \, A b^{5} d^{2} e^{7} - 24 \, {\left(29 \, B b c^{4} - 10 \, A c^{5}\right)} d^{7} e^{2} + 12 \, {\left(79 \, B b^{2} c^{3} - 62 \, A b c^{4}\right)} d^{6} e^{3} - {\left(763 \, B b^{3} c^{2} - 1622 \, A b^{2} c^{3}\right)} d^{5} e^{4} + 3 \, {\left(152 \, B b^{4} c - 669 \, A b^{3} c^{2}\right)} d^{4} e^{5} - 21 \, {\left(5 \, B b^{5} - 54 \, A b^{4} c\right)} d^{3} e^{6}\right)} x^{3} + 2 \, {\left(320 \, B c^{5} d^{9} - 448 \, A b^{5} d^{3} e^{6} - 480 \, {\left(3 \, B b c^{4} - A c^{5}\right)} d^{8} e + 24 \, {\left(88 \, B b^{2} c^{3} - 65 \, A b c^{4}\right)} d^{7} e^{2} - {\left(1691 \, B b^{3} c^{2} - 3178 \, A b^{2} c^{3}\right)} d^{6} e^{3} + 33 \, {\left(27 \, B b^{4} c - 113 \, A b^{3} c^{2}\right)} d^{5} e^{4} - 3 \, {\left(64 \, B b^{5} - 693 \, A b^{4} c\right)} d^{4} e^{5}\right)} x^{2} - 10 \, {\left(79 \, A b^{5} d^{4} e^{5} - 16 \, {\left(B b c^{4} + 6 \, A c^{5}\right)} d^{9} + 28 \, {\left(5 \, B b^{2} c^{3} + 12 \, A b c^{4}\right)} d^{8} e - {\left(211 \, B b^{3} c^{2} + 642 \, A b^{2} c^{3}\right)} d^{7} e^{2} + {\left(108 \, B b^{4} c + 697 \, A b^{3} c^{2}\right)} d^{6} e^{3} - {\left(21 \, B b^{5} + 374 \, A b^{4} c\right)} d^{5} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, {\left(c^{5} d^{15} - 5 \, b c^{4} d^{14} e + 10 \, b^{2} c^{3} d^{13} e^{2} - 10 \, b^{3} c^{2} d^{12} e^{3} + 5 \, b^{4} c d^{11} e^{4} - b^{5} d^{10} e^{5} + {\left(c^{5} d^{10} e^{5} - 5 \, b c^{4} d^{9} e^{6} + 10 \, b^{2} c^{3} d^{8} e^{7} - 10 \, b^{3} c^{2} d^{7} e^{8} + 5 \, b^{4} c d^{6} e^{9} - b^{5} d^{5} e^{10}\right)} x^{5} + 5 \, {\left(c^{5} d^{11} e^{4} - 5 \, b c^{4} d^{10} e^{5} + 10 \, b^{2} c^{3} d^{9} e^{6} - 10 \, b^{3} c^{2} d^{8} e^{7} + 5 \, b^{4} c d^{7} e^{8} - b^{5} d^{6} e^{9}\right)} x^{4} + 10 \, {\left(c^{5} d^{12} e^{3} - 5 \, b c^{4} d^{11} e^{4} + 10 \, b^{2} c^{3} d^{10} e^{5} - 10 \, b^{3} c^{2} d^{9} e^{6} + 5 \, b^{4} c d^{8} e^{7} - b^{5} d^{7} e^{8}\right)} x^{3} + 10 \, {\left(c^{5} d^{13} e^{2} - 5 \, b c^{4} d^{12} e^{3} + 10 \, b^{2} c^{3} d^{11} e^{4} - 10 \, b^{3} c^{2} d^{10} e^{5} + 5 \, b^{4} c d^{9} e^{6} - b^{5} d^{8} e^{7}\right)} x^{2} + 5 \, {\left(c^{5} d^{14} e - 5 \, b c^{4} d^{13} e^{2} + 10 \, b^{2} c^{3} d^{12} e^{3} - 10 \, b^{3} c^{2} d^{11} e^{4} + 5 \, b^{4} c d^{10} e^{5} - b^{5} d^{9} e^{6}\right)} x\right)}}\right]"," ",0,"[1/3840*(15*(7*A*b^5*d^5*e^3 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^8 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^7*e + 3*(B*b^5 - 10*A*b^4*c)*d^6*e^2 + (7*A*b^5*e^8 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3*e^5 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^2*e^6 + 3*(B*b^5 - 10*A*b^4*c)*d*e^7)*x^5 + 5*(7*A*b^5*d*e^7 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^4*e^4 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^3*e^5 + 3*(B*b^5 - 10*A*b^4*c)*d^2*e^6)*x^4 + 10*(7*A*b^5*d^2*e^6 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^5*e^3 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^4*e^4 + 3*(B*b^5 - 10*A*b^4*c)*d^3*e^5)*x^3 + 10*(7*A*b^5*d^3*e^5 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^6*e^2 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^5*e^3 + 3*(B*b^5 - 10*A*b^4*c)*d^4*e^4)*x^2 + 5*(7*A*b^5*d^4*e^4 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^7*e - 12*(B*b^4*c - 4*A*b^3*c^2)*d^6*e^2 + 3*(B*b^5 - 10*A*b^4*c)*d^5*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(105*A*b^5*d^5*e^4 - 240*(B*b^2*c^3 - 2*A*b*c^4)*d^9 + 60*(7*B*b^3*c^2 - 20*A*b^2*c^3)*d^8*e - 45*(5*B*b^4*c - 26*A*b^3*c^2)*d^7*e^2 + 15*(3*B*b^5 - 37*A*b^4*c)*d^6*e^3 + (64*B*c^5*d^7*e^2 - 105*A*b^5*d*e^8 - 16*(17*B*b*c^4 - 6*A*c^5)*d^6*e^3 + 32*(11*B*b^2*c^3 - 9*A*b*c^4)*d^5*e^4 - 2*(147*B*b^3*c^2 - 334*A*b^2*c^3)*d^4*e^5 + (195*B*b^4*c - 856*A*b^3*c^2)*d^3*e^6 - 5*(9*B*b^5 - 97*A*b^4*c)*d^2*e^7)*x^4 + 2*(160*B*c^5*d^8*e - 245*A*b^5*d^2*e^7 - 24*(29*B*b*c^4 - 10*A*c^5)*d^7*e^2 + 12*(79*B*b^2*c^3 - 62*A*b*c^4)*d^6*e^3 - (763*B*b^3*c^2 - 1622*A*b^2*c^3)*d^5*e^4 + 3*(152*B*b^4*c - 669*A*b^3*c^2)*d^4*e^5 - 21*(5*B*b^5 - 54*A*b^4*c)*d^3*e^6)*x^3 + 2*(320*B*c^5*d^9 - 448*A*b^5*d^3*e^6 - 480*(3*B*b*c^4 - A*c^5)*d^8*e + 24*(88*B*b^2*c^3 - 65*A*b*c^4)*d^7*e^2 - (1691*B*b^3*c^2 - 3178*A*b^2*c^3)*d^6*e^3 + 33*(27*B*b^4*c - 113*A*b^3*c^2)*d^5*e^4 - 3*(64*B*b^5 - 693*A*b^4*c)*d^4*e^5)*x^2 - 10*(79*A*b^5*d^4*e^5 - 16*(B*b*c^4 + 6*A*c^5)*d^9 + 28*(5*B*b^2*c^3 + 12*A*b*c^4)*d^8*e - (211*B*b^3*c^2 + 642*A*b^2*c^3)*d^7*e^2 + (108*B*b^4*c + 697*A*b^3*c^2)*d^6*e^3 - (21*B*b^5 + 374*A*b^4*c)*d^5*e^4)*x)*sqrt(c*x^2 + b*x))/(c^5*d^15 - 5*b*c^4*d^14*e + 10*b^2*c^3*d^13*e^2 - 10*b^3*c^2*d^12*e^3 + 5*b^4*c*d^11*e^4 - b^5*d^10*e^5 + (c^5*d^10*e^5 - 5*b*c^4*d^9*e^6 + 10*b^2*c^3*d^8*e^7 - 10*b^3*c^2*d^7*e^8 + 5*b^4*c*d^6*e^9 - b^5*d^5*e^10)*x^5 + 5*(c^5*d^11*e^4 - 5*b*c^4*d^10*e^5 + 10*b^2*c^3*d^9*e^6 - 10*b^3*c^2*d^8*e^7 + 5*b^4*c*d^7*e^8 - b^5*d^6*e^9)*x^4 + 10*(c^5*d^12*e^3 - 5*b*c^4*d^11*e^4 + 10*b^2*c^3*d^10*e^5 - 10*b^3*c^2*d^9*e^6 + 5*b^4*c*d^8*e^7 - b^5*d^7*e^8)*x^3 + 10*(c^5*d^13*e^2 - 5*b*c^4*d^12*e^3 + 10*b^2*c^3*d^11*e^4 - 10*b^3*c^2*d^10*e^5 + 5*b^4*c*d^9*e^6 - b^5*d^8*e^7)*x^2 + 5*(c^5*d^14*e - 5*b*c^4*d^13*e^2 + 10*b^2*c^3*d^12*e^3 - 10*b^3*c^2*d^11*e^4 + 5*b^4*c*d^10*e^5 - b^5*d^9*e^6)*x), 1/1920*(15*(7*A*b^5*d^5*e^3 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^8 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^7*e + 3*(B*b^5 - 10*A*b^4*c)*d^6*e^2 + (7*A*b^5*e^8 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3*e^5 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^2*e^6 + 3*(B*b^5 - 10*A*b^4*c)*d*e^7)*x^5 + 5*(7*A*b^5*d*e^7 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^4*e^4 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^3*e^5 + 3*(B*b^5 - 10*A*b^4*c)*d^2*e^6)*x^4 + 10*(7*A*b^5*d^2*e^6 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^5*e^3 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^4*e^4 + 3*(B*b^5 - 10*A*b^4*c)*d^3*e^5)*x^3 + 10*(7*A*b^5*d^3*e^5 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^6*e^2 - 12*(B*b^4*c - 4*A*b^3*c^2)*d^5*e^3 + 3*(B*b^5 - 10*A*b^4*c)*d^4*e^4)*x^2 + 5*(7*A*b^5*d^4*e^4 + 16*(B*b^3*c^2 - 2*A*b^2*c^3)*d^7*e - 12*(B*b^4*c - 4*A*b^3*c^2)*d^6*e^2 + 3*(B*b^5 - 10*A*b^4*c)*d^5*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (105*A*b^5*d^5*e^4 - 240*(B*b^2*c^3 - 2*A*b*c^4)*d^9 + 60*(7*B*b^3*c^2 - 20*A*b^2*c^3)*d^8*e - 45*(5*B*b^4*c - 26*A*b^3*c^2)*d^7*e^2 + 15*(3*B*b^5 - 37*A*b^4*c)*d^6*e^3 + (64*B*c^5*d^7*e^2 - 105*A*b^5*d*e^8 - 16*(17*B*b*c^4 - 6*A*c^5)*d^6*e^3 + 32*(11*B*b^2*c^3 - 9*A*b*c^4)*d^5*e^4 - 2*(147*B*b^3*c^2 - 334*A*b^2*c^3)*d^4*e^5 + (195*B*b^4*c - 856*A*b^3*c^2)*d^3*e^6 - 5*(9*B*b^5 - 97*A*b^4*c)*d^2*e^7)*x^4 + 2*(160*B*c^5*d^8*e - 245*A*b^5*d^2*e^7 - 24*(29*B*b*c^4 - 10*A*c^5)*d^7*e^2 + 12*(79*B*b^2*c^3 - 62*A*b*c^4)*d^6*e^3 - (763*B*b^3*c^2 - 1622*A*b^2*c^3)*d^5*e^4 + 3*(152*B*b^4*c - 669*A*b^3*c^2)*d^4*e^5 - 21*(5*B*b^5 - 54*A*b^4*c)*d^3*e^6)*x^3 + 2*(320*B*c^5*d^9 - 448*A*b^5*d^3*e^6 - 480*(3*B*b*c^4 - A*c^5)*d^8*e + 24*(88*B*b^2*c^3 - 65*A*b*c^4)*d^7*e^2 - (1691*B*b^3*c^2 - 3178*A*b^2*c^3)*d^6*e^3 + 33*(27*B*b^4*c - 113*A*b^3*c^2)*d^5*e^4 - 3*(64*B*b^5 - 693*A*b^4*c)*d^4*e^5)*x^2 - 10*(79*A*b^5*d^4*e^5 - 16*(B*b*c^4 + 6*A*c^5)*d^9 + 28*(5*B*b^2*c^3 + 12*A*b*c^4)*d^8*e - (211*B*b^3*c^2 + 642*A*b^2*c^3)*d^7*e^2 + (108*B*b^4*c + 697*A*b^3*c^2)*d^6*e^3 - (21*B*b^5 + 374*A*b^4*c)*d^5*e^4)*x)*sqrt(c*x^2 + b*x))/(c^5*d^15 - 5*b*c^4*d^14*e + 10*b^2*c^3*d^13*e^2 - 10*b^3*c^2*d^12*e^3 + 5*b^4*c*d^11*e^4 - b^5*d^10*e^5 + (c^5*d^10*e^5 - 5*b*c^4*d^9*e^6 + 10*b^2*c^3*d^8*e^7 - 10*b^3*c^2*d^7*e^8 + 5*b^4*c*d^6*e^9 - b^5*d^5*e^10)*x^5 + 5*(c^5*d^11*e^4 - 5*b*c^4*d^10*e^5 + 10*b^2*c^3*d^9*e^6 - 10*b^3*c^2*d^8*e^7 + 5*b^4*c*d^7*e^8 - b^5*d^6*e^9)*x^4 + 10*(c^5*d^12*e^3 - 5*b*c^4*d^11*e^4 + 10*b^2*c^3*d^10*e^5 - 10*b^3*c^2*d^9*e^6 + 5*b^4*c*d^8*e^7 - b^5*d^7*e^8)*x^3 + 10*(c^5*d^13*e^2 - 5*b*c^4*d^12*e^3 + 10*b^2*c^3*d^11*e^4 - 10*b^3*c^2*d^10*e^5 + 5*b^4*c*d^9*e^6 - b^5*d^8*e^7)*x^2 + 5*(c^5*d^14*e - 5*b*c^4*d^13*e^2 + 10*b^2*c^3*d^12*e^3 - 10*b^3*c^2*d^11*e^4 + 5*b^4*c*d^10*e^5 - b^5*d^9*e^6)*x)]","B",0
1172,1,987,0,0.460380," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{2} - 4 \, {\left(7 \, B b^{6} c - 12 \, A b^{5} c^{2}\right)} d e + {\left(9 \, B b^{7} - 14 \, A b^{6} c\right)} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(15360 \, B c^{7} e^{2} x^{6} + 1280 \, {\left(28 \, B c^{7} d e + {\left(15 \, B b c^{6} + 14 \, A c^{7}\right)} e^{2}\right)} x^{5} + 128 \, {\left(168 \, B c^{7} d^{2} + 28 \, {\left(13 \, B b c^{6} + 12 \, A c^{7}\right)} d e + {\left(3 \, B b^{2} c^{5} + 182 \, A b c^{6}\right)} e^{2}\right)} x^{4} + 48 \, {\left(56 \, {\left(11 \, B b c^{6} + 10 \, A c^{7}\right)} d^{2} + 28 \, {\left(B b^{2} c^{5} + 44 \, A b c^{6}\right)} d e - {\left(9 \, B b^{3} c^{4} - 14 \, A b^{2} c^{5}\right)} e^{2}\right)} x^{3} + 2520 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{2} - 420 \, {\left(7 \, B b^{5} c^{2} - 12 \, A b^{4} c^{3}\right)} d e + 105 \, {\left(9 \, B b^{6} c - 14 \, A b^{5} c^{2}\right)} e^{2} + 56 \, {\left(24 \, {\left(B b^{2} c^{5} + 30 \, A b c^{6}\right)} d^{2} - 4 \, {\left(7 \, B b^{3} c^{4} - 12 \, A b^{2} c^{5}\right)} d e + {\left(9 \, B b^{4} c^{3} - 14 \, A b^{3} c^{4}\right)} e^{2}\right)} x^{2} - 70 \, {\left(24 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{2} - 4 \, {\left(7 \, B b^{4} c^{3} - 12 \, A b^{3} c^{4}\right)} d e + {\left(9 \, B b^{5} c^{2} - 14 \, A b^{4} c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{215040 \, c^{6}}, \frac{105 \, {\left(24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{2} - 4 \, {\left(7 \, B b^{6} c - 12 \, A b^{5} c^{2}\right)} d e + {\left(9 \, B b^{7} - 14 \, A b^{6} c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(15360 \, B c^{7} e^{2} x^{6} + 1280 \, {\left(28 \, B c^{7} d e + {\left(15 \, B b c^{6} + 14 \, A c^{7}\right)} e^{2}\right)} x^{5} + 128 \, {\left(168 \, B c^{7} d^{2} + 28 \, {\left(13 \, B b c^{6} + 12 \, A c^{7}\right)} d e + {\left(3 \, B b^{2} c^{5} + 182 \, A b c^{6}\right)} e^{2}\right)} x^{4} + 48 \, {\left(56 \, {\left(11 \, B b c^{6} + 10 \, A c^{7}\right)} d^{2} + 28 \, {\left(B b^{2} c^{5} + 44 \, A b c^{6}\right)} d e - {\left(9 \, B b^{3} c^{4} - 14 \, A b^{2} c^{5}\right)} e^{2}\right)} x^{3} + 2520 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{2} - 420 \, {\left(7 \, B b^{5} c^{2} - 12 \, A b^{4} c^{3}\right)} d e + 105 \, {\left(9 \, B b^{6} c - 14 \, A b^{5} c^{2}\right)} e^{2} + 56 \, {\left(24 \, {\left(B b^{2} c^{5} + 30 \, A b c^{6}\right)} d^{2} - 4 \, {\left(7 \, B b^{3} c^{4} - 12 \, A b^{2} c^{5}\right)} d e + {\left(9 \, B b^{4} c^{3} - 14 \, A b^{3} c^{4}\right)} e^{2}\right)} x^{2} - 70 \, {\left(24 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{2} - 4 \, {\left(7 \, B b^{4} c^{3} - 12 \, A b^{3} c^{4}\right)} d e + {\left(9 \, B b^{5} c^{2} - 14 \, A b^{4} c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{107520 \, c^{6}}\right]"," ",0,"[-1/215040*(105*(24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^2 - 4*(7*B*b^6*c - 12*A*b^5*c^2)*d*e + (9*B*b^7 - 14*A*b^6*c)*e^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(15360*B*c^7*e^2*x^6 + 1280*(28*B*c^7*d*e + (15*B*b*c^6 + 14*A*c^7)*e^2)*x^5 + 128*(168*B*c^7*d^2 + 28*(13*B*b*c^6 + 12*A*c^7)*d*e + (3*B*b^2*c^5 + 182*A*b*c^6)*e^2)*x^4 + 48*(56*(11*B*b*c^6 + 10*A*c^7)*d^2 + 28*(B*b^2*c^5 + 44*A*b*c^6)*d*e - (9*B*b^3*c^4 - 14*A*b^2*c^5)*e^2)*x^3 + 2520*(B*b^4*c^3 - 2*A*b^3*c^4)*d^2 - 420*(7*B*b^5*c^2 - 12*A*b^4*c^3)*d*e + 105*(9*B*b^6*c - 14*A*b^5*c^2)*e^2 + 56*(24*(B*b^2*c^5 + 30*A*b*c^6)*d^2 - 4*(7*B*b^3*c^4 - 12*A*b^2*c^5)*d*e + (9*B*b^4*c^3 - 14*A*b^3*c^4)*e^2)*x^2 - 70*(24*(B*b^3*c^4 - 2*A*b^2*c^5)*d^2 - 4*(7*B*b^4*c^3 - 12*A*b^3*c^4)*d*e + (9*B*b^5*c^2 - 14*A*b^4*c^3)*e^2)*x)*sqrt(c*x^2 + b*x))/c^6, 1/107520*(105*(24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^2 - 4*(7*B*b^6*c - 12*A*b^5*c^2)*d*e + (9*B*b^7 - 14*A*b^6*c)*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (15360*B*c^7*e^2*x^6 + 1280*(28*B*c^7*d*e + (15*B*b*c^6 + 14*A*c^7)*e^2)*x^5 + 128*(168*B*c^7*d^2 + 28*(13*B*b*c^6 + 12*A*c^7)*d*e + (3*B*b^2*c^5 + 182*A*b*c^6)*e^2)*x^4 + 48*(56*(11*B*b*c^6 + 10*A*c^7)*d^2 + 28*(B*b^2*c^5 + 44*A*b*c^6)*d*e - (9*B*b^3*c^4 - 14*A*b^2*c^5)*e^2)*x^3 + 2520*(B*b^4*c^3 - 2*A*b^3*c^4)*d^2 - 420*(7*B*b^5*c^2 - 12*A*b^4*c^3)*d*e + 105*(9*B*b^6*c - 14*A*b^5*c^2)*e^2 + 56*(24*(B*b^2*c^5 + 30*A*b*c^6)*d^2 - 4*(7*B*b^3*c^4 - 12*A*b^2*c^5)*d*e + (9*B*b^4*c^3 - 14*A*b^3*c^4)*e^2)*x^2 - 70*(24*(B*b^3*c^4 - 2*A*b^2*c^5)*d^2 - 4*(7*B*b^4*c^3 - 12*A*b^3*c^4)*d*e + (9*B*b^5*c^2 - 14*A*b^4*c^3)*e^2)*x)*sqrt(c*x^2 + b*x))/c^6]","A",0
1173,1,603,0,0.450746," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d - {\left(7 \, B b^{6} - 12 \, A b^{5} c\right)} e\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(1280 \, B c^{6} e x^{5} + 128 \, {\left(12 \, B c^{6} d + {\left(13 \, B b c^{5} + 12 \, A c^{6}\right)} e\right)} x^{4} + 48 \, {\left(4 \, {\left(11 \, B b c^{5} + 10 \, A c^{6}\right)} d + {\left(B b^{2} c^{4} + 44 \, A b c^{5}\right)} e\right)} x^{3} + 8 \, {\left(12 \, {\left(B b^{2} c^{4} + 30 \, A b c^{5}\right)} d - {\left(7 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} e\right)} x^{2} + 180 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d - 15 \, {\left(7 \, B b^{5} c - 12 \, A b^{4} c^{2}\right)} e - 10 \, {\left(12 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d - {\left(7 \, B b^{4} c^{2} - 12 \, A b^{3} c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x}}{15360 \, c^{5}}, \frac{15 \, {\left(12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d - {\left(7 \, B b^{6} - 12 \, A b^{5} c\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(1280 \, B c^{6} e x^{5} + 128 \, {\left(12 \, B c^{6} d + {\left(13 \, B b c^{5} + 12 \, A c^{6}\right)} e\right)} x^{4} + 48 \, {\left(4 \, {\left(11 \, B b c^{5} + 10 \, A c^{6}\right)} d + {\left(B b^{2} c^{4} + 44 \, A b c^{5}\right)} e\right)} x^{3} + 8 \, {\left(12 \, {\left(B b^{2} c^{4} + 30 \, A b c^{5}\right)} d - {\left(7 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} e\right)} x^{2} + 180 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d - 15 \, {\left(7 \, B b^{5} c - 12 \, A b^{4} c^{2}\right)} e - 10 \, {\left(12 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d - {\left(7 \, B b^{4} c^{2} - 12 \, A b^{3} c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x}}{7680 \, c^{5}}\right]"," ",0,"[1/15360*(15*(12*(B*b^5*c - 2*A*b^4*c^2)*d - (7*B*b^6 - 12*A*b^5*c)*e)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(1280*B*c^6*e*x^5 + 128*(12*B*c^6*d + (13*B*b*c^5 + 12*A*c^6)*e)*x^4 + 48*(4*(11*B*b*c^5 + 10*A*c^6)*d + (B*b^2*c^4 + 44*A*b*c^5)*e)*x^3 + 8*(12*(B*b^2*c^4 + 30*A*b*c^5)*d - (7*B*b^3*c^3 - 12*A*b^2*c^4)*e)*x^2 + 180*(B*b^4*c^2 - 2*A*b^3*c^3)*d - 15*(7*B*b^5*c - 12*A*b^4*c^2)*e - 10*(12*(B*b^3*c^3 - 2*A*b^2*c^4)*d - (7*B*b^4*c^2 - 12*A*b^3*c^3)*e)*x)*sqrt(c*x^2 + b*x))/c^5, 1/7680*(15*(12*(B*b^5*c - 2*A*b^4*c^2)*d - (7*B*b^6 - 12*A*b^5*c)*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (1280*B*c^6*e*x^5 + 128*(12*B*c^6*d + (13*B*b*c^5 + 12*A*c^6)*e)*x^4 + 48*(4*(11*B*b*c^5 + 10*A*c^6)*d + (B*b^2*c^4 + 44*A*b*c^5)*e)*x^3 + 8*(12*(B*b^2*c^4 + 30*A*b*c^5)*d - (7*B*b^3*c^3 - 12*A*b^2*c^4)*e)*x^2 + 180*(B*b^4*c^2 - 2*A*b^3*c^3)*d - 15*(7*B*b^5*c - 12*A*b^4*c^2)*e - 10*(12*(B*b^3*c^3 - 2*A*b^2*c^4)*d - (7*B*b^4*c^2 - 12*A*b^3*c^3)*e)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
1174,1,297,0,0.457073," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B b^{5} - 2 \, A b^{4} c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(128 \, B c^{5} x^{4} + 15 \, B b^{4} c - 30 \, A b^{3} c^{2} + 16 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} x^{3} + 8 \, {\left(B b^{2} c^{3} + 30 \, A b c^{4}\right)} x^{2} - 10 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{1280 \, c^{4}}, \frac{15 \, {\left(B b^{5} - 2 \, A b^{4} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(128 \, B c^{5} x^{4} + 15 \, B b^{4} c - 30 \, A b^{3} c^{2} + 16 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} x^{3} + 8 \, {\left(B b^{2} c^{3} + 30 \, A b c^{4}\right)} x^{2} - 10 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{640 \, c^{4}}\right]"," ",0,"[-1/1280*(15*(B*b^5 - 2*A*b^4*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(128*B*c^5*x^4 + 15*B*b^4*c - 30*A*b^3*c^2 + 16*(11*B*b*c^4 + 10*A*c^5)*x^3 + 8*(B*b^2*c^3 + 30*A*b*c^4)*x^2 - 10*(B*b^3*c^2 - 2*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^4, 1/640*(15*(B*b^5 - 2*A*b^4*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (128*B*c^5*x^4 + 15*B*b^4*c - 30*A*b^3*c^2 + 16*(11*B*b*c^4 + 10*A*c^5)*x^3 + 8*(B*b^2*c^3 + 30*A*b*c^4)*x^2 - 10*(B*b^3*c^2 - 2*A*b^2*c^3)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
1175,1,1695,0,32.555395," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(128 \, B c^{4} d^{4} - 64 \, {\left(3 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e + 48 \, {\left(B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{2} e^{2} + 8 \, {\left(B b^{3} c - 6 \, A b^{2} c^{2}\right)} d e^{3} + {\left(3 \, B b^{4} - 8 \, A b^{3} c\right)} e^{4}\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 384 \, {\left(B c^{4} d^{3} + A b c^{3} d e^{2} - {\left(B b c^{3} + A c^{4}\right)} d^{2} e\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(48 \, B c^{4} e^{4} x^{3} - 192 \, B c^{4} d^{3} e + 48 \, {\left(5 \, B b c^{3} + 4 \, A c^{4}\right)} d^{2} e^{2} - 24 \, {\left(B b^{2} c^{2} + 10 \, A b c^{3}\right)} d e^{3} - 3 \, {\left(3 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} e^{4} - 8 \, {\left(8 \, B c^{4} d e^{3} - {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(48 \, B c^{4} d^{2} e^{2} - 8 \, {\left(7 \, B b c^{3} + 6 \, A c^{4}\right)} d e^{3} + {\left(3 \, B b^{2} c^{2} + 56 \, A b c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, c^{3} e^{5}}, -\frac{768 \, {\left(B c^{4} d^{3} + A b c^{3} d e^{2} - {\left(B b c^{3} + A c^{4}\right)} d^{2} e\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 3 \, {\left(128 \, B c^{4} d^{4} - 64 \, {\left(3 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e + 48 \, {\left(B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{2} e^{2} + 8 \, {\left(B b^{3} c - 6 \, A b^{2} c^{2}\right)} d e^{3} + {\left(3 \, B b^{4} - 8 \, A b^{3} c\right)} e^{4}\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(48 \, B c^{4} e^{4} x^{3} - 192 \, B c^{4} d^{3} e + 48 \, {\left(5 \, B b c^{3} + 4 \, A c^{4}\right)} d^{2} e^{2} - 24 \, {\left(B b^{2} c^{2} + 10 \, A b c^{3}\right)} d e^{3} - 3 \, {\left(3 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} e^{4} - 8 \, {\left(8 \, B c^{4} d e^{3} - {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(48 \, B c^{4} d^{2} e^{2} - 8 \, {\left(7 \, B b c^{3} + 6 \, A c^{4}\right)} d e^{3} + {\left(3 \, B b^{2} c^{2} + 56 \, A b c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, c^{3} e^{5}}, -\frac{3 \, {\left(128 \, B c^{4} d^{4} - 64 \, {\left(3 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e + 48 \, {\left(B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{2} e^{2} + 8 \, {\left(B b^{3} c - 6 \, A b^{2} c^{2}\right)} d e^{3} + {\left(3 \, B b^{4} - 8 \, A b^{3} c\right)} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 192 \, {\left(B c^{4} d^{3} + A b c^{3} d e^{2} - {\left(B b c^{3} + A c^{4}\right)} d^{2} e\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - {\left(48 \, B c^{4} e^{4} x^{3} - 192 \, B c^{4} d^{3} e + 48 \, {\left(5 \, B b c^{3} + 4 \, A c^{4}\right)} d^{2} e^{2} - 24 \, {\left(B b^{2} c^{2} + 10 \, A b c^{3}\right)} d e^{3} - 3 \, {\left(3 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} e^{4} - 8 \, {\left(8 \, B c^{4} d e^{3} - {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(48 \, B c^{4} d^{2} e^{2} - 8 \, {\left(7 \, B b c^{3} + 6 \, A c^{4}\right)} d e^{3} + {\left(3 \, B b^{2} c^{2} + 56 \, A b c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, c^{3} e^{5}}, -\frac{384 \, {\left(B c^{4} d^{3} + A b c^{3} d e^{2} - {\left(B b c^{3} + A c^{4}\right)} d^{2} e\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 3 \, {\left(128 \, B c^{4} d^{4} - 64 \, {\left(3 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e + 48 \, {\left(B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{2} e^{2} + 8 \, {\left(B b^{3} c - 6 \, A b^{2} c^{2}\right)} d e^{3} + {\left(3 \, B b^{4} - 8 \, A b^{3} c\right)} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(48 \, B c^{4} e^{4} x^{3} - 192 \, B c^{4} d^{3} e + 48 \, {\left(5 \, B b c^{3} + 4 \, A c^{4}\right)} d^{2} e^{2} - 24 \, {\left(B b^{2} c^{2} + 10 \, A b c^{3}\right)} d e^{3} - 3 \, {\left(3 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} e^{4} - 8 \, {\left(8 \, B c^{4} d e^{3} - {\left(9 \, B b c^{3} + 8 \, A c^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(48 \, B c^{4} d^{2} e^{2} - 8 \, {\left(7 \, B b c^{3} + 6 \, A c^{4}\right)} d e^{3} + {\left(3 \, B b^{2} c^{2} + 56 \, A b c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, c^{3} e^{5}}\right]"," ",0,"[-1/384*(3*(128*B*c^4*d^4 - 64*(3*B*b*c^3 + 2*A*c^4)*d^3*e + 48*(B*b^2*c^2 + 4*A*b*c^3)*d^2*e^2 + 8*(B*b^3*c - 6*A*b^2*c^2)*d*e^3 + (3*B*b^4 - 8*A*b^3*c)*e^4)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 384*(B*c^4*d^3 + A*b*c^3*d*e^2 - (B*b*c^3 + A*c^4)*d^2*e)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(48*B*c^4*e^4*x^3 - 192*B*c^4*d^3*e + 48*(5*B*b*c^3 + 4*A*c^4)*d^2*e^2 - 24*(B*b^2*c^2 + 10*A*b*c^3)*d*e^3 - 3*(3*B*b^3*c - 8*A*b^2*c^2)*e^4 - 8*(8*B*c^4*d*e^3 - (9*B*b*c^3 + 8*A*c^4)*e^4)*x^2 + 2*(48*B*c^4*d^2*e^2 - 8*(7*B*b*c^3 + 6*A*c^4)*d*e^3 + (3*B*b^2*c^2 + 56*A*b*c^3)*e^4)*x)*sqrt(c*x^2 + b*x))/(c^3*e^5), -1/384*(768*(B*c^4*d^3 + A*b*c^3*d*e^2 - (B*b*c^3 + A*c^4)*d^2*e)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 3*(128*B*c^4*d^4 - 64*(3*B*b*c^3 + 2*A*c^4)*d^3*e + 48*(B*b^2*c^2 + 4*A*b*c^3)*d^2*e^2 + 8*(B*b^3*c - 6*A*b^2*c^2)*d*e^3 + (3*B*b^4 - 8*A*b^3*c)*e^4)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(48*B*c^4*e^4*x^3 - 192*B*c^4*d^3*e + 48*(5*B*b*c^3 + 4*A*c^4)*d^2*e^2 - 24*(B*b^2*c^2 + 10*A*b*c^3)*d*e^3 - 3*(3*B*b^3*c - 8*A*b^2*c^2)*e^4 - 8*(8*B*c^4*d*e^3 - (9*B*b*c^3 + 8*A*c^4)*e^4)*x^2 + 2*(48*B*c^4*d^2*e^2 - 8*(7*B*b*c^3 + 6*A*c^4)*d*e^3 + (3*B*b^2*c^2 + 56*A*b*c^3)*e^4)*x)*sqrt(c*x^2 + b*x))/(c^3*e^5), -1/192*(3*(128*B*c^4*d^4 - 64*(3*B*b*c^3 + 2*A*c^4)*d^3*e + 48*(B*b^2*c^2 + 4*A*b*c^3)*d^2*e^2 + 8*(B*b^3*c - 6*A*b^2*c^2)*d*e^3 + (3*B*b^4 - 8*A*b^3*c)*e^4)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 192*(B*c^4*d^3 + A*b*c^3*d*e^2 - (B*b*c^3 + A*c^4)*d^2*e)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - (48*B*c^4*e^4*x^3 - 192*B*c^4*d^3*e + 48*(5*B*b*c^3 + 4*A*c^4)*d^2*e^2 - 24*(B*b^2*c^2 + 10*A*b*c^3)*d*e^3 - 3*(3*B*b^3*c - 8*A*b^2*c^2)*e^4 - 8*(8*B*c^4*d*e^3 - (9*B*b*c^3 + 8*A*c^4)*e^4)*x^2 + 2*(48*B*c^4*d^2*e^2 - 8*(7*B*b*c^3 + 6*A*c^4)*d*e^3 + (3*B*b^2*c^2 + 56*A*b*c^3)*e^4)*x)*sqrt(c*x^2 + b*x))/(c^3*e^5), -1/192*(384*(B*c^4*d^3 + A*b*c^3*d*e^2 - (B*b*c^3 + A*c^4)*d^2*e)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 3*(128*B*c^4*d^4 - 64*(3*B*b*c^3 + 2*A*c^4)*d^3*e + 48*(B*b^2*c^2 + 4*A*b*c^3)*d^2*e^2 + 8*(B*b^3*c - 6*A*b^2*c^2)*d*e^3 + (3*B*b^4 - 8*A*b^3*c)*e^4)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (48*B*c^4*e^4*x^3 - 192*B*c^4*d^3*e + 48*(5*B*b*c^3 + 4*A*c^4)*d^2*e^2 - 24*(B*b^2*c^2 + 10*A*b*c^3)*d*e^3 - 3*(3*B*b^3*c - 8*A*b^2*c^2)*e^4 - 8*(8*B*c^4*d*e^3 - (9*B*b*c^3 + 8*A*c^4)*e^4)*x^2 + 2*(48*B*c^4*d^2*e^2 - 8*(7*B*b*c^3 + 6*A*c^4)*d*e^3 + (3*B*b^2*c^2 + 56*A*b*c^3)*e^4)*x)*sqrt(c*x^2 + b*x))/(c^3*e^5)]","A",0
1176,1,2017,0,3.862946," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(64 \, B c^{3} d^{4} - 24 \, {\left(3 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e + 12 \, {\left(B b^{2} c + 4 \, A b c^{2}\right)} d^{2} e^{2} + {\left(B b^{3} - 6 \, A b^{2} c\right)} d e^{3} + {\left(64 \, B c^{3} d^{3} e - 24 \, {\left(3 \, B b c^{2} + 2 \, A c^{3}\right)} d^{2} e^{2} + 12 \, {\left(B b^{2} c + 4 \, A b c^{2}\right)} d e^{3} + {\left(B b^{3} - 6 \, A b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 24 \, {\left(8 \, B c^{3} d^{3} + 3 \, A b c^{2} d e^{2} - {\left(5 \, B b c^{2} + 6 \, A c^{3}\right)} d^{2} e + {\left(8 \, B c^{3} d^{2} e + 3 \, A b c^{2} e^{3} - {\left(5 \, B b c^{2} + 6 \, A c^{3}\right)} d e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(8 \, B c^{3} e^{4} x^{3} + 96 \, B c^{3} d^{3} e - 12 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} d^{2} e^{2} + 3 \, {\left(B b^{2} c + 18 \, A b c^{2}\right)} d e^{3} - 2 \, {\left(8 \, B c^{3} d e^{3} - {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} e^{4}\right)} x^{2} + {\left(48 \, B c^{3} d^{2} e^{2} - 2 \, {\left(23 \, B b c^{2} + 18 \, A c^{3}\right)} d e^{3} + 3 \, {\left(B b^{2} c + 10 \, A b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{2} e^{6} x + c^{2} d e^{5}\right)}}, \frac{48 \, {\left(8 \, B c^{3} d^{3} + 3 \, A b c^{2} d e^{2} - {\left(5 \, B b c^{2} + 6 \, A c^{3}\right)} d^{2} e + {\left(8 \, B c^{3} d^{2} e + 3 \, A b c^{2} e^{3} - {\left(5 \, B b c^{2} + 6 \, A c^{3}\right)} d e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 3 \, {\left(64 \, B c^{3} d^{4} - 24 \, {\left(3 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e + 12 \, {\left(B b^{2} c + 4 \, A b c^{2}\right)} d^{2} e^{2} + {\left(B b^{3} - 6 \, A b^{2} c\right)} d e^{3} + {\left(64 \, B c^{3} d^{3} e - 24 \, {\left(3 \, B b c^{2} + 2 \, A c^{3}\right)} d^{2} e^{2} + 12 \, {\left(B b^{2} c + 4 \, A b c^{2}\right)} d e^{3} + {\left(B b^{3} - 6 \, A b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(8 \, B c^{3} e^{4} x^{3} + 96 \, B c^{3} d^{3} e - 12 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} d^{2} e^{2} + 3 \, {\left(B b^{2} c + 18 \, A b c^{2}\right)} d e^{3} - 2 \, {\left(8 \, B c^{3} d e^{3} - {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} e^{4}\right)} x^{2} + {\left(48 \, B c^{3} d^{2} e^{2} - 2 \, {\left(23 \, B b c^{2} + 18 \, A c^{3}\right)} d e^{3} + 3 \, {\left(B b^{2} c + 10 \, A b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{2} e^{6} x + c^{2} d e^{5}\right)}}, \frac{3 \, {\left(64 \, B c^{3} d^{4} - 24 \, {\left(3 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e + 12 \, {\left(B b^{2} c + 4 \, A b c^{2}\right)} d^{2} e^{2} + {\left(B b^{3} - 6 \, A b^{2} c\right)} d e^{3} + {\left(64 \, B c^{3} d^{3} e - 24 \, {\left(3 \, B b c^{2} + 2 \, A c^{3}\right)} d^{2} e^{2} + 12 \, {\left(B b^{2} c + 4 \, A b c^{2}\right)} d e^{3} + {\left(B b^{3} - 6 \, A b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 12 \, {\left(8 \, B c^{3} d^{3} + 3 \, A b c^{2} d e^{2} - {\left(5 \, B b c^{2} + 6 \, A c^{3}\right)} d^{2} e + {\left(8 \, B c^{3} d^{2} e + 3 \, A b c^{2} e^{3} - {\left(5 \, B b c^{2} + 6 \, A c^{3}\right)} d e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + {\left(8 \, B c^{3} e^{4} x^{3} + 96 \, B c^{3} d^{3} e - 12 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} d^{2} e^{2} + 3 \, {\left(B b^{2} c + 18 \, A b c^{2}\right)} d e^{3} - 2 \, {\left(8 \, B c^{3} d e^{3} - {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} e^{4}\right)} x^{2} + {\left(48 \, B c^{3} d^{2} e^{2} - 2 \, {\left(23 \, B b c^{2} + 18 \, A c^{3}\right)} d e^{3} + 3 \, {\left(B b^{2} c + 10 \, A b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{2} e^{6} x + c^{2} d e^{5}\right)}}, \frac{24 \, {\left(8 \, B c^{3} d^{3} + 3 \, A b c^{2} d e^{2} - {\left(5 \, B b c^{2} + 6 \, A c^{3}\right)} d^{2} e + {\left(8 \, B c^{3} d^{2} e + 3 \, A b c^{2} e^{3} - {\left(5 \, B b c^{2} + 6 \, A c^{3}\right)} d e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 3 \, {\left(64 \, B c^{3} d^{4} - 24 \, {\left(3 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e + 12 \, {\left(B b^{2} c + 4 \, A b c^{2}\right)} d^{2} e^{2} + {\left(B b^{3} - 6 \, A b^{2} c\right)} d e^{3} + {\left(64 \, B c^{3} d^{3} e - 24 \, {\left(3 \, B b c^{2} + 2 \, A c^{3}\right)} d^{2} e^{2} + 12 \, {\left(B b^{2} c + 4 \, A b c^{2}\right)} d e^{3} + {\left(B b^{3} - 6 \, A b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, B c^{3} e^{4} x^{3} + 96 \, B c^{3} d^{3} e - 12 \, {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} d^{2} e^{2} + 3 \, {\left(B b^{2} c + 18 \, A b c^{2}\right)} d e^{3} - 2 \, {\left(8 \, B c^{3} d e^{3} - {\left(7 \, B b c^{2} + 6 \, A c^{3}\right)} e^{4}\right)} x^{2} + {\left(48 \, B c^{3} d^{2} e^{2} - 2 \, {\left(23 \, B b c^{2} + 18 \, A c^{3}\right)} d e^{3} + 3 \, {\left(B b^{2} c + 10 \, A b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{2} e^{6} x + c^{2} d e^{5}\right)}}\right]"," ",0,"[-1/48*(3*(64*B*c^3*d^4 - 24*(3*B*b*c^2 + 2*A*c^3)*d^3*e + 12*(B*b^2*c + 4*A*b*c^2)*d^2*e^2 + (B*b^3 - 6*A*b^2*c)*d*e^3 + (64*B*c^3*d^3*e - 24*(3*B*b*c^2 + 2*A*c^3)*d^2*e^2 + 12*(B*b^2*c + 4*A*b*c^2)*d*e^3 + (B*b^3 - 6*A*b^2*c)*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 24*(8*B*c^3*d^3 + 3*A*b*c^2*d*e^2 - (5*B*b*c^2 + 6*A*c^3)*d^2*e + (8*B*c^3*d^2*e + 3*A*b*c^2*e^3 - (5*B*b*c^2 + 6*A*c^3)*d*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(8*B*c^3*e^4*x^3 + 96*B*c^3*d^3*e - 12*(7*B*b*c^2 + 6*A*c^3)*d^2*e^2 + 3*(B*b^2*c + 18*A*b*c^2)*d*e^3 - 2*(8*B*c^3*d*e^3 - (7*B*b*c^2 + 6*A*c^3)*e^4)*x^2 + (48*B*c^3*d^2*e^2 - 2*(23*B*b*c^2 + 18*A*c^3)*d*e^3 + 3*(B*b^2*c + 10*A*b*c^2)*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*e^6*x + c^2*d*e^5), 1/48*(48*(8*B*c^3*d^3 + 3*A*b*c^2*d*e^2 - (5*B*b*c^2 + 6*A*c^3)*d^2*e + (8*B*c^3*d^2*e + 3*A*b*c^2*e^3 - (5*B*b*c^2 + 6*A*c^3)*d*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 3*(64*B*c^3*d^4 - 24*(3*B*b*c^2 + 2*A*c^3)*d^3*e + 12*(B*b^2*c + 4*A*b*c^2)*d^2*e^2 + (B*b^3 - 6*A*b^2*c)*d*e^3 + (64*B*c^3*d^3*e - 24*(3*B*b*c^2 + 2*A*c^3)*d^2*e^2 + 12*(B*b^2*c + 4*A*b*c^2)*d*e^3 + (B*b^3 - 6*A*b^2*c)*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(8*B*c^3*e^4*x^3 + 96*B*c^3*d^3*e - 12*(7*B*b*c^2 + 6*A*c^3)*d^2*e^2 + 3*(B*b^2*c + 18*A*b*c^2)*d*e^3 - 2*(8*B*c^3*d*e^3 - (7*B*b*c^2 + 6*A*c^3)*e^4)*x^2 + (48*B*c^3*d^2*e^2 - 2*(23*B*b*c^2 + 18*A*c^3)*d*e^3 + 3*(B*b^2*c + 10*A*b*c^2)*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*e^6*x + c^2*d*e^5), 1/24*(3*(64*B*c^3*d^4 - 24*(3*B*b*c^2 + 2*A*c^3)*d^3*e + 12*(B*b^2*c + 4*A*b*c^2)*d^2*e^2 + (B*b^3 - 6*A*b^2*c)*d*e^3 + (64*B*c^3*d^3*e - 24*(3*B*b*c^2 + 2*A*c^3)*d^2*e^2 + 12*(B*b^2*c + 4*A*b*c^2)*d*e^3 + (B*b^3 - 6*A*b^2*c)*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 12*(8*B*c^3*d^3 + 3*A*b*c^2*d*e^2 - (5*B*b*c^2 + 6*A*c^3)*d^2*e + (8*B*c^3*d^2*e + 3*A*b*c^2*e^3 - (5*B*b*c^2 + 6*A*c^3)*d*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + (8*B*c^3*e^4*x^3 + 96*B*c^3*d^3*e - 12*(7*B*b*c^2 + 6*A*c^3)*d^2*e^2 + 3*(B*b^2*c + 18*A*b*c^2)*d*e^3 - 2*(8*B*c^3*d*e^3 - (7*B*b*c^2 + 6*A*c^3)*e^4)*x^2 + (48*B*c^3*d^2*e^2 - 2*(23*B*b*c^2 + 18*A*c^3)*d*e^3 + 3*(B*b^2*c + 10*A*b*c^2)*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*e^6*x + c^2*d*e^5), 1/24*(24*(8*B*c^3*d^3 + 3*A*b*c^2*d*e^2 - (5*B*b*c^2 + 6*A*c^3)*d^2*e + (8*B*c^3*d^2*e + 3*A*b*c^2*e^3 - (5*B*b*c^2 + 6*A*c^3)*d*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 3*(64*B*c^3*d^4 - 24*(3*B*b*c^2 + 2*A*c^3)*d^3*e + 12*(B*b^2*c + 4*A*b*c^2)*d^2*e^2 + (B*b^3 - 6*A*b^2*c)*d*e^3 + (64*B*c^3*d^3*e - 24*(3*B*b*c^2 + 2*A*c^3)*d^2*e^2 + 12*(B*b^2*c + 4*A*b*c^2)*d*e^3 + (B*b^3 - 6*A*b^2*c)*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*B*c^3*e^4*x^3 + 96*B*c^3*d^3*e - 12*(7*B*b*c^2 + 6*A*c^3)*d^2*e^2 + 3*(B*b^2*c + 18*A*b*c^2)*d*e^3 - 2*(8*B*c^3*d*e^3 - (7*B*b*c^2 + 6*A*c^3)*e^4)*x^2 + (48*B*c^3*d^2*e^2 - 2*(23*B*b*c^2 + 18*A*c^3)*d*e^3 + 3*(B*b^2*c + 10*A*b*c^2)*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*e^6*x + c^2*d*e^5)]","A",0
1177,1,3342,0,1.846338," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, B c^{3} d^{6} - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{4} e^{2} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d^{3} e^{3} + {\left(16 \, B c^{3} d^{4} e^{2} - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{3} + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{2} e^{4} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d e^{5}\right)} x^{2} + 2 \, {\left(16 \, B c^{3} d^{5} e - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{2} + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{3} e^{3} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 3 \, {\left(16 \, B c^{3} d^{5} - A b^{2} c d^{2} e^{3} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d^{3} e^{2} + {\left(16 \, B c^{3} d^{3} e^{2} - A b^{2} c e^{5} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{2} e^{3} + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d e^{4}\right)} x^{2} + 2 \, {\left(16 \, B c^{3} d^{4} e - A b^{2} c d e^{4} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{2} + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(24 \, B c^{3} d^{5} e - 3 \, A b^{2} c d^{2} e^{4} - 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{2} + 3 \, {\left(4 \, B b^{2} c + 5 \, A b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(B c^{3} d^{2} e^{4} - B b c^{2} d e^{5}\right)} x^{3} + {\left(8 \, B c^{3} d^{3} e^{3} - {\left(13 \, B b c^{2} + 4 \, A c^{3}\right)} d^{2} e^{4} + {\left(5 \, B b^{2} c + 4 \, A b c^{2}\right)} d e^{5}\right)} x^{2} + {\left(36 \, B c^{3} d^{4} e^{2} - 5 \, A b^{2} c d e^{5} - {\left(55 \, B b c^{2} + 18 \, A c^{3}\right)} d^{3} e^{3} + {\left(19 \, B b^{2} c + 23 \, A b c^{2}\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{2} d^{4} e^{5} - b c d^{3} e^{6} + {\left(c^{2} d^{2} e^{7} - b c d e^{8}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e^{6} - b c d^{2} e^{7}\right)} x\right)}}, -\frac{6 \, {\left(16 \, B c^{3} d^{5} - A b^{2} c d^{2} e^{3} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d^{3} e^{2} + {\left(16 \, B c^{3} d^{3} e^{2} - A b^{2} c e^{5} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{2} e^{3} + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d e^{4}\right)} x^{2} + 2 \, {\left(16 \, B c^{3} d^{4} e - A b^{2} c d e^{4} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{2} + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 3 \, {\left(16 \, B c^{3} d^{6} - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{4} e^{2} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d^{3} e^{3} + {\left(16 \, B c^{3} d^{4} e^{2} - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{3} + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{2} e^{4} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d e^{5}\right)} x^{2} + 2 \, {\left(16 \, B c^{3} d^{5} e - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{2} + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{3} e^{3} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(24 \, B c^{3} d^{5} e - 3 \, A b^{2} c d^{2} e^{4} - 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{2} + 3 \, {\left(4 \, B b^{2} c + 5 \, A b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(B c^{3} d^{2} e^{4} - B b c^{2} d e^{5}\right)} x^{3} + {\left(8 \, B c^{3} d^{3} e^{3} - {\left(13 \, B b c^{2} + 4 \, A c^{3}\right)} d^{2} e^{4} + {\left(5 \, B b^{2} c + 4 \, A b c^{2}\right)} d e^{5}\right)} x^{2} + {\left(36 \, B c^{3} d^{4} e^{2} - 5 \, A b^{2} c d e^{5} - {\left(55 \, B b c^{2} + 18 \, A c^{3}\right)} d^{3} e^{3} + {\left(19 \, B b^{2} c + 23 \, A b c^{2}\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{2} d^{4} e^{5} - b c d^{3} e^{6} + {\left(c^{2} d^{2} e^{7} - b c d e^{8}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e^{6} - b c d^{2} e^{7}\right)} x\right)}}, -\frac{6 \, {\left(16 \, B c^{3} d^{6} - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{4} e^{2} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d^{3} e^{3} + {\left(16 \, B c^{3} d^{4} e^{2} - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{3} + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{2} e^{4} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d e^{5}\right)} x^{2} + 2 \, {\left(16 \, B c^{3} d^{5} e - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{2} + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{3} e^{3} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - 3 \, {\left(16 \, B c^{3} d^{5} - A b^{2} c d^{2} e^{3} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d^{3} e^{2} + {\left(16 \, B c^{3} d^{3} e^{2} - A b^{2} c e^{5} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{2} e^{3} + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d e^{4}\right)} x^{2} + 2 \, {\left(16 \, B c^{3} d^{4} e - A b^{2} c d e^{4} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{2} + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(24 \, B c^{3} d^{5} e - 3 \, A b^{2} c d^{2} e^{4} - 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{2} + 3 \, {\left(4 \, B b^{2} c + 5 \, A b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(B c^{3} d^{2} e^{4} - B b c^{2} d e^{5}\right)} x^{3} + {\left(8 \, B c^{3} d^{3} e^{3} - {\left(13 \, B b c^{2} + 4 \, A c^{3}\right)} d^{2} e^{4} + {\left(5 \, B b^{2} c + 4 \, A b c^{2}\right)} d e^{5}\right)} x^{2} + {\left(36 \, B c^{3} d^{4} e^{2} - 5 \, A b^{2} c d e^{5} - {\left(55 \, B b c^{2} + 18 \, A c^{3}\right)} d^{3} e^{3} + {\left(19 \, B b^{2} c + 23 \, A b c^{2}\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{2} d^{4} e^{5} - b c d^{3} e^{6} + {\left(c^{2} d^{2} e^{7} - b c d e^{8}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e^{6} - b c d^{2} e^{7}\right)} x\right)}}, -\frac{3 \, {\left(16 \, B c^{3} d^{5} - A b^{2} c d^{2} e^{3} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d^{3} e^{2} + {\left(16 \, B c^{3} d^{3} e^{2} - A b^{2} c e^{5} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{2} e^{3} + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d e^{4}\right)} x^{2} + 2 \, {\left(16 \, B c^{3} d^{4} e - A b^{2} c d e^{4} - 4 \, {\left(5 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{2} + {\left(5 \, B b^{2} c + 8 \, A b c^{2}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 3 \, {\left(16 \, B c^{3} d^{6} - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{4} e^{2} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d^{3} e^{3} + {\left(16 \, B c^{3} d^{4} e^{2} - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{3} + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{2} e^{4} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d e^{5}\right)} x^{2} + 2 \, {\left(16 \, B c^{3} d^{5} e - 4 \, {\left(7 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{2} + {\left(13 \, B b^{2} c + 12 \, A b c^{2}\right)} d^{3} e^{3} - {\left(B b^{3} + 4 \, A b^{2} c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(24 \, B c^{3} d^{5} e - 3 \, A b^{2} c d^{2} e^{4} - 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{2} + 3 \, {\left(4 \, B b^{2} c + 5 \, A b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(B c^{3} d^{2} e^{4} - B b c^{2} d e^{5}\right)} x^{3} + {\left(8 \, B c^{3} d^{3} e^{3} - {\left(13 \, B b c^{2} + 4 \, A c^{3}\right)} d^{2} e^{4} + {\left(5 \, B b^{2} c + 4 \, A b c^{2}\right)} d e^{5}\right)} x^{2} + {\left(36 \, B c^{3} d^{4} e^{2} - 5 \, A b^{2} c d e^{5} - {\left(55 \, B b c^{2} + 18 \, A c^{3}\right)} d^{3} e^{3} + {\left(19 \, B b^{2} c + 23 \, A b c^{2}\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c^{2} d^{4} e^{5} - b c d^{3} e^{6} + {\left(c^{2} d^{2} e^{7} - b c d e^{8}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e^{6} - b c d^{2} e^{7}\right)} x\right)}}\right]"," ",0,"[1/8*(3*(16*B*c^3*d^6 - 4*(7*B*b*c^2 + 2*A*c^3)*d^5*e + (13*B*b^2*c + 12*A*b*c^2)*d^4*e^2 - (B*b^3 + 4*A*b^2*c)*d^3*e^3 + (16*B*c^3*d^4*e^2 - 4*(7*B*b*c^2 + 2*A*c^3)*d^3*e^3 + (13*B*b^2*c + 12*A*b*c^2)*d^2*e^4 - (B*b^3 + 4*A*b^2*c)*d*e^5)*x^2 + 2*(16*B*c^3*d^5*e - 4*(7*B*b*c^2 + 2*A*c^3)*d^4*e^2 + (13*B*b^2*c + 12*A*b*c^2)*d^3*e^3 - (B*b^3 + 4*A*b^2*c)*d^2*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 3*(16*B*c^3*d^5 - A*b^2*c*d^2*e^3 - 4*(5*B*b*c^2 + 2*A*c^3)*d^4*e + (5*B*b^2*c + 8*A*b*c^2)*d^3*e^2 + (16*B*c^3*d^3*e^2 - A*b^2*c*e^5 - 4*(5*B*b*c^2 + 2*A*c^3)*d^2*e^3 + (5*B*b^2*c + 8*A*b*c^2)*d*e^4)*x^2 + 2*(16*B*c^3*d^4*e - A*b^2*c*d*e^4 - 4*(5*B*b*c^2 + 2*A*c^3)*d^3*e^2 + (5*B*b^2*c + 8*A*b*c^2)*d^2*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(24*B*c^3*d^5*e - 3*A*b^2*c*d^2*e^4 - 12*(3*B*b*c^2 + A*c^3)*d^4*e^2 + 3*(4*B*b^2*c + 5*A*b*c^2)*d^3*e^3 - 2*(B*c^3*d^2*e^4 - B*b*c^2*d*e^5)*x^3 + (8*B*c^3*d^3*e^3 - (13*B*b*c^2 + 4*A*c^3)*d^2*e^4 + (5*B*b^2*c + 4*A*b*c^2)*d*e^5)*x^2 + (36*B*c^3*d^4*e^2 - 5*A*b^2*c*d*e^5 - (55*B*b*c^2 + 18*A*c^3)*d^3*e^3 + (19*B*b^2*c + 23*A*b*c^2)*d^2*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*d^4*e^5 - b*c*d^3*e^6 + (c^2*d^2*e^7 - b*c*d*e^8)*x^2 + 2*(c^2*d^3*e^6 - b*c*d^2*e^7)*x), -1/8*(6*(16*B*c^3*d^5 - A*b^2*c*d^2*e^3 - 4*(5*B*b*c^2 + 2*A*c^3)*d^4*e + (5*B*b^2*c + 8*A*b*c^2)*d^3*e^2 + (16*B*c^3*d^3*e^2 - A*b^2*c*e^5 - 4*(5*B*b*c^2 + 2*A*c^3)*d^2*e^3 + (5*B*b^2*c + 8*A*b*c^2)*d*e^4)*x^2 + 2*(16*B*c^3*d^4*e - A*b^2*c*d*e^4 - 4*(5*B*b*c^2 + 2*A*c^3)*d^3*e^2 + (5*B*b^2*c + 8*A*b*c^2)*d^2*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 3*(16*B*c^3*d^6 - 4*(7*B*b*c^2 + 2*A*c^3)*d^5*e + (13*B*b^2*c + 12*A*b*c^2)*d^4*e^2 - (B*b^3 + 4*A*b^2*c)*d^3*e^3 + (16*B*c^3*d^4*e^2 - 4*(7*B*b*c^2 + 2*A*c^3)*d^3*e^3 + (13*B*b^2*c + 12*A*b*c^2)*d^2*e^4 - (B*b^3 + 4*A*b^2*c)*d*e^5)*x^2 + 2*(16*B*c^3*d^5*e - 4*(7*B*b*c^2 + 2*A*c^3)*d^4*e^2 + (13*B*b^2*c + 12*A*b*c^2)*d^3*e^3 - (B*b^3 + 4*A*b^2*c)*d^2*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(24*B*c^3*d^5*e - 3*A*b^2*c*d^2*e^4 - 12*(3*B*b*c^2 + A*c^3)*d^4*e^2 + 3*(4*B*b^2*c + 5*A*b*c^2)*d^3*e^3 - 2*(B*c^3*d^2*e^4 - B*b*c^2*d*e^5)*x^3 + (8*B*c^3*d^3*e^3 - (13*B*b*c^2 + 4*A*c^3)*d^2*e^4 + (5*B*b^2*c + 4*A*b*c^2)*d*e^5)*x^2 + (36*B*c^3*d^4*e^2 - 5*A*b^2*c*d*e^5 - (55*B*b*c^2 + 18*A*c^3)*d^3*e^3 + (19*B*b^2*c + 23*A*b*c^2)*d^2*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*d^4*e^5 - b*c*d^3*e^6 + (c^2*d^2*e^7 - b*c*d*e^8)*x^2 + 2*(c^2*d^3*e^6 - b*c*d^2*e^7)*x), -1/8*(6*(16*B*c^3*d^6 - 4*(7*B*b*c^2 + 2*A*c^3)*d^5*e + (13*B*b^2*c + 12*A*b*c^2)*d^4*e^2 - (B*b^3 + 4*A*b^2*c)*d^3*e^3 + (16*B*c^3*d^4*e^2 - 4*(7*B*b*c^2 + 2*A*c^3)*d^3*e^3 + (13*B*b^2*c + 12*A*b*c^2)*d^2*e^4 - (B*b^3 + 4*A*b^2*c)*d*e^5)*x^2 + 2*(16*B*c^3*d^5*e - 4*(7*B*b*c^2 + 2*A*c^3)*d^4*e^2 + (13*B*b^2*c + 12*A*b*c^2)*d^3*e^3 - (B*b^3 + 4*A*b^2*c)*d^2*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - 3*(16*B*c^3*d^5 - A*b^2*c*d^2*e^3 - 4*(5*B*b*c^2 + 2*A*c^3)*d^4*e + (5*B*b^2*c + 8*A*b*c^2)*d^3*e^2 + (16*B*c^3*d^3*e^2 - A*b^2*c*e^5 - 4*(5*B*b*c^2 + 2*A*c^3)*d^2*e^3 + (5*B*b^2*c + 8*A*b*c^2)*d*e^4)*x^2 + 2*(16*B*c^3*d^4*e - A*b^2*c*d*e^4 - 4*(5*B*b*c^2 + 2*A*c^3)*d^3*e^2 + (5*B*b^2*c + 8*A*b*c^2)*d^2*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(24*B*c^3*d^5*e - 3*A*b^2*c*d^2*e^4 - 12*(3*B*b*c^2 + A*c^3)*d^4*e^2 + 3*(4*B*b^2*c + 5*A*b*c^2)*d^3*e^3 - 2*(B*c^3*d^2*e^4 - B*b*c^2*d*e^5)*x^3 + (8*B*c^3*d^3*e^3 - (13*B*b*c^2 + 4*A*c^3)*d^2*e^4 + (5*B*b^2*c + 4*A*b*c^2)*d*e^5)*x^2 + (36*B*c^3*d^4*e^2 - 5*A*b^2*c*d*e^5 - (55*B*b*c^2 + 18*A*c^3)*d^3*e^3 + (19*B*b^2*c + 23*A*b*c^2)*d^2*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*d^4*e^5 - b*c*d^3*e^6 + (c^2*d^2*e^7 - b*c*d*e^8)*x^2 + 2*(c^2*d^3*e^6 - b*c*d^2*e^7)*x), -1/4*(3*(16*B*c^3*d^5 - A*b^2*c*d^2*e^3 - 4*(5*B*b*c^2 + 2*A*c^3)*d^4*e + (5*B*b^2*c + 8*A*b*c^2)*d^3*e^2 + (16*B*c^3*d^3*e^2 - A*b^2*c*e^5 - 4*(5*B*b*c^2 + 2*A*c^3)*d^2*e^3 + (5*B*b^2*c + 8*A*b*c^2)*d*e^4)*x^2 + 2*(16*B*c^3*d^4*e - A*b^2*c*d*e^4 - 4*(5*B*b*c^2 + 2*A*c^3)*d^3*e^2 + (5*B*b^2*c + 8*A*b*c^2)*d^2*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 3*(16*B*c^3*d^6 - 4*(7*B*b*c^2 + 2*A*c^3)*d^5*e + (13*B*b^2*c + 12*A*b*c^2)*d^4*e^2 - (B*b^3 + 4*A*b^2*c)*d^3*e^3 + (16*B*c^3*d^4*e^2 - 4*(7*B*b*c^2 + 2*A*c^3)*d^3*e^3 + (13*B*b^2*c + 12*A*b*c^2)*d^2*e^4 - (B*b^3 + 4*A*b^2*c)*d*e^5)*x^2 + 2*(16*B*c^3*d^5*e - 4*(7*B*b*c^2 + 2*A*c^3)*d^4*e^2 + (13*B*b^2*c + 12*A*b*c^2)*d^3*e^3 - (B*b^3 + 4*A*b^2*c)*d^2*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (24*B*c^3*d^5*e - 3*A*b^2*c*d^2*e^4 - 12*(3*B*b*c^2 + A*c^3)*d^4*e^2 + 3*(4*B*b^2*c + 5*A*b*c^2)*d^3*e^3 - 2*(B*c^3*d^2*e^4 - B*b*c^2*d*e^5)*x^3 + (8*B*c^3*d^3*e^3 - (13*B*b*c^2 + 4*A*c^3)*d^2*e^4 + (5*B*b^2*c + 4*A*b*c^2)*d*e^5)*x^2 + (36*B*c^3*d^4*e^2 - 5*A*b^2*c*d*e^5 - (55*B*b*c^2 + 18*A*c^3)*d^3*e^3 + (19*B*b^2*c + 23*A*b*c^2)*d^2*e^4)*x)*sqrt(c*x^2 + b*x))/(c^2*d^4*e^5 - b*c*d^3*e^6 + (c^2*d^2*e^7 - b*c*d*e^8)*x^2 + 2*(c^2*d^3*e^6 - b*c*d^2*e^7)*x)]","B",0
1178,1,5005,0,6.422058," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[-\frac{24 \, {\left(8 \, B c^{3} d^{8} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{7} e + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{6} e^{2} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{5} e^{3} + {\left(8 \, B c^{3} d^{5} e^{3} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{4} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{3} e^{5} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{2} e^{6}\right)} x^{3} + 3 \, {\left(8 \, B c^{3} d^{6} e^{2} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e^{3} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{4} e^{4} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{3} e^{5}\right)} x^{2} + 3 \, {\left(8 \, B c^{3} d^{7} e - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e^{2} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{5} e^{3} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 3 \, {\left(64 \, B c^{3} d^{7} - A b^{3} d^{3} e^{4} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{5} e^{2} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{4} e^{3} + {\left(64 \, B c^{3} d^{4} e^{3} - A b^{3} e^{7} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{4} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{2} e^{5} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d e^{6}\right)} x^{3} + 3 \, {\left(64 \, B c^{3} d^{5} e^{2} - A b^{3} d e^{6} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{3} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{3} e^{4} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 3 \, {\left(64 \, B c^{3} d^{6} e - A b^{3} d^{2} e^{5} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e^{2} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{4} e^{3} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(96 \, B c^{3} d^{7} e - 3 \, A b^{3} d^{3} e^{5} - 12 \, {\left(17 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e^{2} + 3 \, {\left(41 \, B b^{2} c + 14 \, A b c^{2}\right)} d^{5} e^{3} - 15 \, {\left(B b^{3} + A b^{2} c\right)} d^{4} e^{4} + 24 \, {\left(B c^{3} d^{4} e^{4} - 2 \, B b c^{2} d^{3} e^{5} + B b^{2} c d^{2} e^{6}\right)} x^{3} + {\left(176 \, B c^{3} d^{5} e^{3} + 3 \, A b^{3} d e^{7} - 2 \, {\left(191 \, B b c^{2} + 22 \, A c^{3}\right)} d^{4} e^{4} + {\left(239 \, B b^{2} c + 88 \, A b c^{2}\right)} d^{3} e^{5} - {\left(33 \, B b^{3} + 47 \, A b^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(120 \, B c^{3} d^{6} e^{2} - 4 \, A b^{3} d^{2} e^{6} - {\left(257 \, B b c^{2} + 30 \, A c^{3}\right)} d^{5} e^{3} + {\left(157 \, B b^{2} c + 53 \, A b c^{2}\right)} d^{4} e^{4} - {\left(20 \, B b^{3} + 19 \, A b^{2} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{2} d^{7} e^{5} - 2 \, b c d^{6} e^{6} + b^{2} d^{5} e^{7} + {\left(c^{2} d^{4} e^{8} - 2 \, b c d^{3} e^{9} + b^{2} d^{2} e^{10}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{7} - 2 \, b c d^{4} e^{8} + b^{2} d^{3} e^{9}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{6} - 2 \, b c d^{5} e^{7} + b^{2} d^{4} e^{8}\right)} x\right)}}, \frac{3 \, {\left(64 \, B c^{3} d^{7} - A b^{3} d^{3} e^{4} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{5} e^{2} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{4} e^{3} + {\left(64 \, B c^{3} d^{4} e^{3} - A b^{3} e^{7} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{4} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{2} e^{5} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d e^{6}\right)} x^{3} + 3 \, {\left(64 \, B c^{3} d^{5} e^{2} - A b^{3} d e^{6} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{3} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{3} e^{4} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 3 \, {\left(64 \, B c^{3} d^{6} e - A b^{3} d^{2} e^{5} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e^{2} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{4} e^{3} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 12 \, {\left(8 \, B c^{3} d^{8} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{7} e + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{6} e^{2} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{5} e^{3} + {\left(8 \, B c^{3} d^{5} e^{3} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{4} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{3} e^{5} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{2} e^{6}\right)} x^{3} + 3 \, {\left(8 \, B c^{3} d^{6} e^{2} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e^{3} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{4} e^{4} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{3} e^{5}\right)} x^{2} + 3 \, {\left(8 \, B c^{3} d^{7} e - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e^{2} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{5} e^{3} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + {\left(96 \, B c^{3} d^{7} e - 3 \, A b^{3} d^{3} e^{5} - 12 \, {\left(17 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e^{2} + 3 \, {\left(41 \, B b^{2} c + 14 \, A b c^{2}\right)} d^{5} e^{3} - 15 \, {\left(B b^{3} + A b^{2} c\right)} d^{4} e^{4} + 24 \, {\left(B c^{3} d^{4} e^{4} - 2 \, B b c^{2} d^{3} e^{5} + B b^{2} c d^{2} e^{6}\right)} x^{3} + {\left(176 \, B c^{3} d^{5} e^{3} + 3 \, A b^{3} d e^{7} - 2 \, {\left(191 \, B b c^{2} + 22 \, A c^{3}\right)} d^{4} e^{4} + {\left(239 \, B b^{2} c + 88 \, A b c^{2}\right)} d^{3} e^{5} - {\left(33 \, B b^{3} + 47 \, A b^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(120 \, B c^{3} d^{6} e^{2} - 4 \, A b^{3} d^{2} e^{6} - {\left(257 \, B b c^{2} + 30 \, A c^{3}\right)} d^{5} e^{3} + {\left(157 \, B b^{2} c + 53 \, A b c^{2}\right)} d^{4} e^{4} - {\left(20 \, B b^{3} + 19 \, A b^{2} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{2} d^{7} e^{5} - 2 \, b c d^{6} e^{6} + b^{2} d^{5} e^{7} + {\left(c^{2} d^{4} e^{8} - 2 \, b c d^{3} e^{9} + b^{2} d^{2} e^{10}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{7} - 2 \, b c d^{4} e^{8} + b^{2} d^{3} e^{9}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{6} - 2 \, b c d^{5} e^{7} + b^{2} d^{4} e^{8}\right)} x\right)}}, \frac{48 \, {\left(8 \, B c^{3} d^{8} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{7} e + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{6} e^{2} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{5} e^{3} + {\left(8 \, B c^{3} d^{5} e^{3} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{4} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{3} e^{5} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{2} e^{6}\right)} x^{3} + 3 \, {\left(8 \, B c^{3} d^{6} e^{2} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e^{3} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{4} e^{4} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{3} e^{5}\right)} x^{2} + 3 \, {\left(8 \, B c^{3} d^{7} e - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e^{2} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{5} e^{3} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 3 \, {\left(64 \, B c^{3} d^{7} - A b^{3} d^{3} e^{4} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{5} e^{2} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{4} e^{3} + {\left(64 \, B c^{3} d^{4} e^{3} - A b^{3} e^{7} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{4} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{2} e^{5} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d e^{6}\right)} x^{3} + 3 \, {\left(64 \, B c^{3} d^{5} e^{2} - A b^{3} d e^{6} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{3} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{3} e^{4} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 3 \, {\left(64 \, B c^{3} d^{6} e - A b^{3} d^{2} e^{5} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e^{2} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{4} e^{3} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(96 \, B c^{3} d^{7} e - 3 \, A b^{3} d^{3} e^{5} - 12 \, {\left(17 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e^{2} + 3 \, {\left(41 \, B b^{2} c + 14 \, A b c^{2}\right)} d^{5} e^{3} - 15 \, {\left(B b^{3} + A b^{2} c\right)} d^{4} e^{4} + 24 \, {\left(B c^{3} d^{4} e^{4} - 2 \, B b c^{2} d^{3} e^{5} + B b^{2} c d^{2} e^{6}\right)} x^{3} + {\left(176 \, B c^{3} d^{5} e^{3} + 3 \, A b^{3} d e^{7} - 2 \, {\left(191 \, B b c^{2} + 22 \, A c^{3}\right)} d^{4} e^{4} + {\left(239 \, B b^{2} c + 88 \, A b c^{2}\right)} d^{3} e^{5} - {\left(33 \, B b^{3} + 47 \, A b^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(120 \, B c^{3} d^{6} e^{2} - 4 \, A b^{3} d^{2} e^{6} - {\left(257 \, B b c^{2} + 30 \, A c^{3}\right)} d^{5} e^{3} + {\left(157 \, B b^{2} c + 53 \, A b c^{2}\right)} d^{4} e^{4} - {\left(20 \, B b^{3} + 19 \, A b^{2} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{2} d^{7} e^{5} - 2 \, b c d^{6} e^{6} + b^{2} d^{5} e^{7} + {\left(c^{2} d^{4} e^{8} - 2 \, b c d^{3} e^{9} + b^{2} d^{2} e^{10}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{7} - 2 \, b c d^{4} e^{8} + b^{2} d^{3} e^{9}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{6} - 2 \, b c d^{5} e^{7} + b^{2} d^{4} e^{8}\right)} x\right)}}, \frac{3 \, {\left(64 \, B c^{3} d^{7} - A b^{3} d^{3} e^{4} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{5} e^{2} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{4} e^{3} + {\left(64 \, B c^{3} d^{4} e^{3} - A b^{3} e^{7} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{3} e^{4} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{2} e^{5} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d e^{6}\right)} x^{3} + 3 \, {\left(64 \, B c^{3} d^{5} e^{2} - A b^{3} d e^{6} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{3} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{3} e^{4} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 3 \, {\left(64 \, B c^{3} d^{6} e - A b^{3} d^{2} e^{5} - 8 \, {\left(15 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e^{2} + 12 \, {\left(5 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{4} e^{3} - {\left(5 \, B b^{3} + 6 \, A b^{2} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 24 \, {\left(8 \, B c^{3} d^{8} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{7} e + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{6} e^{2} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{5} e^{3} + {\left(8 \, B c^{3} d^{5} e^{3} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{4} e^{4} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{3} e^{5} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{2} e^{6}\right)} x^{3} + 3 \, {\left(8 \, B c^{3} d^{6} e^{2} - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{5} e^{3} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{4} e^{4} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{3} e^{5}\right)} x^{2} + 3 \, {\left(8 \, B c^{3} d^{7} e - {\left(19 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e^{2} + 2 \, {\left(7 \, B b^{2} c + 2 \, A b c^{2}\right)} d^{5} e^{3} - {\left(3 \, B b^{3} + 2 \, A b^{2} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(96 \, B c^{3} d^{7} e - 3 \, A b^{3} d^{3} e^{5} - 12 \, {\left(17 \, B b c^{2} + 2 \, A c^{3}\right)} d^{6} e^{2} + 3 \, {\left(41 \, B b^{2} c + 14 \, A b c^{2}\right)} d^{5} e^{3} - 15 \, {\left(B b^{3} + A b^{2} c\right)} d^{4} e^{4} + 24 \, {\left(B c^{3} d^{4} e^{4} - 2 \, B b c^{2} d^{3} e^{5} + B b^{2} c d^{2} e^{6}\right)} x^{3} + {\left(176 \, B c^{3} d^{5} e^{3} + 3 \, A b^{3} d e^{7} - 2 \, {\left(191 \, B b c^{2} + 22 \, A c^{3}\right)} d^{4} e^{4} + {\left(239 \, B b^{2} c + 88 \, A b c^{2}\right)} d^{3} e^{5} - {\left(33 \, B b^{3} + 47 \, A b^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(120 \, B c^{3} d^{6} e^{2} - 4 \, A b^{3} d^{2} e^{6} - {\left(257 \, B b c^{2} + 30 \, A c^{3}\right)} d^{5} e^{3} + {\left(157 \, B b^{2} c + 53 \, A b c^{2}\right)} d^{4} e^{4} - {\left(20 \, B b^{3} + 19 \, A b^{2} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{2} d^{7} e^{5} - 2 \, b c d^{6} e^{6} + b^{2} d^{5} e^{7} + {\left(c^{2} d^{4} e^{8} - 2 \, b c d^{3} e^{9} + b^{2} d^{2} e^{10}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{7} - 2 \, b c d^{4} e^{8} + b^{2} d^{3} e^{9}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{6} - 2 \, b c d^{5} e^{7} + b^{2} d^{4} e^{8}\right)} x\right)}}\right]"," ",0,"[-1/48*(24*(8*B*c^3*d^8 - (19*B*b*c^2 + 2*A*c^3)*d^7*e + 2*(7*B*b^2*c + 2*A*b*c^2)*d^6*e^2 - (3*B*b^3 + 2*A*b^2*c)*d^5*e^3 + (8*B*c^3*d^5*e^3 - (19*B*b*c^2 + 2*A*c^3)*d^4*e^4 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^3*e^5 - (3*B*b^3 + 2*A*b^2*c)*d^2*e^6)*x^3 + 3*(8*B*c^3*d^6*e^2 - (19*B*b*c^2 + 2*A*c^3)*d^5*e^3 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^4*e^4 - (3*B*b^3 + 2*A*b^2*c)*d^3*e^5)*x^2 + 3*(8*B*c^3*d^7*e - (19*B*b*c^2 + 2*A*c^3)*d^6*e^2 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^5*e^3 - (3*B*b^3 + 2*A*b^2*c)*d^4*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 3*(64*B*c^3*d^7 - A*b^3*d^3*e^4 - 8*(15*B*b*c^2 + 2*A*c^3)*d^6*e + 12*(5*B*b^2*c + 2*A*b*c^2)*d^5*e^2 - (5*B*b^3 + 6*A*b^2*c)*d^4*e^3 + (64*B*c^3*d^4*e^3 - A*b^3*e^7 - 8*(15*B*b*c^2 + 2*A*c^3)*d^3*e^4 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^2*e^5 - (5*B*b^3 + 6*A*b^2*c)*d*e^6)*x^3 + 3*(64*B*c^3*d^5*e^2 - A*b^3*d*e^6 - 8*(15*B*b*c^2 + 2*A*c^3)*d^4*e^3 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^3*e^4 - (5*B*b^3 + 6*A*b^2*c)*d^2*e^5)*x^2 + 3*(64*B*c^3*d^6*e - A*b^3*d^2*e^5 - 8*(15*B*b*c^2 + 2*A*c^3)*d^5*e^2 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^4*e^3 - (5*B*b^3 + 6*A*b^2*c)*d^3*e^4)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(96*B*c^3*d^7*e - 3*A*b^3*d^3*e^5 - 12*(17*B*b*c^2 + 2*A*c^3)*d^6*e^2 + 3*(41*B*b^2*c + 14*A*b*c^2)*d^5*e^3 - 15*(B*b^3 + A*b^2*c)*d^4*e^4 + 24*(B*c^3*d^4*e^4 - 2*B*b*c^2*d^3*e^5 + B*b^2*c*d^2*e^6)*x^3 + (176*B*c^3*d^5*e^3 + 3*A*b^3*d*e^7 - 2*(191*B*b*c^2 + 22*A*c^3)*d^4*e^4 + (239*B*b^2*c + 88*A*b*c^2)*d^3*e^5 - (33*B*b^3 + 47*A*b^2*c)*d^2*e^6)*x^2 + 2*(120*B*c^3*d^6*e^2 - 4*A*b^3*d^2*e^6 - (257*B*b*c^2 + 30*A*c^3)*d^5*e^3 + (157*B*b^2*c + 53*A*b*c^2)*d^4*e^4 - (20*B*b^3 + 19*A*b^2*c)*d^3*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*d^7*e^5 - 2*b*c*d^6*e^6 + b^2*d^5*e^7 + (c^2*d^4*e^8 - 2*b*c*d^3*e^9 + b^2*d^2*e^10)*x^3 + 3*(c^2*d^5*e^7 - 2*b*c*d^4*e^8 + b^2*d^3*e^9)*x^2 + 3*(c^2*d^6*e^6 - 2*b*c*d^5*e^7 + b^2*d^4*e^8)*x), 1/24*(3*(64*B*c^3*d^7 - A*b^3*d^3*e^4 - 8*(15*B*b*c^2 + 2*A*c^3)*d^6*e + 12*(5*B*b^2*c + 2*A*b*c^2)*d^5*e^2 - (5*B*b^3 + 6*A*b^2*c)*d^4*e^3 + (64*B*c^3*d^4*e^3 - A*b^3*e^7 - 8*(15*B*b*c^2 + 2*A*c^3)*d^3*e^4 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^2*e^5 - (5*B*b^3 + 6*A*b^2*c)*d*e^6)*x^3 + 3*(64*B*c^3*d^5*e^2 - A*b^3*d*e^6 - 8*(15*B*b*c^2 + 2*A*c^3)*d^4*e^3 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^3*e^4 - (5*B*b^3 + 6*A*b^2*c)*d^2*e^5)*x^2 + 3*(64*B*c^3*d^6*e - A*b^3*d^2*e^5 - 8*(15*B*b*c^2 + 2*A*c^3)*d^5*e^2 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^4*e^3 - (5*B*b^3 + 6*A*b^2*c)*d^3*e^4)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 12*(8*B*c^3*d^8 - (19*B*b*c^2 + 2*A*c^3)*d^7*e + 2*(7*B*b^2*c + 2*A*b*c^2)*d^6*e^2 - (3*B*b^3 + 2*A*b^2*c)*d^5*e^3 + (8*B*c^3*d^5*e^3 - (19*B*b*c^2 + 2*A*c^3)*d^4*e^4 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^3*e^5 - (3*B*b^3 + 2*A*b^2*c)*d^2*e^6)*x^3 + 3*(8*B*c^3*d^6*e^2 - (19*B*b*c^2 + 2*A*c^3)*d^5*e^3 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^4*e^4 - (3*B*b^3 + 2*A*b^2*c)*d^3*e^5)*x^2 + 3*(8*B*c^3*d^7*e - (19*B*b*c^2 + 2*A*c^3)*d^6*e^2 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^5*e^3 - (3*B*b^3 + 2*A*b^2*c)*d^4*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + (96*B*c^3*d^7*e - 3*A*b^3*d^3*e^5 - 12*(17*B*b*c^2 + 2*A*c^3)*d^6*e^2 + 3*(41*B*b^2*c + 14*A*b*c^2)*d^5*e^3 - 15*(B*b^3 + A*b^2*c)*d^4*e^4 + 24*(B*c^3*d^4*e^4 - 2*B*b*c^2*d^3*e^5 + B*b^2*c*d^2*e^6)*x^3 + (176*B*c^3*d^5*e^3 + 3*A*b^3*d*e^7 - 2*(191*B*b*c^2 + 22*A*c^3)*d^4*e^4 + (239*B*b^2*c + 88*A*b*c^2)*d^3*e^5 - (33*B*b^3 + 47*A*b^2*c)*d^2*e^6)*x^2 + 2*(120*B*c^3*d^6*e^2 - 4*A*b^3*d^2*e^6 - (257*B*b*c^2 + 30*A*c^3)*d^5*e^3 + (157*B*b^2*c + 53*A*b*c^2)*d^4*e^4 - (20*B*b^3 + 19*A*b^2*c)*d^3*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*d^7*e^5 - 2*b*c*d^6*e^6 + b^2*d^5*e^7 + (c^2*d^4*e^8 - 2*b*c*d^3*e^9 + b^2*d^2*e^10)*x^3 + 3*(c^2*d^5*e^7 - 2*b*c*d^4*e^8 + b^2*d^3*e^9)*x^2 + 3*(c^2*d^6*e^6 - 2*b*c*d^5*e^7 + b^2*d^4*e^8)*x), 1/48*(48*(8*B*c^3*d^8 - (19*B*b*c^2 + 2*A*c^3)*d^7*e + 2*(7*B*b^2*c + 2*A*b*c^2)*d^6*e^2 - (3*B*b^3 + 2*A*b^2*c)*d^5*e^3 + (8*B*c^3*d^5*e^3 - (19*B*b*c^2 + 2*A*c^3)*d^4*e^4 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^3*e^5 - (3*B*b^3 + 2*A*b^2*c)*d^2*e^6)*x^3 + 3*(8*B*c^3*d^6*e^2 - (19*B*b*c^2 + 2*A*c^3)*d^5*e^3 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^4*e^4 - (3*B*b^3 + 2*A*b^2*c)*d^3*e^5)*x^2 + 3*(8*B*c^3*d^7*e - (19*B*b*c^2 + 2*A*c^3)*d^6*e^2 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^5*e^3 - (3*B*b^3 + 2*A*b^2*c)*d^4*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 3*(64*B*c^3*d^7 - A*b^3*d^3*e^4 - 8*(15*B*b*c^2 + 2*A*c^3)*d^6*e + 12*(5*B*b^2*c + 2*A*b*c^2)*d^5*e^2 - (5*B*b^3 + 6*A*b^2*c)*d^4*e^3 + (64*B*c^3*d^4*e^3 - A*b^3*e^7 - 8*(15*B*b*c^2 + 2*A*c^3)*d^3*e^4 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^2*e^5 - (5*B*b^3 + 6*A*b^2*c)*d*e^6)*x^3 + 3*(64*B*c^3*d^5*e^2 - A*b^3*d*e^6 - 8*(15*B*b*c^2 + 2*A*c^3)*d^4*e^3 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^3*e^4 - (5*B*b^3 + 6*A*b^2*c)*d^2*e^5)*x^2 + 3*(64*B*c^3*d^6*e - A*b^3*d^2*e^5 - 8*(15*B*b*c^2 + 2*A*c^3)*d^5*e^2 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^4*e^3 - (5*B*b^3 + 6*A*b^2*c)*d^3*e^4)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(96*B*c^3*d^7*e - 3*A*b^3*d^3*e^5 - 12*(17*B*b*c^2 + 2*A*c^3)*d^6*e^2 + 3*(41*B*b^2*c + 14*A*b*c^2)*d^5*e^3 - 15*(B*b^3 + A*b^2*c)*d^4*e^4 + 24*(B*c^3*d^4*e^4 - 2*B*b*c^2*d^3*e^5 + B*b^2*c*d^2*e^6)*x^3 + (176*B*c^3*d^5*e^3 + 3*A*b^3*d*e^7 - 2*(191*B*b*c^2 + 22*A*c^3)*d^4*e^4 + (239*B*b^2*c + 88*A*b*c^2)*d^3*e^5 - (33*B*b^3 + 47*A*b^2*c)*d^2*e^6)*x^2 + 2*(120*B*c^3*d^6*e^2 - 4*A*b^3*d^2*e^6 - (257*B*b*c^2 + 30*A*c^3)*d^5*e^3 + (157*B*b^2*c + 53*A*b*c^2)*d^4*e^4 - (20*B*b^3 + 19*A*b^2*c)*d^3*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*d^7*e^5 - 2*b*c*d^6*e^6 + b^2*d^5*e^7 + (c^2*d^4*e^8 - 2*b*c*d^3*e^9 + b^2*d^2*e^10)*x^3 + 3*(c^2*d^5*e^7 - 2*b*c*d^4*e^8 + b^2*d^3*e^9)*x^2 + 3*(c^2*d^6*e^6 - 2*b*c*d^5*e^7 + b^2*d^4*e^8)*x), 1/24*(3*(64*B*c^3*d^7 - A*b^3*d^3*e^4 - 8*(15*B*b*c^2 + 2*A*c^3)*d^6*e + 12*(5*B*b^2*c + 2*A*b*c^2)*d^5*e^2 - (5*B*b^3 + 6*A*b^2*c)*d^4*e^3 + (64*B*c^3*d^4*e^3 - A*b^3*e^7 - 8*(15*B*b*c^2 + 2*A*c^3)*d^3*e^4 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^2*e^5 - (5*B*b^3 + 6*A*b^2*c)*d*e^6)*x^3 + 3*(64*B*c^3*d^5*e^2 - A*b^3*d*e^6 - 8*(15*B*b*c^2 + 2*A*c^3)*d^4*e^3 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^3*e^4 - (5*B*b^3 + 6*A*b^2*c)*d^2*e^5)*x^2 + 3*(64*B*c^3*d^6*e - A*b^3*d^2*e^5 - 8*(15*B*b*c^2 + 2*A*c^3)*d^5*e^2 + 12*(5*B*b^2*c + 2*A*b*c^2)*d^4*e^3 - (5*B*b^3 + 6*A*b^2*c)*d^3*e^4)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 24*(8*B*c^3*d^8 - (19*B*b*c^2 + 2*A*c^3)*d^7*e + 2*(7*B*b^2*c + 2*A*b*c^2)*d^6*e^2 - (3*B*b^3 + 2*A*b^2*c)*d^5*e^3 + (8*B*c^3*d^5*e^3 - (19*B*b*c^2 + 2*A*c^3)*d^4*e^4 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^3*e^5 - (3*B*b^3 + 2*A*b^2*c)*d^2*e^6)*x^3 + 3*(8*B*c^3*d^6*e^2 - (19*B*b*c^2 + 2*A*c^3)*d^5*e^3 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^4*e^4 - (3*B*b^3 + 2*A*b^2*c)*d^3*e^5)*x^2 + 3*(8*B*c^3*d^7*e - (19*B*b*c^2 + 2*A*c^3)*d^6*e^2 + 2*(7*B*b^2*c + 2*A*b*c^2)*d^5*e^3 - (3*B*b^3 + 2*A*b^2*c)*d^4*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (96*B*c^3*d^7*e - 3*A*b^3*d^3*e^5 - 12*(17*B*b*c^2 + 2*A*c^3)*d^6*e^2 + 3*(41*B*b^2*c + 14*A*b*c^2)*d^5*e^3 - 15*(B*b^3 + A*b^2*c)*d^4*e^4 + 24*(B*c^3*d^4*e^4 - 2*B*b*c^2*d^3*e^5 + B*b^2*c*d^2*e^6)*x^3 + (176*B*c^3*d^5*e^3 + 3*A*b^3*d*e^7 - 2*(191*B*b*c^2 + 22*A*c^3)*d^4*e^4 + (239*B*b^2*c + 88*A*b*c^2)*d^3*e^5 - (33*B*b^3 + 47*A*b^2*c)*d^2*e^6)*x^2 + 2*(120*B*c^3*d^6*e^2 - 4*A*b^3*d^2*e^6 - (257*B*b*c^2 + 30*A*c^3)*d^5*e^3 + (157*B*b^2*c + 53*A*b*c^2)*d^4*e^4 - (20*B*b^3 + 19*A*b^2*c)*d^3*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*d^7*e^5 - 2*b*c*d^6*e^6 + b^2*d^5*e^7 + (c^2*d^4*e^8 - 2*b*c*d^3*e^9 + b^2*d^2*e^10)*x^3 + 3*(c^2*d^5*e^7 - 2*b*c*d^4*e^8 + b^2*d^3*e^9)*x^2 + 3*(c^2*d^6*e^6 - 2*b*c*d^5*e^7 + b^2*d^4*e^8)*x)]","B",0
1179,1,5781,0,21.406759," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[\frac{384 \, {\left(B c^{4} d^{10} - 3 \, B b c^{3} d^{9} e + 3 \, B b^{2} c^{2} d^{8} e^{2} - B b^{3} c d^{7} e^{3} + {\left(B c^{4} d^{6} e^{4} - 3 \, B b c^{3} d^{5} e^{5} + 3 \, B b^{2} c^{2} d^{4} e^{6} - B b^{3} c d^{3} e^{7}\right)} x^{4} + 4 \, {\left(B c^{4} d^{7} e^{3} - 3 \, B b c^{3} d^{6} e^{4} + 3 \, B b^{2} c^{2} d^{5} e^{5} - B b^{3} c d^{4} e^{6}\right)} x^{3} + 6 \, {\left(B c^{4} d^{8} e^{2} - 3 \, B b c^{3} d^{7} e^{3} + 3 \, B b^{2} c^{2} d^{6} e^{4} - B b^{3} c d^{5} e^{5}\right)} x^{2} + 4 \, {\left(B c^{4} d^{9} e - 3 \, B b c^{3} d^{8} e^{2} + 3 \, B b^{2} c^{2} d^{7} e^{3} - B b^{3} c d^{6} e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 3 \, {\left(128 \, B c^{4} d^{9} - 320 \, B b c^{3} d^{8} e + 240 \, B b^{2} c^{2} d^{7} e^{2} - 40 \, B b^{3} c d^{6} e^{3} - 5 \, B b^{4} d^{5} e^{4} - 3 \, A b^{4} d^{4} e^{5} + {\left(128 \, B c^{4} d^{5} e^{4} - 320 \, B b c^{3} d^{4} e^{5} + 240 \, B b^{2} c^{2} d^{3} e^{6} - 40 \, B b^{3} c d^{2} e^{7} - 5 \, B b^{4} d e^{8} - 3 \, A b^{4} e^{9}\right)} x^{4} + 4 \, {\left(128 \, B c^{4} d^{6} e^{3} - 320 \, B b c^{3} d^{5} e^{4} + 240 \, B b^{2} c^{2} d^{4} e^{5} - 40 \, B b^{3} c d^{3} e^{6} - 5 \, B b^{4} d^{2} e^{7} - 3 \, A b^{4} d e^{8}\right)} x^{3} + 6 \, {\left(128 \, B c^{4} d^{7} e^{2} - 320 \, B b c^{3} d^{6} e^{3} + 240 \, B b^{2} c^{2} d^{5} e^{4} - 40 \, B b^{3} c d^{4} e^{5} - 5 \, B b^{4} d^{3} e^{6} - 3 \, A b^{4} d^{2} e^{7}\right)} x^{2} + 4 \, {\left(128 \, B c^{4} d^{8} e - 320 \, B b c^{3} d^{7} e^{2} + 240 \, B b^{2} c^{2} d^{6} e^{3} - 40 \, B b^{3} c d^{5} e^{4} - 5 \, B b^{4} d^{4} e^{5} - 3 \, A b^{4} d^{3} e^{6}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(192 \, B c^{4} d^{9} e - 528 \, B b c^{3} d^{8} e^{2} + 456 \, B b^{2} c^{2} d^{7} e^{3} - 105 \, B b^{3} c d^{6} e^{4} - 9 \, A b^{4} d^{4} e^{6} - 3 \, {\left(5 \, B b^{4} - 3 \, A b^{3} c\right)} d^{5} e^{5} + {\left(400 \, B c^{4} d^{6} e^{4} + 9 \, A b^{4} d e^{9} - 24 \, {\left(49 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{5} + 6 \, {\left(193 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{4} e^{6} - {\left(397 \, B b^{3} c + 78 \, A b^{2} c^{2}\right)} d^{3} e^{7} + 3 \, {\left(5 \, B b^{4} - A b^{3} c\right)} d^{2} e^{8}\right)} x^{3} + {\left(832 \, B c^{4} d^{7} e^{3} - 2312 \, B b c^{3} d^{6} e^{4} + 33 \, A b^{4} d^{2} e^{8} + 12 \, {\left(169 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} d^{5} e^{5} - {\left(475 \, B b^{3} c - 204 \, A b^{2} c^{2}\right)} d^{4} e^{6} - {\left(73 \, B b^{4} + 165 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{2} + {\left(672 \, B c^{4} d^{8} e^{2} - 1856 \, B b c^{3} d^{7} e^{3} + 1614 \, B b^{2} c^{2} d^{6} e^{4} - 33 \, A b^{4} d^{3} e^{7} - 3 \, {\left(125 \, B b^{3} c + 2 \, A b^{2} c^{2}\right)} d^{5} e^{5} - {\left(55 \, B b^{4} - 39 \, A b^{3} c\right)} d^{4} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{3} d^{10} e^{5} - 3 \, b c^{2} d^{9} e^{6} + 3 \, b^{2} c d^{8} e^{7} - b^{3} d^{7} e^{8} + {\left(c^{3} d^{6} e^{9} - 3 \, b c^{2} d^{5} e^{10} + 3 \, b^{2} c d^{4} e^{11} - b^{3} d^{3} e^{12}\right)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{8} - 3 \, b c^{2} d^{6} e^{9} + 3 \, b^{2} c d^{5} e^{10} - b^{3} d^{4} e^{11}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{7} - 3 \, b c^{2} d^{7} e^{8} + 3 \, b^{2} c d^{6} e^{9} - b^{3} d^{5} e^{10}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e^{6} - 3 \, b c^{2} d^{8} e^{7} + 3 \, b^{2} c d^{7} e^{8} - b^{3} d^{6} e^{9}\right)} x\right)}}, -\frac{3 \, {\left(128 \, B c^{4} d^{9} - 320 \, B b c^{3} d^{8} e + 240 \, B b^{2} c^{2} d^{7} e^{2} - 40 \, B b^{3} c d^{6} e^{3} - 5 \, B b^{4} d^{5} e^{4} - 3 \, A b^{4} d^{4} e^{5} + {\left(128 \, B c^{4} d^{5} e^{4} - 320 \, B b c^{3} d^{4} e^{5} + 240 \, B b^{2} c^{2} d^{3} e^{6} - 40 \, B b^{3} c d^{2} e^{7} - 5 \, B b^{4} d e^{8} - 3 \, A b^{4} e^{9}\right)} x^{4} + 4 \, {\left(128 \, B c^{4} d^{6} e^{3} - 320 \, B b c^{3} d^{5} e^{4} + 240 \, B b^{2} c^{2} d^{4} e^{5} - 40 \, B b^{3} c d^{3} e^{6} - 5 \, B b^{4} d^{2} e^{7} - 3 \, A b^{4} d e^{8}\right)} x^{3} + 6 \, {\left(128 \, B c^{4} d^{7} e^{2} - 320 \, B b c^{3} d^{6} e^{3} + 240 \, B b^{2} c^{2} d^{5} e^{4} - 40 \, B b^{3} c d^{4} e^{5} - 5 \, B b^{4} d^{3} e^{6} - 3 \, A b^{4} d^{2} e^{7}\right)} x^{2} + 4 \, {\left(128 \, B c^{4} d^{8} e - 320 \, B b c^{3} d^{7} e^{2} + 240 \, B b^{2} c^{2} d^{6} e^{3} - 40 \, B b^{3} c d^{5} e^{4} - 5 \, B b^{4} d^{4} e^{5} - 3 \, A b^{4} d^{3} e^{6}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 192 \, {\left(B c^{4} d^{10} - 3 \, B b c^{3} d^{9} e + 3 \, B b^{2} c^{2} d^{8} e^{2} - B b^{3} c d^{7} e^{3} + {\left(B c^{4} d^{6} e^{4} - 3 \, B b c^{3} d^{5} e^{5} + 3 \, B b^{2} c^{2} d^{4} e^{6} - B b^{3} c d^{3} e^{7}\right)} x^{4} + 4 \, {\left(B c^{4} d^{7} e^{3} - 3 \, B b c^{3} d^{6} e^{4} + 3 \, B b^{2} c^{2} d^{5} e^{5} - B b^{3} c d^{4} e^{6}\right)} x^{3} + 6 \, {\left(B c^{4} d^{8} e^{2} - 3 \, B b c^{3} d^{7} e^{3} + 3 \, B b^{2} c^{2} d^{6} e^{4} - B b^{3} c d^{5} e^{5}\right)} x^{2} + 4 \, {\left(B c^{4} d^{9} e - 3 \, B b c^{3} d^{8} e^{2} + 3 \, B b^{2} c^{2} d^{7} e^{3} - B b^{3} c d^{6} e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + {\left(192 \, B c^{4} d^{9} e - 528 \, B b c^{3} d^{8} e^{2} + 456 \, B b^{2} c^{2} d^{7} e^{3} - 105 \, B b^{3} c d^{6} e^{4} - 9 \, A b^{4} d^{4} e^{6} - 3 \, {\left(5 \, B b^{4} - 3 \, A b^{3} c\right)} d^{5} e^{5} + {\left(400 \, B c^{4} d^{6} e^{4} + 9 \, A b^{4} d e^{9} - 24 \, {\left(49 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{5} + 6 \, {\left(193 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{4} e^{6} - {\left(397 \, B b^{3} c + 78 \, A b^{2} c^{2}\right)} d^{3} e^{7} + 3 \, {\left(5 \, B b^{4} - A b^{3} c\right)} d^{2} e^{8}\right)} x^{3} + {\left(832 \, B c^{4} d^{7} e^{3} - 2312 \, B b c^{3} d^{6} e^{4} + 33 \, A b^{4} d^{2} e^{8} + 12 \, {\left(169 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} d^{5} e^{5} - {\left(475 \, B b^{3} c - 204 \, A b^{2} c^{2}\right)} d^{4} e^{6} - {\left(73 \, B b^{4} + 165 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{2} + {\left(672 \, B c^{4} d^{8} e^{2} - 1856 \, B b c^{3} d^{7} e^{3} + 1614 \, B b^{2} c^{2} d^{6} e^{4} - 33 \, A b^{4} d^{3} e^{7} - 3 \, {\left(125 \, B b^{3} c + 2 \, A b^{2} c^{2}\right)} d^{5} e^{5} - {\left(55 \, B b^{4} - 39 \, A b^{3} c\right)} d^{4} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{3} d^{10} e^{5} - 3 \, b c^{2} d^{9} e^{6} + 3 \, b^{2} c d^{8} e^{7} - b^{3} d^{7} e^{8} + {\left(c^{3} d^{6} e^{9} - 3 \, b c^{2} d^{5} e^{10} + 3 \, b^{2} c d^{4} e^{11} - b^{3} d^{3} e^{12}\right)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{8} - 3 \, b c^{2} d^{6} e^{9} + 3 \, b^{2} c d^{5} e^{10} - b^{3} d^{4} e^{11}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{7} - 3 \, b c^{2} d^{7} e^{8} + 3 \, b^{2} c d^{6} e^{9} - b^{3} d^{5} e^{10}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e^{6} - 3 \, b c^{2} d^{8} e^{7} + 3 \, b^{2} c d^{7} e^{8} - b^{3} d^{6} e^{9}\right)} x\right)}}, -\frac{768 \, {\left(B c^{4} d^{10} - 3 \, B b c^{3} d^{9} e + 3 \, B b^{2} c^{2} d^{8} e^{2} - B b^{3} c d^{7} e^{3} + {\left(B c^{4} d^{6} e^{4} - 3 \, B b c^{3} d^{5} e^{5} + 3 \, B b^{2} c^{2} d^{4} e^{6} - B b^{3} c d^{3} e^{7}\right)} x^{4} + 4 \, {\left(B c^{4} d^{7} e^{3} - 3 \, B b c^{3} d^{6} e^{4} + 3 \, B b^{2} c^{2} d^{5} e^{5} - B b^{3} c d^{4} e^{6}\right)} x^{3} + 6 \, {\left(B c^{4} d^{8} e^{2} - 3 \, B b c^{3} d^{7} e^{3} + 3 \, B b^{2} c^{2} d^{6} e^{4} - B b^{3} c d^{5} e^{5}\right)} x^{2} + 4 \, {\left(B c^{4} d^{9} e - 3 \, B b c^{3} d^{8} e^{2} + 3 \, B b^{2} c^{2} d^{7} e^{3} - B b^{3} c d^{6} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 3 \, {\left(128 \, B c^{4} d^{9} - 320 \, B b c^{3} d^{8} e + 240 \, B b^{2} c^{2} d^{7} e^{2} - 40 \, B b^{3} c d^{6} e^{3} - 5 \, B b^{4} d^{5} e^{4} - 3 \, A b^{4} d^{4} e^{5} + {\left(128 \, B c^{4} d^{5} e^{4} - 320 \, B b c^{3} d^{4} e^{5} + 240 \, B b^{2} c^{2} d^{3} e^{6} - 40 \, B b^{3} c d^{2} e^{7} - 5 \, B b^{4} d e^{8} - 3 \, A b^{4} e^{9}\right)} x^{4} + 4 \, {\left(128 \, B c^{4} d^{6} e^{3} - 320 \, B b c^{3} d^{5} e^{4} + 240 \, B b^{2} c^{2} d^{4} e^{5} - 40 \, B b^{3} c d^{3} e^{6} - 5 \, B b^{4} d^{2} e^{7} - 3 \, A b^{4} d e^{8}\right)} x^{3} + 6 \, {\left(128 \, B c^{4} d^{7} e^{2} - 320 \, B b c^{3} d^{6} e^{3} + 240 \, B b^{2} c^{2} d^{5} e^{4} - 40 \, B b^{3} c d^{4} e^{5} - 5 \, B b^{4} d^{3} e^{6} - 3 \, A b^{4} d^{2} e^{7}\right)} x^{2} + 4 \, {\left(128 \, B c^{4} d^{8} e - 320 \, B b c^{3} d^{7} e^{2} + 240 \, B b^{2} c^{2} d^{6} e^{3} - 40 \, B b^{3} c d^{5} e^{4} - 5 \, B b^{4} d^{4} e^{5} - 3 \, A b^{4} d^{3} e^{6}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(192 \, B c^{4} d^{9} e - 528 \, B b c^{3} d^{8} e^{2} + 456 \, B b^{2} c^{2} d^{7} e^{3} - 105 \, B b^{3} c d^{6} e^{4} - 9 \, A b^{4} d^{4} e^{6} - 3 \, {\left(5 \, B b^{4} - 3 \, A b^{3} c\right)} d^{5} e^{5} + {\left(400 \, B c^{4} d^{6} e^{4} + 9 \, A b^{4} d e^{9} - 24 \, {\left(49 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{5} + 6 \, {\left(193 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{4} e^{6} - {\left(397 \, B b^{3} c + 78 \, A b^{2} c^{2}\right)} d^{3} e^{7} + 3 \, {\left(5 \, B b^{4} - A b^{3} c\right)} d^{2} e^{8}\right)} x^{3} + {\left(832 \, B c^{4} d^{7} e^{3} - 2312 \, B b c^{3} d^{6} e^{4} + 33 \, A b^{4} d^{2} e^{8} + 12 \, {\left(169 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} d^{5} e^{5} - {\left(475 \, B b^{3} c - 204 \, A b^{2} c^{2}\right)} d^{4} e^{6} - {\left(73 \, B b^{4} + 165 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{2} + {\left(672 \, B c^{4} d^{8} e^{2} - 1856 \, B b c^{3} d^{7} e^{3} + 1614 \, B b^{2} c^{2} d^{6} e^{4} - 33 \, A b^{4} d^{3} e^{7} - 3 \, {\left(125 \, B b^{3} c + 2 \, A b^{2} c^{2}\right)} d^{5} e^{5} - {\left(55 \, B b^{4} - 39 \, A b^{3} c\right)} d^{4} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{3} d^{10} e^{5} - 3 \, b c^{2} d^{9} e^{6} + 3 \, b^{2} c d^{8} e^{7} - b^{3} d^{7} e^{8} + {\left(c^{3} d^{6} e^{9} - 3 \, b c^{2} d^{5} e^{10} + 3 \, b^{2} c d^{4} e^{11} - b^{3} d^{3} e^{12}\right)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{8} - 3 \, b c^{2} d^{6} e^{9} + 3 \, b^{2} c d^{5} e^{10} - b^{3} d^{4} e^{11}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{7} - 3 \, b c^{2} d^{7} e^{8} + 3 \, b^{2} c d^{6} e^{9} - b^{3} d^{5} e^{10}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e^{6} - 3 \, b c^{2} d^{8} e^{7} + 3 \, b^{2} c d^{7} e^{8} - b^{3} d^{6} e^{9}\right)} x\right)}}, -\frac{3 \, {\left(128 \, B c^{4} d^{9} - 320 \, B b c^{3} d^{8} e + 240 \, B b^{2} c^{2} d^{7} e^{2} - 40 \, B b^{3} c d^{6} e^{3} - 5 \, B b^{4} d^{5} e^{4} - 3 \, A b^{4} d^{4} e^{5} + {\left(128 \, B c^{4} d^{5} e^{4} - 320 \, B b c^{3} d^{4} e^{5} + 240 \, B b^{2} c^{2} d^{3} e^{6} - 40 \, B b^{3} c d^{2} e^{7} - 5 \, B b^{4} d e^{8} - 3 \, A b^{4} e^{9}\right)} x^{4} + 4 \, {\left(128 \, B c^{4} d^{6} e^{3} - 320 \, B b c^{3} d^{5} e^{4} + 240 \, B b^{2} c^{2} d^{4} e^{5} - 40 \, B b^{3} c d^{3} e^{6} - 5 \, B b^{4} d^{2} e^{7} - 3 \, A b^{4} d e^{8}\right)} x^{3} + 6 \, {\left(128 \, B c^{4} d^{7} e^{2} - 320 \, B b c^{3} d^{6} e^{3} + 240 \, B b^{2} c^{2} d^{5} e^{4} - 40 \, B b^{3} c d^{4} e^{5} - 5 \, B b^{4} d^{3} e^{6} - 3 \, A b^{4} d^{2} e^{7}\right)} x^{2} + 4 \, {\left(128 \, B c^{4} d^{8} e - 320 \, B b c^{3} d^{7} e^{2} + 240 \, B b^{2} c^{2} d^{6} e^{3} - 40 \, B b^{3} c d^{5} e^{4} - 5 \, B b^{4} d^{4} e^{5} - 3 \, A b^{4} d^{3} e^{6}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 384 \, {\left(B c^{4} d^{10} - 3 \, B b c^{3} d^{9} e + 3 \, B b^{2} c^{2} d^{8} e^{2} - B b^{3} c d^{7} e^{3} + {\left(B c^{4} d^{6} e^{4} - 3 \, B b c^{3} d^{5} e^{5} + 3 \, B b^{2} c^{2} d^{4} e^{6} - B b^{3} c d^{3} e^{7}\right)} x^{4} + 4 \, {\left(B c^{4} d^{7} e^{3} - 3 \, B b c^{3} d^{6} e^{4} + 3 \, B b^{2} c^{2} d^{5} e^{5} - B b^{3} c d^{4} e^{6}\right)} x^{3} + 6 \, {\left(B c^{4} d^{8} e^{2} - 3 \, B b c^{3} d^{7} e^{3} + 3 \, B b^{2} c^{2} d^{6} e^{4} - B b^{3} c d^{5} e^{5}\right)} x^{2} + 4 \, {\left(B c^{4} d^{9} e - 3 \, B b c^{3} d^{8} e^{2} + 3 \, B b^{2} c^{2} d^{7} e^{3} - B b^{3} c d^{6} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(192 \, B c^{4} d^{9} e - 528 \, B b c^{3} d^{8} e^{2} + 456 \, B b^{2} c^{2} d^{7} e^{3} - 105 \, B b^{3} c d^{6} e^{4} - 9 \, A b^{4} d^{4} e^{6} - 3 \, {\left(5 \, B b^{4} - 3 \, A b^{3} c\right)} d^{5} e^{5} + {\left(400 \, B c^{4} d^{6} e^{4} + 9 \, A b^{4} d e^{9} - 24 \, {\left(49 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{5} + 6 \, {\left(193 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{4} e^{6} - {\left(397 \, B b^{3} c + 78 \, A b^{2} c^{2}\right)} d^{3} e^{7} + 3 \, {\left(5 \, B b^{4} - A b^{3} c\right)} d^{2} e^{8}\right)} x^{3} + {\left(832 \, B c^{4} d^{7} e^{3} - 2312 \, B b c^{3} d^{6} e^{4} + 33 \, A b^{4} d^{2} e^{8} + 12 \, {\left(169 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} d^{5} e^{5} - {\left(475 \, B b^{3} c - 204 \, A b^{2} c^{2}\right)} d^{4} e^{6} - {\left(73 \, B b^{4} + 165 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{2} + {\left(672 \, B c^{4} d^{8} e^{2} - 1856 \, B b c^{3} d^{7} e^{3} + 1614 \, B b^{2} c^{2} d^{6} e^{4} - 33 \, A b^{4} d^{3} e^{7} - 3 \, {\left(125 \, B b^{3} c + 2 \, A b^{2} c^{2}\right)} d^{5} e^{5} - {\left(55 \, B b^{4} - 39 \, A b^{3} c\right)} d^{4} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{3} d^{10} e^{5} - 3 \, b c^{2} d^{9} e^{6} + 3 \, b^{2} c d^{8} e^{7} - b^{3} d^{7} e^{8} + {\left(c^{3} d^{6} e^{9} - 3 \, b c^{2} d^{5} e^{10} + 3 \, b^{2} c d^{4} e^{11} - b^{3} d^{3} e^{12}\right)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{8} - 3 \, b c^{2} d^{6} e^{9} + 3 \, b^{2} c d^{5} e^{10} - b^{3} d^{4} e^{11}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{7} - 3 \, b c^{2} d^{7} e^{8} + 3 \, b^{2} c d^{6} e^{9} - b^{3} d^{5} e^{10}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e^{6} - 3 \, b c^{2} d^{8} e^{7} + 3 \, b^{2} c d^{7} e^{8} - b^{3} d^{6} e^{9}\right)} x\right)}}\right]"," ",0,"[1/384*(384*(B*c^4*d^10 - 3*B*b*c^3*d^9*e + 3*B*b^2*c^2*d^8*e^2 - B*b^3*c*d^7*e^3 + (B*c^4*d^6*e^4 - 3*B*b*c^3*d^5*e^5 + 3*B*b^2*c^2*d^4*e^6 - B*b^3*c*d^3*e^7)*x^4 + 4*(B*c^4*d^7*e^3 - 3*B*b*c^3*d^6*e^4 + 3*B*b^2*c^2*d^5*e^5 - B*b^3*c*d^4*e^6)*x^3 + 6*(B*c^4*d^8*e^2 - 3*B*b*c^3*d^7*e^3 + 3*B*b^2*c^2*d^6*e^4 - B*b^3*c*d^5*e^5)*x^2 + 4*(B*c^4*d^9*e - 3*B*b*c^3*d^8*e^2 + 3*B*b^2*c^2*d^7*e^3 - B*b^3*c*d^6*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 3*(128*B*c^4*d^9 - 320*B*b*c^3*d^8*e + 240*B*b^2*c^2*d^7*e^2 - 40*B*b^3*c*d^6*e^3 - 5*B*b^4*d^5*e^4 - 3*A*b^4*d^4*e^5 + (128*B*c^4*d^5*e^4 - 320*B*b*c^3*d^4*e^5 + 240*B*b^2*c^2*d^3*e^6 - 40*B*b^3*c*d^2*e^7 - 5*B*b^4*d*e^8 - 3*A*b^4*e^9)*x^4 + 4*(128*B*c^4*d^6*e^3 - 320*B*b*c^3*d^5*e^4 + 240*B*b^2*c^2*d^4*e^5 - 40*B*b^3*c*d^3*e^6 - 5*B*b^4*d^2*e^7 - 3*A*b^4*d*e^8)*x^3 + 6*(128*B*c^4*d^7*e^2 - 320*B*b*c^3*d^6*e^3 + 240*B*b^2*c^2*d^5*e^4 - 40*B*b^3*c*d^4*e^5 - 5*B*b^4*d^3*e^6 - 3*A*b^4*d^2*e^7)*x^2 + 4*(128*B*c^4*d^8*e - 320*B*b*c^3*d^7*e^2 + 240*B*b^2*c^2*d^6*e^3 - 40*B*b^3*c*d^5*e^4 - 5*B*b^4*d^4*e^5 - 3*A*b^4*d^3*e^6)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(192*B*c^4*d^9*e - 528*B*b*c^3*d^8*e^2 + 456*B*b^2*c^2*d^7*e^3 - 105*B*b^3*c*d^6*e^4 - 9*A*b^4*d^4*e^6 - 3*(5*B*b^4 - 3*A*b^3*c)*d^5*e^5 + (400*B*c^4*d^6*e^4 + 9*A*b^4*d*e^9 - 24*(49*B*b*c^3 + 2*A*c^4)*d^5*e^5 + 6*(193*B*b^2*c^2 + 20*A*b*c^3)*d^4*e^6 - (397*B*b^3*c + 78*A*b^2*c^2)*d^3*e^7 + 3*(5*B*b^4 - A*b^3*c)*d^2*e^8)*x^3 + (832*B*c^4*d^7*e^3 - 2312*B*b*c^3*d^6*e^4 + 33*A*b^4*d^2*e^8 + 12*(169*B*b^2*c^2 - 6*A*b*c^3)*d^5*e^5 - (475*B*b^3*c - 204*A*b^2*c^2)*d^4*e^6 - (73*B*b^4 + 165*A*b^3*c)*d^3*e^7)*x^2 + (672*B*c^4*d^8*e^2 - 1856*B*b*c^3*d^7*e^3 + 1614*B*b^2*c^2*d^6*e^4 - 33*A*b^4*d^3*e^7 - 3*(125*B*b^3*c + 2*A*b^2*c^2)*d^5*e^5 - (55*B*b^4 - 39*A*b^3*c)*d^4*e^6)*x)*sqrt(c*x^2 + b*x))/(c^3*d^10*e^5 - 3*b*c^2*d^9*e^6 + 3*b^2*c*d^8*e^7 - b^3*d^7*e^8 + (c^3*d^6*e^9 - 3*b*c^2*d^5*e^10 + 3*b^2*c*d^4*e^11 - b^3*d^3*e^12)*x^4 + 4*(c^3*d^7*e^8 - 3*b*c^2*d^6*e^9 + 3*b^2*c*d^5*e^10 - b^3*d^4*e^11)*x^3 + 6*(c^3*d^8*e^7 - 3*b*c^2*d^7*e^8 + 3*b^2*c*d^6*e^9 - b^3*d^5*e^10)*x^2 + 4*(c^3*d^9*e^6 - 3*b*c^2*d^8*e^7 + 3*b^2*c*d^7*e^8 - b^3*d^6*e^9)*x), -1/192*(3*(128*B*c^4*d^9 - 320*B*b*c^3*d^8*e + 240*B*b^2*c^2*d^7*e^2 - 40*B*b^3*c*d^6*e^3 - 5*B*b^4*d^5*e^4 - 3*A*b^4*d^4*e^5 + (128*B*c^4*d^5*e^4 - 320*B*b*c^3*d^4*e^5 + 240*B*b^2*c^2*d^3*e^6 - 40*B*b^3*c*d^2*e^7 - 5*B*b^4*d*e^8 - 3*A*b^4*e^9)*x^4 + 4*(128*B*c^4*d^6*e^3 - 320*B*b*c^3*d^5*e^4 + 240*B*b^2*c^2*d^4*e^5 - 40*B*b^3*c*d^3*e^6 - 5*B*b^4*d^2*e^7 - 3*A*b^4*d*e^8)*x^3 + 6*(128*B*c^4*d^7*e^2 - 320*B*b*c^3*d^6*e^3 + 240*B*b^2*c^2*d^5*e^4 - 40*B*b^3*c*d^4*e^5 - 5*B*b^4*d^3*e^6 - 3*A*b^4*d^2*e^7)*x^2 + 4*(128*B*c^4*d^8*e - 320*B*b*c^3*d^7*e^2 + 240*B*b^2*c^2*d^6*e^3 - 40*B*b^3*c*d^5*e^4 - 5*B*b^4*d^4*e^5 - 3*A*b^4*d^3*e^6)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 192*(B*c^4*d^10 - 3*B*b*c^3*d^9*e + 3*B*b^2*c^2*d^8*e^2 - B*b^3*c*d^7*e^3 + (B*c^4*d^6*e^4 - 3*B*b*c^3*d^5*e^5 + 3*B*b^2*c^2*d^4*e^6 - B*b^3*c*d^3*e^7)*x^4 + 4*(B*c^4*d^7*e^3 - 3*B*b*c^3*d^6*e^4 + 3*B*b^2*c^2*d^5*e^5 - B*b^3*c*d^4*e^6)*x^3 + 6*(B*c^4*d^8*e^2 - 3*B*b*c^3*d^7*e^3 + 3*B*b^2*c^2*d^6*e^4 - B*b^3*c*d^5*e^5)*x^2 + 4*(B*c^4*d^9*e - 3*B*b*c^3*d^8*e^2 + 3*B*b^2*c^2*d^7*e^3 - B*b^3*c*d^6*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + (192*B*c^4*d^9*e - 528*B*b*c^3*d^8*e^2 + 456*B*b^2*c^2*d^7*e^3 - 105*B*b^3*c*d^6*e^4 - 9*A*b^4*d^4*e^6 - 3*(5*B*b^4 - 3*A*b^3*c)*d^5*e^5 + (400*B*c^4*d^6*e^4 + 9*A*b^4*d*e^9 - 24*(49*B*b*c^3 + 2*A*c^4)*d^5*e^5 + 6*(193*B*b^2*c^2 + 20*A*b*c^3)*d^4*e^6 - (397*B*b^3*c + 78*A*b^2*c^2)*d^3*e^7 + 3*(5*B*b^4 - A*b^3*c)*d^2*e^8)*x^3 + (832*B*c^4*d^7*e^3 - 2312*B*b*c^3*d^6*e^4 + 33*A*b^4*d^2*e^8 + 12*(169*B*b^2*c^2 - 6*A*b*c^3)*d^5*e^5 - (475*B*b^3*c - 204*A*b^2*c^2)*d^4*e^6 - (73*B*b^4 + 165*A*b^3*c)*d^3*e^7)*x^2 + (672*B*c^4*d^8*e^2 - 1856*B*b*c^3*d^7*e^3 + 1614*B*b^2*c^2*d^6*e^4 - 33*A*b^4*d^3*e^7 - 3*(125*B*b^3*c + 2*A*b^2*c^2)*d^5*e^5 - (55*B*b^4 - 39*A*b^3*c)*d^4*e^6)*x)*sqrt(c*x^2 + b*x))/(c^3*d^10*e^5 - 3*b*c^2*d^9*e^6 + 3*b^2*c*d^8*e^7 - b^3*d^7*e^8 + (c^3*d^6*e^9 - 3*b*c^2*d^5*e^10 + 3*b^2*c*d^4*e^11 - b^3*d^3*e^12)*x^4 + 4*(c^3*d^7*e^8 - 3*b*c^2*d^6*e^9 + 3*b^2*c*d^5*e^10 - b^3*d^4*e^11)*x^3 + 6*(c^3*d^8*e^7 - 3*b*c^2*d^7*e^8 + 3*b^2*c*d^6*e^9 - b^3*d^5*e^10)*x^2 + 4*(c^3*d^9*e^6 - 3*b*c^2*d^8*e^7 + 3*b^2*c*d^7*e^8 - b^3*d^6*e^9)*x), -1/384*(768*(B*c^4*d^10 - 3*B*b*c^3*d^9*e + 3*B*b^2*c^2*d^8*e^2 - B*b^3*c*d^7*e^3 + (B*c^4*d^6*e^4 - 3*B*b*c^3*d^5*e^5 + 3*B*b^2*c^2*d^4*e^6 - B*b^3*c*d^3*e^7)*x^4 + 4*(B*c^4*d^7*e^3 - 3*B*b*c^3*d^6*e^4 + 3*B*b^2*c^2*d^5*e^5 - B*b^3*c*d^4*e^6)*x^3 + 6*(B*c^4*d^8*e^2 - 3*B*b*c^3*d^7*e^3 + 3*B*b^2*c^2*d^6*e^4 - B*b^3*c*d^5*e^5)*x^2 + 4*(B*c^4*d^9*e - 3*B*b*c^3*d^8*e^2 + 3*B*b^2*c^2*d^7*e^3 - B*b^3*c*d^6*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 3*(128*B*c^4*d^9 - 320*B*b*c^3*d^8*e + 240*B*b^2*c^2*d^7*e^2 - 40*B*b^3*c*d^6*e^3 - 5*B*b^4*d^5*e^4 - 3*A*b^4*d^4*e^5 + (128*B*c^4*d^5*e^4 - 320*B*b*c^3*d^4*e^5 + 240*B*b^2*c^2*d^3*e^6 - 40*B*b^3*c*d^2*e^7 - 5*B*b^4*d*e^8 - 3*A*b^4*e^9)*x^4 + 4*(128*B*c^4*d^6*e^3 - 320*B*b*c^3*d^5*e^4 + 240*B*b^2*c^2*d^4*e^5 - 40*B*b^3*c*d^3*e^6 - 5*B*b^4*d^2*e^7 - 3*A*b^4*d*e^8)*x^3 + 6*(128*B*c^4*d^7*e^2 - 320*B*b*c^3*d^6*e^3 + 240*B*b^2*c^2*d^5*e^4 - 40*B*b^3*c*d^4*e^5 - 5*B*b^4*d^3*e^6 - 3*A*b^4*d^2*e^7)*x^2 + 4*(128*B*c^4*d^8*e - 320*B*b*c^3*d^7*e^2 + 240*B*b^2*c^2*d^6*e^3 - 40*B*b^3*c*d^5*e^4 - 5*B*b^4*d^4*e^5 - 3*A*b^4*d^3*e^6)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(192*B*c^4*d^9*e - 528*B*b*c^3*d^8*e^2 + 456*B*b^2*c^2*d^7*e^3 - 105*B*b^3*c*d^6*e^4 - 9*A*b^4*d^4*e^6 - 3*(5*B*b^4 - 3*A*b^3*c)*d^5*e^5 + (400*B*c^4*d^6*e^4 + 9*A*b^4*d*e^9 - 24*(49*B*b*c^3 + 2*A*c^4)*d^5*e^5 + 6*(193*B*b^2*c^2 + 20*A*b*c^3)*d^4*e^6 - (397*B*b^3*c + 78*A*b^2*c^2)*d^3*e^7 + 3*(5*B*b^4 - A*b^3*c)*d^2*e^8)*x^3 + (832*B*c^4*d^7*e^3 - 2312*B*b*c^3*d^6*e^4 + 33*A*b^4*d^2*e^8 + 12*(169*B*b^2*c^2 - 6*A*b*c^3)*d^5*e^5 - (475*B*b^3*c - 204*A*b^2*c^2)*d^4*e^6 - (73*B*b^4 + 165*A*b^3*c)*d^3*e^7)*x^2 + (672*B*c^4*d^8*e^2 - 1856*B*b*c^3*d^7*e^3 + 1614*B*b^2*c^2*d^6*e^4 - 33*A*b^4*d^3*e^7 - 3*(125*B*b^3*c + 2*A*b^2*c^2)*d^5*e^5 - (55*B*b^4 - 39*A*b^3*c)*d^4*e^6)*x)*sqrt(c*x^2 + b*x))/(c^3*d^10*e^5 - 3*b*c^2*d^9*e^6 + 3*b^2*c*d^8*e^7 - b^3*d^7*e^8 + (c^3*d^6*e^9 - 3*b*c^2*d^5*e^10 + 3*b^2*c*d^4*e^11 - b^3*d^3*e^12)*x^4 + 4*(c^3*d^7*e^8 - 3*b*c^2*d^6*e^9 + 3*b^2*c*d^5*e^10 - b^3*d^4*e^11)*x^3 + 6*(c^3*d^8*e^7 - 3*b*c^2*d^7*e^8 + 3*b^2*c*d^6*e^9 - b^3*d^5*e^10)*x^2 + 4*(c^3*d^9*e^6 - 3*b*c^2*d^8*e^7 + 3*b^2*c*d^7*e^8 - b^3*d^6*e^9)*x), -1/192*(3*(128*B*c^4*d^9 - 320*B*b*c^3*d^8*e + 240*B*b^2*c^2*d^7*e^2 - 40*B*b^3*c*d^6*e^3 - 5*B*b^4*d^5*e^4 - 3*A*b^4*d^4*e^5 + (128*B*c^4*d^5*e^4 - 320*B*b*c^3*d^4*e^5 + 240*B*b^2*c^2*d^3*e^6 - 40*B*b^3*c*d^2*e^7 - 5*B*b^4*d*e^8 - 3*A*b^4*e^9)*x^4 + 4*(128*B*c^4*d^6*e^3 - 320*B*b*c^3*d^5*e^4 + 240*B*b^2*c^2*d^4*e^5 - 40*B*b^3*c*d^3*e^6 - 5*B*b^4*d^2*e^7 - 3*A*b^4*d*e^8)*x^3 + 6*(128*B*c^4*d^7*e^2 - 320*B*b*c^3*d^6*e^3 + 240*B*b^2*c^2*d^5*e^4 - 40*B*b^3*c*d^4*e^5 - 5*B*b^4*d^3*e^6 - 3*A*b^4*d^2*e^7)*x^2 + 4*(128*B*c^4*d^8*e - 320*B*b*c^3*d^7*e^2 + 240*B*b^2*c^2*d^6*e^3 - 40*B*b^3*c*d^5*e^4 - 5*B*b^4*d^4*e^5 - 3*A*b^4*d^3*e^6)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 384*(B*c^4*d^10 - 3*B*b*c^3*d^9*e + 3*B*b^2*c^2*d^8*e^2 - B*b^3*c*d^7*e^3 + (B*c^4*d^6*e^4 - 3*B*b*c^3*d^5*e^5 + 3*B*b^2*c^2*d^4*e^6 - B*b^3*c*d^3*e^7)*x^4 + 4*(B*c^4*d^7*e^3 - 3*B*b*c^3*d^6*e^4 + 3*B*b^2*c^2*d^5*e^5 - B*b^3*c*d^4*e^6)*x^3 + 6*(B*c^4*d^8*e^2 - 3*B*b*c^3*d^7*e^3 + 3*B*b^2*c^2*d^6*e^4 - B*b^3*c*d^5*e^5)*x^2 + 4*(B*c^4*d^9*e - 3*B*b*c^3*d^8*e^2 + 3*B*b^2*c^2*d^7*e^3 - B*b^3*c*d^6*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (192*B*c^4*d^9*e - 528*B*b*c^3*d^8*e^2 + 456*B*b^2*c^2*d^7*e^3 - 105*B*b^3*c*d^6*e^4 - 9*A*b^4*d^4*e^6 - 3*(5*B*b^4 - 3*A*b^3*c)*d^5*e^5 + (400*B*c^4*d^6*e^4 + 9*A*b^4*d*e^9 - 24*(49*B*b*c^3 + 2*A*c^4)*d^5*e^5 + 6*(193*B*b^2*c^2 + 20*A*b*c^3)*d^4*e^6 - (397*B*b^3*c + 78*A*b^2*c^2)*d^3*e^7 + 3*(5*B*b^4 - A*b^3*c)*d^2*e^8)*x^3 + (832*B*c^4*d^7*e^3 - 2312*B*b*c^3*d^6*e^4 + 33*A*b^4*d^2*e^8 + 12*(169*B*b^2*c^2 - 6*A*b*c^3)*d^5*e^5 - (475*B*b^3*c - 204*A*b^2*c^2)*d^4*e^6 - (73*B*b^4 + 165*A*b^3*c)*d^3*e^7)*x^2 + (672*B*c^4*d^8*e^2 - 1856*B*b*c^3*d^7*e^3 + 1614*B*b^2*c^2*d^6*e^4 - 33*A*b^4*d^3*e^7 - 3*(125*B*b^3*c + 2*A*b^2*c^2)*d^5*e^5 - (55*B*b^4 - 39*A*b^3*c)*d^4*e^6)*x)*sqrt(c*x^2 + b*x))/(c^3*d^10*e^5 - 3*b*c^2*d^9*e^6 + 3*b^2*c*d^8*e^7 - b^3*d^7*e^8 + (c^3*d^6*e^9 - 3*b*c^2*d^5*e^10 + 3*b^2*c*d^4*e^11 - b^3*d^3*e^12)*x^4 + 4*(c^3*d^7*e^8 - 3*b*c^2*d^6*e^9 + 3*b^2*c*d^5*e^10 - b^3*d^4*e^11)*x^3 + 6*(c^3*d^8*e^7 - 3*b*c^2*d^7*e^8 + 3*b^2*c*d^6*e^9 - b^3*d^5*e^10)*x^2 + 4*(c^3*d^9*e^6 - 3*b*c^2*d^8*e^7 + 3*b^2*c*d^7*e^8 - b^3*d^6*e^9)*x)]","B",0
1180,1,2338,0,0.484749," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(A b^{5} d^{5} e + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{6} + {\left(A b^{5} e^{6} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d e^{5}\right)} x^{5} + 5 \, {\left(A b^{5} d e^{5} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{4} + 10 \, {\left(A b^{5} d^{2} e^{4} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{3} e^{3}\right)} x^{3} + 10 \, {\left(A b^{5} d^{3} e^{3} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{4} e^{2}\right)} x^{2} + 5 \, {\left(A b^{5} d^{4} e^{2} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{5} e\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(15 \, A b^{5} d^{5} e^{2} - 15 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{7} + 15 \, {\left(B b^{5} - 3 \, A b^{4} c\right)} d^{6} e - {\left(128 \, B c^{5} d^{7} + 15 \, A b^{5} d e^{6} - 16 \, {\left(29 \, B b c^{4} - 2 \, A c^{5}\right)} d^{6} e + 8 \, {\left(73 \, B b^{2} c^{3} - 12 \, A b c^{4}\right)} d^{5} e^{2} - 2 \, {\left(129 \, B b^{3} c^{2} - 38 \, A b^{2} c^{3}\right)} d^{4} e^{3} - {\left(5 \, B b^{4} c - 8 \, A b^{3} c^{2}\right)} d^{3} e^{4} + 5 \, {\left(3 \, B b^{5} - 7 \, A b^{4} c\right)} d^{2} e^{5}\right)} x^{4} - 2 \, {\left(35 \, A b^{5} d^{2} e^{5} + 8 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} d^{7} - 8 \, {\left(43 \, B b^{2} c^{3} + 31 \, A b c^{4}\right)} d^{6} e + {\left(489 \, B b^{3} c^{2} + 214 \, A b^{2} c^{3}\right)} d^{5} e^{2} - {\left(268 \, B b^{4} c - A b^{3} c^{2}\right)} d^{4} e^{3} + {\left(35 \, B b^{5} - 82 \, A b^{4} c\right)} d^{3} e^{4}\right)} x^{3} - 2 \, {\left(64 \, A b^{5} d^{3} e^{4} + 4 \, {\left(B b^{2} c^{3} + 30 \, A b c^{4}\right)} d^{7} - {\left(27 \, B b^{3} c^{2} + 454 \, A b^{2} c^{3}\right)} d^{6} e + 3 \, {\left(29 \, B b^{4} c + 189 \, A b^{3} c^{2}\right)} d^{5} e^{2} - {\left(64 \, B b^{5} + 297 \, A b^{4} c\right)} d^{4} e^{3}\right)} x^{2} + 10 \, {\left(7 \, A b^{5} d^{4} e^{3} + {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{7} - {\left(8 \, B b^{4} c - 17 \, A b^{3} c^{2}\right)} d^{6} e + {\left(7 \, B b^{5} - 22 \, A b^{4} c\right)} d^{5} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{1280 \, {\left(c^{4} d^{13} - 4 \, b c^{3} d^{12} e + 6 \, b^{2} c^{2} d^{11} e^{2} - 4 \, b^{3} c d^{10} e^{3} + b^{4} d^{9} e^{4} + {\left(c^{4} d^{8} e^{5} - 4 \, b c^{3} d^{7} e^{6} + 6 \, b^{2} c^{2} d^{6} e^{7} - 4 \, b^{3} c d^{5} e^{8} + b^{4} d^{4} e^{9}\right)} x^{5} + 5 \, {\left(c^{4} d^{9} e^{4} - 4 \, b c^{3} d^{8} e^{5} + 6 \, b^{2} c^{2} d^{7} e^{6} - 4 \, b^{3} c d^{6} e^{7} + b^{4} d^{5} e^{8}\right)} x^{4} + 10 \, {\left(c^{4} d^{10} e^{3} - 4 \, b c^{3} d^{9} e^{4} + 6 \, b^{2} c^{2} d^{8} e^{5} - 4 \, b^{3} c d^{7} e^{6} + b^{4} d^{6} e^{7}\right)} x^{3} + 10 \, {\left(c^{4} d^{11} e^{2} - 4 \, b c^{3} d^{10} e^{3} + 6 \, b^{2} c^{2} d^{9} e^{4} - 4 \, b^{3} c d^{8} e^{5} + b^{4} d^{7} e^{6}\right)} x^{2} + 5 \, {\left(c^{4} d^{12} e - 4 \, b c^{3} d^{11} e^{2} + 6 \, b^{2} c^{2} d^{10} e^{3} - 4 \, b^{3} c d^{9} e^{4} + b^{4} d^{8} e^{5}\right)} x\right)}}, -\frac{15 \, {\left(A b^{5} d^{5} e + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{6} + {\left(A b^{5} e^{6} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d e^{5}\right)} x^{5} + 5 \, {\left(A b^{5} d e^{5} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{4} + 10 \, {\left(A b^{5} d^{2} e^{4} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{3} e^{3}\right)} x^{3} + 10 \, {\left(A b^{5} d^{3} e^{3} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{4} e^{2}\right)} x^{2} + 5 \, {\left(A b^{5} d^{4} e^{2} + {\left(B b^{5} - 2 \, A b^{4} c\right)} d^{5} e\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(15 \, A b^{5} d^{5} e^{2} - 15 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{7} + 15 \, {\left(B b^{5} - 3 \, A b^{4} c\right)} d^{6} e - {\left(128 \, B c^{5} d^{7} + 15 \, A b^{5} d e^{6} - 16 \, {\left(29 \, B b c^{4} - 2 \, A c^{5}\right)} d^{6} e + 8 \, {\left(73 \, B b^{2} c^{3} - 12 \, A b c^{4}\right)} d^{5} e^{2} - 2 \, {\left(129 \, B b^{3} c^{2} - 38 \, A b^{2} c^{3}\right)} d^{4} e^{3} - {\left(5 \, B b^{4} c - 8 \, A b^{3} c^{2}\right)} d^{3} e^{4} + 5 \, {\left(3 \, B b^{5} - 7 \, A b^{4} c\right)} d^{2} e^{5}\right)} x^{4} - 2 \, {\left(35 \, A b^{5} d^{2} e^{5} + 8 \, {\left(11 \, B b c^{4} + 10 \, A c^{5}\right)} d^{7} - 8 \, {\left(43 \, B b^{2} c^{3} + 31 \, A b c^{4}\right)} d^{6} e + {\left(489 \, B b^{3} c^{2} + 214 \, A b^{2} c^{3}\right)} d^{5} e^{2} - {\left(268 \, B b^{4} c - A b^{3} c^{2}\right)} d^{4} e^{3} + {\left(35 \, B b^{5} - 82 \, A b^{4} c\right)} d^{3} e^{4}\right)} x^{3} - 2 \, {\left(64 \, A b^{5} d^{3} e^{4} + 4 \, {\left(B b^{2} c^{3} + 30 \, A b c^{4}\right)} d^{7} - {\left(27 \, B b^{3} c^{2} + 454 \, A b^{2} c^{3}\right)} d^{6} e + 3 \, {\left(29 \, B b^{4} c + 189 \, A b^{3} c^{2}\right)} d^{5} e^{2} - {\left(64 \, B b^{5} + 297 \, A b^{4} c\right)} d^{4} e^{3}\right)} x^{2} + 10 \, {\left(7 \, A b^{5} d^{4} e^{3} + {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{7} - {\left(8 \, B b^{4} c - 17 \, A b^{3} c^{2}\right)} d^{6} e + {\left(7 \, B b^{5} - 22 \, A b^{4} c\right)} d^{5} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{640 \, {\left(c^{4} d^{13} - 4 \, b c^{3} d^{12} e + 6 \, b^{2} c^{2} d^{11} e^{2} - 4 \, b^{3} c d^{10} e^{3} + b^{4} d^{9} e^{4} + {\left(c^{4} d^{8} e^{5} - 4 \, b c^{3} d^{7} e^{6} + 6 \, b^{2} c^{2} d^{6} e^{7} - 4 \, b^{3} c d^{5} e^{8} + b^{4} d^{4} e^{9}\right)} x^{5} + 5 \, {\left(c^{4} d^{9} e^{4} - 4 \, b c^{3} d^{8} e^{5} + 6 \, b^{2} c^{2} d^{7} e^{6} - 4 \, b^{3} c d^{6} e^{7} + b^{4} d^{5} e^{8}\right)} x^{4} + 10 \, {\left(c^{4} d^{10} e^{3} - 4 \, b c^{3} d^{9} e^{4} + 6 \, b^{2} c^{2} d^{8} e^{5} - 4 \, b^{3} c d^{7} e^{6} + b^{4} d^{6} e^{7}\right)} x^{3} + 10 \, {\left(c^{4} d^{11} e^{2} - 4 \, b c^{3} d^{10} e^{3} + 6 \, b^{2} c^{2} d^{9} e^{4} - 4 \, b^{3} c d^{8} e^{5} + b^{4} d^{7} e^{6}\right)} x^{2} + 5 \, {\left(c^{4} d^{12} e - 4 \, b c^{3} d^{11} e^{2} + 6 \, b^{2} c^{2} d^{10} e^{3} - 4 \, b^{3} c d^{9} e^{4} + b^{4} d^{8} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/1280*(15*(A*b^5*d^5*e + (B*b^5 - 2*A*b^4*c)*d^6 + (A*b^5*e^6 + (B*b^5 - 2*A*b^4*c)*d*e^5)*x^5 + 5*(A*b^5*d*e^5 + (B*b^5 - 2*A*b^4*c)*d^2*e^4)*x^4 + 10*(A*b^5*d^2*e^4 + (B*b^5 - 2*A*b^4*c)*d^3*e^3)*x^3 + 10*(A*b^5*d^3*e^3 + (B*b^5 - 2*A*b^4*c)*d^4*e^2)*x^2 + 5*(A*b^5*d^4*e^2 + (B*b^5 - 2*A*b^4*c)*d^5*e)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(15*A*b^5*d^5*e^2 - 15*(B*b^4*c - 2*A*b^3*c^2)*d^7 + 15*(B*b^5 - 3*A*b^4*c)*d^6*e - (128*B*c^5*d^7 + 15*A*b^5*d*e^6 - 16*(29*B*b*c^4 - 2*A*c^5)*d^6*e + 8*(73*B*b^2*c^3 - 12*A*b*c^4)*d^5*e^2 - 2*(129*B*b^3*c^2 - 38*A*b^2*c^3)*d^4*e^3 - (5*B*b^4*c - 8*A*b^3*c^2)*d^3*e^4 + 5*(3*B*b^5 - 7*A*b^4*c)*d^2*e^5)*x^4 - 2*(35*A*b^5*d^2*e^5 + 8*(11*B*b*c^4 + 10*A*c^5)*d^7 - 8*(43*B*b^2*c^3 + 31*A*b*c^4)*d^6*e + (489*B*b^3*c^2 + 214*A*b^2*c^3)*d^5*e^2 - (268*B*b^4*c - A*b^3*c^2)*d^4*e^3 + (35*B*b^5 - 82*A*b^4*c)*d^3*e^4)*x^3 - 2*(64*A*b^5*d^3*e^4 + 4*(B*b^2*c^3 + 30*A*b*c^4)*d^7 - (27*B*b^3*c^2 + 454*A*b^2*c^3)*d^6*e + 3*(29*B*b^4*c + 189*A*b^3*c^2)*d^5*e^2 - (64*B*b^5 + 297*A*b^4*c)*d^4*e^3)*x^2 + 10*(7*A*b^5*d^4*e^3 + (B*b^3*c^2 - 2*A*b^2*c^3)*d^7 - (8*B*b^4*c - 17*A*b^3*c^2)*d^6*e + (7*B*b^5 - 22*A*b^4*c)*d^5*e^2)*x)*sqrt(c*x^2 + b*x))/(c^4*d^13 - 4*b*c^3*d^12*e + 6*b^2*c^2*d^11*e^2 - 4*b^3*c*d^10*e^3 + b^4*d^9*e^4 + (c^4*d^8*e^5 - 4*b*c^3*d^7*e^6 + 6*b^2*c^2*d^6*e^7 - 4*b^3*c*d^5*e^8 + b^4*d^4*e^9)*x^5 + 5*(c^4*d^9*e^4 - 4*b*c^3*d^8*e^5 + 6*b^2*c^2*d^7*e^6 - 4*b^3*c*d^6*e^7 + b^4*d^5*e^8)*x^4 + 10*(c^4*d^10*e^3 - 4*b*c^3*d^9*e^4 + 6*b^2*c^2*d^8*e^5 - 4*b^3*c*d^7*e^6 + b^4*d^6*e^7)*x^3 + 10*(c^4*d^11*e^2 - 4*b*c^3*d^10*e^3 + 6*b^2*c^2*d^9*e^4 - 4*b^3*c*d^8*e^5 + b^4*d^7*e^6)*x^2 + 5*(c^4*d^12*e - 4*b*c^3*d^11*e^2 + 6*b^2*c^2*d^10*e^3 - 4*b^3*c*d^9*e^4 + b^4*d^8*e^5)*x), -1/640*(15*(A*b^5*d^5*e + (B*b^5 - 2*A*b^4*c)*d^6 + (A*b^5*e^6 + (B*b^5 - 2*A*b^4*c)*d*e^5)*x^5 + 5*(A*b^5*d*e^5 + (B*b^5 - 2*A*b^4*c)*d^2*e^4)*x^4 + 10*(A*b^5*d^2*e^4 + (B*b^5 - 2*A*b^4*c)*d^3*e^3)*x^3 + 10*(A*b^5*d^3*e^3 + (B*b^5 - 2*A*b^4*c)*d^4*e^2)*x^2 + 5*(A*b^5*d^4*e^2 + (B*b^5 - 2*A*b^4*c)*d^5*e)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (15*A*b^5*d^5*e^2 - 15*(B*b^4*c - 2*A*b^3*c^2)*d^7 + 15*(B*b^5 - 3*A*b^4*c)*d^6*e - (128*B*c^5*d^7 + 15*A*b^5*d*e^6 - 16*(29*B*b*c^4 - 2*A*c^5)*d^6*e + 8*(73*B*b^2*c^3 - 12*A*b*c^4)*d^5*e^2 - 2*(129*B*b^3*c^2 - 38*A*b^2*c^3)*d^4*e^3 - (5*B*b^4*c - 8*A*b^3*c^2)*d^3*e^4 + 5*(3*B*b^5 - 7*A*b^4*c)*d^2*e^5)*x^4 - 2*(35*A*b^5*d^2*e^5 + 8*(11*B*b*c^4 + 10*A*c^5)*d^7 - 8*(43*B*b^2*c^3 + 31*A*b*c^4)*d^6*e + (489*B*b^3*c^2 + 214*A*b^2*c^3)*d^5*e^2 - (268*B*b^4*c - A*b^3*c^2)*d^4*e^3 + (35*B*b^5 - 82*A*b^4*c)*d^3*e^4)*x^3 - 2*(64*A*b^5*d^3*e^4 + 4*(B*b^2*c^3 + 30*A*b*c^4)*d^7 - (27*B*b^3*c^2 + 454*A*b^2*c^3)*d^6*e + 3*(29*B*b^4*c + 189*A*b^3*c^2)*d^5*e^2 - (64*B*b^5 + 297*A*b^4*c)*d^4*e^3)*x^2 + 10*(7*A*b^5*d^4*e^3 + (B*b^3*c^2 - 2*A*b^2*c^3)*d^7 - (8*B*b^4*c - 17*A*b^3*c^2)*d^6*e + (7*B*b^5 - 22*A*b^4*c)*d^5*e^2)*x)*sqrt(c*x^2 + b*x))/(c^4*d^13 - 4*b*c^3*d^12*e + 6*b^2*c^2*d^11*e^2 - 4*b^3*c*d^10*e^3 + b^4*d^9*e^4 + (c^4*d^8*e^5 - 4*b*c^3*d^7*e^6 + 6*b^2*c^2*d^6*e^7 - 4*b^3*c*d^5*e^8 + b^4*d^4*e^9)*x^5 + 5*(c^4*d^9*e^4 - 4*b*c^3*d^8*e^5 + 6*b^2*c^2*d^7*e^6 - 4*b^3*c*d^6*e^7 + b^4*d^5*e^8)*x^4 + 10*(c^4*d^10*e^3 - 4*b*c^3*d^9*e^4 + 6*b^2*c^2*d^8*e^5 - 4*b^3*c*d^7*e^6 + b^4*d^6*e^7)*x^3 + 10*(c^4*d^11*e^2 - 4*b*c^3*d^10*e^3 + 6*b^2*c^2*d^9*e^4 - 4*b^3*c*d^8*e^5 + b^4*d^7*e^6)*x^2 + 5*(c^4*d^12*e - 4*b*c^3*d^11*e^2 + 6*b^2*c^2*d^10*e^3 - 4*b^3*c*d^9*e^4 + b^4*d^8*e^5)*x)]","B",0
1181,1,3734,0,0.517744," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^7,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, A b^{6} d^{6} e^{2} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{8} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{7} e + {\left(7 \, A b^{6} e^{8} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{2} e^{6} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d e^{7}\right)} x^{6} + 6 \, {\left(7 \, A b^{6} d e^{7} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{3} e^{5} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{5} + 15 \, {\left(7 \, A b^{6} d^{2} e^{6} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{4} e^{4} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{4} + 20 \, {\left(7 \, A b^{6} d^{3} e^{5} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{5} e^{3} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{4} e^{4}\right)} x^{3} + 15 \, {\left(7 \, A b^{6} d^{4} e^{4} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{6} e^{2} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{5} e^{3}\right)} x^{2} + 6 \, {\left(7 \, A b^{6} d^{5} e^{3} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{7} e + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{6} e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(105 \, A b^{6} d^{6} e^{3} + 180 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{9} - 15 \, {\left(17 \, B b^{5} c - 48 \, A b^{4} c^{2}\right)} d^{8} e + 15 \, {\left(5 \, B b^{6} - 31 \, A b^{5} c\right)} d^{7} e^{2} + {\left(256 \, B c^{6} d^{8} e - 105 \, A b^{6} d e^{8} - 64 \, {\left(17 \, B b c^{5} - 2 \, A c^{6}\right)} d^{7} e^{2} + 16 \, {\left(103 \, B b^{2} c^{4} - 28 \, A b c^{5}\right)} d^{6} e^{3} - 32 \, {\left(28 \, B b^{3} c^{3} - 13 \, A b^{2} c^{4}\right)} d^{5} e^{4} - 10 \, {\left(5 \, B b^{4} c^{2} - 8 \, A b^{3} c^{3}\right)} d^{4} e^{5} + {\left(205 \, B b^{5} c - 466 \, A b^{4} c^{2}\right)} d^{3} e^{6} - 5 \, {\left(15 \, B b^{6} - 79 \, A b^{5} c\right)} d^{2} e^{7}\right)} x^{5} + {\left(1536 \, B c^{6} d^{9} - 595 \, A b^{6} d^{2} e^{7} - 256 \, {\left(26 \, B b c^{5} - 3 \, A c^{6}\right)} d^{8} e + 64 \, {\left(163 \, B b^{2} c^{4} - 43 \, A b c^{5}\right)} d^{7} e^{2} - 40 \, {\left(155 \, B b^{3} c^{3} - 68 \, A b^{2} c^{4}\right)} d^{6} e^{3} + 4 \, {\left(37 \, B b^{4} c^{2} + 68 \, A b^{3} c^{3}\right)} d^{5} e^{4} + {\left(1165 \, B b^{5} c - 2656 \, A b^{4} c^{2}\right)} d^{4} e^{5} - {\left(425 \, B b^{6} - 2243 \, A b^{5} c\right)} d^{3} e^{6}\right)} x^{4} - 6 \, {\left(231 \, A b^{6} d^{3} e^{6} - 32 \, {\left(11 \, B b c^{5} + 10 \, A c^{6}\right)} d^{9} + 8 \, {\left(215 \, B b^{2} c^{4} + 148 \, A b c^{5}\right)} d^{8} e - 4 \, {\left(817 \, B b^{3} c^{3} + 318 \, A b^{2} c^{4}\right)} d^{7} e^{2} + 2 \, {\left(1387 \, B b^{4} c^{2} + 18 \, A b^{3} c^{3}\right)} d^{6} e^{3} - {\left(1039 \, B b^{5} c - 1014 \, A b^{4} c^{2}\right)} d^{5} e^{4} + 3 \, {\left(55 \, B b^{6} - 291 \, A b^{5} c\right)} d^{4} e^{5}\right)} x^{3} - 2 \, {\left(843 \, A b^{6} d^{4} e^{5} - 48 \, {\left(B b^{2} c^{4} + 30 \, A b c^{5}\right)} d^{9} + 4 \, {\left(101 \, B b^{3} c^{3} + 1704 \, A b^{2} c^{4}\right)} d^{8} e - 4 \, {\left(421 \, B b^{4} c^{2} + 2879 \, A b^{3} c^{3}\right)} d^{7} e^{2} + {\left(1823 \, B b^{5} c + 9712 \, A b^{4} c^{2}\right)} d^{6} e^{3} - 5 \, {\left(99 \, B b^{6} + 883 \, A b^{5} c\right)} d^{5} e^{4}\right)} x^{2} + 5 \, {\left(119 \, A b^{6} d^{5} e^{4} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{9} + 14 \, {\left(17 \, B b^{4} c^{2} - 36 \, A b^{3} c^{3}\right)} d^{8} e - {\left(299 \, B b^{5} c - 878 \, A b^{4} c^{2}\right)} d^{7} e^{2} + {\left(85 \, B b^{6} - 541 \, A b^{5} c\right)} d^{6} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{15360 \, {\left(c^{5} d^{16} - 5 \, b c^{4} d^{15} e + 10 \, b^{2} c^{3} d^{14} e^{2} - 10 \, b^{3} c^{2} d^{13} e^{3} + 5 \, b^{4} c d^{12} e^{4} - b^{5} d^{11} e^{5} + {\left(c^{5} d^{10} e^{6} - 5 \, b c^{4} d^{9} e^{7} + 10 \, b^{2} c^{3} d^{8} e^{8} - 10 \, b^{3} c^{2} d^{7} e^{9} + 5 \, b^{4} c d^{6} e^{10} - b^{5} d^{5} e^{11}\right)} x^{6} + 6 \, {\left(c^{5} d^{11} e^{5} - 5 \, b c^{4} d^{10} e^{6} + 10 \, b^{2} c^{3} d^{9} e^{7} - 10 \, b^{3} c^{2} d^{8} e^{8} + 5 \, b^{4} c d^{7} e^{9} - b^{5} d^{6} e^{10}\right)} x^{5} + 15 \, {\left(c^{5} d^{12} e^{4} - 5 \, b c^{4} d^{11} e^{5} + 10 \, b^{2} c^{3} d^{10} e^{6} - 10 \, b^{3} c^{2} d^{9} e^{7} + 5 \, b^{4} c d^{8} e^{8} - b^{5} d^{7} e^{9}\right)} x^{4} + 20 \, {\left(c^{5} d^{13} e^{3} - 5 \, b c^{4} d^{12} e^{4} + 10 \, b^{2} c^{3} d^{11} e^{5} - 10 \, b^{3} c^{2} d^{10} e^{6} + 5 \, b^{4} c d^{9} e^{7} - b^{5} d^{8} e^{8}\right)} x^{3} + 15 \, {\left(c^{5} d^{14} e^{2} - 5 \, b c^{4} d^{13} e^{3} + 10 \, b^{2} c^{3} d^{12} e^{4} - 10 \, b^{3} c^{2} d^{11} e^{5} + 5 \, b^{4} c d^{10} e^{6} - b^{5} d^{9} e^{7}\right)} x^{2} + 6 \, {\left(c^{5} d^{15} e - 5 \, b c^{4} d^{14} e^{2} + 10 \, b^{2} c^{3} d^{13} e^{3} - 10 \, b^{3} c^{2} d^{12} e^{4} + 5 \, b^{4} c d^{11} e^{5} - b^{5} d^{10} e^{6}\right)} x\right)}}, \frac{15 \, {\left(7 \, A b^{6} d^{6} e^{2} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{8} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{7} e + {\left(7 \, A b^{6} e^{8} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{2} e^{6} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d e^{7}\right)} x^{6} + 6 \, {\left(7 \, A b^{6} d e^{7} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{3} e^{5} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{5} + 15 \, {\left(7 \, A b^{6} d^{2} e^{6} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{4} e^{4} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{4} + 20 \, {\left(7 \, A b^{6} d^{3} e^{5} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{5} e^{3} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{4} e^{4}\right)} x^{3} + 15 \, {\left(7 \, A b^{6} d^{4} e^{4} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{6} e^{2} + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{5} e^{3}\right)} x^{2} + 6 \, {\left(7 \, A b^{6} d^{5} e^{3} - 12 \, {\left(B b^{5} c - 2 \, A b^{4} c^{2}\right)} d^{7} e + {\left(5 \, B b^{6} - 24 \, A b^{5} c\right)} d^{6} e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(105 \, A b^{6} d^{6} e^{3} + 180 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{9} - 15 \, {\left(17 \, B b^{5} c - 48 \, A b^{4} c^{2}\right)} d^{8} e + 15 \, {\left(5 \, B b^{6} - 31 \, A b^{5} c\right)} d^{7} e^{2} + {\left(256 \, B c^{6} d^{8} e - 105 \, A b^{6} d e^{8} - 64 \, {\left(17 \, B b c^{5} - 2 \, A c^{6}\right)} d^{7} e^{2} + 16 \, {\left(103 \, B b^{2} c^{4} - 28 \, A b c^{5}\right)} d^{6} e^{3} - 32 \, {\left(28 \, B b^{3} c^{3} - 13 \, A b^{2} c^{4}\right)} d^{5} e^{4} - 10 \, {\left(5 \, B b^{4} c^{2} - 8 \, A b^{3} c^{3}\right)} d^{4} e^{5} + {\left(205 \, B b^{5} c - 466 \, A b^{4} c^{2}\right)} d^{3} e^{6} - 5 \, {\left(15 \, B b^{6} - 79 \, A b^{5} c\right)} d^{2} e^{7}\right)} x^{5} + {\left(1536 \, B c^{6} d^{9} - 595 \, A b^{6} d^{2} e^{7} - 256 \, {\left(26 \, B b c^{5} - 3 \, A c^{6}\right)} d^{8} e + 64 \, {\left(163 \, B b^{2} c^{4} - 43 \, A b c^{5}\right)} d^{7} e^{2} - 40 \, {\left(155 \, B b^{3} c^{3} - 68 \, A b^{2} c^{4}\right)} d^{6} e^{3} + 4 \, {\left(37 \, B b^{4} c^{2} + 68 \, A b^{3} c^{3}\right)} d^{5} e^{4} + {\left(1165 \, B b^{5} c - 2656 \, A b^{4} c^{2}\right)} d^{4} e^{5} - {\left(425 \, B b^{6} - 2243 \, A b^{5} c\right)} d^{3} e^{6}\right)} x^{4} - 6 \, {\left(231 \, A b^{6} d^{3} e^{6} - 32 \, {\left(11 \, B b c^{5} + 10 \, A c^{6}\right)} d^{9} + 8 \, {\left(215 \, B b^{2} c^{4} + 148 \, A b c^{5}\right)} d^{8} e - 4 \, {\left(817 \, B b^{3} c^{3} + 318 \, A b^{2} c^{4}\right)} d^{7} e^{2} + 2 \, {\left(1387 \, B b^{4} c^{2} + 18 \, A b^{3} c^{3}\right)} d^{6} e^{3} - {\left(1039 \, B b^{5} c - 1014 \, A b^{4} c^{2}\right)} d^{5} e^{4} + 3 \, {\left(55 \, B b^{6} - 291 \, A b^{5} c\right)} d^{4} e^{5}\right)} x^{3} - 2 \, {\left(843 \, A b^{6} d^{4} e^{5} - 48 \, {\left(B b^{2} c^{4} + 30 \, A b c^{5}\right)} d^{9} + 4 \, {\left(101 \, B b^{3} c^{3} + 1704 \, A b^{2} c^{4}\right)} d^{8} e - 4 \, {\left(421 \, B b^{4} c^{2} + 2879 \, A b^{3} c^{3}\right)} d^{7} e^{2} + {\left(1823 \, B b^{5} c + 9712 \, A b^{4} c^{2}\right)} d^{6} e^{3} - 5 \, {\left(99 \, B b^{6} + 883 \, A b^{5} c\right)} d^{5} e^{4}\right)} x^{2} + 5 \, {\left(119 \, A b^{6} d^{5} e^{4} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{9} + 14 \, {\left(17 \, B b^{4} c^{2} - 36 \, A b^{3} c^{3}\right)} d^{8} e - {\left(299 \, B b^{5} c - 878 \, A b^{4} c^{2}\right)} d^{7} e^{2} + {\left(85 \, B b^{6} - 541 \, A b^{5} c\right)} d^{6} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{7680 \, {\left(c^{5} d^{16} - 5 \, b c^{4} d^{15} e + 10 \, b^{2} c^{3} d^{14} e^{2} - 10 \, b^{3} c^{2} d^{13} e^{3} + 5 \, b^{4} c d^{12} e^{4} - b^{5} d^{11} e^{5} + {\left(c^{5} d^{10} e^{6} - 5 \, b c^{4} d^{9} e^{7} + 10 \, b^{2} c^{3} d^{8} e^{8} - 10 \, b^{3} c^{2} d^{7} e^{9} + 5 \, b^{4} c d^{6} e^{10} - b^{5} d^{5} e^{11}\right)} x^{6} + 6 \, {\left(c^{5} d^{11} e^{5} - 5 \, b c^{4} d^{10} e^{6} + 10 \, b^{2} c^{3} d^{9} e^{7} - 10 \, b^{3} c^{2} d^{8} e^{8} + 5 \, b^{4} c d^{7} e^{9} - b^{5} d^{6} e^{10}\right)} x^{5} + 15 \, {\left(c^{5} d^{12} e^{4} - 5 \, b c^{4} d^{11} e^{5} + 10 \, b^{2} c^{3} d^{10} e^{6} - 10 \, b^{3} c^{2} d^{9} e^{7} + 5 \, b^{4} c d^{8} e^{8} - b^{5} d^{7} e^{9}\right)} x^{4} + 20 \, {\left(c^{5} d^{13} e^{3} - 5 \, b c^{4} d^{12} e^{4} + 10 \, b^{2} c^{3} d^{11} e^{5} - 10 \, b^{3} c^{2} d^{10} e^{6} + 5 \, b^{4} c d^{9} e^{7} - b^{5} d^{8} e^{8}\right)} x^{3} + 15 \, {\left(c^{5} d^{14} e^{2} - 5 \, b c^{4} d^{13} e^{3} + 10 \, b^{2} c^{3} d^{12} e^{4} - 10 \, b^{3} c^{2} d^{11} e^{5} + 5 \, b^{4} c d^{10} e^{6} - b^{5} d^{9} e^{7}\right)} x^{2} + 6 \, {\left(c^{5} d^{15} e - 5 \, b c^{4} d^{14} e^{2} + 10 \, b^{2} c^{3} d^{13} e^{3} - 10 \, b^{3} c^{2} d^{12} e^{4} + 5 \, b^{4} c d^{11} e^{5} - b^{5} d^{10} e^{6}\right)} x\right)}}\right]"," ",0,"[1/15360*(15*(7*A*b^6*d^6*e^2 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^8 + (5*B*b^6 - 24*A*b^5*c)*d^7*e + (7*A*b^6*e^8 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^2*e^6 + (5*B*b^6 - 24*A*b^5*c)*d*e^7)*x^6 + 6*(7*A*b^6*d*e^7 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^3*e^5 + (5*B*b^6 - 24*A*b^5*c)*d^2*e^6)*x^5 + 15*(7*A*b^6*d^2*e^6 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^4*e^4 + (5*B*b^6 - 24*A*b^5*c)*d^3*e^5)*x^4 + 20*(7*A*b^6*d^3*e^5 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^5*e^3 + (5*B*b^6 - 24*A*b^5*c)*d^4*e^4)*x^3 + 15*(7*A*b^6*d^4*e^4 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^6*e^2 + (5*B*b^6 - 24*A*b^5*c)*d^5*e^3)*x^2 + 6*(7*A*b^6*d^5*e^3 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^7*e + (5*B*b^6 - 24*A*b^5*c)*d^6*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(105*A*b^6*d^6*e^3 + 180*(B*b^4*c^2 - 2*A*b^3*c^3)*d^9 - 15*(17*B*b^5*c - 48*A*b^4*c^2)*d^8*e + 15*(5*B*b^6 - 31*A*b^5*c)*d^7*e^2 + (256*B*c^6*d^8*e - 105*A*b^6*d*e^8 - 64*(17*B*b*c^5 - 2*A*c^6)*d^7*e^2 + 16*(103*B*b^2*c^4 - 28*A*b*c^5)*d^6*e^3 - 32*(28*B*b^3*c^3 - 13*A*b^2*c^4)*d^5*e^4 - 10*(5*B*b^4*c^2 - 8*A*b^3*c^3)*d^4*e^5 + (205*B*b^5*c - 466*A*b^4*c^2)*d^3*e^6 - 5*(15*B*b^6 - 79*A*b^5*c)*d^2*e^7)*x^5 + (1536*B*c^6*d^9 - 595*A*b^6*d^2*e^7 - 256*(26*B*b*c^5 - 3*A*c^6)*d^8*e + 64*(163*B*b^2*c^4 - 43*A*b*c^5)*d^7*e^2 - 40*(155*B*b^3*c^3 - 68*A*b^2*c^4)*d^6*e^3 + 4*(37*B*b^4*c^2 + 68*A*b^3*c^3)*d^5*e^4 + (1165*B*b^5*c - 2656*A*b^4*c^2)*d^4*e^5 - (425*B*b^6 - 2243*A*b^5*c)*d^3*e^6)*x^4 - 6*(231*A*b^6*d^3*e^6 - 32*(11*B*b*c^5 + 10*A*c^6)*d^9 + 8*(215*B*b^2*c^4 + 148*A*b*c^5)*d^8*e - 4*(817*B*b^3*c^3 + 318*A*b^2*c^4)*d^7*e^2 + 2*(1387*B*b^4*c^2 + 18*A*b^3*c^3)*d^6*e^3 - (1039*B*b^5*c - 1014*A*b^4*c^2)*d^5*e^4 + 3*(55*B*b^6 - 291*A*b^5*c)*d^4*e^5)*x^3 - 2*(843*A*b^6*d^4*e^5 - 48*(B*b^2*c^4 + 30*A*b*c^5)*d^9 + 4*(101*B*b^3*c^3 + 1704*A*b^2*c^4)*d^8*e - 4*(421*B*b^4*c^2 + 2879*A*b^3*c^3)*d^7*e^2 + (1823*B*b^5*c + 9712*A*b^4*c^2)*d^6*e^3 - 5*(99*B*b^6 + 883*A*b^5*c)*d^5*e^4)*x^2 + 5*(119*A*b^6*d^5*e^4 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^9 + 14*(17*B*b^4*c^2 - 36*A*b^3*c^3)*d^8*e - (299*B*b^5*c - 878*A*b^4*c^2)*d^7*e^2 + (85*B*b^6 - 541*A*b^5*c)*d^6*e^3)*x)*sqrt(c*x^2 + b*x))/(c^5*d^16 - 5*b*c^4*d^15*e + 10*b^2*c^3*d^14*e^2 - 10*b^3*c^2*d^13*e^3 + 5*b^4*c*d^12*e^4 - b^5*d^11*e^5 + (c^5*d^10*e^6 - 5*b*c^4*d^9*e^7 + 10*b^2*c^3*d^8*e^8 - 10*b^3*c^2*d^7*e^9 + 5*b^4*c*d^6*e^10 - b^5*d^5*e^11)*x^6 + 6*(c^5*d^11*e^5 - 5*b*c^4*d^10*e^6 + 10*b^2*c^3*d^9*e^7 - 10*b^3*c^2*d^8*e^8 + 5*b^4*c*d^7*e^9 - b^5*d^6*e^10)*x^5 + 15*(c^5*d^12*e^4 - 5*b*c^4*d^11*e^5 + 10*b^2*c^3*d^10*e^6 - 10*b^3*c^2*d^9*e^7 + 5*b^4*c*d^8*e^8 - b^5*d^7*e^9)*x^4 + 20*(c^5*d^13*e^3 - 5*b*c^4*d^12*e^4 + 10*b^2*c^3*d^11*e^5 - 10*b^3*c^2*d^10*e^6 + 5*b^4*c*d^9*e^7 - b^5*d^8*e^8)*x^3 + 15*(c^5*d^14*e^2 - 5*b*c^4*d^13*e^3 + 10*b^2*c^3*d^12*e^4 - 10*b^3*c^2*d^11*e^5 + 5*b^4*c*d^10*e^6 - b^5*d^9*e^7)*x^2 + 6*(c^5*d^15*e - 5*b*c^4*d^14*e^2 + 10*b^2*c^3*d^13*e^3 - 10*b^3*c^2*d^12*e^4 + 5*b^4*c*d^11*e^5 - b^5*d^10*e^6)*x), 1/7680*(15*(7*A*b^6*d^6*e^2 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^8 + (5*B*b^6 - 24*A*b^5*c)*d^7*e + (7*A*b^6*e^8 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^2*e^6 + (5*B*b^6 - 24*A*b^5*c)*d*e^7)*x^6 + 6*(7*A*b^6*d*e^7 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^3*e^5 + (5*B*b^6 - 24*A*b^5*c)*d^2*e^6)*x^5 + 15*(7*A*b^6*d^2*e^6 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^4*e^4 + (5*B*b^6 - 24*A*b^5*c)*d^3*e^5)*x^4 + 20*(7*A*b^6*d^3*e^5 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^5*e^3 + (5*B*b^6 - 24*A*b^5*c)*d^4*e^4)*x^3 + 15*(7*A*b^6*d^4*e^4 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^6*e^2 + (5*B*b^6 - 24*A*b^5*c)*d^5*e^3)*x^2 + 6*(7*A*b^6*d^5*e^3 - 12*(B*b^5*c - 2*A*b^4*c^2)*d^7*e + (5*B*b^6 - 24*A*b^5*c)*d^6*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (105*A*b^6*d^6*e^3 + 180*(B*b^4*c^2 - 2*A*b^3*c^3)*d^9 - 15*(17*B*b^5*c - 48*A*b^4*c^2)*d^8*e + 15*(5*B*b^6 - 31*A*b^5*c)*d^7*e^2 + (256*B*c^6*d^8*e - 105*A*b^6*d*e^8 - 64*(17*B*b*c^5 - 2*A*c^6)*d^7*e^2 + 16*(103*B*b^2*c^4 - 28*A*b*c^5)*d^6*e^3 - 32*(28*B*b^3*c^3 - 13*A*b^2*c^4)*d^5*e^4 - 10*(5*B*b^4*c^2 - 8*A*b^3*c^3)*d^4*e^5 + (205*B*b^5*c - 466*A*b^4*c^2)*d^3*e^6 - 5*(15*B*b^6 - 79*A*b^5*c)*d^2*e^7)*x^5 + (1536*B*c^6*d^9 - 595*A*b^6*d^2*e^7 - 256*(26*B*b*c^5 - 3*A*c^6)*d^8*e + 64*(163*B*b^2*c^4 - 43*A*b*c^5)*d^7*e^2 - 40*(155*B*b^3*c^3 - 68*A*b^2*c^4)*d^6*e^3 + 4*(37*B*b^4*c^2 + 68*A*b^3*c^3)*d^5*e^4 + (1165*B*b^5*c - 2656*A*b^4*c^2)*d^4*e^5 - (425*B*b^6 - 2243*A*b^5*c)*d^3*e^6)*x^4 - 6*(231*A*b^6*d^3*e^6 - 32*(11*B*b*c^5 + 10*A*c^6)*d^9 + 8*(215*B*b^2*c^4 + 148*A*b*c^5)*d^8*e - 4*(817*B*b^3*c^3 + 318*A*b^2*c^4)*d^7*e^2 + 2*(1387*B*b^4*c^2 + 18*A*b^3*c^3)*d^6*e^3 - (1039*B*b^5*c - 1014*A*b^4*c^2)*d^5*e^4 + 3*(55*B*b^6 - 291*A*b^5*c)*d^4*e^5)*x^3 - 2*(843*A*b^6*d^4*e^5 - 48*(B*b^2*c^4 + 30*A*b*c^5)*d^9 + 4*(101*B*b^3*c^3 + 1704*A*b^2*c^4)*d^8*e - 4*(421*B*b^4*c^2 + 2879*A*b^3*c^3)*d^7*e^2 + (1823*B*b^5*c + 9712*A*b^4*c^2)*d^6*e^3 - 5*(99*B*b^6 + 883*A*b^5*c)*d^5*e^4)*x^2 + 5*(119*A*b^6*d^5*e^4 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^9 + 14*(17*B*b^4*c^2 - 36*A*b^3*c^3)*d^8*e - (299*B*b^5*c - 878*A*b^4*c^2)*d^7*e^2 + (85*B*b^6 - 541*A*b^5*c)*d^6*e^3)*x)*sqrt(c*x^2 + b*x))/(c^5*d^16 - 5*b*c^4*d^15*e + 10*b^2*c^3*d^14*e^2 - 10*b^3*c^2*d^13*e^3 + 5*b^4*c*d^12*e^4 - b^5*d^11*e^5 + (c^5*d^10*e^6 - 5*b*c^4*d^9*e^7 + 10*b^2*c^3*d^8*e^8 - 10*b^3*c^2*d^7*e^9 + 5*b^4*c*d^6*e^10 - b^5*d^5*e^11)*x^6 + 6*(c^5*d^11*e^5 - 5*b*c^4*d^10*e^6 + 10*b^2*c^3*d^9*e^7 - 10*b^3*c^2*d^8*e^8 + 5*b^4*c*d^7*e^9 - b^5*d^6*e^10)*x^5 + 15*(c^5*d^12*e^4 - 5*b*c^4*d^11*e^5 + 10*b^2*c^3*d^10*e^6 - 10*b^3*c^2*d^9*e^7 + 5*b^4*c*d^8*e^8 - b^5*d^7*e^9)*x^4 + 20*(c^5*d^13*e^3 - 5*b*c^4*d^12*e^4 + 10*b^2*c^3*d^11*e^5 - 10*b^3*c^2*d^10*e^6 + 5*b^4*c*d^9*e^7 - b^5*d^8*e^8)*x^3 + 15*(c^5*d^14*e^2 - 5*b*c^4*d^13*e^3 + 10*b^2*c^3*d^12*e^4 - 10*b^3*c^2*d^11*e^5 + 5*b^4*c*d^10*e^6 - b^5*d^9*e^7)*x^2 + 6*(c^5*d^15*e - 5*b*c^4*d^14*e^2 + 10*b^2*c^3*d^13*e^3 - 10*b^3*c^2*d^12*e^4 + 5*b^4*c*d^11*e^5 - b^5*d^10*e^6)*x)]","B",0
1182,1,5398,0,0.565887," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^8,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, A b^{7} d^{7} e^{3} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{10} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{9} e + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{8} e^{2} + {\left(9 \, A b^{7} e^{10} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{3} e^{7} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{2} e^{8} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d e^{9}\right)} x^{7} + 7 \, {\left(9 \, A b^{7} d e^{9} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{4} e^{6} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{3} e^{7} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{2} e^{8}\right)} x^{6} + 21 \, {\left(9 \, A b^{7} d^{2} e^{8} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{5} e^{5} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{4} e^{6} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{3} e^{7}\right)} x^{5} + 35 \, {\left(9 \, A b^{7} d^{3} e^{7} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{6} e^{4} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{5} e^{5} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{4} e^{6}\right)} x^{4} + 35 \, {\left(9 \, A b^{7} d^{4} e^{6} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{7} e^{3} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{6} e^{4} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{5} e^{5}\right)} x^{3} + 21 \, {\left(9 \, A b^{7} d^{5} e^{5} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{8} e^{2} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{7} e^{3} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{6} e^{4}\right)} x^{2} + 7 \, {\left(9 \, A b^{7} d^{6} e^{4} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{9} e - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{8} e^{2} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{7} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(945 \, A b^{7} d^{7} e^{4} - 2520 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{11} + 420 \, {\left(11 \, B b^{5} c^{2} - 30 \, A b^{4} c^{3}\right)} d^{10} e - 105 \, {\left(25 \, B b^{6} c - 114 \, A b^{5} c^{2}\right)} d^{9} e^{2} + 105 \, {\left(5 \, B b^{7} - 51 \, A b^{6} c\right)} d^{8} e^{3} - {\left(1024 \, B c^{7} d^{9} e^{2} + 945 \, A b^{7} d e^{10} - 384 \, {\left(13 \, B b c^{6} - 2 \, A c^{7}\right)} d^{8} e^{3} + 384 \, {\left(23 \, B b^{2} c^{5} - 8 \, A b c^{6}\right)} d^{7} e^{4} - 96 \, {\left(59 \, B b^{3} c^{4} - 34 \, A b^{2} c^{5}\right)} d^{6} e^{5} - 120 \, {\left(5 \, B b^{4} c^{3} - 8 \, A b^{3} c^{4}\right)} d^{5} e^{6} + 6 \, {\left(525 \, B b^{5} c^{2} - 1174 \, A b^{4} c^{3}\right)} d^{4} e^{7} - 7 \, {\left(325 \, B b^{6} c - 1272 \, A b^{5} c^{2}\right)} d^{3} e^{8} + 525 \, {\left(B b^{7} - 9 \, A b^{6} c\right)} d^{2} e^{9}\right)} x^{6} - 2 \, {\left(3584 \, B c^{7} d^{10} e + 3150 \, A b^{7} d^{2} e^{9} - 64 \, {\left(277 \, B b c^{6} - 42 \, A c^{7}\right)} d^{9} e^{2} + 96 \, {\left(335 \, B b^{2} c^{5} - 114 \, A b c^{6}\right)} d^{8} e^{3} - 48 \, {\left(459 \, B b^{3} c^{4} - 254 \, A b^{2} c^{5}\right)} d^{7} e^{4} - 12 \, {\left(57 \, B b^{4} c^{3} - 212 \, A b^{3} c^{4}\right)} d^{6} e^{5} + 3 \, {\left(3515 \, B b^{5} c^{2} - 7878 \, A b^{4} c^{3}\right)} d^{5} e^{6} - 5 \, {\left(1519 \, B b^{6} c - 5955 \, A b^{5} c^{2}\right)} d^{4} e^{7} + 7 \, {\left(250 \, B b^{7} - 2253 \, A b^{6} c\right)} d^{3} e^{8}\right)} x^{5} - {\left(21504 \, B c^{7} d^{11} + 17829 \, A b^{7} d^{3} e^{8} - 896 \, {\left(121 \, B b c^{6} - 18 \, A c^{7}\right)} d^{10} e + 192 \, {\left(1059 \, B b^{2} c^{5} - 350 \, A b c^{6}\right)} d^{9} e^{2} - 48 \, {\left(3161 \, B b^{3} c^{4} - 1658 \, A b^{2} c^{5}\right)} d^{8} e^{3} + 24 \, {\left(439 \, B b^{4} c^{3} + 316 \, A b^{3} c^{4}\right)} d^{7} e^{4} + 48 \, {\left(1207 \, B b^{5} c^{2} - 2785 \, A b^{4} c^{3}\right)} d^{6} e^{5} - 33 \, {\left(1305 \, B b^{6} c - 5126 \, A b^{5} c^{2}\right)} d^{5} e^{6} + {\left(9905 \, B b^{7} - 89403 \, A b^{6} c\right)} d^{4} e^{7}\right)} x^{4} - 4 \, {\left(6912 \, A b^{7} d^{4} e^{7} + 672 \, {\left(11 \, B b c^{6} + 10 \, A c^{7}\right)} d^{11} - 14448 \, {\left(3 \, B b^{2} c^{5} + 2 \, A b c^{6}\right)} d^{10} e + 4 \, {\left(25775 \, B b^{3} c^{4} + 9282 \, A b^{2} c^{5}\right)} d^{9} e^{2} - 12 \, {\left(9883 \, B b^{4} c^{3} + 187 \, A b^{3} c^{4}\right)} d^{8} e^{3} + 3 \, {\left(24291 \, B b^{5} c^{2} - 16846 \, A b^{4} c^{3}\right)} d^{7} e^{4} - {\left(25265 \, B b^{6} c - 65643 \, A b^{5} c^{2}\right)} d^{6} e^{5} + 15 \, {\left(256 \, B b^{7} - 2315 \, A b^{6} c\right)} d^{5} e^{6}\right)} x^{3} - 7 \, {\left(3597 \, A b^{7} d^{5} e^{6} + 192 \, {\left(B b^{2} c^{5} + 30 \, A b c^{6}\right)} d^{11} - 176 \, {\left(11 \, B b^{3} c^{4} + 186 \, A b^{2} c^{5}\right)} d^{10} e + 8 \, {\left(1237 \, B b^{4} c^{3} + 8718 \, A b^{3} c^{4}\right)} d^{9} e^{2} - 6 \, {\left(2357 \, B b^{5} c^{2} + 13498 \, A b^{4} c^{3}\right)} d^{8} e^{3} + 5 \, {\left(1481 \, B b^{6} c + 11292 \, A b^{5} c^{2}\right)} d^{7} e^{4} - {\left(1415 \, B b^{7} + 21837 \, A b^{6} c\right)} d^{6} e^{5}\right)} x^{2} + 70 \, {\left(90 \, A b^{7} d^{6} e^{5} + 24 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{11} - 4 \, {\left(71 \, B b^{4} c^{3} - 150 \, A b^{3} c^{4}\right)} d^{10} e + 3 \, {\left(155 \, B b^{5} c^{2} - 438 \, A b^{4} c^{3}\right)} d^{9} e^{2} - 3 \, {\left(85 \, B b^{6} c - 397 \, A b^{5} c^{2}\right)} d^{8} e^{3} + {\left(50 \, B b^{7} - 519 \, A b^{6} c\right)} d^{7} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{215040 \, {\left(c^{6} d^{19} - 6 \, b c^{5} d^{18} e + 15 \, b^{2} c^{4} d^{17} e^{2} - 20 \, b^{3} c^{3} d^{16} e^{3} + 15 \, b^{4} c^{2} d^{15} e^{4} - 6 \, b^{5} c d^{14} e^{5} + b^{6} d^{13} e^{6} + {\left(c^{6} d^{12} e^{7} - 6 \, b c^{5} d^{11} e^{8} + 15 \, b^{2} c^{4} d^{10} e^{9} - 20 \, b^{3} c^{3} d^{9} e^{10} + 15 \, b^{4} c^{2} d^{8} e^{11} - 6 \, b^{5} c d^{7} e^{12} + b^{6} d^{6} e^{13}\right)} x^{7} + 7 \, {\left(c^{6} d^{13} e^{6} - 6 \, b c^{5} d^{12} e^{7} + 15 \, b^{2} c^{4} d^{11} e^{8} - 20 \, b^{3} c^{3} d^{10} e^{9} + 15 \, b^{4} c^{2} d^{9} e^{10} - 6 \, b^{5} c d^{8} e^{11} + b^{6} d^{7} e^{12}\right)} x^{6} + 21 \, {\left(c^{6} d^{14} e^{5} - 6 \, b c^{5} d^{13} e^{6} + 15 \, b^{2} c^{4} d^{12} e^{7} - 20 \, b^{3} c^{3} d^{11} e^{8} + 15 \, b^{4} c^{2} d^{10} e^{9} - 6 \, b^{5} c d^{9} e^{10} + b^{6} d^{8} e^{11}\right)} x^{5} + 35 \, {\left(c^{6} d^{15} e^{4} - 6 \, b c^{5} d^{14} e^{5} + 15 \, b^{2} c^{4} d^{13} e^{6} - 20 \, b^{3} c^{3} d^{12} e^{7} + 15 \, b^{4} c^{2} d^{11} e^{8} - 6 \, b^{5} c d^{10} e^{9} + b^{6} d^{9} e^{10}\right)} x^{4} + 35 \, {\left(c^{6} d^{16} e^{3} - 6 \, b c^{5} d^{15} e^{4} + 15 \, b^{2} c^{4} d^{14} e^{5} - 20 \, b^{3} c^{3} d^{13} e^{6} + 15 \, b^{4} c^{2} d^{12} e^{7} - 6 \, b^{5} c d^{11} e^{8} + b^{6} d^{10} e^{9}\right)} x^{3} + 21 \, {\left(c^{6} d^{17} e^{2} - 6 \, b c^{5} d^{16} e^{3} + 15 \, b^{2} c^{4} d^{15} e^{4} - 20 \, b^{3} c^{3} d^{14} e^{5} + 15 \, b^{4} c^{2} d^{13} e^{6} - 6 \, b^{5} c d^{12} e^{7} + b^{6} d^{11} e^{8}\right)} x^{2} + 7 \, {\left(c^{6} d^{18} e - 6 \, b c^{5} d^{17} e^{2} + 15 \, b^{2} c^{4} d^{16} e^{3} - 20 \, b^{3} c^{3} d^{15} e^{4} + 15 \, b^{4} c^{2} d^{14} e^{5} - 6 \, b^{5} c d^{13} e^{6} + b^{6} d^{12} e^{7}\right)} x\right)}}, -\frac{105 \, {\left(9 \, A b^{7} d^{7} e^{3} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{10} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{9} e + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{8} e^{2} + {\left(9 \, A b^{7} e^{10} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{3} e^{7} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{2} e^{8} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d e^{9}\right)} x^{7} + 7 \, {\left(9 \, A b^{7} d e^{9} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{4} e^{6} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{3} e^{7} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{2} e^{8}\right)} x^{6} + 21 \, {\left(9 \, A b^{7} d^{2} e^{8} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{5} e^{5} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{4} e^{6} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{3} e^{7}\right)} x^{5} + 35 \, {\left(9 \, A b^{7} d^{3} e^{7} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{6} e^{4} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{5} e^{5} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{4} e^{6}\right)} x^{4} + 35 \, {\left(9 \, A b^{7} d^{4} e^{6} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{7} e^{3} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{6} e^{4} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{5} e^{5}\right)} x^{3} + 21 \, {\left(9 \, A b^{7} d^{5} e^{5} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{8} e^{2} - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{7} e^{3} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{6} e^{4}\right)} x^{2} + 7 \, {\left(9 \, A b^{7} d^{6} e^{4} + 24 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} d^{9} e - 4 \, {\left(5 \, B b^{6} c - 18 \, A b^{5} c^{2}\right)} d^{8} e^{2} + {\left(5 \, B b^{7} - 42 \, A b^{6} c\right)} d^{7} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(945 \, A b^{7} d^{7} e^{4} - 2520 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{11} + 420 \, {\left(11 \, B b^{5} c^{2} - 30 \, A b^{4} c^{3}\right)} d^{10} e - 105 \, {\left(25 \, B b^{6} c - 114 \, A b^{5} c^{2}\right)} d^{9} e^{2} + 105 \, {\left(5 \, B b^{7} - 51 \, A b^{6} c\right)} d^{8} e^{3} - {\left(1024 \, B c^{7} d^{9} e^{2} + 945 \, A b^{7} d e^{10} - 384 \, {\left(13 \, B b c^{6} - 2 \, A c^{7}\right)} d^{8} e^{3} + 384 \, {\left(23 \, B b^{2} c^{5} - 8 \, A b c^{6}\right)} d^{7} e^{4} - 96 \, {\left(59 \, B b^{3} c^{4} - 34 \, A b^{2} c^{5}\right)} d^{6} e^{5} - 120 \, {\left(5 \, B b^{4} c^{3} - 8 \, A b^{3} c^{4}\right)} d^{5} e^{6} + 6 \, {\left(525 \, B b^{5} c^{2} - 1174 \, A b^{4} c^{3}\right)} d^{4} e^{7} - 7 \, {\left(325 \, B b^{6} c - 1272 \, A b^{5} c^{2}\right)} d^{3} e^{8} + 525 \, {\left(B b^{7} - 9 \, A b^{6} c\right)} d^{2} e^{9}\right)} x^{6} - 2 \, {\left(3584 \, B c^{7} d^{10} e + 3150 \, A b^{7} d^{2} e^{9} - 64 \, {\left(277 \, B b c^{6} - 42 \, A c^{7}\right)} d^{9} e^{2} + 96 \, {\left(335 \, B b^{2} c^{5} - 114 \, A b c^{6}\right)} d^{8} e^{3} - 48 \, {\left(459 \, B b^{3} c^{4} - 254 \, A b^{2} c^{5}\right)} d^{7} e^{4} - 12 \, {\left(57 \, B b^{4} c^{3} - 212 \, A b^{3} c^{4}\right)} d^{6} e^{5} + 3 \, {\left(3515 \, B b^{5} c^{2} - 7878 \, A b^{4} c^{3}\right)} d^{5} e^{6} - 5 \, {\left(1519 \, B b^{6} c - 5955 \, A b^{5} c^{2}\right)} d^{4} e^{7} + 7 \, {\left(250 \, B b^{7} - 2253 \, A b^{6} c\right)} d^{3} e^{8}\right)} x^{5} - {\left(21504 \, B c^{7} d^{11} + 17829 \, A b^{7} d^{3} e^{8} - 896 \, {\left(121 \, B b c^{6} - 18 \, A c^{7}\right)} d^{10} e + 192 \, {\left(1059 \, B b^{2} c^{5} - 350 \, A b c^{6}\right)} d^{9} e^{2} - 48 \, {\left(3161 \, B b^{3} c^{4} - 1658 \, A b^{2} c^{5}\right)} d^{8} e^{3} + 24 \, {\left(439 \, B b^{4} c^{3} + 316 \, A b^{3} c^{4}\right)} d^{7} e^{4} + 48 \, {\left(1207 \, B b^{5} c^{2} - 2785 \, A b^{4} c^{3}\right)} d^{6} e^{5} - 33 \, {\left(1305 \, B b^{6} c - 5126 \, A b^{5} c^{2}\right)} d^{5} e^{6} + {\left(9905 \, B b^{7} - 89403 \, A b^{6} c\right)} d^{4} e^{7}\right)} x^{4} - 4 \, {\left(6912 \, A b^{7} d^{4} e^{7} + 672 \, {\left(11 \, B b c^{6} + 10 \, A c^{7}\right)} d^{11} - 14448 \, {\left(3 \, B b^{2} c^{5} + 2 \, A b c^{6}\right)} d^{10} e + 4 \, {\left(25775 \, B b^{3} c^{4} + 9282 \, A b^{2} c^{5}\right)} d^{9} e^{2} - 12 \, {\left(9883 \, B b^{4} c^{3} + 187 \, A b^{3} c^{4}\right)} d^{8} e^{3} + 3 \, {\left(24291 \, B b^{5} c^{2} - 16846 \, A b^{4} c^{3}\right)} d^{7} e^{4} - {\left(25265 \, B b^{6} c - 65643 \, A b^{5} c^{2}\right)} d^{6} e^{5} + 15 \, {\left(256 \, B b^{7} - 2315 \, A b^{6} c\right)} d^{5} e^{6}\right)} x^{3} - 7 \, {\left(3597 \, A b^{7} d^{5} e^{6} + 192 \, {\left(B b^{2} c^{5} + 30 \, A b c^{6}\right)} d^{11} - 176 \, {\left(11 \, B b^{3} c^{4} + 186 \, A b^{2} c^{5}\right)} d^{10} e + 8 \, {\left(1237 \, B b^{4} c^{3} + 8718 \, A b^{3} c^{4}\right)} d^{9} e^{2} - 6 \, {\left(2357 \, B b^{5} c^{2} + 13498 \, A b^{4} c^{3}\right)} d^{8} e^{3} + 5 \, {\left(1481 \, B b^{6} c + 11292 \, A b^{5} c^{2}\right)} d^{7} e^{4} - {\left(1415 \, B b^{7} + 21837 \, A b^{6} c\right)} d^{6} e^{5}\right)} x^{2} + 70 \, {\left(90 \, A b^{7} d^{6} e^{5} + 24 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{11} - 4 \, {\left(71 \, B b^{4} c^{3} - 150 \, A b^{3} c^{4}\right)} d^{10} e + 3 \, {\left(155 \, B b^{5} c^{2} - 438 \, A b^{4} c^{3}\right)} d^{9} e^{2} - 3 \, {\left(85 \, B b^{6} c - 397 \, A b^{5} c^{2}\right)} d^{8} e^{3} + {\left(50 \, B b^{7} - 519 \, A b^{6} c\right)} d^{7} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{107520 \, {\left(c^{6} d^{19} - 6 \, b c^{5} d^{18} e + 15 \, b^{2} c^{4} d^{17} e^{2} - 20 \, b^{3} c^{3} d^{16} e^{3} + 15 \, b^{4} c^{2} d^{15} e^{4} - 6 \, b^{5} c d^{14} e^{5} + b^{6} d^{13} e^{6} + {\left(c^{6} d^{12} e^{7} - 6 \, b c^{5} d^{11} e^{8} + 15 \, b^{2} c^{4} d^{10} e^{9} - 20 \, b^{3} c^{3} d^{9} e^{10} + 15 \, b^{4} c^{2} d^{8} e^{11} - 6 \, b^{5} c d^{7} e^{12} + b^{6} d^{6} e^{13}\right)} x^{7} + 7 \, {\left(c^{6} d^{13} e^{6} - 6 \, b c^{5} d^{12} e^{7} + 15 \, b^{2} c^{4} d^{11} e^{8} - 20 \, b^{3} c^{3} d^{10} e^{9} + 15 \, b^{4} c^{2} d^{9} e^{10} - 6 \, b^{5} c d^{8} e^{11} + b^{6} d^{7} e^{12}\right)} x^{6} + 21 \, {\left(c^{6} d^{14} e^{5} - 6 \, b c^{5} d^{13} e^{6} + 15 \, b^{2} c^{4} d^{12} e^{7} - 20 \, b^{3} c^{3} d^{11} e^{8} + 15 \, b^{4} c^{2} d^{10} e^{9} - 6 \, b^{5} c d^{9} e^{10} + b^{6} d^{8} e^{11}\right)} x^{5} + 35 \, {\left(c^{6} d^{15} e^{4} - 6 \, b c^{5} d^{14} e^{5} + 15 \, b^{2} c^{4} d^{13} e^{6} - 20 \, b^{3} c^{3} d^{12} e^{7} + 15 \, b^{4} c^{2} d^{11} e^{8} - 6 \, b^{5} c d^{10} e^{9} + b^{6} d^{9} e^{10}\right)} x^{4} + 35 \, {\left(c^{6} d^{16} e^{3} - 6 \, b c^{5} d^{15} e^{4} + 15 \, b^{2} c^{4} d^{14} e^{5} - 20 \, b^{3} c^{3} d^{13} e^{6} + 15 \, b^{4} c^{2} d^{12} e^{7} - 6 \, b^{5} c d^{11} e^{8} + b^{6} d^{10} e^{9}\right)} x^{3} + 21 \, {\left(c^{6} d^{17} e^{2} - 6 \, b c^{5} d^{16} e^{3} + 15 \, b^{2} c^{4} d^{15} e^{4} - 20 \, b^{3} c^{3} d^{14} e^{5} + 15 \, b^{4} c^{2} d^{13} e^{6} - 6 \, b^{5} c d^{12} e^{7} + b^{6} d^{11} e^{8}\right)} x^{2} + 7 \, {\left(c^{6} d^{18} e - 6 \, b c^{5} d^{17} e^{2} + 15 \, b^{2} c^{4} d^{16} e^{3} - 20 \, b^{3} c^{3} d^{15} e^{4} + 15 \, b^{4} c^{2} d^{14} e^{5} - 6 \, b^{5} c d^{13} e^{6} + b^{6} d^{12} e^{7}\right)} x\right)}}\right]"," ",0,"[-1/215040*(105*(9*A*b^7*d^7*e^3 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^10 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^9*e + (5*B*b^7 - 42*A*b^6*c)*d^8*e^2 + (9*A*b^7*e^10 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^3*e^7 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^2*e^8 + (5*B*b^7 - 42*A*b^6*c)*d*e^9)*x^7 + 7*(9*A*b^7*d*e^9 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^4*e^6 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^3*e^7 + (5*B*b^7 - 42*A*b^6*c)*d^2*e^8)*x^6 + 21*(9*A*b^7*d^2*e^8 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^5*e^5 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^4*e^6 + (5*B*b^7 - 42*A*b^6*c)*d^3*e^7)*x^5 + 35*(9*A*b^7*d^3*e^7 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^6*e^4 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^5*e^5 + (5*B*b^7 - 42*A*b^6*c)*d^4*e^6)*x^4 + 35*(9*A*b^7*d^4*e^6 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^7*e^3 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^6*e^4 + (5*B*b^7 - 42*A*b^6*c)*d^5*e^5)*x^3 + 21*(9*A*b^7*d^5*e^5 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^8*e^2 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^7*e^3 + (5*B*b^7 - 42*A*b^6*c)*d^6*e^4)*x^2 + 7*(9*A*b^7*d^6*e^4 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^9*e - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^8*e^2 + (5*B*b^7 - 42*A*b^6*c)*d^7*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(945*A*b^7*d^7*e^4 - 2520*(B*b^4*c^3 - 2*A*b^3*c^4)*d^11 + 420*(11*B*b^5*c^2 - 30*A*b^4*c^3)*d^10*e - 105*(25*B*b^6*c - 114*A*b^5*c^2)*d^9*e^2 + 105*(5*B*b^7 - 51*A*b^6*c)*d^8*e^3 - (1024*B*c^7*d^9*e^2 + 945*A*b^7*d*e^10 - 384*(13*B*b*c^6 - 2*A*c^7)*d^8*e^3 + 384*(23*B*b^2*c^5 - 8*A*b*c^6)*d^7*e^4 - 96*(59*B*b^3*c^4 - 34*A*b^2*c^5)*d^6*e^5 - 120*(5*B*b^4*c^3 - 8*A*b^3*c^4)*d^5*e^6 + 6*(525*B*b^5*c^2 - 1174*A*b^4*c^3)*d^4*e^7 - 7*(325*B*b^6*c - 1272*A*b^5*c^2)*d^3*e^8 + 525*(B*b^7 - 9*A*b^6*c)*d^2*e^9)*x^6 - 2*(3584*B*c^7*d^10*e + 3150*A*b^7*d^2*e^9 - 64*(277*B*b*c^6 - 42*A*c^7)*d^9*e^2 + 96*(335*B*b^2*c^5 - 114*A*b*c^6)*d^8*e^3 - 48*(459*B*b^3*c^4 - 254*A*b^2*c^5)*d^7*e^4 - 12*(57*B*b^4*c^3 - 212*A*b^3*c^4)*d^6*e^5 + 3*(3515*B*b^5*c^2 - 7878*A*b^4*c^3)*d^5*e^6 - 5*(1519*B*b^6*c - 5955*A*b^5*c^2)*d^4*e^7 + 7*(250*B*b^7 - 2253*A*b^6*c)*d^3*e^8)*x^5 - (21504*B*c^7*d^11 + 17829*A*b^7*d^3*e^8 - 896*(121*B*b*c^6 - 18*A*c^7)*d^10*e + 192*(1059*B*b^2*c^5 - 350*A*b*c^6)*d^9*e^2 - 48*(3161*B*b^3*c^4 - 1658*A*b^2*c^5)*d^8*e^3 + 24*(439*B*b^4*c^3 + 316*A*b^3*c^4)*d^7*e^4 + 48*(1207*B*b^5*c^2 - 2785*A*b^4*c^3)*d^6*e^5 - 33*(1305*B*b^6*c - 5126*A*b^5*c^2)*d^5*e^6 + (9905*B*b^7 - 89403*A*b^6*c)*d^4*e^7)*x^4 - 4*(6912*A*b^7*d^4*e^7 + 672*(11*B*b*c^6 + 10*A*c^7)*d^11 - 14448*(3*B*b^2*c^5 + 2*A*b*c^6)*d^10*e + 4*(25775*B*b^3*c^4 + 9282*A*b^2*c^5)*d^9*e^2 - 12*(9883*B*b^4*c^3 + 187*A*b^3*c^4)*d^8*e^3 + 3*(24291*B*b^5*c^2 - 16846*A*b^4*c^3)*d^7*e^4 - (25265*B*b^6*c - 65643*A*b^5*c^2)*d^6*e^5 + 15*(256*B*b^7 - 2315*A*b^6*c)*d^5*e^6)*x^3 - 7*(3597*A*b^7*d^5*e^6 + 192*(B*b^2*c^5 + 30*A*b*c^6)*d^11 - 176*(11*B*b^3*c^4 + 186*A*b^2*c^5)*d^10*e + 8*(1237*B*b^4*c^3 + 8718*A*b^3*c^4)*d^9*e^2 - 6*(2357*B*b^5*c^2 + 13498*A*b^4*c^3)*d^8*e^3 + 5*(1481*B*b^6*c + 11292*A*b^5*c^2)*d^7*e^4 - (1415*B*b^7 + 21837*A*b^6*c)*d^6*e^5)*x^2 + 70*(90*A*b^7*d^6*e^5 + 24*(B*b^3*c^4 - 2*A*b^2*c^5)*d^11 - 4*(71*B*b^4*c^3 - 150*A*b^3*c^4)*d^10*e + 3*(155*B*b^5*c^2 - 438*A*b^4*c^3)*d^9*e^2 - 3*(85*B*b^6*c - 397*A*b^5*c^2)*d^8*e^3 + (50*B*b^7 - 519*A*b^6*c)*d^7*e^4)*x)*sqrt(c*x^2 + b*x))/(c^6*d^19 - 6*b*c^5*d^18*e + 15*b^2*c^4*d^17*e^2 - 20*b^3*c^3*d^16*e^3 + 15*b^4*c^2*d^15*e^4 - 6*b^5*c*d^14*e^5 + b^6*d^13*e^6 + (c^6*d^12*e^7 - 6*b*c^5*d^11*e^8 + 15*b^2*c^4*d^10*e^9 - 20*b^3*c^3*d^9*e^10 + 15*b^4*c^2*d^8*e^11 - 6*b^5*c*d^7*e^12 + b^6*d^6*e^13)*x^7 + 7*(c^6*d^13*e^6 - 6*b*c^5*d^12*e^7 + 15*b^2*c^4*d^11*e^8 - 20*b^3*c^3*d^10*e^9 + 15*b^4*c^2*d^9*e^10 - 6*b^5*c*d^8*e^11 + b^6*d^7*e^12)*x^6 + 21*(c^6*d^14*e^5 - 6*b*c^5*d^13*e^6 + 15*b^2*c^4*d^12*e^7 - 20*b^3*c^3*d^11*e^8 + 15*b^4*c^2*d^10*e^9 - 6*b^5*c*d^9*e^10 + b^6*d^8*e^11)*x^5 + 35*(c^6*d^15*e^4 - 6*b*c^5*d^14*e^5 + 15*b^2*c^4*d^13*e^6 - 20*b^3*c^3*d^12*e^7 + 15*b^4*c^2*d^11*e^8 - 6*b^5*c*d^10*e^9 + b^6*d^9*e^10)*x^4 + 35*(c^6*d^16*e^3 - 6*b*c^5*d^15*e^4 + 15*b^2*c^4*d^14*e^5 - 20*b^3*c^3*d^13*e^6 + 15*b^4*c^2*d^12*e^7 - 6*b^5*c*d^11*e^8 + b^6*d^10*e^9)*x^3 + 21*(c^6*d^17*e^2 - 6*b*c^5*d^16*e^3 + 15*b^2*c^4*d^15*e^4 - 20*b^3*c^3*d^14*e^5 + 15*b^4*c^2*d^13*e^6 - 6*b^5*c*d^12*e^7 + b^6*d^11*e^8)*x^2 + 7*(c^6*d^18*e - 6*b*c^5*d^17*e^2 + 15*b^2*c^4*d^16*e^3 - 20*b^3*c^3*d^15*e^4 + 15*b^4*c^2*d^14*e^5 - 6*b^5*c*d^13*e^6 + b^6*d^12*e^7)*x), -1/107520*(105*(9*A*b^7*d^7*e^3 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^10 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^9*e + (5*B*b^7 - 42*A*b^6*c)*d^8*e^2 + (9*A*b^7*e^10 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^3*e^7 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^2*e^8 + (5*B*b^7 - 42*A*b^6*c)*d*e^9)*x^7 + 7*(9*A*b^7*d*e^9 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^4*e^6 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^3*e^7 + (5*B*b^7 - 42*A*b^6*c)*d^2*e^8)*x^6 + 21*(9*A*b^7*d^2*e^8 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^5*e^5 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^4*e^6 + (5*B*b^7 - 42*A*b^6*c)*d^3*e^7)*x^5 + 35*(9*A*b^7*d^3*e^7 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^6*e^4 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^5*e^5 + (5*B*b^7 - 42*A*b^6*c)*d^4*e^6)*x^4 + 35*(9*A*b^7*d^4*e^6 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^7*e^3 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^6*e^4 + (5*B*b^7 - 42*A*b^6*c)*d^5*e^5)*x^3 + 21*(9*A*b^7*d^5*e^5 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^8*e^2 - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^7*e^3 + (5*B*b^7 - 42*A*b^6*c)*d^6*e^4)*x^2 + 7*(9*A*b^7*d^6*e^4 + 24*(B*b^5*c^2 - 2*A*b^4*c^3)*d^9*e - 4*(5*B*b^6*c - 18*A*b^5*c^2)*d^8*e^2 + (5*B*b^7 - 42*A*b^6*c)*d^7*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (945*A*b^7*d^7*e^4 - 2520*(B*b^4*c^3 - 2*A*b^3*c^4)*d^11 + 420*(11*B*b^5*c^2 - 30*A*b^4*c^3)*d^10*e - 105*(25*B*b^6*c - 114*A*b^5*c^2)*d^9*e^2 + 105*(5*B*b^7 - 51*A*b^6*c)*d^8*e^3 - (1024*B*c^7*d^9*e^2 + 945*A*b^7*d*e^10 - 384*(13*B*b*c^6 - 2*A*c^7)*d^8*e^3 + 384*(23*B*b^2*c^5 - 8*A*b*c^6)*d^7*e^4 - 96*(59*B*b^3*c^4 - 34*A*b^2*c^5)*d^6*e^5 - 120*(5*B*b^4*c^3 - 8*A*b^3*c^4)*d^5*e^6 + 6*(525*B*b^5*c^2 - 1174*A*b^4*c^3)*d^4*e^7 - 7*(325*B*b^6*c - 1272*A*b^5*c^2)*d^3*e^8 + 525*(B*b^7 - 9*A*b^6*c)*d^2*e^9)*x^6 - 2*(3584*B*c^7*d^10*e + 3150*A*b^7*d^2*e^9 - 64*(277*B*b*c^6 - 42*A*c^7)*d^9*e^2 + 96*(335*B*b^2*c^5 - 114*A*b*c^6)*d^8*e^3 - 48*(459*B*b^3*c^4 - 254*A*b^2*c^5)*d^7*e^4 - 12*(57*B*b^4*c^3 - 212*A*b^3*c^4)*d^6*e^5 + 3*(3515*B*b^5*c^2 - 7878*A*b^4*c^3)*d^5*e^6 - 5*(1519*B*b^6*c - 5955*A*b^5*c^2)*d^4*e^7 + 7*(250*B*b^7 - 2253*A*b^6*c)*d^3*e^8)*x^5 - (21504*B*c^7*d^11 + 17829*A*b^7*d^3*e^8 - 896*(121*B*b*c^6 - 18*A*c^7)*d^10*e + 192*(1059*B*b^2*c^5 - 350*A*b*c^6)*d^9*e^2 - 48*(3161*B*b^3*c^4 - 1658*A*b^2*c^5)*d^8*e^3 + 24*(439*B*b^4*c^3 + 316*A*b^3*c^4)*d^7*e^4 + 48*(1207*B*b^5*c^2 - 2785*A*b^4*c^3)*d^6*e^5 - 33*(1305*B*b^6*c - 5126*A*b^5*c^2)*d^5*e^6 + (9905*B*b^7 - 89403*A*b^6*c)*d^4*e^7)*x^4 - 4*(6912*A*b^7*d^4*e^7 + 672*(11*B*b*c^6 + 10*A*c^7)*d^11 - 14448*(3*B*b^2*c^5 + 2*A*b*c^6)*d^10*e + 4*(25775*B*b^3*c^4 + 9282*A*b^2*c^5)*d^9*e^2 - 12*(9883*B*b^4*c^3 + 187*A*b^3*c^4)*d^8*e^3 + 3*(24291*B*b^5*c^2 - 16846*A*b^4*c^3)*d^7*e^4 - (25265*B*b^6*c - 65643*A*b^5*c^2)*d^6*e^5 + 15*(256*B*b^7 - 2315*A*b^6*c)*d^5*e^6)*x^3 - 7*(3597*A*b^7*d^5*e^6 + 192*(B*b^2*c^5 + 30*A*b*c^6)*d^11 - 176*(11*B*b^3*c^4 + 186*A*b^2*c^5)*d^10*e + 8*(1237*B*b^4*c^3 + 8718*A*b^3*c^4)*d^9*e^2 - 6*(2357*B*b^5*c^2 + 13498*A*b^4*c^3)*d^8*e^3 + 5*(1481*B*b^6*c + 11292*A*b^5*c^2)*d^7*e^4 - (1415*B*b^7 + 21837*A*b^6*c)*d^6*e^5)*x^2 + 70*(90*A*b^7*d^6*e^5 + 24*(B*b^3*c^4 - 2*A*b^2*c^5)*d^11 - 4*(71*B*b^4*c^3 - 150*A*b^3*c^4)*d^10*e + 3*(155*B*b^5*c^2 - 438*A*b^4*c^3)*d^9*e^2 - 3*(85*B*b^6*c - 397*A*b^5*c^2)*d^8*e^3 + (50*B*b^7 - 519*A*b^6*c)*d^7*e^4)*x)*sqrt(c*x^2 + b*x))/(c^6*d^19 - 6*b*c^5*d^18*e + 15*b^2*c^4*d^17*e^2 - 20*b^3*c^3*d^16*e^3 + 15*b^4*c^2*d^15*e^4 - 6*b^5*c*d^14*e^5 + b^6*d^13*e^6 + (c^6*d^12*e^7 - 6*b*c^5*d^11*e^8 + 15*b^2*c^4*d^10*e^9 - 20*b^3*c^3*d^9*e^10 + 15*b^4*c^2*d^8*e^11 - 6*b^5*c*d^7*e^12 + b^6*d^6*e^13)*x^7 + 7*(c^6*d^13*e^6 - 6*b*c^5*d^12*e^7 + 15*b^2*c^4*d^11*e^8 - 20*b^3*c^3*d^10*e^9 + 15*b^4*c^2*d^9*e^10 - 6*b^5*c*d^8*e^11 + b^6*d^7*e^12)*x^6 + 21*(c^6*d^14*e^5 - 6*b*c^5*d^13*e^6 + 15*b^2*c^4*d^12*e^7 - 20*b^3*c^3*d^11*e^8 + 15*b^4*c^2*d^10*e^9 - 6*b^5*c*d^9*e^10 + b^6*d^8*e^11)*x^5 + 35*(c^6*d^15*e^4 - 6*b*c^5*d^14*e^5 + 15*b^2*c^4*d^13*e^6 - 20*b^3*c^3*d^12*e^7 + 15*b^4*c^2*d^11*e^8 - 6*b^5*c*d^10*e^9 + b^6*d^9*e^10)*x^4 + 35*(c^6*d^16*e^3 - 6*b*c^5*d^15*e^4 + 15*b^2*c^4*d^14*e^5 - 20*b^3*c^3*d^13*e^6 + 15*b^4*c^2*d^12*e^7 - 6*b^5*c*d^11*e^8 + b^6*d^10*e^9)*x^3 + 21*(c^6*d^17*e^2 - 6*b*c^5*d^16*e^3 + 15*b^2*c^4*d^15*e^4 - 20*b^3*c^3*d^14*e^5 + 15*b^4*c^2*d^13*e^6 - 6*b^5*c*d^12*e^7 + b^6*d^11*e^8)*x^2 + 7*(c^6*d^18*e - 6*b*c^5*d^17*e^2 + 15*b^2*c^4*d^16*e^3 - 20*b^3*c^3*d^15*e^4 + 15*b^4*c^2*d^14*e^5 - 6*b^5*c*d^13*e^6 + b^6*d^12*e^7)*x)]","B",0
1183,1,1292,0,0.458445," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(32 \, {\left(B b^{7} c^{2} - 2 \, A b^{6} c^{3}\right)} d^{2} - 4 \, {\left(9 \, B b^{8} c - 16 \, A b^{7} c^{2}\right)} d e + {\left(11 \, B b^{9} - 18 \, A b^{8} c\right)} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(229376 \, B c^{9} e^{2} x^{8} + 14336 \, {\left(36 \, B c^{9} d e + {\left(37 \, B b c^{8} + 18 \, A c^{9}\right)} e^{2}\right)} x^{7} + 3072 \, {\left(96 \, B c^{9} d^{2} + 12 \, {\left(33 \, B b c^{8} + 16 \, A c^{9}\right)} d e + {\left(103 \, B b^{2} c^{7} + 198 \, A b c^{8}\right)} e^{2}\right)} x^{6} + 256 \, {\left(96 \, {\left(29 \, B b c^{8} + 14 \, A c^{9}\right)} d^{2} + 12 \, {\left(243 \, B b^{2} c^{7} + 464 \, A b c^{8}\right)} d e + {\left(5 \, B b^{3} c^{6} + 1458 \, A b^{2} c^{7}\right)} e^{2}\right)} x^{5} + 128 \, {\left(96 \, {\left(37 \, B b^{2} c^{7} + 70 \, A b c^{8}\right)} d^{2} + 12 \, {\left(3 \, B b^{3} c^{6} + 592 \, A b^{2} c^{7}\right)} d e - {\left(11 \, B b^{4} c^{5} - 18 \, A b^{3} c^{6}\right)} e^{2}\right)} x^{4} + 144 \, {\left(32 \, {\left(B b^{3} c^{6} + 126 \, A b^{2} c^{7}\right)} d^{2} - 4 \, {\left(9 \, B b^{4} c^{5} - 16 \, A b^{3} c^{6}\right)} d e + {\left(11 \, B b^{5} c^{4} - 18 \, A b^{4} c^{5}\right)} e^{2}\right)} x^{3} - 10080 \, {\left(B b^{6} c^{3} - 2 \, A b^{5} c^{4}\right)} d^{2} + 1260 \, {\left(9 \, B b^{7} c^{2} - 16 \, A b^{6} c^{3}\right)} d e - 315 \, {\left(11 \, B b^{8} c - 18 \, A b^{7} c^{2}\right)} e^{2} - 168 \, {\left(32 \, {\left(B b^{4} c^{5} - 2 \, A b^{3} c^{6}\right)} d^{2} - 4 \, {\left(9 \, B b^{5} c^{4} - 16 \, A b^{4} c^{5}\right)} d e + {\left(11 \, B b^{6} c^{3} - 18 \, A b^{5} c^{4}\right)} e^{2}\right)} x^{2} + 210 \, {\left(32 \, {\left(B b^{5} c^{4} - 2 \, A b^{4} c^{5}\right)} d^{2} - 4 \, {\left(9 \, B b^{6} c^{3} - 16 \, A b^{5} c^{4}\right)} d e + {\left(11 \, B b^{7} c^{2} - 18 \, A b^{6} c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{4128768 \, c^{7}}, -\frac{315 \, {\left(32 \, {\left(B b^{7} c^{2} - 2 \, A b^{6} c^{3}\right)} d^{2} - 4 \, {\left(9 \, B b^{8} c - 16 \, A b^{7} c^{2}\right)} d e + {\left(11 \, B b^{9} - 18 \, A b^{8} c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(229376 \, B c^{9} e^{2} x^{8} + 14336 \, {\left(36 \, B c^{9} d e + {\left(37 \, B b c^{8} + 18 \, A c^{9}\right)} e^{2}\right)} x^{7} + 3072 \, {\left(96 \, B c^{9} d^{2} + 12 \, {\left(33 \, B b c^{8} + 16 \, A c^{9}\right)} d e + {\left(103 \, B b^{2} c^{7} + 198 \, A b c^{8}\right)} e^{2}\right)} x^{6} + 256 \, {\left(96 \, {\left(29 \, B b c^{8} + 14 \, A c^{9}\right)} d^{2} + 12 \, {\left(243 \, B b^{2} c^{7} + 464 \, A b c^{8}\right)} d e + {\left(5 \, B b^{3} c^{6} + 1458 \, A b^{2} c^{7}\right)} e^{2}\right)} x^{5} + 128 \, {\left(96 \, {\left(37 \, B b^{2} c^{7} + 70 \, A b c^{8}\right)} d^{2} + 12 \, {\left(3 \, B b^{3} c^{6} + 592 \, A b^{2} c^{7}\right)} d e - {\left(11 \, B b^{4} c^{5} - 18 \, A b^{3} c^{6}\right)} e^{2}\right)} x^{4} + 144 \, {\left(32 \, {\left(B b^{3} c^{6} + 126 \, A b^{2} c^{7}\right)} d^{2} - 4 \, {\left(9 \, B b^{4} c^{5} - 16 \, A b^{3} c^{6}\right)} d e + {\left(11 \, B b^{5} c^{4} - 18 \, A b^{4} c^{5}\right)} e^{2}\right)} x^{3} - 10080 \, {\left(B b^{6} c^{3} - 2 \, A b^{5} c^{4}\right)} d^{2} + 1260 \, {\left(9 \, B b^{7} c^{2} - 16 \, A b^{6} c^{3}\right)} d e - 315 \, {\left(11 \, B b^{8} c - 18 \, A b^{7} c^{2}\right)} e^{2} - 168 \, {\left(32 \, {\left(B b^{4} c^{5} - 2 \, A b^{3} c^{6}\right)} d^{2} - 4 \, {\left(9 \, B b^{5} c^{4} - 16 \, A b^{4} c^{5}\right)} d e + {\left(11 \, B b^{6} c^{3} - 18 \, A b^{5} c^{4}\right)} e^{2}\right)} x^{2} + 210 \, {\left(32 \, {\left(B b^{5} c^{4} - 2 \, A b^{4} c^{5}\right)} d^{2} - 4 \, {\left(9 \, B b^{6} c^{3} - 16 \, A b^{5} c^{4}\right)} d e + {\left(11 \, B b^{7} c^{2} - 18 \, A b^{6} c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{2064384 \, c^{7}}\right]"," ",0,"[1/4128768*(315*(32*(B*b^7*c^2 - 2*A*b^6*c^3)*d^2 - 4*(9*B*b^8*c - 16*A*b^7*c^2)*d*e + (11*B*b^9 - 18*A*b^8*c)*e^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(229376*B*c^9*e^2*x^8 + 14336*(36*B*c^9*d*e + (37*B*b*c^8 + 18*A*c^9)*e^2)*x^7 + 3072*(96*B*c^9*d^2 + 12*(33*B*b*c^8 + 16*A*c^9)*d*e + (103*B*b^2*c^7 + 198*A*b*c^8)*e^2)*x^6 + 256*(96*(29*B*b*c^8 + 14*A*c^9)*d^2 + 12*(243*B*b^2*c^7 + 464*A*b*c^8)*d*e + (5*B*b^3*c^6 + 1458*A*b^2*c^7)*e^2)*x^5 + 128*(96*(37*B*b^2*c^7 + 70*A*b*c^8)*d^2 + 12*(3*B*b^3*c^6 + 592*A*b^2*c^7)*d*e - (11*B*b^4*c^5 - 18*A*b^3*c^6)*e^2)*x^4 + 144*(32*(B*b^3*c^6 + 126*A*b^2*c^7)*d^2 - 4*(9*B*b^4*c^5 - 16*A*b^3*c^6)*d*e + (11*B*b^5*c^4 - 18*A*b^4*c^5)*e^2)*x^3 - 10080*(B*b^6*c^3 - 2*A*b^5*c^4)*d^2 + 1260*(9*B*b^7*c^2 - 16*A*b^6*c^3)*d*e - 315*(11*B*b^8*c - 18*A*b^7*c^2)*e^2 - 168*(32*(B*b^4*c^5 - 2*A*b^3*c^6)*d^2 - 4*(9*B*b^5*c^4 - 16*A*b^4*c^5)*d*e + (11*B*b^6*c^3 - 18*A*b^5*c^4)*e^2)*x^2 + 210*(32*(B*b^5*c^4 - 2*A*b^4*c^5)*d^2 - 4*(9*B*b^6*c^3 - 16*A*b^5*c^4)*d*e + (11*B*b^7*c^2 - 18*A*b^6*c^3)*e^2)*x)*sqrt(c*x^2 + b*x))/c^7, -1/2064384*(315*(32*(B*b^7*c^2 - 2*A*b^6*c^3)*d^2 - 4*(9*B*b^8*c - 16*A*b^7*c^2)*d*e + (11*B*b^9 - 18*A*b^8*c)*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (229376*B*c^9*e^2*x^8 + 14336*(36*B*c^9*d*e + (37*B*b*c^8 + 18*A*c^9)*e^2)*x^7 + 3072*(96*B*c^9*d^2 + 12*(33*B*b*c^8 + 16*A*c^9)*d*e + (103*B*b^2*c^7 + 198*A*b*c^8)*e^2)*x^6 + 256*(96*(29*B*b*c^8 + 14*A*c^9)*d^2 + 12*(243*B*b^2*c^7 + 464*A*b*c^8)*d*e + (5*B*b^3*c^6 + 1458*A*b^2*c^7)*e^2)*x^5 + 128*(96*(37*B*b^2*c^7 + 70*A*b*c^8)*d^2 + 12*(3*B*b^3*c^6 + 592*A*b^2*c^7)*d*e - (11*B*b^4*c^5 - 18*A*b^3*c^6)*e^2)*x^4 + 144*(32*(B*b^3*c^6 + 126*A*b^2*c^7)*d^2 - 4*(9*B*b^4*c^5 - 16*A*b^3*c^6)*d*e + (11*B*b^5*c^4 - 18*A*b^4*c^5)*e^2)*x^3 - 10080*(B*b^6*c^3 - 2*A*b^5*c^4)*d^2 + 1260*(9*B*b^7*c^2 - 16*A*b^6*c^3)*d*e - 315*(11*B*b^8*c - 18*A*b^7*c^2)*e^2 - 168*(32*(B*b^4*c^5 - 2*A*b^3*c^6)*d^2 - 4*(9*B*b^5*c^4 - 16*A*b^4*c^5)*d*e + (11*B*b^6*c^3 - 18*A*b^5*c^4)*e^2)*x^2 + 210*(32*(B*b^5*c^4 - 2*A*b^4*c^5)*d^2 - 4*(9*B*b^6*c^3 - 16*A*b^5*c^4)*d*e + (11*B*b^7*c^2 - 18*A*b^6*c^3)*e^2)*x)*sqrt(c*x^2 + b*x))/c^7]","A",0
1184,1,802,0,0.454763," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(16 \, {\left(B b^{7} c - 2 \, A b^{6} c^{2}\right)} d - {\left(9 \, B b^{8} - 16 \, A b^{7} c\right)} e\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(43008 \, B c^{8} e x^{7} + 3072 \, {\left(16 \, B c^{8} d + {\left(33 \, B b c^{7} + 16 \, A c^{8}\right)} e\right)} x^{6} + 256 \, {\left(16 \, {\left(29 \, B b c^{7} + 14 \, A c^{8}\right)} d + {\left(243 \, B b^{2} c^{6} + 464 \, A b c^{7}\right)} e\right)} x^{5} + 128 \, {\left(16 \, {\left(37 \, B b^{2} c^{6} + 70 \, A b c^{7}\right)} d + {\left(3 \, B b^{3} c^{5} + 592 \, A b^{2} c^{6}\right)} e\right)} x^{4} + 48 \, {\left(16 \, {\left(B b^{3} c^{5} + 126 \, A b^{2} c^{6}\right)} d - {\left(9 \, B b^{4} c^{4} - 16 \, A b^{3} c^{5}\right)} e\right)} x^{3} - 56 \, {\left(16 \, {\left(B b^{4} c^{4} - 2 \, A b^{3} c^{5}\right)} d - {\left(9 \, B b^{5} c^{3} - 16 \, A b^{4} c^{4}\right)} e\right)} x^{2} - 1680 \, {\left(B b^{6} c^{2} - 2 \, A b^{5} c^{3}\right)} d + 105 \, {\left(9 \, B b^{7} c - 16 \, A b^{6} c^{2}\right)} e + 70 \, {\left(16 \, {\left(B b^{5} c^{3} - 2 \, A b^{4} c^{4}\right)} d - {\left(9 \, B b^{6} c^{2} - 16 \, A b^{5} c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x}}{688128 \, c^{6}}, -\frac{105 \, {\left(16 \, {\left(B b^{7} c - 2 \, A b^{6} c^{2}\right)} d - {\left(9 \, B b^{8} - 16 \, A b^{7} c\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(43008 \, B c^{8} e x^{7} + 3072 \, {\left(16 \, B c^{8} d + {\left(33 \, B b c^{7} + 16 \, A c^{8}\right)} e\right)} x^{6} + 256 \, {\left(16 \, {\left(29 \, B b c^{7} + 14 \, A c^{8}\right)} d + {\left(243 \, B b^{2} c^{6} + 464 \, A b c^{7}\right)} e\right)} x^{5} + 128 \, {\left(16 \, {\left(37 \, B b^{2} c^{6} + 70 \, A b c^{7}\right)} d + {\left(3 \, B b^{3} c^{5} + 592 \, A b^{2} c^{6}\right)} e\right)} x^{4} + 48 \, {\left(16 \, {\left(B b^{3} c^{5} + 126 \, A b^{2} c^{6}\right)} d - {\left(9 \, B b^{4} c^{4} - 16 \, A b^{3} c^{5}\right)} e\right)} x^{3} - 56 \, {\left(16 \, {\left(B b^{4} c^{4} - 2 \, A b^{3} c^{5}\right)} d - {\left(9 \, B b^{5} c^{3} - 16 \, A b^{4} c^{4}\right)} e\right)} x^{2} - 1680 \, {\left(B b^{6} c^{2} - 2 \, A b^{5} c^{3}\right)} d + 105 \, {\left(9 \, B b^{7} c - 16 \, A b^{6} c^{2}\right)} e + 70 \, {\left(16 \, {\left(B b^{5} c^{3} - 2 \, A b^{4} c^{4}\right)} d - {\left(9 \, B b^{6} c^{2} - 16 \, A b^{5} c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x}}{344064 \, c^{6}}\right]"," ",0,"[1/688128*(105*(16*(B*b^7*c - 2*A*b^6*c^2)*d - (9*B*b^8 - 16*A*b^7*c)*e)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(43008*B*c^8*e*x^7 + 3072*(16*B*c^8*d + (33*B*b*c^7 + 16*A*c^8)*e)*x^6 + 256*(16*(29*B*b*c^7 + 14*A*c^8)*d + (243*B*b^2*c^6 + 464*A*b*c^7)*e)*x^5 + 128*(16*(37*B*b^2*c^6 + 70*A*b*c^7)*d + (3*B*b^3*c^5 + 592*A*b^2*c^6)*e)*x^4 + 48*(16*(B*b^3*c^5 + 126*A*b^2*c^6)*d - (9*B*b^4*c^4 - 16*A*b^3*c^5)*e)*x^3 - 56*(16*(B*b^4*c^4 - 2*A*b^3*c^5)*d - (9*B*b^5*c^3 - 16*A*b^4*c^4)*e)*x^2 - 1680*(B*b^6*c^2 - 2*A*b^5*c^3)*d + 105*(9*B*b^7*c - 16*A*b^6*c^2)*e + 70*(16*(B*b^5*c^3 - 2*A*b^4*c^4)*d - (9*B*b^6*c^2 - 16*A*b^5*c^3)*e)*x)*sqrt(c*x^2 + b*x))/c^6, -1/344064*(105*(16*(B*b^7*c - 2*A*b^6*c^2)*d - (9*B*b^8 - 16*A*b^7*c)*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (43008*B*c^8*e*x^7 + 3072*(16*B*c^8*d + (33*B*b*c^7 + 16*A*c^8)*e)*x^6 + 256*(16*(29*B*b*c^7 + 14*A*c^8)*d + (243*B*b^2*c^6 + 464*A*b*c^7)*e)*x^5 + 128*(16*(37*B*b^2*c^6 + 70*A*b*c^7)*d + (3*B*b^3*c^5 + 592*A*b^2*c^6)*e)*x^4 + 48*(16*(B*b^3*c^5 + 126*A*b^2*c^6)*d - (9*B*b^4*c^4 - 16*A*b^3*c^5)*e)*x^3 - 56*(16*(B*b^4*c^4 - 2*A*b^3*c^5)*d - (9*B*b^5*c^3 - 16*A*b^4*c^4)*e)*x^2 - 1680*(B*b^6*c^2 - 2*A*b^5*c^3)*d + 105*(9*B*b^7*c - 16*A*b^6*c^2)*e + 70*(16*(B*b^5*c^3 - 2*A*b^4*c^4)*d - (9*B*b^6*c^2 - 16*A*b^5*c^3)*e)*x)*sqrt(c*x^2 + b*x))/c^6]","A",0
1185,1,392,0,0.433366," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B b^{7} - 2 \, A b^{6} c\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(3072 \, B c^{7} x^{6} - 105 \, B b^{6} c + 210 \, A b^{5} c^{2} + 256 \, {\left(29 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 128 \, {\left(37 \, B b^{2} c^{5} + 70 \, A b c^{6}\right)} x^{4} + 48 \, {\left(B b^{3} c^{4} + 126 \, A b^{2} c^{5}\right)} x^{3} - 56 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} x^{2} + 70 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{43008 \, c^{5}}, -\frac{105 \, {\left(B b^{7} - 2 \, A b^{6} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(3072 \, B c^{7} x^{6} - 105 \, B b^{6} c + 210 \, A b^{5} c^{2} + 256 \, {\left(29 \, B b c^{6} + 14 \, A c^{7}\right)} x^{5} + 128 \, {\left(37 \, B b^{2} c^{5} + 70 \, A b c^{6}\right)} x^{4} + 48 \, {\left(B b^{3} c^{4} + 126 \, A b^{2} c^{5}\right)} x^{3} - 56 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} x^{2} + 70 \, {\left(B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{21504 \, c^{5}}\right]"," ",0,"[-1/43008*(105*(B*b^7 - 2*A*b^6*c)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(3072*B*c^7*x^6 - 105*B*b^6*c + 210*A*b^5*c^2 + 256*(29*B*b*c^6 + 14*A*c^7)*x^5 + 128*(37*B*b^2*c^5 + 70*A*b*c^6)*x^4 + 48*(B*b^3*c^4 + 126*A*b^2*c^5)*x^3 - 56*(B*b^4*c^3 - 2*A*b^3*c^4)*x^2 + 70*(B*b^5*c^2 - 2*A*b^4*c^3)*x)*sqrt(c*x^2 + b*x))/c^5, -1/21504*(105*(B*b^7 - 2*A*b^6*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (3072*B*c^7*x^6 - 105*B*b^6*c + 210*A*b^5*c^2 + 256*(29*B*b*c^6 + 14*A*c^7)*x^5 + 128*(37*B*b^2*c^5 + 70*A*b*c^6)*x^4 + 48*(B*b^3*c^4 + 126*A*b^2*c^5)*x^3 - 56*(B*b^4*c^3 - 2*A*b^3*c^4)*x^2 + 70*(B*b^5*c^2 - 2*A*b^4*c^3)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
1186,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1187,1,3709,0,77.268748," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(1536 \, B c^{5} d^{6} - 640 \, {\left(5 \, B b c^{4} + 2 \, A c^{5}\right)} d^{5} e + 640 \, {\left(3 \, B b^{2} c^{3} + 4 \, A b c^{4}\right)} d^{4} e^{2} - 240 \, {\left(B b^{3} c^{2} + 6 \, A b^{2} c^{3}\right)} d^{3} e^{3} - 20 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d^{2} e^{4} - {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} d e^{5} + {\left(1536 \, B c^{5} d^{5} e - 640 \, {\left(5 \, B b c^{4} + 2 \, A c^{5}\right)} d^{4} e^{2} + 640 \, {\left(3 \, B b^{2} c^{3} + 4 \, A b c^{4}\right)} d^{3} e^{3} - 240 \, {\left(B b^{3} c^{2} + 6 \, A b^{2} c^{3}\right)} d^{2} e^{4} - 20 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d e^{5} - {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} e^{6}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 1920 \, {\left(12 \, B c^{5} d^{5} - 5 \, A b^{2} c^{3} d^{2} e^{3} - {\left(19 \, B b c^{4} + 10 \, A c^{5}\right)} d^{4} e + {\left(7 \, B b^{2} c^{3} + 15 \, A b c^{4}\right)} d^{3} e^{2} + {\left(12 \, B c^{5} d^{4} e - 5 \, A b^{2} c^{3} d e^{4} - {\left(19 \, B b c^{4} + 10 \, A c^{5}\right)} d^{3} e^{2} + {\left(7 \, B b^{2} c^{3} + 15 \, A b c^{4}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(384 \, B c^{5} e^{6} x^{5} + 11520 \, B c^{5} d^{5} e - 1920 \, {\left(11 \, B b c^{4} + 5 \, A c^{5}\right)} d^{4} e^{2} + 240 \, {\left(41 \, B b^{2} c^{3} + 70 \, A b c^{4}\right)} d^{3} e^{3} - 300 \, {\left(B b^{3} c^{2} + 24 \, A b^{2} c^{3}\right)} d^{2} e^{4} - 15 \, {\left(3 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} d e^{5} - 48 \, {\left(12 \, B c^{5} d e^{5} - {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} e^{6}\right)} x^{4} + 8 \, {\left(120 \, B c^{5} d^{2} e^{4} - 2 \, {\left(107 \, B b c^{4} + 50 \, A c^{5}\right)} d e^{5} + {\left(93 \, B b^{2} c^{3} + 170 \, A b c^{4}\right)} e^{6}\right)} x^{3} - 2 \, {\left(960 \, B c^{5} d^{3} e^{3} - 160 \, {\left(11 \, B b c^{4} + 5 \, A c^{5}\right)} d^{2} e^{4} + 8 \, {\left(101 \, B b^{2} c^{3} + 175 \, A b c^{4}\right)} d e^{5} - 5 \, {\left(3 \, B b^{3} c^{2} + 118 \, A b^{2} c^{3}\right)} e^{6}\right)} x^{2} + 5 \, {\left(1152 \, B c^{5} d^{4} e^{2} - 96 \, {\left(23 \, B b c^{4} + 10 \, A c^{5}\right)} d^{3} e^{3} + 8 \, {\left(139 \, B b^{2} c^{3} + 220 \, A b c^{4}\right)} d^{2} e^{4} - 2 \, {\left(27 \, B b^{3} c^{2} + 410 \, A b^{2} c^{3}\right)} d e^{5} - 3 \, {\left(3 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, {\left(c^{3} e^{8} x + c^{3} d e^{7}\right)}}, \frac{3840 \, {\left(12 \, B c^{5} d^{5} - 5 \, A b^{2} c^{3} d^{2} e^{3} - {\left(19 \, B b c^{4} + 10 \, A c^{5}\right)} d^{4} e + {\left(7 \, B b^{2} c^{3} + 15 \, A b c^{4}\right)} d^{3} e^{2} + {\left(12 \, B c^{5} d^{4} e - 5 \, A b^{2} c^{3} d e^{4} - {\left(19 \, B b c^{4} + 10 \, A c^{5}\right)} d^{3} e^{2} + {\left(7 \, B b^{2} c^{3} + 15 \, A b c^{4}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 15 \, {\left(1536 \, B c^{5} d^{6} - 640 \, {\left(5 \, B b c^{4} + 2 \, A c^{5}\right)} d^{5} e + 640 \, {\left(3 \, B b^{2} c^{3} + 4 \, A b c^{4}\right)} d^{4} e^{2} - 240 \, {\left(B b^{3} c^{2} + 6 \, A b^{2} c^{3}\right)} d^{3} e^{3} - 20 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d^{2} e^{4} - {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} d e^{5} + {\left(1536 \, B c^{5} d^{5} e - 640 \, {\left(5 \, B b c^{4} + 2 \, A c^{5}\right)} d^{4} e^{2} + 640 \, {\left(3 \, B b^{2} c^{3} + 4 \, A b c^{4}\right)} d^{3} e^{3} - 240 \, {\left(B b^{3} c^{2} + 6 \, A b^{2} c^{3}\right)} d^{2} e^{4} - 20 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d e^{5} - {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} e^{6}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(384 \, B c^{5} e^{6} x^{5} + 11520 \, B c^{5} d^{5} e - 1920 \, {\left(11 \, B b c^{4} + 5 \, A c^{5}\right)} d^{4} e^{2} + 240 \, {\left(41 \, B b^{2} c^{3} + 70 \, A b c^{4}\right)} d^{3} e^{3} - 300 \, {\left(B b^{3} c^{2} + 24 \, A b^{2} c^{3}\right)} d^{2} e^{4} - 15 \, {\left(3 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} d e^{5} - 48 \, {\left(12 \, B c^{5} d e^{5} - {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} e^{6}\right)} x^{4} + 8 \, {\left(120 \, B c^{5} d^{2} e^{4} - 2 \, {\left(107 \, B b c^{4} + 50 \, A c^{5}\right)} d e^{5} + {\left(93 \, B b^{2} c^{3} + 170 \, A b c^{4}\right)} e^{6}\right)} x^{3} - 2 \, {\left(960 \, B c^{5} d^{3} e^{3} - 160 \, {\left(11 \, B b c^{4} + 5 \, A c^{5}\right)} d^{2} e^{4} + 8 \, {\left(101 \, B b^{2} c^{3} + 175 \, A b c^{4}\right)} d e^{5} - 5 \, {\left(3 \, B b^{3} c^{2} + 118 \, A b^{2} c^{3}\right)} e^{6}\right)} x^{2} + 5 \, {\left(1152 \, B c^{5} d^{4} e^{2} - 96 \, {\left(23 \, B b c^{4} + 10 \, A c^{5}\right)} d^{3} e^{3} + 8 \, {\left(139 \, B b^{2} c^{3} + 220 \, A b c^{4}\right)} d^{2} e^{4} - 2 \, {\left(27 \, B b^{3} c^{2} + 410 \, A b^{2} c^{3}\right)} d e^{5} - 3 \, {\left(3 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, {\left(c^{3} e^{8} x + c^{3} d e^{7}\right)}}, \frac{15 \, {\left(1536 \, B c^{5} d^{6} - 640 \, {\left(5 \, B b c^{4} + 2 \, A c^{5}\right)} d^{5} e + 640 \, {\left(3 \, B b^{2} c^{3} + 4 \, A b c^{4}\right)} d^{4} e^{2} - 240 \, {\left(B b^{3} c^{2} + 6 \, A b^{2} c^{3}\right)} d^{3} e^{3} - 20 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d^{2} e^{4} - {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} d e^{5} + {\left(1536 \, B c^{5} d^{5} e - 640 \, {\left(5 \, B b c^{4} + 2 \, A c^{5}\right)} d^{4} e^{2} + 640 \, {\left(3 \, B b^{2} c^{3} + 4 \, A b c^{4}\right)} d^{3} e^{3} - 240 \, {\left(B b^{3} c^{2} + 6 \, A b^{2} c^{3}\right)} d^{2} e^{4} - 20 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d e^{5} - {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} e^{6}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - 960 \, {\left(12 \, B c^{5} d^{5} - 5 \, A b^{2} c^{3} d^{2} e^{3} - {\left(19 \, B b c^{4} + 10 \, A c^{5}\right)} d^{4} e + {\left(7 \, B b^{2} c^{3} + 15 \, A b c^{4}\right)} d^{3} e^{2} + {\left(12 \, B c^{5} d^{4} e - 5 \, A b^{2} c^{3} d e^{4} - {\left(19 \, B b c^{4} + 10 \, A c^{5}\right)} d^{3} e^{2} + {\left(7 \, B b^{2} c^{3} + 15 \, A b c^{4}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + {\left(384 \, B c^{5} e^{6} x^{5} + 11520 \, B c^{5} d^{5} e - 1920 \, {\left(11 \, B b c^{4} + 5 \, A c^{5}\right)} d^{4} e^{2} + 240 \, {\left(41 \, B b^{2} c^{3} + 70 \, A b c^{4}\right)} d^{3} e^{3} - 300 \, {\left(B b^{3} c^{2} + 24 \, A b^{2} c^{3}\right)} d^{2} e^{4} - 15 \, {\left(3 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} d e^{5} - 48 \, {\left(12 \, B c^{5} d e^{5} - {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} e^{6}\right)} x^{4} + 8 \, {\left(120 \, B c^{5} d^{2} e^{4} - 2 \, {\left(107 \, B b c^{4} + 50 \, A c^{5}\right)} d e^{5} + {\left(93 \, B b^{2} c^{3} + 170 \, A b c^{4}\right)} e^{6}\right)} x^{3} - 2 \, {\left(960 \, B c^{5} d^{3} e^{3} - 160 \, {\left(11 \, B b c^{4} + 5 \, A c^{5}\right)} d^{2} e^{4} + 8 \, {\left(101 \, B b^{2} c^{3} + 175 \, A b c^{4}\right)} d e^{5} - 5 \, {\left(3 \, B b^{3} c^{2} + 118 \, A b^{2} c^{3}\right)} e^{6}\right)} x^{2} + 5 \, {\left(1152 \, B c^{5} d^{4} e^{2} - 96 \, {\left(23 \, B b c^{4} + 10 \, A c^{5}\right)} d^{3} e^{3} + 8 \, {\left(139 \, B b^{2} c^{3} + 220 \, A b c^{4}\right)} d^{2} e^{4} - 2 \, {\left(27 \, B b^{3} c^{2} + 410 \, A b^{2} c^{3}\right)} d e^{5} - 3 \, {\left(3 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, {\left(c^{3} e^{8} x + c^{3} d e^{7}\right)}}, \frac{1920 \, {\left(12 \, B c^{5} d^{5} - 5 \, A b^{2} c^{3} d^{2} e^{3} - {\left(19 \, B b c^{4} + 10 \, A c^{5}\right)} d^{4} e + {\left(7 \, B b^{2} c^{3} + 15 \, A b c^{4}\right)} d^{3} e^{2} + {\left(12 \, B c^{5} d^{4} e - 5 \, A b^{2} c^{3} d e^{4} - {\left(19 \, B b c^{4} + 10 \, A c^{5}\right)} d^{3} e^{2} + {\left(7 \, B b^{2} c^{3} + 15 \, A b c^{4}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 15 \, {\left(1536 \, B c^{5} d^{6} - 640 \, {\left(5 \, B b c^{4} + 2 \, A c^{5}\right)} d^{5} e + 640 \, {\left(3 \, B b^{2} c^{3} + 4 \, A b c^{4}\right)} d^{4} e^{2} - 240 \, {\left(B b^{3} c^{2} + 6 \, A b^{2} c^{3}\right)} d^{3} e^{3} - 20 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d^{2} e^{4} - {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} d e^{5} + {\left(1536 \, B c^{5} d^{5} e - 640 \, {\left(5 \, B b c^{4} + 2 \, A c^{5}\right)} d^{4} e^{2} + 640 \, {\left(3 \, B b^{2} c^{3} + 4 \, A b c^{4}\right)} d^{3} e^{3} - 240 \, {\left(B b^{3} c^{2} + 6 \, A b^{2} c^{3}\right)} d^{2} e^{4} - 20 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d e^{5} - {\left(3 \, B b^{5} - 10 \, A b^{4} c\right)} e^{6}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(384 \, B c^{5} e^{6} x^{5} + 11520 \, B c^{5} d^{5} e - 1920 \, {\left(11 \, B b c^{4} + 5 \, A c^{5}\right)} d^{4} e^{2} + 240 \, {\left(41 \, B b^{2} c^{3} + 70 \, A b c^{4}\right)} d^{3} e^{3} - 300 \, {\left(B b^{3} c^{2} + 24 \, A b^{2} c^{3}\right)} d^{2} e^{4} - 15 \, {\left(3 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} d e^{5} - 48 \, {\left(12 \, B c^{5} d e^{5} - {\left(21 \, B b c^{4} + 10 \, A c^{5}\right)} e^{6}\right)} x^{4} + 8 \, {\left(120 \, B c^{5} d^{2} e^{4} - 2 \, {\left(107 \, B b c^{4} + 50 \, A c^{5}\right)} d e^{5} + {\left(93 \, B b^{2} c^{3} + 170 \, A b c^{4}\right)} e^{6}\right)} x^{3} - 2 \, {\left(960 \, B c^{5} d^{3} e^{3} - 160 \, {\left(11 \, B b c^{4} + 5 \, A c^{5}\right)} d^{2} e^{4} + 8 \, {\left(101 \, B b^{2} c^{3} + 175 \, A b c^{4}\right)} d e^{5} - 5 \, {\left(3 \, B b^{3} c^{2} + 118 \, A b^{2} c^{3}\right)} e^{6}\right)} x^{2} + 5 \, {\left(1152 \, B c^{5} d^{4} e^{2} - 96 \, {\left(23 \, B b c^{4} + 10 \, A c^{5}\right)} d^{3} e^{3} + 8 \, {\left(139 \, B b^{2} c^{3} + 220 \, A b c^{4}\right)} d^{2} e^{4} - 2 \, {\left(27 \, B b^{3} c^{2} + 410 \, A b^{2} c^{3}\right)} d e^{5} - 3 \, {\left(3 \, B b^{4} c - 10 \, A b^{3} c^{2}\right)} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, {\left(c^{3} e^{8} x + c^{3} d e^{7}\right)}}\right]"," ",0,"[1/3840*(15*(1536*B*c^5*d^6 - 640*(5*B*b*c^4 + 2*A*c^5)*d^5*e + 640*(3*B*b^2*c^3 + 4*A*b*c^4)*d^4*e^2 - 240*(B*b^3*c^2 + 6*A*b^2*c^3)*d^3*e^3 - 20*(B*b^4*c - 8*A*b^3*c^2)*d^2*e^4 - (3*B*b^5 - 10*A*b^4*c)*d*e^5 + (1536*B*c^5*d^5*e - 640*(5*B*b*c^4 + 2*A*c^5)*d^4*e^2 + 640*(3*B*b^2*c^3 + 4*A*b*c^4)*d^3*e^3 - 240*(B*b^3*c^2 + 6*A*b^2*c^3)*d^2*e^4 - 20*(B*b^4*c - 8*A*b^3*c^2)*d*e^5 - (3*B*b^5 - 10*A*b^4*c)*e^6)*x)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 1920*(12*B*c^5*d^5 - 5*A*b^2*c^3*d^2*e^3 - (19*B*b*c^4 + 10*A*c^5)*d^4*e + (7*B*b^2*c^3 + 15*A*b*c^4)*d^3*e^2 + (12*B*c^5*d^4*e - 5*A*b^2*c^3*d*e^4 - (19*B*b*c^4 + 10*A*c^5)*d^3*e^2 + (7*B*b^2*c^3 + 15*A*b*c^4)*d^2*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(384*B*c^5*e^6*x^5 + 11520*B*c^5*d^5*e - 1920*(11*B*b*c^4 + 5*A*c^5)*d^4*e^2 + 240*(41*B*b^2*c^3 + 70*A*b*c^4)*d^3*e^3 - 300*(B*b^3*c^2 + 24*A*b^2*c^3)*d^2*e^4 - 15*(3*B*b^4*c - 10*A*b^3*c^2)*d*e^5 - 48*(12*B*c^5*d*e^5 - (21*B*b*c^4 + 10*A*c^5)*e^6)*x^4 + 8*(120*B*c^5*d^2*e^4 - 2*(107*B*b*c^4 + 50*A*c^5)*d*e^5 + (93*B*b^2*c^3 + 170*A*b*c^4)*e^6)*x^3 - 2*(960*B*c^5*d^3*e^3 - 160*(11*B*b*c^4 + 5*A*c^5)*d^2*e^4 + 8*(101*B*b^2*c^3 + 175*A*b*c^4)*d*e^5 - 5*(3*B*b^3*c^2 + 118*A*b^2*c^3)*e^6)*x^2 + 5*(1152*B*c^5*d^4*e^2 - 96*(23*B*b*c^4 + 10*A*c^5)*d^3*e^3 + 8*(139*B*b^2*c^3 + 220*A*b*c^4)*d^2*e^4 - 2*(27*B*b^3*c^2 + 410*A*b^2*c^3)*d*e^5 - 3*(3*B*b^4*c - 10*A*b^3*c^2)*e^6)*x)*sqrt(c*x^2 + b*x))/(c^3*e^8*x + c^3*d*e^7), 1/3840*(3840*(12*B*c^5*d^5 - 5*A*b^2*c^3*d^2*e^3 - (19*B*b*c^4 + 10*A*c^5)*d^4*e + (7*B*b^2*c^3 + 15*A*b*c^4)*d^3*e^2 + (12*B*c^5*d^4*e - 5*A*b^2*c^3*d*e^4 - (19*B*b*c^4 + 10*A*c^5)*d^3*e^2 + (7*B*b^2*c^3 + 15*A*b*c^4)*d^2*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 15*(1536*B*c^5*d^6 - 640*(5*B*b*c^4 + 2*A*c^5)*d^5*e + 640*(3*B*b^2*c^3 + 4*A*b*c^4)*d^4*e^2 - 240*(B*b^3*c^2 + 6*A*b^2*c^3)*d^3*e^3 - 20*(B*b^4*c - 8*A*b^3*c^2)*d^2*e^4 - (3*B*b^5 - 10*A*b^4*c)*d*e^5 + (1536*B*c^5*d^5*e - 640*(5*B*b*c^4 + 2*A*c^5)*d^4*e^2 + 640*(3*B*b^2*c^3 + 4*A*b*c^4)*d^3*e^3 - 240*(B*b^3*c^2 + 6*A*b^2*c^3)*d^2*e^4 - 20*(B*b^4*c - 8*A*b^3*c^2)*d*e^5 - (3*B*b^5 - 10*A*b^4*c)*e^6)*x)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(384*B*c^5*e^6*x^5 + 11520*B*c^5*d^5*e - 1920*(11*B*b*c^4 + 5*A*c^5)*d^4*e^2 + 240*(41*B*b^2*c^3 + 70*A*b*c^4)*d^3*e^3 - 300*(B*b^3*c^2 + 24*A*b^2*c^3)*d^2*e^4 - 15*(3*B*b^4*c - 10*A*b^3*c^2)*d*e^5 - 48*(12*B*c^5*d*e^5 - (21*B*b*c^4 + 10*A*c^5)*e^6)*x^4 + 8*(120*B*c^5*d^2*e^4 - 2*(107*B*b*c^4 + 50*A*c^5)*d*e^5 + (93*B*b^2*c^3 + 170*A*b*c^4)*e^6)*x^3 - 2*(960*B*c^5*d^3*e^3 - 160*(11*B*b*c^4 + 5*A*c^5)*d^2*e^4 + 8*(101*B*b^2*c^3 + 175*A*b*c^4)*d*e^5 - 5*(3*B*b^3*c^2 + 118*A*b^2*c^3)*e^6)*x^2 + 5*(1152*B*c^5*d^4*e^2 - 96*(23*B*b*c^4 + 10*A*c^5)*d^3*e^3 + 8*(139*B*b^2*c^3 + 220*A*b*c^4)*d^2*e^4 - 2*(27*B*b^3*c^2 + 410*A*b^2*c^3)*d*e^5 - 3*(3*B*b^4*c - 10*A*b^3*c^2)*e^6)*x)*sqrt(c*x^2 + b*x))/(c^3*e^8*x + c^3*d*e^7), 1/1920*(15*(1536*B*c^5*d^6 - 640*(5*B*b*c^4 + 2*A*c^5)*d^5*e + 640*(3*B*b^2*c^3 + 4*A*b*c^4)*d^4*e^2 - 240*(B*b^3*c^2 + 6*A*b^2*c^3)*d^3*e^3 - 20*(B*b^4*c - 8*A*b^3*c^2)*d^2*e^4 - (3*B*b^5 - 10*A*b^4*c)*d*e^5 + (1536*B*c^5*d^5*e - 640*(5*B*b*c^4 + 2*A*c^5)*d^4*e^2 + 640*(3*B*b^2*c^3 + 4*A*b*c^4)*d^3*e^3 - 240*(B*b^3*c^2 + 6*A*b^2*c^3)*d^2*e^4 - 20*(B*b^4*c - 8*A*b^3*c^2)*d*e^5 - (3*B*b^5 - 10*A*b^4*c)*e^6)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - 960*(12*B*c^5*d^5 - 5*A*b^2*c^3*d^2*e^3 - (19*B*b*c^4 + 10*A*c^5)*d^4*e + (7*B*b^2*c^3 + 15*A*b*c^4)*d^3*e^2 + (12*B*c^5*d^4*e - 5*A*b^2*c^3*d*e^4 - (19*B*b*c^4 + 10*A*c^5)*d^3*e^2 + (7*B*b^2*c^3 + 15*A*b*c^4)*d^2*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + (384*B*c^5*e^6*x^5 + 11520*B*c^5*d^5*e - 1920*(11*B*b*c^4 + 5*A*c^5)*d^4*e^2 + 240*(41*B*b^2*c^3 + 70*A*b*c^4)*d^3*e^3 - 300*(B*b^3*c^2 + 24*A*b^2*c^3)*d^2*e^4 - 15*(3*B*b^4*c - 10*A*b^3*c^2)*d*e^5 - 48*(12*B*c^5*d*e^5 - (21*B*b*c^4 + 10*A*c^5)*e^6)*x^4 + 8*(120*B*c^5*d^2*e^4 - 2*(107*B*b*c^4 + 50*A*c^5)*d*e^5 + (93*B*b^2*c^3 + 170*A*b*c^4)*e^6)*x^3 - 2*(960*B*c^5*d^3*e^3 - 160*(11*B*b*c^4 + 5*A*c^5)*d^2*e^4 + 8*(101*B*b^2*c^3 + 175*A*b*c^4)*d*e^5 - 5*(3*B*b^3*c^2 + 118*A*b^2*c^3)*e^6)*x^2 + 5*(1152*B*c^5*d^4*e^2 - 96*(23*B*b*c^4 + 10*A*c^5)*d^3*e^3 + 8*(139*B*b^2*c^3 + 220*A*b*c^4)*d^2*e^4 - 2*(27*B*b^3*c^2 + 410*A*b^2*c^3)*d*e^5 - 3*(3*B*b^4*c - 10*A*b^3*c^2)*e^6)*x)*sqrt(c*x^2 + b*x))/(c^3*e^8*x + c^3*d*e^7), 1/1920*(1920*(12*B*c^5*d^5 - 5*A*b^2*c^3*d^2*e^3 - (19*B*b*c^4 + 10*A*c^5)*d^4*e + (7*B*b^2*c^3 + 15*A*b*c^4)*d^3*e^2 + (12*B*c^5*d^4*e - 5*A*b^2*c^3*d*e^4 - (19*B*b*c^4 + 10*A*c^5)*d^3*e^2 + (7*B*b^2*c^3 + 15*A*b*c^4)*d^2*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 15*(1536*B*c^5*d^6 - 640*(5*B*b*c^4 + 2*A*c^5)*d^5*e + 640*(3*B*b^2*c^3 + 4*A*b*c^4)*d^4*e^2 - 240*(B*b^3*c^2 + 6*A*b^2*c^3)*d^3*e^3 - 20*(B*b^4*c - 8*A*b^3*c^2)*d^2*e^4 - (3*B*b^5 - 10*A*b^4*c)*d*e^5 + (1536*B*c^5*d^5*e - 640*(5*B*b*c^4 + 2*A*c^5)*d^4*e^2 + 640*(3*B*b^2*c^3 + 4*A*b*c^4)*d^3*e^3 - 240*(B*b^3*c^2 + 6*A*b^2*c^3)*d^2*e^4 - 20*(B*b^4*c - 8*A*b^3*c^2)*d*e^5 - (3*B*b^5 - 10*A*b^4*c)*e^6)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (384*B*c^5*e^6*x^5 + 11520*B*c^5*d^5*e - 1920*(11*B*b*c^4 + 5*A*c^5)*d^4*e^2 + 240*(41*B*b^2*c^3 + 70*A*b*c^4)*d^3*e^3 - 300*(B*b^3*c^2 + 24*A*b^2*c^3)*d^2*e^4 - 15*(3*B*b^4*c - 10*A*b^3*c^2)*d*e^5 - 48*(12*B*c^5*d*e^5 - (21*B*b*c^4 + 10*A*c^5)*e^6)*x^4 + 8*(120*B*c^5*d^2*e^4 - 2*(107*B*b*c^4 + 50*A*c^5)*d*e^5 + (93*B*b^2*c^3 + 170*A*b*c^4)*e^6)*x^3 - 2*(960*B*c^5*d^3*e^3 - 160*(11*B*b*c^4 + 5*A*c^5)*d^2*e^4 + 8*(101*B*b^2*c^3 + 175*A*b*c^4)*d*e^5 - 5*(3*B*b^3*c^2 + 118*A*b^2*c^3)*e^6)*x^2 + 5*(1152*B*c^5*d^4*e^2 - 96*(23*B*b*c^4 + 10*A*c^5)*d^3*e^3 + 8*(139*B*b^2*c^3 + 220*A*b*c^4)*d^2*e^4 - 2*(27*B*b^3*c^2 + 410*A*b^2*c^3)*d*e^5 - 3*(3*B*b^4*c - 10*A*b^3*c^2)*e^6)*x)*sqrt(c*x^2 + b*x))/(c^3*e^8*x + c^3*d*e^7)]","A",0
1188,1,4075,0,11.438316," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(384 \, B c^{4} d^{6} - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{4} e^{2} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{3} e^{3} - {\left(B b^{4} - 8 \, A b^{3} c\right)} d^{2} e^{4} + {\left(384 \, B c^{4} d^{4} e^{2} - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e^{3} + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{2} e^{4} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d e^{5} - {\left(B b^{4} - 8 \, A b^{3} c\right)} e^{6}\right)} x^{2} + 2 \, {\left(384 \, B c^{4} d^{5} e - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{2} + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{3} e^{3} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{2} e^{4} - {\left(B b^{4} - 8 \, A b^{3} c\right)} d e^{5}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 240 \, {\left(24 \, B c^{4} d^{5} - 3 \, A b^{2} c^{2} d^{2} e^{3} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{4} e + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d^{3} e^{2} + {\left(24 \, B c^{4} d^{3} e^{2} - 3 \, A b^{2} c^{2} e^{5} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{2} e^{3} + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d e^{4}\right)} x^{2} + 2 \, {\left(24 \, B c^{4} d^{4} e - 3 \, A b^{2} c^{2} d e^{4} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{3} e^{2} + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(48 \, B c^{4} e^{6} x^{5} - 2880 \, B c^{4} d^{5} e + 240 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} d^{4} e^{2} - 120 \, {\left(11 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{3} e^{3} + 15 \, {\left(B b^{3} c + 40 \, A b^{2} c^{2}\right)} d^{2} e^{4} - 8 \, {\left(12 \, B c^{4} d e^{5} - {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left(120 \, B c^{4} d^{2} e^{4} - 16 \, {\left(11 \, B b c^{3} + 5 \, A c^{4}\right)} d e^{5} + {\left(59 \, B b^{2} c^{2} + 104 \, A b c^{3}\right)} e^{6}\right)} x^{3} - {\left(960 \, B c^{4} d^{3} e^{3} - 40 \, {\left(37 \, B b c^{3} + 16 \, A c^{4}\right)} d^{2} e^{4} + 4 \, {\left(139 \, B b^{2} c^{2} + 220 \, A b c^{3}\right)} d e^{5} - 3 \, {\left(5 \, B b^{3} c + 88 \, A b^{2} c^{2}\right)} e^{6}\right)} x^{2} - 10 \, {\left(432 \, B c^{4} d^{4} e^{2} - 48 \, {\left(13 \, B b c^{3} + 6 \, A c^{4}\right)} d^{3} e^{3} + {\left(209 \, B b^{2} c^{2} + 368 \, A b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(B b^{3} c + 32 \, A b^{2} c^{2}\right)} d e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{2} e^{9} x^{2} + 2 \, c^{2} d e^{8} x + c^{2} d^{2} e^{7}\right)}}, -\frac{480 \, {\left(24 \, B c^{4} d^{5} - 3 \, A b^{2} c^{2} d^{2} e^{3} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{4} e + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d^{3} e^{2} + {\left(24 \, B c^{4} d^{3} e^{2} - 3 \, A b^{2} c^{2} e^{5} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{2} e^{3} + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d e^{4}\right)} x^{2} + 2 \, {\left(24 \, B c^{4} d^{4} e - 3 \, A b^{2} c^{2} d e^{4} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{3} e^{2} + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 15 \, {\left(384 \, B c^{4} d^{6} - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{4} e^{2} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{3} e^{3} - {\left(B b^{4} - 8 \, A b^{3} c\right)} d^{2} e^{4} + {\left(384 \, B c^{4} d^{4} e^{2} - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e^{3} + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{2} e^{4} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d e^{5} - {\left(B b^{4} - 8 \, A b^{3} c\right)} e^{6}\right)} x^{2} + 2 \, {\left(384 \, B c^{4} d^{5} e - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{2} + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{3} e^{3} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{2} e^{4} - {\left(B b^{4} - 8 \, A b^{3} c\right)} d e^{5}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(48 \, B c^{4} e^{6} x^{5} - 2880 \, B c^{4} d^{5} e + 240 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} d^{4} e^{2} - 120 \, {\left(11 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{3} e^{3} + 15 \, {\left(B b^{3} c + 40 \, A b^{2} c^{2}\right)} d^{2} e^{4} - 8 \, {\left(12 \, B c^{4} d e^{5} - {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left(120 \, B c^{4} d^{2} e^{4} - 16 \, {\left(11 \, B b c^{3} + 5 \, A c^{4}\right)} d e^{5} + {\left(59 \, B b^{2} c^{2} + 104 \, A b c^{3}\right)} e^{6}\right)} x^{3} - {\left(960 \, B c^{4} d^{3} e^{3} - 40 \, {\left(37 \, B b c^{3} + 16 \, A c^{4}\right)} d^{2} e^{4} + 4 \, {\left(139 \, B b^{2} c^{2} + 220 \, A b c^{3}\right)} d e^{5} - 3 \, {\left(5 \, B b^{3} c + 88 \, A b^{2} c^{2}\right)} e^{6}\right)} x^{2} - 10 \, {\left(432 \, B c^{4} d^{4} e^{2} - 48 \, {\left(13 \, B b c^{3} + 6 \, A c^{4}\right)} d^{3} e^{3} + {\left(209 \, B b^{2} c^{2} + 368 \, A b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(B b^{3} c + 32 \, A b^{2} c^{2}\right)} d e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{2} e^{9} x^{2} + 2 \, c^{2} d e^{8} x + c^{2} d^{2} e^{7}\right)}}, -\frac{15 \, {\left(384 \, B c^{4} d^{6} - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{4} e^{2} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{3} e^{3} - {\left(B b^{4} - 8 \, A b^{3} c\right)} d^{2} e^{4} + {\left(384 \, B c^{4} d^{4} e^{2} - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e^{3} + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{2} e^{4} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d e^{5} - {\left(B b^{4} - 8 \, A b^{3} c\right)} e^{6}\right)} x^{2} + 2 \, {\left(384 \, B c^{4} d^{5} e - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{2} + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{3} e^{3} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{2} e^{4} - {\left(B b^{4} - 8 \, A b^{3} c\right)} d e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - 120 \, {\left(24 \, B c^{4} d^{5} - 3 \, A b^{2} c^{2} d^{2} e^{3} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{4} e + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d^{3} e^{2} + {\left(24 \, B c^{4} d^{3} e^{2} - 3 \, A b^{2} c^{2} e^{5} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{2} e^{3} + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d e^{4}\right)} x^{2} + 2 \, {\left(24 \, B c^{4} d^{4} e - 3 \, A b^{2} c^{2} d e^{4} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{3} e^{2} + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - {\left(48 \, B c^{4} e^{6} x^{5} - 2880 \, B c^{4} d^{5} e + 240 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} d^{4} e^{2} - 120 \, {\left(11 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{3} e^{3} + 15 \, {\left(B b^{3} c + 40 \, A b^{2} c^{2}\right)} d^{2} e^{4} - 8 \, {\left(12 \, B c^{4} d e^{5} - {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left(120 \, B c^{4} d^{2} e^{4} - 16 \, {\left(11 \, B b c^{3} + 5 \, A c^{4}\right)} d e^{5} + {\left(59 \, B b^{2} c^{2} + 104 \, A b c^{3}\right)} e^{6}\right)} x^{3} - {\left(960 \, B c^{4} d^{3} e^{3} - 40 \, {\left(37 \, B b c^{3} + 16 \, A c^{4}\right)} d^{2} e^{4} + 4 \, {\left(139 \, B b^{2} c^{2} + 220 \, A b c^{3}\right)} d e^{5} - 3 \, {\left(5 \, B b^{3} c + 88 \, A b^{2} c^{2}\right)} e^{6}\right)} x^{2} - 10 \, {\left(432 \, B c^{4} d^{4} e^{2} - 48 \, {\left(13 \, B b c^{3} + 6 \, A c^{4}\right)} d^{3} e^{3} + {\left(209 \, B b^{2} c^{2} + 368 \, A b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(B b^{3} c + 32 \, A b^{2} c^{2}\right)} d e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{2} e^{9} x^{2} + 2 \, c^{2} d e^{8} x + c^{2} d^{2} e^{7}\right)}}, -\frac{240 \, {\left(24 \, B c^{4} d^{5} - 3 \, A b^{2} c^{2} d^{2} e^{3} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{4} e + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d^{3} e^{2} + {\left(24 \, B c^{4} d^{3} e^{2} - 3 \, A b^{2} c^{2} e^{5} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{2} e^{3} + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d e^{4}\right)} x^{2} + 2 \, {\left(24 \, B c^{4} d^{4} e - 3 \, A b^{2} c^{2} d e^{4} - 4 \, {\left(7 \, B b c^{3} + 4 \, A c^{4}\right)} d^{3} e^{2} + {\left(7 \, B b^{2} c^{2} + 16 \, A b c^{3}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 15 \, {\left(384 \, B c^{4} d^{6} - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{4} e^{2} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{3} e^{3} - {\left(B b^{4} - 8 \, A b^{3} c\right)} d^{2} e^{4} + {\left(384 \, B c^{4} d^{4} e^{2} - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e^{3} + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{2} e^{4} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d e^{5} - {\left(B b^{4} - 8 \, A b^{3} c\right)} e^{6}\right)} x^{2} + 2 \, {\left(384 \, B c^{4} d^{5} e - 128 \, {\left(5 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{2} + 96 \, {\left(3 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{3} e^{3} - 24 \, {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{2} e^{4} - {\left(B b^{4} - 8 \, A b^{3} c\right)} d e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(48 \, B c^{4} e^{6} x^{5} - 2880 \, B c^{4} d^{5} e + 240 \, {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} d^{4} e^{2} - 120 \, {\left(11 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{3} e^{3} + 15 \, {\left(B b^{3} c + 40 \, A b^{2} c^{2}\right)} d^{2} e^{4} - 8 \, {\left(12 \, B c^{4} d e^{5} - {\left(17 \, B b c^{3} + 8 \, A c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left(120 \, B c^{4} d^{2} e^{4} - 16 \, {\left(11 \, B b c^{3} + 5 \, A c^{4}\right)} d e^{5} + {\left(59 \, B b^{2} c^{2} + 104 \, A b c^{3}\right)} e^{6}\right)} x^{3} - {\left(960 \, B c^{4} d^{3} e^{3} - 40 \, {\left(37 \, B b c^{3} + 16 \, A c^{4}\right)} d^{2} e^{4} + 4 \, {\left(139 \, B b^{2} c^{2} + 220 \, A b c^{3}\right)} d e^{5} - 3 \, {\left(5 \, B b^{3} c + 88 \, A b^{2} c^{2}\right)} e^{6}\right)} x^{2} - 10 \, {\left(432 \, B c^{4} d^{4} e^{2} - 48 \, {\left(13 \, B b c^{3} + 6 \, A c^{4}\right)} d^{3} e^{3} + {\left(209 \, B b^{2} c^{2} + 368 \, A b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(B b^{3} c + 32 \, A b^{2} c^{2}\right)} d e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{2} e^{9} x^{2} + 2 \, c^{2} d e^{8} x + c^{2} d^{2} e^{7}\right)}}\right]"," ",0,"[-1/384*(15*(384*B*c^4*d^6 - 128*(5*B*b*c^3 + 2*A*c^4)*d^5*e + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^4*e^2 - 24*(B*b^3*c + 6*A*b^2*c^2)*d^3*e^3 - (B*b^4 - 8*A*b^3*c)*d^2*e^4 + (384*B*c^4*d^4*e^2 - 128*(5*B*b*c^3 + 2*A*c^4)*d^3*e^3 + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^2*e^4 - 24*(B*b^3*c + 6*A*b^2*c^2)*d*e^5 - (B*b^4 - 8*A*b^3*c)*e^6)*x^2 + 2*(384*B*c^4*d^5*e - 128*(5*B*b*c^3 + 2*A*c^4)*d^4*e^2 + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^3*e^3 - 24*(B*b^3*c + 6*A*b^2*c^2)*d^2*e^4 - (B*b^4 - 8*A*b^3*c)*d*e^5)*x)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 240*(24*B*c^4*d^5 - 3*A*b^2*c^2*d^2*e^3 - 4*(7*B*b*c^3 + 4*A*c^4)*d^4*e + (7*B*b^2*c^2 + 16*A*b*c^3)*d^3*e^2 + (24*B*c^4*d^3*e^2 - 3*A*b^2*c^2*e^5 - 4*(7*B*b*c^3 + 4*A*c^4)*d^2*e^3 + (7*B*b^2*c^2 + 16*A*b*c^3)*d*e^4)*x^2 + 2*(24*B*c^4*d^4*e - 3*A*b^2*c^2*d*e^4 - 4*(7*B*b*c^3 + 4*A*c^4)*d^3*e^2 + (7*B*b^2*c^2 + 16*A*b*c^3)*d^2*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(48*B*c^4*e^6*x^5 - 2880*B*c^4*d^5*e + 240*(17*B*b*c^3 + 8*A*c^4)*d^4*e^2 - 120*(11*B*b^2*c^2 + 20*A*b*c^3)*d^3*e^3 + 15*(B*b^3*c + 40*A*b^2*c^2)*d^2*e^4 - 8*(12*B*c^4*d*e^5 - (17*B*b*c^3 + 8*A*c^4)*e^6)*x^4 + 2*(120*B*c^4*d^2*e^4 - 16*(11*B*b*c^3 + 5*A*c^4)*d*e^5 + (59*B*b^2*c^2 + 104*A*b*c^3)*e^6)*x^3 - (960*B*c^4*d^3*e^3 - 40*(37*B*b*c^3 + 16*A*c^4)*d^2*e^4 + 4*(139*B*b^2*c^2 + 220*A*b*c^3)*d*e^5 - 3*(5*B*b^3*c + 88*A*b^2*c^2)*e^6)*x^2 - 10*(432*B*c^4*d^4*e^2 - 48*(13*B*b*c^3 + 6*A*c^4)*d^3*e^3 + (209*B*b^2*c^2 + 368*A*b*c^3)*d^2*e^4 - 3*(B*b^3*c + 32*A*b^2*c^2)*d*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*e^9*x^2 + 2*c^2*d*e^8*x + c^2*d^2*e^7), -1/384*(480*(24*B*c^4*d^5 - 3*A*b^2*c^2*d^2*e^3 - 4*(7*B*b*c^3 + 4*A*c^4)*d^4*e + (7*B*b^2*c^2 + 16*A*b*c^3)*d^3*e^2 + (24*B*c^4*d^3*e^2 - 3*A*b^2*c^2*e^5 - 4*(7*B*b*c^3 + 4*A*c^4)*d^2*e^3 + (7*B*b^2*c^2 + 16*A*b*c^3)*d*e^4)*x^2 + 2*(24*B*c^4*d^4*e - 3*A*b^2*c^2*d*e^4 - 4*(7*B*b*c^3 + 4*A*c^4)*d^3*e^2 + (7*B*b^2*c^2 + 16*A*b*c^3)*d^2*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 15*(384*B*c^4*d^6 - 128*(5*B*b*c^3 + 2*A*c^4)*d^5*e + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^4*e^2 - 24*(B*b^3*c + 6*A*b^2*c^2)*d^3*e^3 - (B*b^4 - 8*A*b^3*c)*d^2*e^4 + (384*B*c^4*d^4*e^2 - 128*(5*B*b*c^3 + 2*A*c^4)*d^3*e^3 + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^2*e^4 - 24*(B*b^3*c + 6*A*b^2*c^2)*d*e^5 - (B*b^4 - 8*A*b^3*c)*e^6)*x^2 + 2*(384*B*c^4*d^5*e - 128*(5*B*b*c^3 + 2*A*c^4)*d^4*e^2 + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^3*e^3 - 24*(B*b^3*c + 6*A*b^2*c^2)*d^2*e^4 - (B*b^4 - 8*A*b^3*c)*d*e^5)*x)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(48*B*c^4*e^6*x^5 - 2880*B*c^4*d^5*e + 240*(17*B*b*c^3 + 8*A*c^4)*d^4*e^2 - 120*(11*B*b^2*c^2 + 20*A*b*c^3)*d^3*e^3 + 15*(B*b^3*c + 40*A*b^2*c^2)*d^2*e^4 - 8*(12*B*c^4*d*e^5 - (17*B*b*c^3 + 8*A*c^4)*e^6)*x^4 + 2*(120*B*c^4*d^2*e^4 - 16*(11*B*b*c^3 + 5*A*c^4)*d*e^5 + (59*B*b^2*c^2 + 104*A*b*c^3)*e^6)*x^3 - (960*B*c^4*d^3*e^3 - 40*(37*B*b*c^3 + 16*A*c^4)*d^2*e^4 + 4*(139*B*b^2*c^2 + 220*A*b*c^3)*d*e^5 - 3*(5*B*b^3*c + 88*A*b^2*c^2)*e^6)*x^2 - 10*(432*B*c^4*d^4*e^2 - 48*(13*B*b*c^3 + 6*A*c^4)*d^3*e^3 + (209*B*b^2*c^2 + 368*A*b*c^3)*d^2*e^4 - 3*(B*b^3*c + 32*A*b^2*c^2)*d*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*e^9*x^2 + 2*c^2*d*e^8*x + c^2*d^2*e^7), -1/192*(15*(384*B*c^4*d^6 - 128*(5*B*b*c^3 + 2*A*c^4)*d^5*e + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^4*e^2 - 24*(B*b^3*c + 6*A*b^2*c^2)*d^3*e^3 - (B*b^4 - 8*A*b^3*c)*d^2*e^4 + (384*B*c^4*d^4*e^2 - 128*(5*B*b*c^3 + 2*A*c^4)*d^3*e^3 + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^2*e^4 - 24*(B*b^3*c + 6*A*b^2*c^2)*d*e^5 - (B*b^4 - 8*A*b^3*c)*e^6)*x^2 + 2*(384*B*c^4*d^5*e - 128*(5*B*b*c^3 + 2*A*c^4)*d^4*e^2 + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^3*e^3 - 24*(B*b^3*c + 6*A*b^2*c^2)*d^2*e^4 - (B*b^4 - 8*A*b^3*c)*d*e^5)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - 120*(24*B*c^4*d^5 - 3*A*b^2*c^2*d^2*e^3 - 4*(7*B*b*c^3 + 4*A*c^4)*d^4*e + (7*B*b^2*c^2 + 16*A*b*c^3)*d^3*e^2 + (24*B*c^4*d^3*e^2 - 3*A*b^2*c^2*e^5 - 4*(7*B*b*c^3 + 4*A*c^4)*d^2*e^3 + (7*B*b^2*c^2 + 16*A*b*c^3)*d*e^4)*x^2 + 2*(24*B*c^4*d^4*e - 3*A*b^2*c^2*d*e^4 - 4*(7*B*b*c^3 + 4*A*c^4)*d^3*e^2 + (7*B*b^2*c^2 + 16*A*b*c^3)*d^2*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - (48*B*c^4*e^6*x^5 - 2880*B*c^4*d^5*e + 240*(17*B*b*c^3 + 8*A*c^4)*d^4*e^2 - 120*(11*B*b^2*c^2 + 20*A*b*c^3)*d^3*e^3 + 15*(B*b^3*c + 40*A*b^2*c^2)*d^2*e^4 - 8*(12*B*c^4*d*e^5 - (17*B*b*c^3 + 8*A*c^4)*e^6)*x^4 + 2*(120*B*c^4*d^2*e^4 - 16*(11*B*b*c^3 + 5*A*c^4)*d*e^5 + (59*B*b^2*c^2 + 104*A*b*c^3)*e^6)*x^3 - (960*B*c^4*d^3*e^3 - 40*(37*B*b*c^3 + 16*A*c^4)*d^2*e^4 + 4*(139*B*b^2*c^2 + 220*A*b*c^3)*d*e^5 - 3*(5*B*b^3*c + 88*A*b^2*c^2)*e^6)*x^2 - 10*(432*B*c^4*d^4*e^2 - 48*(13*B*b*c^3 + 6*A*c^4)*d^3*e^3 + (209*B*b^2*c^2 + 368*A*b*c^3)*d^2*e^4 - 3*(B*b^3*c + 32*A*b^2*c^2)*d*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*e^9*x^2 + 2*c^2*d*e^8*x + c^2*d^2*e^7), -1/192*(240*(24*B*c^4*d^5 - 3*A*b^2*c^2*d^2*e^3 - 4*(7*B*b*c^3 + 4*A*c^4)*d^4*e + (7*B*b^2*c^2 + 16*A*b*c^3)*d^3*e^2 + (24*B*c^4*d^3*e^2 - 3*A*b^2*c^2*e^5 - 4*(7*B*b*c^3 + 4*A*c^4)*d^2*e^3 + (7*B*b^2*c^2 + 16*A*b*c^3)*d*e^4)*x^2 + 2*(24*B*c^4*d^4*e - 3*A*b^2*c^2*d*e^4 - 4*(7*B*b*c^3 + 4*A*c^4)*d^3*e^2 + (7*B*b^2*c^2 + 16*A*b*c^3)*d^2*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 15*(384*B*c^4*d^6 - 128*(5*B*b*c^3 + 2*A*c^4)*d^5*e + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^4*e^2 - 24*(B*b^3*c + 6*A*b^2*c^2)*d^3*e^3 - (B*b^4 - 8*A*b^3*c)*d^2*e^4 + (384*B*c^4*d^4*e^2 - 128*(5*B*b*c^3 + 2*A*c^4)*d^3*e^3 + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^2*e^4 - 24*(B*b^3*c + 6*A*b^2*c^2)*d*e^5 - (B*b^4 - 8*A*b^3*c)*e^6)*x^2 + 2*(384*B*c^4*d^5*e - 128*(5*B*b*c^3 + 2*A*c^4)*d^4*e^2 + 96*(3*B*b^2*c^2 + 4*A*b*c^3)*d^3*e^3 - 24*(B*b^3*c + 6*A*b^2*c^2)*d^2*e^4 - (B*b^4 - 8*A*b^3*c)*d*e^5)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (48*B*c^4*e^6*x^5 - 2880*B*c^4*d^5*e + 240*(17*B*b*c^3 + 8*A*c^4)*d^4*e^2 - 120*(11*B*b^2*c^2 + 20*A*b*c^3)*d^3*e^3 + 15*(B*b^3*c + 40*A*b^2*c^2)*d^2*e^4 - 8*(12*B*c^4*d*e^5 - (17*B*b*c^3 + 8*A*c^4)*e^6)*x^4 + 2*(120*B*c^4*d^2*e^4 - 16*(11*B*b*c^3 + 5*A*c^4)*d*e^5 + (59*B*b^2*c^2 + 104*A*b*c^3)*e^6)*x^3 - (960*B*c^4*d^3*e^3 - 40*(37*B*b*c^3 + 16*A*c^4)*d^2*e^4 + 4*(139*B*b^2*c^2 + 220*A*b*c^3)*d*e^5 - 3*(5*B*b^3*c + 88*A*b^2*c^2)*e^6)*x^2 - 10*(432*B*c^4*d^4*e^2 - 48*(13*B*b*c^3 + 6*A*c^4)*d^3*e^3 + (209*B*b^2*c^2 + 368*A*b*c^3)*d^2*e^4 - 3*(B*b^3*c + 32*A*b^2*c^2)*d*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*e^9*x^2 + 2*c^2*d*e^8*x + c^2*d^2*e^7)]","B",0
1189,1,5934,0,5.199070," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(64 \, B c^{4} d^{8} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{7} e + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{6} e^{2} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{5} e^{3} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{4} e^{4} + {\left(64 \, B c^{4} d^{5} e^{3} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{4} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{3} e^{5} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{2} e^{6} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d e^{7}\right)} x^{3} + 3 \, {\left(64 \, B c^{4} d^{6} e^{2} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{3} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{4} e^{4} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{3} e^{5} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(64 \, B c^{4} d^{7} e - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e^{2} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{5} e^{3} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{4} e^{4} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 15 \, {\left(64 \, B c^{4} d^{7} + A b^{3} c d^{3} e^{4} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{4} e^{3} + {\left(64 \, B c^{4} d^{4} e^{3} + A b^{3} c e^{7} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e^{4} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{2} e^{5} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d e^{6}\right)} x^{3} + 3 \, {\left(64 \, B c^{4} d^{5} e^{2} + A b^{3} c d e^{6} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{3} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{3} e^{4} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{2} e^{5}\right)} x^{2} + 3 \, {\left(64 \, B c^{4} d^{6} e + A b^{3} c d^{2} e^{5} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{2} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{4} e^{3} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(480 \, B c^{4} d^{7} e + 15 \, A b^{3} c d^{3} e^{5} - 240 \, {\left(4 \, B b c^{3} + A c^{4}\right)} d^{6} e^{2} + 30 \, {\left(19 \, B b^{2} c^{2} + 14 \, A b c^{3}\right)} d^{5} e^{3} - 15 \, {\left(6 \, B b^{3} c + 13 \, A b^{2} c^{2}\right)} d^{4} e^{4} + 8 \, {\left(B c^{4} d^{2} e^{6} - B b c^{3} d e^{7}\right)} x^{5} - 2 \, {\left(12 \, B c^{4} d^{3} e^{5} - {\left(25 \, B b c^{3} + 6 \, A c^{4}\right)} d^{2} e^{6} + {\left(13 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d e^{7}\right)} x^{4} + 3 \, {\left(40 \, B c^{4} d^{4} e^{4} - 2 \, {\left(43 \, B b c^{3} + 10 \, A c^{4}\right)} d^{3} e^{5} + 19 \, {\left(3 \, B b^{2} c^{2} + 2 \, A b c^{3}\right)} d^{2} e^{6} - {\left(11 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d e^{7}\right)} x^{3} + {\left(880 \, B c^{4} d^{5} e^{3} + 33 \, A b^{3} c d e^{7} - 40 \, {\left(45 \, B b c^{3} + 11 \, A c^{4}\right)} d^{4} e^{4} + 158 \, {\left(7 \, B b^{2} c^{2} + 5 \, A b c^{3}\right)} d^{3} e^{5} - {\left(186 \, B b^{3} c + 383 \, A b^{2} c^{2}\right)} d^{2} e^{6}\right)} x^{2} + 5 \, {\left(240 \, B c^{4} d^{6} e^{2} + 8 \, A b^{3} c d^{2} e^{6} - 4 \, {\left(121 \, B b c^{3} + 30 \, A c^{4}\right)} d^{5} e^{3} + {\left(291 \, B b^{2} c^{2} + 212 \, A b c^{3}\right)} d^{4} e^{4} - {\left(47 \, B b^{3} c + 100 \, A b^{2} c^{2}\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{2} d^{5} e^{7} - b c d^{4} e^{8} + {\left(c^{2} d^{2} e^{10} - b c d e^{11}\right)} x^{3} + 3 \, {\left(c^{2} d^{3} e^{9} - b c d^{2} e^{10}\right)} x^{2} + 3 \, {\left(c^{2} d^{4} e^{8} - b c d^{3} e^{9}\right)} x\right)}}, \frac{30 \, {\left(64 \, B c^{4} d^{7} + A b^{3} c d^{3} e^{4} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{4} e^{3} + {\left(64 \, B c^{4} d^{4} e^{3} + A b^{3} c e^{7} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e^{4} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{2} e^{5} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d e^{6}\right)} x^{3} + 3 \, {\left(64 \, B c^{4} d^{5} e^{2} + A b^{3} c d e^{6} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{3} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{3} e^{4} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{2} e^{5}\right)} x^{2} + 3 \, {\left(64 \, B c^{4} d^{6} e + A b^{3} c d^{2} e^{5} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{2} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{4} e^{3} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{3} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 15 \, {\left(64 \, B c^{4} d^{8} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{7} e + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{6} e^{2} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{5} e^{3} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{4} e^{4} + {\left(64 \, B c^{4} d^{5} e^{3} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{4} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{3} e^{5} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{2} e^{6} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d e^{7}\right)} x^{3} + 3 \, {\left(64 \, B c^{4} d^{6} e^{2} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{3} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{4} e^{4} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{3} e^{5} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(64 \, B c^{4} d^{7} e - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e^{2} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{5} e^{3} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{4} e^{4} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(480 \, B c^{4} d^{7} e + 15 \, A b^{3} c d^{3} e^{5} - 240 \, {\left(4 \, B b c^{3} + A c^{4}\right)} d^{6} e^{2} + 30 \, {\left(19 \, B b^{2} c^{2} + 14 \, A b c^{3}\right)} d^{5} e^{3} - 15 \, {\left(6 \, B b^{3} c + 13 \, A b^{2} c^{2}\right)} d^{4} e^{4} + 8 \, {\left(B c^{4} d^{2} e^{6} - B b c^{3} d e^{7}\right)} x^{5} - 2 \, {\left(12 \, B c^{4} d^{3} e^{5} - {\left(25 \, B b c^{3} + 6 \, A c^{4}\right)} d^{2} e^{6} + {\left(13 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d e^{7}\right)} x^{4} + 3 \, {\left(40 \, B c^{4} d^{4} e^{4} - 2 \, {\left(43 \, B b c^{3} + 10 \, A c^{4}\right)} d^{3} e^{5} + 19 \, {\left(3 \, B b^{2} c^{2} + 2 \, A b c^{3}\right)} d^{2} e^{6} - {\left(11 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d e^{7}\right)} x^{3} + {\left(880 \, B c^{4} d^{5} e^{3} + 33 \, A b^{3} c d e^{7} - 40 \, {\left(45 \, B b c^{3} + 11 \, A c^{4}\right)} d^{4} e^{4} + 158 \, {\left(7 \, B b^{2} c^{2} + 5 \, A b c^{3}\right)} d^{3} e^{5} - {\left(186 \, B b^{3} c + 383 \, A b^{2} c^{2}\right)} d^{2} e^{6}\right)} x^{2} + 5 \, {\left(240 \, B c^{4} d^{6} e^{2} + 8 \, A b^{3} c d^{2} e^{6} - 4 \, {\left(121 \, B b c^{3} + 30 \, A c^{4}\right)} d^{5} e^{3} + {\left(291 \, B b^{2} c^{2} + 212 \, A b c^{3}\right)} d^{4} e^{4} - {\left(47 \, B b^{3} c + 100 \, A b^{2} c^{2}\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{2} d^{5} e^{7} - b c d^{4} e^{8} + {\left(c^{2} d^{2} e^{10} - b c d e^{11}\right)} x^{3} + 3 \, {\left(c^{2} d^{3} e^{9} - b c d^{2} e^{10}\right)} x^{2} + 3 \, {\left(c^{2} d^{4} e^{8} - b c d^{3} e^{9}\right)} x\right)}}, \frac{30 \, {\left(64 \, B c^{4} d^{8} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{7} e + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{6} e^{2} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{5} e^{3} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{4} e^{4} + {\left(64 \, B c^{4} d^{5} e^{3} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{4} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{3} e^{5} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{2} e^{6} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d e^{7}\right)} x^{3} + 3 \, {\left(64 \, B c^{4} d^{6} e^{2} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{3} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{4} e^{4} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{3} e^{5} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(64 \, B c^{4} d^{7} e - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e^{2} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{5} e^{3} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{4} e^{4} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - 15 \, {\left(64 \, B c^{4} d^{7} + A b^{3} c d^{3} e^{4} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{4} e^{3} + {\left(64 \, B c^{4} d^{4} e^{3} + A b^{3} c e^{7} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e^{4} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{2} e^{5} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d e^{6}\right)} x^{3} + 3 \, {\left(64 \, B c^{4} d^{5} e^{2} + A b^{3} c d e^{6} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{3} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{3} e^{4} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{2} e^{5}\right)} x^{2} + 3 \, {\left(64 \, B c^{4} d^{6} e + A b^{3} c d^{2} e^{5} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{2} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{4} e^{3} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(480 \, B c^{4} d^{7} e + 15 \, A b^{3} c d^{3} e^{5} - 240 \, {\left(4 \, B b c^{3} + A c^{4}\right)} d^{6} e^{2} + 30 \, {\left(19 \, B b^{2} c^{2} + 14 \, A b c^{3}\right)} d^{5} e^{3} - 15 \, {\left(6 \, B b^{3} c + 13 \, A b^{2} c^{2}\right)} d^{4} e^{4} + 8 \, {\left(B c^{4} d^{2} e^{6} - B b c^{3} d e^{7}\right)} x^{5} - 2 \, {\left(12 \, B c^{4} d^{3} e^{5} - {\left(25 \, B b c^{3} + 6 \, A c^{4}\right)} d^{2} e^{6} + {\left(13 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d e^{7}\right)} x^{4} + 3 \, {\left(40 \, B c^{4} d^{4} e^{4} - 2 \, {\left(43 \, B b c^{3} + 10 \, A c^{4}\right)} d^{3} e^{5} + 19 \, {\left(3 \, B b^{2} c^{2} + 2 \, A b c^{3}\right)} d^{2} e^{6} - {\left(11 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d e^{7}\right)} x^{3} + {\left(880 \, B c^{4} d^{5} e^{3} + 33 \, A b^{3} c d e^{7} - 40 \, {\left(45 \, B b c^{3} + 11 \, A c^{4}\right)} d^{4} e^{4} + 158 \, {\left(7 \, B b^{2} c^{2} + 5 \, A b c^{3}\right)} d^{3} e^{5} - {\left(186 \, B b^{3} c + 383 \, A b^{2} c^{2}\right)} d^{2} e^{6}\right)} x^{2} + 5 \, {\left(240 \, B c^{4} d^{6} e^{2} + 8 \, A b^{3} c d^{2} e^{6} - 4 \, {\left(121 \, B b c^{3} + 30 \, A c^{4}\right)} d^{5} e^{3} + {\left(291 \, B b^{2} c^{2} + 212 \, A b c^{3}\right)} d^{4} e^{4} - {\left(47 \, B b^{3} c + 100 \, A b^{2} c^{2}\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{2} d^{5} e^{7} - b c d^{4} e^{8} + {\left(c^{2} d^{2} e^{10} - b c d e^{11}\right)} x^{3} + 3 \, {\left(c^{2} d^{3} e^{9} - b c d^{2} e^{10}\right)} x^{2} + 3 \, {\left(c^{2} d^{4} e^{8} - b c d^{3} e^{9}\right)} x\right)}}, \frac{15 \, {\left(64 \, B c^{4} d^{7} + A b^{3} c d^{3} e^{4} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{4} e^{3} + {\left(64 \, B c^{4} d^{4} e^{3} + A b^{3} c e^{7} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{3} e^{4} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{2} e^{5} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d e^{6}\right)} x^{3} + 3 \, {\left(64 \, B c^{4} d^{5} e^{2} + A b^{3} c d e^{6} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{3} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{3} e^{4} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{2} e^{5}\right)} x^{2} + 3 \, {\left(64 \, B c^{4} d^{6} e + A b^{3} c d^{2} e^{5} - 16 \, {\left(7 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{2} + 8 \, {\left(7 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d^{4} e^{3} - {\left(7 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d^{3} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 15 \, {\left(64 \, B c^{4} d^{8} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{7} e + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{6} e^{2} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{5} e^{3} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{4} e^{4} + {\left(64 \, B c^{4} d^{5} e^{3} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{4} e^{4} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{3} e^{5} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{2} e^{6} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d e^{7}\right)} x^{3} + 3 \, {\left(64 \, B c^{4} d^{6} e^{2} - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{3} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{4} e^{4} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{3} e^{5} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(64 \, B c^{4} d^{7} e - 16 \, {\left(9 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e^{2} + 8 \, {\left(13 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{5} e^{3} - {\left(25 \, B b^{3} c + 38 \, A b^{2} c^{2}\right)} d^{4} e^{4} + {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(480 \, B c^{4} d^{7} e + 15 \, A b^{3} c d^{3} e^{5} - 240 \, {\left(4 \, B b c^{3} + A c^{4}\right)} d^{6} e^{2} + 30 \, {\left(19 \, B b^{2} c^{2} + 14 \, A b c^{3}\right)} d^{5} e^{3} - 15 \, {\left(6 \, B b^{3} c + 13 \, A b^{2} c^{2}\right)} d^{4} e^{4} + 8 \, {\left(B c^{4} d^{2} e^{6} - B b c^{3} d e^{7}\right)} x^{5} - 2 \, {\left(12 \, B c^{4} d^{3} e^{5} - {\left(25 \, B b c^{3} + 6 \, A c^{4}\right)} d^{2} e^{6} + {\left(13 \, B b^{2} c^{2} + 6 \, A b c^{3}\right)} d e^{7}\right)} x^{4} + 3 \, {\left(40 \, B c^{4} d^{4} e^{4} - 2 \, {\left(43 \, B b c^{3} + 10 \, A c^{4}\right)} d^{3} e^{5} + 19 \, {\left(3 \, B b^{2} c^{2} + 2 \, A b c^{3}\right)} d^{2} e^{6} - {\left(11 \, B b^{3} c + 18 \, A b^{2} c^{2}\right)} d e^{7}\right)} x^{3} + {\left(880 \, B c^{4} d^{5} e^{3} + 33 \, A b^{3} c d e^{7} - 40 \, {\left(45 \, B b c^{3} + 11 \, A c^{4}\right)} d^{4} e^{4} + 158 \, {\left(7 \, B b^{2} c^{2} + 5 \, A b c^{3}\right)} d^{3} e^{5} - {\left(186 \, B b^{3} c + 383 \, A b^{2} c^{2}\right)} d^{2} e^{6}\right)} x^{2} + 5 \, {\left(240 \, B c^{4} d^{6} e^{2} + 8 \, A b^{3} c d^{2} e^{6} - 4 \, {\left(121 \, B b c^{3} + 30 \, A c^{4}\right)} d^{5} e^{3} + {\left(291 \, B b^{2} c^{2} + 212 \, A b c^{3}\right)} d^{4} e^{4} - {\left(47 \, B b^{3} c + 100 \, A b^{2} c^{2}\right)} d^{3} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{2} d^{5} e^{7} - b c d^{4} e^{8} + {\left(c^{2} d^{2} e^{10} - b c d e^{11}\right)} x^{3} + 3 \, {\left(c^{2} d^{3} e^{9} - b c d^{2} e^{10}\right)} x^{2} + 3 \, {\left(c^{2} d^{4} e^{8} - b c d^{3} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/48*(15*(64*B*c^4*d^8 - 16*(9*B*b*c^3 + 2*A*c^4)*d^7*e + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^6*e^2 - (25*B*b^3*c + 38*A*b^2*c^2)*d^5*e^3 + (B*b^4 + 6*A*b^3*c)*d^4*e^4 + (64*B*c^4*d^5*e^3 - 16*(9*B*b*c^3 + 2*A*c^4)*d^4*e^4 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^3*e^5 - (25*B*b^3*c + 38*A*b^2*c^2)*d^2*e^6 + (B*b^4 + 6*A*b^3*c)*d*e^7)*x^3 + 3*(64*B*c^4*d^6*e^2 - 16*(9*B*b*c^3 + 2*A*c^4)*d^5*e^3 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^4*e^4 - (25*B*b^3*c + 38*A*b^2*c^2)*d^3*e^5 + (B*b^4 + 6*A*b^3*c)*d^2*e^6)*x^2 + 3*(64*B*c^4*d^7*e - 16*(9*B*b*c^3 + 2*A*c^4)*d^6*e^2 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^5*e^3 - (25*B*b^3*c + 38*A*b^2*c^2)*d^4*e^4 + (B*b^4 + 6*A*b^3*c)*d^3*e^5)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 15*(64*B*c^4*d^7 + A*b^3*c*d^3*e^4 - 16*(7*B*b*c^3 + 2*A*c^4)*d^6*e + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^5*e^2 - (7*B*b^3*c + 18*A*b^2*c^2)*d^4*e^3 + (64*B*c^4*d^4*e^3 + A*b^3*c*e^7 - 16*(7*B*b*c^3 + 2*A*c^4)*d^3*e^4 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^2*e^5 - (7*B*b^3*c + 18*A*b^2*c^2)*d*e^6)*x^3 + 3*(64*B*c^4*d^5*e^2 + A*b^3*c*d*e^6 - 16*(7*B*b*c^3 + 2*A*c^4)*d^4*e^3 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^3*e^4 - (7*B*b^3*c + 18*A*b^2*c^2)*d^2*e^5)*x^2 + 3*(64*B*c^4*d^6*e + A*b^3*c*d^2*e^5 - 16*(7*B*b*c^3 + 2*A*c^4)*d^5*e^2 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^4*e^3 - (7*B*b^3*c + 18*A*b^2*c^2)*d^3*e^4)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(480*B*c^4*d^7*e + 15*A*b^3*c*d^3*e^5 - 240*(4*B*b*c^3 + A*c^4)*d^6*e^2 + 30*(19*B*b^2*c^2 + 14*A*b*c^3)*d^5*e^3 - 15*(6*B*b^3*c + 13*A*b^2*c^2)*d^4*e^4 + 8*(B*c^4*d^2*e^6 - B*b*c^3*d*e^7)*x^5 - 2*(12*B*c^4*d^3*e^5 - (25*B*b*c^3 + 6*A*c^4)*d^2*e^6 + (13*B*b^2*c^2 + 6*A*b*c^3)*d*e^7)*x^4 + 3*(40*B*c^4*d^4*e^4 - 2*(43*B*b*c^3 + 10*A*c^4)*d^3*e^5 + 19*(3*B*b^2*c^2 + 2*A*b*c^3)*d^2*e^6 - (11*B*b^3*c + 18*A*b^2*c^2)*d*e^7)*x^3 + (880*B*c^4*d^5*e^3 + 33*A*b^3*c*d*e^7 - 40*(45*B*b*c^3 + 11*A*c^4)*d^4*e^4 + 158*(7*B*b^2*c^2 + 5*A*b*c^3)*d^3*e^5 - (186*B*b^3*c + 383*A*b^2*c^2)*d^2*e^6)*x^2 + 5*(240*B*c^4*d^6*e^2 + 8*A*b^3*c*d^2*e^6 - 4*(121*B*b*c^3 + 30*A*c^4)*d^5*e^3 + (291*B*b^2*c^2 + 212*A*b*c^3)*d^4*e^4 - (47*B*b^3*c + 100*A*b^2*c^2)*d^3*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*d^5*e^7 - b*c*d^4*e^8 + (c^2*d^2*e^10 - b*c*d*e^11)*x^3 + 3*(c^2*d^3*e^9 - b*c*d^2*e^10)*x^2 + 3*(c^2*d^4*e^8 - b*c*d^3*e^9)*x), 1/48*(30*(64*B*c^4*d^7 + A*b^3*c*d^3*e^4 - 16*(7*B*b*c^3 + 2*A*c^4)*d^6*e + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^5*e^2 - (7*B*b^3*c + 18*A*b^2*c^2)*d^4*e^3 + (64*B*c^4*d^4*e^3 + A*b^3*c*e^7 - 16*(7*B*b*c^3 + 2*A*c^4)*d^3*e^4 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^2*e^5 - (7*B*b^3*c + 18*A*b^2*c^2)*d*e^6)*x^3 + 3*(64*B*c^4*d^5*e^2 + A*b^3*c*d*e^6 - 16*(7*B*b*c^3 + 2*A*c^4)*d^4*e^3 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^3*e^4 - (7*B*b^3*c + 18*A*b^2*c^2)*d^2*e^5)*x^2 + 3*(64*B*c^4*d^6*e + A*b^3*c*d^2*e^5 - 16*(7*B*b*c^3 + 2*A*c^4)*d^5*e^2 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^4*e^3 - (7*B*b^3*c + 18*A*b^2*c^2)*d^3*e^4)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 15*(64*B*c^4*d^8 - 16*(9*B*b*c^3 + 2*A*c^4)*d^7*e + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^6*e^2 - (25*B*b^3*c + 38*A*b^2*c^2)*d^5*e^3 + (B*b^4 + 6*A*b^3*c)*d^4*e^4 + (64*B*c^4*d^5*e^3 - 16*(9*B*b*c^3 + 2*A*c^4)*d^4*e^4 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^3*e^5 - (25*B*b^3*c + 38*A*b^2*c^2)*d^2*e^6 + (B*b^4 + 6*A*b^3*c)*d*e^7)*x^3 + 3*(64*B*c^4*d^6*e^2 - 16*(9*B*b*c^3 + 2*A*c^4)*d^5*e^3 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^4*e^4 - (25*B*b^3*c + 38*A*b^2*c^2)*d^3*e^5 + (B*b^4 + 6*A*b^3*c)*d^2*e^6)*x^2 + 3*(64*B*c^4*d^7*e - 16*(9*B*b*c^3 + 2*A*c^4)*d^6*e^2 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^5*e^3 - (25*B*b^3*c + 38*A*b^2*c^2)*d^4*e^4 + (B*b^4 + 6*A*b^3*c)*d^3*e^5)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(480*B*c^4*d^7*e + 15*A*b^3*c*d^3*e^5 - 240*(4*B*b*c^3 + A*c^4)*d^6*e^2 + 30*(19*B*b^2*c^2 + 14*A*b*c^3)*d^5*e^3 - 15*(6*B*b^3*c + 13*A*b^2*c^2)*d^4*e^4 + 8*(B*c^4*d^2*e^6 - B*b*c^3*d*e^7)*x^5 - 2*(12*B*c^4*d^3*e^5 - (25*B*b*c^3 + 6*A*c^4)*d^2*e^6 + (13*B*b^2*c^2 + 6*A*b*c^3)*d*e^7)*x^4 + 3*(40*B*c^4*d^4*e^4 - 2*(43*B*b*c^3 + 10*A*c^4)*d^3*e^5 + 19*(3*B*b^2*c^2 + 2*A*b*c^3)*d^2*e^6 - (11*B*b^3*c + 18*A*b^2*c^2)*d*e^7)*x^3 + (880*B*c^4*d^5*e^3 + 33*A*b^3*c*d*e^7 - 40*(45*B*b*c^3 + 11*A*c^4)*d^4*e^4 + 158*(7*B*b^2*c^2 + 5*A*b*c^3)*d^3*e^5 - (186*B*b^3*c + 383*A*b^2*c^2)*d^2*e^6)*x^2 + 5*(240*B*c^4*d^6*e^2 + 8*A*b^3*c*d^2*e^6 - 4*(121*B*b*c^3 + 30*A*c^4)*d^5*e^3 + (291*B*b^2*c^2 + 212*A*b*c^3)*d^4*e^4 - (47*B*b^3*c + 100*A*b^2*c^2)*d^3*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*d^5*e^7 - b*c*d^4*e^8 + (c^2*d^2*e^10 - b*c*d*e^11)*x^3 + 3*(c^2*d^3*e^9 - b*c*d^2*e^10)*x^2 + 3*(c^2*d^4*e^8 - b*c*d^3*e^9)*x), 1/48*(30*(64*B*c^4*d^8 - 16*(9*B*b*c^3 + 2*A*c^4)*d^7*e + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^6*e^2 - (25*B*b^3*c + 38*A*b^2*c^2)*d^5*e^3 + (B*b^4 + 6*A*b^3*c)*d^4*e^4 + (64*B*c^4*d^5*e^3 - 16*(9*B*b*c^3 + 2*A*c^4)*d^4*e^4 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^3*e^5 - (25*B*b^3*c + 38*A*b^2*c^2)*d^2*e^6 + (B*b^4 + 6*A*b^3*c)*d*e^7)*x^3 + 3*(64*B*c^4*d^6*e^2 - 16*(9*B*b*c^3 + 2*A*c^4)*d^5*e^3 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^4*e^4 - (25*B*b^3*c + 38*A*b^2*c^2)*d^3*e^5 + (B*b^4 + 6*A*b^3*c)*d^2*e^6)*x^2 + 3*(64*B*c^4*d^7*e - 16*(9*B*b*c^3 + 2*A*c^4)*d^6*e^2 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^5*e^3 - (25*B*b^3*c + 38*A*b^2*c^2)*d^4*e^4 + (B*b^4 + 6*A*b^3*c)*d^3*e^5)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - 15*(64*B*c^4*d^7 + A*b^3*c*d^3*e^4 - 16*(7*B*b*c^3 + 2*A*c^4)*d^6*e + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^5*e^2 - (7*B*b^3*c + 18*A*b^2*c^2)*d^4*e^3 + (64*B*c^4*d^4*e^3 + A*b^3*c*e^7 - 16*(7*B*b*c^3 + 2*A*c^4)*d^3*e^4 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^2*e^5 - (7*B*b^3*c + 18*A*b^2*c^2)*d*e^6)*x^3 + 3*(64*B*c^4*d^5*e^2 + A*b^3*c*d*e^6 - 16*(7*B*b*c^3 + 2*A*c^4)*d^4*e^3 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^3*e^4 - (7*B*b^3*c + 18*A*b^2*c^2)*d^2*e^5)*x^2 + 3*(64*B*c^4*d^6*e + A*b^3*c*d^2*e^5 - 16*(7*B*b*c^3 + 2*A*c^4)*d^5*e^2 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^4*e^3 - (7*B*b^3*c + 18*A*b^2*c^2)*d^3*e^4)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(480*B*c^4*d^7*e + 15*A*b^3*c*d^3*e^5 - 240*(4*B*b*c^3 + A*c^4)*d^6*e^2 + 30*(19*B*b^2*c^2 + 14*A*b*c^3)*d^5*e^3 - 15*(6*B*b^3*c + 13*A*b^2*c^2)*d^4*e^4 + 8*(B*c^4*d^2*e^6 - B*b*c^3*d*e^7)*x^5 - 2*(12*B*c^4*d^3*e^5 - (25*B*b*c^3 + 6*A*c^4)*d^2*e^6 + (13*B*b^2*c^2 + 6*A*b*c^3)*d*e^7)*x^4 + 3*(40*B*c^4*d^4*e^4 - 2*(43*B*b*c^3 + 10*A*c^4)*d^3*e^5 + 19*(3*B*b^2*c^2 + 2*A*b*c^3)*d^2*e^6 - (11*B*b^3*c + 18*A*b^2*c^2)*d*e^7)*x^3 + (880*B*c^4*d^5*e^3 + 33*A*b^3*c*d*e^7 - 40*(45*B*b*c^3 + 11*A*c^4)*d^4*e^4 + 158*(7*B*b^2*c^2 + 5*A*b*c^3)*d^3*e^5 - (186*B*b^3*c + 383*A*b^2*c^2)*d^2*e^6)*x^2 + 5*(240*B*c^4*d^6*e^2 + 8*A*b^3*c*d^2*e^6 - 4*(121*B*b*c^3 + 30*A*c^4)*d^5*e^3 + (291*B*b^2*c^2 + 212*A*b*c^3)*d^4*e^4 - (47*B*b^3*c + 100*A*b^2*c^2)*d^3*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*d^5*e^7 - b*c*d^4*e^8 + (c^2*d^2*e^10 - b*c*d*e^11)*x^3 + 3*(c^2*d^3*e^9 - b*c*d^2*e^10)*x^2 + 3*(c^2*d^4*e^8 - b*c*d^3*e^9)*x), 1/24*(15*(64*B*c^4*d^7 + A*b^3*c*d^3*e^4 - 16*(7*B*b*c^3 + 2*A*c^4)*d^6*e + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^5*e^2 - (7*B*b^3*c + 18*A*b^2*c^2)*d^4*e^3 + (64*B*c^4*d^4*e^3 + A*b^3*c*e^7 - 16*(7*B*b*c^3 + 2*A*c^4)*d^3*e^4 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^2*e^5 - (7*B*b^3*c + 18*A*b^2*c^2)*d*e^6)*x^3 + 3*(64*B*c^4*d^5*e^2 + A*b^3*c*d*e^6 - 16*(7*B*b*c^3 + 2*A*c^4)*d^4*e^3 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^3*e^4 - (7*B*b^3*c + 18*A*b^2*c^2)*d^2*e^5)*x^2 + 3*(64*B*c^4*d^6*e + A*b^3*c*d^2*e^5 - 16*(7*B*b*c^3 + 2*A*c^4)*d^5*e^2 + 8*(7*B*b^2*c^2 + 6*A*b*c^3)*d^4*e^3 - (7*B*b^3*c + 18*A*b^2*c^2)*d^3*e^4)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 15*(64*B*c^4*d^8 - 16*(9*B*b*c^3 + 2*A*c^4)*d^7*e + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^6*e^2 - (25*B*b^3*c + 38*A*b^2*c^2)*d^5*e^3 + (B*b^4 + 6*A*b^3*c)*d^4*e^4 + (64*B*c^4*d^5*e^3 - 16*(9*B*b*c^3 + 2*A*c^4)*d^4*e^4 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^3*e^5 - (25*B*b^3*c + 38*A*b^2*c^2)*d^2*e^6 + (B*b^4 + 6*A*b^3*c)*d*e^7)*x^3 + 3*(64*B*c^4*d^6*e^2 - 16*(9*B*b*c^3 + 2*A*c^4)*d^5*e^3 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^4*e^4 - (25*B*b^3*c + 38*A*b^2*c^2)*d^3*e^5 + (B*b^4 + 6*A*b^3*c)*d^2*e^6)*x^2 + 3*(64*B*c^4*d^7*e - 16*(9*B*b*c^3 + 2*A*c^4)*d^6*e^2 + 8*(13*B*b^2*c^2 + 8*A*b*c^3)*d^5*e^3 - (25*B*b^3*c + 38*A*b^2*c^2)*d^4*e^4 + (B*b^4 + 6*A*b^3*c)*d^3*e^5)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (480*B*c^4*d^7*e + 15*A*b^3*c*d^3*e^5 - 240*(4*B*b*c^3 + A*c^4)*d^6*e^2 + 30*(19*B*b^2*c^2 + 14*A*b*c^3)*d^5*e^3 - 15*(6*B*b^3*c + 13*A*b^2*c^2)*d^4*e^4 + 8*(B*c^4*d^2*e^6 - B*b*c^3*d*e^7)*x^5 - 2*(12*B*c^4*d^3*e^5 - (25*B*b*c^3 + 6*A*c^4)*d^2*e^6 + (13*B*b^2*c^2 + 6*A*b*c^3)*d*e^7)*x^4 + 3*(40*B*c^4*d^4*e^4 - 2*(43*B*b*c^3 + 10*A*c^4)*d^3*e^5 + 19*(3*B*b^2*c^2 + 2*A*b*c^3)*d^2*e^6 - (11*B*b^3*c + 18*A*b^2*c^2)*d*e^7)*x^3 + (880*B*c^4*d^5*e^3 + 33*A*b^3*c*d*e^7 - 40*(45*B*b*c^3 + 11*A*c^4)*d^4*e^4 + 158*(7*B*b^2*c^2 + 5*A*b*c^3)*d^3*e^5 - (186*B*b^3*c + 383*A*b^2*c^2)*d^2*e^6)*x^2 + 5*(240*B*c^4*d^6*e^2 + 8*A*b^3*c*d^2*e^6 - 4*(121*B*b*c^3 + 30*A*c^4)*d^5*e^3 + (291*B*b^2*c^2 + 212*A*b*c^3)*d^4*e^4 - (47*B*b^3*c + 100*A*b^2*c^2)*d^3*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*d^5*e^7 - b*c*d^4*e^8 + (c^2*d^2*e^10 - b*c*d*e^11)*x^3 + 3*(c^2*d^3*e^9 - b*c*d^2*e^10)*x^2 + 3*(c^2*d^4*e^8 - b*c*d^3*e^9)*x)]","B",0
1190,1,8045,0,15.834549," ","integrate((B*x+A)*(c*x^2+b*x)^(5/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[\frac{240 \, {\left(24 \, B c^{4} d^{10} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{9} e + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{8} e^{2} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{7} e^{3} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{6} e^{4} + {\left(24 \, B c^{4} d^{6} e^{4} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{5} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{4} e^{6} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{3} e^{7} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{2} e^{8}\right)} x^{4} + 4 \, {\left(24 \, B c^{4} d^{7} e^{3} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e^{4} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{5} e^{5} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{4} e^{6} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{3} + 6 \, {\left(24 \, B c^{4} d^{8} e^{2} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{7} e^{3} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{6} e^{4} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{5} e^{5} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{4} e^{6}\right)} x^{2} + 4 \, {\left(24 \, B c^{4} d^{9} e - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{8} e^{2} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{7} e^{3} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{6} e^{4} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{5} e^{5}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 15 \, {\left(384 \, B c^{4} d^{9} + A b^{4} d^{4} e^{5} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{8} e + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{7} e^{2} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{6} e^{3} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{5} e^{4} + {\left(384 \, B c^{4} d^{5} e^{4} + A b^{4} e^{9} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{4} e^{5} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{3} e^{6} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{2} e^{7} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d e^{8}\right)} x^{4} + 4 \, {\left(384 \, B c^{4} d^{6} e^{3} + A b^{4} d e^{8} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{5} e^{4} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{4} e^{5} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{3} e^{6} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{2} e^{7}\right)} x^{3} + 6 \, {\left(384 \, B c^{4} d^{7} e^{2} + A b^{4} d^{2} e^{7} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{6} e^{3} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{5} e^{4} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{4} e^{5} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{3} e^{6}\right)} x^{2} + 4 \, {\left(384 \, B c^{4} d^{8} e + A b^{4} d^{3} e^{6} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{7} e^{2} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{6} e^{3} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{5} e^{4} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{4} e^{5}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(2880 \, B c^{4} d^{9} e + 15 \, A b^{4} d^{4} e^{6} - 240 \, {\left(31 \, B b c^{3} + 4 \, A c^{4}\right)} d^{8} e^{2} + 120 \, {\left(53 \, B b^{2} c^{2} + 18 \, A b c^{3}\right)} d^{7} e^{3} - 15 \, {\left(127 \, B b^{3} c + 96 \, A b^{2} c^{2}\right)} d^{6} e^{4} + 15 \, {\left(7 \, B b^{4} + 15 \, A b^{3} c\right)} d^{5} e^{5} - 96 \, {\left(B c^{4} d^{4} e^{6} - 2 \, B b c^{3} d^{3} e^{7} + B b^{2} c^{2} d^{2} e^{8}\right)} x^{5} + 48 \, {\left(12 \, B c^{4} d^{5} e^{5} - {\left(33 \, B b c^{3} + 4 \, A c^{4}\right)} d^{4} e^{6} + 2 \, {\left(15 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{3} e^{7} - {\left(9 \, B b^{3} c + 4 \, A b^{2} c^{2}\right)} d^{2} e^{8}\right)} x^{4} + {\left(6000 \, B c^{4} d^{6} e^{4} - 15 \, A b^{4} d e^{9} - 8 \, {\left(1981 \, B b c^{3} + 250 \, A c^{4}\right)} d^{5} e^{5} + 2 \, {\left(6995 \, B b^{2} c^{2} + 2308 \, A b c^{3}\right)} d^{4} e^{6} - {\left(4421 \, B b^{3} c + 3262 \, A b^{2} c^{2}\right)} d^{3} e^{7} + {\left(279 \, B b^{4} + 661 \, A b^{3} c\right)} d^{2} e^{8}\right)} x^{3} + {\left(12480 \, B c^{4} d^{7} e^{3} + 73 \, A b^{4} d^{2} e^{8} - 40 \, {\left(815 \, B b c^{3} + 104 \, A c^{4}\right)} d^{6} e^{4} + 4 \, {\left(7079 \, B b^{2} c^{2} + 2370 \, A b c^{3}\right)} d^{5} e^{5} - {\left(8707 \, B b^{3} c + 6452 \, A b^{2} c^{2}\right)} d^{4} e^{6} + {\left(511 \, B b^{4} + 1059 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{2} + 5 \, {\left(2016 \, B c^{4} d^{8} e^{2} + 11 \, A b^{4} d^{3} e^{7} - 48 \, {\left(109 \, B b c^{3} + 14 \, A c^{4}\right)} d^{7} e^{3} + 2 \, {\left(2251 \, B b^{2} c^{2} + 760 \, A b c^{3}\right)} d^{6} e^{4} - {\left(1363 \, B b^{3} c + 1022 \, A b^{2} c^{2}\right)} d^{5} e^{5} + {\left(77 \, B b^{4} + 163 \, A b^{3} c\right)} d^{4} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{2} d^{8} e^{7} - 2 \, b c d^{7} e^{8} + b^{2} d^{6} e^{9} + {\left(c^{2} d^{4} e^{11} - 2 \, b c d^{3} e^{12} + b^{2} d^{2} e^{13}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{10} - 2 \, b c d^{4} e^{11} + b^{2} d^{3} e^{12}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{9} - 2 \, b c d^{5} e^{10} + b^{2} d^{4} e^{11}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{8} - 2 \, b c d^{6} e^{9} + b^{2} d^{5} e^{10}\right)} x\right)}}, -\frac{15 \, {\left(384 \, B c^{4} d^{9} + A b^{4} d^{4} e^{5} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{8} e + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{7} e^{2} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{6} e^{3} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{5} e^{4} + {\left(384 \, B c^{4} d^{5} e^{4} + A b^{4} e^{9} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{4} e^{5} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{3} e^{6} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{2} e^{7} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d e^{8}\right)} x^{4} + 4 \, {\left(384 \, B c^{4} d^{6} e^{3} + A b^{4} d e^{8} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{5} e^{4} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{4} e^{5} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{3} e^{6} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{2} e^{7}\right)} x^{3} + 6 \, {\left(384 \, B c^{4} d^{7} e^{2} + A b^{4} d^{2} e^{7} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{6} e^{3} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{5} e^{4} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{4} e^{5} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{3} e^{6}\right)} x^{2} + 4 \, {\left(384 \, B c^{4} d^{8} e + A b^{4} d^{3} e^{6} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{7} e^{2} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{6} e^{3} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{5} e^{4} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{4} e^{5}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 120 \, {\left(24 \, B c^{4} d^{10} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{9} e + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{8} e^{2} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{7} e^{3} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{6} e^{4} + {\left(24 \, B c^{4} d^{6} e^{4} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{5} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{4} e^{6} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{3} e^{7} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{2} e^{8}\right)} x^{4} + 4 \, {\left(24 \, B c^{4} d^{7} e^{3} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e^{4} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{5} e^{5} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{4} e^{6} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{3} + 6 \, {\left(24 \, B c^{4} d^{8} e^{2} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{7} e^{3} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{6} e^{4} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{5} e^{5} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{4} e^{6}\right)} x^{2} + 4 \, {\left(24 \, B c^{4} d^{9} e - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{8} e^{2} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{7} e^{3} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{6} e^{4} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{5} e^{5}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + {\left(2880 \, B c^{4} d^{9} e + 15 \, A b^{4} d^{4} e^{6} - 240 \, {\left(31 \, B b c^{3} + 4 \, A c^{4}\right)} d^{8} e^{2} + 120 \, {\left(53 \, B b^{2} c^{2} + 18 \, A b c^{3}\right)} d^{7} e^{3} - 15 \, {\left(127 \, B b^{3} c + 96 \, A b^{2} c^{2}\right)} d^{6} e^{4} + 15 \, {\left(7 \, B b^{4} + 15 \, A b^{3} c\right)} d^{5} e^{5} - 96 \, {\left(B c^{4} d^{4} e^{6} - 2 \, B b c^{3} d^{3} e^{7} + B b^{2} c^{2} d^{2} e^{8}\right)} x^{5} + 48 \, {\left(12 \, B c^{4} d^{5} e^{5} - {\left(33 \, B b c^{3} + 4 \, A c^{4}\right)} d^{4} e^{6} + 2 \, {\left(15 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{3} e^{7} - {\left(9 \, B b^{3} c + 4 \, A b^{2} c^{2}\right)} d^{2} e^{8}\right)} x^{4} + {\left(6000 \, B c^{4} d^{6} e^{4} - 15 \, A b^{4} d e^{9} - 8 \, {\left(1981 \, B b c^{3} + 250 \, A c^{4}\right)} d^{5} e^{5} + 2 \, {\left(6995 \, B b^{2} c^{2} + 2308 \, A b c^{3}\right)} d^{4} e^{6} - {\left(4421 \, B b^{3} c + 3262 \, A b^{2} c^{2}\right)} d^{3} e^{7} + {\left(279 \, B b^{4} + 661 \, A b^{3} c\right)} d^{2} e^{8}\right)} x^{3} + {\left(12480 \, B c^{4} d^{7} e^{3} + 73 \, A b^{4} d^{2} e^{8} - 40 \, {\left(815 \, B b c^{3} + 104 \, A c^{4}\right)} d^{6} e^{4} + 4 \, {\left(7079 \, B b^{2} c^{2} + 2370 \, A b c^{3}\right)} d^{5} e^{5} - {\left(8707 \, B b^{3} c + 6452 \, A b^{2} c^{2}\right)} d^{4} e^{6} + {\left(511 \, B b^{4} + 1059 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{2} + 5 \, {\left(2016 \, B c^{4} d^{8} e^{2} + 11 \, A b^{4} d^{3} e^{7} - 48 \, {\left(109 \, B b c^{3} + 14 \, A c^{4}\right)} d^{7} e^{3} + 2 \, {\left(2251 \, B b^{2} c^{2} + 760 \, A b c^{3}\right)} d^{6} e^{4} - {\left(1363 \, B b^{3} c + 1022 \, A b^{2} c^{2}\right)} d^{5} e^{5} + {\left(77 \, B b^{4} + 163 \, A b^{3} c\right)} d^{4} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{2} d^{8} e^{7} - 2 \, b c d^{7} e^{8} + b^{2} d^{6} e^{9} + {\left(c^{2} d^{4} e^{11} - 2 \, b c d^{3} e^{12} + b^{2} d^{2} e^{13}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{10} - 2 \, b c d^{4} e^{11} + b^{2} d^{3} e^{12}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{9} - 2 \, b c d^{5} e^{10} + b^{2} d^{4} e^{11}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{8} - 2 \, b c d^{6} e^{9} + b^{2} d^{5} e^{10}\right)} x\right)}}, -\frac{480 \, {\left(24 \, B c^{4} d^{10} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{9} e + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{8} e^{2} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{7} e^{3} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{6} e^{4} + {\left(24 \, B c^{4} d^{6} e^{4} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{5} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{4} e^{6} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{3} e^{7} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{2} e^{8}\right)} x^{4} + 4 \, {\left(24 \, B c^{4} d^{7} e^{3} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e^{4} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{5} e^{5} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{4} e^{6} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{3} + 6 \, {\left(24 \, B c^{4} d^{8} e^{2} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{7} e^{3} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{6} e^{4} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{5} e^{5} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{4} e^{6}\right)} x^{2} + 4 \, {\left(24 \, B c^{4} d^{9} e - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{8} e^{2} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{7} e^{3} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{6} e^{4} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{5} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 15 \, {\left(384 \, B c^{4} d^{9} + A b^{4} d^{4} e^{5} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{8} e + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{7} e^{2} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{6} e^{3} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{5} e^{4} + {\left(384 \, B c^{4} d^{5} e^{4} + A b^{4} e^{9} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{4} e^{5} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{3} e^{6} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{2} e^{7} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d e^{8}\right)} x^{4} + 4 \, {\left(384 \, B c^{4} d^{6} e^{3} + A b^{4} d e^{8} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{5} e^{4} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{4} e^{5} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{3} e^{6} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{2} e^{7}\right)} x^{3} + 6 \, {\left(384 \, B c^{4} d^{7} e^{2} + A b^{4} d^{2} e^{7} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{6} e^{3} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{5} e^{4} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{4} e^{5} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{3} e^{6}\right)} x^{2} + 4 \, {\left(384 \, B c^{4} d^{8} e + A b^{4} d^{3} e^{6} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{7} e^{2} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{6} e^{3} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{5} e^{4} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{4} e^{5}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(2880 \, B c^{4} d^{9} e + 15 \, A b^{4} d^{4} e^{6} - 240 \, {\left(31 \, B b c^{3} + 4 \, A c^{4}\right)} d^{8} e^{2} + 120 \, {\left(53 \, B b^{2} c^{2} + 18 \, A b c^{3}\right)} d^{7} e^{3} - 15 \, {\left(127 \, B b^{3} c + 96 \, A b^{2} c^{2}\right)} d^{6} e^{4} + 15 \, {\left(7 \, B b^{4} + 15 \, A b^{3} c\right)} d^{5} e^{5} - 96 \, {\left(B c^{4} d^{4} e^{6} - 2 \, B b c^{3} d^{3} e^{7} + B b^{2} c^{2} d^{2} e^{8}\right)} x^{5} + 48 \, {\left(12 \, B c^{4} d^{5} e^{5} - {\left(33 \, B b c^{3} + 4 \, A c^{4}\right)} d^{4} e^{6} + 2 \, {\left(15 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{3} e^{7} - {\left(9 \, B b^{3} c + 4 \, A b^{2} c^{2}\right)} d^{2} e^{8}\right)} x^{4} + {\left(6000 \, B c^{4} d^{6} e^{4} - 15 \, A b^{4} d e^{9} - 8 \, {\left(1981 \, B b c^{3} + 250 \, A c^{4}\right)} d^{5} e^{5} + 2 \, {\left(6995 \, B b^{2} c^{2} + 2308 \, A b c^{3}\right)} d^{4} e^{6} - {\left(4421 \, B b^{3} c + 3262 \, A b^{2} c^{2}\right)} d^{3} e^{7} + {\left(279 \, B b^{4} + 661 \, A b^{3} c\right)} d^{2} e^{8}\right)} x^{3} + {\left(12480 \, B c^{4} d^{7} e^{3} + 73 \, A b^{4} d^{2} e^{8} - 40 \, {\left(815 \, B b c^{3} + 104 \, A c^{4}\right)} d^{6} e^{4} + 4 \, {\left(7079 \, B b^{2} c^{2} + 2370 \, A b c^{3}\right)} d^{5} e^{5} - {\left(8707 \, B b^{3} c + 6452 \, A b^{2} c^{2}\right)} d^{4} e^{6} + {\left(511 \, B b^{4} + 1059 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{2} + 5 \, {\left(2016 \, B c^{4} d^{8} e^{2} + 11 \, A b^{4} d^{3} e^{7} - 48 \, {\left(109 \, B b c^{3} + 14 \, A c^{4}\right)} d^{7} e^{3} + 2 \, {\left(2251 \, B b^{2} c^{2} + 760 \, A b c^{3}\right)} d^{6} e^{4} - {\left(1363 \, B b^{3} c + 1022 \, A b^{2} c^{2}\right)} d^{5} e^{5} + {\left(77 \, B b^{4} + 163 \, A b^{3} c\right)} d^{4} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{2} d^{8} e^{7} - 2 \, b c d^{7} e^{8} + b^{2} d^{6} e^{9} + {\left(c^{2} d^{4} e^{11} - 2 \, b c d^{3} e^{12} + b^{2} d^{2} e^{13}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{10} - 2 \, b c d^{4} e^{11} + b^{2} d^{3} e^{12}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{9} - 2 \, b c d^{5} e^{10} + b^{2} d^{4} e^{11}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{8} - 2 \, b c d^{6} e^{9} + b^{2} d^{5} e^{10}\right)} x\right)}}, -\frac{15 \, {\left(384 \, B c^{4} d^{9} + A b^{4} d^{4} e^{5} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{8} e + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{7} e^{2} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{6} e^{3} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{5} e^{4} + {\left(384 \, B c^{4} d^{5} e^{4} + A b^{4} e^{9} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{4} e^{5} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{3} e^{6} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{2} e^{7} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d e^{8}\right)} x^{4} + 4 \, {\left(384 \, B c^{4} d^{6} e^{3} + A b^{4} d e^{8} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{5} e^{4} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{4} e^{5} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{3} e^{6} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{2} e^{7}\right)} x^{3} + 6 \, {\left(384 \, B c^{4} d^{7} e^{2} + A b^{4} d^{2} e^{7} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{6} e^{3} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{5} e^{4} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{4} e^{5} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{3} e^{6}\right)} x^{2} + 4 \, {\left(384 \, B c^{4} d^{8} e + A b^{4} d^{3} e^{6} - 128 \, {\left(7 \, B b c^{3} + A c^{4}\right)} d^{7} e^{2} + 32 \, {\left(21 \, B b^{2} c^{2} + 8 \, A b c^{3}\right)} d^{6} e^{3} - 24 \, {\left(7 \, B b^{3} c + 6 \, A b^{2} c^{2}\right)} d^{5} e^{4} + {\left(7 \, B b^{4} + 16 \, A b^{3} c\right)} d^{4} e^{5}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 240 \, {\left(24 \, B c^{4} d^{10} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{9} e + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{8} e^{2} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{7} e^{3} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{6} e^{4} + {\left(24 \, B c^{4} d^{6} e^{4} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{5} e^{5} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{4} e^{6} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{3} e^{7} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{2} e^{8}\right)} x^{4} + 4 \, {\left(24 \, B c^{4} d^{7} e^{3} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{6} e^{4} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{5} e^{5} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{4} e^{6} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{3} + 6 \, {\left(24 \, B c^{4} d^{8} e^{2} - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{7} e^{3} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{6} e^{4} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{5} e^{5} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{4} e^{6}\right)} x^{2} + 4 \, {\left(24 \, B c^{4} d^{9} e - 4 \, {\left(17 \, B b c^{3} + 2 \, A c^{4}\right)} d^{8} e^{2} + {\left(67 \, B b^{2} c^{2} + 20 \, A b c^{3}\right)} d^{7} e^{3} - 2 \, {\left(13 \, B b^{3} c + 8 \, A b^{2} c^{2}\right)} d^{6} e^{4} + {\left(3 \, B b^{4} + 4 \, A b^{3} c\right)} d^{5} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(2880 \, B c^{4} d^{9} e + 15 \, A b^{4} d^{4} e^{6} - 240 \, {\left(31 \, B b c^{3} + 4 \, A c^{4}\right)} d^{8} e^{2} + 120 \, {\left(53 \, B b^{2} c^{2} + 18 \, A b c^{3}\right)} d^{7} e^{3} - 15 \, {\left(127 \, B b^{3} c + 96 \, A b^{2} c^{2}\right)} d^{6} e^{4} + 15 \, {\left(7 \, B b^{4} + 15 \, A b^{3} c\right)} d^{5} e^{5} - 96 \, {\left(B c^{4} d^{4} e^{6} - 2 \, B b c^{3} d^{3} e^{7} + B b^{2} c^{2} d^{2} e^{8}\right)} x^{5} + 48 \, {\left(12 \, B c^{4} d^{5} e^{5} - {\left(33 \, B b c^{3} + 4 \, A c^{4}\right)} d^{4} e^{6} + 2 \, {\left(15 \, B b^{2} c^{2} + 4 \, A b c^{3}\right)} d^{3} e^{7} - {\left(9 \, B b^{3} c + 4 \, A b^{2} c^{2}\right)} d^{2} e^{8}\right)} x^{4} + {\left(6000 \, B c^{4} d^{6} e^{4} - 15 \, A b^{4} d e^{9} - 8 \, {\left(1981 \, B b c^{3} + 250 \, A c^{4}\right)} d^{5} e^{5} + 2 \, {\left(6995 \, B b^{2} c^{2} + 2308 \, A b c^{3}\right)} d^{4} e^{6} - {\left(4421 \, B b^{3} c + 3262 \, A b^{2} c^{2}\right)} d^{3} e^{7} + {\left(279 \, B b^{4} + 661 \, A b^{3} c\right)} d^{2} e^{8}\right)} x^{3} + {\left(12480 \, B c^{4} d^{7} e^{3} + 73 \, A b^{4} d^{2} e^{8} - 40 \, {\left(815 \, B b c^{3} + 104 \, A c^{4}\right)} d^{6} e^{4} + 4 \, {\left(7079 \, B b^{2} c^{2} + 2370 \, A b c^{3}\right)} d^{5} e^{5} - {\left(8707 \, B b^{3} c + 6452 \, A b^{2} c^{2}\right)} d^{4} e^{6} + {\left(511 \, B b^{4} + 1059 \, A b^{3} c\right)} d^{3} e^{7}\right)} x^{2} + 5 \, {\left(2016 \, B c^{4} d^{8} e^{2} + 11 \, A b^{4} d^{3} e^{7} - 48 \, {\left(109 \, B b c^{3} + 14 \, A c^{4}\right)} d^{7} e^{3} + 2 \, {\left(2251 \, B b^{2} c^{2} + 760 \, A b c^{3}\right)} d^{6} e^{4} - {\left(1363 \, B b^{3} c + 1022 \, A b^{2} c^{2}\right)} d^{5} e^{5} + {\left(77 \, B b^{4} + 163 \, A b^{3} c\right)} d^{4} e^{6}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{2} d^{8} e^{7} - 2 \, b c d^{7} e^{8} + b^{2} d^{6} e^{9} + {\left(c^{2} d^{4} e^{11} - 2 \, b c d^{3} e^{12} + b^{2} d^{2} e^{13}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{10} - 2 \, b c d^{4} e^{11} + b^{2} d^{3} e^{12}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{9} - 2 \, b c d^{5} e^{10} + b^{2} d^{4} e^{11}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{8} - 2 \, b c d^{6} e^{9} + b^{2} d^{5} e^{10}\right)} x\right)}}\right]"," ",0,"[1/384*(240*(24*B*c^4*d^10 - 4*(17*B*b*c^3 + 2*A*c^4)*d^9*e + (67*B*b^2*c^2 + 20*A*b*c^3)*d^8*e^2 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^7*e^3 + (3*B*b^4 + 4*A*b^3*c)*d^6*e^4 + (24*B*c^4*d^6*e^4 - 4*(17*B*b*c^3 + 2*A*c^4)*d^5*e^5 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^4*e^6 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^3*e^7 + (3*B*b^4 + 4*A*b^3*c)*d^2*e^8)*x^4 + 4*(24*B*c^4*d^7*e^3 - 4*(17*B*b*c^3 + 2*A*c^4)*d^6*e^4 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^5*e^5 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^4*e^6 + (3*B*b^4 + 4*A*b^3*c)*d^3*e^7)*x^3 + 6*(24*B*c^4*d^8*e^2 - 4*(17*B*b*c^3 + 2*A*c^4)*d^7*e^3 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^6*e^4 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^5*e^5 + (3*B*b^4 + 4*A*b^3*c)*d^4*e^6)*x^2 + 4*(24*B*c^4*d^9*e - 4*(17*B*b*c^3 + 2*A*c^4)*d^8*e^2 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^7*e^3 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^6*e^4 + (3*B*b^4 + 4*A*b^3*c)*d^5*e^5)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 15*(384*B*c^4*d^9 + A*b^4*d^4*e^5 - 128*(7*B*b*c^3 + A*c^4)*d^8*e + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^7*e^2 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^6*e^3 + (7*B*b^4 + 16*A*b^3*c)*d^5*e^4 + (384*B*c^4*d^5*e^4 + A*b^4*e^9 - 128*(7*B*b*c^3 + A*c^4)*d^4*e^5 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^3*e^6 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^2*e^7 + (7*B*b^4 + 16*A*b^3*c)*d*e^8)*x^4 + 4*(384*B*c^4*d^6*e^3 + A*b^4*d*e^8 - 128*(7*B*b*c^3 + A*c^4)*d^5*e^4 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^4*e^5 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^3*e^6 + (7*B*b^4 + 16*A*b^3*c)*d^2*e^7)*x^3 + 6*(384*B*c^4*d^7*e^2 + A*b^4*d^2*e^7 - 128*(7*B*b*c^3 + A*c^4)*d^6*e^3 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^5*e^4 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^4*e^5 + (7*B*b^4 + 16*A*b^3*c)*d^3*e^6)*x^2 + 4*(384*B*c^4*d^8*e + A*b^4*d^3*e^6 - 128*(7*B*b*c^3 + A*c^4)*d^7*e^2 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^6*e^3 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^5*e^4 + (7*B*b^4 + 16*A*b^3*c)*d^4*e^5)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(2880*B*c^4*d^9*e + 15*A*b^4*d^4*e^6 - 240*(31*B*b*c^3 + 4*A*c^4)*d^8*e^2 + 120*(53*B*b^2*c^2 + 18*A*b*c^3)*d^7*e^3 - 15*(127*B*b^3*c + 96*A*b^2*c^2)*d^6*e^4 + 15*(7*B*b^4 + 15*A*b^3*c)*d^5*e^5 - 96*(B*c^4*d^4*e^6 - 2*B*b*c^3*d^3*e^7 + B*b^2*c^2*d^2*e^8)*x^5 + 48*(12*B*c^4*d^5*e^5 - (33*B*b*c^3 + 4*A*c^4)*d^4*e^6 + 2*(15*B*b^2*c^2 + 4*A*b*c^3)*d^3*e^7 - (9*B*b^3*c + 4*A*b^2*c^2)*d^2*e^8)*x^4 + (6000*B*c^4*d^6*e^4 - 15*A*b^4*d*e^9 - 8*(1981*B*b*c^3 + 250*A*c^4)*d^5*e^5 + 2*(6995*B*b^2*c^2 + 2308*A*b*c^3)*d^4*e^6 - (4421*B*b^3*c + 3262*A*b^2*c^2)*d^3*e^7 + (279*B*b^4 + 661*A*b^3*c)*d^2*e^8)*x^3 + (12480*B*c^4*d^7*e^3 + 73*A*b^4*d^2*e^8 - 40*(815*B*b*c^3 + 104*A*c^4)*d^6*e^4 + 4*(7079*B*b^2*c^2 + 2370*A*b*c^3)*d^5*e^5 - (8707*B*b^3*c + 6452*A*b^2*c^2)*d^4*e^6 + (511*B*b^4 + 1059*A*b^3*c)*d^3*e^7)*x^2 + 5*(2016*B*c^4*d^8*e^2 + 11*A*b^4*d^3*e^7 - 48*(109*B*b*c^3 + 14*A*c^4)*d^7*e^3 + 2*(2251*B*b^2*c^2 + 760*A*b*c^3)*d^6*e^4 - (1363*B*b^3*c + 1022*A*b^2*c^2)*d^5*e^5 + (77*B*b^4 + 163*A*b^3*c)*d^4*e^6)*x)*sqrt(c*x^2 + b*x))/(c^2*d^8*e^7 - 2*b*c*d^7*e^8 + b^2*d^6*e^9 + (c^2*d^4*e^11 - 2*b*c*d^3*e^12 + b^2*d^2*e^13)*x^4 + 4*(c^2*d^5*e^10 - 2*b*c*d^4*e^11 + b^2*d^3*e^12)*x^3 + 6*(c^2*d^6*e^9 - 2*b*c*d^5*e^10 + b^2*d^4*e^11)*x^2 + 4*(c^2*d^7*e^8 - 2*b*c*d^6*e^9 + b^2*d^5*e^10)*x), -1/192*(15*(384*B*c^4*d^9 + A*b^4*d^4*e^5 - 128*(7*B*b*c^3 + A*c^4)*d^8*e + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^7*e^2 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^6*e^3 + (7*B*b^4 + 16*A*b^3*c)*d^5*e^4 + (384*B*c^4*d^5*e^4 + A*b^4*e^9 - 128*(7*B*b*c^3 + A*c^4)*d^4*e^5 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^3*e^6 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^2*e^7 + (7*B*b^4 + 16*A*b^3*c)*d*e^8)*x^4 + 4*(384*B*c^4*d^6*e^3 + A*b^4*d*e^8 - 128*(7*B*b*c^3 + A*c^4)*d^5*e^4 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^4*e^5 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^3*e^6 + (7*B*b^4 + 16*A*b^3*c)*d^2*e^7)*x^3 + 6*(384*B*c^4*d^7*e^2 + A*b^4*d^2*e^7 - 128*(7*B*b*c^3 + A*c^4)*d^6*e^3 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^5*e^4 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^4*e^5 + (7*B*b^4 + 16*A*b^3*c)*d^3*e^6)*x^2 + 4*(384*B*c^4*d^8*e + A*b^4*d^3*e^6 - 128*(7*B*b*c^3 + A*c^4)*d^7*e^2 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^6*e^3 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^5*e^4 + (7*B*b^4 + 16*A*b^3*c)*d^4*e^5)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 120*(24*B*c^4*d^10 - 4*(17*B*b*c^3 + 2*A*c^4)*d^9*e + (67*B*b^2*c^2 + 20*A*b*c^3)*d^8*e^2 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^7*e^3 + (3*B*b^4 + 4*A*b^3*c)*d^6*e^4 + (24*B*c^4*d^6*e^4 - 4*(17*B*b*c^3 + 2*A*c^4)*d^5*e^5 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^4*e^6 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^3*e^7 + (3*B*b^4 + 4*A*b^3*c)*d^2*e^8)*x^4 + 4*(24*B*c^4*d^7*e^3 - 4*(17*B*b*c^3 + 2*A*c^4)*d^6*e^4 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^5*e^5 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^4*e^6 + (3*B*b^4 + 4*A*b^3*c)*d^3*e^7)*x^3 + 6*(24*B*c^4*d^8*e^2 - 4*(17*B*b*c^3 + 2*A*c^4)*d^7*e^3 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^6*e^4 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^5*e^5 + (3*B*b^4 + 4*A*b^3*c)*d^4*e^6)*x^2 + 4*(24*B*c^4*d^9*e - 4*(17*B*b*c^3 + 2*A*c^4)*d^8*e^2 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^7*e^3 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^6*e^4 + (3*B*b^4 + 4*A*b^3*c)*d^5*e^5)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + (2880*B*c^4*d^9*e + 15*A*b^4*d^4*e^6 - 240*(31*B*b*c^3 + 4*A*c^4)*d^8*e^2 + 120*(53*B*b^2*c^2 + 18*A*b*c^3)*d^7*e^3 - 15*(127*B*b^3*c + 96*A*b^2*c^2)*d^6*e^4 + 15*(7*B*b^4 + 15*A*b^3*c)*d^5*e^5 - 96*(B*c^4*d^4*e^6 - 2*B*b*c^3*d^3*e^7 + B*b^2*c^2*d^2*e^8)*x^5 + 48*(12*B*c^4*d^5*e^5 - (33*B*b*c^3 + 4*A*c^4)*d^4*e^6 + 2*(15*B*b^2*c^2 + 4*A*b*c^3)*d^3*e^7 - (9*B*b^3*c + 4*A*b^2*c^2)*d^2*e^8)*x^4 + (6000*B*c^4*d^6*e^4 - 15*A*b^4*d*e^9 - 8*(1981*B*b*c^3 + 250*A*c^4)*d^5*e^5 + 2*(6995*B*b^2*c^2 + 2308*A*b*c^3)*d^4*e^6 - (4421*B*b^3*c + 3262*A*b^2*c^2)*d^3*e^7 + (279*B*b^4 + 661*A*b^3*c)*d^2*e^8)*x^3 + (12480*B*c^4*d^7*e^3 + 73*A*b^4*d^2*e^8 - 40*(815*B*b*c^3 + 104*A*c^4)*d^6*e^4 + 4*(7079*B*b^2*c^2 + 2370*A*b*c^3)*d^5*e^5 - (8707*B*b^3*c + 6452*A*b^2*c^2)*d^4*e^6 + (511*B*b^4 + 1059*A*b^3*c)*d^3*e^7)*x^2 + 5*(2016*B*c^4*d^8*e^2 + 11*A*b^4*d^3*e^7 - 48*(109*B*b*c^3 + 14*A*c^4)*d^7*e^3 + 2*(2251*B*b^2*c^2 + 760*A*b*c^3)*d^6*e^4 - (1363*B*b^3*c + 1022*A*b^2*c^2)*d^5*e^5 + (77*B*b^4 + 163*A*b^3*c)*d^4*e^6)*x)*sqrt(c*x^2 + b*x))/(c^2*d^8*e^7 - 2*b*c*d^7*e^8 + b^2*d^6*e^9 + (c^2*d^4*e^11 - 2*b*c*d^3*e^12 + b^2*d^2*e^13)*x^4 + 4*(c^2*d^5*e^10 - 2*b*c*d^4*e^11 + b^2*d^3*e^12)*x^3 + 6*(c^2*d^6*e^9 - 2*b*c*d^5*e^10 + b^2*d^4*e^11)*x^2 + 4*(c^2*d^7*e^8 - 2*b*c*d^6*e^9 + b^2*d^5*e^10)*x), -1/384*(480*(24*B*c^4*d^10 - 4*(17*B*b*c^3 + 2*A*c^4)*d^9*e + (67*B*b^2*c^2 + 20*A*b*c^3)*d^8*e^2 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^7*e^3 + (3*B*b^4 + 4*A*b^3*c)*d^6*e^4 + (24*B*c^4*d^6*e^4 - 4*(17*B*b*c^3 + 2*A*c^4)*d^5*e^5 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^4*e^6 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^3*e^7 + (3*B*b^4 + 4*A*b^3*c)*d^2*e^8)*x^4 + 4*(24*B*c^4*d^7*e^3 - 4*(17*B*b*c^3 + 2*A*c^4)*d^6*e^4 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^5*e^5 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^4*e^6 + (3*B*b^4 + 4*A*b^3*c)*d^3*e^7)*x^3 + 6*(24*B*c^4*d^8*e^2 - 4*(17*B*b*c^3 + 2*A*c^4)*d^7*e^3 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^6*e^4 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^5*e^5 + (3*B*b^4 + 4*A*b^3*c)*d^4*e^6)*x^2 + 4*(24*B*c^4*d^9*e - 4*(17*B*b*c^3 + 2*A*c^4)*d^8*e^2 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^7*e^3 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^6*e^4 + (3*B*b^4 + 4*A*b^3*c)*d^5*e^5)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 15*(384*B*c^4*d^9 + A*b^4*d^4*e^5 - 128*(7*B*b*c^3 + A*c^4)*d^8*e + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^7*e^2 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^6*e^3 + (7*B*b^4 + 16*A*b^3*c)*d^5*e^4 + (384*B*c^4*d^5*e^4 + A*b^4*e^9 - 128*(7*B*b*c^3 + A*c^4)*d^4*e^5 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^3*e^6 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^2*e^7 + (7*B*b^4 + 16*A*b^3*c)*d*e^8)*x^4 + 4*(384*B*c^4*d^6*e^3 + A*b^4*d*e^8 - 128*(7*B*b*c^3 + A*c^4)*d^5*e^4 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^4*e^5 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^3*e^6 + (7*B*b^4 + 16*A*b^3*c)*d^2*e^7)*x^3 + 6*(384*B*c^4*d^7*e^2 + A*b^4*d^2*e^7 - 128*(7*B*b*c^3 + A*c^4)*d^6*e^3 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^5*e^4 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^4*e^5 + (7*B*b^4 + 16*A*b^3*c)*d^3*e^6)*x^2 + 4*(384*B*c^4*d^8*e + A*b^4*d^3*e^6 - 128*(7*B*b*c^3 + A*c^4)*d^7*e^2 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^6*e^3 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^5*e^4 + (7*B*b^4 + 16*A*b^3*c)*d^4*e^5)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(2880*B*c^4*d^9*e + 15*A*b^4*d^4*e^6 - 240*(31*B*b*c^3 + 4*A*c^4)*d^8*e^2 + 120*(53*B*b^2*c^2 + 18*A*b*c^3)*d^7*e^3 - 15*(127*B*b^3*c + 96*A*b^2*c^2)*d^6*e^4 + 15*(7*B*b^4 + 15*A*b^3*c)*d^5*e^5 - 96*(B*c^4*d^4*e^6 - 2*B*b*c^3*d^3*e^7 + B*b^2*c^2*d^2*e^8)*x^5 + 48*(12*B*c^4*d^5*e^5 - (33*B*b*c^3 + 4*A*c^4)*d^4*e^6 + 2*(15*B*b^2*c^2 + 4*A*b*c^3)*d^3*e^7 - (9*B*b^3*c + 4*A*b^2*c^2)*d^2*e^8)*x^4 + (6000*B*c^4*d^6*e^4 - 15*A*b^4*d*e^9 - 8*(1981*B*b*c^3 + 250*A*c^4)*d^5*e^5 + 2*(6995*B*b^2*c^2 + 2308*A*b*c^3)*d^4*e^6 - (4421*B*b^3*c + 3262*A*b^2*c^2)*d^3*e^7 + (279*B*b^4 + 661*A*b^3*c)*d^2*e^8)*x^3 + (12480*B*c^4*d^7*e^3 + 73*A*b^4*d^2*e^8 - 40*(815*B*b*c^3 + 104*A*c^4)*d^6*e^4 + 4*(7079*B*b^2*c^2 + 2370*A*b*c^3)*d^5*e^5 - (8707*B*b^3*c + 6452*A*b^2*c^2)*d^4*e^6 + (511*B*b^4 + 1059*A*b^3*c)*d^3*e^7)*x^2 + 5*(2016*B*c^4*d^8*e^2 + 11*A*b^4*d^3*e^7 - 48*(109*B*b*c^3 + 14*A*c^4)*d^7*e^3 + 2*(2251*B*b^2*c^2 + 760*A*b*c^3)*d^6*e^4 - (1363*B*b^3*c + 1022*A*b^2*c^2)*d^5*e^5 + (77*B*b^4 + 163*A*b^3*c)*d^4*e^6)*x)*sqrt(c*x^2 + b*x))/(c^2*d^8*e^7 - 2*b*c*d^7*e^8 + b^2*d^6*e^9 + (c^2*d^4*e^11 - 2*b*c*d^3*e^12 + b^2*d^2*e^13)*x^4 + 4*(c^2*d^5*e^10 - 2*b*c*d^4*e^11 + b^2*d^3*e^12)*x^3 + 6*(c^2*d^6*e^9 - 2*b*c*d^5*e^10 + b^2*d^4*e^11)*x^2 + 4*(c^2*d^7*e^8 - 2*b*c*d^6*e^9 + b^2*d^5*e^10)*x), -1/192*(15*(384*B*c^4*d^9 + A*b^4*d^4*e^5 - 128*(7*B*b*c^3 + A*c^4)*d^8*e + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^7*e^2 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^6*e^3 + (7*B*b^4 + 16*A*b^3*c)*d^5*e^4 + (384*B*c^4*d^5*e^4 + A*b^4*e^9 - 128*(7*B*b*c^3 + A*c^4)*d^4*e^5 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^3*e^6 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^2*e^7 + (7*B*b^4 + 16*A*b^3*c)*d*e^8)*x^4 + 4*(384*B*c^4*d^6*e^3 + A*b^4*d*e^8 - 128*(7*B*b*c^3 + A*c^4)*d^5*e^4 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^4*e^5 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^3*e^6 + (7*B*b^4 + 16*A*b^3*c)*d^2*e^7)*x^3 + 6*(384*B*c^4*d^7*e^2 + A*b^4*d^2*e^7 - 128*(7*B*b*c^3 + A*c^4)*d^6*e^3 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^5*e^4 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^4*e^5 + (7*B*b^4 + 16*A*b^3*c)*d^3*e^6)*x^2 + 4*(384*B*c^4*d^8*e + A*b^4*d^3*e^6 - 128*(7*B*b*c^3 + A*c^4)*d^7*e^2 + 32*(21*B*b^2*c^2 + 8*A*b*c^3)*d^6*e^3 - 24*(7*B*b^3*c + 6*A*b^2*c^2)*d^5*e^4 + (7*B*b^4 + 16*A*b^3*c)*d^4*e^5)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 240*(24*B*c^4*d^10 - 4*(17*B*b*c^3 + 2*A*c^4)*d^9*e + (67*B*b^2*c^2 + 20*A*b*c^3)*d^8*e^2 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^7*e^3 + (3*B*b^4 + 4*A*b^3*c)*d^6*e^4 + (24*B*c^4*d^6*e^4 - 4*(17*B*b*c^3 + 2*A*c^4)*d^5*e^5 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^4*e^6 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^3*e^7 + (3*B*b^4 + 4*A*b^3*c)*d^2*e^8)*x^4 + 4*(24*B*c^4*d^7*e^3 - 4*(17*B*b*c^3 + 2*A*c^4)*d^6*e^4 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^5*e^5 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^4*e^6 + (3*B*b^4 + 4*A*b^3*c)*d^3*e^7)*x^3 + 6*(24*B*c^4*d^8*e^2 - 4*(17*B*b*c^3 + 2*A*c^4)*d^7*e^3 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^6*e^4 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^5*e^5 + (3*B*b^4 + 4*A*b^3*c)*d^4*e^6)*x^2 + 4*(24*B*c^4*d^9*e - 4*(17*B*b*c^3 + 2*A*c^4)*d^8*e^2 + (67*B*b^2*c^2 + 20*A*b*c^3)*d^7*e^3 - 2*(13*B*b^3*c + 8*A*b^2*c^2)*d^6*e^4 + (3*B*b^4 + 4*A*b^3*c)*d^5*e^5)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (2880*B*c^4*d^9*e + 15*A*b^4*d^4*e^6 - 240*(31*B*b*c^3 + 4*A*c^4)*d^8*e^2 + 120*(53*B*b^2*c^2 + 18*A*b*c^3)*d^7*e^3 - 15*(127*B*b^3*c + 96*A*b^2*c^2)*d^6*e^4 + 15*(7*B*b^4 + 15*A*b^3*c)*d^5*e^5 - 96*(B*c^4*d^4*e^6 - 2*B*b*c^3*d^3*e^7 + B*b^2*c^2*d^2*e^8)*x^5 + 48*(12*B*c^4*d^5*e^5 - (33*B*b*c^3 + 4*A*c^4)*d^4*e^6 + 2*(15*B*b^2*c^2 + 4*A*b*c^3)*d^3*e^7 - (9*B*b^3*c + 4*A*b^2*c^2)*d^2*e^8)*x^4 + (6000*B*c^4*d^6*e^4 - 15*A*b^4*d*e^9 - 8*(1981*B*b*c^3 + 250*A*c^4)*d^5*e^5 + 2*(6995*B*b^2*c^2 + 2308*A*b*c^3)*d^4*e^6 - (4421*B*b^3*c + 3262*A*b^2*c^2)*d^3*e^7 + (279*B*b^4 + 661*A*b^3*c)*d^2*e^8)*x^3 + (12480*B*c^4*d^7*e^3 + 73*A*b^4*d^2*e^8 - 40*(815*B*b*c^3 + 104*A*c^4)*d^6*e^4 + 4*(7079*B*b^2*c^2 + 2370*A*b*c^3)*d^5*e^5 - (8707*B*b^3*c + 6452*A*b^2*c^2)*d^4*e^6 + (511*B*b^4 + 1059*A*b^3*c)*d^3*e^7)*x^2 + 5*(2016*B*c^4*d^8*e^2 + 11*A*b^4*d^3*e^7 - 48*(109*B*b*c^3 + 14*A*c^4)*d^7*e^3 + 2*(2251*B*b^2*c^2 + 760*A*b*c^3)*d^6*e^4 - (1363*B*b^3*c + 1022*A*b^2*c^2)*d^5*e^5 + (77*B*b^4 + 163*A*b^3*c)*d^4*e^6)*x)*sqrt(c*x^2 + b*x))/(c^2*d^8*e^7 - 2*b*c*d^7*e^8 + b^2*d^6*e^9 + (c^2*d^4*e^11 - 2*b*c*d^3*e^12 + b^2*d^2*e^13)*x^4 + 4*(c^2*d^5*e^10 - 2*b*c*d^4*e^11 + b^2*d^3*e^12)*x^3 + 6*(c^2*d^6*e^9 - 2*b*c*d^5*e^10 + b^2*d^4*e^11)*x^2 + 4*(c^2*d^7*e^8 - 2*b*c*d^6*e^9 + b^2*d^5*e^10)*x)]","B",0
1191,1,621,0,0.451742," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(64 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} - 48 \, {\left(3 \, B b^{2} c^{2} - 4 \, A b c^{3}\right)} d^{2} e + 24 \, {\left(5 \, B b^{3} c - 6 \, A b^{2} c^{2}\right)} d e^{2} - 5 \, {\left(7 \, B b^{4} - 8 \, A b^{3} c\right)} e^{3}\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(48 \, B c^{4} e^{3} x^{3} + 192 \, B c^{4} d^{3} - 144 \, {\left(3 \, B b c^{3} - 4 \, A c^{4}\right)} d^{2} e + 72 \, {\left(5 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} d e^{2} - 15 \, {\left(7 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} e^{3} + 8 \, {\left(24 \, B c^{4} d e^{2} - {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(144 \, B c^{4} d^{2} e - 24 \, {\left(5 \, B b c^{3} - 6 \, A c^{4}\right)} d e^{2} + 5 \, {\left(7 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, c^{5}}, \frac{3 \, {\left(64 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} - 48 \, {\left(3 \, B b^{2} c^{2} - 4 \, A b c^{3}\right)} d^{2} e + 24 \, {\left(5 \, B b^{3} c - 6 \, A b^{2} c^{2}\right)} d e^{2} - 5 \, {\left(7 \, B b^{4} - 8 \, A b^{3} c\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(48 \, B c^{4} e^{3} x^{3} + 192 \, B c^{4} d^{3} - 144 \, {\left(3 \, B b c^{3} - 4 \, A c^{4}\right)} d^{2} e + 72 \, {\left(5 \, B b^{2} c^{2} - 6 \, A b c^{3}\right)} d e^{2} - 15 \, {\left(7 \, B b^{3} c - 8 \, A b^{2} c^{2}\right)} e^{3} + 8 \, {\left(24 \, B c^{4} d e^{2} - {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(144 \, B c^{4} d^{2} e - 24 \, {\left(5 \, B b c^{3} - 6 \, A c^{4}\right)} d e^{2} + 5 \, {\left(7 \, B b^{2} c^{2} - 8 \, A b c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, c^{5}}\right]"," ",0,"[1/384*(3*(64*(B*b*c^3 - 2*A*c^4)*d^3 - 48*(3*B*b^2*c^2 - 4*A*b*c^3)*d^2*e + 24*(5*B*b^3*c - 6*A*b^2*c^2)*d*e^2 - 5*(7*B*b^4 - 8*A*b^3*c)*e^3)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(48*B*c^4*e^3*x^3 + 192*B*c^4*d^3 - 144*(3*B*b*c^3 - 4*A*c^4)*d^2*e + 72*(5*B*b^2*c^2 - 6*A*b*c^3)*d*e^2 - 15*(7*B*b^3*c - 8*A*b^2*c^2)*e^3 + 8*(24*B*c^4*d*e^2 - (7*B*b*c^3 - 8*A*c^4)*e^3)*x^2 + 2*(144*B*c^4*d^2*e - 24*(5*B*b*c^3 - 6*A*c^4)*d*e^2 + 5*(7*B*b^2*c^2 - 8*A*b*c^3)*e^3)*x)*sqrt(c*x^2 + b*x))/c^5, 1/192*(3*(64*(B*b*c^3 - 2*A*c^4)*d^3 - 48*(3*B*b^2*c^2 - 4*A*b*c^3)*d^2*e + 24*(5*B*b^3*c - 6*A*b^2*c^2)*d*e^2 - 5*(7*B*b^4 - 8*A*b^3*c)*e^3)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (48*B*c^4*e^3*x^3 + 192*B*c^4*d^3 - 144*(3*B*b*c^3 - 4*A*c^4)*d^2*e + 72*(5*B*b^2*c^2 - 6*A*b*c^3)*d*e^2 - 15*(7*B*b^3*c - 8*A*b^2*c^2)*e^3 + 8*(24*B*c^4*d*e^2 - (7*B*b*c^3 - 8*A*c^4)*e^3)*x^2 + 2*(144*B*c^4*d^2*e - 24*(5*B*b*c^3 - 6*A*c^4)*d*e^2 + 5*(7*B*b^2*c^2 - 8*A*b*c^3)*e^3)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
1192,1,391,0,0.434489," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - 4 \, {\left(3 \, B b^{2} c - 4 \, A b c^{2}\right)} d e + {\left(5 \, B b^{3} - 6 \, A b^{2} c\right)} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(8 \, B c^{3} e^{2} x^{2} + 24 \, B c^{3} d^{2} - 12 \, {\left(3 \, B b c^{2} - 4 \, A c^{3}\right)} d e + 3 \, {\left(5 \, B b^{2} c - 6 \, A b c^{2}\right)} e^{2} + 2 \, {\left(12 \, B c^{3} d e - {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c^{4}}, \frac{3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - 4 \, {\left(3 \, B b^{2} c - 4 \, A b c^{2}\right)} d e + {\left(5 \, B b^{3} - 6 \, A b^{2} c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, B c^{3} e^{2} x^{2} + 24 \, B c^{3} d^{2} - 12 \, {\left(3 \, B b c^{2} - 4 \, A c^{3}\right)} d e + 3 \, {\left(5 \, B b^{2} c - 6 \, A b c^{2}\right)} e^{2} + 2 \, {\left(12 \, B c^{3} d e - {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c^{4}}\right]"," ",0,"[-1/48*(3*(8*(B*b*c^2 - 2*A*c^3)*d^2 - 4*(3*B*b^2*c - 4*A*b*c^2)*d*e + (5*B*b^3 - 6*A*b^2*c)*e^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(8*B*c^3*e^2*x^2 + 24*B*c^3*d^2 - 12*(3*B*b*c^2 - 4*A*c^3)*d*e + 3*(5*B*b^2*c - 6*A*b*c^2)*e^2 + 2*(12*B*c^3*d*e - (5*B*b*c^2 - 6*A*c^3)*e^2)*x)*sqrt(c*x^2 + b*x))/c^4, 1/24*(3*(8*(B*b*c^2 - 2*A*c^3)*d^2 - 4*(3*B*b^2*c - 4*A*b*c^2)*d*e + (5*B*b^3 - 6*A*b^2*c)*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*B*c^3*e^2*x^2 + 24*B*c^3*d^2 - 12*(3*B*b*c^2 - 4*A*c^3)*d*e + 3*(5*B*b^2*c - 6*A*b*c^2)*e^2 + 2*(12*B*c^3*d*e - (5*B*b*c^2 - 6*A*c^3)*e^2)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
1193,1,217,0,0.429961," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d - {\left(3 \, B b^{2} - 4 \, A b c\right)} e\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, B c^{2} e x + 4 \, B c^{2} d - {\left(3 \, B b c - 4 \, A c^{2}\right)} e\right)} \sqrt{c x^{2} + b x}}{8 \, c^{3}}, \frac{{\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d - {\left(3 \, B b^{2} - 4 \, A b c\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(2 \, B c^{2} e x + 4 \, B c^{2} d - {\left(3 \, B b c - 4 \, A c^{2}\right)} e\right)} \sqrt{c x^{2} + b x}}{4 \, c^{3}}\right]"," ",0,"[1/8*((4*(B*b*c - 2*A*c^2)*d - (3*B*b^2 - 4*A*b*c)*e)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*B*c^2*e*x + 4*B*c^2*d - (3*B*b*c - 4*A*c^2)*e)*sqrt(c*x^2 + b*x))/c^3, 1/4*((4*(B*b*c - 2*A*c^2)*d - (3*B*b^2 - 4*A*b*c)*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (2*B*c^2*e*x + 4*B*c^2*d - (3*B*b*c - 4*A*c^2)*e)*sqrt(c*x^2 + b*x))/c^3]","A",0
1194,1,115,0,0.424297," ","integrate((B*x+A)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c x^{2} + b x} B c - {\left(B b - 2 \, A c\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right)}{2 \, c^{2}}, \frac{\sqrt{c x^{2} + b x} B c + {\left(B b - 2 \, A c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right)}{c^{2}}\right]"," ",0,"[1/2*(2*sqrt(c*x^2 + b*x)*B*c - (B*b - 2*A*c)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)))/c^2, (sqrt(c*x^2 + b*x)*B*c + (B*b - 2*A*c)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)))/c^2]","A",0
1195,1,534,0,0.493515," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(B c d^{2} - B b d e\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - {\left(B c d - A c e\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right)}{c^{2} d^{2} e - b c d e^{2}}, -\frac{2 \, {\left(B c d - A c e\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(B c d^{2} - B b d e\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right)}{c^{2} d^{2} e - b c d e^{2}}, -\frac{2 \, {\left(B c d^{2} - B b d e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(B c d - A c e\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right)}{c^{2} d^{2} e - b c d e^{2}}, -\frac{2 \, {\left({\left(B c d - A c e\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(B c d^{2} - B b d e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right)\right)}}{c^{2} d^{2} e - b c d e^{2}}\right]"," ",0,"[((B*c*d^2 - B*b*d*e)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - (B*c*d - A*c*e)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)))/(c^2*d^2*e - b*c*d*e^2), -(2*(B*c*d - A*c*e)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (B*c*d^2 - B*b*d*e)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)))/(c^2*d^2*e - b*c*d*e^2), -(2*(B*c*d^2 - B*b*d*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (B*c*d - A*c*e)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)))/(c^2*d^2*e - b*c*d*e^2), -2*((B*c*d - A*c*e)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (B*c*d^2 - B*b*d*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)))/(c^2*d^2*e - b*c*d*e^2)]","A",0
1196,1,399,0,0.436028," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(A b d e + {\left(B b - 2 \, A c\right)} d^{2} + {\left(A b e^{2} + {\left(B b - 2 \, A c\right)} d e\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(B c d^{3} + A b d e^{2} - {\left(B b + A c\right)} d^{2} e\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e + b^{2} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} x\right)}}, -\frac{{\left(A b d e + {\left(B b - 2 \, A c\right)} d^{2} + {\left(A b e^{2} + {\left(B b - 2 \, A c\right)} d e\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(B c d^{3} + A b d e^{2} - {\left(B b + A c\right)} d^{2} e\right)} \sqrt{c x^{2} + b x}}{c^{2} d^{5} - 2 \, b c d^{4} e + b^{2} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} x}\right]"," ",0,"[-1/2*((A*b*d*e + (B*b - 2*A*c)*d^2 + (A*b*e^2 + (B*b - 2*A*c)*d*e)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(B*c*d^3 + A*b*d*e^2 - (B*b + A*c)*d^2*e)*sqrt(c*x^2 + b*x))/(c^2*d^5 - 2*b*c*d^4*e + b^2*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3)*x), -((A*b*d*e + (B*b - 2*A*c)*d^2 + (A*b*e^2 + (B*b - 2*A*c)*d*e)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (B*c*d^3 + A*b*d*e^2 - (B*b + A*c)*d^2*e)*sqrt(c*x^2 + b*x))/(c^2*d^5 - 2*b*c*d^4*e + b^2*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3)*x)]","A",0
1197,1,954,0,0.455802," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, A b^{2} d^{2} e^{2} - 4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{4} + {\left(B b^{2} - 8 \, A b c\right)} d^{3} e + {\left(3 \, A b^{2} e^{4} - 4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{2} e^{2} + {\left(B b^{2} - 8 \, A b c\right)} d e^{3}\right)} x^{2} + 2 \, {\left(3 \, A b^{2} d e^{3} - 4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{3} e + {\left(B b^{2} - 8 \, A b c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(4 \, B c^{2} d^{5} - 5 \, A b^{2} d^{2} e^{3} - {\left(5 \, B b c + 8 \, A c^{2}\right)} d^{4} e + {\left(B b^{2} + 13 \, A b c\right)} d^{3} e^{2} + {\left(2 \, B c^{2} d^{4} e - 3 \, A b^{2} d e^{4} - {\left(B b c + 6 \, A c^{2}\right)} d^{3} e^{2} - {\left(B b^{2} - 9 \, A b c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e + 3 \, b^{2} c d^{6} e^{2} - b^{3} d^{5} e^{3} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} + 3 \, b^{2} c d^{4} e^{4} - b^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} + 3 \, b^{2} c d^{5} e^{3} - b^{3} d^{4} e^{4}\right)} x\right)}}, \frac{{\left(3 \, A b^{2} d^{2} e^{2} - 4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{4} + {\left(B b^{2} - 8 \, A b c\right)} d^{3} e + {\left(3 \, A b^{2} e^{4} - 4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{2} e^{2} + {\left(B b^{2} - 8 \, A b c\right)} d e^{3}\right)} x^{2} + 2 \, {\left(3 \, A b^{2} d e^{3} - 4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{3} e + {\left(B b^{2} - 8 \, A b c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(4 \, B c^{2} d^{5} - 5 \, A b^{2} d^{2} e^{3} - {\left(5 \, B b c + 8 \, A c^{2}\right)} d^{4} e + {\left(B b^{2} + 13 \, A b c\right)} d^{3} e^{2} + {\left(2 \, B c^{2} d^{4} e - 3 \, A b^{2} d e^{4} - {\left(B b c + 6 \, A c^{2}\right)} d^{3} e^{2} - {\left(B b^{2} - 9 \, A b c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e + 3 \, b^{2} c d^{6} e^{2} - b^{3} d^{5} e^{3} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} + 3 \, b^{2} c d^{4} e^{4} - b^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} + 3 \, b^{2} c d^{5} e^{3} - b^{3} d^{4} e^{4}\right)} x\right)}}\right]"," ",0,"[1/8*((3*A*b^2*d^2*e^2 - 4*(B*b*c - 2*A*c^2)*d^4 + (B*b^2 - 8*A*b*c)*d^3*e + (3*A*b^2*e^4 - 4*(B*b*c - 2*A*c^2)*d^2*e^2 + (B*b^2 - 8*A*b*c)*d*e^3)*x^2 + 2*(3*A*b^2*d*e^3 - 4*(B*b*c - 2*A*c^2)*d^3*e + (B*b^2 - 8*A*b*c)*d^2*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(4*B*c^2*d^5 - 5*A*b^2*d^2*e^3 - (5*B*b*c + 8*A*c^2)*d^4*e + (B*b^2 + 13*A*b*c)*d^3*e^2 + (2*B*c^2*d^4*e - 3*A*b^2*d*e^4 - (B*b*c + 6*A*c^2)*d^3*e^2 - (B*b^2 - 9*A*b*c)*d^2*e^3)*x)*sqrt(c*x^2 + b*x))/(c^3*d^8 - 3*b*c^2*d^7*e + 3*b^2*c*d^6*e^2 - b^3*d^5*e^3 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 + 3*b^2*c*d^4*e^4 - b^3*d^3*e^5)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 + 3*b^2*c*d^5*e^3 - b^3*d^4*e^4)*x), 1/4*((3*A*b^2*d^2*e^2 - 4*(B*b*c - 2*A*c^2)*d^4 + (B*b^2 - 8*A*b*c)*d^3*e + (3*A*b^2*e^4 - 4*(B*b*c - 2*A*c^2)*d^2*e^2 + (B*b^2 - 8*A*b*c)*d*e^3)*x^2 + 2*(3*A*b^2*d*e^3 - 4*(B*b*c - 2*A*c^2)*d^3*e + (B*b^2 - 8*A*b*c)*d^2*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (4*B*c^2*d^5 - 5*A*b^2*d^2*e^3 - (5*B*b*c + 8*A*c^2)*d^4*e + (B*b^2 + 13*A*b*c)*d^3*e^2 + (2*B*c^2*d^4*e - 3*A*b^2*d*e^4 - (B*b*c + 6*A*c^2)*d^3*e^2 - (B*b^2 - 9*A*b*c)*d^2*e^3)*x)*sqrt(c*x^2 + b*x))/(c^3*d^8 - 3*b*c^2*d^7*e + 3*b^2*c*d^6*e^2 - b^3*d^5*e^3 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 + 3*b^2*c*d^4*e^4 - b^3*d^3*e^5)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 + 3*b^2*c*d^5*e^3 - b^3*d^4*e^4)*x)]","B",0
1198,1,1781,0,0.489722," ","integrate((B*x+A)/(e*x+d)^4/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, A b^{3} d^{3} e^{3} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{6} - 4 \, {\left(B b^{2} c - 6 \, A b c^{2}\right)} d^{5} e + {\left(B b^{3} - 18 \, A b^{2} c\right)} d^{4} e^{2} + {\left(5 \, A b^{3} e^{6} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} e^{3} - 4 \, {\left(B b^{2} c - 6 \, A b c^{2}\right)} d^{2} e^{4} + {\left(B b^{3} - 18 \, A b^{2} c\right)} d e^{5}\right)} x^{3} + 3 \, {\left(5 \, A b^{3} d e^{5} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{4} e^{2} - 4 \, {\left(B b^{2} c - 6 \, A b c^{2}\right)} d^{3} e^{3} + {\left(B b^{3} - 18 \, A b^{2} c\right)} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(5 \, A b^{3} d^{2} e^{4} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{5} e - 4 \, {\left(B b^{2} c - 6 \, A b c^{2}\right)} d^{4} e^{2} + {\left(B b^{3} - 18 \, A b^{2} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(24 \, B c^{3} d^{7} + 33 \, A b^{3} d^{3} e^{4} - 36 \, {\left(B b c^{2} + 2 \, A c^{3}\right)} d^{6} e + 3 \, {\left(5 \, B b^{2} c + 54 \, A b c^{2}\right)} d^{5} e^{2} - 3 \, {\left(B b^{3} + 41 \, A b^{2} c\right)} d^{4} e^{3} + {\left(8 \, B c^{3} d^{5} e^{2} + 15 \, A b^{3} d e^{6} + 2 \, {\left(B b c^{2} - 22 \, A c^{3}\right)} d^{4} e^{3} - {\left(13 \, B b^{2} c - 88 \, A b c^{2}\right)} d^{3} e^{4} + {\left(3 \, B b^{3} - 59 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(12 \, B c^{3} d^{6} e + 20 \, A b^{3} d^{2} e^{5} - {\left(5 \, B b c^{2} + 54 \, A c^{3}\right)} d^{5} e^{2} - {\left(11 \, B b^{2} c - 113 \, A b c^{2}\right)} d^{4} e^{3} + {\left(4 \, B b^{3} - 79 \, A b^{2} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{4} d^{11} - 4 \, b c^{3} d^{10} e + 6 \, b^{2} c^{2} d^{9} e^{2} - 4 \, b^{3} c d^{8} e^{3} + b^{4} d^{7} e^{4} + {\left(c^{4} d^{8} e^{3} - 4 \, b c^{3} d^{7} e^{4} + 6 \, b^{2} c^{2} d^{6} e^{5} - 4 \, b^{3} c d^{5} e^{6} + b^{4} d^{4} e^{7}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} - 4 \, b c^{3} d^{8} e^{3} + 6 \, b^{2} c^{2} d^{7} e^{4} - 4 \, b^{3} c d^{6} e^{5} + b^{4} d^{5} e^{6}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e - 4 \, b c^{3} d^{9} e^{2} + 6 \, b^{2} c^{2} d^{8} e^{3} - 4 \, b^{3} c d^{7} e^{4} + b^{4} d^{6} e^{5}\right)} x\right)}}, -\frac{3 \, {\left(5 \, A b^{3} d^{3} e^{3} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{6} - 4 \, {\left(B b^{2} c - 6 \, A b c^{2}\right)} d^{5} e + {\left(B b^{3} - 18 \, A b^{2} c\right)} d^{4} e^{2} + {\left(5 \, A b^{3} e^{6} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} e^{3} - 4 \, {\left(B b^{2} c - 6 \, A b c^{2}\right)} d^{2} e^{4} + {\left(B b^{3} - 18 \, A b^{2} c\right)} d e^{5}\right)} x^{3} + 3 \, {\left(5 \, A b^{3} d e^{5} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{4} e^{2} - 4 \, {\left(B b^{2} c - 6 \, A b c^{2}\right)} d^{3} e^{3} + {\left(B b^{3} - 18 \, A b^{2} c\right)} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(5 \, A b^{3} d^{2} e^{4} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{5} e - 4 \, {\left(B b^{2} c - 6 \, A b c^{2}\right)} d^{4} e^{2} + {\left(B b^{3} - 18 \, A b^{2} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(24 \, B c^{3} d^{7} + 33 \, A b^{3} d^{3} e^{4} - 36 \, {\left(B b c^{2} + 2 \, A c^{3}\right)} d^{6} e + 3 \, {\left(5 \, B b^{2} c + 54 \, A b c^{2}\right)} d^{5} e^{2} - 3 \, {\left(B b^{3} + 41 \, A b^{2} c\right)} d^{4} e^{3} + {\left(8 \, B c^{3} d^{5} e^{2} + 15 \, A b^{3} d e^{6} + 2 \, {\left(B b c^{2} - 22 \, A c^{3}\right)} d^{4} e^{3} - {\left(13 \, B b^{2} c - 88 \, A b c^{2}\right)} d^{3} e^{4} + {\left(3 \, B b^{3} - 59 \, A b^{2} c\right)} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(12 \, B c^{3} d^{6} e + 20 \, A b^{3} d^{2} e^{5} - {\left(5 \, B b c^{2} + 54 \, A c^{3}\right)} d^{5} e^{2} - {\left(11 \, B b^{2} c - 113 \, A b c^{2}\right)} d^{4} e^{3} + {\left(4 \, B b^{3} - 79 \, A b^{2} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{4} d^{11} - 4 \, b c^{3} d^{10} e + 6 \, b^{2} c^{2} d^{9} e^{2} - 4 \, b^{3} c d^{8} e^{3} + b^{4} d^{7} e^{4} + {\left(c^{4} d^{8} e^{3} - 4 \, b c^{3} d^{7} e^{4} + 6 \, b^{2} c^{2} d^{6} e^{5} - 4 \, b^{3} c d^{5} e^{6} + b^{4} d^{4} e^{7}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} - 4 \, b c^{3} d^{8} e^{3} + 6 \, b^{2} c^{2} d^{7} e^{4} - 4 \, b^{3} c d^{6} e^{5} + b^{4} d^{5} e^{6}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e - 4 \, b c^{3} d^{9} e^{2} + 6 \, b^{2} c^{2} d^{8} e^{3} - 4 \, b^{3} c d^{7} e^{4} + b^{4} d^{6} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(5*A*b^3*d^3*e^3 + 8*(B*b*c^2 - 2*A*c^3)*d^6 - 4*(B*b^2*c - 6*A*b*c^2)*d^5*e + (B*b^3 - 18*A*b^2*c)*d^4*e^2 + (5*A*b^3*e^6 + 8*(B*b*c^2 - 2*A*c^3)*d^3*e^3 - 4*(B*b^2*c - 6*A*b*c^2)*d^2*e^4 + (B*b^3 - 18*A*b^2*c)*d*e^5)*x^3 + 3*(5*A*b^3*d*e^5 + 8*(B*b*c^2 - 2*A*c^3)*d^4*e^2 - 4*(B*b^2*c - 6*A*b*c^2)*d^3*e^3 + (B*b^3 - 18*A*b^2*c)*d^2*e^4)*x^2 + 3*(5*A*b^3*d^2*e^4 + 8*(B*b*c^2 - 2*A*c^3)*d^5*e - 4*(B*b^2*c - 6*A*b*c^2)*d^4*e^2 + (B*b^3 - 18*A*b^2*c)*d^3*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(24*B*c^3*d^7 + 33*A*b^3*d^3*e^4 - 36*(B*b*c^2 + 2*A*c^3)*d^6*e + 3*(5*B*b^2*c + 54*A*b*c^2)*d^5*e^2 - 3*(B*b^3 + 41*A*b^2*c)*d^4*e^3 + (8*B*c^3*d^5*e^2 + 15*A*b^3*d*e^6 + 2*(B*b*c^2 - 22*A*c^3)*d^4*e^3 - (13*B*b^2*c - 88*A*b*c^2)*d^3*e^4 + (3*B*b^3 - 59*A*b^2*c)*d^2*e^5)*x^2 + 2*(12*B*c^3*d^6*e + 20*A*b^3*d^2*e^5 - (5*B*b*c^2 + 54*A*c^3)*d^5*e^2 - (11*B*b^2*c - 113*A*b*c^2)*d^4*e^3 + (4*B*b^3 - 79*A*b^2*c)*d^3*e^4)*x)*sqrt(c*x^2 + b*x))/(c^4*d^11 - 4*b*c^3*d^10*e + 6*b^2*c^2*d^9*e^2 - 4*b^3*c*d^8*e^3 + b^4*d^7*e^4 + (c^4*d^8*e^3 - 4*b*c^3*d^7*e^4 + 6*b^2*c^2*d^6*e^5 - 4*b^3*c*d^5*e^6 + b^4*d^4*e^7)*x^3 + 3*(c^4*d^9*e^2 - 4*b*c^3*d^8*e^3 + 6*b^2*c^2*d^7*e^4 - 4*b^3*c*d^6*e^5 + b^4*d^5*e^6)*x^2 + 3*(c^4*d^10*e - 4*b*c^3*d^9*e^2 + 6*b^2*c^2*d^8*e^3 - 4*b^3*c*d^7*e^4 + b^4*d^6*e^5)*x), -1/24*(3*(5*A*b^3*d^3*e^3 + 8*(B*b*c^2 - 2*A*c^3)*d^6 - 4*(B*b^2*c - 6*A*b*c^2)*d^5*e + (B*b^3 - 18*A*b^2*c)*d^4*e^2 + (5*A*b^3*e^6 + 8*(B*b*c^2 - 2*A*c^3)*d^3*e^3 - 4*(B*b^2*c - 6*A*b*c^2)*d^2*e^4 + (B*b^3 - 18*A*b^2*c)*d*e^5)*x^3 + 3*(5*A*b^3*d*e^5 + 8*(B*b*c^2 - 2*A*c^3)*d^4*e^2 - 4*(B*b^2*c - 6*A*b*c^2)*d^3*e^3 + (B*b^3 - 18*A*b^2*c)*d^2*e^4)*x^2 + 3*(5*A*b^3*d^2*e^4 + 8*(B*b*c^2 - 2*A*c^3)*d^5*e - 4*(B*b^2*c - 6*A*b*c^2)*d^4*e^2 + (B*b^3 - 18*A*b^2*c)*d^3*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (24*B*c^3*d^7 + 33*A*b^3*d^3*e^4 - 36*(B*b*c^2 + 2*A*c^3)*d^6*e + 3*(5*B*b^2*c + 54*A*b*c^2)*d^5*e^2 - 3*(B*b^3 + 41*A*b^2*c)*d^4*e^3 + (8*B*c^3*d^5*e^2 + 15*A*b^3*d*e^6 + 2*(B*b*c^2 - 22*A*c^3)*d^4*e^3 - (13*B*b^2*c - 88*A*b*c^2)*d^3*e^4 + (3*B*b^3 - 59*A*b^2*c)*d^2*e^5)*x^2 + 2*(12*B*c^3*d^6*e + 20*A*b^3*d^2*e^5 - (5*B*b*c^2 + 54*A*c^3)*d^5*e^2 - (11*B*b^2*c - 113*A*b*c^2)*d^4*e^3 + (4*B*b^3 - 79*A*b^2*c)*d^3*e^4)*x)*sqrt(c*x^2 + b*x))/(c^4*d^11 - 4*b*c^3*d^10*e + 6*b^2*c^2*d^9*e^2 - 4*b^3*c*d^8*e^3 + b^4*d^7*e^4 + (c^4*d^8*e^3 - 4*b*c^3*d^7*e^4 + 6*b^2*c^2*d^6*e^5 - 4*b^3*c*d^5*e^6 + b^4*d^4*e^7)*x^3 + 3*(c^4*d^9*e^2 - 4*b*c^3*d^8*e^3 + 6*b^2*c^2*d^7*e^4 - 4*b^3*c*d^6*e^5 + b^4*d^5*e^6)*x^2 + 3*(c^4*d^10*e - 4*b*c^3*d^9*e^2 + 6*b^2*c^2*d^8*e^3 - 4*b^3*c*d^7*e^4 + b^4*d^6*e^5)*x)]","B",0
1199,1,694,0,0.438944," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, B b^{2} c^{3} d^{2} e - 4 \, {\left(3 \, B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d e^{2} + {\left(5 \, B b^{4} c - 4 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, B b^{3} c^{2} d^{2} e - 4 \, {\left(3 \, B b^{4} c - 2 \, A b^{3} c^{2}\right)} d e^{2} + {\left(5 \, B b^{5} - 4 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, B b^{2} c^{3} e^{3} x^{3} - 8 \, A b c^{4} d^{3} + {\left(12 \, B b^{2} c^{3} d e^{2} - {\left(5 \, B b^{3} c^{2} - 4 \, A b^{2} c^{3}\right)} e^{3}\right)} x^{2} + {\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} - 24 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{2} e + 12 \, {\left(3 \, B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d e^{2} - 3 \, {\left(5 \, B b^{4} c - 4 \, A b^{3} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(b^{2} c^{5} x^{2} + b^{3} c^{4} x\right)}}, -\frac{3 \, {\left({\left(8 \, B b^{2} c^{3} d^{2} e - 4 \, {\left(3 \, B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d e^{2} + {\left(5 \, B b^{4} c - 4 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, B b^{3} c^{2} d^{2} e - 4 \, {\left(3 \, B b^{4} c - 2 \, A b^{3} c^{2}\right)} d e^{2} + {\left(5 \, B b^{5} - 4 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, B b^{2} c^{3} e^{3} x^{3} - 8 \, A b c^{4} d^{3} + {\left(12 \, B b^{2} c^{3} d e^{2} - {\left(5 \, B b^{3} c^{2} - 4 \, A b^{2} c^{3}\right)} e^{3}\right)} x^{2} + {\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} - 24 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{2} e + 12 \, {\left(3 \, B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d e^{2} - 3 \, {\left(5 \, B b^{4} c - 4 \, A b^{3} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(b^{2} c^{5} x^{2} + b^{3} c^{4} x\right)}}\right]"," ",0,"[1/8*(3*((8*B*b^2*c^3*d^2*e - 4*(3*B*b^3*c^2 - 2*A*b^2*c^3)*d*e^2 + (5*B*b^4*c - 4*A*b^3*c^2)*e^3)*x^2 + (8*B*b^3*c^2*d^2*e - 4*(3*B*b^4*c - 2*A*b^3*c^2)*d*e^2 + (5*B*b^5 - 4*A*b^4*c)*e^3)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*B*b^2*c^3*e^3*x^3 - 8*A*b*c^4*d^3 + (12*B*b^2*c^3*d*e^2 - (5*B*b^3*c^2 - 4*A*b^2*c^3)*e^3)*x^2 + (8*(B*b*c^4 - 2*A*c^5)*d^3 - 24*(B*b^2*c^3 - A*b*c^4)*d^2*e + 12*(3*B*b^3*c^2 - 2*A*b^2*c^3)*d*e^2 - 3*(5*B*b^4*c - 4*A*b^3*c^2)*e^3)*x)*sqrt(c*x^2 + b*x))/(b^2*c^5*x^2 + b^3*c^4*x), -1/4*(3*((8*B*b^2*c^3*d^2*e - 4*(3*B*b^3*c^2 - 2*A*b^2*c^3)*d*e^2 + (5*B*b^4*c - 4*A*b^3*c^2)*e^3)*x^2 + (8*B*b^3*c^2*d^2*e - 4*(3*B*b^4*c - 2*A*b^3*c^2)*d*e^2 + (5*B*b^5 - 4*A*b^4*c)*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*B*b^2*c^3*e^3*x^3 - 8*A*b*c^4*d^3 + (12*B*b^2*c^3*d*e^2 - (5*B*b^3*c^2 - 4*A*b^2*c^3)*e^3)*x^2 + (8*(B*b*c^4 - 2*A*c^5)*d^3 - 24*(B*b^2*c^3 - A*b*c^4)*d^2*e + 12*(3*B*b^3*c^2 - 2*A*b^2*c^3)*d*e^2 - 3*(5*B*b^4*c - 4*A*b^3*c^2)*e^3)*x)*sqrt(c*x^2 + b*x))/(b^2*c^5*x^2 + b^3*c^4*x)]","A",0
1200,1,446,0,0.431487," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, B b^{2} c^{2} d e - {\left(3 \, B b^{3} c - 2 \, A b^{2} c^{2}\right)} e^{2}\right)} x^{2} + {\left(4 \, B b^{3} c d e - {\left(3 \, B b^{4} - 2 \, A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(B b^{2} c^{2} e^{2} x^{2} - 2 \, A b c^{3} d^{2} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} - 4 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d e + {\left(3 \, B b^{3} c - 2 \, A b^{2} c^{2}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(b^{2} c^{4} x^{2} + b^{3} c^{3} x\right)}}, -\frac{{\left({\left(4 \, B b^{2} c^{2} d e - {\left(3 \, B b^{3} c - 2 \, A b^{2} c^{2}\right)} e^{2}\right)} x^{2} + {\left(4 \, B b^{3} c d e - {\left(3 \, B b^{4} - 2 \, A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(B b^{2} c^{2} e^{2} x^{2} - 2 \, A b c^{3} d^{2} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} - 4 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d e + {\left(3 \, B b^{3} c - 2 \, A b^{2} c^{2}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{b^{2} c^{4} x^{2} + b^{3} c^{3} x}\right]"," ",0,"[1/2*(((4*B*b^2*c^2*d*e - (3*B*b^3*c - 2*A*b^2*c^2)*e^2)*x^2 + (4*B*b^3*c*d*e - (3*B*b^4 - 2*A*b^3*c)*e^2)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(B*b^2*c^2*e^2*x^2 - 2*A*b*c^3*d^2 + (2*(B*b*c^3 - 2*A*c^4)*d^2 - 4*(B*b^2*c^2 - A*b*c^3)*d*e + (3*B*b^3*c - 2*A*b^2*c^2)*e^2)*x)*sqrt(c*x^2 + b*x))/(b^2*c^4*x^2 + b^3*c^3*x), -(((4*B*b^2*c^2*d*e - (3*B*b^3*c - 2*A*b^2*c^2)*e^2)*x^2 + (4*B*b^3*c*d*e - (3*B*b^4 - 2*A*b^3*c)*e^2)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (B*b^2*c^2*e^2*x^2 - 2*A*b*c^3*d^2 + (2*(B*b*c^3 - 2*A*c^4)*d^2 - 4*(B*b^2*c^2 - A*b*c^3)*d*e + (3*B*b^3*c - 2*A*b^2*c^2)*e^2)*x)*sqrt(c*x^2 + b*x))/(b^2*c^4*x^2 + b^3*c^3*x)]","A",0
1201,1,254,0,0.442121," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B b^{2} c e x^{2} + B b^{3} e x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(A b c^{2} d - {\left({\left(B b c^{2} - 2 \, A c^{3}\right)} d - {\left(B b^{2} c - A b c^{2}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x}}{b^{2} c^{3} x^{2} + b^{3} c^{2} x}, -\frac{2 \, {\left({\left(B b^{2} c e x^{2} + B b^{3} e x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(A b c^{2} d - {\left({\left(B b c^{2} - 2 \, A c^{3}\right)} d - {\left(B b^{2} c - A b c^{2}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x}\right)}}{b^{2} c^{3} x^{2} + b^{3} c^{2} x}\right]"," ",0,"[((B*b^2*c*e*x^2 + B*b^3*e*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(A*b*c^2*d - ((B*b*c^2 - 2*A*c^3)*d - (B*b^2*c - A*b*c^2)*e)*x)*sqrt(c*x^2 + b*x))/(b^2*c^3*x^2 + b^3*c^2*x), -2*((B*b^2*c*e*x^2 + B*b^3*e*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (A*b*c^2*d - ((B*b*c^2 - 2*A*c^3)*d - (B*b^2*c - A*b*c^2)*e)*x)*sqrt(c*x^2 + b*x))/(b^2*c^3*x^2 + b^3*c^2*x)]","A",0
1202,1,44,0,0.409951," ","integrate((B*x+A)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x} {\left(A b - {\left(B b - 2 \, A c\right)} x\right)}}{b^{2} c x^{2} + b^{3} x}"," ",0,"-2*sqrt(c*x^2 + b*x)*(A*b - (B*b - 2*A*c)*x)/(b^2*c*x^2 + b^3*x)","A",0
1203,1,543,0,0.426948," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d^{2} - b d e} {\left({\left(B b^{2} c d e - A b^{2} c e^{2}\right)} x^{2} + {\left(B b^{3} d e - A b^{3} e^{2}\right)} x\right)} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(A b c^{2} d^{3} - 2 \, A b^{2} c d^{2} e + A b^{3} d e^{2} + {\left(A b^{2} c d e^{2} - {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} + {\left(B b^{2} c - 3 \, A b c^{2}\right)} d^{2} e\right)} x\right)} \sqrt{c x^{2} + b x}}{{\left(b^{2} c^{3} d^{4} - 2 \, b^{3} c^{2} d^{3} e + b^{4} c d^{2} e^{2}\right)} x^{2} + {\left(b^{3} c^{2} d^{4} - 2 \, b^{4} c d^{3} e + b^{5} d^{2} e^{2}\right)} x}, -\frac{2 \, {\left(\sqrt{-c d^{2} + b d e} {\left({\left(B b^{2} c d e - A b^{2} c e^{2}\right)} x^{2} + {\left(B b^{3} d e - A b^{3} e^{2}\right)} x\right)} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(A b c^{2} d^{3} - 2 \, A b^{2} c d^{2} e + A b^{3} d e^{2} + {\left(A b^{2} c d e^{2} - {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} + {\left(B b^{2} c - 3 \, A b c^{2}\right)} d^{2} e\right)} x\right)} \sqrt{c x^{2} + b x}\right)}}{{\left(b^{2} c^{3} d^{4} - 2 \, b^{3} c^{2} d^{3} e + b^{4} c d^{2} e^{2}\right)} x^{2} + {\left(b^{3} c^{2} d^{4} - 2 \, b^{4} c d^{3} e + b^{5} d^{2} e^{2}\right)} x}\right]"," ",0,"[(sqrt(c*d^2 - b*d*e)*((B*b^2*c*d*e - A*b^2*c*e^2)*x^2 + (B*b^3*d*e - A*b^3*e^2)*x)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(A*b*c^2*d^3 - 2*A*b^2*c*d^2*e + A*b^3*d*e^2 + (A*b^2*c*d*e^2 - (B*b*c^2 - 2*A*c^3)*d^3 + (B*b^2*c - 3*A*b*c^2)*d^2*e)*x)*sqrt(c*x^2 + b*x))/((b^2*c^3*d^4 - 2*b^3*c^2*d^3*e + b^4*c*d^2*e^2)*x^2 + (b^3*c^2*d^4 - 2*b^4*c*d^3*e + b^5*d^2*e^2)*x), -2*(sqrt(-c*d^2 + b*d*e)*((B*b^2*c*d*e - A*b^2*c*e^2)*x^2 + (B*b^3*d*e - A*b^3*e^2)*x)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (A*b*c^2*d^3 - 2*A*b^2*c*d^2*e + A*b^3*d*e^2 + (A*b^2*c*d*e^2 - (B*b*c^2 - 2*A*c^3)*d^3 + (B*b^2*c - 3*A*b*c^2)*d^2*e)*x)*sqrt(c*x^2 + b*x))/((b^2*c^3*d^4 - 2*b^3*c^2*d^3*e + b^4*c*d^2*e^2)*x^2 + (b^3*c^2*d^4 - 2*b^4*c*d^3*e + b^5*d^2*e^2)*x)]","B",0
1204,1,1240,0,0.466329," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, B b^{2} c^{2} d^{2} e^{2} + 3 \, A b^{3} c e^{4} - {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(4 \, B b^{2} c^{2} d^{3} e + 3 \, A b^{4} e^{4} + 3 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{2} e^{2} - {\left(B b^{4} + 3 \, A b^{3} c\right)} d e^{3}\right)} x^{2} + {\left(4 \, B b^{3} c d^{3} e + 3 \, A b^{4} d e^{3} - {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(2 \, A b c^{3} d^{5} - 6 \, A b^{2} c^{2} d^{4} e + 6 \, A b^{3} c d^{3} e^{2} - 2 \, A b^{4} d^{2} e^{3} - {\left(3 \, A b^{3} c d e^{4} + 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} e - {\left(B b^{2} c^{2} - 8 \, A b c^{3}\right)} d^{3} e^{2} - {\left(B b^{3} c + 7 \, A b^{2} c^{2}\right)} d^{2} e^{3}\right)} x^{2} - {\left(B b^{3} c d^{3} e^{2} + 3 \, A b^{4} d e^{4} + 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{5} - 2 \, {\left(B b^{2} c^{2} - 3 \, A b c^{3}\right)} d^{4} e - {\left(B b^{4} + 5 \, A b^{3} c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{2 \, {\left({\left(b^{2} c^{4} d^{6} e - 3 \, b^{3} c^{3} d^{5} e^{2} + 3 \, b^{4} c^{2} d^{4} e^{3} - b^{5} c d^{3} e^{4}\right)} x^{3} + {\left(b^{2} c^{4} d^{7} - 2 \, b^{3} c^{3} d^{6} e + 2 \, b^{5} c d^{4} e^{3} - b^{6} d^{3} e^{4}\right)} x^{2} + {\left(b^{3} c^{3} d^{7} - 3 \, b^{4} c^{2} d^{6} e + 3 \, b^{5} c d^{5} e^{2} - b^{6} d^{4} e^{3}\right)} x\right)}}, -\frac{{\left({\left(4 \, B b^{2} c^{2} d^{2} e^{2} + 3 \, A b^{3} c e^{4} - {\left(B b^{3} c + 6 \, A b^{2} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(4 \, B b^{2} c^{2} d^{3} e + 3 \, A b^{4} e^{4} + 3 \, {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d^{2} e^{2} - {\left(B b^{4} + 3 \, A b^{3} c\right)} d e^{3}\right)} x^{2} + {\left(4 \, B b^{3} c d^{3} e + 3 \, A b^{4} d e^{3} - {\left(B b^{4} + 6 \, A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(2 \, A b c^{3} d^{5} - 6 \, A b^{2} c^{2} d^{4} e + 6 \, A b^{3} c d^{3} e^{2} - 2 \, A b^{4} d^{2} e^{3} - {\left(3 \, A b^{3} c d e^{4} + 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} e - {\left(B b^{2} c^{2} - 8 \, A b c^{3}\right)} d^{3} e^{2} - {\left(B b^{3} c + 7 \, A b^{2} c^{2}\right)} d^{2} e^{3}\right)} x^{2} - {\left(B b^{3} c d^{3} e^{2} + 3 \, A b^{4} d e^{4} + 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{5} - 2 \, {\left(B b^{2} c^{2} - 3 \, A b c^{3}\right)} d^{4} e - {\left(B b^{4} + 5 \, A b^{3} c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{{\left(b^{2} c^{4} d^{6} e - 3 \, b^{3} c^{3} d^{5} e^{2} + 3 \, b^{4} c^{2} d^{4} e^{3} - b^{5} c d^{3} e^{4}\right)} x^{3} + {\left(b^{2} c^{4} d^{7} - 2 \, b^{3} c^{3} d^{6} e + 2 \, b^{5} c d^{4} e^{3} - b^{6} d^{3} e^{4}\right)} x^{2} + {\left(b^{3} c^{3} d^{7} - 3 \, b^{4} c^{2} d^{6} e + 3 \, b^{5} c d^{5} e^{2} - b^{6} d^{4} e^{3}\right)} x}\right]"," ",0,"[1/2*(((4*B*b^2*c^2*d^2*e^2 + 3*A*b^3*c*e^4 - (B*b^3*c + 6*A*b^2*c^2)*d*e^3)*x^3 + (4*B*b^2*c^2*d^3*e + 3*A*b^4*e^4 + 3*(B*b^3*c - 2*A*b^2*c^2)*d^2*e^2 - (B*b^4 + 3*A*b^3*c)*d*e^3)*x^2 + (4*B*b^3*c*d^3*e + 3*A*b^4*d*e^3 - (B*b^4 + 6*A*b^3*c)*d^2*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(2*A*b*c^3*d^5 - 6*A*b^2*c^2*d^4*e + 6*A*b^3*c*d^3*e^2 - 2*A*b^4*d^2*e^3 - (3*A*b^3*c*d*e^4 + 2*(B*b*c^3 - 2*A*c^4)*d^4*e - (B*b^2*c^2 - 8*A*b*c^3)*d^3*e^2 - (B*b^3*c + 7*A*b^2*c^2)*d^2*e^3)*x^2 - (B*b^3*c*d^3*e^2 + 3*A*b^4*d*e^4 + 2*(B*b*c^3 - 2*A*c^4)*d^5 - 2*(B*b^2*c^2 - 3*A*b*c^3)*d^4*e - (B*b^4 + 5*A*b^3*c)*d^2*e^3)*x)*sqrt(c*x^2 + b*x))/((b^2*c^4*d^6*e - 3*b^3*c^3*d^5*e^2 + 3*b^4*c^2*d^4*e^3 - b^5*c*d^3*e^4)*x^3 + (b^2*c^4*d^7 - 2*b^3*c^3*d^6*e + 2*b^5*c*d^4*e^3 - b^6*d^3*e^4)*x^2 + (b^3*c^3*d^7 - 3*b^4*c^2*d^6*e + 3*b^5*c*d^5*e^2 - b^6*d^4*e^3)*x), -(((4*B*b^2*c^2*d^2*e^2 + 3*A*b^3*c*e^4 - (B*b^3*c + 6*A*b^2*c^2)*d*e^3)*x^3 + (4*B*b^2*c^2*d^3*e + 3*A*b^4*e^4 + 3*(B*b^3*c - 2*A*b^2*c^2)*d^2*e^2 - (B*b^4 + 3*A*b^3*c)*d*e^3)*x^2 + (4*B*b^3*c*d^3*e + 3*A*b^4*d*e^3 - (B*b^4 + 6*A*b^3*c)*d^2*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (2*A*b*c^3*d^5 - 6*A*b^2*c^2*d^4*e + 6*A*b^3*c*d^3*e^2 - 2*A*b^4*d^2*e^3 - (3*A*b^3*c*d*e^4 + 2*(B*b*c^3 - 2*A*c^4)*d^4*e - (B*b^2*c^2 - 8*A*b*c^3)*d^3*e^2 - (B*b^3*c + 7*A*b^2*c^2)*d^2*e^3)*x^2 - (B*b^3*c*d^3*e^2 + 3*A*b^4*d*e^4 + 2*(B*b*c^3 - 2*A*c^4)*d^5 - 2*(B*b^2*c^2 - 3*A*b*c^3)*d^4*e - (B*b^4 + 5*A*b^3*c)*d^2*e^3)*x)*sqrt(c*x^2 + b*x))/((b^2*c^4*d^6*e - 3*b^3*c^3*d^5*e^2 + 3*b^4*c^2*d^4*e^3 - b^5*c*d^3*e^4)*x^3 + (b^2*c^4*d^7 - 2*b^3*c^3*d^6*e + 2*b^5*c*d^4*e^3 - b^6*d^3*e^4)*x^2 + (b^3*c^3*d^7 - 3*b^4*c^2*d^6*e + 3*b^5*c*d^5*e^2 - b^6*d^4*e^3)*x)]","B",0
1205,1,2282,0,0.529024," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(8 \, B b^{2} c^{3} d^{3} e^{3} - 5 \, A b^{4} c e^{6} - 4 \, {\left(B b^{3} c^{2} + 4 \, A b^{2} c^{3}\right)} d^{2} e^{4} + {\left(B b^{4} c + 16 \, A b^{3} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(16 \, B b^{2} c^{3} d^{4} e^{2} - 32 \, A b^{2} c^{3} d^{3} e^{3} - 5 \, A b^{5} e^{6} - 2 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d^{2} e^{4} + {\left(B b^{5} + 6 \, A b^{4} c\right)} d e^{5}\right)} x^{3} + {\left(8 \, B b^{2} c^{3} d^{5} e - 10 \, A b^{5} d e^{5} + 4 \, {\left(3 \, B b^{3} c^{2} - 4 \, A b^{2} c^{3}\right)} d^{4} e^{2} - {\left(7 \, B b^{4} c + 16 \, A b^{3} c^{2}\right)} d^{3} e^{3} + {\left(2 \, B b^{5} + 27 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(8 \, B b^{3} c^{2} d^{5} e - 5 \, A b^{5} d^{2} e^{4} - 4 \, {\left(B b^{4} c + 4 \, A b^{3} c^{2}\right)} d^{4} e^{2} + {\left(B b^{5} + 16 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(8 \, A b c^{4} d^{7} - 32 \, A b^{2} c^{3} d^{6} e + 48 \, A b^{3} c^{2} d^{5} e^{2} - 32 \, A b^{4} c d^{4} e^{3} + 8 \, A b^{5} d^{3} e^{4} + {\left(15 \, A b^{4} c d e^{6} - 8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e^{2} - 2 \, {\left(B b^{2} c^{3} + 20 \, A b c^{4}\right)} d^{4} e^{3} + {\left(13 \, B b^{3} c^{2} + 62 \, A b^{2} c^{3}\right)} d^{3} e^{4} - {\left(3 \, B b^{4} c + 53 \, A b^{3} c^{2}\right)} d^{2} e^{5}\right)} x^{3} + {\left(15 \, A b^{5} d e^{6} - 16 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} e + 4 \, {\left(B b^{2} c^{3} - 18 \, A b c^{4}\right)} d^{5} e^{2} + {\left(7 \, B b^{3} c^{2} + 80 \, A b^{2} c^{3}\right)} d^{4} e^{3} + {\left(8 \, B b^{4} c - 27 \, A b^{3} c^{2}\right)} d^{3} e^{4} - {\left(3 \, B b^{5} + 28 \, A b^{4} c\right)} d^{2} e^{5}\right)} x^{2} + {\left(25 \, A b^{5} d^{2} e^{5} - 8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{7} + 8 \, {\left(B b^{2} c^{3} - 3 \, A b c^{4}\right)} d^{6} e - 4 \, {\left(3 \, B b^{3} c^{2} + 4 \, A b^{2} c^{3}\right)} d^{5} e^{2} + {\left(17 \, B b^{4} c + 80 \, A b^{3} c^{2}\right)} d^{4} e^{3} - {\left(5 \, B b^{5} + 81 \, A b^{4} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left({\left(b^{2} c^{5} d^{8} e^{2} - 4 \, b^{3} c^{4} d^{7} e^{3} + 6 \, b^{4} c^{3} d^{6} e^{4} - 4 \, b^{5} c^{2} d^{5} e^{5} + b^{6} c d^{4} e^{6}\right)} x^{4} + {\left(2 \, b^{2} c^{5} d^{9} e - 7 \, b^{3} c^{4} d^{8} e^{2} + 8 \, b^{4} c^{3} d^{7} e^{3} - 2 \, b^{5} c^{2} d^{6} e^{4} - 2 \, b^{6} c d^{5} e^{5} + b^{7} d^{4} e^{6}\right)} x^{3} + {\left(b^{2} c^{5} d^{10} - 2 \, b^{3} c^{4} d^{9} e - 2 \, b^{4} c^{3} d^{8} e^{2} + 8 \, b^{5} c^{2} d^{7} e^{3} - 7 \, b^{6} c d^{6} e^{4} + 2 \, b^{7} d^{5} e^{5}\right)} x^{2} + {\left(b^{3} c^{4} d^{10} - 4 \, b^{4} c^{3} d^{9} e + 6 \, b^{5} c^{2} d^{8} e^{2} - 4 \, b^{6} c d^{7} e^{3} + b^{7} d^{6} e^{4}\right)} x\right)}}, -\frac{3 \, {\left({\left(8 \, B b^{2} c^{3} d^{3} e^{3} - 5 \, A b^{4} c e^{6} - 4 \, {\left(B b^{3} c^{2} + 4 \, A b^{2} c^{3}\right)} d^{2} e^{4} + {\left(B b^{4} c + 16 \, A b^{3} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(16 \, B b^{2} c^{3} d^{4} e^{2} - 32 \, A b^{2} c^{3} d^{3} e^{3} - 5 \, A b^{5} e^{6} - 2 \, {\left(B b^{4} c - 8 \, A b^{3} c^{2}\right)} d^{2} e^{4} + {\left(B b^{5} + 6 \, A b^{4} c\right)} d e^{5}\right)} x^{3} + {\left(8 \, B b^{2} c^{3} d^{5} e - 10 \, A b^{5} d e^{5} + 4 \, {\left(3 \, B b^{3} c^{2} - 4 \, A b^{2} c^{3}\right)} d^{4} e^{2} - {\left(7 \, B b^{4} c + 16 \, A b^{3} c^{2}\right)} d^{3} e^{3} + {\left(2 \, B b^{5} + 27 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(8 \, B b^{3} c^{2} d^{5} e - 5 \, A b^{5} d^{2} e^{4} - 4 \, {\left(B b^{4} c + 4 \, A b^{3} c^{2}\right)} d^{4} e^{2} + {\left(B b^{5} + 16 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(8 \, A b c^{4} d^{7} - 32 \, A b^{2} c^{3} d^{6} e + 48 \, A b^{3} c^{2} d^{5} e^{2} - 32 \, A b^{4} c d^{4} e^{3} + 8 \, A b^{5} d^{3} e^{4} + {\left(15 \, A b^{4} c d e^{6} - 8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e^{2} - 2 \, {\left(B b^{2} c^{3} + 20 \, A b c^{4}\right)} d^{4} e^{3} + {\left(13 \, B b^{3} c^{2} + 62 \, A b^{2} c^{3}\right)} d^{3} e^{4} - {\left(3 \, B b^{4} c + 53 \, A b^{3} c^{2}\right)} d^{2} e^{5}\right)} x^{3} + {\left(15 \, A b^{5} d e^{6} - 16 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} e + 4 \, {\left(B b^{2} c^{3} - 18 \, A b c^{4}\right)} d^{5} e^{2} + {\left(7 \, B b^{3} c^{2} + 80 \, A b^{2} c^{3}\right)} d^{4} e^{3} + {\left(8 \, B b^{4} c - 27 \, A b^{3} c^{2}\right)} d^{3} e^{4} - {\left(3 \, B b^{5} + 28 \, A b^{4} c\right)} d^{2} e^{5}\right)} x^{2} + {\left(25 \, A b^{5} d^{2} e^{5} - 8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{7} + 8 \, {\left(B b^{2} c^{3} - 3 \, A b c^{4}\right)} d^{6} e - 4 \, {\left(3 \, B b^{3} c^{2} + 4 \, A b^{2} c^{3}\right)} d^{5} e^{2} + {\left(17 \, B b^{4} c + 80 \, A b^{3} c^{2}\right)} d^{4} e^{3} - {\left(5 \, B b^{5} + 81 \, A b^{4} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left({\left(b^{2} c^{5} d^{8} e^{2} - 4 \, b^{3} c^{4} d^{7} e^{3} + 6 \, b^{4} c^{3} d^{6} e^{4} - 4 \, b^{5} c^{2} d^{5} e^{5} + b^{6} c d^{4} e^{6}\right)} x^{4} + {\left(2 \, b^{2} c^{5} d^{9} e - 7 \, b^{3} c^{4} d^{8} e^{2} + 8 \, b^{4} c^{3} d^{7} e^{3} - 2 \, b^{5} c^{2} d^{6} e^{4} - 2 \, b^{6} c d^{5} e^{5} + b^{7} d^{4} e^{6}\right)} x^{3} + {\left(b^{2} c^{5} d^{10} - 2 \, b^{3} c^{4} d^{9} e - 2 \, b^{4} c^{3} d^{8} e^{2} + 8 \, b^{5} c^{2} d^{7} e^{3} - 7 \, b^{6} c d^{6} e^{4} + 2 \, b^{7} d^{5} e^{5}\right)} x^{2} + {\left(b^{3} c^{4} d^{10} - 4 \, b^{4} c^{3} d^{9} e + 6 \, b^{5} c^{2} d^{8} e^{2} - 4 \, b^{6} c d^{7} e^{3} + b^{7} d^{6} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/8*(3*((8*B*b^2*c^3*d^3*e^3 - 5*A*b^4*c*e^6 - 4*(B*b^3*c^2 + 4*A*b^2*c^3)*d^2*e^4 + (B*b^4*c + 16*A*b^3*c^2)*d*e^5)*x^4 + (16*B*b^2*c^3*d^4*e^2 - 32*A*b^2*c^3*d^3*e^3 - 5*A*b^5*e^6 - 2*(B*b^4*c - 8*A*b^3*c^2)*d^2*e^4 + (B*b^5 + 6*A*b^4*c)*d*e^5)*x^3 + (8*B*b^2*c^3*d^5*e - 10*A*b^5*d*e^5 + 4*(3*B*b^3*c^2 - 4*A*b^2*c^3)*d^4*e^2 - (7*B*b^4*c + 16*A*b^3*c^2)*d^3*e^3 + (2*B*b^5 + 27*A*b^4*c)*d^2*e^4)*x^2 + (8*B*b^3*c^2*d^5*e - 5*A*b^5*d^2*e^4 - 4*(B*b^4*c + 4*A*b^3*c^2)*d^4*e^2 + (B*b^5 + 16*A*b^4*c)*d^3*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(8*A*b*c^4*d^7 - 32*A*b^2*c^3*d^6*e + 48*A*b^3*c^2*d^5*e^2 - 32*A*b^4*c*d^4*e^3 + 8*A*b^5*d^3*e^4 + (15*A*b^4*c*d*e^6 - 8*(B*b*c^4 - 2*A*c^5)*d^5*e^2 - 2*(B*b^2*c^3 + 20*A*b*c^4)*d^4*e^3 + (13*B*b^3*c^2 + 62*A*b^2*c^3)*d^3*e^4 - (3*B*b^4*c + 53*A*b^3*c^2)*d^2*e^5)*x^3 + (15*A*b^5*d*e^6 - 16*(B*b*c^4 - 2*A*c^5)*d^6*e + 4*(B*b^2*c^3 - 18*A*b*c^4)*d^5*e^2 + (7*B*b^3*c^2 + 80*A*b^2*c^3)*d^4*e^3 + (8*B*b^4*c - 27*A*b^3*c^2)*d^3*e^4 - (3*B*b^5 + 28*A*b^4*c)*d^2*e^5)*x^2 + (25*A*b^5*d^2*e^5 - 8*(B*b*c^4 - 2*A*c^5)*d^7 + 8*(B*b^2*c^3 - 3*A*b*c^4)*d^6*e - 4*(3*B*b^3*c^2 + 4*A*b^2*c^3)*d^5*e^2 + (17*B*b^4*c + 80*A*b^3*c^2)*d^4*e^3 - (5*B*b^5 + 81*A*b^4*c)*d^3*e^4)*x)*sqrt(c*x^2 + b*x))/((b^2*c^5*d^8*e^2 - 4*b^3*c^4*d^7*e^3 + 6*b^4*c^3*d^6*e^4 - 4*b^5*c^2*d^5*e^5 + b^6*c*d^4*e^6)*x^4 + (2*b^2*c^5*d^9*e - 7*b^3*c^4*d^8*e^2 + 8*b^4*c^3*d^7*e^3 - 2*b^5*c^2*d^6*e^4 - 2*b^6*c*d^5*e^5 + b^7*d^4*e^6)*x^3 + (b^2*c^5*d^10 - 2*b^3*c^4*d^9*e - 2*b^4*c^3*d^8*e^2 + 8*b^5*c^2*d^7*e^3 - 7*b^6*c*d^6*e^4 + 2*b^7*d^5*e^5)*x^2 + (b^3*c^4*d^10 - 4*b^4*c^3*d^9*e + 6*b^5*c^2*d^8*e^2 - 4*b^6*c*d^7*e^3 + b^7*d^6*e^4)*x), -1/4*(3*((8*B*b^2*c^3*d^3*e^3 - 5*A*b^4*c*e^6 - 4*(B*b^3*c^2 + 4*A*b^2*c^3)*d^2*e^4 + (B*b^4*c + 16*A*b^3*c^2)*d*e^5)*x^4 + (16*B*b^2*c^3*d^4*e^2 - 32*A*b^2*c^3*d^3*e^3 - 5*A*b^5*e^6 - 2*(B*b^4*c - 8*A*b^3*c^2)*d^2*e^4 + (B*b^5 + 6*A*b^4*c)*d*e^5)*x^3 + (8*B*b^2*c^3*d^5*e - 10*A*b^5*d*e^5 + 4*(3*B*b^3*c^2 - 4*A*b^2*c^3)*d^4*e^2 - (7*B*b^4*c + 16*A*b^3*c^2)*d^3*e^3 + (2*B*b^5 + 27*A*b^4*c)*d^2*e^4)*x^2 + (8*B*b^3*c^2*d^5*e - 5*A*b^5*d^2*e^4 - 4*(B*b^4*c + 4*A*b^3*c^2)*d^4*e^2 + (B*b^5 + 16*A*b^4*c)*d^3*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (8*A*b*c^4*d^7 - 32*A*b^2*c^3*d^6*e + 48*A*b^3*c^2*d^5*e^2 - 32*A*b^4*c*d^4*e^3 + 8*A*b^5*d^3*e^4 + (15*A*b^4*c*d*e^6 - 8*(B*b*c^4 - 2*A*c^5)*d^5*e^2 - 2*(B*b^2*c^3 + 20*A*b*c^4)*d^4*e^3 + (13*B*b^3*c^2 + 62*A*b^2*c^3)*d^3*e^4 - (3*B*b^4*c + 53*A*b^3*c^2)*d^2*e^5)*x^3 + (15*A*b^5*d*e^6 - 16*(B*b*c^4 - 2*A*c^5)*d^6*e + 4*(B*b^2*c^3 - 18*A*b*c^4)*d^5*e^2 + (7*B*b^3*c^2 + 80*A*b^2*c^3)*d^4*e^3 + (8*B*b^4*c - 27*A*b^3*c^2)*d^3*e^4 - (3*B*b^5 + 28*A*b^4*c)*d^2*e^5)*x^2 + (25*A*b^5*d^2*e^5 - 8*(B*b*c^4 - 2*A*c^5)*d^7 + 8*(B*b^2*c^3 - 3*A*b*c^4)*d^6*e - 4*(3*B*b^3*c^2 + 4*A*b^2*c^3)*d^5*e^2 + (17*B*b^4*c + 80*A*b^3*c^2)*d^4*e^3 - (5*B*b^5 + 81*A*b^4*c)*d^3*e^4)*x)*sqrt(c*x^2 + b*x))/((b^2*c^5*d^8*e^2 - 4*b^3*c^4*d^7*e^3 + 6*b^4*c^3*d^6*e^4 - 4*b^5*c^2*d^5*e^5 + b^6*c*d^4*e^6)*x^4 + (2*b^2*c^5*d^9*e - 7*b^3*c^4*d^8*e^2 + 8*b^4*c^3*d^7*e^3 - 2*b^5*c^2*d^6*e^4 - 2*b^6*c*d^5*e^5 + b^7*d^4*e^6)*x^3 + (b^2*c^5*d^10 - 2*b^3*c^4*d^9*e - 2*b^4*c^3*d^8*e^2 + 8*b^5*c^2*d^7*e^3 - 7*b^6*c*d^6*e^4 + 2*b^7*d^5*e^5)*x^2 + (b^3*c^4*d^10 - 4*b^4*c^3*d^9*e + 6*b^5*c^2*d^8*e^2 - 4*b^6*c*d^7*e^3 + b^7*d^6*e^4)*x)]","B",0
1206,1,974,0,0.462619," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, B b^{4} c^{3} d e^{3} - {\left(5 \, B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(8 \, B b^{5} c^{2} d e^{3} - {\left(5 \, B b^{6} c - 2 \, A b^{5} c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, B b^{6} c d e^{3} - {\left(5 \, B b^{7} - 2 \, A b^{6} c\right)} e^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(3 \, B b^{4} c^{3} e^{4} x^{4} - 2 \, A b^{3} c^{4} d^{4} - 4 \, {\left(4 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} - 4 \, {\left(B b^{2} c^{5} - 4 \, A b c^{6}\right)} d^{3} e - 3 \, {\left(B b^{3} c^{4} + 2 \, A b^{2} c^{5}\right)} d^{2} e^{2} + 2 \, {\left(4 \, B b^{4} c^{3} - A b^{3} c^{4}\right)} d e^{3} - {\left(5 \, B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(12 \, A b^{3} c^{4} d^{2} e^{2} - 8 \, B b^{5} c^{2} d e^{3} - 8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} + 8 \, {\left(B b^{3} c^{4} - 4 \, A b^{2} c^{5}\right)} d^{3} e + {\left(5 \, B b^{6} c - 2 \, A b^{5} c^{2}\right)} e^{4}\right)} x^{2} - 6 \, {\left(4 \, A b^{3} c^{4} d^{3} e + {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{6 \, {\left(b^{4} c^{6} x^{4} + 2 \, b^{5} c^{5} x^{3} + b^{6} c^{4} x^{2}\right)}}, -\frac{3 \, {\left({\left(8 \, B b^{4} c^{3} d e^{3} - {\left(5 \, B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(8 \, B b^{5} c^{2} d e^{3} - {\left(5 \, B b^{6} c - 2 \, A b^{5} c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, B b^{6} c d e^{3} - {\left(5 \, B b^{7} - 2 \, A b^{6} c\right)} e^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(3 \, B b^{4} c^{3} e^{4} x^{4} - 2 \, A b^{3} c^{4} d^{4} - 4 \, {\left(4 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} - 4 \, {\left(B b^{2} c^{5} - 4 \, A b c^{6}\right)} d^{3} e - 3 \, {\left(B b^{3} c^{4} + 2 \, A b^{2} c^{5}\right)} d^{2} e^{2} + 2 \, {\left(4 \, B b^{4} c^{3} - A b^{3} c^{4}\right)} d e^{3} - {\left(5 \, B b^{5} c^{2} - 2 \, A b^{4} c^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(12 \, A b^{3} c^{4} d^{2} e^{2} - 8 \, B b^{5} c^{2} d e^{3} - 8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} + 8 \, {\left(B b^{3} c^{4} - 4 \, A b^{2} c^{5}\right)} d^{3} e + {\left(5 \, B b^{6} c - 2 \, A b^{5} c^{2}\right)} e^{4}\right)} x^{2} - 6 \, {\left(4 \, A b^{3} c^{4} d^{3} e + {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{6} x^{4} + 2 \, b^{5} c^{5} x^{3} + b^{6} c^{4} x^{2}\right)}}\right]"," ",0,"[1/6*(3*((8*B*b^4*c^3*d*e^3 - (5*B*b^5*c^2 - 2*A*b^4*c^3)*e^4)*x^4 + 2*(8*B*b^5*c^2*d*e^3 - (5*B*b^6*c - 2*A*b^5*c^2)*e^4)*x^3 + (8*B*b^6*c*d*e^3 - (5*B*b^7 - 2*A*b^6*c)*e^4)*x^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(3*B*b^4*c^3*e^4*x^4 - 2*A*b^3*c^4*d^4 - 4*(4*(B*b*c^6 - 2*A*c^7)*d^4 - 4*(B*b^2*c^5 - 4*A*b*c^6)*d^3*e - 3*(B*b^3*c^4 + 2*A*b^2*c^5)*d^2*e^2 + 2*(4*B*b^4*c^3 - A*b^3*c^4)*d*e^3 - (5*B*b^5*c^2 - 2*A*b^4*c^3)*e^4)*x^3 + 3*(12*A*b^3*c^4*d^2*e^2 - 8*B*b^5*c^2*d*e^3 - 8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 + 8*(B*b^3*c^4 - 4*A*b^2*c^5)*d^3*e + (5*B*b^6*c - 2*A*b^5*c^2)*e^4)*x^2 - 6*(4*A*b^3*c^4*d^3*e + (B*b^3*c^4 - 2*A*b^2*c^5)*d^4)*x)*sqrt(c*x^2 + b*x))/(b^4*c^6*x^4 + 2*b^5*c^5*x^3 + b^6*c^4*x^2), -1/3*(3*((8*B*b^4*c^3*d*e^3 - (5*B*b^5*c^2 - 2*A*b^4*c^3)*e^4)*x^4 + 2*(8*B*b^5*c^2*d*e^3 - (5*B*b^6*c - 2*A*b^5*c^2)*e^4)*x^3 + (8*B*b^6*c*d*e^3 - (5*B*b^7 - 2*A*b^6*c)*e^4)*x^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (3*B*b^4*c^3*e^4*x^4 - 2*A*b^3*c^4*d^4 - 4*(4*(B*b*c^6 - 2*A*c^7)*d^4 - 4*(B*b^2*c^5 - 4*A*b*c^6)*d^3*e - 3*(B*b^3*c^4 + 2*A*b^2*c^5)*d^2*e^2 + 2*(4*B*b^4*c^3 - A*b^3*c^4)*d*e^3 - (5*B*b^5*c^2 - 2*A*b^4*c^3)*e^4)*x^3 + 3*(12*A*b^3*c^4*d^2*e^2 - 8*B*b^5*c^2*d*e^3 - 8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 + 8*(B*b^3*c^4 - 4*A*b^2*c^5)*d^3*e + (5*B*b^6*c - 2*A*b^5*c^2)*e^4)*x^2 - 6*(4*A*b^3*c^4*d^3*e + (B*b^3*c^4 - 2*A*b^2*c^5)*d^4)*x)*sqrt(c*x^2 + b*x))/(b^4*c^6*x^4 + 2*b^5*c^5*x^3 + b^6*c^4*x^2)]","A",0
1207,1,671,0,0.429514," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B b^{4} c^{2} e^{3} x^{4} + 2 \, B b^{5} c e^{3} x^{3} + B b^{6} e^{3} x^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(A b^{3} c^{3} d^{3} + {\left(8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 6 \, {\left(B b^{2} c^{4} - 4 \, A b c^{5}\right)} d^{2} e - 3 \, {\left(B b^{3} c^{3} + 2 \, A b^{2} c^{4}\right)} d e^{2} + {\left(4 \, B b^{4} c^{2} - A b^{3} c^{3}\right)} e^{3}\right)} x^{3} - 3 \, {\left(3 \, A b^{3} c^{3} d e^{2} - B b^{5} c e^{3} - 4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + 3 \, {\left(B b^{3} c^{3} - 4 \, A b^{2} c^{4}\right)} d^{2} e\right)} x^{2} + 3 \, {\left(3 \, A b^{3} c^{3} d^{2} e + {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{5} x^{4} + 2 \, b^{5} c^{4} x^{3} + b^{6} c^{3} x^{2}\right)}}, -\frac{2 \, {\left(3 \, {\left(B b^{4} c^{2} e^{3} x^{4} + 2 \, B b^{5} c e^{3} x^{3} + B b^{6} e^{3} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(A b^{3} c^{3} d^{3} + {\left(8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 6 \, {\left(B b^{2} c^{4} - 4 \, A b c^{5}\right)} d^{2} e - 3 \, {\left(B b^{3} c^{3} + 2 \, A b^{2} c^{4}\right)} d e^{2} + {\left(4 \, B b^{4} c^{2} - A b^{3} c^{3}\right)} e^{3}\right)} x^{3} - 3 \, {\left(3 \, A b^{3} c^{3} d e^{2} - B b^{5} c e^{3} - 4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + 3 \, {\left(B b^{3} c^{3} - 4 \, A b^{2} c^{4}\right)} d^{2} e\right)} x^{2} + 3 \, {\left(3 \, A b^{3} c^{3} d^{2} e + {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3}\right)} x\right)} \sqrt{c x^{2} + b x}\right)}}{3 \, {\left(b^{4} c^{5} x^{4} + 2 \, b^{5} c^{4} x^{3} + b^{6} c^{3} x^{2}\right)}}\right]"," ",0,"[1/3*(3*(B*b^4*c^2*e^3*x^4 + 2*B*b^5*c*e^3*x^3 + B*b^6*e^3*x^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(A*b^3*c^3*d^3 + (8*(B*b*c^5 - 2*A*c^6)*d^3 - 6*(B*b^2*c^4 - 4*A*b*c^5)*d^2*e - 3*(B*b^3*c^3 + 2*A*b^2*c^4)*d*e^2 + (4*B*b^4*c^2 - A*b^3*c^3)*e^3)*x^3 - 3*(3*A*b^3*c^3*d*e^2 - B*b^5*c*e^3 - 4*(B*b^2*c^4 - 2*A*b*c^5)*d^3 + 3*(B*b^3*c^3 - 4*A*b^2*c^4)*d^2*e)*x^2 + 3*(3*A*b^3*c^3*d^2*e + (B*b^3*c^3 - 2*A*b^2*c^4)*d^3)*x)*sqrt(c*x^2 + b*x))/(b^4*c^5*x^4 + 2*b^5*c^4*x^3 + b^6*c^3*x^2), -2/3*(3*(B*b^4*c^2*e^3*x^4 + 2*B*b^5*c*e^3*x^3 + B*b^6*e^3*x^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (A*b^3*c^3*d^3 + (8*(B*b*c^5 - 2*A*c^6)*d^3 - 6*(B*b^2*c^4 - 4*A*b*c^5)*d^2*e - 3*(B*b^3*c^3 + 2*A*b^2*c^4)*d*e^2 + (4*B*b^4*c^2 - A*b^3*c^3)*e^3)*x^3 - 3*(3*A*b^3*c^3*d*e^2 - B*b^5*c*e^3 - 4*(B*b^2*c^4 - 2*A*b*c^5)*d^3 + 3*(B*b^3*c^3 - 4*A*b^2*c^4)*d^2*e)*x^2 + 3*(3*A*b^3*c^3*d^2*e + (B*b^3*c^3 - 2*A*b^2*c^4)*d^3)*x)*sqrt(c*x^2 + b*x))/(b^4*c^5*x^4 + 2*b^5*c^4*x^3 + b^6*c^3*x^2)]","A",0
1208,1,189,0,0.428225," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A b^{3} d^{2} + {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - 4 \, {\left(B b^{2} c - 4 \, A b c^{2}\right)} d e - {\left(B b^{3} + 2 \, A b^{2} c\right)} e^{2}\right)} x^{3} - 3 \, {\left(A b^{3} e^{2} - 4 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} + 2 \, {\left(B b^{3} - 4 \, A b^{2} c\right)} d e\right)} x^{2} + 3 \, {\left(2 \, A b^{3} d e + {\left(B b^{3} - 2 \, A b^{2} c\right)} d^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}"," ",0,"-2/3*(A*b^3*d^2 + (8*(B*b*c^2 - 2*A*c^3)*d^2 - 4*(B*b^2*c - 4*A*b*c^2)*d*e - (B*b^3 + 2*A*b^2*c)*e^2)*x^3 - 3*(A*b^3*e^2 - 4*(B*b^2*c - 2*A*b*c^2)*d^2 + 2*(B*b^3 - 4*A*b^2*c)*d*e)*x^2 + 3*(2*A*b^3*d*e + (B*b^3 - 2*A*b^2*c)*d^2)*x)*sqrt(c*x^2 + b*x)/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)","B",0
1209,1,152,0,0.409624," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A b^{3} d + 2 \, {\left(4 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d - {\left(B b^{2} c - 4 \, A b c^{2}\right)} e\right)} x^{3} + 3 \, {\left(4 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d - {\left(B b^{3} - 4 \, A b^{2} c\right)} e\right)} x^{2} + 3 \, {\left(A b^{3} e + {\left(B b^{3} - 2 \, A b^{2} c\right)} d\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}"," ",0,"-2/3*(A*b^3*d + 2*(4*(B*b*c^2 - 2*A*c^3)*d - (B*b^2*c - 4*A*b*c^2)*e)*x^3 + 3*(4*(B*b^2*c - 2*A*b*c^2)*d - (B*b^3 - 4*A*b^2*c)*e)*x^2 + 3*(A*b^3*e + (B*b^3 - 2*A*b^2*c)*d)*x)*sqrt(c*x^2 + b*x)/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)","A",0
1210,1,101,0,0.397149," ","integrate((B*x+A)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A b^{3} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} x^{3} + 12 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} x^{2} + 3 \, {\left(B b^{3} - 2 \, A b^{2} c\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}"," ",0,"-2/3*(A*b^3 + 8*(B*b*c^2 - 2*A*c^3)*x^3 + 12*(B*b^2*c - 2*A*b*c^2)*x^2 + 3*(B*b^3 - 2*A*b^2*c)*x)*sqrt(c*x^2 + b*x)/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)","A",0
1211,1,1390,0,0.463945," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(B b^{4} c^{2} d e^{3} - A b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(B b^{5} c d e^{3} - A b^{5} c e^{4}\right)} x^{3} + {\left(B b^{6} d e^{3} - A b^{6} e^{4}\right)} x^{2}\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(A b^{3} c^{3} d^{5} - 3 \, A b^{4} c^{2} d^{4} e + 3 \, A b^{5} c d^{3} e^{2} - A b^{6} d^{2} e^{3} + {\left(3 \, A b^{4} c^{2} d e^{4} + 8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} - 2 \, {\left(11 \, B b^{2} c^{4} - 20 \, A b c^{5}\right)} d^{4} e + {\left(17 \, B b^{3} c^{3} - 26 \, A b^{2} c^{4}\right)} d^{3} e^{2} - {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} d^{2} e^{3}\right)} x^{3} + 3 \, {\left(2 \, A b^{5} c d e^{4} + 4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} - {\left(11 \, B b^{3} c^{3} - 20 \, A b^{2} c^{4}\right)} d^{4} e + {\left(9 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} d^{3} e^{2} - {\left(2 \, B b^{5} c + A b^{4} c^{2}\right)} d^{2} e^{3}\right)} x^{2} + 3 \, {\left(A b^{6} d e^{4} + {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{5} - {\left(3 \, B b^{4} c^{2} - 5 \, A b^{3} c^{3}\right)} d^{4} e + 3 \, {\left(B b^{5} c - A b^{4} c^{2}\right)} d^{3} e^{2} - {\left(B b^{6} + A b^{5} c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left({\left(b^{4} c^{5} d^{6} - 3 \, b^{5} c^{4} d^{5} e + 3 \, b^{6} c^{3} d^{4} e^{2} - b^{7} c^{2} d^{3} e^{3}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} d^{6} - 3 \, b^{6} c^{3} d^{5} e + 3 \, b^{7} c^{2} d^{4} e^{2} - b^{8} c d^{3} e^{3}\right)} x^{3} + {\left(b^{6} c^{3} d^{6} - 3 \, b^{7} c^{2} d^{5} e + 3 \, b^{8} c d^{4} e^{2} - b^{9} d^{3} e^{3}\right)} x^{2}\right)}}, -\frac{2 \, {\left(3 \, {\left({\left(B b^{4} c^{2} d e^{3} - A b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(B b^{5} c d e^{3} - A b^{5} c e^{4}\right)} x^{3} + {\left(B b^{6} d e^{3} - A b^{6} e^{4}\right)} x^{2}\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(A b^{3} c^{3} d^{5} - 3 \, A b^{4} c^{2} d^{4} e + 3 \, A b^{5} c d^{3} e^{2} - A b^{6} d^{2} e^{3} + {\left(3 \, A b^{4} c^{2} d e^{4} + 8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} - 2 \, {\left(11 \, B b^{2} c^{4} - 20 \, A b c^{5}\right)} d^{4} e + {\left(17 \, B b^{3} c^{3} - 26 \, A b^{2} c^{4}\right)} d^{3} e^{2} - {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} d^{2} e^{3}\right)} x^{3} + 3 \, {\left(2 \, A b^{5} c d e^{4} + 4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} - {\left(11 \, B b^{3} c^{3} - 20 \, A b^{2} c^{4}\right)} d^{4} e + {\left(9 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} d^{3} e^{2} - {\left(2 \, B b^{5} c + A b^{4} c^{2}\right)} d^{2} e^{3}\right)} x^{2} + 3 \, {\left(A b^{6} d e^{4} + {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{5} - {\left(3 \, B b^{4} c^{2} - 5 \, A b^{3} c^{3}\right)} d^{4} e + 3 \, {\left(B b^{5} c - A b^{4} c^{2}\right)} d^{3} e^{2} - {\left(B b^{6} + A b^{5} c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}\right)}}{3 \, {\left({\left(b^{4} c^{5} d^{6} - 3 \, b^{5} c^{4} d^{5} e + 3 \, b^{6} c^{3} d^{4} e^{2} - b^{7} c^{2} d^{3} e^{3}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} d^{6} - 3 \, b^{6} c^{3} d^{5} e + 3 \, b^{7} c^{2} d^{4} e^{2} - b^{8} c d^{3} e^{3}\right)} x^{3} + {\left(b^{6} c^{3} d^{6} - 3 \, b^{7} c^{2} d^{5} e + 3 \, b^{8} c d^{4} e^{2} - b^{9} d^{3} e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/3*(3*((B*b^4*c^2*d*e^3 - A*b^4*c^2*e^4)*x^4 + 2*(B*b^5*c*d*e^3 - A*b^5*c*e^4)*x^3 + (B*b^6*d*e^3 - A*b^6*e^4)*x^2)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(A*b^3*c^3*d^5 - 3*A*b^4*c^2*d^4*e + 3*A*b^5*c*d^3*e^2 - A*b^6*d^2*e^3 + (3*A*b^4*c^2*d*e^4 + 8*(B*b*c^5 - 2*A*c^6)*d^5 - 2*(11*B*b^2*c^4 - 20*A*b*c^5)*d^4*e + (17*B*b^3*c^3 - 26*A*b^2*c^4)*d^3*e^2 - (3*B*b^4*c^2 + A*b^3*c^3)*d^2*e^3)*x^3 + 3*(2*A*b^5*c*d*e^4 + 4*(B*b^2*c^4 - 2*A*b*c^5)*d^5 - (11*B*b^3*c^3 - 20*A*b^2*c^4)*d^4*e + (9*B*b^4*c^2 - 13*A*b^3*c^3)*d^3*e^2 - (2*B*b^5*c + A*b^4*c^2)*d^2*e^3)*x^2 + 3*(A*b^6*d*e^4 + (B*b^3*c^3 - 2*A*b^2*c^4)*d^5 - (3*B*b^4*c^2 - 5*A*b^3*c^3)*d^4*e + 3*(B*b^5*c - A*b^4*c^2)*d^3*e^2 - (B*b^6 + A*b^5*c)*d^2*e^3)*x)*sqrt(c*x^2 + b*x))/((b^4*c^5*d^6 - 3*b^5*c^4*d^5*e + 3*b^6*c^3*d^4*e^2 - b^7*c^2*d^3*e^3)*x^4 + 2*(b^5*c^4*d^6 - 3*b^6*c^3*d^5*e + 3*b^7*c^2*d^4*e^2 - b^8*c*d^3*e^3)*x^3 + (b^6*c^3*d^6 - 3*b^7*c^2*d^5*e + 3*b^8*c*d^4*e^2 - b^9*d^3*e^3)*x^2), -2/3*(3*((B*b^4*c^2*d*e^3 - A*b^4*c^2*e^4)*x^4 + 2*(B*b^5*c*d*e^3 - A*b^5*c*e^4)*x^3 + (B*b^6*d*e^3 - A*b^6*e^4)*x^2)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (A*b^3*c^3*d^5 - 3*A*b^4*c^2*d^4*e + 3*A*b^5*c*d^3*e^2 - A*b^6*d^2*e^3 + (3*A*b^4*c^2*d*e^4 + 8*(B*b*c^5 - 2*A*c^6)*d^5 - 2*(11*B*b^2*c^4 - 20*A*b*c^5)*d^4*e + (17*B*b^3*c^3 - 26*A*b^2*c^4)*d^3*e^2 - (3*B*b^4*c^2 + A*b^3*c^3)*d^2*e^3)*x^3 + 3*(2*A*b^5*c*d*e^4 + 4*(B*b^2*c^4 - 2*A*b*c^5)*d^5 - (11*B*b^3*c^3 - 20*A*b^2*c^4)*d^4*e + (9*B*b^4*c^2 - 13*A*b^3*c^3)*d^3*e^2 - (2*B*b^5*c + A*b^4*c^2)*d^2*e^3)*x^2 + 3*(A*b^6*d*e^4 + (B*b^3*c^3 - 2*A*b^2*c^4)*d^5 - (3*B*b^4*c^2 - 5*A*b^3*c^3)*d^4*e + 3*(B*b^5*c - A*b^4*c^2)*d^3*e^2 - (B*b^6 + A*b^5*c)*d^2*e^3)*x)*sqrt(c*x^2 + b*x))/((b^4*c^5*d^6 - 3*b^5*c^4*d^5*e + 3*b^6*c^3*d^4*e^2 - b^7*c^2*d^3*e^3)*x^4 + 2*(b^5*c^4*d^6 - 3*b^6*c^3*d^5*e + 3*b^7*c^2*d^4*e^2 - b^8*c*d^3*e^3)*x^3 + (b^6*c^3*d^6 - 3*b^7*c^2*d^5*e + 3*b^8*c*d^4*e^2 - b^9*d^3*e^3)*x^2)]","B",0
1212,1,2582,0,0.538315," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(8 \, B b^{4} c^{3} d^{2} e^{4} + 5 \, A b^{5} c^{2} e^{6} - {\left(3 \, B b^{5} c^{2} + 10 \, A b^{4} c^{3}\right)} d e^{5}\right)} x^{5} + {\left(8 \, B b^{4} c^{3} d^{3} e^{3} + 10 \, A b^{6} c e^{6} + {\left(13 \, B b^{5} c^{2} - 10 \, A b^{4} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(2 \, B b^{6} c + 5 \, A b^{5} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(16 \, B b^{5} c^{2} d^{3} e^{3} - 3 \, B b^{7} d e^{5} + 5 \, A b^{7} e^{6} + 2 \, {\left(B b^{6} c - 10 \, A b^{5} c^{2}\right)} d^{2} e^{4}\right)} x^{3} + {\left(8 \, B b^{6} c d^{3} e^{3} + 5 \, A b^{7} d e^{5} - {\left(3 \, B b^{7} + 10 \, A b^{6} c\right)} d^{2} e^{4}\right)} x^{2}\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(2 \, A b^{3} c^{4} d^{7} - 8 \, A b^{4} c^{3} d^{6} e + 12 \, A b^{5} c^{2} d^{5} e^{2} - 8 \, A b^{6} c d^{4} e^{3} + 2 \, A b^{7} d^{3} e^{4} - {\left(15 \, A b^{5} c^{2} d e^{6} - 16 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} e + 8 \, {\left(7 \, B b^{2} c^{5} - 12 \, A b c^{6}\right)} d^{5} e^{2} - 2 \, {\left(29 \, B b^{3} c^{4} - 38 \, A b^{2} c^{5}\right)} d^{4} e^{3} + {\left(27 \, B b^{4} c^{3} + 8 \, A b^{3} c^{4}\right)} d^{3} e^{4} - {\left(9 \, B b^{5} c^{2} + 35 \, A b^{4} c^{3}\right)} d^{2} e^{5}\right)} x^{4} - 2 \, {\left(15 \, A b^{6} c d e^{6} - 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{7} + 8 \, {\left(2 \, B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{6} e + {\left(13 \, B b^{3} c^{4} - 34 \, A b^{2} c^{5}\right)} d^{5} e^{2} - {\left(36 \, B b^{4} c^{3} - 61 \, A b^{3} c^{4}\right)} d^{4} e^{3} + 4 \, {\left(6 \, B b^{5} c^{2} - A b^{4} c^{3}\right)} d^{3} e^{4} - 3 \, {\left(3 \, B b^{6} c + 10 \, A b^{5} c^{2}\right)} d^{2} e^{5}\right)} x^{3} - 3 \, {\left(5 \, A b^{7} d e^{6} - 8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{7} + 2 \, {\left(13 \, B b^{3} c^{4} - 22 \, A b^{2} c^{5}\right)} d^{6} e - 2 \, {\left(12 \, B b^{4} c^{3} - 13 \, A b^{3} c^{4}\right)} d^{5} e^{2} + 4 \, {\left(B b^{5} c^{2} + 4 \, A b^{4} c^{3}\right)} d^{4} e^{3} + {\left(5 \, B b^{6} c - 14 \, A b^{5} c^{2}\right)} d^{3} e^{4} - {\left(3 \, B b^{7} + 5 \, A b^{6} c\right)} d^{2} e^{5}\right)} x^{2} - 2 \, {\left(5 \, A b^{7} d^{2} e^{5} - 3 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{7} + {\left(12 \, B b^{4} c^{3} - 19 \, A b^{3} c^{4}\right)} d^{6} e - 2 \, {\left(9 \, B b^{5} c^{2} - 8 \, A b^{4} c^{3}\right)} d^{5} e^{2} + 6 \, {\left(2 \, B b^{6} c + A b^{5} c^{2}\right)} d^{4} e^{3} - {\left(3 \, B b^{7} + 14 \, A b^{6} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{6 \, {\left({\left(b^{4} c^{6} d^{8} e - 4 \, b^{5} c^{5} d^{7} e^{2} + 6 \, b^{6} c^{4} d^{6} e^{3} - 4 \, b^{7} c^{3} d^{5} e^{4} + b^{8} c^{2} d^{4} e^{5}\right)} x^{5} + {\left(b^{4} c^{6} d^{9} - 2 \, b^{5} c^{5} d^{8} e - 2 \, b^{6} c^{4} d^{7} e^{2} + 8 \, b^{7} c^{3} d^{6} e^{3} - 7 \, b^{8} c^{2} d^{5} e^{4} + 2 \, b^{9} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{5} c^{5} d^{9} - 7 \, b^{6} c^{4} d^{8} e + 8 \, b^{7} c^{3} d^{7} e^{2} - 2 \, b^{8} c^{2} d^{6} e^{3} - 2 \, b^{9} c d^{5} e^{4} + b^{10} d^{4} e^{5}\right)} x^{3} + {\left(b^{6} c^{4} d^{9} - 4 \, b^{7} c^{3} d^{8} e + 6 \, b^{8} c^{2} d^{7} e^{2} - 4 \, b^{9} c d^{6} e^{3} + b^{10} d^{5} e^{4}\right)} x^{2}\right)}}, -\frac{3 \, {\left({\left(8 \, B b^{4} c^{3} d^{2} e^{4} + 5 \, A b^{5} c^{2} e^{6} - {\left(3 \, B b^{5} c^{2} + 10 \, A b^{4} c^{3}\right)} d e^{5}\right)} x^{5} + {\left(8 \, B b^{4} c^{3} d^{3} e^{3} + 10 \, A b^{6} c e^{6} + {\left(13 \, B b^{5} c^{2} - 10 \, A b^{4} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(2 \, B b^{6} c + 5 \, A b^{5} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(16 \, B b^{5} c^{2} d^{3} e^{3} - 3 \, B b^{7} d e^{5} + 5 \, A b^{7} e^{6} + 2 \, {\left(B b^{6} c - 10 \, A b^{5} c^{2}\right)} d^{2} e^{4}\right)} x^{3} + {\left(8 \, B b^{6} c d^{3} e^{3} + 5 \, A b^{7} d e^{5} - {\left(3 \, B b^{7} + 10 \, A b^{6} c\right)} d^{2} e^{4}\right)} x^{2}\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(2 \, A b^{3} c^{4} d^{7} - 8 \, A b^{4} c^{3} d^{6} e + 12 \, A b^{5} c^{2} d^{5} e^{2} - 8 \, A b^{6} c d^{4} e^{3} + 2 \, A b^{7} d^{3} e^{4} - {\left(15 \, A b^{5} c^{2} d e^{6} - 16 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} e + 8 \, {\left(7 \, B b^{2} c^{5} - 12 \, A b c^{6}\right)} d^{5} e^{2} - 2 \, {\left(29 \, B b^{3} c^{4} - 38 \, A b^{2} c^{5}\right)} d^{4} e^{3} + {\left(27 \, B b^{4} c^{3} + 8 \, A b^{3} c^{4}\right)} d^{3} e^{4} - {\left(9 \, B b^{5} c^{2} + 35 \, A b^{4} c^{3}\right)} d^{2} e^{5}\right)} x^{4} - 2 \, {\left(15 \, A b^{6} c d e^{6} - 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{7} + 8 \, {\left(2 \, B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{6} e + {\left(13 \, B b^{3} c^{4} - 34 \, A b^{2} c^{5}\right)} d^{5} e^{2} - {\left(36 \, B b^{4} c^{3} - 61 \, A b^{3} c^{4}\right)} d^{4} e^{3} + 4 \, {\left(6 \, B b^{5} c^{2} - A b^{4} c^{3}\right)} d^{3} e^{4} - 3 \, {\left(3 \, B b^{6} c + 10 \, A b^{5} c^{2}\right)} d^{2} e^{5}\right)} x^{3} - 3 \, {\left(5 \, A b^{7} d e^{6} - 8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{7} + 2 \, {\left(13 \, B b^{3} c^{4} - 22 \, A b^{2} c^{5}\right)} d^{6} e - 2 \, {\left(12 \, B b^{4} c^{3} - 13 \, A b^{3} c^{4}\right)} d^{5} e^{2} + 4 \, {\left(B b^{5} c^{2} + 4 \, A b^{4} c^{3}\right)} d^{4} e^{3} + {\left(5 \, B b^{6} c - 14 \, A b^{5} c^{2}\right)} d^{3} e^{4} - {\left(3 \, B b^{7} + 5 \, A b^{6} c\right)} d^{2} e^{5}\right)} x^{2} - 2 \, {\left(5 \, A b^{7} d^{2} e^{5} - 3 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{7} + {\left(12 \, B b^{4} c^{3} - 19 \, A b^{3} c^{4}\right)} d^{6} e - 2 \, {\left(9 \, B b^{5} c^{2} - 8 \, A b^{4} c^{3}\right)} d^{5} e^{2} + 6 \, {\left(2 \, B b^{6} c + A b^{5} c^{2}\right)} d^{4} e^{3} - {\left(3 \, B b^{7} + 14 \, A b^{6} c\right)} d^{3} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left({\left(b^{4} c^{6} d^{8} e - 4 \, b^{5} c^{5} d^{7} e^{2} + 6 \, b^{6} c^{4} d^{6} e^{3} - 4 \, b^{7} c^{3} d^{5} e^{4} + b^{8} c^{2} d^{4} e^{5}\right)} x^{5} + {\left(b^{4} c^{6} d^{9} - 2 \, b^{5} c^{5} d^{8} e - 2 \, b^{6} c^{4} d^{7} e^{2} + 8 \, b^{7} c^{3} d^{6} e^{3} - 7 \, b^{8} c^{2} d^{5} e^{4} + 2 \, b^{9} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{5} c^{5} d^{9} - 7 \, b^{6} c^{4} d^{8} e + 8 \, b^{7} c^{3} d^{7} e^{2} - 2 \, b^{8} c^{2} d^{6} e^{3} - 2 \, b^{9} c d^{5} e^{4} + b^{10} d^{4} e^{5}\right)} x^{3} + {\left(b^{6} c^{4} d^{9} - 4 \, b^{7} c^{3} d^{8} e + 6 \, b^{8} c^{2} d^{7} e^{2} - 4 \, b^{9} c d^{6} e^{3} + b^{10} d^{5} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/6*(3*((8*B*b^4*c^3*d^2*e^4 + 5*A*b^5*c^2*e^6 - (3*B*b^5*c^2 + 10*A*b^4*c^3)*d*e^5)*x^5 + (8*B*b^4*c^3*d^3*e^3 + 10*A*b^6*c*e^6 + (13*B*b^5*c^2 - 10*A*b^4*c^3)*d^2*e^4 - 3*(2*B*b^6*c + 5*A*b^5*c^2)*d*e^5)*x^4 + (16*B*b^5*c^2*d^3*e^3 - 3*B*b^7*d*e^5 + 5*A*b^7*e^6 + 2*(B*b^6*c - 10*A*b^5*c^2)*d^2*e^4)*x^3 + (8*B*b^6*c*d^3*e^3 + 5*A*b^7*d*e^5 - (3*B*b^7 + 10*A*b^6*c)*d^2*e^4)*x^2)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(2*A*b^3*c^4*d^7 - 8*A*b^4*c^3*d^6*e + 12*A*b^5*c^2*d^5*e^2 - 8*A*b^6*c*d^4*e^3 + 2*A*b^7*d^3*e^4 - (15*A*b^5*c^2*d*e^6 - 16*(B*b*c^6 - 2*A*c^7)*d^6*e + 8*(7*B*b^2*c^5 - 12*A*b*c^6)*d^5*e^2 - 2*(29*B*b^3*c^4 - 38*A*b^2*c^5)*d^4*e^3 + (27*B*b^4*c^3 + 8*A*b^3*c^4)*d^3*e^4 - (9*B*b^5*c^2 + 35*A*b^4*c^3)*d^2*e^5)*x^4 - 2*(15*A*b^6*c*d*e^6 - 8*(B*b*c^6 - 2*A*c^7)*d^7 + 8*(2*B*b^2*c^5 - 3*A*b*c^6)*d^6*e + (13*B*b^3*c^4 - 34*A*b^2*c^5)*d^5*e^2 - (36*B*b^4*c^3 - 61*A*b^3*c^4)*d^4*e^3 + 4*(6*B*b^5*c^2 - A*b^4*c^3)*d^3*e^4 - 3*(3*B*b^6*c + 10*A*b^5*c^2)*d^2*e^5)*x^3 - 3*(5*A*b^7*d*e^6 - 8*(B*b^2*c^5 - 2*A*b*c^6)*d^7 + 2*(13*B*b^3*c^4 - 22*A*b^2*c^5)*d^6*e - 2*(12*B*b^4*c^3 - 13*A*b^3*c^4)*d^5*e^2 + 4*(B*b^5*c^2 + 4*A*b^4*c^3)*d^4*e^3 + (5*B*b^6*c - 14*A*b^5*c^2)*d^3*e^4 - (3*B*b^7 + 5*A*b^6*c)*d^2*e^5)*x^2 - 2*(5*A*b^7*d^2*e^5 - 3*(B*b^3*c^4 - 2*A*b^2*c^5)*d^7 + (12*B*b^4*c^3 - 19*A*b^3*c^4)*d^6*e - 2*(9*B*b^5*c^2 - 8*A*b^4*c^3)*d^5*e^2 + 6*(2*B*b^6*c + A*b^5*c^2)*d^4*e^3 - (3*B*b^7 + 14*A*b^6*c)*d^3*e^4)*x)*sqrt(c*x^2 + b*x))/((b^4*c^6*d^8*e - 4*b^5*c^5*d^7*e^2 + 6*b^6*c^4*d^6*e^3 - 4*b^7*c^3*d^5*e^4 + b^8*c^2*d^4*e^5)*x^5 + (b^4*c^6*d^9 - 2*b^5*c^5*d^8*e - 2*b^6*c^4*d^7*e^2 + 8*b^7*c^3*d^6*e^3 - 7*b^8*c^2*d^5*e^4 + 2*b^9*c*d^4*e^5)*x^4 + (2*b^5*c^5*d^9 - 7*b^6*c^4*d^8*e + 8*b^7*c^3*d^7*e^2 - 2*b^8*c^2*d^6*e^3 - 2*b^9*c*d^5*e^4 + b^10*d^4*e^5)*x^3 + (b^6*c^4*d^9 - 4*b^7*c^3*d^8*e + 6*b^8*c^2*d^7*e^2 - 4*b^9*c*d^6*e^3 + b^10*d^5*e^4)*x^2), -1/3*(3*((8*B*b^4*c^3*d^2*e^4 + 5*A*b^5*c^2*e^6 - (3*B*b^5*c^2 + 10*A*b^4*c^3)*d*e^5)*x^5 + (8*B*b^4*c^3*d^3*e^3 + 10*A*b^6*c*e^6 + (13*B*b^5*c^2 - 10*A*b^4*c^3)*d^2*e^4 - 3*(2*B*b^6*c + 5*A*b^5*c^2)*d*e^5)*x^4 + (16*B*b^5*c^2*d^3*e^3 - 3*B*b^7*d*e^5 + 5*A*b^7*e^6 + 2*(B*b^6*c - 10*A*b^5*c^2)*d^2*e^4)*x^3 + (8*B*b^6*c*d^3*e^3 + 5*A*b^7*d*e^5 - (3*B*b^7 + 10*A*b^6*c)*d^2*e^4)*x^2)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (2*A*b^3*c^4*d^7 - 8*A*b^4*c^3*d^6*e + 12*A*b^5*c^2*d^5*e^2 - 8*A*b^6*c*d^4*e^3 + 2*A*b^7*d^3*e^4 - (15*A*b^5*c^2*d*e^6 - 16*(B*b*c^6 - 2*A*c^7)*d^6*e + 8*(7*B*b^2*c^5 - 12*A*b*c^6)*d^5*e^2 - 2*(29*B*b^3*c^4 - 38*A*b^2*c^5)*d^4*e^3 + (27*B*b^4*c^3 + 8*A*b^3*c^4)*d^3*e^4 - (9*B*b^5*c^2 + 35*A*b^4*c^3)*d^2*e^5)*x^4 - 2*(15*A*b^6*c*d*e^6 - 8*(B*b*c^6 - 2*A*c^7)*d^7 + 8*(2*B*b^2*c^5 - 3*A*b*c^6)*d^6*e + (13*B*b^3*c^4 - 34*A*b^2*c^5)*d^5*e^2 - (36*B*b^4*c^3 - 61*A*b^3*c^4)*d^4*e^3 + 4*(6*B*b^5*c^2 - A*b^4*c^3)*d^3*e^4 - 3*(3*B*b^6*c + 10*A*b^5*c^2)*d^2*e^5)*x^3 - 3*(5*A*b^7*d*e^6 - 8*(B*b^2*c^5 - 2*A*b*c^6)*d^7 + 2*(13*B*b^3*c^4 - 22*A*b^2*c^5)*d^6*e - 2*(12*B*b^4*c^3 - 13*A*b^3*c^4)*d^5*e^2 + 4*(B*b^5*c^2 + 4*A*b^4*c^3)*d^4*e^3 + (5*B*b^6*c - 14*A*b^5*c^2)*d^3*e^4 - (3*B*b^7 + 5*A*b^6*c)*d^2*e^5)*x^2 - 2*(5*A*b^7*d^2*e^5 - 3*(B*b^3*c^4 - 2*A*b^2*c^5)*d^7 + (12*B*b^4*c^3 - 19*A*b^3*c^4)*d^6*e - 2*(9*B*b^5*c^2 - 8*A*b^4*c^3)*d^5*e^2 + 6*(2*B*b^6*c + A*b^5*c^2)*d^4*e^3 - (3*B*b^7 + 14*A*b^6*c)*d^3*e^4)*x)*sqrt(c*x^2 + b*x))/((b^4*c^6*d^8*e - 4*b^5*c^5*d^7*e^2 + 6*b^6*c^4*d^6*e^3 - 4*b^7*c^3*d^5*e^4 + b^8*c^2*d^4*e^5)*x^5 + (b^4*c^6*d^9 - 2*b^5*c^5*d^8*e - 2*b^6*c^4*d^7*e^2 + 8*b^7*c^3*d^6*e^3 - 7*b^8*c^2*d^5*e^4 + 2*b^9*c*d^4*e^5)*x^4 + (2*b^5*c^5*d^9 - 7*b^6*c^4*d^8*e + 8*b^7*c^3*d^7*e^2 - 2*b^8*c^2*d^6*e^3 - 2*b^9*c*d^5*e^4 + b^10*d^4*e^5)*x^3 + (b^6*c^4*d^9 - 4*b^7*c^3*d^8*e + 6*b^8*c^2*d^7*e^2 - 4*b^9*c*d^6*e^3 + b^10*d^5*e^4)*x^2)]","B",0
1213,1,271,0,0.409841," ","integrate((B*x+A)*(e*x+d)^(7/2)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, {\left(429 \, B c e^{7} x^{7} - 16 \, B c d^{7} - 130 \, A b d^{5} e^{2} + 40 \, {\left(B b + A c\right)} d^{6} e + 33 \, {\left(46 \, B c d e^{6} + 15 \, {\left(B b + A c\right)} e^{7}\right)} x^{6} + 9 \, {\left(206 \, B c d^{2} e^{5} + 65 \, A b e^{7} + 200 \, {\left(B b + A c\right)} d e^{6}\right)} x^{5} + 10 \, {\left(80 \, B c d^{3} e^{4} + 221 \, A b d e^{6} + 229 \, {\left(B b + A c\right)} d^{2} e^{5}\right)} x^{4} + 5 \, {\left(B c d^{4} e^{3} + 598 \, A b d^{2} e^{5} + 212 \, {\left(B b + A c\right)} d^{3} e^{4}\right)} x^{3} - 3 \, {\left(2 \, B c d^{5} e^{2} - 520 \, A b d^{3} e^{4} - 5 \, {\left(B b + A c\right)} d^{4} e^{3}\right)} x^{2} + {\left(8 \, B c d^{6} e + 65 \, A b d^{4} e^{3} - 20 \, {\left(B b + A c\right)} d^{5} e^{2}\right)} x\right)} \sqrt{e x + d}}{6435 \, e^{4}}"," ",0,"2/6435*(429*B*c*e^7*x^7 - 16*B*c*d^7 - 130*A*b*d^5*e^2 + 40*(B*b + A*c)*d^6*e + 33*(46*B*c*d*e^6 + 15*(B*b + A*c)*e^7)*x^6 + 9*(206*B*c*d^2*e^5 + 65*A*b*e^7 + 200*(B*b + A*c)*d*e^6)*x^5 + 10*(80*B*c*d^3*e^4 + 221*A*b*d*e^6 + 229*(B*b + A*c)*d^2*e^5)*x^4 + 5*(B*c*d^4*e^3 + 598*A*b*d^2*e^5 + 212*(B*b + A*c)*d^3*e^4)*x^3 - 3*(2*B*c*d^5*e^2 - 520*A*b*d^3*e^4 - 5*(B*b + A*c)*d^4*e^3)*x^2 + (8*B*c*d^6*e + 65*A*b*d^4*e^3 - 20*(B*b + A*c)*d^5*e^2)*x)*sqrt(e*x + d)/e^4","B",0
1214,1,230,0,0.397523," ","integrate((B*x+A)*(e*x+d)^(5/2)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, B c e^{6} x^{6} - 48 \, B c d^{6} - 286 \, A b d^{4} e^{2} + 104 \, {\left(B b + A c\right)} d^{5} e + 63 \, {\left(27 \, B c d e^{5} + 13 \, {\left(B b + A c\right)} e^{6}\right)} x^{5} + 7 \, {\left(159 \, B c d^{2} e^{4} + 143 \, A b e^{6} + 299 \, {\left(B b + A c\right)} d e^{5}\right)} x^{4} + {\left(15 \, B c d^{3} e^{3} + 2717 \, A b d e^{5} + 1469 \, {\left(B b + A c\right)} d^{2} e^{4}\right)} x^{3} - 3 \, {\left(6 \, B c d^{4} e^{2} - 715 \, A b d^{2} e^{4} - 13 \, {\left(B b + A c\right)} d^{3} e^{3}\right)} x^{2} + {\left(24 \, B c d^{5} e + 143 \, A b d^{3} e^{3} - 52 \, {\left(B b + A c\right)} d^{4} e^{2}\right)} x\right)} \sqrt{e x + d}}{9009 \, e^{4}}"," ",0,"2/9009*(693*B*c*e^6*x^6 - 48*B*c*d^6 - 286*A*b*d^4*e^2 + 104*(B*b + A*c)*d^5*e + 63*(27*B*c*d*e^5 + 13*(B*b + A*c)*e^6)*x^5 + 7*(159*B*c*d^2*e^4 + 143*A*b*e^6 + 299*(B*b + A*c)*d*e^5)*x^4 + (15*B*c*d^3*e^3 + 2717*A*b*d*e^5 + 1469*(B*b + A*c)*d^2*e^4)*x^3 - 3*(6*B*c*d^4*e^2 - 715*A*b*d^2*e^4 - 13*(B*b + A*c)*d^3*e^3)*x^2 + (24*B*c*d^5*e + 143*A*b*d^3*e^3 - 52*(B*b + A*c)*d^4*e^2)*x)*sqrt(e*x + d)/e^4","B",0
1215,1,190,0,0.404255," ","integrate((B*x+A)*(e*x+d)^(3/2)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B c e^{5} x^{5} - 48 \, B c d^{5} - 198 \, A b d^{3} e^{2} + 88 \, {\left(B b + A c\right)} d^{4} e + 35 \, {\left(12 \, B c d e^{4} + 11 \, {\left(B b + A c\right)} e^{5}\right)} x^{4} + 5 \, {\left(3 \, B c d^{2} e^{3} + 99 \, A b e^{5} + 110 \, {\left(B b + A c\right)} d e^{4}\right)} x^{3} - 3 \, {\left(6 \, B c d^{3} e^{2} - 264 \, A b d e^{4} - 11 \, {\left(B b + A c\right)} d^{2} e^{3}\right)} x^{2} + {\left(24 \, B c d^{4} e + 99 \, A b d^{2} e^{3} - 44 \, {\left(B b + A c\right)} d^{3} e^{2}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{4}}"," ",0,"2/3465*(315*B*c*e^5*x^5 - 48*B*c*d^5 - 198*A*b*d^3*e^2 + 88*(B*b + A*c)*d^4*e + 35*(12*B*c*d*e^4 + 11*(B*b + A*c)*e^5)*x^4 + 5*(3*B*c*d^2*e^3 + 99*A*b*e^5 + 110*(B*b + A*c)*d*e^4)*x^3 - 3*(6*B*c*d^3*e^2 - 264*A*b*d*e^4 - 11*(B*b + A*c)*d^2*e^3)*x^2 + (24*B*c*d^4*e + 99*A*b*d^2*e^3 - 44*(B*b + A*c)*d^3*e^2)*x)*sqrt(e*x + d)/e^4","A",0
1216,1,148,0,0.397438," ","integrate((B*x+A)*(e*x+d)^(1/2)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c e^{4} x^{4} - 16 \, B c d^{4} - 42 \, A b d^{2} e^{2} + 24 \, {\left(B b + A c\right)} d^{3} e + 5 \, {\left(B c d e^{3} + 9 \, {\left(B b + A c\right)} e^{4}\right)} x^{3} - 3 \, {\left(2 \, B c d^{2} e^{2} - 21 \, A b e^{4} - 3 \, {\left(B b + A c\right)} d e^{3}\right)} x^{2} + {\left(8 \, B c d^{3} e + 21 \, A b d e^{3} - 12 \, {\left(B b + A c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{4}}"," ",0,"2/315*(35*B*c*e^4*x^4 - 16*B*c*d^4 - 42*A*b*d^2*e^2 + 24*(B*b + A*c)*d^3*e + 5*(B*c*d*e^3 + 9*(B*b + A*c)*e^4)*x^3 - 3*(2*B*c*d^2*e^2 - 21*A*b*e^4 - 3*(B*b + A*c)*d*e^3)*x^2 + (8*B*c*d^3*e + 21*A*b*d*e^3 - 12*(B*b + A*c)*d^2*e^2)*x)*sqrt(e*x + d)/e^4","A",0
1217,1,108,0,0.403774," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c e^{3} x^{3} - 48 \, B c d^{3} - 70 \, A b d e^{2} + 56 \, {\left(B b + A c\right)} d^{2} e - 3 \, {\left(6 \, B c d e^{2} - 7 \, {\left(B b + A c\right)} e^{3}\right)} x^{2} + {\left(24 \, B c d^{2} e + 35 \, A b e^{3} - 28 \, {\left(B b + A c\right)} d e^{2}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{4}}"," ",0,"2/105*(15*B*c*e^3*x^3 - 48*B*c*d^3 - 70*A*b*d*e^2 + 56*(B*b + A*c)*d^2*e - 3*(6*B*c*d*e^2 - 7*(B*b + A*c)*e^3)*x^2 + (24*B*c*d^2*e + 35*A*b*e^3 - 28*(B*b + A*c)*d*e^2)*x)*sqrt(e*x + d)/e^4","A",0
1218,1,118,0,0.405722," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c e^{3} x^{3} + 48 \, B c d^{3} + 30 \, A b d e^{2} - 40 \, {\left(B b + A c\right)} d^{2} e - {\left(6 \, B c d e^{2} - 5 \, {\left(B b + A c\right)} e^{3}\right)} x^{2} + {\left(24 \, B c d^{2} e + 15 \, A b e^{3} - 20 \, {\left(B b + A c\right)} d e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"2/15*(3*B*c*e^3*x^3 + 48*B*c*d^3 + 30*A*b*d*e^2 - 40*(B*b + A*c)*d^2*e - (6*B*c*d*e^2 - 5*(B*b + A*c)*e^3)*x^2 + (24*B*c*d^2*e + 15*A*b*e^3 - 20*(B*b + A*c)*d*e^2)*x)*sqrt(e*x + d)/(e^5*x + d*e^4)","A",0
1219,1,128,0,0.409580," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c e^{3} x^{3} - 16 \, B c d^{3} - 2 \, A b d e^{2} + 8 \, {\left(B b + A c\right)} d^{2} e - 3 \, {\left(2 \, B c d e^{2} - {\left(B b + A c\right)} e^{3}\right)} x^{2} - 3 \, {\left(8 \, B c d^{2} e + A b e^{3} - 4 \, {\left(B b + A c\right)} d e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"2/3*(B*c*e^3*x^3 - 16*B*c*d^3 - 2*A*b*d*e^2 + 8*(B*b + A*c)*d^2*e - 3*(2*B*c*d*e^2 - (B*b + A*c)*e^3)*x^2 - 3*(8*B*c*d^2*e + A*b*e^3 - 4*(B*b + A*c)*d*e^2)*x)*sqrt(e*x + d)/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1220,1,141,0,0.414999," ","integrate((B*x+A)*(c*x^2+b*x)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c e^{3} x^{3} + 48 \, B c d^{3} - 2 \, A b d e^{2} - 8 \, {\left(B b + A c\right)} d^{2} e + 15 \, {\left(6 \, B c d e^{2} - {\left(B b + A c\right)} e^{3}\right)} x^{2} + 5 \, {\left(24 \, B c d^{2} e - A b e^{3} - 4 \, {\left(B b + A c\right)} d e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"2/15*(15*B*c*e^3*x^3 + 48*B*c*d^3 - 2*A*b*d*e^2 - 8*(B*b + A*c)*d^2*e + 15*(6*B*c*d*e^2 - (B*b + A*c)*e^3)*x^2 + 5*(24*B*c*d^2*e - A*b*e^3 - 4*(B*b + A*c)*d*e^2)*x)*sqrt(e*x + d)/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1221,1,562,0,0.422354," ","integrate((B*x+A)*(e*x+d)^(7/2)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(109395 \, B c^{2} e^{9} x^{9} - 1280 \, B c^{2} d^{9} + 12920 \, A b^{2} d^{6} e^{3} + 2432 \, {\left(2 \, B b c + A c^{2}\right)} d^{8} e - 5168 \, {\left(B b^{2} + 2 \, A b c\right)} d^{7} e^{2} + 6435 \, {\left(58 \, B c^{2} d e^{8} + 19 \, {\left(2 \, B b c + A c^{2}\right)} e^{9}\right)} x^{8} + 429 \, {\left(1010 \, B c^{2} d^{2} e^{7} + 988 \, {\left(2 \, B b c + A c^{2}\right)} d e^{8} + 323 \, {\left(B b^{2} + 2 \, A b c\right)} e^{9}\right)} x^{7} + 33 \, {\left(5240 \, B c^{2} d^{3} e^{6} + 4845 \, A b^{2} e^{9} + 15238 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{7} + 14858 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{8}\right)} x^{6} + 9 \, {\left(35 \, B c^{2} d^{4} e^{5} + 64600 \, A b^{2} d e^{8} + 23028 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{6} + 66538 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{7}\right)} x^{5} - 5 \, {\left(70 \, B c^{2} d^{5} e^{4} - 147934 \, A b^{2} d^{2} e^{7} - 133 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e^{5} - 51680 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{6}\right)} x^{4} + 5 \, {\left(80 \, B c^{2} d^{6} e^{3} + 68476 \, A b^{2} d^{3} e^{6} - 152 \, {\left(2 \, B b c + A c^{2}\right)} d^{5} e^{4} + 323 \, {\left(B b^{2} + 2 \, A b c\right)} d^{4} e^{5}\right)} x^{3} - 3 \, {\left(160 \, B c^{2} d^{7} e^{2} - 1615 \, A b^{2} d^{4} e^{5} - 304 \, {\left(2 \, B b c + A c^{2}\right)} d^{6} e^{3} + 646 \, {\left(B b^{2} + 2 \, A b c\right)} d^{5} e^{4}\right)} x^{2} + 4 \, {\left(160 \, B c^{2} d^{8} e - 1615 \, A b^{2} d^{5} e^{4} - 304 \, {\left(2 \, B b c + A c^{2}\right)} d^{7} e^{2} + 646 \, {\left(B b^{2} + 2 \, A b c\right)} d^{6} e^{3}\right)} x\right)} \sqrt{e x + d}}{2078505 \, e^{6}}"," ",0,"2/2078505*(109395*B*c^2*e^9*x^9 - 1280*B*c^2*d^9 + 12920*A*b^2*d^6*e^3 + 2432*(2*B*b*c + A*c^2)*d^8*e - 5168*(B*b^2 + 2*A*b*c)*d^7*e^2 + 6435*(58*B*c^2*d*e^8 + 19*(2*B*b*c + A*c^2)*e^9)*x^8 + 429*(1010*B*c^2*d^2*e^7 + 988*(2*B*b*c + A*c^2)*d*e^8 + 323*(B*b^2 + 2*A*b*c)*e^9)*x^7 + 33*(5240*B*c^2*d^3*e^6 + 4845*A*b^2*e^9 + 15238*(2*B*b*c + A*c^2)*d^2*e^7 + 14858*(B*b^2 + 2*A*b*c)*d*e^8)*x^6 + 9*(35*B*c^2*d^4*e^5 + 64600*A*b^2*d*e^8 + 23028*(2*B*b*c + A*c^2)*d^3*e^6 + 66538*(B*b^2 + 2*A*b*c)*d^2*e^7)*x^5 - 5*(70*B*c^2*d^5*e^4 - 147934*A*b^2*d^2*e^7 - 133*(2*B*b*c + A*c^2)*d^4*e^5 - 51680*(B*b^2 + 2*A*b*c)*d^3*e^6)*x^4 + 5*(80*B*c^2*d^6*e^3 + 68476*A*b^2*d^3*e^6 - 152*(2*B*b*c + A*c^2)*d^5*e^4 + 323*(B*b^2 + 2*A*b*c)*d^4*e^5)*x^3 - 3*(160*B*c^2*d^7*e^2 - 1615*A*b^2*d^4*e^5 - 304*(2*B*b*c + A*c^2)*d^6*e^3 + 646*(B*b^2 + 2*A*b*c)*d^5*e^4)*x^2 + 4*(160*B*c^2*d^8*e - 1615*A*b^2*d^5*e^4 - 304*(2*B*b*c + A*c^2)*d^7*e^2 + 646*(B*b^2 + 2*A*b*c)*d^6*e^3)*x)*sqrt(e*x + d)/e^6","B",0
1222,1,494,0,0.419206," ","integrate((B*x+A)*(e*x+d)^(5/2)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(45045 \, B c^{2} e^{8} x^{8} - 1280 \, B c^{2} d^{8} + 8840 \, A b^{2} d^{5} e^{3} + 2176 \, {\left(2 \, B b c + A c^{2}\right)} d^{7} e - 4080 \, {\left(B b^{2} + 2 \, A b c\right)} d^{6} e^{2} + 3003 \, {\left(35 \, B c^{2} d e^{7} + 17 \, {\left(2 \, B b c + A c^{2}\right)} e^{8}\right)} x^{7} + 231 \, {\left(275 \, B c^{2} d^{2} e^{6} + 527 \, {\left(2 \, B b c + A c^{2}\right)} d e^{7} + 255 \, {\left(B b^{2} + 2 \, A b c\right)} e^{8}\right)} x^{6} + 63 \, {\left(5 \, B c^{2} d^{3} e^{5} + 1105 \, A b^{2} e^{8} + 1207 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{6} + 2295 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{7}\right)} x^{5} - 35 \, {\left(10 \, B c^{2} d^{4} e^{4} - 5083 \, A b^{2} d e^{7} - 17 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{5} - 2703 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{6}\right)} x^{4} + 5 \, {\left(80 \, B c^{2} d^{5} e^{3} + 24973 \, A b^{2} d^{2} e^{6} - 136 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e^{4} + 255 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{5}\right)} x^{3} - 3 \, {\left(160 \, B c^{2} d^{6} e^{2} - 1105 \, A b^{2} d^{3} e^{5} - 272 \, {\left(2 \, B b c + A c^{2}\right)} d^{5} e^{3} + 510 \, {\left(B b^{2} + 2 \, A b c\right)} d^{4} e^{4}\right)} x^{2} + 4 \, {\left(160 \, B c^{2} d^{7} e - 1105 \, A b^{2} d^{4} e^{4} - 272 \, {\left(2 \, B b c + A c^{2}\right)} d^{6} e^{2} + 510 \, {\left(B b^{2} + 2 \, A b c\right)} d^{5} e^{3}\right)} x\right)} \sqrt{e x + d}}{765765 \, e^{6}}"," ",0,"2/765765*(45045*B*c^2*e^8*x^8 - 1280*B*c^2*d^8 + 8840*A*b^2*d^5*e^3 + 2176*(2*B*b*c + A*c^2)*d^7*e - 4080*(B*b^2 + 2*A*b*c)*d^6*e^2 + 3003*(35*B*c^2*d*e^7 + 17*(2*B*b*c + A*c^2)*e^8)*x^7 + 231*(275*B*c^2*d^2*e^6 + 527*(2*B*b*c + A*c^2)*d*e^7 + 255*(B*b^2 + 2*A*b*c)*e^8)*x^6 + 63*(5*B*c^2*d^3*e^5 + 1105*A*b^2*e^8 + 1207*(2*B*b*c + A*c^2)*d^2*e^6 + 2295*(B*b^2 + 2*A*b*c)*d*e^7)*x^5 - 35*(10*B*c^2*d^4*e^4 - 5083*A*b^2*d*e^7 - 17*(2*B*b*c + A*c^2)*d^3*e^5 - 2703*(B*b^2 + 2*A*b*c)*d^2*e^6)*x^4 + 5*(80*B*c^2*d^5*e^3 + 24973*A*b^2*d^2*e^6 - 136*(2*B*b*c + A*c^2)*d^4*e^4 + 255*(B*b^2 + 2*A*b*c)*d^3*e^5)*x^3 - 3*(160*B*c^2*d^6*e^2 - 1105*A*b^2*d^3*e^5 - 272*(2*B*b*c + A*c^2)*d^5*e^3 + 510*(B*b^2 + 2*A*b*c)*d^4*e^4)*x^2 + 4*(160*B*c^2*d^7*e - 1105*A*b^2*d^4*e^4 - 272*(2*B*b*c + A*c^2)*d^6*e^2 + 510*(B*b^2 + 2*A*b*c)*d^5*e^3)*x)*sqrt(e*x + d)/e^6","B",0
1223,1,425,0,0.423820," ","integrate((B*x+A)*(e*x+d)^(3/2)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B c^{2} e^{7} x^{7} - 256 \, B c^{2} d^{7} + 1144 \, A b^{2} d^{4} e^{3} + 384 \, {\left(2 \, B b c + A c^{2}\right)} d^{6} e - 624 \, {\left(B b^{2} + 2 \, A b c\right)} d^{5} e^{2} + 231 \, {\left(16 \, B c^{2} d e^{6} + 15 \, {\left(2 \, B b c + A c^{2}\right)} e^{7}\right)} x^{6} + 63 \, {\left(B c^{2} d^{2} e^{5} + 70 \, {\left(2 \, B b c + A c^{2}\right)} d e^{6} + 65 \, {\left(B b^{2} + 2 \, A b c\right)} e^{7}\right)} x^{5} - 35 \, {\left(2 \, B c^{2} d^{3} e^{4} - 143 \, A b^{2} e^{7} - 3 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{5} - 156 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{6}\right)} x^{4} + 5 \, {\left(16 \, B c^{2} d^{4} e^{3} + 1430 \, A b^{2} d e^{6} - 24 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{4} + 39 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{5}\right)} x^{3} - 3 \, {\left(32 \, B c^{2} d^{5} e^{2} - 143 \, A b^{2} d^{2} e^{5} - 48 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e^{3} + 78 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{4}\right)} x^{2} + 4 \, {\left(32 \, B c^{2} d^{6} e - 143 \, A b^{2} d^{3} e^{4} - 48 \, {\left(2 \, B b c + A c^{2}\right)} d^{5} e^{2} + 78 \, {\left(B b^{2} + 2 \, A b c\right)} d^{4} e^{3}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{6}}"," ",0,"2/45045*(3003*B*c^2*e^7*x^7 - 256*B*c^2*d^7 + 1144*A*b^2*d^4*e^3 + 384*(2*B*b*c + A*c^2)*d^6*e - 624*(B*b^2 + 2*A*b*c)*d^5*e^2 + 231*(16*B*c^2*d*e^6 + 15*(2*B*b*c + A*c^2)*e^7)*x^6 + 63*(B*c^2*d^2*e^5 + 70*(2*B*b*c + A*c^2)*d*e^6 + 65*(B*b^2 + 2*A*b*c)*e^7)*x^5 - 35*(2*B*c^2*d^3*e^4 - 143*A*b^2*e^7 - 3*(2*B*b*c + A*c^2)*d^2*e^5 - 156*(B*b^2 + 2*A*b*c)*d*e^6)*x^4 + 5*(16*B*c^2*d^4*e^3 + 1430*A*b^2*d*e^6 - 24*(2*B*b*c + A*c^2)*d^3*e^4 + 39*(B*b^2 + 2*A*b*c)*d^2*e^5)*x^3 - 3*(32*B*c^2*d^5*e^2 - 143*A*b^2*d^2*e^5 - 48*(2*B*b*c + A*c^2)*d^4*e^3 + 78*(B*b^2 + 2*A*b*c)*d^3*e^4)*x^2 + 4*(32*B*c^2*d^6*e - 143*A*b^2*d^3*e^4 - 48*(2*B*b*c + A*c^2)*d^5*e^2 + 78*(B*b^2 + 2*A*b*c)*d^4*e^3)*x)*sqrt(e*x + d)/e^6","A",0
1224,1,357,0,0.428381," ","integrate((B*x+A)*(e*x+d)^(1/2)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, B c^{2} e^{6} x^{6} - 1280 \, B c^{2} d^{6} + 3432 \, A b^{2} d^{3} e^{3} + 1664 \, {\left(2 \, B b c + A c^{2}\right)} d^{5} e - 2288 \, {\left(B b^{2} + 2 \, A b c\right)} d^{4} e^{2} + 315 \, {\left(B c^{2} d e^{5} + 13 \, {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} x^{5} - 35 \, {\left(10 \, B c^{2} d^{2} e^{4} - 13 \, {\left(2 \, B b c + A c^{2}\right)} d e^{5} - 143 \, {\left(B b^{2} + 2 \, A b c\right)} e^{6}\right)} x^{4} + 5 \, {\left(80 \, B c^{2} d^{3} e^{3} + 1287 \, A b^{2} e^{6} - 104 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{4} + 143 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{5}\right)} x^{3} - 3 \, {\left(160 \, B c^{2} d^{4} e^{2} - 429 \, A b^{2} d e^{5} - 208 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{3} + 286 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(160 \, B c^{2} d^{5} e - 429 \, A b^{2} d^{2} e^{4} - 208 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e^{2} + 286 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{6}}"," ",0,"2/45045*(3465*B*c^2*e^6*x^6 - 1280*B*c^2*d^6 + 3432*A*b^2*d^3*e^3 + 1664*(2*B*b*c + A*c^2)*d^5*e - 2288*(B*b^2 + 2*A*b*c)*d^4*e^2 + 315*(B*c^2*d*e^5 + 13*(2*B*b*c + A*c^2)*e^6)*x^5 - 35*(10*B*c^2*d^2*e^4 - 13*(2*B*b*c + A*c^2)*d*e^5 - 143*(B*b^2 + 2*A*b*c)*e^6)*x^4 + 5*(80*B*c^2*d^3*e^3 + 1287*A*b^2*e^6 - 104*(2*B*b*c + A*c^2)*d^2*e^4 + 143*(B*b^2 + 2*A*b*c)*d*e^5)*x^3 - 3*(160*B*c^2*d^4*e^2 - 429*A*b^2*d*e^5 - 208*(2*B*b*c + A*c^2)*d^3*e^3 + 286*(B*b^2 + 2*A*b*c)*d^2*e^4)*x^2 + 4*(160*B*c^2*d^5*e - 429*A*b^2*d^2*e^4 - 208*(2*B*b*c + A*c^2)*d^4*e^2 + 286*(B*b^2 + 2*A*b*c)*d^3*e^3)*x)*sqrt(e*x + d)/e^6","A",0
1225,1,290,0,0.423106," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B c^{2} e^{5} x^{5} - 1280 \, B c^{2} d^{5} + 1848 \, A b^{2} d^{2} e^{3} + 1408 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e - 1584 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} - 35 \, {\left(10 \, B c^{2} d e^{4} - 11 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 5 \, {\left(80 \, B c^{2} d^{2} e^{3} - 88 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 99 \, {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} - 3 \, {\left(160 \, B c^{2} d^{3} e^{2} - 231 \, A b^{2} e^{5} - 176 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 198 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 4 \, {\left(160 \, B c^{2} d^{4} e - 231 \, A b^{2} d e^{4} - 176 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 198 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{6}}"," ",0,"2/3465*(315*B*c^2*e^5*x^5 - 1280*B*c^2*d^5 + 1848*A*b^2*d^2*e^3 + 1408*(2*B*b*c + A*c^2)*d^4*e - 1584*(B*b^2 + 2*A*b*c)*d^3*e^2 - 35*(10*B*c^2*d*e^4 - 11*(2*B*b*c + A*c^2)*e^5)*x^4 + 5*(80*B*c^2*d^2*e^3 - 88*(2*B*b*c + A*c^2)*d*e^4 + 99*(B*b^2 + 2*A*b*c)*e^5)*x^3 - 3*(160*B*c^2*d^3*e^2 - 231*A*b^2*e^5 - 176*(2*B*b*c + A*c^2)*d^2*e^3 + 198*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 4*(160*B*c^2*d^4*e - 231*A*b^2*d*e^4 - 176*(2*B*b*c + A*c^2)*d^3*e^2 + 198*(B*b^2 + 2*A*b*c)*d^2*e^3)*x)*sqrt(e*x + d)/e^6","A",0
1226,1,299,0,0.400135," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{2} e^{5} x^{5} + 1280 \, B c^{2} d^{5} - 840 \, A b^{2} d^{2} e^{3} - 1152 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 1008 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} - 5 \, {\left(10 \, B c^{2} d e^{4} - 9 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + {\left(80 \, B c^{2} d^{2} e^{3} - 72 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 63 \, {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} - {\left(160 \, B c^{2} d^{3} e^{2} - 105 \, A b^{2} e^{5} - 144 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 126 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 4 \, {\left(160 \, B c^{2} d^{4} e - 105 \, A b^{2} d e^{4} - 144 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 126 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"2/315*(35*B*c^2*e^5*x^5 + 1280*B*c^2*d^5 - 840*A*b^2*d^2*e^3 - 1152*(2*B*b*c + A*c^2)*d^4*e + 1008*(B*b^2 + 2*A*b*c)*d^3*e^2 - 5*(10*B*c^2*d*e^4 - 9*(2*B*b*c + A*c^2)*e^5)*x^4 + (80*B*c^2*d^2*e^3 - 72*(2*B*b*c + A*c^2)*d*e^4 + 63*(B*b^2 + 2*A*b*c)*e^5)*x^3 - (160*B*c^2*d^3*e^2 - 105*A*b^2*e^5 - 144*(2*B*b*c + A*c^2)*d^2*e^3 + 126*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 4*(160*B*c^2*d^4*e - 105*A*b^2*d*e^4 - 144*(2*B*b*c + A*c^2)*d^3*e^2 + 126*(B*b^2 + 2*A*b*c)*d^2*e^3)*x)*sqrt(e*x + d)/(e^7*x + d*e^6)","A",0
1227,1,310,0,0.415308," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c^{2} e^{5} x^{5} - 1280 \, B c^{2} d^{5} + 280 \, A b^{2} d^{2} e^{3} + 896 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e - 560 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} - 3 \, {\left(10 \, B c^{2} d e^{4} - 7 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + {\left(80 \, B c^{2} d^{2} e^{3} - 56 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 35 \, {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} - 3 \, {\left(160 \, B c^{2} d^{3} e^{2} - 35 \, A b^{2} e^{5} - 112 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 70 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} - 12 \, {\left(160 \, B c^{2} d^{4} e - 35 \, A b^{2} d e^{4} - 112 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 70 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"2/105*(15*B*c^2*e^5*x^5 - 1280*B*c^2*d^5 + 280*A*b^2*d^2*e^3 + 896*(2*B*b*c + A*c^2)*d^4*e - 560*(B*b^2 + 2*A*b*c)*d^3*e^2 - 3*(10*B*c^2*d*e^4 - 7*(2*B*b*c + A*c^2)*e^5)*x^4 + (80*B*c^2*d^2*e^3 - 56*(2*B*b*c + A*c^2)*d*e^4 + 35*(B*b^2 + 2*A*b*c)*e^5)*x^3 - 3*(160*B*c^2*d^3*e^2 - 35*A*b^2*e^5 - 112*(2*B*b*c + A*c^2)*d^2*e^3 + 70*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 - 12*(160*B*c^2*d^4*e - 35*A*b^2*d*e^4 - 112*(2*B*b*c + A*c^2)*d^3*e^2 + 70*(B*b^2 + 2*A*b*c)*d^2*e^3)*x)*sqrt(e*x + d)/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","A",0
1228,1,322,0,0.409799," ","integrate((B*x+A)*(c*x^2+b*x)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{2} e^{5} x^{5} + 256 \, B c^{2} d^{5} - 8 \, A b^{2} d^{2} e^{3} - 128 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 48 \, {\left(B b^{2} + 2 \, A b c\right)} d^{3} e^{2} - 5 \, {\left(2 \, B c^{2} d e^{4} - {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 5 \, {\left(16 \, B c^{2} d^{2} e^{3} - 8 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 3 \, {\left(B b^{2} + 2 \, A b c\right)} e^{5}\right)} x^{3} + 15 \, {\left(32 \, B c^{2} d^{3} e^{2} - A b^{2} e^{5} - 16 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 6 \, {\left(B b^{2} + 2 \, A b c\right)} d e^{4}\right)} x^{2} + 20 \, {\left(32 \, B c^{2} d^{4} e - A b^{2} d e^{4} - 16 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 6 \, {\left(B b^{2} + 2 \, A b c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"2/15*(3*B*c^2*e^5*x^5 + 256*B*c^2*d^5 - 8*A*b^2*d^2*e^3 - 128*(2*B*b*c + A*c^2)*d^4*e + 48*(B*b^2 + 2*A*b*c)*d^3*e^2 - 5*(2*B*c^2*d*e^4 - (2*B*b*c + A*c^2)*e^5)*x^4 + 5*(16*B*c^2*d^2*e^3 - 8*(2*B*b*c + A*c^2)*d*e^4 + 3*(B*b^2 + 2*A*b*c)*e^5)*x^3 + 15*(32*B*c^2*d^3*e^2 - A*b^2*e^5 - 16*(2*B*b*c + A*c^2)*d^2*e^3 + 6*(B*b^2 + 2*A*b*c)*d*e^4)*x^2 + 20*(32*B*c^2*d^4*e - A*b^2*d*e^4 - 16*(2*B*b*c + A*c^2)*d^3*e^2 + 6*(B*b^2 + 2*A*b*c)*d^2*e^3)*x)*sqrt(e*x + d)/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","A",0
1229,1,1474,0,15.889591," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{105 \, A c^{4} d^{\frac{7}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 105 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{3} - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{2} e + 3 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e^{2} - {\left(B b^{4} - A b^{3} c\right)} e^{3}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(15 \, B b c^{3} e^{3} x^{3} + 176 \, B b c^{3} d^{3} - 406 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{2} e + 350 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e^{2} - 105 \, {\left(B b^{4} - A b^{3} c\right)} e^{3} + 3 \, {\left(22 \, B b c^{3} d e^{2} - 7 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} e^{3}\right)} x^{2} + {\left(122 \, B b c^{3} d^{2} e - 112 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d e^{2} + 35 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, b c^{4}}, \frac{105 \, A c^{4} d^{\frac{7}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 210 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{3} - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{2} e + 3 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e^{2} - {\left(B b^{4} - A b^{3} c\right)} e^{3}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 2 \, {\left(15 \, B b c^{3} e^{3} x^{3} + 176 \, B b c^{3} d^{3} - 406 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{2} e + 350 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e^{2} - 105 \, {\left(B b^{4} - A b^{3} c\right)} e^{3} + 3 \, {\left(22 \, B b c^{3} d e^{2} - 7 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} e^{3}\right)} x^{2} + {\left(122 \, B b c^{3} d^{2} e - 112 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d e^{2} + 35 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, b c^{4}}, \frac{210 \, A c^{4} \sqrt{-d} d^{3} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 105 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{3} - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{2} e + 3 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e^{2} - {\left(B b^{4} - A b^{3} c\right)} e^{3}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(15 \, B b c^{3} e^{3} x^{3} + 176 \, B b c^{3} d^{3} - 406 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{2} e + 350 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e^{2} - 105 \, {\left(B b^{4} - A b^{3} c\right)} e^{3} + 3 \, {\left(22 \, B b c^{3} d e^{2} - 7 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} e^{3}\right)} x^{2} + {\left(122 \, B b c^{3} d^{2} e - 112 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d e^{2} + 35 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, b c^{4}}, \frac{2 \, {\left(105 \, A c^{4} \sqrt{-d} d^{3} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 105 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{3} - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{2} e + 3 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e^{2} - {\left(B b^{4} - A b^{3} c\right)} e^{3}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left(15 \, B b c^{3} e^{3} x^{3} + 176 \, B b c^{3} d^{3} - 406 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{2} e + 350 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e^{2} - 105 \, {\left(B b^{4} - A b^{3} c\right)} e^{3} + 3 \, {\left(22 \, B b c^{3} d e^{2} - 7 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} e^{3}\right)} x^{2} + {\left(122 \, B b c^{3} d^{2} e - 112 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d e^{2} + 35 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{105 \, b c^{4}}\right]"," ",0,"[1/105*(105*A*c^4*d^(7/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 105*((B*b*c^3 - A*c^4)*d^3 - 3*(B*b^2*c^2 - A*b*c^3)*d^2*e + 3*(B*b^3*c - A*b^2*c^2)*d*e^2 - (B*b^4 - A*b^3*c)*e^3)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(15*B*b*c^3*e^3*x^3 + 176*B*b*c^3*d^3 - 406*(B*b^2*c^2 - A*b*c^3)*d^2*e + 350*(B*b^3*c - A*b^2*c^2)*d*e^2 - 105*(B*b^4 - A*b^3*c)*e^3 + 3*(22*B*b*c^3*d*e^2 - 7*(B*b^2*c^2 - A*b*c^3)*e^3)*x^2 + (122*B*b*c^3*d^2*e - 112*(B*b^2*c^2 - A*b*c^3)*d*e^2 + 35*(B*b^3*c - A*b^2*c^2)*e^3)*x)*sqrt(e*x + d))/(b*c^4), 1/105*(105*A*c^4*d^(7/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 210*((B*b*c^3 - A*c^4)*d^3 - 3*(B*b^2*c^2 - A*b*c^3)*d^2*e + 3*(B*b^3*c - A*b^2*c^2)*d*e^2 - (B*b^4 - A*b^3*c)*e^3)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 2*(15*B*b*c^3*e^3*x^3 + 176*B*b*c^3*d^3 - 406*(B*b^2*c^2 - A*b*c^3)*d^2*e + 350*(B*b^3*c - A*b^2*c^2)*d*e^2 - 105*(B*b^4 - A*b^3*c)*e^3 + 3*(22*B*b*c^3*d*e^2 - 7*(B*b^2*c^2 - A*b*c^3)*e^3)*x^2 + (122*B*b*c^3*d^2*e - 112*(B*b^2*c^2 - A*b*c^3)*d*e^2 + 35*(B*b^3*c - A*b^2*c^2)*e^3)*x)*sqrt(e*x + d))/(b*c^4), 1/105*(210*A*c^4*sqrt(-d)*d^3*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 105*((B*b*c^3 - A*c^4)*d^3 - 3*(B*b^2*c^2 - A*b*c^3)*d^2*e + 3*(B*b^3*c - A*b^2*c^2)*d*e^2 - (B*b^4 - A*b^3*c)*e^3)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(15*B*b*c^3*e^3*x^3 + 176*B*b*c^3*d^3 - 406*(B*b^2*c^2 - A*b*c^3)*d^2*e + 350*(B*b^3*c - A*b^2*c^2)*d*e^2 - 105*(B*b^4 - A*b^3*c)*e^3 + 3*(22*B*b*c^3*d*e^2 - 7*(B*b^2*c^2 - A*b*c^3)*e^3)*x^2 + (122*B*b*c^3*d^2*e - 112*(B*b^2*c^2 - A*b*c^3)*d*e^2 + 35*(B*b^3*c - A*b^2*c^2)*e^3)*x)*sqrt(e*x + d))/(b*c^4), 2/105*(105*A*c^4*sqrt(-d)*d^3*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 105*((B*b*c^3 - A*c^4)*d^3 - 3*(B*b^2*c^2 - A*b*c^3)*d^2*e + 3*(B*b^3*c - A*b^2*c^2)*d*e^2 - (B*b^4 - A*b^3*c)*e^3)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + (15*B*b*c^3*e^3*x^3 + 176*B*b*c^3*d^3 - 406*(B*b^2*c^2 - A*b*c^3)*d^2*e + 350*(B*b^3*c - A*b^2*c^2)*d*e^2 - 105*(B*b^4 - A*b^3*c)*e^3 + 3*(22*B*b*c^3*d*e^2 - 7*(B*b^2*c^2 - A*b*c^3)*e^3)*x^2 + (122*B*b*c^3*d^2*e - 112*(B*b^2*c^2 - A*b*c^3)*d*e^2 + 35*(B*b^3*c - A*b^2*c^2)*e^3)*x)*sqrt(e*x + d))/(b*c^4)]","A",0
1230,1,1006,0,4.203617," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{15 \, A c^{3} d^{\frac{5}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 15 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{2} - 2 \, {\left(B b^{2} c - A b c^{2}\right)} d e + {\left(B b^{3} - A b^{2} c\right)} e^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(3 \, B b c^{2} e^{2} x^{2} + 23 \, B b c^{2} d^{2} - 35 \, {\left(B b^{2} c - A b c^{2}\right)} d e + 15 \, {\left(B b^{3} - A b^{2} c\right)} e^{2} + {\left(11 \, B b c^{2} d e - 5 \, {\left(B b^{2} c - A b c^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, b c^{3}}, \frac{15 \, A c^{3} d^{\frac{5}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 30 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{2} - 2 \, {\left(B b^{2} c - A b c^{2}\right)} d e + {\left(B b^{3} - A b^{2} c\right)} e^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 2 \, {\left(3 \, B b c^{2} e^{2} x^{2} + 23 \, B b c^{2} d^{2} - 35 \, {\left(B b^{2} c - A b c^{2}\right)} d e + 15 \, {\left(B b^{3} - A b^{2} c\right)} e^{2} + {\left(11 \, B b c^{2} d e - 5 \, {\left(B b^{2} c - A b c^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, b c^{3}}, \frac{30 \, A c^{3} \sqrt{-d} d^{2} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 15 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{2} - 2 \, {\left(B b^{2} c - A b c^{2}\right)} d e + {\left(B b^{3} - A b^{2} c\right)} e^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(3 \, B b c^{2} e^{2} x^{2} + 23 \, B b c^{2} d^{2} - 35 \, {\left(B b^{2} c - A b c^{2}\right)} d e + 15 \, {\left(B b^{3} - A b^{2} c\right)} e^{2} + {\left(11 \, B b c^{2} d e - 5 \, {\left(B b^{2} c - A b c^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, b c^{3}}, \frac{2 \, {\left(15 \, A c^{3} \sqrt{-d} d^{2} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 15 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{2} - 2 \, {\left(B b^{2} c - A b c^{2}\right)} d e + {\left(B b^{3} - A b^{2} c\right)} e^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left(3 \, B b c^{2} e^{2} x^{2} + 23 \, B b c^{2} d^{2} - 35 \, {\left(B b^{2} c - A b c^{2}\right)} d e + 15 \, {\left(B b^{3} - A b^{2} c\right)} e^{2} + {\left(11 \, B b c^{2} d e - 5 \, {\left(B b^{2} c - A b c^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, b c^{3}}\right]"," ",0,"[1/15*(15*A*c^3*d^(5/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 15*((B*b*c^2 - A*c^3)*d^2 - 2*(B*b^2*c - A*b*c^2)*d*e + (B*b^3 - A*b^2*c)*e^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(3*B*b*c^2*e^2*x^2 + 23*B*b*c^2*d^2 - 35*(B*b^2*c - A*b*c^2)*d*e + 15*(B*b^3 - A*b^2*c)*e^2 + (11*B*b*c^2*d*e - 5*(B*b^2*c - A*b*c^2)*e^2)*x)*sqrt(e*x + d))/(b*c^3), 1/15*(15*A*c^3*d^(5/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 30*((B*b*c^2 - A*c^3)*d^2 - 2*(B*b^2*c - A*b*c^2)*d*e + (B*b^3 - A*b^2*c)*e^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 2*(3*B*b*c^2*e^2*x^2 + 23*B*b*c^2*d^2 - 35*(B*b^2*c - A*b*c^2)*d*e + 15*(B*b^3 - A*b^2*c)*e^2 + (11*B*b*c^2*d*e - 5*(B*b^2*c - A*b*c^2)*e^2)*x)*sqrt(e*x + d))/(b*c^3), 1/15*(30*A*c^3*sqrt(-d)*d^2*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 15*((B*b*c^2 - A*c^3)*d^2 - 2*(B*b^2*c - A*b*c^2)*d*e + (B*b^3 - A*b^2*c)*e^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(3*B*b*c^2*e^2*x^2 + 23*B*b*c^2*d^2 - 35*(B*b^2*c - A*b*c^2)*d*e + 15*(B*b^3 - A*b^2*c)*e^2 + (11*B*b*c^2*d*e - 5*(B*b^2*c - A*b*c^2)*e^2)*x)*sqrt(e*x + d))/(b*c^3), 2/15*(15*A*c^3*sqrt(-d)*d^2*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 15*((B*b*c^2 - A*c^3)*d^2 - 2*(B*b^2*c - A*b*c^2)*d*e + (B*b^3 - A*b^2*c)*e^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + (3*B*b*c^2*e^2*x^2 + 23*B*b*c^2*d^2 - 35*(B*b^2*c - A*b*c^2)*d*e + 15*(B*b^3 - A*b^2*c)*e^2 + (11*B*b*c^2*d*e - 5*(B*b^2*c - A*b*c^2)*e^2)*x)*sqrt(e*x + d))/(b*c^3)]","A",0
1231,1,646,0,1.061301," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{3 \, A c^{2} d^{\frac{3}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 3 \, {\left({\left(B b c - A c^{2}\right)} d - {\left(B b^{2} - A b c\right)} e\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(B b c e x + 4 \, B b c d - 3 \, {\left(B b^{2} - A b c\right)} e\right)} \sqrt{e x + d}}{3 \, b c^{2}}, \frac{3 \, A c^{2} d^{\frac{3}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 6 \, {\left({\left(B b c - A c^{2}\right)} d - {\left(B b^{2} - A b c\right)} e\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 2 \, {\left(B b c e x + 4 \, B b c d - 3 \, {\left(B b^{2} - A b c\right)} e\right)} \sqrt{e x + d}}{3 \, b c^{2}}, \frac{6 \, A c^{2} \sqrt{-d} d \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 3 \, {\left({\left(B b c - A c^{2}\right)} d - {\left(B b^{2} - A b c\right)} e\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(B b c e x + 4 \, B b c d - 3 \, {\left(B b^{2} - A b c\right)} e\right)} \sqrt{e x + d}}{3 \, b c^{2}}, \frac{2 \, {\left(3 \, A c^{2} \sqrt{-d} d \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 3 \, {\left({\left(B b c - A c^{2}\right)} d - {\left(B b^{2} - A b c\right)} e\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left(B b c e x + 4 \, B b c d - 3 \, {\left(B b^{2} - A b c\right)} e\right)} \sqrt{e x + d}\right)}}{3 \, b c^{2}}\right]"," ",0,"[1/3*(3*A*c^2*d^(3/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 3*((B*b*c - A*c^2)*d - (B*b^2 - A*b*c)*e)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(B*b*c*e*x + 4*B*b*c*d - 3*(B*b^2 - A*b*c)*e)*sqrt(e*x + d))/(b*c^2), 1/3*(3*A*c^2*d^(3/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 6*((B*b*c - A*c^2)*d - (B*b^2 - A*b*c)*e)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 2*(B*b*c*e*x + 4*B*b*c*d - 3*(B*b^2 - A*b*c)*e)*sqrt(e*x + d))/(b*c^2), 1/3*(6*A*c^2*sqrt(-d)*d*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 3*((B*b*c - A*c^2)*d - (B*b^2 - A*b*c)*e)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(B*b*c*e*x + 4*B*b*c*d - 3*(B*b^2 - A*b*c)*e)*sqrt(e*x + d))/(b*c^2), 2/3*(3*A*c^2*sqrt(-d)*d*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 3*((B*b*c - A*c^2)*d - (B*b^2 - A*b*c)*e)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + (B*b*c*e*x + 4*B*b*c*d - 3*(B*b^2 - A*b*c)*e)*sqrt(e*x + d))/(b*c^2)]","A",0
1232,1,450,0,0.519020," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{A c \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, \sqrt{e x + d} B b - {\left(B b - A c\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right)}{b c}, \frac{A c \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, \sqrt{e x + d} B b - 2 \, {\left(B b - A c\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right)}{b c}, \frac{2 \, A c \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 2 \, \sqrt{e x + d} B b - {\left(B b - A c\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right)}{b c}, \frac{2 \, {\left(A c \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + \sqrt{e x + d} B b - {\left(B b - A c\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right)\right)}}{b c}\right]"," ",0,"[(A*c*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*sqrt(e*x + d)*B*b - (B*b - A*c)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)))/(b*c), (A*c*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*sqrt(e*x + d)*B*b - 2*(B*b - A*c)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)))/(b*c), (2*A*c*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 2*sqrt(e*x + d)*B*b - (B*b - A*c)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)))/(b*c), 2*(A*c*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + sqrt(e*x + d)*B*b - (B*b - A*c)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)))/(b*c)]","A",0
1233,1,489,0,0.491754," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{\sqrt{c^{2} d - b c e} {\left(B b - A c\right)} d \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{c^{2} d - b c e} \sqrt{e x + d}}{c x + b}\right) - {\left(A c^{2} d - A b c e\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{b c^{2} d^{2} - b^{2} c d e}, \frac{2 \, \sqrt{-c^{2} d + b c e} {\left(B b - A c\right)} d \arctan\left(\frac{\sqrt{-c^{2} d + b c e} \sqrt{e x + d}}{c e x + c d}\right) + {\left(A c^{2} d - A b c e\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{b c^{2} d^{2} - b^{2} c d e}, -\frac{\sqrt{c^{2} d - b c e} {\left(B b - A c\right)} d \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{c^{2} d - b c e} \sqrt{e x + d}}{c x + b}\right) - 2 \, {\left(A c^{2} d - A b c e\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right)}{b c^{2} d^{2} - b^{2} c d e}, \frac{2 \, {\left(\sqrt{-c^{2} d + b c e} {\left(B b - A c\right)} d \arctan\left(\frac{\sqrt{-c^{2} d + b c e} \sqrt{e x + d}}{c e x + c d}\right) + {\left(A c^{2} d - A b c e\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right)\right)}}{b c^{2} d^{2} - b^{2} c d e}\right]"," ",0,"[-(sqrt(c^2*d - b*c*e)*(B*b - A*c)*d*log((c*e*x + 2*c*d - b*e + 2*sqrt(c^2*d - b*c*e)*sqrt(e*x + d))/(c*x + b)) - (A*c^2*d - A*b*c*e)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/(b*c^2*d^2 - b^2*c*d*e), (2*sqrt(-c^2*d + b*c*e)*(B*b - A*c)*d*arctan(sqrt(-c^2*d + b*c*e)*sqrt(e*x + d)/(c*e*x + c*d)) + (A*c^2*d - A*b*c*e)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/(b*c^2*d^2 - b^2*c*d*e), -(sqrt(c^2*d - b*c*e)*(B*b - A*c)*d*log((c*e*x + 2*c*d - b*e + 2*sqrt(c^2*d - b*c*e)*sqrt(e*x + d))/(c*x + b)) - 2*(A*c^2*d - A*b*c*e)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d))/(b*c^2*d^2 - b^2*c*d*e), 2*(sqrt(-c^2*d + b*c*e)*(B*b - A*c)*d*arctan(sqrt(-c^2*d + b*c*e)*sqrt(e*x + d)/(c*e*x + c*d)) + (A*c^2*d - A*b*c*e)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d))/(b*c^2*d^2 - b^2*c*d*e)]","A",0
1234,1,835,0,0.729065," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{{\left({\left(B b - A c\right)} d^{2} e x + {\left(B b - A c\right)} d^{3}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + {\left(A c d^{2} - A b d e + {\left(A c d e - A b e^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(B b d^{2} - A b d e\right)} \sqrt{e x + d}}{b c d^{4} - b^{2} d^{3} e + {\left(b c d^{3} e - b^{2} d^{2} e^{2}\right)} x}, -\frac{2 \, {\left({\left(B b - A c\right)} d^{2} e x + {\left(B b - A c\right)} d^{3}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left(A c d^{2} - A b d e + {\left(A c d e - A b e^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(B b d^{2} - A b d e\right)} \sqrt{e x + d}}{b c d^{4} - b^{2} d^{3} e + {\left(b c d^{3} e - b^{2} d^{2} e^{2}\right)} x}, \frac{2 \, {\left(A c d^{2} - A b d e + {\left(A c d e - A b e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left({\left(B b - A c\right)} d^{2} e x + {\left(B b - A c\right)} d^{3}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(B b d^{2} - A b d e\right)} \sqrt{e x + d}}{b c d^{4} - b^{2} d^{3} e + {\left(b c d^{3} e - b^{2} d^{2} e^{2}\right)} x}, -\frac{2 \, {\left({\left({\left(B b - A c\right)} d^{2} e x + {\left(B b - A c\right)} d^{3}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left(A c d^{2} - A b d e + {\left(A c d e - A b e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(B b d^{2} - A b d e\right)} \sqrt{e x + d}\right)}}{b c d^{4} - b^{2} d^{3} e + {\left(b c d^{3} e - b^{2} d^{2} e^{2}\right)} x}\right]"," ",0,"[(((B*b - A*c)*d^2*e*x + (B*b - A*c)*d^3)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + (A*c*d^2 - A*b*d*e + (A*c*d*e - A*b*e^2)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(B*b*d^2 - A*b*d*e)*sqrt(e*x + d))/(b*c*d^4 - b^2*d^3*e + (b*c*d^3*e - b^2*d^2*e^2)*x), -(2*((B*b - A*c)*d^2*e*x + (B*b - A*c)*d^3)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - (A*c*d^2 - A*b*d*e + (A*c*d*e - A*b*e^2)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(B*b*d^2 - A*b*d*e)*sqrt(e*x + d))/(b*c*d^4 - b^2*d^3*e + (b*c*d^3*e - b^2*d^2*e^2)*x), (2*(A*c*d^2 - A*b*d*e + (A*c*d*e - A*b*e^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + ((B*b - A*c)*d^2*e*x + (B*b - A*c)*d^3)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(B*b*d^2 - A*b*d*e)*sqrt(e*x + d))/(b*c*d^4 - b^2*d^3*e + (b*c*d^3*e - b^2*d^2*e^2)*x), -2*(((B*b - A*c)*d^2*e*x + (B*b - A*c)*d^3)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - (A*c*d^2 - A*b*d*e + (A*c*d*e - A*b*e^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (B*b*d^2 - A*b*d*e)*sqrt(e*x + d))/(b*c*d^4 - b^2*d^3*e + (b*c*d^3*e - b^2*d^2*e^2)*x)]","B",0
1235,1,1709,0,2.060176," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(B b c - A c^{2}\right)} d^{3} e^{2} x^{2} + 2 \, {\left(B b c - A c^{2}\right)} d^{4} e x + {\left(B b c - A c^{2}\right)} d^{5}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 3 \, {\left(A c^{2} d^{4} - 2 \, A b c d^{3} e + A b^{2} d^{2} e^{2} + {\left(A c^{2} d^{2} e^{2} - 2 \, A b c d e^{3} + A b^{2} e^{4}\right)} x^{2} + 2 \, {\left(A c^{2} d^{3} e - 2 \, A b c d^{2} e^{2} + A b^{2} d e^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(4 \, B b c d^{4} + 4 \, A b^{2} d^{2} e^{2} - {\left(B b^{2} + 7 \, A b c\right)} d^{3} e + 3 \, {\left(B b c d^{3} e - 2 \, A b c d^{2} e^{2} + A b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b c^{2} d^{7} - 2 \, b^{2} c d^{6} e + b^{3} d^{5} e^{2} + {\left(b c^{2} d^{5} e^{2} - 2 \, b^{2} c d^{4} e^{3} + b^{3} d^{3} e^{4}\right)} x^{2} + 2 \, {\left(b c^{2} d^{6} e - 2 \, b^{2} c d^{5} e^{2} + b^{3} d^{4} e^{3}\right)} x\right)}}, -\frac{6 \, {\left({\left(B b c - A c^{2}\right)} d^{3} e^{2} x^{2} + 2 \, {\left(B b c - A c^{2}\right)} d^{4} e x + {\left(B b c - A c^{2}\right)} d^{5}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 3 \, {\left(A c^{2} d^{4} - 2 \, A b c d^{3} e + A b^{2} d^{2} e^{2} + {\left(A c^{2} d^{2} e^{2} - 2 \, A b c d e^{3} + A b^{2} e^{4}\right)} x^{2} + 2 \, {\left(A c^{2} d^{3} e - 2 \, A b c d^{2} e^{2} + A b^{2} d e^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(4 \, B b c d^{4} + 4 \, A b^{2} d^{2} e^{2} - {\left(B b^{2} + 7 \, A b c\right)} d^{3} e + 3 \, {\left(B b c d^{3} e - 2 \, A b c d^{2} e^{2} + A b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b c^{2} d^{7} - 2 \, b^{2} c d^{6} e + b^{3} d^{5} e^{2} + {\left(b c^{2} d^{5} e^{2} - 2 \, b^{2} c d^{4} e^{3} + b^{3} d^{3} e^{4}\right)} x^{2} + 2 \, {\left(b c^{2} d^{6} e - 2 \, b^{2} c d^{5} e^{2} + b^{3} d^{4} e^{3}\right)} x\right)}}, \frac{6 \, {\left(A c^{2} d^{4} - 2 \, A b c d^{3} e + A b^{2} d^{2} e^{2} + {\left(A c^{2} d^{2} e^{2} - 2 \, A b c d e^{3} + A b^{2} e^{4}\right)} x^{2} + 2 \, {\left(A c^{2} d^{3} e - 2 \, A b c d^{2} e^{2} + A b^{2} d e^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 3 \, {\left({\left(B b c - A c^{2}\right)} d^{3} e^{2} x^{2} + 2 \, {\left(B b c - A c^{2}\right)} d^{4} e x + {\left(B b c - A c^{2}\right)} d^{5}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(4 \, B b c d^{4} + 4 \, A b^{2} d^{2} e^{2} - {\left(B b^{2} + 7 \, A b c\right)} d^{3} e + 3 \, {\left(B b c d^{3} e - 2 \, A b c d^{2} e^{2} + A b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b c^{2} d^{7} - 2 \, b^{2} c d^{6} e + b^{3} d^{5} e^{2} + {\left(b c^{2} d^{5} e^{2} - 2 \, b^{2} c d^{4} e^{3} + b^{3} d^{3} e^{4}\right)} x^{2} + 2 \, {\left(b c^{2} d^{6} e - 2 \, b^{2} c d^{5} e^{2} + b^{3} d^{4} e^{3}\right)} x\right)}}, -\frac{2 \, {\left(3 \, {\left({\left(B b c - A c^{2}\right)} d^{3} e^{2} x^{2} + 2 \, {\left(B b c - A c^{2}\right)} d^{4} e x + {\left(B b c - A c^{2}\right)} d^{5}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 3 \, {\left(A c^{2} d^{4} - 2 \, A b c d^{3} e + A b^{2} d^{2} e^{2} + {\left(A c^{2} d^{2} e^{2} - 2 \, A b c d e^{3} + A b^{2} e^{4}\right)} x^{2} + 2 \, {\left(A c^{2} d^{3} e - 2 \, A b c d^{2} e^{2} + A b^{2} d e^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(4 \, B b c d^{4} + 4 \, A b^{2} d^{2} e^{2} - {\left(B b^{2} + 7 \, A b c\right)} d^{3} e + 3 \, {\left(B b c d^{3} e - 2 \, A b c d^{2} e^{2} + A b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{3 \, {\left(b c^{2} d^{7} - 2 \, b^{2} c d^{6} e + b^{3} d^{5} e^{2} + {\left(b c^{2} d^{5} e^{2} - 2 \, b^{2} c d^{4} e^{3} + b^{3} d^{3} e^{4}\right)} x^{2} + 2 \, {\left(b c^{2} d^{6} e - 2 \, b^{2} c d^{5} e^{2} + b^{3} d^{4} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/3*(3*((B*b*c - A*c^2)*d^3*e^2*x^2 + 2*(B*b*c - A*c^2)*d^4*e*x + (B*b*c - A*c^2)*d^5)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 3*(A*c^2*d^4 - 2*A*b*c*d^3*e + A*b^2*d^2*e^2 + (A*c^2*d^2*e^2 - 2*A*b*c*d*e^3 + A*b^2*e^4)*x^2 + 2*(A*c^2*d^3*e - 2*A*b*c*d^2*e^2 + A*b^2*d*e^3)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(4*B*b*c*d^4 + 4*A*b^2*d^2*e^2 - (B*b^2 + 7*A*b*c)*d^3*e + 3*(B*b*c*d^3*e - 2*A*b*c*d^2*e^2 + A*b^2*d*e^3)*x)*sqrt(e*x + d))/(b*c^2*d^7 - 2*b^2*c*d^6*e + b^3*d^5*e^2 + (b*c^2*d^5*e^2 - 2*b^2*c*d^4*e^3 + b^3*d^3*e^4)*x^2 + 2*(b*c^2*d^6*e - 2*b^2*c*d^5*e^2 + b^3*d^4*e^3)*x), -1/3*(6*((B*b*c - A*c^2)*d^3*e^2*x^2 + 2*(B*b*c - A*c^2)*d^4*e*x + (B*b*c - A*c^2)*d^5)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 3*(A*c^2*d^4 - 2*A*b*c*d^3*e + A*b^2*d^2*e^2 + (A*c^2*d^2*e^2 - 2*A*b*c*d*e^3 + A*b^2*e^4)*x^2 + 2*(A*c^2*d^3*e - 2*A*b*c*d^2*e^2 + A*b^2*d*e^3)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(4*B*b*c*d^4 + 4*A*b^2*d^2*e^2 - (B*b^2 + 7*A*b*c)*d^3*e + 3*(B*b*c*d^3*e - 2*A*b*c*d^2*e^2 + A*b^2*d*e^3)*x)*sqrt(e*x + d))/(b*c^2*d^7 - 2*b^2*c*d^6*e + b^3*d^5*e^2 + (b*c^2*d^5*e^2 - 2*b^2*c*d^4*e^3 + b^3*d^3*e^4)*x^2 + 2*(b*c^2*d^6*e - 2*b^2*c*d^5*e^2 + b^3*d^4*e^3)*x), 1/3*(6*(A*c^2*d^4 - 2*A*b*c*d^3*e + A*b^2*d^2*e^2 + (A*c^2*d^2*e^2 - 2*A*b*c*d*e^3 + A*b^2*e^4)*x^2 + 2*(A*c^2*d^3*e - 2*A*b*c*d^2*e^2 + A*b^2*d*e^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 3*((B*b*c - A*c^2)*d^3*e^2*x^2 + 2*(B*b*c - A*c^2)*d^4*e*x + (B*b*c - A*c^2)*d^5)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(4*B*b*c*d^4 + 4*A*b^2*d^2*e^2 - (B*b^2 + 7*A*b*c)*d^3*e + 3*(B*b*c*d^3*e - 2*A*b*c*d^2*e^2 + A*b^2*d*e^3)*x)*sqrt(e*x + d))/(b*c^2*d^7 - 2*b^2*c*d^6*e + b^3*d^5*e^2 + (b*c^2*d^5*e^2 - 2*b^2*c*d^4*e^3 + b^3*d^3*e^4)*x^2 + 2*(b*c^2*d^6*e - 2*b^2*c*d^5*e^2 + b^3*d^4*e^3)*x), -2/3*(3*((B*b*c - A*c^2)*d^3*e^2*x^2 + 2*(B*b*c - A*c^2)*d^4*e*x + (B*b*c - A*c^2)*d^5)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 3*(A*c^2*d^4 - 2*A*b*c*d^3*e + A*b^2*d^2*e^2 + (A*c^2*d^2*e^2 - 2*A*b*c*d*e^3 + A*b^2*e^4)*x^2 + 2*(A*c^2*d^3*e - 2*A*b*c*d^2*e^2 + A*b^2*d*e^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (4*B*b*c*d^4 + 4*A*b^2*d^2*e^2 - (B*b^2 + 7*A*b*c)*d^3*e + 3*(B*b*c*d^3*e - 2*A*b*c*d^2*e^2 + A*b^2*d*e^3)*x)*sqrt(e*x + d))/(b*c^2*d^7 - 2*b^2*c*d^6*e + b^3*d^5*e^2 + (b*c^2*d^5*e^2 - 2*b^2*c*d^4*e^3 + b^3*d^3*e^4)*x^2 + 2*(b*c^2*d^6*e - 2*b^2*c*d^5*e^2 + b^3*d^4*e^3)*x)]","B",0
1236,1,3081,0,7.484245," ","integrate((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{4} e^{3} x^{3} + 3 \, {\left(B b c^{2} - A c^{3}\right)} d^{5} e^{2} x^{2} + 3 \, {\left(B b c^{2} - A c^{3}\right)} d^{6} e x + {\left(B b c^{2} - A c^{3}\right)} d^{7}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 15 \, {\left(A c^{3} d^{6} - 3 \, A b c^{2} d^{5} e + 3 \, A b^{2} c d^{4} e^{2} - A b^{3} d^{3} e^{3} + {\left(A c^{3} d^{3} e^{3} - 3 \, A b c^{2} d^{2} e^{4} + 3 \, A b^{2} c d e^{5} - A b^{3} e^{6}\right)} x^{3} + 3 \, {\left(A c^{3} d^{4} e^{2} - 3 \, A b c^{2} d^{3} e^{3} + 3 \, A b^{2} c d^{2} e^{4} - A b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(A c^{3} d^{5} e - 3 \, A b c^{2} d^{4} e^{2} + 3 \, A b^{2} c d^{3} e^{3} - A b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(23 \, B b c^{2} d^{6} - 23 \, A b^{3} d^{3} e^{3} - {\left(11 \, B b^{2} c + 58 \, A b c^{2}\right)} d^{5} e + 3 \, {\left(B b^{3} + 22 \, A b^{2} c\right)} d^{4} e^{2} + 15 \, {\left(B b c^{2} d^{4} e^{2} - 3 \, A b c^{2} d^{3} e^{3} + 3 \, A b^{2} c d^{2} e^{4} - A b^{3} d e^{5}\right)} x^{2} + 5 \, {\left(7 \, B b c^{2} d^{5} e + 21 \, A b^{2} c d^{3} e^{3} - 7 \, A b^{3} d^{2} e^{4} - {\left(B b^{2} c + 20 \, A b c^{2}\right)} d^{4} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b c^{3} d^{10} - 3 \, b^{2} c^{2} d^{9} e + 3 \, b^{3} c d^{8} e^{2} - b^{4} d^{7} e^{3} + {\left(b c^{3} d^{7} e^{3} - 3 \, b^{2} c^{2} d^{6} e^{4} + 3 \, b^{3} c d^{5} e^{5} - b^{4} d^{4} e^{6}\right)} x^{3} + 3 \, {\left(b c^{3} d^{8} e^{2} - 3 \, b^{2} c^{2} d^{7} e^{3} + 3 \, b^{3} c d^{6} e^{4} - b^{4} d^{5} e^{5}\right)} x^{2} + 3 \, {\left(b c^{3} d^{9} e - 3 \, b^{2} c^{2} d^{8} e^{2} + 3 \, b^{3} c d^{7} e^{3} - b^{4} d^{6} e^{4}\right)} x\right)}}, -\frac{30 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{4} e^{3} x^{3} + 3 \, {\left(B b c^{2} - A c^{3}\right)} d^{5} e^{2} x^{2} + 3 \, {\left(B b c^{2} - A c^{3}\right)} d^{6} e x + {\left(B b c^{2} - A c^{3}\right)} d^{7}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 15 \, {\left(A c^{3} d^{6} - 3 \, A b c^{2} d^{5} e + 3 \, A b^{2} c d^{4} e^{2} - A b^{3} d^{3} e^{3} + {\left(A c^{3} d^{3} e^{3} - 3 \, A b c^{2} d^{2} e^{4} + 3 \, A b^{2} c d e^{5} - A b^{3} e^{6}\right)} x^{3} + 3 \, {\left(A c^{3} d^{4} e^{2} - 3 \, A b c^{2} d^{3} e^{3} + 3 \, A b^{2} c d^{2} e^{4} - A b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(A c^{3} d^{5} e - 3 \, A b c^{2} d^{4} e^{2} + 3 \, A b^{2} c d^{3} e^{3} - A b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(23 \, B b c^{2} d^{6} - 23 \, A b^{3} d^{3} e^{3} - {\left(11 \, B b^{2} c + 58 \, A b c^{2}\right)} d^{5} e + 3 \, {\left(B b^{3} + 22 \, A b^{2} c\right)} d^{4} e^{2} + 15 \, {\left(B b c^{2} d^{4} e^{2} - 3 \, A b c^{2} d^{3} e^{3} + 3 \, A b^{2} c d^{2} e^{4} - A b^{3} d e^{5}\right)} x^{2} + 5 \, {\left(7 \, B b c^{2} d^{5} e + 21 \, A b^{2} c d^{3} e^{3} - 7 \, A b^{3} d^{2} e^{4} - {\left(B b^{2} c + 20 \, A b c^{2}\right)} d^{4} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b c^{3} d^{10} - 3 \, b^{2} c^{2} d^{9} e + 3 \, b^{3} c d^{8} e^{2} - b^{4} d^{7} e^{3} + {\left(b c^{3} d^{7} e^{3} - 3 \, b^{2} c^{2} d^{6} e^{4} + 3 \, b^{3} c d^{5} e^{5} - b^{4} d^{4} e^{6}\right)} x^{3} + 3 \, {\left(b c^{3} d^{8} e^{2} - 3 \, b^{2} c^{2} d^{7} e^{3} + 3 \, b^{3} c d^{6} e^{4} - b^{4} d^{5} e^{5}\right)} x^{2} + 3 \, {\left(b c^{3} d^{9} e - 3 \, b^{2} c^{2} d^{8} e^{2} + 3 \, b^{3} c d^{7} e^{3} - b^{4} d^{6} e^{4}\right)} x\right)}}, \frac{30 \, {\left(A c^{3} d^{6} - 3 \, A b c^{2} d^{5} e + 3 \, A b^{2} c d^{4} e^{2} - A b^{3} d^{3} e^{3} + {\left(A c^{3} d^{3} e^{3} - 3 \, A b c^{2} d^{2} e^{4} + 3 \, A b^{2} c d e^{5} - A b^{3} e^{6}\right)} x^{3} + 3 \, {\left(A c^{3} d^{4} e^{2} - 3 \, A b c^{2} d^{3} e^{3} + 3 \, A b^{2} c d^{2} e^{4} - A b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(A c^{3} d^{5} e - 3 \, A b c^{2} d^{4} e^{2} + 3 \, A b^{2} c d^{3} e^{3} - A b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 15 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{4} e^{3} x^{3} + 3 \, {\left(B b c^{2} - A c^{3}\right)} d^{5} e^{2} x^{2} + 3 \, {\left(B b c^{2} - A c^{3}\right)} d^{6} e x + {\left(B b c^{2} - A c^{3}\right)} d^{7}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(23 \, B b c^{2} d^{6} - 23 \, A b^{3} d^{3} e^{3} - {\left(11 \, B b^{2} c + 58 \, A b c^{2}\right)} d^{5} e + 3 \, {\left(B b^{3} + 22 \, A b^{2} c\right)} d^{4} e^{2} + 15 \, {\left(B b c^{2} d^{4} e^{2} - 3 \, A b c^{2} d^{3} e^{3} + 3 \, A b^{2} c d^{2} e^{4} - A b^{3} d e^{5}\right)} x^{2} + 5 \, {\left(7 \, B b c^{2} d^{5} e + 21 \, A b^{2} c d^{3} e^{3} - 7 \, A b^{3} d^{2} e^{4} - {\left(B b^{2} c + 20 \, A b c^{2}\right)} d^{4} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b c^{3} d^{10} - 3 \, b^{2} c^{2} d^{9} e + 3 \, b^{3} c d^{8} e^{2} - b^{4} d^{7} e^{3} + {\left(b c^{3} d^{7} e^{3} - 3 \, b^{2} c^{2} d^{6} e^{4} + 3 \, b^{3} c d^{5} e^{5} - b^{4} d^{4} e^{6}\right)} x^{3} + 3 \, {\left(b c^{3} d^{8} e^{2} - 3 \, b^{2} c^{2} d^{7} e^{3} + 3 \, b^{3} c d^{6} e^{4} - b^{4} d^{5} e^{5}\right)} x^{2} + 3 \, {\left(b c^{3} d^{9} e - 3 \, b^{2} c^{2} d^{8} e^{2} + 3 \, b^{3} c d^{7} e^{3} - b^{4} d^{6} e^{4}\right)} x\right)}}, -\frac{2 \, {\left(15 \, {\left({\left(B b c^{2} - A c^{3}\right)} d^{4} e^{3} x^{3} + 3 \, {\left(B b c^{2} - A c^{3}\right)} d^{5} e^{2} x^{2} + 3 \, {\left(B b c^{2} - A c^{3}\right)} d^{6} e x + {\left(B b c^{2} - A c^{3}\right)} d^{7}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 15 \, {\left(A c^{3} d^{6} - 3 \, A b c^{2} d^{5} e + 3 \, A b^{2} c d^{4} e^{2} - A b^{3} d^{3} e^{3} + {\left(A c^{3} d^{3} e^{3} - 3 \, A b c^{2} d^{2} e^{4} + 3 \, A b^{2} c d e^{5} - A b^{3} e^{6}\right)} x^{3} + 3 \, {\left(A c^{3} d^{4} e^{2} - 3 \, A b c^{2} d^{3} e^{3} + 3 \, A b^{2} c d^{2} e^{4} - A b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(A c^{3} d^{5} e - 3 \, A b c^{2} d^{4} e^{2} + 3 \, A b^{2} c d^{3} e^{3} - A b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(23 \, B b c^{2} d^{6} - 23 \, A b^{3} d^{3} e^{3} - {\left(11 \, B b^{2} c + 58 \, A b c^{2}\right)} d^{5} e + 3 \, {\left(B b^{3} + 22 \, A b^{2} c\right)} d^{4} e^{2} + 15 \, {\left(B b c^{2} d^{4} e^{2} - 3 \, A b c^{2} d^{3} e^{3} + 3 \, A b^{2} c d^{2} e^{4} - A b^{3} d e^{5}\right)} x^{2} + 5 \, {\left(7 \, B b c^{2} d^{5} e + 21 \, A b^{2} c d^{3} e^{3} - 7 \, A b^{3} d^{2} e^{4} - {\left(B b^{2} c + 20 \, A b c^{2}\right)} d^{4} e^{2}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, {\left(b c^{3} d^{10} - 3 \, b^{2} c^{2} d^{9} e + 3 \, b^{3} c d^{8} e^{2} - b^{4} d^{7} e^{3} + {\left(b c^{3} d^{7} e^{3} - 3 \, b^{2} c^{2} d^{6} e^{4} + 3 \, b^{3} c d^{5} e^{5} - b^{4} d^{4} e^{6}\right)} x^{3} + 3 \, {\left(b c^{3} d^{8} e^{2} - 3 \, b^{2} c^{2} d^{7} e^{3} + 3 \, b^{3} c d^{6} e^{4} - b^{4} d^{5} e^{5}\right)} x^{2} + 3 \, {\left(b c^{3} d^{9} e - 3 \, b^{2} c^{2} d^{8} e^{2} + 3 \, b^{3} c d^{7} e^{3} - b^{4} d^{6} e^{4}\right)} x\right)}}\right]"," ",0,"[1/15*(15*((B*b*c^2 - A*c^3)*d^4*e^3*x^3 + 3*(B*b*c^2 - A*c^3)*d^5*e^2*x^2 + 3*(B*b*c^2 - A*c^3)*d^6*e*x + (B*b*c^2 - A*c^3)*d^7)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 15*(A*c^3*d^6 - 3*A*b*c^2*d^5*e + 3*A*b^2*c*d^4*e^2 - A*b^3*d^3*e^3 + (A*c^3*d^3*e^3 - 3*A*b*c^2*d^2*e^4 + 3*A*b^2*c*d*e^5 - A*b^3*e^6)*x^3 + 3*(A*c^3*d^4*e^2 - 3*A*b*c^2*d^3*e^3 + 3*A*b^2*c*d^2*e^4 - A*b^3*d*e^5)*x^2 + 3*(A*c^3*d^5*e - 3*A*b*c^2*d^4*e^2 + 3*A*b^2*c*d^3*e^3 - A*b^3*d^2*e^4)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(23*B*b*c^2*d^6 - 23*A*b^3*d^3*e^3 - (11*B*b^2*c + 58*A*b*c^2)*d^5*e + 3*(B*b^3 + 22*A*b^2*c)*d^4*e^2 + 15*(B*b*c^2*d^4*e^2 - 3*A*b*c^2*d^3*e^3 + 3*A*b^2*c*d^2*e^4 - A*b^3*d*e^5)*x^2 + 5*(7*B*b*c^2*d^5*e + 21*A*b^2*c*d^3*e^3 - 7*A*b^3*d^2*e^4 - (B*b^2*c + 20*A*b*c^2)*d^4*e^2)*x)*sqrt(e*x + d))/(b*c^3*d^10 - 3*b^2*c^2*d^9*e + 3*b^3*c*d^8*e^2 - b^4*d^7*e^3 + (b*c^3*d^7*e^3 - 3*b^2*c^2*d^6*e^4 + 3*b^3*c*d^5*e^5 - b^4*d^4*e^6)*x^3 + 3*(b*c^3*d^8*e^2 - 3*b^2*c^2*d^7*e^3 + 3*b^3*c*d^6*e^4 - b^4*d^5*e^5)*x^2 + 3*(b*c^3*d^9*e - 3*b^2*c^2*d^8*e^2 + 3*b^3*c*d^7*e^3 - b^4*d^6*e^4)*x), -1/15*(30*((B*b*c^2 - A*c^3)*d^4*e^3*x^3 + 3*(B*b*c^2 - A*c^3)*d^5*e^2*x^2 + 3*(B*b*c^2 - A*c^3)*d^6*e*x + (B*b*c^2 - A*c^3)*d^7)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 15*(A*c^3*d^6 - 3*A*b*c^2*d^5*e + 3*A*b^2*c*d^4*e^2 - A*b^3*d^3*e^3 + (A*c^3*d^3*e^3 - 3*A*b*c^2*d^2*e^4 + 3*A*b^2*c*d*e^5 - A*b^3*e^6)*x^3 + 3*(A*c^3*d^4*e^2 - 3*A*b*c^2*d^3*e^3 + 3*A*b^2*c*d^2*e^4 - A*b^3*d*e^5)*x^2 + 3*(A*c^3*d^5*e - 3*A*b*c^2*d^4*e^2 + 3*A*b^2*c*d^3*e^3 - A*b^3*d^2*e^4)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(23*B*b*c^2*d^6 - 23*A*b^3*d^3*e^3 - (11*B*b^2*c + 58*A*b*c^2)*d^5*e + 3*(B*b^3 + 22*A*b^2*c)*d^4*e^2 + 15*(B*b*c^2*d^4*e^2 - 3*A*b*c^2*d^3*e^3 + 3*A*b^2*c*d^2*e^4 - A*b^3*d*e^5)*x^2 + 5*(7*B*b*c^2*d^5*e + 21*A*b^2*c*d^3*e^3 - 7*A*b^3*d^2*e^4 - (B*b^2*c + 20*A*b*c^2)*d^4*e^2)*x)*sqrt(e*x + d))/(b*c^3*d^10 - 3*b^2*c^2*d^9*e + 3*b^3*c*d^8*e^2 - b^4*d^7*e^3 + (b*c^3*d^7*e^3 - 3*b^2*c^2*d^6*e^4 + 3*b^3*c*d^5*e^5 - b^4*d^4*e^6)*x^3 + 3*(b*c^3*d^8*e^2 - 3*b^2*c^2*d^7*e^3 + 3*b^3*c*d^6*e^4 - b^4*d^5*e^5)*x^2 + 3*(b*c^3*d^9*e - 3*b^2*c^2*d^8*e^2 + 3*b^3*c*d^7*e^3 - b^4*d^6*e^4)*x), 1/15*(30*(A*c^3*d^6 - 3*A*b*c^2*d^5*e + 3*A*b^2*c*d^4*e^2 - A*b^3*d^3*e^3 + (A*c^3*d^3*e^3 - 3*A*b*c^2*d^2*e^4 + 3*A*b^2*c*d*e^5 - A*b^3*e^6)*x^3 + 3*(A*c^3*d^4*e^2 - 3*A*b*c^2*d^3*e^3 + 3*A*b^2*c*d^2*e^4 - A*b^3*d*e^5)*x^2 + 3*(A*c^3*d^5*e - 3*A*b*c^2*d^4*e^2 + 3*A*b^2*c*d^3*e^3 - A*b^3*d^2*e^4)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 15*((B*b*c^2 - A*c^3)*d^4*e^3*x^3 + 3*(B*b*c^2 - A*c^3)*d^5*e^2*x^2 + 3*(B*b*c^2 - A*c^3)*d^6*e*x + (B*b*c^2 - A*c^3)*d^7)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(23*B*b*c^2*d^6 - 23*A*b^3*d^3*e^3 - (11*B*b^2*c + 58*A*b*c^2)*d^5*e + 3*(B*b^3 + 22*A*b^2*c)*d^4*e^2 + 15*(B*b*c^2*d^4*e^2 - 3*A*b*c^2*d^3*e^3 + 3*A*b^2*c*d^2*e^4 - A*b^3*d*e^5)*x^2 + 5*(7*B*b*c^2*d^5*e + 21*A*b^2*c*d^3*e^3 - 7*A*b^3*d^2*e^4 - (B*b^2*c + 20*A*b*c^2)*d^4*e^2)*x)*sqrt(e*x + d))/(b*c^3*d^10 - 3*b^2*c^2*d^9*e + 3*b^3*c*d^8*e^2 - b^4*d^7*e^3 + (b*c^3*d^7*e^3 - 3*b^2*c^2*d^6*e^4 + 3*b^3*c*d^5*e^5 - b^4*d^4*e^6)*x^3 + 3*(b*c^3*d^8*e^2 - 3*b^2*c^2*d^7*e^3 + 3*b^3*c*d^6*e^4 - b^4*d^5*e^5)*x^2 + 3*(b*c^3*d^9*e - 3*b^2*c^2*d^8*e^2 + 3*b^3*c*d^7*e^3 - b^4*d^6*e^4)*x), -2/15*(15*((B*b*c^2 - A*c^3)*d^4*e^3*x^3 + 3*(B*b*c^2 - A*c^3)*d^5*e^2*x^2 + 3*(B*b*c^2 - A*c^3)*d^6*e*x + (B*b*c^2 - A*c^3)*d^7)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 15*(A*c^3*d^6 - 3*A*b*c^2*d^5*e + 3*A*b^2*c*d^4*e^2 - A*b^3*d^3*e^3 + (A*c^3*d^3*e^3 - 3*A*b*c^2*d^2*e^4 + 3*A*b^2*c*d*e^5 - A*b^3*e^6)*x^3 + 3*(A*c^3*d^4*e^2 - 3*A*b*c^2*d^3*e^3 + 3*A*b^2*c*d^2*e^4 - A*b^3*d*e^5)*x^2 + 3*(A*c^3*d^5*e - 3*A*b*c^2*d^4*e^2 + 3*A*b^2*c*d^3*e^3 - A*b^3*d^2*e^4)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (23*B*b*c^2*d^6 - 23*A*b^3*d^3*e^3 - (11*B*b^2*c + 58*A*b*c^2)*d^5*e + 3*(B*b^3 + 22*A*b^2*c)*d^4*e^2 + 15*(B*b*c^2*d^4*e^2 - 3*A*b*c^2*d^3*e^3 + 3*A*b^2*c*d^2*e^4 - A*b^3*d*e^5)*x^2 + 5*(7*B*b*c^2*d^5*e + 21*A*b^2*c*d^3*e^3 - 7*A*b^3*d^2*e^4 - (B*b^2*c + 20*A*b*c^2)*d^4*e^2)*x)*sqrt(e*x + d))/(b*c^3*d^10 - 3*b^2*c^2*d^9*e + 3*b^3*c*d^8*e^2 - b^4*d^7*e^3 + (b*c^3*d^7*e^3 - 3*b^2*c^2*d^6*e^4 + 3*b^3*c*d^5*e^5 - b^4*d^4*e^6)*x^3 + 3*(b*c^3*d^8*e^2 - 3*b^2*c^2*d^7*e^3 + 3*b^3*c*d^6*e^4 - b^4*d^5*e^5)*x^2 + 3*(b*c^3*d^9*e - 3*b^2*c^2*d^8*e^2 + 3*b^3*c*d^7*e^3 - b^4*d^6*e^4)*x)]","B",0
1237,1,4757,0,25.166513," ","integrate((B*x+A)/(e*x+d)^(9/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{5} e^{4} x^{4} + 4 \, {\left(B b c^{3} - A c^{4}\right)} d^{6} e^{3} x^{3} + 6 \, {\left(B b c^{3} - A c^{4}\right)} d^{7} e^{2} x^{2} + 4 \, {\left(B b c^{3} - A c^{4}\right)} d^{8} e x + {\left(B b c^{3} - A c^{4}\right)} d^{9}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 105 \, {\left(A c^{4} d^{8} - 4 \, A b c^{3} d^{7} e + 6 \, A b^{2} c^{2} d^{6} e^{2} - 4 \, A b^{3} c d^{5} e^{3} + A b^{4} d^{4} e^{4} + {\left(A c^{4} d^{4} e^{4} - 4 \, A b c^{3} d^{3} e^{5} + 6 \, A b^{2} c^{2} d^{2} e^{6} - 4 \, A b^{3} c d e^{7} + A b^{4} e^{8}\right)} x^{4} + 4 \, {\left(A c^{4} d^{5} e^{3} - 4 \, A b c^{3} d^{4} e^{4} + 6 \, A b^{2} c^{2} d^{3} e^{5} - 4 \, A b^{3} c d^{2} e^{6} + A b^{4} d e^{7}\right)} x^{3} + 6 \, {\left(A c^{4} d^{6} e^{2} - 4 \, A b c^{3} d^{5} e^{3} + 6 \, A b^{2} c^{2} d^{4} e^{4} - 4 \, A b^{3} c d^{3} e^{5} + A b^{4} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(A c^{4} d^{7} e - 4 \, A b c^{3} d^{6} e^{2} + 6 \, A b^{2} c^{2} d^{5} e^{3} - 4 \, A b^{3} c d^{4} e^{4} + A b^{4} d^{3} e^{5}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(176 \, B b c^{3} d^{8} + 176 \, A b^{4} d^{4} e^{4} - 2 \, {\left(61 \, B b^{2} c^{2} + 291 \, A b c^{3}\right)} d^{7} e + 66 \, {\left(B b^{3} c + 15 \, A b^{2} c^{2}\right)} d^{6} e^{2} - {\left(15 \, B b^{4} + 689 \, A b^{3} c\right)} d^{5} e^{3} + 105 \, {\left(B b c^{3} d^{5} e^{3} - 4 \, A b c^{3} d^{4} e^{4} + 6 \, A b^{2} c^{2} d^{3} e^{5} - 4 \, A b^{3} c d^{2} e^{6} + A b^{4} d e^{7}\right)} x^{3} + 35 \, {\left(10 \, B b c^{3} d^{6} e^{2} + 60 \, A b^{2} c^{2} d^{4} e^{4} - 40 \, A b^{3} c d^{3} e^{5} + 10 \, A b^{4} d^{2} e^{6} - {\left(B b^{2} c^{2} + 39 \, A b c^{3}\right)} d^{5} e^{3}\right)} x^{2} + 7 \, {\left(58 \, B b c^{3} d^{7} e - 232 \, A b^{3} c d^{4} e^{4} + 58 \, A b^{4} d^{3} e^{5} - 8 \, {\left(2 \, B b^{2} c^{2} + 27 \, A b c^{3}\right)} d^{6} e^{2} + 3 \, {\left(B b^{3} c + 115 \, A b^{2} c^{2}\right)} d^{5} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(b c^{4} d^{13} - 4 \, b^{2} c^{3} d^{12} e + 6 \, b^{3} c^{2} d^{11} e^{2} - 4 \, b^{4} c d^{10} e^{3} + b^{5} d^{9} e^{4} + {\left(b c^{4} d^{9} e^{4} - 4 \, b^{2} c^{3} d^{8} e^{5} + 6 \, b^{3} c^{2} d^{7} e^{6} - 4 \, b^{4} c d^{6} e^{7} + b^{5} d^{5} e^{8}\right)} x^{4} + 4 \, {\left(b c^{4} d^{10} e^{3} - 4 \, b^{2} c^{3} d^{9} e^{4} + 6 \, b^{3} c^{2} d^{8} e^{5} - 4 \, b^{4} c d^{7} e^{6} + b^{5} d^{6} e^{7}\right)} x^{3} + 6 \, {\left(b c^{4} d^{11} e^{2} - 4 \, b^{2} c^{3} d^{10} e^{3} + 6 \, b^{3} c^{2} d^{9} e^{4} - 4 \, b^{4} c d^{8} e^{5} + b^{5} d^{7} e^{6}\right)} x^{2} + 4 \, {\left(b c^{4} d^{12} e - 4 \, b^{2} c^{3} d^{11} e^{2} + 6 \, b^{3} c^{2} d^{10} e^{3} - 4 \, b^{4} c d^{9} e^{4} + b^{5} d^{8} e^{5}\right)} x\right)}}, -\frac{210 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{5} e^{4} x^{4} + 4 \, {\left(B b c^{3} - A c^{4}\right)} d^{6} e^{3} x^{3} + 6 \, {\left(B b c^{3} - A c^{4}\right)} d^{7} e^{2} x^{2} + 4 \, {\left(B b c^{3} - A c^{4}\right)} d^{8} e x + {\left(B b c^{3} - A c^{4}\right)} d^{9}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 105 \, {\left(A c^{4} d^{8} - 4 \, A b c^{3} d^{7} e + 6 \, A b^{2} c^{2} d^{6} e^{2} - 4 \, A b^{3} c d^{5} e^{3} + A b^{4} d^{4} e^{4} + {\left(A c^{4} d^{4} e^{4} - 4 \, A b c^{3} d^{3} e^{5} + 6 \, A b^{2} c^{2} d^{2} e^{6} - 4 \, A b^{3} c d e^{7} + A b^{4} e^{8}\right)} x^{4} + 4 \, {\left(A c^{4} d^{5} e^{3} - 4 \, A b c^{3} d^{4} e^{4} + 6 \, A b^{2} c^{2} d^{3} e^{5} - 4 \, A b^{3} c d^{2} e^{6} + A b^{4} d e^{7}\right)} x^{3} + 6 \, {\left(A c^{4} d^{6} e^{2} - 4 \, A b c^{3} d^{5} e^{3} + 6 \, A b^{2} c^{2} d^{4} e^{4} - 4 \, A b^{3} c d^{3} e^{5} + A b^{4} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(A c^{4} d^{7} e - 4 \, A b c^{3} d^{6} e^{2} + 6 \, A b^{2} c^{2} d^{5} e^{3} - 4 \, A b^{3} c d^{4} e^{4} + A b^{4} d^{3} e^{5}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(176 \, B b c^{3} d^{8} + 176 \, A b^{4} d^{4} e^{4} - 2 \, {\left(61 \, B b^{2} c^{2} + 291 \, A b c^{3}\right)} d^{7} e + 66 \, {\left(B b^{3} c + 15 \, A b^{2} c^{2}\right)} d^{6} e^{2} - {\left(15 \, B b^{4} + 689 \, A b^{3} c\right)} d^{5} e^{3} + 105 \, {\left(B b c^{3} d^{5} e^{3} - 4 \, A b c^{3} d^{4} e^{4} + 6 \, A b^{2} c^{2} d^{3} e^{5} - 4 \, A b^{3} c d^{2} e^{6} + A b^{4} d e^{7}\right)} x^{3} + 35 \, {\left(10 \, B b c^{3} d^{6} e^{2} + 60 \, A b^{2} c^{2} d^{4} e^{4} - 40 \, A b^{3} c d^{3} e^{5} + 10 \, A b^{4} d^{2} e^{6} - {\left(B b^{2} c^{2} + 39 \, A b c^{3}\right)} d^{5} e^{3}\right)} x^{2} + 7 \, {\left(58 \, B b c^{3} d^{7} e - 232 \, A b^{3} c d^{4} e^{4} + 58 \, A b^{4} d^{3} e^{5} - 8 \, {\left(2 \, B b^{2} c^{2} + 27 \, A b c^{3}\right)} d^{6} e^{2} + 3 \, {\left(B b^{3} c + 115 \, A b^{2} c^{2}\right)} d^{5} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(b c^{4} d^{13} - 4 \, b^{2} c^{3} d^{12} e + 6 \, b^{3} c^{2} d^{11} e^{2} - 4 \, b^{4} c d^{10} e^{3} + b^{5} d^{9} e^{4} + {\left(b c^{4} d^{9} e^{4} - 4 \, b^{2} c^{3} d^{8} e^{5} + 6 \, b^{3} c^{2} d^{7} e^{6} - 4 \, b^{4} c d^{6} e^{7} + b^{5} d^{5} e^{8}\right)} x^{4} + 4 \, {\left(b c^{4} d^{10} e^{3} - 4 \, b^{2} c^{3} d^{9} e^{4} + 6 \, b^{3} c^{2} d^{8} e^{5} - 4 \, b^{4} c d^{7} e^{6} + b^{5} d^{6} e^{7}\right)} x^{3} + 6 \, {\left(b c^{4} d^{11} e^{2} - 4 \, b^{2} c^{3} d^{10} e^{3} + 6 \, b^{3} c^{2} d^{9} e^{4} - 4 \, b^{4} c d^{8} e^{5} + b^{5} d^{7} e^{6}\right)} x^{2} + 4 \, {\left(b c^{4} d^{12} e - 4 \, b^{2} c^{3} d^{11} e^{2} + 6 \, b^{3} c^{2} d^{10} e^{3} - 4 \, b^{4} c d^{9} e^{4} + b^{5} d^{8} e^{5}\right)} x\right)}}, \frac{210 \, {\left(A c^{4} d^{8} - 4 \, A b c^{3} d^{7} e + 6 \, A b^{2} c^{2} d^{6} e^{2} - 4 \, A b^{3} c d^{5} e^{3} + A b^{4} d^{4} e^{4} + {\left(A c^{4} d^{4} e^{4} - 4 \, A b c^{3} d^{3} e^{5} + 6 \, A b^{2} c^{2} d^{2} e^{6} - 4 \, A b^{3} c d e^{7} + A b^{4} e^{8}\right)} x^{4} + 4 \, {\left(A c^{4} d^{5} e^{3} - 4 \, A b c^{3} d^{4} e^{4} + 6 \, A b^{2} c^{2} d^{3} e^{5} - 4 \, A b^{3} c d^{2} e^{6} + A b^{4} d e^{7}\right)} x^{3} + 6 \, {\left(A c^{4} d^{6} e^{2} - 4 \, A b c^{3} d^{5} e^{3} + 6 \, A b^{2} c^{2} d^{4} e^{4} - 4 \, A b^{3} c d^{3} e^{5} + A b^{4} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(A c^{4} d^{7} e - 4 \, A b c^{3} d^{6} e^{2} + 6 \, A b^{2} c^{2} d^{5} e^{3} - 4 \, A b^{3} c d^{4} e^{4} + A b^{4} d^{3} e^{5}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 105 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{5} e^{4} x^{4} + 4 \, {\left(B b c^{3} - A c^{4}\right)} d^{6} e^{3} x^{3} + 6 \, {\left(B b c^{3} - A c^{4}\right)} d^{7} e^{2} x^{2} + 4 \, {\left(B b c^{3} - A c^{4}\right)} d^{8} e x + {\left(B b c^{3} - A c^{4}\right)} d^{9}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(176 \, B b c^{3} d^{8} + 176 \, A b^{4} d^{4} e^{4} - 2 \, {\left(61 \, B b^{2} c^{2} + 291 \, A b c^{3}\right)} d^{7} e + 66 \, {\left(B b^{3} c + 15 \, A b^{2} c^{2}\right)} d^{6} e^{2} - {\left(15 \, B b^{4} + 689 \, A b^{3} c\right)} d^{5} e^{3} + 105 \, {\left(B b c^{3} d^{5} e^{3} - 4 \, A b c^{3} d^{4} e^{4} + 6 \, A b^{2} c^{2} d^{3} e^{5} - 4 \, A b^{3} c d^{2} e^{6} + A b^{4} d e^{7}\right)} x^{3} + 35 \, {\left(10 \, B b c^{3} d^{6} e^{2} + 60 \, A b^{2} c^{2} d^{4} e^{4} - 40 \, A b^{3} c d^{3} e^{5} + 10 \, A b^{4} d^{2} e^{6} - {\left(B b^{2} c^{2} + 39 \, A b c^{3}\right)} d^{5} e^{3}\right)} x^{2} + 7 \, {\left(58 \, B b c^{3} d^{7} e - 232 \, A b^{3} c d^{4} e^{4} + 58 \, A b^{4} d^{3} e^{5} - 8 \, {\left(2 \, B b^{2} c^{2} + 27 \, A b c^{3}\right)} d^{6} e^{2} + 3 \, {\left(B b^{3} c + 115 \, A b^{2} c^{2}\right)} d^{5} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(b c^{4} d^{13} - 4 \, b^{2} c^{3} d^{12} e + 6 \, b^{3} c^{2} d^{11} e^{2} - 4 \, b^{4} c d^{10} e^{3} + b^{5} d^{9} e^{4} + {\left(b c^{4} d^{9} e^{4} - 4 \, b^{2} c^{3} d^{8} e^{5} + 6 \, b^{3} c^{2} d^{7} e^{6} - 4 \, b^{4} c d^{6} e^{7} + b^{5} d^{5} e^{8}\right)} x^{4} + 4 \, {\left(b c^{4} d^{10} e^{3} - 4 \, b^{2} c^{3} d^{9} e^{4} + 6 \, b^{3} c^{2} d^{8} e^{5} - 4 \, b^{4} c d^{7} e^{6} + b^{5} d^{6} e^{7}\right)} x^{3} + 6 \, {\left(b c^{4} d^{11} e^{2} - 4 \, b^{2} c^{3} d^{10} e^{3} + 6 \, b^{3} c^{2} d^{9} e^{4} - 4 \, b^{4} c d^{8} e^{5} + b^{5} d^{7} e^{6}\right)} x^{2} + 4 \, {\left(b c^{4} d^{12} e - 4 \, b^{2} c^{3} d^{11} e^{2} + 6 \, b^{3} c^{2} d^{10} e^{3} - 4 \, b^{4} c d^{9} e^{4} + b^{5} d^{8} e^{5}\right)} x\right)}}, -\frac{2 \, {\left(105 \, {\left({\left(B b c^{3} - A c^{4}\right)} d^{5} e^{4} x^{4} + 4 \, {\left(B b c^{3} - A c^{4}\right)} d^{6} e^{3} x^{3} + 6 \, {\left(B b c^{3} - A c^{4}\right)} d^{7} e^{2} x^{2} + 4 \, {\left(B b c^{3} - A c^{4}\right)} d^{8} e x + {\left(B b c^{3} - A c^{4}\right)} d^{9}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 105 \, {\left(A c^{4} d^{8} - 4 \, A b c^{3} d^{7} e + 6 \, A b^{2} c^{2} d^{6} e^{2} - 4 \, A b^{3} c d^{5} e^{3} + A b^{4} d^{4} e^{4} + {\left(A c^{4} d^{4} e^{4} - 4 \, A b c^{3} d^{3} e^{5} + 6 \, A b^{2} c^{2} d^{2} e^{6} - 4 \, A b^{3} c d e^{7} + A b^{4} e^{8}\right)} x^{4} + 4 \, {\left(A c^{4} d^{5} e^{3} - 4 \, A b c^{3} d^{4} e^{4} + 6 \, A b^{2} c^{2} d^{3} e^{5} - 4 \, A b^{3} c d^{2} e^{6} + A b^{4} d e^{7}\right)} x^{3} + 6 \, {\left(A c^{4} d^{6} e^{2} - 4 \, A b c^{3} d^{5} e^{3} + 6 \, A b^{2} c^{2} d^{4} e^{4} - 4 \, A b^{3} c d^{3} e^{5} + A b^{4} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(A c^{4} d^{7} e - 4 \, A b c^{3} d^{6} e^{2} + 6 \, A b^{2} c^{2} d^{5} e^{3} - 4 \, A b^{3} c d^{4} e^{4} + A b^{4} d^{3} e^{5}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(176 \, B b c^{3} d^{8} + 176 \, A b^{4} d^{4} e^{4} - 2 \, {\left(61 \, B b^{2} c^{2} + 291 \, A b c^{3}\right)} d^{7} e + 66 \, {\left(B b^{3} c + 15 \, A b^{2} c^{2}\right)} d^{6} e^{2} - {\left(15 \, B b^{4} + 689 \, A b^{3} c\right)} d^{5} e^{3} + 105 \, {\left(B b c^{3} d^{5} e^{3} - 4 \, A b c^{3} d^{4} e^{4} + 6 \, A b^{2} c^{2} d^{3} e^{5} - 4 \, A b^{3} c d^{2} e^{6} + A b^{4} d e^{7}\right)} x^{3} + 35 \, {\left(10 \, B b c^{3} d^{6} e^{2} + 60 \, A b^{2} c^{2} d^{4} e^{4} - 40 \, A b^{3} c d^{3} e^{5} + 10 \, A b^{4} d^{2} e^{6} - {\left(B b^{2} c^{2} + 39 \, A b c^{3}\right)} d^{5} e^{3}\right)} x^{2} + 7 \, {\left(58 \, B b c^{3} d^{7} e - 232 \, A b^{3} c d^{4} e^{4} + 58 \, A b^{4} d^{3} e^{5} - 8 \, {\left(2 \, B b^{2} c^{2} + 27 \, A b c^{3}\right)} d^{6} e^{2} + 3 \, {\left(B b^{3} c + 115 \, A b^{2} c^{2}\right)} d^{5} e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{105 \, {\left(b c^{4} d^{13} - 4 \, b^{2} c^{3} d^{12} e + 6 \, b^{3} c^{2} d^{11} e^{2} - 4 \, b^{4} c d^{10} e^{3} + b^{5} d^{9} e^{4} + {\left(b c^{4} d^{9} e^{4} - 4 \, b^{2} c^{3} d^{8} e^{5} + 6 \, b^{3} c^{2} d^{7} e^{6} - 4 \, b^{4} c d^{6} e^{7} + b^{5} d^{5} e^{8}\right)} x^{4} + 4 \, {\left(b c^{4} d^{10} e^{3} - 4 \, b^{2} c^{3} d^{9} e^{4} + 6 \, b^{3} c^{2} d^{8} e^{5} - 4 \, b^{4} c d^{7} e^{6} + b^{5} d^{6} e^{7}\right)} x^{3} + 6 \, {\left(b c^{4} d^{11} e^{2} - 4 \, b^{2} c^{3} d^{10} e^{3} + 6 \, b^{3} c^{2} d^{9} e^{4} - 4 \, b^{4} c d^{8} e^{5} + b^{5} d^{7} e^{6}\right)} x^{2} + 4 \, {\left(b c^{4} d^{12} e - 4 \, b^{2} c^{3} d^{11} e^{2} + 6 \, b^{3} c^{2} d^{10} e^{3} - 4 \, b^{4} c d^{9} e^{4} + b^{5} d^{8} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/105*(105*((B*b*c^3 - A*c^4)*d^5*e^4*x^4 + 4*(B*b*c^3 - A*c^4)*d^6*e^3*x^3 + 6*(B*b*c^3 - A*c^4)*d^7*e^2*x^2 + 4*(B*b*c^3 - A*c^4)*d^8*e*x + (B*b*c^3 - A*c^4)*d^9)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 105*(A*c^4*d^8 - 4*A*b*c^3*d^7*e + 6*A*b^2*c^2*d^6*e^2 - 4*A*b^3*c*d^5*e^3 + A*b^4*d^4*e^4 + (A*c^4*d^4*e^4 - 4*A*b*c^3*d^3*e^5 + 6*A*b^2*c^2*d^2*e^6 - 4*A*b^3*c*d*e^7 + A*b^4*e^8)*x^4 + 4*(A*c^4*d^5*e^3 - 4*A*b*c^3*d^4*e^4 + 6*A*b^2*c^2*d^3*e^5 - 4*A*b^3*c*d^2*e^6 + A*b^4*d*e^7)*x^3 + 6*(A*c^4*d^6*e^2 - 4*A*b*c^3*d^5*e^3 + 6*A*b^2*c^2*d^4*e^4 - 4*A*b^3*c*d^3*e^5 + A*b^4*d^2*e^6)*x^2 + 4*(A*c^4*d^7*e - 4*A*b*c^3*d^6*e^2 + 6*A*b^2*c^2*d^5*e^3 - 4*A*b^3*c*d^4*e^4 + A*b^4*d^3*e^5)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(176*B*b*c^3*d^8 + 176*A*b^4*d^4*e^4 - 2*(61*B*b^2*c^2 + 291*A*b*c^3)*d^7*e + 66*(B*b^3*c + 15*A*b^2*c^2)*d^6*e^2 - (15*B*b^4 + 689*A*b^3*c)*d^5*e^3 + 105*(B*b*c^3*d^5*e^3 - 4*A*b*c^3*d^4*e^4 + 6*A*b^2*c^2*d^3*e^5 - 4*A*b^3*c*d^2*e^6 + A*b^4*d*e^7)*x^3 + 35*(10*B*b*c^3*d^6*e^2 + 60*A*b^2*c^2*d^4*e^4 - 40*A*b^3*c*d^3*e^5 + 10*A*b^4*d^2*e^6 - (B*b^2*c^2 + 39*A*b*c^3)*d^5*e^3)*x^2 + 7*(58*B*b*c^3*d^7*e - 232*A*b^3*c*d^4*e^4 + 58*A*b^4*d^3*e^5 - 8*(2*B*b^2*c^2 + 27*A*b*c^3)*d^6*e^2 + 3*(B*b^3*c + 115*A*b^2*c^2)*d^5*e^3)*x)*sqrt(e*x + d))/(b*c^4*d^13 - 4*b^2*c^3*d^12*e + 6*b^3*c^2*d^11*e^2 - 4*b^4*c*d^10*e^3 + b^5*d^9*e^4 + (b*c^4*d^9*e^4 - 4*b^2*c^3*d^8*e^5 + 6*b^3*c^2*d^7*e^6 - 4*b^4*c*d^6*e^7 + b^5*d^5*e^8)*x^4 + 4*(b*c^4*d^10*e^3 - 4*b^2*c^3*d^9*e^4 + 6*b^3*c^2*d^8*e^5 - 4*b^4*c*d^7*e^6 + b^5*d^6*e^7)*x^3 + 6*(b*c^4*d^11*e^2 - 4*b^2*c^3*d^10*e^3 + 6*b^3*c^2*d^9*e^4 - 4*b^4*c*d^8*e^5 + b^5*d^7*e^6)*x^2 + 4*(b*c^4*d^12*e - 4*b^2*c^3*d^11*e^2 + 6*b^3*c^2*d^10*e^3 - 4*b^4*c*d^9*e^4 + b^5*d^8*e^5)*x), -1/105*(210*((B*b*c^3 - A*c^4)*d^5*e^4*x^4 + 4*(B*b*c^3 - A*c^4)*d^6*e^3*x^3 + 6*(B*b*c^3 - A*c^4)*d^7*e^2*x^2 + 4*(B*b*c^3 - A*c^4)*d^8*e*x + (B*b*c^3 - A*c^4)*d^9)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 105*(A*c^4*d^8 - 4*A*b*c^3*d^7*e + 6*A*b^2*c^2*d^6*e^2 - 4*A*b^3*c*d^5*e^3 + A*b^4*d^4*e^4 + (A*c^4*d^4*e^4 - 4*A*b*c^3*d^3*e^5 + 6*A*b^2*c^2*d^2*e^6 - 4*A*b^3*c*d*e^7 + A*b^4*e^8)*x^4 + 4*(A*c^4*d^5*e^3 - 4*A*b*c^3*d^4*e^4 + 6*A*b^2*c^2*d^3*e^5 - 4*A*b^3*c*d^2*e^6 + A*b^4*d*e^7)*x^3 + 6*(A*c^4*d^6*e^2 - 4*A*b*c^3*d^5*e^3 + 6*A*b^2*c^2*d^4*e^4 - 4*A*b^3*c*d^3*e^5 + A*b^4*d^2*e^6)*x^2 + 4*(A*c^4*d^7*e - 4*A*b*c^3*d^6*e^2 + 6*A*b^2*c^2*d^5*e^3 - 4*A*b^3*c*d^4*e^4 + A*b^4*d^3*e^5)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(176*B*b*c^3*d^8 + 176*A*b^4*d^4*e^4 - 2*(61*B*b^2*c^2 + 291*A*b*c^3)*d^7*e + 66*(B*b^3*c + 15*A*b^2*c^2)*d^6*e^2 - (15*B*b^4 + 689*A*b^3*c)*d^5*e^3 + 105*(B*b*c^3*d^5*e^3 - 4*A*b*c^3*d^4*e^4 + 6*A*b^2*c^2*d^3*e^5 - 4*A*b^3*c*d^2*e^6 + A*b^4*d*e^7)*x^3 + 35*(10*B*b*c^3*d^6*e^2 + 60*A*b^2*c^2*d^4*e^4 - 40*A*b^3*c*d^3*e^5 + 10*A*b^4*d^2*e^6 - (B*b^2*c^2 + 39*A*b*c^3)*d^5*e^3)*x^2 + 7*(58*B*b*c^3*d^7*e - 232*A*b^3*c*d^4*e^4 + 58*A*b^4*d^3*e^5 - 8*(2*B*b^2*c^2 + 27*A*b*c^3)*d^6*e^2 + 3*(B*b^3*c + 115*A*b^2*c^2)*d^5*e^3)*x)*sqrt(e*x + d))/(b*c^4*d^13 - 4*b^2*c^3*d^12*e + 6*b^3*c^2*d^11*e^2 - 4*b^4*c*d^10*e^3 + b^5*d^9*e^4 + (b*c^4*d^9*e^4 - 4*b^2*c^3*d^8*e^5 + 6*b^3*c^2*d^7*e^6 - 4*b^4*c*d^6*e^7 + b^5*d^5*e^8)*x^4 + 4*(b*c^4*d^10*e^3 - 4*b^2*c^3*d^9*e^4 + 6*b^3*c^2*d^8*e^5 - 4*b^4*c*d^7*e^6 + b^5*d^6*e^7)*x^3 + 6*(b*c^4*d^11*e^2 - 4*b^2*c^3*d^10*e^3 + 6*b^3*c^2*d^9*e^4 - 4*b^4*c*d^8*e^5 + b^5*d^7*e^6)*x^2 + 4*(b*c^4*d^12*e - 4*b^2*c^3*d^11*e^2 + 6*b^3*c^2*d^10*e^3 - 4*b^4*c*d^9*e^4 + b^5*d^8*e^5)*x), 1/105*(210*(A*c^4*d^8 - 4*A*b*c^3*d^7*e + 6*A*b^2*c^2*d^6*e^2 - 4*A*b^3*c*d^5*e^3 + A*b^4*d^4*e^4 + (A*c^4*d^4*e^4 - 4*A*b*c^3*d^3*e^5 + 6*A*b^2*c^2*d^2*e^6 - 4*A*b^3*c*d*e^7 + A*b^4*e^8)*x^4 + 4*(A*c^4*d^5*e^3 - 4*A*b*c^3*d^4*e^4 + 6*A*b^2*c^2*d^3*e^5 - 4*A*b^3*c*d^2*e^6 + A*b^4*d*e^7)*x^3 + 6*(A*c^4*d^6*e^2 - 4*A*b*c^3*d^5*e^3 + 6*A*b^2*c^2*d^4*e^4 - 4*A*b^3*c*d^3*e^5 + A*b^4*d^2*e^6)*x^2 + 4*(A*c^4*d^7*e - 4*A*b*c^3*d^6*e^2 + 6*A*b^2*c^2*d^5*e^3 - 4*A*b^3*c*d^4*e^4 + A*b^4*d^3*e^5)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 105*((B*b*c^3 - A*c^4)*d^5*e^4*x^4 + 4*(B*b*c^3 - A*c^4)*d^6*e^3*x^3 + 6*(B*b*c^3 - A*c^4)*d^7*e^2*x^2 + 4*(B*b*c^3 - A*c^4)*d^8*e*x + (B*b*c^3 - A*c^4)*d^9)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(176*B*b*c^3*d^8 + 176*A*b^4*d^4*e^4 - 2*(61*B*b^2*c^2 + 291*A*b*c^3)*d^7*e + 66*(B*b^3*c + 15*A*b^2*c^2)*d^6*e^2 - (15*B*b^4 + 689*A*b^3*c)*d^5*e^3 + 105*(B*b*c^3*d^5*e^3 - 4*A*b*c^3*d^4*e^4 + 6*A*b^2*c^2*d^3*e^5 - 4*A*b^3*c*d^2*e^6 + A*b^4*d*e^7)*x^3 + 35*(10*B*b*c^3*d^6*e^2 + 60*A*b^2*c^2*d^4*e^4 - 40*A*b^3*c*d^3*e^5 + 10*A*b^4*d^2*e^6 - (B*b^2*c^2 + 39*A*b*c^3)*d^5*e^3)*x^2 + 7*(58*B*b*c^3*d^7*e - 232*A*b^3*c*d^4*e^4 + 58*A*b^4*d^3*e^5 - 8*(2*B*b^2*c^2 + 27*A*b*c^3)*d^6*e^2 + 3*(B*b^3*c + 115*A*b^2*c^2)*d^5*e^3)*x)*sqrt(e*x + d))/(b*c^4*d^13 - 4*b^2*c^3*d^12*e + 6*b^3*c^2*d^11*e^2 - 4*b^4*c*d^10*e^3 + b^5*d^9*e^4 + (b*c^4*d^9*e^4 - 4*b^2*c^3*d^8*e^5 + 6*b^3*c^2*d^7*e^6 - 4*b^4*c*d^6*e^7 + b^5*d^5*e^8)*x^4 + 4*(b*c^4*d^10*e^3 - 4*b^2*c^3*d^9*e^4 + 6*b^3*c^2*d^8*e^5 - 4*b^4*c*d^7*e^6 + b^5*d^6*e^7)*x^3 + 6*(b*c^4*d^11*e^2 - 4*b^2*c^3*d^10*e^3 + 6*b^3*c^2*d^9*e^4 - 4*b^4*c*d^8*e^5 + b^5*d^7*e^6)*x^2 + 4*(b*c^4*d^12*e - 4*b^2*c^3*d^11*e^2 + 6*b^3*c^2*d^10*e^3 - 4*b^4*c*d^9*e^4 + b^5*d^8*e^5)*x), -2/105*(105*((B*b*c^3 - A*c^4)*d^5*e^4*x^4 + 4*(B*b*c^3 - A*c^4)*d^6*e^3*x^3 + 6*(B*b*c^3 - A*c^4)*d^7*e^2*x^2 + 4*(B*b*c^3 - A*c^4)*d^8*e*x + (B*b*c^3 - A*c^4)*d^9)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 105*(A*c^4*d^8 - 4*A*b*c^3*d^7*e + 6*A*b^2*c^2*d^6*e^2 - 4*A*b^3*c*d^5*e^3 + A*b^4*d^4*e^4 + (A*c^4*d^4*e^4 - 4*A*b*c^3*d^3*e^5 + 6*A*b^2*c^2*d^2*e^6 - 4*A*b^3*c*d*e^7 + A*b^4*e^8)*x^4 + 4*(A*c^4*d^5*e^3 - 4*A*b*c^3*d^4*e^4 + 6*A*b^2*c^2*d^3*e^5 - 4*A*b^3*c*d^2*e^6 + A*b^4*d*e^7)*x^3 + 6*(A*c^4*d^6*e^2 - 4*A*b*c^3*d^5*e^3 + 6*A*b^2*c^2*d^4*e^4 - 4*A*b^3*c*d^3*e^5 + A*b^4*d^2*e^6)*x^2 + 4*(A*c^4*d^7*e - 4*A*b*c^3*d^6*e^2 + 6*A*b^2*c^2*d^5*e^3 - 4*A*b^3*c*d^4*e^4 + A*b^4*d^3*e^5)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (176*B*b*c^3*d^8 + 176*A*b^4*d^4*e^4 - 2*(61*B*b^2*c^2 + 291*A*b*c^3)*d^7*e + 66*(B*b^3*c + 15*A*b^2*c^2)*d^6*e^2 - (15*B*b^4 + 689*A*b^3*c)*d^5*e^3 + 105*(B*b*c^3*d^5*e^3 - 4*A*b*c^3*d^4*e^4 + 6*A*b^2*c^2*d^3*e^5 - 4*A*b^3*c*d^2*e^6 + A*b^4*d*e^7)*x^3 + 35*(10*B*b*c^3*d^6*e^2 + 60*A*b^2*c^2*d^4*e^4 - 40*A*b^3*c*d^3*e^5 + 10*A*b^4*d^2*e^6 - (B*b^2*c^2 + 39*A*b*c^3)*d^5*e^3)*x^2 + 7*(58*B*b*c^3*d^7*e - 232*A*b^3*c*d^4*e^4 + 58*A*b^4*d^3*e^5 - 8*(2*B*b^2*c^2 + 27*A*b*c^3)*d^6*e^2 + 3*(B*b^3*c + 115*A*b^2*c^2)*d^5*e^3)*x)*sqrt(e*x + d))/(b*c^4*d^13 - 4*b^2*c^3*d^12*e + 6*b^3*c^2*d^11*e^2 - 4*b^4*c*d^10*e^3 + b^5*d^9*e^4 + (b*c^4*d^9*e^4 - 4*b^2*c^3*d^8*e^5 + 6*b^3*c^2*d^7*e^6 - 4*b^4*c*d^6*e^7 + b^5*d^5*e^8)*x^4 + 4*(b*c^4*d^10*e^3 - 4*b^2*c^3*d^9*e^4 + 6*b^3*c^2*d^8*e^5 - 4*b^4*c*d^7*e^6 + b^5*d^6*e^7)*x^3 + 6*(b*c^4*d^11*e^2 - 4*b^2*c^3*d^10*e^3 + 6*b^3*c^2*d^9*e^4 - 4*b^4*c*d^8*e^5 + b^5*d^7*e^6)*x^2 + 4*(b*c^4*d^12*e - 4*b^2*c^3*d^11*e^2 + 6*b^3*c^2*d^10*e^3 - 4*b^4*c*d^9*e^4 + b^5*d^8*e^5)*x)]","B",0
1238,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^(9/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1239,1,2104,0,73.696635," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} + {\left(B b^{2} c^{3} + 5 \, A b c^{4}\right)} d^{2} e - 2 \, {\left(4 \, B b^{3} c^{2} - A b^{2} c^{3}\right)} d e^{2} + {\left(5 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + {\left(B b^{3} c^{2} + 5 \, A b^{2} c^{3}\right)} d^{2} e - 2 \, {\left(4 \, B b^{4} c - A b^{3} c^{2}\right)} d e^{2} + {\left(5 \, B b^{5} - 3 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - 3 \, {\left({\left(7 \, A b c^{4} d^{2} e + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3}\right)} x^{2} + {\left(7 \, A b^{2} c^{3} d^{2} e + 2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, B b^{3} c^{2} e^{3} x^{3} - 3 \, A b^{2} c^{3} d^{3} + 2 \, {\left(10 \, B b^{3} c^{2} d e^{2} - {\left(5 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 9 \, {\left(B b^{3} c^{2} - A b^{2} c^{3}\right)} d^{2} e + {\left(29 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} d e^{2} - 3 \, {\left(5 \, B b^{5} - 3 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{3} c^{4} x^{2} + b^{4} c^{3} x\right)}}, \frac{6 \, {\left({\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} + {\left(B b^{2} c^{3} + 5 \, A b c^{4}\right)} d^{2} e - 2 \, {\left(4 \, B b^{3} c^{2} - A b^{2} c^{3}\right)} d e^{2} + {\left(5 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + {\left(B b^{3} c^{2} + 5 \, A b^{2} c^{3}\right)} d^{2} e - 2 \, {\left(4 \, B b^{4} c - A b^{3} c^{2}\right)} d e^{2} + {\left(5 \, B b^{5} - 3 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 3 \, {\left({\left(7 \, A b c^{4} d^{2} e + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3}\right)} x^{2} + {\left(7 \, A b^{2} c^{3} d^{2} e + 2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, B b^{3} c^{2} e^{3} x^{3} - 3 \, A b^{2} c^{3} d^{3} + 2 \, {\left(10 \, B b^{3} c^{2} d e^{2} - {\left(5 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 9 \, {\left(B b^{3} c^{2} - A b^{2} c^{3}\right)} d^{2} e + {\left(29 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} d e^{2} - 3 \, {\left(5 \, B b^{5} - 3 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{3} c^{4} x^{2} + b^{4} c^{3} x\right)}}, \frac{6 \, {\left({\left(7 \, A b c^{4} d^{2} e + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3}\right)} x^{2} + {\left(7 \, A b^{2} c^{3} d^{2} e + 2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 3 \, {\left({\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} + {\left(B b^{2} c^{3} + 5 \, A b c^{4}\right)} d^{2} e - 2 \, {\left(4 \, B b^{3} c^{2} - A b^{2} c^{3}\right)} d e^{2} + {\left(5 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + {\left(B b^{3} c^{2} + 5 \, A b^{2} c^{3}\right)} d^{2} e - 2 \, {\left(4 \, B b^{4} c - A b^{3} c^{2}\right)} d e^{2} + {\left(5 \, B b^{5} - 3 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(2 \, B b^{3} c^{2} e^{3} x^{3} - 3 \, A b^{2} c^{3} d^{3} + 2 \, {\left(10 \, B b^{3} c^{2} d e^{2} - {\left(5 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 9 \, {\left(B b^{3} c^{2} - A b^{2} c^{3}\right)} d^{2} e + {\left(29 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} d e^{2} - 3 \, {\left(5 \, B b^{5} - 3 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{3} c^{4} x^{2} + b^{4} c^{3} x\right)}}, \frac{3 \, {\left({\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} + {\left(B b^{2} c^{3} + 5 \, A b c^{4}\right)} d^{2} e - 2 \, {\left(4 \, B b^{3} c^{2} - A b^{2} c^{3}\right)} d e^{2} + {\left(5 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + {\left(B b^{3} c^{2} + 5 \, A b^{2} c^{3}\right)} d^{2} e - 2 \, {\left(4 \, B b^{4} c - A b^{3} c^{2}\right)} d e^{2} + {\left(5 \, B b^{5} - 3 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 3 \, {\left({\left(7 \, A b c^{4} d^{2} e + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3}\right)} x^{2} + {\left(7 \, A b^{2} c^{3} d^{2} e + 2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(2 \, B b^{3} c^{2} e^{3} x^{3} - 3 \, A b^{2} c^{3} d^{3} + 2 \, {\left(10 \, B b^{3} c^{2} d e^{2} - {\left(5 \, B b^{4} c - 3 \, A b^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 9 \, {\left(B b^{3} c^{2} - A b^{2} c^{3}\right)} d^{2} e + {\left(29 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} d e^{2} - 3 \, {\left(5 \, B b^{5} - 3 \, A b^{4} c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b^{3} c^{4} x^{2} + b^{4} c^{3} x\right)}}\right]"," ",0,"[-1/6*(3*((2*(B*b*c^4 - 2*A*c^5)*d^3 + (B*b^2*c^3 + 5*A*b*c^4)*d^2*e - 2*(4*B*b^3*c^2 - A*b^2*c^3)*d*e^2 + (5*B*b^4*c - 3*A*b^3*c^2)*e^3)*x^2 + (2*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + (B*b^3*c^2 + 5*A*b^2*c^3)*d^2*e - 2*(4*B*b^4*c - A*b^3*c^2)*d*e^2 + (5*B*b^5 - 3*A*b^4*c)*e^3)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - 3*((7*A*b*c^4*d^2*e + 2*(B*b*c^4 - 2*A*c^5)*d^3)*x^2 + (7*A*b^2*c^3*d^2*e + 2*(B*b^2*c^3 - 2*A*b*c^4)*d^3)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*B*b^3*c^2*e^3*x^3 - 3*A*b^2*c^3*d^3 + 2*(10*B*b^3*c^2*d*e^2 - (5*B*b^4*c - 3*A*b^3*c^2)*e^3)*x^2 + (3*(B*b^2*c^3 - 2*A*b*c^4)*d^3 - 9*(B*b^3*c^2 - A*b^2*c^3)*d^2*e + (29*B*b^4*c - 9*A*b^3*c^2)*d*e^2 - 3*(5*B*b^5 - 3*A*b^4*c)*e^3)*x)*sqrt(e*x + d))/(b^3*c^4*x^2 + b^4*c^3*x), 1/6*(6*((2*(B*b*c^4 - 2*A*c^5)*d^3 + (B*b^2*c^3 + 5*A*b*c^4)*d^2*e - 2*(4*B*b^3*c^2 - A*b^2*c^3)*d*e^2 + (5*B*b^4*c - 3*A*b^3*c^2)*e^3)*x^2 + (2*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + (B*b^3*c^2 + 5*A*b^2*c^3)*d^2*e - 2*(4*B*b^4*c - A*b^3*c^2)*d*e^2 + (5*B*b^5 - 3*A*b^4*c)*e^3)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 3*((7*A*b*c^4*d^2*e + 2*(B*b*c^4 - 2*A*c^5)*d^3)*x^2 + (7*A*b^2*c^3*d^2*e + 2*(B*b^2*c^3 - 2*A*b*c^4)*d^3)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*B*b^3*c^2*e^3*x^3 - 3*A*b^2*c^3*d^3 + 2*(10*B*b^3*c^2*d*e^2 - (5*B*b^4*c - 3*A*b^3*c^2)*e^3)*x^2 + (3*(B*b^2*c^3 - 2*A*b*c^4)*d^3 - 9*(B*b^3*c^2 - A*b^2*c^3)*d^2*e + (29*B*b^4*c - 9*A*b^3*c^2)*d*e^2 - 3*(5*B*b^5 - 3*A*b^4*c)*e^3)*x)*sqrt(e*x + d))/(b^3*c^4*x^2 + b^4*c^3*x), 1/6*(6*((7*A*b*c^4*d^2*e + 2*(B*b*c^4 - 2*A*c^5)*d^3)*x^2 + (7*A*b^2*c^3*d^2*e + 2*(B*b^2*c^3 - 2*A*b*c^4)*d^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 3*((2*(B*b*c^4 - 2*A*c^5)*d^3 + (B*b^2*c^3 + 5*A*b*c^4)*d^2*e - 2*(4*B*b^3*c^2 - A*b^2*c^3)*d*e^2 + (5*B*b^4*c - 3*A*b^3*c^2)*e^3)*x^2 + (2*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + (B*b^3*c^2 + 5*A*b^2*c^3)*d^2*e - 2*(4*B*b^4*c - A*b^3*c^2)*d*e^2 + (5*B*b^5 - 3*A*b^4*c)*e^3)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(2*B*b^3*c^2*e^3*x^3 - 3*A*b^2*c^3*d^3 + 2*(10*B*b^3*c^2*d*e^2 - (5*B*b^4*c - 3*A*b^3*c^2)*e^3)*x^2 + (3*(B*b^2*c^3 - 2*A*b*c^4)*d^3 - 9*(B*b^3*c^2 - A*b^2*c^3)*d^2*e + (29*B*b^4*c - 9*A*b^3*c^2)*d*e^2 - 3*(5*B*b^5 - 3*A*b^4*c)*e^3)*x)*sqrt(e*x + d))/(b^3*c^4*x^2 + b^4*c^3*x), 1/3*(3*((2*(B*b*c^4 - 2*A*c^5)*d^3 + (B*b^2*c^3 + 5*A*b*c^4)*d^2*e - 2*(4*B*b^3*c^2 - A*b^2*c^3)*d*e^2 + (5*B*b^4*c - 3*A*b^3*c^2)*e^3)*x^2 + (2*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + (B*b^3*c^2 + 5*A*b^2*c^3)*d^2*e - 2*(4*B*b^4*c - A*b^3*c^2)*d*e^2 + (5*B*b^5 - 3*A*b^4*c)*e^3)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 3*((7*A*b*c^4*d^2*e + 2*(B*b*c^4 - 2*A*c^5)*d^3)*x^2 + (7*A*b^2*c^3*d^2*e + 2*(B*b^2*c^3 - 2*A*b*c^4)*d^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (2*B*b^3*c^2*e^3*x^3 - 3*A*b^2*c^3*d^3 + 2*(10*B*b^3*c^2*d*e^2 - (5*B*b^4*c - 3*A*b^3*c^2)*e^3)*x^2 + (3*(B*b^2*c^3 - 2*A*b*c^4)*d^3 - 9*(B*b^3*c^2 - A*b^2*c^3)*d^2*e + (29*B*b^4*c - 9*A*b^3*c^2)*d*e^2 - 3*(5*B*b^5 - 3*A*b^4*c)*e^3)*x)*sqrt(e*x + d))/(b^3*c^4*x^2 + b^4*c^3*x)]","A",0
1240,1,1589,0,10.826492," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} + {\left(B b^{2} c^{2} + 3 \, A b c^{3}\right)} d e - {\left(3 \, B b^{3} c - A b^{2} c^{2}\right)} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} + {\left(B b^{3} c + 3 \, A b^{2} c^{2}\right)} d e - {\left(3 \, B b^{4} - A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + {\left({\left(5 \, A b c^{3} d e + 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2}\right)} x^{2} + {\left(5 \, A b^{2} c^{2} d e + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, B b^{3} c e^{2} x^{2} - A b^{2} c^{2} d^{2} + {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} - 2 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e + {\left(3 \, B b^{4} - A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{3} x^{2} + b^{4} c^{2} x\right)}}, \frac{2 \, {\left({\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} + {\left(B b^{2} c^{2} + 3 \, A b c^{3}\right)} d e - {\left(3 \, B b^{3} c - A b^{2} c^{2}\right)} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} + {\left(B b^{3} c + 3 \, A b^{2} c^{2}\right)} d e - {\left(3 \, B b^{4} - A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(5 \, A b c^{3} d e + 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2}\right)} x^{2} + {\left(5 \, A b^{2} c^{2} d e + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, B b^{3} c e^{2} x^{2} - A b^{2} c^{2} d^{2} + {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} - 2 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e + {\left(3 \, B b^{4} - A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{3} x^{2} + b^{4} c^{2} x\right)}}, \frac{2 \, {\left({\left(5 \, A b c^{3} d e + 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2}\right)} x^{2} + {\left(5 \, A b^{2} c^{2} d e + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left({\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} + {\left(B b^{2} c^{2} + 3 \, A b c^{3}\right)} d e - {\left(3 \, B b^{3} c - A b^{2} c^{2}\right)} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} + {\left(B b^{3} c + 3 \, A b^{2} c^{2}\right)} d e - {\left(3 \, B b^{4} - A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(2 \, B b^{3} c e^{2} x^{2} - A b^{2} c^{2} d^{2} + {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} - 2 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e + {\left(3 \, B b^{4} - A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{3} x^{2} + b^{4} c^{2} x\right)}}, \frac{{\left({\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} + {\left(B b^{2} c^{2} + 3 \, A b c^{3}\right)} d e - {\left(3 \, B b^{3} c - A b^{2} c^{2}\right)} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} + {\left(B b^{3} c + 3 \, A b^{2} c^{2}\right)} d e - {\left(3 \, B b^{4} - A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(5 \, A b c^{3} d e + 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2}\right)} x^{2} + {\left(5 \, A b^{2} c^{2} d e + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(2 \, B b^{3} c e^{2} x^{2} - A b^{2} c^{2} d^{2} + {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} - 2 \, {\left(B b^{3} c - A b^{2} c^{2}\right)} d e + {\left(3 \, B b^{4} - A b^{3} c\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{b^{3} c^{3} x^{2} + b^{4} c^{2} x}\right]"," ",0,"[1/2*(((2*(B*b*c^3 - 2*A*c^4)*d^2 + (B*b^2*c^2 + 3*A*b*c^3)*d*e - (3*B*b^3*c - A*b^2*c^2)*e^2)*x^2 + (2*(B*b^2*c^2 - 2*A*b*c^3)*d^2 + (B*b^3*c + 3*A*b^2*c^2)*d*e - (3*B*b^4 - A*b^3*c)*e^2)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + ((5*A*b*c^3*d*e + 2*(B*b*c^3 - 2*A*c^4)*d^2)*x^2 + (5*A*b^2*c^2*d*e + 2*(B*b^2*c^2 - 2*A*b*c^3)*d^2)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*B*b^3*c*e^2*x^2 - A*b^2*c^2*d^2 + ((B*b^2*c^2 - 2*A*b*c^3)*d^2 - 2*(B*b^3*c - A*b^2*c^2)*d*e + (3*B*b^4 - A*b^3*c)*e^2)*x)*sqrt(e*x + d))/(b^3*c^3*x^2 + b^4*c^2*x), 1/2*(2*((2*(B*b*c^3 - 2*A*c^4)*d^2 + (B*b^2*c^2 + 3*A*b*c^3)*d*e - (3*B*b^3*c - A*b^2*c^2)*e^2)*x^2 + (2*(B*b^2*c^2 - 2*A*b*c^3)*d^2 + (B*b^3*c + 3*A*b^2*c^2)*d*e - (3*B*b^4 - A*b^3*c)*e^2)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((5*A*b*c^3*d*e + 2*(B*b*c^3 - 2*A*c^4)*d^2)*x^2 + (5*A*b^2*c^2*d*e + 2*(B*b^2*c^2 - 2*A*b*c^3)*d^2)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*B*b^3*c*e^2*x^2 - A*b^2*c^2*d^2 + ((B*b^2*c^2 - 2*A*b*c^3)*d^2 - 2*(B*b^3*c - A*b^2*c^2)*d*e + (3*B*b^4 - A*b^3*c)*e^2)*x)*sqrt(e*x + d))/(b^3*c^3*x^2 + b^4*c^2*x), 1/2*(2*((5*A*b*c^3*d*e + 2*(B*b*c^3 - 2*A*c^4)*d^2)*x^2 + (5*A*b^2*c^2*d*e + 2*(B*b^2*c^2 - 2*A*b*c^3)*d^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + ((2*(B*b*c^3 - 2*A*c^4)*d^2 + (B*b^2*c^2 + 3*A*b*c^3)*d*e - (3*B*b^3*c - A*b^2*c^2)*e^2)*x^2 + (2*(B*b^2*c^2 - 2*A*b*c^3)*d^2 + (B*b^3*c + 3*A*b^2*c^2)*d*e - (3*B*b^4 - A*b^3*c)*e^2)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(2*B*b^3*c*e^2*x^2 - A*b^2*c^2*d^2 + ((B*b^2*c^2 - 2*A*b*c^3)*d^2 - 2*(B*b^3*c - A*b^2*c^2)*d*e + (3*B*b^4 - A*b^3*c)*e^2)*x)*sqrt(e*x + d))/(b^3*c^3*x^2 + b^4*c^2*x), (((2*(B*b*c^3 - 2*A*c^4)*d^2 + (B*b^2*c^2 + 3*A*b*c^3)*d*e - (3*B*b^3*c - A*b^2*c^2)*e^2)*x^2 + (2*(B*b^2*c^2 - 2*A*b*c^3)*d^2 + (B*b^3*c + 3*A*b^2*c^2)*d*e - (3*B*b^4 - A*b^3*c)*e^2)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((5*A*b*c^3*d*e + 2*(B*b*c^3 - 2*A*c^4)*d^2)*x^2 + (5*A*b^2*c^2*d*e + 2*(B*b^2*c^2 - 2*A*b*c^3)*d^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (2*B*b^3*c*e^2*x^2 - A*b^2*c^2*d^2 + ((B*b^2*c^2 - 2*A*b*c^3)*d^2 - 2*(B*b^3*c - A*b^2*c^2)*d*e + (3*B*b^4 - A*b^3*c)*e^2)*x)*sqrt(e*x + d))/(b^3*c^3*x^2 + b^4*c^2*x)]","A",0
1241,1,1146,0,1.261814," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d + {\left(B b^{2} c + A b c^{2}\right)} e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d + {\left(B b^{3} + A b^{2} c\right)} e\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + {\left({\left(3 \, A b c^{2} e + 2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d\right)} x^{2} + {\left(3 \, A b^{2} c e + 2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(A b^{2} c d - {\left({\left(B b^{2} c - 2 \, A b c^{2}\right)} d - {\left(B b^{3} - A b^{2} c\right)} e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{2} x^{2} + b^{4} c x\right)}}, \frac{2 \, {\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d + {\left(B b^{2} c + A b c^{2}\right)} e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d + {\left(B b^{3} + A b^{2} c\right)} e\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(3 \, A b c^{2} e + 2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d\right)} x^{2} + {\left(3 \, A b^{2} c e + 2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(A b^{2} c d - {\left({\left(B b^{2} c - 2 \, A b c^{2}\right)} d - {\left(B b^{3} - A b^{2} c\right)} e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{2} x^{2} + b^{4} c x\right)}}, \frac{2 \, {\left({\left(3 \, A b c^{2} e + 2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d\right)} x^{2} + {\left(3 \, A b^{2} c e + 2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d + {\left(B b^{2} c + A b c^{2}\right)} e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d + {\left(B b^{3} + A b^{2} c\right)} e\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - 2 \, {\left(A b^{2} c d - {\left({\left(B b^{2} c - 2 \, A b c^{2}\right)} d - {\left(B b^{3} - A b^{2} c\right)} e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{2} x^{2} + b^{4} c x\right)}}, \frac{{\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d + {\left(B b^{2} c + A b c^{2}\right)} e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d + {\left(B b^{3} + A b^{2} c\right)} e\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(3 \, A b c^{2} e + 2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d\right)} x^{2} + {\left(3 \, A b^{2} c e + 2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(A b^{2} c d - {\left({\left(B b^{2} c - 2 \, A b c^{2}\right)} d - {\left(B b^{3} - A b^{2} c\right)} e\right)} x\right)} \sqrt{e x + d}}{b^{3} c^{2} x^{2} + b^{4} c x}\right]"," ",0,"[1/2*(((2*(B*b*c^2 - 2*A*c^3)*d + (B*b^2*c + A*b*c^2)*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d + (B*b^3 + A*b^2*c)*e)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + ((3*A*b*c^2*e + 2*(B*b*c^2 - 2*A*c^3)*d)*x^2 + (3*A*b^2*c*e + 2*(B*b^2*c - 2*A*b*c^2)*d)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(A*b^2*c*d - ((B*b^2*c - 2*A*b*c^2)*d - (B*b^3 - A*b^2*c)*e)*x)*sqrt(e*x + d))/(b^3*c^2*x^2 + b^4*c*x), 1/2*(2*((2*(B*b*c^2 - 2*A*c^3)*d + (B*b^2*c + A*b*c^2)*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d + (B*b^3 + A*b^2*c)*e)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((3*A*b*c^2*e + 2*(B*b*c^2 - 2*A*c^3)*d)*x^2 + (3*A*b^2*c*e + 2*(B*b^2*c - 2*A*b*c^2)*d)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(A*b^2*c*d - ((B*b^2*c - 2*A*b*c^2)*d - (B*b^3 - A*b^2*c)*e)*x)*sqrt(e*x + d))/(b^3*c^2*x^2 + b^4*c*x), 1/2*(2*((3*A*b*c^2*e + 2*(B*b*c^2 - 2*A*c^3)*d)*x^2 + (3*A*b^2*c*e + 2*(B*b^2*c - 2*A*b*c^2)*d)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + ((2*(B*b*c^2 - 2*A*c^3)*d + (B*b^2*c + A*b*c^2)*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d + (B*b^3 + A*b^2*c)*e)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - 2*(A*b^2*c*d - ((B*b^2*c - 2*A*b*c^2)*d - (B*b^3 - A*b^2*c)*e)*x)*sqrt(e*x + d))/(b^3*c^2*x^2 + b^4*c*x), (((2*(B*b*c^2 - 2*A*c^3)*d + (B*b^2*c + A*b*c^2)*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d + (B*b^3 + A*b^2*c)*e)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((3*A*b*c^2*e + 2*(B*b*c^2 - 2*A*c^3)*d)*x^2 + (3*A*b^2*c*e + 2*(B*b^2*c - 2*A*b*c^2)*d)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (A*b^2*c*d - ((B*b^2*c - 2*A*b*c^2)*d - (B*b^3 - A*b^2*c)*e)*x)*sqrt(e*x + d))/(b^3*c^2*x^2 + b^4*c*x)]","A",0
1242,1,1574,0,0.878988," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{\sqrt{c^{2} d - b c e} {\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - {\left(B b^{2} c - 3 \, A b c^{2}\right)} d e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} - {\left(B b^{3} - 3 \, A b^{2} c\right)} d e\right)} x\right)} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{c^{2} d - b c e} \sqrt{e x + d}}{c x + b}\right) - {\left({\left(A b^{2} c^{2} e^{2} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} + {\left(2 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} d e\right)} x^{2} + {\left(A b^{3} c e^{2} - 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} + {\left(2 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} d e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(A b^{2} c^{2} d^{2} - A b^{3} c d e - {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} - {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{3} d^{2} - b^{4} c^{2} d e\right)} x^{2} + {\left(b^{4} c^{2} d^{2} - b^{5} c d e\right)} x\right)}}, -\frac{2 \, \sqrt{-c^{2} d + b c e} {\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - {\left(B b^{2} c - 3 \, A b c^{2}\right)} d e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} - {\left(B b^{3} - 3 \, A b^{2} c\right)} d e\right)} x\right)} \arctan\left(\frac{\sqrt{-c^{2} d + b c e} \sqrt{e x + d}}{c e x + c d}\right) + {\left({\left(A b^{2} c^{2} e^{2} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} + {\left(2 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} d e\right)} x^{2} + {\left(A b^{3} c e^{2} - 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} + {\left(2 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} d e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(A b^{2} c^{2} d^{2} - A b^{3} c d e - {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} - {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{3} d^{2} - b^{4} c^{2} d e\right)} x^{2} + {\left(b^{4} c^{2} d^{2} - b^{5} c d e\right)} x\right)}}, -\frac{2 \, {\left({\left(A b^{2} c^{2} e^{2} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} + {\left(2 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} d e\right)} x^{2} + {\left(A b^{3} c e^{2} - 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} + {\left(2 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} d e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - \sqrt{c^{2} d - b c e} {\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - {\left(B b^{2} c - 3 \, A b c^{2}\right)} d e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} - {\left(B b^{3} - 3 \, A b^{2} c\right)} d e\right)} x\right)} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{c^{2} d - b c e} \sqrt{e x + d}}{c x + b}\right) + 2 \, {\left(A b^{2} c^{2} d^{2} - A b^{3} c d e - {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} - {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{3} d^{2} - b^{4} c^{2} d e\right)} x^{2} + {\left(b^{4} c^{2} d^{2} - b^{5} c d e\right)} x\right)}}, -\frac{\sqrt{-c^{2} d + b c e} {\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - {\left(B b^{2} c - 3 \, A b c^{2}\right)} d e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} - {\left(B b^{3} - 3 \, A b^{2} c\right)} d e\right)} x\right)} \arctan\left(\frac{\sqrt{-c^{2} d + b c e} \sqrt{e x + d}}{c e x + c d}\right) + {\left({\left(A b^{2} c^{2} e^{2} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} + {\left(2 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} d e\right)} x^{2} + {\left(A b^{3} c e^{2} - 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} + {\left(2 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} d e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(A b^{2} c^{2} d^{2} - A b^{3} c d e - {\left({\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{2} - {\left(B b^{3} c - 2 \, A b^{2} c^{2}\right)} d e\right)} x\right)} \sqrt{e x + d}}{{\left(b^{3} c^{3} d^{2} - b^{4} c^{2} d e\right)} x^{2} + {\left(b^{4} c^{2} d^{2} - b^{5} c d e\right)} x}\right]"," ",0,"[1/2*(sqrt(c^2*d - b*c*e)*((2*(B*b*c^2 - 2*A*c^3)*d^2 - (B*b^2*c - 3*A*b*c^2)*d*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d^2 - (B*b^3 - 3*A*b^2*c)*d*e)*x)*log((c*e*x + 2*c*d - b*e + 2*sqrt(c^2*d - b*c*e)*sqrt(e*x + d))/(c*x + b)) - ((A*b^2*c^2*e^2 - 2*(B*b*c^3 - 2*A*c^4)*d^2 + (2*B*b^2*c^2 - 5*A*b*c^3)*d*e)*x^2 + (A*b^3*c*e^2 - 2*(B*b^2*c^2 - 2*A*b*c^3)*d^2 + (2*B*b^3*c - 5*A*b^2*c^2)*d*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(A*b^2*c^2*d^2 - A*b^3*c*d*e - ((B*b^2*c^2 - 2*A*b*c^3)*d^2 - (B*b^3*c - 2*A*b^2*c^2)*d*e)*x)*sqrt(e*x + d))/((b^3*c^3*d^2 - b^4*c^2*d*e)*x^2 + (b^4*c^2*d^2 - b^5*c*d*e)*x), -1/2*(2*sqrt(-c^2*d + b*c*e)*((2*(B*b*c^2 - 2*A*c^3)*d^2 - (B*b^2*c - 3*A*b*c^2)*d*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d^2 - (B*b^3 - 3*A*b^2*c)*d*e)*x)*arctan(sqrt(-c^2*d + b*c*e)*sqrt(e*x + d)/(c*e*x + c*d)) + ((A*b^2*c^2*e^2 - 2*(B*b*c^3 - 2*A*c^4)*d^2 + (2*B*b^2*c^2 - 5*A*b*c^3)*d*e)*x^2 + (A*b^3*c*e^2 - 2*(B*b^2*c^2 - 2*A*b*c^3)*d^2 + (2*B*b^3*c - 5*A*b^2*c^2)*d*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(A*b^2*c^2*d^2 - A*b^3*c*d*e - ((B*b^2*c^2 - 2*A*b*c^3)*d^2 - (B*b^3*c - 2*A*b^2*c^2)*d*e)*x)*sqrt(e*x + d))/((b^3*c^3*d^2 - b^4*c^2*d*e)*x^2 + (b^4*c^2*d^2 - b^5*c*d*e)*x), -1/2*(2*((A*b^2*c^2*e^2 - 2*(B*b*c^3 - 2*A*c^4)*d^2 + (2*B*b^2*c^2 - 5*A*b*c^3)*d*e)*x^2 + (A*b^3*c*e^2 - 2*(B*b^2*c^2 - 2*A*b*c^3)*d^2 + (2*B*b^3*c - 5*A*b^2*c^2)*d*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - sqrt(c^2*d - b*c*e)*((2*(B*b*c^2 - 2*A*c^3)*d^2 - (B*b^2*c - 3*A*b*c^2)*d*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d^2 - (B*b^3 - 3*A*b^2*c)*d*e)*x)*log((c*e*x + 2*c*d - b*e + 2*sqrt(c^2*d - b*c*e)*sqrt(e*x + d))/(c*x + b)) + 2*(A*b^2*c^2*d^2 - A*b^3*c*d*e - ((B*b^2*c^2 - 2*A*b*c^3)*d^2 - (B*b^3*c - 2*A*b^2*c^2)*d*e)*x)*sqrt(e*x + d))/((b^3*c^3*d^2 - b^4*c^2*d*e)*x^2 + (b^4*c^2*d^2 - b^5*c*d*e)*x), -(sqrt(-c^2*d + b*c*e)*((2*(B*b*c^2 - 2*A*c^3)*d^2 - (B*b^2*c - 3*A*b*c^2)*d*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d^2 - (B*b^3 - 3*A*b^2*c)*d*e)*x)*arctan(sqrt(-c^2*d + b*c*e)*sqrt(e*x + d)/(c*e*x + c*d)) + ((A*b^2*c^2*e^2 - 2*(B*b*c^3 - 2*A*c^4)*d^2 + (2*B*b^2*c^2 - 5*A*b*c^3)*d*e)*x^2 + (A*b^3*c*e^2 - 2*(B*b^2*c^2 - 2*A*b*c^3)*d^2 + (2*B*b^3*c - 5*A*b^2*c^2)*d*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (A*b^2*c^2*d^2 - A*b^3*c*d*e - ((B*b^2*c^2 - 2*A*b*c^3)*d^2 - (B*b^3*c - 2*A*b^2*c^2)*d*e)*x)*sqrt(e*x + d))/((b^3*c^3*d^2 - b^4*c^2*d*e)*x^2 + (b^4*c^2*d^2 - b^5*c*d*e)*x)]","B",0
1243,1,1540,0,2.918696," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} - {\left(3 \, B b^{2} c - 5 \, A b c^{2}\right)} d^{2} e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{3} - {\left(3 \, B b^{3} - 5 \, A b^{2} c\right)} d^{2} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + {\left({\left(A b^{2} c e^{2} + 2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - {\left(2 \, B b^{2} c - 3 \, A b c^{2}\right)} d e\right)} x^{2} + {\left(A b^{3} e^{2} + 2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} - {\left(2 \, B b^{3} - 3 \, A b^{2} c\right)} d e\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(A b^{2} c d^{2} - A b^{3} d e - {\left(A b^{2} c d e + {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{2} d^{3} - b^{4} c d^{2} e\right)} x^{2} + {\left(b^{4} c d^{3} - b^{5} d^{2} e\right)} x\right)}}, \frac{2 \, {\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} - {\left(3 \, B b^{2} c - 5 \, A b c^{2}\right)} d^{2} e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{3} - {\left(3 \, B b^{3} - 5 \, A b^{2} c\right)} d^{2} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left({\left(A b^{2} c e^{2} + 2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - {\left(2 \, B b^{2} c - 3 \, A b c^{2}\right)} d e\right)} x^{2} + {\left(A b^{3} e^{2} + 2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} - {\left(2 \, B b^{3} - 3 \, A b^{2} c\right)} d e\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(A b^{2} c d^{2} - A b^{3} d e - {\left(A b^{2} c d e + {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{2} d^{3} - b^{4} c d^{2} e\right)} x^{2} + {\left(b^{4} c d^{3} - b^{5} d^{2} e\right)} x\right)}}, \frac{2 \, {\left({\left(A b^{2} c e^{2} + 2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - {\left(2 \, B b^{2} c - 3 \, A b c^{2}\right)} d e\right)} x^{2} + {\left(A b^{3} e^{2} + 2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} - {\left(2 \, B b^{3} - 3 \, A b^{2} c\right)} d e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} - {\left(3 \, B b^{2} c - 5 \, A b c^{2}\right)} d^{2} e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{3} - {\left(3 \, B b^{3} - 5 \, A b^{2} c\right)} d^{2} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(A b^{2} c d^{2} - A b^{3} d e - {\left(A b^{2} c d e + {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{2} d^{3} - b^{4} c d^{2} e\right)} x^{2} + {\left(b^{4} c d^{3} - b^{5} d^{2} e\right)} x\right)}}, \frac{{\left({\left(2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} - {\left(3 \, B b^{2} c - 5 \, A b c^{2}\right)} d^{2} e\right)} x^{2} + {\left(2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{3} - {\left(3 \, B b^{3} - 5 \, A b^{2} c\right)} d^{2} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + {\left({\left(A b^{2} c e^{2} + 2 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - {\left(2 \, B b^{2} c - 3 \, A b c^{2}\right)} d e\right)} x^{2} + {\left(A b^{3} e^{2} + 2 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} - {\left(2 \, B b^{3} - 3 \, A b^{2} c\right)} d e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(A b^{2} c d^{2} - A b^{3} d e - {\left(A b^{2} c d e + {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{e x + d}}{{\left(b^{3} c^{2} d^{3} - b^{4} c d^{2} e\right)} x^{2} + {\left(b^{4} c d^{3} - b^{5} d^{2} e\right)} x}\right]"," ",0,"[-1/2*(((2*(B*b*c^2 - 2*A*c^3)*d^3 - (3*B*b^2*c - 5*A*b*c^2)*d^2*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d^3 - (3*B*b^3 - 5*A*b^2*c)*d^2*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + ((A*b^2*c*e^2 + 2*(B*b*c^2 - 2*A*c^3)*d^2 - (2*B*b^2*c - 3*A*b*c^2)*d*e)*x^2 + (A*b^3*e^2 + 2*(B*b^2*c - 2*A*b*c^2)*d^2 - (2*B*b^3 - 3*A*b^2*c)*d*e)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(A*b^2*c*d^2 - A*b^3*d*e - (A*b^2*c*d*e + (B*b^2*c - 2*A*b*c^2)*d^2)*x)*sqrt(e*x + d))/((b^3*c^2*d^3 - b^4*c*d^2*e)*x^2 + (b^4*c*d^3 - b^5*d^2*e)*x), 1/2*(2*((2*(B*b*c^2 - 2*A*c^3)*d^3 - (3*B*b^2*c - 5*A*b*c^2)*d^2*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d^3 - (3*B*b^3 - 5*A*b^2*c)*d^2*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - ((A*b^2*c*e^2 + 2*(B*b*c^2 - 2*A*c^3)*d^2 - (2*B*b^2*c - 3*A*b*c^2)*d*e)*x^2 + (A*b^3*e^2 + 2*(B*b^2*c - 2*A*b*c^2)*d^2 - (2*B*b^3 - 3*A*b^2*c)*d*e)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(A*b^2*c*d^2 - A*b^3*d*e - (A*b^2*c*d*e + (B*b^2*c - 2*A*b*c^2)*d^2)*x)*sqrt(e*x + d))/((b^3*c^2*d^3 - b^4*c*d^2*e)*x^2 + (b^4*c*d^3 - b^5*d^2*e)*x), 1/2*(2*((A*b^2*c*e^2 + 2*(B*b*c^2 - 2*A*c^3)*d^2 - (2*B*b^2*c - 3*A*b*c^2)*d*e)*x^2 + (A*b^3*e^2 + 2*(B*b^2*c - 2*A*b*c^2)*d^2 - (2*B*b^3 - 3*A*b^2*c)*d*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - ((2*(B*b*c^2 - 2*A*c^3)*d^3 - (3*B*b^2*c - 5*A*b*c^2)*d^2*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d^3 - (3*B*b^3 - 5*A*b^2*c)*d^2*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(A*b^2*c*d^2 - A*b^3*d*e - (A*b^2*c*d*e + (B*b^2*c - 2*A*b*c^2)*d^2)*x)*sqrt(e*x + d))/((b^3*c^2*d^3 - b^4*c*d^2*e)*x^2 + (b^4*c*d^3 - b^5*d^2*e)*x), (((2*(B*b*c^2 - 2*A*c^3)*d^3 - (3*B*b^2*c - 5*A*b*c^2)*d^2*e)*x^2 + (2*(B*b^2*c - 2*A*b*c^2)*d^3 - (3*B*b^3 - 5*A*b^2*c)*d^2*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + ((A*b^2*c*e^2 + 2*(B*b*c^2 - 2*A*c^3)*d^2 - (2*B*b^2*c - 3*A*b*c^2)*d*e)*x^2 + (A*b^3*e^2 + 2*(B*b^2*c - 2*A*b*c^2)*d^2 - (2*B*b^3 - 3*A*b^2*c)*d*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (A*b^2*c*d^2 - A*b^3*d*e - (A*b^2*c*d*e + (B*b^2*c - 2*A*b*c^2)*d^2)*x)*sqrt(e*x + d))/((b^3*c^2*d^3 - b^4*c*d^2*e)*x^2 + (b^4*c*d^3 - b^5*d^2*e)*x)]","B",0
1244,1,3240,0,18.118788," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} e - {\left(5 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} d^{3} e^{2}\right)} x^{3} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{5} - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{4} e - {\left(5 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{3} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{5} - {\left(5 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{4} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + {\left({\left(3 \, A b^{3} c e^{4} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} e + {\left(4 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} d^{2} e^{2} - 2 \, {\left(B b^{3} c + A b^{2} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(3 \, A b^{4} e^{4} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} + {\left(2 \, B b^{2} c^{2} - A b c^{3}\right)} d^{3} e + {\left(2 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{2} e^{2} - {\left(2 \, B b^{4} - A b^{3} c\right)} d e^{3}\right)} x^{2} + {\left(3 \, A b^{4} d e^{3} - 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{4} + {\left(4 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} d^{3} e - 2 \, {\left(B b^{4} + A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(A b^{2} c^{2} d^{4} - 2 \, A b^{3} c d^{3} e + A b^{4} d^{2} e^{2} + {\left(3 \, A b^{3} c d e^{3} - {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{3} e - 2 \, {\left(B b^{3} c + A b^{2} c^{2}\right)} d^{2} e^{2}\right)} x^{2} - {\left(A b^{2} c^{2} d^{3} e - 3 \, A b^{4} d e^{3} + {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{4} + {\left(2 \, B b^{4} + A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{3} d^{5} e - 2 \, b^{4} c^{2} d^{4} e^{2} + b^{5} c d^{3} e^{3}\right)} x^{3} + {\left(b^{3} c^{3} d^{6} - b^{4} c^{2} d^{5} e - b^{5} c d^{4} e^{2} + b^{6} d^{3} e^{3}\right)} x^{2} + {\left(b^{4} c^{2} d^{6} - 2 \, b^{5} c d^{5} e + b^{6} d^{4} e^{2}\right)} x\right)}}, \frac{2 \, {\left({\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} e - {\left(5 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} d^{3} e^{2}\right)} x^{3} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{5} - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{4} e - {\left(5 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{3} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{5} - {\left(5 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{4} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + {\left({\left(3 \, A b^{3} c e^{4} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} e + {\left(4 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} d^{2} e^{2} - 2 \, {\left(B b^{3} c + A b^{2} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(3 \, A b^{4} e^{4} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} + {\left(2 \, B b^{2} c^{2} - A b c^{3}\right)} d^{3} e + {\left(2 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{2} e^{2} - {\left(2 \, B b^{4} - A b^{3} c\right)} d e^{3}\right)} x^{2} + {\left(3 \, A b^{4} d e^{3} - 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{4} + {\left(4 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} d^{3} e - 2 \, {\left(B b^{4} + A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(A b^{2} c^{2} d^{4} - 2 \, A b^{3} c d^{3} e + A b^{4} d^{2} e^{2} + {\left(3 \, A b^{3} c d e^{3} - {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{3} e - 2 \, {\left(B b^{3} c + A b^{2} c^{2}\right)} d^{2} e^{2}\right)} x^{2} - {\left(A b^{2} c^{2} d^{3} e - 3 \, A b^{4} d e^{3} + {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{4} + {\left(2 \, B b^{4} + A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{3} d^{5} e - 2 \, b^{4} c^{2} d^{4} e^{2} + b^{5} c d^{3} e^{3}\right)} x^{3} + {\left(b^{3} c^{3} d^{6} - b^{4} c^{2} d^{5} e - b^{5} c d^{4} e^{2} + b^{6} d^{3} e^{3}\right)} x^{2} + {\left(b^{4} c^{2} d^{6} - 2 \, b^{5} c d^{5} e + b^{6} d^{4} e^{2}\right)} x\right)}}, -\frac{2 \, {\left({\left(3 \, A b^{3} c e^{4} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} e + {\left(4 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} d^{2} e^{2} - 2 \, {\left(B b^{3} c + A b^{2} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(3 \, A b^{4} e^{4} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} + {\left(2 \, B b^{2} c^{2} - A b c^{3}\right)} d^{3} e + {\left(2 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{2} e^{2} - {\left(2 \, B b^{4} - A b^{3} c\right)} d e^{3}\right)} x^{2} + {\left(3 \, A b^{4} d e^{3} - 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{4} + {\left(4 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} d^{3} e - 2 \, {\left(B b^{4} + A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left({\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} e - {\left(5 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} d^{3} e^{2}\right)} x^{3} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{5} - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{4} e - {\left(5 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{3} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{5} - {\left(5 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{4} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(A b^{2} c^{2} d^{4} - 2 \, A b^{3} c d^{3} e + A b^{4} d^{2} e^{2} + {\left(3 \, A b^{3} c d e^{3} - {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{3} e - 2 \, {\left(B b^{3} c + A b^{2} c^{2}\right)} d^{2} e^{2}\right)} x^{2} - {\left(A b^{2} c^{2} d^{3} e - 3 \, A b^{4} d e^{3} + {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{4} + {\left(2 \, B b^{4} + A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{3} d^{5} e - 2 \, b^{4} c^{2} d^{4} e^{2} + b^{5} c d^{3} e^{3}\right)} x^{3} + {\left(b^{3} c^{3} d^{6} - b^{4} c^{2} d^{5} e - b^{5} c d^{4} e^{2} + b^{6} d^{3} e^{3}\right)} x^{2} + {\left(b^{4} c^{2} d^{6} - 2 \, b^{5} c d^{5} e + b^{6} d^{4} e^{2}\right)} x\right)}}, \frac{{\left({\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} e - {\left(5 \, B b^{2} c^{2} - 7 \, A b c^{3}\right)} d^{3} e^{2}\right)} x^{3} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{5} - 3 \, {\left(B b^{2} c^{2} - A b c^{3}\right)} d^{4} e - {\left(5 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{3} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{5} - {\left(5 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{4} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left({\left(3 \, A b^{3} c e^{4} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} e + {\left(4 \, B b^{2} c^{2} - 5 \, A b c^{3}\right)} d^{2} e^{2} - 2 \, {\left(B b^{3} c + A b^{2} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(3 \, A b^{4} e^{4} - 2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} + {\left(2 \, B b^{2} c^{2} - A b c^{3}\right)} d^{3} e + {\left(2 \, B b^{3} c - 7 \, A b^{2} c^{2}\right)} d^{2} e^{2} - {\left(2 \, B b^{4} - A b^{3} c\right)} d e^{3}\right)} x^{2} + {\left(3 \, A b^{4} d e^{3} - 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{4} + {\left(4 \, B b^{3} c - 5 \, A b^{2} c^{2}\right)} d^{3} e - 2 \, {\left(B b^{4} + A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(A b^{2} c^{2} d^{4} - 2 \, A b^{3} c d^{3} e + A b^{4} d^{2} e^{2} + {\left(3 \, A b^{3} c d e^{3} - {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{3} e - 2 \, {\left(B b^{3} c + A b^{2} c^{2}\right)} d^{2} e^{2}\right)} x^{2} - {\left(A b^{2} c^{2} d^{3} e - 3 \, A b^{4} d e^{3} + {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} d^{4} + {\left(2 \, B b^{4} + A b^{3} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{{\left(b^{3} c^{3} d^{5} e - 2 \, b^{4} c^{2} d^{4} e^{2} + b^{5} c d^{3} e^{3}\right)} x^{3} + {\left(b^{3} c^{3} d^{6} - b^{4} c^{2} d^{5} e - b^{5} c d^{4} e^{2} + b^{6} d^{3} e^{3}\right)} x^{2} + {\left(b^{4} c^{2} d^{6} - 2 \, b^{5} c d^{5} e + b^{6} d^{4} e^{2}\right)} x}\right]"," ",0,"[1/2*(((2*(B*b*c^3 - 2*A*c^4)*d^4*e - (5*B*b^2*c^2 - 7*A*b*c^3)*d^3*e^2)*x^3 + (2*(B*b*c^3 - 2*A*c^4)*d^5 - 3*(B*b^2*c^2 - A*b*c^3)*d^4*e - (5*B*b^3*c - 7*A*b^2*c^2)*d^3*e^2)*x^2 + (2*(B*b^2*c^2 - 2*A*b*c^3)*d^5 - (5*B*b^3*c - 7*A*b^2*c^2)*d^4*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + ((3*A*b^3*c*e^4 - 2*(B*b*c^3 - 2*A*c^4)*d^3*e + (4*B*b^2*c^2 - 5*A*b*c^3)*d^2*e^2 - 2*(B*b^3*c + A*b^2*c^2)*d*e^3)*x^3 + (3*A*b^4*e^4 - 2*(B*b*c^3 - 2*A*c^4)*d^4 + (2*B*b^2*c^2 - A*b*c^3)*d^3*e + (2*B*b^3*c - 7*A*b^2*c^2)*d^2*e^2 - (2*B*b^4 - A*b^3*c)*d*e^3)*x^2 + (3*A*b^4*d*e^3 - 2*(B*b^2*c^2 - 2*A*b*c^3)*d^4 + (4*B*b^3*c - 5*A*b^2*c^2)*d^3*e - 2*(B*b^4 + A*b^3*c)*d^2*e^2)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(A*b^2*c^2*d^4 - 2*A*b^3*c*d^3*e + A*b^4*d^2*e^2 + (3*A*b^3*c*d*e^3 - (B*b^2*c^2 - 2*A*b*c^3)*d^3*e - 2*(B*b^3*c + A*b^2*c^2)*d^2*e^2)*x^2 - (A*b^2*c^2*d^3*e - 3*A*b^4*d*e^3 + (B*b^2*c^2 - 2*A*b*c^3)*d^4 + (2*B*b^4 + A*b^3*c)*d^2*e^2)*x)*sqrt(e*x + d))/((b^3*c^3*d^5*e - 2*b^4*c^2*d^4*e^2 + b^5*c*d^3*e^3)*x^3 + (b^3*c^3*d^6 - b^4*c^2*d^5*e - b^5*c*d^4*e^2 + b^6*d^3*e^3)*x^2 + (b^4*c^2*d^6 - 2*b^5*c*d^5*e + b^6*d^4*e^2)*x), 1/2*(2*((2*(B*b*c^3 - 2*A*c^4)*d^4*e - (5*B*b^2*c^2 - 7*A*b*c^3)*d^3*e^2)*x^3 + (2*(B*b*c^3 - 2*A*c^4)*d^5 - 3*(B*b^2*c^2 - A*b*c^3)*d^4*e - (5*B*b^3*c - 7*A*b^2*c^2)*d^3*e^2)*x^2 + (2*(B*b^2*c^2 - 2*A*b*c^3)*d^5 - (5*B*b^3*c - 7*A*b^2*c^2)*d^4*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + ((3*A*b^3*c*e^4 - 2*(B*b*c^3 - 2*A*c^4)*d^3*e + (4*B*b^2*c^2 - 5*A*b*c^3)*d^2*e^2 - 2*(B*b^3*c + A*b^2*c^2)*d*e^3)*x^3 + (3*A*b^4*e^4 - 2*(B*b*c^3 - 2*A*c^4)*d^4 + (2*B*b^2*c^2 - A*b*c^3)*d^3*e + (2*B*b^3*c - 7*A*b^2*c^2)*d^2*e^2 - (2*B*b^4 - A*b^3*c)*d*e^3)*x^2 + (3*A*b^4*d*e^3 - 2*(B*b^2*c^2 - 2*A*b*c^3)*d^4 + (4*B*b^3*c - 5*A*b^2*c^2)*d^3*e - 2*(B*b^4 + A*b^3*c)*d^2*e^2)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(A*b^2*c^2*d^4 - 2*A*b^3*c*d^3*e + A*b^4*d^2*e^2 + (3*A*b^3*c*d*e^3 - (B*b^2*c^2 - 2*A*b*c^3)*d^3*e - 2*(B*b^3*c + A*b^2*c^2)*d^2*e^2)*x^2 - (A*b^2*c^2*d^3*e - 3*A*b^4*d*e^3 + (B*b^2*c^2 - 2*A*b*c^3)*d^4 + (2*B*b^4 + A*b^3*c)*d^2*e^2)*x)*sqrt(e*x + d))/((b^3*c^3*d^5*e - 2*b^4*c^2*d^4*e^2 + b^5*c*d^3*e^3)*x^3 + (b^3*c^3*d^6 - b^4*c^2*d^5*e - b^5*c*d^4*e^2 + b^6*d^3*e^3)*x^2 + (b^4*c^2*d^6 - 2*b^5*c*d^5*e + b^6*d^4*e^2)*x), -1/2*(2*((3*A*b^3*c*e^4 - 2*(B*b*c^3 - 2*A*c^4)*d^3*e + (4*B*b^2*c^2 - 5*A*b*c^3)*d^2*e^2 - 2*(B*b^3*c + A*b^2*c^2)*d*e^3)*x^3 + (3*A*b^4*e^4 - 2*(B*b*c^3 - 2*A*c^4)*d^4 + (2*B*b^2*c^2 - A*b*c^3)*d^3*e + (2*B*b^3*c - 7*A*b^2*c^2)*d^2*e^2 - (2*B*b^4 - A*b^3*c)*d*e^3)*x^2 + (3*A*b^4*d*e^3 - 2*(B*b^2*c^2 - 2*A*b*c^3)*d^4 + (4*B*b^3*c - 5*A*b^2*c^2)*d^3*e - 2*(B*b^4 + A*b^3*c)*d^2*e^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - ((2*(B*b*c^3 - 2*A*c^4)*d^4*e - (5*B*b^2*c^2 - 7*A*b*c^3)*d^3*e^2)*x^3 + (2*(B*b*c^3 - 2*A*c^4)*d^5 - 3*(B*b^2*c^2 - A*b*c^3)*d^4*e - (5*B*b^3*c - 7*A*b^2*c^2)*d^3*e^2)*x^2 + (2*(B*b^2*c^2 - 2*A*b*c^3)*d^5 - (5*B*b^3*c - 7*A*b^2*c^2)*d^4*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(A*b^2*c^2*d^4 - 2*A*b^3*c*d^3*e + A*b^4*d^2*e^2 + (3*A*b^3*c*d*e^3 - (B*b^2*c^2 - 2*A*b*c^3)*d^3*e - 2*(B*b^3*c + A*b^2*c^2)*d^2*e^2)*x^2 - (A*b^2*c^2*d^3*e - 3*A*b^4*d*e^3 + (B*b^2*c^2 - 2*A*b*c^3)*d^4 + (2*B*b^4 + A*b^3*c)*d^2*e^2)*x)*sqrt(e*x + d))/((b^3*c^3*d^5*e - 2*b^4*c^2*d^4*e^2 + b^5*c*d^3*e^3)*x^3 + (b^3*c^3*d^6 - b^4*c^2*d^5*e - b^5*c*d^4*e^2 + b^6*d^3*e^3)*x^2 + (b^4*c^2*d^6 - 2*b^5*c*d^5*e + b^6*d^4*e^2)*x), (((2*(B*b*c^3 - 2*A*c^4)*d^4*e - (5*B*b^2*c^2 - 7*A*b*c^3)*d^3*e^2)*x^3 + (2*(B*b*c^3 - 2*A*c^4)*d^5 - 3*(B*b^2*c^2 - A*b*c^3)*d^4*e - (5*B*b^3*c - 7*A*b^2*c^2)*d^3*e^2)*x^2 + (2*(B*b^2*c^2 - 2*A*b*c^3)*d^5 - (5*B*b^3*c - 7*A*b^2*c^2)*d^4*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - ((3*A*b^3*c*e^4 - 2*(B*b*c^3 - 2*A*c^4)*d^3*e + (4*B*b^2*c^2 - 5*A*b*c^3)*d^2*e^2 - 2*(B*b^3*c + A*b^2*c^2)*d*e^3)*x^3 + (3*A*b^4*e^4 - 2*(B*b*c^3 - 2*A*c^4)*d^4 + (2*B*b^2*c^2 - A*b*c^3)*d^3*e + (2*B*b^3*c - 7*A*b^2*c^2)*d^2*e^2 - (2*B*b^4 - A*b^3*c)*d*e^3)*x^2 + (3*A*b^4*d*e^3 - 2*(B*b^2*c^2 - 2*A*b*c^3)*d^4 + (4*B*b^3*c - 5*A*b^2*c^2)*d^3*e - 2*(B*b^4 + A*b^3*c)*d^2*e^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (A*b^2*c^2*d^4 - 2*A*b^3*c*d^3*e + A*b^4*d^2*e^2 + (3*A*b^3*c*d*e^3 - (B*b^2*c^2 - 2*A*b*c^3)*d^3*e - 2*(B*b^3*c + A*b^2*c^2)*d^2*e^2)*x^2 - (A*b^2*c^2*d^3*e - 3*A*b^4*d*e^3 + (B*b^2*c^2 - 2*A*b*c^3)*d^4 + (2*B*b^4 + A*b^3*c)*d^2*e^2)*x)*sqrt(e*x + d))/((b^3*c^3*d^5*e - 2*b^4*c^2*d^4*e^2 + b^5*c*d^3*e^3)*x^3 + (b^3*c^3*d^6 - b^4*c^2*d^5*e - b^5*c*d^4*e^2 + b^6*d^3*e^3)*x^2 + (b^4*c^2*d^6 - 2*b^5*c*d^5*e + b^6*d^4*e^2)*x)]","B",0
1245,1,5665,0,49.597607," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e^{2} - {\left(7 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d^{4} e^{3}\right)} x^{4} + {\left(4 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} e - 2 \, {\left(6 \, B b^{2} c^{3} - 7 \, A b c^{4}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{4} e^{3}\right)} x^{3} + {\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{7} - {\left(3 \, B b^{2} c^{3} - A b c^{4}\right)} d^{6} e - 2 \, {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{5} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{7} - {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{6} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 3 \, {\left({\left(5 \, A b^{4} c e^{6} + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} e^{2} - {\left(6 \, B b^{2} c^{3} - 7 \, A b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(2 \, B b^{3} c^{2} + A b^{2} c^{3}\right)} d^{2} e^{4} - {\left(2 \, B b^{4} c + 11 \, A b^{3} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(5 \, A b^{5} e^{6} + 4 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e - 10 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{4} e^{2} + {\left(6 \, B b^{3} c^{2} + 13 \, A b^{2} c^{3}\right)} d^{3} e^{3} + {\left(2 \, B b^{4} c - 19 \, A b^{3} c^{2}\right)} d^{2} e^{4} - {\left(2 \, B b^{5} + A b^{4} c\right)} d e^{5}\right)} x^{3} + {\left(10 \, A b^{5} d e^{5} + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} - {\left(2 \, B b^{2} c^{3} + A b c^{4}\right)} d^{5} e - {\left(6 \, B b^{3} c^{2} - 17 \, A b^{2} c^{3}\right)} d^{4} e^{2} + 5 \, {\left(2 \, B b^{4} c - A b^{3} c^{2}\right)} d^{3} e^{3} - {\left(4 \, B b^{5} + 17 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(5 \, A b^{5} d^{2} e^{4} + 2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{6} - {\left(6 \, B b^{3} c^{2} - 7 \, A b^{2} c^{3}\right)} d^{5} e + 3 \, {\left(2 \, B b^{4} c + A b^{3} c^{2}\right)} d^{4} e^{2} - {\left(2 \, B b^{5} + 11 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(3 \, A b^{2} c^{3} d^{6} - 9 \, A b^{3} c^{2} d^{5} e + 9 \, A b^{4} c d^{4} e^{2} - 3 \, A b^{5} d^{3} e^{3} - 3 \, {\left(5 \, A b^{4} c d e^{5} + {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} e^{2} + 3 \, {\left(2 \, B b^{3} c^{2} + A b^{2} c^{3}\right)} d^{3} e^{3} - {\left(2 \, B b^{4} c + 11 \, A b^{3} c^{2}\right)} d^{2} e^{4}\right)} x^{3} - {\left(15 \, A b^{5} d e^{5} + 6 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{5} e + 5 \, {\left(4 \, B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} d^{4} e^{2} + 5 \, {\left(2 \, B b^{4} c - 7 \, A b^{3} c^{2}\right)} d^{3} e^{3} - {\left(6 \, B b^{5} + 13 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} - {\left(3 \, A b^{2} c^{3} d^{5} e + 20 \, A b^{5} d^{2} e^{4} + 3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{6} + {\left(20 \, B b^{4} c + 9 \, A b^{3} c^{2}\right)} d^{4} e^{2} - {\left(8 \, B b^{5} + 41 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left({\left(b^{3} c^{4} d^{7} e^{2} - 3 \, b^{4} c^{3} d^{6} e^{3} + 3 \, b^{5} c^{2} d^{5} e^{4} - b^{6} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{3} c^{4} d^{8} e - 5 \, b^{4} c^{3} d^{7} e^{2} + 3 \, b^{5} c^{2} d^{6} e^{3} + b^{6} c d^{5} e^{4} - b^{7} d^{4} e^{5}\right)} x^{3} + {\left(b^{3} c^{4} d^{9} - b^{4} c^{3} d^{8} e - 3 \, b^{5} c^{2} d^{7} e^{2} + 5 \, b^{6} c d^{6} e^{3} - 2 \, b^{7} d^{5} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{9} - 3 \, b^{5} c^{2} d^{8} e + 3 \, b^{6} c d^{7} e^{2} - b^{7} d^{6} e^{3}\right)} x\right)}}, \frac{6 \, {\left({\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e^{2} - {\left(7 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d^{4} e^{3}\right)} x^{4} + {\left(4 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} e - 2 \, {\left(6 \, B b^{2} c^{3} - 7 \, A b c^{4}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{4} e^{3}\right)} x^{3} + {\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{7} - {\left(3 \, B b^{2} c^{3} - A b c^{4}\right)} d^{6} e - 2 \, {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{5} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{7} - {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{6} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 3 \, {\left({\left(5 \, A b^{4} c e^{6} + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} e^{2} - {\left(6 \, B b^{2} c^{3} - 7 \, A b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(2 \, B b^{3} c^{2} + A b^{2} c^{3}\right)} d^{2} e^{4} - {\left(2 \, B b^{4} c + 11 \, A b^{3} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(5 \, A b^{5} e^{6} + 4 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e - 10 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{4} e^{2} + {\left(6 \, B b^{3} c^{2} + 13 \, A b^{2} c^{3}\right)} d^{3} e^{3} + {\left(2 \, B b^{4} c - 19 \, A b^{3} c^{2}\right)} d^{2} e^{4} - {\left(2 \, B b^{5} + A b^{4} c\right)} d e^{5}\right)} x^{3} + {\left(10 \, A b^{5} d e^{5} + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} - {\left(2 \, B b^{2} c^{3} + A b c^{4}\right)} d^{5} e - {\left(6 \, B b^{3} c^{2} - 17 \, A b^{2} c^{3}\right)} d^{4} e^{2} + 5 \, {\left(2 \, B b^{4} c - A b^{3} c^{2}\right)} d^{3} e^{3} - {\left(4 \, B b^{5} + 17 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(5 \, A b^{5} d^{2} e^{4} + 2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{6} - {\left(6 \, B b^{3} c^{2} - 7 \, A b^{2} c^{3}\right)} d^{5} e + 3 \, {\left(2 \, B b^{4} c + A b^{3} c^{2}\right)} d^{4} e^{2} - {\left(2 \, B b^{5} + 11 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(3 \, A b^{2} c^{3} d^{6} - 9 \, A b^{3} c^{2} d^{5} e + 9 \, A b^{4} c d^{4} e^{2} - 3 \, A b^{5} d^{3} e^{3} - 3 \, {\left(5 \, A b^{4} c d e^{5} + {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} e^{2} + 3 \, {\left(2 \, B b^{3} c^{2} + A b^{2} c^{3}\right)} d^{3} e^{3} - {\left(2 \, B b^{4} c + 11 \, A b^{3} c^{2}\right)} d^{2} e^{4}\right)} x^{3} - {\left(15 \, A b^{5} d e^{5} + 6 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{5} e + 5 \, {\left(4 \, B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} d^{4} e^{2} + 5 \, {\left(2 \, B b^{4} c - 7 \, A b^{3} c^{2}\right)} d^{3} e^{3} - {\left(6 \, B b^{5} + 13 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} - {\left(3 \, A b^{2} c^{3} d^{5} e + 20 \, A b^{5} d^{2} e^{4} + 3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{6} + {\left(20 \, B b^{4} c + 9 \, A b^{3} c^{2}\right)} d^{4} e^{2} - {\left(8 \, B b^{5} + 41 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left({\left(b^{3} c^{4} d^{7} e^{2} - 3 \, b^{4} c^{3} d^{6} e^{3} + 3 \, b^{5} c^{2} d^{5} e^{4} - b^{6} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{3} c^{4} d^{8} e - 5 \, b^{4} c^{3} d^{7} e^{2} + 3 \, b^{5} c^{2} d^{6} e^{3} + b^{6} c d^{5} e^{4} - b^{7} d^{4} e^{5}\right)} x^{3} + {\left(b^{3} c^{4} d^{9} - b^{4} c^{3} d^{8} e - 3 \, b^{5} c^{2} d^{7} e^{2} + 5 \, b^{6} c d^{6} e^{3} - 2 \, b^{7} d^{5} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{9} - 3 \, b^{5} c^{2} d^{8} e + 3 \, b^{6} c d^{7} e^{2} - b^{7} d^{6} e^{3}\right)} x\right)}}, \frac{6 \, {\left({\left(5 \, A b^{4} c e^{6} + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} e^{2} - {\left(6 \, B b^{2} c^{3} - 7 \, A b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(2 \, B b^{3} c^{2} + A b^{2} c^{3}\right)} d^{2} e^{4} - {\left(2 \, B b^{4} c + 11 \, A b^{3} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(5 \, A b^{5} e^{6} + 4 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e - 10 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{4} e^{2} + {\left(6 \, B b^{3} c^{2} + 13 \, A b^{2} c^{3}\right)} d^{3} e^{3} + {\left(2 \, B b^{4} c - 19 \, A b^{3} c^{2}\right)} d^{2} e^{4} - {\left(2 \, B b^{5} + A b^{4} c\right)} d e^{5}\right)} x^{3} + {\left(10 \, A b^{5} d e^{5} + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} - {\left(2 \, B b^{2} c^{3} + A b c^{4}\right)} d^{5} e - {\left(6 \, B b^{3} c^{2} - 17 \, A b^{2} c^{3}\right)} d^{4} e^{2} + 5 \, {\left(2 \, B b^{4} c - A b^{3} c^{2}\right)} d^{3} e^{3} - {\left(4 \, B b^{5} + 17 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(5 \, A b^{5} d^{2} e^{4} + 2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{6} - {\left(6 \, B b^{3} c^{2} - 7 \, A b^{2} c^{3}\right)} d^{5} e + 3 \, {\left(2 \, B b^{4} c + A b^{3} c^{2}\right)} d^{4} e^{2} - {\left(2 \, B b^{5} + 11 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 3 \, {\left({\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e^{2} - {\left(7 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d^{4} e^{3}\right)} x^{4} + {\left(4 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} e - 2 \, {\left(6 \, B b^{2} c^{3} - 7 \, A b c^{4}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{4} e^{3}\right)} x^{3} + {\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{7} - {\left(3 \, B b^{2} c^{3} - A b c^{4}\right)} d^{6} e - 2 \, {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{5} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{7} - {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{6} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(3 \, A b^{2} c^{3} d^{6} - 9 \, A b^{3} c^{2} d^{5} e + 9 \, A b^{4} c d^{4} e^{2} - 3 \, A b^{5} d^{3} e^{3} - 3 \, {\left(5 \, A b^{4} c d e^{5} + {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} e^{2} + 3 \, {\left(2 \, B b^{3} c^{2} + A b^{2} c^{3}\right)} d^{3} e^{3} - {\left(2 \, B b^{4} c + 11 \, A b^{3} c^{2}\right)} d^{2} e^{4}\right)} x^{3} - {\left(15 \, A b^{5} d e^{5} + 6 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{5} e + 5 \, {\left(4 \, B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} d^{4} e^{2} + 5 \, {\left(2 \, B b^{4} c - 7 \, A b^{3} c^{2}\right)} d^{3} e^{3} - {\left(6 \, B b^{5} + 13 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} - {\left(3 \, A b^{2} c^{3} d^{5} e + 20 \, A b^{5} d^{2} e^{4} + 3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{6} + {\left(20 \, B b^{4} c + 9 \, A b^{3} c^{2}\right)} d^{4} e^{2} - {\left(8 \, B b^{5} + 41 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left({\left(b^{3} c^{4} d^{7} e^{2} - 3 \, b^{4} c^{3} d^{6} e^{3} + 3 \, b^{5} c^{2} d^{5} e^{4} - b^{6} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{3} c^{4} d^{8} e - 5 \, b^{4} c^{3} d^{7} e^{2} + 3 \, b^{5} c^{2} d^{6} e^{3} + b^{6} c d^{5} e^{4} - b^{7} d^{4} e^{5}\right)} x^{3} + {\left(b^{3} c^{4} d^{9} - b^{4} c^{3} d^{8} e - 3 \, b^{5} c^{2} d^{7} e^{2} + 5 \, b^{6} c d^{6} e^{3} - 2 \, b^{7} d^{5} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{9} - 3 \, b^{5} c^{2} d^{8} e + 3 \, b^{6} c d^{7} e^{2} - b^{7} d^{6} e^{3}\right)} x\right)}}, \frac{3 \, {\left({\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e^{2} - {\left(7 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d^{4} e^{3}\right)} x^{4} + {\left(4 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} e - 2 \, {\left(6 \, B b^{2} c^{3} - 7 \, A b c^{4}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{4} e^{3}\right)} x^{3} + {\left(2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{7} - {\left(3 \, B b^{2} c^{3} - A b c^{4}\right)} d^{6} e - 2 \, {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{5} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{7} - {\left(7 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d^{6} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(5 \, A b^{4} c e^{6} + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} e^{2} - {\left(6 \, B b^{2} c^{3} - 7 \, A b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(2 \, B b^{3} c^{2} + A b^{2} c^{3}\right)} d^{2} e^{4} - {\left(2 \, B b^{4} c + 11 \, A b^{3} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(5 \, A b^{5} e^{6} + 4 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e - 10 \, {\left(B b^{2} c^{3} - A b c^{4}\right)} d^{4} e^{2} + {\left(6 \, B b^{3} c^{2} + 13 \, A b^{2} c^{3}\right)} d^{3} e^{3} + {\left(2 \, B b^{4} c - 19 \, A b^{3} c^{2}\right)} d^{2} e^{4} - {\left(2 \, B b^{5} + A b^{4} c\right)} d e^{5}\right)} x^{3} + {\left(10 \, A b^{5} d e^{5} + 2 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} - {\left(2 \, B b^{2} c^{3} + A b c^{4}\right)} d^{5} e - {\left(6 \, B b^{3} c^{2} - 17 \, A b^{2} c^{3}\right)} d^{4} e^{2} + 5 \, {\left(2 \, B b^{4} c - A b^{3} c^{2}\right)} d^{3} e^{3} - {\left(4 \, B b^{5} + 17 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(5 \, A b^{5} d^{2} e^{4} + 2 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{6} - {\left(6 \, B b^{3} c^{2} - 7 \, A b^{2} c^{3}\right)} d^{5} e + 3 \, {\left(2 \, B b^{4} c + A b^{3} c^{2}\right)} d^{4} e^{2} - {\left(2 \, B b^{5} + 11 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(3 \, A b^{2} c^{3} d^{6} - 9 \, A b^{3} c^{2} d^{5} e + 9 \, A b^{4} c d^{4} e^{2} - 3 \, A b^{5} d^{3} e^{3} - 3 \, {\left(5 \, A b^{4} c d e^{5} + {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} e^{2} + 3 \, {\left(2 \, B b^{3} c^{2} + A b^{2} c^{3}\right)} d^{3} e^{3} - {\left(2 \, B b^{4} c + 11 \, A b^{3} c^{2}\right)} d^{2} e^{4}\right)} x^{3} - {\left(15 \, A b^{5} d e^{5} + 6 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{5} e + 5 \, {\left(4 \, B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} d^{4} e^{2} + 5 \, {\left(2 \, B b^{4} c - 7 \, A b^{3} c^{2}\right)} d^{3} e^{3} - {\left(6 \, B b^{5} + 13 \, A b^{4} c\right)} d^{2} e^{4}\right)} x^{2} - {\left(3 \, A b^{2} c^{3} d^{5} e + 20 \, A b^{5} d^{2} e^{4} + 3 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{6} + {\left(20 \, B b^{4} c + 9 \, A b^{3} c^{2}\right)} d^{4} e^{2} - {\left(8 \, B b^{5} + 41 \, A b^{4} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left({\left(b^{3} c^{4} d^{7} e^{2} - 3 \, b^{4} c^{3} d^{6} e^{3} + 3 \, b^{5} c^{2} d^{5} e^{4} - b^{6} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{3} c^{4} d^{8} e - 5 \, b^{4} c^{3} d^{7} e^{2} + 3 \, b^{5} c^{2} d^{6} e^{3} + b^{6} c d^{5} e^{4} - b^{7} d^{4} e^{5}\right)} x^{3} + {\left(b^{3} c^{4} d^{9} - b^{4} c^{3} d^{8} e - 3 \, b^{5} c^{2} d^{7} e^{2} + 5 \, b^{6} c d^{6} e^{3} - 2 \, b^{7} d^{5} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{9} - 3 \, b^{5} c^{2} d^{8} e + 3 \, b^{6} c d^{7} e^{2} - b^{7} d^{6} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/6*(3*((2*(B*b*c^4 - 2*A*c^5)*d^5*e^2 - (7*B*b^2*c^3 - 9*A*b*c^4)*d^4*e^3)*x^4 + (4*(B*b*c^4 - 2*A*c^5)*d^6*e - 2*(6*B*b^2*c^3 - 7*A*b*c^4)*d^5*e^2 - (7*B*b^3*c^2 - 9*A*b^2*c^3)*d^4*e^3)*x^3 + (2*(B*b*c^4 - 2*A*c^5)*d^7 - (3*B*b^2*c^3 - A*b*c^4)*d^6*e - 2*(7*B*b^3*c^2 - 9*A*b^2*c^3)*d^5*e^2)*x^2 + (2*(B*b^2*c^3 - 2*A*b*c^4)*d^7 - (7*B*b^3*c^2 - 9*A*b^2*c^3)*d^6*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 3*((5*A*b^4*c*e^6 + 2*(B*b*c^4 - 2*A*c^5)*d^4*e^2 - (6*B*b^2*c^3 - 7*A*b*c^4)*d^3*e^3 + 3*(2*B*b^3*c^2 + A*b^2*c^3)*d^2*e^4 - (2*B*b^4*c + 11*A*b^3*c^2)*d*e^5)*x^4 + (5*A*b^5*e^6 + 4*(B*b*c^4 - 2*A*c^5)*d^5*e - 10*(B*b^2*c^3 - A*b*c^4)*d^4*e^2 + (6*B*b^3*c^2 + 13*A*b^2*c^3)*d^3*e^3 + (2*B*b^4*c - 19*A*b^3*c^2)*d^2*e^4 - (2*B*b^5 + A*b^4*c)*d*e^5)*x^3 + (10*A*b^5*d*e^5 + 2*(B*b*c^4 - 2*A*c^5)*d^6 - (2*B*b^2*c^3 + A*b*c^4)*d^5*e - (6*B*b^3*c^2 - 17*A*b^2*c^3)*d^4*e^2 + 5*(2*B*b^4*c - A*b^3*c^2)*d^3*e^3 - (4*B*b^5 + 17*A*b^4*c)*d^2*e^4)*x^2 + (5*A*b^5*d^2*e^4 + 2*(B*b^2*c^3 - 2*A*b*c^4)*d^6 - (6*B*b^3*c^2 - 7*A*b^2*c^3)*d^5*e + 3*(2*B*b^4*c + A*b^3*c^2)*d^4*e^2 - (2*B*b^5 + 11*A*b^4*c)*d^3*e^3)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(3*A*b^2*c^3*d^6 - 9*A*b^3*c^2*d^5*e + 9*A*b^4*c*d^4*e^2 - 3*A*b^5*d^3*e^3 - 3*(5*A*b^4*c*d*e^5 + (B*b^2*c^3 - 2*A*b*c^4)*d^4*e^2 + 3*(2*B*b^3*c^2 + A*b^2*c^3)*d^3*e^3 - (2*B*b^4*c + 11*A*b^3*c^2)*d^2*e^4)*x^3 - (15*A*b^5*d*e^5 + 6*(B*b^2*c^3 - 2*A*b*c^4)*d^5*e + 5*(4*B*b^3*c^2 + 3*A*b^2*c^3)*d^4*e^2 + 5*(2*B*b^4*c - 7*A*b^3*c^2)*d^3*e^3 - (6*B*b^5 + 13*A*b^4*c)*d^2*e^4)*x^2 - (3*A*b^2*c^3*d^5*e + 20*A*b^5*d^2*e^4 + 3*(B*b^2*c^3 - 2*A*b*c^4)*d^6 + (20*B*b^4*c + 9*A*b^3*c^2)*d^4*e^2 - (8*B*b^5 + 41*A*b^4*c)*d^3*e^3)*x)*sqrt(e*x + d))/((b^3*c^4*d^7*e^2 - 3*b^4*c^3*d^6*e^3 + 3*b^5*c^2*d^5*e^4 - b^6*c*d^4*e^5)*x^4 + (2*b^3*c^4*d^8*e - 5*b^4*c^3*d^7*e^2 + 3*b^5*c^2*d^6*e^3 + b^6*c*d^5*e^4 - b^7*d^4*e^5)*x^3 + (b^3*c^4*d^9 - b^4*c^3*d^8*e - 3*b^5*c^2*d^7*e^2 + 5*b^6*c*d^6*e^3 - 2*b^7*d^5*e^4)*x^2 + (b^4*c^3*d^9 - 3*b^5*c^2*d^8*e + 3*b^6*c*d^7*e^2 - b^7*d^6*e^3)*x), 1/6*(6*((2*(B*b*c^4 - 2*A*c^5)*d^5*e^2 - (7*B*b^2*c^3 - 9*A*b*c^4)*d^4*e^3)*x^4 + (4*(B*b*c^4 - 2*A*c^5)*d^6*e - 2*(6*B*b^2*c^3 - 7*A*b*c^4)*d^5*e^2 - (7*B*b^3*c^2 - 9*A*b^2*c^3)*d^4*e^3)*x^3 + (2*(B*b*c^4 - 2*A*c^5)*d^7 - (3*B*b^2*c^3 - A*b*c^4)*d^6*e - 2*(7*B*b^3*c^2 - 9*A*b^2*c^3)*d^5*e^2)*x^2 + (2*(B*b^2*c^3 - 2*A*b*c^4)*d^7 - (7*B*b^3*c^2 - 9*A*b^2*c^3)*d^6*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 3*((5*A*b^4*c*e^6 + 2*(B*b*c^4 - 2*A*c^5)*d^4*e^2 - (6*B*b^2*c^3 - 7*A*b*c^4)*d^3*e^3 + 3*(2*B*b^3*c^2 + A*b^2*c^3)*d^2*e^4 - (2*B*b^4*c + 11*A*b^3*c^2)*d*e^5)*x^4 + (5*A*b^5*e^6 + 4*(B*b*c^4 - 2*A*c^5)*d^5*e - 10*(B*b^2*c^3 - A*b*c^4)*d^4*e^2 + (6*B*b^3*c^2 + 13*A*b^2*c^3)*d^3*e^3 + (2*B*b^4*c - 19*A*b^3*c^2)*d^2*e^4 - (2*B*b^5 + A*b^4*c)*d*e^5)*x^3 + (10*A*b^5*d*e^5 + 2*(B*b*c^4 - 2*A*c^5)*d^6 - (2*B*b^2*c^3 + A*b*c^4)*d^5*e - (6*B*b^3*c^2 - 17*A*b^2*c^3)*d^4*e^2 + 5*(2*B*b^4*c - A*b^3*c^2)*d^3*e^3 - (4*B*b^5 + 17*A*b^4*c)*d^2*e^4)*x^2 + (5*A*b^5*d^2*e^4 + 2*(B*b^2*c^3 - 2*A*b*c^4)*d^6 - (6*B*b^3*c^2 - 7*A*b^2*c^3)*d^5*e + 3*(2*B*b^4*c + A*b^3*c^2)*d^4*e^2 - (2*B*b^5 + 11*A*b^4*c)*d^3*e^3)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(3*A*b^2*c^3*d^6 - 9*A*b^3*c^2*d^5*e + 9*A*b^4*c*d^4*e^2 - 3*A*b^5*d^3*e^3 - 3*(5*A*b^4*c*d*e^5 + (B*b^2*c^3 - 2*A*b*c^4)*d^4*e^2 + 3*(2*B*b^3*c^2 + A*b^2*c^3)*d^3*e^3 - (2*B*b^4*c + 11*A*b^3*c^2)*d^2*e^4)*x^3 - (15*A*b^5*d*e^5 + 6*(B*b^2*c^3 - 2*A*b*c^4)*d^5*e + 5*(4*B*b^3*c^2 + 3*A*b^2*c^3)*d^4*e^2 + 5*(2*B*b^4*c - 7*A*b^3*c^2)*d^3*e^3 - (6*B*b^5 + 13*A*b^4*c)*d^2*e^4)*x^2 - (3*A*b^2*c^3*d^5*e + 20*A*b^5*d^2*e^4 + 3*(B*b^2*c^3 - 2*A*b*c^4)*d^6 + (20*B*b^4*c + 9*A*b^3*c^2)*d^4*e^2 - (8*B*b^5 + 41*A*b^4*c)*d^3*e^3)*x)*sqrt(e*x + d))/((b^3*c^4*d^7*e^2 - 3*b^4*c^3*d^6*e^3 + 3*b^5*c^2*d^5*e^4 - b^6*c*d^4*e^5)*x^4 + (2*b^3*c^4*d^8*e - 5*b^4*c^3*d^7*e^2 + 3*b^5*c^2*d^6*e^3 + b^6*c*d^5*e^4 - b^7*d^4*e^5)*x^3 + (b^3*c^4*d^9 - b^4*c^3*d^8*e - 3*b^5*c^2*d^7*e^2 + 5*b^6*c*d^6*e^3 - 2*b^7*d^5*e^4)*x^2 + (b^4*c^3*d^9 - 3*b^5*c^2*d^8*e + 3*b^6*c*d^7*e^2 - b^7*d^6*e^3)*x), 1/6*(6*((5*A*b^4*c*e^6 + 2*(B*b*c^4 - 2*A*c^5)*d^4*e^2 - (6*B*b^2*c^3 - 7*A*b*c^4)*d^3*e^3 + 3*(2*B*b^3*c^2 + A*b^2*c^3)*d^2*e^4 - (2*B*b^4*c + 11*A*b^3*c^2)*d*e^5)*x^4 + (5*A*b^5*e^6 + 4*(B*b*c^4 - 2*A*c^5)*d^5*e - 10*(B*b^2*c^3 - A*b*c^4)*d^4*e^2 + (6*B*b^3*c^2 + 13*A*b^2*c^3)*d^3*e^3 + (2*B*b^4*c - 19*A*b^3*c^2)*d^2*e^4 - (2*B*b^5 + A*b^4*c)*d*e^5)*x^3 + (10*A*b^5*d*e^5 + 2*(B*b*c^4 - 2*A*c^5)*d^6 - (2*B*b^2*c^3 + A*b*c^4)*d^5*e - (6*B*b^3*c^2 - 17*A*b^2*c^3)*d^4*e^2 + 5*(2*B*b^4*c - A*b^3*c^2)*d^3*e^3 - (4*B*b^5 + 17*A*b^4*c)*d^2*e^4)*x^2 + (5*A*b^5*d^2*e^4 + 2*(B*b^2*c^3 - 2*A*b*c^4)*d^6 - (6*B*b^3*c^2 - 7*A*b^2*c^3)*d^5*e + 3*(2*B*b^4*c + A*b^3*c^2)*d^4*e^2 - (2*B*b^5 + 11*A*b^4*c)*d^3*e^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 3*((2*(B*b*c^4 - 2*A*c^5)*d^5*e^2 - (7*B*b^2*c^3 - 9*A*b*c^4)*d^4*e^3)*x^4 + (4*(B*b*c^4 - 2*A*c^5)*d^6*e - 2*(6*B*b^2*c^3 - 7*A*b*c^4)*d^5*e^2 - (7*B*b^3*c^2 - 9*A*b^2*c^3)*d^4*e^3)*x^3 + (2*(B*b*c^4 - 2*A*c^5)*d^7 - (3*B*b^2*c^3 - A*b*c^4)*d^6*e - 2*(7*B*b^3*c^2 - 9*A*b^2*c^3)*d^5*e^2)*x^2 + (2*(B*b^2*c^3 - 2*A*b*c^4)*d^7 - (7*B*b^3*c^2 - 9*A*b^2*c^3)*d^6*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(3*A*b^2*c^3*d^6 - 9*A*b^3*c^2*d^5*e + 9*A*b^4*c*d^4*e^2 - 3*A*b^5*d^3*e^3 - 3*(5*A*b^4*c*d*e^5 + (B*b^2*c^3 - 2*A*b*c^4)*d^4*e^2 + 3*(2*B*b^3*c^2 + A*b^2*c^3)*d^3*e^3 - (2*B*b^4*c + 11*A*b^3*c^2)*d^2*e^4)*x^3 - (15*A*b^5*d*e^5 + 6*(B*b^2*c^3 - 2*A*b*c^4)*d^5*e + 5*(4*B*b^3*c^2 + 3*A*b^2*c^3)*d^4*e^2 + 5*(2*B*b^4*c - 7*A*b^3*c^2)*d^3*e^3 - (6*B*b^5 + 13*A*b^4*c)*d^2*e^4)*x^2 - (3*A*b^2*c^3*d^5*e + 20*A*b^5*d^2*e^4 + 3*(B*b^2*c^3 - 2*A*b*c^4)*d^6 + (20*B*b^4*c + 9*A*b^3*c^2)*d^4*e^2 - (8*B*b^5 + 41*A*b^4*c)*d^3*e^3)*x)*sqrt(e*x + d))/((b^3*c^4*d^7*e^2 - 3*b^4*c^3*d^6*e^3 + 3*b^5*c^2*d^5*e^4 - b^6*c*d^4*e^5)*x^4 + (2*b^3*c^4*d^8*e - 5*b^4*c^3*d^7*e^2 + 3*b^5*c^2*d^6*e^3 + b^6*c*d^5*e^4 - b^7*d^4*e^5)*x^3 + (b^3*c^4*d^9 - b^4*c^3*d^8*e - 3*b^5*c^2*d^7*e^2 + 5*b^6*c*d^6*e^3 - 2*b^7*d^5*e^4)*x^2 + (b^4*c^3*d^9 - 3*b^5*c^2*d^8*e + 3*b^6*c*d^7*e^2 - b^7*d^6*e^3)*x), 1/3*(3*((2*(B*b*c^4 - 2*A*c^5)*d^5*e^2 - (7*B*b^2*c^3 - 9*A*b*c^4)*d^4*e^3)*x^4 + (4*(B*b*c^4 - 2*A*c^5)*d^6*e - 2*(6*B*b^2*c^3 - 7*A*b*c^4)*d^5*e^2 - (7*B*b^3*c^2 - 9*A*b^2*c^3)*d^4*e^3)*x^3 + (2*(B*b*c^4 - 2*A*c^5)*d^7 - (3*B*b^2*c^3 - A*b*c^4)*d^6*e - 2*(7*B*b^3*c^2 - 9*A*b^2*c^3)*d^5*e^2)*x^2 + (2*(B*b^2*c^3 - 2*A*b*c^4)*d^7 - (7*B*b^3*c^2 - 9*A*b^2*c^3)*d^6*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((5*A*b^4*c*e^6 + 2*(B*b*c^4 - 2*A*c^5)*d^4*e^2 - (6*B*b^2*c^3 - 7*A*b*c^4)*d^3*e^3 + 3*(2*B*b^3*c^2 + A*b^2*c^3)*d^2*e^4 - (2*B*b^4*c + 11*A*b^3*c^2)*d*e^5)*x^4 + (5*A*b^5*e^6 + 4*(B*b*c^4 - 2*A*c^5)*d^5*e - 10*(B*b^2*c^3 - A*b*c^4)*d^4*e^2 + (6*B*b^3*c^2 + 13*A*b^2*c^3)*d^3*e^3 + (2*B*b^4*c - 19*A*b^3*c^2)*d^2*e^4 - (2*B*b^5 + A*b^4*c)*d*e^5)*x^3 + (10*A*b^5*d*e^5 + 2*(B*b*c^4 - 2*A*c^5)*d^6 - (2*B*b^2*c^3 + A*b*c^4)*d^5*e - (6*B*b^3*c^2 - 17*A*b^2*c^3)*d^4*e^2 + 5*(2*B*b^4*c - A*b^3*c^2)*d^3*e^3 - (4*B*b^5 + 17*A*b^4*c)*d^2*e^4)*x^2 + (5*A*b^5*d^2*e^4 + 2*(B*b^2*c^3 - 2*A*b*c^4)*d^6 - (6*B*b^3*c^2 - 7*A*b^2*c^3)*d^5*e + 3*(2*B*b^4*c + A*b^3*c^2)*d^4*e^2 - (2*B*b^5 + 11*A*b^4*c)*d^3*e^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (3*A*b^2*c^3*d^6 - 9*A*b^3*c^2*d^5*e + 9*A*b^4*c*d^4*e^2 - 3*A*b^5*d^3*e^3 - 3*(5*A*b^4*c*d*e^5 + (B*b^2*c^3 - 2*A*b*c^4)*d^4*e^2 + 3*(2*B*b^3*c^2 + A*b^2*c^3)*d^3*e^3 - (2*B*b^4*c + 11*A*b^3*c^2)*d^2*e^4)*x^3 - (15*A*b^5*d*e^5 + 6*(B*b^2*c^3 - 2*A*b*c^4)*d^5*e + 5*(4*B*b^3*c^2 + 3*A*b^2*c^3)*d^4*e^2 + 5*(2*B*b^4*c - 7*A*b^3*c^2)*d^3*e^3 - (6*B*b^5 + 13*A*b^4*c)*d^2*e^4)*x^2 - (3*A*b^2*c^3*d^5*e + 20*A*b^5*d^2*e^4 + 3*(B*b^2*c^3 - 2*A*b*c^4)*d^6 + (20*B*b^4*c + 9*A*b^3*c^2)*d^4*e^2 - (8*B*b^5 + 41*A*b^4*c)*d^3*e^3)*x)*sqrt(e*x + d))/((b^3*c^4*d^7*e^2 - 3*b^4*c^3*d^6*e^3 + 3*b^5*c^2*d^5*e^4 - b^6*c*d^4*e^5)*x^4 + (2*b^3*c^4*d^8*e - 5*b^4*c^3*d^7*e^2 + 3*b^5*c^2*d^6*e^3 + b^6*c*d^5*e^4 - b^7*d^4*e^5)*x^3 + (b^3*c^4*d^9 - b^4*c^3*d^8*e - 3*b^5*c^2*d^7*e^2 + 5*b^6*c*d^6*e^3 - 2*b^7*d^5*e^4)*x^2 + (b^4*c^3*d^9 - 3*b^5*c^2*d^8*e + 3*b^6*c*d^7*e^2 - b^7*d^6*e^3)*x)]","B",0
1246,1,8537,0,131.537180," ","integrate((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{6} e^{3} - {\left(9 \, B b^{2} c^{4} - 11 \, A b c^{5}\right)} d^{5} e^{4}\right)} x^{5} + {\left(6 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{7} e^{2} - {\left(25 \, B b^{2} c^{4} - 29 \, A b c^{5}\right)} d^{6} e^{3} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{5} e^{4}\right)} x^{4} + 3 \, {\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{8} e - 7 \, {\left(B b^{2} c^{4} - A b c^{5}\right)} d^{7} e^{2} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{6} e^{3}\right)} x^{3} + {\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{9} - {\left(3 \, B b^{2} c^{4} + A b c^{5}\right)} d^{8} e - 3 \, {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{7} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{9} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{8} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 15 \, {\left({\left(7 \, A b^{5} c e^{8} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} e^{3} + {\left(8 \, B b^{2} c^{4} - 9 \, A b c^{5}\right)} d^{4} e^{4} - 4 \, {\left(3 \, B b^{3} c^{3} + A b^{2} c^{4}\right)} d^{3} e^{5} + 2 \, {\left(4 \, B b^{4} c^{2} + 13 \, A b^{3} c^{3}\right)} d^{2} e^{6} - 2 \, {\left(B b^{5} c + 12 \, A b^{4} c^{2}\right)} d e^{7}\right)} x^{5} + {\left(7 \, A b^{6} e^{8} - 6 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{6} e^{2} + {\left(22 \, B b^{2} c^{4} - 23 \, A b c^{5}\right)} d^{5} e^{3} - 7 \, {\left(4 \, B b^{3} c^{3} + 3 \, A b^{2} c^{4}\right)} d^{4} e^{4} + 2 \, {\left(6 \, B b^{4} c^{2} + 37 \, A b^{3} c^{3}\right)} d^{3} e^{5} + 2 \, {\left(B b^{5} c - 23 \, A b^{4} c^{2}\right)} d^{2} e^{6} - {\left(2 \, B b^{6} + 3 \, A b^{5} c\right)} d e^{7}\right)} x^{4} + 3 \, {\left(7 \, A b^{6} d e^{7} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{7} e + {\left(6 \, B b^{2} c^{4} - 5 \, A b c^{5}\right)} d^{6} e^{2} - {\left(4 \, B b^{3} c^{3} + 13 \, A b^{2} c^{4}\right)} d^{5} e^{3} - 2 \, {\left(2 \, B b^{4} c^{2} - 11 \, A b^{3} c^{3}\right)} d^{4} e^{4} + 2 \, {\left(3 \, B b^{5} c + A b^{4} c^{2}\right)} d^{3} e^{5} - {\left(2 \, B b^{6} + 17 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{3} + {\left(21 \, A b^{6} d^{2} e^{6} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{8} + {\left(2 \, B b^{2} c^{4} + 3 \, A b c^{5}\right)} d^{7} e + {\left(12 \, B b^{3} c^{3} - 31 \, A b^{2} c^{4}\right)} d^{6} e^{2} - 14 \, {\left(2 \, B b^{4} c^{2} - A b^{3} c^{3}\right)} d^{5} e^{3} + 2 \, {\left(11 \, B b^{5} c + 27 \, A b^{4} c^{2}\right)} d^{4} e^{4} - {\left(6 \, B b^{6} + 65 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{2} + {\left(7 \, A b^{6} d^{3} e^{5} - 2 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{8} + {\left(8 \, B b^{3} c^{3} - 9 \, A b^{2} c^{4}\right)} d^{7} e - 4 \, {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(4 \, B b^{5} c + 13 \, A b^{4} c^{2}\right)} d^{5} e^{3} - 2 \, {\left(B b^{6} + 12 \, A b^{5} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(15 \, A b^{2} c^{4} d^{8} - 60 \, A b^{3} c^{3} d^{7} e + 90 \, A b^{4} c^{2} d^{6} e^{2} - 60 \, A b^{5} c d^{5} e^{3} + 15 \, A b^{6} d^{4} e^{4} + 15 \, {\left(7 \, A b^{5} c d e^{7} - {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} e^{3} - 4 \, {\left(3 \, B b^{3} c^{3} + A b^{2} c^{4}\right)} d^{4} e^{4} + 2 \, {\left(4 \, B b^{4} c^{2} + 13 \, A b^{3} c^{3}\right)} d^{3} e^{5} - 2 \, {\left(B b^{5} c + 12 \, A b^{4} c^{2}\right)} d^{2} e^{6}\right)} x^{4} + 5 \, {\left(21 \, A b^{6} d e^{7} - 9 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{6} e^{2} - 3 \, {\left(26 \, B b^{3} c^{3} + 11 \, A b^{2} c^{4}\right)} d^{5} e^{3} + 10 \, {\left(2 \, B b^{4} c^{2} + 17 \, A b^{3} c^{3}\right)} d^{4} e^{4} + 10 \, {\left(B b^{5} c - 9 \, A b^{4} c^{2}\right)} d^{3} e^{5} - {\left(6 \, B b^{6} + 23 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{3} + {\left(245 \, A b^{6} d^{2} e^{6} - 45 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{7} e - 27 \, {\left(8 \, B b^{3} c^{3} + 5 \, A b^{2} c^{4}\right)} d^{6} e^{2} - 218 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{5} e^{3} + 2 \, {\left(117 \, B b^{5} c + 179 \, A b^{4} c^{2}\right)} d^{4} e^{4} - 7 \, {\left(10 \, B b^{6} + 97 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{2} - {\left(15 \, A b^{2} c^{4} d^{7} e - 161 \, A b^{6} d^{3} e^{5} + 15 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{8} + 18 \, {\left(12 \, B b^{4} c^{2} + 5 \, A b^{3} c^{3}\right)} d^{6} e^{2} - 4 \, {\left(43 \, B b^{5} c + 139 \, A b^{4} c^{2}\right)} d^{5} e^{3} + {\left(46 \, B b^{6} + 537 \, A b^{5} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left({\left(b^{3} c^{5} d^{9} e^{3} - 4 \, b^{4} c^{4} d^{8} e^{4} + 6 \, b^{5} c^{3} d^{7} e^{5} - 4 \, b^{6} c^{2} d^{6} e^{6} + b^{7} c d^{5} e^{7}\right)} x^{5} + {\left(3 \, b^{3} c^{5} d^{10} e^{2} - 11 \, b^{4} c^{4} d^{9} e^{3} + 14 \, b^{5} c^{3} d^{8} e^{4} - 6 \, b^{6} c^{2} d^{7} e^{5} - b^{7} c d^{6} e^{6} + b^{8} d^{5} e^{7}\right)} x^{4} + 3 \, {\left(b^{3} c^{5} d^{11} e - 3 \, b^{4} c^{4} d^{10} e^{2} + 2 \, b^{5} c^{3} d^{9} e^{3} + 2 \, b^{6} c^{2} d^{8} e^{4} - 3 \, b^{7} c d^{7} e^{5} + b^{8} d^{6} e^{6}\right)} x^{3} + {\left(b^{3} c^{5} d^{12} - b^{4} c^{4} d^{11} e - 6 \, b^{5} c^{3} d^{10} e^{2} + 14 \, b^{6} c^{2} d^{9} e^{3} - 11 \, b^{7} c d^{8} e^{4} + 3 \, b^{8} d^{7} e^{5}\right)} x^{2} + {\left(b^{4} c^{4} d^{12} - 4 \, b^{5} c^{3} d^{11} e + 6 \, b^{6} c^{2} d^{10} e^{2} - 4 \, b^{7} c d^{9} e^{3} + b^{8} d^{8} e^{4}\right)} x\right)}}, \frac{30 \, {\left({\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{6} e^{3} - {\left(9 \, B b^{2} c^{4} - 11 \, A b c^{5}\right)} d^{5} e^{4}\right)} x^{5} + {\left(6 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{7} e^{2} - {\left(25 \, B b^{2} c^{4} - 29 \, A b c^{5}\right)} d^{6} e^{3} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{5} e^{4}\right)} x^{4} + 3 \, {\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{8} e - 7 \, {\left(B b^{2} c^{4} - A b c^{5}\right)} d^{7} e^{2} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{6} e^{3}\right)} x^{3} + {\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{9} - {\left(3 \, B b^{2} c^{4} + A b c^{5}\right)} d^{8} e - 3 \, {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{7} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{9} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{8} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 15 \, {\left({\left(7 \, A b^{5} c e^{8} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} e^{3} + {\left(8 \, B b^{2} c^{4} - 9 \, A b c^{5}\right)} d^{4} e^{4} - 4 \, {\left(3 \, B b^{3} c^{3} + A b^{2} c^{4}\right)} d^{3} e^{5} + 2 \, {\left(4 \, B b^{4} c^{2} + 13 \, A b^{3} c^{3}\right)} d^{2} e^{6} - 2 \, {\left(B b^{5} c + 12 \, A b^{4} c^{2}\right)} d e^{7}\right)} x^{5} + {\left(7 \, A b^{6} e^{8} - 6 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{6} e^{2} + {\left(22 \, B b^{2} c^{4} - 23 \, A b c^{5}\right)} d^{5} e^{3} - 7 \, {\left(4 \, B b^{3} c^{3} + 3 \, A b^{2} c^{4}\right)} d^{4} e^{4} + 2 \, {\left(6 \, B b^{4} c^{2} + 37 \, A b^{3} c^{3}\right)} d^{3} e^{5} + 2 \, {\left(B b^{5} c - 23 \, A b^{4} c^{2}\right)} d^{2} e^{6} - {\left(2 \, B b^{6} + 3 \, A b^{5} c\right)} d e^{7}\right)} x^{4} + 3 \, {\left(7 \, A b^{6} d e^{7} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{7} e + {\left(6 \, B b^{2} c^{4} - 5 \, A b c^{5}\right)} d^{6} e^{2} - {\left(4 \, B b^{3} c^{3} + 13 \, A b^{2} c^{4}\right)} d^{5} e^{3} - 2 \, {\left(2 \, B b^{4} c^{2} - 11 \, A b^{3} c^{3}\right)} d^{4} e^{4} + 2 \, {\left(3 \, B b^{5} c + A b^{4} c^{2}\right)} d^{3} e^{5} - {\left(2 \, B b^{6} + 17 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{3} + {\left(21 \, A b^{6} d^{2} e^{6} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{8} + {\left(2 \, B b^{2} c^{4} + 3 \, A b c^{5}\right)} d^{7} e + {\left(12 \, B b^{3} c^{3} - 31 \, A b^{2} c^{4}\right)} d^{6} e^{2} - 14 \, {\left(2 \, B b^{4} c^{2} - A b^{3} c^{3}\right)} d^{5} e^{3} + 2 \, {\left(11 \, B b^{5} c + 27 \, A b^{4} c^{2}\right)} d^{4} e^{4} - {\left(6 \, B b^{6} + 65 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{2} + {\left(7 \, A b^{6} d^{3} e^{5} - 2 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{8} + {\left(8 \, B b^{3} c^{3} - 9 \, A b^{2} c^{4}\right)} d^{7} e - 4 \, {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(4 \, B b^{5} c + 13 \, A b^{4} c^{2}\right)} d^{5} e^{3} - 2 \, {\left(B b^{6} + 12 \, A b^{5} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(15 \, A b^{2} c^{4} d^{8} - 60 \, A b^{3} c^{3} d^{7} e + 90 \, A b^{4} c^{2} d^{6} e^{2} - 60 \, A b^{5} c d^{5} e^{3} + 15 \, A b^{6} d^{4} e^{4} + 15 \, {\left(7 \, A b^{5} c d e^{7} - {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} e^{3} - 4 \, {\left(3 \, B b^{3} c^{3} + A b^{2} c^{4}\right)} d^{4} e^{4} + 2 \, {\left(4 \, B b^{4} c^{2} + 13 \, A b^{3} c^{3}\right)} d^{3} e^{5} - 2 \, {\left(B b^{5} c + 12 \, A b^{4} c^{2}\right)} d^{2} e^{6}\right)} x^{4} + 5 \, {\left(21 \, A b^{6} d e^{7} - 9 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{6} e^{2} - 3 \, {\left(26 \, B b^{3} c^{3} + 11 \, A b^{2} c^{4}\right)} d^{5} e^{3} + 10 \, {\left(2 \, B b^{4} c^{2} + 17 \, A b^{3} c^{3}\right)} d^{4} e^{4} + 10 \, {\left(B b^{5} c - 9 \, A b^{4} c^{2}\right)} d^{3} e^{5} - {\left(6 \, B b^{6} + 23 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{3} + {\left(245 \, A b^{6} d^{2} e^{6} - 45 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{7} e - 27 \, {\left(8 \, B b^{3} c^{3} + 5 \, A b^{2} c^{4}\right)} d^{6} e^{2} - 218 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{5} e^{3} + 2 \, {\left(117 \, B b^{5} c + 179 \, A b^{4} c^{2}\right)} d^{4} e^{4} - 7 \, {\left(10 \, B b^{6} + 97 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{2} - {\left(15 \, A b^{2} c^{4} d^{7} e - 161 \, A b^{6} d^{3} e^{5} + 15 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{8} + 18 \, {\left(12 \, B b^{4} c^{2} + 5 \, A b^{3} c^{3}\right)} d^{6} e^{2} - 4 \, {\left(43 \, B b^{5} c + 139 \, A b^{4} c^{2}\right)} d^{5} e^{3} + {\left(46 \, B b^{6} + 537 \, A b^{5} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left({\left(b^{3} c^{5} d^{9} e^{3} - 4 \, b^{4} c^{4} d^{8} e^{4} + 6 \, b^{5} c^{3} d^{7} e^{5} - 4 \, b^{6} c^{2} d^{6} e^{6} + b^{7} c d^{5} e^{7}\right)} x^{5} + {\left(3 \, b^{3} c^{5} d^{10} e^{2} - 11 \, b^{4} c^{4} d^{9} e^{3} + 14 \, b^{5} c^{3} d^{8} e^{4} - 6 \, b^{6} c^{2} d^{7} e^{5} - b^{7} c d^{6} e^{6} + b^{8} d^{5} e^{7}\right)} x^{4} + 3 \, {\left(b^{3} c^{5} d^{11} e - 3 \, b^{4} c^{4} d^{10} e^{2} + 2 \, b^{5} c^{3} d^{9} e^{3} + 2 \, b^{6} c^{2} d^{8} e^{4} - 3 \, b^{7} c d^{7} e^{5} + b^{8} d^{6} e^{6}\right)} x^{3} + {\left(b^{3} c^{5} d^{12} - b^{4} c^{4} d^{11} e - 6 \, b^{5} c^{3} d^{10} e^{2} + 14 \, b^{6} c^{2} d^{9} e^{3} - 11 \, b^{7} c d^{8} e^{4} + 3 \, b^{8} d^{7} e^{5}\right)} x^{2} + {\left(b^{4} c^{4} d^{12} - 4 \, b^{5} c^{3} d^{11} e + 6 \, b^{6} c^{2} d^{10} e^{2} - 4 \, b^{7} c d^{9} e^{3} + b^{8} d^{8} e^{4}\right)} x\right)}}, -\frac{30 \, {\left({\left(7 \, A b^{5} c e^{8} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} e^{3} + {\left(8 \, B b^{2} c^{4} - 9 \, A b c^{5}\right)} d^{4} e^{4} - 4 \, {\left(3 \, B b^{3} c^{3} + A b^{2} c^{4}\right)} d^{3} e^{5} + 2 \, {\left(4 \, B b^{4} c^{2} + 13 \, A b^{3} c^{3}\right)} d^{2} e^{6} - 2 \, {\left(B b^{5} c + 12 \, A b^{4} c^{2}\right)} d e^{7}\right)} x^{5} + {\left(7 \, A b^{6} e^{8} - 6 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{6} e^{2} + {\left(22 \, B b^{2} c^{4} - 23 \, A b c^{5}\right)} d^{5} e^{3} - 7 \, {\left(4 \, B b^{3} c^{3} + 3 \, A b^{2} c^{4}\right)} d^{4} e^{4} + 2 \, {\left(6 \, B b^{4} c^{2} + 37 \, A b^{3} c^{3}\right)} d^{3} e^{5} + 2 \, {\left(B b^{5} c - 23 \, A b^{4} c^{2}\right)} d^{2} e^{6} - {\left(2 \, B b^{6} + 3 \, A b^{5} c\right)} d e^{7}\right)} x^{4} + 3 \, {\left(7 \, A b^{6} d e^{7} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{7} e + {\left(6 \, B b^{2} c^{4} - 5 \, A b c^{5}\right)} d^{6} e^{2} - {\left(4 \, B b^{3} c^{3} + 13 \, A b^{2} c^{4}\right)} d^{5} e^{3} - 2 \, {\left(2 \, B b^{4} c^{2} - 11 \, A b^{3} c^{3}\right)} d^{4} e^{4} + 2 \, {\left(3 \, B b^{5} c + A b^{4} c^{2}\right)} d^{3} e^{5} - {\left(2 \, B b^{6} + 17 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{3} + {\left(21 \, A b^{6} d^{2} e^{6} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{8} + {\left(2 \, B b^{2} c^{4} + 3 \, A b c^{5}\right)} d^{7} e + {\left(12 \, B b^{3} c^{3} - 31 \, A b^{2} c^{4}\right)} d^{6} e^{2} - 14 \, {\left(2 \, B b^{4} c^{2} - A b^{3} c^{3}\right)} d^{5} e^{3} + 2 \, {\left(11 \, B b^{5} c + 27 \, A b^{4} c^{2}\right)} d^{4} e^{4} - {\left(6 \, B b^{6} + 65 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{2} + {\left(7 \, A b^{6} d^{3} e^{5} - 2 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{8} + {\left(8 \, B b^{3} c^{3} - 9 \, A b^{2} c^{4}\right)} d^{7} e - 4 \, {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(4 \, B b^{5} c + 13 \, A b^{4} c^{2}\right)} d^{5} e^{3} - 2 \, {\left(B b^{6} + 12 \, A b^{5} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 15 \, {\left({\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{6} e^{3} - {\left(9 \, B b^{2} c^{4} - 11 \, A b c^{5}\right)} d^{5} e^{4}\right)} x^{5} + {\left(6 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{7} e^{2} - {\left(25 \, B b^{2} c^{4} - 29 \, A b c^{5}\right)} d^{6} e^{3} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{5} e^{4}\right)} x^{4} + 3 \, {\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{8} e - 7 \, {\left(B b^{2} c^{4} - A b c^{5}\right)} d^{7} e^{2} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{6} e^{3}\right)} x^{3} + {\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{9} - {\left(3 \, B b^{2} c^{4} + A b c^{5}\right)} d^{8} e - 3 \, {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{7} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{9} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{8} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(15 \, A b^{2} c^{4} d^{8} - 60 \, A b^{3} c^{3} d^{7} e + 90 \, A b^{4} c^{2} d^{6} e^{2} - 60 \, A b^{5} c d^{5} e^{3} + 15 \, A b^{6} d^{4} e^{4} + 15 \, {\left(7 \, A b^{5} c d e^{7} - {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} e^{3} - 4 \, {\left(3 \, B b^{3} c^{3} + A b^{2} c^{4}\right)} d^{4} e^{4} + 2 \, {\left(4 \, B b^{4} c^{2} + 13 \, A b^{3} c^{3}\right)} d^{3} e^{5} - 2 \, {\left(B b^{5} c + 12 \, A b^{4} c^{2}\right)} d^{2} e^{6}\right)} x^{4} + 5 \, {\left(21 \, A b^{6} d e^{7} - 9 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{6} e^{2} - 3 \, {\left(26 \, B b^{3} c^{3} + 11 \, A b^{2} c^{4}\right)} d^{5} e^{3} + 10 \, {\left(2 \, B b^{4} c^{2} + 17 \, A b^{3} c^{3}\right)} d^{4} e^{4} + 10 \, {\left(B b^{5} c - 9 \, A b^{4} c^{2}\right)} d^{3} e^{5} - {\left(6 \, B b^{6} + 23 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{3} + {\left(245 \, A b^{6} d^{2} e^{6} - 45 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{7} e - 27 \, {\left(8 \, B b^{3} c^{3} + 5 \, A b^{2} c^{4}\right)} d^{6} e^{2} - 218 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{5} e^{3} + 2 \, {\left(117 \, B b^{5} c + 179 \, A b^{4} c^{2}\right)} d^{4} e^{4} - 7 \, {\left(10 \, B b^{6} + 97 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{2} - {\left(15 \, A b^{2} c^{4} d^{7} e - 161 \, A b^{6} d^{3} e^{5} + 15 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{8} + 18 \, {\left(12 \, B b^{4} c^{2} + 5 \, A b^{3} c^{3}\right)} d^{6} e^{2} - 4 \, {\left(43 \, B b^{5} c + 139 \, A b^{4} c^{2}\right)} d^{5} e^{3} + {\left(46 \, B b^{6} + 537 \, A b^{5} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left({\left(b^{3} c^{5} d^{9} e^{3} - 4 \, b^{4} c^{4} d^{8} e^{4} + 6 \, b^{5} c^{3} d^{7} e^{5} - 4 \, b^{6} c^{2} d^{6} e^{6} + b^{7} c d^{5} e^{7}\right)} x^{5} + {\left(3 \, b^{3} c^{5} d^{10} e^{2} - 11 \, b^{4} c^{4} d^{9} e^{3} + 14 \, b^{5} c^{3} d^{8} e^{4} - 6 \, b^{6} c^{2} d^{7} e^{5} - b^{7} c d^{6} e^{6} + b^{8} d^{5} e^{7}\right)} x^{4} + 3 \, {\left(b^{3} c^{5} d^{11} e - 3 \, b^{4} c^{4} d^{10} e^{2} + 2 \, b^{5} c^{3} d^{9} e^{3} + 2 \, b^{6} c^{2} d^{8} e^{4} - 3 \, b^{7} c d^{7} e^{5} + b^{8} d^{6} e^{6}\right)} x^{3} + {\left(b^{3} c^{5} d^{12} - b^{4} c^{4} d^{11} e - 6 \, b^{5} c^{3} d^{10} e^{2} + 14 \, b^{6} c^{2} d^{9} e^{3} - 11 \, b^{7} c d^{8} e^{4} + 3 \, b^{8} d^{7} e^{5}\right)} x^{2} + {\left(b^{4} c^{4} d^{12} - 4 \, b^{5} c^{3} d^{11} e + 6 \, b^{6} c^{2} d^{10} e^{2} - 4 \, b^{7} c d^{9} e^{3} + b^{8} d^{8} e^{4}\right)} x\right)}}, \frac{15 \, {\left({\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{6} e^{3} - {\left(9 \, B b^{2} c^{4} - 11 \, A b c^{5}\right)} d^{5} e^{4}\right)} x^{5} + {\left(6 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{7} e^{2} - {\left(25 \, B b^{2} c^{4} - 29 \, A b c^{5}\right)} d^{6} e^{3} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{5} e^{4}\right)} x^{4} + 3 \, {\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{8} e - 7 \, {\left(B b^{2} c^{4} - A b c^{5}\right)} d^{7} e^{2} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{6} e^{3}\right)} x^{3} + {\left(2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{9} - {\left(3 \, B b^{2} c^{4} + A b c^{5}\right)} d^{8} e - 3 \, {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{7} e^{2}\right)} x^{2} + {\left(2 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{9} - {\left(9 \, B b^{3} c^{3} - 11 \, A b^{2} c^{4}\right)} d^{8} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 15 \, {\left({\left(7 \, A b^{5} c e^{8} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} e^{3} + {\left(8 \, B b^{2} c^{4} - 9 \, A b c^{5}\right)} d^{4} e^{4} - 4 \, {\left(3 \, B b^{3} c^{3} + A b^{2} c^{4}\right)} d^{3} e^{5} + 2 \, {\left(4 \, B b^{4} c^{2} + 13 \, A b^{3} c^{3}\right)} d^{2} e^{6} - 2 \, {\left(B b^{5} c + 12 \, A b^{4} c^{2}\right)} d e^{7}\right)} x^{5} + {\left(7 \, A b^{6} e^{8} - 6 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{6} e^{2} + {\left(22 \, B b^{2} c^{4} - 23 \, A b c^{5}\right)} d^{5} e^{3} - 7 \, {\left(4 \, B b^{3} c^{3} + 3 \, A b^{2} c^{4}\right)} d^{4} e^{4} + 2 \, {\left(6 \, B b^{4} c^{2} + 37 \, A b^{3} c^{3}\right)} d^{3} e^{5} + 2 \, {\left(B b^{5} c - 23 \, A b^{4} c^{2}\right)} d^{2} e^{6} - {\left(2 \, B b^{6} + 3 \, A b^{5} c\right)} d e^{7}\right)} x^{4} + 3 \, {\left(7 \, A b^{6} d e^{7} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{7} e + {\left(6 \, B b^{2} c^{4} - 5 \, A b c^{5}\right)} d^{6} e^{2} - {\left(4 \, B b^{3} c^{3} + 13 \, A b^{2} c^{4}\right)} d^{5} e^{3} - 2 \, {\left(2 \, B b^{4} c^{2} - 11 \, A b^{3} c^{3}\right)} d^{4} e^{4} + 2 \, {\left(3 \, B b^{5} c + A b^{4} c^{2}\right)} d^{3} e^{5} - {\left(2 \, B b^{6} + 17 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{3} + {\left(21 \, A b^{6} d^{2} e^{6} - 2 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{8} + {\left(2 \, B b^{2} c^{4} + 3 \, A b c^{5}\right)} d^{7} e + {\left(12 \, B b^{3} c^{3} - 31 \, A b^{2} c^{4}\right)} d^{6} e^{2} - 14 \, {\left(2 \, B b^{4} c^{2} - A b^{3} c^{3}\right)} d^{5} e^{3} + 2 \, {\left(11 \, B b^{5} c + 27 \, A b^{4} c^{2}\right)} d^{4} e^{4} - {\left(6 \, B b^{6} + 65 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{2} + {\left(7 \, A b^{6} d^{3} e^{5} - 2 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{8} + {\left(8 \, B b^{3} c^{3} - 9 \, A b^{2} c^{4}\right)} d^{7} e - 4 \, {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(4 \, B b^{5} c + 13 \, A b^{4} c^{2}\right)} d^{5} e^{3} - 2 \, {\left(B b^{6} + 12 \, A b^{5} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(15 \, A b^{2} c^{4} d^{8} - 60 \, A b^{3} c^{3} d^{7} e + 90 \, A b^{4} c^{2} d^{6} e^{2} - 60 \, A b^{5} c d^{5} e^{3} + 15 \, A b^{6} d^{4} e^{4} + 15 \, {\left(7 \, A b^{5} c d e^{7} - {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} e^{3} - 4 \, {\left(3 \, B b^{3} c^{3} + A b^{2} c^{4}\right)} d^{4} e^{4} + 2 \, {\left(4 \, B b^{4} c^{2} + 13 \, A b^{3} c^{3}\right)} d^{3} e^{5} - 2 \, {\left(B b^{5} c + 12 \, A b^{4} c^{2}\right)} d^{2} e^{6}\right)} x^{4} + 5 \, {\left(21 \, A b^{6} d e^{7} - 9 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{6} e^{2} - 3 \, {\left(26 \, B b^{3} c^{3} + 11 \, A b^{2} c^{4}\right)} d^{5} e^{3} + 10 \, {\left(2 \, B b^{4} c^{2} + 17 \, A b^{3} c^{3}\right)} d^{4} e^{4} + 10 \, {\left(B b^{5} c - 9 \, A b^{4} c^{2}\right)} d^{3} e^{5} - {\left(6 \, B b^{6} + 23 \, A b^{5} c\right)} d^{2} e^{6}\right)} x^{3} + {\left(245 \, A b^{6} d^{2} e^{6} - 45 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{7} e - 27 \, {\left(8 \, B b^{3} c^{3} + 5 \, A b^{2} c^{4}\right)} d^{6} e^{2} - 218 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{5} e^{3} + 2 \, {\left(117 \, B b^{5} c + 179 \, A b^{4} c^{2}\right)} d^{4} e^{4} - 7 \, {\left(10 \, B b^{6} + 97 \, A b^{5} c\right)} d^{3} e^{5}\right)} x^{2} - {\left(15 \, A b^{2} c^{4} d^{7} e - 161 \, A b^{6} d^{3} e^{5} + 15 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{8} + 18 \, {\left(12 \, B b^{4} c^{2} + 5 \, A b^{3} c^{3}\right)} d^{6} e^{2} - 4 \, {\left(43 \, B b^{5} c + 139 \, A b^{4} c^{2}\right)} d^{5} e^{3} + {\left(46 \, B b^{6} + 537 \, A b^{5} c\right)} d^{4} e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left({\left(b^{3} c^{5} d^{9} e^{3} - 4 \, b^{4} c^{4} d^{8} e^{4} + 6 \, b^{5} c^{3} d^{7} e^{5} - 4 \, b^{6} c^{2} d^{6} e^{6} + b^{7} c d^{5} e^{7}\right)} x^{5} + {\left(3 \, b^{3} c^{5} d^{10} e^{2} - 11 \, b^{4} c^{4} d^{9} e^{3} + 14 \, b^{5} c^{3} d^{8} e^{4} - 6 \, b^{6} c^{2} d^{7} e^{5} - b^{7} c d^{6} e^{6} + b^{8} d^{5} e^{7}\right)} x^{4} + 3 \, {\left(b^{3} c^{5} d^{11} e - 3 \, b^{4} c^{4} d^{10} e^{2} + 2 \, b^{5} c^{3} d^{9} e^{3} + 2 \, b^{6} c^{2} d^{8} e^{4} - 3 \, b^{7} c d^{7} e^{5} + b^{8} d^{6} e^{6}\right)} x^{3} + {\left(b^{3} c^{5} d^{12} - b^{4} c^{4} d^{11} e - 6 \, b^{5} c^{3} d^{10} e^{2} + 14 \, b^{6} c^{2} d^{9} e^{3} - 11 \, b^{7} c d^{8} e^{4} + 3 \, b^{8} d^{7} e^{5}\right)} x^{2} + {\left(b^{4} c^{4} d^{12} - 4 \, b^{5} c^{3} d^{11} e + 6 \, b^{6} c^{2} d^{10} e^{2} - 4 \, b^{7} c d^{9} e^{3} + b^{8} d^{8} e^{4}\right)} x\right)}}\right]"," ",0,"[1/30*(15*((2*(B*b*c^5 - 2*A*c^6)*d^6*e^3 - (9*B*b^2*c^4 - 11*A*b*c^5)*d^5*e^4)*x^5 + (6*(B*b*c^5 - 2*A*c^6)*d^7*e^2 - (25*B*b^2*c^4 - 29*A*b*c^5)*d^6*e^3 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^5*e^4)*x^4 + 3*(2*(B*b*c^5 - 2*A*c^6)*d^8*e - 7*(B*b^2*c^4 - A*b*c^5)*d^7*e^2 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^6*e^3)*x^3 + (2*(B*b*c^5 - 2*A*c^6)*d^9 - (3*B*b^2*c^4 + A*b*c^5)*d^8*e - 3*(9*B*b^3*c^3 - 11*A*b^2*c^4)*d^7*e^2)*x^2 + (2*(B*b^2*c^4 - 2*A*b*c^5)*d^9 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^8*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 15*((7*A*b^5*c*e^8 - 2*(B*b*c^5 - 2*A*c^6)*d^5*e^3 + (8*B*b^2*c^4 - 9*A*b*c^5)*d^4*e^4 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^3*e^5 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^2*e^6 - 2*(B*b^5*c + 12*A*b^4*c^2)*d*e^7)*x^5 + (7*A*b^6*e^8 - 6*(B*b*c^5 - 2*A*c^6)*d^6*e^2 + (22*B*b^2*c^4 - 23*A*b*c^5)*d^5*e^3 - 7*(4*B*b^3*c^3 + 3*A*b^2*c^4)*d^4*e^4 + 2*(6*B*b^4*c^2 + 37*A*b^3*c^3)*d^3*e^5 + 2*(B*b^5*c - 23*A*b^4*c^2)*d^2*e^6 - (2*B*b^6 + 3*A*b^5*c)*d*e^7)*x^4 + 3*(7*A*b^6*d*e^7 - 2*(B*b*c^5 - 2*A*c^6)*d^7*e + (6*B*b^2*c^4 - 5*A*b*c^5)*d^6*e^2 - (4*B*b^3*c^3 + 13*A*b^2*c^4)*d^5*e^3 - 2*(2*B*b^4*c^2 - 11*A*b^3*c^3)*d^4*e^4 + 2*(3*B*b^5*c + A*b^4*c^2)*d^3*e^5 - (2*B*b^6 + 17*A*b^5*c)*d^2*e^6)*x^3 + (21*A*b^6*d^2*e^6 - 2*(B*b*c^5 - 2*A*c^6)*d^8 + (2*B*b^2*c^4 + 3*A*b*c^5)*d^7*e + (12*B*b^3*c^3 - 31*A*b^2*c^4)*d^6*e^2 - 14*(2*B*b^4*c^2 - A*b^3*c^3)*d^5*e^3 + 2*(11*B*b^5*c + 27*A*b^4*c^2)*d^4*e^4 - (6*B*b^6 + 65*A*b^5*c)*d^3*e^5)*x^2 + (7*A*b^6*d^3*e^5 - 2*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + (8*B*b^3*c^3 - 9*A*b^2*c^4)*d^7*e - 4*(3*B*b^4*c^2 + A*b^3*c^3)*d^6*e^2 + 2*(4*B*b^5*c + 13*A*b^4*c^2)*d^5*e^3 - 2*(B*b^6 + 12*A*b^5*c)*d^4*e^4)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(15*A*b^2*c^4*d^8 - 60*A*b^3*c^3*d^7*e + 90*A*b^4*c^2*d^6*e^2 - 60*A*b^5*c*d^5*e^3 + 15*A*b^6*d^4*e^4 + 15*(7*A*b^5*c*d*e^7 - (B*b^2*c^4 - 2*A*b*c^5)*d^5*e^3 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^4*e^4 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^3*e^5 - 2*(B*b^5*c + 12*A*b^4*c^2)*d^2*e^6)*x^4 + 5*(21*A*b^6*d*e^7 - 9*(B*b^2*c^4 - 2*A*b*c^5)*d^6*e^2 - 3*(26*B*b^3*c^3 + 11*A*b^2*c^4)*d^5*e^3 + 10*(2*B*b^4*c^2 + 17*A*b^3*c^3)*d^4*e^4 + 10*(B*b^5*c - 9*A*b^4*c^2)*d^3*e^5 - (6*B*b^6 + 23*A*b^5*c)*d^2*e^6)*x^3 + (245*A*b^6*d^2*e^6 - 45*(B*b^2*c^4 - 2*A*b*c^5)*d^7*e - 27*(8*B*b^3*c^3 + 5*A*b^2*c^4)*d^6*e^2 - 218*(B*b^4*c^2 - 2*A*b^3*c^3)*d^5*e^3 + 2*(117*B*b^5*c + 179*A*b^4*c^2)*d^4*e^4 - 7*(10*B*b^6 + 97*A*b^5*c)*d^3*e^5)*x^2 - (15*A*b^2*c^4*d^7*e - 161*A*b^6*d^3*e^5 + 15*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + 18*(12*B*b^4*c^2 + 5*A*b^3*c^3)*d^6*e^2 - 4*(43*B*b^5*c + 139*A*b^4*c^2)*d^5*e^3 + (46*B*b^6 + 537*A*b^5*c)*d^4*e^4)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x), 1/30*(30*((2*(B*b*c^5 - 2*A*c^6)*d^6*e^3 - (9*B*b^2*c^4 - 11*A*b*c^5)*d^5*e^4)*x^5 + (6*(B*b*c^5 - 2*A*c^6)*d^7*e^2 - (25*B*b^2*c^4 - 29*A*b*c^5)*d^6*e^3 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^5*e^4)*x^4 + 3*(2*(B*b*c^5 - 2*A*c^6)*d^8*e - 7*(B*b^2*c^4 - A*b*c^5)*d^7*e^2 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^6*e^3)*x^3 + (2*(B*b*c^5 - 2*A*c^6)*d^9 - (3*B*b^2*c^4 + A*b*c^5)*d^8*e - 3*(9*B*b^3*c^3 - 11*A*b^2*c^4)*d^7*e^2)*x^2 + (2*(B*b^2*c^4 - 2*A*b*c^5)*d^9 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^8*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 15*((7*A*b^5*c*e^8 - 2*(B*b*c^5 - 2*A*c^6)*d^5*e^3 + (8*B*b^2*c^4 - 9*A*b*c^5)*d^4*e^4 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^3*e^5 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^2*e^6 - 2*(B*b^5*c + 12*A*b^4*c^2)*d*e^7)*x^5 + (7*A*b^6*e^8 - 6*(B*b*c^5 - 2*A*c^6)*d^6*e^2 + (22*B*b^2*c^4 - 23*A*b*c^5)*d^5*e^3 - 7*(4*B*b^3*c^3 + 3*A*b^2*c^4)*d^4*e^4 + 2*(6*B*b^4*c^2 + 37*A*b^3*c^3)*d^3*e^5 + 2*(B*b^5*c - 23*A*b^4*c^2)*d^2*e^6 - (2*B*b^6 + 3*A*b^5*c)*d*e^7)*x^4 + 3*(7*A*b^6*d*e^7 - 2*(B*b*c^5 - 2*A*c^6)*d^7*e + (6*B*b^2*c^4 - 5*A*b*c^5)*d^6*e^2 - (4*B*b^3*c^3 + 13*A*b^2*c^4)*d^5*e^3 - 2*(2*B*b^4*c^2 - 11*A*b^3*c^3)*d^4*e^4 + 2*(3*B*b^5*c + A*b^4*c^2)*d^3*e^5 - (2*B*b^6 + 17*A*b^5*c)*d^2*e^6)*x^3 + (21*A*b^6*d^2*e^6 - 2*(B*b*c^5 - 2*A*c^6)*d^8 + (2*B*b^2*c^4 + 3*A*b*c^5)*d^7*e + (12*B*b^3*c^3 - 31*A*b^2*c^4)*d^6*e^2 - 14*(2*B*b^4*c^2 - A*b^3*c^3)*d^5*e^3 + 2*(11*B*b^5*c + 27*A*b^4*c^2)*d^4*e^4 - (6*B*b^6 + 65*A*b^5*c)*d^3*e^5)*x^2 + (7*A*b^6*d^3*e^5 - 2*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + (8*B*b^3*c^3 - 9*A*b^2*c^4)*d^7*e - 4*(3*B*b^4*c^2 + A*b^3*c^3)*d^6*e^2 + 2*(4*B*b^5*c + 13*A*b^4*c^2)*d^5*e^3 - 2*(B*b^6 + 12*A*b^5*c)*d^4*e^4)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(15*A*b^2*c^4*d^8 - 60*A*b^3*c^3*d^7*e + 90*A*b^4*c^2*d^6*e^2 - 60*A*b^5*c*d^5*e^3 + 15*A*b^6*d^4*e^4 + 15*(7*A*b^5*c*d*e^7 - (B*b^2*c^4 - 2*A*b*c^5)*d^5*e^3 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^4*e^4 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^3*e^5 - 2*(B*b^5*c + 12*A*b^4*c^2)*d^2*e^6)*x^4 + 5*(21*A*b^6*d*e^7 - 9*(B*b^2*c^4 - 2*A*b*c^5)*d^6*e^2 - 3*(26*B*b^3*c^3 + 11*A*b^2*c^4)*d^5*e^3 + 10*(2*B*b^4*c^2 + 17*A*b^3*c^3)*d^4*e^4 + 10*(B*b^5*c - 9*A*b^4*c^2)*d^3*e^5 - (6*B*b^6 + 23*A*b^5*c)*d^2*e^6)*x^3 + (245*A*b^6*d^2*e^6 - 45*(B*b^2*c^4 - 2*A*b*c^5)*d^7*e - 27*(8*B*b^3*c^3 + 5*A*b^2*c^4)*d^6*e^2 - 218*(B*b^4*c^2 - 2*A*b^3*c^3)*d^5*e^3 + 2*(117*B*b^5*c + 179*A*b^4*c^2)*d^4*e^4 - 7*(10*B*b^6 + 97*A*b^5*c)*d^3*e^5)*x^2 - (15*A*b^2*c^4*d^7*e - 161*A*b^6*d^3*e^5 + 15*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + 18*(12*B*b^4*c^2 + 5*A*b^3*c^3)*d^6*e^2 - 4*(43*B*b^5*c + 139*A*b^4*c^2)*d^5*e^3 + (46*B*b^6 + 537*A*b^5*c)*d^4*e^4)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x), -1/30*(30*((7*A*b^5*c*e^8 - 2*(B*b*c^5 - 2*A*c^6)*d^5*e^3 + (8*B*b^2*c^4 - 9*A*b*c^5)*d^4*e^4 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^3*e^5 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^2*e^6 - 2*(B*b^5*c + 12*A*b^4*c^2)*d*e^7)*x^5 + (7*A*b^6*e^8 - 6*(B*b*c^5 - 2*A*c^6)*d^6*e^2 + (22*B*b^2*c^4 - 23*A*b*c^5)*d^5*e^3 - 7*(4*B*b^3*c^3 + 3*A*b^2*c^4)*d^4*e^4 + 2*(6*B*b^4*c^2 + 37*A*b^3*c^3)*d^3*e^5 + 2*(B*b^5*c - 23*A*b^4*c^2)*d^2*e^6 - (2*B*b^6 + 3*A*b^5*c)*d*e^7)*x^4 + 3*(7*A*b^6*d*e^7 - 2*(B*b*c^5 - 2*A*c^6)*d^7*e + (6*B*b^2*c^4 - 5*A*b*c^5)*d^6*e^2 - (4*B*b^3*c^3 + 13*A*b^2*c^4)*d^5*e^3 - 2*(2*B*b^4*c^2 - 11*A*b^3*c^3)*d^4*e^4 + 2*(3*B*b^5*c + A*b^4*c^2)*d^3*e^5 - (2*B*b^6 + 17*A*b^5*c)*d^2*e^6)*x^3 + (21*A*b^6*d^2*e^6 - 2*(B*b*c^5 - 2*A*c^6)*d^8 + (2*B*b^2*c^4 + 3*A*b*c^5)*d^7*e + (12*B*b^3*c^3 - 31*A*b^2*c^4)*d^6*e^2 - 14*(2*B*b^4*c^2 - A*b^3*c^3)*d^5*e^3 + 2*(11*B*b^5*c + 27*A*b^4*c^2)*d^4*e^4 - (6*B*b^6 + 65*A*b^5*c)*d^3*e^5)*x^2 + (7*A*b^6*d^3*e^5 - 2*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + (8*B*b^3*c^3 - 9*A*b^2*c^4)*d^7*e - 4*(3*B*b^4*c^2 + A*b^3*c^3)*d^6*e^2 + 2*(4*B*b^5*c + 13*A*b^4*c^2)*d^5*e^3 - 2*(B*b^6 + 12*A*b^5*c)*d^4*e^4)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 15*((2*(B*b*c^5 - 2*A*c^6)*d^6*e^3 - (9*B*b^2*c^4 - 11*A*b*c^5)*d^5*e^4)*x^5 + (6*(B*b*c^5 - 2*A*c^6)*d^7*e^2 - (25*B*b^2*c^4 - 29*A*b*c^5)*d^6*e^3 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^5*e^4)*x^4 + 3*(2*(B*b*c^5 - 2*A*c^6)*d^8*e - 7*(B*b^2*c^4 - A*b*c^5)*d^7*e^2 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^6*e^3)*x^3 + (2*(B*b*c^5 - 2*A*c^6)*d^9 - (3*B*b^2*c^4 + A*b*c^5)*d^8*e - 3*(9*B*b^3*c^3 - 11*A*b^2*c^4)*d^7*e^2)*x^2 + (2*(B*b^2*c^4 - 2*A*b*c^5)*d^9 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^8*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(15*A*b^2*c^4*d^8 - 60*A*b^3*c^3*d^7*e + 90*A*b^4*c^2*d^6*e^2 - 60*A*b^5*c*d^5*e^3 + 15*A*b^6*d^4*e^4 + 15*(7*A*b^5*c*d*e^7 - (B*b^2*c^4 - 2*A*b*c^5)*d^5*e^3 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^4*e^4 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^3*e^5 - 2*(B*b^5*c + 12*A*b^4*c^2)*d^2*e^6)*x^4 + 5*(21*A*b^6*d*e^7 - 9*(B*b^2*c^4 - 2*A*b*c^5)*d^6*e^2 - 3*(26*B*b^3*c^3 + 11*A*b^2*c^4)*d^5*e^3 + 10*(2*B*b^4*c^2 + 17*A*b^3*c^3)*d^4*e^4 + 10*(B*b^5*c - 9*A*b^4*c^2)*d^3*e^5 - (6*B*b^6 + 23*A*b^5*c)*d^2*e^6)*x^3 + (245*A*b^6*d^2*e^6 - 45*(B*b^2*c^4 - 2*A*b*c^5)*d^7*e - 27*(8*B*b^3*c^3 + 5*A*b^2*c^4)*d^6*e^2 - 218*(B*b^4*c^2 - 2*A*b^3*c^3)*d^5*e^3 + 2*(117*B*b^5*c + 179*A*b^4*c^2)*d^4*e^4 - 7*(10*B*b^6 + 97*A*b^5*c)*d^3*e^5)*x^2 - (15*A*b^2*c^4*d^7*e - 161*A*b^6*d^3*e^5 + 15*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + 18*(12*B*b^4*c^2 + 5*A*b^3*c^3)*d^6*e^2 - 4*(43*B*b^5*c + 139*A*b^4*c^2)*d^5*e^3 + (46*B*b^6 + 537*A*b^5*c)*d^4*e^4)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x), 1/15*(15*((2*(B*b*c^5 - 2*A*c^6)*d^6*e^3 - (9*B*b^2*c^4 - 11*A*b*c^5)*d^5*e^4)*x^5 + (6*(B*b*c^5 - 2*A*c^6)*d^7*e^2 - (25*B*b^2*c^4 - 29*A*b*c^5)*d^6*e^3 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^5*e^4)*x^4 + 3*(2*(B*b*c^5 - 2*A*c^6)*d^8*e - 7*(B*b^2*c^4 - A*b*c^5)*d^7*e^2 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^6*e^3)*x^3 + (2*(B*b*c^5 - 2*A*c^6)*d^9 - (3*B*b^2*c^4 + A*b*c^5)*d^8*e - 3*(9*B*b^3*c^3 - 11*A*b^2*c^4)*d^7*e^2)*x^2 + (2*(B*b^2*c^4 - 2*A*b*c^5)*d^9 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^8*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 15*((7*A*b^5*c*e^8 - 2*(B*b*c^5 - 2*A*c^6)*d^5*e^3 + (8*B*b^2*c^4 - 9*A*b*c^5)*d^4*e^4 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^3*e^5 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^2*e^6 - 2*(B*b^5*c + 12*A*b^4*c^2)*d*e^7)*x^5 + (7*A*b^6*e^8 - 6*(B*b*c^5 - 2*A*c^6)*d^6*e^2 + (22*B*b^2*c^4 - 23*A*b*c^5)*d^5*e^3 - 7*(4*B*b^3*c^3 + 3*A*b^2*c^4)*d^4*e^4 + 2*(6*B*b^4*c^2 + 37*A*b^3*c^3)*d^3*e^5 + 2*(B*b^5*c - 23*A*b^4*c^2)*d^2*e^6 - (2*B*b^6 + 3*A*b^5*c)*d*e^7)*x^4 + 3*(7*A*b^6*d*e^7 - 2*(B*b*c^5 - 2*A*c^6)*d^7*e + (6*B*b^2*c^4 - 5*A*b*c^5)*d^6*e^2 - (4*B*b^3*c^3 + 13*A*b^2*c^4)*d^5*e^3 - 2*(2*B*b^4*c^2 - 11*A*b^3*c^3)*d^4*e^4 + 2*(3*B*b^5*c + A*b^4*c^2)*d^3*e^5 - (2*B*b^6 + 17*A*b^5*c)*d^2*e^6)*x^3 + (21*A*b^6*d^2*e^6 - 2*(B*b*c^5 - 2*A*c^6)*d^8 + (2*B*b^2*c^4 + 3*A*b*c^5)*d^7*e + (12*B*b^3*c^3 - 31*A*b^2*c^4)*d^6*e^2 - 14*(2*B*b^4*c^2 - A*b^3*c^3)*d^5*e^3 + 2*(11*B*b^5*c + 27*A*b^4*c^2)*d^4*e^4 - (6*B*b^6 + 65*A*b^5*c)*d^3*e^5)*x^2 + (7*A*b^6*d^3*e^5 - 2*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + (8*B*b^3*c^3 - 9*A*b^2*c^4)*d^7*e - 4*(3*B*b^4*c^2 + A*b^3*c^3)*d^6*e^2 + 2*(4*B*b^5*c + 13*A*b^4*c^2)*d^5*e^3 - 2*(B*b^6 + 12*A*b^5*c)*d^4*e^4)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (15*A*b^2*c^4*d^8 - 60*A*b^3*c^3*d^7*e + 90*A*b^4*c^2*d^6*e^2 - 60*A*b^5*c*d^5*e^3 + 15*A*b^6*d^4*e^4 + 15*(7*A*b^5*c*d*e^7 - (B*b^2*c^4 - 2*A*b*c^5)*d^5*e^3 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^4*e^4 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^3*e^5 - 2*(B*b^5*c + 12*A*b^4*c^2)*d^2*e^6)*x^4 + 5*(21*A*b^6*d*e^7 - 9*(B*b^2*c^4 - 2*A*b*c^5)*d^6*e^2 - 3*(26*B*b^3*c^3 + 11*A*b^2*c^4)*d^5*e^3 + 10*(2*B*b^4*c^2 + 17*A*b^3*c^3)*d^4*e^4 + 10*(B*b^5*c - 9*A*b^4*c^2)*d^3*e^5 - (6*B*b^6 + 23*A*b^5*c)*d^2*e^6)*x^3 + (245*A*b^6*d^2*e^6 - 45*(B*b^2*c^4 - 2*A*b*c^5)*d^7*e - 27*(8*B*b^3*c^3 + 5*A*b^2*c^4)*d^6*e^2 - 218*(B*b^4*c^2 - 2*A*b^3*c^3)*d^5*e^3 + 2*(117*B*b^5*c + 179*A*b^4*c^2)*d^4*e^4 - 7*(10*B*b^6 + 97*A*b^5*c)*d^3*e^5)*x^2 - (15*A*b^2*c^4*d^7*e - 161*A*b^6*d^3*e^5 + 15*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + 18*(12*B*b^4*c^2 + 5*A*b^3*c^3)*d^6*e^2 - 4*(43*B*b^5*c + 139*A*b^4*c^2)*d^5*e^3 + (46*B*b^6 + 537*A*b^5*c)*d^4*e^4)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x)]","B",0
1247,1,3989,0,141.136557," ","integrate((B*x+A)*(e*x+d)^(9/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} - 4 \, {\left(2 \, B b^{2} c^{5} - 7 \, A b c^{6}\right)} d^{3} e - 3 \, {\left(B b^{3} c^{4} + 3 \, A b^{2} c^{5}\right)} d^{2} e^{2} - 2 \, {\left(B b^{4} c^{3} + A b^{3} c^{4}\right)} d e^{3} + {\left(5 \, B b^{5} c^{2} - A b^{4} c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 4 \, {\left(2 \, B b^{3} c^{4} - 7 \, A b^{2} c^{5}\right)} d^{3} e - 3 \, {\left(B b^{4} c^{3} + 3 \, A b^{3} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(B b^{5} c^{2} + A b^{4} c^{3}\right)} d e^{3} + {\left(5 \, B b^{6} c - A b^{5} c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} - 4 \, {\left(2 \, B b^{4} c^{3} - 7 \, A b^{3} c^{4}\right)} d^{3} e - 3 \, {\left(B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(B b^{6} c + A b^{5} c^{2}\right)} d e^{3} + {\left(5 \, B b^{7} - A b^{6} c\right)} e^{4}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 3 \, {\left({\left(21 \, A b^{2} c^{5} d^{2} e^{2} - 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} + 12 \, {\left(B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{3} e\right)} x^{4} + 2 \, {\left(21 \, A b^{3} c^{4} d^{2} e^{2} - 8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} + 12 \, {\left(B b^{3} c^{4} - 3 \, A b^{2} c^{5}\right)} d^{3} e\right)} x^{3} + {\left(21 \, A b^{4} c^{3} d^{2} e^{2} - 8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} + 12 \, {\left(B b^{4} c^{3} - 3 \, A b^{3} c^{4}\right)} d^{3} e\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(8 \, B b^{5} c^{2} e^{4} x^{4} - 2 \, A b^{4} c^{3} d^{4} - {\left(12 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 3 \, {\left(5 \, B b^{3} c^{4} - 16 \, A b^{2} c^{5}\right)} d^{3} e - 3 \, {\left(B b^{4} c^{3} + 7 \, A b^{3} c^{4}\right)} d^{2} e^{2} + {\left(19 \, B b^{5} c^{2} - 3 \, A b^{4} c^{3}\right)} d e^{3} - 5 \, {\left(5 \, B b^{6} c - A b^{5} c^{2}\right)} e^{4}\right)} x^{3} - {\left(18 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} - {\left(23 \, B b^{4} c^{3} - 73 \, A b^{3} c^{4}\right)} d^{3} e + 3 \, {\left(3 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{2} e^{2} + {\left(11 \, B b^{6} c + 5 \, A b^{5} c^{2}\right)} d e^{3} - 3 \, {\left(5 \, B b^{7} - A b^{6} c\right)} e^{4}\right)} x^{2} - {\left(17 \, A b^{4} c^{3} d^{3} e + 4 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{4}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{5} x^{4} + 2 \, b^{6} c^{4} x^{3} + b^{7} c^{3} x^{2}\right)}}, -\frac{6 \, {\left({\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} - 4 \, {\left(2 \, B b^{2} c^{5} - 7 \, A b c^{6}\right)} d^{3} e - 3 \, {\left(B b^{3} c^{4} + 3 \, A b^{2} c^{5}\right)} d^{2} e^{2} - 2 \, {\left(B b^{4} c^{3} + A b^{3} c^{4}\right)} d e^{3} + {\left(5 \, B b^{5} c^{2} - A b^{4} c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 4 \, {\left(2 \, B b^{3} c^{4} - 7 \, A b^{2} c^{5}\right)} d^{3} e - 3 \, {\left(B b^{4} c^{3} + 3 \, A b^{3} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(B b^{5} c^{2} + A b^{4} c^{3}\right)} d e^{3} + {\left(5 \, B b^{6} c - A b^{5} c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} - 4 \, {\left(2 \, B b^{4} c^{3} - 7 \, A b^{3} c^{4}\right)} d^{3} e - 3 \, {\left(B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(B b^{6} c + A b^{5} c^{2}\right)} d e^{3} + {\left(5 \, B b^{7} - A b^{6} c\right)} e^{4}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) - 3 \, {\left({\left(21 \, A b^{2} c^{5} d^{2} e^{2} - 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} + 12 \, {\left(B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{3} e\right)} x^{4} + 2 \, {\left(21 \, A b^{3} c^{4} d^{2} e^{2} - 8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} + 12 \, {\left(B b^{3} c^{4} - 3 \, A b^{2} c^{5}\right)} d^{3} e\right)} x^{3} + {\left(21 \, A b^{4} c^{3} d^{2} e^{2} - 8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} + 12 \, {\left(B b^{4} c^{3} - 3 \, A b^{3} c^{4}\right)} d^{3} e\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(8 \, B b^{5} c^{2} e^{4} x^{4} - 2 \, A b^{4} c^{3} d^{4} - {\left(12 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 3 \, {\left(5 \, B b^{3} c^{4} - 16 \, A b^{2} c^{5}\right)} d^{3} e - 3 \, {\left(B b^{4} c^{3} + 7 \, A b^{3} c^{4}\right)} d^{2} e^{2} + {\left(19 \, B b^{5} c^{2} - 3 \, A b^{4} c^{3}\right)} d e^{3} - 5 \, {\left(5 \, B b^{6} c - A b^{5} c^{2}\right)} e^{4}\right)} x^{3} - {\left(18 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} - {\left(23 \, B b^{4} c^{3} - 73 \, A b^{3} c^{4}\right)} d^{3} e + 3 \, {\left(3 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{2} e^{2} + {\left(11 \, B b^{6} c + 5 \, A b^{5} c^{2}\right)} d e^{3} - 3 \, {\left(5 \, B b^{7} - A b^{6} c\right)} e^{4}\right)} x^{2} - {\left(17 \, A b^{4} c^{3} d^{3} e + 4 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{4}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{5} x^{4} + 2 \, b^{6} c^{4} x^{3} + b^{7} c^{3} x^{2}\right)}}, \frac{6 \, {\left({\left(21 \, A b^{2} c^{5} d^{2} e^{2} - 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} + 12 \, {\left(B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{3} e\right)} x^{4} + 2 \, {\left(21 \, A b^{3} c^{4} d^{2} e^{2} - 8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} + 12 \, {\left(B b^{3} c^{4} - 3 \, A b^{2} c^{5}\right)} d^{3} e\right)} x^{3} + {\left(21 \, A b^{4} c^{3} d^{2} e^{2} - 8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} + 12 \, {\left(B b^{4} c^{3} - 3 \, A b^{3} c^{4}\right)} d^{3} e\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left({\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} - 4 \, {\left(2 \, B b^{2} c^{5} - 7 \, A b c^{6}\right)} d^{3} e - 3 \, {\left(B b^{3} c^{4} + 3 \, A b^{2} c^{5}\right)} d^{2} e^{2} - 2 \, {\left(B b^{4} c^{3} + A b^{3} c^{4}\right)} d e^{3} + {\left(5 \, B b^{5} c^{2} - A b^{4} c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 4 \, {\left(2 \, B b^{3} c^{4} - 7 \, A b^{2} c^{5}\right)} d^{3} e - 3 \, {\left(B b^{4} c^{3} + 3 \, A b^{3} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(B b^{5} c^{2} + A b^{4} c^{3}\right)} d e^{3} + {\left(5 \, B b^{6} c - A b^{5} c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} - 4 \, {\left(2 \, B b^{4} c^{3} - 7 \, A b^{3} c^{4}\right)} d^{3} e - 3 \, {\left(B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(B b^{6} c + A b^{5} c^{2}\right)} d e^{3} + {\left(5 \, B b^{7} - A b^{6} c\right)} e^{4}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(8 \, B b^{5} c^{2} e^{4} x^{4} - 2 \, A b^{4} c^{3} d^{4} - {\left(12 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 3 \, {\left(5 \, B b^{3} c^{4} - 16 \, A b^{2} c^{5}\right)} d^{3} e - 3 \, {\left(B b^{4} c^{3} + 7 \, A b^{3} c^{4}\right)} d^{2} e^{2} + {\left(19 \, B b^{5} c^{2} - 3 \, A b^{4} c^{3}\right)} d e^{3} - 5 \, {\left(5 \, B b^{6} c - A b^{5} c^{2}\right)} e^{4}\right)} x^{3} - {\left(18 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} - {\left(23 \, B b^{4} c^{3} - 73 \, A b^{3} c^{4}\right)} d^{3} e + 3 \, {\left(3 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{2} e^{2} + {\left(11 \, B b^{6} c + 5 \, A b^{5} c^{2}\right)} d e^{3} - 3 \, {\left(5 \, B b^{7} - A b^{6} c\right)} e^{4}\right)} x^{2} - {\left(17 \, A b^{4} c^{3} d^{3} e + 4 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{4}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{5} x^{4} + 2 \, b^{6} c^{4} x^{3} + b^{7} c^{3} x^{2}\right)}}, -\frac{3 \, {\left({\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} - 4 \, {\left(2 \, B b^{2} c^{5} - 7 \, A b c^{6}\right)} d^{3} e - 3 \, {\left(B b^{3} c^{4} + 3 \, A b^{2} c^{5}\right)} d^{2} e^{2} - 2 \, {\left(B b^{4} c^{3} + A b^{3} c^{4}\right)} d e^{3} + {\left(5 \, B b^{5} c^{2} - A b^{4} c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 4 \, {\left(2 \, B b^{3} c^{4} - 7 \, A b^{2} c^{5}\right)} d^{3} e - 3 \, {\left(B b^{4} c^{3} + 3 \, A b^{3} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(B b^{5} c^{2} + A b^{4} c^{3}\right)} d e^{3} + {\left(5 \, B b^{6} c - A b^{5} c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} - 4 \, {\left(2 \, B b^{4} c^{3} - 7 \, A b^{3} c^{4}\right)} d^{3} e - 3 \, {\left(B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(B b^{6} c + A b^{5} c^{2}\right)} d e^{3} + {\left(5 \, B b^{7} - A b^{6} c\right)} e^{4}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) - 3 \, {\left({\left(21 \, A b^{2} c^{5} d^{2} e^{2} - 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} + 12 \, {\left(B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{3} e\right)} x^{4} + 2 \, {\left(21 \, A b^{3} c^{4} d^{2} e^{2} - 8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} + 12 \, {\left(B b^{3} c^{4} - 3 \, A b^{2} c^{5}\right)} d^{3} e\right)} x^{3} + {\left(21 \, A b^{4} c^{3} d^{2} e^{2} - 8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} + 12 \, {\left(B b^{4} c^{3} - 3 \, A b^{3} c^{4}\right)} d^{3} e\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(8 \, B b^{5} c^{2} e^{4} x^{4} - 2 \, A b^{4} c^{3} d^{4} - {\left(12 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 3 \, {\left(5 \, B b^{3} c^{4} - 16 \, A b^{2} c^{5}\right)} d^{3} e - 3 \, {\left(B b^{4} c^{3} + 7 \, A b^{3} c^{4}\right)} d^{2} e^{2} + {\left(19 \, B b^{5} c^{2} - 3 \, A b^{4} c^{3}\right)} d e^{3} - 5 \, {\left(5 \, B b^{6} c - A b^{5} c^{2}\right)} e^{4}\right)} x^{3} - {\left(18 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{4} - {\left(23 \, B b^{4} c^{3} - 73 \, A b^{3} c^{4}\right)} d^{3} e + 3 \, {\left(3 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{2} e^{2} + {\left(11 \, B b^{6} c + 5 \, A b^{5} c^{2}\right)} d e^{3} - 3 \, {\left(5 \, B b^{7} - A b^{6} c\right)} e^{4}\right)} x^{2} - {\left(17 \, A b^{4} c^{3} d^{3} e + 4 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{4}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(b^{5} c^{5} x^{4} + 2 \, b^{6} c^{4} x^{3} + b^{7} c^{3} x^{2}\right)}}\right]"," ",0,"[1/8*(3*((8*(B*b*c^6 - 2*A*c^7)*d^4 - 4*(2*B*b^2*c^5 - 7*A*b*c^6)*d^3*e - 3*(B*b^3*c^4 + 3*A*b^2*c^5)*d^2*e^2 - 2*(B*b^4*c^3 + A*b^3*c^4)*d*e^3 + (5*B*b^5*c^2 - A*b^4*c^3)*e^4)*x^4 + 2*(8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 4*(2*B*b^3*c^4 - 7*A*b^2*c^5)*d^3*e - 3*(B*b^4*c^3 + 3*A*b^3*c^4)*d^2*e^2 - 2*(B*b^5*c^2 + A*b^4*c^3)*d*e^3 + (5*B*b^6*c - A*b^5*c^2)*e^4)*x^3 + (8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 - 4*(2*B*b^4*c^3 - 7*A*b^3*c^4)*d^3*e - 3*(B*b^5*c^2 + 3*A*b^4*c^3)*d^2*e^2 - 2*(B*b^6*c + A*b^5*c^2)*d*e^3 + (5*B*b^7 - A*b^6*c)*e^4)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 3*((21*A*b^2*c^5*d^2*e^2 - 8*(B*b*c^6 - 2*A*c^7)*d^4 + 12*(B*b^2*c^5 - 3*A*b*c^6)*d^3*e)*x^4 + 2*(21*A*b^3*c^4*d^2*e^2 - 8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 + 12*(B*b^3*c^4 - 3*A*b^2*c^5)*d^3*e)*x^3 + (21*A*b^4*c^3*d^2*e^2 - 8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 + 12*(B*b^4*c^3 - 3*A*b^3*c^4)*d^3*e)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(8*B*b^5*c^2*e^4*x^4 - 2*A*b^4*c^3*d^4 - (12*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 3*(5*B*b^3*c^4 - 16*A*b^2*c^5)*d^3*e - 3*(B*b^4*c^3 + 7*A*b^3*c^4)*d^2*e^2 + (19*B*b^5*c^2 - 3*A*b^4*c^3)*d*e^3 - 5*(5*B*b^6*c - A*b^5*c^2)*e^4)*x^3 - (18*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 - (23*B*b^4*c^3 - 73*A*b^3*c^4)*d^3*e + 3*(3*B*b^5*c^2 - 11*A*b^4*c^3)*d^2*e^2 + (11*B*b^6*c + 5*A*b^5*c^2)*d*e^3 - 3*(5*B*b^7 - A*b^6*c)*e^4)*x^2 - (17*A*b^4*c^3*d^3*e + 4*(B*b^4*c^3 - 2*A*b^3*c^4)*d^4)*x)*sqrt(e*x + d))/(b^5*c^5*x^4 + 2*b^6*c^4*x^3 + b^7*c^3*x^2), -1/8*(6*((8*(B*b*c^6 - 2*A*c^7)*d^4 - 4*(2*B*b^2*c^5 - 7*A*b*c^6)*d^3*e - 3*(B*b^3*c^4 + 3*A*b^2*c^5)*d^2*e^2 - 2*(B*b^4*c^3 + A*b^3*c^4)*d*e^3 + (5*B*b^5*c^2 - A*b^4*c^3)*e^4)*x^4 + 2*(8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 4*(2*B*b^3*c^4 - 7*A*b^2*c^5)*d^3*e - 3*(B*b^4*c^3 + 3*A*b^3*c^4)*d^2*e^2 - 2*(B*b^5*c^2 + A*b^4*c^3)*d*e^3 + (5*B*b^6*c - A*b^5*c^2)*e^4)*x^3 + (8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 - 4*(2*B*b^4*c^3 - 7*A*b^3*c^4)*d^3*e - 3*(B*b^5*c^2 + 3*A*b^4*c^3)*d^2*e^2 - 2*(B*b^6*c + A*b^5*c^2)*d*e^3 + (5*B*b^7 - A*b^6*c)*e^4)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) - 3*((21*A*b^2*c^5*d^2*e^2 - 8*(B*b*c^6 - 2*A*c^7)*d^4 + 12*(B*b^2*c^5 - 3*A*b*c^6)*d^3*e)*x^4 + 2*(21*A*b^3*c^4*d^2*e^2 - 8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 + 12*(B*b^3*c^4 - 3*A*b^2*c^5)*d^3*e)*x^3 + (21*A*b^4*c^3*d^2*e^2 - 8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 + 12*(B*b^4*c^3 - 3*A*b^3*c^4)*d^3*e)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(8*B*b^5*c^2*e^4*x^4 - 2*A*b^4*c^3*d^4 - (12*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 3*(5*B*b^3*c^4 - 16*A*b^2*c^5)*d^3*e - 3*(B*b^4*c^3 + 7*A*b^3*c^4)*d^2*e^2 + (19*B*b^5*c^2 - 3*A*b^4*c^3)*d*e^3 - 5*(5*B*b^6*c - A*b^5*c^2)*e^4)*x^3 - (18*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 - (23*B*b^4*c^3 - 73*A*b^3*c^4)*d^3*e + 3*(3*B*b^5*c^2 - 11*A*b^4*c^3)*d^2*e^2 + (11*B*b^6*c + 5*A*b^5*c^2)*d*e^3 - 3*(5*B*b^7 - A*b^6*c)*e^4)*x^2 - (17*A*b^4*c^3*d^3*e + 4*(B*b^4*c^3 - 2*A*b^3*c^4)*d^4)*x)*sqrt(e*x + d))/(b^5*c^5*x^4 + 2*b^6*c^4*x^3 + b^7*c^3*x^2), 1/8*(6*((21*A*b^2*c^5*d^2*e^2 - 8*(B*b*c^6 - 2*A*c^7)*d^4 + 12*(B*b^2*c^5 - 3*A*b*c^6)*d^3*e)*x^4 + 2*(21*A*b^3*c^4*d^2*e^2 - 8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 + 12*(B*b^3*c^4 - 3*A*b^2*c^5)*d^3*e)*x^3 + (21*A*b^4*c^3*d^2*e^2 - 8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 + 12*(B*b^4*c^3 - 3*A*b^3*c^4)*d^3*e)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*((8*(B*b*c^6 - 2*A*c^7)*d^4 - 4*(2*B*b^2*c^5 - 7*A*b*c^6)*d^3*e - 3*(B*b^3*c^4 + 3*A*b^2*c^5)*d^2*e^2 - 2*(B*b^4*c^3 + A*b^3*c^4)*d*e^3 + (5*B*b^5*c^2 - A*b^4*c^3)*e^4)*x^4 + 2*(8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 4*(2*B*b^3*c^4 - 7*A*b^2*c^5)*d^3*e - 3*(B*b^4*c^3 + 3*A*b^3*c^4)*d^2*e^2 - 2*(B*b^5*c^2 + A*b^4*c^3)*d*e^3 + (5*B*b^6*c - A*b^5*c^2)*e^4)*x^3 + (8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 - 4*(2*B*b^4*c^3 - 7*A*b^3*c^4)*d^3*e - 3*(B*b^5*c^2 + 3*A*b^4*c^3)*d^2*e^2 - 2*(B*b^6*c + A*b^5*c^2)*d*e^3 + (5*B*b^7 - A*b^6*c)*e^4)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(8*B*b^5*c^2*e^4*x^4 - 2*A*b^4*c^3*d^4 - (12*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 3*(5*B*b^3*c^4 - 16*A*b^2*c^5)*d^3*e - 3*(B*b^4*c^3 + 7*A*b^3*c^4)*d^2*e^2 + (19*B*b^5*c^2 - 3*A*b^4*c^3)*d*e^3 - 5*(5*B*b^6*c - A*b^5*c^2)*e^4)*x^3 - (18*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 - (23*B*b^4*c^3 - 73*A*b^3*c^4)*d^3*e + 3*(3*B*b^5*c^2 - 11*A*b^4*c^3)*d^2*e^2 + (11*B*b^6*c + 5*A*b^5*c^2)*d*e^3 - 3*(5*B*b^7 - A*b^6*c)*e^4)*x^2 - (17*A*b^4*c^3*d^3*e + 4*(B*b^4*c^3 - 2*A*b^3*c^4)*d^4)*x)*sqrt(e*x + d))/(b^5*c^5*x^4 + 2*b^6*c^4*x^3 + b^7*c^3*x^2), -1/4*(3*((8*(B*b*c^6 - 2*A*c^7)*d^4 - 4*(2*B*b^2*c^5 - 7*A*b*c^6)*d^3*e - 3*(B*b^3*c^4 + 3*A*b^2*c^5)*d^2*e^2 - 2*(B*b^4*c^3 + A*b^3*c^4)*d*e^3 + (5*B*b^5*c^2 - A*b^4*c^3)*e^4)*x^4 + 2*(8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 4*(2*B*b^3*c^4 - 7*A*b^2*c^5)*d^3*e - 3*(B*b^4*c^3 + 3*A*b^3*c^4)*d^2*e^2 - 2*(B*b^5*c^2 + A*b^4*c^3)*d*e^3 + (5*B*b^6*c - A*b^5*c^2)*e^4)*x^3 + (8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 - 4*(2*B*b^4*c^3 - 7*A*b^3*c^4)*d^3*e - 3*(B*b^5*c^2 + 3*A*b^4*c^3)*d^2*e^2 - 2*(B*b^6*c + A*b^5*c^2)*d*e^3 + (5*B*b^7 - A*b^6*c)*e^4)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) - 3*((21*A*b^2*c^5*d^2*e^2 - 8*(B*b*c^6 - 2*A*c^7)*d^4 + 12*(B*b^2*c^5 - 3*A*b*c^6)*d^3*e)*x^4 + 2*(21*A*b^3*c^4*d^2*e^2 - 8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 + 12*(B*b^3*c^4 - 3*A*b^2*c^5)*d^3*e)*x^3 + (21*A*b^4*c^3*d^2*e^2 - 8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 + 12*(B*b^4*c^3 - 3*A*b^3*c^4)*d^3*e)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (8*B*b^5*c^2*e^4*x^4 - 2*A*b^4*c^3*d^4 - (12*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 3*(5*B*b^3*c^4 - 16*A*b^2*c^5)*d^3*e - 3*(B*b^4*c^3 + 7*A*b^3*c^4)*d^2*e^2 + (19*B*b^5*c^2 - 3*A*b^4*c^3)*d*e^3 - 5*(5*B*b^6*c - A*b^5*c^2)*e^4)*x^3 - (18*(B*b^3*c^4 - 2*A*b^2*c^5)*d^4 - (23*B*b^4*c^3 - 73*A*b^3*c^4)*d^3*e + 3*(3*B*b^5*c^2 - 11*A*b^4*c^3)*d^2*e^2 + (11*B*b^6*c + 5*A*b^5*c^2)*d*e^3 - 3*(5*B*b^7 - A*b^6*c)*e^4)*x^2 - (17*A*b^4*c^3*d^3*e + 4*(B*b^4*c^3 - 2*A*b^3*c^4)*d^4)*x)*sqrt(e*x + d))/(b^5*c^5*x^4 + 2*b^6*c^4*x^3 + b^7*c^3*x^2)]","B",0
1248,1,3378,0,34.354388," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 4 \, {\left(4 \, B b^{2} c^{4} - 15 \, A b c^{5}\right)} d^{2} e - {\left(5 \, B b^{3} c^{3} + 11 \, A b^{2} c^{4}\right)} d e^{2} - {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} e^{3}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 4 \, {\left(4 \, B b^{3} c^{3} - 15 \, A b^{2} c^{4}\right)} d^{2} e - {\left(5 \, B b^{4} c^{2} + 11 \, A b^{3} c^{3}\right)} d e^{2} - {\left(3 \, B b^{5} c + A b^{4} c^{2}\right)} e^{3}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 4 \, {\left(4 \, B b^{4} c^{2} - 15 \, A b^{3} c^{3}\right)} d^{2} e - {\left(5 \, B b^{5} c + 11 \, A b^{4} c^{2}\right)} d e^{2} - {\left(3 \, B b^{6} + A b^{5} c\right)} e^{3}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - {\left({\left(35 \, A b^{2} c^{4} d e^{2} - 24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} + 28 \, {\left(B b^{2} c^{4} - 3 \, A b c^{5}\right)} d^{2} e\right)} x^{4} + 2 \, {\left(35 \, A b^{3} c^{3} d e^{2} - 24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + 28 \, {\left(B b^{3} c^{3} - 3 \, A b^{2} c^{4}\right)} d^{2} e\right)} x^{3} + {\left(35 \, A b^{4} c^{2} d e^{2} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} + 28 \, {\left(B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, A b^{4} c^{2} d^{3} + {\left(12 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - {\left(11 \, B b^{3} c^{3} - 36 \, A b^{2} c^{4}\right)} d^{2} e - 2 \, {\left(B b^{4} c^{2} + 5 \, A b^{3} c^{3}\right)} d e^{2} + {\left(5 \, B b^{5} c - A b^{4} c^{2}\right)} e^{3}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - {\left(17 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{2} e + 4 \, {\left(B b^{5} c - 4 \, A b^{4} c^{2}\right)} d e^{2} + {\left(3 \, B b^{6} + A b^{5} c\right)} e^{3}\right)} x^{2} + {\left(13 \, A b^{4} c^{2} d^{2} e + 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}, -\frac{2 \, {\left({\left(24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 4 \, {\left(4 \, B b^{2} c^{4} - 15 \, A b c^{5}\right)} d^{2} e - {\left(5 \, B b^{3} c^{3} + 11 \, A b^{2} c^{4}\right)} d e^{2} - {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} e^{3}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 4 \, {\left(4 \, B b^{3} c^{3} - 15 \, A b^{2} c^{4}\right)} d^{2} e - {\left(5 \, B b^{4} c^{2} + 11 \, A b^{3} c^{3}\right)} d e^{2} - {\left(3 \, B b^{5} c + A b^{4} c^{2}\right)} e^{3}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 4 \, {\left(4 \, B b^{4} c^{2} - 15 \, A b^{3} c^{3}\right)} d^{2} e - {\left(5 \, B b^{5} c + 11 \, A b^{4} c^{2}\right)} d e^{2} - {\left(3 \, B b^{6} + A b^{5} c\right)} e^{3}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) - {\left({\left(35 \, A b^{2} c^{4} d e^{2} - 24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} + 28 \, {\left(B b^{2} c^{4} - 3 \, A b c^{5}\right)} d^{2} e\right)} x^{4} + 2 \, {\left(35 \, A b^{3} c^{3} d e^{2} - 24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + 28 \, {\left(B b^{3} c^{3} - 3 \, A b^{2} c^{4}\right)} d^{2} e\right)} x^{3} + {\left(35 \, A b^{4} c^{2} d e^{2} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} + 28 \, {\left(B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, A b^{4} c^{2} d^{3} + {\left(12 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - {\left(11 \, B b^{3} c^{3} - 36 \, A b^{2} c^{4}\right)} d^{2} e - 2 \, {\left(B b^{4} c^{2} + 5 \, A b^{3} c^{3}\right)} d e^{2} + {\left(5 \, B b^{5} c - A b^{4} c^{2}\right)} e^{3}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - {\left(17 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{2} e + 4 \, {\left(B b^{5} c - 4 \, A b^{4} c^{2}\right)} d e^{2} + {\left(3 \, B b^{6} + A b^{5} c\right)} e^{3}\right)} x^{2} + {\left(13 \, A b^{4} c^{2} d^{2} e + 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}, \frac{2 \, {\left({\left(35 \, A b^{2} c^{4} d e^{2} - 24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} + 28 \, {\left(B b^{2} c^{4} - 3 \, A b c^{5}\right)} d^{2} e\right)} x^{4} + 2 \, {\left(35 \, A b^{3} c^{3} d e^{2} - 24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + 28 \, {\left(B b^{3} c^{3} - 3 \, A b^{2} c^{4}\right)} d^{2} e\right)} x^{3} + {\left(35 \, A b^{4} c^{2} d e^{2} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} + 28 \, {\left(B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left({\left(24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 4 \, {\left(4 \, B b^{2} c^{4} - 15 \, A b c^{5}\right)} d^{2} e - {\left(5 \, B b^{3} c^{3} + 11 \, A b^{2} c^{4}\right)} d e^{2} - {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} e^{3}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 4 \, {\left(4 \, B b^{3} c^{3} - 15 \, A b^{2} c^{4}\right)} d^{2} e - {\left(5 \, B b^{4} c^{2} + 11 \, A b^{3} c^{3}\right)} d e^{2} - {\left(3 \, B b^{5} c + A b^{4} c^{2}\right)} e^{3}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 4 \, {\left(4 \, B b^{4} c^{2} - 15 \, A b^{3} c^{3}\right)} d^{2} e - {\left(5 \, B b^{5} c + 11 \, A b^{4} c^{2}\right)} d e^{2} - {\left(3 \, B b^{6} + A b^{5} c\right)} e^{3}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - 2 \, {\left(2 \, A b^{4} c^{2} d^{3} + {\left(12 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - {\left(11 \, B b^{3} c^{3} - 36 \, A b^{2} c^{4}\right)} d^{2} e - 2 \, {\left(B b^{4} c^{2} + 5 \, A b^{3} c^{3}\right)} d e^{2} + {\left(5 \, B b^{5} c - A b^{4} c^{2}\right)} e^{3}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - {\left(17 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{2} e + 4 \, {\left(B b^{5} c - 4 \, A b^{4} c^{2}\right)} d e^{2} + {\left(3 \, B b^{6} + A b^{5} c\right)} e^{3}\right)} x^{2} + {\left(13 \, A b^{4} c^{2} d^{2} e + 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}, -\frac{{\left({\left(24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 4 \, {\left(4 \, B b^{2} c^{4} - 15 \, A b c^{5}\right)} d^{2} e - {\left(5 \, B b^{3} c^{3} + 11 \, A b^{2} c^{4}\right)} d e^{2} - {\left(3 \, B b^{4} c^{2} + A b^{3} c^{3}\right)} e^{3}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 4 \, {\left(4 \, B b^{3} c^{3} - 15 \, A b^{2} c^{4}\right)} d^{2} e - {\left(5 \, B b^{4} c^{2} + 11 \, A b^{3} c^{3}\right)} d e^{2} - {\left(3 \, B b^{5} c + A b^{4} c^{2}\right)} e^{3}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 4 \, {\left(4 \, B b^{4} c^{2} - 15 \, A b^{3} c^{3}\right)} d^{2} e - {\left(5 \, B b^{5} c + 11 \, A b^{4} c^{2}\right)} d e^{2} - {\left(3 \, B b^{6} + A b^{5} c\right)} e^{3}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) - {\left({\left(35 \, A b^{2} c^{4} d e^{2} - 24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} + 28 \, {\left(B b^{2} c^{4} - 3 \, A b c^{5}\right)} d^{2} e\right)} x^{4} + 2 \, {\left(35 \, A b^{3} c^{3} d e^{2} - 24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} + 28 \, {\left(B b^{3} c^{3} - 3 \, A b^{2} c^{4}\right)} d^{2} e\right)} x^{3} + {\left(35 \, A b^{4} c^{2} d e^{2} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} + 28 \, {\left(B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(2 \, A b^{4} c^{2} d^{3} + {\left(12 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - {\left(11 \, B b^{3} c^{3} - 36 \, A b^{2} c^{4}\right)} d^{2} e - 2 \, {\left(B b^{4} c^{2} + 5 \, A b^{3} c^{3}\right)} d e^{2} + {\left(5 \, B b^{5} c - A b^{4} c^{2}\right)} e^{3}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - {\left(17 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{2} e + 4 \, {\left(B b^{5} c - 4 \, A b^{4} c^{2}\right)} d e^{2} + {\left(3 \, B b^{6} + A b^{5} c\right)} e^{3}\right)} x^{2} + {\left(13 \, A b^{4} c^{2} d^{2} e + 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}\right]"," ",0,"[-1/8*(((24*(B*b*c^5 - 2*A*c^6)*d^3 - 4*(4*B*b^2*c^4 - 15*A*b*c^5)*d^2*e - (5*B*b^3*c^3 + 11*A*b^2*c^4)*d*e^2 - (3*B*b^4*c^2 + A*b^3*c^3)*e^3)*x^4 + 2*(24*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 4*(4*B*b^3*c^3 - 15*A*b^2*c^4)*d^2*e - (5*B*b^4*c^2 + 11*A*b^3*c^3)*d*e^2 - (3*B*b^5*c + A*b^4*c^2)*e^3)*x^3 + (24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 4*(4*B*b^4*c^2 - 15*A*b^3*c^3)*d^2*e - (5*B*b^5*c + 11*A*b^4*c^2)*d*e^2 - (3*B*b^6 + A*b^5*c)*e^3)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - ((35*A*b^2*c^4*d*e^2 - 24*(B*b*c^5 - 2*A*c^6)*d^3 + 28*(B*b^2*c^4 - 3*A*b*c^5)*d^2*e)*x^4 + 2*(35*A*b^3*c^3*d*e^2 - 24*(B*b^2*c^4 - 2*A*b*c^5)*d^3 + 28*(B*b^3*c^3 - 3*A*b^2*c^4)*d^2*e)*x^3 + (35*A*b^4*c^2*d*e^2 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 + 28*(B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*A*b^4*c^2*d^3 + (12*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - (11*B*b^3*c^3 - 36*A*b^2*c^4)*d^2*e - 2*(B*b^4*c^2 + 5*A*b^3*c^3)*d*e^2 + (5*B*b^5*c - A*b^4*c^2)*e^3)*x^3 + (18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - (17*B*b^4*c^2 - 55*A*b^3*c^3)*d^2*e + 4*(B*b^5*c - 4*A*b^4*c^2)*d*e^2 + (3*B*b^6 + A*b^5*c)*e^3)*x^2 + (13*A*b^4*c^2*d^2*e + 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^3)*x)*sqrt(e*x + d))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2), -1/8*(2*((24*(B*b*c^5 - 2*A*c^6)*d^3 - 4*(4*B*b^2*c^4 - 15*A*b*c^5)*d^2*e - (5*B*b^3*c^3 + 11*A*b^2*c^4)*d*e^2 - (3*B*b^4*c^2 + A*b^3*c^3)*e^3)*x^4 + 2*(24*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 4*(4*B*b^3*c^3 - 15*A*b^2*c^4)*d^2*e - (5*B*b^4*c^2 + 11*A*b^3*c^3)*d*e^2 - (3*B*b^5*c + A*b^4*c^2)*e^3)*x^3 + (24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 4*(4*B*b^4*c^2 - 15*A*b^3*c^3)*d^2*e - (5*B*b^5*c + 11*A*b^4*c^2)*d*e^2 - (3*B*b^6 + A*b^5*c)*e^3)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) - ((35*A*b^2*c^4*d*e^2 - 24*(B*b*c^5 - 2*A*c^6)*d^3 + 28*(B*b^2*c^4 - 3*A*b*c^5)*d^2*e)*x^4 + 2*(35*A*b^3*c^3*d*e^2 - 24*(B*b^2*c^4 - 2*A*b*c^5)*d^3 + 28*(B*b^3*c^3 - 3*A*b^2*c^4)*d^2*e)*x^3 + (35*A*b^4*c^2*d*e^2 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 + 28*(B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*A*b^4*c^2*d^3 + (12*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - (11*B*b^3*c^3 - 36*A*b^2*c^4)*d^2*e - 2*(B*b^4*c^2 + 5*A*b^3*c^3)*d*e^2 + (5*B*b^5*c - A*b^4*c^2)*e^3)*x^3 + (18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - (17*B*b^4*c^2 - 55*A*b^3*c^3)*d^2*e + 4*(B*b^5*c - 4*A*b^4*c^2)*d*e^2 + (3*B*b^6 + A*b^5*c)*e^3)*x^2 + (13*A*b^4*c^2*d^2*e + 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^3)*x)*sqrt(e*x + d))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2), 1/8*(2*((35*A*b^2*c^4*d*e^2 - 24*(B*b*c^5 - 2*A*c^6)*d^3 + 28*(B*b^2*c^4 - 3*A*b*c^5)*d^2*e)*x^4 + 2*(35*A*b^3*c^3*d*e^2 - 24*(B*b^2*c^4 - 2*A*b*c^5)*d^3 + 28*(B*b^3*c^3 - 3*A*b^2*c^4)*d^2*e)*x^3 + (35*A*b^4*c^2*d*e^2 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 + 28*(B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - ((24*(B*b*c^5 - 2*A*c^6)*d^3 - 4*(4*B*b^2*c^4 - 15*A*b*c^5)*d^2*e - (5*B*b^3*c^3 + 11*A*b^2*c^4)*d*e^2 - (3*B*b^4*c^2 + A*b^3*c^3)*e^3)*x^4 + 2*(24*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 4*(4*B*b^3*c^3 - 15*A*b^2*c^4)*d^2*e - (5*B*b^4*c^2 + 11*A*b^3*c^3)*d*e^2 - (3*B*b^5*c + A*b^4*c^2)*e^3)*x^3 + (24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 4*(4*B*b^4*c^2 - 15*A*b^3*c^3)*d^2*e - (5*B*b^5*c + 11*A*b^4*c^2)*d*e^2 - (3*B*b^6 + A*b^5*c)*e^3)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - 2*(2*A*b^4*c^2*d^3 + (12*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - (11*B*b^3*c^3 - 36*A*b^2*c^4)*d^2*e - 2*(B*b^4*c^2 + 5*A*b^3*c^3)*d*e^2 + (5*B*b^5*c - A*b^4*c^2)*e^3)*x^3 + (18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - (17*B*b^4*c^2 - 55*A*b^3*c^3)*d^2*e + 4*(B*b^5*c - 4*A*b^4*c^2)*d*e^2 + (3*B*b^6 + A*b^5*c)*e^3)*x^2 + (13*A*b^4*c^2*d^2*e + 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^3)*x)*sqrt(e*x + d))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2), -1/4*(((24*(B*b*c^5 - 2*A*c^6)*d^3 - 4*(4*B*b^2*c^4 - 15*A*b*c^5)*d^2*e - (5*B*b^3*c^3 + 11*A*b^2*c^4)*d*e^2 - (3*B*b^4*c^2 + A*b^3*c^3)*e^3)*x^4 + 2*(24*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 4*(4*B*b^3*c^3 - 15*A*b^2*c^4)*d^2*e - (5*B*b^4*c^2 + 11*A*b^3*c^3)*d*e^2 - (3*B*b^5*c + A*b^4*c^2)*e^3)*x^3 + (24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 4*(4*B*b^4*c^2 - 15*A*b^3*c^3)*d^2*e - (5*B*b^5*c + 11*A*b^4*c^2)*d*e^2 - (3*B*b^6 + A*b^5*c)*e^3)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) - ((35*A*b^2*c^4*d*e^2 - 24*(B*b*c^5 - 2*A*c^6)*d^3 + 28*(B*b^2*c^4 - 3*A*b*c^5)*d^2*e)*x^4 + 2*(35*A*b^3*c^3*d*e^2 - 24*(B*b^2*c^4 - 2*A*b*c^5)*d^3 + 28*(B*b^3*c^3 - 3*A*b^2*c^4)*d^2*e)*x^3 + (35*A*b^4*c^2*d*e^2 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 + 28*(B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (2*A*b^4*c^2*d^3 + (12*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - (11*B*b^3*c^3 - 36*A*b^2*c^4)*d^2*e - 2*(B*b^4*c^2 + 5*A*b^3*c^3)*d*e^2 + (5*B*b^5*c - A*b^4*c^2)*e^3)*x^3 + (18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - (17*B*b^4*c^2 - 55*A*b^3*c^3)*d^2*e + 4*(B*b^5*c - 4*A*b^4*c^2)*d*e^2 + (3*B*b^6 + A*b^5*c)*e^3)*x^2 + (13*A*b^4*c^2*d^2*e + 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^3)*x)*sqrt(e*x + d))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2)]","B",0
1249,1,2754,0,4.026428," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} - 4 \, {\left(2 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d e - {\left(B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} - 4 \, {\left(2 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d e - {\left(B b^{4} c + 3 \, A b^{3} c^{2}\right)} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - 4 \, {\left(2 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} d e - {\left(B b^{5} + 3 \, A b^{4} c\right)} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - {\left({\left(15 \, A b^{2} c^{3} e^{2} - 24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} + 20 \, {\left(B b^{2} c^{3} - 3 \, A b c^{4}\right)} d e\right)} x^{4} + 2 \, {\left(15 \, A b^{3} c^{2} e^{2} - 24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} + 20 \, {\left(B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} d e\right)} x^{3} + {\left(15 \, A b^{4} c e^{2} - 24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} + 20 \, {\left(B b^{4} c - 3 \, A b^{3} c^{2}\right)} d e\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, A b^{4} c d^{2} + {\left(12 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} - {\left(7 \, B b^{3} c^{2} - 24 \, A b^{2} c^{3}\right)} d e - {\left(B b^{4} c + 3 \, A b^{3} c^{2}\right)} e^{2}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - {\left(11 \, B b^{4} c - 37 \, A b^{3} c^{2}\right)} d e + {\left(B b^{5} - 5 \, A b^{4} c\right)} e^{2}\right)} x^{2} + {\left(9 \, A b^{4} c d e + 4 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}, -\frac{2 \, {\left({\left(24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} - 4 \, {\left(2 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d e - {\left(B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} - 4 \, {\left(2 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d e - {\left(B b^{4} c + 3 \, A b^{3} c^{2}\right)} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - 4 \, {\left(2 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} d e - {\left(B b^{5} + 3 \, A b^{4} c\right)} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) - {\left({\left(15 \, A b^{2} c^{3} e^{2} - 24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} + 20 \, {\left(B b^{2} c^{3} - 3 \, A b c^{4}\right)} d e\right)} x^{4} + 2 \, {\left(15 \, A b^{3} c^{2} e^{2} - 24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} + 20 \, {\left(B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} d e\right)} x^{3} + {\left(15 \, A b^{4} c e^{2} - 24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} + 20 \, {\left(B b^{4} c - 3 \, A b^{3} c^{2}\right)} d e\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, A b^{4} c d^{2} + {\left(12 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} - {\left(7 \, B b^{3} c^{2} - 24 \, A b^{2} c^{3}\right)} d e - {\left(B b^{4} c + 3 \, A b^{3} c^{2}\right)} e^{2}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - {\left(11 \, B b^{4} c - 37 \, A b^{3} c^{2}\right)} d e + {\left(B b^{5} - 5 \, A b^{4} c\right)} e^{2}\right)} x^{2} + {\left(9 \, A b^{4} c d e + 4 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}, \frac{2 \, {\left({\left(15 \, A b^{2} c^{3} e^{2} - 24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} + 20 \, {\left(B b^{2} c^{3} - 3 \, A b c^{4}\right)} d e\right)} x^{4} + 2 \, {\left(15 \, A b^{3} c^{2} e^{2} - 24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} + 20 \, {\left(B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} d e\right)} x^{3} + {\left(15 \, A b^{4} c e^{2} - 24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} + 20 \, {\left(B b^{4} c - 3 \, A b^{3} c^{2}\right)} d e\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left({\left(24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} - 4 \, {\left(2 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d e - {\left(B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} - 4 \, {\left(2 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d e - {\left(B b^{4} c + 3 \, A b^{3} c^{2}\right)} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - 4 \, {\left(2 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} d e - {\left(B b^{5} + 3 \, A b^{4} c\right)} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - 2 \, {\left(2 \, A b^{4} c d^{2} + {\left(12 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} - {\left(7 \, B b^{3} c^{2} - 24 \, A b^{2} c^{3}\right)} d e - {\left(B b^{4} c + 3 \, A b^{3} c^{2}\right)} e^{2}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - {\left(11 \, B b^{4} c - 37 \, A b^{3} c^{2}\right)} d e + {\left(B b^{5} - 5 \, A b^{4} c\right)} e^{2}\right)} x^{2} + {\left(9 \, A b^{4} c d e + 4 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}, -\frac{{\left({\left(24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} - 4 \, {\left(2 \, B b^{2} c^{3} - 9 \, A b c^{4}\right)} d e - {\left(B b^{3} c^{2} + 3 \, A b^{2} c^{3}\right)} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} - 4 \, {\left(2 \, B b^{3} c^{2} - 9 \, A b^{2} c^{3}\right)} d e - {\left(B b^{4} c + 3 \, A b^{3} c^{2}\right)} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - 4 \, {\left(2 \, B b^{4} c - 9 \, A b^{3} c^{2}\right)} d e - {\left(B b^{5} + 3 \, A b^{4} c\right)} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) - {\left({\left(15 \, A b^{2} c^{3} e^{2} - 24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} + 20 \, {\left(B b^{2} c^{3} - 3 \, A b c^{4}\right)} d e\right)} x^{4} + 2 \, {\left(15 \, A b^{3} c^{2} e^{2} - 24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} + 20 \, {\left(B b^{3} c^{2} - 3 \, A b^{2} c^{3}\right)} d e\right)} x^{3} + {\left(15 \, A b^{4} c e^{2} - 24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} + 20 \, {\left(B b^{4} c - 3 \, A b^{3} c^{2}\right)} d e\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(2 \, A b^{4} c d^{2} + {\left(12 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} - {\left(7 \, B b^{3} c^{2} - 24 \, A b^{2} c^{3}\right)} d e - {\left(B b^{4} c + 3 \, A b^{3} c^{2}\right)} e^{2}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{2} - {\left(11 \, B b^{4} c - 37 \, A b^{3} c^{2}\right)} d e + {\left(B b^{5} - 5 \, A b^{4} c\right)} e^{2}\right)} x^{2} + {\left(9 \, A b^{4} c d e + 4 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}\right]"," ",0,"[-1/8*(((24*(B*b*c^4 - 2*A*c^5)*d^2 - 4*(2*B*b^2*c^3 - 9*A*b*c^4)*d*e - (B*b^3*c^2 + 3*A*b^2*c^3)*e^2)*x^4 + 2*(24*(B*b^2*c^3 - 2*A*b*c^4)*d^2 - 4*(2*B*b^3*c^2 - 9*A*b^2*c^3)*d*e - (B*b^4*c + 3*A*b^3*c^2)*e^2)*x^3 + (24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - 4*(2*B*b^4*c - 9*A*b^3*c^2)*d*e - (B*b^5 + 3*A*b^4*c)*e^2)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - ((15*A*b^2*c^3*e^2 - 24*(B*b*c^4 - 2*A*c^5)*d^2 + 20*(B*b^2*c^3 - 3*A*b*c^4)*d*e)*x^4 + 2*(15*A*b^3*c^2*e^2 - 24*(B*b^2*c^3 - 2*A*b*c^4)*d^2 + 20*(B*b^3*c^2 - 3*A*b^2*c^3)*d*e)*x^3 + (15*A*b^4*c*e^2 - 24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 + 20*(B*b^4*c - 3*A*b^3*c^2)*d*e)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*A*b^4*c*d^2 + (12*(B*b^2*c^3 - 2*A*b*c^4)*d^2 - (7*B*b^3*c^2 - 24*A*b^2*c^3)*d*e - (B*b^4*c + 3*A*b^3*c^2)*e^2)*x^3 + (18*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - (11*B*b^4*c - 37*A*b^3*c^2)*d*e + (B*b^5 - 5*A*b^4*c)*e^2)*x^2 + (9*A*b^4*c*d*e + 4*(B*b^4*c - 2*A*b^3*c^2)*d^2)*x)*sqrt(e*x + d))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2), -1/8*(2*((24*(B*b*c^4 - 2*A*c^5)*d^2 - 4*(2*B*b^2*c^3 - 9*A*b*c^4)*d*e - (B*b^3*c^2 + 3*A*b^2*c^3)*e^2)*x^4 + 2*(24*(B*b^2*c^3 - 2*A*b*c^4)*d^2 - 4*(2*B*b^3*c^2 - 9*A*b^2*c^3)*d*e - (B*b^4*c + 3*A*b^3*c^2)*e^2)*x^3 + (24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - 4*(2*B*b^4*c - 9*A*b^3*c^2)*d*e - (B*b^5 + 3*A*b^4*c)*e^2)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) - ((15*A*b^2*c^3*e^2 - 24*(B*b*c^4 - 2*A*c^5)*d^2 + 20*(B*b^2*c^3 - 3*A*b*c^4)*d*e)*x^4 + 2*(15*A*b^3*c^2*e^2 - 24*(B*b^2*c^3 - 2*A*b*c^4)*d^2 + 20*(B*b^3*c^2 - 3*A*b^2*c^3)*d*e)*x^3 + (15*A*b^4*c*e^2 - 24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 + 20*(B*b^4*c - 3*A*b^3*c^2)*d*e)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*A*b^4*c*d^2 + (12*(B*b^2*c^3 - 2*A*b*c^4)*d^2 - (7*B*b^3*c^2 - 24*A*b^2*c^3)*d*e - (B*b^4*c + 3*A*b^3*c^2)*e^2)*x^3 + (18*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - (11*B*b^4*c - 37*A*b^3*c^2)*d*e + (B*b^5 - 5*A*b^4*c)*e^2)*x^2 + (9*A*b^4*c*d*e + 4*(B*b^4*c - 2*A*b^3*c^2)*d^2)*x)*sqrt(e*x + d))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2), 1/8*(2*((15*A*b^2*c^3*e^2 - 24*(B*b*c^4 - 2*A*c^5)*d^2 + 20*(B*b^2*c^3 - 3*A*b*c^4)*d*e)*x^4 + 2*(15*A*b^3*c^2*e^2 - 24*(B*b^2*c^3 - 2*A*b*c^4)*d^2 + 20*(B*b^3*c^2 - 3*A*b^2*c^3)*d*e)*x^3 + (15*A*b^4*c*e^2 - 24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 + 20*(B*b^4*c - 3*A*b^3*c^2)*d*e)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - ((24*(B*b*c^4 - 2*A*c^5)*d^2 - 4*(2*B*b^2*c^3 - 9*A*b*c^4)*d*e - (B*b^3*c^2 + 3*A*b^2*c^3)*e^2)*x^4 + 2*(24*(B*b^2*c^3 - 2*A*b*c^4)*d^2 - 4*(2*B*b^3*c^2 - 9*A*b^2*c^3)*d*e - (B*b^4*c + 3*A*b^3*c^2)*e^2)*x^3 + (24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - 4*(2*B*b^4*c - 9*A*b^3*c^2)*d*e - (B*b^5 + 3*A*b^4*c)*e^2)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - 2*(2*A*b^4*c*d^2 + (12*(B*b^2*c^3 - 2*A*b*c^4)*d^2 - (7*B*b^3*c^2 - 24*A*b^2*c^3)*d*e - (B*b^4*c + 3*A*b^3*c^2)*e^2)*x^3 + (18*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - (11*B*b^4*c - 37*A*b^3*c^2)*d*e + (B*b^5 - 5*A*b^4*c)*e^2)*x^2 + (9*A*b^4*c*d*e + 4*(B*b^4*c - 2*A*b^3*c^2)*d^2)*x)*sqrt(e*x + d))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2), -1/4*(((24*(B*b*c^4 - 2*A*c^5)*d^2 - 4*(2*B*b^2*c^3 - 9*A*b*c^4)*d*e - (B*b^3*c^2 + 3*A*b^2*c^3)*e^2)*x^4 + 2*(24*(B*b^2*c^3 - 2*A*b*c^4)*d^2 - 4*(2*B*b^3*c^2 - 9*A*b^2*c^3)*d*e - (B*b^4*c + 3*A*b^3*c^2)*e^2)*x^3 + (24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - 4*(2*B*b^4*c - 9*A*b^3*c^2)*d*e - (B*b^5 + 3*A*b^4*c)*e^2)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) - ((15*A*b^2*c^3*e^2 - 24*(B*b*c^4 - 2*A*c^5)*d^2 + 20*(B*b^2*c^3 - 3*A*b*c^4)*d*e)*x^4 + 2*(15*A*b^3*c^2*e^2 - 24*(B*b^2*c^3 - 2*A*b*c^4)*d^2 + 20*(B*b^3*c^2 - 3*A*b^2*c^3)*d*e)*x^3 + (15*A*b^4*c*e^2 - 24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 + 20*(B*b^4*c - 3*A*b^3*c^2)*d*e)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (2*A*b^4*c*d^2 + (12*(B*b^2*c^3 - 2*A*b*c^4)*d^2 - (7*B*b^3*c^2 - 24*A*b^2*c^3)*d*e - (B*b^4*c + 3*A*b^3*c^2)*e^2)*x^3 + (18*(B*b^3*c^2 - 2*A*b^2*c^3)*d^2 - (11*B*b^4*c - 37*A*b^3*c^2)*d*e + (B*b^5 - 5*A*b^4*c)*e^2)*x^2 + (9*A*b^4*c*d*e + 4*(B*b^4*c - 2*A*b^3*c^2)*d^2)*x)*sqrt(e*x + d))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2)]","B",0
1250,1,3471,0,2.066528," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} - 4 \, {\left(2 \, B b^{2} c^{3} - 5 \, A b c^{4}\right)} d^{2} e + {\left(B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 4 \, {\left(2 \, B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} d^{2} e + {\left(B b^{4} c - 5 \, A b^{3} c^{2}\right)} d e^{2}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} - 4 \, {\left(2 \, B b^{4} c - 5 \, A b^{3} c^{2}\right)} d^{2} e + {\left(B b^{5} - 5 \, A b^{4} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d - b c e} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{c^{2} d - b c e} \sqrt{e x + d}}{c x + b}\right) - 3 \, {\left({\left(A b^{3} c^{3} e^{3} + 8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 4 \, {\left(3 \, B b^{2} c^{4} - 7 \, A b c^{5}\right)} d^{2} e + {\left(4 \, B b^{3} c^{3} - 13 \, A b^{2} c^{4}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(A b^{4} c^{2} e^{3} + 8 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 4 \, {\left(3 \, B b^{3} c^{3} - 7 \, A b^{2} c^{4}\right)} d^{2} e + {\left(4 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} d e^{2}\right)} x^{3} + {\left(A b^{5} c e^{3} + 8 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 4 \, {\left(3 \, B b^{4} c^{2} - 7 \, A b^{3} c^{3}\right)} d^{2} e + {\left(4 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, A b^{4} c^{2} d^{3} - 2 \, A b^{5} c d^{2} e + 3 \, {\left(4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - {\left(5 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} d^{2} e + {\left(B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} d e^{2}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - {\left(23 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{2} e + {\left(5 \, B b^{5} c - 19 \, A b^{4} c^{2}\right)} d e^{2}\right)} x^{2} - {\left(5 \, A b^{5} c d e^{2} - 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{3} + {\left(4 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d^{2} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{4} d^{2} - b^{6} c^{3} d e\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{2} - b^{7} c^{2} d e\right)} x^{3} + {\left(b^{7} c^{2} d^{2} - b^{8} c d e\right)} x^{2}\right)}}, \frac{6 \, {\left({\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} - 4 \, {\left(2 \, B b^{2} c^{3} - 5 \, A b c^{4}\right)} d^{2} e + {\left(B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 4 \, {\left(2 \, B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} d^{2} e + {\left(B b^{4} c - 5 \, A b^{3} c^{2}\right)} d e^{2}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} - 4 \, {\left(2 \, B b^{4} c - 5 \, A b^{3} c^{2}\right)} d^{2} e + {\left(B b^{5} - 5 \, A b^{4} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d + b c e} \arctan\left(\frac{\sqrt{-c^{2} d + b c e} \sqrt{e x + d}}{c e x + c d}\right) - 3 \, {\left({\left(A b^{3} c^{3} e^{3} + 8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 4 \, {\left(3 \, B b^{2} c^{4} - 7 \, A b c^{5}\right)} d^{2} e + {\left(4 \, B b^{3} c^{3} - 13 \, A b^{2} c^{4}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(A b^{4} c^{2} e^{3} + 8 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 4 \, {\left(3 \, B b^{3} c^{3} - 7 \, A b^{2} c^{4}\right)} d^{2} e + {\left(4 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} d e^{2}\right)} x^{3} + {\left(A b^{5} c e^{3} + 8 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 4 \, {\left(3 \, B b^{4} c^{2} - 7 \, A b^{3} c^{3}\right)} d^{2} e + {\left(4 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, A b^{4} c^{2} d^{3} - 2 \, A b^{5} c d^{2} e + 3 \, {\left(4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - {\left(5 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} d^{2} e + {\left(B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} d e^{2}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - {\left(23 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{2} e + {\left(5 \, B b^{5} c - 19 \, A b^{4} c^{2}\right)} d e^{2}\right)} x^{2} - {\left(5 \, A b^{5} c d e^{2} - 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{3} + {\left(4 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d^{2} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{4} d^{2} - b^{6} c^{3} d e\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{2} - b^{7} c^{2} d e\right)} x^{3} + {\left(b^{7} c^{2} d^{2} - b^{8} c d e\right)} x^{2}\right)}}, -\frac{6 \, {\left({\left(A b^{3} c^{3} e^{3} + 8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 4 \, {\left(3 \, B b^{2} c^{4} - 7 \, A b c^{5}\right)} d^{2} e + {\left(4 \, B b^{3} c^{3} - 13 \, A b^{2} c^{4}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(A b^{4} c^{2} e^{3} + 8 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 4 \, {\left(3 \, B b^{3} c^{3} - 7 \, A b^{2} c^{4}\right)} d^{2} e + {\left(4 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} d e^{2}\right)} x^{3} + {\left(A b^{5} c e^{3} + 8 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 4 \, {\left(3 \, B b^{4} c^{2} - 7 \, A b^{3} c^{3}\right)} d^{2} e + {\left(4 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 3 \, {\left({\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} - 4 \, {\left(2 \, B b^{2} c^{3} - 5 \, A b c^{4}\right)} d^{2} e + {\left(B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 4 \, {\left(2 \, B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} d^{2} e + {\left(B b^{4} c - 5 \, A b^{3} c^{2}\right)} d e^{2}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} - 4 \, {\left(2 \, B b^{4} c - 5 \, A b^{3} c^{2}\right)} d^{2} e + {\left(B b^{5} - 5 \, A b^{4} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d - b c e} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{c^{2} d - b c e} \sqrt{e x + d}}{c x + b}\right) + 2 \, {\left(2 \, A b^{4} c^{2} d^{3} - 2 \, A b^{5} c d^{2} e + 3 \, {\left(4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - {\left(5 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} d^{2} e + {\left(B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} d e^{2}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - {\left(23 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{2} e + {\left(5 \, B b^{5} c - 19 \, A b^{4} c^{2}\right)} d e^{2}\right)} x^{2} - {\left(5 \, A b^{5} c d e^{2} - 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{3} + {\left(4 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d^{2} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{4} d^{2} - b^{6} c^{3} d e\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{2} - b^{7} c^{2} d e\right)} x^{3} + {\left(b^{7} c^{2} d^{2} - b^{8} c d e\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} - 4 \, {\left(2 \, B b^{2} c^{3} - 5 \, A b c^{4}\right)} d^{2} e + {\left(B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 4 \, {\left(2 \, B b^{3} c^{2} - 5 \, A b^{2} c^{3}\right)} d^{2} e + {\left(B b^{4} c - 5 \, A b^{3} c^{2}\right)} d e^{2}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} - 4 \, {\left(2 \, B b^{4} c - 5 \, A b^{3} c^{2}\right)} d^{2} e + {\left(B b^{5} - 5 \, A b^{4} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d + b c e} \arctan\left(\frac{\sqrt{-c^{2} d + b c e} \sqrt{e x + d}}{c e x + c d}\right) - 3 \, {\left({\left(A b^{3} c^{3} e^{3} + 8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 4 \, {\left(3 \, B b^{2} c^{4} - 7 \, A b c^{5}\right)} d^{2} e + {\left(4 \, B b^{3} c^{3} - 13 \, A b^{2} c^{4}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(A b^{4} c^{2} e^{3} + 8 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 4 \, {\left(3 \, B b^{3} c^{3} - 7 \, A b^{2} c^{4}\right)} d^{2} e + {\left(4 \, B b^{4} c^{2} - 13 \, A b^{3} c^{3}\right)} d e^{2}\right)} x^{3} + {\left(A b^{5} c e^{3} + 8 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - 4 \, {\left(3 \, B b^{4} c^{2} - 7 \, A b^{3} c^{3}\right)} d^{2} e + {\left(4 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, A b^{4} c^{2} d^{3} - 2 \, A b^{5} c d^{2} e + 3 \, {\left(4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - {\left(5 \, B b^{3} c^{3} - 12 \, A b^{2} c^{4}\right)} d^{2} e + {\left(B b^{4} c^{2} - 4 \, A b^{3} c^{3}\right)} d e^{2}\right)} x^{3} + {\left(18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{3} - {\left(23 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{2} e + {\left(5 \, B b^{5} c - 19 \, A b^{4} c^{2}\right)} d e^{2}\right)} x^{2} - {\left(5 \, A b^{5} c d e^{2} - 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{3} + {\left(4 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d^{2} e\right)} x\right)} \sqrt{e x + d}}{4 \, {\left({\left(b^{5} c^{4} d^{2} - b^{6} c^{3} d e\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{2} - b^{7} c^{2} d e\right)} x^{3} + {\left(b^{7} c^{2} d^{2} - b^{8} c d e\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(3*((8*(B*b*c^4 - 2*A*c^5)*d^3 - 4*(2*B*b^2*c^3 - 5*A*b*c^4)*d^2*e + (B*b^3*c^2 - 5*A*b^2*c^3)*d*e^2)*x^4 + 2*(8*(B*b^2*c^3 - 2*A*b*c^4)*d^3 - 4*(2*B*b^3*c^2 - 5*A*b^2*c^3)*d^2*e + (B*b^4*c - 5*A*b^3*c^2)*d*e^2)*x^3 + (8*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 - 4*(2*B*b^4*c - 5*A*b^3*c^2)*d^2*e + (B*b^5 - 5*A*b^4*c)*d*e^2)*x^2)*sqrt(c^2*d - b*c*e)*log((c*e*x + 2*c*d - b*e - 2*sqrt(c^2*d - b*c*e)*sqrt(e*x + d))/(c*x + b)) - 3*((A*b^3*c^3*e^3 + 8*(B*b*c^5 - 2*A*c^6)*d^3 - 4*(3*B*b^2*c^4 - 7*A*b*c^5)*d^2*e + (4*B*b^3*c^3 - 13*A*b^2*c^4)*d*e^2)*x^4 + 2*(A*b^4*c^2*e^3 + 8*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 4*(3*B*b^3*c^3 - 7*A*b^2*c^4)*d^2*e + (4*B*b^4*c^2 - 13*A*b^3*c^3)*d*e^2)*x^3 + (A*b^5*c*e^3 + 8*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 4*(3*B*b^4*c^2 - 7*A*b^3*c^3)*d^2*e + (4*B*b^5*c - 13*A*b^4*c^2)*d*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*A*b^4*c^2*d^3 - 2*A*b^5*c*d^2*e + 3*(4*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - (5*B*b^3*c^3 - 12*A*b^2*c^4)*d^2*e + (B*b^4*c^2 - 4*A*b^3*c^3)*d*e^2)*x^3 + (18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - (23*B*b^4*c^2 - 55*A*b^3*c^3)*d^2*e + (5*B*b^5*c - 19*A*b^4*c^2)*d*e^2)*x^2 - (5*A*b^5*c*d*e^2 - 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^3 + (4*B*b^5*c - 13*A*b^4*c^2)*d^2*e)*x)*sqrt(e*x + d))/((b^5*c^4*d^2 - b^6*c^3*d*e)*x^4 + 2*(b^6*c^3*d^2 - b^7*c^2*d*e)*x^3 + (b^7*c^2*d^2 - b^8*c*d*e)*x^2), 1/8*(6*((8*(B*b*c^4 - 2*A*c^5)*d^3 - 4*(2*B*b^2*c^3 - 5*A*b*c^4)*d^2*e + (B*b^3*c^2 - 5*A*b^2*c^3)*d*e^2)*x^4 + 2*(8*(B*b^2*c^3 - 2*A*b*c^4)*d^3 - 4*(2*B*b^3*c^2 - 5*A*b^2*c^3)*d^2*e + (B*b^4*c - 5*A*b^3*c^2)*d*e^2)*x^3 + (8*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 - 4*(2*B*b^4*c - 5*A*b^3*c^2)*d^2*e + (B*b^5 - 5*A*b^4*c)*d*e^2)*x^2)*sqrt(-c^2*d + b*c*e)*arctan(sqrt(-c^2*d + b*c*e)*sqrt(e*x + d)/(c*e*x + c*d)) - 3*((A*b^3*c^3*e^3 + 8*(B*b*c^5 - 2*A*c^6)*d^3 - 4*(3*B*b^2*c^4 - 7*A*b*c^5)*d^2*e + (4*B*b^3*c^3 - 13*A*b^2*c^4)*d*e^2)*x^4 + 2*(A*b^4*c^2*e^3 + 8*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 4*(3*B*b^3*c^3 - 7*A*b^2*c^4)*d^2*e + (4*B*b^4*c^2 - 13*A*b^3*c^3)*d*e^2)*x^3 + (A*b^5*c*e^3 + 8*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 4*(3*B*b^4*c^2 - 7*A*b^3*c^3)*d^2*e + (4*B*b^5*c - 13*A*b^4*c^2)*d*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*A*b^4*c^2*d^3 - 2*A*b^5*c*d^2*e + 3*(4*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - (5*B*b^3*c^3 - 12*A*b^2*c^4)*d^2*e + (B*b^4*c^2 - 4*A*b^3*c^3)*d*e^2)*x^3 + (18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - (23*B*b^4*c^2 - 55*A*b^3*c^3)*d^2*e + (5*B*b^5*c - 19*A*b^4*c^2)*d*e^2)*x^2 - (5*A*b^5*c*d*e^2 - 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^3 + (4*B*b^5*c - 13*A*b^4*c^2)*d^2*e)*x)*sqrt(e*x + d))/((b^5*c^4*d^2 - b^6*c^3*d*e)*x^4 + 2*(b^6*c^3*d^2 - b^7*c^2*d*e)*x^3 + (b^7*c^2*d^2 - b^8*c*d*e)*x^2), -1/8*(6*((A*b^3*c^3*e^3 + 8*(B*b*c^5 - 2*A*c^6)*d^3 - 4*(3*B*b^2*c^4 - 7*A*b*c^5)*d^2*e + (4*B*b^3*c^3 - 13*A*b^2*c^4)*d*e^2)*x^4 + 2*(A*b^4*c^2*e^3 + 8*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 4*(3*B*b^3*c^3 - 7*A*b^2*c^4)*d^2*e + (4*B*b^4*c^2 - 13*A*b^3*c^3)*d*e^2)*x^3 + (A*b^5*c*e^3 + 8*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 4*(3*B*b^4*c^2 - 7*A*b^3*c^3)*d^2*e + (4*B*b^5*c - 13*A*b^4*c^2)*d*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 3*((8*(B*b*c^4 - 2*A*c^5)*d^3 - 4*(2*B*b^2*c^3 - 5*A*b*c^4)*d^2*e + (B*b^3*c^2 - 5*A*b^2*c^3)*d*e^2)*x^4 + 2*(8*(B*b^2*c^3 - 2*A*b*c^4)*d^3 - 4*(2*B*b^3*c^2 - 5*A*b^2*c^3)*d^2*e + (B*b^4*c - 5*A*b^3*c^2)*d*e^2)*x^3 + (8*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 - 4*(2*B*b^4*c - 5*A*b^3*c^2)*d^2*e + (B*b^5 - 5*A*b^4*c)*d*e^2)*x^2)*sqrt(c^2*d - b*c*e)*log((c*e*x + 2*c*d - b*e - 2*sqrt(c^2*d - b*c*e)*sqrt(e*x + d))/(c*x + b)) + 2*(2*A*b^4*c^2*d^3 - 2*A*b^5*c*d^2*e + 3*(4*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - (5*B*b^3*c^3 - 12*A*b^2*c^4)*d^2*e + (B*b^4*c^2 - 4*A*b^3*c^3)*d*e^2)*x^3 + (18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - (23*B*b^4*c^2 - 55*A*b^3*c^3)*d^2*e + (5*B*b^5*c - 19*A*b^4*c^2)*d*e^2)*x^2 - (5*A*b^5*c*d*e^2 - 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^3 + (4*B*b^5*c - 13*A*b^4*c^2)*d^2*e)*x)*sqrt(e*x + d))/((b^5*c^4*d^2 - b^6*c^3*d*e)*x^4 + 2*(b^6*c^3*d^2 - b^7*c^2*d*e)*x^3 + (b^7*c^2*d^2 - b^8*c*d*e)*x^2), 1/4*(3*((8*(B*b*c^4 - 2*A*c^5)*d^3 - 4*(2*B*b^2*c^3 - 5*A*b*c^4)*d^2*e + (B*b^3*c^2 - 5*A*b^2*c^3)*d*e^2)*x^4 + 2*(8*(B*b^2*c^3 - 2*A*b*c^4)*d^3 - 4*(2*B*b^3*c^2 - 5*A*b^2*c^3)*d^2*e + (B*b^4*c - 5*A*b^3*c^2)*d*e^2)*x^3 + (8*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 - 4*(2*B*b^4*c - 5*A*b^3*c^2)*d^2*e + (B*b^5 - 5*A*b^4*c)*d*e^2)*x^2)*sqrt(-c^2*d + b*c*e)*arctan(sqrt(-c^2*d + b*c*e)*sqrt(e*x + d)/(c*e*x + c*d)) - 3*((A*b^3*c^3*e^3 + 8*(B*b*c^5 - 2*A*c^6)*d^3 - 4*(3*B*b^2*c^4 - 7*A*b*c^5)*d^2*e + (4*B*b^3*c^3 - 13*A*b^2*c^4)*d*e^2)*x^4 + 2*(A*b^4*c^2*e^3 + 8*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 4*(3*B*b^3*c^3 - 7*A*b^2*c^4)*d^2*e + (4*B*b^4*c^2 - 13*A*b^3*c^3)*d*e^2)*x^3 + (A*b^5*c*e^3 + 8*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - 4*(3*B*b^4*c^2 - 7*A*b^3*c^3)*d^2*e + (4*B*b^5*c - 13*A*b^4*c^2)*d*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*A*b^4*c^2*d^3 - 2*A*b^5*c*d^2*e + 3*(4*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - (5*B*b^3*c^3 - 12*A*b^2*c^4)*d^2*e + (B*b^4*c^2 - 4*A*b^3*c^3)*d*e^2)*x^3 + (18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^3 - (23*B*b^4*c^2 - 55*A*b^3*c^3)*d^2*e + (5*B*b^5*c - 19*A*b^4*c^2)*d*e^2)*x^2 - (5*A*b^5*c*d*e^2 - 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^3 + (4*B*b^5*c - 13*A*b^4*c^2)*d^2*e)*x)*sqrt(e*x + d))/((b^5*c^4*d^2 - b^6*c^3*d*e)*x^4 + 2*(b^6*c^3*d^2 - b^7*c^2*d*e)*x^3 + (b^7*c^2*d^2 - b^8*c*d*e)*x^2)]","B",0
1251,1,3396,0,7.839837," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} - 4 \, {\left(10 \, B b^{2} c^{3} - 21 \, A b c^{4}\right)} d^{3} e + 5 \, {\left(3 \, B b^{3} c^{2} - 7 \, A b^{2} c^{3}\right)} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} - 4 \, {\left(10 \, B b^{3} c^{2} - 21 \, A b^{2} c^{3}\right)} d^{3} e + 5 \, {\left(3 \, B b^{4} c - 7 \, A b^{3} c^{2}\right)} d^{2} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{4} - 4 \, {\left(10 \, B b^{4} c - 21 \, A b^{3} c^{2}\right)} d^{3} e + 5 \, {\left(3 \, B b^{5} - 7 \, A b^{4} c\right)} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - {\left({\left(A b^{3} c^{2} e^{3} - 24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} + 4 \, {\left(7 \, B b^{2} c^{3} - 15 \, A b c^{4}\right)} d^{2} e - {\left(4 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(A b^{4} c e^{3} - 24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + 4 \, {\left(7 \, B b^{3} c^{2} - 15 \, A b^{2} c^{3}\right)} d^{2} e - {\left(4 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} d e^{2}\right)} x^{3} + {\left(A b^{5} e^{3} - 24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} + 4 \, {\left(7 \, B b^{4} c - 15 \, A b^{3} c^{2}\right)} d^{2} e - {\left(4 \, B b^{5} - 11 \, A b^{4} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, A b^{4} c d^{3} - 2 \, A b^{5} d^{2} e - {\left(A b^{3} c^{2} d e^{2} - 12 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + {\left(11 \, B b^{3} c^{2} - 24 \, A b^{2} c^{3}\right)} d^{2} e\right)} x^{3} - {\left(2 \, A b^{4} c d e^{2} - 18 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} + {\left(17 \, B b^{4} c - 37 \, A b^{3} c^{2}\right)} d^{2} e\right)} x^{2} - {\left(A b^{5} d e^{2} - 4 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{3} + {\left(4 \, B b^{5} - 9 \, A b^{4} c\right)} d^{2} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{3} d^{3} - b^{6} c^{2} d^{2} e\right)} x^{4} + 2 \, {\left(b^{6} c^{2} d^{3} - b^{7} c d^{2} e\right)} x^{3} + {\left(b^{7} c d^{3} - b^{8} d^{2} e\right)} x^{2}\right)}}, -\frac{2 \, {\left({\left(24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} - 4 \, {\left(10 \, B b^{2} c^{3} - 21 \, A b c^{4}\right)} d^{3} e + 5 \, {\left(3 \, B b^{3} c^{2} - 7 \, A b^{2} c^{3}\right)} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} - 4 \, {\left(10 \, B b^{3} c^{2} - 21 \, A b^{2} c^{3}\right)} d^{3} e + 5 \, {\left(3 \, B b^{4} c - 7 \, A b^{3} c^{2}\right)} d^{2} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{4} - 4 \, {\left(10 \, B b^{4} c - 21 \, A b^{3} c^{2}\right)} d^{3} e + 5 \, {\left(3 \, B b^{5} - 7 \, A b^{4} c\right)} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + {\left({\left(A b^{3} c^{2} e^{3} - 24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} + 4 \, {\left(7 \, B b^{2} c^{3} - 15 \, A b c^{4}\right)} d^{2} e - {\left(4 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(A b^{4} c e^{3} - 24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + 4 \, {\left(7 \, B b^{3} c^{2} - 15 \, A b^{2} c^{3}\right)} d^{2} e - {\left(4 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} d e^{2}\right)} x^{3} + {\left(A b^{5} e^{3} - 24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} + 4 \, {\left(7 \, B b^{4} c - 15 \, A b^{3} c^{2}\right)} d^{2} e - {\left(4 \, B b^{5} - 11 \, A b^{4} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, A b^{4} c d^{3} - 2 \, A b^{5} d^{2} e - {\left(A b^{3} c^{2} d e^{2} - 12 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + {\left(11 \, B b^{3} c^{2} - 24 \, A b^{2} c^{3}\right)} d^{2} e\right)} x^{3} - {\left(2 \, A b^{4} c d e^{2} - 18 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} + {\left(17 \, B b^{4} c - 37 \, A b^{3} c^{2}\right)} d^{2} e\right)} x^{2} - {\left(A b^{5} d e^{2} - 4 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{3} + {\left(4 \, B b^{5} - 9 \, A b^{4} c\right)} d^{2} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{3} d^{3} - b^{6} c^{2} d^{2} e\right)} x^{4} + 2 \, {\left(b^{6} c^{2} d^{3} - b^{7} c d^{2} e\right)} x^{3} + {\left(b^{7} c d^{3} - b^{8} d^{2} e\right)} x^{2}\right)}}, \frac{2 \, {\left({\left(A b^{3} c^{2} e^{3} - 24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} + 4 \, {\left(7 \, B b^{2} c^{3} - 15 \, A b c^{4}\right)} d^{2} e - {\left(4 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(A b^{4} c e^{3} - 24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + 4 \, {\left(7 \, B b^{3} c^{2} - 15 \, A b^{2} c^{3}\right)} d^{2} e - {\left(4 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} d e^{2}\right)} x^{3} + {\left(A b^{5} e^{3} - 24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} + 4 \, {\left(7 \, B b^{4} c - 15 \, A b^{3} c^{2}\right)} d^{2} e - {\left(4 \, B b^{5} - 11 \, A b^{4} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left({\left(24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} - 4 \, {\left(10 \, B b^{2} c^{3} - 21 \, A b c^{4}\right)} d^{3} e + 5 \, {\left(3 \, B b^{3} c^{2} - 7 \, A b^{2} c^{3}\right)} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} - 4 \, {\left(10 \, B b^{3} c^{2} - 21 \, A b^{2} c^{3}\right)} d^{3} e + 5 \, {\left(3 \, B b^{4} c - 7 \, A b^{3} c^{2}\right)} d^{2} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{4} - 4 \, {\left(10 \, B b^{4} c - 21 \, A b^{3} c^{2}\right)} d^{3} e + 5 \, {\left(3 \, B b^{5} - 7 \, A b^{4} c\right)} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(2 \, A b^{4} c d^{3} - 2 \, A b^{5} d^{2} e - {\left(A b^{3} c^{2} d e^{2} - 12 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + {\left(11 \, B b^{3} c^{2} - 24 \, A b^{2} c^{3}\right)} d^{2} e\right)} x^{3} - {\left(2 \, A b^{4} c d e^{2} - 18 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} + {\left(17 \, B b^{4} c - 37 \, A b^{3} c^{2}\right)} d^{2} e\right)} x^{2} - {\left(A b^{5} d e^{2} - 4 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{3} + {\left(4 \, B b^{5} - 9 \, A b^{4} c\right)} d^{2} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{3} d^{3} - b^{6} c^{2} d^{2} e\right)} x^{4} + 2 \, {\left(b^{6} c^{2} d^{3} - b^{7} c d^{2} e\right)} x^{3} + {\left(b^{7} c d^{3} - b^{8} d^{2} e\right)} x^{2}\right)}}, -\frac{{\left({\left(24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} - 4 \, {\left(10 \, B b^{2} c^{3} - 21 \, A b c^{4}\right)} d^{3} e + 5 \, {\left(3 \, B b^{3} c^{2} - 7 \, A b^{2} c^{3}\right)} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} - 4 \, {\left(10 \, B b^{3} c^{2} - 21 \, A b^{2} c^{3}\right)} d^{3} e + 5 \, {\left(3 \, B b^{4} c - 7 \, A b^{3} c^{2}\right)} d^{2} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{4} - 4 \, {\left(10 \, B b^{4} c - 21 \, A b^{3} c^{2}\right)} d^{3} e + 5 \, {\left(3 \, B b^{5} - 7 \, A b^{4} c\right)} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left({\left(A b^{3} c^{2} e^{3} - 24 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} + 4 \, {\left(7 \, B b^{2} c^{3} - 15 \, A b c^{4}\right)} d^{2} e - {\left(4 \, B b^{3} c^{2} - 11 \, A b^{2} c^{3}\right)} d e^{2}\right)} x^{4} + 2 \, {\left(A b^{4} c e^{3} - 24 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + 4 \, {\left(7 \, B b^{3} c^{2} - 15 \, A b^{2} c^{3}\right)} d^{2} e - {\left(4 \, B b^{4} c - 11 \, A b^{3} c^{2}\right)} d e^{2}\right)} x^{3} + {\left(A b^{5} e^{3} - 24 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} + 4 \, {\left(7 \, B b^{4} c - 15 \, A b^{3} c^{2}\right)} d^{2} e - {\left(4 \, B b^{5} - 11 \, A b^{4} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(2 \, A b^{4} c d^{3} - 2 \, A b^{5} d^{2} e - {\left(A b^{3} c^{2} d e^{2} - 12 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} + {\left(11 \, B b^{3} c^{2} - 24 \, A b^{2} c^{3}\right)} d^{2} e\right)} x^{3} - {\left(2 \, A b^{4} c d e^{2} - 18 \, {\left(B b^{3} c^{2} - 2 \, A b^{2} c^{3}\right)} d^{3} + {\left(17 \, B b^{4} c - 37 \, A b^{3} c^{2}\right)} d^{2} e\right)} x^{2} - {\left(A b^{5} d e^{2} - 4 \, {\left(B b^{4} c - 2 \, A b^{3} c^{2}\right)} d^{3} + {\left(4 \, B b^{5} - 9 \, A b^{4} c\right)} d^{2} e\right)} x\right)} \sqrt{e x + d}}{4 \, {\left({\left(b^{5} c^{3} d^{3} - b^{6} c^{2} d^{2} e\right)} x^{4} + 2 \, {\left(b^{6} c^{2} d^{3} - b^{7} c d^{2} e\right)} x^{3} + {\left(b^{7} c d^{3} - b^{8} d^{2} e\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(((24*(B*b*c^4 - 2*A*c^5)*d^4 - 4*(10*B*b^2*c^3 - 21*A*b*c^4)*d^3*e + 5*(3*B*b^3*c^2 - 7*A*b^2*c^3)*d^2*e^2)*x^4 + 2*(24*(B*b^2*c^3 - 2*A*b*c^4)*d^4 - 4*(10*B*b^3*c^2 - 21*A*b^2*c^3)*d^3*e + 5*(3*B*b^4*c - 7*A*b^3*c^2)*d^2*e^2)*x^3 + (24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^4 - 4*(10*B*b^4*c - 21*A*b^3*c^2)*d^3*e + 5*(3*B*b^5 - 7*A*b^4*c)*d^2*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - ((A*b^3*c^2*e^3 - 24*(B*b*c^4 - 2*A*c^5)*d^3 + 4*(7*B*b^2*c^3 - 15*A*b*c^4)*d^2*e - (4*B*b^3*c^2 - 11*A*b^2*c^3)*d*e^2)*x^4 + 2*(A*b^4*c*e^3 - 24*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + 4*(7*B*b^3*c^2 - 15*A*b^2*c^3)*d^2*e - (4*B*b^4*c - 11*A*b^3*c^2)*d*e^2)*x^3 + (A*b^5*e^3 - 24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 + 4*(7*B*b^4*c - 15*A*b^3*c^2)*d^2*e - (4*B*b^5 - 11*A*b^4*c)*d*e^2)*x^2)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*A*b^4*c*d^3 - 2*A*b^5*d^2*e - (A*b^3*c^2*d*e^2 - 12*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + (11*B*b^3*c^2 - 24*A*b^2*c^3)*d^2*e)*x^3 - (2*A*b^4*c*d*e^2 - 18*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 + (17*B*b^4*c - 37*A*b^3*c^2)*d^2*e)*x^2 - (A*b^5*d*e^2 - 4*(B*b^4*c - 2*A*b^3*c^2)*d^3 + (4*B*b^5 - 9*A*b^4*c)*d^2*e)*x)*sqrt(e*x + d))/((b^5*c^3*d^3 - b^6*c^2*d^2*e)*x^4 + 2*(b^6*c^2*d^3 - b^7*c*d^2*e)*x^3 + (b^7*c*d^3 - b^8*d^2*e)*x^2), -1/8*(2*((24*(B*b*c^4 - 2*A*c^5)*d^4 - 4*(10*B*b^2*c^3 - 21*A*b*c^4)*d^3*e + 5*(3*B*b^3*c^2 - 7*A*b^2*c^3)*d^2*e^2)*x^4 + 2*(24*(B*b^2*c^3 - 2*A*b*c^4)*d^4 - 4*(10*B*b^3*c^2 - 21*A*b^2*c^3)*d^3*e + 5*(3*B*b^4*c - 7*A*b^3*c^2)*d^2*e^2)*x^3 + (24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^4 - 4*(10*B*b^4*c - 21*A*b^3*c^2)*d^3*e + 5*(3*B*b^5 - 7*A*b^4*c)*d^2*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + ((A*b^3*c^2*e^3 - 24*(B*b*c^4 - 2*A*c^5)*d^3 + 4*(7*B*b^2*c^3 - 15*A*b*c^4)*d^2*e - (4*B*b^3*c^2 - 11*A*b^2*c^3)*d*e^2)*x^4 + 2*(A*b^4*c*e^3 - 24*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + 4*(7*B*b^3*c^2 - 15*A*b^2*c^3)*d^2*e - (4*B*b^4*c - 11*A*b^3*c^2)*d*e^2)*x^3 + (A*b^5*e^3 - 24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 + 4*(7*B*b^4*c - 15*A*b^3*c^2)*d^2*e - (4*B*b^5 - 11*A*b^4*c)*d*e^2)*x^2)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*A*b^4*c*d^3 - 2*A*b^5*d^2*e - (A*b^3*c^2*d*e^2 - 12*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + (11*B*b^3*c^2 - 24*A*b^2*c^3)*d^2*e)*x^3 - (2*A*b^4*c*d*e^2 - 18*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 + (17*B*b^4*c - 37*A*b^3*c^2)*d^2*e)*x^2 - (A*b^5*d*e^2 - 4*(B*b^4*c - 2*A*b^3*c^2)*d^3 + (4*B*b^5 - 9*A*b^4*c)*d^2*e)*x)*sqrt(e*x + d))/((b^5*c^3*d^3 - b^6*c^2*d^2*e)*x^4 + 2*(b^6*c^2*d^3 - b^7*c*d^2*e)*x^3 + (b^7*c*d^3 - b^8*d^2*e)*x^2), 1/8*(2*((A*b^3*c^2*e^3 - 24*(B*b*c^4 - 2*A*c^5)*d^3 + 4*(7*B*b^2*c^3 - 15*A*b*c^4)*d^2*e - (4*B*b^3*c^2 - 11*A*b^2*c^3)*d*e^2)*x^4 + 2*(A*b^4*c*e^3 - 24*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + 4*(7*B*b^3*c^2 - 15*A*b^2*c^3)*d^2*e - (4*B*b^4*c - 11*A*b^3*c^2)*d*e^2)*x^3 + (A*b^5*e^3 - 24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 + 4*(7*B*b^4*c - 15*A*b^3*c^2)*d^2*e - (4*B*b^5 - 11*A*b^4*c)*d*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + ((24*(B*b*c^4 - 2*A*c^5)*d^4 - 4*(10*B*b^2*c^3 - 21*A*b*c^4)*d^3*e + 5*(3*B*b^3*c^2 - 7*A*b^2*c^3)*d^2*e^2)*x^4 + 2*(24*(B*b^2*c^3 - 2*A*b*c^4)*d^4 - 4*(10*B*b^3*c^2 - 21*A*b^2*c^3)*d^3*e + 5*(3*B*b^4*c - 7*A*b^3*c^2)*d^2*e^2)*x^3 + (24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^4 - 4*(10*B*b^4*c - 21*A*b^3*c^2)*d^3*e + 5*(3*B*b^5 - 7*A*b^4*c)*d^2*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(2*A*b^4*c*d^3 - 2*A*b^5*d^2*e - (A*b^3*c^2*d*e^2 - 12*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + (11*B*b^3*c^2 - 24*A*b^2*c^3)*d^2*e)*x^3 - (2*A*b^4*c*d*e^2 - 18*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 + (17*B*b^4*c - 37*A*b^3*c^2)*d^2*e)*x^2 - (A*b^5*d*e^2 - 4*(B*b^4*c - 2*A*b^3*c^2)*d^3 + (4*B*b^5 - 9*A*b^4*c)*d^2*e)*x)*sqrt(e*x + d))/((b^5*c^3*d^3 - b^6*c^2*d^2*e)*x^4 + 2*(b^6*c^2*d^3 - b^7*c*d^2*e)*x^3 + (b^7*c*d^3 - b^8*d^2*e)*x^2), -1/4*(((24*(B*b*c^4 - 2*A*c^5)*d^4 - 4*(10*B*b^2*c^3 - 21*A*b*c^4)*d^3*e + 5*(3*B*b^3*c^2 - 7*A*b^2*c^3)*d^2*e^2)*x^4 + 2*(24*(B*b^2*c^3 - 2*A*b*c^4)*d^4 - 4*(10*B*b^3*c^2 - 21*A*b^2*c^3)*d^3*e + 5*(3*B*b^4*c - 7*A*b^3*c^2)*d^2*e^2)*x^3 + (24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^4 - 4*(10*B*b^4*c - 21*A*b^3*c^2)*d^3*e + 5*(3*B*b^5 - 7*A*b^4*c)*d^2*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - ((A*b^3*c^2*e^3 - 24*(B*b*c^4 - 2*A*c^5)*d^3 + 4*(7*B*b^2*c^3 - 15*A*b*c^4)*d^2*e - (4*B*b^3*c^2 - 11*A*b^2*c^3)*d*e^2)*x^4 + 2*(A*b^4*c*e^3 - 24*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + 4*(7*B*b^3*c^2 - 15*A*b^2*c^3)*d^2*e - (4*B*b^4*c - 11*A*b^3*c^2)*d*e^2)*x^3 + (A*b^5*e^3 - 24*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 + 4*(7*B*b^4*c - 15*A*b^3*c^2)*d^2*e - (4*B*b^5 - 11*A*b^4*c)*d*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (2*A*b^4*c*d^3 - 2*A*b^5*d^2*e - (A*b^3*c^2*d*e^2 - 12*(B*b^2*c^3 - 2*A*b*c^4)*d^3 + (11*B*b^3*c^2 - 24*A*b^2*c^3)*d^2*e)*x^3 - (2*A*b^4*c*d*e^2 - 18*(B*b^3*c^2 - 2*A*b^2*c^3)*d^3 + (17*B*b^4*c - 37*A*b^3*c^2)*d^2*e)*x^2 - (A*b^5*d*e^2 - 4*(B*b^4*c - 2*A*b^3*c^2)*d^3 + (4*B*b^5 - 9*A*b^4*c)*d^2*e)*x)*sqrt(e*x + d))/((b^5*c^3*d^3 - b^6*c^2*d^2*e)*x^4 + 2*(b^6*c^2*d^3 - b^7*c*d^2*e)*x^3 + (b^7*c*d^3 - b^8*d^2*e)*x^2)]","B",0
1252,1,4310,0,34.570048," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} - 4 \, {\left(14 \, B b^{2} c^{4} - 27 \, A b c^{5}\right)} d^{4} e + 7 \, {\left(5 \, B b^{3} c^{3} - 9 \, A b^{2} c^{4}\right)} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} - 4 \, {\left(14 \, B b^{3} c^{3} - 27 \, A b^{2} c^{4}\right)} d^{4} e + 7 \, {\left(5 \, B b^{4} c^{2} - 9 \, A b^{3} c^{3}\right)} d^{3} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{5} - 4 \, {\left(14 \, B b^{4} c^{2} - 27 \, A b^{3} c^{3}\right)} d^{4} e + 7 \, {\left(5 \, B b^{5} c - 9 \, A b^{4} c^{2}\right)} d^{3} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - {\left({\left(3 \, A b^{4} c^{2} e^{4} - 24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{4} + 4 \, {\left(11 \, B b^{2} c^{4} - 21 \, A b c^{5}\right)} d^{3} e - {\left(16 \, B b^{3} c^{3} - 27 \, A b^{2} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d e^{3}\right)} x^{4} + 2 \, {\left(3 \, A b^{5} c e^{4} - 24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} + 4 \, {\left(11 \, B b^{3} c^{3} - 21 \, A b^{2} c^{4}\right)} d^{3} e - {\left(16 \, B b^{4} c^{2} - 27 \, A b^{3} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{5} c - 3 \, A b^{4} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(3 \, A b^{6} e^{4} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{4} + 4 \, {\left(11 \, B b^{4} c^{2} - 21 \, A b^{3} c^{3}\right)} d^{3} e - {\left(16 \, B b^{5} c - 27 \, A b^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{6} - 3 \, A b^{5} c\right)} d e^{3}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, A b^{4} c^{2} d^{4} - 4 \, A b^{5} c d^{3} e + 2 \, A b^{6} d^{2} e^{2} - {\left(3 \, A b^{4} c^{2} d e^{3} - 12 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} + {\left(19 \, B b^{3} c^{3} - 36 \, A b^{2} c^{4}\right)} d^{3} e - 2 \, {\left(2 \, B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e^{2}\right)} x^{3} - {\left(6 \, A b^{5} c d e^{3} - 18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{4} + {\left(29 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{3} e - 2 \, {\left(4 \, B b^{5} c - 5 \, A b^{4} c^{2}\right)} d^{2} e^{2}\right)} x^{2} - {\left(3 \, A b^{6} d e^{3} - 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{4} + {\left(8 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d^{3} e - 2 \, {\left(2 \, B b^{6} - A b^{5} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{4} d^{5} - 2 \, b^{6} c^{3} d^{4} e + b^{7} c^{2} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{5} - 2 \, b^{7} c^{2} d^{4} e + b^{8} c d^{3} e^{2}\right)} x^{3} + {\left(b^{7} c^{2} d^{5} - 2 \, b^{8} c d^{4} e + b^{9} d^{3} e^{2}\right)} x^{2}\right)}}, -\frac{2 \, {\left({\left(24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} - 4 \, {\left(14 \, B b^{2} c^{4} - 27 \, A b c^{5}\right)} d^{4} e + 7 \, {\left(5 \, B b^{3} c^{3} - 9 \, A b^{2} c^{4}\right)} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} - 4 \, {\left(14 \, B b^{3} c^{3} - 27 \, A b^{2} c^{4}\right)} d^{4} e + 7 \, {\left(5 \, B b^{4} c^{2} - 9 \, A b^{3} c^{3}\right)} d^{3} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{5} - 4 \, {\left(14 \, B b^{4} c^{2} - 27 \, A b^{3} c^{3}\right)} d^{4} e + 7 \, {\left(5 \, B b^{5} c - 9 \, A b^{4} c^{2}\right)} d^{3} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left({\left(3 \, A b^{4} c^{2} e^{4} - 24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{4} + 4 \, {\left(11 \, B b^{2} c^{4} - 21 \, A b c^{5}\right)} d^{3} e - {\left(16 \, B b^{3} c^{3} - 27 \, A b^{2} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d e^{3}\right)} x^{4} + 2 \, {\left(3 \, A b^{5} c e^{4} - 24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} + 4 \, {\left(11 \, B b^{3} c^{3} - 21 \, A b^{2} c^{4}\right)} d^{3} e - {\left(16 \, B b^{4} c^{2} - 27 \, A b^{3} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{5} c - 3 \, A b^{4} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(3 \, A b^{6} e^{4} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{4} + 4 \, {\left(11 \, B b^{4} c^{2} - 21 \, A b^{3} c^{3}\right)} d^{3} e - {\left(16 \, B b^{5} c - 27 \, A b^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{6} - 3 \, A b^{5} c\right)} d e^{3}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, A b^{4} c^{2} d^{4} - 4 \, A b^{5} c d^{3} e + 2 \, A b^{6} d^{2} e^{2} - {\left(3 \, A b^{4} c^{2} d e^{3} - 12 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} + {\left(19 \, B b^{3} c^{3} - 36 \, A b^{2} c^{4}\right)} d^{3} e - 2 \, {\left(2 \, B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e^{2}\right)} x^{3} - {\left(6 \, A b^{5} c d e^{3} - 18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{4} + {\left(29 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{3} e - 2 \, {\left(4 \, B b^{5} c - 5 \, A b^{4} c^{2}\right)} d^{2} e^{2}\right)} x^{2} - {\left(3 \, A b^{6} d e^{3} - 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{4} + {\left(8 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d^{3} e - 2 \, {\left(2 \, B b^{6} - A b^{5} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{4} d^{5} - 2 \, b^{6} c^{3} d^{4} e + b^{7} c^{2} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{5} - 2 \, b^{7} c^{2} d^{4} e + b^{8} c d^{3} e^{2}\right)} x^{3} + {\left(b^{7} c^{2} d^{5} - 2 \, b^{8} c d^{4} e + b^{9} d^{3} e^{2}\right)} x^{2}\right)}}, \frac{2 \, {\left({\left(3 \, A b^{4} c^{2} e^{4} - 24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{4} + 4 \, {\left(11 \, B b^{2} c^{4} - 21 \, A b c^{5}\right)} d^{3} e - {\left(16 \, B b^{3} c^{3} - 27 \, A b^{2} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d e^{3}\right)} x^{4} + 2 \, {\left(3 \, A b^{5} c e^{4} - 24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} + 4 \, {\left(11 \, B b^{3} c^{3} - 21 \, A b^{2} c^{4}\right)} d^{3} e - {\left(16 \, B b^{4} c^{2} - 27 \, A b^{3} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{5} c - 3 \, A b^{4} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(3 \, A b^{6} e^{4} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{4} + 4 \, {\left(11 \, B b^{4} c^{2} - 21 \, A b^{3} c^{3}\right)} d^{3} e - {\left(16 \, B b^{5} c - 27 \, A b^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{6} - 3 \, A b^{5} c\right)} d e^{3}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left({\left(24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} - 4 \, {\left(14 \, B b^{2} c^{4} - 27 \, A b c^{5}\right)} d^{4} e + 7 \, {\left(5 \, B b^{3} c^{3} - 9 \, A b^{2} c^{4}\right)} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} - 4 \, {\left(14 \, B b^{3} c^{3} - 27 \, A b^{2} c^{4}\right)} d^{4} e + 7 \, {\left(5 \, B b^{4} c^{2} - 9 \, A b^{3} c^{3}\right)} d^{3} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{5} - 4 \, {\left(14 \, B b^{4} c^{2} - 27 \, A b^{3} c^{3}\right)} d^{4} e + 7 \, {\left(5 \, B b^{5} c - 9 \, A b^{4} c^{2}\right)} d^{3} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(2 \, A b^{4} c^{2} d^{4} - 4 \, A b^{5} c d^{3} e + 2 \, A b^{6} d^{2} e^{2} - {\left(3 \, A b^{4} c^{2} d e^{3} - 12 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} + {\left(19 \, B b^{3} c^{3} - 36 \, A b^{2} c^{4}\right)} d^{3} e - 2 \, {\left(2 \, B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e^{2}\right)} x^{3} - {\left(6 \, A b^{5} c d e^{3} - 18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{4} + {\left(29 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{3} e - 2 \, {\left(4 \, B b^{5} c - 5 \, A b^{4} c^{2}\right)} d^{2} e^{2}\right)} x^{2} - {\left(3 \, A b^{6} d e^{3} - 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{4} + {\left(8 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d^{3} e - 2 \, {\left(2 \, B b^{6} - A b^{5} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{4} d^{5} - 2 \, b^{6} c^{3} d^{4} e + b^{7} c^{2} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{5} - 2 \, b^{7} c^{2} d^{4} e + b^{8} c d^{3} e^{2}\right)} x^{3} + {\left(b^{7} c^{2} d^{5} - 2 \, b^{8} c d^{4} e + b^{9} d^{3} e^{2}\right)} x^{2}\right)}}, -\frac{{\left({\left(24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} - 4 \, {\left(14 \, B b^{2} c^{4} - 27 \, A b c^{5}\right)} d^{4} e + 7 \, {\left(5 \, B b^{3} c^{3} - 9 \, A b^{2} c^{4}\right)} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} - 4 \, {\left(14 \, B b^{3} c^{3} - 27 \, A b^{2} c^{4}\right)} d^{4} e + 7 \, {\left(5 \, B b^{4} c^{2} - 9 \, A b^{3} c^{3}\right)} d^{3} e^{2}\right)} x^{3} + {\left(24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{5} - 4 \, {\left(14 \, B b^{4} c^{2} - 27 \, A b^{3} c^{3}\right)} d^{4} e + 7 \, {\left(5 \, B b^{5} c - 9 \, A b^{4} c^{2}\right)} d^{3} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left({\left(3 \, A b^{4} c^{2} e^{4} - 24 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{4} + 4 \, {\left(11 \, B b^{2} c^{4} - 21 \, A b c^{5}\right)} d^{3} e - {\left(16 \, B b^{3} c^{3} - 27 \, A b^{2} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d e^{3}\right)} x^{4} + 2 \, {\left(3 \, A b^{5} c e^{4} - 24 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} + 4 \, {\left(11 \, B b^{3} c^{3} - 21 \, A b^{2} c^{4}\right)} d^{3} e - {\left(16 \, B b^{4} c^{2} - 27 \, A b^{3} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{5} c - 3 \, A b^{4} c^{2}\right)} d e^{3}\right)} x^{3} + {\left(3 \, A b^{6} e^{4} - 24 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{4} + 4 \, {\left(11 \, B b^{4} c^{2} - 21 \, A b^{3} c^{3}\right)} d^{3} e - {\left(16 \, B b^{5} c - 27 \, A b^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B b^{6} - 3 \, A b^{5} c\right)} d e^{3}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(2 \, A b^{4} c^{2} d^{4} - 4 \, A b^{5} c d^{3} e + 2 \, A b^{6} d^{2} e^{2} - {\left(3 \, A b^{4} c^{2} d e^{3} - 12 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{4} + {\left(19 \, B b^{3} c^{3} - 36 \, A b^{2} c^{4}\right)} d^{3} e - 2 \, {\left(2 \, B b^{4} c^{2} - 3 \, A b^{3} c^{3}\right)} d^{2} e^{2}\right)} x^{3} - {\left(6 \, A b^{5} c d e^{3} - 18 \, {\left(B b^{3} c^{3} - 2 \, A b^{2} c^{4}\right)} d^{4} + {\left(29 \, B b^{4} c^{2} - 55 \, A b^{3} c^{3}\right)} d^{3} e - 2 \, {\left(4 \, B b^{5} c - 5 \, A b^{4} c^{2}\right)} d^{2} e^{2}\right)} x^{2} - {\left(3 \, A b^{6} d e^{3} - 4 \, {\left(B b^{4} c^{2} - 2 \, A b^{3} c^{3}\right)} d^{4} + {\left(8 \, B b^{5} c - 13 \, A b^{4} c^{2}\right)} d^{3} e - 2 \, {\left(2 \, B b^{6} - A b^{5} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left({\left(b^{5} c^{4} d^{5} - 2 \, b^{6} c^{3} d^{4} e + b^{7} c^{2} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{5} - 2 \, b^{7} c^{2} d^{4} e + b^{8} c d^{3} e^{2}\right)} x^{3} + {\left(b^{7} c^{2} d^{5} - 2 \, b^{8} c d^{4} e + b^{9} d^{3} e^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(((24*(B*b*c^5 - 2*A*c^6)*d^5 - 4*(14*B*b^2*c^4 - 27*A*b*c^5)*d^4*e + 7*(5*B*b^3*c^3 - 9*A*b^2*c^4)*d^3*e^2)*x^4 + 2*(24*(B*b^2*c^4 - 2*A*b*c^5)*d^5 - 4*(14*B*b^3*c^3 - 27*A*b^2*c^4)*d^4*e + 7*(5*B*b^4*c^2 - 9*A*b^3*c^3)*d^3*e^2)*x^3 + (24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^5 - 4*(14*B*b^4*c^2 - 27*A*b^3*c^3)*d^4*e + 7*(5*B*b^5*c - 9*A*b^4*c^2)*d^3*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - ((3*A*b^4*c^2*e^4 - 24*(B*b*c^5 - 2*A*c^6)*d^4 + 4*(11*B*b^2*c^4 - 21*A*b*c^5)*d^3*e - (16*B*b^3*c^3 - 27*A*b^2*c^4)*d^2*e^2 - 2*(2*B*b^4*c^2 - 3*A*b^3*c^3)*d*e^3)*x^4 + 2*(3*A*b^5*c*e^4 - 24*(B*b^2*c^4 - 2*A*b*c^5)*d^4 + 4*(11*B*b^3*c^3 - 21*A*b^2*c^4)*d^3*e - (16*B*b^4*c^2 - 27*A*b^3*c^3)*d^2*e^2 - 2*(2*B*b^5*c - 3*A*b^4*c^2)*d*e^3)*x^3 + (3*A*b^6*e^4 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^4 + 4*(11*B*b^4*c^2 - 21*A*b^3*c^3)*d^3*e - (16*B*b^5*c - 27*A*b^4*c^2)*d^2*e^2 - 2*(2*B*b^6 - 3*A*b^5*c)*d*e^3)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*A*b^4*c^2*d^4 - 4*A*b^5*c*d^3*e + 2*A*b^6*d^2*e^2 - (3*A*b^4*c^2*d*e^3 - 12*(B*b^2*c^4 - 2*A*b*c^5)*d^4 + (19*B*b^3*c^3 - 36*A*b^2*c^4)*d^3*e - 2*(2*B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e^2)*x^3 - (6*A*b^5*c*d*e^3 - 18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^4 + (29*B*b^4*c^2 - 55*A*b^3*c^3)*d^3*e - 2*(4*B*b^5*c - 5*A*b^4*c^2)*d^2*e^2)*x^2 - (3*A*b^6*d*e^3 - 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^4 + (8*B*b^5*c - 13*A*b^4*c^2)*d^3*e - 2*(2*B*b^6 - A*b^5*c)*d^2*e^2)*x)*sqrt(e*x + d))/((b^5*c^4*d^5 - 2*b^6*c^3*d^4*e + b^7*c^2*d^3*e^2)*x^4 + 2*(b^6*c^3*d^5 - 2*b^7*c^2*d^4*e + b^8*c*d^3*e^2)*x^3 + (b^7*c^2*d^5 - 2*b^8*c*d^4*e + b^9*d^3*e^2)*x^2), -1/8*(2*((24*(B*b*c^5 - 2*A*c^6)*d^5 - 4*(14*B*b^2*c^4 - 27*A*b*c^5)*d^4*e + 7*(5*B*b^3*c^3 - 9*A*b^2*c^4)*d^3*e^2)*x^4 + 2*(24*(B*b^2*c^4 - 2*A*b*c^5)*d^5 - 4*(14*B*b^3*c^3 - 27*A*b^2*c^4)*d^4*e + 7*(5*B*b^4*c^2 - 9*A*b^3*c^3)*d^3*e^2)*x^3 + (24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^5 - 4*(14*B*b^4*c^2 - 27*A*b^3*c^3)*d^4*e + 7*(5*B*b^5*c - 9*A*b^4*c^2)*d^3*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - ((3*A*b^4*c^2*e^4 - 24*(B*b*c^5 - 2*A*c^6)*d^4 + 4*(11*B*b^2*c^4 - 21*A*b*c^5)*d^3*e - (16*B*b^3*c^3 - 27*A*b^2*c^4)*d^2*e^2 - 2*(2*B*b^4*c^2 - 3*A*b^3*c^3)*d*e^3)*x^4 + 2*(3*A*b^5*c*e^4 - 24*(B*b^2*c^4 - 2*A*b*c^5)*d^4 + 4*(11*B*b^3*c^3 - 21*A*b^2*c^4)*d^3*e - (16*B*b^4*c^2 - 27*A*b^3*c^3)*d^2*e^2 - 2*(2*B*b^5*c - 3*A*b^4*c^2)*d*e^3)*x^3 + (3*A*b^6*e^4 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^4 + 4*(11*B*b^4*c^2 - 21*A*b^3*c^3)*d^3*e - (16*B*b^5*c - 27*A*b^4*c^2)*d^2*e^2 - 2*(2*B*b^6 - 3*A*b^5*c)*d*e^3)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*A*b^4*c^2*d^4 - 4*A*b^5*c*d^3*e + 2*A*b^6*d^2*e^2 - (3*A*b^4*c^2*d*e^3 - 12*(B*b^2*c^4 - 2*A*b*c^5)*d^4 + (19*B*b^3*c^3 - 36*A*b^2*c^4)*d^3*e - 2*(2*B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e^2)*x^3 - (6*A*b^5*c*d*e^3 - 18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^4 + (29*B*b^4*c^2 - 55*A*b^3*c^3)*d^3*e - 2*(4*B*b^5*c - 5*A*b^4*c^2)*d^2*e^2)*x^2 - (3*A*b^6*d*e^3 - 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^4 + (8*B*b^5*c - 13*A*b^4*c^2)*d^3*e - 2*(2*B*b^6 - A*b^5*c)*d^2*e^2)*x)*sqrt(e*x + d))/((b^5*c^4*d^5 - 2*b^6*c^3*d^4*e + b^7*c^2*d^3*e^2)*x^4 + 2*(b^6*c^3*d^5 - 2*b^7*c^2*d^4*e + b^8*c*d^3*e^2)*x^3 + (b^7*c^2*d^5 - 2*b^8*c*d^4*e + b^9*d^3*e^2)*x^2), 1/8*(2*((3*A*b^4*c^2*e^4 - 24*(B*b*c^5 - 2*A*c^6)*d^4 + 4*(11*B*b^2*c^4 - 21*A*b*c^5)*d^3*e - (16*B*b^3*c^3 - 27*A*b^2*c^4)*d^2*e^2 - 2*(2*B*b^4*c^2 - 3*A*b^3*c^3)*d*e^3)*x^4 + 2*(3*A*b^5*c*e^4 - 24*(B*b^2*c^4 - 2*A*b*c^5)*d^4 + 4*(11*B*b^3*c^3 - 21*A*b^2*c^4)*d^3*e - (16*B*b^4*c^2 - 27*A*b^3*c^3)*d^2*e^2 - 2*(2*B*b^5*c - 3*A*b^4*c^2)*d*e^3)*x^3 + (3*A*b^6*e^4 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^4 + 4*(11*B*b^4*c^2 - 21*A*b^3*c^3)*d^3*e - (16*B*b^5*c - 27*A*b^4*c^2)*d^2*e^2 - 2*(2*B*b^6 - 3*A*b^5*c)*d*e^3)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - ((24*(B*b*c^5 - 2*A*c^6)*d^5 - 4*(14*B*b^2*c^4 - 27*A*b*c^5)*d^4*e + 7*(5*B*b^3*c^3 - 9*A*b^2*c^4)*d^3*e^2)*x^4 + 2*(24*(B*b^2*c^4 - 2*A*b*c^5)*d^5 - 4*(14*B*b^3*c^3 - 27*A*b^2*c^4)*d^4*e + 7*(5*B*b^4*c^2 - 9*A*b^3*c^3)*d^3*e^2)*x^3 + (24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^5 - 4*(14*B*b^4*c^2 - 27*A*b^3*c^3)*d^4*e + 7*(5*B*b^5*c - 9*A*b^4*c^2)*d^3*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(2*A*b^4*c^2*d^4 - 4*A*b^5*c*d^3*e + 2*A*b^6*d^2*e^2 - (3*A*b^4*c^2*d*e^3 - 12*(B*b^2*c^4 - 2*A*b*c^5)*d^4 + (19*B*b^3*c^3 - 36*A*b^2*c^4)*d^3*e - 2*(2*B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e^2)*x^3 - (6*A*b^5*c*d*e^3 - 18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^4 + (29*B*b^4*c^2 - 55*A*b^3*c^3)*d^3*e - 2*(4*B*b^5*c - 5*A*b^4*c^2)*d^2*e^2)*x^2 - (3*A*b^6*d*e^3 - 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^4 + (8*B*b^5*c - 13*A*b^4*c^2)*d^3*e - 2*(2*B*b^6 - A*b^5*c)*d^2*e^2)*x)*sqrt(e*x + d))/((b^5*c^4*d^5 - 2*b^6*c^3*d^4*e + b^7*c^2*d^3*e^2)*x^4 + 2*(b^6*c^3*d^5 - 2*b^7*c^2*d^4*e + b^8*c*d^3*e^2)*x^3 + (b^7*c^2*d^5 - 2*b^8*c*d^4*e + b^9*d^3*e^2)*x^2), -1/4*(((24*(B*b*c^5 - 2*A*c^6)*d^5 - 4*(14*B*b^2*c^4 - 27*A*b*c^5)*d^4*e + 7*(5*B*b^3*c^3 - 9*A*b^2*c^4)*d^3*e^2)*x^4 + 2*(24*(B*b^2*c^4 - 2*A*b*c^5)*d^5 - 4*(14*B*b^3*c^3 - 27*A*b^2*c^4)*d^4*e + 7*(5*B*b^4*c^2 - 9*A*b^3*c^3)*d^3*e^2)*x^3 + (24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^5 - 4*(14*B*b^4*c^2 - 27*A*b^3*c^3)*d^4*e + 7*(5*B*b^5*c - 9*A*b^4*c^2)*d^3*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - ((3*A*b^4*c^2*e^4 - 24*(B*b*c^5 - 2*A*c^6)*d^4 + 4*(11*B*b^2*c^4 - 21*A*b*c^5)*d^3*e - (16*B*b^3*c^3 - 27*A*b^2*c^4)*d^2*e^2 - 2*(2*B*b^4*c^2 - 3*A*b^3*c^3)*d*e^3)*x^4 + 2*(3*A*b^5*c*e^4 - 24*(B*b^2*c^4 - 2*A*b*c^5)*d^4 + 4*(11*B*b^3*c^3 - 21*A*b^2*c^4)*d^3*e - (16*B*b^4*c^2 - 27*A*b^3*c^3)*d^2*e^2 - 2*(2*B*b^5*c - 3*A*b^4*c^2)*d*e^3)*x^3 + (3*A*b^6*e^4 - 24*(B*b^3*c^3 - 2*A*b^2*c^4)*d^4 + 4*(11*B*b^4*c^2 - 21*A*b^3*c^3)*d^3*e - (16*B*b^5*c - 27*A*b^4*c^2)*d^2*e^2 - 2*(2*B*b^6 - 3*A*b^5*c)*d*e^3)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (2*A*b^4*c^2*d^4 - 4*A*b^5*c*d^3*e + 2*A*b^6*d^2*e^2 - (3*A*b^4*c^2*d*e^3 - 12*(B*b^2*c^4 - 2*A*b*c^5)*d^4 + (19*B*b^3*c^3 - 36*A*b^2*c^4)*d^3*e - 2*(2*B*b^4*c^2 - 3*A*b^3*c^3)*d^2*e^2)*x^3 - (6*A*b^5*c*d*e^3 - 18*(B*b^3*c^3 - 2*A*b^2*c^4)*d^4 + (29*B*b^4*c^2 - 55*A*b^3*c^3)*d^3*e - 2*(4*B*b^5*c - 5*A*b^4*c^2)*d^2*e^2)*x^2 - (3*A*b^6*d*e^3 - 4*(B*b^4*c^2 - 2*A*b^3*c^3)*d^4 + (8*B*b^5*c - 13*A*b^4*c^2)*d^3*e - 2*(2*B*b^6 - A*b^5*c)*d^2*e^2)*x)*sqrt(e*x + d))/((b^5*c^4*d^5 - 2*b^6*c^3*d^4*e + b^7*c^2*d^3*e^2)*x^4 + 2*(b^6*c^3*d^5 - 2*b^7*c^2*d^4*e + b^8*c*d^3*e^2)*x^3 + (b^7*c^2*d^5 - 2*b^8*c*d^4*e + b^9*d^3*e^2)*x^2)]","B",0
1253,1,7400,0,116.349283," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} e - 4 \, {\left(6 \, B b^{2} c^{5} - 11 \, A b c^{6}\right)} d^{5} e^{2} + 3 \, {\left(7 \, B b^{3} c^{4} - 11 \, A b^{2} c^{5}\right)} d^{4} e^{3}\right)} x^{5} + {\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{7} - 4 \, {\left(2 \, B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{6} e - {\left(27 \, B b^{3} c^{4} - 55 \, A b^{2} c^{5}\right)} d^{5} e^{2} + 6 \, {\left(7 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{4} e^{3}\right)} x^{4} + {\left(16 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{7} - 8 \, {\left(5 \, B b^{3} c^{4} - 9 \, A b^{2} c^{5}\right)} d^{6} e + 2 \, {\left(9 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{5} e^{2} + 3 \, {\left(7 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{4} e^{3}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{7} - 4 \, {\left(6 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{6} e + 3 \, {\left(7 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{5} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 3 \, {\left({\left(5 \, A b^{5} c^{2} e^{6} + 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{5} e - 4 \, {\left(5 \, B b^{2} c^{5} - 9 \, A b c^{6}\right)} d^{4} e^{2} + {\left(12 \, B b^{3} c^{4} - 17 \, A b^{2} c^{5}\right)} d^{3} e^{3} + {\left(4 \, B b^{4} c^{3} - 5 \, A b^{3} c^{4}\right)} d^{2} e^{4} - {\left(4 \, B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d e^{5}\right)} x^{5} + {\left(10 \, A b^{6} c e^{6} + 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} - 4 \, {\left(B b^{2} c^{5} - A b c^{6}\right)} d^{5} e - {\left(28 \, B b^{3} c^{4} - 55 \, A b^{2} c^{5}\right)} d^{4} e^{2} + {\left(28 \, B b^{4} c^{3} - 39 \, A b^{3} c^{4}\right)} d^{3} e^{3} + {\left(4 \, B b^{5} c^{2} - 13 \, A b^{4} c^{3}\right)} d^{2} e^{4} - {\left(8 \, B b^{6} c + A b^{5} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(5 \, A b^{7} e^{6} + 16 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{6} - 8 \, {\left(4 \, B b^{3} c^{4} - 7 \, A b^{2} c^{5}\right)} d^{5} e + 2 \, {\left(2 \, B b^{4} c^{3} + A b^{3} c^{4}\right)} d^{4} e^{2} + {\left(20 \, B b^{5} c^{2} - 27 \, A b^{4} c^{3}\right)} d^{3} e^{3} - {\left(4 \, B b^{6} c + 11 \, A b^{5} c^{2}\right)} d^{2} e^{4} - {\left(4 \, B b^{7} - 7 \, A b^{6} c\right)} d e^{5}\right)} x^{3} + {\left(5 \, A b^{7} d e^{5} + 8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{6} - 4 \, {\left(5 \, B b^{4} c^{3} - 9 \, A b^{3} c^{4}\right)} d^{5} e + {\left(12 \, B b^{5} c^{2} - 17 \, A b^{4} c^{3}\right)} d^{4} e^{2} + {\left(4 \, B b^{6} c - 5 \, A b^{5} c^{2}\right)} d^{3} e^{3} - {\left(4 \, B b^{7} + 3 \, A b^{6} c\right)} d^{2} e^{4}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, A b^{4} c^{3} d^{6} - 6 \, A b^{5} c^{2} d^{5} e + 6 \, A b^{6} c d^{4} e^{2} - 2 \, A b^{7} d^{3} e^{3} + 3 \, {\left(5 \, A b^{5} c^{2} d e^{5} + 4 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{5} e - {\left(9 \, B b^{3} c^{4} - 16 \, A b^{2} c^{5}\right)} d^{4} e^{2} + {\left(4 \, B b^{4} c^{3} - 5 \, A b^{3} c^{4}\right)} d^{3} e^{3} - {\left(4 \, B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d^{2} e^{4}\right)} x^{4} + {\left(30 \, A b^{6} c d e^{5} + 12 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{6} - 3 \, {\left(3 \, B b^{3} c^{4} - 4 \, A b^{2} c^{5}\right)} d^{5} e - 29 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{4} e^{2} + {\left(20 \, B b^{5} c^{2} - 33 \, A b^{4} c^{3}\right)} d^{3} e^{3} - {\left(24 \, B b^{6} c + 13 \, A b^{5} c^{2}\right)} d^{2} e^{4}\right)} x^{3} + {\left(15 \, A b^{7} d e^{5} + 18 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{6} - {\left(37 \, B b^{4} c^{3} - 65 \, A b^{3} c^{4}\right)} d^{5} e + {\left(12 \, B b^{5} c^{2} - 7 \, A b^{4} c^{3}\right)} d^{4} e^{2} + {\left(4 \, B b^{6} c - 23 \, A b^{5} c^{2}\right)} d^{3} e^{3} - {\left(12 \, B b^{7} - A b^{6} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(5 \, A b^{7} d^{2} e^{4} + 4 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{6} - {\left(12 \, B b^{5} c^{2} - 19 \, A b^{4} c^{3}\right)} d^{5} e + 3 \, {\left(4 \, B b^{6} c - 3 \, A b^{5} c^{2}\right)} d^{4} e^{2} - {\left(4 \, B b^{7} + 7 \, A b^{6} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{5} d^{7} e - 3 \, b^{6} c^{4} d^{6} e^{2} + 3 \, b^{7} c^{3} d^{5} e^{3} - b^{8} c^{2} d^{4} e^{4}\right)} x^{5} + {\left(b^{5} c^{5} d^{8} - b^{6} c^{4} d^{7} e - 3 \, b^{7} c^{3} d^{6} e^{2} + 5 \, b^{8} c^{2} d^{5} e^{3} - 2 \, b^{9} c d^{4} e^{4}\right)} x^{4} + {\left(2 \, b^{6} c^{4} d^{8} - 5 \, b^{7} c^{3} d^{7} e + 3 \, b^{8} c^{2} d^{6} e^{2} + b^{9} c d^{5} e^{3} - b^{10} d^{4} e^{4}\right)} x^{3} + {\left(b^{7} c^{3} d^{8} - 3 \, b^{8} c^{2} d^{7} e + 3 \, b^{9} c d^{6} e^{2} - b^{10} d^{5} e^{3}\right)} x^{2}\right)}}, -\frac{6 \, {\left({\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} e - 4 \, {\left(6 \, B b^{2} c^{5} - 11 \, A b c^{6}\right)} d^{5} e^{2} + 3 \, {\left(7 \, B b^{3} c^{4} - 11 \, A b^{2} c^{5}\right)} d^{4} e^{3}\right)} x^{5} + {\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{7} - 4 \, {\left(2 \, B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{6} e - {\left(27 \, B b^{3} c^{4} - 55 \, A b^{2} c^{5}\right)} d^{5} e^{2} + 6 \, {\left(7 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{4} e^{3}\right)} x^{4} + {\left(16 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{7} - 8 \, {\left(5 \, B b^{3} c^{4} - 9 \, A b^{2} c^{5}\right)} d^{6} e + 2 \, {\left(9 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{5} e^{2} + 3 \, {\left(7 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{4} e^{3}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{7} - 4 \, {\left(6 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{6} e + 3 \, {\left(7 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{5} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 3 \, {\left({\left(5 \, A b^{5} c^{2} e^{6} + 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{5} e - 4 \, {\left(5 \, B b^{2} c^{5} - 9 \, A b c^{6}\right)} d^{4} e^{2} + {\left(12 \, B b^{3} c^{4} - 17 \, A b^{2} c^{5}\right)} d^{3} e^{3} + {\left(4 \, B b^{4} c^{3} - 5 \, A b^{3} c^{4}\right)} d^{2} e^{4} - {\left(4 \, B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d e^{5}\right)} x^{5} + {\left(10 \, A b^{6} c e^{6} + 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} - 4 \, {\left(B b^{2} c^{5} - A b c^{6}\right)} d^{5} e - {\left(28 \, B b^{3} c^{4} - 55 \, A b^{2} c^{5}\right)} d^{4} e^{2} + {\left(28 \, B b^{4} c^{3} - 39 \, A b^{3} c^{4}\right)} d^{3} e^{3} + {\left(4 \, B b^{5} c^{2} - 13 \, A b^{4} c^{3}\right)} d^{2} e^{4} - {\left(8 \, B b^{6} c + A b^{5} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(5 \, A b^{7} e^{6} + 16 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{6} - 8 \, {\left(4 \, B b^{3} c^{4} - 7 \, A b^{2} c^{5}\right)} d^{5} e + 2 \, {\left(2 \, B b^{4} c^{3} + A b^{3} c^{4}\right)} d^{4} e^{2} + {\left(20 \, B b^{5} c^{2} - 27 \, A b^{4} c^{3}\right)} d^{3} e^{3} - {\left(4 \, B b^{6} c + 11 \, A b^{5} c^{2}\right)} d^{2} e^{4} - {\left(4 \, B b^{7} - 7 \, A b^{6} c\right)} d e^{5}\right)} x^{3} + {\left(5 \, A b^{7} d e^{5} + 8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{6} - 4 \, {\left(5 \, B b^{4} c^{3} - 9 \, A b^{3} c^{4}\right)} d^{5} e + {\left(12 \, B b^{5} c^{2} - 17 \, A b^{4} c^{3}\right)} d^{4} e^{2} + {\left(4 \, B b^{6} c - 5 \, A b^{5} c^{2}\right)} d^{3} e^{3} - {\left(4 \, B b^{7} + 3 \, A b^{6} c\right)} d^{2} e^{4}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, A b^{4} c^{3} d^{6} - 6 \, A b^{5} c^{2} d^{5} e + 6 \, A b^{6} c d^{4} e^{2} - 2 \, A b^{7} d^{3} e^{3} + 3 \, {\left(5 \, A b^{5} c^{2} d e^{5} + 4 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{5} e - {\left(9 \, B b^{3} c^{4} - 16 \, A b^{2} c^{5}\right)} d^{4} e^{2} + {\left(4 \, B b^{4} c^{3} - 5 \, A b^{3} c^{4}\right)} d^{3} e^{3} - {\left(4 \, B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d^{2} e^{4}\right)} x^{4} + {\left(30 \, A b^{6} c d e^{5} + 12 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{6} - 3 \, {\left(3 \, B b^{3} c^{4} - 4 \, A b^{2} c^{5}\right)} d^{5} e - 29 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{4} e^{2} + {\left(20 \, B b^{5} c^{2} - 33 \, A b^{4} c^{3}\right)} d^{3} e^{3} - {\left(24 \, B b^{6} c + 13 \, A b^{5} c^{2}\right)} d^{2} e^{4}\right)} x^{3} + {\left(15 \, A b^{7} d e^{5} + 18 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{6} - {\left(37 \, B b^{4} c^{3} - 65 \, A b^{3} c^{4}\right)} d^{5} e + {\left(12 \, B b^{5} c^{2} - 7 \, A b^{4} c^{3}\right)} d^{4} e^{2} + {\left(4 \, B b^{6} c - 23 \, A b^{5} c^{2}\right)} d^{3} e^{3} - {\left(12 \, B b^{7} - A b^{6} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(5 \, A b^{7} d^{2} e^{4} + 4 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{6} - {\left(12 \, B b^{5} c^{2} - 19 \, A b^{4} c^{3}\right)} d^{5} e + 3 \, {\left(4 \, B b^{6} c - 3 \, A b^{5} c^{2}\right)} d^{4} e^{2} - {\left(4 \, B b^{7} + 7 \, A b^{6} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{5} d^{7} e - 3 \, b^{6} c^{4} d^{6} e^{2} + 3 \, b^{7} c^{3} d^{5} e^{3} - b^{8} c^{2} d^{4} e^{4}\right)} x^{5} + {\left(b^{5} c^{5} d^{8} - b^{6} c^{4} d^{7} e - 3 \, b^{7} c^{3} d^{6} e^{2} + 5 \, b^{8} c^{2} d^{5} e^{3} - 2 \, b^{9} c d^{4} e^{4}\right)} x^{4} + {\left(2 \, b^{6} c^{4} d^{8} - 5 \, b^{7} c^{3} d^{7} e + 3 \, b^{8} c^{2} d^{6} e^{2} + b^{9} c d^{5} e^{3} - b^{10} d^{4} e^{4}\right)} x^{3} + {\left(b^{7} c^{3} d^{8} - 3 \, b^{8} c^{2} d^{7} e + 3 \, b^{9} c d^{6} e^{2} - b^{10} d^{5} e^{3}\right)} x^{2}\right)}}, -\frac{6 \, {\left({\left(5 \, A b^{5} c^{2} e^{6} + 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{5} e - 4 \, {\left(5 \, B b^{2} c^{5} - 9 \, A b c^{6}\right)} d^{4} e^{2} + {\left(12 \, B b^{3} c^{4} - 17 \, A b^{2} c^{5}\right)} d^{3} e^{3} + {\left(4 \, B b^{4} c^{3} - 5 \, A b^{3} c^{4}\right)} d^{2} e^{4} - {\left(4 \, B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d e^{5}\right)} x^{5} + {\left(10 \, A b^{6} c e^{6} + 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} - 4 \, {\left(B b^{2} c^{5} - A b c^{6}\right)} d^{5} e - {\left(28 \, B b^{3} c^{4} - 55 \, A b^{2} c^{5}\right)} d^{4} e^{2} + {\left(28 \, B b^{4} c^{3} - 39 \, A b^{3} c^{4}\right)} d^{3} e^{3} + {\left(4 \, B b^{5} c^{2} - 13 \, A b^{4} c^{3}\right)} d^{2} e^{4} - {\left(8 \, B b^{6} c + A b^{5} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(5 \, A b^{7} e^{6} + 16 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{6} - 8 \, {\left(4 \, B b^{3} c^{4} - 7 \, A b^{2} c^{5}\right)} d^{5} e + 2 \, {\left(2 \, B b^{4} c^{3} + A b^{3} c^{4}\right)} d^{4} e^{2} + {\left(20 \, B b^{5} c^{2} - 27 \, A b^{4} c^{3}\right)} d^{3} e^{3} - {\left(4 \, B b^{6} c + 11 \, A b^{5} c^{2}\right)} d^{2} e^{4} - {\left(4 \, B b^{7} - 7 \, A b^{6} c\right)} d e^{5}\right)} x^{3} + {\left(5 \, A b^{7} d e^{5} + 8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{6} - 4 \, {\left(5 \, B b^{4} c^{3} - 9 \, A b^{3} c^{4}\right)} d^{5} e + {\left(12 \, B b^{5} c^{2} - 17 \, A b^{4} c^{3}\right)} d^{4} e^{2} + {\left(4 \, B b^{6} c - 5 \, A b^{5} c^{2}\right)} d^{3} e^{3} - {\left(4 \, B b^{7} + 3 \, A b^{6} c\right)} d^{2} e^{4}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left({\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} e - 4 \, {\left(6 \, B b^{2} c^{5} - 11 \, A b c^{6}\right)} d^{5} e^{2} + 3 \, {\left(7 \, B b^{3} c^{4} - 11 \, A b^{2} c^{5}\right)} d^{4} e^{3}\right)} x^{5} + {\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{7} - 4 \, {\left(2 \, B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{6} e - {\left(27 \, B b^{3} c^{4} - 55 \, A b^{2} c^{5}\right)} d^{5} e^{2} + 6 \, {\left(7 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{4} e^{3}\right)} x^{4} + {\left(16 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{7} - 8 \, {\left(5 \, B b^{3} c^{4} - 9 \, A b^{2} c^{5}\right)} d^{6} e + 2 \, {\left(9 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{5} e^{2} + 3 \, {\left(7 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{4} e^{3}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{7} - 4 \, {\left(6 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{6} e + 3 \, {\left(7 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{5} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(2 \, A b^{4} c^{3} d^{6} - 6 \, A b^{5} c^{2} d^{5} e + 6 \, A b^{6} c d^{4} e^{2} - 2 \, A b^{7} d^{3} e^{3} + 3 \, {\left(5 \, A b^{5} c^{2} d e^{5} + 4 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{5} e - {\left(9 \, B b^{3} c^{4} - 16 \, A b^{2} c^{5}\right)} d^{4} e^{2} + {\left(4 \, B b^{4} c^{3} - 5 \, A b^{3} c^{4}\right)} d^{3} e^{3} - {\left(4 \, B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d^{2} e^{4}\right)} x^{4} + {\left(30 \, A b^{6} c d e^{5} + 12 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{6} - 3 \, {\left(3 \, B b^{3} c^{4} - 4 \, A b^{2} c^{5}\right)} d^{5} e - 29 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{4} e^{2} + {\left(20 \, B b^{5} c^{2} - 33 \, A b^{4} c^{3}\right)} d^{3} e^{3} - {\left(24 \, B b^{6} c + 13 \, A b^{5} c^{2}\right)} d^{2} e^{4}\right)} x^{3} + {\left(15 \, A b^{7} d e^{5} + 18 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{6} - {\left(37 \, B b^{4} c^{3} - 65 \, A b^{3} c^{4}\right)} d^{5} e + {\left(12 \, B b^{5} c^{2} - 7 \, A b^{4} c^{3}\right)} d^{4} e^{2} + {\left(4 \, B b^{6} c - 23 \, A b^{5} c^{2}\right)} d^{3} e^{3} - {\left(12 \, B b^{7} - A b^{6} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(5 \, A b^{7} d^{2} e^{4} + 4 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{6} - {\left(12 \, B b^{5} c^{2} - 19 \, A b^{4} c^{3}\right)} d^{5} e + 3 \, {\left(4 \, B b^{6} c - 3 \, A b^{5} c^{2}\right)} d^{4} e^{2} - {\left(4 \, B b^{7} + 7 \, A b^{6} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{5} d^{7} e - 3 \, b^{6} c^{4} d^{6} e^{2} + 3 \, b^{7} c^{3} d^{5} e^{3} - b^{8} c^{2} d^{4} e^{4}\right)} x^{5} + {\left(b^{5} c^{5} d^{8} - b^{6} c^{4} d^{7} e - 3 \, b^{7} c^{3} d^{6} e^{2} + 5 \, b^{8} c^{2} d^{5} e^{3} - 2 \, b^{9} c d^{4} e^{4}\right)} x^{4} + {\left(2 \, b^{6} c^{4} d^{8} - 5 \, b^{7} c^{3} d^{7} e + 3 \, b^{8} c^{2} d^{6} e^{2} + b^{9} c d^{5} e^{3} - b^{10} d^{4} e^{4}\right)} x^{3} + {\left(b^{7} c^{3} d^{8} - 3 \, b^{8} c^{2} d^{7} e + 3 \, b^{9} c d^{6} e^{2} - b^{10} d^{5} e^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left({\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} e - 4 \, {\left(6 \, B b^{2} c^{5} - 11 \, A b c^{6}\right)} d^{5} e^{2} + 3 \, {\left(7 \, B b^{3} c^{4} - 11 \, A b^{2} c^{5}\right)} d^{4} e^{3}\right)} x^{5} + {\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{7} - 4 \, {\left(2 \, B b^{2} c^{5} - 3 \, A b c^{6}\right)} d^{6} e - {\left(27 \, B b^{3} c^{4} - 55 \, A b^{2} c^{5}\right)} d^{5} e^{2} + 6 \, {\left(7 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{4} e^{3}\right)} x^{4} + {\left(16 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{7} - 8 \, {\left(5 \, B b^{3} c^{4} - 9 \, A b^{2} c^{5}\right)} d^{6} e + 2 \, {\left(9 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{5} e^{2} + 3 \, {\left(7 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{4} e^{3}\right)} x^{3} + {\left(8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{7} - 4 \, {\left(6 \, B b^{4} c^{3} - 11 \, A b^{3} c^{4}\right)} d^{6} e + 3 \, {\left(7 \, B b^{5} c^{2} - 11 \, A b^{4} c^{3}\right)} d^{5} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(5 \, A b^{5} c^{2} e^{6} + 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{5} e - 4 \, {\left(5 \, B b^{2} c^{5} - 9 \, A b c^{6}\right)} d^{4} e^{2} + {\left(12 \, B b^{3} c^{4} - 17 \, A b^{2} c^{5}\right)} d^{3} e^{3} + {\left(4 \, B b^{4} c^{3} - 5 \, A b^{3} c^{4}\right)} d^{2} e^{4} - {\left(4 \, B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d e^{5}\right)} x^{5} + {\left(10 \, A b^{6} c e^{6} + 8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} - 4 \, {\left(B b^{2} c^{5} - A b c^{6}\right)} d^{5} e - {\left(28 \, B b^{3} c^{4} - 55 \, A b^{2} c^{5}\right)} d^{4} e^{2} + {\left(28 \, B b^{4} c^{3} - 39 \, A b^{3} c^{4}\right)} d^{3} e^{3} + {\left(4 \, B b^{5} c^{2} - 13 \, A b^{4} c^{3}\right)} d^{2} e^{4} - {\left(8 \, B b^{6} c + A b^{5} c^{2}\right)} d e^{5}\right)} x^{4} + {\left(5 \, A b^{7} e^{6} + 16 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{6} - 8 \, {\left(4 \, B b^{3} c^{4} - 7 \, A b^{2} c^{5}\right)} d^{5} e + 2 \, {\left(2 \, B b^{4} c^{3} + A b^{3} c^{4}\right)} d^{4} e^{2} + {\left(20 \, B b^{5} c^{2} - 27 \, A b^{4} c^{3}\right)} d^{3} e^{3} - {\left(4 \, B b^{6} c + 11 \, A b^{5} c^{2}\right)} d^{2} e^{4} - {\left(4 \, B b^{7} - 7 \, A b^{6} c\right)} d e^{5}\right)} x^{3} + {\left(5 \, A b^{7} d e^{5} + 8 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{6} - 4 \, {\left(5 \, B b^{4} c^{3} - 9 \, A b^{3} c^{4}\right)} d^{5} e + {\left(12 \, B b^{5} c^{2} - 17 \, A b^{4} c^{3}\right)} d^{4} e^{2} + {\left(4 \, B b^{6} c - 5 \, A b^{5} c^{2}\right)} d^{3} e^{3} - {\left(4 \, B b^{7} + 3 \, A b^{6} c\right)} d^{2} e^{4}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(2 \, A b^{4} c^{3} d^{6} - 6 \, A b^{5} c^{2} d^{5} e + 6 \, A b^{6} c d^{4} e^{2} - 2 \, A b^{7} d^{3} e^{3} + 3 \, {\left(5 \, A b^{5} c^{2} d e^{5} + 4 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{5} e - {\left(9 \, B b^{3} c^{4} - 16 \, A b^{2} c^{5}\right)} d^{4} e^{2} + {\left(4 \, B b^{4} c^{3} - 5 \, A b^{3} c^{4}\right)} d^{3} e^{3} - {\left(4 \, B b^{5} c^{2} + 3 \, A b^{4} c^{3}\right)} d^{2} e^{4}\right)} x^{4} + {\left(30 \, A b^{6} c d e^{5} + 12 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{6} - 3 \, {\left(3 \, B b^{3} c^{4} - 4 \, A b^{2} c^{5}\right)} d^{5} e - 29 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{4} e^{2} + {\left(20 \, B b^{5} c^{2} - 33 \, A b^{4} c^{3}\right)} d^{3} e^{3} - {\left(24 \, B b^{6} c + 13 \, A b^{5} c^{2}\right)} d^{2} e^{4}\right)} x^{3} + {\left(15 \, A b^{7} d e^{5} + 18 \, {\left(B b^{3} c^{4} - 2 \, A b^{2} c^{5}\right)} d^{6} - {\left(37 \, B b^{4} c^{3} - 65 \, A b^{3} c^{4}\right)} d^{5} e + {\left(12 \, B b^{5} c^{2} - 7 \, A b^{4} c^{3}\right)} d^{4} e^{2} + {\left(4 \, B b^{6} c - 23 \, A b^{5} c^{2}\right)} d^{3} e^{3} - {\left(12 \, B b^{7} - A b^{6} c\right)} d^{2} e^{4}\right)} x^{2} + {\left(5 \, A b^{7} d^{2} e^{4} + 4 \, {\left(B b^{4} c^{3} - 2 \, A b^{3} c^{4}\right)} d^{6} - {\left(12 \, B b^{5} c^{2} - 19 \, A b^{4} c^{3}\right)} d^{5} e + 3 \, {\left(4 \, B b^{6} c - 3 \, A b^{5} c^{2}\right)} d^{4} e^{2} - {\left(4 \, B b^{7} + 7 \, A b^{6} c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left({\left(b^{5} c^{5} d^{7} e - 3 \, b^{6} c^{4} d^{6} e^{2} + 3 \, b^{7} c^{3} d^{5} e^{3} - b^{8} c^{2} d^{4} e^{4}\right)} x^{5} + {\left(b^{5} c^{5} d^{8} - b^{6} c^{4} d^{7} e - 3 \, b^{7} c^{3} d^{6} e^{2} + 5 \, b^{8} c^{2} d^{5} e^{3} - 2 \, b^{9} c d^{4} e^{4}\right)} x^{4} + {\left(2 \, b^{6} c^{4} d^{8} - 5 \, b^{7} c^{3} d^{7} e + 3 \, b^{8} c^{2} d^{6} e^{2} + b^{9} c d^{5} e^{3} - b^{10} d^{4} e^{4}\right)} x^{3} + {\left(b^{7} c^{3} d^{8} - 3 \, b^{8} c^{2} d^{7} e + 3 \, b^{9} c d^{6} e^{2} - b^{10} d^{5} e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(3*((8*(B*b*c^6 - 2*A*c^7)*d^6*e - 4*(6*B*b^2*c^5 - 11*A*b*c^6)*d^5*e^2 + 3*(7*B*b^3*c^4 - 11*A*b^2*c^5)*d^4*e^3)*x^5 + (8*(B*b*c^6 - 2*A*c^7)*d^7 - 4*(2*B*b^2*c^5 - 3*A*b*c^6)*d^6*e - (27*B*b^3*c^4 - 55*A*b^2*c^5)*d^5*e^2 + 6*(7*B*b^4*c^3 - 11*A*b^3*c^4)*d^4*e^3)*x^4 + (16*(B*b^2*c^5 - 2*A*b*c^6)*d^7 - 8*(5*B*b^3*c^4 - 9*A*b^2*c^5)*d^6*e + 2*(9*B*b^4*c^3 - 11*A*b^3*c^4)*d^5*e^2 + 3*(7*B*b^5*c^2 - 11*A*b^4*c^3)*d^4*e^3)*x^3 + (8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^7 - 4*(6*B*b^4*c^3 - 11*A*b^3*c^4)*d^6*e + 3*(7*B*b^5*c^2 - 11*A*b^4*c^3)*d^5*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 3*((5*A*b^5*c^2*e^6 + 8*(B*b*c^6 - 2*A*c^7)*d^5*e - 4*(5*B*b^2*c^5 - 9*A*b*c^6)*d^4*e^2 + (12*B*b^3*c^4 - 17*A*b^2*c^5)*d^3*e^3 + (4*B*b^4*c^3 - 5*A*b^3*c^4)*d^2*e^4 - (4*B*b^5*c^2 + 3*A*b^4*c^3)*d*e^5)*x^5 + (10*A*b^6*c*e^6 + 8*(B*b*c^6 - 2*A*c^7)*d^6 - 4*(B*b^2*c^5 - A*b*c^6)*d^5*e - (28*B*b^3*c^4 - 55*A*b^2*c^5)*d^4*e^2 + (28*B*b^4*c^3 - 39*A*b^3*c^4)*d^3*e^3 + (4*B*b^5*c^2 - 13*A*b^4*c^3)*d^2*e^4 - (8*B*b^6*c + A*b^5*c^2)*d*e^5)*x^4 + (5*A*b^7*e^6 + 16*(B*b^2*c^5 - 2*A*b*c^6)*d^6 - 8*(4*B*b^3*c^4 - 7*A*b^2*c^5)*d^5*e + 2*(2*B*b^4*c^3 + A*b^3*c^4)*d^4*e^2 + (20*B*b^5*c^2 - 27*A*b^4*c^3)*d^3*e^3 - (4*B*b^6*c + 11*A*b^5*c^2)*d^2*e^4 - (4*B*b^7 - 7*A*b^6*c)*d*e^5)*x^3 + (5*A*b^7*d*e^5 + 8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^6 - 4*(5*B*b^4*c^3 - 9*A*b^3*c^4)*d^5*e + (12*B*b^5*c^2 - 17*A*b^4*c^3)*d^4*e^2 + (4*B*b^6*c - 5*A*b^5*c^2)*d^3*e^3 - (4*B*b^7 + 3*A*b^6*c)*d^2*e^4)*x^2)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*A*b^4*c^3*d^6 - 6*A*b^5*c^2*d^5*e + 6*A*b^6*c*d^4*e^2 - 2*A*b^7*d^3*e^3 + 3*(5*A*b^5*c^2*d*e^5 + 4*(B*b^2*c^5 - 2*A*b*c^6)*d^5*e - (9*B*b^3*c^4 - 16*A*b^2*c^5)*d^4*e^2 + (4*B*b^4*c^3 - 5*A*b^3*c^4)*d^3*e^3 - (4*B*b^5*c^2 + 3*A*b^4*c^3)*d^2*e^4)*x^4 + (30*A*b^6*c*d*e^5 + 12*(B*b^2*c^5 - 2*A*b*c^6)*d^6 - 3*(3*B*b^3*c^4 - 4*A*b^2*c^5)*d^5*e - 29*(B*b^4*c^3 - 2*A*b^3*c^4)*d^4*e^2 + (20*B*b^5*c^2 - 33*A*b^4*c^3)*d^3*e^3 - (24*B*b^6*c + 13*A*b^5*c^2)*d^2*e^4)*x^3 + (15*A*b^7*d*e^5 + 18*(B*b^3*c^4 - 2*A*b^2*c^5)*d^6 - (37*B*b^4*c^3 - 65*A*b^3*c^4)*d^5*e + (12*B*b^5*c^2 - 7*A*b^4*c^3)*d^4*e^2 + (4*B*b^6*c - 23*A*b^5*c^2)*d^3*e^3 - (12*B*b^7 - A*b^6*c)*d^2*e^4)*x^2 + (5*A*b^7*d^2*e^4 + 4*(B*b^4*c^3 - 2*A*b^3*c^4)*d^6 - (12*B*b^5*c^2 - 19*A*b^4*c^3)*d^5*e + 3*(4*B*b^6*c - 3*A*b^5*c^2)*d^4*e^2 - (4*B*b^7 + 7*A*b^6*c)*d^3*e^3)*x)*sqrt(e*x + d))/((b^5*c^5*d^7*e - 3*b^6*c^4*d^6*e^2 + 3*b^7*c^3*d^5*e^3 - b^8*c^2*d^4*e^4)*x^5 + (b^5*c^5*d^8 - b^6*c^4*d^7*e - 3*b^7*c^3*d^6*e^2 + 5*b^8*c^2*d^5*e^3 - 2*b^9*c*d^4*e^4)*x^4 + (2*b^6*c^4*d^8 - 5*b^7*c^3*d^7*e + 3*b^8*c^2*d^6*e^2 + b^9*c*d^5*e^3 - b^10*d^4*e^4)*x^3 + (b^7*c^3*d^8 - 3*b^8*c^2*d^7*e + 3*b^9*c*d^6*e^2 - b^10*d^5*e^3)*x^2), -1/8*(6*((8*(B*b*c^6 - 2*A*c^7)*d^6*e - 4*(6*B*b^2*c^5 - 11*A*b*c^6)*d^5*e^2 + 3*(7*B*b^3*c^4 - 11*A*b^2*c^5)*d^4*e^3)*x^5 + (8*(B*b*c^6 - 2*A*c^7)*d^7 - 4*(2*B*b^2*c^5 - 3*A*b*c^6)*d^6*e - (27*B*b^3*c^4 - 55*A*b^2*c^5)*d^5*e^2 + 6*(7*B*b^4*c^3 - 11*A*b^3*c^4)*d^4*e^3)*x^4 + (16*(B*b^2*c^5 - 2*A*b*c^6)*d^7 - 8*(5*B*b^3*c^4 - 9*A*b^2*c^5)*d^6*e + 2*(9*B*b^4*c^3 - 11*A*b^3*c^4)*d^5*e^2 + 3*(7*B*b^5*c^2 - 11*A*b^4*c^3)*d^4*e^3)*x^3 + (8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^7 - 4*(6*B*b^4*c^3 - 11*A*b^3*c^4)*d^6*e + 3*(7*B*b^5*c^2 - 11*A*b^4*c^3)*d^5*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 3*((5*A*b^5*c^2*e^6 + 8*(B*b*c^6 - 2*A*c^7)*d^5*e - 4*(5*B*b^2*c^5 - 9*A*b*c^6)*d^4*e^2 + (12*B*b^3*c^4 - 17*A*b^2*c^5)*d^3*e^3 + (4*B*b^4*c^3 - 5*A*b^3*c^4)*d^2*e^4 - (4*B*b^5*c^2 + 3*A*b^4*c^3)*d*e^5)*x^5 + (10*A*b^6*c*e^6 + 8*(B*b*c^6 - 2*A*c^7)*d^6 - 4*(B*b^2*c^5 - A*b*c^6)*d^5*e - (28*B*b^3*c^4 - 55*A*b^2*c^5)*d^4*e^2 + (28*B*b^4*c^3 - 39*A*b^3*c^4)*d^3*e^3 + (4*B*b^5*c^2 - 13*A*b^4*c^3)*d^2*e^4 - (8*B*b^6*c + A*b^5*c^2)*d*e^5)*x^4 + (5*A*b^7*e^6 + 16*(B*b^2*c^5 - 2*A*b*c^6)*d^6 - 8*(4*B*b^3*c^4 - 7*A*b^2*c^5)*d^5*e + 2*(2*B*b^4*c^3 + A*b^3*c^4)*d^4*e^2 + (20*B*b^5*c^2 - 27*A*b^4*c^3)*d^3*e^3 - (4*B*b^6*c + 11*A*b^5*c^2)*d^2*e^4 - (4*B*b^7 - 7*A*b^6*c)*d*e^5)*x^3 + (5*A*b^7*d*e^5 + 8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^6 - 4*(5*B*b^4*c^3 - 9*A*b^3*c^4)*d^5*e + (12*B*b^5*c^2 - 17*A*b^4*c^3)*d^4*e^2 + (4*B*b^6*c - 5*A*b^5*c^2)*d^3*e^3 - (4*B*b^7 + 3*A*b^6*c)*d^2*e^4)*x^2)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*A*b^4*c^3*d^6 - 6*A*b^5*c^2*d^5*e + 6*A*b^6*c*d^4*e^2 - 2*A*b^7*d^3*e^3 + 3*(5*A*b^5*c^2*d*e^5 + 4*(B*b^2*c^5 - 2*A*b*c^6)*d^5*e - (9*B*b^3*c^4 - 16*A*b^2*c^5)*d^4*e^2 + (4*B*b^4*c^3 - 5*A*b^3*c^4)*d^3*e^3 - (4*B*b^5*c^2 + 3*A*b^4*c^3)*d^2*e^4)*x^4 + (30*A*b^6*c*d*e^5 + 12*(B*b^2*c^5 - 2*A*b*c^6)*d^6 - 3*(3*B*b^3*c^4 - 4*A*b^2*c^5)*d^5*e - 29*(B*b^4*c^3 - 2*A*b^3*c^4)*d^4*e^2 + (20*B*b^5*c^2 - 33*A*b^4*c^3)*d^3*e^3 - (24*B*b^6*c + 13*A*b^5*c^2)*d^2*e^4)*x^3 + (15*A*b^7*d*e^5 + 18*(B*b^3*c^4 - 2*A*b^2*c^5)*d^6 - (37*B*b^4*c^3 - 65*A*b^3*c^4)*d^5*e + (12*B*b^5*c^2 - 7*A*b^4*c^3)*d^4*e^2 + (4*B*b^6*c - 23*A*b^5*c^2)*d^3*e^3 - (12*B*b^7 - A*b^6*c)*d^2*e^4)*x^2 + (5*A*b^7*d^2*e^4 + 4*(B*b^4*c^3 - 2*A*b^3*c^4)*d^6 - (12*B*b^5*c^2 - 19*A*b^4*c^3)*d^5*e + 3*(4*B*b^6*c - 3*A*b^5*c^2)*d^4*e^2 - (4*B*b^7 + 7*A*b^6*c)*d^3*e^3)*x)*sqrt(e*x + d))/((b^5*c^5*d^7*e - 3*b^6*c^4*d^6*e^2 + 3*b^7*c^3*d^5*e^3 - b^8*c^2*d^4*e^4)*x^5 + (b^5*c^5*d^8 - b^6*c^4*d^7*e - 3*b^7*c^3*d^6*e^2 + 5*b^8*c^2*d^5*e^3 - 2*b^9*c*d^4*e^4)*x^4 + (2*b^6*c^4*d^8 - 5*b^7*c^3*d^7*e + 3*b^8*c^2*d^6*e^2 + b^9*c*d^5*e^3 - b^10*d^4*e^4)*x^3 + (b^7*c^3*d^8 - 3*b^8*c^2*d^7*e + 3*b^9*c*d^6*e^2 - b^10*d^5*e^3)*x^2), -1/8*(6*((5*A*b^5*c^2*e^6 + 8*(B*b*c^6 - 2*A*c^7)*d^5*e - 4*(5*B*b^2*c^5 - 9*A*b*c^6)*d^4*e^2 + (12*B*b^3*c^4 - 17*A*b^2*c^5)*d^3*e^3 + (4*B*b^4*c^3 - 5*A*b^3*c^4)*d^2*e^4 - (4*B*b^5*c^2 + 3*A*b^4*c^3)*d*e^5)*x^5 + (10*A*b^6*c*e^6 + 8*(B*b*c^6 - 2*A*c^7)*d^6 - 4*(B*b^2*c^5 - A*b*c^6)*d^5*e - (28*B*b^3*c^4 - 55*A*b^2*c^5)*d^4*e^2 + (28*B*b^4*c^3 - 39*A*b^3*c^4)*d^3*e^3 + (4*B*b^5*c^2 - 13*A*b^4*c^3)*d^2*e^4 - (8*B*b^6*c + A*b^5*c^2)*d*e^5)*x^4 + (5*A*b^7*e^6 + 16*(B*b^2*c^5 - 2*A*b*c^6)*d^6 - 8*(4*B*b^3*c^4 - 7*A*b^2*c^5)*d^5*e + 2*(2*B*b^4*c^3 + A*b^3*c^4)*d^4*e^2 + (20*B*b^5*c^2 - 27*A*b^4*c^3)*d^3*e^3 - (4*B*b^6*c + 11*A*b^5*c^2)*d^2*e^4 - (4*B*b^7 - 7*A*b^6*c)*d*e^5)*x^3 + (5*A*b^7*d*e^5 + 8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^6 - 4*(5*B*b^4*c^3 - 9*A*b^3*c^4)*d^5*e + (12*B*b^5*c^2 - 17*A*b^4*c^3)*d^4*e^2 + (4*B*b^6*c - 5*A*b^5*c^2)*d^3*e^3 - (4*B*b^7 + 3*A*b^6*c)*d^2*e^4)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*((8*(B*b*c^6 - 2*A*c^7)*d^6*e - 4*(6*B*b^2*c^5 - 11*A*b*c^6)*d^5*e^2 + 3*(7*B*b^3*c^4 - 11*A*b^2*c^5)*d^4*e^3)*x^5 + (8*(B*b*c^6 - 2*A*c^7)*d^7 - 4*(2*B*b^2*c^5 - 3*A*b*c^6)*d^6*e - (27*B*b^3*c^4 - 55*A*b^2*c^5)*d^5*e^2 + 6*(7*B*b^4*c^3 - 11*A*b^3*c^4)*d^4*e^3)*x^4 + (16*(B*b^2*c^5 - 2*A*b*c^6)*d^7 - 8*(5*B*b^3*c^4 - 9*A*b^2*c^5)*d^6*e + 2*(9*B*b^4*c^3 - 11*A*b^3*c^4)*d^5*e^2 + 3*(7*B*b^5*c^2 - 11*A*b^4*c^3)*d^4*e^3)*x^3 + (8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^7 - 4*(6*B*b^4*c^3 - 11*A*b^3*c^4)*d^6*e + 3*(7*B*b^5*c^2 - 11*A*b^4*c^3)*d^5*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(2*A*b^4*c^3*d^6 - 6*A*b^5*c^2*d^5*e + 6*A*b^6*c*d^4*e^2 - 2*A*b^7*d^3*e^3 + 3*(5*A*b^5*c^2*d*e^5 + 4*(B*b^2*c^5 - 2*A*b*c^6)*d^5*e - (9*B*b^3*c^4 - 16*A*b^2*c^5)*d^4*e^2 + (4*B*b^4*c^3 - 5*A*b^3*c^4)*d^3*e^3 - (4*B*b^5*c^2 + 3*A*b^4*c^3)*d^2*e^4)*x^4 + (30*A*b^6*c*d*e^5 + 12*(B*b^2*c^5 - 2*A*b*c^6)*d^6 - 3*(3*B*b^3*c^4 - 4*A*b^2*c^5)*d^5*e - 29*(B*b^4*c^3 - 2*A*b^3*c^4)*d^4*e^2 + (20*B*b^5*c^2 - 33*A*b^4*c^3)*d^3*e^3 - (24*B*b^6*c + 13*A*b^5*c^2)*d^2*e^4)*x^3 + (15*A*b^7*d*e^5 + 18*(B*b^3*c^4 - 2*A*b^2*c^5)*d^6 - (37*B*b^4*c^3 - 65*A*b^3*c^4)*d^5*e + (12*B*b^5*c^2 - 7*A*b^4*c^3)*d^4*e^2 + (4*B*b^6*c - 23*A*b^5*c^2)*d^3*e^3 - (12*B*b^7 - A*b^6*c)*d^2*e^4)*x^2 + (5*A*b^7*d^2*e^4 + 4*(B*b^4*c^3 - 2*A*b^3*c^4)*d^6 - (12*B*b^5*c^2 - 19*A*b^4*c^3)*d^5*e + 3*(4*B*b^6*c - 3*A*b^5*c^2)*d^4*e^2 - (4*B*b^7 + 7*A*b^6*c)*d^3*e^3)*x)*sqrt(e*x + d))/((b^5*c^5*d^7*e - 3*b^6*c^4*d^6*e^2 + 3*b^7*c^3*d^5*e^3 - b^8*c^2*d^4*e^4)*x^5 + (b^5*c^5*d^8 - b^6*c^4*d^7*e - 3*b^7*c^3*d^6*e^2 + 5*b^8*c^2*d^5*e^3 - 2*b^9*c*d^4*e^4)*x^4 + (2*b^6*c^4*d^8 - 5*b^7*c^3*d^7*e + 3*b^8*c^2*d^6*e^2 + b^9*c*d^5*e^3 - b^10*d^4*e^4)*x^3 + (b^7*c^3*d^8 - 3*b^8*c^2*d^7*e + 3*b^9*c*d^6*e^2 - b^10*d^5*e^3)*x^2), -1/4*(3*((8*(B*b*c^6 - 2*A*c^7)*d^6*e - 4*(6*B*b^2*c^5 - 11*A*b*c^6)*d^5*e^2 + 3*(7*B*b^3*c^4 - 11*A*b^2*c^5)*d^4*e^3)*x^5 + (8*(B*b*c^6 - 2*A*c^7)*d^7 - 4*(2*B*b^2*c^5 - 3*A*b*c^6)*d^6*e - (27*B*b^3*c^4 - 55*A*b^2*c^5)*d^5*e^2 + 6*(7*B*b^4*c^3 - 11*A*b^3*c^4)*d^4*e^3)*x^4 + (16*(B*b^2*c^5 - 2*A*b*c^6)*d^7 - 8*(5*B*b^3*c^4 - 9*A*b^2*c^5)*d^6*e + 2*(9*B*b^4*c^3 - 11*A*b^3*c^4)*d^5*e^2 + 3*(7*B*b^5*c^2 - 11*A*b^4*c^3)*d^4*e^3)*x^3 + (8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^7 - 4*(6*B*b^4*c^3 - 11*A*b^3*c^4)*d^6*e + 3*(7*B*b^5*c^2 - 11*A*b^4*c^3)*d^5*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((5*A*b^5*c^2*e^6 + 8*(B*b*c^6 - 2*A*c^7)*d^5*e - 4*(5*B*b^2*c^5 - 9*A*b*c^6)*d^4*e^2 + (12*B*b^3*c^4 - 17*A*b^2*c^5)*d^3*e^3 + (4*B*b^4*c^3 - 5*A*b^3*c^4)*d^2*e^4 - (4*B*b^5*c^2 + 3*A*b^4*c^3)*d*e^5)*x^5 + (10*A*b^6*c*e^6 + 8*(B*b*c^6 - 2*A*c^7)*d^6 - 4*(B*b^2*c^5 - A*b*c^6)*d^5*e - (28*B*b^3*c^4 - 55*A*b^2*c^5)*d^4*e^2 + (28*B*b^4*c^3 - 39*A*b^3*c^4)*d^3*e^3 + (4*B*b^5*c^2 - 13*A*b^4*c^3)*d^2*e^4 - (8*B*b^6*c + A*b^5*c^2)*d*e^5)*x^4 + (5*A*b^7*e^6 + 16*(B*b^2*c^5 - 2*A*b*c^6)*d^6 - 8*(4*B*b^3*c^4 - 7*A*b^2*c^5)*d^5*e + 2*(2*B*b^4*c^3 + A*b^3*c^4)*d^4*e^2 + (20*B*b^5*c^2 - 27*A*b^4*c^3)*d^3*e^3 - (4*B*b^6*c + 11*A*b^5*c^2)*d^2*e^4 - (4*B*b^7 - 7*A*b^6*c)*d*e^5)*x^3 + (5*A*b^7*d*e^5 + 8*(B*b^3*c^4 - 2*A*b^2*c^5)*d^6 - 4*(5*B*b^4*c^3 - 9*A*b^3*c^4)*d^5*e + (12*B*b^5*c^2 - 17*A*b^4*c^3)*d^4*e^2 + (4*B*b^6*c - 5*A*b^5*c^2)*d^3*e^3 - (4*B*b^7 + 3*A*b^6*c)*d^2*e^4)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (2*A*b^4*c^3*d^6 - 6*A*b^5*c^2*d^5*e + 6*A*b^6*c*d^4*e^2 - 2*A*b^7*d^3*e^3 + 3*(5*A*b^5*c^2*d*e^5 + 4*(B*b^2*c^5 - 2*A*b*c^6)*d^5*e - (9*B*b^3*c^4 - 16*A*b^2*c^5)*d^4*e^2 + (4*B*b^4*c^3 - 5*A*b^3*c^4)*d^3*e^3 - (4*B*b^5*c^2 + 3*A*b^4*c^3)*d^2*e^4)*x^4 + (30*A*b^6*c*d*e^5 + 12*(B*b^2*c^5 - 2*A*b*c^6)*d^6 - 3*(3*B*b^3*c^4 - 4*A*b^2*c^5)*d^5*e - 29*(B*b^4*c^3 - 2*A*b^3*c^4)*d^4*e^2 + (20*B*b^5*c^2 - 33*A*b^4*c^3)*d^3*e^3 - (24*B*b^6*c + 13*A*b^5*c^2)*d^2*e^4)*x^3 + (15*A*b^7*d*e^5 + 18*(B*b^3*c^4 - 2*A*b^2*c^5)*d^6 - (37*B*b^4*c^3 - 65*A*b^3*c^4)*d^5*e + (12*B*b^5*c^2 - 7*A*b^4*c^3)*d^4*e^2 + (4*B*b^6*c - 23*A*b^5*c^2)*d^3*e^3 - (12*B*b^7 - A*b^6*c)*d^2*e^4)*x^2 + (5*A*b^7*d^2*e^4 + 4*(B*b^4*c^3 - 2*A*b^3*c^4)*d^6 - (12*B*b^5*c^2 - 19*A*b^4*c^3)*d^5*e + 3*(4*B*b^6*c - 3*A*b^5*c^2)*d^4*e^2 - (4*B*b^7 + 7*A*b^6*c)*d^3*e^3)*x)*sqrt(e*x + d))/((b^5*c^5*d^7*e - 3*b^6*c^4*d^6*e^2 + 3*b^7*c^3*d^5*e^3 - b^8*c^2*d^4*e^4)*x^5 + (b^5*c^5*d^8 - b^6*c^4*d^7*e - 3*b^7*c^3*d^6*e^2 + 5*b^8*c^2*d^5*e^3 - 2*b^9*c*d^4*e^4)*x^4 + (2*b^6*c^4*d^8 - 5*b^7*c^3*d^7*e + 3*b^8*c^2*d^6*e^2 + b^9*c*d^5*e^3 - b^10*d^4*e^4)*x^3 + (b^7*c^3*d^8 - 3*b^8*c^2*d^7*e + 3*b^9*c*d^6*e^2 - b^10*d^5*e^3)*x^2)]","B",0
1254,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1255,0,0,0,0.528061," ","integrate((B*x+A)*(e*x+d)^(1/2)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d), x)","F",0
1256,0,0,0,0.550810," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)}}{\sqrt{e x + d}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)/sqrt(e*x + d), x)","F",0
1257,0,0,0,0.510584," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
1258,0,0,0,0.531031," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
1259,0,0,0,0.453907," ","integrate((B*x+A)*(c*x^2+b*x)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
1260,0,0,0,0.564093," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A b x + {\left(B b + A c\right)} x^{2}\right)} \sqrt{c x^{2} + b x}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((B*c*x^3 + A*b*x + (B*b + A*c)*x^2)*sqrt(c*x^2 + b*x)/sqrt(e*x + d), x)","F",0
1261,0,0,0,0.577623," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A b x + {\left(B b + A c\right)} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((B*c*x^3 + A*b*x + (B*b + A*c)*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
1262,0,0,0,0.575829," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A b x + {\left(B b + A c\right)} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((B*c*x^3 + A*b*x + (B*b + A*c)*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
1263,0,0,0,0.582155," ","integrate((B*x+A)*(c*x^2+b*x)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A b x + {\left(B b + A c\right)} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((B*c*x^3 + A*b*x + (B*b + A*c)*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
1264,0,0,0,0.557832," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{3} + A d^{2} + {\left(2 \, B d e + A e^{2}\right)} x^{2} + {\left(B d^{2} + 2 \, A d e\right)} x\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x}}, x\right)"," ",0,"integral((B*e^2*x^3 + A*d^2 + (2*B*d*e + A*e^2)*x^2 + (B*d^2 + 2*A*d*e)*x)*sqrt(e*x + d)/sqrt(c*x^2 + b*x), x)","F",0
1265,0,0,0,0.540135," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A d + {\left(B d + A e\right)} x\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x}}, x\right)"," ",0,"integral((B*e*x^2 + A*d + (B*d + A*e)*x)*sqrt(e*x + d)/sqrt(c*x^2 + b*x), x)","F",0
1266,0,0,0,0.491436," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x}}, x\right)"," ",0,"integral((B*x + A)*sqrt(e*x + d)/sqrt(c*x^2 + b*x), x)","F",0
1267,0,0,0,0.493099," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c e x^{3} + b d x + {\left(c d + b e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c*e*x^3 + b*d*x + (c*d + b*e)*x^2), x)","F",0
1268,0,0,0,0.463756," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c e^{2} x^{4} + b d^{2} x + {\left(2 \, c d e + b e^{2}\right)} x^{3} + {\left(c d^{2} + 2 \, b d e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c*e^2*x^4 + b*d^2*x + (2*c*d*e + b*e^2)*x^3 + (c*d^2 + 2*b*d*e)*x^2), x)","F",0
1269,0,0,0,0.452462," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c e^{3} x^{5} + b d^{3} x + {\left(3 \, c d e^{2} + b e^{3}\right)} x^{4} + 3 \, {\left(c d^{2} e + b d e^{2}\right)} x^{3} + {\left(c d^{3} + 3 \, b d^{2} e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c*e^3*x^5 + b*d^3*x + (3*c*d*e^2 + b*e^3)*x^4 + 3*(c*d^2*e + b*d*e^2)*x^3 + (c*d^3 + 3*b*d^2*e)*x^2), x)","F",0
1270,0,0,0,0.462845," ","integrate((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c e^{4} x^{6} + b d^{4} x + {\left(4 \, c d e^{3} + b e^{4}\right)} x^{5} + 2 \, {\left(3 \, c d^{2} e^{2} + 2 \, b d e^{3}\right)} x^{4} + 2 \, {\left(2 \, c d^{3} e + 3 \, b d^{2} e^{2}\right)} x^{3} + {\left(c d^{4} + 4 \, b d^{3} e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c*e^4*x^6 + b*d^4*x + (4*c*d*e^3 + b*e^4)*x^5 + 2*(3*c*d^2*e^2 + 2*b*d*e^3)*x^4 + 2*(2*c*d^3*e + 3*b*d^2*e^2)*x^3 + (c*d^4 + 4*b*d^3*e)*x^2), x)","F",0
1271,0,0,0,0.563503," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{3} x^{4} + A d^{3} + {\left(3 \, B d e^{2} + A e^{3}\right)} x^{3} + 3 \, {\left(B d^{2} e + A d e^{2}\right)} x^{2} + {\left(B d^{3} + 3 \, A d^{2} e\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral((B*e^3*x^4 + A*d^3 + (3*B*d*e^2 + A*e^3)*x^3 + 3*(B*d^2*e + A*d*e^2)*x^2 + (B*d^3 + 3*A*d^2*e)*x)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
1272,0,0,0,0.525090," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{3} + A d^{2} + {\left(2 \, B d e + A e^{2}\right)} x^{2} + {\left(B d^{2} + 2 \, A d e\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral((B*e^2*x^3 + A*d^2 + (2*B*d*e + A*e^2)*x^2 + (B*d^2 + 2*A*d*e)*x)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
1273,0,0,0,0.515940," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A d + {\left(B d + A e\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral((B*e*x^2 + A*d + (B*d + A*e)*x)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
1274,0,0,0,0.445551," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
1275,0,0,0,0.470122," ","integrate((B*x+A)/(c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c^{2} e x^{5} + b^{2} d x^{2} + {\left(c^{2} d + 2 \, b c e\right)} x^{4} + {\left(2 \, b c d + b^{2} e\right)} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c^2*e*x^5 + b^2*d*x^2 + (c^2*d + 2*b*c*e)*x^4 + (2*b*c*d + b^2*e)*x^3), x)","F",0
1276,0,0,0,0.466505," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c^{2} e^{2} x^{6} + b^{2} d^{2} x^{2} + 2 \, {\left(c^{2} d e + b c e^{2}\right)} x^{5} + {\left(c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2}\right)} x^{4} + 2 \, {\left(b c d^{2} + b^{2} d e\right)} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c^2*e^2*x^6 + b^2*d^2*x^2 + 2*(c^2*d*e + b*c*e^2)*x^5 + (c^2*d^2 + 4*b*c*d*e + b^2*e^2)*x^4 + 2*(b*c*d^2 + b^2*d*e)*x^3), x)","F",0
1277,0,0,0,0.509494," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c^{2} e^{3} x^{7} + b^{2} d^{3} x^{2} + {\left(3 \, c^{2} d e^{2} + 2 \, b c e^{3}\right)} x^{6} + {\left(3 \, c^{2} d^{2} e + 6 \, b c d e^{2} + b^{2} e^{3}\right)} x^{5} + {\left(c^{2} d^{3} + 6 \, b c d^{2} e + 3 \, b^{2} d e^{2}\right)} x^{4} + {\left(2 \, b c d^{3} + 3 \, b^{2} d^{2} e\right)} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c^2*e^3*x^7 + b^2*d^3*x^2 + (3*c^2*d*e^2 + 2*b*c*e^3)*x^6 + (3*c^2*d^2*e + 6*b*c*d*e^2 + b^2*e^3)*x^5 + (c^2*d^3 + 6*b*c*d^2*e + 3*b^2*d*e^2)*x^4 + (2*b*c*d^3 + 3*b^2*d^2*e)*x^3), x)","F",0
1278,0,0,0,0.597832," ","integrate((B*x+A)*(e*x+d)^(7/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{3} x^{4} + A d^{3} + {\left(3 \, B d e^{2} + A e^{3}\right)} x^{3} + 3 \, {\left(B d^{2} e + A d e^{2}\right)} x^{2} + {\left(B d^{3} + 3 \, A d^{2} e\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral((B*e^3*x^4 + A*d^3 + (3*B*d*e^2 + A*e^3)*x^3 + 3*(B*d^2*e + A*d*e^2)*x^2 + (B*d^3 + 3*A*d^2*e)*x)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
1279,0,0,0,0.467962," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{3} + A d^{2} + {\left(2 \, B d e + A e^{2}\right)} x^{2} + {\left(B d^{2} + 2 \, A d e\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral((B*e^2*x^3 + A*d^2 + (2*B*d*e + A*e^2)*x^2 + (B*d^2 + 2*A*d*e)*x)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
1280,0,0,0,0.452618," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A d + {\left(B d + A e\right)} x\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral((B*e*x^2 + A*d + (B*d + A*e)*x)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
1281,0,0,0,0.459675," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
1282,0,0,0,0.464585," ","integrate((B*x+A)/(c*x^2+b*x)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c^{3} e x^{7} + b^{3} d x^{3} + {\left(c^{3} d + 3 \, b c^{2} e\right)} x^{6} + 3 \, {\left(b c^{2} d + b^{2} c e\right)} x^{5} + {\left(3 \, b^{2} c d + b^{3} e\right)} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c^3*e*x^7 + b^3*d*x^3 + (c^3*d + 3*b*c^2*e)*x^6 + 3*(b*c^2*d + b^2*c*e)*x^5 + (3*b^2*c*d + b^3*e)*x^4), x)","F",0
1283,0,0,0,0.506577," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(B x + A\right)} \sqrt{e x + d}}{c^{3} e^{2} x^{8} + b^{3} d^{2} x^{3} + {\left(2 \, c^{3} d e + 3 \, b c^{2} e^{2}\right)} x^{7} + {\left(c^{3} d^{2} + 6 \, b c^{2} d e + 3 \, b^{2} c e^{2}\right)} x^{6} + {\left(3 \, b c^{2} d^{2} + 6 \, b^{2} c d e + b^{3} e^{2}\right)} x^{5} + {\left(3 \, b^{2} c d^{2} + 2 \, b^{3} d e\right)} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(B*x + A)*sqrt(e*x + d)/(c^3*e^2*x^8 + b^3*d^2*x^3 + (2*c^3*d*e + 3*b*c^2*e^2)*x^7 + (c^3*d^2 + 6*b*c^2*d*e + 3*b^2*c*e^2)*x^6 + (3*b*c^2*d^2 + 6*b^2*c*d*e + b^3*e^2)*x^5 + (3*b^2*c*d^2 + 2*b^3*d*e)*x^4), x)","F",0
1284,1,268,0,0.386605," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{5} c B + \frac{5}{8} x^{8} e^{4} d c B + \frac{1}{8} x^{8} e^{5} c A + \frac{10}{7} x^{7} e^{3} d^{2} c B + \frac{1}{7} x^{7} e^{5} a B + \frac{5}{7} x^{7} e^{4} d c A + \frac{5}{3} x^{6} e^{2} d^{3} c B + \frac{5}{6} x^{6} e^{4} d a B + \frac{5}{3} x^{6} e^{3} d^{2} c A + \frac{1}{6} x^{6} e^{5} a A + x^{5} e d^{4} c B + 2 x^{5} e^{3} d^{2} a B + 2 x^{5} e^{2} d^{3} c A + x^{5} e^{4} d a A + \frac{1}{4} x^{4} d^{5} c B + \frac{5}{2} x^{4} e^{2} d^{3} a B + \frac{5}{4} x^{4} e d^{4} c A + \frac{5}{2} x^{4} e^{3} d^{2} a A + \frac{5}{3} x^{3} e d^{4} a B + \frac{1}{3} x^{3} d^{5} c A + \frac{10}{3} x^{3} e^{2} d^{3} a A + \frac{1}{2} x^{2} d^{5} a B + \frac{5}{2} x^{2} e d^{4} a A + x d^{5} a A"," ",0,"1/9*x^9*e^5*c*B + 5/8*x^8*e^4*d*c*B + 1/8*x^8*e^5*c*A + 10/7*x^7*e^3*d^2*c*B + 1/7*x^7*e^5*a*B + 5/7*x^7*e^4*d*c*A + 5/3*x^6*e^2*d^3*c*B + 5/6*x^6*e^4*d*a*B + 5/3*x^6*e^3*d^2*c*A + 1/6*x^6*e^5*a*A + x^5*e*d^4*c*B + 2*x^5*e^3*d^2*a*B + 2*x^5*e^2*d^3*c*A + x^5*e^4*d*a*A + 1/4*x^4*d^5*c*B + 5/2*x^4*e^2*d^3*a*B + 5/4*x^4*e*d^4*c*A + 5/2*x^4*e^3*d^2*a*A + 5/3*x^3*e*d^4*a*B + 1/3*x^3*d^5*c*A + 10/3*x^3*e^2*d^3*a*A + 1/2*x^2*d^5*a*B + 5/2*x^2*e*d^4*a*A + x*d^5*a*A","B",0
1285,1,215,0,0.363860," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{4} c B + \frac{4}{7} x^{7} e^{3} d c B + \frac{1}{7} x^{7} e^{4} c A + x^{6} e^{2} d^{2} c B + \frac{1}{6} x^{6} e^{4} a B + \frac{2}{3} x^{6} e^{3} d c A + \frac{4}{5} x^{5} e d^{3} c B + \frac{4}{5} x^{5} e^{3} d a B + \frac{6}{5} x^{5} e^{2} d^{2} c A + \frac{1}{5} x^{5} e^{4} a A + \frac{1}{4} x^{4} d^{4} c B + \frac{3}{2} x^{4} e^{2} d^{2} a B + x^{4} e d^{3} c A + x^{4} e^{3} d a A + \frac{4}{3} x^{3} e d^{3} a B + \frac{1}{3} x^{3} d^{4} c A + 2 x^{3} e^{2} d^{2} a A + \frac{1}{2} x^{2} d^{4} a B + 2 x^{2} e d^{3} a A + x d^{4} a A"," ",0,"1/8*x^8*e^4*c*B + 4/7*x^7*e^3*d*c*B + 1/7*x^7*e^4*c*A + x^6*e^2*d^2*c*B + 1/6*x^6*e^4*a*B + 2/3*x^6*e^3*d*c*A + 4/5*x^5*e*d^3*c*B + 4/5*x^5*e^3*d*a*B + 6/5*x^5*e^2*d^2*c*A + 1/5*x^5*e^4*a*A + 1/4*x^4*d^4*c*B + 3/2*x^4*e^2*d^2*a*B + x^4*e*d^3*c*A + x^4*e^3*d*a*A + 4/3*x^3*e*d^3*a*B + 1/3*x^3*d^4*c*A + 2*x^3*e^2*d^2*a*A + 1/2*x^2*d^4*a*B + 2*x^2*e*d^3*a*A + x*d^4*a*A","B",0
1286,1,164,0,0.354489," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{3} c B + \frac{1}{2} x^{6} e^{2} d c B + \frac{1}{6} x^{6} e^{3} c A + \frac{3}{5} x^{5} e d^{2} c B + \frac{1}{5} x^{5} e^{3} a B + \frac{3}{5} x^{5} e^{2} d c A + \frac{1}{4} x^{4} d^{3} c B + \frac{3}{4} x^{4} e^{2} d a B + \frac{3}{4} x^{4} e d^{2} c A + \frac{1}{4} x^{4} e^{3} a A + x^{3} e d^{2} a B + \frac{1}{3} x^{3} d^{3} c A + x^{3} e^{2} d a A + \frac{1}{2} x^{2} d^{3} a B + \frac{3}{2} x^{2} e d^{2} a A + x d^{3} a A"," ",0,"1/7*x^7*e^3*c*B + 1/2*x^6*e^2*d*c*B + 1/6*x^6*e^3*c*A + 3/5*x^5*e*d^2*c*B + 1/5*x^5*e^3*a*B + 3/5*x^5*e^2*d*c*A + 1/4*x^4*d^3*c*B + 3/4*x^4*e^2*d*a*B + 3/4*x^4*e*d^2*c*A + 1/4*x^4*e^3*a*A + x^3*e*d^2*a*B + 1/3*x^3*d^3*c*A + x^3*e^2*d*a*A + 1/2*x^2*d^3*a*B + 3/2*x^2*e*d^2*a*A + x*d^3*a*A","A",0
1287,1,113,0,0.509146," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{2} c B + \frac{2}{5} x^{5} e d c B + \frac{1}{5} x^{5} e^{2} c A + \frac{1}{4} x^{4} d^{2} c B + \frac{1}{4} x^{4} e^{2} a B + \frac{1}{2} x^{4} e d c A + \frac{2}{3} x^{3} e d a B + \frac{1}{3} x^{3} d^{2} c A + \frac{1}{3} x^{3} e^{2} a A + \frac{1}{2} x^{2} d^{2} a B + x^{2} e d a A + x d^{2} a A"," ",0,"1/6*x^6*e^2*c*B + 2/5*x^5*e*d*c*B + 1/5*x^5*e^2*c*A + 1/4*x^4*d^2*c*B + 1/4*x^4*e^2*a*B + 1/2*x^4*e*d*c*A + 2/3*x^3*e*d*a*B + 1/3*x^3*d^2*c*A + 1/3*x^3*e^2*a*A + 1/2*x^2*d^2*a*B + x^2*e*d*a*A + x*d^2*a*A","A",0
1288,1,62,0,0.390645," ","integrate((B*x+A)*(e*x+d)*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e c B + \frac{1}{4} x^{4} d c B + \frac{1}{4} x^{4} e c A + \frac{1}{3} x^{3} e a B + \frac{1}{3} x^{3} d c A + \frac{1}{2} x^{2} d a B + \frac{1}{2} x^{2} e a A + x d a A"," ",0,"1/5*x^5*e*c*B + 1/4*x^4*d*c*B + 1/4*x^4*e*c*A + 1/3*x^3*e*a*B + 1/3*x^3*d*c*A + 1/2*x^2*d*a*B + 1/2*x^2*e*a*A + x*d*a*A","A",0
1289,1,26,0,0.371632," ","integrate((B*x+A)*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} a B + x a A"," ",0,"1/4*x^4*c*B + 1/3*x^3*c*A + 1/2*x^2*a*B + x*a*A","A",0
1290,1,98,0,0.405948," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d),x, algorithm=""fricas"")","\frac{2 \, B c e^{3} x^{3} - 3 \, {\left(B c d e^{2} - A c e^{3}\right)} x^{2} + 6 \, {\left(B c d^{2} e - A c d e^{2} + B a e^{3}\right)} x - 6 \, {\left(B c d^{3} - A c d^{2} e + B a d e^{2} - A a e^{3}\right)} \log\left(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(2*B*c*e^3*x^3 - 3*(B*c*d*e^2 - A*c*e^3)*x^2 + 6*(B*c*d^2*e - A*c*d*e^2 + B*a*e^3)*x - 6*(B*c*d^3 - A*c*d^2*e + B*a*d*e^2 - A*a*e^3)*log(e*x + d))/e^4","A",0
1291,1,152,0,0.423855," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{B c e^{3} x^{3} + 2 \, B c d^{3} - 2 \, A c d^{2} e + 2 \, B a d e^{2} - 2 \, A a e^{3} - {\left(3 \, B c d e^{2} - 2 \, A c e^{3}\right)} x^{2} - 2 \, {\left(2 \, B c d^{2} e - A c d e^{2}\right)} x + 2 \, {\left(3 \, B c d^{3} - 2 \, A c d^{2} e + B a d e^{2} + {\left(3 \, B c d^{2} e - 2 \, A c d e^{2} + B a e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(B*c*e^3*x^3 + 2*B*c*d^3 - 2*A*c*d^2*e + 2*B*a*d*e^2 - 2*A*a*e^3 - (3*B*c*d*e^2 - 2*A*c*e^3)*x^2 - 2*(2*B*c*d^2*e - A*c*d*e^2)*x + 2*(3*B*c*d^3 - 2*A*c*d^2*e + B*a*d*e^2 + (3*B*c*d^2*e - 2*A*c*d*e^2 + B*a*e^3)*x)*log(e*x + d))/(e^5*x + d*e^4)","A",0
1292,1,168,0,0.410611," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, B c e^{3} x^{3} + 4 \, B c d e^{2} x^{2} - 5 \, B c d^{3} + 3 \, A c d^{2} e - B a d e^{2} - A a e^{3} - 2 \, {\left(2 \, B c d^{2} e - 2 \, A c d e^{2} + B a e^{3}\right)} x - 2 \, {\left(3 \, B c d^{3} - A c d^{2} e + {\left(3 \, B c d e^{2} - A c e^{3}\right)} x^{2} + 2 \, {\left(3 \, B c d^{2} e - A c d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(2*B*c*e^3*x^3 + 4*B*c*d*e^2*x^2 - 5*B*c*d^3 + 3*A*c*d^2*e - B*a*d*e^2 - A*a*e^3 - 2*(2*B*c*d^2*e - 2*A*c*d*e^2 + B*a*e^3)*x - 2*(3*B*c*d^3 - A*c*d^2*e + (3*B*c*d*e^2 - A*c*e^3)*x^2 + 2*(3*B*c*d^2*e - A*c*d*e^2)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1293,1,160,0,0.407010," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{11 \, B c d^{3} - 2 \, A c d^{2} e - B a d e^{2} - 2 \, A a e^{3} + 6 \, {\left(3 \, B c d e^{2} - A c e^{3}\right)} x^{2} + 3 \, {\left(9 \, B c d^{2} e - 2 \, A c d e^{2} - B a e^{3}\right)} x + 6 \, {\left(B c e^{3} x^{3} + 3 \, B c d e^{2} x^{2} + 3 \, B c d^{2} e x + B c d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(11*B*c*d^3 - 2*A*c*d^2*e - B*a*d*e^2 - 2*A*a*e^3 + 6*(3*B*c*d*e^2 - A*c*e^3)*x^2 + 3*(9*B*c*d^2*e - 2*A*c*d*e^2 - B*a*e^3)*x + 6*(B*c*e^3*x^3 + 3*B*c*d*e^2*x^2 + 3*B*c*d^2*e*x + B*c*d^3)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1294,1,132,0,0.401947," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{12 \, B c e^{3} x^{3} + 3 \, B c d^{3} + A c d^{2} e + B a d e^{2} + 3 \, A a e^{3} + 6 \, {\left(3 \, B c d e^{2} + A c e^{3}\right)} x^{2} + 4 \, {\left(3 \, B c d^{2} e + A c d e^{2} + B a e^{3}\right)} x}{12 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-1/12*(12*B*c*e^3*x^3 + 3*B*c*d^3 + A*c*d^2*e + B*a*d*e^2 + 3*A*a*e^3 + 6*(3*B*c*d*e^2 + A*c*e^3)*x^2 + 4*(3*B*c*d^2*e + A*c*d*e^2 + B*a*e^3)*x)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","A",0
1295,1,148,0,0.405944," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{30 \, B c e^{3} x^{3} + 3 \, B c d^{3} + 2 \, A c d^{2} e + 3 \, B a d e^{2} + 12 \, A a e^{3} + 10 \, {\left(3 \, B c d e^{2} + 2 \, A c e^{3}\right)} x^{2} + 5 \, {\left(3 \, B c d^{2} e + 2 \, A c d e^{2} + 3 \, B a e^{3}\right)} x}{60 \, {\left(e^{9} x^{5} + 5 \, d e^{8} x^{4} + 10 \, d^{2} e^{7} x^{3} + 10 \, d^{3} e^{6} x^{2} + 5 \, d^{4} e^{5} x + d^{5} e^{4}\right)}}"," ",0,"-1/60*(30*B*c*e^3*x^3 + 3*B*c*d^3 + 2*A*c*d^2*e + 3*B*a*d*e^2 + 12*A*a*e^3 + 10*(3*B*c*d*e^2 + 2*A*c*e^3)*x^2 + 5*(3*B*c*d^2*e + 2*A*c*d*e^2 + 3*B*a*e^3)*x)/(e^9*x^5 + 5*d*e^8*x^4 + 10*d^2*e^7*x^3 + 10*d^3*e^6*x^2 + 5*d^4*e^5*x + d^5*e^4)","A",0
1296,1,153,0,0.399634," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{20 \, B c e^{3} x^{3} + B c d^{3} + A c d^{2} e + 2 \, B a d e^{2} + 10 \, A a e^{3} + 15 \, {\left(B c d e^{2} + A c e^{3}\right)} x^{2} + 6 \, {\left(B c d^{2} e + A c d e^{2} + 2 \, B a e^{3}\right)} x}{60 \, {\left(e^{10} x^{6} + 6 \, d e^{9} x^{5} + 15 \, d^{2} e^{8} x^{4} + 20 \, d^{3} e^{7} x^{3} + 15 \, d^{4} e^{6} x^{2} + 6 \, d^{5} e^{5} x + d^{6} e^{4}\right)}}"," ",0,"-1/60*(20*B*c*e^3*x^3 + B*c*d^3 + A*c*d^2*e + 2*B*a*d*e^2 + 10*A*a*e^3 + 15*(B*c*d*e^2 + A*c*e^3)*x^2 + 6*(B*c*d^2*e + A*c*d*e^2 + 2*B*a*e^3)*x)/(e^10*x^6 + 6*d*e^9*x^5 + 15*d^2*e^8*x^4 + 20*d^3*e^7*x^3 + 15*d^4*e^6*x^2 + 6*d^5*e^5*x + d^6*e^4)","A",0
1297,1,465,0,0.364953," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{5} c^{2} B + \frac{1}{2} x^{10} e^{4} d c^{2} B + \frac{1}{10} x^{10} e^{5} c^{2} A + \frac{10}{9} x^{9} e^{3} d^{2} c^{2} B + \frac{2}{9} x^{9} e^{5} c a B + \frac{5}{9} x^{9} e^{4} d c^{2} A + \frac{5}{4} x^{8} e^{2} d^{3} c^{2} B + \frac{5}{4} x^{8} e^{4} d c a B + \frac{5}{4} x^{8} e^{3} d^{2} c^{2} A + \frac{1}{4} x^{8} e^{5} c a A + \frac{5}{7} x^{7} e d^{4} c^{2} B + \frac{20}{7} x^{7} e^{3} d^{2} c a B + \frac{1}{7} x^{7} e^{5} a^{2} B + \frac{10}{7} x^{7} e^{2} d^{3} c^{2} A + \frac{10}{7} x^{7} e^{4} d c a A + \frac{1}{6} x^{6} d^{5} c^{2} B + \frac{10}{3} x^{6} e^{2} d^{3} c a B + \frac{5}{6} x^{6} e^{4} d a^{2} B + \frac{5}{6} x^{6} e d^{4} c^{2} A + \frac{10}{3} x^{6} e^{3} d^{2} c a A + \frac{1}{6} x^{6} e^{5} a^{2} A + 2 x^{5} e d^{4} c a B + 2 x^{5} e^{3} d^{2} a^{2} B + \frac{1}{5} x^{5} d^{5} c^{2} A + 4 x^{5} e^{2} d^{3} c a A + x^{5} e^{4} d a^{2} A + \frac{1}{2} x^{4} d^{5} c a B + \frac{5}{2} x^{4} e^{2} d^{3} a^{2} B + \frac{5}{2} x^{4} e d^{4} c a A + \frac{5}{2} x^{4} e^{3} d^{2} a^{2} A + \frac{5}{3} x^{3} e d^{4} a^{2} B + \frac{2}{3} x^{3} d^{5} c a A + \frac{10}{3} x^{3} e^{2} d^{3} a^{2} A + \frac{1}{2} x^{2} d^{5} a^{2} B + \frac{5}{2} x^{2} e d^{4} a^{2} A + x d^{5} a^{2} A"," ",0,"1/11*x^11*e^5*c^2*B + 1/2*x^10*e^4*d*c^2*B + 1/10*x^10*e^5*c^2*A + 10/9*x^9*e^3*d^2*c^2*B + 2/9*x^9*e^5*c*a*B + 5/9*x^9*e^4*d*c^2*A + 5/4*x^8*e^2*d^3*c^2*B + 5/4*x^8*e^4*d*c*a*B + 5/4*x^8*e^3*d^2*c^2*A + 1/4*x^8*e^5*c*a*A + 5/7*x^7*e*d^4*c^2*B + 20/7*x^7*e^3*d^2*c*a*B + 1/7*x^7*e^5*a^2*B + 10/7*x^7*e^2*d^3*c^2*A + 10/7*x^7*e^4*d*c*a*A + 1/6*x^6*d^5*c^2*B + 10/3*x^6*e^2*d^3*c*a*B + 5/6*x^6*e^4*d*a^2*B + 5/6*x^6*e*d^4*c^2*A + 10/3*x^6*e^3*d^2*c*a*A + 1/6*x^6*e^5*a^2*A + 2*x^5*e*d^4*c*a*B + 2*x^5*e^3*d^2*a^2*B + 1/5*x^5*d^5*c^2*A + 4*x^5*e^2*d^3*c*a*A + x^5*e^4*d*a^2*A + 1/2*x^4*d^5*c*a*B + 5/2*x^4*e^2*d^3*a^2*B + 5/2*x^4*e*d^4*c*a*A + 5/2*x^4*e^3*d^2*a^2*A + 5/3*x^3*e*d^4*a^2*B + 2/3*x^3*d^5*c*a*A + 10/3*x^3*e^2*d^3*a^2*A + 1/2*x^2*d^5*a^2*B + 5/2*x^2*e*d^4*a^2*A + x*d^5*a^2*A","B",0
1298,1,377,0,0.355274," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{4} c^{2} B + \frac{4}{9} x^{9} e^{3} d c^{2} B + \frac{1}{9} x^{9} e^{4} c^{2} A + \frac{3}{4} x^{8} e^{2} d^{2} c^{2} B + \frac{1}{4} x^{8} e^{4} c a B + \frac{1}{2} x^{8} e^{3} d c^{2} A + \frac{4}{7} x^{7} e d^{3} c^{2} B + \frac{8}{7} x^{7} e^{3} d c a B + \frac{6}{7} x^{7} e^{2} d^{2} c^{2} A + \frac{2}{7} x^{7} e^{4} c a A + \frac{1}{6} x^{6} d^{4} c^{2} B + 2 x^{6} e^{2} d^{2} c a B + \frac{1}{6} x^{6} e^{4} a^{2} B + \frac{2}{3} x^{6} e d^{3} c^{2} A + \frac{4}{3} x^{6} e^{3} d c a A + \frac{8}{5} x^{5} e d^{3} c a B + \frac{4}{5} x^{5} e^{3} d a^{2} B + \frac{1}{5} x^{5} d^{4} c^{2} A + \frac{12}{5} x^{5} e^{2} d^{2} c a A + \frac{1}{5} x^{5} e^{4} a^{2} A + \frac{1}{2} x^{4} d^{4} c a B + \frac{3}{2} x^{4} e^{2} d^{2} a^{2} B + 2 x^{4} e d^{3} c a A + x^{4} e^{3} d a^{2} A + \frac{4}{3} x^{3} e d^{3} a^{2} B + \frac{2}{3} x^{3} d^{4} c a A + 2 x^{3} e^{2} d^{2} a^{2} A + \frac{1}{2} x^{2} d^{4} a^{2} B + 2 x^{2} e d^{3} a^{2} A + x d^{4} a^{2} A"," ",0,"1/10*x^10*e^4*c^2*B + 4/9*x^9*e^3*d*c^2*B + 1/9*x^9*e^4*c^2*A + 3/4*x^8*e^2*d^2*c^2*B + 1/4*x^8*e^4*c*a*B + 1/2*x^8*e^3*d*c^2*A + 4/7*x^7*e*d^3*c^2*B + 8/7*x^7*e^3*d*c*a*B + 6/7*x^7*e^2*d^2*c^2*A + 2/7*x^7*e^4*c*a*A + 1/6*x^6*d^4*c^2*B + 2*x^6*e^2*d^2*c*a*B + 1/6*x^6*e^4*a^2*B + 2/3*x^6*e*d^3*c^2*A + 4/3*x^6*e^3*d*c*a*A + 8/5*x^5*e*d^3*c*a*B + 4/5*x^5*e^3*d*a^2*B + 1/5*x^5*d^4*c^2*A + 12/5*x^5*e^2*d^2*c*a*A + 1/5*x^5*e^4*a^2*A + 1/2*x^4*d^4*c*a*B + 3/2*x^4*e^2*d^2*a^2*B + 2*x^4*e*d^3*c*a*A + x^4*e^3*d*a^2*A + 4/3*x^3*e*d^3*a^2*B + 2/3*x^3*d^4*c*a*A + 2*x^3*e^2*d^2*a^2*A + 1/2*x^2*d^4*a^2*B + 2*x^2*e*d^3*a^2*A + x*d^4*a^2*A","A",0
1299,1,287,0,0.363264," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{3} c^{2} B + \frac{3}{8} x^{8} e^{2} d c^{2} B + \frac{1}{8} x^{8} e^{3} c^{2} A + \frac{3}{7} x^{7} e d^{2} c^{2} B + \frac{2}{7} x^{7} e^{3} c a B + \frac{3}{7} x^{7} e^{2} d c^{2} A + \frac{1}{6} x^{6} d^{3} c^{2} B + x^{6} e^{2} d c a B + \frac{1}{2} x^{6} e d^{2} c^{2} A + \frac{1}{3} x^{6} e^{3} c a A + \frac{6}{5} x^{5} e d^{2} c a B + \frac{1}{5} x^{5} e^{3} a^{2} B + \frac{1}{5} x^{5} d^{3} c^{2} A + \frac{6}{5} x^{5} e^{2} d c a A + \frac{1}{2} x^{4} d^{3} c a B + \frac{3}{4} x^{4} e^{2} d a^{2} B + \frac{3}{2} x^{4} e d^{2} c a A + \frac{1}{4} x^{4} e^{3} a^{2} A + x^{3} e d^{2} a^{2} B + \frac{2}{3} x^{3} d^{3} c a A + x^{3} e^{2} d a^{2} A + \frac{1}{2} x^{2} d^{3} a^{2} B + \frac{3}{2} x^{2} e d^{2} a^{2} A + x d^{3} a^{2} A"," ",0,"1/9*x^9*e^3*c^2*B + 3/8*x^8*e^2*d*c^2*B + 1/8*x^8*e^3*c^2*A + 3/7*x^7*e*d^2*c^2*B + 2/7*x^7*e^3*c*a*B + 3/7*x^7*e^2*d*c^2*A + 1/6*x^6*d^3*c^2*B + x^6*e^2*d*c*a*B + 1/2*x^6*e*d^2*c^2*A + 1/3*x^6*e^3*c*a*A + 6/5*x^5*e*d^2*c*a*B + 1/5*x^5*e^3*a^2*B + 1/5*x^5*d^3*c^2*A + 6/5*x^5*e^2*d*c*a*A + 1/2*x^4*d^3*c*a*B + 3/4*x^4*e^2*d*a^2*B + 3/2*x^4*e*d^2*c*a*A + 1/4*x^4*e^3*a^2*A + x^3*e*d^2*a^2*B + 2/3*x^3*d^3*c*a*A + x^3*e^2*d*a^2*A + 1/2*x^2*d^3*a^2*B + 3/2*x^2*e*d^2*a^2*A + x*d^3*a^2*A","A",0
1300,1,200,0,0.356553," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{2} c^{2} B + \frac{2}{7} x^{7} e d c^{2} B + \frac{1}{7} x^{7} e^{2} c^{2} A + \frac{1}{6} x^{6} d^{2} c^{2} B + \frac{1}{3} x^{6} e^{2} c a B + \frac{1}{3} x^{6} e d c^{2} A + \frac{4}{5} x^{5} e d c a B + \frac{1}{5} x^{5} d^{2} c^{2} A + \frac{2}{5} x^{5} e^{2} c a A + \frac{1}{2} x^{4} d^{2} c a B + \frac{1}{4} x^{4} e^{2} a^{2} B + x^{4} e d c a A + \frac{2}{3} x^{3} e d a^{2} B + \frac{2}{3} x^{3} d^{2} c a A + \frac{1}{3} x^{3} e^{2} a^{2} A + \frac{1}{2} x^{2} d^{2} a^{2} B + x^{2} e d a^{2} A + x d^{2} a^{2} A"," ",0,"1/8*x^8*e^2*c^2*B + 2/7*x^7*e*d*c^2*B + 1/7*x^7*e^2*c^2*A + 1/6*x^6*d^2*c^2*B + 1/3*x^6*e^2*c*a*B + 1/3*x^6*e*d*c^2*A + 4/5*x^5*e*d*c*a*B + 1/5*x^5*d^2*c^2*A + 2/5*x^5*e^2*c*a*A + 1/2*x^4*d^2*c*a*B + 1/4*x^4*e^2*a^2*B + x^4*e*d*c*a*A + 2/3*x^3*e*d*a^2*B + 2/3*x^3*d^2*c*a*A + 1/3*x^3*e^2*a^2*A + 1/2*x^2*d^2*a^2*B + x^2*e*d*a^2*A + x*d^2*a^2*A","A",0
1301,1,114,0,0.353773," ","integrate((B*x+A)*(e*x+d)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e c^{2} B + \frac{1}{6} x^{6} d c^{2} B + \frac{1}{6} x^{6} e c^{2} A + \frac{2}{5} x^{5} e c a B + \frac{1}{5} x^{5} d c^{2} A + \frac{1}{2} x^{4} d c a B + \frac{1}{2} x^{4} e c a A + \frac{1}{3} x^{3} e a^{2} B + \frac{2}{3} x^{3} d c a A + \frac{1}{2} x^{2} d a^{2} B + \frac{1}{2} x^{2} e a^{2} A + x d a^{2} A"," ",0,"1/7*x^7*e*c^2*B + 1/6*x^6*d*c^2*B + 1/6*x^6*e*c^2*A + 2/5*x^5*e*c*a*B + 1/5*x^5*d*c^2*A + 1/2*x^4*d*c*a*B + 1/2*x^4*e*c*a*A + 1/3*x^3*e*a^2*B + 2/3*x^3*d*c*a*A + 1/2*x^2*d*a^2*B + 1/2*x^2*e*a^2*A + x*d*a^2*A","A",0
1302,1,50,0,0.349930," ","integrate((B*x+A)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} c^{2} B + \frac{1}{5} x^{5} c^{2} A + \frac{1}{2} x^{4} c a B + \frac{2}{3} x^{3} c a A + \frac{1}{2} x^{2} a^{2} B + x a^{2} A"," ",0,"1/6*x^6*c^2*B + 1/5*x^5*c^2*A + 1/2*x^4*c*a*B + 2/3*x^3*c*a*A + 1/2*x^2*a^2*B + x*a^2*A","A",0
1303,1,243,0,0.394646," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d),x, algorithm=""fricas"")","\frac{12 \, B c^{2} e^{5} x^{5} - 15 \, {\left(B c^{2} d e^{4} - A c^{2} e^{5}\right)} x^{4} + 20 \, {\left(B c^{2} d^{2} e^{3} - A c^{2} d e^{4} + 2 \, B a c e^{5}\right)} x^{3} - 30 \, {\left(B c^{2} d^{3} e^{2} - A c^{2} d^{2} e^{3} + 2 \, B a c d e^{4} - 2 \, A a c e^{5}\right)} x^{2} + 60 \, {\left(B c^{2} d^{4} e - A c^{2} d^{3} e^{2} + 2 \, B a c d^{2} e^{3} - 2 \, A a c d e^{4} + B a^{2} e^{5}\right)} x - 60 \, {\left(B c^{2} d^{5} - A c^{2} d^{4} e + 2 \, B a c d^{3} e^{2} - 2 \, A a c d^{2} e^{3} + B a^{2} d e^{4} - A a^{2} e^{5}\right)} \log\left(e x + d\right)}{60 \, e^{6}}"," ",0,"1/60*(12*B*c^2*e^5*x^5 - 15*(B*c^2*d*e^4 - A*c^2*e^5)*x^4 + 20*(B*c^2*d^2*e^3 - A*c^2*d*e^4 + 2*B*a*c*e^5)*x^3 - 30*(B*c^2*d^3*e^2 - A*c^2*d^2*e^3 + 2*B*a*c*d*e^4 - 2*A*a*c*e^5)*x^2 + 60*(B*c^2*d^4*e - A*c^2*d^3*e^2 + 2*B*a*c*d^2*e^3 - 2*A*a*c*d*e^4 + B*a^2*e^5)*x - 60*(B*c^2*d^5 - A*c^2*d^4*e + 2*B*a*c*d^3*e^2 - 2*A*a*c*d^2*e^3 + B*a^2*d*e^4 - A*a^2*e^5)*log(e*x + d))/e^6","A",0
1304,1,354,0,0.406842," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{3 \, B c^{2} e^{5} x^{5} + 12 \, B c^{2} d^{5} - 12 \, A c^{2} d^{4} e + 24 \, B a c d^{3} e^{2} - 24 \, A a c d^{2} e^{3} + 12 \, B a^{2} d e^{4} - 12 \, A a^{2} e^{5} - {\left(5 \, B c^{2} d e^{4} - 4 \, A c^{2} e^{5}\right)} x^{4} + 2 \, {\left(5 \, B c^{2} d^{2} e^{3} - 4 \, A c^{2} d e^{4} + 6 \, B a c e^{5}\right)} x^{3} - 6 \, {\left(5 \, B c^{2} d^{3} e^{2} - 4 \, A c^{2} d^{2} e^{3} + 6 \, B a c d e^{4} - 4 \, A a c e^{5}\right)} x^{2} - 12 \, {\left(4 \, B c^{2} d^{4} e - 3 \, A c^{2} d^{3} e^{2} + 4 \, B a c d^{2} e^{3} - 2 \, A a c d e^{4}\right)} x + 12 \, {\left(5 \, B c^{2} d^{5} - 4 \, A c^{2} d^{4} e + 6 \, B a c d^{3} e^{2} - 4 \, A a c d^{2} e^{3} + B a^{2} d e^{4} + {\left(5 \, B c^{2} d^{4} e - 4 \, A c^{2} d^{3} e^{2} + 6 \, B a c d^{2} e^{3} - 4 \, A a c d e^{4} + B a^{2} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"1/12*(3*B*c^2*e^5*x^5 + 12*B*c^2*d^5 - 12*A*c^2*d^4*e + 24*B*a*c*d^3*e^2 - 24*A*a*c*d^2*e^3 + 12*B*a^2*d*e^4 - 12*A*a^2*e^5 - (5*B*c^2*d*e^4 - 4*A*c^2*e^5)*x^4 + 2*(5*B*c^2*d^2*e^3 - 4*A*c^2*d*e^4 + 6*B*a*c*e^5)*x^3 - 6*(5*B*c^2*d^3*e^2 - 4*A*c^2*d^2*e^3 + 6*B*a*c*d*e^4 - 4*A*a*c*e^5)*x^2 - 12*(4*B*c^2*d^4*e - 3*A*c^2*d^3*e^2 + 4*B*a*c*d^2*e^3 - 2*A*a*c*d*e^4)*x + 12*(5*B*c^2*d^5 - 4*A*c^2*d^4*e + 6*B*a*c*d^3*e^2 - 4*A*a*c*d^2*e^3 + B*a^2*d*e^4 + (5*B*c^2*d^4*e - 4*A*c^2*d^3*e^2 + 6*B*a*c*d^2*e^3 - 4*A*a*c*d*e^4 + B*a^2*e^5)*x)*log(e*x + d))/(e^7*x + d*e^6)","B",0
1305,1,394,0,0.396789," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, B c^{2} e^{5} x^{5} - 27 \, B c^{2} d^{5} + 21 \, A c^{2} d^{4} e - 30 \, B a c d^{3} e^{2} + 18 \, A a c d^{2} e^{3} - 3 \, B a^{2} d e^{4} - 3 \, A a^{2} e^{5} - {\left(5 \, B c^{2} d e^{4} - 3 \, A c^{2} e^{5}\right)} x^{4} + 4 \, {\left(5 \, B c^{2} d^{2} e^{3} - 3 \, A c^{2} d e^{4} + 3 \, B a c e^{5}\right)} x^{3} + 3 \, {\left(21 \, B c^{2} d^{3} e^{2} - 11 \, A c^{2} d^{2} e^{3} + 8 \, B a c d e^{4}\right)} x^{2} + 6 \, {\left(B c^{2} d^{4} e + A c^{2} d^{3} e^{2} - 4 \, B a c d^{2} e^{3} + 4 \, A a c d e^{4} - B a^{2} e^{5}\right)} x - 12 \, {\left(5 \, B c^{2} d^{5} - 3 \, A c^{2} d^{4} e + 3 \, B a c d^{3} e^{2} - A a c d^{2} e^{3} + {\left(5 \, B c^{2} d^{3} e^{2} - 3 \, A c^{2} d^{2} e^{3} + 3 \, B a c d e^{4} - A a c e^{5}\right)} x^{2} + 2 \, {\left(5 \, B c^{2} d^{4} e - 3 \, A c^{2} d^{3} e^{2} + 3 \, B a c d^{2} e^{3} - A a c d e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"1/6*(2*B*c^2*e^5*x^5 - 27*B*c^2*d^5 + 21*A*c^2*d^4*e - 30*B*a*c*d^3*e^2 + 18*A*a*c*d^2*e^3 - 3*B*a^2*d*e^4 - 3*A*a^2*e^5 - (5*B*c^2*d*e^4 - 3*A*c^2*e^5)*x^4 + 4*(5*B*c^2*d^2*e^3 - 3*A*c^2*d*e^4 + 3*B*a*c*e^5)*x^3 + 3*(21*B*c^2*d^3*e^2 - 11*A*c^2*d^2*e^3 + 8*B*a*c*d*e^4)*x^2 + 6*(B*c^2*d^4*e + A*c^2*d^3*e^2 - 4*B*a*c*d^2*e^3 + 4*A*a*c*d*e^4 - B*a^2*e^5)*x - 12*(5*B*c^2*d^5 - 3*A*c^2*d^4*e + 3*B*a*c*d^3*e^2 - A*a*c*d^2*e^3 + (5*B*c^2*d^3*e^2 - 3*A*c^2*d^2*e^3 + 3*B*a*c*d*e^4 - A*a*c*e^5)*x^2 + 2*(5*B*c^2*d^4*e - 3*A*c^2*d^3*e^2 + 3*B*a*c*d^2*e^3 - A*a*c*d*e^4)*x)*log(e*x + d))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","B",0
1306,1,411,0,0.406940," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, B c^{2} e^{5} x^{5} + 47 \, B c^{2} d^{5} - 26 \, A c^{2} d^{4} e + 22 \, B a c d^{3} e^{2} - 4 \, A a c d^{2} e^{3} - B a^{2} d e^{4} - 2 \, A a^{2} e^{5} - 3 \, {\left(5 \, B c^{2} d e^{4} - 2 \, A c^{2} e^{5}\right)} x^{4} - 9 \, {\left(7 \, B c^{2} d^{2} e^{3} - 2 \, A c^{2} d e^{4}\right)} x^{3} - 3 \, {\left(3 \, B c^{2} d^{3} e^{2} + 6 \, A c^{2} d^{2} e^{3} - 12 \, B a c d e^{4} + 4 \, A a c e^{5}\right)} x^{2} + 3 \, {\left(27 \, B c^{2} d^{4} e - 18 \, A c^{2} d^{3} e^{2} + 18 \, B a c d^{2} e^{3} - 4 \, A a c d e^{4} - B a^{2} e^{5}\right)} x + 12 \, {\left(5 \, B c^{2} d^{5} - 2 \, A c^{2} d^{4} e + B a c d^{3} e^{2} + {\left(5 \, B c^{2} d^{2} e^{3} - 2 \, A c^{2} d e^{4} + B a c e^{5}\right)} x^{3} + 3 \, {\left(5 \, B c^{2} d^{3} e^{2} - 2 \, A c^{2} d^{2} e^{3} + B a c d e^{4}\right)} x^{2} + 3 \, {\left(5 \, B c^{2} d^{4} e - 2 \, A c^{2} d^{3} e^{2} + B a c d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"1/6*(3*B*c^2*e^5*x^5 + 47*B*c^2*d^5 - 26*A*c^2*d^4*e + 22*B*a*c*d^3*e^2 - 4*A*a*c*d^2*e^3 - B*a^2*d*e^4 - 2*A*a^2*e^5 - 3*(5*B*c^2*d*e^4 - 2*A*c^2*e^5)*x^4 - 9*(7*B*c^2*d^2*e^3 - 2*A*c^2*d*e^4)*x^3 - 3*(3*B*c^2*d^3*e^2 + 6*A*c^2*d^2*e^3 - 12*B*a*c*d*e^4 + 4*A*a*c*e^5)*x^2 + 3*(27*B*c^2*d^4*e - 18*A*c^2*d^3*e^2 + 18*B*a*c*d^2*e^3 - 4*A*a*c*d*e^4 - B*a^2*e^5)*x + 12*(5*B*c^2*d^5 - 2*A*c^2*d^4*e + B*a*c*d^3*e^2 + (5*B*c^2*d^2*e^3 - 2*A*c^2*d*e^4 + B*a*c*e^5)*x^3 + 3*(5*B*c^2*d^3*e^2 - 2*A*c^2*d^2*e^3 + B*a*c*d*e^4)*x^2 + 3*(5*B*c^2*d^4*e - 2*A*c^2*d^3*e^2 + B*a*c*d^2*e^3)*x)*log(e*x + d))/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","B",0
1307,1,405,0,0.394592," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{12 \, B c^{2} e^{5} x^{5} + 48 \, B c^{2} d e^{4} x^{4} - 77 \, B c^{2} d^{5} + 25 \, A c^{2} d^{4} e - 6 \, B a c d^{3} e^{2} - 2 \, A a c d^{2} e^{3} - B a^{2} d e^{4} - 3 \, A a^{2} e^{5} - 24 \, {\left(2 \, B c^{2} d^{2} e^{3} - 2 \, A c^{2} d e^{4} + B a c e^{5}\right)} x^{3} - 12 \, {\left(21 \, B c^{2} d^{3} e^{2} - 9 \, A c^{2} d^{2} e^{3} + 3 \, B a c d e^{4} + A a c e^{5}\right)} x^{2} - 4 \, {\left(62 \, B c^{2} d^{4} e - 22 \, A c^{2} d^{3} e^{2} + 6 \, B a c d^{2} e^{3} + 2 \, A a c d e^{4} + B a^{2} e^{5}\right)} x - 12 \, {\left(5 \, B c^{2} d^{5} - A c^{2} d^{4} e + {\left(5 \, B c^{2} d e^{4} - A c^{2} e^{5}\right)} x^{4} + 4 \, {\left(5 \, B c^{2} d^{2} e^{3} - A c^{2} d e^{4}\right)} x^{3} + 6 \, {\left(5 \, B c^{2} d^{3} e^{2} - A c^{2} d^{2} e^{3}\right)} x^{2} + 4 \, {\left(5 \, B c^{2} d^{4} e - A c^{2} d^{3} e^{2}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{10} x^{4} + 4 \, d e^{9} x^{3} + 6 \, d^{2} e^{8} x^{2} + 4 \, d^{3} e^{7} x + d^{4} e^{6}\right)}}"," ",0,"1/12*(12*B*c^2*e^5*x^5 + 48*B*c^2*d*e^4*x^4 - 77*B*c^2*d^5 + 25*A*c^2*d^4*e - 6*B*a*c*d^3*e^2 - 2*A*a*c*d^2*e^3 - B*a^2*d*e^4 - 3*A*a^2*e^5 - 24*(2*B*c^2*d^2*e^3 - 2*A*c^2*d*e^4 + B*a*c*e^5)*x^3 - 12*(21*B*c^2*d^3*e^2 - 9*A*c^2*d^2*e^3 + 3*B*a*c*d*e^4 + A*a*c*e^5)*x^2 - 4*(62*B*c^2*d^4*e - 22*A*c^2*d^3*e^2 + 6*B*a*c*d^2*e^3 + 2*A*a*c*d*e^4 + B*a^2*e^5)*x - 12*(5*B*c^2*d^5 - A*c^2*d^4*e + (5*B*c^2*d*e^4 - A*c^2*e^5)*x^4 + 4*(5*B*c^2*d^2*e^3 - A*c^2*d*e^4)*x^3 + 6*(5*B*c^2*d^3*e^2 - A*c^2*d^2*e^3)*x^2 + 4*(5*B*c^2*d^4*e - A*c^2*d^3*e^2)*x)*log(e*x + d))/(e^10*x^4 + 4*d*e^9*x^3 + 6*d^2*e^8*x^2 + 4*d^3*e^7*x + d^4*e^6)","B",0
1308,1,365,0,0.400939," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^6,x, algorithm=""fricas"")","\frac{137 \, B c^{2} d^{5} - 12 \, A c^{2} d^{4} e - 6 \, B a c d^{3} e^{2} - 4 \, A a c d^{2} e^{3} - 3 \, B a^{2} d e^{4} - 12 \, A a^{2} e^{5} + 60 \, {\left(5 \, B c^{2} d e^{4} - A c^{2} e^{5}\right)} x^{4} + 60 \, {\left(15 \, B c^{2} d^{2} e^{3} - 2 \, A c^{2} d e^{4} - B a c e^{5}\right)} x^{3} + 20 \, {\left(55 \, B c^{2} d^{3} e^{2} - 6 \, A c^{2} d^{2} e^{3} - 3 \, B a c d e^{4} - 2 \, A a c e^{5}\right)} x^{2} + 5 \, {\left(125 \, B c^{2} d^{4} e - 12 \, A c^{2} d^{3} e^{2} - 6 \, B a c d^{2} e^{3} - 4 \, A a c d e^{4} - 3 \, B a^{2} e^{5}\right)} x + 60 \, {\left(B c^{2} e^{5} x^{5} + 5 \, B c^{2} d e^{4} x^{4} + 10 \, B c^{2} d^{2} e^{3} x^{3} + 10 \, B c^{2} d^{3} e^{2} x^{2} + 5 \, B c^{2} d^{4} e x + B c^{2} d^{5}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{11} x^{5} + 5 \, d e^{10} x^{4} + 10 \, d^{2} e^{9} x^{3} + 10 \, d^{3} e^{8} x^{2} + 5 \, d^{4} e^{7} x + d^{5} e^{6}\right)}}"," ",0,"1/60*(137*B*c^2*d^5 - 12*A*c^2*d^4*e - 6*B*a*c*d^3*e^2 - 4*A*a*c*d^2*e^3 - 3*B*a^2*d*e^4 - 12*A*a^2*e^5 + 60*(5*B*c^2*d*e^4 - A*c^2*e^5)*x^4 + 60*(15*B*c^2*d^2*e^3 - 2*A*c^2*d*e^4 - B*a*c*e^5)*x^3 + 20*(55*B*c^2*d^3*e^2 - 6*A*c^2*d^2*e^3 - 3*B*a*c*d*e^4 - 2*A*a*c*e^5)*x^2 + 5*(125*B*c^2*d^4*e - 12*A*c^2*d^3*e^2 - 6*B*a*c*d^2*e^3 - 4*A*a*c*d*e^4 - 3*B*a^2*e^5)*x + 60*(B*c^2*e^5*x^5 + 5*B*c^2*d*e^4*x^4 + 10*B*c^2*d^2*e^3*x^3 + 10*B*c^2*d^3*e^2*x^2 + 5*B*c^2*d^4*e*x + B*c^2*d^5)*log(e*x + d))/(e^11*x^5 + 5*d*e^10*x^4 + 10*d^2*e^9*x^3 + 10*d^3*e^8*x^2 + 5*d^4*e^7*x + d^5*e^6)","A",0
1309,1,292,0,0.396622," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{30 \, B c^{2} e^{5} x^{5} + 5 \, B c^{2} d^{5} + A c^{2} d^{4} e + B a c d^{3} e^{2} + A a c d^{2} e^{3} + B a^{2} d e^{4} + 5 \, A a^{2} e^{5} + 15 \, {\left(5 \, B c^{2} d e^{4} + A c^{2} e^{5}\right)} x^{4} + 20 \, {\left(5 \, B c^{2} d^{2} e^{3} + A c^{2} d e^{4} + B a c e^{5}\right)} x^{3} + 15 \, {\left(5 \, B c^{2} d^{3} e^{2} + A c^{2} d^{2} e^{3} + B a c d e^{4} + A a c e^{5}\right)} x^{2} + 6 \, {\left(5 \, B c^{2} d^{4} e + A c^{2} d^{3} e^{2} + B a c d^{2} e^{3} + A a c d e^{4} + B a^{2} e^{5}\right)} x}{30 \, {\left(e^{12} x^{6} + 6 \, d e^{11} x^{5} + 15 \, d^{2} e^{10} x^{4} + 20 \, d^{3} e^{9} x^{3} + 15 \, d^{4} e^{8} x^{2} + 6 \, d^{5} e^{7} x + d^{6} e^{6}\right)}}"," ",0,"-1/30*(30*B*c^2*e^5*x^5 + 5*B*c^2*d^5 + A*c^2*d^4*e + B*a*c*d^3*e^2 + A*a*c*d^2*e^3 + B*a^2*d*e^4 + 5*A*a^2*e^5 + 15*(5*B*c^2*d*e^4 + A*c^2*e^5)*x^4 + 20*(5*B*c^2*d^2*e^3 + A*c^2*d*e^4 + B*a*c*e^5)*x^3 + 15*(5*B*c^2*d^3*e^2 + A*c^2*d^2*e^3 + B*a*c*d*e^4 + A*a*c*e^5)*x^2 + 6*(5*B*c^2*d^4*e + A*c^2*d^3*e^2 + B*a*c*d^2*e^3 + A*a*c*d*e^4 + B*a^2*e^5)*x)/(e^12*x^6 + 6*d*e^11*x^5 + 15*d^2*e^10*x^4 + 20*d^3*e^9*x^3 + 15*d^4*e^8*x^2 + 6*d^5*e^7*x + d^6*e^6)","A",0
1310,1,317,0,0.403537," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{105 \, B c^{2} e^{5} x^{5} + 5 \, B c^{2} d^{5} + 2 \, A c^{2} d^{4} e + 3 \, B a c d^{3} e^{2} + 4 \, A a c d^{2} e^{3} + 5 \, B a^{2} d e^{4} + 30 \, A a^{2} e^{5} + 35 \, {\left(5 \, B c^{2} d e^{4} + 2 \, A c^{2} e^{5}\right)} x^{4} + 35 \, {\left(5 \, B c^{2} d^{2} e^{3} + 2 \, A c^{2} d e^{4} + 3 \, B a c e^{5}\right)} x^{3} + 21 \, {\left(5 \, B c^{2} d^{3} e^{2} + 2 \, A c^{2} d^{2} e^{3} + 3 \, B a c d e^{4} + 4 \, A a c e^{5}\right)} x^{2} + 7 \, {\left(5 \, B c^{2} d^{4} e + 2 \, A c^{2} d^{3} e^{2} + 3 \, B a c d^{2} e^{3} + 4 \, A a c d e^{4} + 5 \, B a^{2} e^{5}\right)} x}{210 \, {\left(e^{13} x^{7} + 7 \, d e^{12} x^{6} + 21 \, d^{2} e^{11} x^{5} + 35 \, d^{3} e^{10} x^{4} + 35 \, d^{4} e^{9} x^{3} + 21 \, d^{5} e^{8} x^{2} + 7 \, d^{6} e^{7} x + d^{7} e^{6}\right)}}"," ",0,"-1/210*(105*B*c^2*e^5*x^5 + 5*B*c^2*d^5 + 2*A*c^2*d^4*e + 3*B*a*c*d^3*e^2 + 4*A*a*c*d^2*e^3 + 5*B*a^2*d*e^4 + 30*A*a^2*e^5 + 35*(5*B*c^2*d*e^4 + 2*A*c^2*e^5)*x^4 + 35*(5*B*c^2*d^2*e^3 + 2*A*c^2*d*e^4 + 3*B*a*c*e^5)*x^3 + 21*(5*B*c^2*d^3*e^2 + 2*A*c^2*d^2*e^3 + 3*B*a*c*d*e^4 + 4*A*a*c*e^5)*x^2 + 7*(5*B*c^2*d^4*e + 2*A*c^2*d^3*e^2 + 3*B*a*c*d^2*e^3 + 4*A*a*c*d*e^4 + 5*B*a^2*e^5)*x)/(e^13*x^7 + 7*d*e^12*x^6 + 21*d^2*e^11*x^5 + 35*d^3*e^10*x^4 + 35*d^4*e^9*x^3 + 21*d^5*e^8*x^2 + 7*d^6*e^7*x + d^7*e^6)","A",0
1311,1,328,0,0.396838," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{280 \, B c^{2} e^{5} x^{5} + 5 \, B c^{2} d^{5} + 3 \, A c^{2} d^{4} e + 6 \, B a c d^{3} e^{2} + 10 \, A a c d^{2} e^{3} + 15 \, B a^{2} d e^{4} + 105 \, A a^{2} e^{5} + 70 \, {\left(5 \, B c^{2} d e^{4} + 3 \, A c^{2} e^{5}\right)} x^{4} + 56 \, {\left(5 \, B c^{2} d^{2} e^{3} + 3 \, A c^{2} d e^{4} + 6 \, B a c e^{5}\right)} x^{3} + 28 \, {\left(5 \, B c^{2} d^{3} e^{2} + 3 \, A c^{2} d^{2} e^{3} + 6 \, B a c d e^{4} + 10 \, A a c e^{5}\right)} x^{2} + 8 \, {\left(5 \, B c^{2} d^{4} e + 3 \, A c^{2} d^{3} e^{2} + 6 \, B a c d^{2} e^{3} + 10 \, A a c d e^{4} + 15 \, B a^{2} e^{5}\right)} x}{840 \, {\left(e^{14} x^{8} + 8 \, d e^{13} x^{7} + 28 \, d^{2} e^{12} x^{6} + 56 \, d^{3} e^{11} x^{5} + 70 \, d^{4} e^{10} x^{4} + 56 \, d^{5} e^{9} x^{3} + 28 \, d^{6} e^{8} x^{2} + 8 \, d^{7} e^{7} x + d^{8} e^{6}\right)}}"," ",0,"-1/840*(280*B*c^2*e^5*x^5 + 5*B*c^2*d^5 + 3*A*c^2*d^4*e + 6*B*a*c*d^3*e^2 + 10*A*a*c*d^2*e^3 + 15*B*a^2*d*e^4 + 105*A*a^2*e^5 + 70*(5*B*c^2*d*e^4 + 3*A*c^2*e^5)*x^4 + 56*(5*B*c^2*d^2*e^3 + 3*A*c^2*d*e^4 + 6*B*a*c*e^5)*x^3 + 28*(5*B*c^2*d^3*e^2 + 3*A*c^2*d^2*e^3 + 6*B*a*c*d*e^4 + 10*A*a*c*e^5)*x^2 + 8*(5*B*c^2*d^4*e + 3*A*c^2*d^3*e^2 + 6*B*a*c*d^2*e^3 + 10*A*a*c*d*e^4 + 15*B*a^2*e^5)*x)/(e^14*x^8 + 8*d*e^13*x^7 + 28*d^2*e^12*x^6 + 56*d^3*e^11*x^5 + 70*d^4*e^10*x^4 + 56*d^5*e^9*x^3 + 28*d^6*e^8*x^2 + 8*d^7*e^7*x + d^8*e^6)","A",0
1312,1,339,0,0.389928," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{630 \, B c^{2} e^{5} x^{5} + 5 \, B c^{2} d^{5} + 4 \, A c^{2} d^{4} e + 10 \, B a c d^{3} e^{2} + 20 \, A a c d^{2} e^{3} + 35 \, B a^{2} d e^{4} + 280 \, A a^{2} e^{5} + 126 \, {\left(5 \, B c^{2} d e^{4} + 4 \, A c^{2} e^{5}\right)} x^{4} + 84 \, {\left(5 \, B c^{2} d^{2} e^{3} + 4 \, A c^{2} d e^{4} + 10 \, B a c e^{5}\right)} x^{3} + 36 \, {\left(5 \, B c^{2} d^{3} e^{2} + 4 \, A c^{2} d^{2} e^{3} + 10 \, B a c d e^{4} + 20 \, A a c e^{5}\right)} x^{2} + 9 \, {\left(5 \, B c^{2} d^{4} e + 4 \, A c^{2} d^{3} e^{2} + 10 \, B a c d^{2} e^{3} + 20 \, A a c d e^{4} + 35 \, B a^{2} e^{5}\right)} x}{2520 \, {\left(e^{15} x^{9} + 9 \, d e^{14} x^{8} + 36 \, d^{2} e^{13} x^{7} + 84 \, d^{3} e^{12} x^{6} + 126 \, d^{4} e^{11} x^{5} + 126 \, d^{5} e^{10} x^{4} + 84 \, d^{6} e^{9} x^{3} + 36 \, d^{7} e^{8} x^{2} + 9 \, d^{8} e^{7} x + d^{9} e^{6}\right)}}"," ",0,"-1/2520*(630*B*c^2*e^5*x^5 + 5*B*c^2*d^5 + 4*A*c^2*d^4*e + 10*B*a*c*d^3*e^2 + 20*A*a*c*d^2*e^3 + 35*B*a^2*d*e^4 + 280*A*a^2*e^5 + 126*(5*B*c^2*d*e^4 + 4*A*c^2*e^5)*x^4 + 84*(5*B*c^2*d^2*e^3 + 4*A*c^2*d*e^4 + 10*B*a*c*e^5)*x^3 + 36*(5*B*c^2*d^3*e^2 + 4*A*c^2*d^2*e^3 + 10*B*a*c*d*e^4 + 20*A*a*c*e^5)*x^2 + 9*(5*B*c^2*d^4*e + 4*A*c^2*d^3*e^2 + 10*B*a*c*d^2*e^3 + 20*A*a*c*d*e^4 + 35*B*a^2*e^5)*x)/(e^15*x^9 + 9*d*e^14*x^8 + 36*d^2*e^13*x^7 + 84*d^3*e^12*x^6 + 126*d^4*e^11*x^5 + 126*d^5*e^10*x^4 + 84*d^6*e^9*x^3 + 36*d^7*e^8*x^2 + 9*d^8*e^7*x + d^9*e^6)","A",0
1313,1,658,0,0.344913," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{5} c^{3} B + \frac{5}{12} x^{12} e^{4} d c^{3} B + \frac{1}{12} x^{12} e^{5} c^{3} A + \frac{10}{11} x^{11} e^{3} d^{2} c^{3} B + \frac{3}{11} x^{11} e^{5} c^{2} a B + \frac{5}{11} x^{11} e^{4} d c^{3} A + x^{10} e^{2} d^{3} c^{3} B + \frac{3}{2} x^{10} e^{4} d c^{2} a B + x^{10} e^{3} d^{2} c^{3} A + \frac{3}{10} x^{10} e^{5} c^{2} a A + \frac{5}{9} x^{9} e d^{4} c^{3} B + \frac{10}{3} x^{9} e^{3} d^{2} c^{2} a B + \frac{1}{3} x^{9} e^{5} c a^{2} B + \frac{10}{9} x^{9} e^{2} d^{3} c^{3} A + \frac{5}{3} x^{9} e^{4} d c^{2} a A + \frac{1}{8} x^{8} d^{5} c^{3} B + \frac{15}{4} x^{8} e^{2} d^{3} c^{2} a B + \frac{15}{8} x^{8} e^{4} d c a^{2} B + \frac{5}{8} x^{8} e d^{4} c^{3} A + \frac{15}{4} x^{8} e^{3} d^{2} c^{2} a A + \frac{3}{8} x^{8} e^{5} c a^{2} A + \frac{15}{7} x^{7} e d^{4} c^{2} a B + \frac{30}{7} x^{7} e^{3} d^{2} c a^{2} B + \frac{1}{7} x^{7} e^{5} a^{3} B + \frac{1}{7} x^{7} d^{5} c^{3} A + \frac{30}{7} x^{7} e^{2} d^{3} c^{2} a A + \frac{15}{7} x^{7} e^{4} d c a^{2} A + \frac{1}{2} x^{6} d^{5} c^{2} a B + 5 x^{6} e^{2} d^{3} c a^{2} B + \frac{5}{6} x^{6} e^{4} d a^{3} B + \frac{5}{2} x^{6} e d^{4} c^{2} a A + 5 x^{6} e^{3} d^{2} c a^{2} A + \frac{1}{6} x^{6} e^{5} a^{3} A + 3 x^{5} e d^{4} c a^{2} B + 2 x^{5} e^{3} d^{2} a^{3} B + \frac{3}{5} x^{5} d^{5} c^{2} a A + 6 x^{5} e^{2} d^{3} c a^{2} A + x^{5} e^{4} d a^{3} A + \frac{3}{4} x^{4} d^{5} c a^{2} B + \frac{5}{2} x^{4} e^{2} d^{3} a^{3} B + \frac{15}{4} x^{4} e d^{4} c a^{2} A + \frac{5}{2} x^{4} e^{3} d^{2} a^{3} A + \frac{5}{3} x^{3} e d^{4} a^{3} B + x^{3} d^{5} c a^{2} A + \frac{10}{3} x^{3} e^{2} d^{3} a^{3} A + \frac{1}{2} x^{2} d^{5} a^{3} B + \frac{5}{2} x^{2} e d^{4} a^{3} A + x d^{5} a^{3} A"," ",0,"1/13*x^13*e^5*c^3*B + 5/12*x^12*e^4*d*c^3*B + 1/12*x^12*e^5*c^3*A + 10/11*x^11*e^3*d^2*c^3*B + 3/11*x^11*e^5*c^2*a*B + 5/11*x^11*e^4*d*c^3*A + x^10*e^2*d^3*c^3*B + 3/2*x^10*e^4*d*c^2*a*B + x^10*e^3*d^2*c^3*A + 3/10*x^10*e^5*c^2*a*A + 5/9*x^9*e*d^4*c^3*B + 10/3*x^9*e^3*d^2*c^2*a*B + 1/3*x^9*e^5*c*a^2*B + 10/9*x^9*e^2*d^3*c^3*A + 5/3*x^9*e^4*d*c^2*a*A + 1/8*x^8*d^5*c^3*B + 15/4*x^8*e^2*d^3*c^2*a*B + 15/8*x^8*e^4*d*c*a^2*B + 5/8*x^8*e*d^4*c^3*A + 15/4*x^8*e^3*d^2*c^2*a*A + 3/8*x^8*e^5*c*a^2*A + 15/7*x^7*e*d^4*c^2*a*B + 30/7*x^7*e^3*d^2*c*a^2*B + 1/7*x^7*e^5*a^3*B + 1/7*x^7*d^5*c^3*A + 30/7*x^7*e^2*d^3*c^2*a*A + 15/7*x^7*e^4*d*c*a^2*A + 1/2*x^6*d^5*c^2*a*B + 5*x^6*e^2*d^3*c*a^2*B + 5/6*x^6*e^4*d*a^3*B + 5/2*x^6*e*d^4*c^2*a*A + 5*x^6*e^3*d^2*c*a^2*A + 1/6*x^6*e^5*a^3*A + 3*x^5*e*d^4*c*a^2*B + 2*x^5*e^3*d^2*a^3*B + 3/5*x^5*d^5*c^2*a*A + 6*x^5*e^2*d^3*c*a^2*A + x^5*e^4*d*a^3*A + 3/4*x^4*d^5*c*a^2*B + 5/2*x^4*e^2*d^3*a^3*B + 15/4*x^4*e*d^4*c*a^2*A + 5/2*x^4*e^3*d^2*a^3*A + 5/3*x^3*e*d^4*a^3*B + x^3*d^5*c*a^2*A + 10/3*x^3*e^2*d^3*a^3*A + 1/2*x^2*d^5*a^3*B + 5/2*x^2*e*d^4*a^3*A + x*d^5*a^3*A","B",0
1314,1,536,0,0.356472," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{4} c^{3} B + \frac{4}{11} x^{11} e^{3} d c^{3} B + \frac{1}{11} x^{11} e^{4} c^{3} A + \frac{3}{5} x^{10} e^{2} d^{2} c^{3} B + \frac{3}{10} x^{10} e^{4} c^{2} a B + \frac{2}{5} x^{10} e^{3} d c^{3} A + \frac{4}{9} x^{9} e d^{3} c^{3} B + \frac{4}{3} x^{9} e^{3} d c^{2} a B + \frac{2}{3} x^{9} e^{2} d^{2} c^{3} A + \frac{1}{3} x^{9} e^{4} c^{2} a A + \frac{1}{8} x^{8} d^{4} c^{3} B + \frac{9}{4} x^{8} e^{2} d^{2} c^{2} a B + \frac{3}{8} x^{8} e^{4} c a^{2} B + \frac{1}{2} x^{8} e d^{3} c^{3} A + \frac{3}{2} x^{8} e^{3} d c^{2} a A + \frac{12}{7} x^{7} e d^{3} c^{2} a B + \frac{12}{7} x^{7} e^{3} d c a^{2} B + \frac{1}{7} x^{7} d^{4} c^{3} A + \frac{18}{7} x^{7} e^{2} d^{2} c^{2} a A + \frac{3}{7} x^{7} e^{4} c a^{2} A + \frac{1}{2} x^{6} d^{4} c^{2} a B + 3 x^{6} e^{2} d^{2} c a^{2} B + \frac{1}{6} x^{6} e^{4} a^{3} B + 2 x^{6} e d^{3} c^{2} a A + 2 x^{6} e^{3} d c a^{2} A + \frac{12}{5} x^{5} e d^{3} c a^{2} B + \frac{4}{5} x^{5} e^{3} d a^{3} B + \frac{3}{5} x^{5} d^{4} c^{2} a A + \frac{18}{5} x^{5} e^{2} d^{2} c a^{2} A + \frac{1}{5} x^{5} e^{4} a^{3} A + \frac{3}{4} x^{4} d^{4} c a^{2} B + \frac{3}{2} x^{4} e^{2} d^{2} a^{3} B + 3 x^{4} e d^{3} c a^{2} A + x^{4} e^{3} d a^{3} A + \frac{4}{3} x^{3} e d^{3} a^{3} B + x^{3} d^{4} c a^{2} A + 2 x^{3} e^{2} d^{2} a^{3} A + \frac{1}{2} x^{2} d^{4} a^{3} B + 2 x^{2} e d^{3} a^{3} A + x d^{4} a^{3} A"," ",0,"1/12*x^12*e^4*c^3*B + 4/11*x^11*e^3*d*c^3*B + 1/11*x^11*e^4*c^3*A + 3/5*x^10*e^2*d^2*c^3*B + 3/10*x^10*e^4*c^2*a*B + 2/5*x^10*e^3*d*c^3*A + 4/9*x^9*e*d^3*c^3*B + 4/3*x^9*e^3*d*c^2*a*B + 2/3*x^9*e^2*d^2*c^3*A + 1/3*x^9*e^4*c^2*a*A + 1/8*x^8*d^4*c^3*B + 9/4*x^8*e^2*d^2*c^2*a*B + 3/8*x^8*e^4*c*a^2*B + 1/2*x^8*e*d^3*c^3*A + 3/2*x^8*e^3*d*c^2*a*A + 12/7*x^7*e*d^3*c^2*a*B + 12/7*x^7*e^3*d*c*a^2*B + 1/7*x^7*d^4*c^3*A + 18/7*x^7*e^2*d^2*c^2*a*A + 3/7*x^7*e^4*c*a^2*A + 1/2*x^6*d^4*c^2*a*B + 3*x^6*e^2*d^2*c*a^2*B + 1/6*x^6*e^4*a^3*B + 2*x^6*e*d^3*c^2*a*A + 2*x^6*e^3*d*c*a^2*A + 12/5*x^5*e*d^3*c*a^2*B + 4/5*x^5*e^3*d*a^3*B + 3/5*x^5*d^4*c^2*a*A + 18/5*x^5*e^2*d^2*c*a^2*A + 1/5*x^5*e^4*a^3*A + 3/4*x^4*d^4*c*a^2*B + 3/2*x^4*e^2*d^2*a^3*B + 3*x^4*e*d^3*c*a^2*A + x^4*e^3*d*a^3*A + 4/3*x^3*e*d^3*a^3*B + x^3*d^4*c*a^2*A + 2*x^3*e^2*d^2*a^3*A + 1/2*x^2*d^4*a^3*B + 2*x^2*e*d^3*a^3*A + x*d^4*a^3*A","A",0
1315,1,411,0,0.364950," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{3} c^{3} B + \frac{3}{10} x^{10} e^{2} d c^{3} B + \frac{1}{10} x^{10} e^{3} c^{3} A + \frac{1}{3} x^{9} e d^{2} c^{3} B + \frac{1}{3} x^{9} e^{3} c^{2} a B + \frac{1}{3} x^{9} e^{2} d c^{3} A + \frac{1}{8} x^{8} d^{3} c^{3} B + \frac{9}{8} x^{8} e^{2} d c^{2} a B + \frac{3}{8} x^{8} e d^{2} c^{3} A + \frac{3}{8} x^{8} e^{3} c^{2} a A + \frac{9}{7} x^{7} e d^{2} c^{2} a B + \frac{3}{7} x^{7} e^{3} c a^{2} B + \frac{1}{7} x^{7} d^{3} c^{3} A + \frac{9}{7} x^{7} e^{2} d c^{2} a A + \frac{1}{2} x^{6} d^{3} c^{2} a B + \frac{3}{2} x^{6} e^{2} d c a^{2} B + \frac{3}{2} x^{6} e d^{2} c^{2} a A + \frac{1}{2} x^{6} e^{3} c a^{2} A + \frac{9}{5} x^{5} e d^{2} c a^{2} B + \frac{1}{5} x^{5} e^{3} a^{3} B + \frac{3}{5} x^{5} d^{3} c^{2} a A + \frac{9}{5} x^{5} e^{2} d c a^{2} A + \frac{3}{4} x^{4} d^{3} c a^{2} B + \frac{3}{4} x^{4} e^{2} d a^{3} B + \frac{9}{4} x^{4} e d^{2} c a^{2} A + \frac{1}{4} x^{4} e^{3} a^{3} A + x^{3} e d^{2} a^{3} B + x^{3} d^{3} c a^{2} A + x^{3} e^{2} d a^{3} A + \frac{1}{2} x^{2} d^{3} a^{3} B + \frac{3}{2} x^{2} e d^{2} a^{3} A + x d^{3} a^{3} A"," ",0,"1/11*x^11*e^3*c^3*B + 3/10*x^10*e^2*d*c^3*B + 1/10*x^10*e^3*c^3*A + 1/3*x^9*e*d^2*c^3*B + 1/3*x^9*e^3*c^2*a*B + 1/3*x^9*e^2*d*c^3*A + 1/8*x^8*d^3*c^3*B + 9/8*x^8*e^2*d*c^2*a*B + 3/8*x^8*e*d^2*c^3*A + 3/8*x^8*e^3*c^2*a*A + 9/7*x^7*e*d^2*c^2*a*B + 3/7*x^7*e^3*c*a^2*B + 1/7*x^7*d^3*c^3*A + 9/7*x^7*e^2*d*c^2*a*A + 1/2*x^6*d^3*c^2*a*B + 3/2*x^6*e^2*d*c*a^2*B + 3/2*x^6*e*d^2*c^2*a*A + 1/2*x^6*e^3*c*a^2*A + 9/5*x^5*e*d^2*c*a^2*B + 1/5*x^5*e^3*a^3*B + 3/5*x^5*d^3*c^2*a*A + 9/5*x^5*e^2*d*c*a^2*A + 3/4*x^4*d^3*c*a^2*B + 3/4*x^4*e^2*d*a^3*B + 9/4*x^4*e*d^2*c*a^2*A + 1/4*x^4*e^3*a^3*A + x^3*e*d^2*a^3*B + x^3*d^3*c*a^2*A + x^3*e^2*d*a^3*A + 1/2*x^2*d^3*a^3*B + 3/2*x^2*e*d^2*a^3*A + x*d^3*a^3*A","A",0
1316,1,287,0,0.359262," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{2} c^{3} B + \frac{2}{9} x^{9} e d c^{3} B + \frac{1}{9} x^{9} e^{2} c^{3} A + \frac{1}{8} x^{8} d^{2} c^{3} B + \frac{3}{8} x^{8} e^{2} c^{2} a B + \frac{1}{4} x^{8} e d c^{3} A + \frac{6}{7} x^{7} e d c^{2} a B + \frac{1}{7} x^{7} d^{2} c^{3} A + \frac{3}{7} x^{7} e^{2} c^{2} a A + \frac{1}{2} x^{6} d^{2} c^{2} a B + \frac{1}{2} x^{6} e^{2} c a^{2} B + x^{6} e d c^{2} a A + \frac{6}{5} x^{5} e d c a^{2} B + \frac{3}{5} x^{5} d^{2} c^{2} a A + \frac{3}{5} x^{5} e^{2} c a^{2} A + \frac{3}{4} x^{4} d^{2} c a^{2} B + \frac{1}{4} x^{4} e^{2} a^{3} B + \frac{3}{2} x^{4} e d c a^{2} A + \frac{2}{3} x^{3} e d a^{3} B + x^{3} d^{2} c a^{2} A + \frac{1}{3} x^{3} e^{2} a^{3} A + \frac{1}{2} x^{2} d^{2} a^{3} B + x^{2} e d a^{3} A + x d^{2} a^{3} A"," ",0,"1/10*x^10*e^2*c^3*B + 2/9*x^9*e*d*c^3*B + 1/9*x^9*e^2*c^3*A + 1/8*x^8*d^2*c^3*B + 3/8*x^8*e^2*c^2*a*B + 1/4*x^8*e*d*c^3*A + 6/7*x^7*e*d*c^2*a*B + 1/7*x^7*d^2*c^3*A + 3/7*x^7*e^2*c^2*a*A + 1/2*x^6*d^2*c^2*a*B + 1/2*x^6*e^2*c*a^2*B + x^6*e*d*c^2*a*A + 6/5*x^5*e*d*c*a^2*B + 3/5*x^5*d^2*c^2*a*A + 3/5*x^5*e^2*c*a^2*A + 3/4*x^4*d^2*c*a^2*B + 1/4*x^4*e^2*a^3*B + 3/2*x^4*e*d*c*a^2*A + 2/3*x^3*e*d*a^3*B + x^3*d^2*c*a^2*A + 1/3*x^3*e^2*a^3*A + 1/2*x^2*d^2*a^3*B + x^2*e*d*a^3*A + x*d^2*a^3*A","A",0
1317,1,165,0,0.373660," ","integrate((B*x+A)*(e*x+d)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e c^{3} B + \frac{1}{8} x^{8} d c^{3} B + \frac{1}{8} x^{8} e c^{3} A + \frac{3}{7} x^{7} e c^{2} a B + \frac{1}{7} x^{7} d c^{3} A + \frac{1}{2} x^{6} d c^{2} a B + \frac{1}{2} x^{6} e c^{2} a A + \frac{3}{5} x^{5} e c a^{2} B + \frac{3}{5} x^{5} d c^{2} a A + \frac{3}{4} x^{4} d c a^{2} B + \frac{3}{4} x^{4} e c a^{2} A + \frac{1}{3} x^{3} e a^{3} B + x^{3} d c a^{2} A + \frac{1}{2} x^{2} d a^{3} B + \frac{1}{2} x^{2} e a^{3} A + x d a^{3} A"," ",0,"1/9*x^9*e*c^3*B + 1/8*x^8*d*c^3*B + 1/8*x^8*e*c^3*A + 3/7*x^7*e*c^2*a*B + 1/7*x^7*d*c^3*A + 1/2*x^6*d*c^2*a*B + 1/2*x^6*e*c^2*a*A + 3/5*x^5*e*c*a^2*B + 3/5*x^5*d*c^2*a*A + 3/4*x^4*d*c*a^2*B + 3/4*x^4*e*c*a^2*A + 1/3*x^3*e*a^3*B + x^3*d*c*a^2*A + 1/2*x^2*d*a^3*B + 1/2*x^2*e*a^3*A + x*d*a^3*A","A",0
1318,1,73,0,0.358792," ","integrate((B*x+A)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{3} B + \frac{1}{7} x^{7} c^{3} A + \frac{1}{2} x^{6} c^{2} a B + \frac{3}{5} x^{5} c^{2} a A + \frac{3}{4} x^{4} c a^{2} B + x^{3} c a^{2} A + \frac{1}{2} x^{2} a^{3} B + x a^{3} A"," ",0,"1/8*x^8*c^3*B + 1/7*x^7*c^3*A + 1/2*x^6*c^2*a*B + 3/5*x^5*c^2*a*A + 3/4*x^4*c*a^2*B + x^3*c*a^2*A + 1/2*x^2*a^3*B + x*a^3*A","A",0
1319,1,448,0,0.385630," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d),x, algorithm=""fricas"")","\frac{60 \, B c^{3} e^{7} x^{7} - 70 \, {\left(B c^{3} d e^{6} - A c^{3} e^{7}\right)} x^{6} + 84 \, {\left(B c^{3} d^{2} e^{5} - A c^{3} d e^{6} + 3 \, B a c^{2} e^{7}\right)} x^{5} - 105 \, {\left(B c^{3} d^{3} e^{4} - A c^{3} d^{2} e^{5} + 3 \, B a c^{2} d e^{6} - 3 \, A a c^{2} e^{7}\right)} x^{4} + 140 \, {\left(B c^{3} d^{4} e^{3} - A c^{3} d^{3} e^{4} + 3 \, B a c^{2} d^{2} e^{5} - 3 \, A a c^{2} d e^{6} + 3 \, B a^{2} c e^{7}\right)} x^{3} - 210 \, {\left(B c^{3} d^{5} e^{2} - A c^{3} d^{4} e^{3} + 3 \, B a c^{2} d^{3} e^{4} - 3 \, A a c^{2} d^{2} e^{5} + 3 \, B a^{2} c d e^{6} - 3 \, A a^{2} c e^{7}\right)} x^{2} + 420 \, {\left(B c^{3} d^{6} e - A c^{3} d^{5} e^{2} + 3 \, B a c^{2} d^{4} e^{3} - 3 \, A a c^{2} d^{3} e^{4} + 3 \, B a^{2} c d^{2} e^{5} - 3 \, A a^{2} c d e^{6} + B a^{3} e^{7}\right)} x - 420 \, {\left(B c^{3} d^{7} - A c^{3} d^{6} e + 3 \, B a c^{2} d^{5} e^{2} - 3 \, A a c^{2} d^{4} e^{3} + 3 \, B a^{2} c d^{3} e^{4} - 3 \, A a^{2} c d^{2} e^{5} + B a^{3} d e^{6} - A a^{3} e^{7}\right)} \log\left(e x + d\right)}{420 \, e^{8}}"," ",0,"1/420*(60*B*c^3*e^7*x^7 - 70*(B*c^3*d*e^6 - A*c^3*e^7)*x^6 + 84*(B*c^3*d^2*e^5 - A*c^3*d*e^6 + 3*B*a*c^2*e^7)*x^5 - 105*(B*c^3*d^3*e^4 - A*c^3*d^2*e^5 + 3*B*a*c^2*d*e^6 - 3*A*a*c^2*e^7)*x^4 + 140*(B*c^3*d^4*e^3 - A*c^3*d^3*e^4 + 3*B*a*c^2*d^2*e^5 - 3*A*a*c^2*d*e^6 + 3*B*a^2*c*e^7)*x^3 - 210*(B*c^3*d^5*e^2 - A*c^3*d^4*e^3 + 3*B*a*c^2*d^3*e^4 - 3*A*a*c^2*d^2*e^5 + 3*B*a^2*c*d*e^6 - 3*A*a^2*c*e^7)*x^2 + 420*(B*c^3*d^6*e - A*c^3*d^5*e^2 + 3*B*a*c^2*d^4*e^3 - 3*A*a*c^2*d^3*e^4 + 3*B*a^2*c*d^2*e^5 - 3*A*a^2*c*d*e^6 + B*a^3*e^7)*x - 420*(B*c^3*d^7 - A*c^3*d^6*e + 3*B*a*c^2*d^5*e^2 - 3*A*a*c^2*d^4*e^3 + 3*B*a^2*c*d^3*e^4 - 3*A*a^2*c*d^2*e^5 + B*a^3*d*e^6 - A*a^3*e^7)*log(e*x + d))/e^8","A",0
1320,1,621,0,0.420480," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{10 \, B c^{3} e^{7} x^{7} + 60 \, B c^{3} d^{7} - 60 \, A c^{3} d^{6} e + 180 \, B a c^{2} d^{5} e^{2} - 180 \, A a c^{2} d^{4} e^{3} + 180 \, B a^{2} c d^{3} e^{4} - 180 \, A a^{2} c d^{2} e^{5} + 60 \, B a^{3} d e^{6} - 60 \, A a^{3} e^{7} - 2 \, {\left(7 \, B c^{3} d e^{6} - 6 \, A c^{3} e^{7}\right)} x^{6} + 3 \, {\left(7 \, B c^{3} d^{2} e^{5} - 6 \, A c^{3} d e^{6} + 15 \, B a c^{2} e^{7}\right)} x^{5} - 5 \, {\left(7 \, B c^{3} d^{3} e^{4} - 6 \, A c^{3} d^{2} e^{5} + 15 \, B a c^{2} d e^{6} - 12 \, A a c^{2} e^{7}\right)} x^{4} + 10 \, {\left(7 \, B c^{3} d^{4} e^{3} - 6 \, A c^{3} d^{3} e^{4} + 15 \, B a c^{2} d^{2} e^{5} - 12 \, A a c^{2} d e^{6} + 9 \, B a^{2} c e^{7}\right)} x^{3} - 30 \, {\left(7 \, B c^{3} d^{5} e^{2} - 6 \, A c^{3} d^{4} e^{3} + 15 \, B a c^{2} d^{3} e^{4} - 12 \, A a c^{2} d^{2} e^{5} + 9 \, B a^{2} c d e^{6} - 6 \, A a^{2} c e^{7}\right)} x^{2} - 60 \, {\left(6 \, B c^{3} d^{6} e - 5 \, A c^{3} d^{5} e^{2} + 12 \, B a c^{2} d^{4} e^{3} - 9 \, A a c^{2} d^{3} e^{4} + 6 \, B a^{2} c d^{2} e^{5} - 3 \, A a^{2} c d e^{6}\right)} x + 60 \, {\left(7 \, B c^{3} d^{7} - 6 \, A c^{3} d^{6} e + 15 \, B a c^{2} d^{5} e^{2} - 12 \, A a c^{2} d^{4} e^{3} + 9 \, B a^{2} c d^{3} e^{4} - 6 \, A a^{2} c d^{2} e^{5} + B a^{3} d e^{6} + {\left(7 \, B c^{3} d^{6} e - 6 \, A c^{3} d^{5} e^{2} + 15 \, B a c^{2} d^{4} e^{3} - 12 \, A a c^{2} d^{3} e^{4} + 9 \, B a^{2} c d^{2} e^{5} - 6 \, A a^{2} c d e^{6} + B a^{3} e^{7}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"1/60*(10*B*c^3*e^7*x^7 + 60*B*c^3*d^7 - 60*A*c^3*d^6*e + 180*B*a*c^2*d^5*e^2 - 180*A*a*c^2*d^4*e^3 + 180*B*a^2*c*d^3*e^4 - 180*A*a^2*c*d^2*e^5 + 60*B*a^3*d*e^6 - 60*A*a^3*e^7 - 2*(7*B*c^3*d*e^6 - 6*A*c^3*e^7)*x^6 + 3*(7*B*c^3*d^2*e^5 - 6*A*c^3*d*e^6 + 15*B*a*c^2*e^7)*x^5 - 5*(7*B*c^3*d^3*e^4 - 6*A*c^3*d^2*e^5 + 15*B*a*c^2*d*e^6 - 12*A*a*c^2*e^7)*x^4 + 10*(7*B*c^3*d^4*e^3 - 6*A*c^3*d^3*e^4 + 15*B*a*c^2*d^2*e^5 - 12*A*a*c^2*d*e^6 + 9*B*a^2*c*e^7)*x^3 - 30*(7*B*c^3*d^5*e^2 - 6*A*c^3*d^4*e^3 + 15*B*a*c^2*d^3*e^4 - 12*A*a*c^2*d^2*e^5 + 9*B*a^2*c*d*e^6 - 6*A*a^2*c*e^7)*x^2 - 60*(6*B*c^3*d^6*e - 5*A*c^3*d^5*e^2 + 12*B*a*c^2*d^4*e^3 - 9*A*a*c^2*d^3*e^4 + 6*B*a^2*c*d^2*e^5 - 3*A*a^2*c*d*e^6)*x + 60*(7*B*c^3*d^7 - 6*A*c^3*d^6*e + 15*B*a*c^2*d^5*e^2 - 12*A*a*c^2*d^4*e^3 + 9*B*a^2*c*d^3*e^4 - 6*A*a^2*c*d^2*e^5 + B*a^3*d*e^6 + (7*B*c^3*d^6*e - 6*A*c^3*d^5*e^2 + 15*B*a*c^2*d^4*e^3 - 12*A*a*c^2*d^3*e^4 + 9*B*a^2*c*d^2*e^5 - 6*A*a^2*c*d*e^6 + B*a^3*e^7)*x)*log(e*x + d))/(e^9*x + d*e^8)","B",0
1321,1,691,0,0.399282," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{4 \, B c^{3} e^{7} x^{7} - 130 \, B c^{3} d^{7} + 110 \, A c^{3} d^{6} e - 270 \, B a c^{2} d^{5} e^{2} + 210 \, A a c^{2} d^{4} e^{3} - 150 \, B a^{2} c d^{3} e^{4} + 90 \, A a^{2} c d^{2} e^{5} - 10 \, B a^{3} d e^{6} - 10 \, A a^{3} e^{7} - {\left(7 \, B c^{3} d e^{6} - 5 \, A c^{3} e^{7}\right)} x^{6} + 2 \, {\left(7 \, B c^{3} d^{2} e^{5} - 5 \, A c^{3} d e^{6} + 10 \, B a c^{2} e^{7}\right)} x^{5} - 5 \, {\left(7 \, B c^{3} d^{3} e^{4} - 5 \, A c^{3} d^{2} e^{5} + 10 \, B a c^{2} d e^{6} - 6 \, A a c^{2} e^{7}\right)} x^{4} + 20 \, {\left(7 \, B c^{3} d^{4} e^{3} - 5 \, A c^{3} d^{3} e^{4} + 10 \, B a c^{2} d^{2} e^{5} - 6 \, A a c^{2} d e^{6} + 3 \, B a^{2} c e^{7}\right)} x^{3} + 10 \, {\left(50 \, B c^{3} d^{5} e^{2} - 34 \, A c^{3} d^{4} e^{3} + 63 \, B a c^{2} d^{3} e^{4} - 33 \, A a c^{2} d^{2} e^{5} + 12 \, B a^{2} c d e^{6}\right)} x^{2} + 20 \, {\left(8 \, B c^{3} d^{6} e - 4 \, A c^{3} d^{5} e^{2} + 3 \, B a c^{2} d^{4} e^{3} + 3 \, A a c^{2} d^{3} e^{4} - 6 \, B a^{2} c d^{2} e^{5} + 6 \, A a^{2} c d e^{6} - B a^{3} e^{7}\right)} x - 60 \, {\left(7 \, B c^{3} d^{7} - 5 \, A c^{3} d^{6} e + 10 \, B a c^{2} d^{5} e^{2} - 6 \, A a c^{2} d^{4} e^{3} + 3 \, B a^{2} c d^{3} e^{4} - A a^{2} c d^{2} e^{5} + {\left(7 \, B c^{3} d^{5} e^{2} - 5 \, A c^{3} d^{4} e^{3} + 10 \, B a c^{2} d^{3} e^{4} - 6 \, A a c^{2} d^{2} e^{5} + 3 \, B a^{2} c d e^{6} - A a^{2} c e^{7}\right)} x^{2} + 2 \, {\left(7 \, B c^{3} d^{6} e - 5 \, A c^{3} d^{5} e^{2} + 10 \, B a c^{2} d^{4} e^{3} - 6 \, A a c^{2} d^{3} e^{4} + 3 \, B a^{2} c d^{2} e^{5} - A a^{2} c d e^{6}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"1/20*(4*B*c^3*e^7*x^7 - 130*B*c^3*d^7 + 110*A*c^3*d^6*e - 270*B*a*c^2*d^5*e^2 + 210*A*a*c^2*d^4*e^3 - 150*B*a^2*c*d^3*e^4 + 90*A*a^2*c*d^2*e^5 - 10*B*a^3*d*e^6 - 10*A*a^3*e^7 - (7*B*c^3*d*e^6 - 5*A*c^3*e^7)*x^6 + 2*(7*B*c^3*d^2*e^5 - 5*A*c^3*d*e^6 + 10*B*a*c^2*e^7)*x^5 - 5*(7*B*c^3*d^3*e^4 - 5*A*c^3*d^2*e^5 + 10*B*a*c^2*d*e^6 - 6*A*a*c^2*e^7)*x^4 + 20*(7*B*c^3*d^4*e^3 - 5*A*c^3*d^3*e^4 + 10*B*a*c^2*d^2*e^5 - 6*A*a*c^2*d*e^6 + 3*B*a^2*c*e^7)*x^3 + 10*(50*B*c^3*d^5*e^2 - 34*A*c^3*d^4*e^3 + 63*B*a*c^2*d^3*e^4 - 33*A*a*c^2*d^2*e^5 + 12*B*a^2*c*d*e^6)*x^2 + 20*(8*B*c^3*d^6*e - 4*A*c^3*d^5*e^2 + 3*B*a*c^2*d^4*e^3 + 3*A*a*c^2*d^3*e^4 - 6*B*a^2*c*d^2*e^5 + 6*A*a^2*c*d*e^6 - B*a^3*e^7)*x - 60*(7*B*c^3*d^7 - 5*A*c^3*d^6*e + 10*B*a*c^2*d^5*e^2 - 6*A*a*c^2*d^4*e^3 + 3*B*a^2*c*d^3*e^4 - A*a^2*c*d^2*e^5 + (7*B*c^3*d^5*e^2 - 5*A*c^3*d^4*e^3 + 10*B*a*c^2*d^3*e^4 - 6*A*a*c^2*d^2*e^5 + 3*B*a^2*c*d*e^6 - A*a^2*c*e^7)*x^2 + 2*(7*B*c^3*d^6*e - 5*A*c^3*d^5*e^2 + 10*B*a*c^2*d^4*e^3 - 6*A*a*c^2*d^3*e^4 + 3*B*a^2*c*d^2*e^5 - A*a^2*c*d*e^6)*x)*log(e*x + d))/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","B",0
1322,1,732,0,0.407230," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, B c^{3} e^{7} x^{7} + 214 \, B c^{3} d^{7} - 148 \, A c^{3} d^{6} e + 282 \, B a c^{2} d^{5} e^{2} - 156 \, A a c^{2} d^{4} e^{3} + 66 \, B a^{2} c d^{3} e^{4} - 12 \, A a^{2} c d^{2} e^{5} - 2 \, B a^{3} d e^{6} - 4 \, A a^{3} e^{7} - {\left(7 \, B c^{3} d e^{6} - 4 \, A c^{3} e^{7}\right)} x^{6} + 3 \, {\left(7 \, B c^{3} d^{2} e^{5} - 4 \, A c^{3} d e^{6} + 6 \, B a c^{2} e^{7}\right)} x^{5} - 3 \, {\left(35 \, B c^{3} d^{3} e^{4} - 20 \, A c^{3} d^{2} e^{5} + 30 \, B a c^{2} d e^{6} - 12 \, A a c^{2} e^{7}\right)} x^{4} - 2 \, {\left(278 \, B c^{3} d^{4} e^{3} - 146 \, A c^{3} d^{3} e^{4} + 189 \, B a c^{2} d^{2} e^{5} - 54 \, A a c^{2} d e^{6}\right)} x^{3} - 6 \, {\left(68 \, B c^{3} d^{5} e^{2} - 26 \, A c^{3} d^{4} e^{3} + 9 \, B a c^{2} d^{3} e^{4} + 18 \, A a c^{2} d^{2} e^{5} - 18 \, B a^{2} c d e^{6} + 6 \, A a^{2} c e^{7}\right)} x^{2} + 6 \, {\left(37 \, B c^{3} d^{6} e - 34 \, A c^{3} d^{5} e^{2} + 81 \, B a c^{2} d^{4} e^{3} - 54 \, A a c^{2} d^{3} e^{4} + 27 \, B a^{2} c d^{2} e^{5} - 6 \, A a^{2} c d e^{6} - B a^{3} e^{7}\right)} x + 12 \, {\left(35 \, B c^{3} d^{7} - 20 \, A c^{3} d^{6} e + 30 \, B a c^{2} d^{5} e^{2} - 12 \, A a c^{2} d^{4} e^{3} + 3 \, B a^{2} c d^{3} e^{4} + {\left(35 \, B c^{3} d^{4} e^{3} - 20 \, A c^{3} d^{3} e^{4} + 30 \, B a c^{2} d^{2} e^{5} - 12 \, A a c^{2} d e^{6} + 3 \, B a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(35 \, B c^{3} d^{5} e^{2} - 20 \, A c^{3} d^{4} e^{3} + 30 \, B a c^{2} d^{3} e^{4} - 12 \, A a c^{2} d^{2} e^{5} + 3 \, B a^{2} c d e^{6}\right)} x^{2} + 3 \, {\left(35 \, B c^{3} d^{6} e - 20 \, A c^{3} d^{5} e^{2} + 30 \, B a c^{2} d^{4} e^{3} - 12 \, A a c^{2} d^{3} e^{4} + 3 \, B a^{2} c d^{2} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right)}}"," ",0,"1/12*(3*B*c^3*e^7*x^7 + 214*B*c^3*d^7 - 148*A*c^3*d^6*e + 282*B*a*c^2*d^5*e^2 - 156*A*a*c^2*d^4*e^3 + 66*B*a^2*c*d^3*e^4 - 12*A*a^2*c*d^2*e^5 - 2*B*a^3*d*e^6 - 4*A*a^3*e^7 - (7*B*c^3*d*e^6 - 4*A*c^3*e^7)*x^6 + 3*(7*B*c^3*d^2*e^5 - 4*A*c^3*d*e^6 + 6*B*a*c^2*e^7)*x^5 - 3*(35*B*c^3*d^3*e^4 - 20*A*c^3*d^2*e^5 + 30*B*a*c^2*d*e^6 - 12*A*a*c^2*e^7)*x^4 - 2*(278*B*c^3*d^4*e^3 - 146*A*c^3*d^3*e^4 + 189*B*a*c^2*d^2*e^5 - 54*A*a*c^2*d*e^6)*x^3 - 6*(68*B*c^3*d^5*e^2 - 26*A*c^3*d^4*e^3 + 9*B*a*c^2*d^3*e^4 + 18*A*a*c^2*d^2*e^5 - 18*B*a^2*c*d*e^6 + 6*A*a^2*c*e^7)*x^2 + 6*(37*B*c^3*d^6*e - 34*A*c^3*d^5*e^2 + 81*B*a*c^2*d^4*e^3 - 54*A*a*c^2*d^3*e^4 + 27*B*a^2*c*d^2*e^5 - 6*A*a^2*c*d*e^6 - B*a^3*e^7)*x + 12*(35*B*c^3*d^7 - 20*A*c^3*d^6*e + 30*B*a*c^2*d^5*e^2 - 12*A*a*c^2*d^4*e^3 + 3*B*a^2*c*d^3*e^4 + (35*B*c^3*d^4*e^3 - 20*A*c^3*d^3*e^4 + 30*B*a*c^2*d^2*e^5 - 12*A*a*c^2*d*e^6 + 3*B*a^2*c*e^7)*x^3 + 3*(35*B*c^3*d^5*e^2 - 20*A*c^3*d^4*e^3 + 30*B*a*c^2*d^3*e^4 - 12*A*a*c^2*d^2*e^5 + 3*B*a^2*c*d*e^6)*x^2 + 3*(35*B*c^3*d^6*e - 20*A*c^3*d^5*e^2 + 30*B*a*c^2*d^4*e^3 - 12*A*a*c^2*d^3*e^4 + 3*B*a^2*c*d^2*e^5)*x)*log(e*x + d))/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8)","B",0
1323,1,746,0,0.418148," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^5,x, algorithm=""fricas"")","\frac{4 \, B c^{3} e^{7} x^{7} - 319 \, B c^{3} d^{7} + 171 \, A c^{3} d^{6} e - 231 \, B a c^{2} d^{5} e^{2} + 75 \, A a c^{2} d^{4} e^{3} - 9 \, B a^{2} c d^{3} e^{4} - 3 \, A a^{2} c d^{2} e^{5} - B a^{3} d e^{6} - 3 \, A a^{3} e^{7} - 2 \, {\left(7 \, B c^{3} d e^{6} - 3 \, A c^{3} e^{7}\right)} x^{6} + 12 \, {\left(7 \, B c^{3} d^{2} e^{5} - 3 \, A c^{3} d e^{6} + 3 \, B a c^{2} e^{7}\right)} x^{5} + 4 \, {\left(139 \, B c^{3} d^{3} e^{4} - 51 \, A c^{3} d^{2} e^{5} + 36 \, B a c^{2} d e^{6}\right)} x^{4} + 4 \, {\left(136 \, B c^{3} d^{4} e^{3} - 24 \, A c^{3} d^{3} e^{4} - 36 \, B a c^{2} d^{2} e^{5} + 36 \, A a c^{2} d e^{6} - 9 \, B a^{2} c e^{7}\right)} x^{3} - 6 \, {\left(74 \, B c^{3} d^{5} e^{2} - 66 \, A c^{3} d^{4} e^{3} + 126 \, B a c^{2} d^{3} e^{4} - 54 \, A a c^{2} d^{2} e^{5} + 9 \, B a^{2} c d e^{6} + 3 \, A a^{2} c e^{7}\right)} x^{2} - 4 \, {\left(214 \, B c^{3} d^{6} e - 126 \, A c^{3} d^{5} e^{2} + 186 \, B a c^{2} d^{4} e^{3} - 66 \, A a c^{2} d^{3} e^{4} + 9 \, B a^{2} c d^{2} e^{5} + 3 \, A a^{2} c d e^{6} + B a^{3} e^{7}\right)} x - 12 \, {\left(35 \, B c^{3} d^{7} - 15 \, A c^{3} d^{6} e + 15 \, B a c^{2} d^{5} e^{2} - 3 \, A a c^{2} d^{4} e^{3} + {\left(35 \, B c^{3} d^{3} e^{4} - 15 \, A c^{3} d^{2} e^{5} + 15 \, B a c^{2} d e^{6} - 3 \, A a c^{2} e^{7}\right)} x^{4} + 4 \, {\left(35 \, B c^{3} d^{4} e^{3} - 15 \, A c^{3} d^{3} e^{4} + 15 \, B a c^{2} d^{2} e^{5} - 3 \, A a c^{2} d e^{6}\right)} x^{3} + 6 \, {\left(35 \, B c^{3} d^{5} e^{2} - 15 \, A c^{3} d^{4} e^{3} + 15 \, B a c^{2} d^{3} e^{4} - 3 \, A a c^{2} d^{2} e^{5}\right)} x^{2} + 4 \, {\left(35 \, B c^{3} d^{6} e - 15 \, A c^{3} d^{5} e^{2} + 15 \, B a c^{2} d^{4} e^{3} - 3 \, A a c^{2} d^{3} e^{4}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{12} x^{4} + 4 \, d e^{11} x^{3} + 6 \, d^{2} e^{10} x^{2} + 4 \, d^{3} e^{9} x + d^{4} e^{8}\right)}}"," ",0,"1/12*(4*B*c^3*e^7*x^7 - 319*B*c^3*d^7 + 171*A*c^3*d^6*e - 231*B*a*c^2*d^5*e^2 + 75*A*a*c^2*d^4*e^3 - 9*B*a^2*c*d^3*e^4 - 3*A*a^2*c*d^2*e^5 - B*a^3*d*e^6 - 3*A*a^3*e^7 - 2*(7*B*c^3*d*e^6 - 3*A*c^3*e^7)*x^6 + 12*(7*B*c^3*d^2*e^5 - 3*A*c^3*d*e^6 + 3*B*a*c^2*e^7)*x^5 + 4*(139*B*c^3*d^3*e^4 - 51*A*c^3*d^2*e^5 + 36*B*a*c^2*d*e^6)*x^4 + 4*(136*B*c^3*d^4*e^3 - 24*A*c^3*d^3*e^4 - 36*B*a*c^2*d^2*e^5 + 36*A*a*c^2*d*e^6 - 9*B*a^2*c*e^7)*x^3 - 6*(74*B*c^3*d^5*e^2 - 66*A*c^3*d^4*e^3 + 126*B*a*c^2*d^3*e^4 - 54*A*a*c^2*d^2*e^5 + 9*B*a^2*c*d*e^6 + 3*A*a^2*c*e^7)*x^2 - 4*(214*B*c^3*d^6*e - 126*A*c^3*d^5*e^2 + 186*B*a*c^2*d^4*e^3 - 66*A*a*c^2*d^3*e^4 + 9*B*a^2*c*d^2*e^5 + 3*A*a^2*c*d*e^6 + B*a^3*e^7)*x - 12*(35*B*c^3*d^7 - 15*A*c^3*d^6*e + 15*B*a*c^2*d^5*e^2 - 3*A*a*c^2*d^4*e^3 + (35*B*c^3*d^3*e^4 - 15*A*c^3*d^2*e^5 + 15*B*a*c^2*d*e^6 - 3*A*a*c^2*e^7)*x^4 + 4*(35*B*c^3*d^4*e^3 - 15*A*c^3*d^3*e^4 + 15*B*a*c^2*d^2*e^5 - 3*A*a*c^2*d*e^6)*x^3 + 6*(35*B*c^3*d^5*e^2 - 15*A*c^3*d^4*e^3 + 15*B*a*c^2*d^3*e^4 - 3*A*a*c^2*d^2*e^5)*x^2 + 4*(35*B*c^3*d^6*e - 15*A*c^3*d^5*e^2 + 15*B*a*c^2*d^4*e^3 - 3*A*a*c^2*d^3*e^4)*x)*log(e*x + d))/(e^12*x^4 + 4*d*e^11*x^3 + 6*d^2*e^10*x^2 + 4*d^3*e^9*x + d^4*e^8)","B",0
1324,1,730,0,0.413859," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^6,x, algorithm=""fricas"")","\frac{10 \, B c^{3} e^{7} x^{7} + 459 \, B c^{3} d^{7} - 174 \, A c^{3} d^{6} e + 137 \, B a c^{2} d^{5} e^{2} - 12 \, A a c^{2} d^{4} e^{3} - 3 \, B a^{2} c d^{3} e^{4} - 2 \, A a^{2} c d^{2} e^{5} - B a^{3} d e^{6} - 4 \, A a^{3} e^{7} - 10 \, {\left(7 \, B c^{3} d e^{6} - 2 \, A c^{3} e^{7}\right)} x^{6} - 100 \, {\left(5 \, B c^{3} d^{2} e^{5} - A c^{3} d e^{6}\right)} x^{5} - 20 \, {\left(20 \, B c^{3} d^{3} e^{4} + 5 \, A c^{3} d^{2} e^{5} - 15 \, B a c^{2} d e^{6} + 3 \, A a c^{2} e^{7}\right)} x^{4} + 10 \, {\left(130 \, B c^{3} d^{4} e^{3} - 80 \, A c^{3} d^{3} e^{4} + 90 \, B a c^{2} d^{2} e^{5} - 12 \, A a c^{2} d e^{6} - 3 \, B a^{2} c e^{7}\right)} x^{3} + 10 \, {\left(270 \, B c^{3} d^{5} e^{2} - 120 \, A c^{3} d^{4} e^{3} + 110 \, B a c^{2} d^{3} e^{4} - 12 \, A a c^{2} d^{2} e^{5} - 3 \, B a^{2} c d e^{6} - 2 \, A a^{2} c e^{7}\right)} x^{2} + 5 \, {\left(375 \, B c^{3} d^{6} e - 150 \, A c^{3} d^{5} e^{2} + 125 \, B a c^{2} d^{4} e^{3} - 12 \, A a c^{2} d^{3} e^{4} - 3 \, B a^{2} c d^{2} e^{5} - 2 \, A a^{2} c d e^{6} - B a^{3} e^{7}\right)} x + 60 \, {\left(7 \, B c^{3} d^{7} - 2 \, A c^{3} d^{6} e + B a c^{2} d^{5} e^{2} + {\left(7 \, B c^{3} d^{2} e^{5} - 2 \, A c^{3} d e^{6} + B a c^{2} e^{7}\right)} x^{5} + 5 \, {\left(7 \, B c^{3} d^{3} e^{4} - 2 \, A c^{3} d^{2} e^{5} + B a c^{2} d e^{6}\right)} x^{4} + 10 \, {\left(7 \, B c^{3} d^{4} e^{3} - 2 \, A c^{3} d^{3} e^{4} + B a c^{2} d^{2} e^{5}\right)} x^{3} + 10 \, {\left(7 \, B c^{3} d^{5} e^{2} - 2 \, A c^{3} d^{4} e^{3} + B a c^{2} d^{3} e^{4}\right)} x^{2} + 5 \, {\left(7 \, B c^{3} d^{6} e - 2 \, A c^{3} d^{5} e^{2} + B a c^{2} d^{4} e^{3}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{13} x^{5} + 5 \, d e^{12} x^{4} + 10 \, d^{2} e^{11} x^{3} + 10 \, d^{3} e^{10} x^{2} + 5 \, d^{4} e^{9} x + d^{5} e^{8}\right)}}"," ",0,"1/20*(10*B*c^3*e^7*x^7 + 459*B*c^3*d^7 - 174*A*c^3*d^6*e + 137*B*a*c^2*d^5*e^2 - 12*A*a*c^2*d^4*e^3 - 3*B*a^2*c*d^3*e^4 - 2*A*a^2*c*d^2*e^5 - B*a^3*d*e^6 - 4*A*a^3*e^7 - 10*(7*B*c^3*d*e^6 - 2*A*c^3*e^7)*x^6 - 100*(5*B*c^3*d^2*e^5 - A*c^3*d*e^6)*x^5 - 20*(20*B*c^3*d^3*e^4 + 5*A*c^3*d^2*e^5 - 15*B*a*c^2*d*e^6 + 3*A*a*c^2*e^7)*x^4 + 10*(130*B*c^3*d^4*e^3 - 80*A*c^3*d^3*e^4 + 90*B*a*c^2*d^2*e^5 - 12*A*a*c^2*d*e^6 - 3*B*a^2*c*e^7)*x^3 + 10*(270*B*c^3*d^5*e^2 - 120*A*c^3*d^4*e^3 + 110*B*a*c^2*d^3*e^4 - 12*A*a*c^2*d^2*e^5 - 3*B*a^2*c*d*e^6 - 2*A*a^2*c*e^7)*x^2 + 5*(375*B*c^3*d^6*e - 150*A*c^3*d^5*e^2 + 125*B*a*c^2*d^4*e^3 - 12*A*a*c^2*d^3*e^4 - 3*B*a^2*c*d^2*e^5 - 2*A*a^2*c*d*e^6 - B*a^3*e^7)*x + 60*(7*B*c^3*d^7 - 2*A*c^3*d^6*e + B*a*c^2*d^5*e^2 + (7*B*c^3*d^2*e^5 - 2*A*c^3*d*e^6 + B*a*c^2*e^7)*x^5 + 5*(7*B*c^3*d^3*e^4 - 2*A*c^3*d^2*e^5 + B*a*c^2*d*e^6)*x^4 + 10*(7*B*c^3*d^4*e^3 - 2*A*c^3*d^3*e^4 + B*a*c^2*d^2*e^5)*x^3 + 10*(7*B*c^3*d^5*e^2 - 2*A*c^3*d^4*e^3 + B*a*c^2*d^3*e^4)*x^2 + 5*(7*B*c^3*d^6*e - 2*A*c^3*d^5*e^2 + B*a*c^2*d^4*e^3)*x)*log(e*x + d))/(e^13*x^5 + 5*d*e^12*x^4 + 10*d^2*e^11*x^3 + 10*d^3*e^10*x^2 + 5*d^4*e^9*x + d^5*e^8)","B",0
1325,1,695,0,0.411212," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^7,x, algorithm=""fricas"")","\frac{60 \, B c^{3} e^{7} x^{7} + 360 \, B c^{3} d e^{6} x^{6} - 669 \, B c^{3} d^{7} + 147 \, A c^{3} d^{6} e - 30 \, B a c^{2} d^{5} e^{2} - 6 \, A a c^{2} d^{4} e^{3} - 3 \, B a^{2} c d^{3} e^{4} - 3 \, A a^{2} c d^{2} e^{5} - 2 \, B a^{3} d e^{6} - 10 \, A a^{3} e^{7} - 180 \, {\left(2 \, B c^{3} d^{2} e^{5} - 2 \, A c^{3} d e^{6} + B a c^{2} e^{7}\right)} x^{5} - 90 \, {\left(45 \, B c^{3} d^{3} e^{4} - 15 \, A c^{3} d^{2} e^{5} + 5 \, B a c^{2} d e^{6} + A a c^{2} e^{7}\right)} x^{4} - 20 \, {\left(410 \, B c^{3} d^{4} e^{3} - 110 \, A c^{3} d^{3} e^{4} + 30 \, B a c^{2} d^{2} e^{5} + 6 \, A a c^{2} d e^{6} + 3 \, B a^{2} c e^{7}\right)} x^{3} - 15 \, {\left(515 \, B c^{3} d^{5} e^{2} - 125 \, A c^{3} d^{4} e^{3} + 30 \, B a c^{2} d^{3} e^{4} + 6 \, A a c^{2} d^{2} e^{5} + 3 \, B a^{2} c d e^{6} + 3 \, A a^{2} c e^{7}\right)} x^{2} - 6 \, {\left(599 \, B c^{3} d^{6} e - 137 \, A c^{3} d^{5} e^{2} + 30 \, B a c^{2} d^{4} e^{3} + 6 \, A a c^{2} d^{3} e^{4} + 3 \, B a^{2} c d^{2} e^{5} + 3 \, A a^{2} c d e^{6} + 2 \, B a^{3} e^{7}\right)} x - 60 \, {\left(7 \, B c^{3} d^{7} - A c^{3} d^{6} e + {\left(7 \, B c^{3} d e^{6} - A c^{3} e^{7}\right)} x^{6} + 6 \, {\left(7 \, B c^{3} d^{2} e^{5} - A c^{3} d e^{6}\right)} x^{5} + 15 \, {\left(7 \, B c^{3} d^{3} e^{4} - A c^{3} d^{2} e^{5}\right)} x^{4} + 20 \, {\left(7 \, B c^{3} d^{4} e^{3} - A c^{3} d^{3} e^{4}\right)} x^{3} + 15 \, {\left(7 \, B c^{3} d^{5} e^{2} - A c^{3} d^{4} e^{3}\right)} x^{2} + 6 \, {\left(7 \, B c^{3} d^{6} e - A c^{3} d^{5} e^{2}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{14} x^{6} + 6 \, d e^{13} x^{5} + 15 \, d^{2} e^{12} x^{4} + 20 \, d^{3} e^{11} x^{3} + 15 \, d^{4} e^{10} x^{2} + 6 \, d^{5} e^{9} x + d^{6} e^{8}\right)}}"," ",0,"1/60*(60*B*c^3*e^7*x^7 + 360*B*c^3*d*e^6*x^6 - 669*B*c^3*d^7 + 147*A*c^3*d^6*e - 30*B*a*c^2*d^5*e^2 - 6*A*a*c^2*d^4*e^3 - 3*B*a^2*c*d^3*e^4 - 3*A*a^2*c*d^2*e^5 - 2*B*a^3*d*e^6 - 10*A*a^3*e^7 - 180*(2*B*c^3*d^2*e^5 - 2*A*c^3*d*e^6 + B*a*c^2*e^7)*x^5 - 90*(45*B*c^3*d^3*e^4 - 15*A*c^3*d^2*e^5 + 5*B*a*c^2*d*e^6 + A*a*c^2*e^7)*x^4 - 20*(410*B*c^3*d^4*e^3 - 110*A*c^3*d^3*e^4 + 30*B*a*c^2*d^2*e^5 + 6*A*a*c^2*d*e^6 + 3*B*a^2*c*e^7)*x^3 - 15*(515*B*c^3*d^5*e^2 - 125*A*c^3*d^4*e^3 + 30*B*a*c^2*d^3*e^4 + 6*A*a*c^2*d^2*e^5 + 3*B*a^2*c*d*e^6 + 3*A*a^2*c*e^7)*x^2 - 6*(599*B*c^3*d^6*e - 137*A*c^3*d^5*e^2 + 30*B*a*c^2*d^4*e^3 + 6*A*a*c^2*d^3*e^4 + 3*B*a^2*c*d^2*e^5 + 3*A*a^2*c*d*e^6 + 2*B*a^3*e^7)*x - 60*(7*B*c^3*d^7 - A*c^3*d^6*e + (7*B*c^3*d*e^6 - A*c^3*e^7)*x^6 + 6*(7*B*c^3*d^2*e^5 - A*c^3*d*e^6)*x^5 + 15*(7*B*c^3*d^3*e^4 - A*c^3*d^2*e^5)*x^4 + 20*(7*B*c^3*d^4*e^3 - A*c^3*d^3*e^4)*x^3 + 15*(7*B*c^3*d^5*e^2 - A*c^3*d^4*e^3)*x^2 + 6*(7*B*c^3*d^6*e - A*c^3*d^5*e^2)*x)*log(e*x + d))/(e^14*x^6 + 6*d*e^13*x^5 + 15*d^2*e^12*x^4 + 20*d^3*e^11*x^3 + 15*d^4*e^10*x^2 + 6*d^5*e^9*x + d^6*e^8)","B",0
1326,1,624,0,0.411575," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^8,x, algorithm=""fricas"")","\frac{1089 \, B c^{3} d^{7} - 60 \, A c^{3} d^{6} e - 30 \, B a c^{2} d^{5} e^{2} - 12 \, A a c^{2} d^{4} e^{3} - 9 \, B a^{2} c d^{3} e^{4} - 12 \, A a^{2} c d^{2} e^{5} - 10 \, B a^{3} d e^{6} - 60 \, A a^{3} e^{7} + 420 \, {\left(7 \, B c^{3} d e^{6} - A c^{3} e^{7}\right)} x^{6} + 630 \, {\left(21 \, B c^{3} d^{2} e^{5} - 2 \, A c^{3} d e^{6} - B a c^{2} e^{7}\right)} x^{5} + 70 \, {\left(385 \, B c^{3} d^{3} e^{4} - 30 \, A c^{3} d^{2} e^{5} - 15 \, B a c^{2} d e^{6} - 6 \, A a c^{2} e^{7}\right)} x^{4} + 35 \, {\left(875 \, B c^{3} d^{4} e^{3} - 60 \, A c^{3} d^{3} e^{4} - 30 \, B a c^{2} d^{2} e^{5} - 12 \, A a c^{2} d e^{6} - 9 \, B a^{2} c e^{7}\right)} x^{3} + 21 \, {\left(959 \, B c^{3} d^{5} e^{2} - 60 \, A c^{3} d^{4} e^{3} - 30 \, B a c^{2} d^{3} e^{4} - 12 \, A a c^{2} d^{2} e^{5} - 9 \, B a^{2} c d e^{6} - 12 \, A a^{2} c e^{7}\right)} x^{2} + 7 \, {\left(1029 \, B c^{3} d^{6} e - 60 \, A c^{3} d^{5} e^{2} - 30 \, B a c^{2} d^{4} e^{3} - 12 \, A a c^{2} d^{3} e^{4} - 9 \, B a^{2} c d^{2} e^{5} - 12 \, A a^{2} c d e^{6} - 10 \, B a^{3} e^{7}\right)} x + 420 \, {\left(B c^{3} e^{7} x^{7} + 7 \, B c^{3} d e^{6} x^{6} + 21 \, B c^{3} d^{2} e^{5} x^{5} + 35 \, B c^{3} d^{3} e^{4} x^{4} + 35 \, B c^{3} d^{4} e^{3} x^{3} + 21 \, B c^{3} d^{5} e^{2} x^{2} + 7 \, B c^{3} d^{6} e x + B c^{3} d^{7}\right)} \log\left(e x + d\right)}{420 \, {\left(e^{15} x^{7} + 7 \, d e^{14} x^{6} + 21 \, d^{2} e^{13} x^{5} + 35 \, d^{3} e^{12} x^{4} + 35 \, d^{4} e^{11} x^{3} + 21 \, d^{5} e^{10} x^{2} + 7 \, d^{6} e^{9} x + d^{7} e^{8}\right)}}"," ",0,"1/420*(1089*B*c^3*d^7 - 60*A*c^3*d^6*e - 30*B*a*c^2*d^5*e^2 - 12*A*a*c^2*d^4*e^3 - 9*B*a^2*c*d^3*e^4 - 12*A*a^2*c*d^2*e^5 - 10*B*a^3*d*e^6 - 60*A*a^3*e^7 + 420*(7*B*c^3*d*e^6 - A*c^3*e^7)*x^6 + 630*(21*B*c^3*d^2*e^5 - 2*A*c^3*d*e^6 - B*a*c^2*e^7)*x^5 + 70*(385*B*c^3*d^3*e^4 - 30*A*c^3*d^2*e^5 - 15*B*a*c^2*d*e^6 - 6*A*a*c^2*e^7)*x^4 + 35*(875*B*c^3*d^4*e^3 - 60*A*c^3*d^3*e^4 - 30*B*a*c^2*d^2*e^5 - 12*A*a*c^2*d*e^6 - 9*B*a^2*c*e^7)*x^3 + 21*(959*B*c^3*d^5*e^2 - 60*A*c^3*d^4*e^3 - 30*B*a*c^2*d^3*e^4 - 12*A*a*c^2*d^2*e^5 - 9*B*a^2*c*d*e^6 - 12*A*a^2*c*e^7)*x^2 + 7*(1029*B*c^3*d^6*e - 60*A*c^3*d^5*e^2 - 30*B*a*c^2*d^4*e^3 - 12*A*a*c^2*d^3*e^4 - 9*B*a^2*c*d^2*e^5 - 12*A*a^2*c*d*e^6 - 10*B*a^3*e^7)*x + 420*(B*c^3*e^7*x^7 + 7*B*c^3*d*e^6*x^6 + 21*B*c^3*d^2*e^5*x^5 + 35*B*c^3*d^3*e^4*x^4 + 35*B*c^3*d^4*e^3*x^3 + 21*B*c^3*d^5*e^2*x^2 + 7*B*c^3*d^6*e*x + B*c^3*d^7)*log(e*x + d))/(e^15*x^7 + 7*d*e^14*x^6 + 21*d^2*e^13*x^5 + 35*d^3*e^12*x^4 + 35*d^4*e^11*x^3 + 21*d^5*e^10*x^2 + 7*d^6*e^9*x + d^7*e^8)","A",0
1327,1,532,0,0.388256," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{280 \, B c^{3} e^{7} x^{7} + 35 \, B c^{3} d^{7} + 5 \, A c^{3} d^{6} e + 5 \, B a c^{2} d^{5} e^{2} + 3 \, A a c^{2} d^{4} e^{3} + 3 \, B a^{2} c d^{3} e^{4} + 5 \, A a^{2} c d^{2} e^{5} + 5 \, B a^{3} d e^{6} + 35 \, A a^{3} e^{7} + 140 \, {\left(7 \, B c^{3} d e^{6} + A c^{3} e^{7}\right)} x^{6} + 280 \, {\left(7 \, B c^{3} d^{2} e^{5} + A c^{3} d e^{6} + B a c^{2} e^{7}\right)} x^{5} + 70 \, {\left(35 \, B c^{3} d^{3} e^{4} + 5 \, A c^{3} d^{2} e^{5} + 5 \, B a c^{2} d e^{6} + 3 \, A a c^{2} e^{7}\right)} x^{4} + 56 \, {\left(35 \, B c^{3} d^{4} e^{3} + 5 \, A c^{3} d^{3} e^{4} + 5 \, B a c^{2} d^{2} e^{5} + 3 \, A a c^{2} d e^{6} + 3 \, B a^{2} c e^{7}\right)} x^{3} + 28 \, {\left(35 \, B c^{3} d^{5} e^{2} + 5 \, A c^{3} d^{4} e^{3} + 5 \, B a c^{2} d^{3} e^{4} + 3 \, A a c^{2} d^{2} e^{5} + 3 \, B a^{2} c d e^{6} + 5 \, A a^{2} c e^{7}\right)} x^{2} + 8 \, {\left(35 \, B c^{3} d^{6} e + 5 \, A c^{3} d^{5} e^{2} + 5 \, B a c^{2} d^{4} e^{3} + 3 \, A a c^{2} d^{3} e^{4} + 3 \, B a^{2} c d^{2} e^{5} + 5 \, A a^{2} c d e^{6} + 5 \, B a^{3} e^{7}\right)} x}{280 \, {\left(e^{16} x^{8} + 8 \, d e^{15} x^{7} + 28 \, d^{2} e^{14} x^{6} + 56 \, d^{3} e^{13} x^{5} + 70 \, d^{4} e^{12} x^{4} + 56 \, d^{5} e^{11} x^{3} + 28 \, d^{6} e^{10} x^{2} + 8 \, d^{7} e^{9} x + d^{8} e^{8}\right)}}"," ",0,"-1/280*(280*B*c^3*e^7*x^7 + 35*B*c^3*d^7 + 5*A*c^3*d^6*e + 5*B*a*c^2*d^5*e^2 + 3*A*a*c^2*d^4*e^3 + 3*B*a^2*c*d^3*e^4 + 5*A*a^2*c*d^2*e^5 + 5*B*a^3*d*e^6 + 35*A*a^3*e^7 + 140*(7*B*c^3*d*e^6 + A*c^3*e^7)*x^6 + 280*(7*B*c^3*d^2*e^5 + A*c^3*d*e^6 + B*a*c^2*e^7)*x^5 + 70*(35*B*c^3*d^3*e^4 + 5*A*c^3*d^2*e^5 + 5*B*a*c^2*d*e^6 + 3*A*a*c^2*e^7)*x^4 + 56*(35*B*c^3*d^4*e^3 + 5*A*c^3*d^3*e^4 + 5*B*a*c^2*d^2*e^5 + 3*A*a*c^2*d*e^6 + 3*B*a^2*c*e^7)*x^3 + 28*(35*B*c^3*d^5*e^2 + 5*A*c^3*d^4*e^3 + 5*B*a*c^2*d^3*e^4 + 3*A*a*c^2*d^2*e^5 + 3*B*a^2*c*d*e^6 + 5*A*a^2*c*e^7)*x^2 + 8*(35*B*c^3*d^6*e + 5*A*c^3*d^5*e^2 + 5*B*a*c^2*d^4*e^3 + 3*A*a*c^2*d^3*e^4 + 3*B*a^2*c*d^2*e^5 + 5*A*a^2*c*d*e^6 + 5*B*a^3*e^7)*x)/(e^16*x^8 + 8*d*e^15*x^7 + 28*d^2*e^14*x^6 + 56*d^3*e^13*x^5 + 70*d^4*e^12*x^4 + 56*d^5*e^11*x^3 + 28*d^6*e^10*x^2 + 8*d^7*e^9*x + d^8*e^8)","A",0
1328,1,546,0,0.386183," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{1260 \, B c^{3} e^{7} x^{7} + 35 \, B c^{3} d^{7} + 10 \, A c^{3} d^{6} e + 15 \, B a c^{2} d^{5} e^{2} + 12 \, A a c^{2} d^{4} e^{3} + 15 \, B a^{2} c d^{3} e^{4} + 30 \, A a^{2} c d^{2} e^{5} + 35 \, B a^{3} d e^{6} + 280 \, A a^{3} e^{7} + 420 \, {\left(7 \, B c^{3} d e^{6} + 2 \, A c^{3} e^{7}\right)} x^{6} + 630 \, {\left(7 \, B c^{3} d^{2} e^{5} + 2 \, A c^{3} d e^{6} + 3 \, B a c^{2} e^{7}\right)} x^{5} + 126 \, {\left(35 \, B c^{3} d^{3} e^{4} + 10 \, A c^{3} d^{2} e^{5} + 15 \, B a c^{2} d e^{6} + 12 \, A a c^{2} e^{7}\right)} x^{4} + 84 \, {\left(35 \, B c^{3} d^{4} e^{3} + 10 \, A c^{3} d^{3} e^{4} + 15 \, B a c^{2} d^{2} e^{5} + 12 \, A a c^{2} d e^{6} + 15 \, B a^{2} c e^{7}\right)} x^{3} + 36 \, {\left(35 \, B c^{3} d^{5} e^{2} + 10 \, A c^{3} d^{4} e^{3} + 15 \, B a c^{2} d^{3} e^{4} + 12 \, A a c^{2} d^{2} e^{5} + 15 \, B a^{2} c d e^{6} + 30 \, A a^{2} c e^{7}\right)} x^{2} + 9 \, {\left(35 \, B c^{3} d^{6} e + 10 \, A c^{3} d^{5} e^{2} + 15 \, B a c^{2} d^{4} e^{3} + 12 \, A a c^{2} d^{3} e^{4} + 15 \, B a^{2} c d^{2} e^{5} + 30 \, A a^{2} c d e^{6} + 35 \, B a^{3} e^{7}\right)} x}{2520 \, {\left(e^{17} x^{9} + 9 \, d e^{16} x^{8} + 36 \, d^{2} e^{15} x^{7} + 84 \, d^{3} e^{14} x^{6} + 126 \, d^{4} e^{13} x^{5} + 126 \, d^{5} e^{12} x^{4} + 84 \, d^{6} e^{11} x^{3} + 36 \, d^{7} e^{10} x^{2} + 9 \, d^{8} e^{9} x + d^{9} e^{8}\right)}}"," ",0,"-1/2520*(1260*B*c^3*e^7*x^7 + 35*B*c^3*d^7 + 10*A*c^3*d^6*e + 15*B*a*c^2*d^5*e^2 + 12*A*a*c^2*d^4*e^3 + 15*B*a^2*c*d^3*e^4 + 30*A*a^2*c*d^2*e^5 + 35*B*a^3*d*e^6 + 280*A*a^3*e^7 + 420*(7*B*c^3*d*e^6 + 2*A*c^3*e^7)*x^6 + 630*(7*B*c^3*d^2*e^5 + 2*A*c^3*d*e^6 + 3*B*a*c^2*e^7)*x^5 + 126*(35*B*c^3*d^3*e^4 + 10*A*c^3*d^2*e^5 + 15*B*a*c^2*d*e^6 + 12*A*a*c^2*e^7)*x^4 + 84*(35*B*c^3*d^4*e^3 + 10*A*c^3*d^3*e^4 + 15*B*a*c^2*d^2*e^5 + 12*A*a*c^2*d*e^6 + 15*B*a^2*c*e^7)*x^3 + 36*(35*B*c^3*d^5*e^2 + 10*A*c^3*d^4*e^3 + 15*B*a*c^2*d^3*e^4 + 12*A*a*c^2*d^2*e^5 + 15*B*a^2*c*d*e^6 + 30*A*a^2*c*e^7)*x^2 + 9*(35*B*c^3*d^6*e + 10*A*c^3*d^5*e^2 + 15*B*a*c^2*d^4*e^3 + 12*A*a*c^2*d^3*e^4 + 15*B*a^2*c*d^2*e^5 + 30*A*a^2*c*d*e^6 + 35*B*a^3*e^7)*x)/(e^17*x^9 + 9*d*e^16*x^8 + 36*d^2*e^15*x^7 + 84*d^3*e^14*x^6 + 126*d^4*e^13*x^5 + 126*d^5*e^12*x^4 + 84*d^6*e^11*x^3 + 36*d^7*e^10*x^2 + 9*d^8*e^9*x + d^9*e^8)","A",0
1329,1,557,0,0.404253," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{840 \, B c^{3} e^{7} x^{7} + 7 \, B c^{3} d^{7} + 3 \, A c^{3} d^{6} e + 6 \, B a c^{2} d^{5} e^{2} + 6 \, A a c^{2} d^{4} e^{3} + 9 \, B a^{2} c d^{3} e^{4} + 21 \, A a^{2} c d^{2} e^{5} + 28 \, B a^{3} d e^{6} + 252 \, A a^{3} e^{7} + 210 \, {\left(7 \, B c^{3} d e^{6} + 3 \, A c^{3} e^{7}\right)} x^{6} + 252 \, {\left(7 \, B c^{3} d^{2} e^{5} + 3 \, A c^{3} d e^{6} + 6 \, B a c^{2} e^{7}\right)} x^{5} + 210 \, {\left(7 \, B c^{3} d^{3} e^{4} + 3 \, A c^{3} d^{2} e^{5} + 6 \, B a c^{2} d e^{6} + 6 \, A a c^{2} e^{7}\right)} x^{4} + 120 \, {\left(7 \, B c^{3} d^{4} e^{3} + 3 \, A c^{3} d^{3} e^{4} + 6 \, B a c^{2} d^{2} e^{5} + 6 \, A a c^{2} d e^{6} + 9 \, B a^{2} c e^{7}\right)} x^{3} + 45 \, {\left(7 \, B c^{3} d^{5} e^{2} + 3 \, A c^{3} d^{4} e^{3} + 6 \, B a c^{2} d^{3} e^{4} + 6 \, A a c^{2} d^{2} e^{5} + 9 \, B a^{2} c d e^{6} + 21 \, A a^{2} c e^{7}\right)} x^{2} + 10 \, {\left(7 \, B c^{3} d^{6} e + 3 \, A c^{3} d^{5} e^{2} + 6 \, B a c^{2} d^{4} e^{3} + 6 \, A a c^{2} d^{3} e^{4} + 9 \, B a^{2} c d^{2} e^{5} + 21 \, A a^{2} c d e^{6} + 28 \, B a^{3} e^{7}\right)} x}{2520 \, {\left(e^{18} x^{10} + 10 \, d e^{17} x^{9} + 45 \, d^{2} e^{16} x^{8} + 120 \, d^{3} e^{15} x^{7} + 210 \, d^{4} e^{14} x^{6} + 252 \, d^{5} e^{13} x^{5} + 210 \, d^{6} e^{12} x^{4} + 120 \, d^{7} e^{11} x^{3} + 45 \, d^{8} e^{10} x^{2} + 10 \, d^{9} e^{9} x + d^{10} e^{8}\right)}}"," ",0,"-1/2520*(840*B*c^3*e^7*x^7 + 7*B*c^3*d^7 + 3*A*c^3*d^6*e + 6*B*a*c^2*d^5*e^2 + 6*A*a*c^2*d^4*e^3 + 9*B*a^2*c*d^3*e^4 + 21*A*a^2*c*d^2*e^5 + 28*B*a^3*d*e^6 + 252*A*a^3*e^7 + 210*(7*B*c^3*d*e^6 + 3*A*c^3*e^7)*x^6 + 252*(7*B*c^3*d^2*e^5 + 3*A*c^3*d*e^6 + 6*B*a*c^2*e^7)*x^5 + 210*(7*B*c^3*d^3*e^4 + 3*A*c^3*d^2*e^5 + 6*B*a*c^2*d*e^6 + 6*A*a*c^2*e^7)*x^4 + 120*(7*B*c^3*d^4*e^3 + 3*A*c^3*d^3*e^4 + 6*B*a*c^2*d^2*e^5 + 6*A*a*c^2*d*e^6 + 9*B*a^2*c*e^7)*x^3 + 45*(7*B*c^3*d^5*e^2 + 3*A*c^3*d^4*e^3 + 6*B*a*c^2*d^3*e^4 + 6*A*a*c^2*d^2*e^5 + 9*B*a^2*c*d*e^6 + 21*A*a^2*c*e^7)*x^2 + 10*(7*B*c^3*d^6*e + 3*A*c^3*d^5*e^2 + 6*B*a*c^2*d^4*e^3 + 6*A*a*c^2*d^3*e^4 + 9*B*a^2*c*d^2*e^5 + 21*A*a^2*c*d*e^6 + 28*B*a^3*e^7)*x)/(e^18*x^10 + 10*d*e^17*x^9 + 45*d^2*e^16*x^8 + 120*d^3*e^15*x^7 + 210*d^4*e^14*x^6 + 252*d^5*e^13*x^5 + 210*d^6*e^12*x^4 + 120*d^7*e^11*x^3 + 45*d^8*e^10*x^2 + 10*d^9*e^9*x + d^10*e^8)","A",0
1330,1,550,0,0.440758," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, B a c^{2} e^{4} x^{4} + 4 \, {\left(4 \, B a c^{2} d e^{3} + A a c^{2} e^{4}\right)} x^{3} + 6 \, {\left(6 \, B a c^{2} d^{2} e^{2} + 4 \, A a c^{2} d e^{3} - B a^{2} c e^{4}\right)} x^{2} - 6 \, {\left(A c^{2} d^{4} - 4 \, B a c d^{3} e - 6 \, A a c d^{2} e^{2} + 4 \, B a^{2} d e^{3} + A a^{2} e^{4}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 12 \, {\left(4 \, B a c^{2} d^{3} e + 6 \, A a c^{2} d^{2} e^{2} - 4 \, B a^{2} c d e^{3} - A a^{2} c e^{4}\right)} x + 6 \, {\left(B a c^{2} d^{4} + 4 \, A a c^{2} d^{3} e - 6 \, B a^{2} c d^{2} e^{2} - 4 \, A a^{2} c d e^{3} + B a^{3} e^{4}\right)} \log\left(c x^{2} + a\right)}{12 \, a c^{3}}, \frac{3 \, B a c^{2} e^{4} x^{4} + 4 \, {\left(4 \, B a c^{2} d e^{3} + A a c^{2} e^{4}\right)} x^{3} + 6 \, {\left(6 \, B a c^{2} d^{2} e^{2} + 4 \, A a c^{2} d e^{3} - B a^{2} c e^{4}\right)} x^{2} + 12 \, {\left(A c^{2} d^{4} - 4 \, B a c d^{3} e - 6 \, A a c d^{2} e^{2} + 4 \, B a^{2} d e^{3} + A a^{2} e^{4}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 12 \, {\left(4 \, B a c^{2} d^{3} e + 6 \, A a c^{2} d^{2} e^{2} - 4 \, B a^{2} c d e^{3} - A a^{2} c e^{4}\right)} x + 6 \, {\left(B a c^{2} d^{4} + 4 \, A a c^{2} d^{3} e - 6 \, B a^{2} c d^{2} e^{2} - 4 \, A a^{2} c d e^{3} + B a^{3} e^{4}\right)} \log\left(c x^{2} + a\right)}{12 \, a c^{3}}\right]"," ",0,"[1/12*(3*B*a*c^2*e^4*x^4 + 4*(4*B*a*c^2*d*e^3 + A*a*c^2*e^4)*x^3 + 6*(6*B*a*c^2*d^2*e^2 + 4*A*a*c^2*d*e^3 - B*a^2*c*e^4)*x^2 - 6*(A*c^2*d^4 - 4*B*a*c*d^3*e - 6*A*a*c*d^2*e^2 + 4*B*a^2*d*e^3 + A*a^2*e^4)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 12*(4*B*a*c^2*d^3*e + 6*A*a*c^2*d^2*e^2 - 4*B*a^2*c*d*e^3 - A*a^2*c*e^4)*x + 6*(B*a*c^2*d^4 + 4*A*a*c^2*d^3*e - 6*B*a^2*c*d^2*e^2 - 4*A*a^2*c*d*e^3 + B*a^3*e^4)*log(c*x^2 + a))/(a*c^3), 1/12*(3*B*a*c^2*e^4*x^4 + 4*(4*B*a*c^2*d*e^3 + A*a*c^2*e^4)*x^3 + 6*(6*B*a*c^2*d^2*e^2 + 4*A*a*c^2*d*e^3 - B*a^2*c*e^4)*x^2 + 12*(A*c^2*d^4 - 4*B*a*c*d^3*e - 6*A*a*c*d^2*e^2 + 4*B*a^2*d*e^3 + A*a^2*e^4)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 12*(4*B*a*c^2*d^3*e + 6*A*a*c^2*d^2*e^2 - 4*B*a^2*c*d*e^3 - A*a^2*c*e^4)*x + 6*(B*a*c^2*d^4 + 4*A*a*c^2*d^3*e - 6*B*a^2*c*d^2*e^2 - 4*A*a^2*c*d*e^3 + B*a^3*e^4)*log(c*x^2 + a))/(a*c^3)]","A",0
1331,1,398,0,0.420220," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, B a c^{2} e^{3} x^{3} + 3 \, {\left(3 \, B a c^{2} d e^{2} + A a c^{2} e^{3}\right)} x^{2} - 3 \, {\left(A c^{2} d^{3} - 3 \, B a c d^{2} e - 3 \, A a c d e^{2} + B a^{2} e^{3}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 6 \, {\left(3 \, B a c^{2} d^{2} e + 3 \, A a c^{2} d e^{2} - B a^{2} c e^{3}\right)} x + 3 \, {\left(B a c^{2} d^{3} + 3 \, A a c^{2} d^{2} e - 3 \, B a^{2} c d e^{2} - A a^{2} c e^{3}\right)} \log\left(c x^{2} + a\right)}{6 \, a c^{3}}, \frac{2 \, B a c^{2} e^{3} x^{3} + 3 \, {\left(3 \, B a c^{2} d e^{2} + A a c^{2} e^{3}\right)} x^{2} + 6 \, {\left(A c^{2} d^{3} - 3 \, B a c d^{2} e - 3 \, A a c d e^{2} + B a^{2} e^{3}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 6 \, {\left(3 \, B a c^{2} d^{2} e + 3 \, A a c^{2} d e^{2} - B a^{2} c e^{3}\right)} x + 3 \, {\left(B a c^{2} d^{3} + 3 \, A a c^{2} d^{2} e - 3 \, B a^{2} c d e^{2} - A a^{2} c e^{3}\right)} \log\left(c x^{2} + a\right)}{6 \, a c^{3}}\right]"," ",0,"[1/6*(2*B*a*c^2*e^3*x^3 + 3*(3*B*a*c^2*d*e^2 + A*a*c^2*e^3)*x^2 - 3*(A*c^2*d^3 - 3*B*a*c*d^2*e - 3*A*a*c*d*e^2 + B*a^2*e^3)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 6*(3*B*a*c^2*d^2*e + 3*A*a*c^2*d*e^2 - B*a^2*c*e^3)*x + 3*(B*a*c^2*d^3 + 3*A*a*c^2*d^2*e - 3*B*a^2*c*d*e^2 - A*a^2*c*e^3)*log(c*x^2 + a))/(a*c^3), 1/6*(2*B*a*c^2*e^3*x^3 + 3*(3*B*a*c^2*d*e^2 + A*a*c^2*e^3)*x^2 + 6*(A*c^2*d^3 - 3*B*a*c*d^2*e - 3*A*a*c*d*e^2 + B*a^2*e^3)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 6*(3*B*a*c^2*d^2*e + 3*A*a*c^2*d*e^2 - B*a^2*c*e^3)*x + 3*(B*a*c^2*d^3 + 3*A*a*c^2*d^2*e - 3*B*a^2*c*d*e^2 - A*a^2*c*e^3)*log(c*x^2 + a))/(a*c^3)]","A",0
1332,1,235,0,0.422678," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{B a c e^{2} x^{2} + {\left(A c d^{2} - 2 \, B a d e - A a e^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(2 \, B a c d e + A a c e^{2}\right)} x + {\left(B a c d^{2} + 2 \, A a c d e - B a^{2} e^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, a c^{2}}, \frac{B a c e^{2} x^{2} + 2 \, {\left(A c d^{2} - 2 \, B a d e - A a e^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 2 \, {\left(2 \, B a c d e + A a c e^{2}\right)} x + {\left(B a c d^{2} + 2 \, A a c d e - B a^{2} e^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, a c^{2}}\right]"," ",0,"[1/2*(B*a*c*e^2*x^2 + (A*c*d^2 - 2*B*a*d*e - A*a*e^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(2*B*a*c*d*e + A*a*c*e^2)*x + (B*a*c*d^2 + 2*A*a*c*d*e - B*a^2*e^2)*log(c*x^2 + a))/(a*c^2), 1/2*(B*a*c*e^2*x^2 + 2*(A*c*d^2 - 2*B*a*d*e - A*a*e^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 2*(2*B*a*c*d*e + A*a*c*e^2)*x + (B*a*c*d^2 + 2*A*a*c*d*e - B*a^2*e^2)*log(c*x^2 + a))/(a*c^2)]","A",0
1333,1,147,0,0.429260," ","integrate((B*x+A)*(e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, B a c e x + {\left(A c d - B a e\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + {\left(B a c d + A a c e\right)} \log\left(c x^{2} + a\right)}{2 \, a c^{2}}, \frac{2 \, B a c e x + 2 \, {\left(A c d - B a e\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(B a c d + A a c e\right)} \log\left(c x^{2} + a\right)}{2 \, a c^{2}}\right]"," ",0,"[1/2*(2*B*a*c*e*x + (A*c*d - B*a*e)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + (B*a*c*d + A*a*c*e)*log(c*x^2 + a))/(a*c^2), 1/2*(2*B*a*c*e*x + 2*(A*c*d - B*a*e)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (B*a*c*d + A*a*c*e)*log(c*x^2 + a))/(a*c^2)]","A",0
1334,1,98,0,0.409078," ","integrate((B*x+A)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{B a \log\left(c x^{2} + a\right) - \sqrt{-a c} A \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{2 \, a c}, \frac{B a \log\left(c x^{2} + a\right) + 2 \, \sqrt{a c} A \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{2 \, a c}\right]"," ",0,"[1/2*(B*a*log(c*x^2 + a) - sqrt(-a*c)*A*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a*c), 1/2*(B*a*log(c*x^2 + a) + 2*sqrt(a*c)*A*arctan(sqrt(a*c)*x/a))/(a*c)]","A",0
1335,1,200,0,1.347591," ","integrate((B*x+A)/(e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[-\frac{{\left(A c d + B a e\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - {\left(B a c d - A a c e\right)} \log\left(c x^{2} + a\right) + 2 \, {\left(B a c d - A a c e\right)} \log\left(e x + d\right)}{2 \, {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)}}, \frac{2 \, {\left(A c d + B a e\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(B a c d - A a c e\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(B a c d - A a c e\right)} \log\left(e x + d\right)}{2 \, {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)}}\right]"," ",0,"[-1/2*((A*c*d + B*a*e)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - (B*a*c*d - A*a*c*e)*log(c*x^2 + a) + 2*(B*a*c*d - A*a*c*e)*log(e*x + d))/(a*c^2*d^2 + a^2*c*e^2), 1/2*(2*(A*c*d + B*a*e)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (B*a*c*d - A*a*c*e)*log(c*x^2 + a) - 2*(B*a*c*d - A*a*c*e)*log(e*x + d))/(a*c^2*d^2 + a^2*c*e^2)]","A",0
1336,1,562,0,6.944085," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, B c d^{3} - 2 \, A c d^{2} e + 2 \, B a d e^{2} - 2 \, A a e^{3} - {\left(A c d^{3} + 2 \, B a d^{2} e - A a d e^{2} + {\left(A c d^{2} e + 2 \, B a d e^{2} - A a e^{3}\right)} x\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + {\left(B c d^{3} - 2 \, A c d^{2} e - B a d e^{2} + {\left(B c d^{2} e - 2 \, A c d e^{2} - B a e^{3}\right)} x\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(B c d^{3} - 2 \, A c d^{2} e - B a d e^{2} + {\left(B c d^{2} e - 2 \, A c d e^{2} - B a e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)}}, \frac{2 \, B c d^{3} - 2 \, A c d^{2} e + 2 \, B a d e^{2} - 2 \, A a e^{3} + 2 \, {\left(A c d^{3} + 2 \, B a d^{2} e - A a d e^{2} + {\left(A c d^{2} e + 2 \, B a d e^{2} - A a e^{3}\right)} x\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + {\left(B c d^{3} - 2 \, A c d^{2} e - B a d e^{2} + {\left(B c d^{2} e - 2 \, A c d e^{2} - B a e^{3}\right)} x\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(B c d^{3} - 2 \, A c d^{2} e - B a d e^{2} + {\left(B c d^{2} e - 2 \, A c d e^{2} - B a e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[1/2*(2*B*c*d^3 - 2*A*c*d^2*e + 2*B*a*d*e^2 - 2*A*a*e^3 - (A*c*d^3 + 2*B*a*d^2*e - A*a*d*e^2 + (A*c*d^2*e + 2*B*a*d*e^2 - A*a*e^3)*x)*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + (B*c*d^3 - 2*A*c*d^2*e - B*a*d*e^2 + (B*c*d^2*e - 2*A*c*d*e^2 - B*a*e^3)*x)*log(c*x^2 + a) - 2*(B*c*d^3 - 2*A*c*d^2*e - B*a*d*e^2 + (B*c*d^2*e - 2*A*c*d*e^2 - B*a*e^3)*x)*log(e*x + d))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x), 1/2*(2*B*c*d^3 - 2*A*c*d^2*e + 2*B*a*d*e^2 - 2*A*a*e^3 + 2*(A*c*d^3 + 2*B*a*d^2*e - A*a*d*e^2 + (A*c*d^2*e + 2*B*a*d*e^2 - A*a*e^3)*x)*sqrt(c/a)*arctan(x*sqrt(c/a)) + (B*c*d^3 - 2*A*c*d^2*e - B*a*d*e^2 + (B*c*d^2*e - 2*A*c*d*e^2 - B*a*e^3)*x)*log(c*x^2 + a) - 2*(B*c*d^3 - 2*A*c*d^2*e - B*a*d*e^2 + (B*c*d^2*e - 2*A*c*d*e^2 - B*a*e^3)*x)*log(e*x + d))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)]","A",0
1337,1,1350,0,35.124406," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, B c^{2} d^{5} - 5 \, A c^{2} d^{4} e + 2 \, B a c d^{3} e^{2} - 6 \, A a c d^{2} e^{3} - B a^{2} d e^{4} - A a^{2} e^{5} - {\left(A c^{2} d^{5} + 3 \, B a c d^{4} e - 3 \, A a c d^{3} e^{2} - B a^{2} d^{2} e^{3} + {\left(A c^{2} d^{3} e^{2} + 3 \, B a c d^{2} e^{3} - 3 \, A a c d e^{4} - B a^{2} e^{5}\right)} x^{2} + 2 \, {\left(A c^{2} d^{4} e + 3 \, B a c d^{3} e^{2} - 3 \, A a c d^{2} e^{3} - B a^{2} d e^{4}\right)} x\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 2 \, {\left(B c^{2} d^{4} e - 2 \, A c^{2} d^{3} e^{2} - 2 \, A a c d e^{4} - B a^{2} e^{5}\right)} x + {\left(B c^{2} d^{5} - 3 \, A c^{2} d^{4} e - 3 \, B a c d^{3} e^{2} + A a c d^{2} e^{3} + {\left(B c^{2} d^{3} e^{2} - 3 \, A c^{2} d^{2} e^{3} - 3 \, B a c d e^{4} + A a c e^{5}\right)} x^{2} + 2 \, {\left(B c^{2} d^{4} e - 3 \, A c^{2} d^{3} e^{2} - 3 \, B a c d^{2} e^{3} + A a c d e^{4}\right)} x\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(B c^{2} d^{5} - 3 \, A c^{2} d^{4} e - 3 \, B a c d^{3} e^{2} + A a c d^{2} e^{3} + {\left(B c^{2} d^{3} e^{2} - 3 \, A c^{2} d^{2} e^{3} - 3 \, B a c d e^{4} + A a c e^{5}\right)} x^{2} + 2 \, {\left(B c^{2} d^{4} e - 3 \, A c^{2} d^{3} e^{2} - 3 \, B a c d^{2} e^{3} + A a c d e^{4}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{3} d^{8} + 3 \, a c^{2} d^{6} e^{2} + 3 \, a^{2} c d^{4} e^{4} + a^{3} d^{2} e^{6} + {\left(c^{3} d^{6} e^{2} + 3 \, a c^{2} d^{4} e^{4} + 3 \, a^{2} c d^{2} e^{6} + a^{3} e^{8}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e + 3 \, a c^{2} d^{5} e^{3} + 3 \, a^{2} c d^{3} e^{5} + a^{3} d e^{7}\right)} x\right)}}, \frac{3 \, B c^{2} d^{5} - 5 \, A c^{2} d^{4} e + 2 \, B a c d^{3} e^{2} - 6 \, A a c d^{2} e^{3} - B a^{2} d e^{4} - A a^{2} e^{5} + 2 \, {\left(A c^{2} d^{5} + 3 \, B a c d^{4} e - 3 \, A a c d^{3} e^{2} - B a^{2} d^{2} e^{3} + {\left(A c^{2} d^{3} e^{2} + 3 \, B a c d^{2} e^{3} - 3 \, A a c d e^{4} - B a^{2} e^{5}\right)} x^{2} + 2 \, {\left(A c^{2} d^{4} e + 3 \, B a c d^{3} e^{2} - 3 \, A a c d^{2} e^{3} - B a^{2} d e^{4}\right)} x\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + 2 \, {\left(B c^{2} d^{4} e - 2 \, A c^{2} d^{3} e^{2} - 2 \, A a c d e^{4} - B a^{2} e^{5}\right)} x + {\left(B c^{2} d^{5} - 3 \, A c^{2} d^{4} e - 3 \, B a c d^{3} e^{2} + A a c d^{2} e^{3} + {\left(B c^{2} d^{3} e^{2} - 3 \, A c^{2} d^{2} e^{3} - 3 \, B a c d e^{4} + A a c e^{5}\right)} x^{2} + 2 \, {\left(B c^{2} d^{4} e - 3 \, A c^{2} d^{3} e^{2} - 3 \, B a c d^{2} e^{3} + A a c d e^{4}\right)} x\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(B c^{2} d^{5} - 3 \, A c^{2} d^{4} e - 3 \, B a c d^{3} e^{2} + A a c d^{2} e^{3} + {\left(B c^{2} d^{3} e^{2} - 3 \, A c^{2} d^{2} e^{3} - 3 \, B a c d e^{4} + A a c e^{5}\right)} x^{2} + 2 \, {\left(B c^{2} d^{4} e - 3 \, A c^{2} d^{3} e^{2} - 3 \, B a c d^{2} e^{3} + A a c d e^{4}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{3} d^{8} + 3 \, a c^{2} d^{6} e^{2} + 3 \, a^{2} c d^{4} e^{4} + a^{3} d^{2} e^{6} + {\left(c^{3} d^{6} e^{2} + 3 \, a c^{2} d^{4} e^{4} + 3 \, a^{2} c d^{2} e^{6} + a^{3} e^{8}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e + 3 \, a c^{2} d^{5} e^{3} + 3 \, a^{2} c d^{3} e^{5} + a^{3} d e^{7}\right)} x\right)}}\right]"," ",0,"[1/2*(3*B*c^2*d^5 - 5*A*c^2*d^4*e + 2*B*a*c*d^3*e^2 - 6*A*a*c*d^2*e^3 - B*a^2*d*e^4 - A*a^2*e^5 - (A*c^2*d^5 + 3*B*a*c*d^4*e - 3*A*a*c*d^3*e^2 - B*a^2*d^2*e^3 + (A*c^2*d^3*e^2 + 3*B*a*c*d^2*e^3 - 3*A*a*c*d*e^4 - B*a^2*e^5)*x^2 + 2*(A*c^2*d^4*e + 3*B*a*c*d^3*e^2 - 3*A*a*c*d^2*e^3 - B*a^2*d*e^4)*x)*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 2*(B*c^2*d^4*e - 2*A*c^2*d^3*e^2 - 2*A*a*c*d*e^4 - B*a^2*e^5)*x + (B*c^2*d^5 - 3*A*c^2*d^4*e - 3*B*a*c*d^3*e^2 + A*a*c*d^2*e^3 + (B*c^2*d^3*e^2 - 3*A*c^2*d^2*e^3 - 3*B*a*c*d*e^4 + A*a*c*e^5)*x^2 + 2*(B*c^2*d^4*e - 3*A*c^2*d^3*e^2 - 3*B*a*c*d^2*e^3 + A*a*c*d*e^4)*x)*log(c*x^2 + a) - 2*(B*c^2*d^5 - 3*A*c^2*d^4*e - 3*B*a*c*d^3*e^2 + A*a*c*d^2*e^3 + (B*c^2*d^3*e^2 - 3*A*c^2*d^2*e^3 - 3*B*a*c*d*e^4 + A*a*c*e^5)*x^2 + 2*(B*c^2*d^4*e - 3*A*c^2*d^3*e^2 - 3*B*a*c*d^2*e^3 + A*a*c*d*e^4)*x)*log(e*x + d))/(c^3*d^8 + 3*a*c^2*d^6*e^2 + 3*a^2*c*d^4*e^4 + a^3*d^2*e^6 + (c^3*d^6*e^2 + 3*a*c^2*d^4*e^4 + 3*a^2*c*d^2*e^6 + a^3*e^8)*x^2 + 2*(c^3*d^7*e + 3*a*c^2*d^5*e^3 + 3*a^2*c*d^3*e^5 + a^3*d*e^7)*x), 1/2*(3*B*c^2*d^5 - 5*A*c^2*d^4*e + 2*B*a*c*d^3*e^2 - 6*A*a*c*d^2*e^3 - B*a^2*d*e^4 - A*a^2*e^5 + 2*(A*c^2*d^5 + 3*B*a*c*d^4*e - 3*A*a*c*d^3*e^2 - B*a^2*d^2*e^3 + (A*c^2*d^3*e^2 + 3*B*a*c*d^2*e^3 - 3*A*a*c*d*e^4 - B*a^2*e^5)*x^2 + 2*(A*c^2*d^4*e + 3*B*a*c*d^3*e^2 - 3*A*a*c*d^2*e^3 - B*a^2*d*e^4)*x)*sqrt(c/a)*arctan(x*sqrt(c/a)) + 2*(B*c^2*d^4*e - 2*A*c^2*d^3*e^2 - 2*A*a*c*d*e^4 - B*a^2*e^5)*x + (B*c^2*d^5 - 3*A*c^2*d^4*e - 3*B*a*c*d^3*e^2 + A*a*c*d^2*e^3 + (B*c^2*d^3*e^2 - 3*A*c^2*d^2*e^3 - 3*B*a*c*d*e^4 + A*a*c*e^5)*x^2 + 2*(B*c^2*d^4*e - 3*A*c^2*d^3*e^2 - 3*B*a*c*d^2*e^3 + A*a*c*d*e^4)*x)*log(c*x^2 + a) - 2*(B*c^2*d^5 - 3*A*c^2*d^4*e - 3*B*a*c*d^3*e^2 + A*a*c*d^2*e^3 + (B*c^2*d^3*e^2 - 3*A*c^2*d^2*e^3 - 3*B*a*c*d*e^4 + A*a*c*e^5)*x^2 + 2*(B*c^2*d^4*e - 3*A*c^2*d^3*e^2 - 3*B*a*c*d^2*e^3 + A*a*c*d*e^4)*x)*log(e*x + d))/(c^3*d^8 + 3*a*c^2*d^6*e^2 + 3*a^2*c*d^4*e^4 + a^3*d^2*e^6 + (c^3*d^6*e^2 + 3*a*c^2*d^4*e^4 + 3*a^2*c*d^2*e^6 + a^3*e^8)*x^2 + 2*(c^3*d^7*e + 3*a*c^2*d^5*e^3 + 3*a^2*c*d^3*e^5 + a^3*d*e^7)*x)]","B",0
1338,1,1190,0,0.432153," ","integrate((B*x+A)*(e*x+d)^5/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, B a^{2} c^{3} e^{5} x^{5} - 6 \, B a^{2} c^{3} d^{5} - 30 \, A a^{2} c^{3} d^{4} e + 60 \, B a^{3} c^{2} d^{3} e^{2} + 60 \, A a^{3} c^{2} d^{2} e^{3} - 30 \, B a^{4} c d e^{4} - 6 \, A a^{4} c e^{5} + 6 \, {\left(5 \, B a^{2} c^{3} d e^{4} + A a^{2} c^{3} e^{5}\right)} x^{4} + 20 \, {\left(6 \, B a^{2} c^{3} d^{2} e^{3} + 3 \, A a^{2} c^{3} d e^{4} - B a^{3} c^{2} e^{5}\right)} x^{3} + 6 \, {\left(5 \, B a^{3} c^{2} d e^{4} + A a^{3} c^{2} e^{5}\right)} x^{2} - 3 \, {\left(A a c^{3} d^{5} + 5 \, B a^{2} c^{2} d^{4} e + 10 \, A a^{2} c^{2} d^{3} e^{2} - 30 \, B a^{3} c d^{2} e^{3} - 15 \, A a^{3} c d e^{4} + 5 \, B a^{4} e^{5} + {\left(A c^{4} d^{5} + 5 \, B a c^{3} d^{4} e + 10 \, A a c^{3} d^{3} e^{2} - 30 \, B a^{2} c^{2} d^{2} e^{3} - 15 \, A a^{2} c^{2} d e^{4} + 5 \, B a^{3} c e^{5}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 6 \, {\left(A a c^{4} d^{5} - 5 \, B a^{2} c^{3} d^{4} e - 10 \, A a^{2} c^{3} d^{3} e^{2} + 30 \, B a^{3} c^{2} d^{2} e^{3} + 15 \, A a^{3} c^{2} d e^{4} - 5 \, B a^{4} c e^{5}\right)} x + 12 \, {\left(5 \, B a^{3} c^{2} d^{3} e^{2} + 5 \, A a^{3} c^{2} d^{2} e^{3} - 5 \, B a^{4} c d e^{4} - A a^{4} c e^{5} + {\left(5 \, B a^{2} c^{3} d^{3} e^{2} + 5 \, A a^{2} c^{3} d^{2} e^{3} - 5 \, B a^{3} c^{2} d e^{4} - A a^{3} c^{2} e^{5}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{12 \, {\left(a^{2} c^{5} x^{2} + a^{3} c^{4}\right)}}, \frac{2 \, B a^{2} c^{3} e^{5} x^{5} - 3 \, B a^{2} c^{3} d^{5} - 15 \, A a^{2} c^{3} d^{4} e + 30 \, B a^{3} c^{2} d^{3} e^{2} + 30 \, A a^{3} c^{2} d^{2} e^{3} - 15 \, B a^{4} c d e^{4} - 3 \, A a^{4} c e^{5} + 3 \, {\left(5 \, B a^{2} c^{3} d e^{4} + A a^{2} c^{3} e^{5}\right)} x^{4} + 10 \, {\left(6 \, B a^{2} c^{3} d^{2} e^{3} + 3 \, A a^{2} c^{3} d e^{4} - B a^{3} c^{2} e^{5}\right)} x^{3} + 3 \, {\left(5 \, B a^{3} c^{2} d e^{4} + A a^{3} c^{2} e^{5}\right)} x^{2} + 3 \, {\left(A a c^{3} d^{5} + 5 \, B a^{2} c^{2} d^{4} e + 10 \, A a^{2} c^{2} d^{3} e^{2} - 30 \, B a^{3} c d^{2} e^{3} - 15 \, A a^{3} c d e^{4} + 5 \, B a^{4} e^{5} + {\left(A c^{4} d^{5} + 5 \, B a c^{3} d^{4} e + 10 \, A a c^{3} d^{3} e^{2} - 30 \, B a^{2} c^{2} d^{2} e^{3} - 15 \, A a^{2} c^{2} d e^{4} + 5 \, B a^{3} c e^{5}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 3 \, {\left(A a c^{4} d^{5} - 5 \, B a^{2} c^{3} d^{4} e - 10 \, A a^{2} c^{3} d^{3} e^{2} + 30 \, B a^{3} c^{2} d^{2} e^{3} + 15 \, A a^{3} c^{2} d e^{4} - 5 \, B a^{4} c e^{5}\right)} x + 6 \, {\left(5 \, B a^{3} c^{2} d^{3} e^{2} + 5 \, A a^{3} c^{2} d^{2} e^{3} - 5 \, B a^{4} c d e^{4} - A a^{4} c e^{5} + {\left(5 \, B a^{2} c^{3} d^{3} e^{2} + 5 \, A a^{2} c^{3} d^{2} e^{3} - 5 \, B a^{3} c^{2} d e^{4} - A a^{3} c^{2} e^{5}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{6 \, {\left(a^{2} c^{5} x^{2} + a^{3} c^{4}\right)}}\right]"," ",0,"[1/12*(4*B*a^2*c^3*e^5*x^5 - 6*B*a^2*c^3*d^5 - 30*A*a^2*c^3*d^4*e + 60*B*a^3*c^2*d^3*e^2 + 60*A*a^3*c^2*d^2*e^3 - 30*B*a^4*c*d*e^4 - 6*A*a^4*c*e^5 + 6*(5*B*a^2*c^3*d*e^4 + A*a^2*c^3*e^5)*x^4 + 20*(6*B*a^2*c^3*d^2*e^3 + 3*A*a^2*c^3*d*e^4 - B*a^3*c^2*e^5)*x^3 + 6*(5*B*a^3*c^2*d*e^4 + A*a^3*c^2*e^5)*x^2 - 3*(A*a*c^3*d^5 + 5*B*a^2*c^2*d^4*e + 10*A*a^2*c^2*d^3*e^2 - 30*B*a^3*c*d^2*e^3 - 15*A*a^3*c*d*e^4 + 5*B*a^4*e^5 + (A*c^4*d^5 + 5*B*a*c^3*d^4*e + 10*A*a*c^3*d^3*e^2 - 30*B*a^2*c^2*d^2*e^3 - 15*A*a^2*c^2*d*e^4 + 5*B*a^3*c*e^5)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 6*(A*a*c^4*d^5 - 5*B*a^2*c^3*d^4*e - 10*A*a^2*c^3*d^3*e^2 + 30*B*a^3*c^2*d^2*e^3 + 15*A*a^3*c^2*d*e^4 - 5*B*a^4*c*e^5)*x + 12*(5*B*a^3*c^2*d^3*e^2 + 5*A*a^3*c^2*d^2*e^3 - 5*B*a^4*c*d*e^4 - A*a^4*c*e^5 + (5*B*a^2*c^3*d^3*e^2 + 5*A*a^2*c^3*d^2*e^3 - 5*B*a^3*c^2*d*e^4 - A*a^3*c^2*e^5)*x^2)*log(c*x^2 + a))/(a^2*c^5*x^2 + a^3*c^4), 1/6*(2*B*a^2*c^3*e^5*x^5 - 3*B*a^2*c^3*d^5 - 15*A*a^2*c^3*d^4*e + 30*B*a^3*c^2*d^3*e^2 + 30*A*a^3*c^2*d^2*e^3 - 15*B*a^4*c*d*e^4 - 3*A*a^4*c*e^5 + 3*(5*B*a^2*c^3*d*e^4 + A*a^2*c^3*e^5)*x^4 + 10*(6*B*a^2*c^3*d^2*e^3 + 3*A*a^2*c^3*d*e^4 - B*a^3*c^2*e^5)*x^3 + 3*(5*B*a^3*c^2*d*e^4 + A*a^3*c^2*e^5)*x^2 + 3*(A*a*c^3*d^5 + 5*B*a^2*c^2*d^4*e + 10*A*a^2*c^2*d^3*e^2 - 30*B*a^3*c*d^2*e^3 - 15*A*a^3*c*d*e^4 + 5*B*a^4*e^5 + (A*c^4*d^5 + 5*B*a*c^3*d^4*e + 10*A*a*c^3*d^3*e^2 - 30*B*a^2*c^2*d^2*e^3 - 15*A*a^2*c^2*d*e^4 + 5*B*a^3*c*e^5)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 3*(A*a*c^4*d^5 - 5*B*a^2*c^3*d^4*e - 10*A*a^2*c^3*d^3*e^2 + 30*B*a^3*c^2*d^2*e^3 + 15*A*a^3*c^2*d*e^4 - 5*B*a^4*c*e^5)*x + 6*(5*B*a^3*c^2*d^3*e^2 + 5*A*a^3*c^2*d^2*e^3 - 5*B*a^4*c*d*e^4 - A*a^4*c*e^5 + (5*B*a^2*c^3*d^3*e^2 + 5*A*a^2*c^3*d^2*e^3 - 5*B*a^3*c^2*d*e^4 - A*a^3*c^2*e^5)*x^2)*log(c*x^2 + a))/(a^2*c^5*x^2 + a^3*c^4)]","B",0
1339,1,849,0,0.426053," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, B a^{2} c^{2} e^{4} x^{4} + 2 \, B a^{3} c e^{4} x^{2} - 2 \, B a^{2} c^{2} d^{4} - 8 \, A a^{2} c^{2} d^{3} e + 12 \, B a^{3} c d^{2} e^{2} + 8 \, A a^{3} c d e^{3} - 2 \, B a^{4} e^{4} + 4 \, {\left(4 \, B a^{2} c^{2} d e^{3} + A a^{2} c^{2} e^{4}\right)} x^{3} + {\left(A a c^{2} d^{4} + 4 \, B a^{2} c d^{3} e + 6 \, A a^{2} c d^{2} e^{2} - 12 \, B a^{3} d e^{3} - 3 \, A a^{3} e^{4} + {\left(A c^{3} d^{4} + 4 \, B a c^{2} d^{3} e + 6 \, A a c^{2} d^{2} e^{2} - 12 \, B a^{2} c d e^{3} - 3 \, A a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(A a c^{3} d^{4} - 4 \, B a^{2} c^{2} d^{3} e - 6 \, A a^{2} c^{2} d^{2} e^{2} + 12 \, B a^{3} c d e^{3} + 3 \, A a^{3} c e^{4}\right)} x + 4 \, {\left(3 \, B a^{3} c d^{2} e^{2} + 2 \, A a^{3} c d e^{3} - B a^{4} e^{4} + {\left(3 \, B a^{2} c^{2} d^{2} e^{2} + 2 \, A a^{2} c^{2} d e^{3} - B a^{3} c e^{4}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}, \frac{B a^{2} c^{2} e^{4} x^{4} + B a^{3} c e^{4} x^{2} - B a^{2} c^{2} d^{4} - 4 \, A a^{2} c^{2} d^{3} e + 6 \, B a^{3} c d^{2} e^{2} + 4 \, A a^{3} c d e^{3} - B a^{4} e^{4} + 2 \, {\left(4 \, B a^{2} c^{2} d e^{3} + A a^{2} c^{2} e^{4}\right)} x^{3} + {\left(A a c^{2} d^{4} + 4 \, B a^{2} c d^{3} e + 6 \, A a^{2} c d^{2} e^{2} - 12 \, B a^{3} d e^{3} - 3 \, A a^{3} e^{4} + {\left(A c^{3} d^{4} + 4 \, B a c^{2} d^{3} e + 6 \, A a c^{2} d^{2} e^{2} - 12 \, B a^{2} c d e^{3} - 3 \, A a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(A a c^{3} d^{4} - 4 \, B a^{2} c^{2} d^{3} e - 6 \, A a^{2} c^{2} d^{2} e^{2} + 12 \, B a^{3} c d e^{3} + 3 \, A a^{3} c e^{4}\right)} x + 2 \, {\left(3 \, B a^{3} c d^{2} e^{2} + 2 \, A a^{3} c d e^{3} - B a^{4} e^{4} + {\left(3 \, B a^{2} c^{2} d^{2} e^{2} + 2 \, A a^{2} c^{2} d e^{3} - B a^{3} c e^{4}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}\right]"," ",0,"[1/4*(2*B*a^2*c^2*e^4*x^4 + 2*B*a^3*c*e^4*x^2 - 2*B*a^2*c^2*d^4 - 8*A*a^2*c^2*d^3*e + 12*B*a^3*c*d^2*e^2 + 8*A*a^3*c*d*e^3 - 2*B*a^4*e^4 + 4*(4*B*a^2*c^2*d*e^3 + A*a^2*c^2*e^4)*x^3 + (A*a*c^2*d^4 + 4*B*a^2*c*d^3*e + 6*A*a^2*c*d^2*e^2 - 12*B*a^3*d*e^3 - 3*A*a^3*e^4 + (A*c^3*d^4 + 4*B*a*c^2*d^3*e + 6*A*a*c^2*d^2*e^2 - 12*B*a^2*c*d*e^3 - 3*A*a^2*c*e^4)*x^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(A*a*c^3*d^4 - 4*B*a^2*c^2*d^3*e - 6*A*a^2*c^2*d^2*e^2 + 12*B*a^3*c*d*e^3 + 3*A*a^3*c*e^4)*x + 4*(3*B*a^3*c*d^2*e^2 + 2*A*a^3*c*d*e^3 - B*a^4*e^4 + (3*B*a^2*c^2*d^2*e^2 + 2*A*a^2*c^2*d*e^3 - B*a^3*c*e^4)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3), 1/2*(B*a^2*c^2*e^4*x^4 + B*a^3*c*e^4*x^2 - B*a^2*c^2*d^4 - 4*A*a^2*c^2*d^3*e + 6*B*a^3*c*d^2*e^2 + 4*A*a^3*c*d*e^3 - B*a^4*e^4 + 2*(4*B*a^2*c^2*d*e^3 + A*a^2*c^2*e^4)*x^3 + (A*a*c^2*d^4 + 4*B*a^2*c*d^3*e + 6*A*a^2*c*d^2*e^2 - 12*B*a^3*d*e^3 - 3*A*a^3*e^4 + (A*c^3*d^4 + 4*B*a*c^2*d^3*e + 6*A*a*c^2*d^2*e^2 - 12*B*a^2*c*d*e^3 - 3*A*a^2*c*e^4)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (A*a*c^3*d^4 - 4*B*a^2*c^2*d^3*e - 6*A*a^2*c^2*d^2*e^2 + 12*B*a^3*c*d*e^3 + 3*A*a^3*c*e^4)*x + 2*(3*B*a^3*c*d^2*e^2 + 2*A*a^3*c*d*e^3 - B*a^4*e^4 + (3*B*a^2*c^2*d^2*e^2 + 2*A*a^2*c^2*d*e^3 - B*a^3*c*e^4)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3)]","B",0
1340,1,609,0,0.421277," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, B a^{2} c^{2} e^{3} x^{3} - 2 \, B a^{2} c^{2} d^{3} - 6 \, A a^{2} c^{2} d^{2} e + 6 \, B a^{3} c d e^{2} + 2 \, A a^{3} c e^{3} + {\left(A a c^{2} d^{3} + 3 \, B a^{2} c d^{2} e + 3 \, A a^{2} c d e^{2} - 3 \, B a^{3} e^{3} + {\left(A c^{3} d^{3} + 3 \, B a c^{2} d^{2} e + 3 \, A a c^{2} d e^{2} - 3 \, B a^{2} c e^{3}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(A a c^{3} d^{3} - 3 \, B a^{2} c^{2} d^{2} e - 3 \, A a^{2} c^{2} d e^{2} + 3 \, B a^{3} c e^{3}\right)} x + 2 \, {\left(3 \, B a^{3} c d e^{2} + A a^{3} c e^{3} + {\left(3 \, B a^{2} c^{2} d e^{2} + A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}, \frac{2 \, B a^{2} c^{2} e^{3} x^{3} - B a^{2} c^{2} d^{3} - 3 \, A a^{2} c^{2} d^{2} e + 3 \, B a^{3} c d e^{2} + A a^{3} c e^{3} + {\left(A a c^{2} d^{3} + 3 \, B a^{2} c d^{2} e + 3 \, A a^{2} c d e^{2} - 3 \, B a^{3} e^{3} + {\left(A c^{3} d^{3} + 3 \, B a c^{2} d^{2} e + 3 \, A a c^{2} d e^{2} - 3 \, B a^{2} c e^{3}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(A a c^{3} d^{3} - 3 \, B a^{2} c^{2} d^{2} e - 3 \, A a^{2} c^{2} d e^{2} + 3 \, B a^{3} c e^{3}\right)} x + {\left(3 \, B a^{3} c d e^{2} + A a^{3} c e^{3} + {\left(3 \, B a^{2} c^{2} d e^{2} + A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}\right]"," ",0,"[1/4*(4*B*a^2*c^2*e^3*x^3 - 2*B*a^2*c^2*d^3 - 6*A*a^2*c^2*d^2*e + 6*B*a^3*c*d*e^2 + 2*A*a^3*c*e^3 + (A*a*c^2*d^3 + 3*B*a^2*c*d^2*e + 3*A*a^2*c*d*e^2 - 3*B*a^3*e^3 + (A*c^3*d^3 + 3*B*a*c^2*d^2*e + 3*A*a*c^2*d*e^2 - 3*B*a^2*c*e^3)*x^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(A*a*c^3*d^3 - 3*B*a^2*c^2*d^2*e - 3*A*a^2*c^2*d*e^2 + 3*B*a^3*c*e^3)*x + 2*(3*B*a^3*c*d*e^2 + A*a^3*c*e^3 + (3*B*a^2*c^2*d*e^2 + A*a^2*c^2*e^3)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3), 1/2*(2*B*a^2*c^2*e^3*x^3 - B*a^2*c^2*d^3 - 3*A*a^2*c^2*d^2*e + 3*B*a^3*c*d*e^2 + A*a^3*c*e^3 + (A*a*c^2*d^3 + 3*B*a^2*c*d^2*e + 3*A*a^2*c*d*e^2 - 3*B*a^3*e^3 + (A*c^3*d^3 + 3*B*a*c^2*d^2*e + 3*A*a*c^2*d*e^2 - 3*B*a^2*c*e^3)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (A*a*c^3*d^3 - 3*B*a^2*c^2*d^2*e - 3*A*a^2*c^2*d*e^2 + 3*B*a^3*c*e^3)*x + (3*B*a^3*c*d*e^2 + A*a^3*c*e^3 + (3*B*a^2*c^2*d*e^2 + A*a^2*c^2*e^3)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3)]","B",0
1341,1,384,0,0.422974," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a^{2} c d^{2} + 4 \, A a^{2} c d e - 2 \, B a^{3} e^{2} + {\left(A a c d^{2} + 2 \, B a^{2} d e + A a^{2} e^{2} + {\left(A c^{2} d^{2} + 2 \, B a c d e + A a c e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(A a c^{2} d^{2} - 2 \, B a^{2} c d e - A a^{2} c e^{2}\right)} x - 2 \, {\left(B a^{2} c e^{2} x^{2} + B a^{3} e^{2}\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}, -\frac{B a^{2} c d^{2} + 2 \, A a^{2} c d e - B a^{3} e^{2} - {\left(A a c d^{2} + 2 \, B a^{2} d e + A a^{2} e^{2} + {\left(A c^{2} d^{2} + 2 \, B a c d e + A a c e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(A a c^{2} d^{2} - 2 \, B a^{2} c d e - A a^{2} c e^{2}\right)} x - {\left(B a^{2} c e^{2} x^{2} + B a^{3} e^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}\right]"," ",0,"[-1/4*(2*B*a^2*c*d^2 + 4*A*a^2*c*d*e - 2*B*a^3*e^2 + (A*a*c*d^2 + 2*B*a^2*d*e + A*a^2*e^2 + (A*c^2*d^2 + 2*B*a*c*d*e + A*a*c*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(A*a*c^2*d^2 - 2*B*a^2*c*d*e - A*a^2*c*e^2)*x - 2*(B*a^2*c*e^2*x^2 + B*a^3*e^2)*log(c*x^2 + a))/(a^2*c^3*x^2 + a^3*c^2), -1/2*(B*a^2*c*d^2 + 2*A*a^2*c*d*e - B*a^3*e^2 - (A*a*c*d^2 + 2*B*a^2*d*e + A*a^2*e^2 + (A*c^2*d^2 + 2*B*a*c*d*e + A*a*c*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (A*a*c^2*d^2 - 2*B*a^2*c*d*e - A*a^2*c*e^2)*x - (B*a^2*c*e^2*x^2 + B*a^3*e^2)*log(c*x^2 + a))/(a^2*c^3*x^2 + a^3*c^2)]","A",0
1342,1,225,0,0.406001," ","integrate((B*x+A)*(e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a^{2} c d + 2 \, A a^{2} c e + {\left(A a c d + B a^{2} e + {\left(A c^{2} d + B a c e\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(A a c^{2} d - B a^{2} c e\right)} x}{4 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}, -\frac{B a^{2} c d + A a^{2} c e - {\left(A a c d + B a^{2} e + {\left(A c^{2} d + B a c e\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(A a c^{2} d - B a^{2} c e\right)} x}{2 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}\right]"," ",0,"[-1/4*(2*B*a^2*c*d + 2*A*a^2*c*e + (A*a*c*d + B*a^2*e + (A*c^2*d + B*a*c*e)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(A*a*c^2*d - B*a^2*c*e)*x)/(a^2*c^3*x^2 + a^3*c^2), -1/2*(B*a^2*c*d + A*a^2*c*e - (A*a*c*d + B*a^2*e + (A*c^2*d + B*a*c*e)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (A*a*c^2*d - B*a^2*c*e)*x)/(a^2*c^3*x^2 + a^3*c^2)]","A",0
1343,1,140,0,0.421582," ","integrate((B*x+A)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, A a c x - 2 \, B a^{2} - {\left(A c x^{2} + A a\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{4 \, {\left(a^{2} c^{2} x^{2} + a^{3} c\right)}}, \frac{A a c x - B a^{2} + {\left(A c x^{2} + A a\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{2 \, {\left(a^{2} c^{2} x^{2} + a^{3} c\right)}}\right]"," ",0,"[1/4*(2*A*a*c*x - 2*B*a^2 - (A*c*x^2 + A*a)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a^2*c^2*x^2 + a^3*c), 1/2*(A*a*c*x - B*a^2 + (A*c*x^2 + A*a)*sqrt(a*c)*arctan(sqrt(a*c)*x/a))/(a^2*c^2*x^2 + a^3*c)]","A",0
1344,1,795,0,16.504624," ","integrate((B*x+A)/(e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a^{2} c^{2} d^{3} - 2 \, A a^{2} c^{2} d^{2} e + 2 \, B a^{3} c d e^{2} - 2 \, A a^{3} c e^{3} + {\left(A a c^{2} d^{3} - B a^{2} c d^{2} e + 3 \, A a^{2} c d e^{2} + B a^{3} e^{3} + {\left(A c^{3} d^{3} - B a c^{2} d^{2} e + 3 \, A a c^{2} d e^{2} + B a^{2} c e^{3}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(A a c^{3} d^{3} + B a^{2} c^{2} d^{2} e + A a^{2} c^{2} d e^{2} + B a^{3} c e^{3}\right)} x - 2 \, {\left(B a^{3} c d e^{2} - A a^{3} c e^{3} + {\left(B a^{2} c^{2} d e^{2} - A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(c x^{2} + a\right) + 4 \, {\left(B a^{3} c d e^{2} - A a^{3} c e^{3} + {\left(B a^{2} c^{2} d e^{2} - A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(e x + d\right)}{4 \, {\left(a^{3} c^{3} d^{4} + 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4} + {\left(a^{2} c^{4} d^{4} + 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{2}\right)}}, -\frac{B a^{2} c^{2} d^{3} - A a^{2} c^{2} d^{2} e + B a^{3} c d e^{2} - A a^{3} c e^{3} - {\left(A a c^{2} d^{3} - B a^{2} c d^{2} e + 3 \, A a^{2} c d e^{2} + B a^{3} e^{3} + {\left(A c^{3} d^{3} - B a c^{2} d^{2} e + 3 \, A a c^{2} d e^{2} + B a^{2} c e^{3}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(A a c^{3} d^{3} + B a^{2} c^{2} d^{2} e + A a^{2} c^{2} d e^{2} + B a^{3} c e^{3}\right)} x - {\left(B a^{3} c d e^{2} - A a^{3} c e^{3} + {\left(B a^{2} c^{2} d e^{2} - A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(c x^{2} + a\right) + 2 \, {\left(B a^{3} c d e^{2} - A a^{3} c e^{3} + {\left(B a^{2} c^{2} d e^{2} - A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(a^{3} c^{3} d^{4} + 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4} + {\left(a^{2} c^{4} d^{4} + 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*B*a^2*c^2*d^3 - 2*A*a^2*c^2*d^2*e + 2*B*a^3*c*d*e^2 - 2*A*a^3*c*e^3 + (A*a*c^2*d^3 - B*a^2*c*d^2*e + 3*A*a^2*c*d*e^2 + B*a^3*e^3 + (A*c^3*d^3 - B*a*c^2*d^2*e + 3*A*a*c^2*d*e^2 + B*a^2*c*e^3)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(A*a*c^3*d^3 + B*a^2*c^2*d^2*e + A*a^2*c^2*d*e^2 + B*a^3*c*e^3)*x - 2*(B*a^3*c*d*e^2 - A*a^3*c*e^3 + (B*a^2*c^2*d*e^2 - A*a^2*c^2*e^3)*x^2)*log(c*x^2 + a) + 4*(B*a^3*c*d*e^2 - A*a^3*c*e^3 + (B*a^2*c^2*d*e^2 - A*a^2*c^2*e^3)*x^2)*log(e*x + d))/(a^3*c^3*d^4 + 2*a^4*c^2*d^2*e^2 + a^5*c*e^4 + (a^2*c^4*d^4 + 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^2), -1/2*(B*a^2*c^2*d^3 - A*a^2*c^2*d^2*e + B*a^3*c*d*e^2 - A*a^3*c*e^3 - (A*a*c^2*d^3 - B*a^2*c*d^2*e + 3*A*a^2*c*d*e^2 + B*a^3*e^3 + (A*c^3*d^3 - B*a*c^2*d^2*e + 3*A*a*c^2*d*e^2 + B*a^2*c*e^3)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (A*a*c^3*d^3 + B*a^2*c^2*d^2*e + A*a^2*c^2*d*e^2 + B*a^3*c*e^3)*x - (B*a^3*c*d*e^2 - A*a^3*c*e^3 + (B*a^2*c^2*d*e^2 - A*a^2*c^2*e^3)*x^2)*log(c*x^2 + a) + 2*(B*a^3*c*d*e^2 - A*a^3*c*e^3 + (B*a^2*c^2*d*e^2 - A*a^2*c^2*e^3)*x^2)*log(e*x + d))/(a^3*c^3*d^4 + 2*a^4*c^2*d^2*e^2 + a^5*c*e^4 + (a^2*c^4*d^4 + 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^2)]","B",0
1345,1,1940,0,57.637933," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a c^{2} d^{5} - 4 \, A a c^{2} d^{4} e - 4 \, B a^{2} c d^{3} e^{2} - 6 \, B a^{3} d e^{4} + 4 \, A a^{3} e^{5} - 2 \, {\left(A c^{3} d^{4} e + 4 \, B a c^{2} d^{3} e^{2} - 2 \, A a c^{2} d^{2} e^{3} + 4 \, B a^{2} c d e^{4} - 3 \, A a^{2} c e^{5}\right)} x^{2} + {\left(A a c^{2} d^{5} - 2 \, B a^{2} c d^{4} e + 6 \, A a^{2} c d^{3} e^{2} + 6 \, B a^{3} d^{2} e^{3} - 3 \, A a^{3} d e^{4} + {\left(A c^{3} d^{4} e - 2 \, B a c^{2} d^{3} e^{2} + 6 \, A a c^{2} d^{2} e^{3} + 6 \, B a^{2} c d e^{4} - 3 \, A a^{2} c e^{5}\right)} x^{3} + {\left(A c^{3} d^{5} - 2 \, B a c^{2} d^{4} e + 6 \, A a c^{2} d^{3} e^{2} + 6 \, B a^{2} c d^{2} e^{3} - 3 \, A a^{2} c d e^{4}\right)} x^{2} + {\left(A a c^{2} d^{4} e - 2 \, B a^{2} c d^{3} e^{2} + 6 \, A a^{2} c d^{2} e^{3} + 6 \, B a^{3} d e^{4} - 3 \, A a^{3} e^{5}\right)} x\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) - 2 \, {\left(A c^{3} d^{5} + B a c^{2} d^{4} e + 2 \, A a c^{2} d^{3} e^{2} + 2 \, B a^{2} c d^{2} e^{3} + A a^{2} c d e^{4} + B a^{3} e^{5}\right)} x - 2 \, {\left(3 \, B a^{2} c d^{3} e^{2} - 4 \, A a^{2} c d^{2} e^{3} - B a^{3} d e^{4} + {\left(3 \, B a c^{2} d^{2} e^{3} - 4 \, A a c^{2} d e^{4} - B a^{2} c e^{5}\right)} x^{3} + {\left(3 \, B a c^{2} d^{3} e^{2} - 4 \, A a c^{2} d^{2} e^{3} - B a^{2} c d e^{4}\right)} x^{2} + {\left(3 \, B a^{2} c d^{2} e^{3} - 4 \, A a^{2} c d e^{4} - B a^{3} e^{5}\right)} x\right)} \log\left(c x^{2} + a\right) + 4 \, {\left(3 \, B a^{2} c d^{3} e^{2} - 4 \, A a^{2} c d^{2} e^{3} - B a^{3} d e^{4} + {\left(3 \, B a c^{2} d^{2} e^{3} - 4 \, A a c^{2} d e^{4} - B a^{2} c e^{5}\right)} x^{3} + {\left(3 \, B a c^{2} d^{3} e^{2} - 4 \, A a c^{2} d^{2} e^{3} - B a^{2} c d e^{4}\right)} x^{2} + {\left(3 \, B a^{2} c d^{2} e^{3} - 4 \, A a^{2} c d e^{4} - B a^{3} e^{5}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(a^{2} c^{3} d^{7} + 3 \, a^{3} c^{2} d^{5} e^{2} + 3 \, a^{4} c d^{3} e^{4} + a^{5} d e^{6} + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} x^{3} + {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} x^{2} + {\left(a^{2} c^{3} d^{6} e + 3 \, a^{3} c^{2} d^{4} e^{3} + 3 \, a^{4} c d^{2} e^{5} + a^{5} e^{7}\right)} x\right)}}, -\frac{B a c^{2} d^{5} - 2 \, A a c^{2} d^{4} e - 2 \, B a^{2} c d^{3} e^{2} - 3 \, B a^{3} d e^{4} + 2 \, A a^{3} e^{5} - {\left(A c^{3} d^{4} e + 4 \, B a c^{2} d^{3} e^{2} - 2 \, A a c^{2} d^{2} e^{3} + 4 \, B a^{2} c d e^{4} - 3 \, A a^{2} c e^{5}\right)} x^{2} - {\left(A a c^{2} d^{5} - 2 \, B a^{2} c d^{4} e + 6 \, A a^{2} c d^{3} e^{2} + 6 \, B a^{3} d^{2} e^{3} - 3 \, A a^{3} d e^{4} + {\left(A c^{3} d^{4} e - 2 \, B a c^{2} d^{3} e^{2} + 6 \, A a c^{2} d^{2} e^{3} + 6 \, B a^{2} c d e^{4} - 3 \, A a^{2} c e^{5}\right)} x^{3} + {\left(A c^{3} d^{5} - 2 \, B a c^{2} d^{4} e + 6 \, A a c^{2} d^{3} e^{2} + 6 \, B a^{2} c d^{2} e^{3} - 3 \, A a^{2} c d e^{4}\right)} x^{2} + {\left(A a c^{2} d^{4} e - 2 \, B a^{2} c d^{3} e^{2} + 6 \, A a^{2} c d^{2} e^{3} + 6 \, B a^{3} d e^{4} - 3 \, A a^{3} e^{5}\right)} x\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) - {\left(A c^{3} d^{5} + B a c^{2} d^{4} e + 2 \, A a c^{2} d^{3} e^{2} + 2 \, B a^{2} c d^{2} e^{3} + A a^{2} c d e^{4} + B a^{3} e^{5}\right)} x - {\left(3 \, B a^{2} c d^{3} e^{2} - 4 \, A a^{2} c d^{2} e^{3} - B a^{3} d e^{4} + {\left(3 \, B a c^{2} d^{2} e^{3} - 4 \, A a c^{2} d e^{4} - B a^{2} c e^{5}\right)} x^{3} + {\left(3 \, B a c^{2} d^{3} e^{2} - 4 \, A a c^{2} d^{2} e^{3} - B a^{2} c d e^{4}\right)} x^{2} + {\left(3 \, B a^{2} c d^{2} e^{3} - 4 \, A a^{2} c d e^{4} - B a^{3} e^{5}\right)} x\right)} \log\left(c x^{2} + a\right) + 2 \, {\left(3 \, B a^{2} c d^{3} e^{2} - 4 \, A a^{2} c d^{2} e^{3} - B a^{3} d e^{4} + {\left(3 \, B a c^{2} d^{2} e^{3} - 4 \, A a c^{2} d e^{4} - B a^{2} c e^{5}\right)} x^{3} + {\left(3 \, B a c^{2} d^{3} e^{2} - 4 \, A a c^{2} d^{2} e^{3} - B a^{2} c d e^{4}\right)} x^{2} + {\left(3 \, B a^{2} c d^{2} e^{3} - 4 \, A a^{2} c d e^{4} - B a^{3} e^{5}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} c^{3} d^{7} + 3 \, a^{3} c^{2} d^{5} e^{2} + 3 \, a^{4} c d^{3} e^{4} + a^{5} d e^{6} + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} x^{3} + {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} x^{2} + {\left(a^{2} c^{3} d^{6} e + 3 \, a^{3} c^{2} d^{4} e^{3} + 3 \, a^{4} c d^{2} e^{5} + a^{5} e^{7}\right)} x\right)}}\right]"," ",0,"[-1/4*(2*B*a*c^2*d^5 - 4*A*a*c^2*d^4*e - 4*B*a^2*c*d^3*e^2 - 6*B*a^3*d*e^4 + 4*A*a^3*e^5 - 2*(A*c^3*d^4*e + 4*B*a*c^2*d^3*e^2 - 2*A*a*c^2*d^2*e^3 + 4*B*a^2*c*d*e^4 - 3*A*a^2*c*e^5)*x^2 + (A*a*c^2*d^5 - 2*B*a^2*c*d^4*e + 6*A*a^2*c*d^3*e^2 + 6*B*a^3*d^2*e^3 - 3*A*a^3*d*e^4 + (A*c^3*d^4*e - 2*B*a*c^2*d^3*e^2 + 6*A*a*c^2*d^2*e^3 + 6*B*a^2*c*d*e^4 - 3*A*a^2*c*e^5)*x^3 + (A*c^3*d^5 - 2*B*a*c^2*d^4*e + 6*A*a*c^2*d^3*e^2 + 6*B*a^2*c*d^2*e^3 - 3*A*a^2*c*d*e^4)*x^2 + (A*a*c^2*d^4*e - 2*B*a^2*c*d^3*e^2 + 6*A*a^2*c*d^2*e^3 + 6*B*a^3*d*e^4 - 3*A*a^3*e^5)*x)*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) - 2*(A*c^3*d^5 + B*a*c^2*d^4*e + 2*A*a*c^2*d^3*e^2 + 2*B*a^2*c*d^2*e^3 + A*a^2*c*d*e^4 + B*a^3*e^5)*x - 2*(3*B*a^2*c*d^3*e^2 - 4*A*a^2*c*d^2*e^3 - B*a^3*d*e^4 + (3*B*a*c^2*d^2*e^3 - 4*A*a*c^2*d*e^4 - B*a^2*c*e^5)*x^3 + (3*B*a*c^2*d^3*e^2 - 4*A*a*c^2*d^2*e^3 - B*a^2*c*d*e^4)*x^2 + (3*B*a^2*c*d^2*e^3 - 4*A*a^2*c*d*e^4 - B*a^3*e^5)*x)*log(c*x^2 + a) + 4*(3*B*a^2*c*d^3*e^2 - 4*A*a^2*c*d^2*e^3 - B*a^3*d*e^4 + (3*B*a*c^2*d^2*e^3 - 4*A*a*c^2*d*e^4 - B*a^2*c*e^5)*x^3 + (3*B*a*c^2*d^3*e^2 - 4*A*a*c^2*d^2*e^3 - B*a^2*c*d*e^4)*x^2 + (3*B*a^2*c*d^2*e^3 - 4*A*a^2*c*d*e^4 - B*a^3*e^5)*x)*log(e*x + d))/(a^2*c^3*d^7 + 3*a^3*c^2*d^5*e^2 + 3*a^4*c*d^3*e^4 + a^5*d*e^6 + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*x^3 + (a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*x^2 + (a^2*c^3*d^6*e + 3*a^3*c^2*d^4*e^3 + 3*a^4*c*d^2*e^5 + a^5*e^7)*x), -1/2*(B*a*c^2*d^5 - 2*A*a*c^2*d^4*e - 2*B*a^2*c*d^3*e^2 - 3*B*a^3*d*e^4 + 2*A*a^3*e^5 - (A*c^3*d^4*e + 4*B*a*c^2*d^3*e^2 - 2*A*a*c^2*d^2*e^3 + 4*B*a^2*c*d*e^4 - 3*A*a^2*c*e^5)*x^2 - (A*a*c^2*d^5 - 2*B*a^2*c*d^4*e + 6*A*a^2*c*d^3*e^2 + 6*B*a^3*d^2*e^3 - 3*A*a^3*d*e^4 + (A*c^3*d^4*e - 2*B*a*c^2*d^3*e^2 + 6*A*a*c^2*d^2*e^3 + 6*B*a^2*c*d*e^4 - 3*A*a^2*c*e^5)*x^3 + (A*c^3*d^5 - 2*B*a*c^2*d^4*e + 6*A*a*c^2*d^3*e^2 + 6*B*a^2*c*d^2*e^3 - 3*A*a^2*c*d*e^4)*x^2 + (A*a*c^2*d^4*e - 2*B*a^2*c*d^3*e^2 + 6*A*a^2*c*d^2*e^3 + 6*B*a^3*d*e^4 - 3*A*a^3*e^5)*x)*sqrt(c/a)*arctan(x*sqrt(c/a)) - (A*c^3*d^5 + B*a*c^2*d^4*e + 2*A*a*c^2*d^3*e^2 + 2*B*a^2*c*d^2*e^3 + A*a^2*c*d*e^4 + B*a^3*e^5)*x - (3*B*a^2*c*d^3*e^2 - 4*A*a^2*c*d^2*e^3 - B*a^3*d*e^4 + (3*B*a*c^2*d^2*e^3 - 4*A*a*c^2*d*e^4 - B*a^2*c*e^5)*x^3 + (3*B*a*c^2*d^3*e^2 - 4*A*a*c^2*d^2*e^3 - B*a^2*c*d*e^4)*x^2 + (3*B*a^2*c*d^2*e^3 - 4*A*a^2*c*d*e^4 - B*a^3*e^5)*x)*log(c*x^2 + a) + 2*(3*B*a^2*c*d^3*e^2 - 4*A*a^2*c*d^2*e^3 - B*a^3*d*e^4 + (3*B*a*c^2*d^2*e^3 - 4*A*a*c^2*d*e^4 - B*a^2*c*e^5)*x^3 + (3*B*a*c^2*d^3*e^2 - 4*A*a*c^2*d^2*e^3 - B*a^2*c*d*e^4)*x^2 + (3*B*a^2*c*d^2*e^3 - 4*A*a^2*c*d*e^4 - B*a^3*e^5)*x)*log(e*x + d))/(a^2*c^3*d^7 + 3*a^3*c^2*d^5*e^2 + 3*a^4*c*d^3*e^4 + a^5*d*e^6 + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*x^3 + (a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*x^2 + (a^2*c^3*d^6*e + 3*a^3*c^2*d^4*e^3 + 3*a^4*c*d^2*e^5 + a^5*e^7)*x)]","B",0
1346,1,1403,0,0.456252," ","integrate((B*x+A)*(e*x+d)^5/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{16 \, B a^{3} c^{3} e^{5} x^{5} - 4 \, B a^{3} c^{3} d^{5} - 20 \, A a^{3} c^{3} d^{4} e - 40 \, B a^{4} c^{2} d^{3} e^{2} - 40 \, A a^{4} c^{2} d^{2} e^{3} + 60 \, B a^{5} c d e^{4} + 12 \, A a^{5} c e^{5} + 2 \, {\left(3 \, A a c^{5} d^{5} + 5 \, B a^{2} c^{4} d^{4} e + 10 \, A a^{2} c^{4} d^{3} e^{2} - 50 \, B a^{3} c^{3} d^{2} e^{3} - 25 \, A a^{3} c^{3} d e^{4} + 25 \, B a^{4} c^{2} e^{5}\right)} x^{3} - 16 \, {\left(5 \, B a^{3} c^{3} d^{3} e^{2} + 5 \, A a^{3} c^{3} d^{2} e^{3} - 5 \, B a^{4} c^{2} d e^{4} - A a^{4} c^{2} e^{5}\right)} x^{2} + {\left(3 \, A a^{2} c^{3} d^{5} + 5 \, B a^{3} c^{2} d^{4} e + 10 \, A a^{3} c^{2} d^{3} e^{2} + 30 \, B a^{4} c d^{2} e^{3} + 15 \, A a^{4} c d e^{4} - 15 \, B a^{5} e^{5} + {\left(3 \, A c^{5} d^{5} + 5 \, B a c^{4} d^{4} e + 10 \, A a c^{4} d^{3} e^{2} + 30 \, B a^{2} c^{3} d^{2} e^{3} + 15 \, A a^{2} c^{3} d e^{4} - 15 \, B a^{3} c^{2} e^{5}\right)} x^{4} + 2 \, {\left(3 \, A a c^{4} d^{5} + 5 \, B a^{2} c^{3} d^{4} e + 10 \, A a^{2} c^{3} d^{3} e^{2} + 30 \, B a^{3} c^{2} d^{2} e^{3} + 15 \, A a^{3} c^{2} d e^{4} - 15 \, B a^{4} c e^{5}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 10 \, {\left(A a^{2} c^{4} d^{5} - B a^{3} c^{3} d^{4} e - 2 \, A a^{3} c^{3} d^{3} e^{2} - 6 \, B a^{4} c^{2} d^{2} e^{3} - 3 \, A a^{4} c^{2} d e^{4} + 3 \, B a^{5} c e^{5}\right)} x + 8 \, {\left(5 \, B a^{5} c d e^{4} + A a^{5} c e^{5} + {\left(5 \, B a^{3} c^{3} d e^{4} + A a^{3} c^{3} e^{5}\right)} x^{4} + 2 \, {\left(5 \, B a^{4} c^{2} d e^{4} + A a^{4} c^{2} e^{5}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{16 \, {\left(a^{3} c^{6} x^{4} + 2 \, a^{4} c^{5} x^{2} + a^{5} c^{4}\right)}}, \frac{8 \, B a^{3} c^{3} e^{5} x^{5} - 2 \, B a^{3} c^{3} d^{5} - 10 \, A a^{3} c^{3} d^{4} e - 20 \, B a^{4} c^{2} d^{3} e^{2} - 20 \, A a^{4} c^{2} d^{2} e^{3} + 30 \, B a^{5} c d e^{4} + 6 \, A a^{5} c e^{5} + {\left(3 \, A a c^{5} d^{5} + 5 \, B a^{2} c^{4} d^{4} e + 10 \, A a^{2} c^{4} d^{3} e^{2} - 50 \, B a^{3} c^{3} d^{2} e^{3} - 25 \, A a^{3} c^{3} d e^{4} + 25 \, B a^{4} c^{2} e^{5}\right)} x^{3} - 8 \, {\left(5 \, B a^{3} c^{3} d^{3} e^{2} + 5 \, A a^{3} c^{3} d^{2} e^{3} - 5 \, B a^{4} c^{2} d e^{4} - A a^{4} c^{2} e^{5}\right)} x^{2} + {\left(3 \, A a^{2} c^{3} d^{5} + 5 \, B a^{3} c^{2} d^{4} e + 10 \, A a^{3} c^{2} d^{3} e^{2} + 30 \, B a^{4} c d^{2} e^{3} + 15 \, A a^{4} c d e^{4} - 15 \, B a^{5} e^{5} + {\left(3 \, A c^{5} d^{5} + 5 \, B a c^{4} d^{4} e + 10 \, A a c^{4} d^{3} e^{2} + 30 \, B a^{2} c^{3} d^{2} e^{3} + 15 \, A a^{2} c^{3} d e^{4} - 15 \, B a^{3} c^{2} e^{5}\right)} x^{4} + 2 \, {\left(3 \, A a c^{4} d^{5} + 5 \, B a^{2} c^{3} d^{4} e + 10 \, A a^{2} c^{3} d^{3} e^{2} + 30 \, B a^{3} c^{2} d^{2} e^{3} + 15 \, A a^{3} c^{2} d e^{4} - 15 \, B a^{4} c e^{5}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 5 \, {\left(A a^{2} c^{4} d^{5} - B a^{3} c^{3} d^{4} e - 2 \, A a^{3} c^{3} d^{3} e^{2} - 6 \, B a^{4} c^{2} d^{2} e^{3} - 3 \, A a^{4} c^{2} d e^{4} + 3 \, B a^{5} c e^{5}\right)} x + 4 \, {\left(5 \, B a^{5} c d e^{4} + A a^{5} c e^{5} + {\left(5 \, B a^{3} c^{3} d e^{4} + A a^{3} c^{3} e^{5}\right)} x^{4} + 2 \, {\left(5 \, B a^{4} c^{2} d e^{4} + A a^{4} c^{2} e^{5}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{8 \, {\left(a^{3} c^{6} x^{4} + 2 \, a^{4} c^{5} x^{2} + a^{5} c^{4}\right)}}\right]"," ",0,"[1/16*(16*B*a^3*c^3*e^5*x^5 - 4*B*a^3*c^3*d^5 - 20*A*a^3*c^3*d^4*e - 40*B*a^4*c^2*d^3*e^2 - 40*A*a^4*c^2*d^2*e^3 + 60*B*a^5*c*d*e^4 + 12*A*a^5*c*e^5 + 2*(3*A*a*c^5*d^5 + 5*B*a^2*c^4*d^4*e + 10*A*a^2*c^4*d^3*e^2 - 50*B*a^3*c^3*d^2*e^3 - 25*A*a^3*c^3*d*e^4 + 25*B*a^4*c^2*e^5)*x^3 - 16*(5*B*a^3*c^3*d^3*e^2 + 5*A*a^3*c^3*d^2*e^3 - 5*B*a^4*c^2*d*e^4 - A*a^4*c^2*e^5)*x^2 + (3*A*a^2*c^3*d^5 + 5*B*a^3*c^2*d^4*e + 10*A*a^3*c^2*d^3*e^2 + 30*B*a^4*c*d^2*e^3 + 15*A*a^4*c*d*e^4 - 15*B*a^5*e^5 + (3*A*c^5*d^5 + 5*B*a*c^4*d^4*e + 10*A*a*c^4*d^3*e^2 + 30*B*a^2*c^3*d^2*e^3 + 15*A*a^2*c^3*d*e^4 - 15*B*a^3*c^2*e^5)*x^4 + 2*(3*A*a*c^4*d^5 + 5*B*a^2*c^3*d^4*e + 10*A*a^2*c^3*d^3*e^2 + 30*B*a^3*c^2*d^2*e^3 + 15*A*a^3*c^2*d*e^4 - 15*B*a^4*c*e^5)*x^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 10*(A*a^2*c^4*d^5 - B*a^3*c^3*d^4*e - 2*A*a^3*c^3*d^3*e^2 - 6*B*a^4*c^2*d^2*e^3 - 3*A*a^4*c^2*d*e^4 + 3*B*a^5*c*e^5)*x + 8*(5*B*a^5*c*d*e^4 + A*a^5*c*e^5 + (5*B*a^3*c^3*d*e^4 + A*a^3*c^3*e^5)*x^4 + 2*(5*B*a^4*c^2*d*e^4 + A*a^4*c^2*e^5)*x^2)*log(c*x^2 + a))/(a^3*c^6*x^4 + 2*a^4*c^5*x^2 + a^5*c^4), 1/8*(8*B*a^3*c^3*e^5*x^5 - 2*B*a^3*c^3*d^5 - 10*A*a^3*c^3*d^4*e - 20*B*a^4*c^2*d^3*e^2 - 20*A*a^4*c^2*d^2*e^3 + 30*B*a^5*c*d*e^4 + 6*A*a^5*c*e^5 + (3*A*a*c^5*d^5 + 5*B*a^2*c^4*d^4*e + 10*A*a^2*c^4*d^3*e^2 - 50*B*a^3*c^3*d^2*e^3 - 25*A*a^3*c^3*d*e^4 + 25*B*a^4*c^2*e^5)*x^3 - 8*(5*B*a^3*c^3*d^3*e^2 + 5*A*a^3*c^3*d^2*e^3 - 5*B*a^4*c^2*d*e^4 - A*a^4*c^2*e^5)*x^2 + (3*A*a^2*c^3*d^5 + 5*B*a^3*c^2*d^4*e + 10*A*a^3*c^2*d^3*e^2 + 30*B*a^4*c*d^2*e^3 + 15*A*a^4*c*d*e^4 - 15*B*a^5*e^5 + (3*A*c^5*d^5 + 5*B*a*c^4*d^4*e + 10*A*a*c^4*d^3*e^2 + 30*B*a^2*c^3*d^2*e^3 + 15*A*a^2*c^3*d*e^4 - 15*B*a^3*c^2*e^5)*x^4 + 2*(3*A*a*c^4*d^5 + 5*B*a^2*c^3*d^4*e + 10*A*a^2*c^3*d^3*e^2 + 30*B*a^3*c^2*d^2*e^3 + 15*A*a^3*c^2*d*e^4 - 15*B*a^4*c*e^5)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 5*(A*a^2*c^4*d^5 - B*a^3*c^3*d^4*e - 2*A*a^3*c^3*d^3*e^2 - 6*B*a^4*c^2*d^2*e^3 - 3*A*a^4*c^2*d*e^4 + 3*B*a^5*c*e^5)*x + 4*(5*B*a^5*c*d*e^4 + A*a^5*c*e^5 + (5*B*a^3*c^3*d*e^4 + A*a^3*c^3*e^5)*x^4 + 2*(5*B*a^4*c^2*d*e^4 + A*a^4*c^2*e^5)*x^2)*log(c*x^2 + a))/(a^3*c^6*x^4 + 2*a^4*c^5*x^2 + a^5*c^4)]","B",0
1347,1,1055,0,0.446697," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, B a^{3} c^{2} d^{4} + 16 \, A a^{3} c^{2} d^{3} e + 24 \, B a^{4} c d^{2} e^{2} + 16 \, A a^{4} c d e^{3} - 12 \, B a^{5} e^{4} - 2 \, {\left(3 \, A a c^{4} d^{4} + 4 \, B a^{2} c^{3} d^{3} e + 6 \, A a^{2} c^{3} d^{2} e^{2} - 20 \, B a^{3} c^{2} d e^{3} - 5 \, A a^{3} c^{2} e^{4}\right)} x^{3} + 16 \, {\left(3 \, B a^{3} c^{2} d^{2} e^{2} + 2 \, A a^{3} c^{2} d e^{3} - B a^{4} c e^{4}\right)} x^{2} + {\left(3 \, A a^{2} c^{2} d^{4} + 4 \, B a^{3} c d^{3} e + 6 \, A a^{3} c d^{2} e^{2} + 12 \, B a^{4} d e^{3} + 3 \, A a^{4} e^{4} + {\left(3 \, A c^{4} d^{4} + 4 \, B a c^{3} d^{3} e + 6 \, A a c^{3} d^{2} e^{2} + 12 \, B a^{2} c^{2} d e^{3} + 3 \, A a^{2} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(3 \, A a c^{3} d^{4} + 4 \, B a^{2} c^{2} d^{3} e + 6 \, A a^{2} c^{2} d^{2} e^{2} + 12 \, B a^{3} c d e^{3} + 3 \, A a^{3} c e^{4}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(5 \, A a^{2} c^{3} d^{4} - 4 \, B a^{3} c^{2} d^{3} e - 6 \, A a^{3} c^{2} d^{2} e^{2} - 12 \, B a^{4} c d e^{3} - 3 \, A a^{4} c e^{4}\right)} x - 8 \, {\left(B a^{3} c^{2} e^{4} x^{4} + 2 \, B a^{4} c e^{4} x^{2} + B a^{5} e^{4}\right)} \log\left(c x^{2} + a\right)}{16 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}, -\frac{2 \, B a^{3} c^{2} d^{4} + 8 \, A a^{3} c^{2} d^{3} e + 12 \, B a^{4} c d^{2} e^{2} + 8 \, A a^{4} c d e^{3} - 6 \, B a^{5} e^{4} - {\left(3 \, A a c^{4} d^{4} + 4 \, B a^{2} c^{3} d^{3} e + 6 \, A a^{2} c^{3} d^{2} e^{2} - 20 \, B a^{3} c^{2} d e^{3} - 5 \, A a^{3} c^{2} e^{4}\right)} x^{3} + 8 \, {\left(3 \, B a^{3} c^{2} d^{2} e^{2} + 2 \, A a^{3} c^{2} d e^{3} - B a^{4} c e^{4}\right)} x^{2} - {\left(3 \, A a^{2} c^{2} d^{4} + 4 \, B a^{3} c d^{3} e + 6 \, A a^{3} c d^{2} e^{2} + 12 \, B a^{4} d e^{3} + 3 \, A a^{4} e^{4} + {\left(3 \, A c^{4} d^{4} + 4 \, B a c^{3} d^{3} e + 6 \, A a c^{3} d^{2} e^{2} + 12 \, B a^{2} c^{2} d e^{3} + 3 \, A a^{2} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(3 \, A a c^{3} d^{4} + 4 \, B a^{2} c^{2} d^{3} e + 6 \, A a^{2} c^{2} d^{2} e^{2} + 12 \, B a^{3} c d e^{3} + 3 \, A a^{3} c e^{4}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(5 \, A a^{2} c^{3} d^{4} - 4 \, B a^{3} c^{2} d^{3} e - 6 \, A a^{3} c^{2} d^{2} e^{2} - 12 \, B a^{4} c d e^{3} - 3 \, A a^{4} c e^{4}\right)} x - 4 \, {\left(B a^{3} c^{2} e^{4} x^{4} + 2 \, B a^{4} c e^{4} x^{2} + B a^{5} e^{4}\right)} \log\left(c x^{2} + a\right)}{8 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}\right]"," ",0,"[-1/16*(4*B*a^3*c^2*d^4 + 16*A*a^3*c^2*d^3*e + 24*B*a^4*c*d^2*e^2 + 16*A*a^4*c*d*e^3 - 12*B*a^5*e^4 - 2*(3*A*a*c^4*d^4 + 4*B*a^2*c^3*d^3*e + 6*A*a^2*c^3*d^2*e^2 - 20*B*a^3*c^2*d*e^3 - 5*A*a^3*c^2*e^4)*x^3 + 16*(3*B*a^3*c^2*d^2*e^2 + 2*A*a^3*c^2*d*e^3 - B*a^4*c*e^4)*x^2 + (3*A*a^2*c^2*d^4 + 4*B*a^3*c*d^3*e + 6*A*a^3*c*d^2*e^2 + 12*B*a^4*d*e^3 + 3*A*a^4*e^4 + (3*A*c^4*d^4 + 4*B*a*c^3*d^3*e + 6*A*a*c^3*d^2*e^2 + 12*B*a^2*c^2*d*e^3 + 3*A*a^2*c^2*e^4)*x^4 + 2*(3*A*a*c^3*d^4 + 4*B*a^2*c^2*d^3*e + 6*A*a^2*c^2*d^2*e^2 + 12*B*a^3*c*d*e^3 + 3*A*a^3*c*e^4)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(5*A*a^2*c^3*d^4 - 4*B*a^3*c^2*d^3*e - 6*A*a^3*c^2*d^2*e^2 - 12*B*a^4*c*d*e^3 - 3*A*a^4*c*e^4)*x - 8*(B*a^3*c^2*e^4*x^4 + 2*B*a^4*c*e^4*x^2 + B*a^5*e^4)*log(c*x^2 + a))/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3), -1/8*(2*B*a^3*c^2*d^4 + 8*A*a^3*c^2*d^3*e + 12*B*a^4*c*d^2*e^2 + 8*A*a^4*c*d*e^3 - 6*B*a^5*e^4 - (3*A*a*c^4*d^4 + 4*B*a^2*c^3*d^3*e + 6*A*a^2*c^3*d^2*e^2 - 20*B*a^3*c^2*d*e^3 - 5*A*a^3*c^2*e^4)*x^3 + 8*(3*B*a^3*c^2*d^2*e^2 + 2*A*a^3*c^2*d*e^3 - B*a^4*c*e^4)*x^2 - (3*A*a^2*c^2*d^4 + 4*B*a^3*c*d^3*e + 6*A*a^3*c*d^2*e^2 + 12*B*a^4*d*e^3 + 3*A*a^4*e^4 + (3*A*c^4*d^4 + 4*B*a*c^3*d^3*e + 6*A*a*c^3*d^2*e^2 + 12*B*a^2*c^2*d*e^3 + 3*A*a^2*c^2*e^4)*x^4 + 2*(3*A*a*c^3*d^4 + 4*B*a^2*c^2*d^3*e + 6*A*a^2*c^2*d^2*e^2 + 12*B*a^3*c*d*e^3 + 3*A*a^3*c*e^4)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (5*A*a^2*c^3*d^4 - 4*B*a^3*c^2*d^3*e - 6*A*a^3*c^2*d^2*e^2 - 12*B*a^4*c*d*e^3 - 3*A*a^4*c*e^4)*x - 4*(B*a^3*c^2*e^4*x^4 + 2*B*a^4*c*e^4*x^2 + B*a^5*e^4)*log(c*x^2 + a))/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3)]","B",0
1348,1,752,0,0.442436," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, B a^{3} c^{2} d^{3} + 12 \, A a^{3} c^{2} d^{2} e + 12 \, B a^{4} c d e^{2} + 4 \, A a^{4} c e^{3} - 2 \, {\left(3 \, A a c^{4} d^{3} + 3 \, B a^{2} c^{3} d^{2} e + 3 \, A a^{2} c^{3} d e^{2} - 5 \, B a^{3} c^{2} e^{3}\right)} x^{3} + 8 \, {\left(3 \, B a^{3} c^{2} d e^{2} + A a^{3} c^{2} e^{3}\right)} x^{2} + 3 \, {\left(A a^{2} c^{2} d^{3} + B a^{3} c d^{2} e + A a^{3} c d e^{2} + B a^{4} e^{3} + {\left(A c^{4} d^{3} + B a c^{3} d^{2} e + A a c^{3} d e^{2} + B a^{2} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(A a c^{3} d^{3} + B a^{2} c^{2} d^{2} e + A a^{2} c^{2} d e^{2} + B a^{3} c e^{3}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(5 \, A a^{2} c^{3} d^{3} - 3 \, B a^{3} c^{2} d^{2} e - 3 \, A a^{3} c^{2} d e^{2} - 3 \, B a^{4} c e^{3}\right)} x}{16 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}, -\frac{2 \, B a^{3} c^{2} d^{3} + 6 \, A a^{3} c^{2} d^{2} e + 6 \, B a^{4} c d e^{2} + 2 \, A a^{4} c e^{3} - {\left(3 \, A a c^{4} d^{3} + 3 \, B a^{2} c^{3} d^{2} e + 3 \, A a^{2} c^{3} d e^{2} - 5 \, B a^{3} c^{2} e^{3}\right)} x^{3} + 4 \, {\left(3 \, B a^{3} c^{2} d e^{2} + A a^{3} c^{2} e^{3}\right)} x^{2} - 3 \, {\left(A a^{2} c^{2} d^{3} + B a^{3} c d^{2} e + A a^{3} c d e^{2} + B a^{4} e^{3} + {\left(A c^{4} d^{3} + B a c^{3} d^{2} e + A a c^{3} d e^{2} + B a^{2} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(A a c^{3} d^{3} + B a^{2} c^{2} d^{2} e + A a^{2} c^{2} d e^{2} + B a^{3} c e^{3}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(5 \, A a^{2} c^{3} d^{3} - 3 \, B a^{3} c^{2} d^{2} e - 3 \, A a^{3} c^{2} d e^{2} - 3 \, B a^{4} c e^{3}\right)} x}{8 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}\right]"," ",0,"[-1/16*(4*B*a^3*c^2*d^3 + 12*A*a^3*c^2*d^2*e + 12*B*a^4*c*d*e^2 + 4*A*a^4*c*e^3 - 2*(3*A*a*c^4*d^3 + 3*B*a^2*c^3*d^2*e + 3*A*a^2*c^3*d*e^2 - 5*B*a^3*c^2*e^3)*x^3 + 8*(3*B*a^3*c^2*d*e^2 + A*a^3*c^2*e^3)*x^2 + 3*(A*a^2*c^2*d^3 + B*a^3*c*d^2*e + A*a^3*c*d*e^2 + B*a^4*e^3 + (A*c^4*d^3 + B*a*c^3*d^2*e + A*a*c^3*d*e^2 + B*a^2*c^2*e^3)*x^4 + 2*(A*a*c^3*d^3 + B*a^2*c^2*d^2*e + A*a^2*c^2*d*e^2 + B*a^3*c*e^3)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(5*A*a^2*c^3*d^3 - 3*B*a^3*c^2*d^2*e - 3*A*a^3*c^2*d*e^2 - 3*B*a^4*c*e^3)*x)/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3), -1/8*(2*B*a^3*c^2*d^3 + 6*A*a^3*c^2*d^2*e + 6*B*a^4*c*d*e^2 + 2*A*a^4*c*e^3 - (3*A*a*c^4*d^3 + 3*B*a^2*c^3*d^2*e + 3*A*a^2*c^3*d*e^2 - 5*B*a^3*c^2*e^3)*x^3 + 4*(3*B*a^3*c^2*d*e^2 + A*a^3*c^2*e^3)*x^2 - 3*(A*a^2*c^2*d^3 + B*a^3*c*d^2*e + A*a^3*c*d*e^2 + B*a^4*e^3 + (A*c^4*d^3 + B*a*c^3*d^2*e + A*a*c^3*d*e^2 + B*a^2*c^2*e^3)*x^4 + 2*(A*a*c^3*d^3 + B*a^2*c^2*d^2*e + A*a^2*c^2*d*e^2 + B*a^3*c*e^3)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (5*A*a^2*c^3*d^3 - 3*B*a^3*c^2*d^2*e - 3*A*a^3*c^2*d*e^2 - 3*B*a^4*c*e^3)*x)/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3)]","B",0
1349,1,537,0,0.427817," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{8 \, B a^{3} c e^{2} x^{2} + 4 \, B a^{3} c d^{2} + 8 \, A a^{3} c d e + 4 \, B a^{4} e^{2} - 2 \, {\left(3 \, A a c^{3} d^{2} + 2 \, B a^{2} c^{2} d e + A a^{2} c^{2} e^{2}\right)} x^{3} + {\left(3 \, A a^{2} c d^{2} + 2 \, B a^{3} d e + A a^{3} e^{2} + {\left(3 \, A c^{3} d^{2} + 2 \, B a c^{2} d e + A a c^{2} e^{2}\right)} x^{4} + 2 \, {\left(3 \, A a c^{2} d^{2} + 2 \, B a^{2} c d e + A a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(5 \, A a^{2} c^{2} d^{2} - 2 \, B a^{3} c d e - A a^{3} c e^{2}\right)} x}{16 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}, -\frac{4 \, B a^{3} c e^{2} x^{2} + 2 \, B a^{3} c d^{2} + 4 \, A a^{3} c d e + 2 \, B a^{4} e^{2} - {\left(3 \, A a c^{3} d^{2} + 2 \, B a^{2} c^{2} d e + A a^{2} c^{2} e^{2}\right)} x^{3} - {\left(3 \, A a^{2} c d^{2} + 2 \, B a^{3} d e + A a^{3} e^{2} + {\left(3 \, A c^{3} d^{2} + 2 \, B a c^{2} d e + A a c^{2} e^{2}\right)} x^{4} + 2 \, {\left(3 \, A a c^{2} d^{2} + 2 \, B a^{2} c d e + A a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(5 \, A a^{2} c^{2} d^{2} - 2 \, B a^{3} c d e - A a^{3} c e^{2}\right)} x}{8 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}\right]"," ",0,"[-1/16*(8*B*a^3*c*e^2*x^2 + 4*B*a^3*c*d^2 + 8*A*a^3*c*d*e + 4*B*a^4*e^2 - 2*(3*A*a*c^3*d^2 + 2*B*a^2*c^2*d*e + A*a^2*c^2*e^2)*x^3 + (3*A*a^2*c*d^2 + 2*B*a^3*d*e + A*a^3*e^2 + (3*A*c^3*d^2 + 2*B*a*c^2*d*e + A*a*c^2*e^2)*x^4 + 2*(3*A*a*c^2*d^2 + 2*B*a^2*c*d*e + A*a^2*c*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(5*A*a^2*c^2*d^2 - 2*B*a^3*c*d*e - A*a^3*c*e^2)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2), -1/8*(4*B*a^3*c*e^2*x^2 + 2*B*a^3*c*d^2 + 4*A*a^3*c*d*e + 2*B*a^4*e^2 - (3*A*a*c^3*d^2 + 2*B*a^2*c^2*d*e + A*a^2*c^2*e^2)*x^3 - (3*A*a^2*c*d^2 + 2*B*a^3*d*e + A*a^3*e^2 + (3*A*c^3*d^2 + 2*B*a*c^2*d*e + A*a*c^2*e^2)*x^4 + 2*(3*A*a*c^2*d^2 + 2*B*a^2*c*d*e + A*a^2*c*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (5*A*a^2*c^2*d^2 - 2*B*a^3*c*d*e - A*a^3*c*e^2)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2)]","B",0
1350,1,355,0,0.425194," ","integrate((B*x+A)*(e*x+d)/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, B a^{3} c d + 4 \, A a^{3} c e - 2 \, {\left(3 \, A a c^{3} d + B a^{2} c^{2} e\right)} x^{3} + {\left(3 \, A a^{2} c d + B a^{3} e + {\left(3 \, A c^{3} d + B a c^{2} e\right)} x^{4} + 2 \, {\left(3 \, A a c^{2} d + B a^{2} c e\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(5 \, A a^{2} c^{2} d - B a^{3} c e\right)} x}{16 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}, -\frac{2 \, B a^{3} c d + 2 \, A a^{3} c e - {\left(3 \, A a c^{3} d + B a^{2} c^{2} e\right)} x^{3} - {\left(3 \, A a^{2} c d + B a^{3} e + {\left(3 \, A c^{3} d + B a c^{2} e\right)} x^{4} + 2 \, {\left(3 \, A a c^{2} d + B a^{2} c e\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(5 \, A a^{2} c^{2} d - B a^{3} c e\right)} x}{8 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}\right]"," ",0,"[-1/16*(4*B*a^3*c*d + 4*A*a^3*c*e - 2*(3*A*a*c^3*d + B*a^2*c^2*e)*x^3 + (3*A*a^2*c*d + B*a^3*e + (3*A*c^3*d + B*a*c^2*e)*x^4 + 2*(3*A*a*c^2*d + B*a^2*c*e)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(5*A*a^2*c^2*d - B*a^3*c*e)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2), -1/8*(2*B*a^3*c*d + 2*A*a^3*c*e - (3*A*a*c^3*d + B*a^2*c^2*e)*x^3 - (3*A*a^2*c*d + B*a^3*e + (3*A*c^3*d + B*a*c^2*e)*x^4 + 2*(3*A*a*c^2*d + B*a^2*c*e)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (5*A*a^2*c^2*d - B*a^3*c*e)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2)]","A",0
1351,1,212,0,0.426980," ","integrate((B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{6 \, A a c^{2} x^{3} + 10 \, A a^{2} c x - 4 \, B a^{3} - 3 \, {\left(A c^{2} x^{4} + 2 \, A a c x^{2} + A a^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{16 \, {\left(a^{3} c^{3} x^{4} + 2 \, a^{4} c^{2} x^{2} + a^{5} c\right)}}, \frac{3 \, A a c^{2} x^{3} + 5 \, A a^{2} c x - 2 \, B a^{3} + 3 \, {\left(A c^{2} x^{4} + 2 \, A a c x^{2} + A a^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{8 \, {\left(a^{3} c^{3} x^{4} + 2 \, a^{4} c^{2} x^{2} + a^{5} c\right)}}\right]"," ",0,"[1/16*(6*A*a*c^2*x^3 + 10*A*a^2*c*x - 4*B*a^3 - 3*(A*c^2*x^4 + 2*A*a*c*x^2 + A*a^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a^3*c^3*x^4 + 2*a^4*c^2*x^2 + a^5*c), 1/8*(3*A*a*c^2*x^3 + 5*A*a^2*c*x - 2*B*a^3 + 3*(A*c^2*x^4 + 2*A*a*c*x^2 + A*a^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a))/(a^3*c^3*x^4 + 2*a^4*c^2*x^2 + a^5*c)]","A",0
1352,1,1797,0,135.503244," ","integrate((B*x+A)/(e*x+d)/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, B a^{3} c^{3} d^{5} - 4 \, A a^{3} c^{3} d^{4} e + 16 \, B a^{4} c^{2} d^{3} e^{2} - 16 \, A a^{4} c^{2} d^{2} e^{3} + 12 \, B a^{5} c d e^{4} - 12 \, A a^{5} c e^{5} - 2 \, {\left(3 \, A a c^{5} d^{5} - B a^{2} c^{4} d^{4} e + 10 \, A a^{2} c^{4} d^{3} e^{2} + 2 \, B a^{3} c^{3} d^{2} e^{3} + 7 \, A a^{3} c^{3} d e^{4} + 3 \, B a^{4} c^{2} e^{5}\right)} x^{3} + 8 \, {\left(B a^{3} c^{3} d^{3} e^{2} - A a^{3} c^{3} d^{2} e^{3} + B a^{4} c^{2} d e^{4} - A a^{4} c^{2} e^{5}\right)} x^{2} + {\left(3 \, A a^{2} c^{3} d^{5} - B a^{3} c^{2} d^{4} e + 10 \, A a^{3} c^{2} d^{3} e^{2} - 6 \, B a^{4} c d^{2} e^{3} + 15 \, A a^{4} c d e^{4} + 3 \, B a^{5} e^{5} + {\left(3 \, A c^{5} d^{5} - B a c^{4} d^{4} e + 10 \, A a c^{4} d^{3} e^{2} - 6 \, B a^{2} c^{3} d^{2} e^{3} + 15 \, A a^{2} c^{3} d e^{4} + 3 \, B a^{3} c^{2} e^{5}\right)} x^{4} + 2 \, {\left(3 \, A a c^{4} d^{5} - B a^{2} c^{3} d^{4} e + 10 \, A a^{2} c^{3} d^{3} e^{2} - 6 \, B a^{3} c^{2} d^{2} e^{3} + 15 \, A a^{3} c^{2} d e^{4} + 3 \, B a^{4} c e^{5}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(5 \, A a^{2} c^{4} d^{5} + B a^{3} c^{3} d^{4} e + 14 \, A a^{3} c^{3} d^{3} e^{2} + 6 \, B a^{4} c^{2} d^{2} e^{3} + 9 \, A a^{4} c^{2} d e^{4} + 5 \, B a^{5} c e^{5}\right)} x - 8 \, {\left(B a^{5} c d e^{4} - A a^{5} c e^{5} + {\left(B a^{3} c^{3} d e^{4} - A a^{3} c^{3} e^{5}\right)} x^{4} + 2 \, {\left(B a^{4} c^{2} d e^{4} - A a^{4} c^{2} e^{5}\right)} x^{2}\right)} \log\left(c x^{2} + a\right) + 16 \, {\left(B a^{5} c d e^{4} - A a^{5} c e^{5} + {\left(B a^{3} c^{3} d e^{4} - A a^{3} c^{3} e^{5}\right)} x^{4} + 2 \, {\left(B a^{4} c^{2} d e^{4} - A a^{4} c^{2} e^{5}\right)} x^{2}\right)} \log\left(e x + d\right)}{16 \, {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6} + {\left(a^{3} c^{6} d^{6} + 3 \, a^{4} c^{5} d^{4} e^{2} + 3 \, a^{5} c^{4} d^{2} e^{4} + a^{6} c^{3} e^{6}\right)} x^{4} + 2 \, {\left(a^{4} c^{5} d^{6} + 3 \, a^{5} c^{4} d^{4} e^{2} + 3 \, a^{6} c^{3} d^{2} e^{4} + a^{7} c^{2} e^{6}\right)} x^{2}\right)}}, -\frac{2 \, B a^{3} c^{3} d^{5} - 2 \, A a^{3} c^{3} d^{4} e + 8 \, B a^{4} c^{2} d^{3} e^{2} - 8 \, A a^{4} c^{2} d^{2} e^{3} + 6 \, B a^{5} c d e^{4} - 6 \, A a^{5} c e^{5} - {\left(3 \, A a c^{5} d^{5} - B a^{2} c^{4} d^{4} e + 10 \, A a^{2} c^{4} d^{3} e^{2} + 2 \, B a^{3} c^{3} d^{2} e^{3} + 7 \, A a^{3} c^{3} d e^{4} + 3 \, B a^{4} c^{2} e^{5}\right)} x^{3} + 4 \, {\left(B a^{3} c^{3} d^{3} e^{2} - A a^{3} c^{3} d^{2} e^{3} + B a^{4} c^{2} d e^{4} - A a^{4} c^{2} e^{5}\right)} x^{2} - {\left(3 \, A a^{2} c^{3} d^{5} - B a^{3} c^{2} d^{4} e + 10 \, A a^{3} c^{2} d^{3} e^{2} - 6 \, B a^{4} c d^{2} e^{3} + 15 \, A a^{4} c d e^{4} + 3 \, B a^{5} e^{5} + {\left(3 \, A c^{5} d^{5} - B a c^{4} d^{4} e + 10 \, A a c^{4} d^{3} e^{2} - 6 \, B a^{2} c^{3} d^{2} e^{3} + 15 \, A a^{2} c^{3} d e^{4} + 3 \, B a^{3} c^{2} e^{5}\right)} x^{4} + 2 \, {\left(3 \, A a c^{4} d^{5} - B a^{2} c^{3} d^{4} e + 10 \, A a^{2} c^{3} d^{3} e^{2} - 6 \, B a^{3} c^{2} d^{2} e^{3} + 15 \, A a^{3} c^{2} d e^{4} + 3 \, B a^{4} c e^{5}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(5 \, A a^{2} c^{4} d^{5} + B a^{3} c^{3} d^{4} e + 14 \, A a^{3} c^{3} d^{3} e^{2} + 6 \, B a^{4} c^{2} d^{2} e^{3} + 9 \, A a^{4} c^{2} d e^{4} + 5 \, B a^{5} c e^{5}\right)} x - 4 \, {\left(B a^{5} c d e^{4} - A a^{5} c e^{5} + {\left(B a^{3} c^{3} d e^{4} - A a^{3} c^{3} e^{5}\right)} x^{4} + 2 \, {\left(B a^{4} c^{2} d e^{4} - A a^{4} c^{2} e^{5}\right)} x^{2}\right)} \log\left(c x^{2} + a\right) + 8 \, {\left(B a^{5} c d e^{4} - A a^{5} c e^{5} + {\left(B a^{3} c^{3} d e^{4} - A a^{3} c^{3} e^{5}\right)} x^{4} + 2 \, {\left(B a^{4} c^{2} d e^{4} - A a^{4} c^{2} e^{5}\right)} x^{2}\right)} \log\left(e x + d\right)}{8 \, {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6} + {\left(a^{3} c^{6} d^{6} + 3 \, a^{4} c^{5} d^{4} e^{2} + 3 \, a^{5} c^{4} d^{2} e^{4} + a^{6} c^{3} e^{6}\right)} x^{4} + 2 \, {\left(a^{4} c^{5} d^{6} + 3 \, a^{5} c^{4} d^{4} e^{2} + 3 \, a^{6} c^{3} d^{2} e^{4} + a^{7} c^{2} e^{6}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(4*B*a^3*c^3*d^5 - 4*A*a^3*c^3*d^4*e + 16*B*a^4*c^2*d^3*e^2 - 16*A*a^4*c^2*d^2*e^3 + 12*B*a^5*c*d*e^4 - 12*A*a^5*c*e^5 - 2*(3*A*a*c^5*d^5 - B*a^2*c^4*d^4*e + 10*A*a^2*c^4*d^3*e^2 + 2*B*a^3*c^3*d^2*e^3 + 7*A*a^3*c^3*d*e^4 + 3*B*a^4*c^2*e^5)*x^3 + 8*(B*a^3*c^3*d^3*e^2 - A*a^3*c^3*d^2*e^3 + B*a^4*c^2*d*e^4 - A*a^4*c^2*e^5)*x^2 + (3*A*a^2*c^3*d^5 - B*a^3*c^2*d^4*e + 10*A*a^3*c^2*d^3*e^2 - 6*B*a^4*c*d^2*e^3 + 15*A*a^4*c*d*e^4 + 3*B*a^5*e^5 + (3*A*c^5*d^5 - B*a*c^4*d^4*e + 10*A*a*c^4*d^3*e^2 - 6*B*a^2*c^3*d^2*e^3 + 15*A*a^2*c^3*d*e^4 + 3*B*a^3*c^2*e^5)*x^4 + 2*(3*A*a*c^4*d^5 - B*a^2*c^3*d^4*e + 10*A*a^2*c^3*d^3*e^2 - 6*B*a^3*c^2*d^2*e^3 + 15*A*a^3*c^2*d*e^4 + 3*B*a^4*c*e^5)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(5*A*a^2*c^4*d^5 + B*a^3*c^3*d^4*e + 14*A*a^3*c^3*d^3*e^2 + 6*B*a^4*c^2*d^2*e^3 + 9*A*a^4*c^2*d*e^4 + 5*B*a^5*c*e^5)*x - 8*(B*a^5*c*d*e^4 - A*a^5*c*e^5 + (B*a^3*c^3*d*e^4 - A*a^3*c^3*e^5)*x^4 + 2*(B*a^4*c^2*d*e^4 - A*a^4*c^2*e^5)*x^2)*log(c*x^2 + a) + 16*(B*a^5*c*d*e^4 - A*a^5*c*e^5 + (B*a^3*c^3*d*e^4 - A*a^3*c^3*e^5)*x^4 + 2*(B*a^4*c^2*d*e^4 - A*a^4*c^2*e^5)*x^2)*log(e*x + d))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6 + (a^3*c^6*d^6 + 3*a^4*c^5*d^4*e^2 + 3*a^5*c^4*d^2*e^4 + a^6*c^3*e^6)*x^4 + 2*(a^4*c^5*d^6 + 3*a^5*c^4*d^4*e^2 + 3*a^6*c^3*d^2*e^4 + a^7*c^2*e^6)*x^2), -1/8*(2*B*a^3*c^3*d^5 - 2*A*a^3*c^3*d^4*e + 8*B*a^4*c^2*d^3*e^2 - 8*A*a^4*c^2*d^2*e^3 + 6*B*a^5*c*d*e^4 - 6*A*a^5*c*e^5 - (3*A*a*c^5*d^5 - B*a^2*c^4*d^4*e + 10*A*a^2*c^4*d^3*e^2 + 2*B*a^3*c^3*d^2*e^3 + 7*A*a^3*c^3*d*e^4 + 3*B*a^4*c^2*e^5)*x^3 + 4*(B*a^3*c^3*d^3*e^2 - A*a^3*c^3*d^2*e^3 + B*a^4*c^2*d*e^4 - A*a^4*c^2*e^5)*x^2 - (3*A*a^2*c^3*d^5 - B*a^3*c^2*d^4*e + 10*A*a^3*c^2*d^3*e^2 - 6*B*a^4*c*d^2*e^3 + 15*A*a^4*c*d*e^4 + 3*B*a^5*e^5 + (3*A*c^5*d^5 - B*a*c^4*d^4*e + 10*A*a*c^4*d^3*e^2 - 6*B*a^2*c^3*d^2*e^3 + 15*A*a^2*c^3*d*e^4 + 3*B*a^3*c^2*e^5)*x^4 + 2*(3*A*a*c^4*d^5 - B*a^2*c^3*d^4*e + 10*A*a^2*c^3*d^3*e^2 - 6*B*a^3*c^2*d^2*e^3 + 15*A*a^3*c^2*d*e^4 + 3*B*a^4*c*e^5)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (5*A*a^2*c^4*d^5 + B*a^3*c^3*d^4*e + 14*A*a^3*c^3*d^3*e^2 + 6*B*a^4*c^2*d^2*e^3 + 9*A*a^4*c^2*d*e^4 + 5*B*a^5*c*e^5)*x - 4*(B*a^5*c*d*e^4 - A*a^5*c*e^5 + (B*a^3*c^3*d*e^4 - A*a^3*c^3*e^5)*x^4 + 2*(B*a^4*c^2*d*e^4 - A*a^4*c^2*e^5)*x^2)*log(c*x^2 + a) + 8*(B*a^5*c*d*e^4 - A*a^5*c*e^5 + (B*a^3*c^3*d*e^4 - A*a^3*c^3*e^5)*x^4 + 2*(B*a^4*c^2*d*e^4 - A*a^4*c^2*e^5)*x^2)*log(e*x + d))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6 + (a^3*c^6*d^6 + 3*a^4*c^5*d^4*e^2 + 3*a^5*c^4*d^2*e^4 + a^6*c^3*e^6)*x^4 + 2*(a^4*c^5*d^6 + 3*a^5*c^4*d^4*e^2 + 3*a^6*c^3*d^2*e^4 + a^7*c^2*e^6)*x^2)]","B",0
1353,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1354,1,21,0,0.417755," ","integrate((-11+6*x)/(-1+2*x)/(x^2-1),x, algorithm=""fricas"")","\frac{16}{3} \, \log\left(2 \, x - 1\right) - \frac{17}{6} \, \log\left(x + 1\right) - \frac{5}{2} \, \log\left(x - 1\right)"," ",0,"16/3*log(2*x - 1) - 17/6*log(x + 1) - 5/2*log(x - 1)","A",0
1355,1,40,0,0.409530," ","integrate(x*(1+x)^2/(x^2+1)^3,x, algorithm=""fricas"")","\frac{x^{3} - 2 \, x^{2} + {\left(x^{4} + 2 \, x^{2} + 1\right)} \arctan\left(x\right) - x - 2}{4 \, {\left(x^{4} + 2 \, x^{2} + 1\right)}}"," ",0,"1/4*(x^3 - 2*x^2 + (x^4 + 2*x^2 + 1)*arctan(x) - x - 2)/(x^4 + 2*x^2 + 1)","A",0
1356,1,70,0,0.427731," ","integrate((5-x)*(3+2*x)^4*(3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{5670} \, {\left(12960 \, x^{6} + 15120 \, x^{5} - 297648 \, x^{4} - 1222200 \, x^{3} - 1956174 \, x^{2} - 1558935 \, x - 1167988\right)} \sqrt{3 \, x^{2} + 2} + \frac{2341}{54} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/5670*(12960*x^6 + 15120*x^5 - 297648*x^4 - 1222200*x^3 - 1956174*x^2 - 1558935*x - 1167988)*sqrt(3*x^2 + 2) + 2341/54*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1357,1,65,0,0.419556," ","integrate((5-x)*(3+2*x)^3*(3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{270} \, {\left(360 \, x^{5} - 216 \, x^{4} - 8445 \, x^{3} - 21918 \, x^{2} - 21120 \, x - 14516\right)} \sqrt{3 \, x^{2} + 2} + \frac{511}{27} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/270*(360*x^5 - 216*x^4 - 8445*x^3 - 21918*x^2 - 21120*x - 14516)*sqrt(3*x^2 + 2) + 511/27*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1358,1,60,0,0.411464," ","integrate((5-x)*(3+2*x)^2*(3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{270} \, {\left(216 \, x^{4} - 540 \, x^{3} - 4542 \, x^{2} - 6255 \, x - 3124\right)} \sqrt{3 \, x^{2} + 2} + \frac{131}{18} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/270*(216*x^4 - 540*x^3 - 4542*x^2 - 6255*x - 3124)*sqrt(3*x^2 + 2) + 131/18*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1359,1,55,0,0.417222," ","integrate((5-x)*(3+2*x)*(3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{18} \, {\left(9 \, x^{3} - 42 \, x^{2} - 132 \, x - 28\right)} \sqrt{3 \, x^{2} + 2} + \frac{23}{9} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/18*(9*x^3 - 42*x^2 - 132*x - 28)*sqrt(3*x^2 + 2) + 23/9*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1360,1,50,0,0.425264," ","integrate((5-x)*(3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{18} \, {\left(6 \, x^{2} - 45 \, x + 4\right)} \sqrt{3 \, x^{2} + 2} + \frac{5}{6} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/18*(6*x^2 - 45*x + 4)*sqrt(3*x^2 + 2) + 5/6*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1361,1,90,0,0.425733," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{3 \, x^{2} + 2} {\left(x - 13\right)} + \frac{121}{48} \, \sqrt{3} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + \frac{13}{16} \, \sqrt{35} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right)"," ",0,"-1/4*sqrt(3*x^2 + 2)*(x - 13) + 121/48*sqrt(3)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 13/16*sqrt(35)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9))","A",0
1362,1,109,0,0.427167," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^2,x, algorithm=""fricas"")","\frac{70 \, \sqrt{3} {\left(2 \, x + 3\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 19 \, \sqrt{35} {\left(2 \, x + 3\right)} \log\left(\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} - 93 \, x^{2} + 36 \, x - 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, \sqrt{3 \, x^{2} + 2} {\left(x + 8\right)}}{70 \, {\left(2 \, x + 3\right)}}"," ",0,"1/70*(70*sqrt(3)*(2*x + 3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 19*sqrt(35)*(2*x + 3)*log((sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) - 93*x^2 + 36*x - 43)/(4*x^2 + 12*x + 9)) - 35*sqrt(3*x^2 + 2)*(x + 8))/(2*x + 3)","A",0
1363,1,126,0,0.432990," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^3,x, algorithm=""fricas"")","\frac{1225 \, \sqrt{3} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 471 \, \sqrt{35} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) + 140 \, \sqrt{3 \, x^{2} + 2} {\left(187 \, x + 53\right)}}{19600 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/19600*(1225*sqrt(3)*(4*x^2 + 12*x + 9)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 471*sqrt(35)*(4*x^2 + 12*x + 9)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) + 140*sqrt(3*x^2 + 2)*(187*x + 53))/(4*x^2 + 12*x + 9)","B",0
1364,1,104,0,0.423430," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^4,x, algorithm=""fricas"")","\frac{369 \, \sqrt{35} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(516 \, x^{2} - 2337 \, x + 3296\right)} \sqrt{3 \, x^{2} + 2}}{257250 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/257250*(369*sqrt(35)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(516*x^2 - 2337*x + 3296)*sqrt(3*x^2 + 2))/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
1365,1,119,0,0.408824," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^5,x, algorithm=""fricas"")","\frac{594 \, \sqrt{35} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(2217 \, x^{3} + 10134 \, x^{2} - 304 \, x + 26028\right)} \sqrt{3 \, x^{2} + 2}}{1800750 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"1/1800750*(594*sqrt(35)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(2217*x^3 + 10134*x^2 - 304*x + 26028)*sqrt(3*x^2 + 2))/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
1366,1,134,0,0.419937," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^6,x, algorithm=""fricas"")","\frac{1017 \, \sqrt{35} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(11712 \, x^{4} + 76992 \, x^{3} + 186392 \, x^{2} + 108167 \, x + 222112\right)} \sqrt{3 \, x^{2} + 2}}{15006250 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"1/15006250*(1017*sqrt(35)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(11712*x^4 + 76992*x^3 + 186392*x^2 + 108167*x + 222112)*sqrt(3*x^2 + 2))/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
1367,1,149,0,0.423018," ","integrate((5-x)*(3*x^2+2)^(1/2)/(3+2*x)^7,x, algorithm=""fricas"")","\frac{18306 \, \sqrt{35} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(642132 \, x^{5} + 5388660 \, x^{4} + 18236055 \, x^{3} + 30753930 \, x^{2} + 18651300 \, x + 22308548\right)} \sqrt{3 \, x^{2} + 2}}{1575656250 \, {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)}}"," ",0,"1/1575656250*(18306*sqrt(35)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(642132*x^5 + 5388660*x^4 + 18236055*x^3 + 30753930*x^2 + 18651300*x + 22308548)*sqrt(3*x^2 + 2))/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)","A",0
1368,1,80,0,0.432913," ","integrate((5-x)*(3+2*x)^4*(3*x^2+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{34020} \, {\left(181440 \, x^{8} + 204120 \, x^{7} - 3676320 \, x^{6} - 14492520 \, x^{5} - 24490404 \, x^{4} - 27468315 \, x^{3} - 27537072 \, x^{2} - 19683405 \, x - 8598544\right)} \sqrt{3 \, x^{2} + 2} + \frac{2777}{36} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/34020*(181440*x^8 + 204120*x^7 - 3676320*x^6 - 14492520*x^5 - 24490404*x^4 - 27468315*x^3 - 27537072*x^2 - 19683405*x - 8598544)*sqrt(3*x^2 + 2) + 2777/36*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1369,1,75,0,0.416976," ","integrate((5-x)*(3+2*x)^3*(3*x^2+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{1260} \, {\left(3780 \, x^{7} - 2160 \, x^{6} - 75600 \, x^{5} - 186012 \, x^{4} - 219975 \, x^{3} - 245136 \, x^{2} - 226065 \, x - 81392\right)} \sqrt{3 \, x^{2} + 2} + \frac{1087}{36} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/1260*(3780*x^7 - 2160*x^6 - 75600*x^5 - 186012*x^4 - 219975*x^3 - 245136*x^2 - 226065*x - 81392)*sqrt(3*x^2 + 2) + 1087/36*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1370,1,70,0,0.421662," ","integrate((5-x)*(3+2*x)^2*(3*x^2+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{1260} \, {\left(2160 \, x^{6} - 5040 \, x^{5} - 36252 \, x^{4} - 48405 \, x^{3} - 51216 \, x^{2} - 71715 \, x - 17392\right)} \sqrt{3 \, x^{2} + 2} + \frac{397}{36} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/1260*(2160*x^6 - 5040*x^5 - 36252*x^4 - 48405*x^3 - 51216*x^2 - 71715*x - 17392)*sqrt(3*x^2 + 2) + 397/36*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1371,1,65,0,0.431818," ","integrate((5-x)*(3+2*x)*(3*x^2+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{60} \, {\left(60 \, x^{5} - 252 \, x^{4} - 605 \, x^{3} - 336 \, x^{2} - 1115 \, x - 112\right)} \sqrt{3 \, x^{2} + 2} + \frac{137}{36} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/60*(60*x^5 - 252*x^4 - 605*x^3 - 336*x^2 - 1115*x - 112)*sqrt(3*x^2 + 2) + 137/36*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1372,1,60,0,0.411784," ","integrate((5-x)*(3*x^2+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{60} \, {\left(36 \, x^{4} - 225 \, x^{3} + 48 \, x^{2} - 375 \, x + 16\right)} \sqrt{3 \, x^{2} + 2} + \frac{5}{4} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/60*(36*x^4 - 225*x^3 + 48*x^2 - 375*x + 16)*sqrt(3*x^2 + 2) + 5/4*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1373,1,102,0,0.468719," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x),x, algorithm=""fricas"")","-\frac{1}{48} \, {\left(18 \, x^{3} - 156 \, x^{2} + 381 \, x - 1469\right)} \sqrt{3 \, x^{2} + 2} + \frac{1529}{64} \, \sqrt{3} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + \frac{455}{64} \, \sqrt{35} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right)"," ",0,"-1/48*(18*x^3 - 156*x^2 + 381*x - 1469)*sqrt(3*x^2 + 2) + 1529/64*sqrt(3)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 455/64*sqrt(35)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9))","A",0
1374,1,121,0,0.444903," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^2,x, algorithm=""fricas"")","\frac{1989 \, \sqrt{3} {\left(2 \, x + 3\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 579 \, \sqrt{35} {\left(2 \, x + 3\right)} \log\left(\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} - 93 \, x^{2} + 36 \, x - 43}{4 \, x^{2} + 12 \, x + 9}\right) - 4 \, {\left(12 \, x^{3} - 126 \, x^{2} + 599 \, x + 1905\right)} \sqrt{3 \, x^{2} + 2}}{96 \, {\left(2 \, x + 3\right)}}"," ",0,"1/96*(1989*sqrt(3)*(2*x + 3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 579*sqrt(35)*(2*x + 3)*log((sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) - 93*x^2 + 36*x - 43)/(4*x^2 + 12*x + 9)) - 4*(12*x^3 - 126*x^2 + 599*x + 1905)*sqrt(3*x^2 + 2))/(2*x + 3)","A",0
1375,1,136,0,0.431219," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^3,x, algorithm=""fricas"")","\frac{3885 \, \sqrt{3} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 1143 \, \sqrt{35} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 140 \, {\left(3 \, x^{3} - 48 \, x^{2} - 328 \, x - 317\right)} \sqrt{3 \, x^{2} + 2}}{560 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/560*(3885*sqrt(3)*(4*x^2 + 12*x + 9)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 1143*sqrt(35)*(4*x^2 + 12*x + 9)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 140*(3*x^3 - 48*x^2 - 328*x - 317)*sqrt(3*x^2 + 2))/(4*x^2 + 12*x + 9)","A",0
1376,1,151,0,0.443693," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^4,x, algorithm=""fricas"")","\frac{121275 \, \sqrt{3} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 35181 \, \sqrt{35} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} - 93 \, x^{2} + 36 \, x - 43}{4 \, x^{2} + 12 \, x + 9}\right) - 140 \, {\left(1260 \, x^{3} + 24474 \, x^{2} + 48747 \, x + 30269\right)} \sqrt{3 \, x^{2} + 2}}{117600 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/117600*(121275*sqrt(3)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 35181*sqrt(35)*(8*x^3 + 36*x^2 + 54*x + 27)*log((sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) - 93*x^2 + 36*x - 43)/(4*x^2 + 12*x + 9)) - 140*(1260*x^3 + 24474*x^2 + 48747*x + 30269)*sqrt(3*x^2 + 2))/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
1377,1,166,0,0.437518," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^5,x, algorithm=""fricas"")","\frac{385875 \, \sqrt{3} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 118989 \, \sqrt{35} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) + 140 \, {\left(250602 \, x^{3} + 559764 \, x^{2} + 718441 \, x + 245943\right)} \sqrt{3 \, x^{2} + 2}}{8232000 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"1/8232000*(385875*sqrt(3)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 118989*sqrt(35)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) + 140*(250602*x^3 + 559764*x^2 + 718441*x + 245943)*sqrt(3*x^2 + 2))/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
1378,1,134,0,0.429489," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^6,x, algorithm=""fricas"")","\frac{1107 \, \sqrt{35} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(10602 \, x^{4} - 189543 \, x^{3} + 26682 \, x^{2} - 64493 \, x + 125252\right)} \sqrt{3 \, x^{2} + 2}}{6002500 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"1/6002500*(1107*sqrt(35)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(10602*x^4 - 189543*x^3 + 26682*x^2 - 64493*x + 125252)*sqrt(3*x^2 + 2))/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
1379,1,149,0,0.439812," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^7,x, algorithm=""fricas"")","\frac{81 \, \sqrt{35} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(432 \, x^{5} + 2160 \, x^{4} - 39195 \, x^{3} + 33180 \, x^{2} + 3675 \, x + 39748\right)} \sqrt{3 \, x^{2} + 2}}{1837500 \, {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)}}"," ",0,"1/1837500*(81*sqrt(35)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(432*x^5 + 2160*x^4 - 39195*x^3 + 33180*x^2 + 3675*x + 39748)*sqrt(3*x^2 + 2))/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)","A",0
1380,1,164,0,0.429438," ","integrate((5-x)*(3*x^2+2)^(3/2)/(3+2*x)^8,x, algorithm=""fricas"")","\frac{217809 \, \sqrt{35} {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(5104296 \, x^{6} + 44301924 \, x^{5} + 148868010 \, x^{4} - 98810025 \, x^{3} + 740031210 \, x^{2} + 256388969 \, x + 471103116\right)} \sqrt{3 \, x^{2} + 2}}{22059187500 \, {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)}}"," ",0,"1/22059187500*(217809*sqrt(35)*(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(5104296*x^6 + 44301924*x^5 + 148868010*x^4 - 98810025*x^3 + 740031210*x^2 + 256388969*x + 471103116)*sqrt(3*x^2 + 2))/(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)","A",0
1381,1,90,0,0.421962," ","integrate((5-x)*(3+2*x)^4*(3*x^2+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{53460} \, {\left(699840 \, x^{10} + 769824 \, x^{9} - 12921120 \, x^{8} - 50615928 \, x^{7} - 93646260 \, x^{6} - 129966606 \, x^{5} - 150762600 \, x^{4} - 127123425 \, x^{3} - 92160240 \, x^{2} - 64370295 \, x - 19537120\right)} \sqrt{3 \, x^{2} + 2} + \frac{4991}{36} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/53460*(699840*x^10 + 769824*x^9 - 12921120*x^8 - 50615928*x^7 - 93646260*x^6 - 129966606*x^5 - 150762600*x^4 - 127123425*x^3 - 92160240*x^2 - 64370295*x - 19537120)*sqrt(3*x^2 + 2) + 4991/36*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1382,1,85,0,0.418154," ","integrate((5-x)*(3+2*x)^3*(3*x^2+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{3240} \, {\left(23328 \, x^{9} - 12960 \, x^{8} - 418446 \, x^{7} - 1035720 \, x^{6} - 1503522 \, x^{5} - 2036880 \, x^{4} - 1922805 \, x^{3} - 1350240 \, x^{2} - 1245915 \, x - 299200\right)} \sqrt{3 \, x^{2} + 2} + \frac{3731}{72} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/3240*(23328*x^9 - 12960*x^8 - 418446*x^7 - 1035720*x^6 - 1503522*x^5 - 2036880*x^4 - 1922805*x^3 - 1350240*x^2 - 1245915*x - 299200)*sqrt(3*x^2 + 2) + 3731/72*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1383,1,80,0,0.426790," ","integrate((5-x)*(3+2*x)^2*(3*x^2+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{324} \, {\left(1296 \, x^{8} - 2916 \, x^{7} - 18900 \, x^{6} - 27378 \, x^{5} - 41256 \, x^{4} - 50571 \, x^{3} - 28272 \, x^{2} - 40365 \, x - 6368\right)} \sqrt{3 \, x^{2} + 2} + \frac{665}{36} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/324*(1296*x^8 - 2916*x^7 - 18900*x^6 - 27378*x^5 - 41256*x^4 - 50571*x^3 - 28272*x^2 - 40365*x - 6368)*sqrt(3*x^2 + 2) + 665/36*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1384,1,75,0,0.418255," ","integrate((5-x)*(3+2*x)*(3*x^2+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{24} \, {\left(54 \, x^{7} - 216 \, x^{6} - 438 \, x^{5} - 432 \, x^{4} - 1111 \, x^{3} - 288 \, x^{2} - 985 \, x - 64\right)} \sqrt{3 \, x^{2} + 2} + \frac{455}{72} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/24*(54*x^7 - 216*x^6 - 438*x^5 - 432*x^4 - 1111*x^3 - 288*x^2 - 985*x - 64)*sqrt(3*x^2 + 2) + 455/72*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1385,1,70,0,0.421829," ","integrate((5-x)*(3*x^2+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{84} \, {\left(108 \, x^{6} - 630 \, x^{5} + 216 \, x^{4} - 1365 \, x^{3} + 144 \, x^{2} - 1155 \, x + 32\right)} \sqrt{3 \, x^{2} + 2} + \frac{25}{12} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/84*(108*x^6 - 630*x^5 + 216*x^4 - 1365*x^3 + 144*x^2 - 1155*x + 32)*sqrt(3*x^2 + 2) + 25/12*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1386,1,112,0,0.438055," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x),x, algorithm=""fricas"")","-\frac{1}{960} \, {\left(720 \, x^{5} - 5616 \, x^{4} + 12090 \, x^{3} - 34788 \, x^{2} + 80295 \, x - 259571\right)} \sqrt{3 \, x^{2} + 2} + \frac{162673}{768} \, \sqrt{3} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + \frac{15925}{256} \, \sqrt{35} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right)"," ",0,"-1/960*(720*x^5 - 5616*x^4 + 12090*x^3 - 34788*x^2 + 80295*x - 259571)*sqrt(3*x^2 + 2) + 162673/768*sqrt(3)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 15925/256*sqrt(35)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9))","A",0
1387,1,131,0,0.439520," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^2,x, algorithm=""fricas"")","\frac{278145 \, \sqrt{3} {\left(2 \, x + 3\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 81375 \, \sqrt{35} {\left(2 \, x + 3\right)} \log\left(\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} - 93 \, x^{2} + 36 \, x - 43}{4 \, x^{2} + 12 \, x + 9}\right) - 4 \, {\left(216 \, x^{5} - 1836 \, x^{4} + 5118 \, x^{3} - 19458 \, x^{2} + 89521 \, x + 265989\right)} \sqrt{3 \, x^{2} + 2}}{960 \, {\left(2 \, x + 3\right)}}"," ",0,"1/960*(278145*sqrt(3)*(2*x + 3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 81375*sqrt(35)*(2*x + 3)*log((sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) - 93*x^2 + 36*x - 43)/(4*x^2 + 12*x + 9)) - 4*(216*x^5 - 1836*x^4 + 5118*x^3 - 19458*x^2 + 89521*x + 265989)*sqrt(3*x^2 + 2))/(2*x + 3)","A",0
1388,1,146,0,0.433666," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^3,x, algorithm=""fricas"")","\frac{43995 \, \sqrt{3} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 12885 \, \sqrt{35} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 4 \, {\left(72 \, x^{5} - 696 \, x^{4} + 2826 \, x^{3} - 19268 \, x^{2} - 127403 \, x - 126181\right)} \sqrt{3 \, x^{2} + 2}}{256 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/256*(43995*sqrt(3)*(4*x^2 + 12*x + 9)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 12885*sqrt(35)*(4*x^2 + 12*x + 9)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 4*(72*x^5 - 696*x^4 + 2826*x^3 - 19268*x^2 - 127403*x - 126181)*sqrt(3*x^2 + 2))/(4*x^2 + 12*x + 9)","A",0
1389,1,167,0,0.441430," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^4,x, algorithm=""fricas"")","\frac{10971 \, \sqrt{7} \sqrt{5} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(\frac{\sqrt{7} \sqrt{5} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} - 93 \, x^{2} + 36 \, x - 43}{4 \, x^{2} + 12 \, x + 9}\right) + 37485 \, \sqrt{3} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) - 28 \, {\left(36 \, x^{5} - 432 \, x^{4} + 3408 \, x^{3} + 37974 \, x^{2} + 77061 \, x + 46103\right)} \sqrt{3 \, x^{2} + 2}}{672 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/672*(10971*sqrt(7)*sqrt(5)*(8*x^3 + 36*x^2 + 54*x + 27)*log((sqrt(7)*sqrt(5)*sqrt(3*x^2 + 2)*(9*x - 4) - 93*x^2 + 36*x - 43)/(4*x^2 + 12*x + 9)) + 37485*sqrt(3)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) - 28*(36*x^5 - 432*x^4 + 3408*x^3 + 37974*x^2 + 77061*x + 46103)*sqrt(3*x^2 + 2))/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
1390,1,176,0,0.455951," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^5,x, algorithm=""fricas"")","\frac{1929375 \, \sqrt{3} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 565137 \, \sqrt{35} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 140 \, {\left(3024 \, x^{5} - 57456 \, x^{4} - 898734 \, x^{3} - 2762820 \, x^{2} - 3335009 \, x - 1421955\right)} \sqrt{3 \, x^{2} + 2}}{188160 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"1/188160*(1929375*sqrt(3)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 565137*sqrt(35)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 140*(3024*x^5 - 57456*x^4 - 898734*x^3 - 2762820*x^2 - 3335009*x - 1421955)*sqrt(3*x^2 + 2))/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
1391,1,191,0,0.434852," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^6,x, algorithm=""fricas"")","\frac{2701125 \, \sqrt{3} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 789723 \, \sqrt{35} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} - 93 \, x^{2} + 36 \, x - 43}{4 \, x^{2} + 12 \, x + 9}\right) - 140 \, {\left(88200 \, x^{5} + 2740188 \, x^{4} + 11367738 \, x^{3} + 20911298 \, x^{2} + 17940463 \, x + 5999363\right)} \sqrt{3 \, x^{2} + 2}}{2744000 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"1/2744000*(2701125*sqrt(3)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 789723*sqrt(35)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log((sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) - 93*x^2 + 36*x - 43)/(4*x^2 + 12*x + 9)) - 140*(88200*x^5 + 2740188*x^4 + 11367738*x^3 + 20911298*x^2 + 17940463*x + 5999363)*sqrt(3*x^2 + 2))/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
1392,1,206,0,0.446518," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^7,x, algorithm=""fricas"")","\frac{1620675 \, \sqrt{3} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 479277 \, \sqrt{35} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) + 140 \, {\left(4369608 \, x^{5} + 18915336 \, x^{4} + 47453802 \, x^{3} + 59256588 \, x^{2} + 39843609 \, x + 10361807\right)} \sqrt{3 \, x^{2} + 2}}{46099200 \, {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)}}"," ",0,"1/46099200*(1620675*sqrt(3)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 479277*sqrt(35)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) + 140*(4369608*x^5 + 18915336*x^4 + 47453802*x^3 + 59256588*x^2 + 39843609*x + 10361807)*sqrt(3*x^2 + 2))/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)","A",0
1393,1,164,0,0.441278," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^8,x, algorithm=""fricas"")","\frac{3321 \, \sqrt{35} {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(656424 \, x^{6} - 9455994 \, x^{5} - 2997810 \, x^{4} - 15015225 \, x^{3} + 3488490 \, x^{2} - 593639 \, x + 4499004\right)} \sqrt{3 \, x^{2} + 2}}{126052500 \, {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)}}"," ",0,"1/126052500*(3321*sqrt(35)*(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(656424*x^6 - 9455994*x^5 - 2997810*x^4 - 15015225*x^3 + 3488490*x^2 - 593639*x + 4499004)*sqrt(3*x^2 + 2))/(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)","A",0
1394,1,179,0,0.461498," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^9,x, algorithm=""fricas"")","\frac{18873 \, \sqrt{35} {\left(256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) + 35 \, {\left(49626 \, x^{7} + 2206008 \, x^{6} + 210306726 \, x^{5} + 33613440 \, x^{4} + 226355535 \, x^{3} - 178164896 \, x^{2} - 38788883 \, x - 104577556\right)} \sqrt{3 \, x^{2} + 2}}{2941225000 \, {\left(256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561\right)}}"," ",0,"1/2941225000*(18873*sqrt(35)*(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) + 35*(49626*x^7 + 2206008*x^6 + 210306726*x^5 + 33613440*x^4 + 226355535*x^3 - 178164896*x^2 - 38788883*x - 104577556)*sqrt(3*x^2 + 2))/(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561)","A",0
1395,1,194,0,0.449847," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^10,x, algorithm=""fricas"")","\frac{691821 \, \sqrt{35} {\left(512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(10968696 \, x^{8} + 30006612 \, x^{7} - 620594352 \, x^{6} - 25197346566 \, x^{5} + 9750269970 \, x^{4} - 11567526201 \, x^{3} + 42455611758 \, x^{2} + 11990965797 \, x + 15948113036\right)} \sqrt{3 \, x^{2} + 2}}{463242937500 \, {\left(512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right)}}"," ",0,"1/463242937500*(691821*sqrt(35)*(512*x^9 + 6912*x^8 + 41472*x^7 + 145152*x^6 + 326592*x^5 + 489888*x^4 + 489888*x^3 + 314928*x^2 + 118098*x + 19683)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(10968696*x^8 + 30006612*x^7 - 620594352*x^6 - 25197346566*x^5 + 9750269970*x^4 - 11567526201*x^3 + 42455611758*x^2 + 11990965797*x + 15948113036)*sqrt(3*x^2 + 2))/(512*x^9 + 6912*x^8 + 41472*x^7 + 145152*x^6 + 326592*x^5 + 489888*x^4 + 489888*x^3 + 314928*x^2 + 118098*x + 19683)","A",0
1396,1,209,0,0.446176," ","integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^11,x, algorithm=""fricas"")","\frac{53386857 \, \sqrt{35} {\left(1024 \, x^{10} + 15360 \, x^{9} + 103680 \, x^{8} + 414720 \, x^{7} + 1088640 \, x^{6} + 1959552 \, x^{5} + 2449440 \, x^{4} + 2099520 \, x^{3} + 1180980 \, x^{2} + 393660 \, x + 59049\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(7968937464 \, x^{9} + 101311348104 \, x^{8} + 544524933294 \, x^{7} + 1541962687104 \, x^{6} - 3078520541586 \, x^{5} + 11369945485836 \, x^{4} + 4704132871221 \, x^{3} + 18888919063956 \, x^{2} + 5421307926571 \, x + 5288003538036\right)} \sqrt{3 \, x^{2} + 2}}{162135028125000 \, {\left(1024 \, x^{10} + 15360 \, x^{9} + 103680 \, x^{8} + 414720 \, x^{7} + 1088640 \, x^{6} + 1959552 \, x^{5} + 2449440 \, x^{4} + 2099520 \, x^{3} + 1180980 \, x^{2} + 393660 \, x + 59049\right)}}"," ",0,"1/162135028125000*(53386857*sqrt(35)*(1024*x^10 + 15360*x^9 + 103680*x^8 + 414720*x^7 + 1088640*x^6 + 1959552*x^5 + 2449440*x^4 + 2099520*x^3 + 1180980*x^2 + 393660*x + 59049)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(7968937464*x^9 + 101311348104*x^8 + 544524933294*x^7 + 1541962687104*x^6 - 3078520541586*x^5 + 11369945485836*x^4 + 4704132871221*x^3 + 18888919063956*x^2 + 5421307926571*x + 5288003538036)*sqrt(3*x^2 + 2))/(1024*x^10 + 15360*x^9 + 103680*x^8 + 414720*x^7 + 1088640*x^6 + 1959552*x^5 + 2449440*x^4 + 2099520*x^3 + 1180980*x^2 + 393660*x + 59049)","A",0
1397,1,60,0,0.426747," ","integrate((5-x)*(3+2*x)^4/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{405} \, {\left(432 \, x^{4} + 540 \, x^{3} - 12264 \, x^{2} - 58860 \, x - 118513\right)} \sqrt{3 \, x^{2} + 2} + \frac{343}{18} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/405*(432*x^4 + 540*x^3 - 12264*x^2 - 58860*x - 118513)*sqrt(3*x^2 + 2) + 343/18*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1398,1,55,0,0.432250," ","integrate((5-x)*(3+2*x)^3/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{27} \, {\left(18 \, x^{3} - 12 \, x^{2} - 585 \, x - 2171\right)} \sqrt{3 \, x^{2} + 2} + \frac{275}{18} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/27*(18*x^3 - 12*x^2 - 585*x - 2171)*sqrt(3*x^2 + 2) + 275/18*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1399,1,50,0,0.414375," ","integrate((5-x)*(3+2*x)^2/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{27} \, {\left(12 \, x^{2} - 36 \, x - 475\right)} \sqrt{3 \, x^{2} + 2} + \frac{127}{18} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/27*(12*x^2 - 36*x - 475)*sqrt(3*x^2 + 2) + 127/18*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1400,1,43,0,0.419658," ","integrate((5-x)*(3+2*x)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, \sqrt{3 \, x^{2} + 2} {\left(x - 7\right)} + \frac{47}{18} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"-1/3*sqrt(3*x^2 + 2)*(x - 7) + 47/18*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
1401,1,40,0,0.417061," ","integrate((5-x)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{5}{6} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) - \frac{1}{3} \, \sqrt{3 \, x^{2} + 2}"," ",0,"5/6*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) - 1/3*sqrt(3*x^2 + 2)","A",0
1402,1,76,0,0.427364," ","integrate((5-x)/(3+2*x)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + \frac{13}{140} \, \sqrt{35} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right)"," ",0,"1/12*sqrt(3)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 13/140*sqrt(35)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9))","A",0
1403,1,74,0,0.421973," ","integrate((5-x)/(3+2*x)^2/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{41 \, \sqrt{35} {\left(2 \, x + 3\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 910 \, \sqrt{3 \, x^{2} + 2}}{2450 \, {\left(2 \, x + 3\right)}}"," ",0,"1/2450*(41*sqrt(35)*(2*x + 3)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 910*sqrt(3*x^2 + 2))/(2*x + 3)","A",0
1404,1,89,0,0.413269," ","integrate((5-x)/(3+2*x)^3/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{291 \, \sqrt{35} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 70 \, \sqrt{3 \, x^{2} + 2} {\left(281 \, x + 649\right)}}{85750 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/85750*(291*sqrt(35)*(4*x^2 + 12*x + 9)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 70*sqrt(3*x^2 + 2)*(281*x + 649))/(4*x^2 + 12*x + 9)","A",0
1405,1,104,0,0.445456," ","integrate((5-x)/(3+2*x)^4/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{171 \, \sqrt{35} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 70 \, {\left(600 \, x^{2} + 2472 \, x + 2995\right)} \sqrt{3 \, x^{2} + 2}}{360150 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/360150*(171*sqrt(35)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 70*(600*x^2 + 2472*x + 2995)*sqrt(3*x^2 + 2))/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
1406,1,118,0,0.442765," ","integrate((5-x)/(3+2*x)^5/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{81 \, \sqrt{35} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} - 93 \, x^{2} + 36 \, x - 43}{4 \, x^{2} + 12 \, x + 9}\right) - 70 \, {\left(5946 \, x^{3} + 35892 \, x^{2} + 79423 \, x + 70389\right)} \sqrt{3 \, x^{2} + 2}}{9003750 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"1/9003750*(81*sqrt(35)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log((sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) - 93*x^2 + 36*x - 43)/(4*x^2 + 12*x + 9)) - 70*(5946*x^3 + 35892*x^2 + 79423*x + 70389)*sqrt(3*x^2 + 2))/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
1407,1,133,0,0.447883," ","integrate((5-x)/(3+2*x)^6/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{19737 \, \sqrt{35} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} - 93 \, x^{2} + 36 \, x - 43}{4 \, x^{2} + 12 \, x + 9}\right) - 70 \, {\left(80184 \, x^{4} + 706644 \, x^{3} + 2487944 \, x^{2} + 4314244 \, x + 3409859\right)} \sqrt{3 \, x^{2} + 2}}{525218750 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"1/525218750*(19737*sqrt(35)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log((sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) - 93*x^2 + 36*x - 43)/(4*x^2 + 12*x + 9)) - 70*(80184*x^4 + 706644*x^3 + 2487944*x^2 + 4314244*x + 3409859)*sqrt(3*x^2 + 2))/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
1408,1,78,0,0.414535," ","integrate((5-x)*(3+2*x)^4/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{7920 \, \sqrt{3} {\left(3 \, x^{2} + 2\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) - {\left(288 \, x^{4} + 432 \, x^{3} - 15024 \, x^{2} + 14715 \, x + 33914\right)} \sqrt{3 \, x^{2} + 2}}{162 \, {\left(3 \, x^{2} + 2\right)}}"," ",0,"1/162*(7920*sqrt(3)*(3*x^2 + 2)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) - (288*x^4 + 432*x^3 - 15024*x^2 + 14715*x + 33914)*sqrt(3*x^2 + 2))/(3*x^2 + 2)","A",0
1409,1,73,0,0.489643," ","integrate((5-x)*(3+2*x)^3/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{134 \, \sqrt{3} {\left(3 \, x^{2} + 2\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) - {\left(24 \, x^{3} - 24 \, x^{2} - 411 \, x + 1426\right)} \sqrt{3 \, x^{2} + 2}}{18 \, {\left(3 \, x^{2} + 2\right)}}"," ",0,"1/18*(134*sqrt(3)*(3*x^2 + 2)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) - (24*x^3 - 24*x^2 - 411*x + 1426)*sqrt(3*x^2 + 2))/(3*x^2 + 2)","A",0
1410,1,68,0,0.422459," ","integrate((5-x)*(3+2*x)^2/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{3} {\left(3 \, x^{2} + 2\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) - {\left(24 \, x^{2} - 357 \, x + 338\right)} \sqrt{3 \, x^{2} + 2}}{18 \, {\left(3 \, x^{2} + 2\right)}}"," ",0,"1/18*(8*sqrt(3)*(3*x^2 + 2)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) - (24*x^2 - 357*x + 338)*sqrt(3*x^2 + 2))/(3*x^2 + 2)","A",0
1411,1,62,0,0.417153," ","integrate((5-x)*(3+2*x)/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} {\left(3 \, x^{2} + 2\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 21 \, \sqrt{3 \, x^{2} + 2} {\left(7 \, x - 2\right)}}{18 \, {\left(3 \, x^{2} + 2\right)}}"," ",0,"1/18*(2*sqrt(3)*(3*x^2 + 2)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 21*sqrt(3*x^2 + 2)*(7*x - 2))/(3*x^2 + 2)","B",0
1412,1,16,0,0.405209," ","integrate((5-x)/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{15 \, x + 2}{6 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"1/6*(15*x + 2)/sqrt(3*x^2 + 2)","A",0
1413,1,83,0,0.426903," ","integrate((5-x)/(3+2*x)/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{26 \, \sqrt{35} {\left(3 \, x^{2} + 2\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) + 35 \, \sqrt{3 \, x^{2} + 2} {\left(41 \, x + 26\right)}}{2450 \, {\left(3 \, x^{2} + 2\right)}}"," ",0,"1/2450*(26*sqrt(35)*(3*x^2 + 2)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) + 35*sqrt(3*x^2 + 2)*(41*x + 26))/(3*x^2 + 2)","A",0
1414,1,104,0,0.468762," ","integrate((5-x)/(3+2*x)^2/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{632 \, \sqrt{35} {\left(6 \, x^{3} + 9 \, x^{2} + 4 \, x + 6\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) + 35 \, {\left(114 \, x^{2} + 1435 \, x + 986\right)} \sqrt{3 \, x^{2} + 2}}{85750 \, {\left(6 \, x^{3} + 9 \, x^{2} + 4 \, x + 6\right)}}"," ",0,"1/85750*(632*sqrt(35)*(6*x^3 + 9*x^2 + 4*x + 6)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) + 35*(114*x^2 + 1435*x + 986)*sqrt(3*x^2 + 2))/(6*x^3 + 9*x^2 + 4*x + 6)","A",0
1415,1,119,0,0.444239," ","integrate((5-x)/(3+2*x)^3/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{1962 \, \sqrt{35} {\left(12 \, x^{4} + 36 \, x^{3} + 35 \, x^{2} + 24 \, x + 18\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(3972 \, x^{3} + 4068 \, x^{2} - 7397 \, x - 3658\right)} \sqrt{3 \, x^{2} + 2}}{600250 \, {\left(12 \, x^{4} + 36 \, x^{3} + 35 \, x^{2} + 24 \, x + 18\right)}}"," ",0,"1/600250*(1962*sqrt(35)*(12*x^4 + 36*x^3 + 35*x^2 + 24*x + 18)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(3972*x^3 + 4068*x^2 - 7397*x - 3658)*sqrt(3*x^2 + 2))/(12*x^4 + 36*x^3 + 35*x^2 + 24*x + 18)","A",0
1416,1,134,0,0.419076," ","integrate((5-x)/(3+2*x)^4/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{9936 \, \sqrt{35} {\left(24 \, x^{5} + 108 \, x^{4} + 178 \, x^{3} + 153 \, x^{2} + 108 \, x + 54\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(75672 \, x^{4} + 261036 \, x^{3} + 237930 \, x^{2} + 23349 \, x + 29438\right)} \sqrt{3 \, x^{2} + 2}}{9003750 \, {\left(24 \, x^{5} + 108 \, x^{4} + 178 \, x^{3} + 153 \, x^{2} + 108 \, x + 54\right)}}"," ",0,"1/9003750*(9936*sqrt(35)*(24*x^5 + 108*x^4 + 178*x^3 + 153*x^2 + 108*x + 54)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(75672*x^4 + 261036*x^3 + 237930*x^2 + 23349*x + 29438)*sqrt(3*x^2 + 2))/(24*x^5 + 108*x^4 + 178*x^3 + 153*x^2 + 108*x + 54)","A",0
1417,1,149,0,0.435220," ","integrate((5-x)/(3+2*x)^5/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{90234 \, \sqrt{35} {\left(48 \, x^{6} + 288 \, x^{5} + 680 \, x^{4} + 840 \, x^{3} + 675 \, x^{2} + 432 \, x + 162\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(2151936 \, x^{5} + 11467872 \, x^{4} + 22188792 \, x^{3} + 18957672 \, x^{2} + 8562487 \, x + 4197366\right)} \sqrt{3 \, x^{2} + 2}}{315131250 \, {\left(48 \, x^{6} + 288 \, x^{5} + 680 \, x^{4} + 840 \, x^{3} + 675 \, x^{2} + 432 \, x + 162\right)}}"," ",0,"1/315131250*(90234*sqrt(35)*(48*x^6 + 288*x^5 + 680*x^4 + 840*x^3 + 675*x^2 + 432*x + 162)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(2151936*x^5 + 11467872*x^4 + 22188792*x^3 + 18957672*x^2 + 8562487*x + 4197366)*sqrt(3*x^2 + 2))/(48*x^6 + 288*x^5 + 680*x^4 + 840*x^3 + 675*x^2 + 432*x + 162)","A",0
1418,1,98,0,0.418624," ","integrate((5-x)*(3+2*x)^6/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{62160 \, \sqrt{3} {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) - {\left(3456 \, x^{6} + 20736 \, x^{5} - 130464 \, x^{4} - 1125999 \, x^{3} + 2363976 \, x^{2} - 139815 \, x + 1798610\right)} \sqrt{3 \, x^{2} + 2}}{486 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/486*(62160*sqrt(3)*(9*x^4 + 12*x^2 + 4)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) - (3456*x^6 + 20736*x^5 - 130464*x^4 - 1125999*x^3 + 2363976*x^2 - 139815*x + 1798610)*sqrt(3*x^2 + 2))/(9*x^4 + 12*x^2 + 4)","A",0
1419,1,93,0,0.419895," ","integrate((5-x)*(3+2*x)^5/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{1600 \, \sqrt{3} {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) - {\left(864 \, x^{5} + 4320 \, x^{4} - 183945 \, x^{3} + 147600 \, x^{2} - 79215 \, x + 134126\right)} \sqrt{3 \, x^{2} + 2}}{162 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/162*(1600*sqrt(3)*(9*x^4 + 12*x^2 + 4)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) - (864*x^5 + 4320*x^4 - 183945*x^3 + 147600*x^2 - 79215*x + 134126)*sqrt(3*x^2 + 2))/(9*x^4 + 12*x^2 + 4)","A",0
1420,1,87,0,0.408106," ","integrate((5-x)*(3+2*x)^4/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{48 \, \sqrt{3} {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) - {\left(864 \, x^{4} - 57285 \, x^{3} + 16560 \, x^{2} - 33381 \, x + 25342\right)} \sqrt{3 \, x^{2} + 2}}{162 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/162*(48*sqrt(3)*(9*x^4 + 12*x^2 + 4)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) - (864*x^4 - 57285*x^3 + 16560*x^2 - 33381*x + 25342)*sqrt(3*x^2 + 2))/(9*x^4 + 12*x^2 + 4)","A",0
1421,1,81,0,0.418753," ","integrate((5-x)*(3+2*x)^3/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{3} {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + {\left(4971 \, x^{3} - 72 \, x^{2} + 3741 \, x - 1490\right)} \sqrt{3 \, x^{2} + 2}}{54 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/54*(8*sqrt(3)*(9*x^4 + 12*x^2 + 4)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + (4971*x^3 - 72*x^2 + 3741*x - 1490)*sqrt(3*x^2 + 2))/(9*x^4 + 12*x^2 + 4)","A",0
1422,1,40,0,0.405383," ","integrate((5-x)*(3+2*x)^2/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(1287 \, x^{3} + 72 \, x^{2} + 1215 \, x - 274\right)} \sqrt{3 \, x^{2} + 2}}{54 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/54*(1287*x^3 + 72*x^2 + 1215*x - 274)*sqrt(3*x^2 + 2)/(9*x^4 + 12*x^2 + 4)","A",0
1423,1,35,0,0.410323," ","integrate((5-x)*(3+2*x)/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(129 \, x^{3} + 135 \, x - 14\right)} \sqrt{3 \, x^{2} + 2}}{18 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/18*(129*x^3 + 135*x - 14)*sqrt(3*x^2 + 2)/(9*x^4 + 12*x^2 + 4)","A",0
1424,1,35,0,0.426373," ","integrate((5-x)/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(45 \, x^{3} + 45 \, x + 2\right)} \sqrt{3 \, x^{2} + 2}}{18 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/18*(45*x^3 + 45*x + 2)*sqrt(3*x^2 + 2)/(9*x^4 + 12*x^2 + 4)","A",0
1425,1,103,0,0.437874," ","integrate((5-x)/(3+2*x)/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{312 \, \sqrt{35} {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) + 35 \, {\left(6411 \, x^{3} + 936 \, x^{2} + 5709 \, x + 1534\right)} \sqrt{3 \, x^{2} + 2}}{257250 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/257250*(312*sqrt(35)*(9*x^4 + 12*x^2 + 4)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) + 35*(6411*x^3 + 936*x^2 + 5709*x + 1534)*sqrt(3*x^2 + 2))/(9*x^4 + 12*x^2 + 4)","A",0
1426,1,134,0,0.434596," ","integrate((5-x)/(3+2*x)^2/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{528 \, \sqrt{35} {\left(18 \, x^{5} + 27 \, x^{4} + 24 \, x^{3} + 36 \, x^{2} + 8 \, x + 12\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) + 35 \, {\left(4986 \, x^{4} + 10647 \, x^{3} + 7362 \, x^{2} + 9107 \, x + 3966\right)} \sqrt{3 \, x^{2} + 2}}{360150 \, {\left(18 \, x^{5} + 27 \, x^{4} + 24 \, x^{3} + 36 \, x^{2} + 8 \, x + 12\right)}}"," ",0,"1/360150*(528*sqrt(35)*(18*x^5 + 27*x^4 + 24*x^3 + 36*x^2 + 8*x + 12)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) + 35*(4986*x^4 + 10647*x^3 + 7362*x^2 + 9107*x + 3966)*sqrt(3*x^2 + 2))/(18*x^5 + 27*x^4 + 24*x^3 + 36*x^2 + 8*x + 12)","A",0
1427,1,149,0,0.440993," ","integrate((5-x)/(3+2*x)^3/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{3072 \, \sqrt{35} {\left(36 \, x^{6} + 108 \, x^{5} + 129 \, x^{4} + 144 \, x^{3} + 124 \, x^{2} + 48 \, x + 36\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) + 35 \, {\left(10284 \, x^{5} + 67716 \, x^{4} + 116367 \, x^{3} + 91268 \, x^{2} + 89749 \, x + 41366\right)} \sqrt{3 \, x^{2} + 2}}{3001250 \, {\left(36 \, x^{6} + 108 \, x^{5} + 129 \, x^{4} + 144 \, x^{3} + 124 \, x^{2} + 48 \, x + 36\right)}}"," ",0,"1/3001250*(3072*sqrt(35)*(36*x^6 + 108*x^5 + 129*x^4 + 144*x^3 + 124*x^2 + 48*x + 36)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) + 35*(10284*x^5 + 67716*x^4 + 116367*x^3 + 91268*x^2 + 89749*x + 41366)*sqrt(3*x^2 + 2))/(36*x^6 + 108*x^5 + 129*x^4 + 144*x^3 + 124*x^2 + 48*x + 36)","A",0
1428,1,164,0,0.449767," ","integrate((5-x)/(3+2*x)^4/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{166032 \, \sqrt{35} {\left(72 \, x^{7} + 324 \, x^{6} + 582 \, x^{5} + 675 \, x^{4} + 680 \, x^{3} + 468 \, x^{2} + 216 \, x + 108\right)} \log\left(-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2} {\left(9 \, x - 4\right)} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right) - 35 \, {\left(1293192 \, x^{6} + 1834596 \, x^{5} - 4920642 \, x^{4} - 9795297 \, x^{3} - 7866162 \, x^{2} - 9103449 \, x - 3788738\right)} \sqrt{3 \, x^{2} + 2}}{315131250 \, {\left(72 \, x^{7} + 324 \, x^{6} + 582 \, x^{5} + 675 \, x^{4} + 680 \, x^{3} + 468 \, x^{2} + 216 \, x + 108\right)}}"," ",0,"1/315131250*(166032*sqrt(35)*(72*x^7 + 324*x^6 + 582*x^5 + 675*x^4 + 680*x^3 + 468*x^2 + 216*x + 108)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(1293192*x^6 + 1834596*x^5 - 4920642*x^4 - 9795297*x^3 - 7866162*x^2 - 9103449*x - 3788738)*sqrt(3*x^2 + 2))/(72*x^7 + 324*x^6 + 582*x^5 + 675*x^4 + 680*x^3 + 468*x^2 + 216*x + 108)","A",0
1429,1,190,0,0.406096," ","integrate((B*x+A)*(e*x+d)^(3/2)*(c*x^2+a),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B c e^{5} x^{5} - 48 \, B c d^{5} + 88 \, A c d^{4} e - 198 \, B a d^{3} e^{2} + 693 \, A a d^{2} e^{3} + 35 \, {\left(12 \, B c d e^{4} + 11 \, A c e^{5}\right)} x^{4} + 5 \, {\left(3 \, B c d^{2} e^{3} + 110 \, A c d e^{4} + 99 \, B a e^{5}\right)} x^{3} - 3 \, {\left(6 \, B c d^{3} e^{2} - 11 \, A c d^{2} e^{3} - 264 \, B a d e^{4} - 231 \, A a e^{5}\right)} x^{2} + {\left(24 \, B c d^{4} e - 44 \, A c d^{3} e^{2} + 99 \, B a d^{2} e^{3} + 1386 \, A a d e^{4}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{4}}"," ",0,"2/3465*(315*B*c*e^5*x^5 - 48*B*c*d^5 + 88*A*c*d^4*e - 198*B*a*d^3*e^2 + 693*A*a*d^2*e^3 + 35*(12*B*c*d*e^4 + 11*A*c*e^5)*x^4 + 5*(3*B*c*d^2*e^3 + 110*A*c*d*e^4 + 99*B*a*e^5)*x^3 - 3*(6*B*c*d^3*e^2 - 11*A*c*d^2*e^3 - 264*B*a*d*e^4 - 231*A*a*e^5)*x^2 + (24*B*c*d^4*e - 44*A*c*d^3*e^2 + 99*B*a*d^2*e^3 + 1386*A*a*d*e^4)*x)*sqrt(e*x + d)/e^4","A",0
1430,1,143,0,0.422309," ","integrate((B*x+A)*(c*x^2+a)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c e^{4} x^{4} - 16 \, B c d^{4} + 24 \, A c d^{3} e - 42 \, B a d^{2} e^{2} + 105 \, A a d e^{3} + 5 \, {\left(B c d e^{3} + 9 \, A c e^{4}\right)} x^{3} - 3 \, {\left(2 \, B c d^{2} e^{2} - 3 \, A c d e^{3} - 21 \, B a e^{4}\right)} x^{2} + {\left(8 \, B c d^{3} e - 12 \, A c d^{2} e^{2} + 21 \, B a d e^{3} + 105 \, A a e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{4}}"," ",0,"2/315*(35*B*c*e^4*x^4 - 16*B*c*d^4 + 24*A*c*d^3*e - 42*B*a*d^2*e^2 + 105*A*a*d*e^3 + 5*(B*c*d*e^3 + 9*A*c*e^4)*x^3 - 3*(2*B*c*d^2*e^2 - 3*A*c*d*e^3 - 21*B*a*e^4)*x^2 + (8*B*c*d^3*e - 12*A*c*d^2*e^2 + 21*B*a*d*e^3 + 105*A*a*e^4)*x)*sqrt(e*x + d)/e^4","A",0
1431,1,100,0,0.433661," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c e^{3} x^{3} - 48 \, B c d^{3} + 56 \, A c d^{2} e - 70 \, B a d e^{2} + 105 \, A a e^{3} - 3 \, {\left(6 \, B c d e^{2} - 7 \, A c e^{3}\right)} x^{2} + {\left(24 \, B c d^{2} e - 28 \, A c d e^{2} + 35 \, B a e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{4}}"," ",0,"2/105*(15*B*c*e^3*x^3 - 48*B*c*d^3 + 56*A*c*d^2*e - 70*B*a*d*e^2 + 105*A*a*e^3 - 3*(6*B*c*d*e^2 - 7*A*c*e^3)*x^2 + (24*B*c*d^2*e - 28*A*c*d*e^2 + 35*B*a*e^3)*x)*sqrt(e*x + d)/e^4","A",0
1432,1,110,0,0.418455," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c e^{3} x^{3} + 48 \, B c d^{3} - 40 \, A c d^{2} e + 30 \, B a d e^{2} - 15 \, A a e^{3} - {\left(6 \, B c d e^{2} - 5 \, A c e^{3}\right)} x^{2} + {\left(24 \, B c d^{2} e - 20 \, A c d e^{2} + 15 \, B a e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"2/15*(3*B*c*e^3*x^3 + 48*B*c*d^3 - 40*A*c*d^2*e + 30*B*a*d*e^2 - 15*A*a*e^3 - (6*B*c*d*e^2 - 5*A*c*e^3)*x^2 + (24*B*c*d^2*e - 20*A*c*d*e^2 + 15*B*a*e^3)*x)*sqrt(e*x + d)/(e^5*x + d*e^4)","A",0
1433,1,120,0,0.407992," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B c e^{3} x^{3} - 16 \, B c d^{3} + 8 \, A c d^{2} e - 2 \, B a d e^{2} - A a e^{3} - 3 \, {\left(2 \, B c d e^{2} - A c e^{3}\right)} x^{2} - 3 \, {\left(8 \, B c d^{2} e - 4 \, A c d e^{2} + B a e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"2/3*(B*c*e^3*x^3 - 16*B*c*d^3 + 8*A*c*d^2*e - 2*B*a*d*e^2 - A*a*e^3 - 3*(2*B*c*d*e^2 - A*c*e^3)*x^2 - 3*(8*B*c*d^2*e - 4*A*c*d*e^2 + B*a*e^3)*x)*sqrt(e*x + d)/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1434,1,133,0,0.409919," ","integrate((B*x+A)*(c*x^2+a)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c e^{3} x^{3} + 48 \, B c d^{3} - 8 \, A c d^{2} e - 2 \, B a d e^{2} - 3 \, A a e^{3} + 15 \, {\left(6 \, B c d e^{2} - A c e^{3}\right)} x^{2} + 5 \, {\left(24 \, B c d^{2} e - 4 \, A c d e^{2} - B a e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"2/15*(15*B*c*e^3*x^3 + 48*B*c*d^3 - 8*A*c*d^2*e - 2*B*a*d*e^2 - 3*A*a*e^3 + 15*(6*B*c*d*e^2 - A*c*e^3)*x^2 + 5*(24*B*c*d^2*e - 4*A*c*d*e^2 - B*a*e^3)*x)*sqrt(e*x + d)/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1435,1,320,0,0.417839," ","integrate((B*x+A)*(c*x^2+a)^2*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, B c^{2} e^{6} x^{6} - 1280 \, B c^{2} d^{6} + 1664 \, A c^{2} d^{5} e - 4576 \, B a c d^{4} e^{2} + 6864 \, A a c d^{3} e^{3} - 6006 \, B a^{2} d^{2} e^{4} + 15015 \, A a^{2} d e^{5} + 315 \, {\left(B c^{2} d e^{5} + 13 \, A c^{2} e^{6}\right)} x^{5} - 35 \, {\left(10 \, B c^{2} d^{2} e^{4} - 13 \, A c^{2} d e^{5} - 286 \, B a c e^{6}\right)} x^{4} + 10 \, {\left(40 \, B c^{2} d^{3} e^{3} - 52 \, A c^{2} d^{2} e^{4} + 143 \, B a c d e^{5} + 1287 \, A a c e^{6}\right)} x^{3} - 3 \, {\left(160 \, B c^{2} d^{4} e^{2} - 208 \, A c^{2} d^{3} e^{3} + 572 \, B a c d^{2} e^{4} - 858 \, A a c d e^{5} - 3003 \, B a^{2} e^{6}\right)} x^{2} + {\left(640 \, B c^{2} d^{5} e - 832 \, A c^{2} d^{4} e^{2} + 2288 \, B a c d^{3} e^{3} - 3432 \, A a c d^{2} e^{4} + 3003 \, B a^{2} d e^{5} + 15015 \, A a^{2} e^{6}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{6}}"," ",0,"2/45045*(3465*B*c^2*e^6*x^6 - 1280*B*c^2*d^6 + 1664*A*c^2*d^5*e - 4576*B*a*c*d^4*e^2 + 6864*A*a*c*d^3*e^3 - 6006*B*a^2*d^2*e^4 + 15015*A*a^2*d*e^5 + 315*(B*c^2*d*e^5 + 13*A*c^2*e^6)*x^5 - 35*(10*B*c^2*d^2*e^4 - 13*A*c^2*d*e^5 - 286*B*a*c*e^6)*x^4 + 10*(40*B*c^2*d^3*e^3 - 52*A*c^2*d^2*e^4 + 143*B*a*c*d*e^5 + 1287*A*a*c*e^6)*x^3 - 3*(160*B*c^2*d^4*e^2 - 208*A*c^2*d^3*e^3 + 572*B*a*c*d^2*e^4 - 858*A*a*c*d*e^5 - 3003*B*a^2*e^6)*x^2 + (640*B*c^2*d^5*e - 832*A*c^2*d^4*e^2 + 2288*B*a*c*d^3*e^3 - 3432*A*a*c*d^2*e^4 + 3003*B*a^2*d*e^5 + 15015*A*a^2*e^6)*x)*sqrt(e*x + d)/e^6","A",0
1436,1,247,0,0.393269," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B c^{2} e^{5} x^{5} - 1280 \, B c^{2} d^{5} + 1408 \, A c^{2} d^{4} e - 3168 \, B a c d^{3} e^{2} + 3696 \, A a c d^{2} e^{3} - 2310 \, B a^{2} d e^{4} + 3465 \, A a^{2} e^{5} - 35 \, {\left(10 \, B c^{2} d e^{4} - 11 \, A c^{2} e^{5}\right)} x^{4} + 10 \, {\left(40 \, B c^{2} d^{2} e^{3} - 44 \, A c^{2} d e^{4} + 99 \, B a c e^{5}\right)} x^{3} - 6 \, {\left(80 \, B c^{2} d^{3} e^{2} - 88 \, A c^{2} d^{2} e^{3} + 198 \, B a c d e^{4} - 231 \, A a c e^{5}\right)} x^{2} + {\left(640 \, B c^{2} d^{4} e - 704 \, A c^{2} d^{3} e^{2} + 1584 \, B a c d^{2} e^{3} - 1848 \, A a c d e^{4} + 1155 \, B a^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{6}}"," ",0,"2/3465*(315*B*c^2*e^5*x^5 - 1280*B*c^2*d^5 + 1408*A*c^2*d^4*e - 3168*B*a*c*d^3*e^2 + 3696*A*a*c*d^2*e^3 - 2310*B*a^2*d*e^4 + 3465*A*a^2*e^5 - 35*(10*B*c^2*d*e^4 - 11*A*c^2*e^5)*x^4 + 10*(40*B*c^2*d^2*e^3 - 44*A*c^2*d*e^4 + 99*B*a*c*e^5)*x^3 - 6*(80*B*c^2*d^3*e^2 - 88*A*c^2*d^2*e^3 + 198*B*a*c*d*e^4 - 231*A*a*c*e^5)*x^2 + (640*B*c^2*d^4*e - 704*A*c^2*d^3*e^2 + 1584*B*a*c*d^2*e^3 - 1848*A*a*c*d*e^4 + 1155*B*a^2*e^5)*x)*sqrt(e*x + d)/e^6","A",0
1437,1,257,0,0.405985," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{2} e^{5} x^{5} + 1280 \, B c^{2} d^{5} - 1152 \, A c^{2} d^{4} e + 2016 \, B a c d^{3} e^{2} - 1680 \, A a c d^{2} e^{3} + 630 \, B a^{2} d e^{4} - 315 \, A a^{2} e^{5} - 5 \, {\left(10 \, B c^{2} d e^{4} - 9 \, A c^{2} e^{5}\right)} x^{4} + 2 \, {\left(40 \, B c^{2} d^{2} e^{3} - 36 \, A c^{2} d e^{4} + 63 \, B a c e^{5}\right)} x^{3} - 2 \, {\left(80 \, B c^{2} d^{3} e^{2} - 72 \, A c^{2} d^{2} e^{3} + 126 \, B a c d e^{4} - 105 \, A a c e^{5}\right)} x^{2} + {\left(640 \, B c^{2} d^{4} e - 576 \, A c^{2} d^{3} e^{2} + 1008 \, B a c d^{2} e^{3} - 840 \, A a c d e^{4} + 315 \, B a^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"2/315*(35*B*c^2*e^5*x^5 + 1280*B*c^2*d^5 - 1152*A*c^2*d^4*e + 2016*B*a*c*d^3*e^2 - 1680*A*a*c*d^2*e^3 + 630*B*a^2*d*e^4 - 315*A*a^2*e^5 - 5*(10*B*c^2*d*e^4 - 9*A*c^2*e^5)*x^4 + 2*(40*B*c^2*d^2*e^3 - 36*A*c^2*d*e^4 + 63*B*a*c*e^5)*x^3 - 2*(80*B*c^2*d^3*e^2 - 72*A*c^2*d^2*e^3 + 126*B*a*c*d*e^4 - 105*A*a*c*e^5)*x^2 + (640*B*c^2*d^4*e - 576*A*c^2*d^3*e^2 + 1008*B*a*c*d^2*e^3 - 840*A*a*c*d*e^4 + 315*B*a^2*e^5)*x)*sqrt(e*x + d)/(e^7*x + d*e^6)","A",0
1438,1,269,0,0.399870," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c^{2} e^{5} x^{5} - 1280 \, B c^{2} d^{5} + 896 \, A c^{2} d^{4} e - 1120 \, B a c d^{3} e^{2} + 560 \, A a c d^{2} e^{3} - 70 \, B a^{2} d e^{4} - 35 \, A a^{2} e^{5} - 3 \, {\left(10 \, B c^{2} d e^{4} - 7 \, A c^{2} e^{5}\right)} x^{4} + 2 \, {\left(40 \, B c^{2} d^{2} e^{3} - 28 \, A c^{2} d e^{4} + 35 \, B a c e^{5}\right)} x^{3} - 6 \, {\left(80 \, B c^{2} d^{3} e^{2} - 56 \, A c^{2} d^{2} e^{3} + 70 \, B a c d e^{4} - 35 \, A a c e^{5}\right)} x^{2} - 3 \, {\left(640 \, B c^{2} d^{4} e - 448 \, A c^{2} d^{3} e^{2} + 560 \, B a c d^{2} e^{3} - 280 \, A a c d e^{4} + 35 \, B a^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"2/105*(15*B*c^2*e^5*x^5 - 1280*B*c^2*d^5 + 896*A*c^2*d^4*e - 1120*B*a*c*d^3*e^2 + 560*A*a*c*d^2*e^3 - 70*B*a^2*d*e^4 - 35*A*a^2*e^5 - 3*(10*B*c^2*d*e^4 - 7*A*c^2*e^5)*x^4 + 2*(40*B*c^2*d^2*e^3 - 28*A*c^2*d*e^4 + 35*B*a*c*e^5)*x^3 - 6*(80*B*c^2*d^3*e^2 - 56*A*c^2*d^2*e^3 + 70*B*a*c*d*e^4 - 35*A*a*c*e^5)*x^2 - 3*(640*B*c^2*d^4*e - 448*A*c^2*d^3*e^2 + 560*B*a*c*d^2*e^3 - 280*A*a*c*d*e^4 + 35*B*a^2*e^5)*x)*sqrt(e*x + d)/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","A",0
1439,1,280,0,0.415529," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c^{2} e^{5} x^{5} + 256 \, B c^{2} d^{5} - 128 \, A c^{2} d^{4} e + 96 \, B a c d^{3} e^{2} - 16 \, A a c d^{2} e^{3} - 2 \, B a^{2} d e^{4} - 3 \, A a^{2} e^{5} - 5 \, {\left(2 \, B c^{2} d e^{4} - A c^{2} e^{5}\right)} x^{4} + 10 \, {\left(8 \, B c^{2} d^{2} e^{3} - 4 \, A c^{2} d e^{4} + 3 \, B a c e^{5}\right)} x^{3} + 30 \, {\left(16 \, B c^{2} d^{3} e^{2} - 8 \, A c^{2} d^{2} e^{3} + 6 \, B a c d e^{4} - A a c e^{5}\right)} x^{2} + 5 \, {\left(128 \, B c^{2} d^{4} e - 64 \, A c^{2} d^{3} e^{2} + 48 \, B a c d^{2} e^{3} - 8 \, A a c d e^{4} - B a^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"2/15*(3*B*c^2*e^5*x^5 + 256*B*c^2*d^5 - 128*A*c^2*d^4*e + 96*B*a*c*d^3*e^2 - 16*A*a*c*d^2*e^3 - 2*B*a^2*d*e^4 - 3*A*a^2*e^5 - 5*(2*B*c^2*d*e^4 - A*c^2*e^5)*x^4 + 10*(8*B*c^2*d^2*e^3 - 4*A*c^2*d*e^4 + 3*B*a*c*e^5)*x^3 + 30*(16*B*c^2*d^3*e^2 - 8*A*c^2*d^2*e^3 + 6*B*a*c*d*e^4 - A*a*c*e^5)*x^2 + 5*(128*B*c^2*d^4*e - 64*A*c^2*d^3*e^2 + 48*B*a*c*d^2*e^3 - 8*A*a*c*d*e^4 - B*a^2*e^5)*x)*sqrt(e*x + d)/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","A",0
1440,1,290,0,0.420210," ","integrate((B*x+A)*(c*x^2+a)^2/(e*x+d)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{2} e^{5} x^{5} - 1280 \, B c^{2} d^{5} + 384 \, A c^{2} d^{4} e - 96 \, B a c d^{3} e^{2} - 16 \, A a c d^{2} e^{3} - 6 \, B a^{2} d e^{4} - 15 \, A a^{2} e^{5} - 35 \, {\left(10 \, B c^{2} d e^{4} - 3 \, A c^{2} e^{5}\right)} x^{4} - 70 \, {\left(40 \, B c^{2} d^{2} e^{3} - 12 \, A c^{2} d e^{4} + 3 \, B a c e^{5}\right)} x^{3} - 70 \, {\left(80 \, B c^{2} d^{3} e^{2} - 24 \, A c^{2} d^{2} e^{3} + 6 \, B a c d e^{4} + A a c e^{5}\right)} x^{2} - 7 \, {\left(640 \, B c^{2} d^{4} e - 192 \, A c^{2} d^{3} e^{2} + 48 \, B a c d^{2} e^{3} + 8 \, A a c d e^{4} + 3 \, B a^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(e^{10} x^{4} + 4 \, d e^{9} x^{3} + 6 \, d^{2} e^{8} x^{2} + 4 \, d^{3} e^{7} x + d^{4} e^{6}\right)}}"," ",0,"2/105*(35*B*c^2*e^5*x^5 - 1280*B*c^2*d^5 + 384*A*c^2*d^4*e - 96*B*a*c*d^3*e^2 - 16*A*a*c*d^2*e^3 - 6*B*a^2*d*e^4 - 15*A*a^2*e^5 - 35*(10*B*c^2*d*e^4 - 3*A*c^2*e^5)*x^4 - 70*(40*B*c^2*d^2*e^3 - 12*A*c^2*d*e^4 + 3*B*a*c*e^5)*x^3 - 70*(80*B*c^2*d^3*e^2 - 24*A*c^2*d^2*e^3 + 6*B*a*c*d*e^4 + A*a*c*e^5)*x^2 - 7*(640*B*c^2*d^4*e - 192*A*c^2*d^3*e^2 + 48*B*a*c*d^2*e^3 + 8*A*a*c*d*e^4 + 3*B*a^2*e^5)*x)*sqrt(e*x + d)/(e^10*x^4 + 4*d*e^9*x^3 + 6*d^2*e^8*x^2 + 4*d^3*e^7*x + d^4*e^6)","A",0
1441,1,454,0,0.412610," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B c^{3} e^{7} x^{7} - 14336 \, B c^{3} d^{7} + 15360 \, A c^{3} d^{6} e - 49920 \, B a c^{2} d^{5} e^{2} + 54912 \, A a c^{2} d^{4} e^{3} - 61776 \, B a^{2} c d^{3} e^{4} + 72072 \, A a^{2} c d^{2} e^{5} - 30030 \, B a^{3} d e^{6} + 45045 \, A a^{3} e^{7} - 231 \, {\left(14 \, B c^{3} d e^{6} - 15 \, A c^{3} e^{7}\right)} x^{6} + 63 \, {\left(56 \, B c^{3} d^{2} e^{5} - 60 \, A c^{3} d e^{6} + 195 \, B a c^{2} e^{7}\right)} x^{5} - 35 \, {\left(112 \, B c^{3} d^{3} e^{4} - 120 \, A c^{3} d^{2} e^{5} + 390 \, B a c^{2} d e^{6} - 429 \, A a c^{2} e^{7}\right)} x^{4} + 5 \, {\left(896 \, B c^{3} d^{4} e^{3} - 960 \, A c^{3} d^{3} e^{4} + 3120 \, B a c^{2} d^{2} e^{5} - 3432 \, A a c^{2} d e^{6} + 3861 \, B a^{2} c e^{7}\right)} x^{3} - 3 \, {\left(1792 \, B c^{3} d^{5} e^{2} - 1920 \, A c^{3} d^{4} e^{3} + 6240 \, B a c^{2} d^{3} e^{4} - 6864 \, A a c^{2} d^{2} e^{5} + 7722 \, B a^{2} c d e^{6} - 9009 \, A a^{2} c e^{7}\right)} x^{2} + {\left(7168 \, B c^{3} d^{6} e - 7680 \, A c^{3} d^{5} e^{2} + 24960 \, B a c^{2} d^{4} e^{3} - 27456 \, A a c^{2} d^{3} e^{4} + 30888 \, B a^{2} c d^{2} e^{5} - 36036 \, A a^{2} c d e^{6} + 15015 \, B a^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{8}}"," ",0,"2/45045*(3003*B*c^3*e^7*x^7 - 14336*B*c^3*d^7 + 15360*A*c^3*d^6*e - 49920*B*a*c^2*d^5*e^2 + 54912*A*a*c^2*d^4*e^3 - 61776*B*a^2*c*d^3*e^4 + 72072*A*a^2*c*d^2*e^5 - 30030*B*a^3*d*e^6 + 45045*A*a^3*e^7 - 231*(14*B*c^3*d*e^6 - 15*A*c^3*e^7)*x^6 + 63*(56*B*c^3*d^2*e^5 - 60*A*c^3*d*e^6 + 195*B*a*c^2*e^7)*x^5 - 35*(112*B*c^3*d^3*e^4 - 120*A*c^3*d^2*e^5 + 390*B*a*c^2*d*e^6 - 429*A*a*c^2*e^7)*x^4 + 5*(896*B*c^3*d^4*e^3 - 960*A*c^3*d^3*e^4 + 3120*B*a*c^2*d^2*e^5 - 3432*A*a*c^2*d*e^6 + 3861*B*a^2*c*e^7)*x^3 - 3*(1792*B*c^3*d^5*e^2 - 1920*A*c^3*d^4*e^3 + 6240*B*a*c^2*d^3*e^4 - 6864*A*a*c^2*d^2*e^5 + 7722*B*a^2*c*d*e^6 - 9009*A*a^2*c*e^7)*x^2 + (7168*B*c^3*d^6*e - 7680*A*c^3*d^5*e^2 + 24960*B*a*c^2*d^4*e^3 - 27456*A*a*c^2*d^3*e^4 + 30888*B*a^2*c*d^2*e^5 - 36036*A*a^2*c*d*e^6 + 15015*B*a^3*e^7)*x)*sqrt(e*x + d)/e^8","A",0
1442,1,463,0,0.427903," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, B c^{3} e^{7} x^{7} + 71680 \, B c^{3} d^{7} - 66560 \, A c^{3} d^{6} e + 183040 \, B a c^{2} d^{5} e^{2} - 164736 \, A a c^{2} d^{4} e^{3} + 144144 \, B a^{2} c d^{3} e^{4} - 120120 \, A a^{2} c d^{2} e^{5} + 30030 \, B a^{3} d e^{6} - 15015 \, A a^{3} e^{7} - 105 \, {\left(14 \, B c^{3} d e^{6} - 13 \, A c^{3} e^{7}\right)} x^{6} + 35 \, {\left(56 \, B c^{3} d^{2} e^{5} - 52 \, A c^{3} d e^{6} + 143 \, B a c^{2} e^{7}\right)} x^{5} - 5 \, {\left(560 \, B c^{3} d^{3} e^{4} - 520 \, A c^{3} d^{2} e^{5} + 1430 \, B a c^{2} d e^{6} - 1287 \, A a c^{2} e^{7}\right)} x^{4} + {\left(4480 \, B c^{3} d^{4} e^{3} - 4160 \, A c^{3} d^{3} e^{4} + 11440 \, B a c^{2} d^{2} e^{5} - 10296 \, A a c^{2} d e^{6} + 9009 \, B a^{2} c e^{7}\right)} x^{3} - {\left(8960 \, B c^{3} d^{5} e^{2} - 8320 \, A c^{3} d^{4} e^{3} + 22880 \, B a c^{2} d^{3} e^{4} - 20592 \, A a c^{2} d^{2} e^{5} + 18018 \, B a^{2} c d e^{6} - 15015 \, A a^{2} c e^{7}\right)} x^{2} + {\left(35840 \, B c^{3} d^{6} e - 33280 \, A c^{3} d^{5} e^{2} + 91520 \, B a c^{2} d^{4} e^{3} - 82368 \, A a c^{2} d^{3} e^{4} + 72072 \, B a^{2} c d^{2} e^{5} - 60060 \, A a^{2} c d e^{6} + 15015 \, B a^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{15015 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"2/15015*(1155*B*c^3*e^7*x^7 + 71680*B*c^3*d^7 - 66560*A*c^3*d^6*e + 183040*B*a*c^2*d^5*e^2 - 164736*A*a*c^2*d^4*e^3 + 144144*B*a^2*c*d^3*e^4 - 120120*A*a^2*c*d^2*e^5 + 30030*B*a^3*d*e^6 - 15015*A*a^3*e^7 - 105*(14*B*c^3*d*e^6 - 13*A*c^3*e^7)*x^6 + 35*(56*B*c^3*d^2*e^5 - 52*A*c^3*d*e^6 + 143*B*a*c^2*e^7)*x^5 - 5*(560*B*c^3*d^3*e^4 - 520*A*c^3*d^2*e^5 + 1430*B*a*c^2*d*e^6 - 1287*A*a*c^2*e^7)*x^4 + (4480*B*c^3*d^4*e^3 - 4160*A*c^3*d^3*e^4 + 11440*B*a*c^2*d^2*e^5 - 10296*A*a*c^2*d*e^6 + 9009*B*a^2*c*e^7)*x^3 - (8960*B*c^3*d^5*e^2 - 8320*A*c^3*d^4*e^3 + 22880*B*a*c^2*d^3*e^4 - 20592*A*a*c^2*d^2*e^5 + 18018*B*a^2*c*d*e^6 - 15015*A*a^2*c*e^7)*x^2 + (35840*B*c^3*d^6*e - 33280*A*c^3*d^5*e^2 + 91520*B*a*c^2*d^4*e^3 - 82368*A*a*c^2*d^3*e^4 + 72072*B*a^2*c*d^2*e^5 - 60060*A*a^2*c*d*e^6 + 15015*B*a^3*e^7)*x)*sqrt(e*x + d)/(e^9*x + d*e^8)","A",0
1443,1,475,0,0.417631," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B c^{3} e^{7} x^{7} - 71680 \, B c^{3} d^{7} + 56320 \, A c^{3} d^{6} e - 126720 \, B a c^{2} d^{5} e^{2} + 88704 \, A a c^{2} d^{4} e^{3} - 55440 \, B a^{2} c d^{3} e^{4} + 27720 \, A a^{2} c d^{2} e^{5} - 2310 \, B a^{3} d e^{6} - 1155 \, A a^{3} e^{7} - 35 \, {\left(14 \, B c^{3} d e^{6} - 11 \, A c^{3} e^{7}\right)} x^{6} + 15 \, {\left(56 \, B c^{3} d^{2} e^{5} - 44 \, A c^{3} d e^{6} + 99 \, B a c^{2} e^{7}\right)} x^{5} - 3 \, {\left(560 \, B c^{3} d^{3} e^{4} - 440 \, A c^{3} d^{2} e^{5} + 990 \, B a c^{2} d e^{6} - 693 \, A a c^{2} e^{7}\right)} x^{4} + {\left(4480 \, B c^{3} d^{4} e^{3} - 3520 \, A c^{3} d^{3} e^{4} + 7920 \, B a c^{2} d^{2} e^{5} - 5544 \, A a c^{2} d e^{6} + 3465 \, B a^{2} c e^{7}\right)} x^{3} - 3 \, {\left(8960 \, B c^{3} d^{5} e^{2} - 7040 \, A c^{3} d^{4} e^{3} + 15840 \, B a c^{2} d^{3} e^{4} - 11088 \, A a c^{2} d^{2} e^{5} + 6930 \, B a^{2} c d e^{6} - 3465 \, A a^{2} c e^{7}\right)} x^{2} - 3 \, {\left(35840 \, B c^{3} d^{6} e - 28160 \, A c^{3} d^{5} e^{2} + 63360 \, B a c^{2} d^{4} e^{3} - 44352 \, A a c^{2} d^{3} e^{4} + 27720 \, B a^{2} c d^{2} e^{5} - 13860 \, A a^{2} c d e^{6} + 1155 \, B a^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{3465 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"2/3465*(315*B*c^3*e^7*x^7 - 71680*B*c^3*d^7 + 56320*A*c^3*d^6*e - 126720*B*a*c^2*d^5*e^2 + 88704*A*a*c^2*d^4*e^3 - 55440*B*a^2*c*d^3*e^4 + 27720*A*a^2*c*d^2*e^5 - 2310*B*a^3*d*e^6 - 1155*A*a^3*e^7 - 35*(14*B*c^3*d*e^6 - 11*A*c^3*e^7)*x^6 + 15*(56*B*c^3*d^2*e^5 - 44*A*c^3*d*e^6 + 99*B*a*c^2*e^7)*x^5 - 3*(560*B*c^3*d^3*e^4 - 440*A*c^3*d^2*e^5 + 990*B*a*c^2*d*e^6 - 693*A*a*c^2*e^7)*x^4 + (4480*B*c^3*d^4*e^3 - 3520*A*c^3*d^3*e^4 + 7920*B*a*c^2*d^2*e^5 - 5544*A*a*c^2*d*e^6 + 3465*B*a^2*c*e^7)*x^3 - 3*(8960*B*c^3*d^5*e^2 - 7040*A*c^3*d^4*e^3 + 15840*B*a*c^2*d^3*e^4 - 11088*A*a*c^2*d^2*e^5 + 6930*B*a^2*c*d*e^6 - 3465*A*a^2*c*e^7)*x^2 - 3*(35840*B*c^3*d^6*e - 28160*A*c^3*d^5*e^2 + 63360*B*a*c^2*d^4*e^3 - 44352*A*a*c^2*d^3*e^4 + 27720*B*a^2*c*d^2*e^5 - 13860*A*a^2*c*d*e^6 + 1155*B*a^3*e^7)*x)*sqrt(e*x + d)/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","A",0
1444,1,487,0,0.433125," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B c^{3} e^{7} x^{7} + 14336 \, B c^{3} d^{7} - 9216 \, A c^{3} d^{6} e + 16128 \, B a c^{2} d^{5} e^{2} - 8064 \, A a c^{2} d^{4} e^{3} + 3024 \, B a^{2} c d^{3} e^{4} - 504 \, A a^{2} c d^{2} e^{5} - 42 \, B a^{3} d e^{6} - 63 \, A a^{3} e^{7} - 5 \, {\left(14 \, B c^{3} d e^{6} - 9 \, A c^{3} e^{7}\right)} x^{6} + 3 \, {\left(56 \, B c^{3} d^{2} e^{5} - 36 \, A c^{3} d e^{6} + 63 \, B a c^{2} e^{7}\right)} x^{5} - 5 \, {\left(112 \, B c^{3} d^{3} e^{4} - 72 \, A c^{3} d^{2} e^{5} + 126 \, B a c^{2} d e^{6} - 63 \, A a c^{2} e^{7}\right)} x^{4} + 5 \, {\left(896 \, B c^{3} d^{4} e^{3} - 576 \, A c^{3} d^{3} e^{4} + 1008 \, B a c^{2} d^{2} e^{5} - 504 \, A a c^{2} d e^{6} + 189 \, B a^{2} c e^{7}\right)} x^{3} + 15 \, {\left(1792 \, B c^{3} d^{5} e^{2} - 1152 \, A c^{3} d^{4} e^{3} + 2016 \, B a c^{2} d^{3} e^{4} - 1008 \, A a c^{2} d^{2} e^{5} + 378 \, B a^{2} c d e^{6} - 63 \, A a^{2} c e^{7}\right)} x^{2} + 5 \, {\left(7168 \, B c^{3} d^{6} e - 4608 \, A c^{3} d^{5} e^{2} + 8064 \, B a c^{2} d^{4} e^{3} - 4032 \, A a c^{2} d^{3} e^{4} + 1512 \, B a^{2} c d^{2} e^{5} - 252 \, A a^{2} c d e^{6} - 21 \, B a^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right)}}"," ",0,"2/315*(35*B*c^3*e^7*x^7 + 14336*B*c^3*d^7 - 9216*A*c^3*d^6*e + 16128*B*a*c^2*d^5*e^2 - 8064*A*a*c^2*d^4*e^3 + 3024*B*a^2*c*d^3*e^4 - 504*A*a^2*c*d^2*e^5 - 42*B*a^3*d*e^6 - 63*A*a^3*e^7 - 5*(14*B*c^3*d*e^6 - 9*A*c^3*e^7)*x^6 + 3*(56*B*c^3*d^2*e^5 - 36*A*c^3*d*e^6 + 63*B*a*c^2*e^7)*x^5 - 5*(112*B*c^3*d^3*e^4 - 72*A*c^3*d^2*e^5 + 126*B*a*c^2*d*e^6 - 63*A*a*c^2*e^7)*x^4 + 5*(896*B*c^3*d^4*e^3 - 576*A*c^3*d^3*e^4 + 1008*B*a*c^2*d^2*e^5 - 504*A*a*c^2*d*e^6 + 189*B*a^2*c*e^7)*x^3 + 15*(1792*B*c^3*d^5*e^2 - 1152*A*c^3*d^4*e^3 + 2016*B*a*c^2*d^3*e^4 - 1008*A*a*c^2*d^2*e^5 + 378*B*a^2*c*d*e^6 - 63*A*a^2*c*e^7)*x^2 + 5*(7168*B*c^3*d^6*e - 4608*A*c^3*d^5*e^2 + 8064*B*a*c^2*d^4*e^3 - 4032*A*a*c^2*d^3*e^4 + 1512*B*a^2*c*d^2*e^5 - 252*A*a^2*c*d*e^6 - 21*B*a^3*e^7)*x)*sqrt(e*x + d)/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8)","A",0
1445,1,496,0,0.428331," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B c^{3} e^{7} x^{7} - 2048 \, B c^{3} d^{7} + 1024 \, A c^{3} d^{6} e - 1280 \, B a c^{2} d^{5} e^{2} + 384 \, A a c^{2} d^{4} e^{3} - 48 \, B a^{2} c d^{3} e^{4} - 8 \, A a^{2} c d^{2} e^{5} - 2 \, B a^{3} d e^{6} - 5 \, A a^{3} e^{7} - 7 \, {\left(2 \, B c^{3} d e^{6} - A c^{3} e^{7}\right)} x^{6} + 7 \, {\left(8 \, B c^{3} d^{2} e^{5} - 4 \, A c^{3} d e^{6} + 5 \, B a c^{2} e^{7}\right)} x^{5} - 35 \, {\left(16 \, B c^{3} d^{3} e^{4} - 8 \, A c^{3} d^{2} e^{5} + 10 \, B a c^{2} d e^{6} - 3 \, A a c^{2} e^{7}\right)} x^{4} - 35 \, {\left(128 \, B c^{3} d^{4} e^{3} - 64 \, A c^{3} d^{3} e^{4} + 80 \, B a c^{2} d^{2} e^{5} - 24 \, A a c^{2} d e^{6} + 3 \, B a^{2} c e^{7}\right)} x^{3} - 35 \, {\left(256 \, B c^{3} d^{5} e^{2} - 128 \, A c^{3} d^{4} e^{3} + 160 \, B a c^{2} d^{3} e^{4} - 48 \, A a c^{2} d^{2} e^{5} + 6 \, B a^{2} c d e^{6} + A a^{2} c e^{7}\right)} x^{2} - 7 \, {\left(1024 \, B c^{3} d^{6} e - 512 \, A c^{3} d^{5} e^{2} + 640 \, B a c^{2} d^{4} e^{3} - 192 \, A a c^{2} d^{3} e^{4} + 24 \, B a^{2} c d^{2} e^{5} + 4 \, A a^{2} c d e^{6} + B a^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{12} x^{4} + 4 \, d e^{11} x^{3} + 6 \, d^{2} e^{10} x^{2} + 4 \, d^{3} e^{9} x + d^{4} e^{8}\right)}}"," ",0,"2/35*(5*B*c^3*e^7*x^7 - 2048*B*c^3*d^7 + 1024*A*c^3*d^6*e - 1280*B*a*c^2*d^5*e^2 + 384*A*a*c^2*d^4*e^3 - 48*B*a^2*c*d^3*e^4 - 8*A*a^2*c*d^2*e^5 - 2*B*a^3*d*e^6 - 5*A*a^3*e^7 - 7*(2*B*c^3*d*e^6 - A*c^3*e^7)*x^6 + 7*(8*B*c^3*d^2*e^5 - 4*A*c^3*d*e^6 + 5*B*a*c^2*e^7)*x^5 - 35*(16*B*c^3*d^3*e^4 - 8*A*c^3*d^2*e^5 + 10*B*a*c^2*d*e^6 - 3*A*a*c^2*e^7)*x^4 - 35*(128*B*c^3*d^4*e^3 - 64*A*c^3*d^3*e^4 + 80*B*a*c^2*d^2*e^5 - 24*A*a*c^2*d*e^6 + 3*B*a^2*c*e^7)*x^3 - 35*(256*B*c^3*d^5*e^2 - 128*A*c^3*d^4*e^3 + 160*B*a*c^2*d^3*e^4 - 48*A*a*c^2*d^2*e^5 + 6*B*a^2*c*d*e^6 + A*a^2*c*e^7)*x^2 - 7*(1024*B*c^3*d^6*e - 512*A*c^3*d^5*e^2 + 640*B*a*c^2*d^4*e^3 - 192*A*a*c^2*d^3*e^4 + 24*B*a^2*c*d^2*e^5 + 4*A*a^2*c*d*e^6 + B*a^3*e^7)*x)*sqrt(e*x + d)/(e^12*x^4 + 4*d*e^11*x^3 + 6*d^2*e^10*x^2 + 4*d^3*e^9*x + d^4*e^8)","A",0
1446,1,509,0,0.401695," ","integrate((B*x+A)*(c*x^2+a)^3/(e*x+d)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B c^{3} e^{7} x^{7} + 14336 \, B c^{3} d^{7} - 5120 \, A c^{3} d^{6} e + 3840 \, B a c^{2} d^{5} e^{2} - 384 \, A a c^{2} d^{4} e^{3} - 48 \, B a^{2} c d^{3} e^{4} - 24 \, A a^{2} c d^{2} e^{5} - 10 \, B a^{3} d e^{6} - 35 \, A a^{3} e^{7} - 21 \, {\left(14 \, B c^{3} d e^{6} - 5 \, A c^{3} e^{7}\right)} x^{6} + 63 \, {\left(56 \, B c^{3} d^{2} e^{5} - 20 \, A c^{3} d e^{6} + 15 \, B a c^{2} e^{7}\right)} x^{5} + 315 \, {\left(112 \, B c^{3} d^{3} e^{4} - 40 \, A c^{3} d^{2} e^{5} + 30 \, B a c^{2} d e^{6} - 3 \, A a c^{2} e^{7}\right)} x^{4} + 105 \, {\left(896 \, B c^{3} d^{4} e^{3} - 320 \, A c^{3} d^{3} e^{4} + 240 \, B a c^{2} d^{2} e^{5} - 24 \, A a c^{2} d e^{6} - 3 \, B a^{2} c e^{7}\right)} x^{3} + 63 \, {\left(1792 \, B c^{3} d^{5} e^{2} - 640 \, A c^{3} d^{4} e^{3} + 480 \, B a c^{2} d^{3} e^{4} - 48 \, A a c^{2} d^{2} e^{5} - 6 \, B a^{2} c d e^{6} - 3 \, A a^{2} c e^{7}\right)} x^{2} + 9 \, {\left(7168 \, B c^{3} d^{6} e - 2560 \, A c^{3} d^{5} e^{2} + 1920 \, B a c^{2} d^{4} e^{3} - 192 \, A a c^{2} d^{3} e^{4} - 24 \, B a^{2} c d^{2} e^{5} - 12 \, A a^{2} c d e^{6} - 5 \, B a^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{13} x^{5} + 5 \, d e^{12} x^{4} + 10 \, d^{2} e^{11} x^{3} + 10 \, d^{3} e^{10} x^{2} + 5 \, d^{4} e^{9} x + d^{5} e^{8}\right)}}"," ",0,"2/315*(63*B*c^3*e^7*x^7 + 14336*B*c^3*d^7 - 5120*A*c^3*d^6*e + 3840*B*a*c^2*d^5*e^2 - 384*A*a*c^2*d^4*e^3 - 48*B*a^2*c*d^3*e^4 - 24*A*a^2*c*d^2*e^5 - 10*B*a^3*d*e^6 - 35*A*a^3*e^7 - 21*(14*B*c^3*d*e^6 - 5*A*c^3*e^7)*x^6 + 63*(56*B*c^3*d^2*e^5 - 20*A*c^3*d*e^6 + 15*B*a*c^2*e^7)*x^5 + 315*(112*B*c^3*d^3*e^4 - 40*A*c^3*d^2*e^5 + 30*B*a*c^2*d*e^6 - 3*A*a*c^2*e^7)*x^4 + 105*(896*B*c^3*d^4*e^3 - 320*A*c^3*d^3*e^4 + 240*B*a*c^2*d^2*e^5 - 24*A*a*c^2*d*e^6 - 3*B*a^2*c*e^7)*x^3 + 63*(1792*B*c^3*d^5*e^2 - 640*A*c^3*d^4*e^3 + 480*B*a*c^2*d^3*e^4 - 48*A*a*c^2*d^2*e^5 - 6*B*a^2*c*d*e^6 - 3*A*a^2*c*e^7)*x^2 + 9*(7168*B*c^3*d^6*e - 2560*A*c^3*d^5*e^2 + 1920*B*a*c^2*d^4*e^3 - 192*A*a*c^2*d^3*e^4 - 24*B*a^2*c*d^2*e^5 - 12*A*a^2*c*d*e^6 - 5*B*a^3*e^7)*x)*sqrt(e*x + d)/(e^13*x^5 + 5*d*e^12*x^4 + 10*d^2*e^11*x^3 + 10*d^3*e^10*x^2 + 5*d^4*e^9*x + d^5*e^8)","A",0
1447,1,7410,0,9.104610," ","integrate((B*x+A)*(e*x+d)^(5/2)/(-c*x^2+a),x, algorithm=""fricas"")","-\frac{15 \, c^{2} \sqrt{\frac{10 \, A B a c^{2} d^{4} e + 20 \, A B a^{2} c d^{2} e^{3} + 2 \, A B a^{3} e^{5} + {\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{5} + 10 \, {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{3} e^{2} + 5 \, {\left(B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4} + a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}}{a c^{4}}} \log\left(-{\left(2 \, {\left(A B^{3} a c^{5} - A^{3} B c^{6}\right)} d^{9} + 5 \, {\left(B^{4} a^{2} c^{4} - A^{4} c^{6}\right)} d^{8} e + 16 \, {\left(A B^{3} a^{2} c^{4} - A^{3} B a c^{5}\right)} d^{7} e^{2} - 28 \, {\left(A B^{3} a^{3} c^{3} - A^{3} B a^{2} c^{4}\right)} d^{5} e^{4} - 14 \, {\left(B^{4} a^{4} c^{2} - A^{4} a^{2} c^{4}\right)} d^{4} e^{5} + 8 \, {\left(B^{4} a^{5} c - A^{4} a^{3} c^{3}\right)} d^{2} e^{7} + 10 \, {\left(A B^{3} a^{5} c - A^{3} B a^{4} c^{2}\right)} d e^{8} + {\left(B^{4} a^{6} - A^{4} a^{4} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{6} d^{7} + {\left(5 \, B^{3} a^{2} c^{5} + 9 \, A^{2} B a c^{6}\right)} d^{6} e + 2 \, {\left(16 \, A B^{2} a^{2} c^{5} + 5 \, A^{3} a c^{6}\right)} d^{5} e^{2} + 5 \, {\left(3 \, B^{3} a^{3} c^{4} + 11 \, A^{2} B a^{2} c^{5}\right)} d^{4} e^{3} + 10 \, {\left(5 \, A B^{2} a^{3} c^{4} + 2 \, A^{3} a^{2} c^{5}\right)} d^{3} e^{4} + {\left(11 \, B^{3} a^{4} c^{3} + 31 \, A^{2} B a^{3} c^{4}\right)} d^{2} e^{5} + 2 \, {\left(6 \, A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} d e^{6} + {\left(B^{3} a^{5} c^{2} + A^{2} B a^{4} c^{3}\right)} e^{7} - {\left(A a c^{8} d^{2} + 2 \, B a^{2} c^{7} d e + A a^{2} c^{7} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}\right)} \sqrt{\frac{10 \, A B a c^{2} d^{4} e + 20 \, A B a^{2} c d^{2} e^{3} + 2 \, A B a^{3} e^{5} + {\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{5} + 10 \, {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{3} e^{2} + 5 \, {\left(B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4} + a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}}{a c^{4}}}\right) - 15 \, c^{2} \sqrt{\frac{10 \, A B a c^{2} d^{4} e + 20 \, A B a^{2} c d^{2} e^{3} + 2 \, A B a^{3} e^{5} + {\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{5} + 10 \, {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{3} e^{2} + 5 \, {\left(B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4} + a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}}{a c^{4}}} \log\left(-{\left(2 \, {\left(A B^{3} a c^{5} - A^{3} B c^{6}\right)} d^{9} + 5 \, {\left(B^{4} a^{2} c^{4} - A^{4} c^{6}\right)} d^{8} e + 16 \, {\left(A B^{3} a^{2} c^{4} - A^{3} B a c^{5}\right)} d^{7} e^{2} - 28 \, {\left(A B^{3} a^{3} c^{3} - A^{3} B a^{2} c^{4}\right)} d^{5} e^{4} - 14 \, {\left(B^{4} a^{4} c^{2} - A^{4} a^{2} c^{4}\right)} d^{4} e^{5} + 8 \, {\left(B^{4} a^{5} c - A^{4} a^{3} c^{3}\right)} d^{2} e^{7} + 10 \, {\left(A B^{3} a^{5} c - A^{3} B a^{4} c^{2}\right)} d e^{8} + {\left(B^{4} a^{6} - A^{4} a^{4} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{6} d^{7} + {\left(5 \, B^{3} a^{2} c^{5} + 9 \, A^{2} B a c^{6}\right)} d^{6} e + 2 \, {\left(16 \, A B^{2} a^{2} c^{5} + 5 \, A^{3} a c^{6}\right)} d^{5} e^{2} + 5 \, {\left(3 \, B^{3} a^{3} c^{4} + 11 \, A^{2} B a^{2} c^{5}\right)} d^{4} e^{3} + 10 \, {\left(5 \, A B^{2} a^{3} c^{4} + 2 \, A^{3} a^{2} c^{5}\right)} d^{3} e^{4} + {\left(11 \, B^{3} a^{4} c^{3} + 31 \, A^{2} B a^{3} c^{4}\right)} d^{2} e^{5} + 2 \, {\left(6 \, A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} d e^{6} + {\left(B^{3} a^{5} c^{2} + A^{2} B a^{4} c^{3}\right)} e^{7} - {\left(A a c^{8} d^{2} + 2 \, B a^{2} c^{7} d e + A a^{2} c^{7} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}\right)} \sqrt{\frac{10 \, A B a c^{2} d^{4} e + 20 \, A B a^{2} c d^{2} e^{3} + 2 \, A B a^{3} e^{5} + {\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{5} + 10 \, {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{3} e^{2} + 5 \, {\left(B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4} + a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}}{a c^{4}}}\right) + 15 \, c^{2} \sqrt{\frac{10 \, A B a c^{2} d^{4} e + 20 \, A B a^{2} c d^{2} e^{3} + 2 \, A B a^{3} e^{5} + {\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{5} + 10 \, {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{3} e^{2} + 5 \, {\left(B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4} - a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}}{a c^{4}}} \log\left(-{\left(2 \, {\left(A B^{3} a c^{5} - A^{3} B c^{6}\right)} d^{9} + 5 \, {\left(B^{4} a^{2} c^{4} - A^{4} c^{6}\right)} d^{8} e + 16 \, {\left(A B^{3} a^{2} c^{4} - A^{3} B a c^{5}\right)} d^{7} e^{2} - 28 \, {\left(A B^{3} a^{3} c^{3} - A^{3} B a^{2} c^{4}\right)} d^{5} e^{4} - 14 \, {\left(B^{4} a^{4} c^{2} - A^{4} a^{2} c^{4}\right)} d^{4} e^{5} + 8 \, {\left(B^{4} a^{5} c - A^{4} a^{3} c^{3}\right)} d^{2} e^{7} + 10 \, {\left(A B^{3} a^{5} c - A^{3} B a^{4} c^{2}\right)} d e^{8} + {\left(B^{4} a^{6} - A^{4} a^{4} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{6} d^{7} + {\left(5 \, B^{3} a^{2} c^{5} + 9 \, A^{2} B a c^{6}\right)} d^{6} e + 2 \, {\left(16 \, A B^{2} a^{2} c^{5} + 5 \, A^{3} a c^{6}\right)} d^{5} e^{2} + 5 \, {\left(3 \, B^{3} a^{3} c^{4} + 11 \, A^{2} B a^{2} c^{5}\right)} d^{4} e^{3} + 10 \, {\left(5 \, A B^{2} a^{3} c^{4} + 2 \, A^{3} a^{2} c^{5}\right)} d^{3} e^{4} + {\left(11 \, B^{3} a^{4} c^{3} + 31 \, A^{2} B a^{3} c^{4}\right)} d^{2} e^{5} + 2 \, {\left(6 \, A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} d e^{6} + {\left(B^{3} a^{5} c^{2} + A^{2} B a^{4} c^{3}\right)} e^{7} + {\left(A a c^{8} d^{2} + 2 \, B a^{2} c^{7} d e + A a^{2} c^{7} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}\right)} \sqrt{\frac{10 \, A B a c^{2} d^{4} e + 20 \, A B a^{2} c d^{2} e^{3} + 2 \, A B a^{3} e^{5} + {\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{5} + 10 \, {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{3} e^{2} + 5 \, {\left(B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4} - a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}}{a c^{4}}}\right) - 15 \, c^{2} \sqrt{\frac{10 \, A B a c^{2} d^{4} e + 20 \, A B a^{2} c d^{2} e^{3} + 2 \, A B a^{3} e^{5} + {\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{5} + 10 \, {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{3} e^{2} + 5 \, {\left(B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4} - a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}}{a c^{4}}} \log\left(-{\left(2 \, {\left(A B^{3} a c^{5} - A^{3} B c^{6}\right)} d^{9} + 5 \, {\left(B^{4} a^{2} c^{4} - A^{4} c^{6}\right)} d^{8} e + 16 \, {\left(A B^{3} a^{2} c^{4} - A^{3} B a c^{5}\right)} d^{7} e^{2} - 28 \, {\left(A B^{3} a^{3} c^{3} - A^{3} B a^{2} c^{4}\right)} d^{5} e^{4} - 14 \, {\left(B^{4} a^{4} c^{2} - A^{4} a^{2} c^{4}\right)} d^{4} e^{5} + 8 \, {\left(B^{4} a^{5} c - A^{4} a^{3} c^{3}\right)} d^{2} e^{7} + 10 \, {\left(A B^{3} a^{5} c - A^{3} B a^{4} c^{2}\right)} d e^{8} + {\left(B^{4} a^{6} - A^{4} a^{4} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{6} d^{7} + {\left(5 \, B^{3} a^{2} c^{5} + 9 \, A^{2} B a c^{6}\right)} d^{6} e + 2 \, {\left(16 \, A B^{2} a^{2} c^{5} + 5 \, A^{3} a c^{6}\right)} d^{5} e^{2} + 5 \, {\left(3 \, B^{3} a^{3} c^{4} + 11 \, A^{2} B a^{2} c^{5}\right)} d^{4} e^{3} + 10 \, {\left(5 \, A B^{2} a^{3} c^{4} + 2 \, A^{3} a^{2} c^{5}\right)} d^{3} e^{4} + {\left(11 \, B^{3} a^{4} c^{3} + 31 \, A^{2} B a^{3} c^{4}\right)} d^{2} e^{5} + 2 \, {\left(6 \, A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} d e^{6} + {\left(B^{3} a^{5} c^{2} + A^{2} B a^{4} c^{3}\right)} e^{7} + {\left(A a c^{8} d^{2} + 2 \, B a^{2} c^{7} d e + A a^{2} c^{7} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}\right)} \sqrt{\frac{10 \, A B a c^{2} d^{4} e + 20 \, A B a^{2} c d^{2} e^{3} + 2 \, A B a^{3} e^{5} + {\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{5} + 10 \, {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{3} e^{2} + 5 \, {\left(B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4} - a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{6} d^{10} + 20 \, {\left(A B^{3} a c^{5} + A^{3} B c^{6}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{4} + 26 \, A^{2} B^{2} a c^{5} + 5 \, A^{4} c^{6}\right)} d^{8} e^{2} + 240 \, {\left(A B^{3} a^{2} c^{4} + A^{3} B a c^{5}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{3} + 32 \, A^{2} B^{2} a^{2} c^{4} + 5 \, A^{4} a c^{5}\right)} d^{6} e^{4} + 504 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{2} + 62 \, A^{2} B^{2} a^{3} c^{3} + 11 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{6} + 240 \, {\left(A B^{3} a^{4} c^{2} + A^{3} B a^{3} c^{3}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c + 7 \, A^{2} B^{2} a^{4} c^{2} + A^{4} a^{3} c^{3}\right)} d^{2} e^{8} + 20 \, {\left(A B^{3} a^{5} c + A^{3} B a^{4} c^{2}\right)} d e^{9} + {\left(B^{4} a^{6} + 2 \, A^{2} B^{2} a^{5} c + A^{4} a^{4} c^{2}\right)} e^{10}}{a c^{9}}}}{a c^{4}}}\right) + 4 \, {\left(3 \, B c e^{2} x^{2} + 23 \, B c d^{2} + 35 \, A c d e + 15 \, B a e^{2} + {\left(11 \, B c d e + 5 \, A c e^{2}\right)} x\right)} \sqrt{e x + d}}{30 \, c^{2}}"," ",0,"-1/30*(15*c^2*sqrt((10*A*B*a*c^2*d^4*e + 20*A*B*a^2*c*d^2*e^3 + 2*A*B*a^3*e^5 + (B^2*a*c^2 + A^2*c^3)*d^5 + 10*(B^2*a^2*c + A^2*a*c^2)*d^3*e^2 + 5*(B^2*a^3 + A^2*a^2*c)*d*e^4 + a*c^4*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))/(a*c^4))*log(-(2*(A*B^3*a*c^5 - A^3*B*c^6)*d^9 + 5*(B^4*a^2*c^4 - A^4*c^6)*d^8*e + 16*(A*B^3*a^2*c^4 - A^3*B*a*c^5)*d^7*e^2 - 28*(A*B^3*a^3*c^3 - A^3*B*a^2*c^4)*d^5*e^4 - 14*(B^4*a^4*c^2 - A^4*a^2*c^4)*d^4*e^5 + 8*(B^4*a^5*c - A^4*a^3*c^3)*d^2*e^7 + 10*(A*B^3*a^5*c - A^3*B*a^4*c^2)*d*e^8 + (B^4*a^6 - A^4*a^4*c^2)*e^9)*sqrt(e*x + d) + (2*A*B^2*a*c^6*d^7 + (5*B^3*a^2*c^5 + 9*A^2*B*a*c^6)*d^6*e + 2*(16*A*B^2*a^2*c^5 + 5*A^3*a*c^6)*d^5*e^2 + 5*(3*B^3*a^3*c^4 + 11*A^2*B*a^2*c^5)*d^4*e^3 + 10*(5*A*B^2*a^3*c^4 + 2*A^3*a^2*c^5)*d^3*e^4 + (11*B^3*a^4*c^3 + 31*A^2*B*a^3*c^4)*d^2*e^5 + 2*(6*A*B^2*a^4*c^3 + A^3*a^3*c^4)*d*e^6 + (B^3*a^5*c^2 + A^2*B*a^4*c^3)*e^7 - (A*a*c^8*d^2 + 2*B*a^2*c^7*d*e + A*a^2*c^7*e^2)*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))*sqrt((10*A*B*a*c^2*d^4*e + 20*A*B*a^2*c*d^2*e^3 + 2*A*B*a^3*e^5 + (B^2*a*c^2 + A^2*c^3)*d^5 + 10*(B^2*a^2*c + A^2*a*c^2)*d^3*e^2 + 5*(B^2*a^3 + A^2*a^2*c)*d*e^4 + a*c^4*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))/(a*c^4))) - 15*c^2*sqrt((10*A*B*a*c^2*d^4*e + 20*A*B*a^2*c*d^2*e^3 + 2*A*B*a^3*e^5 + (B^2*a*c^2 + A^2*c^3)*d^5 + 10*(B^2*a^2*c + A^2*a*c^2)*d^3*e^2 + 5*(B^2*a^3 + A^2*a^2*c)*d*e^4 + a*c^4*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))/(a*c^4))*log(-(2*(A*B^3*a*c^5 - A^3*B*c^6)*d^9 + 5*(B^4*a^2*c^4 - A^4*c^6)*d^8*e + 16*(A*B^3*a^2*c^4 - A^3*B*a*c^5)*d^7*e^2 - 28*(A*B^3*a^3*c^3 - A^3*B*a^2*c^4)*d^5*e^4 - 14*(B^4*a^4*c^2 - A^4*a^2*c^4)*d^4*e^5 + 8*(B^4*a^5*c - A^4*a^3*c^3)*d^2*e^7 + 10*(A*B^3*a^5*c - A^3*B*a^4*c^2)*d*e^8 + (B^4*a^6 - A^4*a^4*c^2)*e^9)*sqrt(e*x + d) - (2*A*B^2*a*c^6*d^7 + (5*B^3*a^2*c^5 + 9*A^2*B*a*c^6)*d^6*e + 2*(16*A*B^2*a^2*c^5 + 5*A^3*a*c^6)*d^5*e^2 + 5*(3*B^3*a^3*c^4 + 11*A^2*B*a^2*c^5)*d^4*e^3 + 10*(5*A*B^2*a^3*c^4 + 2*A^3*a^2*c^5)*d^3*e^4 + (11*B^3*a^4*c^3 + 31*A^2*B*a^3*c^4)*d^2*e^5 + 2*(6*A*B^2*a^4*c^3 + A^3*a^3*c^4)*d*e^6 + (B^3*a^5*c^2 + A^2*B*a^4*c^3)*e^7 - (A*a*c^8*d^2 + 2*B*a^2*c^7*d*e + A*a^2*c^7*e^2)*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))*sqrt((10*A*B*a*c^2*d^4*e + 20*A*B*a^2*c*d^2*e^3 + 2*A*B*a^3*e^5 + (B^2*a*c^2 + A^2*c^3)*d^5 + 10*(B^2*a^2*c + A^2*a*c^2)*d^3*e^2 + 5*(B^2*a^3 + A^2*a^2*c)*d*e^4 + a*c^4*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))/(a*c^4))) + 15*c^2*sqrt((10*A*B*a*c^2*d^4*e + 20*A*B*a^2*c*d^2*e^3 + 2*A*B*a^3*e^5 + (B^2*a*c^2 + A^2*c^3)*d^5 + 10*(B^2*a^2*c + A^2*a*c^2)*d^3*e^2 + 5*(B^2*a^3 + A^2*a^2*c)*d*e^4 - a*c^4*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))/(a*c^4))*log(-(2*(A*B^3*a*c^5 - A^3*B*c^6)*d^9 + 5*(B^4*a^2*c^4 - A^4*c^6)*d^8*e + 16*(A*B^3*a^2*c^4 - A^3*B*a*c^5)*d^7*e^2 - 28*(A*B^3*a^3*c^3 - A^3*B*a^2*c^4)*d^5*e^4 - 14*(B^4*a^4*c^2 - A^4*a^2*c^4)*d^4*e^5 + 8*(B^4*a^5*c - A^4*a^3*c^3)*d^2*e^7 + 10*(A*B^3*a^5*c - A^3*B*a^4*c^2)*d*e^8 + (B^4*a^6 - A^4*a^4*c^2)*e^9)*sqrt(e*x + d) + (2*A*B^2*a*c^6*d^7 + (5*B^3*a^2*c^5 + 9*A^2*B*a*c^6)*d^6*e + 2*(16*A*B^2*a^2*c^5 + 5*A^3*a*c^6)*d^5*e^2 + 5*(3*B^3*a^3*c^4 + 11*A^2*B*a^2*c^5)*d^4*e^3 + 10*(5*A*B^2*a^3*c^4 + 2*A^3*a^2*c^5)*d^3*e^4 + (11*B^3*a^4*c^3 + 31*A^2*B*a^3*c^4)*d^2*e^5 + 2*(6*A*B^2*a^4*c^3 + A^3*a^3*c^4)*d*e^6 + (B^3*a^5*c^2 + A^2*B*a^4*c^3)*e^7 + (A*a*c^8*d^2 + 2*B*a^2*c^7*d*e + A*a^2*c^7*e^2)*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))*sqrt((10*A*B*a*c^2*d^4*e + 20*A*B*a^2*c*d^2*e^3 + 2*A*B*a^3*e^5 + (B^2*a*c^2 + A^2*c^3)*d^5 + 10*(B^2*a^2*c + A^2*a*c^2)*d^3*e^2 + 5*(B^2*a^3 + A^2*a^2*c)*d*e^4 - a*c^4*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))/(a*c^4))) - 15*c^2*sqrt((10*A*B*a*c^2*d^4*e + 20*A*B*a^2*c*d^2*e^3 + 2*A*B*a^3*e^5 + (B^2*a*c^2 + A^2*c^3)*d^5 + 10*(B^2*a^2*c + A^2*a*c^2)*d^3*e^2 + 5*(B^2*a^3 + A^2*a^2*c)*d*e^4 - a*c^4*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))/(a*c^4))*log(-(2*(A*B^3*a*c^5 - A^3*B*c^6)*d^9 + 5*(B^4*a^2*c^4 - A^4*c^6)*d^8*e + 16*(A*B^3*a^2*c^4 - A^3*B*a*c^5)*d^7*e^2 - 28*(A*B^3*a^3*c^3 - A^3*B*a^2*c^4)*d^5*e^4 - 14*(B^4*a^4*c^2 - A^4*a^2*c^4)*d^4*e^5 + 8*(B^4*a^5*c - A^4*a^3*c^3)*d^2*e^7 + 10*(A*B^3*a^5*c - A^3*B*a^4*c^2)*d*e^8 + (B^4*a^6 - A^4*a^4*c^2)*e^9)*sqrt(e*x + d) - (2*A*B^2*a*c^6*d^7 + (5*B^3*a^2*c^5 + 9*A^2*B*a*c^6)*d^6*e + 2*(16*A*B^2*a^2*c^5 + 5*A^3*a*c^6)*d^5*e^2 + 5*(3*B^3*a^3*c^4 + 11*A^2*B*a^2*c^5)*d^4*e^3 + 10*(5*A*B^2*a^3*c^4 + 2*A^3*a^2*c^5)*d^3*e^4 + (11*B^3*a^4*c^3 + 31*A^2*B*a^3*c^4)*d^2*e^5 + 2*(6*A*B^2*a^4*c^3 + A^3*a^3*c^4)*d*e^6 + (B^3*a^5*c^2 + A^2*B*a^4*c^3)*e^7 + (A*a*c^8*d^2 + 2*B*a^2*c^7*d*e + A*a^2*c^7*e^2)*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))*sqrt((10*A*B*a*c^2*d^4*e + 20*A*B*a^2*c*d^2*e^3 + 2*A*B*a^3*e^5 + (B^2*a*c^2 + A^2*c^3)*d^5 + 10*(B^2*a^2*c + A^2*a*c^2)*d^3*e^2 + 5*(B^2*a^3 + A^2*a^2*c)*d*e^4 - a*c^4*sqrt((4*A^2*B^2*c^6*d^10 + 20*(A*B^3*a*c^5 + A^3*B*c^6)*d^9*e + 5*(5*B^4*a^2*c^4 + 26*A^2*B^2*a*c^5 + 5*A^4*c^6)*d^8*e^2 + 240*(A*B^3*a^2*c^4 + A^3*B*a*c^5)*d^7*e^3 + 20*(5*B^4*a^3*c^3 + 32*A^2*B^2*a^2*c^4 + 5*A^4*a*c^5)*d^6*e^4 + 504*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^5 + 10*(11*B^4*a^4*c^2 + 62*A^2*B^2*a^3*c^3 + 11*A^4*a^2*c^4)*d^4*e^6 + 240*(A*B^3*a^4*c^2 + A^3*B*a^3*c^3)*d^3*e^7 + 20*(B^4*a^5*c + 7*A^2*B^2*a^4*c^2 + A^4*a^3*c^3)*d^2*e^8 + 20*(A*B^3*a^5*c + A^3*B*a^4*c^2)*d*e^9 + (B^4*a^6 + 2*A^2*B^2*a^5*c + A^4*a^4*c^2)*e^10)/(a*c^9)))/(a*c^4))) + 4*(3*B*c*e^2*x^2 + 23*B*c*d^2 + 35*A*c*d*e + 15*B*a*e^2 + (11*B*c*d*e + 5*A*c*e^2)*x)*sqrt(e*x + d))/c^2","B",0
1448,1,4480,0,1.858207," ","integrate((B*x+A)*(e*x+d)^(3/2)/(-c*x^2+a),x, algorithm=""fricas"")","\frac{3 \, c \sqrt{\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + a c^{3} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}} + {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} + 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2}}{a c^{3}}} \log\left({\left(2 \, {\left(A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} + 3 \, {\left(B^{4} a^{2} c^{2} - A^{4} c^{4}\right)} d^{4} e + 4 \, {\left(A B^{3} a^{2} c^{2} - A^{3} B a c^{3}\right)} d^{3} e^{2} - 2 \, {\left(B^{4} a^{3} c - A^{4} a c^{3}\right)} d^{2} e^{3} - 6 \, {\left(A B^{3} a^{3} c - A^{3} B a^{2} c^{2}\right)} d e^{4} - {\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} e^{5}\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{4} d^{4} + {\left(3 \, B^{3} a^{2} c^{3} + 5 \, A^{2} B a c^{4}\right)} d^{3} e + 3 \, {\left(3 \, A B^{2} a^{2} c^{3} + A^{3} a c^{4}\right)} d^{2} e^{2} + {\left(B^{3} a^{3} c^{2} + 7 \, A^{2} B a^{2} c^{3}\right)} d e^{3} + {\left(A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} e^{4} - {\left(A a c^{6} d + B a^{2} c^{5} e\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}}\right)} \sqrt{\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + a c^{3} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}} + {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} + 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2}}{a c^{3}}}\right) - 3 \, c \sqrt{\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + a c^{3} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}} + {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} + 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2}}{a c^{3}}} \log\left({\left(2 \, {\left(A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} + 3 \, {\left(B^{4} a^{2} c^{2} - A^{4} c^{4}\right)} d^{4} e + 4 \, {\left(A B^{3} a^{2} c^{2} - A^{3} B a c^{3}\right)} d^{3} e^{2} - 2 \, {\left(B^{4} a^{3} c - A^{4} a c^{3}\right)} d^{2} e^{3} - 6 \, {\left(A B^{3} a^{3} c - A^{3} B a^{2} c^{2}\right)} d e^{4} - {\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} e^{5}\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{4} d^{4} + {\left(3 \, B^{3} a^{2} c^{3} + 5 \, A^{2} B a c^{4}\right)} d^{3} e + 3 \, {\left(3 \, A B^{2} a^{2} c^{3} + A^{3} a c^{4}\right)} d^{2} e^{2} + {\left(B^{3} a^{3} c^{2} + 7 \, A^{2} B a^{2} c^{3}\right)} d e^{3} + {\left(A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} e^{4} - {\left(A a c^{6} d + B a^{2} c^{5} e\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}}\right)} \sqrt{\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + a c^{3} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}} + {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} + 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2}}{a c^{3}}}\right) + 3 \, c \sqrt{\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - a c^{3} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}} + {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} + 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2}}{a c^{3}}} \log\left({\left(2 \, {\left(A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} + 3 \, {\left(B^{4} a^{2} c^{2} - A^{4} c^{4}\right)} d^{4} e + 4 \, {\left(A B^{3} a^{2} c^{2} - A^{3} B a c^{3}\right)} d^{3} e^{2} - 2 \, {\left(B^{4} a^{3} c - A^{4} a c^{3}\right)} d^{2} e^{3} - 6 \, {\left(A B^{3} a^{3} c - A^{3} B a^{2} c^{2}\right)} d e^{4} - {\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} e^{5}\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{4} d^{4} + {\left(3 \, B^{3} a^{2} c^{3} + 5 \, A^{2} B a c^{4}\right)} d^{3} e + 3 \, {\left(3 \, A B^{2} a^{2} c^{3} + A^{3} a c^{4}\right)} d^{2} e^{2} + {\left(B^{3} a^{3} c^{2} + 7 \, A^{2} B a^{2} c^{3}\right)} d e^{3} + {\left(A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} e^{4} + {\left(A a c^{6} d + B a^{2} c^{5} e\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}}\right)} \sqrt{\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - a c^{3} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}} + {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} + 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2}}{a c^{3}}}\right) - 3 \, c \sqrt{\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - a c^{3} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}} + {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} + 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2}}{a c^{3}}} \log\left({\left(2 \, {\left(A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} + 3 \, {\left(B^{4} a^{2} c^{2} - A^{4} c^{4}\right)} d^{4} e + 4 \, {\left(A B^{3} a^{2} c^{2} - A^{3} B a c^{3}\right)} d^{3} e^{2} - 2 \, {\left(B^{4} a^{3} c - A^{4} a c^{3}\right)} d^{2} e^{3} - 6 \, {\left(A B^{3} a^{3} c - A^{3} B a^{2} c^{2}\right)} d e^{4} - {\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} e^{5}\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{4} d^{4} + {\left(3 \, B^{3} a^{2} c^{3} + 5 \, A^{2} B a c^{4}\right)} d^{3} e + 3 \, {\left(3 \, A B^{2} a^{2} c^{3} + A^{3} a c^{4}\right)} d^{2} e^{2} + {\left(B^{3} a^{3} c^{2} + 7 \, A^{2} B a^{2} c^{3}\right)} d e^{3} + {\left(A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} e^{4} + {\left(A a c^{6} d + B a^{2} c^{5} e\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}}\right)} \sqrt{\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - a c^{3} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} + 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} + 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} + 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7}}} + {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} + 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2}}{a c^{3}}}\right) - 4 \, {\left(B e x + 4 \, B d + 3 \, A e\right)} \sqrt{e x + d}}{6 \, c}"," ",0,"1/6*(3*c*sqrt((6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + a*c^3*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)) + (B^2*a*c + A^2*c^2)*d^3 + 3*(B^2*a^2 + A^2*a*c)*d*e^2)/(a*c^3))*log((2*(A*B^3*a*c^3 - A^3*B*c^4)*d^5 + 3*(B^4*a^2*c^2 - A^4*c^4)*d^4*e + 4*(A*B^3*a^2*c^2 - A^3*B*a*c^3)*d^3*e^2 - 2*(B^4*a^3*c - A^4*a*c^3)*d^2*e^3 - 6*(A*B^3*a^3*c - A^3*B*a^2*c^2)*d*e^4 - (B^4*a^4 - A^4*a^2*c^2)*e^5)*sqrt(e*x + d) + (2*A*B^2*a*c^4*d^4 + (3*B^3*a^2*c^3 + 5*A^2*B*a*c^4)*d^3*e + 3*(3*A*B^2*a^2*c^3 + A^3*a*c^4)*d^2*e^2 + (B^3*a^3*c^2 + 7*A^2*B*a^2*c^3)*d*e^3 + (A*B^2*a^3*c^2 + A^3*a^2*c^3)*e^4 - (A*a*c^6*d + B*a^2*c^5*e)*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)))*sqrt((6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + a*c^3*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)) + (B^2*a*c + A^2*c^2)*d^3 + 3*(B^2*a^2 + A^2*a*c)*d*e^2)/(a*c^3))) - 3*c*sqrt((6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + a*c^3*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)) + (B^2*a*c + A^2*c^2)*d^3 + 3*(B^2*a^2 + A^2*a*c)*d*e^2)/(a*c^3))*log((2*(A*B^3*a*c^3 - A^3*B*c^4)*d^5 + 3*(B^4*a^2*c^2 - A^4*c^4)*d^4*e + 4*(A*B^3*a^2*c^2 - A^3*B*a*c^3)*d^3*e^2 - 2*(B^4*a^3*c - A^4*a*c^3)*d^2*e^3 - 6*(A*B^3*a^3*c - A^3*B*a^2*c^2)*d*e^4 - (B^4*a^4 - A^4*a^2*c^2)*e^5)*sqrt(e*x + d) - (2*A*B^2*a*c^4*d^4 + (3*B^3*a^2*c^3 + 5*A^2*B*a*c^4)*d^3*e + 3*(3*A*B^2*a^2*c^3 + A^3*a*c^4)*d^2*e^2 + (B^3*a^3*c^2 + 7*A^2*B*a^2*c^3)*d*e^3 + (A*B^2*a^3*c^2 + A^3*a^2*c^3)*e^4 - (A*a*c^6*d + B*a^2*c^5*e)*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)))*sqrt((6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + a*c^3*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)) + (B^2*a*c + A^2*c^2)*d^3 + 3*(B^2*a^2 + A^2*a*c)*d*e^2)/(a*c^3))) + 3*c*sqrt((6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - a*c^3*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)) + (B^2*a*c + A^2*c^2)*d^3 + 3*(B^2*a^2 + A^2*a*c)*d*e^2)/(a*c^3))*log((2*(A*B^3*a*c^3 - A^3*B*c^4)*d^5 + 3*(B^4*a^2*c^2 - A^4*c^4)*d^4*e + 4*(A*B^3*a^2*c^2 - A^3*B*a*c^3)*d^3*e^2 - 2*(B^4*a^3*c - A^4*a*c^3)*d^2*e^3 - 6*(A*B^3*a^3*c - A^3*B*a^2*c^2)*d*e^4 - (B^4*a^4 - A^4*a^2*c^2)*e^5)*sqrt(e*x + d) + (2*A*B^2*a*c^4*d^4 + (3*B^3*a^2*c^3 + 5*A^2*B*a*c^4)*d^3*e + 3*(3*A*B^2*a^2*c^3 + A^3*a*c^4)*d^2*e^2 + (B^3*a^3*c^2 + 7*A^2*B*a^2*c^3)*d*e^3 + (A*B^2*a^3*c^2 + A^3*a^2*c^3)*e^4 + (A*a*c^6*d + B*a^2*c^5*e)*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)))*sqrt((6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - a*c^3*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)) + (B^2*a*c + A^2*c^2)*d^3 + 3*(B^2*a^2 + A^2*a*c)*d*e^2)/(a*c^3))) - 3*c*sqrt((6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - a*c^3*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)) + (B^2*a*c + A^2*c^2)*d^3 + 3*(B^2*a^2 + A^2*a*c)*d*e^2)/(a*c^3))*log((2*(A*B^3*a*c^3 - A^3*B*c^4)*d^5 + 3*(B^4*a^2*c^2 - A^4*c^4)*d^4*e + 4*(A*B^3*a^2*c^2 - A^3*B*a*c^3)*d^3*e^2 - 2*(B^4*a^3*c - A^4*a*c^3)*d^2*e^3 - 6*(A*B^3*a^3*c - A^3*B*a^2*c^2)*d*e^4 - (B^4*a^4 - A^4*a^2*c^2)*e^5)*sqrt(e*x + d) - (2*A*B^2*a*c^4*d^4 + (3*B^3*a^2*c^3 + 5*A^2*B*a*c^4)*d^3*e + 3*(3*A*B^2*a^2*c^3 + A^3*a*c^4)*d^2*e^2 + (B^3*a^3*c^2 + 7*A^2*B*a^2*c^3)*d*e^3 + (A*B^2*a^3*c^2 + A^3*a^2*c^3)*e^4 + (A*a*c^6*d + B*a^2*c^5*e)*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)))*sqrt((6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - a*c^3*sqrt((4*A^2*B^2*c^4*d^6 + 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 + 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 + 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7)) + (B^2*a*c + A^2*c^2)*d^3 + 3*(B^2*a^2 + A^2*a*c)*d*e^2)/(a*c^3))) - 4*(B*e*x + 4*B*d + 3*A*e)*sqrt(e*x + d))/c","B",0
1449,1,1538,0,0.465255," ","integrate((B*x+A)*(e*x+d)^(1/2)/(-c*x^2+a),x, algorithm=""fricas"")","-\frac{c \sqrt{\frac{2 \, A B a e + a c^{2} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{2} a + A^{2} c\right)} d}{a c^{2}}} \log\left(-{\left(2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{2} d - A a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{3} a^{2} c + A^{2} B a c^{2}\right)} e\right)} \sqrt{\frac{2 \, A B a e + a c^{2} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{2} a + A^{2} c\right)} d}{a c^{2}}}\right) - c \sqrt{\frac{2 \, A B a e + a c^{2} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{2} a + A^{2} c\right)} d}{a c^{2}}} \log\left(-{\left(2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{2} d - A a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{3} a^{2} c + A^{2} B a c^{2}\right)} e\right)} \sqrt{\frac{2 \, A B a e + a c^{2} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{2} a + A^{2} c\right)} d}{a c^{2}}}\right) + c \sqrt{\frac{2 \, A B a e - a c^{2} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{2} a + A^{2} c\right)} d}{a c^{2}}} \log\left(-{\left(2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{2} d + A a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{3} a^{2} c + A^{2} B a c^{2}\right)} e\right)} \sqrt{\frac{2 \, A B a e - a c^{2} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{2} a + A^{2} c\right)} d}{a c^{2}}}\right) - c \sqrt{\frac{2 \, A B a e - a c^{2} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{2} a + A^{2} c\right)} d}{a c^{2}}} \log\left(-{\left(2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{2} d + A a c^{4} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{3} a^{2} c + A^{2} B a c^{2}\right)} e\right)} \sqrt{\frac{2 \, A B a e - a c^{2} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5}}} + {\left(B^{2} a + A^{2} c\right)} d}{a c^{2}}}\right) + 4 \, \sqrt{e x + d} B}{2 \, c}"," ",0,"-1/2*(c*sqrt((2*A*B*a*e + a*c^2*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^2*a + A^2*c)*d)/(a*c^2))*log(-(2*(A*B^3*a*c - A^3*B*c^2)*d + (B^4*a^2 - A^4*c^2)*e)*sqrt(e*x + d) + (2*A*B^2*a*c^2*d - A*a*c^4*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^3*a^2*c + A^2*B*a*c^2)*e)*sqrt((2*A*B*a*e + a*c^2*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^2*a + A^2*c)*d)/(a*c^2))) - c*sqrt((2*A*B*a*e + a*c^2*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^2*a + A^2*c)*d)/(a*c^2))*log(-(2*(A*B^3*a*c - A^3*B*c^2)*d + (B^4*a^2 - A^4*c^2)*e)*sqrt(e*x + d) - (2*A*B^2*a*c^2*d - A*a*c^4*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^3*a^2*c + A^2*B*a*c^2)*e)*sqrt((2*A*B*a*e + a*c^2*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^2*a + A^2*c)*d)/(a*c^2))) + c*sqrt((2*A*B*a*e - a*c^2*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^2*a + A^2*c)*d)/(a*c^2))*log(-(2*(A*B^3*a*c - A^3*B*c^2)*d + (B^4*a^2 - A^4*c^2)*e)*sqrt(e*x + d) + (2*A*B^2*a*c^2*d + A*a*c^4*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^3*a^2*c + A^2*B*a*c^2)*e)*sqrt((2*A*B*a*e - a*c^2*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^2*a + A^2*c)*d)/(a*c^2))) - c*sqrt((2*A*B*a*e - a*c^2*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^2*a + A^2*c)*d)/(a*c^2))*log(-(2*(A*B^3*a*c - A^3*B*c^2)*d + (B^4*a^2 - A^4*c^2)*e)*sqrt(e*x + d) - (2*A*B^2*a*c^2*d + A*a*c^4*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^3*a^2*c + A^2*B*a*c^2)*e)*sqrt((2*A*B*a*e - a*c^2*sqrt((4*A^2*B^2*c^2*d^2 + 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5)) + (B^2*a + A^2*c)*d)/(a*c^2))) + 4*sqrt(e*x + d)*B)/c","B",0
1450,1,2385,0,0.513973," ","integrate((B*x+A)/(e*x+d)^(1/2)/(-c*x^2+a),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-\frac{2 \, A B a e - {\left(B^{2} a + A^{2} c\right)} d + {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}}{a c^{2} d^{2} - a^{2} c e^{2}}} \log\left({\left(2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d - {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{2} d^{2} - {\left(B^{3} a^{2} c + 3 \, A^{2} B a c^{2}\right)} d e + {\left(A B^{2} a^{2} c + A^{3} a c^{2}\right)} e^{2} + {\left(A a c^{4} d^{3} - B a^{2} c^{3} d^{2} e - A a^{2} c^{3} d e^{2} + B a^{3} c^{2} e^{3}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}\right)} \sqrt{-\frac{2 \, A B a e - {\left(B^{2} a + A^{2} c\right)} d + {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}}{a c^{2} d^{2} - a^{2} c e^{2}}}\right) - \frac{1}{2} \, \sqrt{-\frac{2 \, A B a e - {\left(B^{2} a + A^{2} c\right)} d + {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}}{a c^{2} d^{2} - a^{2} c e^{2}}} \log\left({\left(2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d - {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{2} d^{2} - {\left(B^{3} a^{2} c + 3 \, A^{2} B a c^{2}\right)} d e + {\left(A B^{2} a^{2} c + A^{3} a c^{2}\right)} e^{2} + {\left(A a c^{4} d^{3} - B a^{2} c^{3} d^{2} e - A a^{2} c^{3} d e^{2} + B a^{3} c^{2} e^{3}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}\right)} \sqrt{-\frac{2 \, A B a e - {\left(B^{2} a + A^{2} c\right)} d + {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}}{a c^{2} d^{2} - a^{2} c e^{2}}}\right) + \frac{1}{2} \, \sqrt{-\frac{2 \, A B a e - {\left(B^{2} a + A^{2} c\right)} d - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}}{a c^{2} d^{2} - a^{2} c e^{2}}} \log\left({\left(2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d - {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{2} d^{2} - {\left(B^{3} a^{2} c + 3 \, A^{2} B a c^{2}\right)} d e + {\left(A B^{2} a^{2} c + A^{3} a c^{2}\right)} e^{2} - {\left(A a c^{4} d^{3} - B a^{2} c^{3} d^{2} e - A a^{2} c^{3} d e^{2} + B a^{3} c^{2} e^{3}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}\right)} \sqrt{-\frac{2 \, A B a e - {\left(B^{2} a + A^{2} c\right)} d - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}}{a c^{2} d^{2} - a^{2} c e^{2}}}\right) - \frac{1}{2} \, \sqrt{-\frac{2 \, A B a e - {\left(B^{2} a + A^{2} c\right)} d - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}}{a c^{2} d^{2} - a^{2} c e^{2}}} \log\left({\left(2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d - {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{2} d^{2} - {\left(B^{3} a^{2} c + 3 \, A^{2} B a c^{2}\right)} d e + {\left(A B^{2} a^{2} c + A^{3} a c^{2}\right)} e^{2} - {\left(A a c^{4} d^{3} - B a^{2} c^{3} d^{2} e - A a^{2} c^{3} d e^{2} + B a^{3} c^{2} e^{3}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}\right)} \sqrt{-\frac{2 \, A B a e - {\left(B^{2} a + A^{2} c\right)} d - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2}}{a c^{5} d^{4} - 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}}}}{a c^{2} d^{2} - a^{2} c e^{2}}}\right)"," ",0,"1/2*sqrt(-(2*A*B*a*e - (B^2*a + A^2*c)*d + (a*c^2*d^2 - a^2*c*e^2)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))/(a*c^2*d^2 - a^2*c*e^2))*log((2*(A*B^3*a*c - A^3*B*c^2)*d - (B^4*a^2 - A^4*c^2)*e)*sqrt(e*x + d) + (2*A*B^2*a*c^2*d^2 - (B^3*a^2*c + 3*A^2*B*a*c^2)*d*e + (A*B^2*a^2*c + A^3*a*c^2)*e^2 + (A*a*c^4*d^3 - B*a^2*c^3*d^2*e - A*a^2*c^3*d*e^2 + B*a^3*c^2*e^3)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))*sqrt(-(2*A*B*a*e - (B^2*a + A^2*c)*d + (a*c^2*d^2 - a^2*c*e^2)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))/(a*c^2*d^2 - a^2*c*e^2))) - 1/2*sqrt(-(2*A*B*a*e - (B^2*a + A^2*c)*d + (a*c^2*d^2 - a^2*c*e^2)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))/(a*c^2*d^2 - a^2*c*e^2))*log((2*(A*B^3*a*c - A^3*B*c^2)*d - (B^4*a^2 - A^4*c^2)*e)*sqrt(e*x + d) - (2*A*B^2*a*c^2*d^2 - (B^3*a^2*c + 3*A^2*B*a*c^2)*d*e + (A*B^2*a^2*c + A^3*a*c^2)*e^2 + (A*a*c^4*d^3 - B*a^2*c^3*d^2*e - A*a^2*c^3*d*e^2 + B*a^3*c^2*e^3)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))*sqrt(-(2*A*B*a*e - (B^2*a + A^2*c)*d + (a*c^2*d^2 - a^2*c*e^2)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))/(a*c^2*d^2 - a^2*c*e^2))) + 1/2*sqrt(-(2*A*B*a*e - (B^2*a + A^2*c)*d - (a*c^2*d^2 - a^2*c*e^2)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))/(a*c^2*d^2 - a^2*c*e^2))*log((2*(A*B^3*a*c - A^3*B*c^2)*d - (B^4*a^2 - A^4*c^2)*e)*sqrt(e*x + d) + (2*A*B^2*a*c^2*d^2 - (B^3*a^2*c + 3*A^2*B*a*c^2)*d*e + (A*B^2*a^2*c + A^3*a*c^2)*e^2 - (A*a*c^4*d^3 - B*a^2*c^3*d^2*e - A*a^2*c^3*d*e^2 + B*a^3*c^2*e^3)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))*sqrt(-(2*A*B*a*e - (B^2*a + A^2*c)*d - (a*c^2*d^2 - a^2*c*e^2)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))/(a*c^2*d^2 - a^2*c*e^2))) - 1/2*sqrt(-(2*A*B*a*e - (B^2*a + A^2*c)*d - (a*c^2*d^2 - a^2*c*e^2)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))/(a*c^2*d^2 - a^2*c*e^2))*log((2*(A*B^3*a*c - A^3*B*c^2)*d - (B^4*a^2 - A^4*c^2)*e)*sqrt(e*x + d) - (2*A*B^2*a*c^2*d^2 - (B^3*a^2*c + 3*A^2*B*a*c^2)*d*e + (A*B^2*a^2*c + A^3*a*c^2)*e^2 - (A*a*c^4*d^3 - B*a^2*c^3*d^2*e - A*a^2*c^3*d*e^2 + B*a^3*c^2*e^3)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))*sqrt(-(2*A*B*a*e - (B^2*a + A^2*c)*d - (a*c^2*d^2 - a^2*c*e^2)*sqrt((4*A^2*B^2*c^2*d^2 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^2)/(a*c^5*d^4 - 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)))/(a*c^2*d^2 - a^2*c*e^2)))","B",0
1451,1,6448,0,2.761559," ","integrate((B*x+A)/(e*x+d)^(3/2)/(-c*x^2+a),x, algorithm=""fricas"")","\frac{{\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{-\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} - 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2} + {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}}{a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}}} \log\left({\left(2 \, {\left(A B^{3} a c^{2} - A^{3} B c^{3}\right)} d^{3} - 3 \, {\left(B^{4} a^{2} c - A^{4} c^{3}\right)} d^{2} e + 6 \, {\left(A B^{3} a^{2} c - A^{3} B a c^{2}\right)} d e^{2} - {\left(B^{4} a^{3} - A^{4} a c^{2}\right)} e^{3}\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{3} d^{5} - {\left(3 \, B^{3} a^{2} c^{2} + 7 \, A^{2} B a c^{3}\right)} d^{4} e + 2 \, {\left(7 \, A B^{2} a^{2} c^{2} + 3 \, A^{3} a c^{3}\right)} d^{3} e^{2} - 4 \, {\left(B^{3} a^{3} c + 4 \, A^{2} B a^{2} c^{2}\right)} d^{2} e^{3} + 2 \, {\left(4 \, A B^{2} a^{3} c + A^{3} a^{2} c^{2}\right)} d e^{4} - {\left(B^{3} a^{4} + A^{2} B a^{3} c\right)} e^{5} + {\left(A a c^{5} d^{8} - 2 \, B a^{2} c^{4} d^{7} e - 2 \, A a^{2} c^{4} d^{6} e^{2} + 6 \, B a^{3} c^{3} d^{5} e^{3} - 6 \, B a^{4} c^{2} d^{3} e^{5} + 2 \, A a^{4} c^{2} d^{2} e^{6} + 2 \, B a^{5} c d e^{7} - A a^{5} c e^{8}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}\right)} \sqrt{-\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} - 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2} + {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}}{a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}}}\right) - {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{-\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} - 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2} + {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}}{a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}}} \log\left({\left(2 \, {\left(A B^{3} a c^{2} - A^{3} B c^{3}\right)} d^{3} - 3 \, {\left(B^{4} a^{2} c - A^{4} c^{3}\right)} d^{2} e + 6 \, {\left(A B^{3} a^{2} c - A^{3} B a c^{2}\right)} d e^{2} - {\left(B^{4} a^{3} - A^{4} a c^{2}\right)} e^{3}\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{3} d^{5} - {\left(3 \, B^{3} a^{2} c^{2} + 7 \, A^{2} B a c^{3}\right)} d^{4} e + 2 \, {\left(7 \, A B^{2} a^{2} c^{2} + 3 \, A^{3} a c^{3}\right)} d^{3} e^{2} - 4 \, {\left(B^{3} a^{3} c + 4 \, A^{2} B a^{2} c^{2}\right)} d^{2} e^{3} + 2 \, {\left(4 \, A B^{2} a^{3} c + A^{3} a^{2} c^{2}\right)} d e^{4} - {\left(B^{3} a^{4} + A^{2} B a^{3} c\right)} e^{5} + {\left(A a c^{5} d^{8} - 2 \, B a^{2} c^{4} d^{7} e - 2 \, A a^{2} c^{4} d^{6} e^{2} + 6 \, B a^{3} c^{3} d^{5} e^{3} - 6 \, B a^{4} c^{2} d^{3} e^{5} + 2 \, A a^{4} c^{2} d^{2} e^{6} + 2 \, B a^{5} c d e^{7} - A a^{5} c e^{8}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}\right)} \sqrt{-\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} - 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2} + {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}}{a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}}}\right) + {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{-\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} - 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2} - {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}}{a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}}} \log\left({\left(2 \, {\left(A B^{3} a c^{2} - A^{3} B c^{3}\right)} d^{3} - 3 \, {\left(B^{4} a^{2} c - A^{4} c^{3}\right)} d^{2} e + 6 \, {\left(A B^{3} a^{2} c - A^{3} B a c^{2}\right)} d e^{2} - {\left(B^{4} a^{3} - A^{4} a c^{2}\right)} e^{3}\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{3} d^{5} - {\left(3 \, B^{3} a^{2} c^{2} + 7 \, A^{2} B a c^{3}\right)} d^{4} e + 2 \, {\left(7 \, A B^{2} a^{2} c^{2} + 3 \, A^{3} a c^{3}\right)} d^{3} e^{2} - 4 \, {\left(B^{3} a^{3} c + 4 \, A^{2} B a^{2} c^{2}\right)} d^{2} e^{3} + 2 \, {\left(4 \, A B^{2} a^{3} c + A^{3} a^{2} c^{2}\right)} d e^{4} - {\left(B^{3} a^{4} + A^{2} B a^{3} c\right)} e^{5} - {\left(A a c^{5} d^{8} - 2 \, B a^{2} c^{4} d^{7} e - 2 \, A a^{2} c^{4} d^{6} e^{2} + 6 \, B a^{3} c^{3} d^{5} e^{3} - 6 \, B a^{4} c^{2} d^{3} e^{5} + 2 \, A a^{4} c^{2} d^{2} e^{6} + 2 \, B a^{5} c d e^{7} - A a^{5} c e^{8}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}\right)} \sqrt{-\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} - 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2} - {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}}{a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}}}\right) - {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{-\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} - 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2} - {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}}{a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}}} \log\left({\left(2 \, {\left(A B^{3} a c^{2} - A^{3} B c^{3}\right)} d^{3} - 3 \, {\left(B^{4} a^{2} c - A^{4} c^{3}\right)} d^{2} e + 6 \, {\left(A B^{3} a^{2} c - A^{3} B a c^{2}\right)} d e^{2} - {\left(B^{4} a^{3} - A^{4} a c^{2}\right)} e^{3}\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{3} d^{5} - {\left(3 \, B^{3} a^{2} c^{2} + 7 \, A^{2} B a c^{3}\right)} d^{4} e + 2 \, {\left(7 \, A B^{2} a^{2} c^{2} + 3 \, A^{3} a c^{3}\right)} d^{3} e^{2} - 4 \, {\left(B^{3} a^{3} c + 4 \, A^{2} B a^{2} c^{2}\right)} d^{2} e^{3} + 2 \, {\left(4 \, A B^{2} a^{3} c + A^{3} a^{2} c^{2}\right)} d e^{4} - {\left(B^{3} a^{4} + A^{2} B a^{3} c\right)} e^{5} - {\left(A a c^{5} d^{8} - 2 \, B a^{2} c^{4} d^{7} e - 2 \, A a^{2} c^{4} d^{6} e^{2} + 6 \, B a^{3} c^{3} d^{5} e^{3} - 6 \, B a^{4} c^{2} d^{3} e^{5} + 2 \, A a^{4} c^{2} d^{2} e^{6} + 2 \, B a^{5} c d e^{7} - A a^{5} c e^{8}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}\right)} \sqrt{-\frac{6 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} - {\left(B^{2} a c + A^{2} c^{2}\right)} d^{3} - 3 \, {\left(B^{2} a^{2} + A^{2} a c\right)} d e^{2} - {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{4} d^{6} - 12 \, {\left(A B^{3} a c^{3} + A^{3} B c^{4}\right)} d^{5} e + 3 \, {\left(3 \, B^{4} a^{2} c^{2} + 14 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{2} - 40 \, {\left(A B^{3} a^{2} c^{2} + A^{3} B a c^{3}\right)} d^{3} e^{3} + 6 \, {\left(B^{4} a^{3} c + 8 \, A^{2} B^{2} a^{2} c^{2} + A^{4} a c^{3}\right)} d^{2} e^{4} - 12 \, {\left(A B^{3} a^{3} c + A^{3} B a^{2} c^{2}\right)} d e^{5} + {\left(B^{4} a^{4} + 2 \, A^{2} B^{2} a^{3} c + A^{4} a^{2} c^{2}\right)} e^{6}}{a c^{7} d^{12} - 6 \, a^{2} c^{6} d^{10} e^{2} + 15 \, a^{3} c^{5} d^{8} e^{4} - 20 \, a^{4} c^{4} d^{6} e^{6} + 15 \, a^{5} c^{3} d^{4} e^{8} - 6 \, a^{6} c^{2} d^{2} e^{10} + a^{7} c e^{12}}}}{a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}}}\right) - 4 \, {\left(B d - A e\right)} \sqrt{e x + d}}{2 \, {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)}}"," ",0,"1/2*((c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(-(6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - (B^2*a*c + A^2*c^2)*d^3 - 3*(B^2*a^2 + A^2*a*c)*d*e^2 + (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))/(a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6))*log((2*(A*B^3*a*c^2 - A^3*B*c^3)*d^3 - 3*(B^4*a^2*c - A^4*c^3)*d^2*e + 6*(A*B^3*a^2*c - A^3*B*a*c^2)*d*e^2 - (B^4*a^3 - A^4*a*c^2)*e^3)*sqrt(e*x + d) + (2*A*B^2*a*c^3*d^5 - (3*B^3*a^2*c^2 + 7*A^2*B*a*c^3)*d^4*e + 2*(7*A*B^2*a^2*c^2 + 3*A^3*a*c^3)*d^3*e^2 - 4*(B^3*a^3*c + 4*A^2*B*a^2*c^2)*d^2*e^3 + 2*(4*A*B^2*a^3*c + A^3*a^2*c^2)*d*e^4 - (B^3*a^4 + A^2*B*a^3*c)*e^5 + (A*a*c^5*d^8 - 2*B*a^2*c^4*d^7*e - 2*A*a^2*c^4*d^6*e^2 + 6*B*a^3*c^3*d^5*e^3 - 6*B*a^4*c^2*d^3*e^5 + 2*A*a^4*c^2*d^2*e^6 + 2*B*a^5*c*d*e^7 - A*a^5*c*e^8)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))*sqrt(-(6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - (B^2*a*c + A^2*c^2)*d^3 - 3*(B^2*a^2 + A^2*a*c)*d*e^2 + (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))/(a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6))) - (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(-(6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - (B^2*a*c + A^2*c^2)*d^3 - 3*(B^2*a^2 + A^2*a*c)*d*e^2 + (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))/(a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6))*log((2*(A*B^3*a*c^2 - A^3*B*c^3)*d^3 - 3*(B^4*a^2*c - A^4*c^3)*d^2*e + 6*(A*B^3*a^2*c - A^3*B*a*c^2)*d*e^2 - (B^4*a^3 - A^4*a*c^2)*e^3)*sqrt(e*x + d) - (2*A*B^2*a*c^3*d^5 - (3*B^3*a^2*c^2 + 7*A^2*B*a*c^3)*d^4*e + 2*(7*A*B^2*a^2*c^2 + 3*A^3*a*c^3)*d^3*e^2 - 4*(B^3*a^3*c + 4*A^2*B*a^2*c^2)*d^2*e^3 + 2*(4*A*B^2*a^3*c + A^3*a^2*c^2)*d*e^4 - (B^3*a^4 + A^2*B*a^3*c)*e^5 + (A*a*c^5*d^8 - 2*B*a^2*c^4*d^7*e - 2*A*a^2*c^4*d^6*e^2 + 6*B*a^3*c^3*d^5*e^3 - 6*B*a^4*c^2*d^3*e^5 + 2*A*a^4*c^2*d^2*e^6 + 2*B*a^5*c*d*e^7 - A*a^5*c*e^8)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))*sqrt(-(6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - (B^2*a*c + A^2*c^2)*d^3 - 3*(B^2*a^2 + A^2*a*c)*d*e^2 + (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))/(a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6))) + (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(-(6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - (B^2*a*c + A^2*c^2)*d^3 - 3*(B^2*a^2 + A^2*a*c)*d*e^2 - (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))/(a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6))*log((2*(A*B^3*a*c^2 - A^3*B*c^3)*d^3 - 3*(B^4*a^2*c - A^4*c^3)*d^2*e + 6*(A*B^3*a^2*c - A^3*B*a*c^2)*d*e^2 - (B^4*a^3 - A^4*a*c^2)*e^3)*sqrt(e*x + d) + (2*A*B^2*a*c^3*d^5 - (3*B^3*a^2*c^2 + 7*A^2*B*a*c^3)*d^4*e + 2*(7*A*B^2*a^2*c^2 + 3*A^3*a*c^3)*d^3*e^2 - 4*(B^3*a^3*c + 4*A^2*B*a^2*c^2)*d^2*e^3 + 2*(4*A*B^2*a^3*c + A^3*a^2*c^2)*d*e^4 - (B^3*a^4 + A^2*B*a^3*c)*e^5 - (A*a*c^5*d^8 - 2*B*a^2*c^4*d^7*e - 2*A*a^2*c^4*d^6*e^2 + 6*B*a^3*c^3*d^5*e^3 - 6*B*a^4*c^2*d^3*e^5 + 2*A*a^4*c^2*d^2*e^6 + 2*B*a^5*c*d*e^7 - A*a^5*c*e^8)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))*sqrt(-(6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - (B^2*a*c + A^2*c^2)*d^3 - 3*(B^2*a^2 + A^2*a*c)*d*e^2 - (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))/(a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6))) - (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(-(6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - (B^2*a*c + A^2*c^2)*d^3 - 3*(B^2*a^2 + A^2*a*c)*d*e^2 - (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))/(a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6))*log((2*(A*B^3*a*c^2 - A^3*B*c^3)*d^3 - 3*(B^4*a^2*c - A^4*c^3)*d^2*e + 6*(A*B^3*a^2*c - A^3*B*a*c^2)*d*e^2 - (B^4*a^3 - A^4*a*c^2)*e^3)*sqrt(e*x + d) - (2*A*B^2*a*c^3*d^5 - (3*B^3*a^2*c^2 + 7*A^2*B*a*c^3)*d^4*e + 2*(7*A*B^2*a^2*c^2 + 3*A^3*a*c^3)*d^3*e^2 - 4*(B^3*a^3*c + 4*A^2*B*a^2*c^2)*d^2*e^3 + 2*(4*A*B^2*a^3*c + A^3*a^2*c^2)*d*e^4 - (B^3*a^4 + A^2*B*a^3*c)*e^5 - (A*a*c^5*d^8 - 2*B*a^2*c^4*d^7*e - 2*A*a^2*c^4*d^6*e^2 + 6*B*a^3*c^3*d^5*e^3 - 6*B*a^4*c^2*d^3*e^5 + 2*A*a^4*c^2*d^2*e^6 + 2*B*a^5*c*d*e^7 - A*a^5*c*e^8)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))*sqrt(-(6*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 - (B^2*a*c + A^2*c^2)*d^3 - 3*(B^2*a^2 + A^2*a*c)*d*e^2 - (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*sqrt((4*A^2*B^2*c^4*d^6 - 12*(A*B^3*a*c^3 + A^3*B*c^4)*d^5*e + 3*(3*B^4*a^2*c^2 + 14*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^2 - 40*(A*B^3*a^2*c^2 + A^3*B*a*c^3)*d^3*e^3 + 6*(B^4*a^3*c + 8*A^2*B^2*a^2*c^2 + A^4*a*c^3)*d^2*e^4 - 12*(A*B^3*a^3*c + A^3*B*a^2*c^2)*d*e^5 + (B^4*a^4 + 2*A^2*B^2*a^3*c + A^4*a^2*c^2)*e^6)/(a*c^7*d^12 - 6*a^2*c^6*d^10*e^2 + 15*a^3*c^5*d^8*e^4 - 20*a^4*c^4*d^6*e^6 + 15*a^5*c^3*d^4*e^8 - 6*a^6*c^2*d^2*e^10 + a^7*c*e^12)))/(a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6))) - 4*(B*d - A*e)*sqrt(e*x + d))/(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)","B",0
1452,1,11231,0,15.759475," ","integrate((B*x+A)/(e*x+d)^(5/2)/(-c*x^2+a),x, algorithm=""fricas"")","\frac{3 \, {\left(c^{2} d^{6} - 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{-\frac{10 \, A B a c^{3} d^{4} e + 20 \, A B a^{2} c^{2} d^{2} e^{3} + 2 \, A B a^{3} c e^{5} - {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{5} - 10 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{3} e^{2} - 5 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d e^{4} + {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}} \log\left({\left(2 \, {\left(A B^{3} a c^{4} - A^{3} B c^{5}\right)} d^{5} - 5 \, {\left(B^{4} a^{2} c^{3} - A^{4} c^{5}\right)} d^{4} e + 20 \, {\left(A B^{3} a^{2} c^{3} - A^{3} B a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(B^{4} a^{3} c^{2} - A^{4} a c^{4}\right)} d^{2} e^{3} + 10 \, {\left(A B^{3} a^{3} c^{2} - A^{3} B a^{2} c^{3}\right)} d e^{4} - {\left(B^{4} a^{4} c - A^{4} a^{2} c^{3}\right)} e^{5}\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{5} d^{8} - {\left(5 \, B^{3} a^{2} c^{4} + 11 \, A^{2} B a c^{5}\right)} d^{7} e + {\left(41 \, A B^{2} a^{2} c^{4} + 15 \, A^{3} a c^{5}\right)} d^{6} e^{2} - {\left(25 \, B^{3} a^{3} c^{3} + 87 \, A^{2} B a^{2} c^{4}\right)} d^{5} e^{3} + 35 \, {\left(3 \, A B^{2} a^{3} c^{3} + A^{3} a^{2} c^{4}\right)} d^{4} e^{4} - {\left(31 \, B^{3} a^{4} c^{2} + 81 \, A^{2} B a^{3} c^{3}\right)} d^{3} e^{5} + {\left(43 \, A B^{2} a^{4} c^{2} + 13 \, A^{3} a^{3} c^{3}\right)} d^{2} e^{6} - {\left(3 \, B^{3} a^{5} c + 13 \, A^{2} B a^{4} c^{2}\right)} d e^{7} + {\left(A B^{2} a^{5} c + A^{3} a^{4} c^{2}\right)} e^{8} + {\left(A a c^{7} d^{13} - 3 \, B a^{2} c^{6} d^{12} e - 2 \, A a^{2} c^{6} d^{11} e^{2} + 14 \, B a^{3} c^{5} d^{10} e^{3} - 5 \, A a^{3} c^{5} d^{9} e^{4} - 25 \, B a^{4} c^{4} d^{8} e^{5} + 20 \, A a^{4} c^{4} d^{7} e^{6} + 20 \, B a^{5} c^{3} d^{6} e^{7} - 25 \, A a^{5} c^{3} d^{5} e^{8} - 5 \, B a^{6} c^{2} d^{4} e^{9} + 14 \, A a^{6} c^{2} d^{3} e^{10} - 2 \, B a^{7} c d^{2} e^{11} - 3 \, A a^{7} c d e^{12} + B a^{8} e^{13}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{-\frac{10 \, A B a c^{3} d^{4} e + 20 \, A B a^{2} c^{2} d^{2} e^{3} + 2 \, A B a^{3} c e^{5} - {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{5} - 10 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{3} e^{2} - 5 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d e^{4} + {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}}\right) - 3 \, {\left(c^{2} d^{6} - 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{-\frac{10 \, A B a c^{3} d^{4} e + 20 \, A B a^{2} c^{2} d^{2} e^{3} + 2 \, A B a^{3} c e^{5} - {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{5} - 10 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{3} e^{2} - 5 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d e^{4} + {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}} \log\left({\left(2 \, {\left(A B^{3} a c^{4} - A^{3} B c^{5}\right)} d^{5} - 5 \, {\left(B^{4} a^{2} c^{3} - A^{4} c^{5}\right)} d^{4} e + 20 \, {\left(A B^{3} a^{2} c^{3} - A^{3} B a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(B^{4} a^{3} c^{2} - A^{4} a c^{4}\right)} d^{2} e^{3} + 10 \, {\left(A B^{3} a^{3} c^{2} - A^{3} B a^{2} c^{3}\right)} d e^{4} - {\left(B^{4} a^{4} c - A^{4} a^{2} c^{3}\right)} e^{5}\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{5} d^{8} - {\left(5 \, B^{3} a^{2} c^{4} + 11 \, A^{2} B a c^{5}\right)} d^{7} e + {\left(41 \, A B^{2} a^{2} c^{4} + 15 \, A^{3} a c^{5}\right)} d^{6} e^{2} - {\left(25 \, B^{3} a^{3} c^{3} + 87 \, A^{2} B a^{2} c^{4}\right)} d^{5} e^{3} + 35 \, {\left(3 \, A B^{2} a^{3} c^{3} + A^{3} a^{2} c^{4}\right)} d^{4} e^{4} - {\left(31 \, B^{3} a^{4} c^{2} + 81 \, A^{2} B a^{3} c^{3}\right)} d^{3} e^{5} + {\left(43 \, A B^{2} a^{4} c^{2} + 13 \, A^{3} a^{3} c^{3}\right)} d^{2} e^{6} - {\left(3 \, B^{3} a^{5} c + 13 \, A^{2} B a^{4} c^{2}\right)} d e^{7} + {\left(A B^{2} a^{5} c + A^{3} a^{4} c^{2}\right)} e^{8} + {\left(A a c^{7} d^{13} - 3 \, B a^{2} c^{6} d^{12} e - 2 \, A a^{2} c^{6} d^{11} e^{2} + 14 \, B a^{3} c^{5} d^{10} e^{3} - 5 \, A a^{3} c^{5} d^{9} e^{4} - 25 \, B a^{4} c^{4} d^{8} e^{5} + 20 \, A a^{4} c^{4} d^{7} e^{6} + 20 \, B a^{5} c^{3} d^{6} e^{7} - 25 \, A a^{5} c^{3} d^{5} e^{8} - 5 \, B a^{6} c^{2} d^{4} e^{9} + 14 \, A a^{6} c^{2} d^{3} e^{10} - 2 \, B a^{7} c d^{2} e^{11} - 3 \, A a^{7} c d e^{12} + B a^{8} e^{13}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{-\frac{10 \, A B a c^{3} d^{4} e + 20 \, A B a^{2} c^{2} d^{2} e^{3} + 2 \, A B a^{3} c e^{5} - {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{5} - 10 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{3} e^{2} - 5 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d e^{4} + {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}}\right) + 3 \, {\left(c^{2} d^{6} - 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{-\frac{10 \, A B a c^{3} d^{4} e + 20 \, A B a^{2} c^{2} d^{2} e^{3} + 2 \, A B a^{3} c e^{5} - {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{5} - 10 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{3} e^{2} - 5 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d e^{4} - {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}} \log\left({\left(2 \, {\left(A B^{3} a c^{4} - A^{3} B c^{5}\right)} d^{5} - 5 \, {\left(B^{4} a^{2} c^{3} - A^{4} c^{5}\right)} d^{4} e + 20 \, {\left(A B^{3} a^{2} c^{3} - A^{3} B a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(B^{4} a^{3} c^{2} - A^{4} a c^{4}\right)} d^{2} e^{3} + 10 \, {\left(A B^{3} a^{3} c^{2} - A^{3} B a^{2} c^{3}\right)} d e^{4} - {\left(B^{4} a^{4} c - A^{4} a^{2} c^{3}\right)} e^{5}\right)} \sqrt{e x + d} + {\left(2 \, A B^{2} a c^{5} d^{8} - {\left(5 \, B^{3} a^{2} c^{4} + 11 \, A^{2} B a c^{5}\right)} d^{7} e + {\left(41 \, A B^{2} a^{2} c^{4} + 15 \, A^{3} a c^{5}\right)} d^{6} e^{2} - {\left(25 \, B^{3} a^{3} c^{3} + 87 \, A^{2} B a^{2} c^{4}\right)} d^{5} e^{3} + 35 \, {\left(3 \, A B^{2} a^{3} c^{3} + A^{3} a^{2} c^{4}\right)} d^{4} e^{4} - {\left(31 \, B^{3} a^{4} c^{2} + 81 \, A^{2} B a^{3} c^{3}\right)} d^{3} e^{5} + {\left(43 \, A B^{2} a^{4} c^{2} + 13 \, A^{3} a^{3} c^{3}\right)} d^{2} e^{6} - {\left(3 \, B^{3} a^{5} c + 13 \, A^{2} B a^{4} c^{2}\right)} d e^{7} + {\left(A B^{2} a^{5} c + A^{3} a^{4} c^{2}\right)} e^{8} - {\left(A a c^{7} d^{13} - 3 \, B a^{2} c^{6} d^{12} e - 2 \, A a^{2} c^{6} d^{11} e^{2} + 14 \, B a^{3} c^{5} d^{10} e^{3} - 5 \, A a^{3} c^{5} d^{9} e^{4} - 25 \, B a^{4} c^{4} d^{8} e^{5} + 20 \, A a^{4} c^{4} d^{7} e^{6} + 20 \, B a^{5} c^{3} d^{6} e^{7} - 25 \, A a^{5} c^{3} d^{5} e^{8} - 5 \, B a^{6} c^{2} d^{4} e^{9} + 14 \, A a^{6} c^{2} d^{3} e^{10} - 2 \, B a^{7} c d^{2} e^{11} - 3 \, A a^{7} c d e^{12} + B a^{8} e^{13}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{-\frac{10 \, A B a c^{3} d^{4} e + 20 \, A B a^{2} c^{2} d^{2} e^{3} + 2 \, A B a^{3} c e^{5} - {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{5} - 10 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{3} e^{2} - 5 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d e^{4} - {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}}\right) - 3 \, {\left(c^{2} d^{6} - 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{-\frac{10 \, A B a c^{3} d^{4} e + 20 \, A B a^{2} c^{2} d^{2} e^{3} + 2 \, A B a^{3} c e^{5} - {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{5} - 10 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{3} e^{2} - 5 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d e^{4} - {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}} \log\left({\left(2 \, {\left(A B^{3} a c^{4} - A^{3} B c^{5}\right)} d^{5} - 5 \, {\left(B^{4} a^{2} c^{3} - A^{4} c^{5}\right)} d^{4} e + 20 \, {\left(A B^{3} a^{2} c^{3} - A^{3} B a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(B^{4} a^{3} c^{2} - A^{4} a c^{4}\right)} d^{2} e^{3} + 10 \, {\left(A B^{3} a^{3} c^{2} - A^{3} B a^{2} c^{3}\right)} d e^{4} - {\left(B^{4} a^{4} c - A^{4} a^{2} c^{3}\right)} e^{5}\right)} \sqrt{e x + d} - {\left(2 \, A B^{2} a c^{5} d^{8} - {\left(5 \, B^{3} a^{2} c^{4} + 11 \, A^{2} B a c^{5}\right)} d^{7} e + {\left(41 \, A B^{2} a^{2} c^{4} + 15 \, A^{3} a c^{5}\right)} d^{6} e^{2} - {\left(25 \, B^{3} a^{3} c^{3} + 87 \, A^{2} B a^{2} c^{4}\right)} d^{5} e^{3} + 35 \, {\left(3 \, A B^{2} a^{3} c^{3} + A^{3} a^{2} c^{4}\right)} d^{4} e^{4} - {\left(31 \, B^{3} a^{4} c^{2} + 81 \, A^{2} B a^{3} c^{3}\right)} d^{3} e^{5} + {\left(43 \, A B^{2} a^{4} c^{2} + 13 \, A^{3} a^{3} c^{3}\right)} d^{2} e^{6} - {\left(3 \, B^{3} a^{5} c + 13 \, A^{2} B a^{4} c^{2}\right)} d e^{7} + {\left(A B^{2} a^{5} c + A^{3} a^{4} c^{2}\right)} e^{8} - {\left(A a c^{7} d^{13} - 3 \, B a^{2} c^{6} d^{12} e - 2 \, A a^{2} c^{6} d^{11} e^{2} + 14 \, B a^{3} c^{5} d^{10} e^{3} - 5 \, A a^{3} c^{5} d^{9} e^{4} - 25 \, B a^{4} c^{4} d^{8} e^{5} + 20 \, A a^{4} c^{4} d^{7} e^{6} + 20 \, B a^{5} c^{3} d^{6} e^{7} - 25 \, A a^{5} c^{3} d^{5} e^{8} - 5 \, B a^{6} c^{2} d^{4} e^{9} + 14 \, A a^{6} c^{2} d^{3} e^{10} - 2 \, B a^{7} c d^{2} e^{11} - 3 \, A a^{7} c d e^{12} + B a^{8} e^{13}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{-\frac{10 \, A B a c^{3} d^{4} e + 20 \, A B a^{2} c^{2} d^{2} e^{3} + 2 \, A B a^{3} c e^{5} - {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{5} - 10 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{3} e^{2} - 5 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d e^{4} - {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{7} d^{10} - 20 \, {\left(A B^{3} a c^{6} + A^{3} B c^{7}\right)} d^{9} e + 5 \, {\left(5 \, B^{4} a^{2} c^{5} + 26 \, A^{2} B^{2} a c^{6} + 5 \, A^{4} c^{7}\right)} d^{8} e^{2} - 240 \, {\left(A B^{3} a^{2} c^{5} + A^{3} B a c^{6}\right)} d^{7} e^{3} + 20 \, {\left(5 \, B^{4} a^{3} c^{4} + 32 \, A^{2} B^{2} a^{2} c^{5} + 5 \, A^{4} a c^{6}\right)} d^{6} e^{4} - 504 \, {\left(A B^{3} a^{3} c^{4} + A^{3} B a^{2} c^{5}\right)} d^{5} e^{5} + 10 \, {\left(11 \, B^{4} a^{4} c^{3} + 62 \, A^{2} B^{2} a^{3} c^{4} + 11 \, A^{4} a^{2} c^{5}\right)} d^{4} e^{6} - 240 \, {\left(A B^{3} a^{4} c^{3} + A^{3} B a^{3} c^{4}\right)} d^{3} e^{7} + 20 \, {\left(B^{4} a^{5} c^{2} + 7 \, A^{2} B^{2} a^{4} c^{3} + A^{4} a^{3} c^{4}\right)} d^{2} e^{8} - 20 \, {\left(A B^{3} a^{5} c^{2} + A^{3} B a^{4} c^{3}\right)} d e^{9} + {\left(B^{4} a^{6} c + 2 \, A^{2} B^{2} a^{5} c^{2} + A^{4} a^{4} c^{3}\right)} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}}\right) - 4 \, {\left(4 \, B c d^{3} - 7 \, A c d^{2} e + 2 \, B a d e^{2} + A a e^{3} + 3 \, {\left(B c d^{2} e - 2 \, A c d e^{2} + B a e^{3}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(c^{2} d^{6} - 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)}}"," ",0,"1/6*(3*(c^2*d^6 - 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + 2*(c^2*d^5*e - 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(-(10*A*B*a*c^3*d^4*e + 20*A*B*a^2*c^2*d^2*e^3 + 2*A*B*a^3*c*e^5 - (B^2*a*c^3 + A^2*c^4)*d^5 - 10*(B^2*a^2*c^2 + A^2*a*c^3)*d^3*e^2 - 5*(B^2*a^3*c + A^2*a^2*c^2)*d*e^4 + (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))*log((2*(A*B^3*a*c^4 - A^3*B*c^5)*d^5 - 5*(B^4*a^2*c^3 - A^4*c^5)*d^4*e + 20*(A*B^3*a^2*c^3 - A^3*B*a*c^4)*d^3*e^2 - 10*(B^4*a^3*c^2 - A^4*a*c^4)*d^2*e^3 + 10*(A*B^3*a^3*c^2 - A^3*B*a^2*c^3)*d*e^4 - (B^4*a^4*c - A^4*a^2*c^3)*e^5)*sqrt(e*x + d) + (2*A*B^2*a*c^5*d^8 - (5*B^3*a^2*c^4 + 11*A^2*B*a*c^5)*d^7*e + (41*A*B^2*a^2*c^4 + 15*A^3*a*c^5)*d^6*e^2 - (25*B^3*a^3*c^3 + 87*A^2*B*a^2*c^4)*d^5*e^3 + 35*(3*A*B^2*a^3*c^3 + A^3*a^2*c^4)*d^4*e^4 - (31*B^3*a^4*c^2 + 81*A^2*B*a^3*c^3)*d^3*e^5 + (43*A*B^2*a^4*c^2 + 13*A^3*a^3*c^3)*d^2*e^6 - (3*B^3*a^5*c + 13*A^2*B*a^4*c^2)*d*e^7 + (A*B^2*a^5*c + A^3*a^4*c^2)*e^8 + (A*a*c^7*d^13 - 3*B*a^2*c^6*d^12*e - 2*A*a^2*c^6*d^11*e^2 + 14*B*a^3*c^5*d^10*e^3 - 5*A*a^3*c^5*d^9*e^4 - 25*B*a^4*c^4*d^8*e^5 + 20*A*a^4*c^4*d^7*e^6 + 20*B*a^5*c^3*d^6*e^7 - 25*A*a^5*c^3*d^5*e^8 - 5*B*a^6*c^2*d^4*e^9 + 14*A*a^6*c^2*d^3*e^10 - 2*B*a^7*c*d^2*e^11 - 3*A*a^7*c*d*e^12 + B*a^8*e^13)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt(-(10*A*B*a*c^3*d^4*e + 20*A*B*a^2*c^2*d^2*e^3 + 2*A*B*a^3*c*e^5 - (B^2*a*c^3 + A^2*c^4)*d^5 - 10*(B^2*a^2*c^2 + A^2*a*c^3)*d^3*e^2 - 5*(B^2*a^3*c + A^2*a^2*c^2)*d*e^4 + (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))) - 3*(c^2*d^6 - 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + 2*(c^2*d^5*e - 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(-(10*A*B*a*c^3*d^4*e + 20*A*B*a^2*c^2*d^2*e^3 + 2*A*B*a^3*c*e^5 - (B^2*a*c^3 + A^2*c^4)*d^5 - 10*(B^2*a^2*c^2 + A^2*a*c^3)*d^3*e^2 - 5*(B^2*a^3*c + A^2*a^2*c^2)*d*e^4 + (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))*log((2*(A*B^3*a*c^4 - A^3*B*c^5)*d^5 - 5*(B^4*a^2*c^3 - A^4*c^5)*d^4*e + 20*(A*B^3*a^2*c^3 - A^3*B*a*c^4)*d^3*e^2 - 10*(B^4*a^3*c^2 - A^4*a*c^4)*d^2*e^3 + 10*(A*B^3*a^3*c^2 - A^3*B*a^2*c^3)*d*e^4 - (B^4*a^4*c - A^4*a^2*c^3)*e^5)*sqrt(e*x + d) - (2*A*B^2*a*c^5*d^8 - (5*B^3*a^2*c^4 + 11*A^2*B*a*c^5)*d^7*e + (41*A*B^2*a^2*c^4 + 15*A^3*a*c^5)*d^6*e^2 - (25*B^3*a^3*c^3 + 87*A^2*B*a^2*c^4)*d^5*e^3 + 35*(3*A*B^2*a^3*c^3 + A^3*a^2*c^4)*d^4*e^4 - (31*B^3*a^4*c^2 + 81*A^2*B*a^3*c^3)*d^3*e^5 + (43*A*B^2*a^4*c^2 + 13*A^3*a^3*c^3)*d^2*e^6 - (3*B^3*a^5*c + 13*A^2*B*a^4*c^2)*d*e^7 + (A*B^2*a^5*c + A^3*a^4*c^2)*e^8 + (A*a*c^7*d^13 - 3*B*a^2*c^6*d^12*e - 2*A*a^2*c^6*d^11*e^2 + 14*B*a^3*c^5*d^10*e^3 - 5*A*a^3*c^5*d^9*e^4 - 25*B*a^4*c^4*d^8*e^5 + 20*A*a^4*c^4*d^7*e^6 + 20*B*a^5*c^3*d^6*e^7 - 25*A*a^5*c^3*d^5*e^8 - 5*B*a^6*c^2*d^4*e^9 + 14*A*a^6*c^2*d^3*e^10 - 2*B*a^7*c*d^2*e^11 - 3*A*a^7*c*d*e^12 + B*a^8*e^13)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt(-(10*A*B*a*c^3*d^4*e + 20*A*B*a^2*c^2*d^2*e^3 + 2*A*B*a^3*c*e^5 - (B^2*a*c^3 + A^2*c^4)*d^5 - 10*(B^2*a^2*c^2 + A^2*a*c^3)*d^3*e^2 - 5*(B^2*a^3*c + A^2*a^2*c^2)*d*e^4 + (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))) + 3*(c^2*d^6 - 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + 2*(c^2*d^5*e - 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(-(10*A*B*a*c^3*d^4*e + 20*A*B*a^2*c^2*d^2*e^3 + 2*A*B*a^3*c*e^5 - (B^2*a*c^3 + A^2*c^4)*d^5 - 10*(B^2*a^2*c^2 + A^2*a*c^3)*d^3*e^2 - 5*(B^2*a^3*c + A^2*a^2*c^2)*d*e^4 - (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))*log((2*(A*B^3*a*c^4 - A^3*B*c^5)*d^5 - 5*(B^4*a^2*c^3 - A^4*c^5)*d^4*e + 20*(A*B^3*a^2*c^3 - A^3*B*a*c^4)*d^3*e^2 - 10*(B^4*a^3*c^2 - A^4*a*c^4)*d^2*e^3 + 10*(A*B^3*a^3*c^2 - A^3*B*a^2*c^3)*d*e^4 - (B^4*a^4*c - A^4*a^2*c^3)*e^5)*sqrt(e*x + d) + (2*A*B^2*a*c^5*d^8 - (5*B^3*a^2*c^4 + 11*A^2*B*a*c^5)*d^7*e + (41*A*B^2*a^2*c^4 + 15*A^3*a*c^5)*d^6*e^2 - (25*B^3*a^3*c^3 + 87*A^2*B*a^2*c^4)*d^5*e^3 + 35*(3*A*B^2*a^3*c^3 + A^3*a^2*c^4)*d^4*e^4 - (31*B^3*a^4*c^2 + 81*A^2*B*a^3*c^3)*d^3*e^5 + (43*A*B^2*a^4*c^2 + 13*A^3*a^3*c^3)*d^2*e^6 - (3*B^3*a^5*c + 13*A^2*B*a^4*c^2)*d*e^7 + (A*B^2*a^5*c + A^3*a^4*c^2)*e^8 - (A*a*c^7*d^13 - 3*B*a^2*c^6*d^12*e - 2*A*a^2*c^6*d^11*e^2 + 14*B*a^3*c^5*d^10*e^3 - 5*A*a^3*c^5*d^9*e^4 - 25*B*a^4*c^4*d^8*e^5 + 20*A*a^4*c^4*d^7*e^6 + 20*B*a^5*c^3*d^6*e^7 - 25*A*a^5*c^3*d^5*e^8 - 5*B*a^6*c^2*d^4*e^9 + 14*A*a^6*c^2*d^3*e^10 - 2*B*a^7*c*d^2*e^11 - 3*A*a^7*c*d*e^12 + B*a^8*e^13)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt(-(10*A*B*a*c^3*d^4*e + 20*A*B*a^2*c^2*d^2*e^3 + 2*A*B*a^3*c*e^5 - (B^2*a*c^3 + A^2*c^4)*d^5 - 10*(B^2*a^2*c^2 + A^2*a*c^3)*d^3*e^2 - 5*(B^2*a^3*c + A^2*a^2*c^2)*d*e^4 - (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))) - 3*(c^2*d^6 - 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + 2*(c^2*d^5*e - 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(-(10*A*B*a*c^3*d^4*e + 20*A*B*a^2*c^2*d^2*e^3 + 2*A*B*a^3*c*e^5 - (B^2*a*c^3 + A^2*c^4)*d^5 - 10*(B^2*a^2*c^2 + A^2*a*c^3)*d^3*e^2 - 5*(B^2*a^3*c + A^2*a^2*c^2)*d*e^4 - (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))*log((2*(A*B^3*a*c^4 - A^3*B*c^5)*d^5 - 5*(B^4*a^2*c^3 - A^4*c^5)*d^4*e + 20*(A*B^3*a^2*c^3 - A^3*B*a*c^4)*d^3*e^2 - 10*(B^4*a^3*c^2 - A^4*a*c^4)*d^2*e^3 + 10*(A*B^3*a^3*c^2 - A^3*B*a^2*c^3)*d*e^4 - (B^4*a^4*c - A^4*a^2*c^3)*e^5)*sqrt(e*x + d) - (2*A*B^2*a*c^5*d^8 - (5*B^3*a^2*c^4 + 11*A^2*B*a*c^5)*d^7*e + (41*A*B^2*a^2*c^4 + 15*A^3*a*c^5)*d^6*e^2 - (25*B^3*a^3*c^3 + 87*A^2*B*a^2*c^4)*d^5*e^3 + 35*(3*A*B^2*a^3*c^3 + A^3*a^2*c^4)*d^4*e^4 - (31*B^3*a^4*c^2 + 81*A^2*B*a^3*c^3)*d^3*e^5 + (43*A*B^2*a^4*c^2 + 13*A^3*a^3*c^3)*d^2*e^6 - (3*B^3*a^5*c + 13*A^2*B*a^4*c^2)*d*e^7 + (A*B^2*a^5*c + A^3*a^4*c^2)*e^8 - (A*a*c^7*d^13 - 3*B*a^2*c^6*d^12*e - 2*A*a^2*c^6*d^11*e^2 + 14*B*a^3*c^5*d^10*e^3 - 5*A*a^3*c^5*d^9*e^4 - 25*B*a^4*c^4*d^8*e^5 + 20*A*a^4*c^4*d^7*e^6 + 20*B*a^5*c^3*d^6*e^7 - 25*A*a^5*c^3*d^5*e^8 - 5*B*a^6*c^2*d^4*e^9 + 14*A*a^6*c^2*d^3*e^10 - 2*B*a^7*c*d^2*e^11 - 3*A*a^7*c*d*e^12 + B*a^8*e^13)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt(-(10*A*B*a*c^3*d^4*e + 20*A*B*a^2*c^2*d^2*e^3 + 2*A*B*a^3*c*e^5 - (B^2*a*c^3 + A^2*c^4)*d^5 - 10*(B^2*a^2*c^2 + A^2*a*c^3)*d^3*e^2 - 5*(B^2*a^3*c + A^2*a^2*c^2)*d*e^4 - (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((4*A^2*B^2*c^7*d^10 - 20*(A*B^3*a*c^6 + A^3*B*c^7)*d^9*e + 5*(5*B^4*a^2*c^5 + 26*A^2*B^2*a*c^6 + 5*A^4*c^7)*d^8*e^2 - 240*(A*B^3*a^2*c^5 + A^3*B*a*c^6)*d^7*e^3 + 20*(5*B^4*a^3*c^4 + 32*A^2*B^2*a^2*c^5 + 5*A^4*a*c^6)*d^6*e^4 - 504*(A*B^3*a^3*c^4 + A^3*B*a^2*c^5)*d^5*e^5 + 10*(11*B^4*a^4*c^3 + 62*A^2*B^2*a^3*c^4 + 11*A^4*a^2*c^5)*d^4*e^6 - 240*(A*B^3*a^4*c^3 + A^3*B*a^3*c^4)*d^3*e^7 + 20*(B^4*a^5*c^2 + 7*A^2*B^2*a^4*c^3 + A^4*a^3*c^4)*d^2*e^8 - 20*(A*B^3*a^5*c^2 + A^3*B*a^4*c^3)*d*e^9 + (B^4*a^6*c + 2*A^2*B^2*a^5*c^2 + A^4*a^4*c^3)*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))) - 4*(4*B*c*d^3 - 7*A*c*d^2*e + 2*B*a*d*e^2 + A*a*e^3 + 3*(B*c*d^2*e - 2*A*c*d*e^2 + B*a*e^3)*x)*sqrt(e*x + d))/(c^2*d^6 - 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + 2*(c^2*d^5*e - 2*a*c*d^3*e^3 + a^2*d*e^5)*x)","B",0
1453,1,5611,0,8.659575," ","integrate((B*x+A)*(e*x+d)^(5/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a c^{3} x^{2} - a^{2} c^{2}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} - 20 \, A B a c^{2} d^{4} e + 30 \, A B a^{2} c d^{2} e^{3} + 30 \, A B a^{3} e^{5} + a^{3} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}} + 5 \, {\left(5 \, B^{2} a^{2} c - 3 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 15 \, {\left(5 \, B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4}}{a^{3} c^{4}}} \log\left(-{\left(120 \, A^{3} B c^{5} d^{7} e^{2} - 20 \, {\left(45 \, A^{2} B^{2} a c^{4} - A^{4} c^{5}\right)} d^{6} e^{3} + 10 \, {\left(225 \, A B^{3} a^{2} c^{3} - 77 \, A^{3} B a c^{4}\right)} d^{5} e^{4} - {\left(1875 \, B^{4} a^{3} c^{2} - 3000 \, A^{2} B^{2} a^{2} c^{3} + 101 \, A^{4} a c^{4}\right)} d^{4} e^{5} - 20 \, {\left(175 \, A B^{3} a^{3} c^{2} - 73 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{6} + 2 \, {\left(625 \, B^{4} a^{4} c - 1050 \, A^{2} B^{2} a^{3} c^{2} + 81 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{7} + 10 \, {\left(125 \, A B^{3} a^{4} c - 81 \, A^{3} B a^{3} c^{2}\right)} d e^{8} + {\left(625 \, B^{4} a^{5} - 81 \, A^{4} a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + {\left(30 \, A^{2} B a^{2} c^{5} d^{4} e^{3} + 5 \, {\left(15 \, A B^{2} a^{3} c^{4} + A^{3} a^{2} c^{5}\right)} d^{3} e^{4} - 15 \, {\left(25 \, B^{3} a^{4} c^{3} + 3 \, A^{2} B a^{3} c^{4}\right)} d^{2} e^{5} - 3 \, {\left(125 \, A B^{2} a^{4} c^{3} + 3 \, A^{3} a^{3} c^{4}\right)} d e^{6} - 5 \, {\left(25 \, B^{3} a^{5} c^{2} + 9 \, A^{2} B a^{4} c^{3}\right)} e^{7} - {\left(2 \, A a^{3} c^{8} d^{2} - 5 \, B a^{4} c^{7} d e - 3 \, A a^{4} c^{7} e^{2}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} - 20 \, A B a c^{2} d^{4} e + 30 \, A B a^{2} c d^{2} e^{3} + 30 \, A B a^{3} e^{5} + a^{3} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}} + 5 \, {\left(5 \, B^{2} a^{2} c - 3 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 15 \, {\left(5 \, B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4}}{a^{3} c^{4}}}\right) - {\left(a c^{3} x^{2} - a^{2} c^{2}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} - 20 \, A B a c^{2} d^{4} e + 30 \, A B a^{2} c d^{2} e^{3} + 30 \, A B a^{3} e^{5} + a^{3} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}} + 5 \, {\left(5 \, B^{2} a^{2} c - 3 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 15 \, {\left(5 \, B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4}}{a^{3} c^{4}}} \log\left(-{\left(120 \, A^{3} B c^{5} d^{7} e^{2} - 20 \, {\left(45 \, A^{2} B^{2} a c^{4} - A^{4} c^{5}\right)} d^{6} e^{3} + 10 \, {\left(225 \, A B^{3} a^{2} c^{3} - 77 \, A^{3} B a c^{4}\right)} d^{5} e^{4} - {\left(1875 \, B^{4} a^{3} c^{2} - 3000 \, A^{2} B^{2} a^{2} c^{3} + 101 \, A^{4} a c^{4}\right)} d^{4} e^{5} - 20 \, {\left(175 \, A B^{3} a^{3} c^{2} - 73 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{6} + 2 \, {\left(625 \, B^{4} a^{4} c - 1050 \, A^{2} B^{2} a^{3} c^{2} + 81 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{7} + 10 \, {\left(125 \, A B^{3} a^{4} c - 81 \, A^{3} B a^{3} c^{2}\right)} d e^{8} + {\left(625 \, B^{4} a^{5} - 81 \, A^{4} a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - {\left(30 \, A^{2} B a^{2} c^{5} d^{4} e^{3} + 5 \, {\left(15 \, A B^{2} a^{3} c^{4} + A^{3} a^{2} c^{5}\right)} d^{3} e^{4} - 15 \, {\left(25 \, B^{3} a^{4} c^{3} + 3 \, A^{2} B a^{3} c^{4}\right)} d^{2} e^{5} - 3 \, {\left(125 \, A B^{2} a^{4} c^{3} + 3 \, A^{3} a^{3} c^{4}\right)} d e^{6} - 5 \, {\left(25 \, B^{3} a^{5} c^{2} + 9 \, A^{2} B a^{4} c^{3}\right)} e^{7} - {\left(2 \, A a^{3} c^{8} d^{2} - 5 \, B a^{4} c^{7} d e - 3 \, A a^{4} c^{7} e^{2}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} - 20 \, A B a c^{2} d^{4} e + 30 \, A B a^{2} c d^{2} e^{3} + 30 \, A B a^{3} e^{5} + a^{3} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}} + 5 \, {\left(5 \, B^{2} a^{2} c - 3 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 15 \, {\left(5 \, B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4}}{a^{3} c^{4}}}\right) + {\left(a c^{3} x^{2} - a^{2} c^{2}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} - 20 \, A B a c^{2} d^{4} e + 30 \, A B a^{2} c d^{2} e^{3} + 30 \, A B a^{3} e^{5} - a^{3} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}} + 5 \, {\left(5 \, B^{2} a^{2} c - 3 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 15 \, {\left(5 \, B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4}}{a^{3} c^{4}}} \log\left(-{\left(120 \, A^{3} B c^{5} d^{7} e^{2} - 20 \, {\left(45 \, A^{2} B^{2} a c^{4} - A^{4} c^{5}\right)} d^{6} e^{3} + 10 \, {\left(225 \, A B^{3} a^{2} c^{3} - 77 \, A^{3} B a c^{4}\right)} d^{5} e^{4} - {\left(1875 \, B^{4} a^{3} c^{2} - 3000 \, A^{2} B^{2} a^{2} c^{3} + 101 \, A^{4} a c^{4}\right)} d^{4} e^{5} - 20 \, {\left(175 \, A B^{3} a^{3} c^{2} - 73 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{6} + 2 \, {\left(625 \, B^{4} a^{4} c - 1050 \, A^{2} B^{2} a^{3} c^{2} + 81 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{7} + 10 \, {\left(125 \, A B^{3} a^{4} c - 81 \, A^{3} B a^{3} c^{2}\right)} d e^{8} + {\left(625 \, B^{4} a^{5} - 81 \, A^{4} a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + {\left(30 \, A^{2} B a^{2} c^{5} d^{4} e^{3} + 5 \, {\left(15 \, A B^{2} a^{3} c^{4} + A^{3} a^{2} c^{5}\right)} d^{3} e^{4} - 15 \, {\left(25 \, B^{3} a^{4} c^{3} + 3 \, A^{2} B a^{3} c^{4}\right)} d^{2} e^{5} - 3 \, {\left(125 \, A B^{2} a^{4} c^{3} + 3 \, A^{3} a^{3} c^{4}\right)} d e^{6} - 5 \, {\left(25 \, B^{3} a^{5} c^{2} + 9 \, A^{2} B a^{4} c^{3}\right)} e^{7} + {\left(2 \, A a^{3} c^{8} d^{2} - 5 \, B a^{4} c^{7} d e - 3 \, A a^{4} c^{7} e^{2}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} - 20 \, A B a c^{2} d^{4} e + 30 \, A B a^{2} c d^{2} e^{3} + 30 \, A B a^{3} e^{5} - a^{3} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}} + 5 \, {\left(5 \, B^{2} a^{2} c - 3 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 15 \, {\left(5 \, B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4}}{a^{3} c^{4}}}\right) - {\left(a c^{3} x^{2} - a^{2} c^{2}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} - 20 \, A B a c^{2} d^{4} e + 30 \, A B a^{2} c d^{2} e^{3} + 30 \, A B a^{3} e^{5} - a^{3} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}} + 5 \, {\left(5 \, B^{2} a^{2} c - 3 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 15 \, {\left(5 \, B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4}}{a^{3} c^{4}}} \log\left(-{\left(120 \, A^{3} B c^{5} d^{7} e^{2} - 20 \, {\left(45 \, A^{2} B^{2} a c^{4} - A^{4} c^{5}\right)} d^{6} e^{3} + 10 \, {\left(225 \, A B^{3} a^{2} c^{3} - 77 \, A^{3} B a c^{4}\right)} d^{5} e^{4} - {\left(1875 \, B^{4} a^{3} c^{2} - 3000 \, A^{2} B^{2} a^{2} c^{3} + 101 \, A^{4} a c^{4}\right)} d^{4} e^{5} - 20 \, {\left(175 \, A B^{3} a^{3} c^{2} - 73 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{6} + 2 \, {\left(625 \, B^{4} a^{4} c - 1050 \, A^{2} B^{2} a^{3} c^{2} + 81 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{7} + 10 \, {\left(125 \, A B^{3} a^{4} c - 81 \, A^{3} B a^{3} c^{2}\right)} d e^{8} + {\left(625 \, B^{4} a^{5} - 81 \, A^{4} a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - {\left(30 \, A^{2} B a^{2} c^{5} d^{4} e^{3} + 5 \, {\left(15 \, A B^{2} a^{3} c^{4} + A^{3} a^{2} c^{5}\right)} d^{3} e^{4} - 15 \, {\left(25 \, B^{3} a^{4} c^{3} + 3 \, A^{2} B a^{3} c^{4}\right)} d^{2} e^{5} - 3 \, {\left(125 \, A B^{2} a^{4} c^{3} + 3 \, A^{3} a^{3} c^{4}\right)} d e^{6} - 5 \, {\left(25 \, B^{3} a^{5} c^{2} + 9 \, A^{2} B a^{4} c^{3}\right)} e^{7} + {\left(2 \, A a^{3} c^{8} d^{2} - 5 \, B a^{4} c^{7} d e - 3 \, A a^{4} c^{7} e^{2}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} - 20 \, A B a c^{2} d^{4} e + 30 \, A B a^{2} c d^{2} e^{3} + 30 \, A B a^{3} e^{5} - a^{3} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{4} - 300 \, {\left(15 \, A B^{3} a c^{3} - A^{3} B c^{4}\right)} d^{5} e^{5} + 25 \, {\left(225 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{6} + 40 \, {\left(225 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 30 \, {\left(125 \, B^{4} a^{3} c + 200 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{8} + 140 \, {\left(25 \, A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9}}} + 5 \, {\left(5 \, B^{2} a^{2} c - 3 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 15 \, {\left(5 \, B^{2} a^{3} + A^{2} a^{2} c\right)} d e^{4}}{a^{3} c^{4}}}\right) - 4 \, {\left(4 \, B a c e^{2} x^{2} - B a c d^{2} - 2 \, A a c d e - 5 \, B a^{2} e^{2} - {\left(A c^{2} d^{2} + 2 \, B a c d e + A a c e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a c^{3} x^{2} - a^{2} c^{2}\right)}}"," ",0,"-1/8*((a*c^3*x^2 - a^2*c^2)*sqrt((4*A^2*c^3*d^5 - 20*A*B*a*c^2*d^4*e + 30*A*B*a^2*c*d^2*e^3 + 30*A*B*a^3*e^5 + a^3*c^4*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)) + 5*(5*B^2*a^2*c - 3*A^2*a*c^2)*d^3*e^2 + 15*(5*B^2*a^3 + A^2*a^2*c)*d*e^4)/(a^3*c^4))*log(-(120*A^3*B*c^5*d^7*e^2 - 20*(45*A^2*B^2*a*c^4 - A^4*c^5)*d^6*e^3 + 10*(225*A*B^3*a^2*c^3 - 77*A^3*B*a*c^4)*d^5*e^4 - (1875*B^4*a^3*c^2 - 3000*A^2*B^2*a^2*c^3 + 101*A^4*a*c^4)*d^4*e^5 - 20*(175*A*B^3*a^3*c^2 - 73*A^3*B*a^2*c^3)*d^3*e^6 + 2*(625*B^4*a^4*c - 1050*A^2*B^2*a^3*c^2 + 81*A^4*a^2*c^3)*d^2*e^7 + 10*(125*A*B^3*a^4*c - 81*A^3*B*a^3*c^2)*d*e^8 + (625*B^4*a^5 - 81*A^4*a^3*c^2)*e^9)*sqrt(e*x + d) + (30*A^2*B*a^2*c^5*d^4*e^3 + 5*(15*A*B^2*a^3*c^4 + A^3*a^2*c^5)*d^3*e^4 - 15*(25*B^3*a^4*c^3 + 3*A^2*B*a^3*c^4)*d^2*e^5 - 3*(125*A*B^2*a^4*c^3 + 3*A^3*a^3*c^4)*d*e^6 - 5*(25*B^3*a^5*c^2 + 9*A^2*B*a^4*c^3)*e^7 - (2*A*a^3*c^8*d^2 - 5*B*a^4*c^7*d*e - 3*A*a^4*c^7*e^2)*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)))*sqrt((4*A^2*c^3*d^5 - 20*A*B*a*c^2*d^4*e + 30*A*B*a^2*c*d^2*e^3 + 30*A*B*a^3*e^5 + a^3*c^4*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)) + 5*(5*B^2*a^2*c - 3*A^2*a*c^2)*d^3*e^2 + 15*(5*B^2*a^3 + A^2*a^2*c)*d*e^4)/(a^3*c^4))) - (a*c^3*x^2 - a^2*c^2)*sqrt((4*A^2*c^3*d^5 - 20*A*B*a*c^2*d^4*e + 30*A*B*a^2*c*d^2*e^3 + 30*A*B*a^3*e^5 + a^3*c^4*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)) + 5*(5*B^2*a^2*c - 3*A^2*a*c^2)*d^3*e^2 + 15*(5*B^2*a^3 + A^2*a^2*c)*d*e^4)/(a^3*c^4))*log(-(120*A^3*B*c^5*d^7*e^2 - 20*(45*A^2*B^2*a*c^4 - A^4*c^5)*d^6*e^3 + 10*(225*A*B^3*a^2*c^3 - 77*A^3*B*a*c^4)*d^5*e^4 - (1875*B^4*a^3*c^2 - 3000*A^2*B^2*a^2*c^3 + 101*A^4*a*c^4)*d^4*e^5 - 20*(175*A*B^3*a^3*c^2 - 73*A^3*B*a^2*c^3)*d^3*e^6 + 2*(625*B^4*a^4*c - 1050*A^2*B^2*a^3*c^2 + 81*A^4*a^2*c^3)*d^2*e^7 + 10*(125*A*B^3*a^4*c - 81*A^3*B*a^3*c^2)*d*e^8 + (625*B^4*a^5 - 81*A^4*a^3*c^2)*e^9)*sqrt(e*x + d) - (30*A^2*B*a^2*c^5*d^4*e^3 + 5*(15*A*B^2*a^3*c^4 + A^3*a^2*c^5)*d^3*e^4 - 15*(25*B^3*a^4*c^3 + 3*A^2*B*a^3*c^4)*d^2*e^5 - 3*(125*A*B^2*a^4*c^3 + 3*A^3*a^3*c^4)*d*e^6 - 5*(25*B^3*a^5*c^2 + 9*A^2*B*a^4*c^3)*e^7 - (2*A*a^3*c^8*d^2 - 5*B*a^4*c^7*d*e - 3*A*a^4*c^7*e^2)*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)))*sqrt((4*A^2*c^3*d^5 - 20*A*B*a*c^2*d^4*e + 30*A*B*a^2*c*d^2*e^3 + 30*A*B*a^3*e^5 + a^3*c^4*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)) + 5*(5*B^2*a^2*c - 3*A^2*a*c^2)*d^3*e^2 + 15*(5*B^2*a^3 + A^2*a^2*c)*d*e^4)/(a^3*c^4))) + (a*c^3*x^2 - a^2*c^2)*sqrt((4*A^2*c^3*d^5 - 20*A*B*a*c^2*d^4*e + 30*A*B*a^2*c*d^2*e^3 + 30*A*B*a^3*e^5 - a^3*c^4*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)) + 5*(5*B^2*a^2*c - 3*A^2*a*c^2)*d^3*e^2 + 15*(5*B^2*a^3 + A^2*a^2*c)*d*e^4)/(a^3*c^4))*log(-(120*A^3*B*c^5*d^7*e^2 - 20*(45*A^2*B^2*a*c^4 - A^4*c^5)*d^6*e^3 + 10*(225*A*B^3*a^2*c^3 - 77*A^3*B*a*c^4)*d^5*e^4 - (1875*B^4*a^3*c^2 - 3000*A^2*B^2*a^2*c^3 + 101*A^4*a*c^4)*d^4*e^5 - 20*(175*A*B^3*a^3*c^2 - 73*A^3*B*a^2*c^3)*d^3*e^6 + 2*(625*B^4*a^4*c - 1050*A^2*B^2*a^3*c^2 + 81*A^4*a^2*c^3)*d^2*e^7 + 10*(125*A*B^3*a^4*c - 81*A^3*B*a^3*c^2)*d*e^8 + (625*B^4*a^5 - 81*A^4*a^3*c^2)*e^9)*sqrt(e*x + d) + (30*A^2*B*a^2*c^5*d^4*e^3 + 5*(15*A*B^2*a^3*c^4 + A^3*a^2*c^5)*d^3*e^4 - 15*(25*B^3*a^4*c^3 + 3*A^2*B*a^3*c^4)*d^2*e^5 - 3*(125*A*B^2*a^4*c^3 + 3*A^3*a^3*c^4)*d*e^6 - 5*(25*B^3*a^5*c^2 + 9*A^2*B*a^4*c^3)*e^7 + (2*A*a^3*c^8*d^2 - 5*B*a^4*c^7*d*e - 3*A*a^4*c^7*e^2)*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)))*sqrt((4*A^2*c^3*d^5 - 20*A*B*a*c^2*d^4*e + 30*A*B*a^2*c*d^2*e^3 + 30*A*B*a^3*e^5 - a^3*c^4*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)) + 5*(5*B^2*a^2*c - 3*A^2*a*c^2)*d^3*e^2 + 15*(5*B^2*a^3 + A^2*a^2*c)*d*e^4)/(a^3*c^4))) - (a*c^3*x^2 - a^2*c^2)*sqrt((4*A^2*c^3*d^5 - 20*A*B*a*c^2*d^4*e + 30*A*B*a^2*c*d^2*e^3 + 30*A*B*a^3*e^5 - a^3*c^4*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)) + 5*(5*B^2*a^2*c - 3*A^2*a*c^2)*d^3*e^2 + 15*(5*B^2*a^3 + A^2*a^2*c)*d*e^4)/(a^3*c^4))*log(-(120*A^3*B*c^5*d^7*e^2 - 20*(45*A^2*B^2*a*c^4 - A^4*c^5)*d^6*e^3 + 10*(225*A*B^3*a^2*c^3 - 77*A^3*B*a*c^4)*d^5*e^4 - (1875*B^4*a^3*c^2 - 3000*A^2*B^2*a^2*c^3 + 101*A^4*a*c^4)*d^4*e^5 - 20*(175*A*B^3*a^3*c^2 - 73*A^3*B*a^2*c^3)*d^3*e^6 + 2*(625*B^4*a^4*c - 1050*A^2*B^2*a^3*c^2 + 81*A^4*a^2*c^3)*d^2*e^7 + 10*(125*A*B^3*a^4*c - 81*A^3*B*a^3*c^2)*d*e^8 + (625*B^4*a^5 - 81*A^4*a^3*c^2)*e^9)*sqrt(e*x + d) - (30*A^2*B*a^2*c^5*d^4*e^3 + 5*(15*A*B^2*a^3*c^4 + A^3*a^2*c^5)*d^3*e^4 - 15*(25*B^3*a^4*c^3 + 3*A^2*B*a^3*c^4)*d^2*e^5 - 3*(125*A*B^2*a^4*c^3 + 3*A^3*a^3*c^4)*d*e^6 - 5*(25*B^3*a^5*c^2 + 9*A^2*B*a^4*c^3)*e^7 + (2*A*a^3*c^8*d^2 - 5*B*a^4*c^7*d*e - 3*A*a^4*c^7*e^2)*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)))*sqrt((4*A^2*c^3*d^5 - 20*A*B*a*c^2*d^4*e + 30*A*B*a^2*c*d^2*e^3 + 30*A*B*a^3*e^5 - a^3*c^4*sqrt((900*A^2*B^2*c^4*d^6*e^4 - 300*(15*A*B^3*a*c^3 - A^3*B*c^4)*d^5*e^5 + 25*(225*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^6 + 40*(225*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 30*(125*B^4*a^3*c + 200*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^8 + 140*(25*A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (625*B^4*a^4 + 450*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9)) + 5*(5*B^2*a^2*c - 3*A^2*a*c^2)*d^3*e^2 + 15*(5*B^2*a^3 + A^2*a^2*c)*d*e^4)/(a^3*c^4))) - 4*(4*B*a*c*e^2*x^2 - B*a*c*d^2 - 2*A*a*c*d*e - 5*B*a^2*e^2 - (A*c^2*d^2 + 2*B*a*c*d*e + A*a*c*e^2)*x)*sqrt(e*x + d))/(a*c^3*x^2 - a^2*c^2)","B",0
1454,1,2327,0,0.645366," ","integrate((B*x+A)*(e*x+d)^(3/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 12 \, A B a c d^{2} e + 6 \, A B a^{2} e^{3} + a^{3} c^{3} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}} + 3 \, {\left(3 \, B^{2} a^{2} - A^{2} a c\right)} d e^{2}}{a^{3} c^{3}}} \log\left({\left(24 \, A^{3} B c^{3} d^{3} e^{2} - 4 \, {\left(27 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}\right)} d^{2} e^{3} + 6 \, {\left(27 \, A B^{3} a^{2} c + A^{3} B a c^{2}\right)} d e^{4} - {\left(81 \, B^{4} a^{3} - A^{4} a c^{2}\right)} e^{5}\right)} \sqrt{e x + d} + {\left(6 \, A^{2} B a^{2} c^{3} d e^{3} - {\left(9 \, A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} e^{4} - {\left(2 \, A a^{3} c^{6} d - 3 \, B a^{4} c^{5} e\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}}\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 12 \, A B a c d^{2} e + 6 \, A B a^{2} e^{3} + a^{3} c^{3} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}} + 3 \, {\left(3 \, B^{2} a^{2} - A^{2} a c\right)} d e^{2}}{a^{3} c^{3}}}\right) - {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 12 \, A B a c d^{2} e + 6 \, A B a^{2} e^{3} + a^{3} c^{3} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}} + 3 \, {\left(3 \, B^{2} a^{2} - A^{2} a c\right)} d e^{2}}{a^{3} c^{3}}} \log\left({\left(24 \, A^{3} B c^{3} d^{3} e^{2} - 4 \, {\left(27 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}\right)} d^{2} e^{3} + 6 \, {\left(27 \, A B^{3} a^{2} c + A^{3} B a c^{2}\right)} d e^{4} - {\left(81 \, B^{4} a^{3} - A^{4} a c^{2}\right)} e^{5}\right)} \sqrt{e x + d} - {\left(6 \, A^{2} B a^{2} c^{3} d e^{3} - {\left(9 \, A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} e^{4} - {\left(2 \, A a^{3} c^{6} d - 3 \, B a^{4} c^{5} e\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}}\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 12 \, A B a c d^{2} e + 6 \, A B a^{2} e^{3} + a^{3} c^{3} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}} + 3 \, {\left(3 \, B^{2} a^{2} - A^{2} a c\right)} d e^{2}}{a^{3} c^{3}}}\right) + {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 12 \, A B a c d^{2} e + 6 \, A B a^{2} e^{3} - a^{3} c^{3} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}} + 3 \, {\left(3 \, B^{2} a^{2} - A^{2} a c\right)} d e^{2}}{a^{3} c^{3}}} \log\left({\left(24 \, A^{3} B c^{3} d^{3} e^{2} - 4 \, {\left(27 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}\right)} d^{2} e^{3} + 6 \, {\left(27 \, A B^{3} a^{2} c + A^{3} B a c^{2}\right)} d e^{4} - {\left(81 \, B^{4} a^{3} - A^{4} a c^{2}\right)} e^{5}\right)} \sqrt{e x + d} + {\left(6 \, A^{2} B a^{2} c^{3} d e^{3} - {\left(9 \, A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} e^{4} + {\left(2 \, A a^{3} c^{6} d - 3 \, B a^{4} c^{5} e\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}}\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 12 \, A B a c d^{2} e + 6 \, A B a^{2} e^{3} - a^{3} c^{3} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}} + 3 \, {\left(3 \, B^{2} a^{2} - A^{2} a c\right)} d e^{2}}{a^{3} c^{3}}}\right) - {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 12 \, A B a c d^{2} e + 6 \, A B a^{2} e^{3} - a^{3} c^{3} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}} + 3 \, {\left(3 \, B^{2} a^{2} - A^{2} a c\right)} d e^{2}}{a^{3} c^{3}}} \log\left({\left(24 \, A^{3} B c^{3} d^{3} e^{2} - 4 \, {\left(27 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}\right)} d^{2} e^{3} + 6 \, {\left(27 \, A B^{3} a^{2} c + A^{3} B a c^{2}\right)} d e^{4} - {\left(81 \, B^{4} a^{3} - A^{4} a c^{2}\right)} e^{5}\right)} \sqrt{e x + d} - {\left(6 \, A^{2} B a^{2} c^{3} d e^{3} - {\left(9 \, A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} e^{4} + {\left(2 \, A a^{3} c^{6} d - 3 \, B a^{4} c^{5} e\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}}\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 12 \, A B a c d^{2} e + 6 \, A B a^{2} e^{3} - a^{3} c^{3} \sqrt{\frac{36 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 12 \, {\left(9 \, A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(81 \, B^{4} a^{2} + 18 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7}}} + 3 \, {\left(3 \, B^{2} a^{2} - A^{2} a c\right)} d e^{2}}{a^{3} c^{3}}}\right) - 4 \, {\left(B a d + A a e + {\left(A c d + B a e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a c^{2} x^{2} - a^{2} c\right)}}"," ",0,"1/8*((a*c^2*x^2 - a^2*c)*sqrt((4*A^2*c^2*d^3 - 12*A*B*a*c*d^2*e + 6*A*B*a^2*e^3 + a^3*c^3*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)) + 3*(3*B^2*a^2 - A^2*a*c)*d*e^2)/(a^3*c^3))*log((24*A^3*B*c^3*d^3*e^2 - 4*(27*A^2*B^2*a*c^2 + A^4*c^3)*d^2*e^3 + 6*(27*A*B^3*a^2*c + A^3*B*a*c^2)*d*e^4 - (81*B^4*a^3 - A^4*a*c^2)*e^5)*sqrt(e*x + d) + (6*A^2*B*a^2*c^3*d*e^3 - (9*A*B^2*a^3*c^2 + A^3*a^2*c^3)*e^4 - (2*A*a^3*c^6*d - 3*B*a^4*c^5*e)*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)))*sqrt((4*A^2*c^2*d^3 - 12*A*B*a*c*d^2*e + 6*A*B*a^2*e^3 + a^3*c^3*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)) + 3*(3*B^2*a^2 - A^2*a*c)*d*e^2)/(a^3*c^3))) - (a*c^2*x^2 - a^2*c)*sqrt((4*A^2*c^2*d^3 - 12*A*B*a*c*d^2*e + 6*A*B*a^2*e^3 + a^3*c^3*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)) + 3*(3*B^2*a^2 - A^2*a*c)*d*e^2)/(a^3*c^3))*log((24*A^3*B*c^3*d^3*e^2 - 4*(27*A^2*B^2*a*c^2 + A^4*c^3)*d^2*e^3 + 6*(27*A*B^3*a^2*c + A^3*B*a*c^2)*d*e^4 - (81*B^4*a^3 - A^4*a*c^2)*e^5)*sqrt(e*x + d) - (6*A^2*B*a^2*c^3*d*e^3 - (9*A*B^2*a^3*c^2 + A^3*a^2*c^3)*e^4 - (2*A*a^3*c^6*d - 3*B*a^4*c^5*e)*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)))*sqrt((4*A^2*c^2*d^3 - 12*A*B*a*c*d^2*e + 6*A*B*a^2*e^3 + a^3*c^3*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)) + 3*(3*B^2*a^2 - A^2*a*c)*d*e^2)/(a^3*c^3))) + (a*c^2*x^2 - a^2*c)*sqrt((4*A^2*c^2*d^3 - 12*A*B*a*c*d^2*e + 6*A*B*a^2*e^3 - a^3*c^3*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)) + 3*(3*B^2*a^2 - A^2*a*c)*d*e^2)/(a^3*c^3))*log((24*A^3*B*c^3*d^3*e^2 - 4*(27*A^2*B^2*a*c^2 + A^4*c^3)*d^2*e^3 + 6*(27*A*B^3*a^2*c + A^3*B*a*c^2)*d*e^4 - (81*B^4*a^3 - A^4*a*c^2)*e^5)*sqrt(e*x + d) + (6*A^2*B*a^2*c^3*d*e^3 - (9*A*B^2*a^3*c^2 + A^3*a^2*c^3)*e^4 + (2*A*a^3*c^6*d - 3*B*a^4*c^5*e)*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)))*sqrt((4*A^2*c^2*d^3 - 12*A*B*a*c*d^2*e + 6*A*B*a^2*e^3 - a^3*c^3*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)) + 3*(3*B^2*a^2 - A^2*a*c)*d*e^2)/(a^3*c^3))) - (a*c^2*x^2 - a^2*c)*sqrt((4*A^2*c^2*d^3 - 12*A*B*a*c*d^2*e + 6*A*B*a^2*e^3 - a^3*c^3*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)) + 3*(3*B^2*a^2 - A^2*a*c)*d*e^2)/(a^3*c^3))*log((24*A^3*B*c^3*d^3*e^2 - 4*(27*A^2*B^2*a*c^2 + A^4*c^3)*d^2*e^3 + 6*(27*A*B^3*a^2*c + A^3*B*a*c^2)*d*e^4 - (81*B^4*a^3 - A^4*a*c^2)*e^5)*sqrt(e*x + d) - (6*A^2*B*a^2*c^3*d*e^3 - (9*A*B^2*a^3*c^2 + A^3*a^2*c^3)*e^4 + (2*A*a^3*c^6*d - 3*B*a^4*c^5*e)*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)))*sqrt((4*A^2*c^2*d^3 - 12*A*B*a*c*d^2*e + 6*A*B*a^2*e^3 - a^3*c^3*sqrt((36*A^2*B^2*c^2*d^2*e^4 - 12*(9*A*B^3*a*c + A^3*B*c^2)*d*e^5 + (81*B^4*a^2 + 18*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7)) + 3*(3*B^2*a^2 - A^2*a*c)*d*e^2)/(a^3*c^3))) - 4*(B*a*d + A*a*e + (A*c*d + B*a*e)*x)*sqrt(e*x + d))/(a*c^2*x^2 - a^2*c)","B",0
1455,1,3195,0,2.427706," ","integrate((B*x+A)*(e*x+d)^(1/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 4 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + {\left(B^{2} a^{2} - 3 \, A^{2} a c\right)} d e^{2} + {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}}{a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}}} \log\left({\left(8 \, A^{3} B c^{3} d^{3} e^{2} - 4 \, {\left(3 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}\right)} d^{2} e^{3} + 2 \, {\left(3 \, A B^{3} a^{2} c + A^{3} B a c^{2}\right)} d e^{4} - {\left(B^{4} a^{3} - A^{4} a c^{2}\right)} e^{5}\right)} \sqrt{e x + d} + {\left(2 \, A^{2} B a^{2} c^{3} d^{2} e^{3} - {\left(3 \, A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} d e^{4} + {\left(B^{3} a^{4} c + A^{2} B a^{3} c^{2}\right)} e^{5} + {\left(2 \, A a^{3} c^{6} d^{4} - B a^{4} c^{5} d^{3} e - 3 \, A a^{4} c^{5} d^{2} e^{2} + B a^{5} c^{4} d e^{3} + A a^{5} c^{4} e^{4}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 4 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + {\left(B^{2} a^{2} - 3 \, A^{2} a c\right)} d e^{2} + {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}}{a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}}}\right) - {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 4 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + {\left(B^{2} a^{2} - 3 \, A^{2} a c\right)} d e^{2} + {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}}{a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}}} \log\left({\left(8 \, A^{3} B c^{3} d^{3} e^{2} - 4 \, {\left(3 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}\right)} d^{2} e^{3} + 2 \, {\left(3 \, A B^{3} a^{2} c + A^{3} B a c^{2}\right)} d e^{4} - {\left(B^{4} a^{3} - A^{4} a c^{2}\right)} e^{5}\right)} \sqrt{e x + d} - {\left(2 \, A^{2} B a^{2} c^{3} d^{2} e^{3} - {\left(3 \, A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} d e^{4} + {\left(B^{3} a^{4} c + A^{2} B a^{3} c^{2}\right)} e^{5} + {\left(2 \, A a^{3} c^{6} d^{4} - B a^{4} c^{5} d^{3} e - 3 \, A a^{4} c^{5} d^{2} e^{2} + B a^{5} c^{4} d e^{3} + A a^{5} c^{4} e^{4}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 4 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + {\left(B^{2} a^{2} - 3 \, A^{2} a c\right)} d e^{2} + {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}}{a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}}}\right) + {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 4 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + {\left(B^{2} a^{2} - 3 \, A^{2} a c\right)} d e^{2} - {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}}{a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}}} \log\left({\left(8 \, A^{3} B c^{3} d^{3} e^{2} - 4 \, {\left(3 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}\right)} d^{2} e^{3} + 2 \, {\left(3 \, A B^{3} a^{2} c + A^{3} B a c^{2}\right)} d e^{4} - {\left(B^{4} a^{3} - A^{4} a c^{2}\right)} e^{5}\right)} \sqrt{e x + d} + {\left(2 \, A^{2} B a^{2} c^{3} d^{2} e^{3} - {\left(3 \, A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} d e^{4} + {\left(B^{3} a^{4} c + A^{2} B a^{3} c^{2}\right)} e^{5} - {\left(2 \, A a^{3} c^{6} d^{4} - B a^{4} c^{5} d^{3} e - 3 \, A a^{4} c^{5} d^{2} e^{2} + B a^{5} c^{4} d e^{3} + A a^{5} c^{4} e^{4}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 4 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + {\left(B^{2} a^{2} - 3 \, A^{2} a c\right)} d e^{2} - {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}}{a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}}}\right) - {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 4 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + {\left(B^{2} a^{2} - 3 \, A^{2} a c\right)} d e^{2} - {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}}{a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}}} \log\left({\left(8 \, A^{3} B c^{3} d^{3} e^{2} - 4 \, {\left(3 \, A^{2} B^{2} a c^{2} + A^{4} c^{3}\right)} d^{2} e^{3} + 2 \, {\left(3 \, A B^{3} a^{2} c + A^{3} B a c^{2}\right)} d e^{4} - {\left(B^{4} a^{3} - A^{4} a c^{2}\right)} e^{5}\right)} \sqrt{e x + d} - {\left(2 \, A^{2} B a^{2} c^{3} d^{2} e^{3} - {\left(3 \, A B^{2} a^{3} c^{2} + A^{3} a^{2} c^{3}\right)} d e^{4} + {\left(B^{3} a^{4} c + A^{2} B a^{3} c^{2}\right)} e^{5} - {\left(2 \, A a^{3} c^{6} d^{4} - B a^{4} c^{5} d^{3} e - 3 \, A a^{4} c^{5} d^{2} e^{2} + B a^{5} c^{4} d e^{3} + A a^{5} c^{4} e^{4}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}\right)} \sqrt{\frac{4 \, A^{2} c^{2} d^{3} - 4 \, A B a c d^{2} e + 2 \, A B a^{2} e^{3} + {\left(B^{2} a^{2} - 3 \, A^{2} a c\right)} d e^{2} - {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{4} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{5} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{6}}{a^{3} c^{7} d^{4} - 2 \, a^{4} c^{6} d^{2} e^{2} + a^{5} c^{5} e^{4}}}}{a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}}}\right) - 4 \, {\left(A c x + B a\right)} \sqrt{e x + d}}{8 \, {\left(a c^{2} x^{2} - a^{2} c\right)}}"," ",0,"1/8*((a*c^2*x^2 - a^2*c)*sqrt((4*A^2*c^2*d^3 - 4*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + (B^2*a^2 - 3*A^2*a*c)*d*e^2 + (a^3*c^3*d^2 - a^4*c^2*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))/(a^3*c^3*d^2 - a^4*c^2*e^2))*log((8*A^3*B*c^3*d^3*e^2 - 4*(3*A^2*B^2*a*c^2 + A^4*c^3)*d^2*e^3 + 2*(3*A*B^3*a^2*c + A^3*B*a*c^2)*d*e^4 - (B^4*a^3 - A^4*a*c^2)*e^5)*sqrt(e*x + d) + (2*A^2*B*a^2*c^3*d^2*e^3 - (3*A*B^2*a^3*c^2 + A^3*a^2*c^3)*d*e^4 + (B^3*a^4*c + A^2*B*a^3*c^2)*e^5 + (2*A*a^3*c^6*d^4 - B*a^4*c^5*d^3*e - 3*A*a^4*c^5*d^2*e^2 + B*a^5*c^4*d*e^3 + A*a^5*c^4*e^4)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))*sqrt((4*A^2*c^2*d^3 - 4*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + (B^2*a^2 - 3*A^2*a*c)*d*e^2 + (a^3*c^3*d^2 - a^4*c^2*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))/(a^3*c^3*d^2 - a^4*c^2*e^2))) - (a*c^2*x^2 - a^2*c)*sqrt((4*A^2*c^2*d^3 - 4*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + (B^2*a^2 - 3*A^2*a*c)*d*e^2 + (a^3*c^3*d^2 - a^4*c^2*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))/(a^3*c^3*d^2 - a^4*c^2*e^2))*log((8*A^3*B*c^3*d^3*e^2 - 4*(3*A^2*B^2*a*c^2 + A^4*c^3)*d^2*e^3 + 2*(3*A*B^3*a^2*c + A^3*B*a*c^2)*d*e^4 - (B^4*a^3 - A^4*a*c^2)*e^5)*sqrt(e*x + d) - (2*A^2*B*a^2*c^3*d^2*e^3 - (3*A*B^2*a^3*c^2 + A^3*a^2*c^3)*d*e^4 + (B^3*a^4*c + A^2*B*a^3*c^2)*e^5 + (2*A*a^3*c^6*d^4 - B*a^4*c^5*d^3*e - 3*A*a^4*c^5*d^2*e^2 + B*a^5*c^4*d*e^3 + A*a^5*c^4*e^4)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))*sqrt((4*A^2*c^2*d^3 - 4*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + (B^2*a^2 - 3*A^2*a*c)*d*e^2 + (a^3*c^3*d^2 - a^4*c^2*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))/(a^3*c^3*d^2 - a^4*c^2*e^2))) + (a*c^2*x^2 - a^2*c)*sqrt((4*A^2*c^2*d^3 - 4*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + (B^2*a^2 - 3*A^2*a*c)*d*e^2 - (a^3*c^3*d^2 - a^4*c^2*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))/(a^3*c^3*d^2 - a^4*c^2*e^2))*log((8*A^3*B*c^3*d^3*e^2 - 4*(3*A^2*B^2*a*c^2 + A^4*c^3)*d^2*e^3 + 2*(3*A*B^3*a^2*c + A^3*B*a*c^2)*d*e^4 - (B^4*a^3 - A^4*a*c^2)*e^5)*sqrt(e*x + d) + (2*A^2*B*a^2*c^3*d^2*e^3 - (3*A*B^2*a^3*c^2 + A^3*a^2*c^3)*d*e^4 + (B^3*a^4*c + A^2*B*a^3*c^2)*e^5 - (2*A*a^3*c^6*d^4 - B*a^4*c^5*d^3*e - 3*A*a^4*c^5*d^2*e^2 + B*a^5*c^4*d*e^3 + A*a^5*c^4*e^4)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))*sqrt((4*A^2*c^2*d^3 - 4*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + (B^2*a^2 - 3*A^2*a*c)*d*e^2 - (a^3*c^3*d^2 - a^4*c^2*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))/(a^3*c^3*d^2 - a^4*c^2*e^2))) - (a*c^2*x^2 - a^2*c)*sqrt((4*A^2*c^2*d^3 - 4*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + (B^2*a^2 - 3*A^2*a*c)*d*e^2 - (a^3*c^3*d^2 - a^4*c^2*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))/(a^3*c^3*d^2 - a^4*c^2*e^2))*log((8*A^3*B*c^3*d^3*e^2 - 4*(3*A^2*B^2*a*c^2 + A^4*c^3)*d^2*e^3 + 2*(3*A*B^3*a^2*c + A^3*B*a*c^2)*d*e^4 - (B^4*a^3 - A^4*a*c^2)*e^5)*sqrt(e*x + d) - (2*A^2*B*a^2*c^3*d^2*e^3 - (3*A*B^2*a^3*c^2 + A^3*a^2*c^3)*d*e^4 + (B^3*a^4*c + A^2*B*a^3*c^2)*e^5 - (2*A*a^3*c^6*d^4 - B*a^4*c^5*d^3*e - 3*A*a^4*c^5*d^2*e^2 + B*a^5*c^4*d*e^3 + A*a^5*c^4*e^4)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))*sqrt((4*A^2*c^2*d^3 - 4*A*B*a*c*d^2*e + 2*A*B*a^2*e^3 + (B^2*a^2 - 3*A^2*a*c)*d*e^2 - (a^3*c^3*d^2 - a^4*c^2*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^4 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^5 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^6)/(a^3*c^7*d^4 - 2*a^4*c^6*d^2*e^2 + a^5*c^5*e^4)))/(a^3*c^3*d^2 - a^4*c^2*e^2))) - 4*(A*c*x + B*a)*sqrt(e*x + d))/(a*c^2*x^2 - a^2*c)","B",0
1456,1,7506,0,30.614504," ","integrate((B*x+A)/(e*x+d)^(1/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} + 4 \, A B a c^{2} d^{4} e - 6 \, A B a^{2} c d^{2} e^{3} - 6 \, A B a^{3} e^{5} + {\left(B^{2} a^{2} c - 15 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B^{2} a^{3} + 5 \, A^{2} a^{2} c\right)} d e^{4} + {\left(a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}}{a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}}} \log\left(-{\left(24 \, A^{3} B c^{4} d^{5} e^{2} + 4 \, {\left(9 \, A^{2} B^{2} a c^{3} - 5 \, A^{4} c^{4}\right)} d^{4} e^{3} + 2 \, {\left(9 \, A B^{3} a^{2} c^{2} - 65 \, A^{3} B a c^{3}\right)} d^{3} e^{4} + 3 \, {\left(B^{4} a^{3} c - 28 \, A^{2} B^{2} a^{2} c^{2} + 27 \, A^{4} a c^{3}\right)} d^{2} e^{5} - 2 \, {\left(5 \, A B^{3} a^{3} c - 81 \, A^{3} B a^{2} c^{2}\right)} d e^{6} + {\left(B^{4} a^{4} - 81 \, A^{4} a^{2} c^{2}\right)} e^{7}\right)} \sqrt{e x + d} + {\left(6 \, A^{2} B a^{2} c^{4} d^{5} e^{3} + 5 \, {\left(3 \, A B^{2} a^{3} c^{3} - A^{3} a^{2} c^{4}\right)} d^{4} e^{4} + 6 \, {\left(B^{3} a^{4} c^{2} - 7 \, A^{2} B a^{3} c^{3}\right)} d^{3} e^{5} - 12 \, {\left(3 \, A B^{2} a^{4} c^{2} - 2 \, A^{3} a^{3} c^{3}\right)} d^{2} e^{6} + 2 \, {\left(B^{3} a^{5} c + 30 \, A^{2} B a^{4} c^{2}\right)} d e^{7} - 3 \, {\left(A B^{2} a^{5} c + 9 \, A^{3} a^{4} c^{2}\right)} e^{8} - {\left(2 \, A a^{3} c^{7} d^{9} + B a^{4} c^{6} d^{8} e - 10 \, A a^{4} c^{6} d^{7} e^{2} - 2 \, B a^{5} c^{5} d^{6} e^{3} + 18 \, A a^{5} c^{5} d^{5} e^{4} - 14 \, A a^{6} c^{4} d^{3} e^{6} + 2 \, B a^{7} c^{3} d^{2} e^{7} + 4 \, A a^{7} c^{3} d e^{8} - B a^{8} c^{2} e^{9}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} + 4 \, A B a c^{2} d^{4} e - 6 \, A B a^{2} c d^{2} e^{3} - 6 \, A B a^{3} e^{5} + {\left(B^{2} a^{2} c - 15 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B^{2} a^{3} + 5 \, A^{2} a^{2} c\right)} d e^{4} + {\left(a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}}{a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}}}\right) - {\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} + 4 \, A B a c^{2} d^{4} e - 6 \, A B a^{2} c d^{2} e^{3} - 6 \, A B a^{3} e^{5} + {\left(B^{2} a^{2} c - 15 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B^{2} a^{3} + 5 \, A^{2} a^{2} c\right)} d e^{4} + {\left(a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}}{a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}}} \log\left(-{\left(24 \, A^{3} B c^{4} d^{5} e^{2} + 4 \, {\left(9 \, A^{2} B^{2} a c^{3} - 5 \, A^{4} c^{4}\right)} d^{4} e^{3} + 2 \, {\left(9 \, A B^{3} a^{2} c^{2} - 65 \, A^{3} B a c^{3}\right)} d^{3} e^{4} + 3 \, {\left(B^{4} a^{3} c - 28 \, A^{2} B^{2} a^{2} c^{2} + 27 \, A^{4} a c^{3}\right)} d^{2} e^{5} - 2 \, {\left(5 \, A B^{3} a^{3} c - 81 \, A^{3} B a^{2} c^{2}\right)} d e^{6} + {\left(B^{4} a^{4} - 81 \, A^{4} a^{2} c^{2}\right)} e^{7}\right)} \sqrt{e x + d} - {\left(6 \, A^{2} B a^{2} c^{4} d^{5} e^{3} + 5 \, {\left(3 \, A B^{2} a^{3} c^{3} - A^{3} a^{2} c^{4}\right)} d^{4} e^{4} + 6 \, {\left(B^{3} a^{4} c^{2} - 7 \, A^{2} B a^{3} c^{3}\right)} d^{3} e^{5} - 12 \, {\left(3 \, A B^{2} a^{4} c^{2} - 2 \, A^{3} a^{3} c^{3}\right)} d^{2} e^{6} + 2 \, {\left(B^{3} a^{5} c + 30 \, A^{2} B a^{4} c^{2}\right)} d e^{7} - 3 \, {\left(A B^{2} a^{5} c + 9 \, A^{3} a^{4} c^{2}\right)} e^{8} - {\left(2 \, A a^{3} c^{7} d^{9} + B a^{4} c^{6} d^{8} e - 10 \, A a^{4} c^{6} d^{7} e^{2} - 2 \, B a^{5} c^{5} d^{6} e^{3} + 18 \, A a^{5} c^{5} d^{5} e^{4} - 14 \, A a^{6} c^{4} d^{3} e^{6} + 2 \, B a^{7} c^{3} d^{2} e^{7} + 4 \, A a^{7} c^{3} d e^{8} - B a^{8} c^{2} e^{9}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} + 4 \, A B a c^{2} d^{4} e - 6 \, A B a^{2} c d^{2} e^{3} - 6 \, A B a^{3} e^{5} + {\left(B^{2} a^{2} c - 15 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B^{2} a^{3} + 5 \, A^{2} a^{2} c\right)} d e^{4} + {\left(a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}}{a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}}}\right) + {\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} + 4 \, A B a c^{2} d^{4} e - 6 \, A B a^{2} c d^{2} e^{3} - 6 \, A B a^{3} e^{5} + {\left(B^{2} a^{2} c - 15 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B^{2} a^{3} + 5 \, A^{2} a^{2} c\right)} d e^{4} - {\left(a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}}{a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}}} \log\left(-{\left(24 \, A^{3} B c^{4} d^{5} e^{2} + 4 \, {\left(9 \, A^{2} B^{2} a c^{3} - 5 \, A^{4} c^{4}\right)} d^{4} e^{3} + 2 \, {\left(9 \, A B^{3} a^{2} c^{2} - 65 \, A^{3} B a c^{3}\right)} d^{3} e^{4} + 3 \, {\left(B^{4} a^{3} c - 28 \, A^{2} B^{2} a^{2} c^{2} + 27 \, A^{4} a c^{3}\right)} d^{2} e^{5} - 2 \, {\left(5 \, A B^{3} a^{3} c - 81 \, A^{3} B a^{2} c^{2}\right)} d e^{6} + {\left(B^{4} a^{4} - 81 \, A^{4} a^{2} c^{2}\right)} e^{7}\right)} \sqrt{e x + d} + {\left(6 \, A^{2} B a^{2} c^{4} d^{5} e^{3} + 5 \, {\left(3 \, A B^{2} a^{3} c^{3} - A^{3} a^{2} c^{4}\right)} d^{4} e^{4} + 6 \, {\left(B^{3} a^{4} c^{2} - 7 \, A^{2} B a^{3} c^{3}\right)} d^{3} e^{5} - 12 \, {\left(3 \, A B^{2} a^{4} c^{2} - 2 \, A^{3} a^{3} c^{3}\right)} d^{2} e^{6} + 2 \, {\left(B^{3} a^{5} c + 30 \, A^{2} B a^{4} c^{2}\right)} d e^{7} - 3 \, {\left(A B^{2} a^{5} c + 9 \, A^{3} a^{4} c^{2}\right)} e^{8} + {\left(2 \, A a^{3} c^{7} d^{9} + B a^{4} c^{6} d^{8} e - 10 \, A a^{4} c^{6} d^{7} e^{2} - 2 \, B a^{5} c^{5} d^{6} e^{3} + 18 \, A a^{5} c^{5} d^{5} e^{4} - 14 \, A a^{6} c^{4} d^{3} e^{6} + 2 \, B a^{7} c^{3} d^{2} e^{7} + 4 \, A a^{7} c^{3} d e^{8} - B a^{8} c^{2} e^{9}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} + 4 \, A B a c^{2} d^{4} e - 6 \, A B a^{2} c d^{2} e^{3} - 6 \, A B a^{3} e^{5} + {\left(B^{2} a^{2} c - 15 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B^{2} a^{3} + 5 \, A^{2} a^{2} c\right)} d e^{4} - {\left(a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}}{a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}}}\right) - {\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} + 4 \, A B a c^{2} d^{4} e - 6 \, A B a^{2} c d^{2} e^{3} - 6 \, A B a^{3} e^{5} + {\left(B^{2} a^{2} c - 15 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B^{2} a^{3} + 5 \, A^{2} a^{2} c\right)} d e^{4} - {\left(a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}}{a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}}} \log\left(-{\left(24 \, A^{3} B c^{4} d^{5} e^{2} + 4 \, {\left(9 \, A^{2} B^{2} a c^{3} - 5 \, A^{4} c^{4}\right)} d^{4} e^{3} + 2 \, {\left(9 \, A B^{3} a^{2} c^{2} - 65 \, A^{3} B a c^{3}\right)} d^{3} e^{4} + 3 \, {\left(B^{4} a^{3} c - 28 \, A^{2} B^{2} a^{2} c^{2} + 27 \, A^{4} a c^{3}\right)} d^{2} e^{5} - 2 \, {\left(5 \, A B^{3} a^{3} c - 81 \, A^{3} B a^{2} c^{2}\right)} d e^{6} + {\left(B^{4} a^{4} - 81 \, A^{4} a^{2} c^{2}\right)} e^{7}\right)} \sqrt{e x + d} - {\left(6 \, A^{2} B a^{2} c^{4} d^{5} e^{3} + 5 \, {\left(3 \, A B^{2} a^{3} c^{3} - A^{3} a^{2} c^{4}\right)} d^{4} e^{4} + 6 \, {\left(B^{3} a^{4} c^{2} - 7 \, A^{2} B a^{3} c^{3}\right)} d^{3} e^{5} - 12 \, {\left(3 \, A B^{2} a^{4} c^{2} - 2 \, A^{3} a^{3} c^{3}\right)} d^{2} e^{6} + 2 \, {\left(B^{3} a^{5} c + 30 \, A^{2} B a^{4} c^{2}\right)} d e^{7} - 3 \, {\left(A B^{2} a^{5} c + 9 \, A^{3} a^{4} c^{2}\right)} e^{8} + {\left(2 \, A a^{3} c^{7} d^{9} + B a^{4} c^{6} d^{8} e - 10 \, A a^{4} c^{6} d^{7} e^{2} - 2 \, B a^{5} c^{5} d^{6} e^{3} + 18 \, A a^{5} c^{5} d^{5} e^{4} - 14 \, A a^{6} c^{4} d^{3} e^{6} + 2 \, B a^{7} c^{3} d^{2} e^{7} + 4 \, A a^{7} c^{3} d e^{8} - B a^{8} c^{2} e^{9}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}\right)} \sqrt{\frac{4 \, A^{2} c^{3} d^{5} + 4 \, A B a c^{2} d^{4} e - 6 \, A B a^{2} c d^{2} e^{3} - 6 \, A B a^{3} e^{5} + {\left(B^{2} a^{2} c - 15 \, A^{2} a c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B^{2} a^{3} + 5 \, A^{2} a^{2} c\right)} d e^{4} - {\left(a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}\right)} \sqrt{\frac{36 \, A^{2} B^{2} c^{4} d^{6} e^{4} + 12 \, {\left(3 \, A B^{3} a c^{3} - 5 \, A^{3} B c^{4}\right)} d^{5} e^{5} + {\left(9 \, B^{4} a^{2} c^{2} - 198 \, A^{2} B^{2} a c^{3} + 25 \, A^{4} c^{4}\right)} d^{4} e^{6} - 8 \, {\left(9 \, A B^{3} a^{2} c^{2} - 31 \, A^{3} B a c^{3}\right)} d^{3} e^{7} + 6 \, {\left(B^{4} a^{3} c + 40 \, A^{2} B^{2} a^{2} c^{2} - 15 \, A^{4} a c^{3}\right)} d^{2} e^{8} - 28 \, {\left(A B^{3} a^{3} c + 9 \, A^{3} B a^{2} c^{2}\right)} d e^{9} + {\left(B^{4} a^{4} + 18 \, A^{2} B^{2} a^{3} c + 81 \, A^{4} a^{2} c^{2}\right)} e^{10}}{a^{3} c^{9} d^{12} - 6 \, a^{4} c^{8} d^{10} e^{2} + 15 \, a^{5} c^{7} d^{8} e^{4} - 20 \, a^{6} c^{6} d^{6} e^{6} + 15 \, a^{7} c^{5} d^{4} e^{8} - 6 \, a^{8} c^{4} d^{2} e^{10} + a^{9} c^{3} e^{12}}}}{a^{3} c^{4} d^{6} - 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} - a^{6} c e^{6}}}\right) - 4 \, {\left(B a d - A a e + {\left(A c d - B a e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)}}"," ",0,"-1/8*((a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)*sqrt((4*A^2*c^3*d^5 + 4*A*B*a*c^2*d^4*e - 6*A*B*a^2*c*d^2*e^3 - 6*A*B*a^3*e^5 + (B^2*a^2*c - 15*A^2*a*c^2)*d^3*e^2 + 3*(B^2*a^3 + 5*A^2*a^2*c)*d*e^4 + (a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))/(a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6))*log(-(24*A^3*B*c^4*d^5*e^2 + 4*(9*A^2*B^2*a*c^3 - 5*A^4*c^4)*d^4*e^3 + 2*(9*A*B^3*a^2*c^2 - 65*A^3*B*a*c^3)*d^3*e^4 + 3*(B^4*a^3*c - 28*A^2*B^2*a^2*c^2 + 27*A^4*a*c^3)*d^2*e^5 - 2*(5*A*B^3*a^3*c - 81*A^3*B*a^2*c^2)*d*e^6 + (B^4*a^4 - 81*A^4*a^2*c^2)*e^7)*sqrt(e*x + d) + (6*A^2*B*a^2*c^4*d^5*e^3 + 5*(3*A*B^2*a^3*c^3 - A^3*a^2*c^4)*d^4*e^4 + 6*(B^3*a^4*c^2 - 7*A^2*B*a^3*c^3)*d^3*e^5 - 12*(3*A*B^2*a^4*c^2 - 2*A^3*a^3*c^3)*d^2*e^6 + 2*(B^3*a^5*c + 30*A^2*B*a^4*c^2)*d*e^7 - 3*(A*B^2*a^5*c + 9*A^3*a^4*c^2)*e^8 - (2*A*a^3*c^7*d^9 + B*a^4*c^6*d^8*e - 10*A*a^4*c^6*d^7*e^2 - 2*B*a^5*c^5*d^6*e^3 + 18*A*a^5*c^5*d^5*e^4 - 14*A*a^6*c^4*d^3*e^6 + 2*B*a^7*c^3*d^2*e^7 + 4*A*a^7*c^3*d*e^8 - B*a^8*c^2*e^9)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))*sqrt((4*A^2*c^3*d^5 + 4*A*B*a*c^2*d^4*e - 6*A*B*a^2*c*d^2*e^3 - 6*A*B*a^3*e^5 + (B^2*a^2*c - 15*A^2*a*c^2)*d^3*e^2 + 3*(B^2*a^3 + 5*A^2*a^2*c)*d*e^4 + (a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))/(a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6))) - (a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)*sqrt((4*A^2*c^3*d^5 + 4*A*B*a*c^2*d^4*e - 6*A*B*a^2*c*d^2*e^3 - 6*A*B*a^3*e^5 + (B^2*a^2*c - 15*A^2*a*c^2)*d^3*e^2 + 3*(B^2*a^3 + 5*A^2*a^2*c)*d*e^4 + (a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))/(a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6))*log(-(24*A^3*B*c^4*d^5*e^2 + 4*(9*A^2*B^2*a*c^3 - 5*A^4*c^4)*d^4*e^3 + 2*(9*A*B^3*a^2*c^2 - 65*A^3*B*a*c^3)*d^3*e^4 + 3*(B^4*a^3*c - 28*A^2*B^2*a^2*c^2 + 27*A^4*a*c^3)*d^2*e^5 - 2*(5*A*B^3*a^3*c - 81*A^3*B*a^2*c^2)*d*e^6 + (B^4*a^4 - 81*A^4*a^2*c^2)*e^7)*sqrt(e*x + d) - (6*A^2*B*a^2*c^4*d^5*e^3 + 5*(3*A*B^2*a^3*c^3 - A^3*a^2*c^4)*d^4*e^4 + 6*(B^3*a^4*c^2 - 7*A^2*B*a^3*c^3)*d^3*e^5 - 12*(3*A*B^2*a^4*c^2 - 2*A^3*a^3*c^3)*d^2*e^6 + 2*(B^3*a^5*c + 30*A^2*B*a^4*c^2)*d*e^7 - 3*(A*B^2*a^5*c + 9*A^3*a^4*c^2)*e^8 - (2*A*a^3*c^7*d^9 + B*a^4*c^6*d^8*e - 10*A*a^4*c^6*d^7*e^2 - 2*B*a^5*c^5*d^6*e^3 + 18*A*a^5*c^5*d^5*e^4 - 14*A*a^6*c^4*d^3*e^6 + 2*B*a^7*c^3*d^2*e^7 + 4*A*a^7*c^3*d*e^8 - B*a^8*c^2*e^9)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))*sqrt((4*A^2*c^3*d^5 + 4*A*B*a*c^2*d^4*e - 6*A*B*a^2*c*d^2*e^3 - 6*A*B*a^3*e^5 + (B^2*a^2*c - 15*A^2*a*c^2)*d^3*e^2 + 3*(B^2*a^3 + 5*A^2*a^2*c)*d*e^4 + (a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))/(a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6))) + (a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)*sqrt((4*A^2*c^3*d^5 + 4*A*B*a*c^2*d^4*e - 6*A*B*a^2*c*d^2*e^3 - 6*A*B*a^3*e^5 + (B^2*a^2*c - 15*A^2*a*c^2)*d^3*e^2 + 3*(B^2*a^3 + 5*A^2*a^2*c)*d*e^4 - (a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))/(a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6))*log(-(24*A^3*B*c^4*d^5*e^2 + 4*(9*A^2*B^2*a*c^3 - 5*A^4*c^4)*d^4*e^3 + 2*(9*A*B^3*a^2*c^2 - 65*A^3*B*a*c^3)*d^3*e^4 + 3*(B^4*a^3*c - 28*A^2*B^2*a^2*c^2 + 27*A^4*a*c^3)*d^2*e^5 - 2*(5*A*B^3*a^3*c - 81*A^3*B*a^2*c^2)*d*e^6 + (B^4*a^4 - 81*A^4*a^2*c^2)*e^7)*sqrt(e*x + d) + (6*A^2*B*a^2*c^4*d^5*e^3 + 5*(3*A*B^2*a^3*c^3 - A^3*a^2*c^4)*d^4*e^4 + 6*(B^3*a^4*c^2 - 7*A^2*B*a^3*c^3)*d^3*e^5 - 12*(3*A*B^2*a^4*c^2 - 2*A^3*a^3*c^3)*d^2*e^6 + 2*(B^3*a^5*c + 30*A^2*B*a^4*c^2)*d*e^7 - 3*(A*B^2*a^5*c + 9*A^3*a^4*c^2)*e^8 + (2*A*a^3*c^7*d^9 + B*a^4*c^6*d^8*e - 10*A*a^4*c^6*d^7*e^2 - 2*B*a^5*c^5*d^6*e^3 + 18*A*a^5*c^5*d^5*e^4 - 14*A*a^6*c^4*d^3*e^6 + 2*B*a^7*c^3*d^2*e^7 + 4*A*a^7*c^3*d*e^8 - B*a^8*c^2*e^9)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))*sqrt((4*A^2*c^3*d^5 + 4*A*B*a*c^2*d^4*e - 6*A*B*a^2*c*d^2*e^3 - 6*A*B*a^3*e^5 + (B^2*a^2*c - 15*A^2*a*c^2)*d^3*e^2 + 3*(B^2*a^3 + 5*A^2*a^2*c)*d*e^4 - (a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))/(a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6))) - (a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)*sqrt((4*A^2*c^3*d^5 + 4*A*B*a*c^2*d^4*e - 6*A*B*a^2*c*d^2*e^3 - 6*A*B*a^3*e^5 + (B^2*a^2*c - 15*A^2*a*c^2)*d^3*e^2 + 3*(B^2*a^3 + 5*A^2*a^2*c)*d*e^4 - (a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))/(a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6))*log(-(24*A^3*B*c^4*d^5*e^2 + 4*(9*A^2*B^2*a*c^3 - 5*A^4*c^4)*d^4*e^3 + 2*(9*A*B^3*a^2*c^2 - 65*A^3*B*a*c^3)*d^3*e^4 + 3*(B^4*a^3*c - 28*A^2*B^2*a^2*c^2 + 27*A^4*a*c^3)*d^2*e^5 - 2*(5*A*B^3*a^3*c - 81*A^3*B*a^2*c^2)*d*e^6 + (B^4*a^4 - 81*A^4*a^2*c^2)*e^7)*sqrt(e*x + d) - (6*A^2*B*a^2*c^4*d^5*e^3 + 5*(3*A*B^2*a^3*c^3 - A^3*a^2*c^4)*d^4*e^4 + 6*(B^3*a^4*c^2 - 7*A^2*B*a^3*c^3)*d^3*e^5 - 12*(3*A*B^2*a^4*c^2 - 2*A^3*a^3*c^3)*d^2*e^6 + 2*(B^3*a^5*c + 30*A^2*B*a^4*c^2)*d*e^7 - 3*(A*B^2*a^5*c + 9*A^3*a^4*c^2)*e^8 + (2*A*a^3*c^7*d^9 + B*a^4*c^6*d^8*e - 10*A*a^4*c^6*d^7*e^2 - 2*B*a^5*c^5*d^6*e^3 + 18*A*a^5*c^5*d^5*e^4 - 14*A*a^6*c^4*d^3*e^6 + 2*B*a^7*c^3*d^2*e^7 + 4*A*a^7*c^3*d*e^8 - B*a^8*c^2*e^9)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))*sqrt((4*A^2*c^3*d^5 + 4*A*B*a*c^2*d^4*e - 6*A*B*a^2*c*d^2*e^3 - 6*A*B*a^3*e^5 + (B^2*a^2*c - 15*A^2*a*c^2)*d^3*e^2 + 3*(B^2*a^3 + 5*A^2*a^2*c)*d*e^4 - (a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6)*sqrt((36*A^2*B^2*c^4*d^6*e^4 + 12*(3*A*B^3*a*c^3 - 5*A^3*B*c^4)*d^5*e^5 + (9*B^4*a^2*c^2 - 198*A^2*B^2*a*c^3 + 25*A^4*c^4)*d^4*e^6 - 8*(9*A*B^3*a^2*c^2 - 31*A^3*B*a*c^3)*d^3*e^7 + 6*(B^4*a^3*c + 40*A^2*B^2*a^2*c^2 - 15*A^4*a*c^3)*d^2*e^8 - 28*(A*B^3*a^3*c + 9*A^3*B*a^2*c^2)*d*e^9 + (B^4*a^4 + 18*A^2*B^2*a^3*c + 81*A^4*a^2*c^2)*e^10)/(a^3*c^9*d^12 - 6*a^4*c^8*d^10*e^2 + 15*a^5*c^7*d^8*e^4 - 20*a^6*c^6*d^6*e^6 + 15*a^7*c^5*d^4*e^8 - 6*a^8*c^4*d^2*e^10 + a^9*c^3*e^12)))/(a^3*c^4*d^6 - 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 - a^6*c*e^6))) - 4*(B*a*d - A*a*e + (A*c*d - B*a*e)*x)*sqrt(e*x + d))/(a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)","B",0
1457,1,12458,0,113.382601," ","integrate((B*x+A)/(e*x+d)^(3/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{4 \, A^{2} c^{4} d^{7} + 12 \, A B a c^{3} d^{6} e - 30 \, A B a^{2} c^{2} d^{4} e^{3} - 240 \, A B a^{3} c d^{2} e^{5} - 30 \, A B a^{4} e^{7} + {\left(9 \, B^{2} a^{2} c^{2} - 35 \, A^{2} a c^{3}\right)} d^{5} e^{2} + 10 \, {\left(9 \, B^{2} a^{3} c + 7 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B^{2} a^{4} + 7 \, A^{2} a^{3} c\right)} d e^{6} + {\left(a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}}{a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}}} \log\left(-{\left(120 \, A^{3} B c^{5} d^{7} e^{2} + 20 \, {\left(27 \, A^{2} B^{2} a c^{4} - 7 \, A^{4} c^{5}\right)} d^{6} e^{3} + 270 \, {\left(3 \, A B^{3} a^{2} c^{3} - 7 \, A^{3} B a c^{4}\right)} d^{5} e^{4} + 3 \, {\left(135 \, B^{4} a^{3} c^{2} - 1080 \, A^{2} B^{2} a^{2} c^{3} + 497 \, A^{4} a c^{4}\right)} d^{4} e^{5} - 36 \, {\left(15 \, A B^{3} a^{3} c^{2} - 161 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{6} + 6 \, {\left(135 \, B^{4} a^{4} c - 414 \, A^{2} B^{2} a^{3} c^{2} - 625 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{7} - 6 \, {\left(189 \, A B^{3} a^{4} c - 625 \, A^{3} B a^{3} c^{2}\right)} d e^{8} + {\left(81 \, B^{4} a^{5} - 625 \, A^{4} a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + {\left(30 \, A^{2} B a^{2} c^{5} d^{8} e^{3} + 35 \, {\left(9 \, A B^{2} a^{3} c^{4} - A^{3} a^{2} c^{5}\right)} d^{7} e^{4} + 15 \, {\left(27 \, B^{3} a^{4} c^{3} - 59 \, A^{2} B a^{3} c^{4}\right)} d^{6} e^{5} - 3 \, {\left(675 \, A B^{2} a^{4} c^{3} - 203 \, A^{3} a^{3} c^{4}\right)} d^{5} e^{6} + 27 \, {\left(35 \, B^{3} a^{5} c^{2} + 129 \, A^{2} B a^{4} c^{3}\right)} d^{4} e^{7} - 3 \, {\left(981 \, A B^{2} a^{5} c^{2} + 659 \, A^{3} a^{4} c^{3}\right)} d^{3} e^{8} + 3 \, {\left(117 \, B^{3} a^{6} c + 827 \, A^{2} B a^{5} c^{2}\right)} d^{2} e^{9} - {\left(531 \, A B^{2} a^{6} c + 325 \, A^{3} a^{5} c^{2}\right)} d e^{10} + 3 \, {\left(9 \, B^{3} a^{7} + 25 \, A^{2} B a^{6} c\right)} e^{11} - {\left(2 \, A a^{3} c^{8} d^{14} + 3 \, B a^{4} c^{7} d^{13} e - 19 \, A a^{4} c^{7} d^{12} e^{2} - 6 \, B a^{5} c^{6} d^{11} e^{3} + 60 \, A a^{5} c^{6} d^{10} e^{4} - 15 \, B a^{6} c^{5} d^{9} e^{5} - 85 \, A a^{6} c^{5} d^{8} e^{6} + 60 \, B a^{7} c^{4} d^{7} e^{7} + 50 \, A a^{7} c^{4} d^{6} e^{8} - 75 \, B a^{8} c^{3} d^{5} e^{9} + 3 \, A a^{8} c^{3} d^{4} e^{10} + 42 \, B a^{9} c^{2} d^{3} e^{11} - 16 \, A a^{9} c^{2} d^{2} e^{12} - 9 \, B a^{10} c d e^{13} + 5 \, A a^{10} c e^{14}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}\right)} \sqrt{\frac{4 \, A^{2} c^{4} d^{7} + 12 \, A B a c^{3} d^{6} e - 30 \, A B a^{2} c^{2} d^{4} e^{3} - 240 \, A B a^{3} c d^{2} e^{5} - 30 \, A B a^{4} e^{7} + {\left(9 \, B^{2} a^{2} c^{2} - 35 \, A^{2} a c^{3}\right)} d^{5} e^{2} + 10 \, {\left(9 \, B^{2} a^{3} c + 7 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B^{2} a^{4} + 7 \, A^{2} a^{3} c\right)} d e^{6} + {\left(a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}}{a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}}}\right) - {\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{4 \, A^{2} c^{4} d^{7} + 12 \, A B a c^{3} d^{6} e - 30 \, A B a^{2} c^{2} d^{4} e^{3} - 240 \, A B a^{3} c d^{2} e^{5} - 30 \, A B a^{4} e^{7} + {\left(9 \, B^{2} a^{2} c^{2} - 35 \, A^{2} a c^{3}\right)} d^{5} e^{2} + 10 \, {\left(9 \, B^{2} a^{3} c + 7 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B^{2} a^{4} + 7 \, A^{2} a^{3} c\right)} d e^{6} + {\left(a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}}{a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}}} \log\left(-{\left(120 \, A^{3} B c^{5} d^{7} e^{2} + 20 \, {\left(27 \, A^{2} B^{2} a c^{4} - 7 \, A^{4} c^{5}\right)} d^{6} e^{3} + 270 \, {\left(3 \, A B^{3} a^{2} c^{3} - 7 \, A^{3} B a c^{4}\right)} d^{5} e^{4} + 3 \, {\left(135 \, B^{4} a^{3} c^{2} - 1080 \, A^{2} B^{2} a^{2} c^{3} + 497 \, A^{4} a c^{4}\right)} d^{4} e^{5} - 36 \, {\left(15 \, A B^{3} a^{3} c^{2} - 161 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{6} + 6 \, {\left(135 \, B^{4} a^{4} c - 414 \, A^{2} B^{2} a^{3} c^{2} - 625 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{7} - 6 \, {\left(189 \, A B^{3} a^{4} c - 625 \, A^{3} B a^{3} c^{2}\right)} d e^{8} + {\left(81 \, B^{4} a^{5} - 625 \, A^{4} a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - {\left(30 \, A^{2} B a^{2} c^{5} d^{8} e^{3} + 35 \, {\left(9 \, A B^{2} a^{3} c^{4} - A^{3} a^{2} c^{5}\right)} d^{7} e^{4} + 15 \, {\left(27 \, B^{3} a^{4} c^{3} - 59 \, A^{2} B a^{3} c^{4}\right)} d^{6} e^{5} - 3 \, {\left(675 \, A B^{2} a^{4} c^{3} - 203 \, A^{3} a^{3} c^{4}\right)} d^{5} e^{6} + 27 \, {\left(35 \, B^{3} a^{5} c^{2} + 129 \, A^{2} B a^{4} c^{3}\right)} d^{4} e^{7} - 3 \, {\left(981 \, A B^{2} a^{5} c^{2} + 659 \, A^{3} a^{4} c^{3}\right)} d^{3} e^{8} + 3 \, {\left(117 \, B^{3} a^{6} c + 827 \, A^{2} B a^{5} c^{2}\right)} d^{2} e^{9} - {\left(531 \, A B^{2} a^{6} c + 325 \, A^{3} a^{5} c^{2}\right)} d e^{10} + 3 \, {\left(9 \, B^{3} a^{7} + 25 \, A^{2} B a^{6} c\right)} e^{11} - {\left(2 \, A a^{3} c^{8} d^{14} + 3 \, B a^{4} c^{7} d^{13} e - 19 \, A a^{4} c^{7} d^{12} e^{2} - 6 \, B a^{5} c^{6} d^{11} e^{3} + 60 \, A a^{5} c^{6} d^{10} e^{4} - 15 \, B a^{6} c^{5} d^{9} e^{5} - 85 \, A a^{6} c^{5} d^{8} e^{6} + 60 \, B a^{7} c^{4} d^{7} e^{7} + 50 \, A a^{7} c^{4} d^{6} e^{8} - 75 \, B a^{8} c^{3} d^{5} e^{9} + 3 \, A a^{8} c^{3} d^{4} e^{10} + 42 \, B a^{9} c^{2} d^{3} e^{11} - 16 \, A a^{9} c^{2} d^{2} e^{12} - 9 \, B a^{10} c d e^{13} + 5 \, A a^{10} c e^{14}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}\right)} \sqrt{\frac{4 \, A^{2} c^{4} d^{7} + 12 \, A B a c^{3} d^{6} e - 30 \, A B a^{2} c^{2} d^{4} e^{3} - 240 \, A B a^{3} c d^{2} e^{5} - 30 \, A B a^{4} e^{7} + {\left(9 \, B^{2} a^{2} c^{2} - 35 \, A^{2} a c^{3}\right)} d^{5} e^{2} + 10 \, {\left(9 \, B^{2} a^{3} c + 7 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B^{2} a^{4} + 7 \, A^{2} a^{3} c\right)} d e^{6} + {\left(a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}}{a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}}}\right) + {\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{4 \, A^{2} c^{4} d^{7} + 12 \, A B a c^{3} d^{6} e - 30 \, A B a^{2} c^{2} d^{4} e^{3} - 240 \, A B a^{3} c d^{2} e^{5} - 30 \, A B a^{4} e^{7} + {\left(9 \, B^{2} a^{2} c^{2} - 35 \, A^{2} a c^{3}\right)} d^{5} e^{2} + 10 \, {\left(9 \, B^{2} a^{3} c + 7 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B^{2} a^{4} + 7 \, A^{2} a^{3} c\right)} d e^{6} - {\left(a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}}{a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}}} \log\left(-{\left(120 \, A^{3} B c^{5} d^{7} e^{2} + 20 \, {\left(27 \, A^{2} B^{2} a c^{4} - 7 \, A^{4} c^{5}\right)} d^{6} e^{3} + 270 \, {\left(3 \, A B^{3} a^{2} c^{3} - 7 \, A^{3} B a c^{4}\right)} d^{5} e^{4} + 3 \, {\left(135 \, B^{4} a^{3} c^{2} - 1080 \, A^{2} B^{2} a^{2} c^{3} + 497 \, A^{4} a c^{4}\right)} d^{4} e^{5} - 36 \, {\left(15 \, A B^{3} a^{3} c^{2} - 161 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{6} + 6 \, {\left(135 \, B^{4} a^{4} c - 414 \, A^{2} B^{2} a^{3} c^{2} - 625 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{7} - 6 \, {\left(189 \, A B^{3} a^{4} c - 625 \, A^{3} B a^{3} c^{2}\right)} d e^{8} + {\left(81 \, B^{4} a^{5} - 625 \, A^{4} a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + {\left(30 \, A^{2} B a^{2} c^{5} d^{8} e^{3} + 35 \, {\left(9 \, A B^{2} a^{3} c^{4} - A^{3} a^{2} c^{5}\right)} d^{7} e^{4} + 15 \, {\left(27 \, B^{3} a^{4} c^{3} - 59 \, A^{2} B a^{3} c^{4}\right)} d^{6} e^{5} - 3 \, {\left(675 \, A B^{2} a^{4} c^{3} - 203 \, A^{3} a^{3} c^{4}\right)} d^{5} e^{6} + 27 \, {\left(35 \, B^{3} a^{5} c^{2} + 129 \, A^{2} B a^{4} c^{3}\right)} d^{4} e^{7} - 3 \, {\left(981 \, A B^{2} a^{5} c^{2} + 659 \, A^{3} a^{4} c^{3}\right)} d^{3} e^{8} + 3 \, {\left(117 \, B^{3} a^{6} c + 827 \, A^{2} B a^{5} c^{2}\right)} d^{2} e^{9} - {\left(531 \, A B^{2} a^{6} c + 325 \, A^{3} a^{5} c^{2}\right)} d e^{10} + 3 \, {\left(9 \, B^{3} a^{7} + 25 \, A^{2} B a^{6} c\right)} e^{11} + {\left(2 \, A a^{3} c^{8} d^{14} + 3 \, B a^{4} c^{7} d^{13} e - 19 \, A a^{4} c^{7} d^{12} e^{2} - 6 \, B a^{5} c^{6} d^{11} e^{3} + 60 \, A a^{5} c^{6} d^{10} e^{4} - 15 \, B a^{6} c^{5} d^{9} e^{5} - 85 \, A a^{6} c^{5} d^{8} e^{6} + 60 \, B a^{7} c^{4} d^{7} e^{7} + 50 \, A a^{7} c^{4} d^{6} e^{8} - 75 \, B a^{8} c^{3} d^{5} e^{9} + 3 \, A a^{8} c^{3} d^{4} e^{10} + 42 \, B a^{9} c^{2} d^{3} e^{11} - 16 \, A a^{9} c^{2} d^{2} e^{12} - 9 \, B a^{10} c d e^{13} + 5 \, A a^{10} c e^{14}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}\right)} \sqrt{\frac{4 \, A^{2} c^{4} d^{7} + 12 \, A B a c^{3} d^{6} e - 30 \, A B a^{2} c^{2} d^{4} e^{3} - 240 \, A B a^{3} c d^{2} e^{5} - 30 \, A B a^{4} e^{7} + {\left(9 \, B^{2} a^{2} c^{2} - 35 \, A^{2} a c^{3}\right)} d^{5} e^{2} + 10 \, {\left(9 \, B^{2} a^{3} c + 7 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B^{2} a^{4} + 7 \, A^{2} a^{3} c\right)} d e^{6} - {\left(a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}}{a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}}}\right) - {\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{4 \, A^{2} c^{4} d^{7} + 12 \, A B a c^{3} d^{6} e - 30 \, A B a^{2} c^{2} d^{4} e^{3} - 240 \, A B a^{3} c d^{2} e^{5} - 30 \, A B a^{4} e^{7} + {\left(9 \, B^{2} a^{2} c^{2} - 35 \, A^{2} a c^{3}\right)} d^{5} e^{2} + 10 \, {\left(9 \, B^{2} a^{3} c + 7 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B^{2} a^{4} + 7 \, A^{2} a^{3} c\right)} d e^{6} - {\left(a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}}{a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}}} \log\left(-{\left(120 \, A^{3} B c^{5} d^{7} e^{2} + 20 \, {\left(27 \, A^{2} B^{2} a c^{4} - 7 \, A^{4} c^{5}\right)} d^{6} e^{3} + 270 \, {\left(3 \, A B^{3} a^{2} c^{3} - 7 \, A^{3} B a c^{4}\right)} d^{5} e^{4} + 3 \, {\left(135 \, B^{4} a^{3} c^{2} - 1080 \, A^{2} B^{2} a^{2} c^{3} + 497 \, A^{4} a c^{4}\right)} d^{4} e^{5} - 36 \, {\left(15 \, A B^{3} a^{3} c^{2} - 161 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{6} + 6 \, {\left(135 \, B^{4} a^{4} c - 414 \, A^{2} B^{2} a^{3} c^{2} - 625 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{7} - 6 \, {\left(189 \, A B^{3} a^{4} c - 625 \, A^{3} B a^{3} c^{2}\right)} d e^{8} + {\left(81 \, B^{4} a^{5} - 625 \, A^{4} a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - {\left(30 \, A^{2} B a^{2} c^{5} d^{8} e^{3} + 35 \, {\left(9 \, A B^{2} a^{3} c^{4} - A^{3} a^{2} c^{5}\right)} d^{7} e^{4} + 15 \, {\left(27 \, B^{3} a^{4} c^{3} - 59 \, A^{2} B a^{3} c^{4}\right)} d^{6} e^{5} - 3 \, {\left(675 \, A B^{2} a^{4} c^{3} - 203 \, A^{3} a^{3} c^{4}\right)} d^{5} e^{6} + 27 \, {\left(35 \, B^{3} a^{5} c^{2} + 129 \, A^{2} B a^{4} c^{3}\right)} d^{4} e^{7} - 3 \, {\left(981 \, A B^{2} a^{5} c^{2} + 659 \, A^{3} a^{4} c^{3}\right)} d^{3} e^{8} + 3 \, {\left(117 \, B^{3} a^{6} c + 827 \, A^{2} B a^{5} c^{2}\right)} d^{2} e^{9} - {\left(531 \, A B^{2} a^{6} c + 325 \, A^{3} a^{5} c^{2}\right)} d e^{10} + 3 \, {\left(9 \, B^{3} a^{7} + 25 \, A^{2} B a^{6} c\right)} e^{11} + {\left(2 \, A a^{3} c^{8} d^{14} + 3 \, B a^{4} c^{7} d^{13} e - 19 \, A a^{4} c^{7} d^{12} e^{2} - 6 \, B a^{5} c^{6} d^{11} e^{3} + 60 \, A a^{5} c^{6} d^{10} e^{4} - 15 \, B a^{6} c^{5} d^{9} e^{5} - 85 \, A a^{6} c^{5} d^{8} e^{6} + 60 \, B a^{7} c^{4} d^{7} e^{7} + 50 \, A a^{7} c^{4} d^{6} e^{8} - 75 \, B a^{8} c^{3} d^{5} e^{9} + 3 \, A a^{8} c^{3} d^{4} e^{10} + 42 \, B a^{9} c^{2} d^{3} e^{11} - 16 \, A a^{9} c^{2} d^{2} e^{12} - 9 \, B a^{10} c d e^{13} + 5 \, A a^{10} c e^{14}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}\right)} \sqrt{\frac{4 \, A^{2} c^{4} d^{7} + 12 \, A B a c^{3} d^{6} e - 30 \, A B a^{2} c^{2} d^{4} e^{3} - 240 \, A B a^{3} c d^{2} e^{5} - 30 \, A B a^{4} e^{7} + {\left(9 \, B^{2} a^{2} c^{2} - 35 \, A^{2} a c^{3}\right)} d^{5} e^{2} + 10 \, {\left(9 \, B^{2} a^{3} c + 7 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B^{2} a^{4} + 7 \, A^{2} a^{3} c\right)} d e^{6} - {\left(a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{6} d^{10} e^{4} + 300 \, {\left(9 \, A B^{3} a c^{5} - 7 \, A^{3} B c^{6}\right)} d^{9} e^{5} + 25 \, {\left(81 \, B^{4} a^{2} c^{4} - 558 \, A^{2} B^{2} a c^{5} + 49 \, A^{4} c^{6}\right)} d^{8} e^{6} - 240 \, {\left(45 \, A B^{3} a^{2} c^{4} - 91 \, A^{3} B a c^{5}\right)} d^{7} e^{7} + 20 \, {\left(405 \, B^{4} a^{3} c^{3} + 1584 \, A^{2} B^{2} a^{2} c^{4} - 539 \, A^{4} a c^{5}\right)} d^{6} e^{8} - 44280 \, {\left(A B^{3} a^{3} c^{3} + A^{3} B a^{2} c^{4}\right)} d^{5} e^{9} + 6 \, {\left(1485 \, B^{4} a^{4} c^{2} + 13170 \, A^{2} B^{2} a^{3} c^{3} + 3661 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{10} - 48 \, {\left(585 \, A B^{3} a^{4} c^{2} + 1073 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{11} + 4 \, {\left(405 \, B^{4} a^{5} c + 6579 \, A^{2} B^{2} a^{4} c^{2} + 1925 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{12} - 276 \, {\left(9 \, A B^{3} a^{5} c + 25 \, A^{3} B a^{4} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{6} + 450 \, A^{2} B^{2} a^{5} c + 625 \, A^{4} a^{4} c^{2}\right)} e^{14}}{a^{3} c^{11} d^{20} - 10 \, a^{4} c^{10} d^{18} e^{2} + 45 \, a^{5} c^{9} d^{16} e^{4} - 120 \, a^{6} c^{8} d^{14} e^{6} + 210 \, a^{7} c^{7} d^{12} e^{8} - 252 \, a^{8} c^{6} d^{10} e^{10} + 210 \, a^{9} c^{5} d^{8} e^{12} - 120 \, a^{10} c^{4} d^{6} e^{14} + 45 \, a^{11} c^{3} d^{4} e^{16} - 10 \, a^{12} c^{2} d^{2} e^{18} + a^{13} c e^{20}}}}{a^{3} c^{5} d^{10} - 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} - 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} - a^{8} e^{10}}}\right) - 4 \, {\left(B a c d^{3} - 2 \, A a c d^{2} e + 5 \, B a^{2} d e^{2} - 4 \, A a^{2} e^{3} + {\left(A c^{2} d^{2} e - 6 \, B a c d e^{2} + 5 \, A a c e^{3}\right)} x^{2} + {\left(A c^{2} d^{3} - B a c d^{2} e - A a c d e^{2} + B a^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)}}"," ",0,"-1/8*((a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt((4*A^2*c^4*d^7 + 12*A*B*a*c^3*d^6*e - 30*A*B*a^2*c^2*d^4*e^3 - 240*A*B*a^3*c*d^2*e^5 - 30*A*B*a^4*e^7 + (9*B^2*a^2*c^2 - 35*A^2*a*c^3)*d^5*e^2 + 10*(9*B^2*a^3*c + 7*A^2*a^2*c^2)*d^3*e^4 + 15*(3*B^2*a^4 + 7*A^2*a^3*c)*d*e^6 + (a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))/(a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10))*log(-(120*A^3*B*c^5*d^7*e^2 + 20*(27*A^2*B^2*a*c^4 - 7*A^4*c^5)*d^6*e^3 + 270*(3*A*B^3*a^2*c^3 - 7*A^3*B*a*c^4)*d^5*e^4 + 3*(135*B^4*a^3*c^2 - 1080*A^2*B^2*a^2*c^3 + 497*A^4*a*c^4)*d^4*e^5 - 36*(15*A*B^3*a^3*c^2 - 161*A^3*B*a^2*c^3)*d^3*e^6 + 6*(135*B^4*a^4*c - 414*A^2*B^2*a^3*c^2 - 625*A^4*a^2*c^3)*d^2*e^7 - 6*(189*A*B^3*a^4*c - 625*A^3*B*a^3*c^2)*d*e^8 + (81*B^4*a^5 - 625*A^4*a^3*c^2)*e^9)*sqrt(e*x + d) + (30*A^2*B*a^2*c^5*d^8*e^3 + 35*(9*A*B^2*a^3*c^4 - A^3*a^2*c^5)*d^7*e^4 + 15*(27*B^3*a^4*c^3 - 59*A^2*B*a^3*c^4)*d^6*e^5 - 3*(675*A*B^2*a^4*c^3 - 203*A^3*a^3*c^4)*d^5*e^6 + 27*(35*B^3*a^5*c^2 + 129*A^2*B*a^4*c^3)*d^4*e^7 - 3*(981*A*B^2*a^5*c^2 + 659*A^3*a^4*c^3)*d^3*e^8 + 3*(117*B^3*a^6*c + 827*A^2*B*a^5*c^2)*d^2*e^9 - (531*A*B^2*a^6*c + 325*A^3*a^5*c^2)*d*e^10 + 3*(9*B^3*a^7 + 25*A^2*B*a^6*c)*e^11 - (2*A*a^3*c^8*d^14 + 3*B*a^4*c^7*d^13*e - 19*A*a^4*c^7*d^12*e^2 - 6*B*a^5*c^6*d^11*e^3 + 60*A*a^5*c^6*d^10*e^4 - 15*B*a^6*c^5*d^9*e^5 - 85*A*a^6*c^5*d^8*e^6 + 60*B*a^7*c^4*d^7*e^7 + 50*A*a^7*c^4*d^6*e^8 - 75*B*a^8*c^3*d^5*e^9 + 3*A*a^8*c^3*d^4*e^10 + 42*B*a^9*c^2*d^3*e^11 - 16*A*a^9*c^2*d^2*e^12 - 9*B*a^10*c*d*e^13 + 5*A*a^10*c*e^14)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))*sqrt((4*A^2*c^4*d^7 + 12*A*B*a*c^3*d^6*e - 30*A*B*a^2*c^2*d^4*e^3 - 240*A*B*a^3*c*d^2*e^5 - 30*A*B*a^4*e^7 + (9*B^2*a^2*c^2 - 35*A^2*a*c^3)*d^5*e^2 + 10*(9*B^2*a^3*c + 7*A^2*a^2*c^2)*d^3*e^4 + 15*(3*B^2*a^4 + 7*A^2*a^3*c)*d*e^6 + (a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))/(a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10))) - (a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt((4*A^2*c^4*d^7 + 12*A*B*a*c^3*d^6*e - 30*A*B*a^2*c^2*d^4*e^3 - 240*A*B*a^3*c*d^2*e^5 - 30*A*B*a^4*e^7 + (9*B^2*a^2*c^2 - 35*A^2*a*c^3)*d^5*e^2 + 10*(9*B^2*a^3*c + 7*A^2*a^2*c^2)*d^3*e^4 + 15*(3*B^2*a^4 + 7*A^2*a^3*c)*d*e^6 + (a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))/(a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10))*log(-(120*A^3*B*c^5*d^7*e^2 + 20*(27*A^2*B^2*a*c^4 - 7*A^4*c^5)*d^6*e^3 + 270*(3*A*B^3*a^2*c^3 - 7*A^3*B*a*c^4)*d^5*e^4 + 3*(135*B^4*a^3*c^2 - 1080*A^2*B^2*a^2*c^3 + 497*A^4*a*c^4)*d^4*e^5 - 36*(15*A*B^3*a^3*c^2 - 161*A^3*B*a^2*c^3)*d^3*e^6 + 6*(135*B^4*a^4*c - 414*A^2*B^2*a^3*c^2 - 625*A^4*a^2*c^3)*d^2*e^7 - 6*(189*A*B^3*a^4*c - 625*A^3*B*a^3*c^2)*d*e^8 + (81*B^4*a^5 - 625*A^4*a^3*c^2)*e^9)*sqrt(e*x + d) - (30*A^2*B*a^2*c^5*d^8*e^3 + 35*(9*A*B^2*a^3*c^4 - A^3*a^2*c^5)*d^7*e^4 + 15*(27*B^3*a^4*c^3 - 59*A^2*B*a^3*c^4)*d^6*e^5 - 3*(675*A*B^2*a^4*c^3 - 203*A^3*a^3*c^4)*d^5*e^6 + 27*(35*B^3*a^5*c^2 + 129*A^2*B*a^4*c^3)*d^4*e^7 - 3*(981*A*B^2*a^5*c^2 + 659*A^3*a^4*c^3)*d^3*e^8 + 3*(117*B^3*a^6*c + 827*A^2*B*a^5*c^2)*d^2*e^9 - (531*A*B^2*a^6*c + 325*A^3*a^5*c^2)*d*e^10 + 3*(9*B^3*a^7 + 25*A^2*B*a^6*c)*e^11 - (2*A*a^3*c^8*d^14 + 3*B*a^4*c^7*d^13*e - 19*A*a^4*c^7*d^12*e^2 - 6*B*a^5*c^6*d^11*e^3 + 60*A*a^5*c^6*d^10*e^4 - 15*B*a^6*c^5*d^9*e^5 - 85*A*a^6*c^5*d^8*e^6 + 60*B*a^7*c^4*d^7*e^7 + 50*A*a^7*c^4*d^6*e^8 - 75*B*a^8*c^3*d^5*e^9 + 3*A*a^8*c^3*d^4*e^10 + 42*B*a^9*c^2*d^3*e^11 - 16*A*a^9*c^2*d^2*e^12 - 9*B*a^10*c*d*e^13 + 5*A*a^10*c*e^14)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))*sqrt((4*A^2*c^4*d^7 + 12*A*B*a*c^3*d^6*e - 30*A*B*a^2*c^2*d^4*e^3 - 240*A*B*a^3*c*d^2*e^5 - 30*A*B*a^4*e^7 + (9*B^2*a^2*c^2 - 35*A^2*a*c^3)*d^5*e^2 + 10*(9*B^2*a^3*c + 7*A^2*a^2*c^2)*d^3*e^4 + 15*(3*B^2*a^4 + 7*A^2*a^3*c)*d*e^6 + (a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))/(a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10))) + (a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt((4*A^2*c^4*d^7 + 12*A*B*a*c^3*d^6*e - 30*A*B*a^2*c^2*d^4*e^3 - 240*A*B*a^3*c*d^2*e^5 - 30*A*B*a^4*e^7 + (9*B^2*a^2*c^2 - 35*A^2*a*c^3)*d^5*e^2 + 10*(9*B^2*a^3*c + 7*A^2*a^2*c^2)*d^3*e^4 + 15*(3*B^2*a^4 + 7*A^2*a^3*c)*d*e^6 - (a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))/(a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10))*log(-(120*A^3*B*c^5*d^7*e^2 + 20*(27*A^2*B^2*a*c^4 - 7*A^4*c^5)*d^6*e^3 + 270*(3*A*B^3*a^2*c^3 - 7*A^3*B*a*c^4)*d^5*e^4 + 3*(135*B^4*a^3*c^2 - 1080*A^2*B^2*a^2*c^3 + 497*A^4*a*c^4)*d^4*e^5 - 36*(15*A*B^3*a^3*c^2 - 161*A^3*B*a^2*c^3)*d^3*e^6 + 6*(135*B^4*a^4*c - 414*A^2*B^2*a^3*c^2 - 625*A^4*a^2*c^3)*d^2*e^7 - 6*(189*A*B^3*a^4*c - 625*A^3*B*a^3*c^2)*d*e^8 + (81*B^4*a^5 - 625*A^4*a^3*c^2)*e^9)*sqrt(e*x + d) + (30*A^2*B*a^2*c^5*d^8*e^3 + 35*(9*A*B^2*a^3*c^4 - A^3*a^2*c^5)*d^7*e^4 + 15*(27*B^3*a^4*c^3 - 59*A^2*B*a^3*c^4)*d^6*e^5 - 3*(675*A*B^2*a^4*c^3 - 203*A^3*a^3*c^4)*d^5*e^6 + 27*(35*B^3*a^5*c^2 + 129*A^2*B*a^4*c^3)*d^4*e^7 - 3*(981*A*B^2*a^5*c^2 + 659*A^3*a^4*c^3)*d^3*e^8 + 3*(117*B^3*a^6*c + 827*A^2*B*a^5*c^2)*d^2*e^9 - (531*A*B^2*a^6*c + 325*A^3*a^5*c^2)*d*e^10 + 3*(9*B^3*a^7 + 25*A^2*B*a^6*c)*e^11 + (2*A*a^3*c^8*d^14 + 3*B*a^4*c^7*d^13*e - 19*A*a^4*c^7*d^12*e^2 - 6*B*a^5*c^6*d^11*e^3 + 60*A*a^5*c^6*d^10*e^4 - 15*B*a^6*c^5*d^9*e^5 - 85*A*a^6*c^5*d^8*e^6 + 60*B*a^7*c^4*d^7*e^7 + 50*A*a^7*c^4*d^6*e^8 - 75*B*a^8*c^3*d^5*e^9 + 3*A*a^8*c^3*d^4*e^10 + 42*B*a^9*c^2*d^3*e^11 - 16*A*a^9*c^2*d^2*e^12 - 9*B*a^10*c*d*e^13 + 5*A*a^10*c*e^14)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))*sqrt((4*A^2*c^4*d^7 + 12*A*B*a*c^3*d^6*e - 30*A*B*a^2*c^2*d^4*e^3 - 240*A*B*a^3*c*d^2*e^5 - 30*A*B*a^4*e^7 + (9*B^2*a^2*c^2 - 35*A^2*a*c^3)*d^5*e^2 + 10*(9*B^2*a^3*c + 7*A^2*a^2*c^2)*d^3*e^4 + 15*(3*B^2*a^4 + 7*A^2*a^3*c)*d*e^6 - (a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))/(a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10))) - (a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt((4*A^2*c^4*d^7 + 12*A*B*a*c^3*d^6*e - 30*A*B*a^2*c^2*d^4*e^3 - 240*A*B*a^3*c*d^2*e^5 - 30*A*B*a^4*e^7 + (9*B^2*a^2*c^2 - 35*A^2*a*c^3)*d^5*e^2 + 10*(9*B^2*a^3*c + 7*A^2*a^2*c^2)*d^3*e^4 + 15*(3*B^2*a^4 + 7*A^2*a^3*c)*d*e^6 - (a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))/(a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10))*log(-(120*A^3*B*c^5*d^7*e^2 + 20*(27*A^2*B^2*a*c^4 - 7*A^4*c^5)*d^6*e^3 + 270*(3*A*B^3*a^2*c^3 - 7*A^3*B*a*c^4)*d^5*e^4 + 3*(135*B^4*a^3*c^2 - 1080*A^2*B^2*a^2*c^3 + 497*A^4*a*c^4)*d^4*e^5 - 36*(15*A*B^3*a^3*c^2 - 161*A^3*B*a^2*c^3)*d^3*e^6 + 6*(135*B^4*a^4*c - 414*A^2*B^2*a^3*c^2 - 625*A^4*a^2*c^3)*d^2*e^7 - 6*(189*A*B^3*a^4*c - 625*A^3*B*a^3*c^2)*d*e^8 + (81*B^4*a^5 - 625*A^4*a^3*c^2)*e^9)*sqrt(e*x + d) - (30*A^2*B*a^2*c^5*d^8*e^3 + 35*(9*A*B^2*a^3*c^4 - A^3*a^2*c^5)*d^7*e^4 + 15*(27*B^3*a^4*c^3 - 59*A^2*B*a^3*c^4)*d^6*e^5 - 3*(675*A*B^2*a^4*c^3 - 203*A^3*a^3*c^4)*d^5*e^6 + 27*(35*B^3*a^5*c^2 + 129*A^2*B*a^4*c^3)*d^4*e^7 - 3*(981*A*B^2*a^5*c^2 + 659*A^3*a^4*c^3)*d^3*e^8 + 3*(117*B^3*a^6*c + 827*A^2*B*a^5*c^2)*d^2*e^9 - (531*A*B^2*a^6*c + 325*A^3*a^5*c^2)*d*e^10 + 3*(9*B^3*a^7 + 25*A^2*B*a^6*c)*e^11 + (2*A*a^3*c^8*d^14 + 3*B*a^4*c^7*d^13*e - 19*A*a^4*c^7*d^12*e^2 - 6*B*a^5*c^6*d^11*e^3 + 60*A*a^5*c^6*d^10*e^4 - 15*B*a^6*c^5*d^9*e^5 - 85*A*a^6*c^5*d^8*e^6 + 60*B*a^7*c^4*d^7*e^7 + 50*A*a^7*c^4*d^6*e^8 - 75*B*a^8*c^3*d^5*e^9 + 3*A*a^8*c^3*d^4*e^10 + 42*B*a^9*c^2*d^3*e^11 - 16*A*a^9*c^2*d^2*e^12 - 9*B*a^10*c*d*e^13 + 5*A*a^10*c*e^14)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))*sqrt((4*A^2*c^4*d^7 + 12*A*B*a*c^3*d^6*e - 30*A*B*a^2*c^2*d^4*e^3 - 240*A*B*a^3*c*d^2*e^5 - 30*A*B*a^4*e^7 + (9*B^2*a^2*c^2 - 35*A^2*a*c^3)*d^5*e^2 + 10*(9*B^2*a^3*c + 7*A^2*a^2*c^2)*d^3*e^4 + 15*(3*B^2*a^4 + 7*A^2*a^3*c)*d*e^6 - (a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10)*sqrt((900*A^2*B^2*c^6*d^10*e^4 + 300*(9*A*B^3*a*c^5 - 7*A^3*B*c^6)*d^9*e^5 + 25*(81*B^4*a^2*c^4 - 558*A^2*B^2*a*c^5 + 49*A^4*c^6)*d^8*e^6 - 240*(45*A*B^3*a^2*c^4 - 91*A^3*B*a*c^5)*d^7*e^7 + 20*(405*B^4*a^3*c^3 + 1584*A^2*B^2*a^2*c^4 - 539*A^4*a*c^5)*d^6*e^8 - 44280*(A*B^3*a^3*c^3 + A^3*B*a^2*c^4)*d^5*e^9 + 6*(1485*B^4*a^4*c^2 + 13170*A^2*B^2*a^3*c^3 + 3661*A^4*a^2*c^4)*d^4*e^10 - 48*(585*A*B^3*a^4*c^2 + 1073*A^3*B*a^3*c^3)*d^3*e^11 + 4*(405*B^4*a^5*c + 6579*A^2*B^2*a^4*c^2 + 1925*A^4*a^3*c^3)*d^2*e^12 - 276*(9*A*B^3*a^5*c + 25*A^3*B*a^4*c^2)*d*e^13 + (81*B^4*a^6 + 450*A^2*B^2*a^5*c + 625*A^4*a^4*c^2)*e^14)/(a^3*c^11*d^20 - 10*a^4*c^10*d^18*e^2 + 45*a^5*c^9*d^16*e^4 - 120*a^6*c^8*d^14*e^6 + 210*a^7*c^7*d^12*e^8 - 252*a^8*c^6*d^10*e^10 + 210*a^9*c^5*d^8*e^12 - 120*a^10*c^4*d^6*e^14 + 45*a^11*c^3*d^4*e^16 - 10*a^12*c^2*d^2*e^18 + a^13*c*e^20)))/(a^3*c^5*d^10 - 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 - 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 - a^8*e^10))) - 4*(B*a*c*d^3 - 2*A*a*c*d^2*e + 5*B*a^2*d*e^2 - 4*A*a^2*e^3 + (A*c^2*d^2*e - 6*B*a*c*d*e^2 + 5*A*a*c*e^3)*x^2 + (A*c^2*d^3 - B*a*c*d^2*e - A*a*c*d*e^2 + B*a^2*e^3)*x)*sqrt(e*x + d))/(a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)","B",0
1458,1,6669,0,11.785471," ","integrate((B*x+A)*(e*x+d)^(7/2)/(-c*x^2+a)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 336 \, A B a c^{3} d^{6} e + 1120 \, A B a^{2} c^{2} d^{4} e^{3} - 1050 \, A B a^{3} c d^{2} e^{5} + 210 \, A B a^{4} e^{7} + a^{5} c^{5} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}} + 28 \, {\left(7 \, B^{2} a^{2} c^{2} - 15 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 35 \, {\left(21 \, B^{2} a^{3} c - 11 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 105 \, {\left(7 \, B^{2} a^{4} - A^{2} a^{3} c\right)} d e^{6}}{a^{5} c^{5}}} \log\left(-{\left(30240 \, A^{3} B c^{6} d^{9} e^{4} - 3024 \, {\left(35 \, A^{2} B^{2} a c^{5} + A^{4} c^{6}\right)} d^{8} e^{5} + 504 \, {\left(245 \, A B^{3} a^{2} c^{4} - 207 \, A^{3} B a c^{5}\right)} d^{7} e^{6} - 4 \, {\left(12005 \, B^{4} a^{3} c^{3} - 108486 \, A^{2} B^{2} a^{2} c^{4} - 2727 \, A^{4} a c^{5}\right)} d^{6} e^{7} - 14 \, {\left(40523 \, A B^{3} a^{3} c^{3} - 8019 \, A^{3} B a^{2} c^{4}\right)} d^{5} e^{8} + {\left(242501 \, B^{4} a^{4} c^{2} - 573888 \, A^{2} B^{2} a^{3} c^{3} - 13509 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{9} + 28 \, {\left(29743 \, A B^{3} a^{4} c^{2} - 1051 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{10} - 2 \, {\left(194481 \, B^{4} a^{5} c - 122892 \, A^{2} B^{2} a^{4} c^{2} - 3125 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{11} - 14 \, {\left(27783 \, A B^{3} a^{5} c + 625 \, A^{3} B a^{4} c^{2}\right)} d e^{12} + {\left(194481 \, B^{4} a^{6} - 625 \, A^{4} a^{4} c^{2}\right)} e^{13}\right)} \sqrt{e x + d} + {\left(1260 \, A^{2} B a^{3} c^{6} d^{5} e^{5} - 42 \, {\left(70 \, A B^{2} a^{4} c^{5} + 3 \, A^{3} a^{3} c^{6}\right)} d^{4} e^{6} + 49 \, {\left(35 \, B^{3} a^{5} c^{4} - 51 \, A^{2} B a^{4} c^{5}\right)} d^{3} e^{7} + 3 \, {\left(1911 \, A B^{2} a^{5} c^{4} + 85 \, A^{3} a^{4} c^{5}\right)} d^{2} e^{8} - 21 \, {\left(147 \, B^{3} a^{6} c^{3} - 55 \, A^{2} B a^{5} c^{4}\right)} d e^{9} - 5 \, {\left(441 \, A B^{2} a^{6} c^{3} + 25 \, A^{3} a^{5} c^{4}\right)} e^{10} + {\left(12 \, A a^{5} c^{10} d^{3} - 14 \, B a^{6} c^{9} d^{2} e - 13 \, A a^{6} c^{9} d e^{2} + 21 \, B a^{7} c^{8} e^{3}\right)} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 336 \, A B a c^{3} d^{6} e + 1120 \, A B a^{2} c^{2} d^{4} e^{3} - 1050 \, A B a^{3} c d^{2} e^{5} + 210 \, A B a^{4} e^{7} + a^{5} c^{5} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}} + 28 \, {\left(7 \, B^{2} a^{2} c^{2} - 15 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 35 \, {\left(21 \, B^{2} a^{3} c - 11 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 105 \, {\left(7 \, B^{2} a^{4} - A^{2} a^{3} c\right)} d e^{6}}{a^{5} c^{5}}}\right) - {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 336 \, A B a c^{3} d^{6} e + 1120 \, A B a^{2} c^{2} d^{4} e^{3} - 1050 \, A B a^{3} c d^{2} e^{5} + 210 \, A B a^{4} e^{7} + a^{5} c^{5} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}} + 28 \, {\left(7 \, B^{2} a^{2} c^{2} - 15 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 35 \, {\left(21 \, B^{2} a^{3} c - 11 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 105 \, {\left(7 \, B^{2} a^{4} - A^{2} a^{3} c\right)} d e^{6}}{a^{5} c^{5}}} \log\left(-{\left(30240 \, A^{3} B c^{6} d^{9} e^{4} - 3024 \, {\left(35 \, A^{2} B^{2} a c^{5} + A^{4} c^{6}\right)} d^{8} e^{5} + 504 \, {\left(245 \, A B^{3} a^{2} c^{4} - 207 \, A^{3} B a c^{5}\right)} d^{7} e^{6} - 4 \, {\left(12005 \, B^{4} a^{3} c^{3} - 108486 \, A^{2} B^{2} a^{2} c^{4} - 2727 \, A^{4} a c^{5}\right)} d^{6} e^{7} - 14 \, {\left(40523 \, A B^{3} a^{3} c^{3} - 8019 \, A^{3} B a^{2} c^{4}\right)} d^{5} e^{8} + {\left(242501 \, B^{4} a^{4} c^{2} - 573888 \, A^{2} B^{2} a^{3} c^{3} - 13509 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{9} + 28 \, {\left(29743 \, A B^{3} a^{4} c^{2} - 1051 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{10} - 2 \, {\left(194481 \, B^{4} a^{5} c - 122892 \, A^{2} B^{2} a^{4} c^{2} - 3125 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{11} - 14 \, {\left(27783 \, A B^{3} a^{5} c + 625 \, A^{3} B a^{4} c^{2}\right)} d e^{12} + {\left(194481 \, B^{4} a^{6} - 625 \, A^{4} a^{4} c^{2}\right)} e^{13}\right)} \sqrt{e x + d} - {\left(1260 \, A^{2} B a^{3} c^{6} d^{5} e^{5} - 42 \, {\left(70 \, A B^{2} a^{4} c^{5} + 3 \, A^{3} a^{3} c^{6}\right)} d^{4} e^{6} + 49 \, {\left(35 \, B^{3} a^{5} c^{4} - 51 \, A^{2} B a^{4} c^{5}\right)} d^{3} e^{7} + 3 \, {\left(1911 \, A B^{2} a^{5} c^{4} + 85 \, A^{3} a^{4} c^{5}\right)} d^{2} e^{8} - 21 \, {\left(147 \, B^{3} a^{6} c^{3} - 55 \, A^{2} B a^{5} c^{4}\right)} d e^{9} - 5 \, {\left(441 \, A B^{2} a^{6} c^{3} + 25 \, A^{3} a^{5} c^{4}\right)} e^{10} + {\left(12 \, A a^{5} c^{10} d^{3} - 14 \, B a^{6} c^{9} d^{2} e - 13 \, A a^{6} c^{9} d e^{2} + 21 \, B a^{7} c^{8} e^{3}\right)} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 336 \, A B a c^{3} d^{6} e + 1120 \, A B a^{2} c^{2} d^{4} e^{3} - 1050 \, A B a^{3} c d^{2} e^{5} + 210 \, A B a^{4} e^{7} + a^{5} c^{5} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}} + 28 \, {\left(7 \, B^{2} a^{2} c^{2} - 15 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 35 \, {\left(21 \, B^{2} a^{3} c - 11 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 105 \, {\left(7 \, B^{2} a^{4} - A^{2} a^{3} c\right)} d e^{6}}{a^{5} c^{5}}}\right) + {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 336 \, A B a c^{3} d^{6} e + 1120 \, A B a^{2} c^{2} d^{4} e^{3} - 1050 \, A B a^{3} c d^{2} e^{5} + 210 \, A B a^{4} e^{7} - a^{5} c^{5} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}} + 28 \, {\left(7 \, B^{2} a^{2} c^{2} - 15 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 35 \, {\left(21 \, B^{2} a^{3} c - 11 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 105 \, {\left(7 \, B^{2} a^{4} - A^{2} a^{3} c\right)} d e^{6}}{a^{5} c^{5}}} \log\left(-{\left(30240 \, A^{3} B c^{6} d^{9} e^{4} - 3024 \, {\left(35 \, A^{2} B^{2} a c^{5} + A^{4} c^{6}\right)} d^{8} e^{5} + 504 \, {\left(245 \, A B^{3} a^{2} c^{4} - 207 \, A^{3} B a c^{5}\right)} d^{7} e^{6} - 4 \, {\left(12005 \, B^{4} a^{3} c^{3} - 108486 \, A^{2} B^{2} a^{2} c^{4} - 2727 \, A^{4} a c^{5}\right)} d^{6} e^{7} - 14 \, {\left(40523 \, A B^{3} a^{3} c^{3} - 8019 \, A^{3} B a^{2} c^{4}\right)} d^{5} e^{8} + {\left(242501 \, B^{4} a^{4} c^{2} - 573888 \, A^{2} B^{2} a^{3} c^{3} - 13509 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{9} + 28 \, {\left(29743 \, A B^{3} a^{4} c^{2} - 1051 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{10} - 2 \, {\left(194481 \, B^{4} a^{5} c - 122892 \, A^{2} B^{2} a^{4} c^{2} - 3125 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{11} - 14 \, {\left(27783 \, A B^{3} a^{5} c + 625 \, A^{3} B a^{4} c^{2}\right)} d e^{12} + {\left(194481 \, B^{4} a^{6} - 625 \, A^{4} a^{4} c^{2}\right)} e^{13}\right)} \sqrt{e x + d} + {\left(1260 \, A^{2} B a^{3} c^{6} d^{5} e^{5} - 42 \, {\left(70 \, A B^{2} a^{4} c^{5} + 3 \, A^{3} a^{3} c^{6}\right)} d^{4} e^{6} + 49 \, {\left(35 \, B^{3} a^{5} c^{4} - 51 \, A^{2} B a^{4} c^{5}\right)} d^{3} e^{7} + 3 \, {\left(1911 \, A B^{2} a^{5} c^{4} + 85 \, A^{3} a^{4} c^{5}\right)} d^{2} e^{8} - 21 \, {\left(147 \, B^{3} a^{6} c^{3} - 55 \, A^{2} B a^{5} c^{4}\right)} d e^{9} - 5 \, {\left(441 \, A B^{2} a^{6} c^{3} + 25 \, A^{3} a^{5} c^{4}\right)} e^{10} - {\left(12 \, A a^{5} c^{10} d^{3} - 14 \, B a^{6} c^{9} d^{2} e - 13 \, A a^{6} c^{9} d e^{2} + 21 \, B a^{7} c^{8} e^{3}\right)} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 336 \, A B a c^{3} d^{6} e + 1120 \, A B a^{2} c^{2} d^{4} e^{3} - 1050 \, A B a^{3} c d^{2} e^{5} + 210 \, A B a^{4} e^{7} - a^{5} c^{5} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}} + 28 \, {\left(7 \, B^{2} a^{2} c^{2} - 15 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 35 \, {\left(21 \, B^{2} a^{3} c - 11 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 105 \, {\left(7 \, B^{2} a^{4} - A^{2} a^{3} c\right)} d e^{6}}{a^{5} c^{5}}}\right) - {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 336 \, A B a c^{3} d^{6} e + 1120 \, A B a^{2} c^{2} d^{4} e^{3} - 1050 \, A B a^{3} c d^{2} e^{5} + 210 \, A B a^{4} e^{7} - a^{5} c^{5} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}} + 28 \, {\left(7 \, B^{2} a^{2} c^{2} - 15 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 35 \, {\left(21 \, B^{2} a^{3} c - 11 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 105 \, {\left(7 \, B^{2} a^{4} - A^{2} a^{3} c\right)} d e^{6}}{a^{5} c^{5}}} \log\left(-{\left(30240 \, A^{3} B c^{6} d^{9} e^{4} - 3024 \, {\left(35 \, A^{2} B^{2} a c^{5} + A^{4} c^{6}\right)} d^{8} e^{5} + 504 \, {\left(245 \, A B^{3} a^{2} c^{4} - 207 \, A^{3} B a c^{5}\right)} d^{7} e^{6} - 4 \, {\left(12005 \, B^{4} a^{3} c^{3} - 108486 \, A^{2} B^{2} a^{2} c^{4} - 2727 \, A^{4} a c^{5}\right)} d^{6} e^{7} - 14 \, {\left(40523 \, A B^{3} a^{3} c^{3} - 8019 \, A^{3} B a^{2} c^{4}\right)} d^{5} e^{8} + {\left(242501 \, B^{4} a^{4} c^{2} - 573888 \, A^{2} B^{2} a^{3} c^{3} - 13509 \, A^{4} a^{2} c^{4}\right)} d^{4} e^{9} + 28 \, {\left(29743 \, A B^{3} a^{4} c^{2} - 1051 \, A^{3} B a^{3} c^{3}\right)} d^{3} e^{10} - 2 \, {\left(194481 \, B^{4} a^{5} c - 122892 \, A^{2} B^{2} a^{4} c^{2} - 3125 \, A^{4} a^{3} c^{3}\right)} d^{2} e^{11} - 14 \, {\left(27783 \, A B^{3} a^{5} c + 625 \, A^{3} B a^{4} c^{2}\right)} d e^{12} + {\left(194481 \, B^{4} a^{6} - 625 \, A^{4} a^{4} c^{2}\right)} e^{13}\right)} \sqrt{e x + d} - {\left(1260 \, A^{2} B a^{3} c^{6} d^{5} e^{5} - 42 \, {\left(70 \, A B^{2} a^{4} c^{5} + 3 \, A^{3} a^{3} c^{6}\right)} d^{4} e^{6} + 49 \, {\left(35 \, B^{3} a^{5} c^{4} - 51 \, A^{2} B a^{4} c^{5}\right)} d^{3} e^{7} + 3 \, {\left(1911 \, A B^{2} a^{5} c^{4} + 85 \, A^{3} a^{4} c^{5}\right)} d^{2} e^{8} - 21 \, {\left(147 \, B^{3} a^{6} c^{3} - 55 \, A^{2} B a^{5} c^{4}\right)} d e^{9} - 5 \, {\left(441 \, A B^{2} a^{6} c^{3} + 25 \, A^{3} a^{5} c^{4}\right)} e^{10} - {\left(12 \, A a^{5} c^{10} d^{3} - 14 \, B a^{6} c^{9} d^{2} e - 13 \, A a^{6} c^{9} d e^{2} + 21 \, B a^{7} c^{8} e^{3}\right)} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 336 \, A B a c^{3} d^{6} e + 1120 \, A B a^{2} c^{2} d^{4} e^{3} - 1050 \, A B a^{3} c d^{2} e^{5} + 210 \, A B a^{4} e^{7} - a^{5} c^{5} \sqrt{\frac{44100 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 2940 \, {\left(35 \, A B^{3} a c^{3} + 3 \, A^{3} B c^{4}\right)} d^{5} e^{9} + 49 \, {\left(1225 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 9 \, A^{4} c^{4}\right)} d^{4} e^{10} + 56 \, {\left(5635 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 42 \, {\left(5145 \, B^{4} a^{3} c - 952 \, A^{2} B^{2} a^{2} c^{2} + 25 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 532 \, {\left(441 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(194481 \, B^{4} a^{4} + 22050 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11}}} + 28 \, {\left(7 \, B^{2} a^{2} c^{2} - 15 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 35 \, {\left(21 \, B^{2} a^{3} c - 11 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 105 \, {\left(7 \, B^{2} a^{4} - A^{2} a^{3} c\right)} d e^{6}}{a^{5} c^{5}}}\right) - 4 \, {\left(4 \, B a^{2} c d^{3} + 11 \, A a^{2} c d^{2} e - 14 \, B a^{3} d e^{2} - 5 \, A a^{3} e^{3} - {\left(6 \, A c^{3} d^{3} - 7 \, B a c^{2} d^{2} e - 8 \, A a c^{2} d e^{2} - 11 \, B a^{2} c e^{3}\right)} x^{3} + {\left(A a c^{2} d^{2} e + 26 \, B a^{2} c d e^{2} + 9 \, A a^{2} c e^{3}\right)} x^{2} + {\left(10 \, A a c^{2} d^{3} + 5 \, B a^{2} c d^{2} e + 4 \, A a^{2} c d e^{2} - 7 \, B a^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)}}"," ",0,"-1/64*((a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*A^2*c^4*d^7 - 336*A*B*a*c^3*d^6*e + 1120*A*B*a^2*c^2*d^4*e^3 - 1050*A*B*a^3*c*d^2*e^5 + 210*A*B*a^4*e^7 + a^5*c^5*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)) + 28*(7*B^2*a^2*c^2 - 15*A^2*a*c^3)*d^5*e^2 - 35*(21*B^2*a^3*c - 11*A^2*a^2*c^2)*d^3*e^4 + 105*(7*B^2*a^4 - A^2*a^3*c)*d*e^6)/(a^5*c^5))*log(-(30240*A^3*B*c^6*d^9*e^4 - 3024*(35*A^2*B^2*a*c^5 + A^4*c^6)*d^8*e^5 + 504*(245*A*B^3*a^2*c^4 - 207*A^3*B*a*c^5)*d^7*e^6 - 4*(12005*B^4*a^3*c^3 - 108486*A^2*B^2*a^2*c^4 - 2727*A^4*a*c^5)*d^6*e^7 - 14*(40523*A*B^3*a^3*c^3 - 8019*A^3*B*a^2*c^4)*d^5*e^8 + (242501*B^4*a^4*c^2 - 573888*A^2*B^2*a^3*c^3 - 13509*A^4*a^2*c^4)*d^4*e^9 + 28*(29743*A*B^3*a^4*c^2 - 1051*A^3*B*a^3*c^3)*d^3*e^10 - 2*(194481*B^4*a^5*c - 122892*A^2*B^2*a^4*c^2 - 3125*A^4*a^3*c^3)*d^2*e^11 - 14*(27783*A*B^3*a^5*c + 625*A^3*B*a^4*c^2)*d*e^12 + (194481*B^4*a^6 - 625*A^4*a^4*c^2)*e^13)*sqrt(e*x + d) + (1260*A^2*B*a^3*c^6*d^5*e^5 - 42*(70*A*B^2*a^4*c^5 + 3*A^3*a^3*c^6)*d^4*e^6 + 49*(35*B^3*a^5*c^4 - 51*A^2*B*a^4*c^5)*d^3*e^7 + 3*(1911*A*B^2*a^5*c^4 + 85*A^3*a^4*c^5)*d^2*e^8 - 21*(147*B^3*a^6*c^3 - 55*A^2*B*a^5*c^4)*d*e^9 - 5*(441*A*B^2*a^6*c^3 + 25*A^3*a^5*c^4)*e^10 + (12*A*a^5*c^10*d^3 - 14*B*a^6*c^9*d^2*e - 13*A*a^6*c^9*d*e^2 + 21*B*a^7*c^8*e^3)*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)))*sqrt((144*A^2*c^4*d^7 - 336*A*B*a*c^3*d^6*e + 1120*A*B*a^2*c^2*d^4*e^3 - 1050*A*B*a^3*c*d^2*e^5 + 210*A*B*a^4*e^7 + a^5*c^5*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)) + 28*(7*B^2*a^2*c^2 - 15*A^2*a*c^3)*d^5*e^2 - 35*(21*B^2*a^3*c - 11*A^2*a^2*c^2)*d^3*e^4 + 105*(7*B^2*a^4 - A^2*a^3*c)*d*e^6)/(a^5*c^5))) - (a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*A^2*c^4*d^7 - 336*A*B*a*c^3*d^6*e + 1120*A*B*a^2*c^2*d^4*e^3 - 1050*A*B*a^3*c*d^2*e^5 + 210*A*B*a^4*e^7 + a^5*c^5*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)) + 28*(7*B^2*a^2*c^2 - 15*A^2*a*c^3)*d^5*e^2 - 35*(21*B^2*a^3*c - 11*A^2*a^2*c^2)*d^3*e^4 + 105*(7*B^2*a^4 - A^2*a^3*c)*d*e^6)/(a^5*c^5))*log(-(30240*A^3*B*c^6*d^9*e^4 - 3024*(35*A^2*B^2*a*c^5 + A^4*c^6)*d^8*e^5 + 504*(245*A*B^3*a^2*c^4 - 207*A^3*B*a*c^5)*d^7*e^6 - 4*(12005*B^4*a^3*c^3 - 108486*A^2*B^2*a^2*c^4 - 2727*A^4*a*c^5)*d^6*e^7 - 14*(40523*A*B^3*a^3*c^3 - 8019*A^3*B*a^2*c^4)*d^5*e^8 + (242501*B^4*a^4*c^2 - 573888*A^2*B^2*a^3*c^3 - 13509*A^4*a^2*c^4)*d^4*e^9 + 28*(29743*A*B^3*a^4*c^2 - 1051*A^3*B*a^3*c^3)*d^3*e^10 - 2*(194481*B^4*a^5*c - 122892*A^2*B^2*a^4*c^2 - 3125*A^4*a^3*c^3)*d^2*e^11 - 14*(27783*A*B^3*a^5*c + 625*A^3*B*a^4*c^2)*d*e^12 + (194481*B^4*a^6 - 625*A^4*a^4*c^2)*e^13)*sqrt(e*x + d) - (1260*A^2*B*a^3*c^6*d^5*e^5 - 42*(70*A*B^2*a^4*c^5 + 3*A^3*a^3*c^6)*d^4*e^6 + 49*(35*B^3*a^5*c^4 - 51*A^2*B*a^4*c^5)*d^3*e^7 + 3*(1911*A*B^2*a^5*c^4 + 85*A^3*a^4*c^5)*d^2*e^8 - 21*(147*B^3*a^6*c^3 - 55*A^2*B*a^5*c^4)*d*e^9 - 5*(441*A*B^2*a^6*c^3 + 25*A^3*a^5*c^4)*e^10 + (12*A*a^5*c^10*d^3 - 14*B*a^6*c^9*d^2*e - 13*A*a^6*c^9*d*e^2 + 21*B*a^7*c^8*e^3)*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)))*sqrt((144*A^2*c^4*d^7 - 336*A*B*a*c^3*d^6*e + 1120*A*B*a^2*c^2*d^4*e^3 - 1050*A*B*a^3*c*d^2*e^5 + 210*A*B*a^4*e^7 + a^5*c^5*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)) + 28*(7*B^2*a^2*c^2 - 15*A^2*a*c^3)*d^5*e^2 - 35*(21*B^2*a^3*c - 11*A^2*a^2*c^2)*d^3*e^4 + 105*(7*B^2*a^4 - A^2*a^3*c)*d*e^6)/(a^5*c^5))) + (a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*A^2*c^4*d^7 - 336*A*B*a*c^3*d^6*e + 1120*A*B*a^2*c^2*d^4*e^3 - 1050*A*B*a^3*c*d^2*e^5 + 210*A*B*a^4*e^7 - a^5*c^5*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)) + 28*(7*B^2*a^2*c^2 - 15*A^2*a*c^3)*d^5*e^2 - 35*(21*B^2*a^3*c - 11*A^2*a^2*c^2)*d^3*e^4 + 105*(7*B^2*a^4 - A^2*a^3*c)*d*e^6)/(a^5*c^5))*log(-(30240*A^3*B*c^6*d^9*e^4 - 3024*(35*A^2*B^2*a*c^5 + A^4*c^6)*d^8*e^5 + 504*(245*A*B^3*a^2*c^4 - 207*A^3*B*a*c^5)*d^7*e^6 - 4*(12005*B^4*a^3*c^3 - 108486*A^2*B^2*a^2*c^4 - 2727*A^4*a*c^5)*d^6*e^7 - 14*(40523*A*B^3*a^3*c^3 - 8019*A^3*B*a^2*c^4)*d^5*e^8 + (242501*B^4*a^4*c^2 - 573888*A^2*B^2*a^3*c^3 - 13509*A^4*a^2*c^4)*d^4*e^9 + 28*(29743*A*B^3*a^4*c^2 - 1051*A^3*B*a^3*c^3)*d^3*e^10 - 2*(194481*B^4*a^5*c - 122892*A^2*B^2*a^4*c^2 - 3125*A^4*a^3*c^3)*d^2*e^11 - 14*(27783*A*B^3*a^5*c + 625*A^3*B*a^4*c^2)*d*e^12 + (194481*B^4*a^6 - 625*A^4*a^4*c^2)*e^13)*sqrt(e*x + d) + (1260*A^2*B*a^3*c^6*d^5*e^5 - 42*(70*A*B^2*a^4*c^5 + 3*A^3*a^3*c^6)*d^4*e^6 + 49*(35*B^3*a^5*c^4 - 51*A^2*B*a^4*c^5)*d^3*e^7 + 3*(1911*A*B^2*a^5*c^4 + 85*A^3*a^4*c^5)*d^2*e^8 - 21*(147*B^3*a^6*c^3 - 55*A^2*B*a^5*c^4)*d*e^9 - 5*(441*A*B^2*a^6*c^3 + 25*A^3*a^5*c^4)*e^10 - (12*A*a^5*c^10*d^3 - 14*B*a^6*c^9*d^2*e - 13*A*a^6*c^9*d*e^2 + 21*B*a^7*c^8*e^3)*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)))*sqrt((144*A^2*c^4*d^7 - 336*A*B*a*c^3*d^6*e + 1120*A*B*a^2*c^2*d^4*e^3 - 1050*A*B*a^3*c*d^2*e^5 + 210*A*B*a^4*e^7 - a^5*c^5*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)) + 28*(7*B^2*a^2*c^2 - 15*A^2*a*c^3)*d^5*e^2 - 35*(21*B^2*a^3*c - 11*A^2*a^2*c^2)*d^3*e^4 + 105*(7*B^2*a^4 - A^2*a^3*c)*d*e^6)/(a^5*c^5))) - (a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*A^2*c^4*d^7 - 336*A*B*a*c^3*d^6*e + 1120*A*B*a^2*c^2*d^4*e^3 - 1050*A*B*a^3*c*d^2*e^5 + 210*A*B*a^4*e^7 - a^5*c^5*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)) + 28*(7*B^2*a^2*c^2 - 15*A^2*a*c^3)*d^5*e^2 - 35*(21*B^2*a^3*c - 11*A^2*a^2*c^2)*d^3*e^4 + 105*(7*B^2*a^4 - A^2*a^3*c)*d*e^6)/(a^5*c^5))*log(-(30240*A^3*B*c^6*d^9*e^4 - 3024*(35*A^2*B^2*a*c^5 + A^4*c^6)*d^8*e^5 + 504*(245*A*B^3*a^2*c^4 - 207*A^3*B*a*c^5)*d^7*e^6 - 4*(12005*B^4*a^3*c^3 - 108486*A^2*B^2*a^2*c^4 - 2727*A^4*a*c^5)*d^6*e^7 - 14*(40523*A*B^3*a^3*c^3 - 8019*A^3*B*a^2*c^4)*d^5*e^8 + (242501*B^4*a^4*c^2 - 573888*A^2*B^2*a^3*c^3 - 13509*A^4*a^2*c^4)*d^4*e^9 + 28*(29743*A*B^3*a^4*c^2 - 1051*A^3*B*a^3*c^3)*d^3*e^10 - 2*(194481*B^4*a^5*c - 122892*A^2*B^2*a^4*c^2 - 3125*A^4*a^3*c^3)*d^2*e^11 - 14*(27783*A*B^3*a^5*c + 625*A^3*B*a^4*c^2)*d*e^12 + (194481*B^4*a^6 - 625*A^4*a^4*c^2)*e^13)*sqrt(e*x + d) - (1260*A^2*B*a^3*c^6*d^5*e^5 - 42*(70*A*B^2*a^4*c^5 + 3*A^3*a^3*c^6)*d^4*e^6 + 49*(35*B^3*a^5*c^4 - 51*A^2*B*a^4*c^5)*d^3*e^7 + 3*(1911*A*B^2*a^5*c^4 + 85*A^3*a^4*c^5)*d^2*e^8 - 21*(147*B^3*a^6*c^3 - 55*A^2*B*a^5*c^4)*d*e^9 - 5*(441*A*B^2*a^6*c^3 + 25*A^3*a^5*c^4)*e^10 - (12*A*a^5*c^10*d^3 - 14*B*a^6*c^9*d^2*e - 13*A*a^6*c^9*d*e^2 + 21*B*a^7*c^8*e^3)*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)))*sqrt((144*A^2*c^4*d^7 - 336*A*B*a*c^3*d^6*e + 1120*A*B*a^2*c^2*d^4*e^3 - 1050*A*B*a^3*c*d^2*e^5 + 210*A*B*a^4*e^7 - a^5*c^5*sqrt((44100*A^2*B^2*c^4*d^6*e^8 - 2940*(35*A*B^3*a*c^3 + 3*A^3*B*c^4)*d^5*e^9 + 49*(1225*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 9*A^4*c^4)*d^4*e^10 + 56*(5635*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 42*(5145*B^4*a^3*c - 952*A^2*B^2*a^2*c^2 + 25*A^4*a*c^3)*d^2*e^12 - 532*(441*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (194481*B^4*a^4 + 22050*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11)) + 28*(7*B^2*a^2*c^2 - 15*A^2*a*c^3)*d^5*e^2 - 35*(21*B^2*a^3*c - 11*A^2*a^2*c^2)*d^3*e^4 + 105*(7*B^2*a^4 - A^2*a^3*c)*d*e^6)/(a^5*c^5))) - 4*(4*B*a^2*c*d^3 + 11*A*a^2*c*d^2*e - 14*B*a^3*d*e^2 - 5*A*a^3*e^3 - (6*A*c^3*d^3 - 7*B*a*c^2*d^2*e - 8*A*a*c^2*d*e^2 - 11*B*a^2*c*e^3)*x^3 + (A*a*c^2*d^2*e + 26*B*a^2*c*d*e^2 + 9*A*a^2*c*e^3)*x^2 + (10*A*a*c^2*d^3 + 5*B*a^2*c*d^2*e + 4*A*a^2*c*d*e^2 - 7*B*a^3*e^3)*x)*sqrt(e*x + d))/(a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)","B",0
1459,1,3382,0,1.217216," ","integrate((B*x+A)*(e*x+d)^(5/2)/(-c*x^2+a)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{3} d^{5} - 240 \, A B a c^{2} d^{4} e + 240 \, A B a^{2} c d^{2} e^{3} - 30 \, A B a^{3} e^{5} + a^{5} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}} + 20 \, {\left(5 \, B^{2} a^{2} c - 9 \, A^{2} a c^{2}\right)} d^{3} e^{2} - 15 \, {\left(5 \, B^{2} a^{3} - 3 \, A^{2} a^{2} c\right)} d e^{4}}{a^{5} c^{4}}} \log\left(-{\left(4320 \, A^{3} B c^{4} d^{5} e^{4} - 432 \, {\left(25 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{5} + 360 \, {\left(25 \, A B^{3} a^{2} c^{2} - 3 \, A^{3} B a c^{3}\right)} d^{3} e^{6} - 4 \, {\left(625 \, B^{4} a^{3} c - 1350 \, A^{2} B^{2} a^{2} c^{2} - 243 \, A^{4} a c^{3}\right)} d^{2} e^{7} - 30 \, {\left(125 \, A B^{3} a^{3} c + 27 \, A^{3} B a^{2} c^{2}\right)} d e^{8} + {\left(625 \, B^{4} a^{4} - 81 \, A^{4} a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + {\left(180 \, A^{2} B a^{3} c^{4} d^{2} e^{5} - 6 \, {\left(50 \, A B^{2} a^{4} c^{3} + 9 \, A^{3} a^{3} c^{4}\right)} d e^{6} + 5 \, {\left(25 \, B^{3} a^{5} c^{2} + 9 \, A^{2} B a^{4} c^{3}\right)} e^{7} - {\left(12 \, A a^{5} c^{8} d^{2} - 10 \, B a^{6} c^{7} d e - 3 \, A a^{6} c^{7} e^{2}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}}\right)} \sqrt{\frac{144 \, A^{2} c^{3} d^{5} - 240 \, A B a c^{2} d^{4} e + 240 \, A B a^{2} c d^{2} e^{3} - 30 \, A B a^{3} e^{5} + a^{5} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}} + 20 \, {\left(5 \, B^{2} a^{2} c - 9 \, A^{2} a c^{2}\right)} d^{3} e^{2} - 15 \, {\left(5 \, B^{2} a^{3} - 3 \, A^{2} a^{2} c\right)} d e^{4}}{a^{5} c^{4}}}\right) - {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{3} d^{5} - 240 \, A B a c^{2} d^{4} e + 240 \, A B a^{2} c d^{2} e^{3} - 30 \, A B a^{3} e^{5} + a^{5} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}} + 20 \, {\left(5 \, B^{2} a^{2} c - 9 \, A^{2} a c^{2}\right)} d^{3} e^{2} - 15 \, {\left(5 \, B^{2} a^{3} - 3 \, A^{2} a^{2} c\right)} d e^{4}}{a^{5} c^{4}}} \log\left(-{\left(4320 \, A^{3} B c^{4} d^{5} e^{4} - 432 \, {\left(25 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{5} + 360 \, {\left(25 \, A B^{3} a^{2} c^{2} - 3 \, A^{3} B a c^{3}\right)} d^{3} e^{6} - 4 \, {\left(625 \, B^{4} a^{3} c - 1350 \, A^{2} B^{2} a^{2} c^{2} - 243 \, A^{4} a c^{3}\right)} d^{2} e^{7} - 30 \, {\left(125 \, A B^{3} a^{3} c + 27 \, A^{3} B a^{2} c^{2}\right)} d e^{8} + {\left(625 \, B^{4} a^{4} - 81 \, A^{4} a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - {\left(180 \, A^{2} B a^{3} c^{4} d^{2} e^{5} - 6 \, {\left(50 \, A B^{2} a^{4} c^{3} + 9 \, A^{3} a^{3} c^{4}\right)} d e^{6} + 5 \, {\left(25 \, B^{3} a^{5} c^{2} + 9 \, A^{2} B a^{4} c^{3}\right)} e^{7} - {\left(12 \, A a^{5} c^{8} d^{2} - 10 \, B a^{6} c^{7} d e - 3 \, A a^{6} c^{7} e^{2}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}}\right)} \sqrt{\frac{144 \, A^{2} c^{3} d^{5} - 240 \, A B a c^{2} d^{4} e + 240 \, A B a^{2} c d^{2} e^{3} - 30 \, A B a^{3} e^{5} + a^{5} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}} + 20 \, {\left(5 \, B^{2} a^{2} c - 9 \, A^{2} a c^{2}\right)} d^{3} e^{2} - 15 \, {\left(5 \, B^{2} a^{3} - 3 \, A^{2} a^{2} c\right)} d e^{4}}{a^{5} c^{4}}}\right) + {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{3} d^{5} - 240 \, A B a c^{2} d^{4} e + 240 \, A B a^{2} c d^{2} e^{3} - 30 \, A B a^{3} e^{5} - a^{5} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}} + 20 \, {\left(5 \, B^{2} a^{2} c - 9 \, A^{2} a c^{2}\right)} d^{3} e^{2} - 15 \, {\left(5 \, B^{2} a^{3} - 3 \, A^{2} a^{2} c\right)} d e^{4}}{a^{5} c^{4}}} \log\left(-{\left(4320 \, A^{3} B c^{4} d^{5} e^{4} - 432 \, {\left(25 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{5} + 360 \, {\left(25 \, A B^{3} a^{2} c^{2} - 3 \, A^{3} B a c^{3}\right)} d^{3} e^{6} - 4 \, {\left(625 \, B^{4} a^{3} c - 1350 \, A^{2} B^{2} a^{2} c^{2} - 243 \, A^{4} a c^{3}\right)} d^{2} e^{7} - 30 \, {\left(125 \, A B^{3} a^{3} c + 27 \, A^{3} B a^{2} c^{2}\right)} d e^{8} + {\left(625 \, B^{4} a^{4} - 81 \, A^{4} a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + {\left(180 \, A^{2} B a^{3} c^{4} d^{2} e^{5} - 6 \, {\left(50 \, A B^{2} a^{4} c^{3} + 9 \, A^{3} a^{3} c^{4}\right)} d e^{6} + 5 \, {\left(25 \, B^{3} a^{5} c^{2} + 9 \, A^{2} B a^{4} c^{3}\right)} e^{7} + {\left(12 \, A a^{5} c^{8} d^{2} - 10 \, B a^{6} c^{7} d e - 3 \, A a^{6} c^{7} e^{2}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}}\right)} \sqrt{\frac{144 \, A^{2} c^{3} d^{5} - 240 \, A B a c^{2} d^{4} e + 240 \, A B a^{2} c d^{2} e^{3} - 30 \, A B a^{3} e^{5} - a^{5} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}} + 20 \, {\left(5 \, B^{2} a^{2} c - 9 \, A^{2} a c^{2}\right)} d^{3} e^{2} - 15 \, {\left(5 \, B^{2} a^{3} - 3 \, A^{2} a^{2} c\right)} d e^{4}}{a^{5} c^{4}}}\right) - {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{3} d^{5} - 240 \, A B a c^{2} d^{4} e + 240 \, A B a^{2} c d^{2} e^{3} - 30 \, A B a^{3} e^{5} - a^{5} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}} + 20 \, {\left(5 \, B^{2} a^{2} c - 9 \, A^{2} a c^{2}\right)} d^{3} e^{2} - 15 \, {\left(5 \, B^{2} a^{3} - 3 \, A^{2} a^{2} c\right)} d e^{4}}{a^{5} c^{4}}} \log\left(-{\left(4320 \, A^{3} B c^{4} d^{5} e^{4} - 432 \, {\left(25 \, A^{2} B^{2} a c^{3} + 3 \, A^{4} c^{4}\right)} d^{4} e^{5} + 360 \, {\left(25 \, A B^{3} a^{2} c^{2} - 3 \, A^{3} B a c^{3}\right)} d^{3} e^{6} - 4 \, {\left(625 \, B^{4} a^{3} c - 1350 \, A^{2} B^{2} a^{2} c^{2} - 243 \, A^{4} a c^{3}\right)} d^{2} e^{7} - 30 \, {\left(125 \, A B^{3} a^{3} c + 27 \, A^{3} B a^{2} c^{2}\right)} d e^{8} + {\left(625 \, B^{4} a^{4} - 81 \, A^{4} a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - {\left(180 \, A^{2} B a^{3} c^{4} d^{2} e^{5} - 6 \, {\left(50 \, A B^{2} a^{4} c^{3} + 9 \, A^{3} a^{3} c^{4}\right)} d e^{6} + 5 \, {\left(25 \, B^{3} a^{5} c^{2} + 9 \, A^{2} B a^{4} c^{3}\right)} e^{7} + {\left(12 \, A a^{5} c^{8} d^{2} - 10 \, B a^{6} c^{7} d e - 3 \, A a^{6} c^{7} e^{2}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}}\right)} \sqrt{\frac{144 \, A^{2} c^{3} d^{5} - 240 \, A B a c^{2} d^{4} e + 240 \, A B a^{2} c d^{2} e^{3} - 30 \, A B a^{3} e^{5} - a^{5} c^{4} \sqrt{\frac{900 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 60 \, {\left(25 \, A B^{3} a c + 9 \, A^{3} B c^{2}\right)} d e^{9} + {\left(625 \, B^{4} a^{2} + 450 \, A^{2} B^{2} a c + 81 \, A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9}}} + 20 \, {\left(5 \, B^{2} a^{2} c - 9 \, A^{2} a c^{2}\right)} d^{3} e^{2} - 15 \, {\left(5 \, B^{2} a^{3} - 3 \, A^{2} a^{2} c\right)} d e^{4}}{a^{5} c^{4}}}\right) - 4 \, {\left(4 \, B a^{2} c d^{2} + 7 \, A a^{2} c d e - 5 \, B a^{3} e^{2} - {\left(6 \, A c^{3} d^{2} - 5 \, B a c^{2} d e - 3 \, A a c^{2} e^{2}\right)} x^{3} + {\left(A a c^{2} d e + 9 \, B a^{2} c e^{2}\right)} x^{2} + {\left(10 \, A a c^{2} d^{2} + 3 \, B a^{2} c d e + A a^{2} c e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)}}"," ",0,"-1/64*((a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*A^2*c^3*d^5 - 240*A*B*a*c^2*d^4*e + 240*A*B*a^2*c*d^2*e^3 - 30*A*B*a^3*e^5 + a^5*c^4*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)) + 20*(5*B^2*a^2*c - 9*A^2*a*c^2)*d^3*e^2 - 15*(5*B^2*a^3 - 3*A^2*a^2*c)*d*e^4)/(a^5*c^4))*log(-(4320*A^3*B*c^4*d^5*e^4 - 432*(25*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^5 + 360*(25*A*B^3*a^2*c^2 - 3*A^3*B*a*c^3)*d^3*e^6 - 4*(625*B^4*a^3*c - 1350*A^2*B^2*a^2*c^2 - 243*A^4*a*c^3)*d^2*e^7 - 30*(125*A*B^3*a^3*c + 27*A^3*B*a^2*c^2)*d*e^8 + (625*B^4*a^4 - 81*A^4*a^2*c^2)*e^9)*sqrt(e*x + d) + (180*A^2*B*a^3*c^4*d^2*e^5 - 6*(50*A*B^2*a^4*c^3 + 9*A^3*a^3*c^4)*d*e^6 + 5*(25*B^3*a^5*c^2 + 9*A^2*B*a^4*c^3)*e^7 - (12*A*a^5*c^8*d^2 - 10*B*a^6*c^7*d*e - 3*A*a^6*c^7*e^2)*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)))*sqrt((144*A^2*c^3*d^5 - 240*A*B*a*c^2*d^4*e + 240*A*B*a^2*c*d^2*e^3 - 30*A*B*a^3*e^5 + a^5*c^4*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)) + 20*(5*B^2*a^2*c - 9*A^2*a*c^2)*d^3*e^2 - 15*(5*B^2*a^3 - 3*A^2*a^2*c)*d*e^4)/(a^5*c^4))) - (a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*A^2*c^3*d^5 - 240*A*B*a*c^2*d^4*e + 240*A*B*a^2*c*d^2*e^3 - 30*A*B*a^3*e^5 + a^5*c^4*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)) + 20*(5*B^2*a^2*c - 9*A^2*a*c^2)*d^3*e^2 - 15*(5*B^2*a^3 - 3*A^2*a^2*c)*d*e^4)/(a^5*c^4))*log(-(4320*A^3*B*c^4*d^5*e^4 - 432*(25*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^5 + 360*(25*A*B^3*a^2*c^2 - 3*A^3*B*a*c^3)*d^3*e^6 - 4*(625*B^4*a^3*c - 1350*A^2*B^2*a^2*c^2 - 243*A^4*a*c^3)*d^2*e^7 - 30*(125*A*B^3*a^3*c + 27*A^3*B*a^2*c^2)*d*e^8 + (625*B^4*a^4 - 81*A^4*a^2*c^2)*e^9)*sqrt(e*x + d) - (180*A^2*B*a^3*c^4*d^2*e^5 - 6*(50*A*B^2*a^4*c^3 + 9*A^3*a^3*c^4)*d*e^6 + 5*(25*B^3*a^5*c^2 + 9*A^2*B*a^4*c^3)*e^7 - (12*A*a^5*c^8*d^2 - 10*B*a^6*c^7*d*e - 3*A*a^6*c^7*e^2)*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)))*sqrt((144*A^2*c^3*d^5 - 240*A*B*a*c^2*d^4*e + 240*A*B*a^2*c*d^2*e^3 - 30*A*B*a^3*e^5 + a^5*c^4*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)) + 20*(5*B^2*a^2*c - 9*A^2*a*c^2)*d^3*e^2 - 15*(5*B^2*a^3 - 3*A^2*a^2*c)*d*e^4)/(a^5*c^4))) + (a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*A^2*c^3*d^5 - 240*A*B*a*c^2*d^4*e + 240*A*B*a^2*c*d^2*e^3 - 30*A*B*a^3*e^5 - a^5*c^4*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)) + 20*(5*B^2*a^2*c - 9*A^2*a*c^2)*d^3*e^2 - 15*(5*B^2*a^3 - 3*A^2*a^2*c)*d*e^4)/(a^5*c^4))*log(-(4320*A^3*B*c^4*d^5*e^4 - 432*(25*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^5 + 360*(25*A*B^3*a^2*c^2 - 3*A^3*B*a*c^3)*d^3*e^6 - 4*(625*B^4*a^3*c - 1350*A^2*B^2*a^2*c^2 - 243*A^4*a*c^3)*d^2*e^7 - 30*(125*A*B^3*a^3*c + 27*A^3*B*a^2*c^2)*d*e^8 + (625*B^4*a^4 - 81*A^4*a^2*c^2)*e^9)*sqrt(e*x + d) + (180*A^2*B*a^3*c^4*d^2*e^5 - 6*(50*A*B^2*a^4*c^3 + 9*A^3*a^3*c^4)*d*e^6 + 5*(25*B^3*a^5*c^2 + 9*A^2*B*a^4*c^3)*e^7 + (12*A*a^5*c^8*d^2 - 10*B*a^6*c^7*d*e - 3*A*a^6*c^7*e^2)*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)))*sqrt((144*A^2*c^3*d^5 - 240*A*B*a*c^2*d^4*e + 240*A*B*a^2*c*d^2*e^3 - 30*A*B*a^3*e^5 - a^5*c^4*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)) + 20*(5*B^2*a^2*c - 9*A^2*a*c^2)*d^3*e^2 - 15*(5*B^2*a^3 - 3*A^2*a^2*c)*d*e^4)/(a^5*c^4))) - (a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*A^2*c^3*d^5 - 240*A*B*a*c^2*d^4*e + 240*A*B*a^2*c*d^2*e^3 - 30*A*B*a^3*e^5 - a^5*c^4*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)) + 20*(5*B^2*a^2*c - 9*A^2*a*c^2)*d^3*e^2 - 15*(5*B^2*a^3 - 3*A^2*a^2*c)*d*e^4)/(a^5*c^4))*log(-(4320*A^3*B*c^4*d^5*e^4 - 432*(25*A^2*B^2*a*c^3 + 3*A^4*c^4)*d^4*e^5 + 360*(25*A*B^3*a^2*c^2 - 3*A^3*B*a*c^3)*d^3*e^6 - 4*(625*B^4*a^3*c - 1350*A^2*B^2*a^2*c^2 - 243*A^4*a*c^3)*d^2*e^7 - 30*(125*A*B^3*a^3*c + 27*A^3*B*a^2*c^2)*d*e^8 + (625*B^4*a^4 - 81*A^4*a^2*c^2)*e^9)*sqrt(e*x + d) - (180*A^2*B*a^3*c^4*d^2*e^5 - 6*(50*A*B^2*a^4*c^3 + 9*A^3*a^3*c^4)*d*e^6 + 5*(25*B^3*a^5*c^2 + 9*A^2*B*a^4*c^3)*e^7 + (12*A*a^5*c^8*d^2 - 10*B*a^6*c^7*d*e - 3*A*a^6*c^7*e^2)*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)))*sqrt((144*A^2*c^3*d^5 - 240*A*B*a*c^2*d^4*e + 240*A*B*a^2*c*d^2*e^3 - 30*A*B*a^3*e^5 - a^5*c^4*sqrt((900*A^2*B^2*c^2*d^2*e^8 - 60*(25*A*B^3*a*c + 9*A^3*B*c^2)*d*e^9 + (625*B^4*a^2 + 450*A^2*B^2*a*c + 81*A^4*c^2)*e^10)/(a^5*c^9)) + 20*(5*B^2*a^2*c - 9*A^2*a*c^2)*d^3*e^2 - 15*(5*B^2*a^3 - 3*A^2*a^2*c)*d*e^4)/(a^5*c^4))) - 4*(4*B*a^2*c*d^2 + 7*A*a^2*c*d*e - 5*B*a^3*e^2 - (6*A*c^3*d^2 - 5*B*a*c^2*d*e - 3*A*a*c^2*e^2)*x^3 + (A*a*c^2*d*e + 9*B*a^2*c*e^2)*x^2 + (10*A*a*c^2*d^2 + 3*B*a^2*c*d*e + A*a^2*c*e^2)*x)*sqrt(e*x + d))/(a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)","B",0
1460,1,4176,0,1.855723," ","integrate((B*x+A)*(e*x+d)^(3/2)/(-c*x^2+a)^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{16 \, A^{2} c^{3} d^{5} - 16 \, A B a c^{2} d^{4} e + 16 \, A B a^{2} c d^{2} e^{3} - 2 \, A B a^{3} e^{5} + 4 \, {\left(B^{2} a^{2} c - 5 \, A^{2} a c^{2}\right)} d^{3} e^{2} - {\left(3 \, B^{2} a^{3} - 5 \, A^{2} a^{2} c\right)} d e^{4} + {\left(a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}}{a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}}} \log\left(-27 \, {\left(32 \, A^{3} B c^{4} d^{5} e^{4} - 16 \, {\left(3 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{5} + 8 \, {\left(3 \, A B^{3} a^{2} c^{2} - A^{3} B a c^{3}\right)} d^{3} e^{6} - 4 \, {\left(B^{4} a^{3} c - 6 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{7} - 2 \, {\left(5 \, A B^{3} a^{3} c + 3 \, A^{3} B a^{2} c^{2}\right)} d e^{8} + {\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(4 \, A^{2} B a^{3} c^{4} d^{3} e^{5} - 2 \, {\left(2 \, A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} d^{2} e^{6} + {\left(B^{3} a^{5} c^{2} - A^{2} B a^{4} c^{3}\right)} d e^{7} + {\left(A B^{2} a^{5} c^{2} + A^{3} a^{4} c^{3}\right)} e^{8} + {\left(4 \, A a^{5} c^{8} d^{5} - 2 \, B a^{6} c^{7} d^{4} e - 7 \, A a^{6} c^{7} d^{3} e^{2} + 3 \, B a^{7} c^{6} d^{2} e^{3} + 3 \, A a^{7} c^{6} d e^{4} - B a^{8} c^{5} e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}\right)} \sqrt{\frac{16 \, A^{2} c^{3} d^{5} - 16 \, A B a c^{2} d^{4} e + 16 \, A B a^{2} c d^{2} e^{3} - 2 \, A B a^{3} e^{5} + 4 \, {\left(B^{2} a^{2} c - 5 \, A^{2} a c^{2}\right)} d^{3} e^{2} - {\left(3 \, B^{2} a^{3} - 5 \, A^{2} a^{2} c\right)} d e^{4} + {\left(a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}}{a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{16 \, A^{2} c^{3} d^{5} - 16 \, A B a c^{2} d^{4} e + 16 \, A B a^{2} c d^{2} e^{3} - 2 \, A B a^{3} e^{5} + 4 \, {\left(B^{2} a^{2} c - 5 \, A^{2} a c^{2}\right)} d^{3} e^{2} - {\left(3 \, B^{2} a^{3} - 5 \, A^{2} a^{2} c\right)} d e^{4} + {\left(a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}}{a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}}} \log\left(-27 \, {\left(32 \, A^{3} B c^{4} d^{5} e^{4} - 16 \, {\left(3 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{5} + 8 \, {\left(3 \, A B^{3} a^{2} c^{2} - A^{3} B a c^{3}\right)} d^{3} e^{6} - 4 \, {\left(B^{4} a^{3} c - 6 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{7} - 2 \, {\left(5 \, A B^{3} a^{3} c + 3 \, A^{3} B a^{2} c^{2}\right)} d e^{8} + {\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(4 \, A^{2} B a^{3} c^{4} d^{3} e^{5} - 2 \, {\left(2 \, A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} d^{2} e^{6} + {\left(B^{3} a^{5} c^{2} - A^{2} B a^{4} c^{3}\right)} d e^{7} + {\left(A B^{2} a^{5} c^{2} + A^{3} a^{4} c^{3}\right)} e^{8} + {\left(4 \, A a^{5} c^{8} d^{5} - 2 \, B a^{6} c^{7} d^{4} e - 7 \, A a^{6} c^{7} d^{3} e^{2} + 3 \, B a^{7} c^{6} d^{2} e^{3} + 3 \, A a^{7} c^{6} d e^{4} - B a^{8} c^{5} e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}\right)} \sqrt{\frac{16 \, A^{2} c^{3} d^{5} - 16 \, A B a c^{2} d^{4} e + 16 \, A B a^{2} c d^{2} e^{3} - 2 \, A B a^{3} e^{5} + 4 \, {\left(B^{2} a^{2} c - 5 \, A^{2} a c^{2}\right)} d^{3} e^{2} - {\left(3 \, B^{2} a^{3} - 5 \, A^{2} a^{2} c\right)} d e^{4} + {\left(a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}}{a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}}}\right) + 3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{16 \, A^{2} c^{3} d^{5} - 16 \, A B a c^{2} d^{4} e + 16 \, A B a^{2} c d^{2} e^{3} - 2 \, A B a^{3} e^{5} + 4 \, {\left(B^{2} a^{2} c - 5 \, A^{2} a c^{2}\right)} d^{3} e^{2} - {\left(3 \, B^{2} a^{3} - 5 \, A^{2} a^{2} c\right)} d e^{4} - {\left(a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}}{a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}}} \log\left(-27 \, {\left(32 \, A^{3} B c^{4} d^{5} e^{4} - 16 \, {\left(3 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{5} + 8 \, {\left(3 \, A B^{3} a^{2} c^{2} - A^{3} B a c^{3}\right)} d^{3} e^{6} - 4 \, {\left(B^{4} a^{3} c - 6 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{7} - 2 \, {\left(5 \, A B^{3} a^{3} c + 3 \, A^{3} B a^{2} c^{2}\right)} d e^{8} + {\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(4 \, A^{2} B a^{3} c^{4} d^{3} e^{5} - 2 \, {\left(2 \, A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} d^{2} e^{6} + {\left(B^{3} a^{5} c^{2} - A^{2} B a^{4} c^{3}\right)} d e^{7} + {\left(A B^{2} a^{5} c^{2} + A^{3} a^{4} c^{3}\right)} e^{8} - {\left(4 \, A a^{5} c^{8} d^{5} - 2 \, B a^{6} c^{7} d^{4} e - 7 \, A a^{6} c^{7} d^{3} e^{2} + 3 \, B a^{7} c^{6} d^{2} e^{3} + 3 \, A a^{7} c^{6} d e^{4} - B a^{8} c^{5} e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}\right)} \sqrt{\frac{16 \, A^{2} c^{3} d^{5} - 16 \, A B a c^{2} d^{4} e + 16 \, A B a^{2} c d^{2} e^{3} - 2 \, A B a^{3} e^{5} + 4 \, {\left(B^{2} a^{2} c - 5 \, A^{2} a c^{2}\right)} d^{3} e^{2} - {\left(3 \, B^{2} a^{3} - 5 \, A^{2} a^{2} c\right)} d e^{4} - {\left(a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}}{a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{16 \, A^{2} c^{3} d^{5} - 16 \, A B a c^{2} d^{4} e + 16 \, A B a^{2} c d^{2} e^{3} - 2 \, A B a^{3} e^{5} + 4 \, {\left(B^{2} a^{2} c - 5 \, A^{2} a c^{2}\right)} d^{3} e^{2} - {\left(3 \, B^{2} a^{3} - 5 \, A^{2} a^{2} c\right)} d e^{4} - {\left(a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}}{a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}}} \log\left(-27 \, {\left(32 \, A^{3} B c^{4} d^{5} e^{4} - 16 \, {\left(3 \, A^{2} B^{2} a c^{3} + A^{4} c^{4}\right)} d^{4} e^{5} + 8 \, {\left(3 \, A B^{3} a^{2} c^{2} - A^{3} B a c^{3}\right)} d^{3} e^{6} - 4 \, {\left(B^{4} a^{3} c - 6 \, A^{2} B^{2} a^{2} c^{2} - 3 \, A^{4} a c^{3}\right)} d^{2} e^{7} - 2 \, {\left(5 \, A B^{3} a^{3} c + 3 \, A^{3} B a^{2} c^{2}\right)} d e^{8} + {\left(B^{4} a^{4} - A^{4} a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(4 \, A^{2} B a^{3} c^{4} d^{3} e^{5} - 2 \, {\left(2 \, A B^{2} a^{4} c^{3} + A^{3} a^{3} c^{4}\right)} d^{2} e^{6} + {\left(B^{3} a^{5} c^{2} - A^{2} B a^{4} c^{3}\right)} d e^{7} + {\left(A B^{2} a^{5} c^{2} + A^{3} a^{4} c^{3}\right)} e^{8} - {\left(4 \, A a^{5} c^{8} d^{5} - 2 \, B a^{6} c^{7} d^{4} e - 7 \, A a^{6} c^{7} d^{3} e^{2} + 3 \, B a^{7} c^{6} d^{2} e^{3} + 3 \, A a^{7} c^{6} d e^{4} - B a^{8} c^{5} e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}\right)} \sqrt{\frac{16 \, A^{2} c^{3} d^{5} - 16 \, A B a c^{2} d^{4} e + 16 \, A B a^{2} c d^{2} e^{3} - 2 \, A B a^{3} e^{5} + 4 \, {\left(B^{2} a^{2} c - 5 \, A^{2} a c^{2}\right)} d^{3} e^{2} - {\left(3 \, B^{2} a^{3} - 5 \, A^{2} a^{2} c\right)} d e^{4} - {\left(a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} c^{2} d^{2} e^{8} - 4 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e^{9} + {\left(B^{4} a^{2} + 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{10}}{a^{5} c^{9} d^{4} - 2 \, a^{6} c^{8} d^{2} e^{2} + a^{7} c^{7} e^{4}}}}{a^{5} c^{4} d^{2} - a^{6} c^{3} e^{2}}}\right) - 4 \, {\left(A a c e x^{2} + 4 \, B a^{2} d + 3 \, A a^{2} e - 3 \, {\left(2 \, A c^{2} d - B a c e\right)} x^{3} + {\left(10 \, A a c d + B a^{2} e\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"-1/64*(3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((16*A^2*c^3*d^5 - 16*A*B*a*c^2*d^4*e + 16*A*B*a^2*c*d^2*e^3 - 2*A*B*a^3*e^5 + 4*(B^2*a^2*c - 5*A^2*a*c^2)*d^3*e^2 - (3*B^2*a^3 - 5*A^2*a^2*c)*d*e^4 + (a^5*c^4*d^2 - a^6*c^3*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))/(a^5*c^4*d^2 - a^6*c^3*e^2))*log(-27*(32*A^3*B*c^4*d^5*e^4 - 16*(3*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^5 + 8*(3*A*B^3*a^2*c^2 - A^3*B*a*c^3)*d^3*e^6 - 4*(B^4*a^3*c - 6*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^7 - 2*(5*A*B^3*a^3*c + 3*A^3*B*a^2*c^2)*d*e^8 + (B^4*a^4 - A^4*a^2*c^2)*e^9)*sqrt(e*x + d) + 27*(4*A^2*B*a^3*c^4*d^3*e^5 - 2*(2*A*B^2*a^4*c^3 + A^3*a^3*c^4)*d^2*e^6 + (B^3*a^5*c^2 - A^2*B*a^4*c^3)*d*e^7 + (A*B^2*a^5*c^2 + A^3*a^4*c^3)*e^8 + (4*A*a^5*c^8*d^5 - 2*B*a^6*c^7*d^4*e - 7*A*a^6*c^7*d^3*e^2 + 3*B*a^7*c^6*d^2*e^3 + 3*A*a^7*c^6*d*e^4 - B*a^8*c^5*e^5)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))*sqrt((16*A^2*c^3*d^5 - 16*A*B*a*c^2*d^4*e + 16*A*B*a^2*c*d^2*e^3 - 2*A*B*a^3*e^5 + 4*(B^2*a^2*c - 5*A^2*a*c^2)*d^3*e^2 - (3*B^2*a^3 - 5*A^2*a^2*c)*d*e^4 + (a^5*c^4*d^2 - a^6*c^3*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))/(a^5*c^4*d^2 - a^6*c^3*e^2))) - 3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((16*A^2*c^3*d^5 - 16*A*B*a*c^2*d^4*e + 16*A*B*a^2*c*d^2*e^3 - 2*A*B*a^3*e^5 + 4*(B^2*a^2*c - 5*A^2*a*c^2)*d^3*e^2 - (3*B^2*a^3 - 5*A^2*a^2*c)*d*e^4 + (a^5*c^4*d^2 - a^6*c^3*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))/(a^5*c^4*d^2 - a^6*c^3*e^2))*log(-27*(32*A^3*B*c^4*d^5*e^4 - 16*(3*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^5 + 8*(3*A*B^3*a^2*c^2 - A^3*B*a*c^3)*d^3*e^6 - 4*(B^4*a^3*c - 6*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^7 - 2*(5*A*B^3*a^3*c + 3*A^3*B*a^2*c^2)*d*e^8 + (B^4*a^4 - A^4*a^2*c^2)*e^9)*sqrt(e*x + d) - 27*(4*A^2*B*a^3*c^4*d^3*e^5 - 2*(2*A*B^2*a^4*c^3 + A^3*a^3*c^4)*d^2*e^6 + (B^3*a^5*c^2 - A^2*B*a^4*c^3)*d*e^7 + (A*B^2*a^5*c^2 + A^3*a^4*c^3)*e^8 + (4*A*a^5*c^8*d^5 - 2*B*a^6*c^7*d^4*e - 7*A*a^6*c^7*d^3*e^2 + 3*B*a^7*c^6*d^2*e^3 + 3*A*a^7*c^6*d*e^4 - B*a^8*c^5*e^5)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))*sqrt((16*A^2*c^3*d^5 - 16*A*B*a*c^2*d^4*e + 16*A*B*a^2*c*d^2*e^3 - 2*A*B*a^3*e^5 + 4*(B^2*a^2*c - 5*A^2*a*c^2)*d^3*e^2 - (3*B^2*a^3 - 5*A^2*a^2*c)*d*e^4 + (a^5*c^4*d^2 - a^6*c^3*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))/(a^5*c^4*d^2 - a^6*c^3*e^2))) + 3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((16*A^2*c^3*d^5 - 16*A*B*a*c^2*d^4*e + 16*A*B*a^2*c*d^2*e^3 - 2*A*B*a^3*e^5 + 4*(B^2*a^2*c - 5*A^2*a*c^2)*d^3*e^2 - (3*B^2*a^3 - 5*A^2*a^2*c)*d*e^4 - (a^5*c^4*d^2 - a^6*c^3*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))/(a^5*c^4*d^2 - a^6*c^3*e^2))*log(-27*(32*A^3*B*c^4*d^5*e^4 - 16*(3*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^5 + 8*(3*A*B^3*a^2*c^2 - A^3*B*a*c^3)*d^3*e^6 - 4*(B^4*a^3*c - 6*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^7 - 2*(5*A*B^3*a^3*c + 3*A^3*B*a^2*c^2)*d*e^8 + (B^4*a^4 - A^4*a^2*c^2)*e^9)*sqrt(e*x + d) + 27*(4*A^2*B*a^3*c^4*d^3*e^5 - 2*(2*A*B^2*a^4*c^3 + A^3*a^3*c^4)*d^2*e^6 + (B^3*a^5*c^2 - A^2*B*a^4*c^3)*d*e^7 + (A*B^2*a^5*c^2 + A^3*a^4*c^3)*e^8 - (4*A*a^5*c^8*d^5 - 2*B*a^6*c^7*d^4*e - 7*A*a^6*c^7*d^3*e^2 + 3*B*a^7*c^6*d^2*e^3 + 3*A*a^7*c^6*d*e^4 - B*a^8*c^5*e^5)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))*sqrt((16*A^2*c^3*d^5 - 16*A*B*a*c^2*d^4*e + 16*A*B*a^2*c*d^2*e^3 - 2*A*B*a^3*e^5 + 4*(B^2*a^2*c - 5*A^2*a*c^2)*d^3*e^2 - (3*B^2*a^3 - 5*A^2*a^2*c)*d*e^4 - (a^5*c^4*d^2 - a^6*c^3*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))/(a^5*c^4*d^2 - a^6*c^3*e^2))) - 3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((16*A^2*c^3*d^5 - 16*A*B*a*c^2*d^4*e + 16*A*B*a^2*c*d^2*e^3 - 2*A*B*a^3*e^5 + 4*(B^2*a^2*c - 5*A^2*a*c^2)*d^3*e^2 - (3*B^2*a^3 - 5*A^2*a^2*c)*d*e^4 - (a^5*c^4*d^2 - a^6*c^3*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))/(a^5*c^4*d^2 - a^6*c^3*e^2))*log(-27*(32*A^3*B*c^4*d^5*e^4 - 16*(3*A^2*B^2*a*c^3 + A^4*c^4)*d^4*e^5 + 8*(3*A*B^3*a^2*c^2 - A^3*B*a*c^3)*d^3*e^6 - 4*(B^4*a^3*c - 6*A^2*B^2*a^2*c^2 - 3*A^4*a*c^3)*d^2*e^7 - 2*(5*A*B^3*a^3*c + 3*A^3*B*a^2*c^2)*d*e^8 + (B^4*a^4 - A^4*a^2*c^2)*e^9)*sqrt(e*x + d) - 27*(4*A^2*B*a^3*c^4*d^3*e^5 - 2*(2*A*B^2*a^4*c^3 + A^3*a^3*c^4)*d^2*e^6 + (B^3*a^5*c^2 - A^2*B*a^4*c^3)*d*e^7 + (A*B^2*a^5*c^2 + A^3*a^4*c^3)*e^8 - (4*A*a^5*c^8*d^5 - 2*B*a^6*c^7*d^4*e - 7*A*a^6*c^7*d^3*e^2 + 3*B*a^7*c^6*d^2*e^3 + 3*A*a^7*c^6*d*e^4 - B*a^8*c^5*e^5)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))*sqrt((16*A^2*c^3*d^5 - 16*A*B*a*c^2*d^4*e + 16*A*B*a^2*c*d^2*e^3 - 2*A*B*a^3*e^5 + 4*(B^2*a^2*c - 5*A^2*a*c^2)*d^3*e^2 - (3*B^2*a^3 - 5*A^2*a^2*c)*d*e^4 - (a^5*c^4*d^2 - a^6*c^3*e^2)*sqrt((4*A^2*B^2*c^2*d^2*e^8 - 4*(A*B^3*a*c + A^3*B*c^2)*d*e^9 + (B^4*a^2 + 2*A^2*B^2*a*c + A^4*c^2)*e^10)/(a^5*c^9*d^4 - 2*a^6*c^8*d^2*e^2 + a^7*c^7*e^4)))/(a^5*c^4*d^2 - a^6*c^3*e^2))) - 4*(A*a*c*e*x^2 + 4*B*a^2*d + 3*A*a^2*e - 3*(2*A*c^2*d - B*a*c*e)*x^3 + (10*A*a*c*d + B*a^2*e)*x)*sqrt(e*x + d))/(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)","B",0
1461,1,8803,0,60.096447," ","integrate((B*x+A)*(e*x+d)^(1/2)/(-c*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(a^{4} c^{2} d^{2} - a^{5} c e^{2} + {\left(a^{2} c^{4} d^{2} - a^{3} c^{3} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} x^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 48 \, A B a c^{3} d^{6} e + 160 \, A B a^{2} c^{2} d^{4} e^{3} - 150 \, A B a^{3} c d^{2} e^{5} + 30 \, A B a^{4} e^{7} + 4 \, {\left(B^{2} a^{2} c^{2} - 105 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, B^{2} a^{3} c - 77 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(B^{2} a^{4} - 7 \, A^{2} a^{3} c\right)} d e^{6} + {\left(a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}}{a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}}} \log\left({\left(4320 \, A^{3} B c^{5} d^{7} e^{4} - 432 \, {\left(5 \, A^{2} B^{2} a c^{4} + 7 \, A^{4} c^{5}\right)} d^{6} e^{5} + 72 \, {\left(5 \, A B^{3} a^{2} c^{3} - 147 \, A^{3} B a c^{4}\right)} d^{5} e^{6} - 4 \, {\left(5 \, B^{4} a^{3} c^{2} - 1674 \, A^{2} B^{2} a^{2} c^{3} - 1971 \, A^{4} a c^{4}\right)} d^{4} e^{7} - 2 \, {\left(647 \, A B^{3} a^{3} c^{2} - 2727 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{8} + 3 \, {\left(27 \, B^{4} a^{4} c - 1672 \, A^{2} B^{2} a^{3} c^{2} - 1875 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{9} + 2 \, {\left(567 \, A B^{3} a^{4} c + 625 \, A^{3} B a^{3} c^{2}\right)} d e^{10} - {\left(81 \, B^{4} a^{5} - 625 \, A^{4} a^{3} c^{2}\right)} e^{11}\right)} \sqrt{e x + d} + {\left(180 \, A^{2} B a^{3} c^{5} d^{6} e^{5} - 6 \, {\left(10 \, A B^{2} a^{4} c^{4} + 21 \, A^{3} a^{3} c^{5}\right)} d^{5} e^{6} + {\left(5 \, B^{3} a^{5} c^{3} - 447 \, A^{2} B a^{4} c^{4}\right)} d^{4} e^{7} + 6 \, {\left(37 \, A B^{2} a^{5} c^{3} + 53 \, A^{3} a^{4} c^{4}\right)} d^{3} e^{8} - 24 \, {\left(B^{3} a^{6} c^{2} - 9 \, A^{2} B a^{5} c^{3}\right)} d^{2} e^{9} - 2 \, {\left(93 \, A B^{2} a^{6} c^{2} + 100 \, A^{3} a^{5} c^{3}\right)} d e^{10} + 3 \, {\left(9 \, B^{3} a^{7} c + 25 \, A^{2} B a^{6} c^{2}\right)} e^{11} - {\left(12 \, A a^{5} c^{9} d^{10} - 2 \, B a^{6} c^{8} d^{9} e - 55 \, A a^{6} c^{8} d^{8} e^{2} + 10 \, B a^{7} c^{7} d^{7} e^{3} + 98 \, A a^{7} c^{7} d^{6} e^{4} - 18 \, B a^{8} c^{6} d^{5} e^{5} - 84 \, A a^{8} c^{6} d^{4} e^{6} + 14 \, B a^{9} c^{5} d^{3} e^{7} + 34 \, A a^{9} c^{5} d^{2} e^{8} - 4 \, B a^{10} c^{4} d e^{9} - 5 \, A a^{10} c^{4} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 48 \, A B a c^{3} d^{6} e + 160 \, A B a^{2} c^{2} d^{4} e^{3} - 150 \, A B a^{3} c d^{2} e^{5} + 30 \, A B a^{4} e^{7} + 4 \, {\left(B^{2} a^{2} c^{2} - 105 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, B^{2} a^{3} c - 77 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(B^{2} a^{4} - 7 \, A^{2} a^{3} c\right)} d e^{6} + {\left(a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}}{a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}}}\right) - {\left(a^{4} c^{2} d^{2} - a^{5} c e^{2} + {\left(a^{2} c^{4} d^{2} - a^{3} c^{3} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} x^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 48 \, A B a c^{3} d^{6} e + 160 \, A B a^{2} c^{2} d^{4} e^{3} - 150 \, A B a^{3} c d^{2} e^{5} + 30 \, A B a^{4} e^{7} + 4 \, {\left(B^{2} a^{2} c^{2} - 105 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, B^{2} a^{3} c - 77 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(B^{2} a^{4} - 7 \, A^{2} a^{3} c\right)} d e^{6} + {\left(a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}}{a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}}} \log\left({\left(4320 \, A^{3} B c^{5} d^{7} e^{4} - 432 \, {\left(5 \, A^{2} B^{2} a c^{4} + 7 \, A^{4} c^{5}\right)} d^{6} e^{5} + 72 \, {\left(5 \, A B^{3} a^{2} c^{3} - 147 \, A^{3} B a c^{4}\right)} d^{5} e^{6} - 4 \, {\left(5 \, B^{4} a^{3} c^{2} - 1674 \, A^{2} B^{2} a^{2} c^{3} - 1971 \, A^{4} a c^{4}\right)} d^{4} e^{7} - 2 \, {\left(647 \, A B^{3} a^{3} c^{2} - 2727 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{8} + 3 \, {\left(27 \, B^{4} a^{4} c - 1672 \, A^{2} B^{2} a^{3} c^{2} - 1875 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{9} + 2 \, {\left(567 \, A B^{3} a^{4} c + 625 \, A^{3} B a^{3} c^{2}\right)} d e^{10} - {\left(81 \, B^{4} a^{5} - 625 \, A^{4} a^{3} c^{2}\right)} e^{11}\right)} \sqrt{e x + d} - {\left(180 \, A^{2} B a^{3} c^{5} d^{6} e^{5} - 6 \, {\left(10 \, A B^{2} a^{4} c^{4} + 21 \, A^{3} a^{3} c^{5}\right)} d^{5} e^{6} + {\left(5 \, B^{3} a^{5} c^{3} - 447 \, A^{2} B a^{4} c^{4}\right)} d^{4} e^{7} + 6 \, {\left(37 \, A B^{2} a^{5} c^{3} + 53 \, A^{3} a^{4} c^{4}\right)} d^{3} e^{8} - 24 \, {\left(B^{3} a^{6} c^{2} - 9 \, A^{2} B a^{5} c^{3}\right)} d^{2} e^{9} - 2 \, {\left(93 \, A B^{2} a^{6} c^{2} + 100 \, A^{3} a^{5} c^{3}\right)} d e^{10} + 3 \, {\left(9 \, B^{3} a^{7} c + 25 \, A^{2} B a^{6} c^{2}\right)} e^{11} - {\left(12 \, A a^{5} c^{9} d^{10} - 2 \, B a^{6} c^{8} d^{9} e - 55 \, A a^{6} c^{8} d^{8} e^{2} + 10 \, B a^{7} c^{7} d^{7} e^{3} + 98 \, A a^{7} c^{7} d^{6} e^{4} - 18 \, B a^{8} c^{6} d^{5} e^{5} - 84 \, A a^{8} c^{6} d^{4} e^{6} + 14 \, B a^{9} c^{5} d^{3} e^{7} + 34 \, A a^{9} c^{5} d^{2} e^{8} - 4 \, B a^{10} c^{4} d e^{9} - 5 \, A a^{10} c^{4} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 48 \, A B a c^{3} d^{6} e + 160 \, A B a^{2} c^{2} d^{4} e^{3} - 150 \, A B a^{3} c d^{2} e^{5} + 30 \, A B a^{4} e^{7} + 4 \, {\left(B^{2} a^{2} c^{2} - 105 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, B^{2} a^{3} c - 77 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(B^{2} a^{4} - 7 \, A^{2} a^{3} c\right)} d e^{6} + {\left(a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}}{a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}}}\right) + {\left(a^{4} c^{2} d^{2} - a^{5} c e^{2} + {\left(a^{2} c^{4} d^{2} - a^{3} c^{3} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} x^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 48 \, A B a c^{3} d^{6} e + 160 \, A B a^{2} c^{2} d^{4} e^{3} - 150 \, A B a^{3} c d^{2} e^{5} + 30 \, A B a^{4} e^{7} + 4 \, {\left(B^{2} a^{2} c^{2} - 105 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, B^{2} a^{3} c - 77 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(B^{2} a^{4} - 7 \, A^{2} a^{3} c\right)} d e^{6} - {\left(a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}}{a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}}} \log\left({\left(4320 \, A^{3} B c^{5} d^{7} e^{4} - 432 \, {\left(5 \, A^{2} B^{2} a c^{4} + 7 \, A^{4} c^{5}\right)} d^{6} e^{5} + 72 \, {\left(5 \, A B^{3} a^{2} c^{3} - 147 \, A^{3} B a c^{4}\right)} d^{5} e^{6} - 4 \, {\left(5 \, B^{4} a^{3} c^{2} - 1674 \, A^{2} B^{2} a^{2} c^{3} - 1971 \, A^{4} a c^{4}\right)} d^{4} e^{7} - 2 \, {\left(647 \, A B^{3} a^{3} c^{2} - 2727 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{8} + 3 \, {\left(27 \, B^{4} a^{4} c - 1672 \, A^{2} B^{2} a^{3} c^{2} - 1875 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{9} + 2 \, {\left(567 \, A B^{3} a^{4} c + 625 \, A^{3} B a^{3} c^{2}\right)} d e^{10} - {\left(81 \, B^{4} a^{5} - 625 \, A^{4} a^{3} c^{2}\right)} e^{11}\right)} \sqrt{e x + d} + {\left(180 \, A^{2} B a^{3} c^{5} d^{6} e^{5} - 6 \, {\left(10 \, A B^{2} a^{4} c^{4} + 21 \, A^{3} a^{3} c^{5}\right)} d^{5} e^{6} + {\left(5 \, B^{3} a^{5} c^{3} - 447 \, A^{2} B a^{4} c^{4}\right)} d^{4} e^{7} + 6 \, {\left(37 \, A B^{2} a^{5} c^{3} + 53 \, A^{3} a^{4} c^{4}\right)} d^{3} e^{8} - 24 \, {\left(B^{3} a^{6} c^{2} - 9 \, A^{2} B a^{5} c^{3}\right)} d^{2} e^{9} - 2 \, {\left(93 \, A B^{2} a^{6} c^{2} + 100 \, A^{3} a^{5} c^{3}\right)} d e^{10} + 3 \, {\left(9 \, B^{3} a^{7} c + 25 \, A^{2} B a^{6} c^{2}\right)} e^{11} + {\left(12 \, A a^{5} c^{9} d^{10} - 2 \, B a^{6} c^{8} d^{9} e - 55 \, A a^{6} c^{8} d^{8} e^{2} + 10 \, B a^{7} c^{7} d^{7} e^{3} + 98 \, A a^{7} c^{7} d^{6} e^{4} - 18 \, B a^{8} c^{6} d^{5} e^{5} - 84 \, A a^{8} c^{6} d^{4} e^{6} + 14 \, B a^{9} c^{5} d^{3} e^{7} + 34 \, A a^{9} c^{5} d^{2} e^{8} - 4 \, B a^{10} c^{4} d e^{9} - 5 \, A a^{10} c^{4} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 48 \, A B a c^{3} d^{6} e + 160 \, A B a^{2} c^{2} d^{4} e^{3} - 150 \, A B a^{3} c d^{2} e^{5} + 30 \, A B a^{4} e^{7} + 4 \, {\left(B^{2} a^{2} c^{2} - 105 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, B^{2} a^{3} c - 77 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(B^{2} a^{4} - 7 \, A^{2} a^{3} c\right)} d e^{6} - {\left(a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}}{a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}}}\right) - {\left(a^{4} c^{2} d^{2} - a^{5} c e^{2} + {\left(a^{2} c^{4} d^{2} - a^{3} c^{3} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} x^{2}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 48 \, A B a c^{3} d^{6} e + 160 \, A B a^{2} c^{2} d^{4} e^{3} - 150 \, A B a^{3} c d^{2} e^{5} + 30 \, A B a^{4} e^{7} + 4 \, {\left(B^{2} a^{2} c^{2} - 105 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, B^{2} a^{3} c - 77 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(B^{2} a^{4} - 7 \, A^{2} a^{3} c\right)} d e^{6} - {\left(a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}}{a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}}} \log\left({\left(4320 \, A^{3} B c^{5} d^{7} e^{4} - 432 \, {\left(5 \, A^{2} B^{2} a c^{4} + 7 \, A^{4} c^{5}\right)} d^{6} e^{5} + 72 \, {\left(5 \, A B^{3} a^{2} c^{3} - 147 \, A^{3} B a c^{4}\right)} d^{5} e^{6} - 4 \, {\left(5 \, B^{4} a^{3} c^{2} - 1674 \, A^{2} B^{2} a^{2} c^{3} - 1971 \, A^{4} a c^{4}\right)} d^{4} e^{7} - 2 \, {\left(647 \, A B^{3} a^{3} c^{2} - 2727 \, A^{3} B a^{2} c^{3}\right)} d^{3} e^{8} + 3 \, {\left(27 \, B^{4} a^{4} c - 1672 \, A^{2} B^{2} a^{3} c^{2} - 1875 \, A^{4} a^{2} c^{3}\right)} d^{2} e^{9} + 2 \, {\left(567 \, A B^{3} a^{4} c + 625 \, A^{3} B a^{3} c^{2}\right)} d e^{10} - {\left(81 \, B^{4} a^{5} - 625 \, A^{4} a^{3} c^{2}\right)} e^{11}\right)} \sqrt{e x + d} - {\left(180 \, A^{2} B a^{3} c^{5} d^{6} e^{5} - 6 \, {\left(10 \, A B^{2} a^{4} c^{4} + 21 \, A^{3} a^{3} c^{5}\right)} d^{5} e^{6} + {\left(5 \, B^{3} a^{5} c^{3} - 447 \, A^{2} B a^{4} c^{4}\right)} d^{4} e^{7} + 6 \, {\left(37 \, A B^{2} a^{5} c^{3} + 53 \, A^{3} a^{4} c^{4}\right)} d^{3} e^{8} - 24 \, {\left(B^{3} a^{6} c^{2} - 9 \, A^{2} B a^{5} c^{3}\right)} d^{2} e^{9} - 2 \, {\left(93 \, A B^{2} a^{6} c^{2} + 100 \, A^{3} a^{5} c^{3}\right)} d e^{10} + 3 \, {\left(9 \, B^{3} a^{7} c + 25 \, A^{2} B a^{6} c^{2}\right)} e^{11} + {\left(12 \, A a^{5} c^{9} d^{10} - 2 \, B a^{6} c^{8} d^{9} e - 55 \, A a^{6} c^{8} d^{8} e^{2} + 10 \, B a^{7} c^{7} d^{7} e^{3} + 98 \, A a^{7} c^{7} d^{6} e^{4} - 18 \, B a^{8} c^{6} d^{5} e^{5} - 84 \, A a^{8} c^{6} d^{4} e^{6} + 14 \, B a^{9} c^{5} d^{3} e^{7} + 34 \, A a^{9} c^{5} d^{2} e^{8} - 4 \, B a^{10} c^{4} d e^{9} - 5 \, A a^{10} c^{4} e^{10}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}\right)} \sqrt{\frac{144 \, A^{2} c^{4} d^{7} - 48 \, A B a c^{3} d^{6} e + 160 \, A B a^{2} c^{2} d^{4} e^{3} - 150 \, A B a^{3} c d^{2} e^{5} + 30 \, A B a^{4} e^{7} + 4 \, {\left(B^{2} a^{2} c^{2} - 105 \, A^{2} a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, B^{2} a^{3} c - 77 \, A^{2} a^{2} c^{2}\right)} d^{3} e^{4} + 15 \, {\left(B^{2} a^{4} - 7 \, A^{2} a^{3} c\right)} d e^{6} - {\left(a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}\right)} \sqrt{\frac{900 \, A^{2} B^{2} c^{4} d^{6} e^{8} - 60 \, {\left(5 \, A B^{3} a c^{3} + 21 \, A^{3} B c^{4}\right)} d^{5} e^{9} + {\left(25 \, B^{4} a^{2} c^{2} - 2070 \, A^{2} B^{2} a c^{3} + 441 \, A^{4} c^{4}\right)} d^{4} e^{10} + 8 \, {\left(115 \, A B^{3} a^{2} c^{2} + 387 \, A^{3} B a c^{3}\right)} d^{3} e^{11} - 6 \, {\left(15 \, B^{4} a^{3} c - 136 \, A^{2} B^{2} a^{2} c^{2} + 175 \, A^{4} a c^{3}\right)} d^{2} e^{12} - 76 \, {\left(9 \, A B^{3} a^{3} c + 25 \, A^{3} B a^{2} c^{2}\right)} d e^{13} + {\left(81 \, B^{4} a^{4} + 450 \, A^{2} B^{2} a^{3} c + 625 \, A^{4} a^{2} c^{2}\right)} e^{14}}{a^{5} c^{11} d^{12} - 6 \, a^{6} c^{10} d^{10} e^{2} + 15 \, a^{7} c^{9} d^{8} e^{4} - 20 \, a^{8} c^{8} d^{6} e^{6} + 15 \, a^{9} c^{7} d^{4} e^{8} - 6 \, a^{10} c^{6} d^{2} e^{10} + a^{11} c^{5} e^{12}}}}{a^{5} c^{5} d^{6} - 3 \, a^{6} c^{4} d^{4} e^{2} + 3 \, a^{7} c^{3} d^{2} e^{4} - a^{8} c^{2} e^{6}}}\right) + 4 \, {\left(4 \, B a^{2} c d^{2} - A a^{2} c d e - 3 \, B a^{3} e^{2} - {\left(6 \, A c^{3} d^{2} - B a c^{2} d e - 5 \, A a c^{2} e^{2}\right)} x^{3} + {\left(A a c^{2} d e - B a^{2} c e^{2}\right)} x^{2} + {\left(10 \, A a c^{2} d^{2} - B a^{2} c d e - 9 \, A a^{2} c e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{4} c^{2} d^{2} - a^{5} c e^{2} + {\left(a^{2} c^{4} d^{2} - a^{3} c^{3} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{2} - a^{4} c^{2} e^{2}\right)} x^{2}\right)}}"," ",0,"1/64*((a^4*c^2*d^2 - a^5*c*e^2 + (a^2*c^4*d^2 - a^3*c^3*e^2)*x^4 - 2*(a^3*c^3*d^2 - a^4*c^2*e^2)*x^2)*sqrt((144*A^2*c^4*d^7 - 48*A*B*a*c^3*d^6*e + 160*A*B*a^2*c^2*d^4*e^3 - 150*A*B*a^3*c*d^2*e^5 + 30*A*B*a^4*e^7 + 4*(B^2*a^2*c^2 - 105*A^2*a*c^3)*d^5*e^2 - 5*(3*B^2*a^3*c - 77*A^2*a^2*c^2)*d^3*e^4 + 15*(B^2*a^4 - 7*A^2*a^3*c)*d*e^6 + (a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))/(a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6))*log((4320*A^3*B*c^5*d^7*e^4 - 432*(5*A^2*B^2*a*c^4 + 7*A^4*c^5)*d^6*e^5 + 72*(5*A*B^3*a^2*c^3 - 147*A^3*B*a*c^4)*d^5*e^6 - 4*(5*B^4*a^3*c^2 - 1674*A^2*B^2*a^2*c^3 - 1971*A^4*a*c^4)*d^4*e^7 - 2*(647*A*B^3*a^3*c^2 - 2727*A^3*B*a^2*c^3)*d^3*e^8 + 3*(27*B^4*a^4*c - 1672*A^2*B^2*a^3*c^2 - 1875*A^4*a^2*c^3)*d^2*e^9 + 2*(567*A*B^3*a^4*c + 625*A^3*B*a^3*c^2)*d*e^10 - (81*B^4*a^5 - 625*A^4*a^3*c^2)*e^11)*sqrt(e*x + d) + (180*A^2*B*a^3*c^5*d^6*e^5 - 6*(10*A*B^2*a^4*c^4 + 21*A^3*a^3*c^5)*d^5*e^6 + (5*B^3*a^5*c^3 - 447*A^2*B*a^4*c^4)*d^4*e^7 + 6*(37*A*B^2*a^5*c^3 + 53*A^3*a^4*c^4)*d^3*e^8 - 24*(B^3*a^6*c^2 - 9*A^2*B*a^5*c^3)*d^2*e^9 - 2*(93*A*B^2*a^6*c^2 + 100*A^3*a^5*c^3)*d*e^10 + 3*(9*B^3*a^7*c + 25*A^2*B*a^6*c^2)*e^11 - (12*A*a^5*c^9*d^10 - 2*B*a^6*c^8*d^9*e - 55*A*a^6*c^8*d^8*e^2 + 10*B*a^7*c^7*d^7*e^3 + 98*A*a^7*c^7*d^6*e^4 - 18*B*a^8*c^6*d^5*e^5 - 84*A*a^8*c^6*d^4*e^6 + 14*B*a^9*c^5*d^3*e^7 + 34*A*a^9*c^5*d^2*e^8 - 4*B*a^10*c^4*d*e^9 - 5*A*a^10*c^4*e^10)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))*sqrt((144*A^2*c^4*d^7 - 48*A*B*a*c^3*d^6*e + 160*A*B*a^2*c^2*d^4*e^3 - 150*A*B*a^3*c*d^2*e^5 + 30*A*B*a^4*e^7 + 4*(B^2*a^2*c^2 - 105*A^2*a*c^3)*d^5*e^2 - 5*(3*B^2*a^3*c - 77*A^2*a^2*c^2)*d^3*e^4 + 15*(B^2*a^4 - 7*A^2*a^3*c)*d*e^6 + (a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))/(a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6))) - (a^4*c^2*d^2 - a^5*c*e^2 + (a^2*c^4*d^2 - a^3*c^3*e^2)*x^4 - 2*(a^3*c^3*d^2 - a^4*c^2*e^2)*x^2)*sqrt((144*A^2*c^4*d^7 - 48*A*B*a*c^3*d^6*e + 160*A*B*a^2*c^2*d^4*e^3 - 150*A*B*a^3*c*d^2*e^5 + 30*A*B*a^4*e^7 + 4*(B^2*a^2*c^2 - 105*A^2*a*c^3)*d^5*e^2 - 5*(3*B^2*a^3*c - 77*A^2*a^2*c^2)*d^3*e^4 + 15*(B^2*a^4 - 7*A^2*a^3*c)*d*e^6 + (a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))/(a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6))*log((4320*A^3*B*c^5*d^7*e^4 - 432*(5*A^2*B^2*a*c^4 + 7*A^4*c^5)*d^6*e^5 + 72*(5*A*B^3*a^2*c^3 - 147*A^3*B*a*c^4)*d^5*e^6 - 4*(5*B^4*a^3*c^2 - 1674*A^2*B^2*a^2*c^3 - 1971*A^4*a*c^4)*d^4*e^7 - 2*(647*A*B^3*a^3*c^2 - 2727*A^3*B*a^2*c^3)*d^3*e^8 + 3*(27*B^4*a^4*c - 1672*A^2*B^2*a^3*c^2 - 1875*A^4*a^2*c^3)*d^2*e^9 + 2*(567*A*B^3*a^4*c + 625*A^3*B*a^3*c^2)*d*e^10 - (81*B^4*a^5 - 625*A^4*a^3*c^2)*e^11)*sqrt(e*x + d) - (180*A^2*B*a^3*c^5*d^6*e^5 - 6*(10*A*B^2*a^4*c^4 + 21*A^3*a^3*c^5)*d^5*e^6 + (5*B^3*a^5*c^3 - 447*A^2*B*a^4*c^4)*d^4*e^7 + 6*(37*A*B^2*a^5*c^3 + 53*A^3*a^4*c^4)*d^3*e^8 - 24*(B^3*a^6*c^2 - 9*A^2*B*a^5*c^3)*d^2*e^9 - 2*(93*A*B^2*a^6*c^2 + 100*A^3*a^5*c^3)*d*e^10 + 3*(9*B^3*a^7*c + 25*A^2*B*a^6*c^2)*e^11 - (12*A*a^5*c^9*d^10 - 2*B*a^6*c^8*d^9*e - 55*A*a^6*c^8*d^8*e^2 + 10*B*a^7*c^7*d^7*e^3 + 98*A*a^7*c^7*d^6*e^4 - 18*B*a^8*c^6*d^5*e^5 - 84*A*a^8*c^6*d^4*e^6 + 14*B*a^9*c^5*d^3*e^7 + 34*A*a^9*c^5*d^2*e^8 - 4*B*a^10*c^4*d*e^9 - 5*A*a^10*c^4*e^10)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))*sqrt((144*A^2*c^4*d^7 - 48*A*B*a*c^3*d^6*e + 160*A*B*a^2*c^2*d^4*e^3 - 150*A*B*a^3*c*d^2*e^5 + 30*A*B*a^4*e^7 + 4*(B^2*a^2*c^2 - 105*A^2*a*c^3)*d^5*e^2 - 5*(3*B^2*a^3*c - 77*A^2*a^2*c^2)*d^3*e^4 + 15*(B^2*a^4 - 7*A^2*a^3*c)*d*e^6 + (a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))/(a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6))) + (a^4*c^2*d^2 - a^5*c*e^2 + (a^2*c^4*d^2 - a^3*c^3*e^2)*x^4 - 2*(a^3*c^3*d^2 - a^4*c^2*e^2)*x^2)*sqrt((144*A^2*c^4*d^7 - 48*A*B*a*c^3*d^6*e + 160*A*B*a^2*c^2*d^4*e^3 - 150*A*B*a^3*c*d^2*e^5 + 30*A*B*a^4*e^7 + 4*(B^2*a^2*c^2 - 105*A^2*a*c^3)*d^5*e^2 - 5*(3*B^2*a^3*c - 77*A^2*a^2*c^2)*d^3*e^4 + 15*(B^2*a^4 - 7*A^2*a^3*c)*d*e^6 - (a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))/(a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6))*log((4320*A^3*B*c^5*d^7*e^4 - 432*(5*A^2*B^2*a*c^4 + 7*A^4*c^5)*d^6*e^5 + 72*(5*A*B^3*a^2*c^3 - 147*A^3*B*a*c^4)*d^5*e^6 - 4*(5*B^4*a^3*c^2 - 1674*A^2*B^2*a^2*c^3 - 1971*A^4*a*c^4)*d^4*e^7 - 2*(647*A*B^3*a^3*c^2 - 2727*A^3*B*a^2*c^3)*d^3*e^8 + 3*(27*B^4*a^4*c - 1672*A^2*B^2*a^3*c^2 - 1875*A^4*a^2*c^3)*d^2*e^9 + 2*(567*A*B^3*a^4*c + 625*A^3*B*a^3*c^2)*d*e^10 - (81*B^4*a^5 - 625*A^4*a^3*c^2)*e^11)*sqrt(e*x + d) + (180*A^2*B*a^3*c^5*d^6*e^5 - 6*(10*A*B^2*a^4*c^4 + 21*A^3*a^3*c^5)*d^5*e^6 + (5*B^3*a^5*c^3 - 447*A^2*B*a^4*c^4)*d^4*e^7 + 6*(37*A*B^2*a^5*c^3 + 53*A^3*a^4*c^4)*d^3*e^8 - 24*(B^3*a^6*c^2 - 9*A^2*B*a^5*c^3)*d^2*e^9 - 2*(93*A*B^2*a^6*c^2 + 100*A^3*a^5*c^3)*d*e^10 + 3*(9*B^3*a^7*c + 25*A^2*B*a^6*c^2)*e^11 + (12*A*a^5*c^9*d^10 - 2*B*a^6*c^8*d^9*e - 55*A*a^6*c^8*d^8*e^2 + 10*B*a^7*c^7*d^7*e^3 + 98*A*a^7*c^7*d^6*e^4 - 18*B*a^8*c^6*d^5*e^5 - 84*A*a^8*c^6*d^4*e^6 + 14*B*a^9*c^5*d^3*e^7 + 34*A*a^9*c^5*d^2*e^8 - 4*B*a^10*c^4*d*e^9 - 5*A*a^10*c^4*e^10)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))*sqrt((144*A^2*c^4*d^7 - 48*A*B*a*c^3*d^6*e + 160*A*B*a^2*c^2*d^4*e^3 - 150*A*B*a^3*c*d^2*e^5 + 30*A*B*a^4*e^7 + 4*(B^2*a^2*c^2 - 105*A^2*a*c^3)*d^5*e^2 - 5*(3*B^2*a^3*c - 77*A^2*a^2*c^2)*d^3*e^4 + 15*(B^2*a^4 - 7*A^2*a^3*c)*d*e^6 - (a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))/(a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6))) - (a^4*c^2*d^2 - a^5*c*e^2 + (a^2*c^4*d^2 - a^3*c^3*e^2)*x^4 - 2*(a^3*c^3*d^2 - a^4*c^2*e^2)*x^2)*sqrt((144*A^2*c^4*d^7 - 48*A*B*a*c^3*d^6*e + 160*A*B*a^2*c^2*d^4*e^3 - 150*A*B*a^3*c*d^2*e^5 + 30*A*B*a^4*e^7 + 4*(B^2*a^2*c^2 - 105*A^2*a*c^3)*d^5*e^2 - 5*(3*B^2*a^3*c - 77*A^2*a^2*c^2)*d^3*e^4 + 15*(B^2*a^4 - 7*A^2*a^3*c)*d*e^6 - (a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))/(a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6))*log((4320*A^3*B*c^5*d^7*e^4 - 432*(5*A^2*B^2*a*c^4 + 7*A^4*c^5)*d^6*e^5 + 72*(5*A*B^3*a^2*c^3 - 147*A^3*B*a*c^4)*d^5*e^6 - 4*(5*B^4*a^3*c^2 - 1674*A^2*B^2*a^2*c^3 - 1971*A^4*a*c^4)*d^4*e^7 - 2*(647*A*B^3*a^3*c^2 - 2727*A^3*B*a^2*c^3)*d^3*e^8 + 3*(27*B^4*a^4*c - 1672*A^2*B^2*a^3*c^2 - 1875*A^4*a^2*c^3)*d^2*e^9 + 2*(567*A*B^3*a^4*c + 625*A^3*B*a^3*c^2)*d*e^10 - (81*B^4*a^5 - 625*A^4*a^3*c^2)*e^11)*sqrt(e*x + d) - (180*A^2*B*a^3*c^5*d^6*e^5 - 6*(10*A*B^2*a^4*c^4 + 21*A^3*a^3*c^5)*d^5*e^6 + (5*B^3*a^5*c^3 - 447*A^2*B*a^4*c^4)*d^4*e^7 + 6*(37*A*B^2*a^5*c^3 + 53*A^3*a^4*c^4)*d^3*e^8 - 24*(B^3*a^6*c^2 - 9*A^2*B*a^5*c^3)*d^2*e^9 - 2*(93*A*B^2*a^6*c^2 + 100*A^3*a^5*c^3)*d*e^10 + 3*(9*B^3*a^7*c + 25*A^2*B*a^6*c^2)*e^11 + (12*A*a^5*c^9*d^10 - 2*B*a^6*c^8*d^9*e - 55*A*a^6*c^8*d^8*e^2 + 10*B*a^7*c^7*d^7*e^3 + 98*A*a^7*c^7*d^6*e^4 - 18*B*a^8*c^6*d^5*e^5 - 84*A*a^8*c^6*d^4*e^6 + 14*B*a^9*c^5*d^3*e^7 + 34*A*a^9*c^5*d^2*e^8 - 4*B*a^10*c^4*d*e^9 - 5*A*a^10*c^4*e^10)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))*sqrt((144*A^2*c^4*d^7 - 48*A*B*a*c^3*d^6*e + 160*A*B*a^2*c^2*d^4*e^3 - 150*A*B*a^3*c*d^2*e^5 + 30*A*B*a^4*e^7 + 4*(B^2*a^2*c^2 - 105*A^2*a*c^3)*d^5*e^2 - 5*(3*B^2*a^3*c - 77*A^2*a^2*c^2)*d^3*e^4 + 15*(B^2*a^4 - 7*A^2*a^3*c)*d*e^6 - (a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6)*sqrt((900*A^2*B^2*c^4*d^6*e^8 - 60*(5*A*B^3*a*c^3 + 21*A^3*B*c^4)*d^5*e^9 + (25*B^4*a^2*c^2 - 2070*A^2*B^2*a*c^3 + 441*A^4*c^4)*d^4*e^10 + 8*(115*A*B^3*a^2*c^2 + 387*A^3*B*a*c^3)*d^3*e^11 - 6*(15*B^4*a^3*c - 136*A^2*B^2*a^2*c^2 + 175*A^4*a*c^3)*d^2*e^12 - 76*(9*A*B^3*a^3*c + 25*A^3*B*a^2*c^2)*d*e^13 + (81*B^4*a^4 + 450*A^2*B^2*a^3*c + 625*A^4*a^2*c^2)*e^14)/(a^5*c^11*d^12 - 6*a^6*c^10*d^10*e^2 + 15*a^7*c^9*d^8*e^4 - 20*a^8*c^8*d^6*e^6 + 15*a^9*c^7*d^4*e^8 - 6*a^10*c^6*d^2*e^10 + a^11*c^5*e^12)))/(a^5*c^5*d^6 - 3*a^6*c^4*d^4*e^2 + 3*a^7*c^3*d^2*e^4 - a^8*c^2*e^6))) + 4*(4*B*a^2*c*d^2 - A*a^2*c*d*e - 3*B*a^3*e^2 - (6*A*c^3*d^2 - B*a*c^2*d*e - 5*A*a*c^2*e^2)*x^3 + (A*a*c^2*d*e - B*a^2*c*e^2)*x^2 + (10*A*a*c^2*d^2 - B*a^2*c*d*e - 9*A*a^2*c*e^2)*x)*sqrt(e*x + d))/(a^4*c^2*d^2 - a^5*c*e^2 + (a^2*c^4*d^2 - a^3*c^3*e^2)*x^4 - 2*(a^3*c^3*d^2 - a^4*c^2*e^2)*x^2)","B",0
1462,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^(1/2)/(-c*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1463,1,236,0,0.442717," ","integrate((B*x+A)/(-B^2*e*x^2-A^2*e+2*A*B*d)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(\frac{B^{2} e^{2} x^{2} + 8 \, B^{2} d^{2} - 6 \, A B d e + A^{2} e^{2} + 4 \, {\left(2 \, B^{2} d e - A B e^{2}\right)} x + \frac{2 \, \sqrt{2} {\left(4 \, B^{3} d^{2} - 4 \, A B^{2} d e + A^{2} B e^{2} + {\left(2 \, B^{3} d e - A B^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{\sqrt{2 \, B^{2} d - A B e}}}{B^{2} e x^{2} - 2 \, A B d + A^{2} e}\right)}{2 \, \sqrt{2 \, B^{2} d - A B e} e}, -\frac{\sqrt{2} \sqrt{-\frac{1}{2 \, B^{2} d - A B e}} \arctan\left(\frac{\sqrt{2} {\left(B e x + 2 \, B d - A e\right)} \sqrt{-\frac{1}{2 \, B^{2} d - A B e}}}{2 \, \sqrt{e x + d}}\right)}{e}\right]"," ",0,"[1/2*sqrt(2)*log((B^2*e^2*x^2 + 8*B^2*d^2 - 6*A*B*d*e + A^2*e^2 + 4*(2*B^2*d*e - A*B*e^2)*x + 2*sqrt(2)*(4*B^3*d^2 - 4*A*B^2*d*e + A^2*B*e^2 + (2*B^3*d*e - A*B^2*e^2)*x)*sqrt(e*x + d)/sqrt(2*B^2*d - A*B*e))/(B^2*e*x^2 - 2*A*B*d + A^2*e))/(sqrt(2*B^2*d - A*B*e)*e), -sqrt(2)*sqrt(-1/(2*B^2*d - A*B*e))*arctan(1/2*sqrt(2)*(B*e*x + 2*B*d - A*e)*sqrt(-1/(2*B^2*d - A*B*e))/sqrt(e*x + d))/e]","A",0
1464,1,164,0,0.440803," ","integrate(2*(B*x+A)/(x^2+1)/(2*(A^2*e-B^2*e)/A/B+4*e*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{2} \sqrt{-\frac{A B}{e}} \log\left(\frac{A^{2} x^{2} - 4 \, A B x - A^{2} + 2 \, B^{2} + 2 \, {\left(A x - B\right)} \sqrt{-\frac{A B}{e}} \sqrt{\frac{2 \, A B e x + {\left(A^{2} - B^{2}\right)} e}{A B}}}{x^{2} + 1}\right), \sqrt{2} \sqrt{\frac{A B}{e}} \arctan\left(\frac{{\left(A x - B\right)} \sqrt{\frac{A B}{e}} \sqrt{\frac{2 \, A B e x + {\left(A^{2} - B^{2}\right)} e}{A B}}}{2 \, A B x + A^{2} - B^{2}}\right)\right]"," ",0,"[1/2*sqrt(2)*sqrt(-A*B/e)*log((A^2*x^2 - 4*A*B*x - A^2 + 2*B^2 + 2*(A*x - B)*sqrt(-A*B/e)*sqrt((2*A*B*e*x + (A^2 - B^2)*e)/(A*B)))/(x^2 + 1)), sqrt(2)*sqrt(A*B/e)*arctan((A*x - B)*sqrt(A*B/e)*sqrt((2*A*B*e*x + (A^2 - B^2)*e)/(A*B))/(2*A*B*x + A^2 - B^2))]","A",0
1465,1,451,0,0.493449," ","integrate((B*x+A)/(-x^2+1)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(A - B\right)} d + {\left(A - B\right)} e\right)} \sqrt{d - e} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d - e} + 2 \, d - e}{x + 1}\right) - {\left({\left(A + B\right)} d - {\left(A + B\right)} e\right)} \sqrt{d + e} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d + e} + 2 \, d + e}{x - 1}\right)}{2 \, {\left(d^{2} - e^{2}\right)}}, -\frac{2 \, {\left({\left(A - B\right)} d + {\left(A - B\right)} e\right)} \sqrt{-d + e} \arctan\left(-\frac{\sqrt{e x + d} \sqrt{-d + e}}{d - e}\right) - {\left({\left(A + B\right)} d - {\left(A + B\right)} e\right)} \sqrt{d + e} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d + e} + 2 \, d + e}{x - 1}\right)}{2 \, {\left(d^{2} - e^{2}\right)}}, -\frac{2 \, {\left({\left(A + B\right)} d - {\left(A + B\right)} e\right)} \sqrt{-d - e} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d - e}}{d + e}\right) + {\left({\left(A - B\right)} d + {\left(A - B\right)} e\right)} \sqrt{d - e} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d - e} + 2 \, d - e}{x + 1}\right)}{2 \, {\left(d^{2} - e^{2}\right)}}, -\frac{{\left({\left(A - B\right)} d + {\left(A - B\right)} e\right)} \sqrt{-d + e} \arctan\left(-\frac{\sqrt{e x + d} \sqrt{-d + e}}{d - e}\right) + {\left({\left(A + B\right)} d - {\left(A + B\right)} e\right)} \sqrt{-d - e} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d - e}}{d + e}\right)}{d^{2} - e^{2}}\right]"," ",0,"[-1/2*(((A - B)*d + (A - B)*e)*sqrt(d - e)*log((e*x + 2*sqrt(e*x + d)*sqrt(d - e) + 2*d - e)/(x + 1)) - ((A + B)*d - (A + B)*e)*sqrt(d + e)*log((e*x + 2*sqrt(e*x + d)*sqrt(d + e) + 2*d + e)/(x - 1)))/(d^2 - e^2), -1/2*(2*((A - B)*d + (A - B)*e)*sqrt(-d + e)*arctan(-sqrt(e*x + d)*sqrt(-d + e)/(d - e)) - ((A + B)*d - (A + B)*e)*sqrt(d + e)*log((e*x + 2*sqrt(e*x + d)*sqrt(d + e) + 2*d + e)/(x - 1)))/(d^2 - e^2), -1/2*(2*((A + B)*d - (A + B)*e)*sqrt(-d - e)*arctan(sqrt(e*x + d)*sqrt(-d - e)/(d + e)) + ((A - B)*d + (A - B)*e)*sqrt(d - e)*log((e*x + 2*sqrt(e*x + d)*sqrt(d - e) + 2*d - e)/(x + 1)))/(d^2 - e^2), -(((A - B)*d + (A - B)*e)*sqrt(-d + e)*arctan(-sqrt(e*x + d)*sqrt(-d + e)/(d - e)) + ((A + B)*d - (A + B)*e)*sqrt(-d - e)*arctan(sqrt(e*x + d)*sqrt(-d - e)/(d + e)))/(d^2 - e^2)]","A",0
1466,1,7715,0,3.556540," ","integrate((B*x+A)/(x^2+1)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(d^{2} + e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} \sqrt{e x + d} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} d^{6} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} d^{5} e + {\left(A^{5} + 4 \, A^{3} B^{2} + 3 \, A B^{4}\right)} d^{4} e^{2} - 2 \, {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} d^{3} e^{3} + 2 \, {\left(A^{5} + A^{3} B^{2}\right)} d^{2} e^{4} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} d e^{5} + {\left(A^{5} - A B^{4}\right)} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} d^{5} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} d^{4} e + 4 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} d^{3} e^{2} - 2 \, {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} d^{2} e^{3} + 2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} d e^{4} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{3}{4}} - \sqrt{2} \sqrt{4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} d^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} d^{2} e + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} d e^{2} + \sqrt{2} {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} d^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} d^{2} e + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} d e^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} e^{3} + {\left(4 \, A^{2} B^{3} d^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} d^{3} e + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} d^{2} e^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} d e^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} e^{4}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}\right)} \sqrt{e x + d} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} d^{2} e - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} d e^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} e^{3}\right)} x + {\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} d^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} d^{3} e + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} d^{2} e^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} d e^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} e^{4}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}} {\left({\left(B d^{5} - A d^{4} e + 2 \, B d^{3} e^{2} - 2 \, A d^{2} e^{3} + B d e^{4} - A e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}} + {\left({\left(A^{2} B + B^{3}\right)} d^{4} + 2 \, {\left(A^{2} B + B^{3}\right)} d^{2} e^{2} + {\left(A^{2} B + B^{3}\right)} e^{4}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{3}{4}} + {\left(2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} d^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} d^{4} e + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} d^{3} e^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} d^{2} e^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} d e^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}} + {\left(2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} d^{4} - {\left(A^{10} + 3 \, A^{8} B^{2} + 2 \, A^{6} B^{4} - 2 \, A^{4} B^{6} - 3 \, A^{2} B^{8} - B^{10}\right)} d^{3} e + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} d^{2} e^{2} - {\left(A^{10} + 3 \, A^{8} B^{2} + 2 \, A^{6} B^{4} - 2 \, A^{4} B^{6} - 3 \, A^{2} B^{8} - B^{10}\right)} d e^{3}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}}}{4 \, {\left(A^{10} B^{2} + 4 \, A^{8} B^{4} + 6 \, A^{6} B^{6} + 4 \, A^{4} B^{8} + A^{2} B^{10}\right)} d^{2} e - 4 \, {\left(A^{11} B + 3 \, A^{9} B^{3} + 2 \, A^{7} B^{5} - 2 \, A^{5} B^{7} - 3 \, A^{3} B^{9} - A B^{11}\right)} d e^{2} + {\left(A^{12} + 2 \, A^{10} B^{2} - A^{8} B^{4} - 4 \, A^{6} B^{6} - A^{4} B^{8} + 2 \, A^{2} B^{10} + B^{12}\right)} e^{3}}\right) + 4 \, \sqrt{2} {\left(d^{2} + e^{2}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} \sqrt{e x + d} {\left({\left(2 \, {\left(A^{3} B^{2} + A B^{4}\right)} d^{6} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} d^{5} e + {\left(A^{5} + 4 \, A^{3} B^{2} + 3 \, A B^{4}\right)} d^{4} e^{2} - 2 \, {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} d^{3} e^{3} + 2 \, {\left(A^{5} + A^{3} B^{2}\right)} d^{2} e^{4} - {\left(3 \, A^{4} B + 2 \, A^{2} B^{3} - B^{5}\right)} d e^{5} + {\left(A^{5} - A B^{4}\right)} e^{6}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}} + {\left(2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} d^{5} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} d^{4} e + 4 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} d^{3} e^{2} - 2 \, {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} d^{2} e^{3} + 2 \, {\left(A^{5} B^{2} + 2 \, A^{3} B^{4} + A B^{6}\right)} d e^{4} - {\left(A^{6} B + A^{4} B^{3} - A^{2} B^{5} - B^{7}\right)} e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{3}{4}} - \sqrt{2} \sqrt{4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} d^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} d^{2} e + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} d e^{2} - \sqrt{2} {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} d^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} d^{2} e + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} d e^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} e^{3} + {\left(4 \, A^{2} B^{3} d^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} d^{3} e + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} d^{2} e^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} d e^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} e^{4}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}\right)} \sqrt{e x + d} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} d^{2} e - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} d e^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} e^{3}\right)} x + {\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} d^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} d^{3} e + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} d^{2} e^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} d e^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} e^{4}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}} {\left({\left(B d^{5} - A d^{4} e + 2 \, B d^{3} e^{2} - 2 \, A d^{2} e^{3} + B d e^{4} - A e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}} + {\left({\left(A^{2} B + B^{3}\right)} d^{4} + 2 \, {\left(A^{2} B + B^{3}\right)} d^{2} e^{2} + {\left(A^{2} B + B^{3}\right)} e^{4}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{3}{4}} - {\left(2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} d^{5} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} d^{4} e + 4 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} d^{3} e^{2} - 2 \, {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} d^{2} e^{3} + 2 \, {\left(A^{7} B + 3 \, A^{5} B^{3} + 3 \, A^{3} B^{5} + A B^{7}\right)} d e^{4} - {\left(A^{8} + 2 \, A^{6} B^{2} - 2 \, A^{2} B^{6} - B^{8}\right)} e^{5}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}} - {\left(2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} d^{4} - {\left(A^{10} + 3 \, A^{8} B^{2} + 2 \, A^{6} B^{4} - 2 \, A^{4} B^{6} - 3 \, A^{2} B^{8} - B^{10}\right)} d^{3} e + 2 \, {\left(A^{9} B + 4 \, A^{7} B^{3} + 6 \, A^{5} B^{5} + 4 \, A^{3} B^{7} + A B^{9}\right)} d^{2} e^{2} - {\left(A^{10} + 3 \, A^{8} B^{2} + 2 \, A^{6} B^{4} - 2 \, A^{4} B^{6} - 3 \, A^{2} B^{8} - B^{10}\right)} d e^{3}\right)} \sqrt{\frac{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}{d^{4} + 2 \, d^{2} e^{2} + e^{4}}}}{4 \, {\left(A^{10} B^{2} + 4 \, A^{8} B^{4} + 6 \, A^{6} B^{6} + 4 \, A^{4} B^{8} + A^{2} B^{10}\right)} d^{2} e - 4 \, {\left(A^{11} B + 3 \, A^{9} B^{3} + 2 \, A^{7} B^{5} - 2 \, A^{5} B^{7} - 3 \, A^{3} B^{9} - A B^{11}\right)} d e^{2} + {\left(A^{12} + 2 \, A^{10} B^{2} - A^{8} B^{4} - 4 \, A^{6} B^{6} - A^{4} B^{8} + 2 \, A^{2} B^{10} + B^{12}\right)} e^{3}}\right) - \sqrt{2} {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4} - {\left(2 \, A B e + {\left(A^{2} - B^{2}\right)} d\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{1}{4}} \log\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} d^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} d^{2} e + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} d e^{2} + \sqrt{2} {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} d^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} d^{2} e + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} d e^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} e^{3} + {\left(4 \, A^{2} B^{3} d^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} d^{3} e + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} d^{2} e^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} d e^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} e^{4}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}\right)} \sqrt{e x + d} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} d^{2} e - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} d e^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} e^{3}\right)} x + {\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} d^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} d^{3} e + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} d^{2} e^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} d e^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} e^{4}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}\right) + \sqrt{2} {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4} - {\left(2 \, A B e + {\left(A^{2} - B^{2}\right)} d\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}\right)} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{1}{4}} \log\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} d^{3} - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} d^{2} e + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} d e^{2} - \sqrt{2} {\left(4 \, {\left(A^{4} B^{3} + A^{2} B^{5}\right)} d^{3} - 4 \, {\left(2 \, A^{5} B^{2} + A^{3} B^{4} - A B^{6}\right)} d^{2} e + {\left(5 \, A^{6} B - A^{4} B^{3} - 5 \, A^{2} B^{5} + B^{7}\right)} d e^{2} - {\left(A^{7} - A^{5} B^{2} - A^{3} B^{4} + A B^{6}\right)} e^{3} + {\left(4 \, A^{2} B^{3} d^{4} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} d^{3} e + {\left(A^{4} B + 2 \, A^{2} B^{3} + B^{5}\right)} d^{2} e^{2} - 4 \, {\left(A^{3} B^{2} - A B^{4}\right)} d e^{3} + {\left(A^{4} B - 2 \, A^{2} B^{3} + B^{5}\right)} e^{4}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}\right)} \sqrt{e x + d} \sqrt{\frac{{\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} d^{2} + {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)} e^{2} + {\left(2 \, A B d^{2} e + 2 \, A B e^{3} + {\left(A^{2} - B^{2}\right)} d^{3} + {\left(A^{2} - B^{2}\right)} d e^{2}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}}{4 \, A^{2} B^{2} d^{2} - 4 \, {\left(A^{3} B - A B^{3}\right)} d e + {\left(A^{4} - 2 \, A^{2} B^{2} + B^{4}\right)} e^{2}}} \left(\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(A^{6} B^{2} + 2 \, A^{4} B^{4} + A^{2} B^{6}\right)} d^{2} e - 4 \, {\left(A^{7} B + A^{5} B^{3} - A^{3} B^{5} - A B^{7}\right)} d e^{2} + {\left(A^{8} - 2 \, A^{4} B^{4} + B^{8}\right)} e^{3}\right)} x + {\left(4 \, {\left(A^{4} B^{2} + A^{2} B^{4}\right)} d^{4} - 4 \, {\left(A^{5} B - A B^{5}\right)} d^{3} e + {\left(A^{6} + 3 \, A^{4} B^{2} + 3 \, A^{2} B^{4} + B^{6}\right)} d^{2} e^{2} - 4 \, {\left(A^{5} B - A B^{5}\right)} d e^{3} + {\left(A^{6} - A^{4} B^{2} - A^{2} B^{4} + B^{6}\right)} e^{4}\right)} \sqrt{\frac{A^{4} + 2 \, A^{2} B^{2} + B^{4}}{d^{2} + e^{2}}}\right)}{4 \, {\left(A^{4} + 2 \, A^{2} B^{2} + B^{4}\right)}}"," ",0,"1/4*(4*sqrt(2)*(d^2 + e^2)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(3/4)*arctan((sqrt(2)*sqrt(e*x + d)*((2*(A^3*B^2 + A*B^4)*d^6 - (3*A^4*B + 2*A^2*B^3 - B^5)*d^5*e + (A^5 + 4*A^3*B^2 + 3*A*B^4)*d^4*e^2 - 2*(3*A^4*B + 2*A^2*B^3 - B^5)*d^3*e^3 + 2*(A^5 + A^3*B^2)*d^2*e^4 - (3*A^4*B + 2*A^2*B^3 - B^5)*d*e^5 + (A^5 - A*B^4)*e^6)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*d^5 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*d^4*e + 4*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*d^3*e^2 - 2*(A^6*B + A^4*B^3 - A^2*B^5 - B^7)*d^2*e^3 + 2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*d*e^4 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*e^5)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4)))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(3/4) - sqrt(2)*sqrt(4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*d^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*d^2*e + (A^8 - 2*A^4*B^4 + B^8)*d*e^2 + sqrt(2)*(4*(A^4*B^3 + A^2*B^5)*d^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*d^2*e + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*d*e^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*e^3 + (4*A^2*B^3*d^4 - 4*(A^3*B^2 - A*B^4)*d^3*e + (A^4*B + 2*A^2*B^3 + B^5)*d^2*e^2 - 4*(A^3*B^2 - A*B^4)*d*e^3 + (A^4*B - 2*A^2*B^3 + B^5)*e^4)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))*sqrt(e*x + d)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*d^2*e - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*d*e^2 + (A^8 - 2*A^4*B^4 + B^8)*e^3)*x + (4*(A^4*B^2 + A^2*B^4)*d^4 - 4*(A^5*B - A*B^5)*d^3*e + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*d^2*e^2 - 4*(A^5*B - A*B^5)*d*e^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*e^4)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))*((B*d^5 - A*d^4*e + 2*B*d^3*e^2 - 2*A*d^2*e^3 + B*d*e^4 - A*e^5)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)) + ((A^2*B + B^3)*d^4 + 2*(A^2*B + B^3)*d^2*e^2 + (A^2*B + B^3)*e^4)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4)))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(3/4) + (2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*d^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*d^4*e + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*d^3*e^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*d^2*e^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*d*e^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*e^5)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)) + (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*d^4 - (A^10 + 3*A^8*B^2 + 2*A^6*B^4 - 2*A^4*B^6 - 3*A^2*B^8 - B^10)*d^3*e + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*d^2*e^2 - (A^10 + 3*A^8*B^2 + 2*A^6*B^4 - 2*A^4*B^6 - 3*A^2*B^8 - B^10)*d*e^3)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4)))/(4*(A^10*B^2 + 4*A^8*B^4 + 6*A^6*B^6 + 4*A^4*B^8 + A^2*B^10)*d^2*e - 4*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*d*e^2 + (A^12 + 2*A^10*B^2 - A^8*B^4 - 4*A^6*B^6 - A^4*B^8 + 2*A^2*B^10 + B^12)*e^3)) + 4*sqrt(2)*(d^2 + e^2)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(3/4)*arctan((sqrt(2)*sqrt(e*x + d)*((2*(A^3*B^2 + A*B^4)*d^6 - (3*A^4*B + 2*A^2*B^3 - B^5)*d^5*e + (A^5 + 4*A^3*B^2 + 3*A*B^4)*d^4*e^2 - 2*(3*A^4*B + 2*A^2*B^3 - B^5)*d^3*e^3 + 2*(A^5 + A^3*B^2)*d^2*e^4 - (3*A^4*B + 2*A^2*B^3 - B^5)*d*e^5 + (A^5 - A*B^4)*e^6)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)) + (2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*d^5 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*d^4*e + 4*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*d^3*e^2 - 2*(A^6*B + A^4*B^3 - A^2*B^5 - B^7)*d^2*e^3 + 2*(A^5*B^2 + 2*A^3*B^4 + A*B^6)*d*e^4 - (A^6*B + A^4*B^3 - A^2*B^5 - B^7)*e^5)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4)))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(3/4) - sqrt(2)*sqrt(4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*d^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*d^2*e + (A^8 - 2*A^4*B^4 + B^8)*d*e^2 - sqrt(2)*(4*(A^4*B^3 + A^2*B^5)*d^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*d^2*e + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*d*e^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*e^3 + (4*A^2*B^3*d^4 - 4*(A^3*B^2 - A*B^4)*d^3*e + (A^4*B + 2*A^2*B^3 + B^5)*d^2*e^2 - 4*(A^3*B^2 - A*B^4)*d*e^3 + (A^4*B - 2*A^2*B^3 + B^5)*e^4)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))*sqrt(e*x + d)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*d^2*e - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*d*e^2 + (A^8 - 2*A^4*B^4 + B^8)*e^3)*x + (4*(A^4*B^2 + A^2*B^4)*d^4 - 4*(A^5*B - A*B^5)*d^3*e + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*d^2*e^2 - 4*(A^5*B - A*B^5)*d*e^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*e^4)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))*((B*d^5 - A*d^4*e + 2*B*d^3*e^2 - 2*A*d^2*e^3 + B*d*e^4 - A*e^5)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)) + ((A^2*B + B^3)*d^4 + 2*(A^2*B + B^3)*d^2*e^2 + (A^2*B + B^3)*e^4)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4)))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(3/4) - (2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*d^5 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*d^4*e + 4*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*d^3*e^2 - 2*(A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*d^2*e^3 + 2*(A^7*B + 3*A^5*B^3 + 3*A^3*B^5 + A*B^7)*d*e^4 - (A^8 + 2*A^6*B^2 - 2*A^2*B^6 - B^8)*e^5)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4))*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)) - (2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*d^4 - (A^10 + 3*A^8*B^2 + 2*A^6*B^4 - 2*A^4*B^6 - 3*A^2*B^8 - B^10)*d^3*e + 2*(A^9*B + 4*A^7*B^3 + 6*A^5*B^5 + 4*A^3*B^7 + A*B^9)*d^2*e^2 - (A^10 + 3*A^8*B^2 + 2*A^6*B^4 - 2*A^4*B^6 - 3*A^2*B^8 - B^10)*d*e^3)*sqrt((4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2)/(d^4 + 2*d^2*e^2 + e^4)))/(4*(A^10*B^2 + 4*A^8*B^4 + 6*A^6*B^6 + 4*A^4*B^8 + A^2*B^10)*d^2*e - 4*(A^11*B + 3*A^9*B^3 + 2*A^7*B^5 - 2*A^5*B^7 - 3*A^3*B^9 - A*B^11)*d*e^2 + (A^12 + 2*A^10*B^2 - A^8*B^4 - 4*A^6*B^6 - A^4*B^8 + 2*A^2*B^10 + B^12)*e^3)) - sqrt(2)*(A^4 + 2*A^2*B^2 + B^4 - (2*A*B*e + (A^2 - B^2)*d)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(1/4)*log(4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*d^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*d^2*e + (A^8 - 2*A^4*B^4 + B^8)*d*e^2 + sqrt(2)*(4*(A^4*B^3 + A^2*B^5)*d^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*d^2*e + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*d*e^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*e^3 + (4*A^2*B^3*d^4 - 4*(A^3*B^2 - A*B^4)*d^3*e + (A^4*B + 2*A^2*B^3 + B^5)*d^2*e^2 - 4*(A^3*B^2 - A*B^4)*d*e^3 + (A^4*B - 2*A^2*B^3 + B^5)*e^4)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))*sqrt(e*x + d)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*d^2*e - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*d*e^2 + (A^8 - 2*A^4*B^4 + B^8)*e^3)*x + (4*(A^4*B^2 + A^2*B^4)*d^4 - 4*(A^5*B - A*B^5)*d^3*e + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*d^2*e^2 - 4*(A^5*B - A*B^5)*d*e^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*e^4)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))) + sqrt(2)*(A^4 + 2*A^2*B^2 + B^4 - (2*A*B*e + (A^2 - B^2)*d)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(1/4)*log(4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*d^3 - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*d^2*e + (A^8 - 2*A^4*B^4 + B^8)*d*e^2 - sqrt(2)*(4*(A^4*B^3 + A^2*B^5)*d^3 - 4*(2*A^5*B^2 + A^3*B^4 - A*B^6)*d^2*e + (5*A^6*B - A^4*B^3 - 5*A^2*B^5 + B^7)*d*e^2 - (A^7 - A^5*B^2 - A^3*B^4 + A*B^6)*e^3 + (4*A^2*B^3*d^4 - 4*(A^3*B^2 - A*B^4)*d^3*e + (A^4*B + 2*A^2*B^3 + B^5)*d^2*e^2 - 4*(A^3*B^2 - A*B^4)*d*e^3 + (A^4*B - 2*A^2*B^3 + B^5)*e^4)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))*sqrt(e*x + d)*sqrt(((A^4 + 2*A^2*B^2 + B^4)*d^2 + (A^4 + 2*A^2*B^2 + B^4)*e^2 + (2*A*B*d^2*e + 2*A*B*e^3 + (A^2 - B^2)*d^3 + (A^2 - B^2)*d*e^2)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2)))/(4*A^2*B^2*d^2 - 4*(A^3*B - A*B^3)*d*e + (A^4 - 2*A^2*B^2 + B^4)*e^2))*((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))^(1/4) + (4*(A^6*B^2 + 2*A^4*B^4 + A^2*B^6)*d^2*e - 4*(A^7*B + A^5*B^3 - A^3*B^5 - A*B^7)*d*e^2 + (A^8 - 2*A^4*B^4 + B^8)*e^3)*x + (4*(A^4*B^2 + A^2*B^4)*d^4 - 4*(A^5*B - A*B^5)*d^3*e + (A^6 + 3*A^4*B^2 + 3*A^2*B^4 + B^6)*d^2*e^2 - 4*(A^5*B - A*B^5)*d*e^3 + (A^6 - A^4*B^2 - A^2*B^4 + B^6)*e^4)*sqrt((A^4 + 2*A^2*B^2 + B^4)/(d^2 + e^2))))/(A^4 + 2*A^2*B^2 + B^4)","B",0
1467,1,294,0,0.456151," ","integrate((1-x)*(1+x)^(1/2)/(x^2+1),x, algorithm=""fricas"")","-\frac{1}{8} \cdot 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(2 \cdot 8^{\frac{1}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) + \frac{1}{8} \cdot 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(-2 \cdot 8^{\frac{1}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \cdot 8^{\frac{1}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 4} - \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} - \sqrt{2} - 1\right) - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{-2 \cdot 8^{\frac{1}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 4} - \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + \sqrt{2} + 1\right) - 2 \, \sqrt{x + 1}"," ",0,"-1/8*8^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(2*8^(1/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) + 1/8*8^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(-2*8^(1/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) - 1/2*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2) + 4)*arctan(1/16*8^(3/4)*sqrt(2)*sqrt(2*8^(1/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*sqrt(2*sqrt(2) + 4) - 1/8*8^(3/4)*sqrt(2)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) - sqrt(2) - 1) - 1/2*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2) + 4)*arctan(1/16*8^(3/4)*sqrt(2)*sqrt(-2*8^(1/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*sqrt(2*sqrt(2) + 4) - 1/8*8^(3/4)*sqrt(2)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + sqrt(2) + 1) - 2*sqrt(x + 1)","A",0
1468,1,22,0,0.423494," ","integrate((3+x)/(x^2+1)/(4+3*x)^(1/2),x, algorithm=""fricas"")","\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(3 \, x - 1\right)}}{2 \, \sqrt{3 \, x + 4}}\right)"," ",0,"sqrt(2)*arctan(1/2*sqrt(2)*(3*x - 1)/sqrt(3*x + 4))","A",0
1469,1,37,0,0.421250," ","integrate((1-3*x)/(x^2+1)/(4+3*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{2 \, \sqrt{2} \sqrt{3 \, x + 4} {\left(x + 3\right)} + x^{2} + 12 \, x + 17}{x^{2} + 1}\right)"," ",0,"1/2*sqrt(2)*log((2*sqrt(2)*sqrt(3*x + 4)*(x + 3) + x^2 + 12*x + 17)/(x^2 + 1))","A",0
1470,1,14,0,0.431510," ","integrate((2+x)/(x^2+1)/(3+4*x)^(1/2),x, algorithm=""fricas"")","\arctan\left(\frac{2 \, x - 1}{\sqrt{4 \, x + 3}}\right)"," ",0,"arctan((2*x - 1)/sqrt(4*x + 3))","A",0
1471,1,19,0,0.401608," ","integrate((-2+x)/(x^2-8)/(-3+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 4\right)}}{4 \, \sqrt{x - 3}}\right)"," ",0,"1/2*sqrt(2)*arctan(1/4*sqrt(2)*(x - 4)/sqrt(x - 3))","A",0
1472,0,0,0,0.439452," ","integrate((B*x+A)*(e*x+d)^(1/2)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x + d}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x + d), x)","F",0
1473,0,0,0,0.440658," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)}}{\sqrt{e x + d}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)/sqrt(e*x + d), x)","F",0
1474,0,0,0,0.437595," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
1475,0,0,0,0.463525," ","integrate((B*x+A)*(c*x^2+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
1476,0,0,0,0.444328," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)/sqrt(e*x + d), x)","F",0
1477,0,0,0,0.480031," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
1478,0,0,0,0.451975," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
1479,0,0,0,0.475770," ","integrate((B*x+A)*(c*x^2+a)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c x^{3} + A c x^{2} + B a x + A a\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((B*c*x^3 + A*c*x^2 + B*a*x + A*a)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
1480,0,0,0,0.450313," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A d + {\left(B d + A e\right)} x\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((B*e*x^2 + A*d + (B*d + A*e)*x)*sqrt(e*x + d)/sqrt(c*x^2 + a), x)","F",0
1481,0,0,0,0.448727," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((B*x + A)*sqrt(e*x + d)/sqrt(c*x^2 + a), x)","F",0
1482,0,0,0,0.457614," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x + d}}{c e x^{3} + c d x^{2} + a e x + a d}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x + d)/(c*e*x^3 + c*d*x^2 + a*e*x + a*d), x)","F",0
1483,0,0,0,0.450751," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x + d}}{c e^{2} x^{4} + 2 \, c d e x^{3} + 2 \, a d e x + a d^{2} + {\left(c d^{2} + a e^{2}\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x + d)/(c*e^2*x^4 + 2*c*d*e*x^3 + 2*a*d*e*x + a*d^2 + (c*d^2 + a*e^2)*x^2), x)","F",0
1484,0,0,0,0.456362," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A d + {\left(B d + A e\right)} x\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e*x^2 + A*d + (B*d + A*e)*x)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
1485,0,0,0,0.454403," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x + d)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
1486,0,0,0,0.468752," ","integrate((B*x+A)/(c*x^2+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(B x + A\right)} \sqrt{e x + d}}{c^{2} e x^{5} + c^{2} d x^{4} + 2 \, a c e x^{3} + 2 \, a c d x^{2} + a^{2} e x + a^{2} d}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(B*x + A)*sqrt(e*x + d)/(c^2*e*x^5 + c^2*d*x^4 + 2*a*c*e*x^3 + 2*a*c*d*x^2 + a^2*e*x + a^2*d), x)","F",0
1487,1,3116,0,0.501004," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(A a^{3} d e^{7} m^{7} - 5040 \, B c^{3} d^{8} + 5760 \, A c^{3} d^{7} e - 20160 \, B a c^{2} d^{6} e^{2} + 24192 \, A a c^{2} d^{5} e^{3} - 30240 \, B a^{2} c d^{4} e^{4} + 40320 \, A a^{2} c d^{3} e^{5} - 20160 \, B a^{3} d^{2} e^{6} + 40320 \, A a^{3} d e^{7} + {\left(B c^{3} e^{8} m^{7} + 28 \, B c^{3} e^{8} m^{6} + 322 \, B c^{3} e^{8} m^{5} + 1960 \, B c^{3} e^{8} m^{4} + 6769 \, B c^{3} e^{8} m^{3} + 13132 \, B c^{3} e^{8} m^{2} + 13068 \, B c^{3} e^{8} m + 5040 \, B c^{3} e^{8}\right)} x^{8} + {\left(5760 \, A c^{3} e^{8} + {\left(B c^{3} d e^{7} + A c^{3} e^{8}\right)} m^{7} + {\left(21 \, B c^{3} d e^{7} + 29 \, A c^{3} e^{8}\right)} m^{6} + 7 \, {\left(25 \, B c^{3} d e^{7} + 49 \, A c^{3} e^{8}\right)} m^{5} + 35 \, {\left(21 \, B c^{3} d e^{7} + 61 \, A c^{3} e^{8}\right)} m^{4} + 56 \, {\left(29 \, B c^{3} d e^{7} + 134 \, A c^{3} e^{8}\right)} m^{3} + 28 \, {\left(63 \, B c^{3} d e^{7} + 527 \, A c^{3} e^{8}\right)} m^{2} + 144 \, {\left(5 \, B c^{3} d e^{7} + 103 \, A c^{3} e^{8}\right)} m\right)} x^{7} - {\left(B a^{3} d^{2} e^{6} - 35 \, A a^{3} d e^{7}\right)} m^{6} + {\left(20160 \, B a c^{2} e^{8} + {\left(A c^{3} d e^{7} + 3 \, B a c^{2} e^{8}\right)} m^{7} - {\left(7 \, B c^{3} d^{2} e^{6} - 23 \, A c^{3} d e^{7} - 90 \, B a c^{2} e^{8}\right)} m^{6} - {\left(105 \, B c^{3} d^{2} e^{6} - 205 \, A c^{3} d e^{7} - 1098 \, B a c^{2} e^{8}\right)} m^{5} - 5 \, {\left(119 \, B c^{3} d^{2} e^{6} - 181 \, A c^{3} d e^{7} - 1404 \, B a c^{2} e^{8}\right)} m^{4} - {\left(1575 \, B c^{3} d^{2} e^{6} - 2074 \, A c^{3} d e^{7} - 25227 \, B a c^{2} e^{8}\right)} m^{3} - 2 \, {\left(959 \, B c^{3} d^{2} e^{6} - 1156 \, A c^{3} d e^{7} - 25245 \, B a c^{2} e^{8}\right)} m^{2} - 24 \, {\left(35 \, B c^{3} d^{2} e^{6} - 40 \, A c^{3} d e^{7} - 2143 \, B a c^{2} e^{8}\right)} m\right)} x^{6} + {\left(6 \, A a^{2} c d^{3} e^{5} - 33 \, B a^{3} d^{2} e^{6} + 511 \, A a^{3} d e^{7}\right)} m^{5} + 3 \, {\left(8064 \, A a c^{2} e^{8} + {\left(B a c^{2} d e^{7} + A a c^{2} e^{8}\right)} m^{7} - {\left(2 \, A c^{3} d^{2} e^{6} - 25 \, B a c^{2} d e^{7} - 31 \, A a c^{2} e^{8}\right)} m^{6} + {\left(14 \, B c^{3} d^{3} e^{5} - 36 \, A c^{3} d^{2} e^{6} + 241 \, B a c^{2} d e^{7} + 391 \, A a c^{2} e^{8}\right)} m^{5} + {\left(140 \, B c^{3} d^{3} e^{5} - 230 \, A c^{3} d^{2} e^{6} + 1135 \, B a c^{2} d e^{7} + 2581 \, A a c^{2} e^{8}\right)} m^{4} + 2 \, {\left(245 \, B c^{3} d^{3} e^{5} - 330 \, A c^{3} d^{2} e^{6} + 1367 \, B a c^{2} d e^{7} + 4772 \, A a c^{2} e^{8}\right)} m^{3} + 4 \, {\left(175 \, B c^{3} d^{3} e^{5} - 212 \, A c^{3} d^{2} e^{6} + 790 \, B a c^{2} d e^{7} + 4891 \, A a c^{2} e^{8}\right)} m^{2} + 48 \, {\left(7 \, B c^{3} d^{3} e^{5} - 8 \, A c^{3} d^{2} e^{6} + 28 \, B a c^{2} d e^{7} + 423 \, A a c^{2} e^{8}\right)} m\right)} x^{5} - {\left(18 \, B a^{2} c d^{4} e^{4} - 180 \, A a^{2} c d^{3} e^{5} + 445 \, B a^{3} d^{2} e^{6} - 4025 \, A a^{3} d e^{7}\right)} m^{4} + 3 \, {\left(10080 \, B a^{2} c e^{8} + {\left(A a c^{2} d e^{7} + B a^{2} c e^{8}\right)} m^{7} - {\left(5 \, B a c^{2} d^{2} e^{6} - 27 \, A a c^{2} d e^{7} - 32 \, B a^{2} c e^{8}\right)} m^{6} + {\left(10 \, A c^{3} d^{3} e^{5} - 105 \, B a c^{2} d^{2} e^{6} + 283 \, A a c^{2} d e^{7} + 418 \, B a^{2} c e^{8}\right)} m^{5} - {\left(70 \, B c^{3} d^{4} e^{4} - 140 \, A c^{3} d^{3} e^{5} + 785 \, B a c^{2} d^{2} e^{6} - 1449 \, A a c^{2} d e^{7} - 2864 \, B a^{2} c e^{8}\right)} m^{4} - {\left(420 \, B c^{3} d^{4} e^{4} - 590 \, A c^{3} d^{3} e^{5} + 2535 \, B a c^{2} d^{2} e^{6} - 3748 \, A a c^{2} d e^{7} - 10993 \, B a^{2} c e^{8}\right)} m^{3} - 2 \, {\left(385 \, B c^{3} d^{4} e^{4} - 470 \, A c^{3} d^{3} e^{5} + 1765 \, B a c^{2} d^{2} e^{6} - 2286 \, A a c^{2} d e^{7} - 11656 \, B a^{2} c e^{8}\right)} m^{2} - 12 \, {\left(35 \, B c^{3} d^{4} e^{4} - 40 \, A c^{3} d^{3} e^{5} + 140 \, B a c^{2} d^{2} e^{6} - 168 \, A a c^{2} d e^{7} - 2073 \, B a^{2} c e^{8}\right)} m\right)} x^{4} + {\left(72 \, A a c^{2} d^{5} e^{3} - 468 \, B a^{2} c d^{4} e^{4} + 2130 \, A a^{2} c d^{3} e^{5} - 3135 \, B a^{3} d^{2} e^{6} + 18424 \, A a^{3} d e^{7}\right)} m^{3} + 3 \, {\left(13440 \, A a^{2} c e^{8} + {\left(B a^{2} c d e^{7} + A a^{2} c e^{8}\right)} m^{7} - {\left(4 \, A a c^{2} d^{2} e^{6} - 29 \, B a^{2} c d e^{7} - 33 \, A a^{2} c e^{8}\right)} m^{6} + {\left(20 \, B a c^{2} d^{3} e^{5} - 96 \, A a c^{2} d^{2} e^{6} + 331 \, B a^{2} c d e^{7} + 447 \, A a^{2} c e^{8}\right)} m^{5} - {\left(40 \, A c^{3} d^{4} e^{4} - 360 \, B a c^{2} d^{3} e^{5} + 844 \, A a c^{2} d^{2} e^{6} - 1871 \, B a^{2} c d e^{7} - 3195 \, A a^{2} c e^{8}\right)} m^{4} + 4 \, {\left(70 \, B c^{3} d^{5} e^{3} - 110 \, A c^{3} d^{4} e^{4} + 515 \, B a c^{2} d^{3} e^{5} - 816 \, A a c^{2} d^{2} e^{6} + 1345 \, B a^{2} c d e^{7} + 3216 \, A a^{2} c e^{8}\right)} m^{3} + 4 \, {\left(210 \, B c^{3} d^{5} e^{3} - 260 \, A c^{3} d^{4} e^{4} + 990 \, B a c^{2} d^{3} e^{5} - 1300 \, A a c^{2} d^{2} e^{6} + 1793 \, B a^{2} c d e^{7} + 7173 \, A a^{2} c e^{8}\right)} m^{2} + 16 \, {\left(35 \, B c^{3} d^{5} e^{3} - 40 \, A c^{3} d^{4} e^{4} + 140 \, B a c^{2} d^{3} e^{5} - 168 \, A a c^{2} d^{2} e^{6} + 210 \, B a^{2} c d e^{7} + 2003 \, A a^{2} c e^{8}\right)} m\right)} x^{3} - 2 \, {\left(180 \, B a c^{2} d^{6} e^{2} - 756 \, A a c^{2} d^{5} e^{3} + 2259 \, B a^{2} c d^{4} e^{4} - 6210 \, A a^{2} c d^{3} e^{5} + 6077 \, B a^{3} d^{2} e^{6} - 24430 \, A a^{3} d e^{7}\right)} m^{2} + {\left(20160 \, B a^{3} e^{8} + {\left(3 \, A a^{2} c d e^{7} + B a^{3} e^{8}\right)} m^{7} - {\left(9 \, B a^{2} c d^{2} e^{6} - 93 \, A a^{2} c d e^{7} - 34 \, B a^{3} e^{8}\right)} m^{6} + {\left(36 \, A a c^{2} d^{3} e^{5} - 243 \, B a^{2} c d^{2} e^{6} + 1155 \, A a^{2} c d e^{7} + 478 \, B a^{3} e^{8}\right)} m^{5} - {\left(180 \, B a c^{2} d^{4} e^{4} - 792 \, A a c^{2} d^{3} e^{5} + 2493 \, B a^{2} c d^{2} e^{6} - 7275 \, A a^{2} c d e^{7} - 3580 \, B a^{3} e^{8}\right)} m^{4} + {\left(360 \, A c^{3} d^{5} e^{3} - 2880 \, B a c^{2} d^{4} e^{4} + 6012 \, A a c^{2} d^{3} e^{5} - 11853 \, B a^{2} c d^{2} e^{6} + 24042 \, A a^{2} c d e^{7} + 15289 \, B a^{3} e^{8}\right)} m^{3} - 2 \, {\left(1260 \, B c^{3} d^{6} e^{2} - 1620 \, A c^{3} d^{5} e^{3} + 6390 \, B a c^{2} d^{4} e^{4} - 8676 \, A a c^{2} d^{3} e^{5} + 12357 \, B a^{2} c d^{2} e^{6} - 18996 \, A a^{2} c d e^{7} - 18353 \, B a^{3} e^{8}\right)} m^{2} - 72 \, {\left(35 \, B c^{3} d^{6} e^{2} - 40 \, A c^{3} d^{5} e^{3} + 140 \, B a c^{2} d^{4} e^{4} - 168 \, A a c^{2} d^{3} e^{5} + 210 \, B a^{2} c d^{2} e^{6} - 280 \, A a^{2} c d e^{7} - 621 \, B a^{3} e^{8}\right)} m\right)} x^{2} + 12 \, {\left(60 \, A c^{3} d^{7} e - 450 \, B a c^{2} d^{6} e^{2} + 876 \, A a c^{2} d^{5} e^{3} - 1599 \, B a^{2} c d^{4} e^{4} + 2972 \, A a^{2} c d^{3} e^{5} - 2046 \, B a^{3} d^{2} e^{6} + 5772 \, A a^{3} d e^{7}\right)} m + {\left(40320 \, A a^{3} e^{8} + {\left(B a^{3} d e^{7} + A a^{3} e^{8}\right)} m^{7} - {\left(6 \, A a^{2} c d^{2} e^{6} - 33 \, B a^{3} d e^{7} - 35 \, A a^{3} e^{8}\right)} m^{6} + {\left(18 \, B a^{2} c d^{3} e^{5} - 180 \, A a^{2} c d^{2} e^{6} + 445 \, B a^{3} d e^{7} + 511 \, A a^{3} e^{8}\right)} m^{5} - {\left(72 \, A a c^{2} d^{4} e^{4} - 468 \, B a^{2} c d^{3} e^{5} + 2130 \, A a^{2} c d^{2} e^{6} - 3135 \, B a^{3} d e^{7} - 4025 \, A a^{3} e^{8}\right)} m^{4} + 2 \, {\left(180 \, B a c^{2} d^{5} e^{3} - 756 \, A a c^{2} d^{4} e^{4} + 2259 \, B a^{2} c d^{3} e^{5} - 6210 \, A a^{2} c d^{2} e^{6} + 6077 \, B a^{3} d e^{7} + 9212 \, A a^{3} e^{8}\right)} m^{3} - 4 \, {\left(180 \, A c^{3} d^{6} e^{2} - 1350 \, B a c^{2} d^{5} e^{3} + 2628 \, A a c^{2} d^{4} e^{4} - 4797 \, B a^{2} c d^{3} e^{5} + 8916 \, A a^{2} c d^{2} e^{6} - 6138 \, B a^{3} d e^{7} - 12215 \, A a^{3} e^{8}\right)} m^{2} + 144 \, {\left(35 \, B c^{3} d^{7} e - 40 \, A c^{3} d^{6} e^{2} + 140 \, B a c^{2} d^{5} e^{3} - 168 \, A a c^{2} d^{4} e^{4} + 210 \, B a^{2} c d^{3} e^{5} - 280 \, A a^{2} c d^{2} e^{6} + 140 \, B a^{3} d e^{7} + 481 \, A a^{3} e^{8}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{8} m^{8} + 36 \, e^{8} m^{7} + 546 \, e^{8} m^{6} + 4536 \, e^{8} m^{5} + 22449 \, e^{8} m^{4} + 67284 \, e^{8} m^{3} + 118124 \, e^{8} m^{2} + 109584 \, e^{8} m + 40320 \, e^{8}}"," ",0,"(A*a^3*d*e^7*m^7 - 5040*B*c^3*d^8 + 5760*A*c^3*d^7*e - 20160*B*a*c^2*d^6*e^2 + 24192*A*a*c^2*d^5*e^3 - 30240*B*a^2*c*d^4*e^4 + 40320*A*a^2*c*d^3*e^5 - 20160*B*a^3*d^2*e^6 + 40320*A*a^3*d*e^7 + (B*c^3*e^8*m^7 + 28*B*c^3*e^8*m^6 + 322*B*c^3*e^8*m^5 + 1960*B*c^3*e^8*m^4 + 6769*B*c^3*e^8*m^3 + 13132*B*c^3*e^8*m^2 + 13068*B*c^3*e^8*m + 5040*B*c^3*e^8)*x^8 + (5760*A*c^3*e^8 + (B*c^3*d*e^7 + A*c^3*e^8)*m^7 + (21*B*c^3*d*e^7 + 29*A*c^3*e^8)*m^6 + 7*(25*B*c^3*d*e^7 + 49*A*c^3*e^8)*m^5 + 35*(21*B*c^3*d*e^7 + 61*A*c^3*e^8)*m^4 + 56*(29*B*c^3*d*e^7 + 134*A*c^3*e^8)*m^3 + 28*(63*B*c^3*d*e^7 + 527*A*c^3*e^8)*m^2 + 144*(5*B*c^3*d*e^7 + 103*A*c^3*e^8)*m)*x^7 - (B*a^3*d^2*e^6 - 35*A*a^3*d*e^7)*m^6 + (20160*B*a*c^2*e^8 + (A*c^3*d*e^7 + 3*B*a*c^2*e^8)*m^7 - (7*B*c^3*d^2*e^6 - 23*A*c^3*d*e^7 - 90*B*a*c^2*e^8)*m^6 - (105*B*c^3*d^2*e^6 - 205*A*c^3*d*e^7 - 1098*B*a*c^2*e^8)*m^5 - 5*(119*B*c^3*d^2*e^6 - 181*A*c^3*d*e^7 - 1404*B*a*c^2*e^8)*m^4 - (1575*B*c^3*d^2*e^6 - 2074*A*c^3*d*e^7 - 25227*B*a*c^2*e^8)*m^3 - 2*(959*B*c^3*d^2*e^6 - 1156*A*c^3*d*e^7 - 25245*B*a*c^2*e^8)*m^2 - 24*(35*B*c^3*d^2*e^6 - 40*A*c^3*d*e^7 - 2143*B*a*c^2*e^8)*m)*x^6 + (6*A*a^2*c*d^3*e^5 - 33*B*a^3*d^2*e^6 + 511*A*a^3*d*e^7)*m^5 + 3*(8064*A*a*c^2*e^8 + (B*a*c^2*d*e^7 + A*a*c^2*e^8)*m^7 - (2*A*c^3*d^2*e^6 - 25*B*a*c^2*d*e^7 - 31*A*a*c^2*e^8)*m^6 + (14*B*c^3*d^3*e^5 - 36*A*c^3*d^2*e^6 + 241*B*a*c^2*d*e^7 + 391*A*a*c^2*e^8)*m^5 + (140*B*c^3*d^3*e^5 - 230*A*c^3*d^2*e^6 + 1135*B*a*c^2*d*e^7 + 2581*A*a*c^2*e^8)*m^4 + 2*(245*B*c^3*d^3*e^5 - 330*A*c^3*d^2*e^6 + 1367*B*a*c^2*d*e^7 + 4772*A*a*c^2*e^8)*m^3 + 4*(175*B*c^3*d^3*e^5 - 212*A*c^3*d^2*e^6 + 790*B*a*c^2*d*e^7 + 4891*A*a*c^2*e^8)*m^2 + 48*(7*B*c^3*d^3*e^5 - 8*A*c^3*d^2*e^6 + 28*B*a*c^2*d*e^7 + 423*A*a*c^2*e^8)*m)*x^5 - (18*B*a^2*c*d^4*e^4 - 180*A*a^2*c*d^3*e^5 + 445*B*a^3*d^2*e^6 - 4025*A*a^3*d*e^7)*m^4 + 3*(10080*B*a^2*c*e^8 + (A*a*c^2*d*e^7 + B*a^2*c*e^8)*m^7 - (5*B*a*c^2*d^2*e^6 - 27*A*a*c^2*d*e^7 - 32*B*a^2*c*e^8)*m^6 + (10*A*c^3*d^3*e^5 - 105*B*a*c^2*d^2*e^6 + 283*A*a*c^2*d*e^7 + 418*B*a^2*c*e^8)*m^5 - (70*B*c^3*d^4*e^4 - 140*A*c^3*d^3*e^5 + 785*B*a*c^2*d^2*e^6 - 1449*A*a*c^2*d*e^7 - 2864*B*a^2*c*e^8)*m^4 - (420*B*c^3*d^4*e^4 - 590*A*c^3*d^3*e^5 + 2535*B*a*c^2*d^2*e^6 - 3748*A*a*c^2*d*e^7 - 10993*B*a^2*c*e^8)*m^3 - 2*(385*B*c^3*d^4*e^4 - 470*A*c^3*d^3*e^5 + 1765*B*a*c^2*d^2*e^6 - 2286*A*a*c^2*d*e^7 - 11656*B*a^2*c*e^8)*m^2 - 12*(35*B*c^3*d^4*e^4 - 40*A*c^3*d^3*e^5 + 140*B*a*c^2*d^2*e^6 - 168*A*a*c^2*d*e^7 - 2073*B*a^2*c*e^8)*m)*x^4 + (72*A*a*c^2*d^5*e^3 - 468*B*a^2*c*d^4*e^4 + 2130*A*a^2*c*d^3*e^5 - 3135*B*a^3*d^2*e^6 + 18424*A*a^3*d*e^7)*m^3 + 3*(13440*A*a^2*c*e^8 + (B*a^2*c*d*e^7 + A*a^2*c*e^8)*m^7 - (4*A*a*c^2*d^2*e^6 - 29*B*a^2*c*d*e^7 - 33*A*a^2*c*e^8)*m^6 + (20*B*a*c^2*d^3*e^5 - 96*A*a*c^2*d^2*e^6 + 331*B*a^2*c*d*e^7 + 447*A*a^2*c*e^8)*m^5 - (40*A*c^3*d^4*e^4 - 360*B*a*c^2*d^3*e^5 + 844*A*a*c^2*d^2*e^6 - 1871*B*a^2*c*d*e^7 - 3195*A*a^2*c*e^8)*m^4 + 4*(70*B*c^3*d^5*e^3 - 110*A*c^3*d^4*e^4 + 515*B*a*c^2*d^3*e^5 - 816*A*a*c^2*d^2*e^6 + 1345*B*a^2*c*d*e^7 + 3216*A*a^2*c*e^8)*m^3 + 4*(210*B*c^3*d^5*e^3 - 260*A*c^3*d^4*e^4 + 990*B*a*c^2*d^3*e^5 - 1300*A*a*c^2*d^2*e^6 + 1793*B*a^2*c*d*e^7 + 7173*A*a^2*c*e^8)*m^2 + 16*(35*B*c^3*d^5*e^3 - 40*A*c^3*d^4*e^4 + 140*B*a*c^2*d^3*e^5 - 168*A*a*c^2*d^2*e^6 + 210*B*a^2*c*d*e^7 + 2003*A*a^2*c*e^8)*m)*x^3 - 2*(180*B*a*c^2*d^6*e^2 - 756*A*a*c^2*d^5*e^3 + 2259*B*a^2*c*d^4*e^4 - 6210*A*a^2*c*d^3*e^5 + 6077*B*a^3*d^2*e^6 - 24430*A*a^3*d*e^7)*m^2 + (20160*B*a^3*e^8 + (3*A*a^2*c*d*e^7 + B*a^3*e^8)*m^7 - (9*B*a^2*c*d^2*e^6 - 93*A*a^2*c*d*e^7 - 34*B*a^3*e^8)*m^6 + (36*A*a*c^2*d^3*e^5 - 243*B*a^2*c*d^2*e^6 + 1155*A*a^2*c*d*e^7 + 478*B*a^3*e^8)*m^5 - (180*B*a*c^2*d^4*e^4 - 792*A*a*c^2*d^3*e^5 + 2493*B*a^2*c*d^2*e^6 - 7275*A*a^2*c*d*e^7 - 3580*B*a^3*e^8)*m^4 + (360*A*c^3*d^5*e^3 - 2880*B*a*c^2*d^4*e^4 + 6012*A*a*c^2*d^3*e^5 - 11853*B*a^2*c*d^2*e^6 + 24042*A*a^2*c*d*e^7 + 15289*B*a^3*e^8)*m^3 - 2*(1260*B*c^3*d^6*e^2 - 1620*A*c^3*d^5*e^3 + 6390*B*a*c^2*d^4*e^4 - 8676*A*a*c^2*d^3*e^5 + 12357*B*a^2*c*d^2*e^6 - 18996*A*a^2*c*d*e^7 - 18353*B*a^3*e^8)*m^2 - 72*(35*B*c^3*d^6*e^2 - 40*A*c^3*d^5*e^3 + 140*B*a*c^2*d^4*e^4 - 168*A*a*c^2*d^3*e^5 + 210*B*a^2*c*d^2*e^6 - 280*A*a^2*c*d*e^7 - 621*B*a^3*e^8)*m)*x^2 + 12*(60*A*c^3*d^7*e - 450*B*a*c^2*d^6*e^2 + 876*A*a*c^2*d^5*e^3 - 1599*B*a^2*c*d^4*e^4 + 2972*A*a^2*c*d^3*e^5 - 2046*B*a^3*d^2*e^6 + 5772*A*a^3*d*e^7)*m + (40320*A*a^3*e^8 + (B*a^3*d*e^7 + A*a^3*e^8)*m^7 - (6*A*a^2*c*d^2*e^6 - 33*B*a^3*d*e^7 - 35*A*a^3*e^8)*m^6 + (18*B*a^2*c*d^3*e^5 - 180*A*a^2*c*d^2*e^6 + 445*B*a^3*d*e^7 + 511*A*a^3*e^8)*m^5 - (72*A*a*c^2*d^4*e^4 - 468*B*a^2*c*d^3*e^5 + 2130*A*a^2*c*d^2*e^6 - 3135*B*a^3*d*e^7 - 4025*A*a^3*e^8)*m^4 + 2*(180*B*a*c^2*d^5*e^3 - 756*A*a*c^2*d^4*e^4 + 2259*B*a^2*c*d^3*e^5 - 6210*A*a^2*c*d^2*e^6 + 6077*B*a^3*d*e^7 + 9212*A*a^3*e^8)*m^3 - 4*(180*A*c^3*d^6*e^2 - 1350*B*a*c^2*d^5*e^3 + 2628*A*a*c^2*d^4*e^4 - 4797*B*a^2*c*d^3*e^5 + 8916*A*a^2*c*d^2*e^6 - 6138*B*a^3*d*e^7 - 12215*A*a^3*e^8)*m^2 + 144*(35*B*c^3*d^7*e - 40*A*c^3*d^6*e^2 + 140*B*a*c^2*d^5*e^3 - 168*A*a*c^2*d^4*e^4 + 210*B*a^2*c*d^3*e^5 - 280*A*a^2*c*d^2*e^6 + 140*B*a^3*d*e^7 + 481*A*a^3*e^8)*m)*x)*(e*x + d)^m/(e^8*m^8 + 36*e^8*m^7 + 546*e^8*m^6 + 4536*e^8*m^5 + 22449*e^8*m^4 + 67284*e^8*m^3 + 118124*e^8*m^2 + 109584*e^8*m + 40320*e^8)","B",0
1488,1,1373,0,0.441595," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(A a^{2} d e^{5} m^{5} - 120 \, B c^{2} d^{6} + 144 \, A c^{2} d^{5} e - 360 \, B a c d^{4} e^{2} + 480 \, A a c d^{3} e^{3} - 360 \, B a^{2} d^{2} e^{4} + 720 \, A a^{2} d e^{5} + {\left(B c^{2} e^{6} m^{5} + 15 \, B c^{2} e^{6} m^{4} + 85 \, B c^{2} e^{6} m^{3} + 225 \, B c^{2} e^{6} m^{2} + 274 \, B c^{2} e^{6} m + 120 \, B c^{2} e^{6}\right)} x^{6} + {\left(144 \, A c^{2} e^{6} + {\left(B c^{2} d e^{5} + A c^{2} e^{6}\right)} m^{5} + 2 \, {\left(5 \, B c^{2} d e^{5} + 8 \, A c^{2} e^{6}\right)} m^{4} + 5 \, {\left(7 \, B c^{2} d e^{5} + 19 \, A c^{2} e^{6}\right)} m^{3} + 10 \, {\left(5 \, B c^{2} d e^{5} + 26 \, A c^{2} e^{6}\right)} m^{2} + 12 \, {\left(2 \, B c^{2} d e^{5} + 27 \, A c^{2} e^{6}\right)} m\right)} x^{5} - {\left(B a^{2} d^{2} e^{4} - 20 \, A a^{2} d e^{5}\right)} m^{4} + {\left(360 \, B a c e^{6} + {\left(A c^{2} d e^{5} + 2 \, B a c e^{6}\right)} m^{5} - {\left(5 \, B c^{2} d^{2} e^{4} - 12 \, A c^{2} d e^{5} - 34 \, B a c e^{6}\right)} m^{4} - {\left(30 \, B c^{2} d^{2} e^{4} - 47 \, A c^{2} d e^{5} - 214 \, B a c e^{6}\right)} m^{3} - {\left(55 \, B c^{2} d^{2} e^{4} - 72 \, A c^{2} d e^{5} - 614 \, B a c e^{6}\right)} m^{2} - 6 \, {\left(5 \, B c^{2} d^{2} e^{4} - 6 \, A c^{2} d e^{5} - 132 \, B a c e^{6}\right)} m\right)} x^{4} + {\left(4 \, A a c d^{3} e^{3} - 18 \, B a^{2} d^{2} e^{4} + 155 \, A a^{2} d e^{5}\right)} m^{3} + 2 \, {\left(240 \, A a c e^{6} + {\left(B a c d e^{5} + A a c e^{6}\right)} m^{5} - 2 \, {\left(A c^{2} d^{2} e^{4} - 7 \, B a c d e^{5} - 9 \, A a c e^{6}\right)} m^{4} + {\left(10 \, B c^{2} d^{3} e^{3} - 18 \, A c^{2} d^{2} e^{4} + 65 \, B a c d e^{5} + 121 \, A a c e^{6}\right)} m^{3} + 2 \, {\left(15 \, B c^{2} d^{3} e^{3} - 20 \, A c^{2} d^{2} e^{4} + 56 \, B a c d e^{5} + 186 \, A a c e^{6}\right)} m^{2} + 4 \, {\left(5 \, B c^{2} d^{3} e^{3} - 6 \, A c^{2} d^{2} e^{4} + 15 \, B a c d e^{5} + 127 \, A a c e^{6}\right)} m\right)} x^{3} - {\left(12 \, B a c d^{4} e^{2} - 60 \, A a c d^{3} e^{3} + 119 \, B a^{2} d^{2} e^{4} - 580 \, A a^{2} d e^{5}\right)} m^{2} + {\left(360 \, B a^{2} e^{6} + {\left(2 \, A a c d e^{5} + B a^{2} e^{6}\right)} m^{5} - {\left(6 \, B a c d^{2} e^{4} - 32 \, A a c d e^{5} - 19 \, B a^{2} e^{6}\right)} m^{4} + {\left(12 \, A c^{2} d^{3} e^{3} - 72 \, B a c d^{2} e^{4} + 178 \, A a c d e^{5} + 137 \, B a^{2} e^{6}\right)} m^{3} - {\left(60 \, B c^{2} d^{4} e^{2} - 84 \, A c^{2} d^{3} e^{3} + 246 \, B a c d^{2} e^{4} - 388 \, A a c d e^{5} - 461 \, B a^{2} e^{6}\right)} m^{2} - 6 \, {\left(10 \, B c^{2} d^{4} e^{2} - 12 \, A c^{2} d^{3} e^{3} + 30 \, B a c d^{2} e^{4} - 40 \, A a c d e^{5} - 117 \, B a^{2} e^{6}\right)} m\right)} x^{2} + 2 \, {\left(12 \, A c^{2} d^{5} e - 66 \, B a c d^{4} e^{2} + 148 \, A a c d^{3} e^{3} - 171 \, B a^{2} d^{2} e^{4} + 522 \, A a^{2} d e^{5}\right)} m + {\left(720 \, A a^{2} e^{6} + {\left(B a^{2} d e^{5} + A a^{2} e^{6}\right)} m^{5} - 2 \, {\left(2 \, A a c d^{2} e^{4} - 9 \, B a^{2} d e^{5} - 10 \, A a^{2} e^{6}\right)} m^{4} + {\left(12 \, B a c d^{3} e^{3} - 60 \, A a c d^{2} e^{4} + 119 \, B a^{2} d e^{5} + 155 \, A a^{2} e^{6}\right)} m^{3} - 2 \, {\left(12 \, A c^{2} d^{4} e^{2} - 66 \, B a c d^{3} e^{3} + 148 \, A a c d^{2} e^{4} - 171 \, B a^{2} d e^{5} - 290 \, A a^{2} e^{6}\right)} m^{2} + 12 \, {\left(10 \, B c^{2} d^{5} e - 12 \, A c^{2} d^{4} e^{2} + 30 \, B a c d^{3} e^{3} - 40 \, A a c d^{2} e^{4} + 30 \, B a^{2} d e^{5} + 87 \, A a^{2} e^{6}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{6} m^{6} + 21 \, e^{6} m^{5} + 175 \, e^{6} m^{4} + 735 \, e^{6} m^{3} + 1624 \, e^{6} m^{2} + 1764 \, e^{6} m + 720 \, e^{6}}"," ",0,"(A*a^2*d*e^5*m^5 - 120*B*c^2*d^6 + 144*A*c^2*d^5*e - 360*B*a*c*d^4*e^2 + 480*A*a*c*d^3*e^3 - 360*B*a^2*d^2*e^4 + 720*A*a^2*d*e^5 + (B*c^2*e^6*m^5 + 15*B*c^2*e^6*m^4 + 85*B*c^2*e^6*m^3 + 225*B*c^2*e^6*m^2 + 274*B*c^2*e^6*m + 120*B*c^2*e^6)*x^6 + (144*A*c^2*e^6 + (B*c^2*d*e^5 + A*c^2*e^6)*m^5 + 2*(5*B*c^2*d*e^5 + 8*A*c^2*e^6)*m^4 + 5*(7*B*c^2*d*e^5 + 19*A*c^2*e^6)*m^3 + 10*(5*B*c^2*d*e^5 + 26*A*c^2*e^6)*m^2 + 12*(2*B*c^2*d*e^5 + 27*A*c^2*e^6)*m)*x^5 - (B*a^2*d^2*e^4 - 20*A*a^2*d*e^5)*m^4 + (360*B*a*c*e^6 + (A*c^2*d*e^5 + 2*B*a*c*e^6)*m^5 - (5*B*c^2*d^2*e^4 - 12*A*c^2*d*e^5 - 34*B*a*c*e^6)*m^4 - (30*B*c^2*d^2*e^4 - 47*A*c^2*d*e^5 - 214*B*a*c*e^6)*m^3 - (55*B*c^2*d^2*e^4 - 72*A*c^2*d*e^5 - 614*B*a*c*e^6)*m^2 - 6*(5*B*c^2*d^2*e^4 - 6*A*c^2*d*e^5 - 132*B*a*c*e^6)*m)*x^4 + (4*A*a*c*d^3*e^3 - 18*B*a^2*d^2*e^4 + 155*A*a^2*d*e^5)*m^3 + 2*(240*A*a*c*e^6 + (B*a*c*d*e^5 + A*a*c*e^6)*m^5 - 2*(A*c^2*d^2*e^4 - 7*B*a*c*d*e^5 - 9*A*a*c*e^6)*m^4 + (10*B*c^2*d^3*e^3 - 18*A*c^2*d^2*e^4 + 65*B*a*c*d*e^5 + 121*A*a*c*e^6)*m^3 + 2*(15*B*c^2*d^3*e^3 - 20*A*c^2*d^2*e^4 + 56*B*a*c*d*e^5 + 186*A*a*c*e^6)*m^2 + 4*(5*B*c^2*d^3*e^3 - 6*A*c^2*d^2*e^4 + 15*B*a*c*d*e^5 + 127*A*a*c*e^6)*m)*x^3 - (12*B*a*c*d^4*e^2 - 60*A*a*c*d^3*e^3 + 119*B*a^2*d^2*e^4 - 580*A*a^2*d*e^5)*m^2 + (360*B*a^2*e^6 + (2*A*a*c*d*e^5 + B*a^2*e^6)*m^5 - (6*B*a*c*d^2*e^4 - 32*A*a*c*d*e^5 - 19*B*a^2*e^6)*m^4 + (12*A*c^2*d^3*e^3 - 72*B*a*c*d^2*e^4 + 178*A*a*c*d*e^5 + 137*B*a^2*e^6)*m^3 - (60*B*c^2*d^4*e^2 - 84*A*c^2*d^3*e^3 + 246*B*a*c*d^2*e^4 - 388*A*a*c*d*e^5 - 461*B*a^2*e^6)*m^2 - 6*(10*B*c^2*d^4*e^2 - 12*A*c^2*d^3*e^3 + 30*B*a*c*d^2*e^4 - 40*A*a*c*d*e^5 - 117*B*a^2*e^6)*m)*x^2 + 2*(12*A*c^2*d^5*e - 66*B*a*c*d^4*e^2 + 148*A*a*c*d^3*e^3 - 171*B*a^2*d^2*e^4 + 522*A*a^2*d*e^5)*m + (720*A*a^2*e^6 + (B*a^2*d*e^5 + A*a^2*e^6)*m^5 - 2*(2*A*a*c*d^2*e^4 - 9*B*a^2*d*e^5 - 10*A*a^2*e^6)*m^4 + (12*B*a*c*d^3*e^3 - 60*A*a*c*d^2*e^4 + 119*B*a^2*d*e^5 + 155*A*a^2*e^6)*m^3 - 2*(12*A*c^2*d^4*e^2 - 66*B*a*c*d^3*e^3 + 148*A*a*c*d^2*e^4 - 171*B*a^2*d*e^5 - 290*A*a^2*e^6)*m^2 + 12*(10*B*c^2*d^5*e - 12*A*c^2*d^4*e^2 + 30*B*a*c*d^3*e^3 - 40*A*a*c*d^2*e^4 + 30*B*a^2*d*e^5 + 87*A*a^2*e^6)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)","B",0
1489,1,434,0,0.449718," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+a),x, algorithm=""fricas"")","\frac{{\left(A a d e^{3} m^{3} - 6 \, B c d^{4} + 8 \, A c d^{3} e - 12 \, B a d^{2} e^{2} + 24 \, A a d e^{3} + {\left(B c e^{4} m^{3} + 6 \, B c e^{4} m^{2} + 11 \, B c e^{4} m + 6 \, B c e^{4}\right)} x^{4} + {\left(8 \, A c e^{4} + {\left(B c d e^{3} + A c e^{4}\right)} m^{3} + {\left(3 \, B c d e^{3} + 7 \, A c e^{4}\right)} m^{2} + 2 \, {\left(B c d e^{3} + 7 \, A c e^{4}\right)} m\right)} x^{3} - {\left(B a d^{2} e^{2} - 9 \, A a d e^{3}\right)} m^{2} + {\left(12 \, B a e^{4} + {\left(A c d e^{3} + B a e^{4}\right)} m^{3} - {\left(3 \, B c d^{2} e^{2} - 5 \, A c d e^{3} - 8 \, B a e^{4}\right)} m^{2} - {\left(3 \, B c d^{2} e^{2} - 4 \, A c d e^{3} - 19 \, B a e^{4}\right)} m\right)} x^{2} + {\left(2 \, A c d^{3} e - 7 \, B a d^{2} e^{2} + 26 \, A a d e^{3}\right)} m + {\left(24 \, A a e^{4} + {\left(B a d e^{3} + A a e^{4}\right)} m^{3} - {\left(2 \, A c d^{2} e^{2} - 7 \, B a d e^{3} - 9 \, A a e^{4}\right)} m^{2} + 2 \, {\left(3 \, B c d^{3} e - 4 \, A c d^{2} e^{2} + 6 \, B a d e^{3} + 13 \, A a e^{4}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"(A*a*d*e^3*m^3 - 6*B*c*d^4 + 8*A*c*d^3*e - 12*B*a*d^2*e^2 + 24*A*a*d*e^3 + (B*c*e^4*m^3 + 6*B*c*e^4*m^2 + 11*B*c*e^4*m + 6*B*c*e^4)*x^4 + (8*A*c*e^4 + (B*c*d*e^3 + A*c*e^4)*m^3 + (3*B*c*d*e^3 + 7*A*c*e^4)*m^2 + 2*(B*c*d*e^3 + 7*A*c*e^4)*m)*x^3 - (B*a*d^2*e^2 - 9*A*a*d*e^3)*m^2 + (12*B*a*e^4 + (A*c*d*e^3 + B*a*e^4)*m^3 - (3*B*c*d^2*e^2 - 5*A*c*d*e^3 - 8*B*a*e^4)*m^2 - (3*B*c*d^2*e^2 - 4*A*c*d*e^3 - 19*B*a*e^4)*m)*x^2 + (2*A*c*d^3*e - 7*B*a*d^2*e^2 + 26*A*a*d*e^3)*m + (24*A*a*e^4 + (B*a*d*e^3 + A*a*e^4)*m^3 - (2*A*c*d^2*e^2 - 7*B*a*d*e^3 - 9*A*a*e^4)*m^2 + 2*(3*B*c*d^3*e - 4*A*c*d^2*e^2 + 6*B*a*d*e^3 + 13*A*a*e^4)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
1490,0,0,0,0.445415," ","integrate((B*x+A)*(e*x+d)^m/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{c x^{2} + a}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^m/(c*x^2 + a), x)","F",0
1491,0,0,0,0.423169," ","integrate((B*x+A)*(e*x+d)^m/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^m/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
1492,0,0,0,0.445456," ","integrate((B*x+A)*(e*x+d)^(1+m)/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m + 1}}{c x^{2} + a}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^(m + 1)/(c*x^2 + a), x)","F",0
1493,1,47,0,0.445162," ","integrate((c*d*x-a*e)*(e*x+d)^(-3-2*p)*(c*x^2+a)^p,x, algorithm=""fricas"")","\frac{{\left(c e x^{3} + c d x^{2} + a e x + a d\right)} {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*e*x^3 + c*d*x^2 + a*e*x + a*d)*(c*x^2 + a)^p*(e*x + d)^(-2*p - 3)/(p + 1)","A",0
1494,1,280,0,0.356142," ","integrate((2*c*x+b)*(e*x+d)^4*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{4} x^{8} e^{4} c^{2} + \frac{8}{7} x^{7} e^{3} d c^{2} + \frac{3}{7} x^{7} e^{4} c b + 2 x^{6} e^{2} d^{2} c^{2} + 2 x^{6} e^{3} d c b + \frac{1}{6} x^{6} e^{4} b^{2} + \frac{1}{3} x^{6} e^{4} c a + \frac{8}{5} x^{5} e d^{3} c^{2} + \frac{18}{5} x^{5} e^{2} d^{2} c b + \frac{4}{5} x^{5} e^{3} d b^{2} + \frac{8}{5} x^{5} e^{3} d c a + \frac{1}{5} x^{5} e^{4} b a + \frac{1}{2} x^{4} d^{4} c^{2} + 3 x^{4} e d^{3} c b + \frac{3}{2} x^{4} e^{2} d^{2} b^{2} + 3 x^{4} e^{2} d^{2} c a + x^{4} e^{3} d b a + x^{3} d^{4} c b + \frac{4}{3} x^{3} e d^{3} b^{2} + \frac{8}{3} x^{3} e d^{3} c a + 2 x^{3} e^{2} d^{2} b a + \frac{1}{2} x^{2} d^{4} b^{2} + x^{2} d^{4} c a + 2 x^{2} e d^{3} b a + x d^{4} b a"," ",0,"1/4*x^8*e^4*c^2 + 8/7*x^7*e^3*d*c^2 + 3/7*x^7*e^4*c*b + 2*x^6*e^2*d^2*c^2 + 2*x^6*e^3*d*c*b + 1/6*x^6*e^4*b^2 + 1/3*x^6*e^4*c*a + 8/5*x^5*e*d^3*c^2 + 18/5*x^5*e^2*d^2*c*b + 4/5*x^5*e^3*d*b^2 + 8/5*x^5*e^3*d*c*a + 1/5*x^5*e^4*b*a + 1/2*x^4*d^4*c^2 + 3*x^4*e*d^3*c*b + 3/2*x^4*e^2*d^2*b^2 + 3*x^4*e^2*d^2*c*a + x^4*e^3*d*b*a + x^3*d^4*c*b + 4/3*x^3*e*d^3*b^2 + 8/3*x^3*e*d^3*c*a + 2*x^3*e^2*d^2*b*a + 1/2*x^2*d^4*b^2 + x^2*d^4*c*a + 2*x^2*e*d^3*b*a + x*d^4*b*a","B",0
1495,1,211,0,0.371241," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{2}{7} x^{7} e^{3} c^{2} + x^{6} e^{2} d c^{2} + \frac{1}{2} x^{6} e^{3} c b + \frac{6}{5} x^{5} e d^{2} c^{2} + \frac{9}{5} x^{5} e^{2} d c b + \frac{1}{5} x^{5} e^{3} b^{2} + \frac{2}{5} x^{5} e^{3} c a + \frac{1}{2} x^{4} d^{3} c^{2} + \frac{9}{4} x^{4} e d^{2} c b + \frac{3}{4} x^{4} e^{2} d b^{2} + \frac{3}{2} x^{4} e^{2} d c a + \frac{1}{4} x^{4} e^{3} b a + x^{3} d^{3} c b + x^{3} e d^{2} b^{2} + 2 x^{3} e d^{2} c a + x^{3} e^{2} d b a + \frac{1}{2} x^{2} d^{3} b^{2} + x^{2} d^{3} c a + \frac{3}{2} x^{2} e d^{2} b a + x d^{3} b a"," ",0,"2/7*x^7*e^3*c^2 + x^6*e^2*d*c^2 + 1/2*x^6*e^3*c*b + 6/5*x^5*e*d^2*c^2 + 9/5*x^5*e^2*d*c*b + 1/5*x^5*e^3*b^2 + 2/5*x^5*e^3*c*a + 1/2*x^4*d^3*c^2 + 9/4*x^4*e*d^2*c*b + 3/4*x^4*e^2*d*b^2 + 3/2*x^4*e^2*d*c*a + 1/4*x^4*e^3*b*a + x^3*d^3*c*b + x^3*e*d^2*b^2 + 2*x^3*e*d^2*c*a + x^3*e^2*d*b*a + 1/2*x^2*d^3*b^2 + x^2*d^3*c*a + 3/2*x^2*e*d^2*b*a + x*d^3*b*a","A",0
1496,1,146,0,0.370315," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{3} x^{6} e^{2} c^{2} + \frac{4}{5} x^{5} e d c^{2} + \frac{3}{5} x^{5} e^{2} c b + \frac{1}{2} x^{4} d^{2} c^{2} + \frac{3}{2} x^{4} e d c b + \frac{1}{4} x^{4} e^{2} b^{2} + \frac{1}{2} x^{4} e^{2} c a + x^{3} d^{2} c b + \frac{2}{3} x^{3} e d b^{2} + \frac{4}{3} x^{3} e d c a + \frac{1}{3} x^{3} e^{2} b a + \frac{1}{2} x^{2} d^{2} b^{2} + x^{2} d^{2} c a + x^{2} e d b a + x d^{2} b a"," ",0,"1/3*x^6*e^2*c^2 + 4/5*x^5*e*d*c^2 + 3/5*x^5*e^2*c*b + 1/2*x^4*d^2*c^2 + 3/2*x^4*e*d*c*b + 1/4*x^4*e^2*b^2 + 1/2*x^4*e^2*c*a + x^3*d^2*c*b + 2/3*x^3*e*d*b^2 + 4/3*x^3*e*d*c*a + 1/3*x^3*e^2*b*a + 1/2*x^2*d^2*b^2 + x^2*d^2*c*a + x^2*e*d*b*a + x*d^2*b*a","A",0
1497,1,80,0,0.363236," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{2}{5} x^{5} e c^{2} + \frac{1}{2} x^{4} d c^{2} + \frac{3}{4} x^{4} e c b + x^{3} d c b + \frac{1}{3} x^{3} e b^{2} + \frac{2}{3} x^{3} e c a + \frac{1}{2} x^{2} d b^{2} + x^{2} d c a + \frac{1}{2} x^{2} e b a + x d b a"," ",0,"2/5*x^5*e*c^2 + 1/2*x^4*d*c^2 + 3/4*x^4*e*c*b + x^3*d*c*b + 1/3*x^3*e*b^2 + 2/3*x^3*e*c*a + 1/2*x^2*d*b^2 + x^2*d*c*a + 1/2*x^2*e*b*a + x*d*b*a","A",0
1498,1,33,0,0.368116," ","integrate((2*c*x+b)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{2} x^{4} c^{2} + x^{3} c b + \frac{1}{2} x^{2} b^{2} + x^{2} c a + x b a"," ",0,"1/2*x^4*c^2 + x^3*c*b + 1/2*x^2*b^2 + x^2*c*a + x*b*a","B",0
1499,1,117,0,0.419802," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d),x, algorithm=""fricas"")","\frac{4 \, c^{2} e^{3} x^{3} - 3 \, {\left(2 \, c^{2} d e^{2} - 3 \, b c e^{3}\right)} x^{2} + 6 \, {\left(2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + {\left(b^{2} + 2 \, a c\right)} e^{3}\right)} x - 6 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e - a b e^{3} + {\left(b^{2} + 2 \, a c\right)} d e^{2}\right)} \log\left(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(4*c^2*e^3*x^3 - 3*(2*c^2*d*e^2 - 3*b*c*e^3)*x^2 + 6*(2*c^2*d^2*e - 3*b*c*d*e^2 + (b^2 + 2*a*c)*e^3)*x - 6*(2*c^2*d^3 - 3*b*c*d^2*e - a*b*e^3 + (b^2 + 2*a*c)*d*e^2)*log(e*x + d))/e^4","A",0
1500,1,172,0,0.420704," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{c^{2} e^{3} x^{3} + 2 \, c^{2} d^{3} - 3 \, b c d^{2} e - a b e^{3} + {\left(b^{2} + 2 \, a c\right)} d e^{2} - 3 \, {\left(c^{2} d e^{2} - b c e^{3}\right)} x^{2} - {\left(4 \, c^{2} d^{2} e - 3 \, b c d e^{2}\right)} x + {\left(6 \, c^{2} d^{3} - 6 \, b c d^{2} e + {\left(b^{2} + 2 \, a c\right)} d e^{2} + {\left(6 \, c^{2} d^{2} e - 6 \, b c d e^{2} + {\left(b^{2} + 2 \, a c\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{e^{5} x + d e^{4}}"," ",0,"(c^2*e^3*x^3 + 2*c^2*d^3 - 3*b*c*d^2*e - a*b*e^3 + (b^2 + 2*a*c)*d*e^2 - 3*(c^2*d*e^2 - b*c*e^3)*x^2 - (4*c^2*d^2*e - 3*b*c*d*e^2)*x + (6*c^2*d^3 - 6*b*c*d^2*e + (b^2 + 2*a*c)*d*e^2 + (6*c^2*d^2*e - 6*b*c*d*e^2 + (b^2 + 2*a*c)*e^3)*x)*log(e*x + d))/(e^5*x + d*e^4)","A",0
1501,1,187,0,0.407208," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{4 \, c^{2} e^{3} x^{3} + 8 \, c^{2} d e^{2} x^{2} - 10 \, c^{2} d^{3} + 9 \, b c d^{2} e - a b e^{3} - {\left(b^{2} + 2 \, a c\right)} d e^{2} - 2 \, {\left(4 \, c^{2} d^{2} e - 6 \, b c d e^{2} + {\left(b^{2} + 2 \, a c\right)} e^{3}\right)} x - 6 \, {\left(2 \, c^{2} d^{3} - b c d^{2} e + {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{2} e - b c d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(4*c^2*e^3*x^3 + 8*c^2*d*e^2*x^2 - 10*c^2*d^3 + 9*b*c*d^2*e - a*b*e^3 - (b^2 + 2*a*c)*d*e^2 - 2*(4*c^2*d^2*e - 6*b*c*d*e^2 + (b^2 + 2*a*c)*e^3)*x - 6*(2*c^2*d^3 - b*c*d^2*e + (2*c^2*d*e^2 - b*c*e^3)*x^2 + 2*(2*c^2*d^2*e - b*c*d*e^2)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1502,1,179,0,0.410672," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{22 \, c^{2} d^{3} - 6 \, b c d^{2} e - 2 \, a b e^{3} - {\left(b^{2} + 2 \, a c\right)} d e^{2} + 18 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} x^{2} + 3 \, {\left(18 \, c^{2} d^{2} e - 6 \, b c d e^{2} - {\left(b^{2} + 2 \, a c\right)} e^{3}\right)} x + 12 \, {\left(c^{2} e^{3} x^{3} + 3 \, c^{2} d e^{2} x^{2} + 3 \, c^{2} d^{2} e x + c^{2} d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(22*c^2*d^3 - 6*b*c*d^2*e - 2*a*b*e^3 - (b^2 + 2*a*c)*d*e^2 + 18*(2*c^2*d*e^2 - b*c*e^3)*x^2 + 3*(18*c^2*d^2*e - 6*b*c*d*e^2 - (b^2 + 2*a*c)*e^3)*x + 12*(c^2*e^3*x^3 + 3*c^2*d*e^2*x^2 + 3*c^2*d^2*e*x + c^2*d^3)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1503,1,150,0,0.438050," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{24 \, c^{2} e^{3} x^{3} + 6 \, c^{2} d^{3} + 3 \, b c d^{2} e + 3 \, a b e^{3} + {\left(b^{2} + 2 \, a c\right)} d e^{2} + 18 \, {\left(2 \, c^{2} d e^{2} + b c e^{3}\right)} x^{2} + 4 \, {\left(6 \, c^{2} d^{2} e + 3 \, b c d e^{2} + {\left(b^{2} + 2 \, a c\right)} e^{3}\right)} x}{12 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-1/12*(24*c^2*e^3*x^3 + 6*c^2*d^3 + 3*b*c*d^2*e + 3*a*b*e^3 + (b^2 + 2*a*c)*d*e^2 + 18*(2*c^2*d*e^2 + b*c*e^3)*x^2 + 4*(6*c^2*d^2*e + 3*b*c*d*e^2 + (b^2 + 2*a*c)*e^3)*x)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","A",0
1504,1,561,0,0.384024," ","integrate((2*c*x+b)*(e*x+d)^4*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{5} x^{10} e^{4} c^{3} + \frac{8}{9} x^{9} e^{3} d c^{3} + \frac{5}{9} x^{9} e^{4} c^{2} b + \frac{3}{2} x^{8} e^{2} d^{2} c^{3} + \frac{5}{2} x^{8} e^{3} d c^{2} b + \frac{1}{2} x^{8} e^{4} c b^{2} + \frac{1}{2} x^{8} e^{4} c^{2} a + \frac{8}{7} x^{7} e d^{3} c^{3} + \frac{30}{7} x^{7} e^{2} d^{2} c^{2} b + \frac{16}{7} x^{7} e^{3} d c b^{2} + \frac{1}{7} x^{7} e^{4} b^{3} + \frac{16}{7} x^{7} e^{3} d c^{2} a + \frac{6}{7} x^{7} e^{4} c b a + \frac{1}{3} x^{6} d^{4} c^{3} + \frac{10}{3} x^{6} e d^{3} c^{2} b + 4 x^{6} e^{2} d^{2} c b^{2} + \frac{2}{3} x^{6} e^{3} d b^{3} + 4 x^{6} e^{2} d^{2} c^{2} a + 4 x^{6} e^{3} d c b a + \frac{1}{3} x^{6} e^{4} b^{2} a + \frac{1}{3} x^{6} e^{4} c a^{2} + x^{5} d^{4} c^{2} b + \frac{16}{5} x^{5} e d^{3} c b^{2} + \frac{6}{5} x^{5} e^{2} d^{2} b^{3} + \frac{16}{5} x^{5} e d^{3} c^{2} a + \frac{36}{5} x^{5} e^{2} d^{2} c b a + \frac{8}{5} x^{5} e^{3} d b^{2} a + \frac{8}{5} x^{5} e^{3} d c a^{2} + \frac{1}{5} x^{5} e^{4} b a^{2} + x^{4} d^{4} c b^{2} + x^{4} e d^{3} b^{3} + x^{4} d^{4} c^{2} a + 6 x^{4} e d^{3} c b a + 3 x^{4} e^{2} d^{2} b^{2} a + 3 x^{4} e^{2} d^{2} c a^{2} + x^{4} e^{3} d b a^{2} + \frac{1}{3} x^{3} d^{4} b^{3} + 2 x^{3} d^{4} c b a + \frac{8}{3} x^{3} e d^{3} b^{2} a + \frac{8}{3} x^{3} e d^{3} c a^{2} + 2 x^{3} e^{2} d^{2} b a^{2} + x^{2} d^{4} b^{2} a + x^{2} d^{4} c a^{2} + 2 x^{2} e d^{3} b a^{2} + x d^{4} b a^{2}"," ",0,"1/5*x^10*e^4*c^3 + 8/9*x^9*e^3*d*c^3 + 5/9*x^9*e^4*c^2*b + 3/2*x^8*e^2*d^2*c^3 + 5/2*x^8*e^3*d*c^2*b + 1/2*x^8*e^4*c*b^2 + 1/2*x^8*e^4*c^2*a + 8/7*x^7*e*d^3*c^3 + 30/7*x^7*e^2*d^2*c^2*b + 16/7*x^7*e^3*d*c*b^2 + 1/7*x^7*e^4*b^3 + 16/7*x^7*e^3*d*c^2*a + 6/7*x^7*e^4*c*b*a + 1/3*x^6*d^4*c^3 + 10/3*x^6*e*d^3*c^2*b + 4*x^6*e^2*d^2*c*b^2 + 2/3*x^6*e^3*d*b^3 + 4*x^6*e^2*d^2*c^2*a + 4*x^6*e^3*d*c*b*a + 1/3*x^6*e^4*b^2*a + 1/3*x^6*e^4*c*a^2 + x^5*d^4*c^2*b + 16/5*x^5*e*d^3*c*b^2 + 6/5*x^5*e^2*d^2*b^3 + 16/5*x^5*e*d^3*c^2*a + 36/5*x^5*e^2*d^2*c*b*a + 8/5*x^5*e^3*d*b^2*a + 8/5*x^5*e^3*d*c*a^2 + 1/5*x^5*e^4*b*a^2 + x^4*d^4*c*b^2 + x^4*e*d^3*b^3 + x^4*d^4*c^2*a + 6*x^4*e*d^3*c*b*a + 3*x^4*e^2*d^2*b^2*a + 3*x^4*e^2*d^2*c*a^2 + x^4*e^3*d*b*a^2 + 1/3*x^3*d^4*b^3 + 2*x^3*d^4*c*b*a + 8/3*x^3*e*d^3*b^2*a + 8/3*x^3*e*d^3*c*a^2 + 2*x^3*e^2*d^2*b*a^2 + x^2*d^4*b^2*a + x^2*d^4*c*a^2 + 2*x^2*e*d^3*b*a^2 + x*d^4*b*a^2","B",0
1505,1,429,0,0.370124," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{2}{9} x^{9} e^{3} c^{3} + \frac{3}{4} x^{8} e^{2} d c^{3} + \frac{5}{8} x^{8} e^{3} c^{2} b + \frac{6}{7} x^{7} e d^{2} c^{3} + \frac{15}{7} x^{7} e^{2} d c^{2} b + \frac{4}{7} x^{7} e^{3} c b^{2} + \frac{4}{7} x^{7} e^{3} c^{2} a + \frac{1}{3} x^{6} d^{3} c^{3} + \frac{5}{2} x^{6} e d^{2} c^{2} b + 2 x^{6} e^{2} d c b^{2} + \frac{1}{6} x^{6} e^{3} b^{3} + 2 x^{6} e^{2} d c^{2} a + x^{6} e^{3} c b a + x^{5} d^{3} c^{2} b + \frac{12}{5} x^{5} e d^{2} c b^{2} + \frac{3}{5} x^{5} e^{2} d b^{3} + \frac{12}{5} x^{5} e d^{2} c^{2} a + \frac{18}{5} x^{5} e^{2} d c b a + \frac{2}{5} x^{5} e^{3} b^{2} a + \frac{2}{5} x^{5} e^{3} c a^{2} + x^{4} d^{3} c b^{2} + \frac{3}{4} x^{4} e d^{2} b^{3} + x^{4} d^{3} c^{2} a + \frac{9}{2} x^{4} e d^{2} c b a + \frac{3}{2} x^{4} e^{2} d b^{2} a + \frac{3}{2} x^{4} e^{2} d c a^{2} + \frac{1}{4} x^{4} e^{3} b a^{2} + \frac{1}{3} x^{3} d^{3} b^{3} + 2 x^{3} d^{3} c b a + 2 x^{3} e d^{2} b^{2} a + 2 x^{3} e d^{2} c a^{2} + x^{3} e^{2} d b a^{2} + x^{2} d^{3} b^{2} a + x^{2} d^{3} c a^{2} + \frac{3}{2} x^{2} e d^{2} b a^{2} + x d^{3} b a^{2}"," ",0,"2/9*x^9*e^3*c^3 + 3/4*x^8*e^2*d*c^3 + 5/8*x^8*e^3*c^2*b + 6/7*x^7*e*d^2*c^3 + 15/7*x^7*e^2*d*c^2*b + 4/7*x^7*e^3*c*b^2 + 4/7*x^7*e^3*c^2*a + 1/3*x^6*d^3*c^3 + 5/2*x^6*e*d^2*c^2*b + 2*x^6*e^2*d*c*b^2 + 1/6*x^6*e^3*b^3 + 2*x^6*e^2*d*c^2*a + x^6*e^3*c*b*a + x^5*d^3*c^2*b + 12/5*x^5*e*d^2*c*b^2 + 3/5*x^5*e^2*d*b^3 + 12/5*x^5*e*d^2*c^2*a + 18/5*x^5*e^2*d*c*b*a + 2/5*x^5*e^3*b^2*a + 2/5*x^5*e^3*c*a^2 + x^4*d^3*c*b^2 + 3/4*x^4*e*d^2*b^3 + x^4*d^3*c^2*a + 9/2*x^4*e*d^2*c*b*a + 3/2*x^4*e^2*d*b^2*a + 3/2*x^4*e^2*d*c*a^2 + 1/4*x^4*e^3*b*a^2 + 1/3*x^3*d^3*b^3 + 2*x^3*d^3*c*b*a + 2*x^3*e*d^2*b^2*a + 2*x^3*e*d^2*c*a^2 + x^3*e^2*d*b*a^2 + x^2*d^3*b^2*a + x^2*d^3*c*a^2 + 3/2*x^2*e*d^2*b*a^2 + x*d^3*b*a^2","A",0
1506,1,298,0,0.400181," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{4} x^{8} e^{2} c^{3} + \frac{4}{7} x^{7} e d c^{3} + \frac{5}{7} x^{7} e^{2} c^{2} b + \frac{1}{3} x^{6} d^{2} c^{3} + \frac{5}{3} x^{6} e d c^{2} b + \frac{2}{3} x^{6} e^{2} c b^{2} + \frac{2}{3} x^{6} e^{2} c^{2} a + x^{5} d^{2} c^{2} b + \frac{8}{5} x^{5} e d c b^{2} + \frac{1}{5} x^{5} e^{2} b^{3} + \frac{8}{5} x^{5} e d c^{2} a + \frac{6}{5} x^{5} e^{2} c b a + x^{4} d^{2} c b^{2} + \frac{1}{2} x^{4} e d b^{3} + x^{4} d^{2} c^{2} a + 3 x^{4} e d c b a + \frac{1}{2} x^{4} e^{2} b^{2} a + \frac{1}{2} x^{4} e^{2} c a^{2} + \frac{1}{3} x^{3} d^{2} b^{3} + 2 x^{3} d^{2} c b a + \frac{4}{3} x^{3} e d b^{2} a + \frac{4}{3} x^{3} e d c a^{2} + \frac{1}{3} x^{3} e^{2} b a^{2} + x^{2} d^{2} b^{2} a + x^{2} d^{2} c a^{2} + x^{2} e d b a^{2} + x d^{2} b a^{2}"," ",0,"1/4*x^8*e^2*c^3 + 4/7*x^7*e*d*c^3 + 5/7*x^7*e^2*c^2*b + 1/3*x^6*d^2*c^3 + 5/3*x^6*e*d*c^2*b + 2/3*x^6*e^2*c*b^2 + 2/3*x^6*e^2*c^2*a + x^5*d^2*c^2*b + 8/5*x^5*e*d*c*b^2 + 1/5*x^5*e^2*b^3 + 8/5*x^5*e*d*c^2*a + 6/5*x^5*e^2*c*b*a + x^4*d^2*c*b^2 + 1/2*x^4*e*d*b^3 + x^4*d^2*c^2*a + 3*x^4*e*d*c*b*a + 1/2*x^4*e^2*b^2*a + 1/2*x^4*e^2*c*a^2 + 1/3*x^3*d^2*b^3 + 2*x^3*d^2*c*b*a + 4/3*x^3*e*d*b^2*a + 4/3*x^3*e*d*c*a^2 + 1/3*x^3*e^2*b*a^2 + x^2*d^2*b^2*a + x^2*d^2*c*a^2 + x^2*e*d*b*a^2 + x*d^2*b*a^2","A",0
1507,1,167,0,0.372393," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{2}{7} x^{7} e c^{3} + \frac{1}{3} x^{6} d c^{3} + \frac{5}{6} x^{6} e c^{2} b + x^{5} d c^{2} b + \frac{4}{5} x^{5} e c b^{2} + \frac{4}{5} x^{5} e c^{2} a + x^{4} d c b^{2} + \frac{1}{4} x^{4} e b^{3} + x^{4} d c^{2} a + \frac{3}{2} x^{4} e c b a + \frac{1}{3} x^{3} d b^{3} + 2 x^{3} d c b a + \frac{2}{3} x^{3} e b^{2} a + \frac{2}{3} x^{3} e c a^{2} + x^{2} d b^{2} a + x^{2} d c a^{2} + \frac{1}{2} x^{2} e b a^{2} + x d b a^{2}"," ",0,"2/7*x^7*e*c^3 + 1/3*x^6*d*c^3 + 5/6*x^6*e*c^2*b + x^5*d*c^2*b + 4/5*x^5*e*c*b^2 + 4/5*x^5*e*c^2*a + x^4*d*c*b^2 + 1/4*x^4*e*b^3 + x^4*d*c^2*a + 3/2*x^4*e*c*b*a + 1/3*x^3*d*b^3 + 2*x^3*d*c*b*a + 2/3*x^3*e*b^2*a + 2/3*x^3*e*c*a^2 + x^2*d*b^2*a + x^2*d*c*a^2 + 1/2*x^2*e*b*a^2 + x*d*b*a^2","A",0
1508,1,71,0,0.371591," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{3} x^{6} c^{3} + x^{5} c^{2} b + x^{4} c b^{2} + x^{4} c^{2} a + \frac{1}{3} x^{3} b^{3} + 2 x^{3} c b a + x^{2} b^{2} a + x^{2} c a^{2} + x b a^{2}"," ",0,"1/3*x^6*c^3 + x^5*c^2*b + x^4*c*b^2 + x^4*c^2*a + 1/3*x^3*b^3 + 2*x^3*c*b*a + x^2*b^2*a + x^2*c*a^2 + x*b*a^2","B",0
1509,1,308,0,0.400437," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d),x, algorithm=""fricas"")","\frac{24 \, c^{3} e^{5} x^{5} - 15 \, {\left(2 \, c^{3} d e^{4} - 5 \, b c^{2} e^{5}\right)} x^{4} + 20 \, {\left(2 \, c^{3} d^{2} e^{3} - 5 \, b c^{2} d e^{4} + 4 \, {\left(b^{2} c + a c^{2}\right)} e^{5}\right)} x^{3} - 30 \, {\left(2 \, c^{3} d^{3} e^{2} - 5 \, b c^{2} d^{2} e^{3} + 4 \, {\left(b^{2} c + a c^{2}\right)} d e^{4} - {\left(b^{3} + 6 \, a b c\right)} e^{5}\right)} x^{2} + 60 \, {\left(2 \, c^{3} d^{4} e - 5 \, b c^{2} d^{3} e^{2} + 4 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d e^{4} + 2 \, {\left(a b^{2} + a^{2} c\right)} e^{5}\right)} x - 60 \, {\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e - a^{2} b e^{5} + 4 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} + 2 \, {\left(a b^{2} + a^{2} c\right)} d e^{4}\right)} \log\left(e x + d\right)}{60 \, e^{6}}"," ",0,"1/60*(24*c^3*e^5*x^5 - 15*(2*c^3*d*e^4 - 5*b*c^2*e^5)*x^4 + 20*(2*c^3*d^2*e^3 - 5*b*c^2*d*e^4 + 4*(b^2*c + a*c^2)*e^5)*x^3 - 30*(2*c^3*d^3*e^2 - 5*b*c^2*d^2*e^3 + 4*(b^2*c + a*c^2)*d*e^4 - (b^3 + 6*a*b*c)*e^5)*x^2 + 60*(2*c^3*d^4*e - 5*b*c^2*d^3*e^2 + 4*(b^2*c + a*c^2)*d^2*e^3 - (b^3 + 6*a*b*c)*d*e^4 + 2*(a*b^2 + a^2*c)*e^5)*x - 60*(2*c^3*d^5 - 5*b*c^2*d^4*e - a^2*b*e^5 + 4*(b^2*c + a*c^2)*d^3*e^2 - (b^3 + 6*a*b*c)*d^2*e^3 + 2*(a*b^2 + a^2*c)*d*e^4)*log(e*x + d))/e^6","A",0
1510,1,444,0,0.414484," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{3 \, c^{3} e^{5} x^{5} + 12 \, c^{3} d^{5} - 30 \, b c^{2} d^{4} e - 6 \, a^{2} b e^{5} + 24 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} - 6 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} + 12 \, {\left(a b^{2} + a^{2} c\right)} d e^{4} - 5 \, {\left(c^{3} d e^{4} - 2 \, b c^{2} e^{5}\right)} x^{4} + 2 \, {\left(5 \, c^{3} d^{2} e^{3} - 10 \, b c^{2} d e^{4} + 6 \, {\left(b^{2} c + a c^{2}\right)} e^{5}\right)} x^{3} - 6 \, {\left(5 \, c^{3} d^{3} e^{2} - 10 \, b c^{2} d^{2} e^{3} + 6 \, {\left(b^{2} c + a c^{2}\right)} d e^{4} - {\left(b^{3} + 6 \, a b c\right)} e^{5}\right)} x^{2} - 6 \, {\left(8 \, c^{3} d^{4} e - 15 \, b c^{2} d^{3} e^{2} + 8 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d e^{4}\right)} x + 12 \, {\left(5 \, c^{3} d^{5} - 10 \, b c^{2} d^{4} e + 6 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} + {\left(a b^{2} + a^{2} c\right)} d e^{4} + {\left(5 \, c^{3} d^{4} e - 10 \, b c^{2} d^{3} e^{2} + 6 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d e^{4} + {\left(a b^{2} + a^{2} c\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"1/6*(3*c^3*e^5*x^5 + 12*c^3*d^5 - 30*b*c^2*d^4*e - 6*a^2*b*e^5 + 24*(b^2*c + a*c^2)*d^3*e^2 - 6*(b^3 + 6*a*b*c)*d^2*e^3 + 12*(a*b^2 + a^2*c)*d*e^4 - 5*(c^3*d*e^4 - 2*b*c^2*e^5)*x^4 + 2*(5*c^3*d^2*e^3 - 10*b*c^2*d*e^4 + 6*(b^2*c + a*c^2)*e^5)*x^3 - 6*(5*c^3*d^3*e^2 - 10*b*c^2*d^2*e^3 + 6*(b^2*c + a*c^2)*d*e^4 - (b^3 + 6*a*b*c)*e^5)*x^2 - 6*(8*c^3*d^4*e - 15*b*c^2*d^3*e^2 + 8*(b^2*c + a*c^2)*d^2*e^3 - (b^3 + 6*a*b*c)*d*e^4)*x + 12*(5*c^3*d^5 - 10*b*c^2*d^4*e + 6*(b^2*c + a*c^2)*d^3*e^2 - (b^3 + 6*a*b*c)*d^2*e^3 + (a*b^2 + a^2*c)*d*e^4 + (5*c^3*d^4*e - 10*b*c^2*d^3*e^2 + 6*(b^2*c + a*c^2)*d^2*e^3 - (b^3 + 6*a*b*c)*d*e^4 + (a*b^2 + a^2*c)*e^5)*x)*log(e*x + d))/(e^7*x + d*e^6)","B",0
1511,1,487,0,0.415862," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{4 \, c^{3} e^{5} x^{5} - 54 \, c^{3} d^{5} + 105 \, b c^{2} d^{4} e - 3 \, a^{2} b e^{5} - 60 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} + 9 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} - 6 \, {\left(a b^{2} + a^{2} c\right)} d e^{4} - 5 \, {\left(2 \, c^{3} d e^{4} - 3 \, b c^{2} e^{5}\right)} x^{4} + 4 \, {\left(10 \, c^{3} d^{2} e^{3} - 15 \, b c^{2} d e^{4} + 6 \, {\left(b^{2} c + a c^{2}\right)} e^{5}\right)} x^{3} + 3 \, {\left(42 \, c^{3} d^{3} e^{2} - 55 \, b c^{2} d^{2} e^{3} + 16 \, {\left(b^{2} c + a c^{2}\right)} d e^{4}\right)} x^{2} + 6 \, {\left(2 \, c^{3} d^{4} e + 5 \, b c^{2} d^{3} e^{2} - 8 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} + 2 \, {\left(b^{3} + 6 \, a b c\right)} d e^{4} - 2 \, {\left(a b^{2} + a^{2} c\right)} e^{5}\right)} x - 6 \, {\left(20 \, c^{3} d^{5} - 30 \, b c^{2} d^{4} e + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} + {\left(20 \, c^{3} d^{3} e^{2} - 30 \, b c^{2} d^{2} e^{3} + 12 \, {\left(b^{2} c + a c^{2}\right)} d e^{4} - {\left(b^{3} + 6 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(20 \, c^{3} d^{4} e - 30 \, b c^{2} d^{3} e^{2} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"1/6*(4*c^3*e^5*x^5 - 54*c^3*d^5 + 105*b*c^2*d^4*e - 3*a^2*b*e^5 - 60*(b^2*c + a*c^2)*d^3*e^2 + 9*(b^3 + 6*a*b*c)*d^2*e^3 - 6*(a*b^2 + a^2*c)*d*e^4 - 5*(2*c^3*d*e^4 - 3*b*c^2*e^5)*x^4 + 4*(10*c^3*d^2*e^3 - 15*b*c^2*d*e^4 + 6*(b^2*c + a*c^2)*e^5)*x^3 + 3*(42*c^3*d^3*e^2 - 55*b*c^2*d^2*e^3 + 16*(b^2*c + a*c^2)*d*e^4)*x^2 + 6*(2*c^3*d^4*e + 5*b*c^2*d^3*e^2 - 8*(b^2*c + a*c^2)*d^2*e^3 + 2*(b^3 + 6*a*b*c)*d*e^4 - 2*(a*b^2 + a^2*c)*e^5)*x - 6*(20*c^3*d^5 - 30*b*c^2*d^4*e + 12*(b^2*c + a*c^2)*d^3*e^2 - (b^3 + 6*a*b*c)*d^2*e^3 + (20*c^3*d^3*e^2 - 30*b*c^2*d^2*e^3 + 12*(b^2*c + a*c^2)*d*e^4 - (b^3 + 6*a*b*c)*e^5)*x^2 + 2*(20*c^3*d^4*e - 30*b*c^2*d^3*e^2 + 12*(b^2*c + a*c^2)*d^2*e^3 - (b^3 + 6*a*b*c)*d*e^4)*x)*log(e*x + d))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","B",0
1512,1,487,0,0.409460," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, c^{3} e^{5} x^{5} + 47 \, c^{3} d^{5} - 65 \, b c^{2} d^{4} e - a^{2} b e^{5} + 22 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} - {\left(a b^{2} + a^{2} c\right)} d e^{4} - 15 \, {\left(c^{3} d e^{4} - b c^{2} e^{5}\right)} x^{4} - 9 \, {\left(7 \, c^{3} d^{2} e^{3} - 5 \, b c^{2} d e^{4}\right)} x^{3} - 3 \, {\left(3 \, c^{3} d^{3} e^{2} + 15 \, b c^{2} d^{2} e^{3} - 12 \, {\left(b^{2} c + a c^{2}\right)} d e^{4} + {\left(b^{3} + 6 \, a b c\right)} e^{5}\right)} x^{2} + 3 \, {\left(27 \, c^{3} d^{4} e - 45 \, b c^{2} d^{3} e^{2} + 18 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d e^{4} - {\left(a b^{2} + a^{2} c\right)} e^{5}\right)} x + 12 \, {\left(5 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} + {\left(5 \, c^{3} d^{2} e^{3} - 5 \, b c^{2} d e^{4} + {\left(b^{2} c + a c^{2}\right)} e^{5}\right)} x^{3} + 3 \, {\left(5 \, c^{3} d^{3} e^{2} - 5 \, b c^{2} d^{2} e^{3} + {\left(b^{2} c + a c^{2}\right)} d e^{4}\right)} x^{2} + 3 \, {\left(5 \, c^{3} d^{4} e - 5 \, b c^{2} d^{3} e^{2} + {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"1/3*(3*c^3*e^5*x^5 + 47*c^3*d^5 - 65*b*c^2*d^4*e - a^2*b*e^5 + 22*(b^2*c + a*c^2)*d^3*e^2 - (b^3 + 6*a*b*c)*d^2*e^3 - (a*b^2 + a^2*c)*d*e^4 - 15*(c^3*d*e^4 - b*c^2*e^5)*x^4 - 9*(7*c^3*d^2*e^3 - 5*b*c^2*d*e^4)*x^3 - 3*(3*c^3*d^3*e^2 + 15*b*c^2*d^2*e^3 - 12*(b^2*c + a*c^2)*d*e^4 + (b^3 + 6*a*b*c)*e^5)*x^2 + 3*(27*c^3*d^4*e - 45*b*c^2*d^3*e^2 + 18*(b^2*c + a*c^2)*d^2*e^3 - (b^3 + 6*a*b*c)*d*e^4 - (a*b^2 + a^2*c)*e^5)*x + 12*(5*c^3*d^5 - 5*b*c^2*d^4*e + (b^2*c + a*c^2)*d^3*e^2 + (5*c^3*d^2*e^3 - 5*b*c^2*d*e^4 + (b^2*c + a*c^2)*e^5)*x^3 + 3*(5*c^3*d^3*e^2 - 5*b*c^2*d^2*e^3 + (b^2*c + a*c^2)*d*e^4)*x^2 + 3*(5*c^3*d^4*e - 5*b*c^2*d^3*e^2 + (b^2*c + a*c^2)*d^2*e^3)*x)*log(e*x + d))/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","B",0
1513,1,458,0,0.425922," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{24 \, c^{3} e^{5} x^{5} + 96 \, c^{3} d e^{4} x^{4} - 154 \, c^{3} d^{5} + 125 \, b c^{2} d^{4} e - 3 \, a^{2} b e^{5} - 12 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} + a^{2} c\right)} d e^{4} - 48 \, {\left(2 \, c^{3} d^{2} e^{3} - 5 \, b c^{2} d e^{4} + {\left(b^{2} c + a c^{2}\right)} e^{5}\right)} x^{3} - 6 \, {\left(84 \, c^{3} d^{3} e^{2} - 90 \, b c^{2} d^{2} e^{3} + 12 \, {\left(b^{2} c + a c^{2}\right)} d e^{4} + {\left(b^{3} + 6 \, a b c\right)} e^{5}\right)} x^{2} - 4 \, {\left(124 \, c^{3} d^{4} e - 110 \, b c^{2} d^{3} e^{2} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} + {\left(b^{3} + 6 \, a b c\right)} d e^{4} + 2 \, {\left(a b^{2} + a^{2} c\right)} e^{5}\right)} x - 60 \, {\left(2 \, c^{3} d^{5} - b c^{2} d^{4} e + {\left(2 \, c^{3} d e^{4} - b c^{2} e^{5}\right)} x^{4} + 4 \, {\left(2 \, c^{3} d^{2} e^{3} - b c^{2} d e^{4}\right)} x^{3} + 6 \, {\left(2 \, c^{3} d^{3} e^{2} - b c^{2} d^{2} e^{3}\right)} x^{2} + 4 \, {\left(2 \, c^{3} d^{4} e - b c^{2} d^{3} e^{2}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{10} x^{4} + 4 \, d e^{9} x^{3} + 6 \, d^{2} e^{8} x^{2} + 4 \, d^{3} e^{7} x + d^{4} e^{6}\right)}}"," ",0,"1/12*(24*c^3*e^5*x^5 + 96*c^3*d*e^4*x^4 - 154*c^3*d^5 + 125*b*c^2*d^4*e - 3*a^2*b*e^5 - 12*(b^2*c + a*c^2)*d^3*e^2 - (b^3 + 6*a*b*c)*d^2*e^3 - 2*(a*b^2 + a^2*c)*d*e^4 - 48*(2*c^3*d^2*e^3 - 5*b*c^2*d*e^4 + (b^2*c + a*c^2)*e^5)*x^3 - 6*(84*c^3*d^3*e^2 - 90*b*c^2*d^2*e^3 + 12*(b^2*c + a*c^2)*d*e^4 + (b^3 + 6*a*b*c)*e^5)*x^2 - 4*(124*c^3*d^4*e - 110*b*c^2*d^3*e^2 + 12*(b^2*c + a*c^2)*d^2*e^3 + (b^3 + 6*a*b*c)*d*e^4 + 2*(a*b^2 + a^2*c)*e^5)*x - 60*(2*c^3*d^5 - b*c^2*d^4*e + (2*c^3*d*e^4 - b*c^2*e^5)*x^4 + 4*(2*c^3*d^2*e^3 - b*c^2*d*e^4)*x^3 + 6*(2*c^3*d^3*e^2 - b*c^2*d^2*e^3)*x^2 + 4*(2*c^3*d^4*e - b*c^2*d^3*e^2)*x)*log(e*x + d))/(e^10*x^4 + 4*d*e^9*x^3 + 6*d^2*e^8*x^2 + 4*d^3*e^7*x + d^4*e^6)","B",0
1514,1,936,0,0.442366," ","integrate((2*c*x+b)*(e*x+d)^4*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{6} x^{12} e^{4} c^{4} + \frac{8}{11} x^{11} e^{3} d c^{4} + \frac{7}{11} x^{11} e^{4} c^{3} b + \frac{6}{5} x^{10} e^{2} d^{2} c^{4} + \frac{14}{5} x^{10} e^{3} d c^{3} b + \frac{9}{10} x^{10} e^{4} c^{2} b^{2} + \frac{3}{5} x^{10} e^{4} c^{3} a + \frac{8}{9} x^{9} e d^{3} c^{4} + \frac{14}{3} x^{9} e^{2} d^{2} c^{3} b + 4 x^{9} e^{3} d c^{2} b^{2} + \frac{5}{9} x^{9} e^{4} c b^{3} + \frac{8}{3} x^{9} e^{3} d c^{3} a + \frac{5}{3} x^{9} e^{4} c^{2} b a + \frac{1}{4} x^{8} d^{4} c^{4} + \frac{7}{2} x^{8} e d^{3} c^{3} b + \frac{27}{4} x^{8} e^{2} d^{2} c^{2} b^{2} + \frac{5}{2} x^{8} e^{3} d c b^{3} + \frac{1}{8} x^{8} e^{4} b^{4} + \frac{9}{2} x^{8} e^{2} d^{2} c^{3} a + \frac{15}{2} x^{8} e^{3} d c^{2} b a + \frac{3}{2} x^{8} e^{4} c b^{2} a + \frac{3}{4} x^{8} e^{4} c^{2} a^{2} + x^{7} d^{4} c^{3} b + \frac{36}{7} x^{7} e d^{3} c^{2} b^{2} + \frac{30}{7} x^{7} e^{2} d^{2} c b^{3} + \frac{4}{7} x^{7} e^{3} d b^{4} + \frac{24}{7} x^{7} e d^{3} c^{3} a + \frac{90}{7} x^{7} e^{2} d^{2} c^{2} b a + \frac{48}{7} x^{7} e^{3} d c b^{2} a + \frac{3}{7} x^{7} e^{4} b^{3} a + \frac{24}{7} x^{7} e^{3} d c^{2} a^{2} + \frac{9}{7} x^{7} e^{4} c b a^{2} + \frac{3}{2} x^{6} d^{4} c^{2} b^{2} + \frac{10}{3} x^{6} e d^{3} c b^{3} + x^{6} e^{2} d^{2} b^{4} + x^{6} d^{4} c^{3} a + 10 x^{6} e d^{3} c^{2} b a + 12 x^{6} e^{2} d^{2} c b^{2} a + 2 x^{6} e^{3} d b^{3} a + 6 x^{6} e^{2} d^{2} c^{2} a^{2} + 6 x^{6} e^{3} d c b a^{2} + \frac{1}{2} x^{6} e^{4} b^{2} a^{2} + \frac{1}{3} x^{6} e^{4} c a^{3} + x^{5} d^{4} c b^{3} + \frac{4}{5} x^{5} e d^{3} b^{4} + 3 x^{5} d^{4} c^{2} b a + \frac{48}{5} x^{5} e d^{3} c b^{2} a + \frac{18}{5} x^{5} e^{2} d^{2} b^{3} a + \frac{24}{5} x^{5} e d^{3} c^{2} a^{2} + \frac{54}{5} x^{5} e^{2} d^{2} c b a^{2} + \frac{12}{5} x^{5} e^{3} d b^{2} a^{2} + \frac{8}{5} x^{5} e^{3} d c a^{3} + \frac{1}{5} x^{5} e^{4} b a^{3} + \frac{1}{4} x^{4} d^{4} b^{4} + 3 x^{4} d^{4} c b^{2} a + 3 x^{4} e d^{3} b^{3} a + \frac{3}{2} x^{4} d^{4} c^{2} a^{2} + 9 x^{4} e d^{3} c b a^{2} + \frac{9}{2} x^{4} e^{2} d^{2} b^{2} a^{2} + 3 x^{4} e^{2} d^{2} c a^{3} + x^{4} e^{3} d b a^{3} + x^{3} d^{4} b^{3} a + 3 x^{3} d^{4} c b a^{2} + 4 x^{3} e d^{3} b^{2} a^{2} + \frac{8}{3} x^{3} e d^{3} c a^{3} + 2 x^{3} e^{2} d^{2} b a^{3} + \frac{3}{2} x^{2} d^{4} b^{2} a^{2} + x^{2} d^{4} c a^{3} + 2 x^{2} e d^{3} b a^{3} + x d^{4} b a^{3}"," ",0,"1/6*x^12*e^4*c^4 + 8/11*x^11*e^3*d*c^4 + 7/11*x^11*e^4*c^3*b + 6/5*x^10*e^2*d^2*c^4 + 14/5*x^10*e^3*d*c^3*b + 9/10*x^10*e^4*c^2*b^2 + 3/5*x^10*e^4*c^3*a + 8/9*x^9*e*d^3*c^4 + 14/3*x^9*e^2*d^2*c^3*b + 4*x^9*e^3*d*c^2*b^2 + 5/9*x^9*e^4*c*b^3 + 8/3*x^9*e^3*d*c^3*a + 5/3*x^9*e^4*c^2*b*a + 1/4*x^8*d^4*c^4 + 7/2*x^8*e*d^3*c^3*b + 27/4*x^8*e^2*d^2*c^2*b^2 + 5/2*x^8*e^3*d*c*b^3 + 1/8*x^8*e^4*b^4 + 9/2*x^8*e^2*d^2*c^3*a + 15/2*x^8*e^3*d*c^2*b*a + 3/2*x^8*e^4*c*b^2*a + 3/4*x^8*e^4*c^2*a^2 + x^7*d^4*c^3*b + 36/7*x^7*e*d^3*c^2*b^2 + 30/7*x^7*e^2*d^2*c*b^3 + 4/7*x^7*e^3*d*b^4 + 24/7*x^7*e*d^3*c^3*a + 90/7*x^7*e^2*d^2*c^2*b*a + 48/7*x^7*e^3*d*c*b^2*a + 3/7*x^7*e^4*b^3*a + 24/7*x^7*e^3*d*c^2*a^2 + 9/7*x^7*e^4*c*b*a^2 + 3/2*x^6*d^4*c^2*b^2 + 10/3*x^6*e*d^3*c*b^3 + x^6*e^2*d^2*b^4 + x^6*d^4*c^3*a + 10*x^6*e*d^3*c^2*b*a + 12*x^6*e^2*d^2*c*b^2*a + 2*x^6*e^3*d*b^3*a + 6*x^6*e^2*d^2*c^2*a^2 + 6*x^6*e^3*d*c*b*a^2 + 1/2*x^6*e^4*b^2*a^2 + 1/3*x^6*e^4*c*a^3 + x^5*d^4*c*b^3 + 4/5*x^5*e*d^3*b^4 + 3*x^5*d^4*c^2*b*a + 48/5*x^5*e*d^3*c*b^2*a + 18/5*x^5*e^2*d^2*b^3*a + 24/5*x^5*e*d^3*c^2*a^2 + 54/5*x^5*e^2*d^2*c*b*a^2 + 12/5*x^5*e^3*d*b^2*a^2 + 8/5*x^5*e^3*d*c*a^3 + 1/5*x^5*e^4*b*a^3 + 1/4*x^4*d^4*b^4 + 3*x^4*d^4*c*b^2*a + 3*x^4*e*d^3*b^3*a + 3/2*x^4*d^4*c^2*a^2 + 9*x^4*e*d^3*c*b*a^2 + 9/2*x^4*e^2*d^2*b^2*a^2 + 3*x^4*e^2*d^2*c*a^3 + x^4*e^3*d*b*a^3 + x^3*d^4*b^3*a + 3*x^3*d^4*c*b*a^2 + 4*x^3*e*d^3*b^2*a^2 + 8/3*x^3*e*d^3*c*a^3 + 2*x^3*e^2*d^2*b*a^3 + 3/2*x^2*d^4*b^2*a^2 + x^2*d^4*c*a^3 + 2*x^2*e*d^3*b*a^3 + x*d^4*b*a^3","B",0
1515,1,719,0,0.391163," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2}{11} x^{11} e^{3} c^{4} + \frac{3}{5} x^{10} e^{2} d c^{4} + \frac{7}{10} x^{10} e^{3} c^{3} b + \frac{2}{3} x^{9} e d^{2} c^{4} + \frac{7}{3} x^{9} e^{2} d c^{3} b + x^{9} e^{3} c^{2} b^{2} + \frac{2}{3} x^{9} e^{3} c^{3} a + \frac{1}{4} x^{8} d^{3} c^{4} + \frac{21}{8} x^{8} e d^{2} c^{3} b + \frac{27}{8} x^{8} e^{2} d c^{2} b^{2} + \frac{5}{8} x^{8} e^{3} c b^{3} + \frac{9}{4} x^{8} e^{2} d c^{3} a + \frac{15}{8} x^{8} e^{3} c^{2} b a + x^{7} d^{3} c^{3} b + \frac{27}{7} x^{7} e d^{2} c^{2} b^{2} + \frac{15}{7} x^{7} e^{2} d c b^{3} + \frac{1}{7} x^{7} e^{3} b^{4} + \frac{18}{7} x^{7} e d^{2} c^{3} a + \frac{45}{7} x^{7} e^{2} d c^{2} b a + \frac{12}{7} x^{7} e^{3} c b^{2} a + \frac{6}{7} x^{7} e^{3} c^{2} a^{2} + \frac{3}{2} x^{6} d^{3} c^{2} b^{2} + \frac{5}{2} x^{6} e d^{2} c b^{3} + \frac{1}{2} x^{6} e^{2} d b^{4} + x^{6} d^{3} c^{3} a + \frac{15}{2} x^{6} e d^{2} c^{2} b a + 6 x^{6} e^{2} d c b^{2} a + \frac{1}{2} x^{6} e^{3} b^{3} a + 3 x^{6} e^{2} d c^{2} a^{2} + \frac{3}{2} x^{6} e^{3} c b a^{2} + x^{5} d^{3} c b^{3} + \frac{3}{5} x^{5} e d^{2} b^{4} + 3 x^{5} d^{3} c^{2} b a + \frac{36}{5} x^{5} e d^{2} c b^{2} a + \frac{9}{5} x^{5} e^{2} d b^{3} a + \frac{18}{5} x^{5} e d^{2} c^{2} a^{2} + \frac{27}{5} x^{5} e^{2} d c b a^{2} + \frac{3}{5} x^{5} e^{3} b^{2} a^{2} + \frac{2}{5} x^{5} e^{3} c a^{3} + \frac{1}{4} x^{4} d^{3} b^{4} + 3 x^{4} d^{3} c b^{2} a + \frac{9}{4} x^{4} e d^{2} b^{3} a + \frac{3}{2} x^{4} d^{3} c^{2} a^{2} + \frac{27}{4} x^{4} e d^{2} c b a^{2} + \frac{9}{4} x^{4} e^{2} d b^{2} a^{2} + \frac{3}{2} x^{4} e^{2} d c a^{3} + \frac{1}{4} x^{4} e^{3} b a^{3} + x^{3} d^{3} b^{3} a + 3 x^{3} d^{3} c b a^{2} + 3 x^{3} e d^{2} b^{2} a^{2} + 2 x^{3} e d^{2} c a^{3} + x^{3} e^{2} d b a^{3} + \frac{3}{2} x^{2} d^{3} b^{2} a^{2} + x^{2} d^{3} c a^{3} + \frac{3}{2} x^{2} e d^{2} b a^{3} + x d^{3} b a^{3}"," ",0,"2/11*x^11*e^3*c^4 + 3/5*x^10*e^2*d*c^4 + 7/10*x^10*e^3*c^3*b + 2/3*x^9*e*d^2*c^4 + 7/3*x^9*e^2*d*c^3*b + x^9*e^3*c^2*b^2 + 2/3*x^9*e^3*c^3*a + 1/4*x^8*d^3*c^4 + 21/8*x^8*e*d^2*c^3*b + 27/8*x^8*e^2*d*c^2*b^2 + 5/8*x^8*e^3*c*b^3 + 9/4*x^8*e^2*d*c^3*a + 15/8*x^8*e^3*c^2*b*a + x^7*d^3*c^3*b + 27/7*x^7*e*d^2*c^2*b^2 + 15/7*x^7*e^2*d*c*b^3 + 1/7*x^7*e^3*b^4 + 18/7*x^7*e*d^2*c^3*a + 45/7*x^7*e^2*d*c^2*b*a + 12/7*x^7*e^3*c*b^2*a + 6/7*x^7*e^3*c^2*a^2 + 3/2*x^6*d^3*c^2*b^2 + 5/2*x^6*e*d^2*c*b^3 + 1/2*x^6*e^2*d*b^4 + x^6*d^3*c^3*a + 15/2*x^6*e*d^2*c^2*b*a + 6*x^6*e^2*d*c*b^2*a + 1/2*x^6*e^3*b^3*a + 3*x^6*e^2*d*c^2*a^2 + 3/2*x^6*e^3*c*b*a^2 + x^5*d^3*c*b^3 + 3/5*x^5*e*d^2*b^4 + 3*x^5*d^3*c^2*b*a + 36/5*x^5*e*d^2*c*b^2*a + 9/5*x^5*e^2*d*b^3*a + 18/5*x^5*e*d^2*c^2*a^2 + 27/5*x^5*e^2*d*c*b*a^2 + 3/5*x^5*e^3*b^2*a^2 + 2/5*x^5*e^3*c*a^3 + 1/4*x^4*d^3*b^4 + 3*x^4*d^3*c*b^2*a + 9/4*x^4*e*d^2*b^3*a + 3/2*x^4*d^3*c^2*a^2 + 27/4*x^4*e*d^2*c*b*a^2 + 9/4*x^4*e^2*d*b^2*a^2 + 3/2*x^4*e^2*d*c*a^3 + 1/4*x^4*e^3*b*a^3 + x^3*d^3*b^3*a + 3*x^3*d^3*c*b*a^2 + 3*x^3*e*d^2*b^2*a^2 + 2*x^3*e*d^2*c*a^3 + x^3*e^2*d*b*a^3 + 3/2*x^2*d^3*b^2*a^2 + x^2*d^3*c*a^3 + 3/2*x^2*e*d^2*b*a^3 + x*d^3*b*a^3","A",0
1516,1,502,0,0.377350," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{5} x^{10} e^{2} c^{4} + \frac{4}{9} x^{9} e d c^{4} + \frac{7}{9} x^{9} e^{2} c^{3} b + \frac{1}{4} x^{8} d^{2} c^{4} + \frac{7}{4} x^{8} e d c^{3} b + \frac{9}{8} x^{8} e^{2} c^{2} b^{2} + \frac{3}{4} x^{8} e^{2} c^{3} a + x^{7} d^{2} c^{3} b + \frac{18}{7} x^{7} e d c^{2} b^{2} + \frac{5}{7} x^{7} e^{2} c b^{3} + \frac{12}{7} x^{7} e d c^{3} a + \frac{15}{7} x^{7} e^{2} c^{2} b a + \frac{3}{2} x^{6} d^{2} c^{2} b^{2} + \frac{5}{3} x^{6} e d c b^{3} + \frac{1}{6} x^{6} e^{2} b^{4} + x^{6} d^{2} c^{3} a + 5 x^{6} e d c^{2} b a + 2 x^{6} e^{2} c b^{2} a + x^{6} e^{2} c^{2} a^{2} + x^{5} d^{2} c b^{3} + \frac{2}{5} x^{5} e d b^{4} + 3 x^{5} d^{2} c^{2} b a + \frac{24}{5} x^{5} e d c b^{2} a + \frac{3}{5} x^{5} e^{2} b^{3} a + \frac{12}{5} x^{5} e d c^{2} a^{2} + \frac{9}{5} x^{5} e^{2} c b a^{2} + \frac{1}{4} x^{4} d^{2} b^{4} + 3 x^{4} d^{2} c b^{2} a + \frac{3}{2} x^{4} e d b^{3} a + \frac{3}{2} x^{4} d^{2} c^{2} a^{2} + \frac{9}{2} x^{4} e d c b a^{2} + \frac{3}{4} x^{4} e^{2} b^{2} a^{2} + \frac{1}{2} x^{4} e^{2} c a^{3} + x^{3} d^{2} b^{3} a + 3 x^{3} d^{2} c b a^{2} + 2 x^{3} e d b^{2} a^{2} + \frac{4}{3} x^{3} e d c a^{3} + \frac{1}{3} x^{3} e^{2} b a^{3} + \frac{3}{2} x^{2} d^{2} b^{2} a^{2} + x^{2} d^{2} c a^{3} + x^{2} e d b a^{3} + x d^{2} b a^{3}"," ",0,"1/5*x^10*e^2*c^4 + 4/9*x^9*e*d*c^4 + 7/9*x^9*e^2*c^3*b + 1/4*x^8*d^2*c^4 + 7/4*x^8*e*d*c^3*b + 9/8*x^8*e^2*c^2*b^2 + 3/4*x^8*e^2*c^3*a + x^7*d^2*c^3*b + 18/7*x^7*e*d*c^2*b^2 + 5/7*x^7*e^2*c*b^3 + 12/7*x^7*e*d*c^3*a + 15/7*x^7*e^2*c^2*b*a + 3/2*x^6*d^2*c^2*b^2 + 5/3*x^6*e*d*c*b^3 + 1/6*x^6*e^2*b^4 + x^6*d^2*c^3*a + 5*x^6*e*d*c^2*b*a + 2*x^6*e^2*c*b^2*a + x^6*e^2*c^2*a^2 + x^5*d^2*c*b^3 + 2/5*x^5*e*d*b^4 + 3*x^5*d^2*c^2*b*a + 24/5*x^5*e*d*c*b^2*a + 3/5*x^5*e^2*b^3*a + 12/5*x^5*e*d*c^2*a^2 + 9/5*x^5*e^2*c*b*a^2 + 1/4*x^4*d^2*b^4 + 3*x^4*d^2*c*b^2*a + 3/2*x^4*e*d*b^3*a + 3/2*x^4*d^2*c^2*a^2 + 9/2*x^4*e*d*c*b*a^2 + 3/4*x^4*e^2*b^2*a^2 + 1/2*x^4*e^2*c*a^3 + x^3*d^2*b^3*a + 3*x^3*d^2*c*b*a^2 + 2*x^3*e*d*b^2*a^2 + 4/3*x^3*e*d*c*a^3 + 1/3*x^3*e^2*b*a^3 + 3/2*x^2*d^2*b^2*a^2 + x^2*d^2*c*a^3 + x^2*e*d*b*a^3 + x*d^2*b*a^3","A",0
1517,1,286,0,0.481577," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2}{9} x^{9} e c^{4} + \frac{1}{4} x^{8} d c^{4} + \frac{7}{8} x^{8} e c^{3} b + x^{7} d c^{3} b + \frac{9}{7} x^{7} e c^{2} b^{2} + \frac{6}{7} x^{7} e c^{3} a + \frac{3}{2} x^{6} d c^{2} b^{2} + \frac{5}{6} x^{6} e c b^{3} + x^{6} d c^{3} a + \frac{5}{2} x^{6} e c^{2} b a + x^{5} d c b^{3} + \frac{1}{5} x^{5} e b^{4} + 3 x^{5} d c^{2} b a + \frac{12}{5} x^{5} e c b^{2} a + \frac{6}{5} x^{5} e c^{2} a^{2} + \frac{1}{4} x^{4} d b^{4} + 3 x^{4} d c b^{2} a + \frac{3}{4} x^{4} e b^{3} a + \frac{3}{2} x^{4} d c^{2} a^{2} + \frac{9}{4} x^{4} e c b a^{2} + x^{3} d b^{3} a + 3 x^{3} d c b a^{2} + x^{3} e b^{2} a^{2} + \frac{2}{3} x^{3} e c a^{3} + \frac{3}{2} x^{2} d b^{2} a^{2} + x^{2} d c a^{3} + \frac{1}{2} x^{2} e b a^{3} + x d b a^{3}"," ",0,"2/9*x^9*e*c^4 + 1/4*x^8*d*c^4 + 7/8*x^8*e*c^3*b + x^7*d*c^3*b + 9/7*x^7*e*c^2*b^2 + 6/7*x^7*e*c^3*a + 3/2*x^6*d*c^2*b^2 + 5/6*x^6*e*c*b^3 + x^6*d*c^3*a + 5/2*x^6*e*c^2*b*a + x^5*d*c*b^3 + 1/5*x^5*e*b^4 + 3*x^5*d*c^2*b*a + 12/5*x^5*e*c*b^2*a + 6/5*x^5*e*c^2*a^2 + 1/4*x^4*d*b^4 + 3*x^4*d*c*b^2*a + 3/4*x^4*e*b^3*a + 3/2*x^4*d*c^2*a^2 + 9/4*x^4*e*c*b*a^2 + x^3*d*b^3*a + 3*x^3*d*c*b*a^2 + x^3*e*b^2*a^2 + 2/3*x^3*e*c*a^3 + 3/2*x^2*d*b^2*a^2 + x^2*d*c*a^3 + 1/2*x^2*e*b*a^3 + x*d*b*a^3","A",0
1518,1,126,0,0.378981," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{4} x^{8} c^{4} + x^{7} c^{3} b + \frac{3}{2} x^{6} c^{2} b^{2} + x^{6} c^{3} a + x^{5} c b^{3} + 3 x^{5} c^{2} b a + \frac{1}{4} x^{4} b^{4} + 3 x^{4} c b^{2} a + \frac{3}{2} x^{4} c^{2} a^{2} + x^{3} b^{3} a + 3 x^{3} c b a^{2} + \frac{3}{2} x^{2} b^{2} a^{2} + x^{2} c a^{3} + x b a^{3}"," ",0,"1/4*x^8*c^4 + x^7*c^3*b + 3/2*x^6*c^2*b^2 + x^6*c^3*a + x^5*c*b^3 + 3*x^5*c^2*b*a + 1/4*x^4*b^4 + 3*x^4*c*b^2*a + 3/2*x^4*c^2*a^2 + x^3*b^3*a + 3*x^3*c*b*a^2 + 3/2*x^2*b^2*a^2 + x^2*c*a^3 + x*b*a^3","B",0
1519,1,645,0,0.441982," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d),x, algorithm=""fricas"")","\frac{120 \, c^{4} e^{7} x^{7} - 70 \, {\left(2 \, c^{4} d e^{6} - 7 \, b c^{3} e^{7}\right)} x^{6} + 84 \, {\left(2 \, c^{4} d^{2} e^{5} - 7 \, b c^{3} d e^{6} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{7}\right)} x^{5} - 105 \, {\left(2 \, c^{4} d^{3} e^{4} - 7 \, b c^{3} d^{2} e^{5} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{6} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{7}\right)} x^{4} + 140 \, {\left(2 \, c^{4} d^{4} e^{3} - 7 \, b c^{3} d^{3} e^{4} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{7}\right)} x^{3} - 210 \, {\left(2 \, c^{4} d^{5} e^{2} - 7 \, b c^{3} d^{4} e^{3} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{7}\right)} x^{2} + 420 \, {\left(2 \, c^{4} d^{6} e - 7 \, b c^{3} d^{5} e^{2} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{7}\right)} x - 420 \, {\left(2 \, c^{4} d^{7} - 7 \, b c^{3} d^{6} e - a^{3} b e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6}\right)} \log\left(e x + d\right)}{420 \, e^{8}}"," ",0,"1/420*(120*c^4*e^7*x^7 - 70*(2*c^4*d*e^6 - 7*b*c^3*e^7)*x^6 + 84*(2*c^4*d^2*e^5 - 7*b*c^3*d*e^6 + 3*(3*b^2*c^2 + 2*a*c^3)*e^7)*x^5 - 105*(2*c^4*d^3*e^4 - 7*b*c^3*d^2*e^5 + 3*(3*b^2*c^2 + 2*a*c^3)*d*e^6 - 5*(b^3*c + 3*a*b*c^2)*e^7)*x^4 + 140*(2*c^4*d^4*e^3 - 7*b*c^3*d^3*e^4 + 3*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 - 5*(b^3*c + 3*a*b*c^2)*d*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^7)*x^3 - 210*(2*c^4*d^5*e^2 - 7*b*c^3*d^4*e^3 + 3*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - 5*(b^3*c + 3*a*b*c^2)*d^2*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6 - 3*(a*b^3 + 3*a^2*b*c)*e^7)*x^2 + 420*(2*c^4*d^6*e - 7*b*c^3*d^5*e^2 + 3*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 5*(b^3*c + 3*a*b*c^2)*d^3*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 - 3*(a*b^3 + 3*a^2*b*c)*d*e^6 + (3*a^2*b^2 + 2*a^3*c)*e^7)*x - 420*(2*c^4*d^7 - 7*b*c^3*d^6*e - a^3*b*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 5*(b^3*c + 3*a*b*c^2)*d^4*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 3*(a*b^3 + 3*a^2*b*c)*d^2*e^5 + (3*a^2*b^2 + 2*a^3*c)*d*e^6)*log(e*x + d))/e^8","A",0
1520,1,903,0,0.422525," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{20 \, c^{4} e^{7} x^{7} + 120 \, c^{4} d^{7} - 420 \, b c^{3} d^{6} e - 60 \, a^{3} b e^{7} + 180 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 300 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + 60 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 180 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} + 60 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6} - 28 \, {\left(c^{4} d e^{6} - 3 \, b c^{3} e^{7}\right)} x^{6} + 3 \, {\left(14 \, c^{4} d^{2} e^{5} - 42 \, b c^{3} d e^{6} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{7}\right)} x^{5} - 5 \, {\left(14 \, c^{4} d^{3} e^{4} - 42 \, b c^{3} d^{2} e^{5} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{6} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{7}\right)} x^{4} + 10 \, {\left(14 \, c^{4} d^{4} e^{3} - 42 \, b c^{3} d^{3} e^{4} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{7}\right)} x^{3} - 30 \, {\left(14 \, c^{4} d^{5} e^{2} - 42 \, b c^{3} d^{4} e^{3} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{7}\right)} x^{2} - 60 \, {\left(12 \, c^{4} d^{6} e - 35 \, b c^{3} d^{5} e^{2} + 12 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 15 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + 2 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6}\right)} x + 60 \, {\left(14 \, c^{4} d^{7} - 42 \, b c^{3} d^{6} e + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6} + {\left(14 \, c^{4} d^{6} e - 42 \, b c^{3} d^{5} e^{2} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{7}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"1/60*(20*c^4*e^7*x^7 + 120*c^4*d^7 - 420*b*c^3*d^6*e - 60*a^3*b*e^7 + 180*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 300*(b^3*c + 3*a*b*c^2)*d^4*e^3 + 60*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 180*(a*b^3 + 3*a^2*b*c)*d^2*e^5 + 60*(3*a^2*b^2 + 2*a^3*c)*d*e^6 - 28*(c^4*d*e^6 - 3*b*c^3*e^7)*x^6 + 3*(14*c^4*d^2*e^5 - 42*b*c^3*d*e^6 + 15*(3*b^2*c^2 + 2*a*c^3)*e^7)*x^5 - 5*(14*c^4*d^3*e^4 - 42*b*c^3*d^2*e^5 + 15*(3*b^2*c^2 + 2*a*c^3)*d*e^6 - 20*(b^3*c + 3*a*b*c^2)*e^7)*x^4 + 10*(14*c^4*d^4*e^3 - 42*b*c^3*d^3*e^4 + 15*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 - 20*(b^3*c + 3*a*b*c^2)*d*e^6 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^7)*x^3 - 30*(14*c^4*d^5*e^2 - 42*b*c^3*d^4*e^3 + 15*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - 20*(b^3*c + 3*a*b*c^2)*d^2*e^5 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6 - 6*(a*b^3 + 3*a^2*b*c)*e^7)*x^2 - 60*(12*c^4*d^6*e - 35*b*c^3*d^5*e^2 + 12*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 15*(b^3*c + 3*a*b*c^2)*d^3*e^4 + 2*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 - 3*(a*b^3 + 3*a^2*b*c)*d*e^6)*x + 60*(14*c^4*d^7 - 42*b*c^3*d^6*e + 15*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 20*(b^3*c + 3*a*b*c^2)*d^4*e^3 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 6*(a*b^3 + 3*a^2*b*c)*d^2*e^5 + (3*a^2*b^2 + 2*a^3*c)*d*e^6 + (14*c^4*d^6*e - 42*b*c^3*d^5*e^2 + 15*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 20*(b^3*c + 3*a*b*c^2)*d^3*e^4 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 - 6*(a*b^3 + 3*a^2*b*c)*d*e^6 + (3*a^2*b^2 + 2*a^3*c)*e^7)*x)*log(e*x + d))/(e^9*x + d*e^8)","B",0
1521,1,990,0,0.417150," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{8 \, c^{4} e^{7} x^{7} - 260 \, c^{4} d^{7} + 770 \, b c^{3} d^{6} e - 10 \, a^{3} b e^{7} - 270 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} + 350 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} - 50 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} + 90 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} - 10 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6} - 7 \, {\left(2 \, c^{4} d e^{6} - 5 \, b c^{3} e^{7}\right)} x^{6} + 2 \, {\left(14 \, c^{4} d^{2} e^{5} - 35 \, b c^{3} d e^{6} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{7}\right)} x^{5} - 5 \, {\left(14 \, c^{4} d^{3} e^{4} - 35 \, b c^{3} d^{2} e^{5} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{6} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{7}\right)} x^{4} + 20 \, {\left(14 \, c^{4} d^{4} e^{3} - 35 \, b c^{3} d^{3} e^{4} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{7}\right)} x^{3} + 10 \, {\left(100 \, c^{4} d^{5} e^{2} - 238 \, b c^{3} d^{4} e^{3} + 63 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - 55 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} + 4 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6}\right)} x^{2} + 20 \, {\left(16 \, c^{4} d^{6} e - 28 \, b c^{3} d^{5} e^{2} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} + 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} - 2 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} + 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{7}\right)} x - 60 \, {\left(14 \, c^{4} d^{7} - 35 \, b c^{3} d^{6} e + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} + {\left(14 \, c^{4} d^{5} e^{2} - 35 \, b c^{3} d^{4} e^{3} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6} - {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{7}\right)} x^{2} + 2 \, {\left(14 \, c^{4} d^{6} e - 35 \, b c^{3} d^{5} e^{2} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"1/20*(8*c^4*e^7*x^7 - 260*c^4*d^7 + 770*b*c^3*d^6*e - 10*a^3*b*e^7 - 270*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 + 350*(b^3*c + 3*a*b*c^2)*d^4*e^3 - 50*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 + 90*(a*b^3 + 3*a^2*b*c)*d^2*e^5 - 10*(3*a^2*b^2 + 2*a^3*c)*d*e^6 - 7*(2*c^4*d*e^6 - 5*b*c^3*e^7)*x^6 + 2*(14*c^4*d^2*e^5 - 35*b*c^3*d*e^6 + 10*(3*b^2*c^2 + 2*a*c^3)*e^7)*x^5 - 5*(14*c^4*d^3*e^4 - 35*b*c^3*d^2*e^5 + 10*(3*b^2*c^2 + 2*a*c^3)*d*e^6 - 10*(b^3*c + 3*a*b*c^2)*e^7)*x^4 + 20*(14*c^4*d^4*e^3 - 35*b*c^3*d^3*e^4 + 10*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 - 10*(b^3*c + 3*a*b*c^2)*d*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^7)*x^3 + 10*(100*c^4*d^5*e^2 - 238*b*c^3*d^4*e^3 + 63*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - 55*(b^3*c + 3*a*b*c^2)*d^2*e^5 + 4*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6)*x^2 + 20*(16*c^4*d^6*e - 28*b*c^3*d^5*e^2 + 3*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 + 5*(b^3*c + 3*a*b*c^2)*d^3*e^4 - 2*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 + 6*(a*b^3 + 3*a^2*b*c)*d*e^6 - (3*a^2*b^2 + 2*a^3*c)*e^7)*x - 60*(14*c^4*d^7 - 35*b*c^3*d^6*e + 10*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 10*(b^3*c + 3*a*b*c^2)*d^4*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - (a*b^3 + 3*a^2*b*c)*d^2*e^5 + (14*c^4*d^5*e^2 - 35*b*c^3*d^4*e^3 + 10*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - 10*(b^3*c + 3*a*b*c^2)*d^2*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6 - (a*b^3 + 3*a^2*b*c)*e^7)*x^2 + 2*(14*c^4*d^6*e - 35*b*c^3*d^5*e^2 + 10*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 10*(b^3*c + 3*a*b*c^2)*d^3*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 - (a*b^3 + 3*a^2*b*c)*d*e^6)*x)*log(e*x + d))/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","B",0
1522,1,1031,0,0.419779," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, c^{4} e^{7} x^{7} + 214 \, c^{4} d^{7} - 518 \, b c^{3} d^{6} e - 2 \, a^{3} b e^{7} + 141 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 130 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + 11 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6} - 7 \, {\left(c^{4} d e^{6} - 2 \, b c^{3} e^{7}\right)} x^{6} + 3 \, {\left(7 \, c^{4} d^{2} e^{5} - 14 \, b c^{3} d e^{6} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{7}\right)} x^{5} - 15 \, {\left(7 \, c^{4} d^{3} e^{4} - 14 \, b c^{3} d^{2} e^{5} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{6} - 2 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{7}\right)} x^{4} - {\left(556 \, c^{4} d^{4} e^{3} - 1022 \, b c^{3} d^{3} e^{4} + 189 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} - 90 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6}\right)} x^{3} - 3 \, {\left(136 \, c^{4} d^{5} e^{2} - 182 \, b c^{3} d^{4} e^{3} + 9 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} + 30 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} - 6 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6} + 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{7}\right)} x^{2} + 3 \, {\left(74 \, c^{4} d^{6} e - 238 \, b c^{3} d^{5} e^{2} + 81 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 90 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + 9 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{7}\right)} x + 6 \, {\left(70 \, c^{4} d^{7} - 140 \, b c^{3} d^{6} e + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} + {\left(70 \, c^{4} d^{4} e^{3} - 140 \, b c^{3} d^{3} e^{4} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{7}\right)} x^{3} + 3 \, {\left(70 \, c^{4} d^{5} e^{2} - 140 \, b c^{3} d^{4} e^{3} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6}\right)} x^{2} + 3 \, {\left(70 \, c^{4} d^{6} e - 140 \, b c^{3} d^{5} e^{2} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right)}}"," ",0,"1/6*(3*c^4*e^7*x^7 + 214*c^4*d^7 - 518*b*c^3*d^6*e - 2*a^3*b*e^7 + 141*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 130*(b^3*c + 3*a*b*c^2)*d^4*e^3 + 11*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 6*(a*b^3 + 3*a^2*b*c)*d^2*e^5 - (3*a^2*b^2 + 2*a^3*c)*d*e^6 - 7*(c^4*d*e^6 - 2*b*c^3*e^7)*x^6 + 3*(7*c^4*d^2*e^5 - 14*b*c^3*d*e^6 + 3*(3*b^2*c^2 + 2*a*c^3)*e^7)*x^5 - 15*(7*c^4*d^3*e^4 - 14*b*c^3*d^2*e^5 + 3*(3*b^2*c^2 + 2*a*c^3)*d*e^6 - 2*(b^3*c + 3*a*b*c^2)*e^7)*x^4 - (556*c^4*d^4*e^3 - 1022*b*c^3*d^3*e^4 + 189*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 - 90*(b^3*c + 3*a*b*c^2)*d*e^6)*x^3 - 3*(136*c^4*d^5*e^2 - 182*b*c^3*d^4*e^3 + 9*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 + 30*(b^3*c + 3*a*b*c^2)*d^2*e^5 - 6*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6 + 6*(a*b^3 + 3*a^2*b*c)*e^7)*x^2 + 3*(74*c^4*d^6*e - 238*b*c^3*d^5*e^2 + 81*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 90*(b^3*c + 3*a*b*c^2)*d^3*e^4 + 9*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 - 6*(a*b^3 + 3*a^2*b*c)*d*e^6 - (3*a^2*b^2 + 2*a^3*c)*e^7)*x + 6*(70*c^4*d^7 - 140*b*c^3*d^6*e + 30*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 20*(b^3*c + 3*a*b*c^2)*d^4*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 + (70*c^4*d^4*e^3 - 140*b*c^3*d^3*e^4 + 30*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 - 20*(b^3*c + 3*a*b*c^2)*d*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^7)*x^3 + 3*(70*c^4*d^5*e^2 - 140*b*c^3*d^4*e^3 + 30*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - 20*(b^3*c + 3*a*b*c^2)*d^2*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6)*x^2 + 3*(70*c^4*d^6*e - 140*b*c^3*d^5*e^2 + 30*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 20*(b^3*c + 3*a*b*c^2)*d^3*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5)*x)*log(e*x + d))/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8)","B",0
1523,1,1017,0,0.415395," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^5,x, algorithm=""fricas"")","\frac{8 \, c^{4} e^{7} x^{7} - 638 \, c^{4} d^{7} + 1197 \, b c^{3} d^{6} e - 3 \, a^{3} b e^{7} - 231 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} + 125 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6} - 14 \, {\left(2 \, c^{4} d e^{6} - 3 \, b c^{3} e^{7}\right)} x^{6} + 12 \, {\left(14 \, c^{4} d^{2} e^{5} - 21 \, b c^{3} d e^{6} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{7}\right)} x^{5} + 4 \, {\left(278 \, c^{4} d^{3} e^{4} - 357 \, b c^{3} d^{2} e^{5} + 36 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{6}\right)} x^{4} + 4 \, {\left(272 \, c^{4} d^{4} e^{3} - 168 \, b c^{3} d^{3} e^{4} - 36 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} + 60 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{7}\right)} x^{3} - 6 \, {\left(148 \, c^{4} d^{5} e^{2} - 462 \, b c^{3} d^{4} e^{3} + 126 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - 90 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{7}\right)} x^{2} - 4 \, {\left(428 \, c^{4} d^{6} e - 882 \, b c^{3} d^{5} e^{2} + 186 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 110 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{7}\right)} x - 60 \, {\left(14 \, c^{4} d^{7} - 21 \, b c^{3} d^{6} e + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + {\left(14 \, c^{4} d^{3} e^{4} - 21 \, b c^{3} d^{2} e^{5} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{6} - {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{7}\right)} x^{4} + 4 \, {\left(14 \, c^{4} d^{4} e^{3} - 21 \, b c^{3} d^{3} e^{4} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} - {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6}\right)} x^{3} + 6 \, {\left(14 \, c^{4} d^{5} e^{2} - 21 \, b c^{3} d^{4} e^{3} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5}\right)} x^{2} + 4 \, {\left(14 \, c^{4} d^{6} e - 21 \, b c^{3} d^{5} e^{2} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{12} x^{4} + 4 \, d e^{11} x^{3} + 6 \, d^{2} e^{10} x^{2} + 4 \, d^{3} e^{9} x + d^{4} e^{8}\right)}}"," ",0,"1/12*(8*c^4*e^7*x^7 - 638*c^4*d^7 + 1197*b*c^3*d^6*e - 3*a^3*b*e^7 - 231*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 + 125*(b^3*c + 3*a*b*c^2)*d^4*e^3 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 3*(a*b^3 + 3*a^2*b*c)*d^2*e^5 - (3*a^2*b^2 + 2*a^3*c)*d*e^6 - 14*(2*c^4*d*e^6 - 3*b*c^3*e^7)*x^6 + 12*(14*c^4*d^2*e^5 - 21*b*c^3*d*e^6 + 3*(3*b^2*c^2 + 2*a*c^3)*e^7)*x^5 + 4*(278*c^4*d^3*e^4 - 357*b*c^3*d^2*e^5 + 36*(3*b^2*c^2 + 2*a*c^3)*d*e^6)*x^4 + 4*(272*c^4*d^4*e^3 - 168*b*c^3*d^3*e^4 - 36*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 + 60*(b^3*c + 3*a*b*c^2)*d*e^6 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^7)*x^3 - 6*(148*c^4*d^5*e^2 - 462*b*c^3*d^4*e^3 + 126*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - 90*(b^3*c + 3*a*b*c^2)*d^2*e^5 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6 + 3*(a*b^3 + 3*a^2*b*c)*e^7)*x^2 - 4*(428*c^4*d^6*e - 882*b*c^3*d^5*e^2 + 186*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 110*(b^3*c + 3*a*b*c^2)*d^3*e^4 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 + 3*(a*b^3 + 3*a^2*b*c)*d*e^6 + (3*a^2*b^2 + 2*a^3*c)*e^7)*x - 60*(14*c^4*d^7 - 21*b*c^3*d^6*e + 3*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - (b^3*c + 3*a*b*c^2)*d^4*e^3 + (14*c^4*d^3*e^4 - 21*b*c^3*d^2*e^5 + 3*(3*b^2*c^2 + 2*a*c^3)*d*e^6 - (b^3*c + 3*a*b*c^2)*e^7)*x^4 + 4*(14*c^4*d^4*e^3 - 21*b*c^3*d^3*e^4 + 3*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 - (b^3*c + 3*a*b*c^2)*d*e^6)*x^3 + 6*(14*c^4*d^5*e^2 - 21*b*c^3*d^4*e^3 + 3*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - (b^3*c + 3*a*b*c^2)*d^2*e^5)*x^2 + 4*(14*c^4*d^6*e - 21*b*c^3*d^5*e^2 + 3*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - (b^3*c + 3*a*b*c^2)*d^3*e^4)*x)*log(e*x + d))/(e^12*x^4 + 4*d*e^11*x^3 + 6*d^2*e^10*x^2 + 4*d^3*e^9*x + d^4*e^8)","B",0
1524,1,709,0,0.435115," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{3 \, c^{4} e^{4} x^{4} + 2 \, {\left(8 \, c^{4} d e^{3} - b c^{3} e^{4}\right)} x^{3} + 3 \, {\left(12 \, c^{4} d^{2} e^{2} - 4 \, b c^{3} d e^{3} + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} e^{4}\right)} x^{2} + 3 \, {\left(4 \, c^{3} d^{3} e - 6 \, b c^{2} d^{2} e^{2} + 4 \, {\left(b^{2} c - a c^{2}\right)} d e^{3} - {\left(b^{3} - 2 \, a b c\right)} e^{4}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 6 \, {\left(8 \, c^{4} d^{3} e - 6 \, b c^{3} d^{2} e^{2} + 4 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{3} - {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{4}\right)} x + 3 \, {\left(2 \, c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{2} - 4 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, c^{4}}, \frac{3 \, c^{4} e^{4} x^{4} + 2 \, {\left(8 \, c^{4} d e^{3} - b c^{3} e^{4}\right)} x^{3} + 3 \, {\left(12 \, c^{4} d^{2} e^{2} - 4 \, b c^{3} d e^{3} + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} e^{4}\right)} x^{2} - 6 \, {\left(4 \, c^{3} d^{3} e - 6 \, b c^{2} d^{2} e^{2} + 4 \, {\left(b^{2} c - a c^{2}\right)} d e^{3} - {\left(b^{3} - 2 \, a b c\right)} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 6 \, {\left(8 \, c^{4} d^{3} e - 6 \, b c^{3} d^{2} e^{2} + 4 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{3} - {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{4}\right)} x + 3 \, {\left(2 \, c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{2} - 4 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, c^{4}}\right]"," ",0,"[1/6*(3*c^4*e^4*x^4 + 2*(8*c^4*d*e^3 - b*c^3*e^4)*x^3 + 3*(12*c^4*d^2*e^2 - 4*b*c^3*d*e^3 + (b^2*c^2 - 2*a*c^3)*e^4)*x^2 + 3*(4*c^3*d^3*e - 6*b*c^2*d^2*e^2 + 4*(b^2*c - a*c^2)*d*e^3 - (b^3 - 2*a*b*c)*e^4)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 6*(8*c^4*d^3*e - 6*b*c^3*d^2*e^2 + 4*(b^2*c^2 - 2*a*c^3)*d*e^3 - (b^3*c - 3*a*b*c^2)*e^4)*x + 3*(2*c^4*d^4 - 4*b*c^3*d^3*e + 6*(b^2*c^2 - 2*a*c^3)*d^2*e^2 - 4*(b^3*c - 3*a*b*c^2)*d*e^3 + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e^4)*log(c*x^2 + b*x + a))/c^4, 1/6*(3*c^4*e^4*x^4 + 2*(8*c^4*d*e^3 - b*c^3*e^4)*x^3 + 3*(12*c^4*d^2*e^2 - 4*b*c^3*d*e^3 + (b^2*c^2 - 2*a*c^3)*e^4)*x^2 - 6*(4*c^3*d^3*e - 6*b*c^2*d^2*e^2 + 4*(b^2*c - a*c^2)*d*e^3 - (b^3 - 2*a*b*c)*e^4)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 6*(8*c^4*d^3*e - 6*b*c^3*d^2*e^2 + 4*(b^2*c^2 - 2*a*c^3)*d*e^3 - (b^3*c - 3*a*b*c^2)*e^4)*x + 3*(2*c^4*d^4 - 4*b*c^3*d^3*e + 6*(b^2*c^2 - 2*a*c^3)*d^2*e^2 - 4*(b^3*c - 3*a*b*c^2)*d*e^3 + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e^4)*log(c*x^2 + b*x + a))/c^4]","A",0
1525,1,458,0,0.437729," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{4 \, c^{3} e^{3} x^{3} + 3 \, {\left(6 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} x^{2} - 3 \, {\left(3 \, c^{2} d^{2} e - 3 \, b c d e^{2} + {\left(b^{2} - a c\right)} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 6 \, {\left(6 \, c^{3} d^{2} e - 3 \, b c^{2} d e^{2} + {\left(b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} x + 3 \, {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, c^{3}}, \frac{4 \, c^{3} e^{3} x^{3} + 3 \, {\left(6 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} x^{2} - 6 \, {\left(3 \, c^{2} d^{2} e - 3 \, b c d e^{2} + {\left(b^{2} - a c\right)} e^{3}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 6 \, {\left(6 \, c^{3} d^{2} e - 3 \, b c^{2} d e^{2} + {\left(b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} x + 3 \, {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, c^{3}}\right]"," ",0,"[1/6*(4*c^3*e^3*x^3 + 3*(6*c^3*d*e^2 - b*c^2*e^3)*x^2 - 3*(3*c^2*d^2*e - 3*b*c*d*e^2 + (b^2 - a*c)*e^3)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 6*(6*c^3*d^2*e - 3*b*c^2*d*e^2 + (b^2*c - 2*a*c^2)*e^3)*x + 3*(2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3)*log(c*x^2 + b*x + a))/c^3, 1/6*(4*c^3*e^3*x^3 + 3*(6*c^3*d*e^2 - b*c^2*e^3)*x^2 - 6*(3*c^2*d^2*e - 3*b*c*d*e^2 + (b^2 - a*c)*e^3)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 6*(6*c^3*d^2*e - 3*b*c^2*d*e^2 + (b^2*c - 2*a*c^2)*e^3)*x + 3*(2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3)*log(c*x^2 + b*x + a))/c^3]","A",0
1526,1,282,0,0.433651," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, c^{2} e^{2} x^{2} - {\left(2 \, c d e - b e^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(4 \, c^{2} d e - b c e^{2}\right)} x + {\left(2 \, c^{2} d^{2} - 2 \, b c d e + {\left(b^{2} - 2 \, a c\right)} e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}}, \frac{2 \, c^{2} e^{2} x^{2} - 2 \, {\left(2 \, c d e - b e^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(4 \, c^{2} d e - b c e^{2}\right)} x + {\left(2 \, c^{2} d^{2} - 2 \, b c d e + {\left(b^{2} - 2 \, a c\right)} e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}}\right]"," ",0,"[1/2*(2*c^2*e^2*x^2 - (2*c*d*e - b*e^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(4*c^2*d*e - b*c*e^2)*x + (2*c^2*d^2 - 2*b*c*d*e + (b^2 - 2*a*c)*e^2)*log(c*x^2 + b*x + a))/c^2, 1/2*(2*c^2*e^2*x^2 - 2*(2*c*d*e - b*e^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(4*c^2*d*e - b*c*e^2)*x + (2*c^2*d^2 - 2*b*c*d*e + (b^2 - 2*a*c)*e^2)*log(c*x^2 + b*x + a))/c^2]","A",0
1527,1,176,0,0.420915," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{4 \, c e x + \sqrt{b^{2} - 4 \, a c} e \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, c d - b e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c}, \frac{4 \, c e x - 2 \, \sqrt{-b^{2} + 4 \, a c} e \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, c d - b e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c}\right]"," ",0,"[1/2*(4*c*e*x + sqrt(b^2 - 4*a*c)*e*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*c*d - b*e)*log(c*x^2 + b*x + a))/c, 1/2*(4*c*e*x - 2*sqrt(-b^2 + 4*a*c)*e*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*c*d - b*e)*log(c*x^2 + b*x + a))/c]","A",0
1528,1,11,0,0.408449," ","integrate((2*c*x+b)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\log\left(c x^{2} + b x + a\right)"," ",0,"log(c*x^2 + b*x + a)","A",0
1529,1,229,0,0.524014," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} e \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, c d - b e\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, c d - b e\right)} \log\left(e x + d\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} e \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, c d - b e\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, c d - b e\right)} \log\left(e x + d\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}}\right]"," ",0,"[1/2*(sqrt(b^2 - 4*a*c)*e*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*c*d - b*e)*log(c*x^2 + b*x + a) - 2*(2*c*d - b*e)*log(e*x + d))/(c*d^2 - b*d*e + a*e^2), 1/2*(2*sqrt(-b^2 + 4*a*c)*e*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*c*d - b*e)*log(c*x^2 + b*x + a) - 2*(2*c*d - b*e)*log(e*x + d))/(c*d^2 - b*d*e + a*e^2)]","A",0
1530,1,745,0,2.256457," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{4 \, c^{2} d^{3} - 6 \, b c d^{2} e - 2 \, a b e^{3} + 2 \, {\left(b^{2} + 2 \, a c\right)} d e^{2} - {\left(2 \, c d^{2} e - b d e^{2} + {\left(2 \, c d e^{2} - b e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, c^{2} d^{3} - 2 \, b c d^{2} e + {\left(b^{2} - 2 \, a c\right)} d e^{2} + {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + {\left(b^{2} - 2 \, a c\right)} e^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, c^{2} d^{3} - 2 \, b c d^{2} e + {\left(b^{2} - 2 \, a c\right)} d e^{2} + {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + {\left(b^{2} - 2 \, a c\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e - 2 \, a b d^{2} e^{3} + a^{2} d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + a^{2} e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)}}, \frac{4 \, c^{2} d^{3} - 6 \, b c d^{2} e - 2 \, a b e^{3} + 2 \, {\left(b^{2} + 2 \, a c\right)} d e^{2} + 2 \, {\left(2 \, c d^{2} e - b d e^{2} + {\left(2 \, c d e^{2} - b e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, c^{2} d^{3} - 2 \, b c d^{2} e + {\left(b^{2} - 2 \, a c\right)} d e^{2} + {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + {\left(b^{2} - 2 \, a c\right)} e^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, c^{2} d^{3} - 2 \, b c d^{2} e + {\left(b^{2} - 2 \, a c\right)} d e^{2} + {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + {\left(b^{2} - 2 \, a c\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e - 2 \, a b d^{2} e^{3} + a^{2} d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + a^{2} e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)}}\right]"," ",0,"[1/2*(4*c^2*d^3 - 6*b*c*d^2*e - 2*a*b*e^3 + 2*(b^2 + 2*a*c)*d*e^2 - (2*c*d^2*e - b*d*e^2 + (2*c*d*e^2 - b*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*c^2*d^3 - 2*b*c*d^2*e + (b^2 - 2*a*c)*d*e^2 + (2*c^2*d^2*e - 2*b*c*d*e^2 + (b^2 - 2*a*c)*e^3)*x)*log(c*x^2 + b*x + a) - 2*(2*c^2*d^3 - 2*b*c*d^2*e + (b^2 - 2*a*c)*d*e^2 + (2*c^2*d^2*e - 2*b*c*d*e^2 + (b^2 - 2*a*c)*e^3)*x)*log(e*x + d))/(c^2*d^5 - 2*b*c*d^4*e - 2*a*b*d^2*e^3 + a^2*d*e^4 + (b^2 + 2*a*c)*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + a^2*e^5 + (b^2 + 2*a*c)*d^2*e^3)*x), 1/2*(4*c^2*d^3 - 6*b*c*d^2*e - 2*a*b*e^3 + 2*(b^2 + 2*a*c)*d*e^2 + 2*(2*c*d^2*e - b*d*e^2 + (2*c*d*e^2 - b*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*c^2*d^3 - 2*b*c*d^2*e + (b^2 - 2*a*c)*d*e^2 + (2*c^2*d^2*e - 2*b*c*d*e^2 + (b^2 - 2*a*c)*e^3)*x)*log(c*x^2 + b*x + a) - 2*(2*c^2*d^3 - 2*b*c*d^2*e + (b^2 - 2*a*c)*d*e^2 + (2*c^2*d^2*e - 2*b*c*d*e^2 + (b^2 - 2*a*c)*e^3)*x)*log(e*x + d))/(c^2*d^5 - 2*b*c*d^4*e - 2*a*b*d^2*e^3 + a^2*d*e^4 + (b^2 + 2*a*c)*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + a^2*e^5 + (b^2 + 2*a*c)*d^2*e^3)*x)]","A",0
1531,1,1961,0,14.969037," ","integrate((2*c*x+b)/(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{6 \, c^{3} d^{5} - 13 \, b c^{2} d^{4} e - a^{2} b e^{5} + 2 \, {\left(5 \, b^{2} c + 2 \, a c^{2}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} + 2 \, a b c\right)} d^{2} e^{3} + 2 \, {\left(2 \, a b^{2} - a^{2} c\right)} d e^{4} - {\left(3 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} + {\left(b^{2} - a c\right)} d^{2} e^{3} + {\left(3 \, c^{2} d^{2} e^{3} - 3 \, b c d e^{4} + {\left(b^{2} - a c\right)} e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + {\left(b^{2} - a c\right)} d e^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(2 \, c^{3} d^{4} e - 4 \, b c^{2} d^{3} e^{2} + 3 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4} + {\left(a b^{2} - 2 \, a^{2} c\right)} e^{5}\right)} x + {\left(2 \, c^{3} d^{5} - 3 \, b c^{2} d^{4} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} - 3 \, a b c\right)} d^{2} e^{3} + {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d^{4} e - 3 \, b c^{2} d^{3} e^{2} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} - 3 \, a b c\right)} d e^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, c^{3} d^{5} - 3 \, b c^{2} d^{4} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} - 3 \, a b c\right)} d^{2} e^{3} + {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d^{4} e - 3 \, b c^{2} d^{3} e^{2} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} - 3 \, a b c\right)} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e - 3 \, a^{2} b d^{3} e^{5} + a^{3} d^{2} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} - 3 \, a^{2} b d e^{7} + a^{3} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} - 3 \, a^{2} b d^{2} e^{6} + a^{3} d e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)}}, \frac{6 \, c^{3} d^{5} - 13 \, b c^{2} d^{4} e - a^{2} b e^{5} + 2 \, {\left(5 \, b^{2} c + 2 \, a c^{2}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} + 2 \, a b c\right)} d^{2} e^{3} + 2 \, {\left(2 \, a b^{2} - a^{2} c\right)} d e^{4} + 2 \, {\left(3 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} + {\left(b^{2} - a c\right)} d^{2} e^{3} + {\left(3 \, c^{2} d^{2} e^{3} - 3 \, b c d e^{4} + {\left(b^{2} - a c\right)} e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + {\left(b^{2} - a c\right)} d e^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(2 \, c^{3} d^{4} e - 4 \, b c^{2} d^{3} e^{2} + 3 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4} + {\left(a b^{2} - 2 \, a^{2} c\right)} e^{5}\right)} x + {\left(2 \, c^{3} d^{5} - 3 \, b c^{2} d^{4} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} - 3 \, a b c\right)} d^{2} e^{3} + {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d^{4} e - 3 \, b c^{2} d^{3} e^{2} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} - 3 \, a b c\right)} d e^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, c^{3} d^{5} - 3 \, b c^{2} d^{4} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} - 3 \, a b c\right)} d^{2} e^{3} + {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d^{4} e - 3 \, b c^{2} d^{3} e^{2} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} - 3 \, a b c\right)} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e - 3 \, a^{2} b d^{3} e^{5} + a^{3} d^{2} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} - 3 \, a^{2} b d e^{7} + a^{3} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} - 3 \, a^{2} b d^{2} e^{6} + a^{3} d e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)}}\right]"," ",0,"[1/2*(6*c^3*d^5 - 13*b*c^2*d^4*e - a^2*b*e^5 + 2*(5*b^2*c + 2*a*c^2)*d^3*e^2 - 3*(b^3 + 2*a*b*c)*d^2*e^3 + 2*(2*a*b^2 - a^2*c)*d*e^4 - (3*c^2*d^4*e - 3*b*c*d^3*e^2 + (b^2 - a*c)*d^2*e^3 + (3*c^2*d^2*e^3 - 3*b*c*d*e^4 + (b^2 - a*c)*e^5)*x^2 + 2*(3*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + (b^2 - a*c)*d*e^4)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(2*c^3*d^4*e - 4*b*c^2*d^3*e^2 + 3*b^2*c*d^2*e^3 - b^3*d*e^4 + (a*b^2 - 2*a^2*c)*e^5)*x + (2*c^3*d^5 - 3*b*c^2*d^4*e + 3*(b^2*c - 2*a*c^2)*d^3*e^2 - (b^3 - 3*a*b*c)*d^2*e^3 + (2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5)*x^2 + 2*(2*c^3*d^4*e - 3*b*c^2*d^3*e^2 + 3*(b^2*c - 2*a*c^2)*d^2*e^3 - (b^3 - 3*a*b*c)*d*e^4)*x)*log(c*x^2 + b*x + a) - 2*(2*c^3*d^5 - 3*b*c^2*d^4*e + 3*(b^2*c - 2*a*c^2)*d^3*e^2 - (b^3 - 3*a*b*c)*d^2*e^3 + (2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5)*x^2 + 2*(2*c^3*d^4*e - 3*b*c^2*d^3*e^2 + 3*(b^2*c - 2*a*c^2)*d^2*e^3 - (b^3 - 3*a*b*c)*d*e^4)*x)*log(e*x + d))/(c^3*d^8 - 3*b*c^2*d^7*e - 3*a^2*b*d^3*e^5 + a^3*d^2*e^6 + 3*(b^2*c + a*c^2)*d^6*e^2 - (b^3 + 6*a*b*c)*d^5*e^3 + 3*(a*b^2 + a^2*c)*d^4*e^4 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 - 3*a^2*b*d*e^7 + a^3*e^8 + 3*(b^2*c + a*c^2)*d^4*e^4 - (b^3 + 6*a*b*c)*d^3*e^5 + 3*(a*b^2 + a^2*c)*d^2*e^6)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 - 3*a^2*b*d^2*e^6 + a^3*d*e^7 + 3*(b^2*c + a*c^2)*d^5*e^3 - (b^3 + 6*a*b*c)*d^4*e^4 + 3*(a*b^2 + a^2*c)*d^3*e^5)*x), 1/2*(6*c^3*d^5 - 13*b*c^2*d^4*e - a^2*b*e^5 + 2*(5*b^2*c + 2*a*c^2)*d^3*e^2 - 3*(b^3 + 2*a*b*c)*d^2*e^3 + 2*(2*a*b^2 - a^2*c)*d*e^4 + 2*(3*c^2*d^4*e - 3*b*c*d^3*e^2 + (b^2 - a*c)*d^2*e^3 + (3*c^2*d^2*e^3 - 3*b*c*d*e^4 + (b^2 - a*c)*e^5)*x^2 + 2*(3*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + (b^2 - a*c)*d*e^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(2*c^3*d^4*e - 4*b*c^2*d^3*e^2 + 3*b^2*c*d^2*e^3 - b^3*d*e^4 + (a*b^2 - 2*a^2*c)*e^5)*x + (2*c^3*d^5 - 3*b*c^2*d^4*e + 3*(b^2*c - 2*a*c^2)*d^3*e^2 - (b^3 - 3*a*b*c)*d^2*e^3 + (2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5)*x^2 + 2*(2*c^3*d^4*e - 3*b*c^2*d^3*e^2 + 3*(b^2*c - 2*a*c^2)*d^2*e^3 - (b^3 - 3*a*b*c)*d*e^4)*x)*log(c*x^2 + b*x + a) - 2*(2*c^3*d^5 - 3*b*c^2*d^4*e + 3*(b^2*c - 2*a*c^2)*d^3*e^2 - (b^3 - 3*a*b*c)*d^2*e^3 + (2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5)*x^2 + 2*(2*c^3*d^4*e - 3*b*c^2*d^3*e^2 + 3*(b^2*c - 2*a*c^2)*d^2*e^3 - (b^3 - 3*a*b*c)*d*e^4)*x)*log(e*x + d))/(c^3*d^8 - 3*b*c^2*d^7*e - 3*a^2*b*d^3*e^5 + a^3*d^2*e^6 + 3*(b^2*c + a*c^2)*d^6*e^2 - (b^3 + 6*a*b*c)*d^5*e^3 + 3*(a*b^2 + a^2*c)*d^4*e^4 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 - 3*a^2*b*d*e^7 + a^3*e^8 + 3*(b^2*c + a*c^2)*d^4*e^4 - (b^3 + 6*a*b*c)*d^3*e^5 + 3*(a*b^2 + a^2*c)*d^2*e^6)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 - 3*a^2*b*d^2*e^6 + a^3*d*e^7 + 3*(b^2*c + a*c^2)*d^5*e^3 - (b^3 + 6*a*b*c)*d^4*e^4 + 3*(a*b^2 + a^2*c)*d^3*e^5)*x)]","B",0
1532,1,1701,0,0.465220," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{4} x^{4} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} + 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} - 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{4} + 2 \, {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{3} + {\left(8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} - {\left(3 \, b^{4} c - 13 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, a c^{3} d^{3} e - 3 \, a b c^{2} d^{2} e^{2} + 3 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} - {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(2 \, c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + 3 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{3} - {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{4}\right)} x^{2} + {\left(2 \, b c^{3} d^{3} e - 3 \, b^{2} c^{2} d^{2} e^{2} + 3 \, {\left(b^{3} c - 2 \, a b c^{2}\right)} d e^{3} - {\left(b^{4} - 3 \, a b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e - 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} + 4 \, {\left(b^{4} c - 7 \, a b^{2} c^{2} + 12 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 9 \, a b^{3} c + 20 \, a^{2} b c^{2}\right)} e^{4}\right)} x + 2 \, {\left(3 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{4} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{2} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} + {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} - 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d e^{3} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x}, \frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{4} x^{4} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} + 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} - 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{4} + 2 \, {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{3} + {\left(8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} - {\left(3 \, b^{4} c - 13 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} - 4 \, {\left(2 \, a c^{3} d^{3} e - 3 \, a b c^{2} d^{2} e^{2} + 3 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} - {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(2 \, c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + 3 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{3} - {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{4}\right)} x^{2} + {\left(2 \, b c^{3} d^{3} e - 3 \, b^{2} c^{2} d^{2} e^{2} + 3 \, {\left(b^{3} c - 2 \, a b c^{2}\right)} d e^{3} - {\left(b^{4} - 3 \, a b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e - 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} + 4 \, {\left(b^{4} c - 7 \, a b^{2} c^{2} + 12 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 9 \, a b^{3} c + 20 \, a^{2} b c^{2}\right)} e^{4}\right)} x + 2 \, {\left(3 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{4} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{2} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} + {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} - 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d e^{3} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x}\right]"," ",0,"[((b^2*c^3 - 4*a*c^4)*e^4*x^4 - (b^2*c^3 - 4*a*c^4)*d^4 + 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 - 4*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^4 + 2*(4*(b^2*c^3 - 4*a*c^4)*d*e^3 - (b^3*c^2 - 4*a*b*c^3)*e^4)*x^3 + (8*(b^3*c^2 - 4*a*b*c^3)*d*e^3 - (3*b^4*c - 13*a*b^2*c^2 + 4*a^2*c^3)*e^4)*x^2 + 2*(2*a*c^3*d^3*e - 3*a*b*c^2*d^2*e^2 + 3*(a*b^2*c - 2*a^2*c^2)*d*e^3 - (a*b^3 - 3*a^2*b*c)*e^4 + (2*c^4*d^3*e - 3*b*c^3*d^2*e^2 + 3*(b^2*c^2 - 2*a*c^3)*d*e^3 - (b^3*c - 3*a*b*c^2)*e^4)*x^2 + (2*b*c^3*d^3*e - 3*b^2*c^2*d^2*e^2 + 3*(b^3*c - 2*a*b*c^2)*d*e^3 - (b^4 - 3*a*b^2*c)*e^4)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (4*(b^2*c^3 - 4*a*c^4)*d^3*e - 6*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 + 4*(b^4*c - 7*a*b^2*c^2 + 12*a^2*c^3)*d*e^3 - (b^5 - 9*a*b^3*c + 20*a^2*b*c^2)*e^4)*x + 2*(3*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 - 3*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^4 + (3*(b^2*c^3 - 4*a*c^4)*d^2*e^2 - 3*(b^3*c^2 - 4*a*b*c^3)*d*e^3 + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^4)*x^2 + (3*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 - 3*(b^4*c - 4*a*b^2*c^2)*d*e^3 + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^4)*x)*log(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x), ((b^2*c^3 - 4*a*c^4)*e^4*x^4 - (b^2*c^3 - 4*a*c^4)*d^4 + 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 - 4*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^4 + 2*(4*(b^2*c^3 - 4*a*c^4)*d*e^3 - (b^3*c^2 - 4*a*b*c^3)*e^4)*x^3 + (8*(b^3*c^2 - 4*a*b*c^3)*d*e^3 - (3*b^4*c - 13*a*b^2*c^2 + 4*a^2*c^3)*e^4)*x^2 - 4*(2*a*c^3*d^3*e - 3*a*b*c^2*d^2*e^2 + 3*(a*b^2*c - 2*a^2*c^2)*d*e^3 - (a*b^3 - 3*a^2*b*c)*e^4 + (2*c^4*d^3*e - 3*b*c^3*d^2*e^2 + 3*(b^2*c^2 - 2*a*c^3)*d*e^3 - (b^3*c - 3*a*b*c^2)*e^4)*x^2 + (2*b*c^3*d^3*e - 3*b^2*c^2*d^2*e^2 + 3*(b^3*c - 2*a*b*c^2)*d*e^3 - (b^4 - 3*a*b^2*c)*e^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (4*(b^2*c^3 - 4*a*c^4)*d^3*e - 6*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 + 4*(b^4*c - 7*a*b^2*c^2 + 12*a^2*c^3)*d*e^3 - (b^5 - 9*a*b^3*c + 20*a^2*b*c^2)*e^4)*x + 2*(3*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 - 3*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^4 + (3*(b^2*c^3 - 4*a*c^4)*d^2*e^2 - 3*(b^3*c^2 - 4*a*b*c^3)*d*e^3 + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^4)*x^2 + (3*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 - 3*(b^4*c - 4*a*b^2*c^2)*d*e^3 + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^4)*x)*log(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x)]","B",0
1533,1,1050,0,0.453279," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{3} x^{3} + 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3} x^{2} - 2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} + 6 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} - 3 \, {\left(2 \, a c^{2} d^{2} e - 2 \, a b c d e^{2} + {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{2} e - 2 \, b c^{2} d e^{2} + {\left(b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, b c^{2} d^{2} e - 2 \, b^{2} c d e^{2} + {\left(b^{3} - 2 \, a b c\right)} e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(b^{4} - 7 \, a b^{2} c + 12 \, a^{2} c^{2}\right)} e^{3}\right)} x + 3 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} - {\left(b^{4} - 4 \, a b^{2} c\right)} e^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}, \frac{4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{3} x^{3} + 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3} x^{2} - 2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} + 6 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} - 6 \, {\left(2 \, a c^{2} d^{2} e - 2 \, a b c d e^{2} + {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{2} e - 2 \, b c^{2} d e^{2} + {\left(b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, b c^{2} d^{2} e - 2 \, b^{2} c d e^{2} + {\left(b^{3} - 2 \, a b c\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(b^{4} - 7 \, a b^{2} c + 12 \, a^{2} c^{2}\right)} e^{3}\right)} x + 3 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} - {\left(b^{4} - 4 \, a b^{2} c\right)} e^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}\right]"," ",0,"[1/2*(4*(b^2*c^2 - 4*a*c^3)*e^3*x^3 + 4*(b^3*c - 4*a*b*c^2)*e^3*x^2 - 2*(b^2*c^2 - 4*a*c^3)*d^3 + 6*(a*b^2*c - 4*a^2*c^2)*d*e^2 - 2*(a*b^3 - 4*a^2*b*c)*e^3 - 3*(2*a*c^2*d^2*e - 2*a*b*c*d*e^2 + (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^2*e - 2*b*c^2*d*e^2 + (b^2*c - 2*a*c^2)*e^3)*x^2 + (2*b*c^2*d^2*e - 2*b^2*c*d*e^2 + (b^3 - 2*a*b*c)*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(3*(b^2*c^2 - 4*a*c^3)*d^2*e - 3*(b^3*c - 4*a*b*c^2)*d*e^2 + (b^4 - 7*a*b^2*c + 12*a^2*c^2)*e^3)*x + 3*(2*(a*b^2*c - 4*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d*e^2 - (b^4 - 4*a*b^2*c)*e^3)*x)*log(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x), 1/2*(4*(b^2*c^2 - 4*a*c^3)*e^3*x^3 + 4*(b^3*c - 4*a*b*c^2)*e^3*x^2 - 2*(b^2*c^2 - 4*a*c^3)*d^3 + 6*(a*b^2*c - 4*a^2*c^2)*d*e^2 - 2*(a*b^3 - 4*a^2*b*c)*e^3 - 6*(2*a*c^2*d^2*e - 2*a*b*c*d*e^2 + (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^2*e - 2*b*c^2*d*e^2 + (b^2*c - 2*a*c^2)*e^3)*x^2 + (2*b*c^2*d^2*e - 2*b^2*c*d*e^2 + (b^3 - 2*a*b*c)*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(3*(b^2*c^2 - 4*a*c^3)*d^2*e - 3*(b^3*c - 4*a*b*c^2)*d*e^2 + (b^4 - 7*a*b^2*c + 12*a^2*c^2)*e^3)*x + 3*(2*(a*b^2*c - 4*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d*e^2 - (b^4 - 4*a*b^2*c)*e^3)*x)*log(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)]","B",0
1534,1,573,0,0.440800," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2} + {\left(2 \, a c d e - a b e^{2} + {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{2} + {\left(2 \, b c d e - b^{2} e^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e - {\left(b^{3} - 4 \, a b c\right)} e^{2}\right)} x - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x}, -\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2} + 2 \, {\left(2 \, a c d e - a b e^{2} + {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{2} + {\left(2 \, b c d e - b^{2} e^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e - {\left(b^{3} - 4 \, a b c\right)} e^{2}\right)} x - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x}\right]"," ",0,"[-((b^2*c - 4*a*c^2)*d^2 - (a*b^2 - 4*a^2*c)*e^2 + (2*a*c*d*e - a*b*e^2 + (2*c^2*d*e - b*c*e^2)*x^2 + (2*b*c*d*e - b^2*e^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*(b^2*c - 4*a*c^2)*d*e - (b^3 - 4*a*b*c)*e^2)*x - ((b^2*c - 4*a*c^2)*e^2*x^2 + (b^3 - 4*a*b*c)*e^2*x + (a*b^2 - 4*a^2*c)*e^2)*log(c*x^2 + b*x + a))/(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x), -((b^2*c - 4*a*c^2)*d^2 - (a*b^2 - 4*a^2*c)*e^2 + 2*(2*a*c*d*e - a*b*e^2 + (2*c^2*d*e - b*c*e^2)*x^2 + (2*b*c*d*e - b^2*e^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*(b^2*c - 4*a*c^2)*d*e - (b^3 - 4*a*b*c)*e^2)*x - ((b^2*c - 4*a*c^2)*e^2*x^2 + (b^3 - 4*a*b*c)*e^2*x + (a*b^2 - 4*a^2*c)*e^2)*log(c*x^2 + b*x + a))/(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)]","B",0
1535,1,269,0,0.444515," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} e x - {\left(c e x^{2} + b e x + a e\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{2} - 4 \, a c\right)} d}{a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x}, -\frac{{\left(b^{2} - 4 \, a c\right)} e x + 2 \, {\left(c e x^{2} + b e x + a e\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{2} - 4 \, a c\right)} d}{a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x}\right]"," ",0,"[-((b^2 - 4*a*c)*e*x - (c*e*x^2 + b*e*x + a*e)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^2 - 4*a*c)*d)/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x), -((b^2 - 4*a*c)*e*x + 2*(c*e*x^2 + b*e*x + a*e)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^2 - 4*a*c)*d)/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)]","B",0
1536,1,14,0,0.408758," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{1}{c x^{2} + b x + a}"," ",0,"-1/(c*x^2 + b*x + a)","A",0
1537,1,1834,0,3.156492," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + 2 \, {\left(b^{4} - 3 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} + {\left(2 \, a c^{2} d^{2} e - 2 \, a b c d e^{2} + {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{2} e - 2 \, b c^{2} d e^{2} + {\left(b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, b c^{2} d^{2} e - 2 \, b^{2} c d e^{2} + {\left(b^{3} - 2 \, a b c\right)} e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)} x - {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} - {\left(b^{4} - 4 \, a b^{2} c\right)} e^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} - {\left(b^{4} - 4 \, a b^{2} c\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)}}, -\frac{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + 2 \, {\left(b^{4} - 3 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} - 2 \, {\left(2 \, a c^{2} d^{2} e - 2 \, a b c d e^{2} + {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{2} e - 2 \, b c^{2} d e^{2} + {\left(b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, b c^{2} d^{2} e - 2 \, b^{2} c d e^{2} + {\left(b^{3} - 2 \, a b c\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)} x - {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} - {\left(b^{4} - 4 \, a b^{2} c\right)} e^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} - {\left(b^{4} - 4 \, a b^{2} c\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(b^2*c^2 - 4*a*c^3)*d^3 - 4*(b^3*c - 4*a*b*c^2)*d^2*e + 2*(b^4 - 3*a*b^2*c - 4*a^2*c^2)*d*e^2 - 2*(a*b^3 - 4*a^2*b*c)*e^3 + (2*a*c^2*d^2*e - 2*a*b*c*d*e^2 + (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^2*e - 2*b*c^2*d*e^2 + (b^2*c - 2*a*c^2)*e^3)*x^2 + (2*b*c^2*d^2*e - 2*b^2*c*d*e^2 + (b^3 - 2*a*b*c)*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*((b^2*c^2 - 4*a*c^3)*d^2*e - (b^3*c - 4*a*b*c^2)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3)*x - (2*(a*b^2*c - 4*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d*e^2 - (b^4 - 4*a*b^2*c)*e^3)*x)*log(c*x^2 + b*x + a) + 2*(2*(a*b^2*c - 4*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d*e^2 - (b^4 - 4*a*b^2*c)*e^3)*x)*log(e*x + d))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x), -1/2*(2*(b^2*c^2 - 4*a*c^3)*d^3 - 4*(b^3*c - 4*a*b*c^2)*d^2*e + 2*(b^4 - 3*a*b^2*c - 4*a^2*c^2)*d*e^2 - 2*(a*b^3 - 4*a^2*b*c)*e^3 - 2*(2*a*c^2*d^2*e - 2*a*b*c*d*e^2 + (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^2*e - 2*b*c^2*d*e^2 + (b^2*c - 2*a*c^2)*e^3)*x^2 + (2*b*c^2*d^2*e - 2*b^2*c*d*e^2 + (b^3 - 2*a*b*c)*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*((b^2*c^2 - 4*a*c^3)*d^2*e - (b^3*c - 4*a*b*c^2)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3)*x - (2*(a*b^2*c - 4*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d*e^2 - (b^4 - 4*a*b^2*c)*e^3)*x)*log(c*x^2 + b*x + a) + 2*(2*(a*b^2*c - 4*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d*e^2 - (b^4 - 4*a*b^2*c)*e^3)*x)*log(e*x + d))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)]","B",0
1538,1,4494,0,43.720744," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + {\left(3 \, b^{4} c - 14 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d^{2} e^{3} - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5} - 2 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{3} + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{4} - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} - {\left(2 \, a c^{3} d^{4} e - 3 \, a b c^{2} d^{3} e^{2} + 3 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{2} e^{3} - {\left(a b^{3} - 3 \, a^{2} b c\right)} d e^{4} + {\left(2 \, c^{4} d^{3} e^{2} - 3 \, b c^{3} d^{2} e^{3} + 3 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{4} - {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{5}\right)} x^{3} + {\left(2 \, c^{4} d^{4} e - b c^{3} d^{3} e^{2} - 6 \, a c^{3} d^{2} e^{3} + {\left(2 \, b^{3} c - 3 \, a b c^{2}\right)} d e^{4} - {\left(b^{4} - 3 \, a b^{2} c\right)} e^{5}\right)} x^{2} + {\left(2 \, b c^{3} d^{4} e - {\left(3 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} e^{2} + 3 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{2} e^{3} - {\left(b^{4} - 6 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{4} - {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{5}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e + 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{2} - {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{2} e^{3} + 2 \, {\left(b^{5} - 3 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{4} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5}\right)} x - {\left(3 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e^{3} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e^{4} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{4} + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - {\left(2 \, b^{4} c - 7 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{4} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} + {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d e^{4} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(3 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e^{3} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e^{4} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{4} + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - {\left(2 \, b^{4} c - 7 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{4} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} + {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d e^{4} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{{\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{7} - 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{6} e + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} e^{2} - {\left(a b^{5} + 2 \, a^{2} b^{3} c - 24 \, a^{3} b c^{2}\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{6} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} e^{2} + 3 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{3} - {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{5} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{6} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{7}\right)} x^{3} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} e + 3 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{5} e^{2} + {\left(2 \, b^{5} c - 11 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d^{4} e^{3} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{5} - 4 \, a^{2} b^{3} c\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{4} - 13 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{7}\right)} x^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} - {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} e + 3 \, {\left(b^{5} c - 4 \, a b^{3} c^{2}\right)} d^{5} e^{2} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} e^{3} + {\left(2 \, a b^{5} - 11 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{6} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{7}\right)} x}, -\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + {\left(3 \, b^{4} c - 14 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d^{2} e^{3} - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5} - 2 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{3} + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{4} - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} - 2 \, {\left(2 \, a c^{3} d^{4} e - 3 \, a b c^{2} d^{3} e^{2} + 3 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{2} e^{3} - {\left(a b^{3} - 3 \, a^{2} b c\right)} d e^{4} + {\left(2 \, c^{4} d^{3} e^{2} - 3 \, b c^{3} d^{2} e^{3} + 3 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{4} - {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{5}\right)} x^{3} + {\left(2 \, c^{4} d^{4} e - b c^{3} d^{3} e^{2} - 6 \, a c^{3} d^{2} e^{3} + {\left(2 \, b^{3} c - 3 \, a b c^{2}\right)} d e^{4} - {\left(b^{4} - 3 \, a b^{2} c\right)} e^{5}\right)} x^{2} + {\left(2 \, b c^{3} d^{4} e - {\left(3 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} e^{2} + 3 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{2} e^{3} - {\left(b^{4} - 6 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{4} - {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e + 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{2} - {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{2} e^{3} + 2 \, {\left(b^{5} - 3 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{4} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5}\right)} x - {\left(3 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e^{3} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e^{4} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{4} + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - {\left(2 \, b^{4} c - 7 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{4} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} + {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d e^{4} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(3 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e^{3} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e^{4} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{4} + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - {\left(2 \, b^{4} c - 7 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{4} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} + {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d e^{4} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{{\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{7} - 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{6} e + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} e^{2} - {\left(a b^{5} + 2 \, a^{2} b^{3} c - 24 \, a^{3} b c^{2}\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{6} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} e^{2} + 3 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{3} - {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{5} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{6} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{7}\right)} x^{3} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} e + 3 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{5} e^{2} + {\left(2 \, b^{5} c - 11 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d^{4} e^{3} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{5} - 4 \, a^{2} b^{3} c\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{4} - 13 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{7}\right)} x^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} - {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} e + 3 \, {\left(b^{5} c - 4 \, a b^{3} c^{2}\right)} d^{5} e^{2} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} e^{3} + {\left(2 \, a b^{5} - 11 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{6} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{7}\right)} x}\right]"," ",0,"[-((b^2*c^3 - 4*a*c^4)*d^5 - 3*(b^3*c^2 - 4*a*b*c^3)*d^4*e + (3*b^4*c - 14*a*b^2*c^2 + 8*a^2*c^3)*d^3*e^2 - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d^2*e^3 - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^4 + (a^2*b^3 - 4*a^3*b*c)*e^5 - 2*(2*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - 3*(b^3*c^2 - 4*a*b*c^3)*d^2*e^3 + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d*e^4 - (a*b^3*c - 4*a^2*b*c^2)*e^5)*x^2 - (2*a*c^3*d^4*e - 3*a*b*c^2*d^3*e^2 + 3*(a*b^2*c - 2*a^2*c^2)*d^2*e^3 - (a*b^3 - 3*a^2*b*c)*d*e^4 + (2*c^4*d^3*e^2 - 3*b*c^3*d^2*e^3 + 3*(b^2*c^2 - 2*a*c^3)*d*e^4 - (b^3*c - 3*a*b*c^2)*e^5)*x^3 + (2*c^4*d^4*e - b*c^3*d^3*e^2 - 6*a*c^3*d^2*e^3 + (2*b^3*c - 3*a*b*c^2)*d*e^4 - (b^4 - 3*a*b^2*c)*e^5)*x^2 + (2*b*c^3*d^4*e - (3*b^2*c^2 - 2*a*c^3)*d^3*e^2 + 3*(b^3*c - 3*a*b*c^2)*d^2*e^3 - (b^4 - 6*a*b^2*c + 6*a^2*c^2)*d*e^4 - (a*b^3 - 3*a^2*b*c)*e^5)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - ((b^2*c^3 - 4*a*c^4)*d^4*e + 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e^2 - (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d^2*e^3 + 2*(b^5 - 3*a*b^3*c - 4*a^2*b*c^2)*d*e^4 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*e^5)*x - (3*(a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - 3*(a*b^3*c - 4*a^2*b*c^2)*d^2*e^3 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d*e^4 + (3*(b^2*c^3 - 4*a*c^4)*d^2*e^3 - 3*(b^3*c^2 - 4*a*b*c^3)*d*e^4 + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^5)*x^3 + (3*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - (2*b^4*c - 7*a*b^2*c^2 - 4*a^2*c^3)*d*e^4 + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^5)*x^2 + (3*(b^3*c^2 - 4*a*b*c^3)*d^3*e^2 - 3*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*e^4 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^5)*x)*log(c*x^2 + b*x + a) + 2*(3*(a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - 3*(a*b^3*c - 4*a^2*b*c^2)*d^2*e^3 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d*e^4 + (3*(b^2*c^3 - 4*a*c^4)*d^2*e^3 - 3*(b^3*c^2 - 4*a*b*c^3)*d*e^4 + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^5)*x^3 + (3*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - (2*b^4*c - 7*a*b^2*c^2 - 4*a^2*c^3)*d*e^4 + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^5)*x^2 + (3*(b^3*c^2 - 4*a*b*c^3)*d^3*e^2 - 3*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*e^4 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^5)*x)*log(e*x + d))/((a*b^2*c^3 - 4*a^2*c^4)*d^7 - 3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^6*e + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^5*e^2 - (a*b^5 + 2*a^2*b^3*c - 24*a^3*b*c^2)*d^4*e^3 + 3*(a^2*b^4 - 3*a^3*b^2*c - 4*a^4*c^2)*d^3*e^4 - 3*(a^3*b^3 - 4*a^4*b*c)*d^2*e^5 + (a^4*b^2 - 4*a^5*c)*d*e^6 + ((b^2*c^4 - 4*a*c^5)*d^6*e - 3*(b^3*c^3 - 4*a*b*c^4)*d^5*e^2 + 3*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e^3 - (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^4 + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^5 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^6 + (a^3*b^2*c - 4*a^4*c^2)*e^7)*x^3 + ((b^2*c^4 - 4*a*c^5)*d^7 - 2*(b^3*c^3 - 4*a*b*c^4)*d^6*e + 3*(a*b^2*c^3 - 4*a^2*c^4)*d^5*e^2 + (2*b^5*c - 11*a*b^3*c^2 + 12*a^2*b*c^3)*d^4*e^3 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^3*e^4 + 3*(a*b^5 - 4*a^2*b^3*c)*d^2*e^5 - (3*a^2*b^4 - 13*a^3*b^2*c + 4*a^4*c^2)*d*e^6 + (a^3*b^3 - 4*a^4*b*c)*e^7)*x^2 + ((b^3*c^3 - 4*a*b*c^4)*d^7 - (3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^6*e + 3*(b^5*c - 4*a*b^3*c^2)*d^5*e^2 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^4*e^3 + (2*a*b^5 - 11*a^2*b^3*c + 12*a^3*b*c^2)*d^3*e^4 + 3*(a^3*b^2*c - 4*a^4*c^2)*d^2*e^5 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^6 + (a^4*b^2 - 4*a^5*c)*e^7)*x), -((b^2*c^3 - 4*a*c^4)*d^5 - 3*(b^3*c^2 - 4*a*b*c^3)*d^4*e + (3*b^4*c - 14*a*b^2*c^2 + 8*a^2*c^3)*d^3*e^2 - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d^2*e^3 - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^4 + (a^2*b^3 - 4*a^3*b*c)*e^5 - 2*(2*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - 3*(b^3*c^2 - 4*a*b*c^3)*d^2*e^3 + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d*e^4 - (a*b^3*c - 4*a^2*b*c^2)*e^5)*x^2 - 2*(2*a*c^3*d^4*e - 3*a*b*c^2*d^3*e^2 + 3*(a*b^2*c - 2*a^2*c^2)*d^2*e^3 - (a*b^3 - 3*a^2*b*c)*d*e^4 + (2*c^4*d^3*e^2 - 3*b*c^3*d^2*e^3 + 3*(b^2*c^2 - 2*a*c^3)*d*e^4 - (b^3*c - 3*a*b*c^2)*e^5)*x^3 + (2*c^4*d^4*e - b*c^3*d^3*e^2 - 6*a*c^3*d^2*e^3 + (2*b^3*c - 3*a*b*c^2)*d*e^4 - (b^4 - 3*a*b^2*c)*e^5)*x^2 + (2*b*c^3*d^4*e - (3*b^2*c^2 - 2*a*c^3)*d^3*e^2 + 3*(b^3*c - 3*a*b*c^2)*d^2*e^3 - (b^4 - 6*a*b^2*c + 6*a^2*c^2)*d*e^4 - (a*b^3 - 3*a^2*b*c)*e^5)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - ((b^2*c^3 - 4*a*c^4)*d^4*e + 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e^2 - (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d^2*e^3 + 2*(b^5 - 3*a*b^3*c - 4*a^2*b*c^2)*d*e^4 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*e^5)*x - (3*(a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - 3*(a*b^3*c - 4*a^2*b*c^2)*d^2*e^3 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d*e^4 + (3*(b^2*c^3 - 4*a*c^4)*d^2*e^3 - 3*(b^3*c^2 - 4*a*b*c^3)*d*e^4 + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^5)*x^3 + (3*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - (2*b^4*c - 7*a*b^2*c^2 - 4*a^2*c^3)*d*e^4 + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^5)*x^2 + (3*(b^3*c^2 - 4*a*b*c^3)*d^3*e^2 - 3*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*e^4 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^5)*x)*log(c*x^2 + b*x + a) + 2*(3*(a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - 3*(a*b^3*c - 4*a^2*b*c^2)*d^2*e^3 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d*e^4 + (3*(b^2*c^3 - 4*a*c^4)*d^2*e^3 - 3*(b^3*c^2 - 4*a*b*c^3)*d*e^4 + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^5)*x^3 + (3*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - (2*b^4*c - 7*a*b^2*c^2 - 4*a^2*c^3)*d*e^4 + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^5)*x^2 + (3*(b^3*c^2 - 4*a*b*c^3)*d^3*e^2 - 3*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*e^4 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^5)*x)*log(e*x + d))/((a*b^2*c^3 - 4*a^2*c^4)*d^7 - 3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^6*e + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^5*e^2 - (a*b^5 + 2*a^2*b^3*c - 24*a^3*b*c^2)*d^4*e^3 + 3*(a^2*b^4 - 3*a^3*b^2*c - 4*a^4*c^2)*d^3*e^4 - 3*(a^3*b^3 - 4*a^4*b*c)*d^2*e^5 + (a^4*b^2 - 4*a^5*c)*d*e^6 + ((b^2*c^4 - 4*a*c^5)*d^6*e - 3*(b^3*c^3 - 4*a*b*c^4)*d^5*e^2 + 3*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e^3 - (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^4 + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^5 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^6 + (a^3*b^2*c - 4*a^4*c^2)*e^7)*x^3 + ((b^2*c^4 - 4*a*c^5)*d^7 - 2*(b^3*c^3 - 4*a*b*c^4)*d^6*e + 3*(a*b^2*c^3 - 4*a^2*c^4)*d^5*e^2 + (2*b^5*c - 11*a*b^3*c^2 + 12*a^2*b*c^3)*d^4*e^3 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^3*e^4 + 3*(a*b^5 - 4*a^2*b^3*c)*d^2*e^5 - (3*a^2*b^4 - 13*a^3*b^2*c + 4*a^4*c^2)*d*e^6 + (a^3*b^3 - 4*a^4*b*c)*e^7)*x^2 + ((b^3*c^3 - 4*a*b*c^4)*d^7 - (3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^6*e + 3*(b^5*c - 4*a*b^3*c^2)*d^5*e^2 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^4*e^3 + (2*a*b^5 - 11*a^2*b^3*c + 12*a^3*b*c^2)*d^3*e^4 + 3*(a^3*b^2*c - 4*a^4*c^2)*d^2*e^5 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^6 + (a^4*b^2 - 4*a^5*c)*e^7)*x)]","B",0
1539,1,3618,0,0.524407," ","integrate((2*c*x+b)*(e*x+d)^5/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e^{5} x^{5} + 8 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5} x^{4} - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{5} - 5 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e + 40 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{3} e^{2} - 30 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(5 \, a^{2} b^{4} c - 32 \, a^{3} b^{2} c^{2} + 48 \, a^{4} c^{3}\right)} d e^{4} - {\left(7 \, a^{2} b^{5} - 51 \, a^{3} b^{3} c + 92 \, a^{4} b c^{2}\right)} e^{5} - 2 \, {\left(5 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} e - 10 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e^{2} + 10 \, {\left(2 \, b^{4} c^{3} - 13 \, a b^{2} c^{4} + 20 \, a^{2} c^{5}\right)} d^{2} e^{3} - 5 \, {\left(3 \, b^{5} c^{2} - 22 \, a b^{3} c^{3} + 40 \, a^{2} b c^{4}\right)} d e^{4} + {\left(2 \, b^{6} c - 21 \, a b^{4} c^{2} + 77 \, a^{2} b^{2} c^{3} - 100 \, a^{3} c^{4}\right)} e^{5}\right)} x^{3} - {\left(15 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e - 10 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} - 32 \, a^{2} c^{5}\right)} d^{3} e^{2} + 30 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 5 \, {\left(5 \, b^{6} c - 30 \, a b^{4} c^{2} + 24 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d e^{4} + {\left(7 \, b^{7} - 57 \, a b^{5} c + 135 \, a^{2} b^{3} c^{2} - 76 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(2 \, a^{2} c^{4} d^{4} e - 4 \, a^{2} b c^{3} d^{3} e^{2} + 12 \, a^{3} c^{3} d^{2} e^{3} + 2 \, {\left(a^{2} b^{3} c - 6 \, a^{3} b c^{2}\right)} d e^{4} - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} e^{5} + {\left(2 \, c^{6} d^{4} e - 4 \, b c^{5} d^{3} e^{2} + 12 \, a c^{5} d^{2} e^{3} + 2 \, {\left(b^{3} c^{3} - 6 \, a b c^{4}\right)} d e^{4} - {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, b c^{5} d^{4} e - 4 \, b^{2} c^{4} d^{3} e^{2} + 12 \, a b c^{4} d^{2} e^{3} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3}\right)} d e^{4} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{4} e - 4 \, {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{3} e^{2} + 12 \, {\left(a b^{2} c^{3} + 2 \, a^{2} c^{4}\right)} d^{2} e^{3} + 2 \, {\left(b^{5} c - 4 \, a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d e^{4} - {\left(b^{6} - 4 \, a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, a b c^{4} d^{4} e - 4 \, a b^{2} c^{3} d^{3} e^{2} + 12 \, a^{2} b c^{3} d^{2} e^{3} + 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2}\right)} d e^{4} - {\left(a b^{5} - 6 \, a^{2} b^{3} c + 6 \, a^{3} b c^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(5 \, {\left(b^{4} c^{3} - 5 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{4} e - 30 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} e^{2} + 30 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{2} e^{3} - 5 \, {\left(5 \, a b^{5} c - 34 \, a^{2} b^{3} c^{2} + 56 \, a^{3} b c^{3}\right)} d e^{4} + {\left(7 \, a b^{6} - 56 \, a^{2} b^{4} c + 127 \, a^{3} b^{2} c^{2} - 60 \, a^{4} c^{3}\right)} e^{5}\right)} x + 5 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}, \frac{4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e^{5} x^{5} + 8 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5} x^{4} - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{5} - 5 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e + 40 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{3} e^{2} - 30 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(5 \, a^{2} b^{4} c - 32 \, a^{3} b^{2} c^{2} + 48 \, a^{4} c^{3}\right)} d e^{4} - {\left(7 \, a^{2} b^{5} - 51 \, a^{3} b^{3} c + 92 \, a^{4} b c^{2}\right)} e^{5} - 2 \, {\left(5 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} e - 10 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e^{2} + 10 \, {\left(2 \, b^{4} c^{3} - 13 \, a b^{2} c^{4} + 20 \, a^{2} c^{5}\right)} d^{2} e^{3} - 5 \, {\left(3 \, b^{5} c^{2} - 22 \, a b^{3} c^{3} + 40 \, a^{2} b c^{4}\right)} d e^{4} + {\left(2 \, b^{6} c - 21 \, a b^{4} c^{2} + 77 \, a^{2} b^{2} c^{3} - 100 \, a^{3} c^{4}\right)} e^{5}\right)} x^{3} - {\left(15 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e - 10 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} - 32 \, a^{2} c^{5}\right)} d^{3} e^{2} + 30 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 5 \, {\left(5 \, b^{6} c - 30 \, a b^{4} c^{2} + 24 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d e^{4} + {\left(7 \, b^{7} - 57 \, a b^{5} c + 135 \, a^{2} b^{3} c^{2} - 76 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 10 \, {\left(2 \, a^{2} c^{4} d^{4} e - 4 \, a^{2} b c^{3} d^{3} e^{2} + 12 \, a^{3} c^{3} d^{2} e^{3} + 2 \, {\left(a^{2} b^{3} c - 6 \, a^{3} b c^{2}\right)} d e^{4} - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} e^{5} + {\left(2 \, c^{6} d^{4} e - 4 \, b c^{5} d^{3} e^{2} + 12 \, a c^{5} d^{2} e^{3} + 2 \, {\left(b^{3} c^{3} - 6 \, a b c^{4}\right)} d e^{4} - {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, b c^{5} d^{4} e - 4 \, b^{2} c^{4} d^{3} e^{2} + 12 \, a b c^{4} d^{2} e^{3} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3}\right)} d e^{4} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{4} e - 4 \, {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{3} e^{2} + 12 \, {\left(a b^{2} c^{3} + 2 \, a^{2} c^{4}\right)} d^{2} e^{3} + 2 \, {\left(b^{5} c - 4 \, a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d e^{4} - {\left(b^{6} - 4 \, a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, a b c^{4} d^{4} e - 4 \, a b^{2} c^{3} d^{3} e^{2} + 12 \, a^{2} b c^{3} d^{2} e^{3} + 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2}\right)} d e^{4} - {\left(a b^{5} - 6 \, a^{2} b^{3} c + 6 \, a^{3} b c^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(5 \, {\left(b^{4} c^{3} - 5 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{4} e - 30 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} e^{2} + 30 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{2} e^{3} - 5 \, {\left(5 \, a b^{5} c - 34 \, a^{2} b^{3} c^{2} + 56 \, a^{3} b c^{3}\right)} d e^{4} + {\left(7 \, a b^{6} - 56 \, a^{2} b^{4} c + 127 \, a^{3} b^{2} c^{2} - 60 \, a^{4} c^{3}\right)} e^{5}\right)} x + 5 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/2*(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*e^5*x^5 + 8*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5*x^4 - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^5 - 5*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e + 40*(a^2*b^2*c^3 - 4*a^3*c^4)*d^3*e^2 - 30*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^2*e^3 + 5*(5*a^2*b^4*c - 32*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^4 - (7*a^2*b^5 - 51*a^3*b^3*c + 92*a^4*b*c^2)*e^5 - 2*(5*(b^2*c^5 - 4*a*c^6)*d^4*e - 10*(b^3*c^4 - 4*a*b*c^5)*d^3*e^2 + 10*(2*b^4*c^3 - 13*a*b^2*c^4 + 20*a^2*c^5)*d^2*e^3 - 5*(3*b^5*c^2 - 22*a*b^3*c^3 + 40*a^2*b*c^4)*d*e^4 + (2*b^6*c - 21*a*b^4*c^2 + 77*a^2*b^2*c^3 - 100*a^3*c^4)*e^5)*x^3 - (15*(b^3*c^4 - 4*a*b*c^5)*d^4*e - 10*(b^4*c^3 + 4*a*b^2*c^4 - 32*a^2*c^5)*d^3*e^2 + 30*(b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e^3 - 5*(5*b^6*c - 30*a*b^4*c^2 + 24*a^2*b^2*c^3 + 64*a^3*c^4)*d*e^4 + (7*b^7 - 57*a*b^5*c + 135*a^2*b^3*c^2 - 76*a^3*b*c^3)*e^5)*x^2 + 5*(2*a^2*c^4*d^4*e - 4*a^2*b*c^3*d^3*e^2 + 12*a^3*c^3*d^2*e^3 + 2*(a^2*b^3*c - 6*a^3*b*c^2)*d*e^4 - (a^2*b^4 - 6*a^3*b^2*c + 6*a^4*c^2)*e^5 + (2*c^6*d^4*e - 4*b*c^5*d^3*e^2 + 12*a*c^5*d^2*e^3 + 2*(b^3*c^3 - 6*a*b*c^4)*d*e^4 - (b^4*c^2 - 6*a*b^2*c^3 + 6*a^2*c^4)*e^5)*x^4 + 2*(2*b*c^5*d^4*e - 4*b^2*c^4*d^3*e^2 + 12*a*b*c^4*d^2*e^3 + 2*(b^4*c^2 - 6*a*b^2*c^3)*d*e^4 - (b^5*c - 6*a*b^3*c^2 + 6*a^2*b*c^3)*e^5)*x^3 + (2*(b^2*c^4 + 2*a*c^5)*d^4*e - 4*(b^3*c^3 + 2*a*b*c^4)*d^3*e^2 + 12*(a*b^2*c^3 + 2*a^2*c^4)*d^2*e^3 + 2*(b^5*c - 4*a*b^3*c^2 - 12*a^2*b*c^3)*d*e^4 - (b^6 - 4*a*b^4*c - 6*a^2*b^2*c^2 + 12*a^3*c^3)*e^5)*x^2 + 2*(2*a*b*c^4*d^4*e - 4*a*b^2*c^3*d^3*e^2 + 12*a^2*b*c^3*d^2*e^3 + 2*(a*b^4*c - 6*a^2*b^2*c^2)*d*e^4 - (a*b^5 - 6*a^2*b^3*c + 6*a^3*b*c^2)*e^5)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(5*(b^4*c^3 - 5*a*b^2*c^4 + 4*a^2*c^5)*d^4*e - 30*(a*b^3*c^3 - 4*a^2*b*c^4)*d^3*e^2 + 30*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d^2*e^3 - 5*(5*a*b^5*c - 34*a^2*b^3*c^2 + 56*a^3*b*c^3)*d*e^4 + (7*a*b^6 - 56*a^2*b^4*c + 127*a^3*b^2*c^2 - 60*a^4*c^3)*e^5)*x + 5*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^4 + 2*(2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^5)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d*e^4 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^5)*x^2 + 2*(2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 - (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^5)*x)*log(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x), 1/2*(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*e^5*x^5 + 8*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5*x^4 - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^5 - 5*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e + 40*(a^2*b^2*c^3 - 4*a^3*c^4)*d^3*e^2 - 30*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^2*e^3 + 5*(5*a^2*b^4*c - 32*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^4 - (7*a^2*b^5 - 51*a^3*b^3*c + 92*a^4*b*c^2)*e^5 - 2*(5*(b^2*c^5 - 4*a*c^6)*d^4*e - 10*(b^3*c^4 - 4*a*b*c^5)*d^3*e^2 + 10*(2*b^4*c^3 - 13*a*b^2*c^4 + 20*a^2*c^5)*d^2*e^3 - 5*(3*b^5*c^2 - 22*a*b^3*c^3 + 40*a^2*b*c^4)*d*e^4 + (2*b^6*c - 21*a*b^4*c^2 + 77*a^2*b^2*c^3 - 100*a^3*c^4)*e^5)*x^3 - (15*(b^3*c^4 - 4*a*b*c^5)*d^4*e - 10*(b^4*c^3 + 4*a*b^2*c^4 - 32*a^2*c^5)*d^3*e^2 + 30*(b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e^3 - 5*(5*b^6*c - 30*a*b^4*c^2 + 24*a^2*b^2*c^3 + 64*a^3*c^4)*d*e^4 + (7*b^7 - 57*a*b^5*c + 135*a^2*b^3*c^2 - 76*a^3*b*c^3)*e^5)*x^2 + 10*(2*a^2*c^4*d^4*e - 4*a^2*b*c^3*d^3*e^2 + 12*a^3*c^3*d^2*e^3 + 2*(a^2*b^3*c - 6*a^3*b*c^2)*d*e^4 - (a^2*b^4 - 6*a^3*b^2*c + 6*a^4*c^2)*e^5 + (2*c^6*d^4*e - 4*b*c^5*d^3*e^2 + 12*a*c^5*d^2*e^3 + 2*(b^3*c^3 - 6*a*b*c^4)*d*e^4 - (b^4*c^2 - 6*a*b^2*c^3 + 6*a^2*c^4)*e^5)*x^4 + 2*(2*b*c^5*d^4*e - 4*b^2*c^4*d^3*e^2 + 12*a*b*c^4*d^2*e^3 + 2*(b^4*c^2 - 6*a*b^2*c^3)*d*e^4 - (b^5*c - 6*a*b^3*c^2 + 6*a^2*b*c^3)*e^5)*x^3 + (2*(b^2*c^4 + 2*a*c^5)*d^4*e - 4*(b^3*c^3 + 2*a*b*c^4)*d^3*e^2 + 12*(a*b^2*c^3 + 2*a^2*c^4)*d^2*e^3 + 2*(b^5*c - 4*a*b^3*c^2 - 12*a^2*b*c^3)*d*e^4 - (b^6 - 4*a*b^4*c - 6*a^2*b^2*c^2 + 12*a^3*c^3)*e^5)*x^2 + 2*(2*a*b*c^4*d^4*e - 4*a*b^2*c^3*d^3*e^2 + 12*a^2*b*c^3*d^2*e^3 + 2*(a*b^4*c - 6*a^2*b^2*c^2)*d*e^4 - (a*b^5 - 6*a^2*b^3*c + 6*a^3*b*c^2)*e^5)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(5*(b^4*c^3 - 5*a*b^2*c^4 + 4*a^2*c^5)*d^4*e - 30*(a*b^3*c^3 - 4*a^2*b*c^4)*d^3*e^2 + 30*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d^2*e^3 - 5*(5*a*b^5*c - 34*a^2*b^3*c^2 + 56*a^3*b*c^3)*d*e^4 + (7*a*b^6 - 56*a^2*b^4*c + 127*a^3*b^2*c^2 - 60*a^4*c^3)*e^5)*x + 5*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^4 + 2*(2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^5)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d*e^4 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^5)*x^2 + 2*(2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 - (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^5)*x)*log(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x)]","B",0
1540,1,2400,0,0.465711," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 4 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e - 24 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{2} + 12 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{3} - {\left(5 \, a^{2} b^{4} - 32 \, a^{3} b^{2} c + 48 \, a^{4} c^{2}\right)} e^{4} + 2 \, {\left(4 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} e - 6 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e^{2} + 4 \, {\left(2 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 20 \, a^{2} c^{4}\right)} d e^{3} - {\left(3 \, b^{5} c - 22 \, a b^{3} c^{2} + 40 \, a^{2} b c^{3}\right)} e^{4}\right)} x^{3} + {\left(12 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e - 6 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} - 32 \, a^{2} c^{4}\right)} d^{2} e^{2} + 12 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{3} - {\left(5 \, b^{6} - 30 \, a b^{4} c + 24 \, a^{2} b^{2} c^{2} + 64 \, a^{3} c^{3}\right)} e^{4}\right)} x^{2} - 2 \, {\left(4 \, a^{2} c^{3} d^{3} e - 6 \, a^{2} b c^{2} d^{2} e^{2} + 12 \, a^{3} c^{2} d e^{3} + {\left(a^{2} b^{3} - 6 \, a^{3} b c\right)} e^{4} + {\left(4 \, c^{5} d^{3} e - 6 \, b c^{4} d^{2} e^{2} + 12 \, a c^{4} d e^{3} + {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(4 \, b c^{4} d^{3} e - 6 \, b^{2} c^{3} d^{2} e^{2} + 12 \, a b c^{3} d e^{3} + {\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} e^{4}\right)} x^{3} + {\left(4 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d^{3} e - 6 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{2} e^{2} + 12 \, {\left(a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{3} + {\left(b^{5} - 4 \, a b^{3} c - 12 \, a^{2} b c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(4 \, a b c^{3} d^{3} e - 6 \, a b^{2} c^{2} d^{2} e^{2} + 12 \, a^{2} b c^{2} d e^{3} + {\left(a b^{4} - 6 \, a^{2} b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(4 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{3} e - 18 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e^{2} + 12 \, {\left(a b^{4} c - 5 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d e^{3} - {\left(5 \, a b^{5} - 34 \, a^{2} b^{3} c + 56 \, a^{3} b c^{2}\right)} e^{4}\right)} x - 2 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{4} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} e^{4} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{4} x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)}}, -\frac{{\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 4 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e - 24 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{2} + 12 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{3} - {\left(5 \, a^{2} b^{4} - 32 \, a^{3} b^{2} c + 48 \, a^{4} c^{2}\right)} e^{4} + 2 \, {\left(4 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} e - 6 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e^{2} + 4 \, {\left(2 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 20 \, a^{2} c^{4}\right)} d e^{3} - {\left(3 \, b^{5} c - 22 \, a b^{3} c^{2} + 40 \, a^{2} b c^{3}\right)} e^{4}\right)} x^{3} + {\left(12 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e - 6 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} - 32 \, a^{2} c^{4}\right)} d^{2} e^{2} + 12 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{3} - {\left(5 \, b^{6} - 30 \, a b^{4} c + 24 \, a^{2} b^{2} c^{2} + 64 \, a^{3} c^{3}\right)} e^{4}\right)} x^{2} - 4 \, {\left(4 \, a^{2} c^{3} d^{3} e - 6 \, a^{2} b c^{2} d^{2} e^{2} + 12 \, a^{3} c^{2} d e^{3} + {\left(a^{2} b^{3} - 6 \, a^{3} b c\right)} e^{4} + {\left(4 \, c^{5} d^{3} e - 6 \, b c^{4} d^{2} e^{2} + 12 \, a c^{4} d e^{3} + {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(4 \, b c^{4} d^{3} e - 6 \, b^{2} c^{3} d^{2} e^{2} + 12 \, a b c^{3} d e^{3} + {\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} e^{4}\right)} x^{3} + {\left(4 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d^{3} e - 6 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{2} e^{2} + 12 \, {\left(a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{3} + {\left(b^{5} - 4 \, a b^{3} c - 12 \, a^{2} b c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(4 \, a b c^{3} d^{3} e - 6 \, a b^{2} c^{2} d^{2} e^{2} + 12 \, a^{2} b c^{2} d e^{3} + {\left(a b^{4} - 6 \, a^{2} b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(4 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{3} e - 18 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e^{2} + 12 \, {\left(a b^{4} c - 5 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d e^{3} - {\left(5 \, a b^{5} - 34 \, a^{2} b^{3} c + 56 \, a^{3} b c^{2}\right)} e^{4}\right)} x - 2 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{4} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} e^{4} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{4} x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/2*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 4*(a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e - 24*(a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^2 + 12*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^3 - (5*a^2*b^4 - 32*a^3*b^2*c + 48*a^4*c^2)*e^4 + 2*(4*(b^2*c^4 - 4*a*c^5)*d^3*e - 6*(b^3*c^3 - 4*a*b*c^4)*d^2*e^2 + 4*(2*b^4*c^2 - 13*a*b^2*c^3 + 20*a^2*c^4)*d*e^3 - (3*b^5*c - 22*a*b^3*c^2 + 40*a^2*b*c^3)*e^4)*x^3 + (12*(b^3*c^3 - 4*a*b*c^4)*d^3*e - 6*(b^4*c^2 + 4*a*b^2*c^3 - 32*a^2*c^4)*d^2*e^2 + 12*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^3 - (5*b^6 - 30*a*b^4*c + 24*a^2*b^2*c^2 + 64*a^3*c^3)*e^4)*x^2 - 2*(4*a^2*c^3*d^3*e - 6*a^2*b*c^2*d^2*e^2 + 12*a^3*c^2*d*e^3 + (a^2*b^3 - 6*a^3*b*c)*e^4 + (4*c^5*d^3*e - 6*b*c^4*d^2*e^2 + 12*a*c^4*d*e^3 + (b^3*c^2 - 6*a*b*c^3)*e^4)*x^4 + 2*(4*b*c^4*d^3*e - 6*b^2*c^3*d^2*e^2 + 12*a*b*c^3*d*e^3 + (b^4*c - 6*a*b^2*c^2)*e^4)*x^3 + (4*(b^2*c^3 + 2*a*c^4)*d^3*e - 6*(b^3*c^2 + 2*a*b*c^3)*d^2*e^2 + 12*(a*b^2*c^2 + 2*a^2*c^3)*d*e^3 + (b^5 - 4*a*b^3*c - 12*a^2*b*c^2)*e^4)*x^2 + 2*(4*a*b*c^3*d^3*e - 6*a*b^2*c^2*d^2*e^2 + 12*a^2*b*c^2*d*e^3 + (a*b^4 - 6*a^2*b^2*c)*e^4)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(4*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d^3*e - 18*(a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e^2 + 12*(a*b^4*c - 5*a^2*b^2*c^2 + 4*a^3*c^3)*d*e^3 - (5*a*b^5 - 34*a^2*b^3*c + 56*a^3*b*c^2)*e^4)*x - 2*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^4*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*e^4*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^4*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e^4)*log(c*x^2 + b*x + a))/(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x), -1/2*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 4*(a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e - 24*(a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^2 + 12*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^3 - (5*a^2*b^4 - 32*a^3*b^2*c + 48*a^4*c^2)*e^4 + 2*(4*(b^2*c^4 - 4*a*c^5)*d^3*e - 6*(b^3*c^3 - 4*a*b*c^4)*d^2*e^2 + 4*(2*b^4*c^2 - 13*a*b^2*c^3 + 20*a^2*c^4)*d*e^3 - (3*b^5*c - 22*a*b^3*c^2 + 40*a^2*b*c^3)*e^4)*x^3 + (12*(b^3*c^3 - 4*a*b*c^4)*d^3*e - 6*(b^4*c^2 + 4*a*b^2*c^3 - 32*a^2*c^4)*d^2*e^2 + 12*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^3 - (5*b^6 - 30*a*b^4*c + 24*a^2*b^2*c^2 + 64*a^3*c^3)*e^4)*x^2 - 4*(4*a^2*c^3*d^3*e - 6*a^2*b*c^2*d^2*e^2 + 12*a^3*c^2*d*e^3 + (a^2*b^3 - 6*a^3*b*c)*e^4 + (4*c^5*d^3*e - 6*b*c^4*d^2*e^2 + 12*a*c^4*d*e^3 + (b^3*c^2 - 6*a*b*c^3)*e^4)*x^4 + 2*(4*b*c^4*d^3*e - 6*b^2*c^3*d^2*e^2 + 12*a*b*c^3*d*e^3 + (b^4*c - 6*a*b^2*c^2)*e^4)*x^3 + (4*(b^2*c^3 + 2*a*c^4)*d^3*e - 6*(b^3*c^2 + 2*a*b*c^3)*d^2*e^2 + 12*(a*b^2*c^2 + 2*a^2*c^3)*d*e^3 + (b^5 - 4*a*b^3*c - 12*a^2*b*c^2)*e^4)*x^2 + 2*(4*a*b*c^3*d^3*e - 6*a*b^2*c^2*d^2*e^2 + 12*a^2*b*c^2*d*e^3 + (a*b^4 - 6*a^2*b^2*c)*e^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(4*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d^3*e - 18*(a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e^2 + 12*(a*b^4*c - 5*a^2*b^2*c^2 + 4*a^3*c^3)*d*e^3 - (5*a*b^5 - 34*a^2*b^3*c + 56*a^3*b*c^2)*e^4)*x - 2*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^4*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*e^4*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^4*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e^4)*log(c*x^2 + b*x + a))/(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)]","B",0
1541,1,1455,0,0.438237," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e - 12 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{2} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{3} + 2 \, {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{2} + {\left(2 \, b^{4} c - 13 \, a b^{2} c^{2} + 20 \, a^{2} c^{3}\right)} e^{3}\right)} x^{3} + 3 \, {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e - {\left(b^{4} c + 4 \, a b^{2} c^{2} - 32 \, a^{2} c^{3}\right)} d e^{2} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{3}\right)} x^{2} + 6 \, {\left(a^{2} c^{2} d^{2} e - a^{2} b c d e^{2} + a^{3} c e^{3} + {\left(c^{4} d^{2} e - b c^{3} d e^{2} + a c^{3} e^{3}\right)} x^{4} + 2 \, {\left(b c^{3} d^{2} e - b^{2} c^{2} d e^{2} + a b c^{2} e^{3}\right)} x^{3} + {\left({\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e - {\left(b^{3} c + 2 \, a b c^{2}\right)} d e^{2} + {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{3}\right)} x^{2} + 2 \, {\left(a b c^{2} d^{2} e - a b^{2} c d e^{2} + a^{2} b c e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 6 \, {\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{2} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{3}\right)} x}{2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)}}, -\frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e - 12 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{2} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{3} + 2 \, {\left(3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{2} + {\left(2 \, b^{4} c - 13 \, a b^{2} c^{2} + 20 \, a^{2} c^{3}\right)} e^{3}\right)} x^{3} + 3 \, {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e - {\left(b^{4} c + 4 \, a b^{2} c^{2} - 32 \, a^{2} c^{3}\right)} d e^{2} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{3}\right)} x^{2} - 12 \, {\left(a^{2} c^{2} d^{2} e - a^{2} b c d e^{2} + a^{3} c e^{3} + {\left(c^{4} d^{2} e - b c^{3} d e^{2} + a c^{3} e^{3}\right)} x^{4} + 2 \, {\left(b c^{3} d^{2} e - b^{2} c^{2} d e^{2} + a b c^{2} e^{3}\right)} x^{3} + {\left({\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e - {\left(b^{3} c + 2 \, a b c^{2}\right)} d e^{2} + {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{3}\right)} x^{2} + 2 \, {\left(a b c^{2} d^{2} e - a b^{2} c d e^{2} + a^{2} b c e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 6 \, {\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{2} + {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{3}\right)} x}{2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)}}\right]"," ",0,"[-1/2*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + 3*(a*b^3*c - 4*a^2*b*c^2)*d^2*e - 12*(a^2*b^2*c - 4*a^3*c^2)*d*e^2 + 3*(a^2*b^3 - 4*a^3*b*c)*e^3 + 2*(3*(b^2*c^3 - 4*a*c^4)*d^2*e - 3*(b^3*c^2 - 4*a*b*c^3)*d*e^2 + (2*b^4*c - 13*a*b^2*c^2 + 20*a^2*c^3)*e^3)*x^3 + 3*(3*(b^3*c^2 - 4*a*b*c^3)*d^2*e - (b^4*c + 4*a*b^2*c^2 - 32*a^2*c^3)*d*e^2 + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^3)*x^2 + 6*(a^2*c^2*d^2*e - a^2*b*c*d*e^2 + a^3*c*e^3 + (c^4*d^2*e - b*c^3*d*e^2 + a*c^3*e^3)*x^4 + 2*(b*c^3*d^2*e - b^2*c^2*d*e^2 + a*b*c^2*e^3)*x^3 + ((b^2*c^2 + 2*a*c^3)*d^2*e - (b^3*c + 2*a*b*c^2)*d*e^2 + (a*b^2*c + 2*a^2*c^2)*e^3)*x^2 + 2*(a*b*c^2*d^2*e - a*b^2*c*d*e^2 + a^2*b*c*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 6*((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e - 3*(a*b^3*c - 4*a^2*b*c^2)*d*e^2 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^3)*x)/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x), -1/2*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + 3*(a*b^3*c - 4*a^2*b*c^2)*d^2*e - 12*(a^2*b^2*c - 4*a^3*c^2)*d*e^2 + 3*(a^2*b^3 - 4*a^3*b*c)*e^3 + 2*(3*(b^2*c^3 - 4*a*c^4)*d^2*e - 3*(b^3*c^2 - 4*a*b*c^3)*d*e^2 + (2*b^4*c - 13*a*b^2*c^2 + 20*a^2*c^3)*e^3)*x^3 + 3*(3*(b^3*c^2 - 4*a*b*c^3)*d^2*e - (b^4*c + 4*a*b^2*c^2 - 32*a^2*c^3)*d*e^2 + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^3)*x^2 - 12*(a^2*c^2*d^2*e - a^2*b*c*d*e^2 + a^3*c*e^3 + (c^4*d^2*e - b*c^3*d*e^2 + a*c^3*e^3)*x^4 + 2*(b*c^3*d^2*e - b^2*c^2*d*e^2 + a*b*c^2*e^3)*x^3 + ((b^2*c^2 + 2*a*c^3)*d^2*e - (b^3*c + 2*a*b*c^2)*d*e^2 + (a*b^2*c + 2*a^2*c^2)*e^3)*x^2 + 2*(a*b*c^2*d^2*e - a*b^2*c*d*e^2 + a^2*b*c*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 6*((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e - 3*(a*b^3*c - 4*a^2*b*c^2)*d*e^2 + (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^3)*x)/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)]","B",0
1542,1,1004,0,0.434147," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{2}\right)} x^{3} + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2} + {\left(6 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e - {\left(b^{4} + 4 \, a b^{2} c - 32 \, a^{2} c^{2}\right)} e^{2}\right)} x^{2} - 2 \, {\left(2 \, a^{2} c d e - a^{2} b e^{2} + {\left(2 \, c^{3} d e - b c^{2} e^{2}\right)} x^{4} + 2 \, {\left(2 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{3} + {\left(2 \, {\left(b^{2} c + 2 \, a c^{2}\right)} d e - {\left(b^{3} + 2 \, a b c\right)} e^{2}\right)} x^{2} + 2 \, {\left(2 \, a b c d e - a b^{2} e^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e - 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{2}\right)} x}{2 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}, -\frac{2 \, {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{2}\right)} x^{3} + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2} + {\left(6 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e - {\left(b^{4} + 4 \, a b^{2} c - 32 \, a^{2} c^{2}\right)} e^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c d e - a^{2} b e^{2} + {\left(2 \, c^{3} d e - b c^{2} e^{2}\right)} x^{4} + 2 \, {\left(2 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{3} + {\left(2 \, {\left(b^{2} c + 2 \, a c^{2}\right)} d e - {\left(b^{3} + 2 \, a b c\right)} e^{2}\right)} x^{2} + 2 \, {\left(2 \, a b c d e - a b^{2} e^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e - 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{2}\right)} x}{2 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(2*(b^2*c^2 - 4*a*c^3)*d*e - (b^3*c - 4*a*b*c^2)*e^2)*x^3 + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^2 + 2*(a*b^3 - 4*a^2*b*c)*d*e - 4*(a^2*b^2 - 4*a^3*c)*e^2 + (6*(b^3*c - 4*a*b*c^2)*d*e - (b^4 + 4*a*b^2*c - 32*a^2*c^2)*e^2)*x^2 - 2*(2*a^2*c*d*e - a^2*b*e^2 + (2*c^3*d*e - b*c^2*e^2)*x^4 + 2*(2*b*c^2*d*e - b^2*c*e^2)*x^3 + (2*(b^2*c + 2*a*c^2)*d*e - (b^3 + 2*a*b*c)*e^2)*x^2 + 2*(2*a*b*c*d*e - a*b^2*e^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e - 3*(a*b^3 - 4*a^2*b*c)*e^2)*x)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x), -1/2*(2*(2*(b^2*c^2 - 4*a*c^3)*d*e - (b^3*c - 4*a*b*c^2)*e^2)*x^3 + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^2 + 2*(a*b^3 - 4*a^2*b*c)*d*e - 4*(a^2*b^2 - 4*a^3*c)*e^2 + (6*(b^3*c - 4*a*b*c^2)*d*e - (b^4 + 4*a*b^2*c - 32*a^2*c^2)*e^2)*x^2 - 4*(2*a^2*c*d*e - a^2*b*e^2 + (2*c^3*d*e - b*c^2*e^2)*x^4 + 2*(2*b*c^2*d*e - b^2*c*e^2)*x^3 + (2*(b^2*c + 2*a*c^2)*d*e - (b^3 + 2*a*b*c)*e^2)*x^2 + 2*(2*a*b*c*d*e - a*b^2*e^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e - 3*(a*b^3 - 4*a^2*b*c)*e^2)*x)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)]","B",0
1543,1,681,0,0.432763," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e x^{3} + 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e x^{2} + 2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e x + 2 \, {\left(c^{3} e x^{4} + 2 \, b c^{2} e x^{3} + 2 \, a b c e x + a^{2} c e + {\left(b^{2} c + 2 \, a c^{2}\right)} e x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d + {\left(a b^{3} - 4 \, a^{2} b c\right)} e}{2 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}, -\frac{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e x^{3} + 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e x^{2} + 2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e x - 4 \, {\left(c^{3} e x^{4} + 2 \, b c^{2} e x^{3} + 2 \, a b c e x + a^{2} c e + {\left(b^{2} c + 2 \, a c^{2}\right)} e x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d + {\left(a b^{3} - 4 \, a^{2} b c\right)} e}{2 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(b^2*c^2 - 4*a*c^3)*e*x^3 + 3*(b^3*c - 4*a*b*c^2)*e*x^2 + 2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*e*x + 2*(c^3*e*x^4 + 2*b*c^2*e*x^3 + 2*a*b*c*e*x + a^2*c*e + (b^2*c + 2*a*c^2)*e*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d + (a*b^3 - 4*a^2*b*c)*e)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x), -1/2*(2*(b^2*c^2 - 4*a*c^3)*e*x^3 + 3*(b^3*c - 4*a*b*c^2)*e*x^2 + 2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*e*x - 4*(c^3*e*x^4 + 2*b*c^2*e*x^3 + 2*a*b*c*e*x + a^2*c*e + (b^2*c + 2*a*c^2)*e*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d + (a*b^3 - 4*a^2*b*c)*e)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)]","B",0
1544,1,39,0,0.407442," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-1/2/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1545,1,6667,0,83.849479," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{5} - {\left(3 \, b^{5} c^{2} - 23 \, a b^{3} c^{3} + 44 \, a^{2} b c^{4}\right)} d^{4} e + {\left(3 \, b^{6} c - 18 \, a b^{4} c^{2} + 8 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(b^{7} + a b^{5} c - 50 \, a^{2} b^{3} c^{2} + 120 \, a^{3} b c^{3}\right)} d^{2} e^{3} + {\left(4 \, a b^{6} - 27 \, a^{2} b^{4} c + 32 \, a^{3} b^{2} c^{2} + 48 \, a^{4} c^{3}\right)} d e^{4} - {\left(3 \, a^{2} b^{5} - 23 \, a^{3} b^{3} c + 44 \, a^{4} b c^{2}\right)} e^{5} - 2 \, {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} e - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e^{2} + 2 \, {\left(b^{4} c^{3} - 5 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{2} e^{3} - {\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d e^{4} + {\left(a b^{4} c^{2} - 7 \, a^{2} b^{2} c^{3} + 12 \, a^{3} c^{4}\right)} e^{5}\right)} x^{3} - {\left(3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e - 8 \, {\left(b^{4} c^{3} - 5 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{3} e^{2} + 9 \, {\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 4 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 6 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d e^{4} + {\left(4 \, a b^{5} c - 29 \, a^{2} b^{3} c^{2} + 52 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} - {\left(2 \, a^{2} c^{4} d^{4} e - 4 \, a^{2} b c^{3} d^{3} e^{2} + 12 \, a^{3} c^{3} d^{2} e^{3} + 2 \, {\left(a^{2} b^{3} c - 6 \, a^{3} b c^{2}\right)} d e^{4} - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} e^{5} + {\left(2 \, c^{6} d^{4} e - 4 \, b c^{5} d^{3} e^{2} + 12 \, a c^{5} d^{2} e^{3} + 2 \, {\left(b^{3} c^{3} - 6 \, a b c^{4}\right)} d e^{4} - {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, b c^{5} d^{4} e - 4 \, b^{2} c^{4} d^{3} e^{2} + 12 \, a b c^{4} d^{2} e^{3} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3}\right)} d e^{4} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{4} e - 4 \, {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{3} e^{2} + 12 \, {\left(a b^{2} c^{3} + 2 \, a^{2} c^{4}\right)} d^{2} e^{3} + 2 \, {\left(b^{5} c - 4 \, a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d e^{4} - {\left(b^{6} - 4 \, a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, a b c^{4} d^{4} e - 4 \, a b^{2} c^{3} d^{3} e^{2} + 12 \, a^{2} b c^{3} d^{2} e^{3} + 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2}\right)} d e^{4} - {\left(a b^{5} - 6 \, a^{2} b^{3} c + 6 \, a^{3} b c^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left({\left(b^{4} c^{3} - 5 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{4} e - 3 \, {\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{3} e^{2} + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 6 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{2} e^{3} - {\left(b^{7} - 4 \, a b^{5} c - 10 \, a^{2} b^{3} c^{2} + 40 \, a^{3} b c^{3}\right)} d e^{4} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 3 \, a^{3} b^{2} c^{2} + 20 \, a^{4} c^{3}\right)} e^{5}\right)} x - {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{6} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e + 3 \, {\left(a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} e^{2} - {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 32 \, a^{4} b^{3} c^{2} + 96 \, a^{5} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} b^{6} - 7 \, a^{4} b^{4} c + 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} + {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{6} - 3 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{5} e + 3 \, {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{4} e^{2} - {\left(b^{7} c^{2} - 2 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 96 \, a^{3} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(a b^{6} c^{2} - 7 \, a^{2} b^{4} c^{3} + 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{5} + {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left({\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{6} - 3 \, {\left(b^{6} c^{3} - 8 \, a b^{4} c^{4} + 16 \, a^{2} b^{2} c^{5}\right)} d^{5} e + 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{2} - {\left(b^{8} c - 2 \, a b^{6} c^{2} - 32 \, a^{2} b^{4} c^{3} + 96 \, a^{3} b^{2} c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{6} c - 8 \, a^{3} b^{4} c^{2} + 16 \, a^{4} b^{2} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} e^{6}\right)} x^{3} + {\left({\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} d^{6} - 3 \, {\left(b^{7} c^{2} - 6 \, a b^{5} c^{3} + 32 \, a^{3} b c^{5}\right)} d^{5} e + 3 \, {\left(b^{8} c - 5 \, a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} + 32 \, a^{4} c^{5}\right)} d^{4} e^{2} - {\left(b^{9} - 36 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} + 192 \, a^{4} b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{8} - 5 \, a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{4} b^{2} c^{3} + 32 \, a^{5} c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{7} - 6 \, a^{3} b^{5} c + 32 \, a^{5} b c^{3}\right)} d e^{5} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{6} - 3 \, {\left(a b^{6} c^{2} - 8 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4}\right)} d^{5} e + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{4} e^{2} - {\left(a b^{8} - 2 \, a^{2} b^{6} c - 32 \, a^{3} b^{4} c^{2} + 96 \, a^{4} b^{2} c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{3} b^{6} - 8 \, a^{4} b^{4} c + 16 \, a^{5} b^{2} c^{2}\right)} d e^{5} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} e^{6}\right)} x\right)}}, -\frac{{\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{5} - {\left(3 \, b^{5} c^{2} - 23 \, a b^{3} c^{3} + 44 \, a^{2} b c^{4}\right)} d^{4} e + {\left(3 \, b^{6} c - 18 \, a b^{4} c^{2} + 8 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(b^{7} + a b^{5} c - 50 \, a^{2} b^{3} c^{2} + 120 \, a^{3} b c^{3}\right)} d^{2} e^{3} + {\left(4 \, a b^{6} - 27 \, a^{2} b^{4} c + 32 \, a^{3} b^{2} c^{2} + 48 \, a^{4} c^{3}\right)} d e^{4} - {\left(3 \, a^{2} b^{5} - 23 \, a^{3} b^{3} c + 44 \, a^{4} b c^{2}\right)} e^{5} - 2 \, {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} e - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e^{2} + 2 \, {\left(b^{4} c^{3} - 5 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{2} e^{3} - {\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d e^{4} + {\left(a b^{4} c^{2} - 7 \, a^{2} b^{2} c^{3} + 12 \, a^{3} c^{4}\right)} e^{5}\right)} x^{3} - {\left(3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e - 8 \, {\left(b^{4} c^{3} - 5 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{3} e^{2} + 9 \, {\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 4 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 6 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d e^{4} + {\left(4 \, a b^{5} c - 29 \, a^{2} b^{3} c^{2} + 52 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, a^{2} c^{4} d^{4} e - 4 \, a^{2} b c^{3} d^{3} e^{2} + 12 \, a^{3} c^{3} d^{2} e^{3} + 2 \, {\left(a^{2} b^{3} c - 6 \, a^{3} b c^{2}\right)} d e^{4} - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} e^{5} + {\left(2 \, c^{6} d^{4} e - 4 \, b c^{5} d^{3} e^{2} + 12 \, a c^{5} d^{2} e^{3} + 2 \, {\left(b^{3} c^{3} - 6 \, a b c^{4}\right)} d e^{4} - {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, b c^{5} d^{4} e - 4 \, b^{2} c^{4} d^{3} e^{2} + 12 \, a b c^{4} d^{2} e^{3} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3}\right)} d e^{4} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{4} e - 4 \, {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{3} e^{2} + 12 \, {\left(a b^{2} c^{3} + 2 \, a^{2} c^{4}\right)} d^{2} e^{3} + 2 \, {\left(b^{5} c - 4 \, a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d e^{4} - {\left(b^{6} - 4 \, a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, a b c^{4} d^{4} e - 4 \, a b^{2} c^{3} d^{3} e^{2} + 12 \, a^{2} b c^{3} d^{2} e^{3} + 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2}\right)} d e^{4} - {\left(a b^{5} - 6 \, a^{2} b^{3} c + 6 \, a^{3} b c^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left({\left(b^{4} c^{3} - 5 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{4} e - 3 \, {\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{3} e^{2} + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 6 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{2} e^{3} - {\left(b^{7} - 4 \, a b^{5} c - 10 \, a^{2} b^{3} c^{2} + 40 \, a^{3} b c^{3}\right)} d e^{4} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 3 \, a^{3} b^{2} c^{2} + 20 \, a^{4} c^{3}\right)} e^{5}\right)} x - {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{6} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e + 3 \, {\left(a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} e^{2} - {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 32 \, a^{4} b^{3} c^{2} + 96 \, a^{5} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} b^{6} - 7 \, a^{4} b^{4} c + 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} + {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{6} - 3 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{5} e + 3 \, {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{4} e^{2} - {\left(b^{7} c^{2} - 2 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 96 \, a^{3} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(a b^{6} c^{2} - 7 \, a^{2} b^{4} c^{3} + 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{5} + {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left({\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{6} - 3 \, {\left(b^{6} c^{3} - 8 \, a b^{4} c^{4} + 16 \, a^{2} b^{2} c^{5}\right)} d^{5} e + 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{2} - {\left(b^{8} c - 2 \, a b^{6} c^{2} - 32 \, a^{2} b^{4} c^{3} + 96 \, a^{3} b^{2} c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{6} c - 8 \, a^{3} b^{4} c^{2} + 16 \, a^{4} b^{2} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} e^{6}\right)} x^{3} + {\left({\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} d^{6} - 3 \, {\left(b^{7} c^{2} - 6 \, a b^{5} c^{3} + 32 \, a^{3} b c^{5}\right)} d^{5} e + 3 \, {\left(b^{8} c - 5 \, a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} + 32 \, a^{4} c^{5}\right)} d^{4} e^{2} - {\left(b^{9} - 36 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} + 192 \, a^{4} b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{8} - 5 \, a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{4} b^{2} c^{3} + 32 \, a^{5} c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{7} - 6 \, a^{3} b^{5} c + 32 \, a^{5} b c^{3}\right)} d e^{5} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{6} - 3 \, {\left(a b^{6} c^{2} - 8 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4}\right)} d^{5} e + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{4} e^{2} - {\left(a b^{8} - 2 \, a^{2} b^{6} c - 32 \, a^{3} b^{4} c^{2} + 96 \, a^{4} b^{2} c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{3} b^{6} - 8 \, a^{4} b^{4} c + 16 \, a^{5} b^{2} c^{2}\right)} d e^{5} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/2*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^5 - (3*b^5*c^2 - 23*a*b^3*c^3 + 44*a^2*b*c^4)*d^4*e + (3*b^6*c - 18*a*b^4*c^2 + 8*a^2*b^2*c^3 + 64*a^3*c^4)*d^3*e^2 - (b^7 + a*b^5*c - 50*a^2*b^3*c^2 + 120*a^3*b*c^3)*d^2*e^3 + (4*a*b^6 - 27*a^2*b^4*c + 32*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^4 - (3*a^2*b^5 - 23*a^3*b^3*c + 44*a^4*b*c^2)*e^5 - 2*((b^2*c^5 - 4*a*c^6)*d^4*e - 2*(b^3*c^4 - 4*a*b*c^5)*d^3*e^2 + 2*(b^4*c^3 - 5*a*b^2*c^4 + 4*a^2*c^5)*d^2*e^3 - (b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d*e^4 + (a*b^4*c^2 - 7*a^2*b^2*c^3 + 12*a^3*c^4)*e^5)*x^3 - (3*(b^3*c^4 - 4*a*b*c^5)*d^4*e - 8*(b^4*c^3 - 5*a*b^2*c^4 + 4*a^2*c^5)*d^3*e^2 + 9*(b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^2*e^3 - 4*(b^6*c - 6*a*b^4*c^2 + 6*a^2*b^2*c^3 + 8*a^3*c^4)*d*e^4 + (4*a*b^5*c - 29*a^2*b^3*c^2 + 52*a^3*b*c^3)*e^5)*x^2 - (2*a^2*c^4*d^4*e - 4*a^2*b*c^3*d^3*e^2 + 12*a^3*c^3*d^2*e^3 + 2*(a^2*b^3*c - 6*a^3*b*c^2)*d*e^4 - (a^2*b^4 - 6*a^3*b^2*c + 6*a^4*c^2)*e^5 + (2*c^6*d^4*e - 4*b*c^5*d^3*e^2 + 12*a*c^5*d^2*e^3 + 2*(b^3*c^3 - 6*a*b*c^4)*d*e^4 - (b^4*c^2 - 6*a*b^2*c^3 + 6*a^2*c^4)*e^5)*x^4 + 2*(2*b*c^5*d^4*e - 4*b^2*c^4*d^3*e^2 + 12*a*b*c^4*d^2*e^3 + 2*(b^4*c^2 - 6*a*b^2*c^3)*d*e^4 - (b^5*c - 6*a*b^3*c^2 + 6*a^2*b*c^3)*e^5)*x^3 + (2*(b^2*c^4 + 2*a*c^5)*d^4*e - 4*(b^3*c^3 + 2*a*b*c^4)*d^3*e^2 + 12*(a*b^2*c^3 + 2*a^2*c^4)*d^2*e^3 + 2*(b^5*c - 4*a*b^3*c^2 - 12*a^2*b*c^3)*d*e^4 - (b^6 - 4*a*b^4*c - 6*a^2*b^2*c^2 + 12*a^3*c^3)*e^5)*x^2 + 2*(2*a*b*c^4*d^4*e - 4*a*b^2*c^3*d^3*e^2 + 12*a^2*b*c^3*d^2*e^3 + 2*(a*b^4*c - 6*a^2*b^2*c^2)*d*e^4 - (a*b^5 - 6*a^2*b^3*c + 6*a^3*b*c^2)*e^5)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*((b^4*c^3 - 5*a*b^2*c^4 + 4*a^2*c^5)*d^4*e - 3*(b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^3*e^2 + 3*(b^6*c - 6*a*b^4*c^2 + 6*a^2*b^2*c^3 + 8*a^3*c^4)*d^2*e^3 - (b^7 - 4*a*b^5*c - 10*a^2*b^3*c^2 + 40*a^3*b*c^3)*d*e^4 + (a*b^6 - 6*a^2*b^4*c + 3*a^3*b^2*c^2 + 20*a^4*c^3)*e^5)*x - (2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^4 + 2*(2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^5)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d*e^4 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^5)*x^2 + 2*(2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 - (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^5)*x)*log(c*x^2 + b*x + a) + 2*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^4 + 2*(2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^5)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d*e^4 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^5)*x^2 + 2*(2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 - (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^5)*x)*log(e*x + d))/((a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^6 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e + 3*(a^2*b^6*c - 7*a^3*b^4*c^2 + 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4*e^2 - (a^2*b^7 - 2*a^3*b^5*c - 32*a^4*b^3*c^2 + 96*a^5*b*c^3)*d^3*e^3 + 3*(a^3*b^6 - 7*a^4*b^4*c + 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^4 - 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 + ((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^6 - 3*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^5*e + 3*(b^6*c^3 - 7*a*b^4*c^4 + 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^4*e^2 - (b^7*c^2 - 2*a*b^5*c^3 - 32*a^2*b^3*c^4 + 96*a^3*b*c^5)*d^3*e^3 + 3*(a*b^6*c^2 - 7*a^2*b^4*c^3 + 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^2*e^4 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^5 + (a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^6)*x^4 + 2*((b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^6 - 3*(b^6*c^3 - 8*a*b^4*c^4 + 16*a^2*b^2*c^5)*d^5*e + 3*(b^7*c^2 - 7*a*b^5*c^3 + 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^2 - (b^8*c - 2*a*b^6*c^2 - 32*a^2*b^4*c^3 + 96*a^3*b^2*c^4)*d^3*e^3 + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^4 - 3*(a^2*b^6*c - 8*a^3*b^4*c^2 + 16*a^4*b^2*c^3)*d*e^5 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*e^6)*x^3 + ((b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*d^6 - 3*(b^7*c^2 - 6*a*b^5*c^3 + 32*a^3*b*c^5)*d^5*e + 3*(b^8*c - 5*a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^3*b^2*c^4 + 32*a^4*c^5)*d^4*e^2 - (b^9 - 36*a^2*b^5*c^2 + 32*a^3*b^3*c^3 + 192*a^4*b*c^4)*d^3*e^3 + 3*(a*b^8 - 5*a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^4*b^2*c^3 + 32*a^5*c^4)*d^2*e^4 - 3*(a^2*b^7 - 6*a^3*b^5*c + 32*a^5*b*c^3)*d*e^5 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*e^6)*x^2 + 2*((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^6 - 3*(a*b^6*c^2 - 8*a^2*b^4*c^3 + 16*a^3*b^2*c^4)*d^5*e + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^4*e^2 - (a*b^8 - 2*a^2*b^6*c - 32*a^3*b^4*c^2 + 96*a^4*b^2*c^3)*d^3*e^3 + 3*(a^2*b^7 - 7*a^3*b^5*c + 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2*e^4 - 3*(a^3*b^6 - 8*a^4*b^4*c + 16*a^5*b^2*c^2)*d*e^5 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*e^6)*x), -1/2*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^5 - (3*b^5*c^2 - 23*a*b^3*c^3 + 44*a^2*b*c^4)*d^4*e + (3*b^6*c - 18*a*b^4*c^2 + 8*a^2*b^2*c^3 + 64*a^3*c^4)*d^3*e^2 - (b^7 + a*b^5*c - 50*a^2*b^3*c^2 + 120*a^3*b*c^3)*d^2*e^3 + (4*a*b^6 - 27*a^2*b^4*c + 32*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^4 - (3*a^2*b^5 - 23*a^3*b^3*c + 44*a^4*b*c^2)*e^5 - 2*((b^2*c^5 - 4*a*c^6)*d^4*e - 2*(b^3*c^4 - 4*a*b*c^5)*d^3*e^2 + 2*(b^4*c^3 - 5*a*b^2*c^4 + 4*a^2*c^5)*d^2*e^3 - (b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d*e^4 + (a*b^4*c^2 - 7*a^2*b^2*c^3 + 12*a^3*c^4)*e^5)*x^3 - (3*(b^3*c^4 - 4*a*b*c^5)*d^4*e - 8*(b^4*c^3 - 5*a*b^2*c^4 + 4*a^2*c^5)*d^3*e^2 + 9*(b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^2*e^3 - 4*(b^6*c - 6*a*b^4*c^2 + 6*a^2*b^2*c^3 + 8*a^3*c^4)*d*e^4 + (4*a*b^5*c - 29*a^2*b^3*c^2 + 52*a^3*b*c^3)*e^5)*x^2 + 2*(2*a^2*c^4*d^4*e - 4*a^2*b*c^3*d^3*e^2 + 12*a^3*c^3*d^2*e^3 + 2*(a^2*b^3*c - 6*a^3*b*c^2)*d*e^4 - (a^2*b^4 - 6*a^3*b^2*c + 6*a^4*c^2)*e^5 + (2*c^6*d^4*e - 4*b*c^5*d^3*e^2 + 12*a*c^5*d^2*e^3 + 2*(b^3*c^3 - 6*a*b*c^4)*d*e^4 - (b^4*c^2 - 6*a*b^2*c^3 + 6*a^2*c^4)*e^5)*x^4 + 2*(2*b*c^5*d^4*e - 4*b^2*c^4*d^3*e^2 + 12*a*b*c^4*d^2*e^3 + 2*(b^4*c^2 - 6*a*b^2*c^3)*d*e^4 - (b^5*c - 6*a*b^3*c^2 + 6*a^2*b*c^3)*e^5)*x^3 + (2*(b^2*c^4 + 2*a*c^5)*d^4*e - 4*(b^3*c^3 + 2*a*b*c^4)*d^3*e^2 + 12*(a*b^2*c^3 + 2*a^2*c^4)*d^2*e^3 + 2*(b^5*c - 4*a*b^3*c^2 - 12*a^2*b*c^3)*d*e^4 - (b^6 - 4*a*b^4*c - 6*a^2*b^2*c^2 + 12*a^3*c^3)*e^5)*x^2 + 2*(2*a*b*c^4*d^4*e - 4*a*b^2*c^3*d^3*e^2 + 12*a^2*b*c^3*d^2*e^3 + 2*(a*b^4*c - 6*a^2*b^2*c^2)*d*e^4 - (a*b^5 - 6*a^2*b^3*c + 6*a^3*b*c^2)*e^5)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*((b^4*c^3 - 5*a*b^2*c^4 + 4*a^2*c^5)*d^4*e - 3*(b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^3*e^2 + 3*(b^6*c - 6*a*b^4*c^2 + 6*a^2*b^2*c^3 + 8*a^3*c^4)*d^2*e^3 - (b^7 - 4*a*b^5*c - 10*a^2*b^3*c^2 + 40*a^3*b*c^3)*d*e^4 + (a*b^6 - 6*a^2*b^4*c + 3*a^3*b^2*c^2 + 20*a^4*c^3)*e^5)*x - (2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^4 + 2*(2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^5)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d*e^4 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^5)*x^2 + 2*(2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 - (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^5)*x)*log(c*x^2 + b*x + a) + 2*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^4 + 2*(2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^5)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d*e^4 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^5)*x^2 + 2*(2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 - (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^5)*x)*log(e*x + d))/((a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^6 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e + 3*(a^2*b^6*c - 7*a^3*b^4*c^2 + 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4*e^2 - (a^2*b^7 - 2*a^3*b^5*c - 32*a^4*b^3*c^2 + 96*a^5*b*c^3)*d^3*e^3 + 3*(a^3*b^6 - 7*a^4*b^4*c + 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^4 - 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 + ((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^6 - 3*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^5*e + 3*(b^6*c^3 - 7*a*b^4*c^4 + 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^4*e^2 - (b^7*c^2 - 2*a*b^5*c^3 - 32*a^2*b^3*c^4 + 96*a^3*b*c^5)*d^3*e^3 + 3*(a*b^6*c^2 - 7*a^2*b^4*c^3 + 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^2*e^4 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^5 + (a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^6)*x^4 + 2*((b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^6 - 3*(b^6*c^3 - 8*a*b^4*c^4 + 16*a^2*b^2*c^5)*d^5*e + 3*(b^7*c^2 - 7*a*b^5*c^3 + 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^2 - (b^8*c - 2*a*b^6*c^2 - 32*a^2*b^4*c^3 + 96*a^3*b^2*c^4)*d^3*e^3 + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^4 - 3*(a^2*b^6*c - 8*a^3*b^4*c^2 + 16*a^4*b^2*c^3)*d*e^5 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*e^6)*x^3 + ((b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*d^6 - 3*(b^7*c^2 - 6*a*b^5*c^3 + 32*a^3*b*c^5)*d^5*e + 3*(b^8*c - 5*a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^3*b^2*c^4 + 32*a^4*c^5)*d^4*e^2 - (b^9 - 36*a^2*b^5*c^2 + 32*a^3*b^3*c^3 + 192*a^4*b*c^4)*d^3*e^3 + 3*(a*b^8 - 5*a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^4*b^2*c^3 + 32*a^5*c^4)*d^2*e^4 - 3*(a^2*b^7 - 6*a^3*b^5*c + 32*a^5*b*c^3)*d*e^5 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*e^6)*x^2 + 2*((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^6 - 3*(a*b^6*c^2 - 8*a^2*b^4*c^3 + 16*a^3*b^2*c^4)*d^5*e + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^4*e^2 - (a*b^8 - 2*a^2*b^6*c - 32*a^3*b^4*c^2 + 96*a^4*b^2*c^3)*d^3*e^3 + 3*(a^2*b^7 - 7*a^3*b^5*c + 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2*e^4 - 3*(a^3*b^6 - 8*a^4*b^4*c + 16*a^5*b^2*c^2)*d*e^5 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*e^6)*x)]","B",0
1546,1,1445,0,0.585461," ","integrate((2*c*x+b)*(e*x+d)^4*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(16 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e - 24 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{2} + 2 \, {\left(7 \, b^{6} c - 60 \, a b^{4} c^{2} + 144 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{3} - {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{4}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(3840 \, c^{7} e^{4} x^{6} + 8960 \, a c^{6} d^{4} + 2560 \, {\left(7 \, c^{7} d e^{3} + b c^{6} e^{4}\right)} x^{5} + 560 \, {\left(3 \, b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{3} e - 168 \, {\left(15 \, b^{4} c^{3} - 100 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} d^{2} e^{2} + 14 \, {\left(105 \, b^{5} c^{2} - 760 \, a b^{3} c^{3} + 1296 \, a^{2} b c^{4}\right)} d e^{3} - {\left(315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4}\right)} e^{4} + 128 \, {\left(252 \, c^{7} d^{2} e^{2} + 98 \, b c^{6} d e^{3} - {\left(b^{2} c^{5} - 6 \, a c^{6}\right)} e^{4}\right)} x^{4} + 16 \, {\left(1680 \, c^{7} d^{3} e + 1512 \, b c^{6} d^{2} e^{2} - 14 \, {\left(3 \, b^{2} c^{5} - 20 \, a c^{6}\right)} d e^{3} + {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} e^{4}\right)} x^{3} + 8 \, {\left(1120 \, c^{7} d^{4} + 2800 \, b c^{6} d^{3} e - 168 \, {\left(b^{2} c^{5} - 8 \, a c^{6}\right)} d^{2} e^{2} + 14 \, {\left(7 \, b^{3} c^{4} - 36 \, a b c^{5}\right)} d e^{3} - {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} e^{4}\right)} x^{2} + 2 \, {\left(4480 \, b c^{6} d^{4} - 560 \, {\left(b^{2} c^{5} - 12 \, a c^{6}\right)} d^{3} e + 168 \, {\left(5 \, b^{3} c^{4} - 28 \, a b c^{5}\right)} d^{2} e^{2} - 14 \, {\left(35 \, b^{4} c^{3} - 216 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} d e^{3} + {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{53760 \, c^{6}}, \frac{105 \, {\left(16 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e - 24 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{2} + 2 \, {\left(7 \, b^{6} c - 60 \, a b^{4} c^{2} + 144 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{3} - {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(3840 \, c^{7} e^{4} x^{6} + 8960 \, a c^{6} d^{4} + 2560 \, {\left(7 \, c^{7} d e^{3} + b c^{6} e^{4}\right)} x^{5} + 560 \, {\left(3 \, b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{3} e - 168 \, {\left(15 \, b^{4} c^{3} - 100 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} d^{2} e^{2} + 14 \, {\left(105 \, b^{5} c^{2} - 760 \, a b^{3} c^{3} + 1296 \, a^{2} b c^{4}\right)} d e^{3} - {\left(315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4}\right)} e^{4} + 128 \, {\left(252 \, c^{7} d^{2} e^{2} + 98 \, b c^{6} d e^{3} - {\left(b^{2} c^{5} - 6 \, a c^{6}\right)} e^{4}\right)} x^{4} + 16 \, {\left(1680 \, c^{7} d^{3} e + 1512 \, b c^{6} d^{2} e^{2} - 14 \, {\left(3 \, b^{2} c^{5} - 20 \, a c^{6}\right)} d e^{3} + {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} e^{4}\right)} x^{3} + 8 \, {\left(1120 \, c^{7} d^{4} + 2800 \, b c^{6} d^{3} e - 168 \, {\left(b^{2} c^{5} - 8 \, a c^{6}\right)} d^{2} e^{2} + 14 \, {\left(7 \, b^{3} c^{4} - 36 \, a b c^{5}\right)} d e^{3} - {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} e^{4}\right)} x^{2} + 2 \, {\left(4480 \, b c^{6} d^{4} - 560 \, {\left(b^{2} c^{5} - 12 \, a c^{6}\right)} d^{3} e + 168 \, {\left(5 \, b^{3} c^{4} - 28 \, a b c^{5}\right)} d^{2} e^{2} - 14 \, {\left(35 \, b^{4} c^{3} - 216 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} d e^{3} + {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{26880 \, c^{6}}\right]"," ",0,"[1/53760*(105*(16*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e - 24*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^2 + 2*(7*b^6*c - 60*a*b^4*c^2 + 144*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^3 - (3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^4)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(3840*c^7*e^4*x^6 + 8960*a*c^6*d^4 + 2560*(7*c^7*d*e^3 + b*c^6*e^4)*x^5 + 560*(3*b^3*c^4 - 20*a*b*c^5)*d^3*e - 168*(15*b^4*c^3 - 100*a*b^2*c^4 + 128*a^2*c^5)*d^2*e^2 + 14*(105*b^5*c^2 - 760*a*b^3*c^3 + 1296*a^2*b*c^4)*d*e^3 - (315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4)*e^4 + 128*(252*c^7*d^2*e^2 + 98*b*c^6*d*e^3 - (b^2*c^5 - 6*a*c^6)*e^4)*x^4 + 16*(1680*c^7*d^3*e + 1512*b*c^6*d^2*e^2 - 14*(3*b^2*c^5 - 20*a*c^6)*d*e^3 + (9*b^3*c^4 - 44*a*b*c^5)*e^4)*x^3 + 8*(1120*c^7*d^4 + 2800*b*c^6*d^3*e - 168*(b^2*c^5 - 8*a*c^6)*d^2*e^2 + 14*(7*b^3*c^4 - 36*a*b*c^5)*d*e^3 - (21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*e^4)*x^2 + 2*(4480*b*c^6*d^4 - 560*(b^2*c^5 - 12*a*c^6)*d^3*e + 168*(5*b^3*c^4 - 28*a*b*c^5)*d^2*e^2 - 14*(35*b^4*c^3 - 216*a*b^2*c^4 + 240*a^2*c^5)*d*e^3 + (105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*e^4)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/26880*(105*(16*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e - 24*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^2 + 2*(7*b^6*c - 60*a*b^4*c^2 + 144*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^3 - (3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^4)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(3840*c^7*e^4*x^6 + 8960*a*c^6*d^4 + 2560*(7*c^7*d*e^3 + b*c^6*e^4)*x^5 + 560*(3*b^3*c^4 - 20*a*b*c^5)*d^3*e - 168*(15*b^4*c^3 - 100*a*b^2*c^4 + 128*a^2*c^5)*d^2*e^2 + 14*(105*b^5*c^2 - 760*a*b^3*c^3 + 1296*a^2*b*c^4)*d*e^3 - (315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4)*e^4 + 128*(252*c^7*d^2*e^2 + 98*b*c^6*d*e^3 - (b^2*c^5 - 6*a*c^6)*e^4)*x^4 + 16*(1680*c^7*d^3*e + 1512*b*c^6*d^2*e^2 - 14*(3*b^2*c^5 - 20*a*c^6)*d*e^3 + (9*b^3*c^4 - 44*a*b*c^5)*e^4)*x^3 + 8*(1120*c^7*d^4 + 2800*b*c^6*d^3*e - 168*(b^2*c^5 - 8*a*c^6)*d^2*e^2 + 14*(7*b^3*c^4 - 36*a*b*c^5)*d*e^3 - (21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*e^4)*x^2 + 2*(4480*b*c^6*d^4 - 560*(b^2*c^5 - 12*a*c^6)*d^3*e + 168*(5*b^3*c^4 - 28*a*b*c^5)*d^2*e^2 - 14*(35*b^4*c^3 - 216*a*b^2*c^4 + 240*a^2*c^5)*d*e^3 + (105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*e^4)*x)*sqrt(c*x^2 + b*x + a))/c^6]","A",0
1547,1,985,0,0.588751," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} e - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{2} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1280 \, c^{6} e^{3} x^{5} + 2560 \, a c^{5} d^{3} + 128 \, {\left(36 \, c^{6} d e^{2} + 7 \, b c^{5} e^{3}\right)} x^{4} + 120 \, {\left(3 \, b^{3} c^{3} - 20 \, a b c^{4}\right)} d^{2} e - 24 \, {\left(15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} d e^{2} + {\left(105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right)} e^{3} + 16 \, {\left(360 \, c^{6} d^{2} e + 216 \, b c^{5} d e^{2} - {\left(3 \, b^{2} c^{4} - 20 \, a c^{5}\right)} e^{3}\right)} x^{3} + 8 \, {\left(320 \, c^{6} d^{3} + 600 \, b c^{5} d^{2} e - 24 \, {\left(b^{2} c^{4} - 8 \, a c^{5}\right)} d e^{2} + {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(1280 \, b c^{5} d^{3} - 120 \, {\left(b^{2} c^{4} - 12 \, a c^{5}\right)} d^{2} e + 24 \, {\left(5 \, b^{3} c^{3} - 28 \, a b c^{4}\right)} d e^{2} - {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{5}}, \frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} e - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{2} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(1280 \, c^{6} e^{3} x^{5} + 2560 \, a c^{5} d^{3} + 128 \, {\left(36 \, c^{6} d e^{2} + 7 \, b c^{5} e^{3}\right)} x^{4} + 120 \, {\left(3 \, b^{3} c^{3} - 20 \, a b c^{4}\right)} d^{2} e - 24 \, {\left(15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} d e^{2} + {\left(105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right)} e^{3} + 16 \, {\left(360 \, c^{6} d^{2} e + 216 \, b c^{5} d e^{2} - {\left(3 \, b^{2} c^{4} - 20 \, a c^{5}\right)} e^{3}\right)} x^{3} + 8 \, {\left(320 \, c^{6} d^{3} + 600 \, b c^{5} d^{2} e - 24 \, {\left(b^{2} c^{4} - 8 \, a c^{5}\right)} d e^{2} + {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(1280 \, b c^{5} d^{3} - 120 \, {\left(b^{2} c^{4} - 12 \, a c^{5}\right)} d^{2} e + 24 \, {\left(5 \, b^{3} c^{3} - 28 \, a b c^{4}\right)} d e^{2} - {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{5}}\right]"," ",0,"[-1/15360*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*e - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^2 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(1280*c^6*e^3*x^5 + 2560*a*c^5*d^3 + 128*(36*c^6*d*e^2 + 7*b*c^5*e^3)*x^4 + 120*(3*b^3*c^3 - 20*a*b*c^4)*d^2*e - 24*(15*b^4*c^2 - 100*a*b^2*c^3 + 128*a^2*c^4)*d*e^2 + (105*b^5*c - 760*a*b^3*c^2 + 1296*a^2*b*c^3)*e^3 + 16*(360*c^6*d^2*e + 216*b*c^5*d*e^2 - (3*b^2*c^4 - 20*a*c^5)*e^3)*x^3 + 8*(320*c^6*d^3 + 600*b*c^5*d^2*e - 24*(b^2*c^4 - 8*a*c^5)*d*e^2 + (7*b^3*c^3 - 36*a*b*c^4)*e^3)*x^2 + 2*(1280*b*c^5*d^3 - 120*(b^2*c^4 - 12*a*c^5)*d^2*e + 24*(5*b^3*c^3 - 28*a*b*c^4)*d*e^2 - (35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^5, 1/7680*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*e - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^2 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(1280*c^6*e^3*x^5 + 2560*a*c^5*d^3 + 128*(36*c^6*d*e^2 + 7*b*c^5*e^3)*x^4 + 120*(3*b^3*c^3 - 20*a*b*c^4)*d^2*e - 24*(15*b^4*c^2 - 100*a*b^2*c^3 + 128*a^2*c^4)*d*e^2 + (105*b^5*c - 760*a*b^3*c^2 + 1296*a^2*b*c^3)*e^3 + 16*(360*c^6*d^2*e + 216*b*c^5*d*e^2 - (3*b^2*c^4 - 20*a*c^5)*e^3)*x^3 + 8*(320*c^6*d^3 + 600*b*c^5*d^2*e - 24*(b^2*c^4 - 8*a*c^5)*d*e^2 + (7*b^3*c^3 - 36*a*b*c^4)*e^3)*x^2 + 2*(1280*b*c^5*d^3 - 120*(b^2*c^4 - 12*a*c^5)*d^2*e + 24*(5*b^3*c^3 - 28*a*b*c^4)*d*e^2 - (35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
1548,1,617,0,0.489781," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(192 \, c^{5} e^{2} x^{4} + 320 \, a c^{4} d^{2} + 48 \, {\left(10 \, c^{5} d e + 3 \, b c^{4} e^{2}\right)} x^{3} + 10 \, {\left(3 \, b^{3} c^{2} - 20 \, a b c^{3}\right)} d e - {\left(15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3}\right)} e^{2} + 8 \, {\left(40 \, c^{5} d^{2} + 50 \, b c^{4} d e - {\left(b^{2} c^{3} - 8 \, a c^{4}\right)} e^{2}\right)} x^{2} + 2 \, {\left(160 \, b c^{4} d^{2} - 10 \, {\left(b^{2} c^{3} - 12 \, a c^{4}\right)} d e + {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1920 \, c^{4}}, \frac{15 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(192 \, c^{5} e^{2} x^{4} + 320 \, a c^{4} d^{2} + 48 \, {\left(10 \, c^{5} d e + 3 \, b c^{4} e^{2}\right)} x^{3} + 10 \, {\left(3 \, b^{3} c^{2} - 20 \, a b c^{3}\right)} d e - {\left(15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3}\right)} e^{2} + 8 \, {\left(40 \, c^{5} d^{2} + 50 \, b c^{4} d e - {\left(b^{2} c^{3} - 8 \, a c^{4}\right)} e^{2}\right)} x^{2} + 2 \, {\left(160 \, b c^{4} d^{2} - 10 \, {\left(b^{2} c^{3} - 12 \, a c^{4}\right)} d e + {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{960 \, c^{4}}\right]"," ",0,"[-1/1920*(15*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(192*c^5*e^2*x^4 + 320*a*c^4*d^2 + 48*(10*c^5*d*e + 3*b*c^4*e^2)*x^3 + 10*(3*b^3*c^2 - 20*a*b*c^3)*d*e - (15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3)*e^2 + 8*(40*c^5*d^2 + 50*b*c^4*d*e - (b^2*c^3 - 8*a*c^4)*e^2)*x^2 + 2*(160*b*c^4*d^2 - 10*(b^2*c^3 - 12*a*c^4)*d*e + (5*b^3*c^2 - 28*a*b*c^3)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/960*(15*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(192*c^5*e^2*x^4 + 320*a*c^4*d^2 + 48*(10*c^5*d*e + 3*b*c^4*e^2)*x^3 + 10*(3*b^3*c^2 - 20*a*b*c^3)*d*e - (15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3)*e^2 + 8*(40*c^5*d^2 + 50*b*c^4*d*e - (b^2*c^3 - 8*a*c^4)*e^2)*x^2 + 2*(160*b*c^4*d^2 - 10*(b^2*c^3 - 12*a*c^4)*d*e + (5*b^3*c^2 - 28*a*b*c^3)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
1549,1,343,0,0.446330," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} e \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, c^{4} e x^{3} + 64 \, a c^{3} d + 8 \, {\left(8 \, c^{4} d + 5 \, b c^{3} e\right)} x^{2} + {\left(3 \, b^{3} c - 20 \, a b c^{2}\right)} e + 2 \, {\left(32 \, b c^{3} d - {\left(b^{2} c^{2} - 12 \, a c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{3}}, \frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} e \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(48 \, c^{4} e x^{3} + 64 \, a c^{3} d + 8 \, {\left(8 \, c^{4} d + 5 \, b c^{3} e\right)} x^{2} + {\left(3 \, b^{3} c - 20 \, a b c^{2}\right)} e + 2 \, {\left(32 \, b c^{3} d - {\left(b^{2} c^{2} - 12 \, a c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{192 \, c^{3}}\right]"," ",0,"[1/384*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(c)*e*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(48*c^4*e*x^3 + 64*a*c^3*d + 8*(8*c^4*d + 5*b*c^3*e)*x^2 + (3*b^3*c - 20*a*b*c^2)*e + 2*(32*b*c^3*d - (b^2*c^2 - 12*a*c^3)*e)*x)*sqrt(c*x^2 + b*x + a))/c^3, 1/192*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*e*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(48*c^4*e*x^3 + 64*a*c^3*d + 8*(8*c^4*d + 5*b*c^3*e)*x^2 + (3*b^3*c - 20*a*b*c^2)*e + 2*(32*b*c^3*d - (b^2*c^2 - 12*a*c^3)*e)*x)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
1550,1,14,0,0.425406," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}"," ",0,"2/3*(c*x^2 + b*x + a)^(3/2)","A",0
1551,1,1196,0,12.658448," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, c^{2} d - b c e\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(2 \, c^{2} e^{2} x - 4 \, c^{2} d e + 3 \, b c e^{2}\right)} \sqrt{c x^{2} + b x + a}}{8 \, c e^{3}}, -\frac{8 \, {\left(2 \, c^{2} d - b c e\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, c^{2} e^{2} x - 4 \, c^{2} d e + 3 \, b c e^{2}\right)} \sqrt{c x^{2} + b x + a}}{8 \, c e^{3}}, -\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(2 \, c^{2} d - b c e\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(2 \, c^{2} e^{2} x - 4 \, c^{2} d e + 3 \, b c e^{2}\right)} \sqrt{c x^{2} + b x + a}}{4 \, c e^{3}}, -\frac{4 \, {\left(2 \, c^{2} d - b c e\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2 \, c^{2} e^{2} x - 4 \, c^{2} d e + 3 \, b c e^{2}\right)} \sqrt{c x^{2} + b x + a}}{4 \, c e^{3}}\right]"," ",0,"[1/8*((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(2*c^2*d - b*c*e)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(2*c^2*e^2*x - 4*c^2*d*e + 3*b*c*e^2)*sqrt(c*x^2 + b*x + a))/(c*e^3), -1/8*(8*(2*c^2*d - b*c*e)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(2*c^2*e^2*x - 4*c^2*d*e + 3*b*c*e^2)*sqrt(c*x^2 + b*x + a))/(c*e^3), -1/4*((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(2*c^2*d - b*c*e)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(2*c^2*e^2*x - 4*c^2*d*e + 3*b*c*e^2)*sqrt(c*x^2 + b*x + a))/(c*e^3), -1/4*(4*(2*c^2*d - b*c*e)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2*c^2*e^2*x - 4*c^2*d*e + 3*b*c*e^2)*sqrt(c*x^2 + b*x + a))/(c*e^3)]","A",0
1552,1,1964,0,21.080902," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(2 \, c^{2} d^{4} - 3 \, b c d^{3} e - a b d e^{3} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} - a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + {\left(b^{2} + 4 \, a c\right)} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + {\left(b^{2} + 4 \, a c\right)} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(4 \, c^{2} d^{3} e - 5 \, b c d^{2} e^{2} - a b e^{4} + {\left(b^{2} + 4 \, a c\right)} d e^{3} + 2 \, {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(c d^{3} e^{3} - b d^{2} e^{4} + a d e^{5} + {\left(c d^{2} e^{4} - b d e^{5} + a e^{6}\right)} x\right)}}, \frac{8 \, {\left(2 \, c^{2} d^{4} - 3 \, b c d^{3} e - a b d e^{3} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} - a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + {\left(b^{2} + 4 \, a c\right)} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + {\left(b^{2} + 4 \, a c\right)} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(4 \, c^{2} d^{3} e - 5 \, b c d^{2} e^{2} - a b e^{4} + {\left(b^{2} + 4 \, a c\right)} d e^{3} + 2 \, {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(c d^{3} e^{3} - b d^{2} e^{4} + a d e^{5} + {\left(c d^{2} e^{4} - b d e^{5} + a e^{6}\right)} x\right)}}, \frac{{\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + {\left(b^{2} + 4 \, a c\right)} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + {\left(b^{2} + 4 \, a c\right)} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, c^{2} d^{4} - 3 \, b c d^{3} e - a b d e^{3} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} - a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, {\left(4 \, c^{2} d^{3} e - 5 \, b c d^{2} e^{2} - a b e^{4} + {\left(b^{2} + 4 \, a c\right)} d e^{3} + 2 \, {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c d^{3} e^{3} - b d^{2} e^{4} + a d e^{5} + {\left(c d^{2} e^{4} - b d e^{5} + a e^{6}\right)} x\right)}}, \frac{{\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + {\left(b^{2} + 4 \, a c\right)} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + {\left(b^{2} + 4 \, a c\right)} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 4 \, {\left(2 \, c^{2} d^{4} - 3 \, b c d^{3} e - a b d e^{3} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} - a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(4 \, c^{2} d^{3} e - 5 \, b c d^{2} e^{2} - a b e^{4} + {\left(b^{2} + 4 \, a c\right)} d e^{3} + 2 \, {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c d^{3} e^{3} - b d^{2} e^{4} + a d e^{5} + {\left(c d^{2} e^{4} - b d e^{5} + a e^{6}\right)} x\right)}}\right]"," ",0,"[-1/4*(4*(2*c^2*d^4 - 3*b*c*d^3*e - a*b*d*e^3 + (b^2 + 2*a*c)*d^2*e^2 + (2*c^2*d^3*e - 3*b*c*d^2*e^2 - a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - (8*c^2*d^3 - 8*b*c*d^2*e + (b^2 + 4*a*c)*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + (b^2 + 4*a*c)*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(4*c^2*d^3*e - 5*b*c*d^2*e^2 - a*b*e^4 + (b^2 + 4*a*c)*d*e^3 + 2*(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*d^3*e^3 - b*d^2*e^4 + a*d*e^5 + (c*d^2*e^4 - b*d*e^5 + a*e^6)*x), 1/4*(8*(2*c^2*d^4 - 3*b*c*d^3*e - a*b*d*e^3 + (b^2 + 2*a*c)*d^2*e^2 + (2*c^2*d^3*e - 3*b*c*d^2*e^2 - a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + (8*c^2*d^3 - 8*b*c*d^2*e + (b^2 + 4*a*c)*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + (b^2 + 4*a*c)*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(4*c^2*d^3*e - 5*b*c*d^2*e^2 - a*b*e^4 + (b^2 + 4*a*c)*d*e^3 + 2*(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*d^3*e^3 - b*d^2*e^4 + a*d*e^5 + (c*d^2*e^4 - b*d*e^5 + a*e^6)*x), 1/2*((8*c^2*d^3 - 8*b*c*d^2*e + (b^2 + 4*a*c)*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + (b^2 + 4*a*c)*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(2*c^2*d^4 - 3*b*c*d^3*e - a*b*d*e^3 + (b^2 + 2*a*c)*d^2*e^2 + (2*c^2*d^3*e - 3*b*c*d^2*e^2 - a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 2*(4*c^2*d^3*e - 5*b*c*d^2*e^2 - a*b*e^4 + (b^2 + 4*a*c)*d*e^3 + 2*(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*d^3*e^3 - b*d^2*e^4 + a*d*e^5 + (c*d^2*e^4 - b*d*e^5 + a*e^6)*x), 1/2*((8*c^2*d^3 - 8*b*c*d^2*e + (b^2 + 4*a*c)*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + (b^2 + 4*a*c)*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 4*(2*c^2*d^4 - 3*b*c*d^3*e - a*b*d*e^3 + (b^2 + 2*a*c)*d^2*e^2 + (2*c^2*d^3*e - 3*b*c*d^2*e^2 - a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(4*c^2*d^3*e - 5*b*c*d^2*e^2 - a*b*e^4 + (b^2 + 4*a*c)*d*e^3 + 2*(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*d^3*e^3 - b*d^2*e^4 + a*d*e^5 + (c*d^2*e^4 - b*d*e^5 + a*e^6)*x)]","B",0
1553,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1554,1,2040,0,3.660864," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{4} x^{3} + 3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d e^{3} x^{2} + 3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} e^{2} x + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} e\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(16 \, a c^{3} d^{5} - 8 \, a^{3} b e^{5} - {\left(3 \, b^{3} c + 28 \, a b c^{2}\right)} d^{4} e + {\left(3 \, b^{4} + 26 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - {\left(17 \, a b^{3} + 12 \, a^{2} b c\right)} d^{2} e^{3} + 2 \, {\left(11 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{4} + {\left(16 \, c^{4} d^{5} - 40 \, b c^{3} d^{4} e + 2 \, {\left(13 \, b^{2} c^{2} + 28 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 84 \, a b c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{4} - 22 \, a b^{2} c - 40 \, a^{2} c^{2}\right)} d e^{4} + {\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(8 \, b c^{3} d^{5} - {\left(23 \, b^{2} c^{2} - 12 \, a c^{3}\right)} d^{4} e + {\left(19 \, b^{3} c + 4 \, a b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(b^{4} + 6 \, a b^{2} c\right)} d^{2} e^{3} + 5 \, {\left(a b^{3} + 4 \, a^{2} b c\right)} d e^{4} - {\left(a^{2} b^{2} + 12 \, a^{3} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(c^{3} d^{9} - 3 \, b c^{2} d^{8} e - 3 \, a^{2} b d^{4} e^{5} + a^{3} d^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{7} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{6} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{5} e^{4} + {\left(c^{3} d^{6} e^{3} - 3 \, b c^{2} d^{5} e^{4} - 3 \, a^{2} b d e^{8} + a^{3} e^{9} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{5} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{2} - 3 \, b c^{2} d^{6} e^{3} - 3 \, a^{2} b d^{2} e^{7} + a^{3} d e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{6}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e - 3 \, b c^{2} d^{7} e^{2} - 3 \, a^{2} b d^{3} e^{6} + a^{3} d^{2} e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{5}\right)} x\right)}}, \frac{3 \, {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{4} x^{3} + 3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d e^{3} x^{2} + 3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} e^{2} x + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} e\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(16 \, a c^{3} d^{5} - 8 \, a^{3} b e^{5} - {\left(3 \, b^{3} c + 28 \, a b c^{2}\right)} d^{4} e + {\left(3 \, b^{4} + 26 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - {\left(17 \, a b^{3} + 12 \, a^{2} b c\right)} d^{2} e^{3} + 2 \, {\left(11 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{4} + {\left(16 \, c^{4} d^{5} - 40 \, b c^{3} d^{4} e + 2 \, {\left(13 \, b^{2} c^{2} + 28 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 84 \, a b c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{4} - 22 \, a b^{2} c - 40 \, a^{2} c^{2}\right)} d e^{4} + {\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(8 \, b c^{3} d^{5} - {\left(23 \, b^{2} c^{2} - 12 \, a c^{3}\right)} d^{4} e + {\left(19 \, b^{3} c + 4 \, a b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(b^{4} + 6 \, a b^{2} c\right)} d^{2} e^{3} + 5 \, {\left(a b^{3} + 4 \, a^{2} b c\right)} d e^{4} - {\left(a^{2} b^{2} + 12 \, a^{3} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(c^{3} d^{9} - 3 \, b c^{2} d^{8} e - 3 \, a^{2} b d^{4} e^{5} + a^{3} d^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{7} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{6} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{5} e^{4} + {\left(c^{3} d^{6} e^{3} - 3 \, b c^{2} d^{5} e^{4} - 3 \, a^{2} b d e^{8} + a^{3} e^{9} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{5} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{2} - 3 \, b c^{2} d^{6} e^{3} - 3 \, a^{2} b d^{2} e^{7} + a^{3} d e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{6}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e - 3 \, b c^{2} d^{7} e^{2} - 3 \, a^{2} b d^{3} e^{6} + a^{3} d^{2} e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{5}\right)} x\right)}}\right]"," ",0,"[1/96*(3*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^4*x^3 + 3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d*e^3*x^2 + 3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^2*e^2*x + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^3*e)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(16*a*c^3*d^5 - 8*a^3*b*e^5 - (3*b^3*c + 28*a*b*c^2)*d^4*e + (3*b^4 + 26*a*b^2*c + 8*a^2*c^2)*d^3*e^2 - (17*a*b^3 + 12*a^2*b*c)*d^2*e^3 + 2*(11*a^2*b^2 - 4*a^3*c)*d*e^4 + (16*c^4*d^5 - 40*b*c^3*d^4*e + 2*(13*b^2*c^2 + 28*a*c^3)*d^3*e^2 + (b^3*c - 84*a*b*c^2)*d^2*e^3 - (3*b^4 - 22*a*b^2*c - 40*a^2*c^2)*d*e^4 + (3*a*b^3 - 20*a^2*b*c)*e^5)*x^2 + 2*(8*b*c^3*d^5 - (23*b^2*c^2 - 12*a*c^3)*d^4*e + (19*b^3*c + 4*a*b*c^2)*d^3*e^2 - 4*(b^4 + 6*a*b^2*c)*d^2*e^3 + 5*(a*b^3 + 4*a^2*b*c)*d*e^4 - (a^2*b^2 + 12*a^3*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^9 - 3*b*c^2*d^8*e - 3*a^2*b*d^4*e^5 + a^3*d^3*e^6 + 3*(b^2*c + a*c^2)*d^7*e^2 - (b^3 + 6*a*b*c)*d^6*e^3 + 3*(a*b^2 + a^2*c)*d^5*e^4 + (c^3*d^6*e^3 - 3*b*c^2*d^5*e^4 - 3*a^2*b*d*e^8 + a^3*e^9 + 3*(b^2*c + a*c^2)*d^4*e^5 - (b^3 + 6*a*b*c)*d^3*e^6 + 3*(a*b^2 + a^2*c)*d^2*e^7)*x^3 + 3*(c^3*d^7*e^2 - 3*b*c^2*d^6*e^3 - 3*a^2*b*d^2*e^7 + a^3*d*e^8 + 3*(b^2*c + a*c^2)*d^5*e^4 - (b^3 + 6*a*b*c)*d^4*e^5 + 3*(a*b^2 + a^2*c)*d^3*e^6)*x^2 + 3*(c^3*d^8*e - 3*b*c^2*d^7*e^2 - 3*a^2*b*d^3*e^6 + a^3*d^2*e^7 + 3*(b^2*c + a*c^2)*d^6*e^3 - (b^3 + 6*a*b*c)*d^5*e^4 + 3*(a*b^2 + a^2*c)*d^4*e^5)*x), 1/48*(3*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^4*x^3 + 3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d*e^3*x^2 + 3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^2*e^2*x + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^3*e)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(16*a*c^3*d^5 - 8*a^3*b*e^5 - (3*b^3*c + 28*a*b*c^2)*d^4*e + (3*b^4 + 26*a*b^2*c + 8*a^2*c^2)*d^3*e^2 - (17*a*b^3 + 12*a^2*b*c)*d^2*e^3 + 2*(11*a^2*b^2 - 4*a^3*c)*d*e^4 + (16*c^4*d^5 - 40*b*c^3*d^4*e + 2*(13*b^2*c^2 + 28*a*c^3)*d^3*e^2 + (b^3*c - 84*a*b*c^2)*d^2*e^3 - (3*b^4 - 22*a*b^2*c - 40*a^2*c^2)*d*e^4 + (3*a*b^3 - 20*a^2*b*c)*e^5)*x^2 + 2*(8*b*c^3*d^5 - (23*b^2*c^2 - 12*a*c^3)*d^4*e + (19*b^3*c + 4*a*b*c^2)*d^3*e^2 - 4*(b^4 + 6*a*b^2*c)*d^2*e^3 + 5*(a*b^3 + 4*a^2*b*c)*d*e^4 - (a^2*b^2 + 12*a^3*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^9 - 3*b*c^2*d^8*e - 3*a^2*b*d^4*e^5 + a^3*d^3*e^6 + 3*(b^2*c + a*c^2)*d^7*e^2 - (b^3 + 6*a*b*c)*d^6*e^3 + 3*(a*b^2 + a^2*c)*d^5*e^4 + (c^3*d^6*e^3 - 3*b*c^2*d^5*e^4 - 3*a^2*b*d*e^8 + a^3*e^9 + 3*(b^2*c + a*c^2)*d^4*e^5 - (b^3 + 6*a*b*c)*d^3*e^6 + 3*(a*b^2 + a^2*c)*d^2*e^7)*x^3 + 3*(c^3*d^7*e^2 - 3*b*c^2*d^6*e^3 - 3*a^2*b*d^2*e^7 + a^3*d*e^8 + 3*(b^2*c + a*c^2)*d^5*e^4 - (b^3 + 6*a*b*c)*d^4*e^5 + 3*(a*b^2 + a^2*c)*d^3*e^6)*x^2 + 3*(c^3*d^8*e - 3*b*c^2*d^7*e^2 - 3*a^2*b*d^3*e^6 + a^3*d^2*e^7 + 3*(b^2*c + a*c^2)*d^6*e^3 - (b^3 + 6*a*b*c)*d^5*e^4 + 3*(a*b^2 + a^2*c)*d^4*e^5)*x)]","B",0
1555,1,3996,0,19.568866," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{5} e - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{4} e^{2} + {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{5} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{6}\right)} x^{4} + 4 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} e^{4} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d e^{5}\right)} x^{3} + 6 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} e^{3} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(128 \, a c^{4} d^{7} - 48 \, a^{4} b e^{7} - 6 \, {\left(5 \, b^{3} c^{2} + 52 \, a b c^{3}\right)} d^{6} e + {\left(45 \, b^{4} c + 448 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d^{5} e^{2} - {\left(15 \, b^{5} + 412 \, a b^{3} c + 112 \, a^{2} b c^{2}\right)} d^{4} e^{3} + {\left(133 \, a b^{4} + 472 \, a^{2} b^{2} c - 176 \, a^{3} c^{2}\right)} d^{3} e^{4} - 2 \, {\left(127 \, a^{2} b^{3} + 44 \, a^{3} b c\right)} d^{2} e^{5} + 8 \, {\left(23 \, a^{3} b^{2} - 4 \, a^{4} c\right)} d e^{6} + {\left(32 \, c^{5} d^{6} e - 96 \, b c^{4} d^{5} e^{2} + 4 \, {\left(19 \, b^{2} c^{3} + 44 \, a c^{4}\right)} d^{4} e^{3} + 8 \, {\left(b^{3} c^{2} - 44 \, a b c^{3}\right)} d^{3} e^{4} - {\left(35 \, b^{4} c - 256 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d^{2} e^{5} + {\left(15 \, b^{5} - 80 \, a b^{3} c - 16 \, a^{2} b c^{2}\right)} d e^{6} - {\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} e^{7}\right)} x^{3} + {\left(128 \, c^{5} d^{7} - 400 \, b c^{4} d^{6} e + 352 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d^{5} e^{2} - 2 \, {\left(3 \, b^{3} c^{2} + 748 \, a b c^{3}\right)} d^{4} e^{3} - {\left(129 \, b^{4} c - 1080 \, a b^{2} c^{2} - 304 \, a^{2} c^{3}\right)} d^{3} e^{4} + {\left(55 \, b^{5} - 268 \, a b^{3} c - 432 \, a^{2} b c^{2}\right)} d^{2} e^{5} - {\left(65 \, a b^{4} - 408 \, a^{2} b^{2} c + 272 \, a^{3} c^{2}\right)} d e^{6} + 2 \, {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} e^{7}\right)} x^{2} + {\left(128 \, b c^{4} d^{7} - 4 \, {\left(123 \, b^{2} c^{3} - 68 \, a c^{4}\right)} d^{6} e + 4 \, {\left(157 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} d^{5} e^{2} - {\left(337 \, b^{4} c + 456 \, a b^{2} c^{2} + 304 \, a^{2} c^{3}\right)} d^{4} e^{3} + {\left(73 \, b^{5} + 360 \, a b^{3} c + 912 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(109 \, a b^{4} + 372 \, a^{2} b^{2} c + 704 \, a^{3} c^{2}\right)} d^{2} e^{5} + 4 \, {\left(11 \, a^{2} b^{3} + 108 \, a^{3} b c\right)} d e^{6} - 8 \, {\left(a^{3} b^{2} + 16 \, a^{4} c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, {\left(c^{4} d^{12} - 4 \, b c^{3} d^{11} e - 4 \, a^{3} b d^{5} e^{7} + a^{4} d^{4} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{10} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{9} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{8} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{7} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{6} e^{6} + {\left(c^{4} d^{8} e^{4} - 4 \, b c^{3} d^{7} e^{5} - 4 \, a^{3} b d e^{11} + a^{4} e^{12} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{6} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{8} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{9} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{10}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, b c^{3} d^{8} e^{4} - 4 \, a^{3} b d^{2} e^{10} + a^{4} d e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{9}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, b c^{3} d^{9} e^{3} - 4 \, a^{3} b d^{3} e^{9} + a^{4} d^{2} e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{8}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, b c^{3} d^{10} e^{2} - 4 \, a^{3} b d^{4} e^{8} + a^{4} d^{3} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{7}\right)} x\right)}}, \frac{15 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{5} e - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{4} e^{2} + {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{5} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{6}\right)} x^{4} + 4 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} e^{4} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d e^{5}\right)} x^{3} + 6 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} e^{3} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(128 \, a c^{4} d^{7} - 48 \, a^{4} b e^{7} - 6 \, {\left(5 \, b^{3} c^{2} + 52 \, a b c^{3}\right)} d^{6} e + {\left(45 \, b^{4} c + 448 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d^{5} e^{2} - {\left(15 \, b^{5} + 412 \, a b^{3} c + 112 \, a^{2} b c^{2}\right)} d^{4} e^{3} + {\left(133 \, a b^{4} + 472 \, a^{2} b^{2} c - 176 \, a^{3} c^{2}\right)} d^{3} e^{4} - 2 \, {\left(127 \, a^{2} b^{3} + 44 \, a^{3} b c\right)} d^{2} e^{5} + 8 \, {\left(23 \, a^{3} b^{2} - 4 \, a^{4} c\right)} d e^{6} + {\left(32 \, c^{5} d^{6} e - 96 \, b c^{4} d^{5} e^{2} + 4 \, {\left(19 \, b^{2} c^{3} + 44 \, a c^{4}\right)} d^{4} e^{3} + 8 \, {\left(b^{3} c^{2} - 44 \, a b c^{3}\right)} d^{3} e^{4} - {\left(35 \, b^{4} c - 256 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d^{2} e^{5} + {\left(15 \, b^{5} - 80 \, a b^{3} c - 16 \, a^{2} b c^{2}\right)} d e^{6} - {\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} e^{7}\right)} x^{3} + {\left(128 \, c^{5} d^{7} - 400 \, b c^{4} d^{6} e + 352 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d^{5} e^{2} - 2 \, {\left(3 \, b^{3} c^{2} + 748 \, a b c^{3}\right)} d^{4} e^{3} - {\left(129 \, b^{4} c - 1080 \, a b^{2} c^{2} - 304 \, a^{2} c^{3}\right)} d^{3} e^{4} + {\left(55 \, b^{5} - 268 \, a b^{3} c - 432 \, a^{2} b c^{2}\right)} d^{2} e^{5} - {\left(65 \, a b^{4} - 408 \, a^{2} b^{2} c + 272 \, a^{3} c^{2}\right)} d e^{6} + 2 \, {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} e^{7}\right)} x^{2} + {\left(128 \, b c^{4} d^{7} - 4 \, {\left(123 \, b^{2} c^{3} - 68 \, a c^{4}\right)} d^{6} e + 4 \, {\left(157 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} d^{5} e^{2} - {\left(337 \, b^{4} c + 456 \, a b^{2} c^{2} + 304 \, a^{2} c^{3}\right)} d^{4} e^{3} + {\left(73 \, b^{5} + 360 \, a b^{3} c + 912 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(109 \, a b^{4} + 372 \, a^{2} b^{2} c + 704 \, a^{3} c^{2}\right)} d^{2} e^{5} + 4 \, {\left(11 \, a^{2} b^{3} + 108 \, a^{3} b c\right)} d e^{6} - 8 \, {\left(a^{3} b^{2} + 16 \, a^{4} c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, {\left(c^{4} d^{12} - 4 \, b c^{3} d^{11} e - 4 \, a^{3} b d^{5} e^{7} + a^{4} d^{4} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{10} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{9} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{8} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{7} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{6} e^{6} + {\left(c^{4} d^{8} e^{4} - 4 \, b c^{3} d^{7} e^{5} - 4 \, a^{3} b d e^{11} + a^{4} e^{12} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{6} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{8} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{9} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{10}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, b c^{3} d^{8} e^{4} - 4 \, a^{3} b d^{2} e^{10} + a^{4} d e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{9}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, b c^{3} d^{9} e^{3} - 4 \, a^{3} b d^{3} e^{9} + a^{4} d^{2} e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{8}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, b c^{3} d^{10} e^{2} - 4 \, a^{3} b d^{4} e^{8} + a^{4} d^{3} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{7}\right)} x\right)}}\right]"," ",0,"[-1/768*(15*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^5*e - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^4*e^2 + (2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^5 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^6)*x^4 + 4*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2*e^4 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*e^5)*x^3 + 6*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3*e^3 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2*e^4)*x^2 + 4*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^4*e^2 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^3*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(128*a*c^4*d^7 - 48*a^4*b*e^7 - 6*(5*b^3*c^2 + 52*a*b*c^3)*d^6*e + (45*b^4*c + 448*a*b^2*c^2 - 16*a^2*c^3)*d^5*e^2 - (15*b^5 + 412*a*b^3*c + 112*a^2*b*c^2)*d^4*e^3 + (133*a*b^4 + 472*a^2*b^2*c - 176*a^3*c^2)*d^3*e^4 - 2*(127*a^2*b^3 + 44*a^3*b*c)*d^2*e^5 + 8*(23*a^3*b^2 - 4*a^4*c)*d*e^6 + (32*c^5*d^6*e - 96*b*c^4*d^5*e^2 + 4*(19*b^2*c^3 + 44*a*c^4)*d^4*e^3 + 8*(b^3*c^2 - 44*a*b*c^3)*d^3*e^4 - (35*b^4*c - 256*a*b^2*c^2 - 16*a^2*c^3)*d^2*e^5 + (15*b^5 - 80*a*b^3*c - 16*a^2*b*c^2)*d*e^6 - (15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*e^7)*x^3 + (128*c^5*d^7 - 400*b*c^4*d^6*e + 352*(b^2*c^3 + 2*a*c^4)*d^5*e^2 - 2*(3*b^3*c^2 + 748*a*b*c^3)*d^4*e^3 - (129*b^4*c - 1080*a*b^2*c^2 - 304*a^2*c^3)*d^3*e^4 + (55*b^5 - 268*a*b^3*c - 432*a^2*b*c^2)*d^2*e^5 - (65*a*b^4 - 408*a^2*b^2*c + 272*a^3*c^2)*d*e^6 + 2*(5*a^2*b^3 - 28*a^3*b*c)*e^7)*x^2 + (128*b*c^4*d^7 - 4*(123*b^2*c^3 - 68*a*c^4)*d^6*e + 4*(157*b^3*c^2 - 28*a*b*c^3)*d^5*e^2 - (337*b^4*c + 456*a*b^2*c^2 + 304*a^2*c^3)*d^4*e^3 + (73*b^5 + 360*a*b^3*c + 912*a^2*b*c^2)*d^3*e^4 - (109*a*b^4 + 372*a^2*b^2*c + 704*a^3*c^2)*d^2*e^5 + 4*(11*a^2*b^3 + 108*a^3*b*c)*d*e^6 - 8*(a^3*b^2 + 16*a^4*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^12 - 4*b*c^3*d^11*e - 4*a^3*b*d^5*e^7 + a^4*d^4*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^10*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^9*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^8*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^7*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^6*e^6 + (c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 - 4*a^3*b*d*e^11 + a^4*e^12 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^6 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^8 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^9 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^10)*x^4 + 4*(c^4*d^9*e^3 - 4*b*c^3*d^8*e^4 - 4*a^3*b*d^2*e^10 + a^4*d*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^9)*x^3 + 6*(c^4*d^10*e^2 - 4*b*c^3*d^9*e^3 - 4*a^3*b*d^3*e^9 + a^4*d^2*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^8)*x^2 + 4*(c^4*d^11*e - 4*b*c^3*d^10*e^2 - 4*a^3*b*d^4*e^8 + a^4*d^3*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^7)*x), 1/384*(15*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^5*e - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^4*e^2 + (2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^5 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^6)*x^4 + 4*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2*e^4 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*e^5)*x^3 + 6*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3*e^3 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2*e^4)*x^2 + 4*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^4*e^2 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^3*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(128*a*c^4*d^7 - 48*a^4*b*e^7 - 6*(5*b^3*c^2 + 52*a*b*c^3)*d^6*e + (45*b^4*c + 448*a*b^2*c^2 - 16*a^2*c^3)*d^5*e^2 - (15*b^5 + 412*a*b^3*c + 112*a^2*b*c^2)*d^4*e^3 + (133*a*b^4 + 472*a^2*b^2*c - 176*a^3*c^2)*d^3*e^4 - 2*(127*a^2*b^3 + 44*a^3*b*c)*d^2*e^5 + 8*(23*a^3*b^2 - 4*a^4*c)*d*e^6 + (32*c^5*d^6*e - 96*b*c^4*d^5*e^2 + 4*(19*b^2*c^3 + 44*a*c^4)*d^4*e^3 + 8*(b^3*c^2 - 44*a*b*c^3)*d^3*e^4 - (35*b^4*c - 256*a*b^2*c^2 - 16*a^2*c^3)*d^2*e^5 + (15*b^5 - 80*a*b^3*c - 16*a^2*b*c^2)*d*e^6 - (15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*e^7)*x^3 + (128*c^5*d^7 - 400*b*c^4*d^6*e + 352*(b^2*c^3 + 2*a*c^4)*d^5*e^2 - 2*(3*b^3*c^2 + 748*a*b*c^3)*d^4*e^3 - (129*b^4*c - 1080*a*b^2*c^2 - 304*a^2*c^3)*d^3*e^4 + (55*b^5 - 268*a*b^3*c - 432*a^2*b*c^2)*d^2*e^5 - (65*a*b^4 - 408*a^2*b^2*c + 272*a^3*c^2)*d*e^6 + 2*(5*a^2*b^3 - 28*a^3*b*c)*e^7)*x^2 + (128*b*c^4*d^7 - 4*(123*b^2*c^3 - 68*a*c^4)*d^6*e + 4*(157*b^3*c^2 - 28*a*b*c^3)*d^5*e^2 - (337*b^4*c + 456*a*b^2*c^2 + 304*a^2*c^3)*d^4*e^3 + (73*b^5 + 360*a*b^3*c + 912*a^2*b*c^2)*d^3*e^4 - (109*a*b^4 + 372*a^2*b^2*c + 704*a^3*c^2)*d^2*e^5 + 4*(11*a^2*b^3 + 108*a^3*b*c)*d*e^6 - 8*(a^3*b^2 + 16*a^4*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^12 - 4*b*c^3*d^11*e - 4*a^3*b*d^5*e^7 + a^4*d^4*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^10*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^9*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^8*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^7*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^6*e^6 + (c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 - 4*a^3*b*d*e^11 + a^4*e^12 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^6 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^8 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^9 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^10)*x^4 + 4*(c^4*d^9*e^3 - 4*b*c^3*d^8*e^4 - 4*a^3*b*d^2*e^10 + a^4*d*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^9)*x^3 + 6*(c^4*d^10*e^2 - 4*b*c^3*d^9*e^3 - 4*a^3*b*d^3*e^9 + a^4*d^2*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^8)*x^2 + 4*(c^4*d^11*e - 4*b*c^3*d^10*e^2 - 4*a^3*b*d^4*e^8 + a^4*d^3*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^7)*x)]","B",0
1556,1,6858,0,86.812748," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} e - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} e^{2} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{5} e^{3} + {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} e^{6} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{7} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{8}\right)} x^{5} + 5 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} e^{5} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} e^{6} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d e^{7}\right)} x^{4} + 10 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} e^{4} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{5} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2} e^{6}\right)} x^{3} + 10 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} e^{3} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} e^{4} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{3} e^{5}\right)} x^{2} + 5 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} e^{2} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{4} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(1280 \, a c^{5} d^{9} - 384 \, a^{5} b e^{9} - 40 \, {\left(9 \, b^{3} c^{3} + 100 \, a b c^{4}\right)} d^{8} e + 16 \, {\left(45 \, b^{4} c^{2} + 485 \, a b^{2} c^{3} - 92 \, a^{2} c^{4}\right)} d^{7} e^{2} - {\left(465 \, b^{5} c + 9520 \, a b^{3} c^{2} - 272 \, a^{2} b c^{3}\right)} d^{6} e^{3} + {\left(105 \, b^{6} + 5690 \, a b^{4} c + 8496 \, a^{2} b^{2} c^{2} - 3616 \, a^{3} c^{3}\right)} d^{5} e^{4} - 5 \, {\left(263 \, a b^{5} + 1984 \, a^{2} b^{3} c - 48 \, a^{3} b c^{2}\right)} d^{4} e^{5} + 2 \, {\left(1657 \, a^{2} b^{4} + 3024 \, a^{3} b^{2} c - 528 \, a^{4} c^{2}\right)} d^{3} e^{6} - 8 \, {\left(449 \, a^{3} b^{3} + 132 \, a^{4} b c\right)} d^{2} e^{7} + 48 \, {\left(39 \, a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{8} + {\left(128 \, c^{6} d^{7} e^{2} - 448 \, b c^{5} d^{6} e^{3} + 32 \, {\left(13 \, b^{2} c^{4} + 32 \, a c^{5}\right)} d^{5} e^{4} + 80 \, {\left(b^{3} c^{3} - 32 \, a b c^{4}\right)} d^{4} e^{5} - 2 \, {\left(233 \, b^{4} c^{2} - 1704 \, a b^{2} c^{3} + 848 \, a^{2} c^{4}\right)} d^{3} e^{6} + {\left(395 \, b^{5} c - 2552 \, a b^{3} c^{2} + 2544 \, a^{2} b c^{3}\right)} d^{2} e^{7} - {\left(105 \, b^{6} - 470 \, a b^{4} c - 672 \, a^{2} b^{2} c^{2} + 2592 \, a^{3} c^{3}\right)} d e^{8} + {\left(105 \, a b^{5} - 760 \, a^{2} b^{3} c + 1296 \, a^{3} b c^{2}\right)} e^{9}\right)} x^{4} + 2 \, {\left(320 \, c^{6} d^{8} e - 1152 \, b c^{5} d^{7} e^{2} + 128 \, {\left(9 \, b^{2} c^{4} + 20 \, a c^{5}\right)} d^{6} e^{3} + 32 \, {\left(3 \, b^{3} c^{3} - 208 \, a b c^{4}\right)} d^{5} e^{4} - 5 \, {\left(219 \, b^{4} c^{2} - 1688 \, a b^{2} c^{3} + 560 \, a^{2} c^{4}\right)} d^{4} e^{5} + 4 \, {\left(231 \, b^{5} c - 1448 \, a b^{3} c^{2} + 976 \, a^{2} b c^{3}\right)} d^{3} e^{6} - {\left(245 \, b^{6} - 958 \, a b^{4} c - 2304 \, a^{2} b^{2} c^{2} + 5280 \, a^{3} c^{3}\right)} d^{2} e^{7} + 8 \, {\left(35 \, a b^{5} - 236 \, a^{2} b^{3} c + 336 \, a^{3} b c^{2}\right)} d e^{8} - {\left(35 \, a^{2} b^{4} - 216 \, a^{3} b^{2} c + 240 \, a^{4} c^{2}\right)} e^{9}\right)} x^{3} + 2 \, {\left(640 \, c^{6} d^{9} - 2400 \, b c^{5} d^{8} e + 24 \, {\left(111 \, b^{2} c^{4} + 212 \, a c^{5}\right)} d^{7} e^{2} - 12 \, {\left(17 \, b^{3} c^{3} + 1164 \, a b c^{4}\right)} d^{6} e^{3} - 3 \, {\left(649 \, b^{4} c^{2} - 5696 \, a b^{2} c^{3} + 752 \, a^{2} c^{4}\right)} d^{5} e^{4} + 15 \, {\left(113 \, b^{5} c - 700 \, a b^{3} c^{2} + 96 \, a^{2} b c^{3}\right)} d^{4} e^{5} - 8 \, {\left(56 \, b^{6} - 171 \, a b^{4} c - 855 \, a^{2} b^{2} c^{2} + 892 \, a^{3} c^{3}\right)} d^{3} e^{6} + 3 \, {\left(203 \, a b^{5} - 1220 \, a^{2} b^{3} c + 928 \, a^{3} b c^{2}\right)} d^{2} e^{7} - 3 \, {\left(63 \, a^{2} b^{4} - 352 \, a^{3} b^{2} c + 144 \, a^{4} c^{2}\right)} d e^{8} + 4 \, {\left(7 \, a^{3} b^{3} - 36 \, a^{4} b c\right)} e^{9}\right)} x^{2} + 2 \, {\left(640 \, b c^{5} d^{9} - 440 \, {\left(7 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} e + 8 \, {\left(665 \, b^{3} c^{3} - 244 \, a b c^{4}\right)} d^{7} e^{2} - {\left(4565 \, b^{4} c^{2} + 1128 \, a b^{2} c^{3} + 4880 \, a^{2} c^{4}\right)} d^{6} e^{3} + 8 \, {\left(260 \, b^{5} c + 337 \, a b^{3} c^{2} + 1548 \, a^{2} b c^{3}\right)} d^{5} e^{4} - 5 \, {\left(79 \, b^{6} + 454 \, a b^{4} c + 1632 \, a^{2} b^{2} c^{2} + 1760 \, a^{3} c^{3}\right)} d^{4} e^{5} + 4 \, {\left(171 \, a b^{5} + 622 \, a^{2} b^{3} c + 2616 \, a^{3} b c^{2}\right)} d^{3} e^{6} - 3 \, {\left(139 \, a^{2} b^{4} + 1272 \, a^{3} b^{2} c + 880 \, a^{4} c^{2}\right)} d^{2} e^{7} + 8 \, {\left(19 \, a^{3} b^{3} + 276 \, a^{4} b c\right)} d e^{8} - 24 \, {\left(a^{4} b^{2} + 20 \, a^{5} c\right)} e^{9}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, {\left(c^{5} d^{15} - 5 \, b c^{4} d^{14} e - 5 \, a^{4} b d^{6} e^{9} + a^{5} d^{5} e^{10} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{13} e^{2} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{12} e^{3} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{11} e^{4} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{10} e^{5} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{9} e^{6} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{8} e^{7} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{7} e^{8} + {\left(c^{5} d^{10} e^{5} - 5 \, b c^{4} d^{9} e^{6} - 5 \, a^{4} b d e^{14} + a^{5} e^{15} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{8} e^{7} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{7} e^{8} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{6} e^{9} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{5} e^{10} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{4} e^{11} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{3} e^{12} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{2} e^{13}\right)} x^{5} + 5 \, {\left(c^{5} d^{11} e^{4} - 5 \, b c^{4} d^{10} e^{5} - 5 \, a^{4} b d^{2} e^{13} + a^{5} d e^{14} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{9} e^{6} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{8} e^{7} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{7} e^{8} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{6} e^{9} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{5} e^{10} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{4} e^{11} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{3} e^{12}\right)} x^{4} + 10 \, {\left(c^{5} d^{12} e^{3} - 5 \, b c^{4} d^{11} e^{4} - 5 \, a^{4} b d^{3} e^{12} + a^{5} d^{2} e^{13} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{10} e^{5} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{9} e^{6} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{8} e^{7} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{7} e^{8} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{6} e^{9} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{5} e^{10} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{4} e^{11}\right)} x^{3} + 10 \, {\left(c^{5} d^{13} e^{2} - 5 \, b c^{4} d^{12} e^{3} - 5 \, a^{4} b d^{4} e^{11} + a^{5} d^{3} e^{12} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{11} e^{4} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{10} e^{5} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{9} e^{6} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{8} e^{7} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{7} e^{8} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{6} e^{9} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{5} e^{10}\right)} x^{2} + 5 \, {\left(c^{5} d^{14} e - 5 \, b c^{4} d^{13} e^{2} - 5 \, a^{4} b d^{5} e^{10} + a^{5} d^{4} e^{11} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{12} e^{3} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{11} e^{4} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{10} e^{5} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{9} e^{6} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{8} e^{7} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{7} e^{8} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{6} e^{9}\right)} x\right)}}, \frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} e - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} e^{2} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{5} e^{3} + {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} e^{6} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{7} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{8}\right)} x^{5} + 5 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} e^{5} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} e^{6} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d e^{7}\right)} x^{4} + 10 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} e^{4} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{5} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2} e^{6}\right)} x^{3} + 10 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} e^{3} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} e^{4} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{3} e^{5}\right)} x^{2} + 5 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} e^{2} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{4} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(1280 \, a c^{5} d^{9} - 384 \, a^{5} b e^{9} - 40 \, {\left(9 \, b^{3} c^{3} + 100 \, a b c^{4}\right)} d^{8} e + 16 \, {\left(45 \, b^{4} c^{2} + 485 \, a b^{2} c^{3} - 92 \, a^{2} c^{4}\right)} d^{7} e^{2} - {\left(465 \, b^{5} c + 9520 \, a b^{3} c^{2} - 272 \, a^{2} b c^{3}\right)} d^{6} e^{3} + {\left(105 \, b^{6} + 5690 \, a b^{4} c + 8496 \, a^{2} b^{2} c^{2} - 3616 \, a^{3} c^{3}\right)} d^{5} e^{4} - 5 \, {\left(263 \, a b^{5} + 1984 \, a^{2} b^{3} c - 48 \, a^{3} b c^{2}\right)} d^{4} e^{5} + 2 \, {\left(1657 \, a^{2} b^{4} + 3024 \, a^{3} b^{2} c - 528 \, a^{4} c^{2}\right)} d^{3} e^{6} - 8 \, {\left(449 \, a^{3} b^{3} + 132 \, a^{4} b c\right)} d^{2} e^{7} + 48 \, {\left(39 \, a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{8} + {\left(128 \, c^{6} d^{7} e^{2} - 448 \, b c^{5} d^{6} e^{3} + 32 \, {\left(13 \, b^{2} c^{4} + 32 \, a c^{5}\right)} d^{5} e^{4} + 80 \, {\left(b^{3} c^{3} - 32 \, a b c^{4}\right)} d^{4} e^{5} - 2 \, {\left(233 \, b^{4} c^{2} - 1704 \, a b^{2} c^{3} + 848 \, a^{2} c^{4}\right)} d^{3} e^{6} + {\left(395 \, b^{5} c - 2552 \, a b^{3} c^{2} + 2544 \, a^{2} b c^{3}\right)} d^{2} e^{7} - {\left(105 \, b^{6} - 470 \, a b^{4} c - 672 \, a^{2} b^{2} c^{2} + 2592 \, a^{3} c^{3}\right)} d e^{8} + {\left(105 \, a b^{5} - 760 \, a^{2} b^{3} c + 1296 \, a^{3} b c^{2}\right)} e^{9}\right)} x^{4} + 2 \, {\left(320 \, c^{6} d^{8} e - 1152 \, b c^{5} d^{7} e^{2} + 128 \, {\left(9 \, b^{2} c^{4} + 20 \, a c^{5}\right)} d^{6} e^{3} + 32 \, {\left(3 \, b^{3} c^{3} - 208 \, a b c^{4}\right)} d^{5} e^{4} - 5 \, {\left(219 \, b^{4} c^{2} - 1688 \, a b^{2} c^{3} + 560 \, a^{2} c^{4}\right)} d^{4} e^{5} + 4 \, {\left(231 \, b^{5} c - 1448 \, a b^{3} c^{2} + 976 \, a^{2} b c^{3}\right)} d^{3} e^{6} - {\left(245 \, b^{6} - 958 \, a b^{4} c - 2304 \, a^{2} b^{2} c^{2} + 5280 \, a^{3} c^{3}\right)} d^{2} e^{7} + 8 \, {\left(35 \, a b^{5} - 236 \, a^{2} b^{3} c + 336 \, a^{3} b c^{2}\right)} d e^{8} - {\left(35 \, a^{2} b^{4} - 216 \, a^{3} b^{2} c + 240 \, a^{4} c^{2}\right)} e^{9}\right)} x^{3} + 2 \, {\left(640 \, c^{6} d^{9} - 2400 \, b c^{5} d^{8} e + 24 \, {\left(111 \, b^{2} c^{4} + 212 \, a c^{5}\right)} d^{7} e^{2} - 12 \, {\left(17 \, b^{3} c^{3} + 1164 \, a b c^{4}\right)} d^{6} e^{3} - 3 \, {\left(649 \, b^{4} c^{2} - 5696 \, a b^{2} c^{3} + 752 \, a^{2} c^{4}\right)} d^{5} e^{4} + 15 \, {\left(113 \, b^{5} c - 700 \, a b^{3} c^{2} + 96 \, a^{2} b c^{3}\right)} d^{4} e^{5} - 8 \, {\left(56 \, b^{6} - 171 \, a b^{4} c - 855 \, a^{2} b^{2} c^{2} + 892 \, a^{3} c^{3}\right)} d^{3} e^{6} + 3 \, {\left(203 \, a b^{5} - 1220 \, a^{2} b^{3} c + 928 \, a^{3} b c^{2}\right)} d^{2} e^{7} - 3 \, {\left(63 \, a^{2} b^{4} - 352 \, a^{3} b^{2} c + 144 \, a^{4} c^{2}\right)} d e^{8} + 4 \, {\left(7 \, a^{3} b^{3} - 36 \, a^{4} b c\right)} e^{9}\right)} x^{2} + 2 \, {\left(640 \, b c^{5} d^{9} - 440 \, {\left(7 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} e + 8 \, {\left(665 \, b^{3} c^{3} - 244 \, a b c^{4}\right)} d^{7} e^{2} - {\left(4565 \, b^{4} c^{2} + 1128 \, a b^{2} c^{3} + 4880 \, a^{2} c^{4}\right)} d^{6} e^{3} + 8 \, {\left(260 \, b^{5} c + 337 \, a b^{3} c^{2} + 1548 \, a^{2} b c^{3}\right)} d^{5} e^{4} - 5 \, {\left(79 \, b^{6} + 454 \, a b^{4} c + 1632 \, a^{2} b^{2} c^{2} + 1760 \, a^{3} c^{3}\right)} d^{4} e^{5} + 4 \, {\left(171 \, a b^{5} + 622 \, a^{2} b^{3} c + 2616 \, a^{3} b c^{2}\right)} d^{3} e^{6} - 3 \, {\left(139 \, a^{2} b^{4} + 1272 \, a^{3} b^{2} c + 880 \, a^{4} c^{2}\right)} d^{2} e^{7} + 8 \, {\left(19 \, a^{3} b^{3} + 276 \, a^{4} b c\right)} d e^{8} - 24 \, {\left(a^{4} b^{2} + 20 \, a^{5} c\right)} e^{9}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, {\left(c^{5} d^{15} - 5 \, b c^{4} d^{14} e - 5 \, a^{4} b d^{6} e^{9} + a^{5} d^{5} e^{10} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{13} e^{2} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{12} e^{3} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{11} e^{4} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{10} e^{5} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{9} e^{6} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{8} e^{7} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{7} e^{8} + {\left(c^{5} d^{10} e^{5} - 5 \, b c^{4} d^{9} e^{6} - 5 \, a^{4} b d e^{14} + a^{5} e^{15} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{8} e^{7} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{7} e^{8} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{6} e^{9} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{5} e^{10} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{4} e^{11} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{3} e^{12} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{2} e^{13}\right)} x^{5} + 5 \, {\left(c^{5} d^{11} e^{4} - 5 \, b c^{4} d^{10} e^{5} - 5 \, a^{4} b d^{2} e^{13} + a^{5} d e^{14} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{9} e^{6} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{8} e^{7} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{7} e^{8} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{6} e^{9} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{5} e^{10} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{4} e^{11} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{3} e^{12}\right)} x^{4} + 10 \, {\left(c^{5} d^{12} e^{3} - 5 \, b c^{4} d^{11} e^{4} - 5 \, a^{4} b d^{3} e^{12} + a^{5} d^{2} e^{13} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{10} e^{5} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{9} e^{6} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{8} e^{7} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{7} e^{8} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{6} e^{9} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{5} e^{10} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{4} e^{11}\right)} x^{3} + 10 \, {\left(c^{5} d^{13} e^{2} - 5 \, b c^{4} d^{12} e^{3} - 5 \, a^{4} b d^{4} e^{11} + a^{5} d^{3} e^{12} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{11} e^{4} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{10} e^{5} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{9} e^{6} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{8} e^{7} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{7} e^{8} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{6} e^{9} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{5} e^{10}\right)} x^{2} + 5 \, {\left(c^{5} d^{14} e - 5 \, b c^{4} d^{13} e^{2} - 5 \, a^{4} b d^{5} e^{10} + a^{5} d^{4} e^{11} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{12} e^{3} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{11} e^{4} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{10} e^{5} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{9} e^{6} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{8} e^{7} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{7} e^{8} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{6} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/7680*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7*e - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6*e^2 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d^5*e^3 + (24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*e^6 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^7 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*e^8)*x^5 + 5*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3*e^5 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*e^6 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d*e^7)*x^4 + 10*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4*e^4 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^5 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d^2*e^6)*x^3 + 10*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5*e^3 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4*e^4 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d^3*e^5)*x^2 + 5*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6*e^2 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5*e^3 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d^4*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(1280*a*c^5*d^9 - 384*a^5*b*e^9 - 40*(9*b^3*c^3 + 100*a*b*c^4)*d^8*e + 16*(45*b^4*c^2 + 485*a*b^2*c^3 - 92*a^2*c^4)*d^7*e^2 - (465*b^5*c + 9520*a*b^3*c^2 - 272*a^2*b*c^3)*d^6*e^3 + (105*b^6 + 5690*a*b^4*c + 8496*a^2*b^2*c^2 - 3616*a^3*c^3)*d^5*e^4 - 5*(263*a*b^5 + 1984*a^2*b^3*c - 48*a^3*b*c^2)*d^4*e^5 + 2*(1657*a^2*b^4 + 3024*a^3*b^2*c - 528*a^4*c^2)*d^3*e^6 - 8*(449*a^3*b^3 + 132*a^4*b*c)*d^2*e^7 + 48*(39*a^4*b^2 - 4*a^5*c)*d*e^8 + (128*c^6*d^7*e^2 - 448*b*c^5*d^6*e^3 + 32*(13*b^2*c^4 + 32*a*c^5)*d^5*e^4 + 80*(b^3*c^3 - 32*a*b*c^4)*d^4*e^5 - 2*(233*b^4*c^2 - 1704*a*b^2*c^3 + 848*a^2*c^4)*d^3*e^6 + (395*b^5*c - 2552*a*b^3*c^2 + 2544*a^2*b*c^3)*d^2*e^7 - (105*b^6 - 470*a*b^4*c - 672*a^2*b^2*c^2 + 2592*a^3*c^3)*d*e^8 + (105*a*b^5 - 760*a^2*b^3*c + 1296*a^3*b*c^2)*e^9)*x^4 + 2*(320*c^6*d^8*e - 1152*b*c^5*d^7*e^2 + 128*(9*b^2*c^4 + 20*a*c^5)*d^6*e^3 + 32*(3*b^3*c^3 - 208*a*b*c^4)*d^5*e^4 - 5*(219*b^4*c^2 - 1688*a*b^2*c^3 + 560*a^2*c^4)*d^4*e^5 + 4*(231*b^5*c - 1448*a*b^3*c^2 + 976*a^2*b*c^3)*d^3*e^6 - (245*b^6 - 958*a*b^4*c - 2304*a^2*b^2*c^2 + 5280*a^3*c^3)*d^2*e^7 + 8*(35*a*b^5 - 236*a^2*b^3*c + 336*a^3*b*c^2)*d*e^8 - (35*a^2*b^4 - 216*a^3*b^2*c + 240*a^4*c^2)*e^9)*x^3 + 2*(640*c^6*d^9 - 2400*b*c^5*d^8*e + 24*(111*b^2*c^4 + 212*a*c^5)*d^7*e^2 - 12*(17*b^3*c^3 + 1164*a*b*c^4)*d^6*e^3 - 3*(649*b^4*c^2 - 5696*a*b^2*c^3 + 752*a^2*c^4)*d^5*e^4 + 15*(113*b^5*c - 700*a*b^3*c^2 + 96*a^2*b*c^3)*d^4*e^5 - 8*(56*b^6 - 171*a*b^4*c - 855*a^2*b^2*c^2 + 892*a^3*c^3)*d^3*e^6 + 3*(203*a*b^5 - 1220*a^2*b^3*c + 928*a^3*b*c^2)*d^2*e^7 - 3*(63*a^2*b^4 - 352*a^3*b^2*c + 144*a^4*c^2)*d*e^8 + 4*(7*a^3*b^3 - 36*a^4*b*c)*e^9)*x^2 + 2*(640*b*c^5*d^9 - 440*(7*b^2*c^4 - 4*a*c^5)*d^8*e + 8*(665*b^3*c^3 - 244*a*b*c^4)*d^7*e^2 - (4565*b^4*c^2 + 1128*a*b^2*c^3 + 4880*a^2*c^4)*d^6*e^3 + 8*(260*b^5*c + 337*a*b^3*c^2 + 1548*a^2*b*c^3)*d^5*e^4 - 5*(79*b^6 + 454*a*b^4*c + 1632*a^2*b^2*c^2 + 1760*a^3*c^3)*d^4*e^5 + 4*(171*a*b^5 + 622*a^2*b^3*c + 2616*a^3*b*c^2)*d^3*e^6 - 3*(139*a^2*b^4 + 1272*a^3*b^2*c + 880*a^4*c^2)*d^2*e^7 + 8*(19*a^3*b^3 + 276*a^4*b*c)*d*e^8 - 24*(a^4*b^2 + 20*a^5*c)*e^9)*x)*sqrt(c*x^2 + b*x + a))/(c^5*d^15 - 5*b*c^4*d^14*e - 5*a^4*b*d^6*e^9 + a^5*d^5*e^10 + 5*(2*b^2*c^3 + a*c^4)*d^13*e^2 - 10*(b^3*c^2 + 2*a*b*c^3)*d^12*e^3 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^11*e^4 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^10*e^5 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^9*e^6 - 10*(a^2*b^3 + 2*a^3*b*c)*d^8*e^7 + 5*(2*a^3*b^2 + a^4*c)*d^7*e^8 + (c^5*d^10*e^5 - 5*b*c^4*d^9*e^6 - 5*a^4*b*d*e^14 + a^5*e^15 + 5*(2*b^2*c^3 + a*c^4)*d^8*e^7 - 10*(b^3*c^2 + 2*a*b*c^3)*d^7*e^8 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^6*e^9 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^5*e^10 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^4*e^11 - 10*(a^2*b^3 + 2*a^3*b*c)*d^3*e^12 + 5*(2*a^3*b^2 + a^4*c)*d^2*e^13)*x^5 + 5*(c^5*d^11*e^4 - 5*b*c^4*d^10*e^5 - 5*a^4*b*d^2*e^13 + a^5*d*e^14 + 5*(2*b^2*c^3 + a*c^4)*d^9*e^6 - 10*(b^3*c^2 + 2*a*b*c^3)*d^8*e^7 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^7*e^8 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^6*e^9 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^5*e^10 - 10*(a^2*b^3 + 2*a^3*b*c)*d^4*e^11 + 5*(2*a^3*b^2 + a^4*c)*d^3*e^12)*x^4 + 10*(c^5*d^12*e^3 - 5*b*c^4*d^11*e^4 - 5*a^4*b*d^3*e^12 + a^5*d^2*e^13 + 5*(2*b^2*c^3 + a*c^4)*d^10*e^5 - 10*(b^3*c^2 + 2*a*b*c^3)*d^9*e^6 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^8*e^7 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^7*e^8 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^6*e^9 - 10*(a^2*b^3 + 2*a^3*b*c)*d^5*e^10 + 5*(2*a^3*b^2 + a^4*c)*d^4*e^11)*x^3 + 10*(c^5*d^13*e^2 - 5*b*c^4*d^12*e^3 - 5*a^4*b*d^4*e^11 + a^5*d^3*e^12 + 5*(2*b^2*c^3 + a*c^4)*d^11*e^4 - 10*(b^3*c^2 + 2*a*b*c^3)*d^10*e^5 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^9*e^6 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^8*e^7 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^7*e^8 - 10*(a^2*b^3 + 2*a^3*b*c)*d^6*e^9 + 5*(2*a^3*b^2 + a^4*c)*d^5*e^10)*x^2 + 5*(c^5*d^14*e - 5*b*c^4*d^13*e^2 - 5*a^4*b*d^5*e^10 + a^5*d^4*e^11 + 5*(2*b^2*c^3 + a*c^4)*d^12*e^3 - 10*(b^3*c^2 + 2*a*b*c^3)*d^11*e^4 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^10*e^5 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^9*e^6 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^8*e^7 - 10*(a^2*b^3 + 2*a^3*b*c)*d^7*e^8 + 5*(2*a^3*b^2 + a^4*c)*d^6*e^9)*x), 1/3840*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7*e - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6*e^2 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d^5*e^3 + (24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*e^6 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^7 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*e^8)*x^5 + 5*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3*e^5 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*e^6 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d*e^7)*x^4 + 10*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4*e^4 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^5 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d^2*e^6)*x^3 + 10*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5*e^3 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4*e^4 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d^3*e^5)*x^2 + 5*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6*e^2 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5*e^3 + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*d^4*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(1280*a*c^5*d^9 - 384*a^5*b*e^9 - 40*(9*b^3*c^3 + 100*a*b*c^4)*d^8*e + 16*(45*b^4*c^2 + 485*a*b^2*c^3 - 92*a^2*c^4)*d^7*e^2 - (465*b^5*c + 9520*a*b^3*c^2 - 272*a^2*b*c^3)*d^6*e^3 + (105*b^6 + 5690*a*b^4*c + 8496*a^2*b^2*c^2 - 3616*a^3*c^3)*d^5*e^4 - 5*(263*a*b^5 + 1984*a^2*b^3*c - 48*a^3*b*c^2)*d^4*e^5 + 2*(1657*a^2*b^4 + 3024*a^3*b^2*c - 528*a^4*c^2)*d^3*e^6 - 8*(449*a^3*b^3 + 132*a^4*b*c)*d^2*e^7 + 48*(39*a^4*b^2 - 4*a^5*c)*d*e^8 + (128*c^6*d^7*e^2 - 448*b*c^5*d^6*e^3 + 32*(13*b^2*c^4 + 32*a*c^5)*d^5*e^4 + 80*(b^3*c^3 - 32*a*b*c^4)*d^4*e^5 - 2*(233*b^4*c^2 - 1704*a*b^2*c^3 + 848*a^2*c^4)*d^3*e^6 + (395*b^5*c - 2552*a*b^3*c^2 + 2544*a^2*b*c^3)*d^2*e^7 - (105*b^6 - 470*a*b^4*c - 672*a^2*b^2*c^2 + 2592*a^3*c^3)*d*e^8 + (105*a*b^5 - 760*a^2*b^3*c + 1296*a^3*b*c^2)*e^9)*x^4 + 2*(320*c^6*d^8*e - 1152*b*c^5*d^7*e^2 + 128*(9*b^2*c^4 + 20*a*c^5)*d^6*e^3 + 32*(3*b^3*c^3 - 208*a*b*c^4)*d^5*e^4 - 5*(219*b^4*c^2 - 1688*a*b^2*c^3 + 560*a^2*c^4)*d^4*e^5 + 4*(231*b^5*c - 1448*a*b^3*c^2 + 976*a^2*b*c^3)*d^3*e^6 - (245*b^6 - 958*a*b^4*c - 2304*a^2*b^2*c^2 + 5280*a^3*c^3)*d^2*e^7 + 8*(35*a*b^5 - 236*a^2*b^3*c + 336*a^3*b*c^2)*d*e^8 - (35*a^2*b^4 - 216*a^3*b^2*c + 240*a^4*c^2)*e^9)*x^3 + 2*(640*c^6*d^9 - 2400*b*c^5*d^8*e + 24*(111*b^2*c^4 + 212*a*c^5)*d^7*e^2 - 12*(17*b^3*c^3 + 1164*a*b*c^4)*d^6*e^3 - 3*(649*b^4*c^2 - 5696*a*b^2*c^3 + 752*a^2*c^4)*d^5*e^4 + 15*(113*b^5*c - 700*a*b^3*c^2 + 96*a^2*b*c^3)*d^4*e^5 - 8*(56*b^6 - 171*a*b^4*c - 855*a^2*b^2*c^2 + 892*a^3*c^3)*d^3*e^6 + 3*(203*a*b^5 - 1220*a^2*b^3*c + 928*a^3*b*c^2)*d^2*e^7 - 3*(63*a^2*b^4 - 352*a^3*b^2*c + 144*a^4*c^2)*d*e^8 + 4*(7*a^3*b^3 - 36*a^4*b*c)*e^9)*x^2 + 2*(640*b*c^5*d^9 - 440*(7*b^2*c^4 - 4*a*c^5)*d^8*e + 8*(665*b^3*c^3 - 244*a*b*c^4)*d^7*e^2 - (4565*b^4*c^2 + 1128*a*b^2*c^3 + 4880*a^2*c^4)*d^6*e^3 + 8*(260*b^5*c + 337*a*b^3*c^2 + 1548*a^2*b*c^3)*d^5*e^4 - 5*(79*b^6 + 454*a*b^4*c + 1632*a^2*b^2*c^2 + 1760*a^3*c^3)*d^4*e^5 + 4*(171*a*b^5 + 622*a^2*b^3*c + 2616*a^3*b*c^2)*d^3*e^6 - 3*(139*a^2*b^4 + 1272*a^3*b^2*c + 880*a^4*c^2)*d^2*e^7 + 8*(19*a^3*b^3 + 276*a^4*b*c)*d*e^8 - 24*(a^4*b^2 + 20*a^5*c)*e^9)*x)*sqrt(c*x^2 + b*x + a))/(c^5*d^15 - 5*b*c^4*d^14*e - 5*a^4*b*d^6*e^9 + a^5*d^5*e^10 + 5*(2*b^2*c^3 + a*c^4)*d^13*e^2 - 10*(b^3*c^2 + 2*a*b*c^3)*d^12*e^3 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^11*e^4 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^10*e^5 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^9*e^6 - 10*(a^2*b^3 + 2*a^3*b*c)*d^8*e^7 + 5*(2*a^3*b^2 + a^4*c)*d^7*e^8 + (c^5*d^10*e^5 - 5*b*c^4*d^9*e^6 - 5*a^4*b*d*e^14 + a^5*e^15 + 5*(2*b^2*c^3 + a*c^4)*d^8*e^7 - 10*(b^3*c^2 + 2*a*b*c^3)*d^7*e^8 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^6*e^9 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^5*e^10 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^4*e^11 - 10*(a^2*b^3 + 2*a^3*b*c)*d^3*e^12 + 5*(2*a^3*b^2 + a^4*c)*d^2*e^13)*x^5 + 5*(c^5*d^11*e^4 - 5*b*c^4*d^10*e^5 - 5*a^4*b*d^2*e^13 + a^5*d*e^14 + 5*(2*b^2*c^3 + a*c^4)*d^9*e^6 - 10*(b^3*c^2 + 2*a*b*c^3)*d^8*e^7 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^7*e^8 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^6*e^9 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^5*e^10 - 10*(a^2*b^3 + 2*a^3*b*c)*d^4*e^11 + 5*(2*a^3*b^2 + a^4*c)*d^3*e^12)*x^4 + 10*(c^5*d^12*e^3 - 5*b*c^4*d^11*e^4 - 5*a^4*b*d^3*e^12 + a^5*d^2*e^13 + 5*(2*b^2*c^3 + a*c^4)*d^10*e^5 - 10*(b^3*c^2 + 2*a*b*c^3)*d^9*e^6 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^8*e^7 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^7*e^8 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^6*e^9 - 10*(a^2*b^3 + 2*a^3*b*c)*d^5*e^10 + 5*(2*a^3*b^2 + a^4*c)*d^4*e^11)*x^3 + 10*(c^5*d^13*e^2 - 5*b*c^4*d^12*e^3 - 5*a^4*b*d^4*e^11 + a^5*d^3*e^12 + 5*(2*b^2*c^3 + a*c^4)*d^11*e^4 - 10*(b^3*c^2 + 2*a*b*c^3)*d^10*e^5 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^9*e^6 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^8*e^7 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^7*e^8 - 10*(a^2*b^3 + 2*a^3*b*c)*d^6*e^9 + 5*(2*a^3*b^2 + a^4*c)*d^5*e^10)*x^2 + 5*(c^5*d^14*e - 5*b*c^4*d^13*e^2 - 5*a^4*b*d^5*e^10 + a^5*d^4*e^11 + 5*(2*b^2*c^3 + a*c^4)*d^12*e^3 - 10*(b^3*c^2 + 2*a*b*c^3)*d^11*e^4 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^10*e^5 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^9*e^6 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^8*e^7 - 10*(a^2*b^3 + 2*a^3*b*c)*d^7*e^8 + 5*(2*a^3*b^2 + a^4*c)*d^6*e^9)*x)]","B",0
1557,1,1587,0,0.630986," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(32 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e - 32 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d e^{2} + {\left(9 \, b^{8} - 112 \, a b^{6} c + 480 \, a^{2} b^{4} c^{2} - 768 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(71680 \, c^{8} e^{3} x^{7} + 114688 \, a^{2} c^{6} d^{3} + 5120 \, {\left(48 \, c^{8} d e^{2} + 25 \, b c^{7} e^{3}\right)} x^{6} + 1280 \, {\left(224 \, c^{8} d^{2} e + 352 \, b c^{7} d e^{2} + {\left(41 \, b^{2} c^{6} + 84 \, a c^{7}\right)} e^{3}\right)} x^{5} + 128 \, {\left(896 \, c^{8} d^{3} + 4256 \, b c^{7} d^{2} e + 32 \, {\left(47 \, b^{2} c^{6} + 96 \, a c^{7}\right)} d e^{2} - 3 \, {\left(b^{3} c^{5} - 188 \, a b c^{6}\right)} e^{3}\right)} x^{4} - 224 \, {\left(15 \, b^{5} c^{3} - 160 \, a b^{3} c^{4} + 528 \, a^{2} b c^{5}\right)} d^{2} e + 32 \, {\left(105 \, b^{6} c^{2} - 1120 \, a b^{4} c^{3} + 3696 \, a^{2} b^{2} c^{4} - 3072 \, a^{3} c^{5}\right)} d e^{2} - {\left(945 \, b^{7} c - 10500 \, a b^{5} c^{2} + 37744 \, a^{2} b^{3} c^{3} - 42432 \, a^{3} b c^{4}\right)} e^{3} + 16 \, {\left(14336 \, b c^{7} d^{3} + 224 \, {\left(69 \, b^{2} c^{6} + 140 \, a c^{7}\right)} d^{2} e - 32 \, {\left(3 \, b^{3} c^{5} - 556 \, a b c^{6}\right)} d e^{2} + {\left(27 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} e^{3}\right)} x^{3} + 8 \, {\left(14336 \, {\left(b^{2} c^{6} + 2 \, a c^{7}\right)} d^{3} - 224 \, {\left(b^{3} c^{5} - 228 \, a b c^{6}\right)} d^{2} e + 32 \, {\left(7 \, b^{4} c^{4} - 60 \, a b^{2} c^{5} + 192 \, a^{2} c^{6}\right)} d e^{2} - {\left(63 \, b^{5} c^{3} - 568 \, a b^{3} c^{4} + 1392 \, a^{2} b c^{5}\right)} e^{3}\right)} x^{2} + 2 \, {\left(114688 \, a b c^{6} d^{3} + 224 \, {\left(5 \, b^{4} c^{4} - 48 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} d^{2} e - 32 \, {\left(35 \, b^{5} c^{3} - 336 \, a b^{3} c^{4} + 912 \, a^{2} b c^{5}\right)} d e^{2} + {\left(315 \, b^{6} c^{2} - 3164 \, a b^{4} c^{3} + 9552 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1146880 \, c^{6}}, -\frac{105 \, {\left(32 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e - 32 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d e^{2} + {\left(9 \, b^{8} - 112 \, a b^{6} c + 480 \, a^{2} b^{4} c^{2} - 768 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(71680 \, c^{8} e^{3} x^{7} + 114688 \, a^{2} c^{6} d^{3} + 5120 \, {\left(48 \, c^{8} d e^{2} + 25 \, b c^{7} e^{3}\right)} x^{6} + 1280 \, {\left(224 \, c^{8} d^{2} e + 352 \, b c^{7} d e^{2} + {\left(41 \, b^{2} c^{6} + 84 \, a c^{7}\right)} e^{3}\right)} x^{5} + 128 \, {\left(896 \, c^{8} d^{3} + 4256 \, b c^{7} d^{2} e + 32 \, {\left(47 \, b^{2} c^{6} + 96 \, a c^{7}\right)} d e^{2} - 3 \, {\left(b^{3} c^{5} - 188 \, a b c^{6}\right)} e^{3}\right)} x^{4} - 224 \, {\left(15 \, b^{5} c^{3} - 160 \, a b^{3} c^{4} + 528 \, a^{2} b c^{5}\right)} d^{2} e + 32 \, {\left(105 \, b^{6} c^{2} - 1120 \, a b^{4} c^{3} + 3696 \, a^{2} b^{2} c^{4} - 3072 \, a^{3} c^{5}\right)} d e^{2} - {\left(945 \, b^{7} c - 10500 \, a b^{5} c^{2} + 37744 \, a^{2} b^{3} c^{3} - 42432 \, a^{3} b c^{4}\right)} e^{3} + 16 \, {\left(14336 \, b c^{7} d^{3} + 224 \, {\left(69 \, b^{2} c^{6} + 140 \, a c^{7}\right)} d^{2} e - 32 \, {\left(3 \, b^{3} c^{5} - 556 \, a b c^{6}\right)} d e^{2} + {\left(27 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} e^{3}\right)} x^{3} + 8 \, {\left(14336 \, {\left(b^{2} c^{6} + 2 \, a c^{7}\right)} d^{3} - 224 \, {\left(b^{3} c^{5} - 228 \, a b c^{6}\right)} d^{2} e + 32 \, {\left(7 \, b^{4} c^{4} - 60 \, a b^{2} c^{5} + 192 \, a^{2} c^{6}\right)} d e^{2} - {\left(63 \, b^{5} c^{3} - 568 \, a b^{3} c^{4} + 1392 \, a^{2} b c^{5}\right)} e^{3}\right)} x^{2} + 2 \, {\left(114688 \, a b c^{6} d^{3} + 224 \, {\left(5 \, b^{4} c^{4} - 48 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} d^{2} e - 32 \, {\left(35 \, b^{5} c^{3} - 336 \, a b^{3} c^{4} + 912 \, a^{2} b c^{5}\right)} d e^{2} + {\left(315 \, b^{6} c^{2} - 3164 \, a b^{4} c^{3} + 9552 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{573440 \, c^{6}}\right]"," ",0,"[1/1146880*(105*(32*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e - 32*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*e^2 + (9*b^8 - 112*a*b^6*c + 480*a^2*b^4*c^2 - 768*a^3*b^2*c^3 + 256*a^4*c^4)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(71680*c^8*e^3*x^7 + 114688*a^2*c^6*d^3 + 5120*(48*c^8*d*e^2 + 25*b*c^7*e^3)*x^6 + 1280*(224*c^8*d^2*e + 352*b*c^7*d*e^2 + (41*b^2*c^6 + 84*a*c^7)*e^3)*x^5 + 128*(896*c^8*d^3 + 4256*b*c^7*d^2*e + 32*(47*b^2*c^6 + 96*a*c^7)*d*e^2 - 3*(b^3*c^5 - 188*a*b*c^6)*e^3)*x^4 - 224*(15*b^5*c^3 - 160*a*b^3*c^4 + 528*a^2*b*c^5)*d^2*e + 32*(105*b^6*c^2 - 1120*a*b^4*c^3 + 3696*a^2*b^2*c^4 - 3072*a^3*c^5)*d*e^2 - (945*b^7*c - 10500*a*b^5*c^2 + 37744*a^2*b^3*c^3 - 42432*a^3*b*c^4)*e^3 + 16*(14336*b*c^7*d^3 + 224*(69*b^2*c^6 + 140*a*c^7)*d^2*e - 32*(3*b^3*c^5 - 556*a*b*c^6)*d*e^2 + (27*b^4*c^4 - 216*a*b^2*c^5 + 560*a^2*c^6)*e^3)*x^3 + 8*(14336*(b^2*c^6 + 2*a*c^7)*d^3 - 224*(b^3*c^5 - 228*a*b*c^6)*d^2*e + 32*(7*b^4*c^4 - 60*a*b^2*c^5 + 192*a^2*c^6)*d*e^2 - (63*b^5*c^3 - 568*a*b^3*c^4 + 1392*a^2*b*c^5)*e^3)*x^2 + 2*(114688*a*b*c^6*d^3 + 224*(5*b^4*c^4 - 48*a*b^2*c^5 + 240*a^2*c^6)*d^2*e - 32*(35*b^5*c^3 - 336*a*b^3*c^4 + 912*a^2*b*c^5)*d*e^2 + (315*b^6*c^2 - 3164*a*b^4*c^3 + 9552*a^2*b^2*c^4 - 6720*a^3*c^5)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^6, -1/573440*(105*(32*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e - 32*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*e^2 + (9*b^8 - 112*a*b^6*c + 480*a^2*b^4*c^2 - 768*a^3*b^2*c^3 + 256*a^4*c^4)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(71680*c^8*e^3*x^7 + 114688*a^2*c^6*d^3 + 5120*(48*c^8*d*e^2 + 25*b*c^7*e^3)*x^6 + 1280*(224*c^8*d^2*e + 352*b*c^7*d*e^2 + (41*b^2*c^6 + 84*a*c^7)*e^3)*x^5 + 128*(896*c^8*d^3 + 4256*b*c^7*d^2*e + 32*(47*b^2*c^6 + 96*a*c^7)*d*e^2 - 3*(b^3*c^5 - 188*a*b*c^6)*e^3)*x^4 - 224*(15*b^5*c^3 - 160*a*b^3*c^4 + 528*a^2*b*c^5)*d^2*e + 32*(105*b^6*c^2 - 1120*a*b^4*c^3 + 3696*a^2*b^2*c^4 - 3072*a^3*c^5)*d*e^2 - (945*b^7*c - 10500*a*b^5*c^2 + 37744*a^2*b^3*c^3 - 42432*a^3*b*c^4)*e^3 + 16*(14336*b*c^7*d^3 + 224*(69*b^2*c^6 + 140*a*c^7)*d^2*e - 32*(3*b^3*c^5 - 556*a*b*c^6)*d*e^2 + (27*b^4*c^4 - 216*a*b^2*c^5 + 560*a^2*c^6)*e^3)*x^3 + 8*(14336*(b^2*c^6 + 2*a*c^7)*d^3 - 224*(b^3*c^5 - 228*a*b*c^6)*d^2*e + 32*(7*b^4*c^4 - 60*a*b^2*c^5 + 192*a^2*c^6)*d*e^2 - (63*b^5*c^3 - 568*a*b^3*c^4 + 1392*a^2*b*c^5)*e^3)*x^2 + 2*(114688*a*b*c^6*d^3 + 224*(5*b^4*c^4 - 48*a*b^2*c^5 + 240*a^2*c^6)*d^2*e - 32*(35*b^5*c^3 - 336*a*b^3*c^4 + 912*a^2*b*c^5)*d*e^2 + (315*b^6*c^2 - 3164*a*b^4*c^3 + 9552*a^2*b^2*c^4 - 6720*a^3*c^5)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^6]","B",0
1558,1,1015,0,0.550966," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(2 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(7680 \, c^{7} e^{2} x^{6} + 10752 \, a^{2} c^{5} d^{2} + 1280 \, {\left(14 \, c^{7} d e + 11 \, b c^{6} e^{2}\right)} x^{5} + 128 \, {\left(84 \, c^{7} d^{2} + 266 \, b c^{6} d e + {\left(47 \, b^{2} c^{5} + 96 \, a c^{6}\right)} e^{2}\right)} x^{4} + 16 \, {\left(1344 \, b c^{6} d^{2} + 14 \, {\left(69 \, b^{2} c^{5} + 140 \, a c^{6}\right)} d e - {\left(3 \, b^{3} c^{4} - 556 \, a b c^{5}\right)} e^{2}\right)} x^{3} - 14 \, {\left(15 \, b^{5} c^{2} - 160 \, a b^{3} c^{3} + 528 \, a^{2} b c^{4}\right)} d e + {\left(105 \, b^{6} c - 1120 \, a b^{4} c^{2} + 3696 \, a^{2} b^{2} c^{3} - 3072 \, a^{3} c^{4}\right)} e^{2} + 8 \, {\left(1344 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{2} - 14 \, {\left(b^{3} c^{4} - 228 \, a b c^{5}\right)} d e + {\left(7 \, b^{4} c^{3} - 60 \, a b^{2} c^{4} + 192 \, a^{2} c^{5}\right)} e^{2}\right)} x^{2} + 2 \, {\left(10752 \, a b c^{5} d^{2} + 14 \, {\left(5 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} d e - {\left(35 \, b^{5} c^{2} - 336 \, a b^{3} c^{3} + 912 \, a^{2} b c^{4}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{107520 \, c^{5}}, -\frac{105 \, {\left(2 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(7680 \, c^{7} e^{2} x^{6} + 10752 \, a^{2} c^{5} d^{2} + 1280 \, {\left(14 \, c^{7} d e + 11 \, b c^{6} e^{2}\right)} x^{5} + 128 \, {\left(84 \, c^{7} d^{2} + 266 \, b c^{6} d e + {\left(47 \, b^{2} c^{5} + 96 \, a c^{6}\right)} e^{2}\right)} x^{4} + 16 \, {\left(1344 \, b c^{6} d^{2} + 14 \, {\left(69 \, b^{2} c^{5} + 140 \, a c^{6}\right)} d e - {\left(3 \, b^{3} c^{4} - 556 \, a b c^{5}\right)} e^{2}\right)} x^{3} - 14 \, {\left(15 \, b^{5} c^{2} - 160 \, a b^{3} c^{3} + 528 \, a^{2} b c^{4}\right)} d e + {\left(105 \, b^{6} c - 1120 \, a b^{4} c^{2} + 3696 \, a^{2} b^{2} c^{3} - 3072 \, a^{3} c^{4}\right)} e^{2} + 8 \, {\left(1344 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{2} - 14 \, {\left(b^{3} c^{4} - 228 \, a b c^{5}\right)} d e + {\left(7 \, b^{4} c^{3} - 60 \, a b^{2} c^{4} + 192 \, a^{2} c^{5}\right)} e^{2}\right)} x^{2} + 2 \, {\left(10752 \, a b c^{5} d^{2} + 14 \, {\left(5 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} d e - {\left(35 \, b^{5} c^{2} - 336 \, a b^{3} c^{3} + 912 \, a^{2} b c^{4}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{53760 \, c^{5}}\right]"," ",0,"[1/107520*(105*(2*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d*e - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(7680*c^7*e^2*x^6 + 10752*a^2*c^5*d^2 + 1280*(14*c^7*d*e + 11*b*c^6*e^2)*x^5 + 128*(84*c^7*d^2 + 266*b*c^6*d*e + (47*b^2*c^5 + 96*a*c^6)*e^2)*x^4 + 16*(1344*b*c^6*d^2 + 14*(69*b^2*c^5 + 140*a*c^6)*d*e - (3*b^3*c^4 - 556*a*b*c^5)*e^2)*x^3 - 14*(15*b^5*c^2 - 160*a*b^3*c^3 + 528*a^2*b*c^4)*d*e + (105*b^6*c - 1120*a*b^4*c^2 + 3696*a^2*b^2*c^3 - 3072*a^3*c^4)*e^2 + 8*(1344*(b^2*c^5 + 2*a*c^6)*d^2 - 14*(b^3*c^4 - 228*a*b*c^5)*d*e + (7*b^4*c^3 - 60*a*b^2*c^4 + 192*a^2*c^5)*e^2)*x^2 + 2*(10752*a*b*c^5*d^2 + 14*(5*b^4*c^3 - 48*a*b^2*c^4 + 240*a^2*c^5)*d*e - (35*b^5*c^2 - 336*a*b^3*c^3 + 912*a^2*b*c^4)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/53760*(105*(2*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d*e - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(7680*c^7*e^2*x^6 + 10752*a^2*c^5*d^2 + 1280*(14*c^7*d*e + 11*b*c^6*e^2)*x^5 + 128*(84*c^7*d^2 + 266*b*c^6*d*e + (47*b^2*c^5 + 96*a*c^6)*e^2)*x^4 + 16*(1344*b*c^6*d^2 + 14*(69*b^2*c^5 + 140*a*c^6)*d*e - (3*b^3*c^4 - 556*a*b*c^5)*e^2)*x^3 - 14*(15*b^5*c^2 - 160*a*b^3*c^3 + 528*a^2*b*c^4)*d*e + (105*b^6*c - 1120*a*b^4*c^2 + 3696*a^2*b^2*c^3 - 3072*a^3*c^4)*e^2 + 8*(1344*(b^2*c^5 + 2*a*c^6)*d^2 - 14*(b^3*c^4 - 228*a*b*c^5)*d*e + (7*b^4*c^3 - 60*a*b^2*c^4 + 192*a^2*c^5)*e^2)*x^2 + 2*(10752*a*b*c^5*d^2 + 14*(5*b^4*c^3 - 48*a*b^2*c^4 + 240*a^2*c^5)*d*e - (35*b^5*c^2 - 336*a*b^3*c^3 + 912*a^2*b*c^4)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^5]","B",0
1559,1,559,0,0.482084," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{c} e \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1280 \, c^{6} e x^{5} + 1536 \, a^{2} c^{4} d + 128 \, {\left(12 \, c^{6} d + 19 \, b c^{5} e\right)} x^{4} + 16 \, {\left(192 \, b c^{5} d + {\left(69 \, b^{2} c^{4} + 140 \, a c^{5}\right)} e\right)} x^{3} + 8 \, {\left(192 \, {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 228 \, a b c^{4}\right)} e\right)} x^{2} - {\left(15 \, b^{5} c - 160 \, a b^{3} c^{2} + 528 \, a^{2} b c^{3}\right)} e + 2 \, {\left(1536 \, a b c^{4} d + {\left(5 \, b^{4} c^{2} - 48 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{4}}, -\frac{15 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-c} e \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(1280 \, c^{6} e x^{5} + 1536 \, a^{2} c^{4} d + 128 \, {\left(12 \, c^{6} d + 19 \, b c^{5} e\right)} x^{4} + 16 \, {\left(192 \, b c^{5} d + {\left(69 \, b^{2} c^{4} + 140 \, a c^{5}\right)} e\right)} x^{3} + 8 \, {\left(192 \, {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 228 \, a b c^{4}\right)} e\right)} x^{2} - {\left(15 \, b^{5} c - 160 \, a b^{3} c^{2} + 528 \, a^{2} b c^{3}\right)} e + 2 \, {\left(1536 \, a b c^{4} d + {\left(5 \, b^{4} c^{2} - 48 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{4}}\right]"," ",0,"[-1/15360*(15*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(c)*e*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(1280*c^6*e*x^5 + 1536*a^2*c^4*d + 128*(12*c^6*d + 19*b*c^5*e)*x^4 + 16*(192*b*c^5*d + (69*b^2*c^4 + 140*a*c^5)*e)*x^3 + 8*(192*(b^2*c^4 + 2*a*c^5)*d - (b^3*c^3 - 228*a*b*c^4)*e)*x^2 - (15*b^5*c - 160*a*b^3*c^2 + 528*a^2*b*c^3)*e + 2*(1536*a*b*c^4*d + (5*b^4*c^2 - 48*a*b^2*c^3 + 240*a^2*c^4)*e)*x)*sqrt(c*x^2 + b*x + a))/c^4, -1/7680*(15*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-c)*e*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(1280*c^6*e*x^5 + 1536*a^2*c^4*d + 128*(12*c^6*d + 19*b*c^5*e)*x^4 + 16*(192*b*c^5*d + (69*b^2*c^4 + 140*a*c^5)*e)*x^3 + 8*(192*(b^2*c^4 + 2*a*c^5)*d - (b^3*c^3 - 228*a*b*c^4)*e)*x^2 - (15*b^5*c - 160*a*b^3*c^2 + 528*a^2*b*c^3)*e + 2*(1536*a*b*c^4*d + (5*b^4*c^2 - 48*a*b^2*c^3 + 240*a^2*c^4)*e)*x)*sqrt(c*x^2 + b*x + a))/c^4]","B",0
1560,1,49,0,0.423918," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2}{5} \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/5*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)","B",0
1561,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1562,1,2231,0,127.987749," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(32 \, c^{3} d^{4} - 48 \, b c^{2} d^{3} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} + 12 \, a b c\right)} d e^{3} + {\left(32 \, c^{3} d^{3} e - 48 \, b c^{2} d^{2} e^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3} - {\left(b^{3} + 12 \, a b c\right)} e^{4}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 6 \, {\left(16 \, c^{3} d^{3} - 16 \, b c^{2} d^{2} e + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} + {\left(16 \, c^{3} d^{2} e - 16 \, b c^{2} d e^{2} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(4 \, c^{3} e^{4} x^{3} + 48 \, c^{3} d^{3} e - 60 \, b c^{2} d^{2} e^{2} - 6 \, a b c e^{4} + {\left(15 \, b^{2} c + 28 \, a c^{2}\right)} d e^{3} - 2 \, {\left(4 \, c^{3} d e^{3} - 5 \, b c^{2} e^{4}\right)} x^{2} + {\left(24 \, c^{3} d^{2} e^{2} - 32 \, b c^{2} d e^{3} + {\left(9 \, b^{2} c + 16 \, a c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{24 \, {\left(c e^{6} x + c d e^{5}\right)}}, \frac{3 \, {\left(32 \, c^{3} d^{4} - 48 \, b c^{2} d^{3} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} + 12 \, a b c\right)} d e^{3} + {\left(32 \, c^{3} d^{3} e - 48 \, b c^{2} d^{2} e^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3} - {\left(b^{3} + 12 \, a b c\right)} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 3 \, {\left(16 \, c^{3} d^{3} - 16 \, b c^{2} d^{2} e + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} + {\left(16 \, c^{3} d^{2} e - 16 \, b c^{2} d e^{2} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(4 \, c^{3} e^{4} x^{3} + 48 \, c^{3} d^{3} e - 60 \, b c^{2} d^{2} e^{2} - 6 \, a b c e^{4} + {\left(15 \, b^{2} c + 28 \, a c^{2}\right)} d e^{3} - 2 \, {\left(4 \, c^{3} d e^{3} - 5 \, b c^{2} e^{4}\right)} x^{2} + {\left(24 \, c^{3} d^{2} e^{2} - 32 \, b c^{2} d e^{3} + {\left(9 \, b^{2} c + 16 \, a c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left(c e^{6} x + c d e^{5}\right)}}, \frac{12 \, {\left(16 \, c^{3} d^{3} - 16 \, b c^{2} d^{2} e + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} + {\left(16 \, c^{3} d^{2} e - 16 \, b c^{2} d e^{2} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 3 \, {\left(32 \, c^{3} d^{4} - 48 \, b c^{2} d^{3} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} + 12 \, a b c\right)} d e^{3} + {\left(32 \, c^{3} d^{3} e - 48 \, b c^{2} d^{2} e^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3} - {\left(b^{3} + 12 \, a b c\right)} e^{4}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(4 \, c^{3} e^{4} x^{3} + 48 \, c^{3} d^{3} e - 60 \, b c^{2} d^{2} e^{2} - 6 \, a b c e^{4} + {\left(15 \, b^{2} c + 28 \, a c^{2}\right)} d e^{3} - 2 \, {\left(4 \, c^{3} d e^{3} - 5 \, b c^{2} e^{4}\right)} x^{2} + {\left(24 \, c^{3} d^{2} e^{2} - 32 \, b c^{2} d e^{3} + {\left(9 \, b^{2} c + 16 \, a c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{24 \, {\left(c e^{6} x + c d e^{5}\right)}}, \frac{6 \, {\left(16 \, c^{3} d^{3} - 16 \, b c^{2} d^{2} e + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} + {\left(16 \, c^{3} d^{2} e - 16 \, b c^{2} d e^{2} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 3 \, {\left(32 \, c^{3} d^{4} - 48 \, b c^{2} d^{3} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} + 12 \, a b c\right)} d e^{3} + {\left(32 \, c^{3} d^{3} e - 48 \, b c^{2} d^{2} e^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3} - {\left(b^{3} + 12 \, a b c\right)} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(4 \, c^{3} e^{4} x^{3} + 48 \, c^{3} d^{3} e - 60 \, b c^{2} d^{2} e^{2} - 6 \, a b c e^{4} + {\left(15 \, b^{2} c + 28 \, a c^{2}\right)} d e^{3} - 2 \, {\left(4 \, c^{3} d e^{3} - 5 \, b c^{2} e^{4}\right)} x^{2} + {\left(24 \, c^{3} d^{2} e^{2} - 32 \, b c^{2} d e^{3} + {\left(9 \, b^{2} c + 16 \, a c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left(c e^{6} x + c d e^{5}\right)}}\right]"," ",0,"[-1/24*(3*(32*c^3*d^4 - 48*b*c^2*d^3*e + 6*(3*b^2*c + 4*a*c^2)*d^2*e^2 - (b^3 + 12*a*b*c)*d*e^3 + (32*c^3*d^3*e - 48*b*c^2*d^2*e^2 + 6*(3*b^2*c + 4*a*c^2)*d*e^3 - (b^3 + 12*a*b*c)*e^4)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 6*(16*c^3*d^3 - 16*b*c^2*d^2*e + (3*b^2*c + 4*a*c^2)*d*e^2 + (16*c^3*d^2*e - 16*b*c^2*d*e^2 + (3*b^2*c + 4*a*c^2)*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(4*c^3*e^4*x^3 + 48*c^3*d^3*e - 60*b*c^2*d^2*e^2 - 6*a*b*c*e^4 + (15*b^2*c + 28*a*c^2)*d*e^3 - 2*(4*c^3*d*e^3 - 5*b*c^2*e^4)*x^2 + (24*c^3*d^2*e^2 - 32*b*c^2*d*e^3 + (9*b^2*c + 16*a*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*e^6*x + c*d*e^5), 1/12*(3*(32*c^3*d^4 - 48*b*c^2*d^3*e + 6*(3*b^2*c + 4*a*c^2)*d^2*e^2 - (b^3 + 12*a*b*c)*d*e^3 + (32*c^3*d^3*e - 48*b*c^2*d^2*e^2 + 6*(3*b^2*c + 4*a*c^2)*d*e^3 - (b^3 + 12*a*b*c)*e^4)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 3*(16*c^3*d^3 - 16*b*c^2*d^2*e + (3*b^2*c + 4*a*c^2)*d*e^2 + (16*c^3*d^2*e - 16*b*c^2*d*e^2 + (3*b^2*c + 4*a*c^2)*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(4*c^3*e^4*x^3 + 48*c^3*d^3*e - 60*b*c^2*d^2*e^2 - 6*a*b*c*e^4 + (15*b^2*c + 28*a*c^2)*d*e^3 - 2*(4*c^3*d*e^3 - 5*b*c^2*e^4)*x^2 + (24*c^3*d^2*e^2 - 32*b*c^2*d*e^3 + (9*b^2*c + 16*a*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*e^6*x + c*d*e^5), 1/24*(12*(16*c^3*d^3 - 16*b*c^2*d^2*e + (3*b^2*c + 4*a*c^2)*d*e^2 + (16*c^3*d^2*e - 16*b*c^2*d*e^2 + (3*b^2*c + 4*a*c^2)*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 3*(32*c^3*d^4 - 48*b*c^2*d^3*e + 6*(3*b^2*c + 4*a*c^2)*d^2*e^2 - (b^3 + 12*a*b*c)*d*e^3 + (32*c^3*d^3*e - 48*b*c^2*d^2*e^2 + 6*(3*b^2*c + 4*a*c^2)*d*e^3 - (b^3 + 12*a*b*c)*e^4)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(4*c^3*e^4*x^3 + 48*c^3*d^3*e - 60*b*c^2*d^2*e^2 - 6*a*b*c*e^4 + (15*b^2*c + 28*a*c^2)*d*e^3 - 2*(4*c^3*d*e^3 - 5*b*c^2*e^4)*x^2 + (24*c^3*d^2*e^2 - 32*b*c^2*d*e^3 + (9*b^2*c + 16*a*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*e^6*x + c*d*e^5), 1/12*(6*(16*c^3*d^3 - 16*b*c^2*d^2*e + (3*b^2*c + 4*a*c^2)*d*e^2 + (16*c^3*d^2*e - 16*b*c^2*d*e^2 + (3*b^2*c + 4*a*c^2)*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 3*(32*c^3*d^4 - 48*b*c^2*d^3*e + 6*(3*b^2*c + 4*a*c^2)*d^2*e^2 - (b^3 + 12*a*b*c)*d*e^3 + (32*c^3*d^3*e - 48*b*c^2*d^2*e^2 + 6*(3*b^2*c + 4*a*c^2)*d*e^3 - (b^3 + 12*a*b*c)*e^4)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(4*c^3*e^4*x^3 + 48*c^3*d^3*e - 60*b*c^2*d^2*e^2 - 6*a*b*c*e^4 + (15*b^2*c + 28*a*c^2)*d*e^3 - 2*(4*c^3*d*e^3 - 5*b*c^2*e^4)*x^2 + (24*c^3*d^2*e^2 - 32*b*c^2*d*e^3 + (9*b^2*c + 16*a*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*e^6*x + c*d*e^5)]","A",0
1563,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1564,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1565,1,2343,0,0.849907," ","integrate((2*c*x+b)*(e*x+d)^3*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(40 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} + 96 \, a^{2} b^{4} c^{4} - 256 \, a^{3} b^{2} c^{5} + 256 \, a^{4} c^{6}\right)} d^{2} e - 40 \, {\left(b^{9} c - 16 \, a b^{7} c^{2} + 96 \, a^{2} b^{5} c^{3} - 256 \, a^{3} b^{3} c^{4} + 256 \, a^{4} b c^{5}\right)} d e^{2} + {\left(11 \, b^{10} - 180 \, a b^{8} c + 1120 \, a^{2} b^{6} c^{2} - 3200 \, a^{3} b^{4} c^{3} + 3840 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1376256 \, c^{10} e^{3} x^{9} + 1966080 \, a^{3} c^{7} d^{3} + 229376 \, {\left(20 \, c^{10} d e^{2} + 17 \, b c^{9} e^{3}\right)} x^{8} + 14336 \, {\left(360 \, c^{10} d^{2} e + 920 \, b c^{9} d e^{2} + {\left(251 \, b^{2} c^{8} + 252 \, a c^{9}\right)} e^{3}\right)} x^{7} + 1024 \, {\left(1920 \, c^{10} d^{3} + 14760 \, b c^{9} d^{2} e + 40 \, {\left(303 \, b^{2} c^{8} + 304 \, a c^{9}\right)} d e^{2} + {\left(1035 \, b^{3} c^{7} + 6268 \, a b c^{8}\right)} e^{3}\right)} x^{6} + 256 \, {\left(23040 \, b c^{9} d^{3} + 120 \, {\left(475 \, b^{2} c^{8} + 476 \, a c^{9}\right)} d^{2} e + 40 \, {\left(367 \, b^{3} c^{7} + 2220 \, a b c^{8}\right)} d e^{2} - {\left(5 \, b^{4} c^{6} - 10200 \, a b^{2} c^{7} - 10416 \, a^{2} c^{8}\right)} e^{3}\right)} x^{5} + 128 \, {\left(46080 \, {\left(b^{2} c^{8} + a c^{9}\right)} d^{3} + 120 \, {\left(299 \, b^{3} c^{7} + 1804 \, a b c^{8}\right)} d^{2} e - 40 \, {\left(b^{4} c^{6} - 1884 \, a b^{2} c^{7} - 1920 \, a^{2} c^{8}\right)} d e^{2} + {\left(11 \, b^{5} c^{5} - 120 \, a b^{3} c^{6} + 13680 \, a^{2} b c^{7}\right)} e^{3}\right)} x^{4} + 120 \, {\left(105 \, b^{7} c^{3} - 1540 \, a b^{5} c^{4} + 8176 \, a^{2} b^{3} c^{5} - 17856 \, a^{3} b c^{6}\right)} d^{2} e - 40 \, {\left(315 \, b^{8} c^{2} - 4620 \, a b^{6} c^{3} + 24528 \, a^{2} b^{4} c^{4} - 53568 \, a^{3} b^{2} c^{5} + 32768 \, a^{4} c^{6}\right)} d e^{2} + {\left(3465 \, b^{9} c - 52080 \, a b^{7} c^{2} + 288288 \, a^{2} b^{5} c^{3} - 687360 \, a^{3} b^{3} c^{4} + 574720 \, a^{4} b c^{5}\right)} e^{3} + 16 \, {\left(122880 \, {\left(b^{3} c^{7} + 6 \, a b c^{8}\right)} d^{3} - 120 \, {\left(3 \, b^{4} c^{6} - 6520 \, a b^{2} c^{7} - 6608 \, a^{2} c^{8}\right)} d^{2} e + 40 \, {\left(9 \, b^{5} c^{5} - 104 \, a b^{3} c^{6} + 10896 \, a^{2} b c^{7}\right)} d e^{2} - {\left(99 \, b^{6} c^{4} - 1180 \, a b^{4} c^{5} + 4560 \, a^{2} b^{2} c^{6} - 6720 \, a^{3} c^{7}\right)} e^{3}\right)} x^{3} + 8 \, {\left(737280 \, {\left(a b^{2} c^{7} + a^{2} c^{8}\right)} d^{3} + 120 \, {\left(7 \, b^{5} c^{5} - 88 \, a b^{3} c^{6} + 10608 \, a^{2} b c^{7}\right)} d^{2} e - 40 \, {\left(21 \, b^{6} c^{4} - 264 \, a b^{4} c^{5} + 1104 \, a^{2} b^{2} c^{6} - 2048 \, a^{3} c^{7}\right)} d e^{2} + {\left(231 \, b^{7} c^{3} - 2988 \, a b^{5} c^{4} + 13200 \, a^{2} b^{3} c^{5} - 20800 \, a^{3} b c^{6}\right)} e^{3}\right)} x^{2} + 2 \, {\left(2949120 \, a^{2} b c^{7} d^{3} - 120 \, {\left(35 \, b^{6} c^{4} - 476 \, a b^{4} c^{5} + 2256 \, a^{2} b^{2} c^{6} - 6720 \, a^{3} c^{7}\right)} d^{2} e + 40 \, {\left(105 \, b^{7} c^{3} - 1428 \, a b^{5} c^{4} + 6768 \, a^{2} b^{3} c^{5} - 11968 \, a^{3} b c^{6}\right)} d e^{2} - {\left(1155 \, b^{8} c^{2} - 16128 \, a b^{6} c^{3} + 80160 \, a^{2} b^{4} c^{4} - 158720 \, a^{3} b^{2} c^{5} + 80640 \, a^{4} c^{6}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{27525120 \, c^{7}}, \frac{315 \, {\left(40 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} + 96 \, a^{2} b^{4} c^{4} - 256 \, a^{3} b^{2} c^{5} + 256 \, a^{4} c^{6}\right)} d^{2} e - 40 \, {\left(b^{9} c - 16 \, a b^{7} c^{2} + 96 \, a^{2} b^{5} c^{3} - 256 \, a^{3} b^{3} c^{4} + 256 \, a^{4} b c^{5}\right)} d e^{2} + {\left(11 \, b^{10} - 180 \, a b^{8} c + 1120 \, a^{2} b^{6} c^{2} - 3200 \, a^{3} b^{4} c^{3} + 3840 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(1376256 \, c^{10} e^{3} x^{9} + 1966080 \, a^{3} c^{7} d^{3} + 229376 \, {\left(20 \, c^{10} d e^{2} + 17 \, b c^{9} e^{3}\right)} x^{8} + 14336 \, {\left(360 \, c^{10} d^{2} e + 920 \, b c^{9} d e^{2} + {\left(251 \, b^{2} c^{8} + 252 \, a c^{9}\right)} e^{3}\right)} x^{7} + 1024 \, {\left(1920 \, c^{10} d^{3} + 14760 \, b c^{9} d^{2} e + 40 \, {\left(303 \, b^{2} c^{8} + 304 \, a c^{9}\right)} d e^{2} + {\left(1035 \, b^{3} c^{7} + 6268 \, a b c^{8}\right)} e^{3}\right)} x^{6} + 256 \, {\left(23040 \, b c^{9} d^{3} + 120 \, {\left(475 \, b^{2} c^{8} + 476 \, a c^{9}\right)} d^{2} e + 40 \, {\left(367 \, b^{3} c^{7} + 2220 \, a b c^{8}\right)} d e^{2} - {\left(5 \, b^{4} c^{6} - 10200 \, a b^{2} c^{7} - 10416 \, a^{2} c^{8}\right)} e^{3}\right)} x^{5} + 128 \, {\left(46080 \, {\left(b^{2} c^{8} + a c^{9}\right)} d^{3} + 120 \, {\left(299 \, b^{3} c^{7} + 1804 \, a b c^{8}\right)} d^{2} e - 40 \, {\left(b^{4} c^{6} - 1884 \, a b^{2} c^{7} - 1920 \, a^{2} c^{8}\right)} d e^{2} + {\left(11 \, b^{5} c^{5} - 120 \, a b^{3} c^{6} + 13680 \, a^{2} b c^{7}\right)} e^{3}\right)} x^{4} + 120 \, {\left(105 \, b^{7} c^{3} - 1540 \, a b^{5} c^{4} + 8176 \, a^{2} b^{3} c^{5} - 17856 \, a^{3} b c^{6}\right)} d^{2} e - 40 \, {\left(315 \, b^{8} c^{2} - 4620 \, a b^{6} c^{3} + 24528 \, a^{2} b^{4} c^{4} - 53568 \, a^{3} b^{2} c^{5} + 32768 \, a^{4} c^{6}\right)} d e^{2} + {\left(3465 \, b^{9} c - 52080 \, a b^{7} c^{2} + 288288 \, a^{2} b^{5} c^{3} - 687360 \, a^{3} b^{3} c^{4} + 574720 \, a^{4} b c^{5}\right)} e^{3} + 16 \, {\left(122880 \, {\left(b^{3} c^{7} + 6 \, a b c^{8}\right)} d^{3} - 120 \, {\left(3 \, b^{4} c^{6} - 6520 \, a b^{2} c^{7} - 6608 \, a^{2} c^{8}\right)} d^{2} e + 40 \, {\left(9 \, b^{5} c^{5} - 104 \, a b^{3} c^{6} + 10896 \, a^{2} b c^{7}\right)} d e^{2} - {\left(99 \, b^{6} c^{4} - 1180 \, a b^{4} c^{5} + 4560 \, a^{2} b^{2} c^{6} - 6720 \, a^{3} c^{7}\right)} e^{3}\right)} x^{3} + 8 \, {\left(737280 \, {\left(a b^{2} c^{7} + a^{2} c^{8}\right)} d^{3} + 120 \, {\left(7 \, b^{5} c^{5} - 88 \, a b^{3} c^{6} + 10608 \, a^{2} b c^{7}\right)} d^{2} e - 40 \, {\left(21 \, b^{6} c^{4} - 264 \, a b^{4} c^{5} + 1104 \, a^{2} b^{2} c^{6} - 2048 \, a^{3} c^{7}\right)} d e^{2} + {\left(231 \, b^{7} c^{3} - 2988 \, a b^{5} c^{4} + 13200 \, a^{2} b^{3} c^{5} - 20800 \, a^{3} b c^{6}\right)} e^{3}\right)} x^{2} + 2 \, {\left(2949120 \, a^{2} b c^{7} d^{3} - 120 \, {\left(35 \, b^{6} c^{4} - 476 \, a b^{4} c^{5} + 2256 \, a^{2} b^{2} c^{6} - 6720 \, a^{3} c^{7}\right)} d^{2} e + 40 \, {\left(105 \, b^{7} c^{3} - 1428 \, a b^{5} c^{4} + 6768 \, a^{2} b^{3} c^{5} - 11968 \, a^{3} b c^{6}\right)} d e^{2} - {\left(1155 \, b^{8} c^{2} - 16128 \, a b^{6} c^{3} + 80160 \, a^{2} b^{4} c^{4} - 158720 \, a^{3} b^{2} c^{5} + 80640 \, a^{4} c^{6}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{13762560 \, c^{7}}\right]"," ",0,"[-1/27525120*(315*(40*(b^8*c^2 - 16*a*b^6*c^3 + 96*a^2*b^4*c^4 - 256*a^3*b^2*c^5 + 256*a^4*c^6)*d^2*e - 40*(b^9*c - 16*a*b^7*c^2 + 96*a^2*b^5*c^3 - 256*a^3*b^3*c^4 + 256*a^4*b*c^5)*d*e^2 + (11*b^10 - 180*a*b^8*c + 1120*a^2*b^6*c^2 - 3200*a^3*b^4*c^3 + 3840*a^4*b^2*c^4 - 1024*a^5*c^5)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(1376256*c^10*e^3*x^9 + 1966080*a^3*c^7*d^3 + 229376*(20*c^10*d*e^2 + 17*b*c^9*e^3)*x^8 + 14336*(360*c^10*d^2*e + 920*b*c^9*d*e^2 + (251*b^2*c^8 + 252*a*c^9)*e^3)*x^7 + 1024*(1920*c^10*d^3 + 14760*b*c^9*d^2*e + 40*(303*b^2*c^8 + 304*a*c^9)*d*e^2 + (1035*b^3*c^7 + 6268*a*b*c^8)*e^3)*x^6 + 256*(23040*b*c^9*d^3 + 120*(475*b^2*c^8 + 476*a*c^9)*d^2*e + 40*(367*b^3*c^7 + 2220*a*b*c^8)*d*e^2 - (5*b^4*c^6 - 10200*a*b^2*c^7 - 10416*a^2*c^8)*e^3)*x^5 + 128*(46080*(b^2*c^8 + a*c^9)*d^3 + 120*(299*b^3*c^7 + 1804*a*b*c^8)*d^2*e - 40*(b^4*c^6 - 1884*a*b^2*c^7 - 1920*a^2*c^8)*d*e^2 + (11*b^5*c^5 - 120*a*b^3*c^6 + 13680*a^2*b*c^7)*e^3)*x^4 + 120*(105*b^7*c^3 - 1540*a*b^5*c^4 + 8176*a^2*b^3*c^5 - 17856*a^3*b*c^6)*d^2*e - 40*(315*b^8*c^2 - 4620*a*b^6*c^3 + 24528*a^2*b^4*c^4 - 53568*a^3*b^2*c^5 + 32768*a^4*c^6)*d*e^2 + (3465*b^9*c - 52080*a*b^7*c^2 + 288288*a^2*b^5*c^3 - 687360*a^3*b^3*c^4 + 574720*a^4*b*c^5)*e^3 + 16*(122880*(b^3*c^7 + 6*a*b*c^8)*d^3 - 120*(3*b^4*c^6 - 6520*a*b^2*c^7 - 6608*a^2*c^8)*d^2*e + 40*(9*b^5*c^5 - 104*a*b^3*c^6 + 10896*a^2*b*c^7)*d*e^2 - (99*b^6*c^4 - 1180*a*b^4*c^5 + 4560*a^2*b^2*c^6 - 6720*a^3*c^7)*e^3)*x^3 + 8*(737280*(a*b^2*c^7 + a^2*c^8)*d^3 + 120*(7*b^5*c^5 - 88*a*b^3*c^6 + 10608*a^2*b*c^7)*d^2*e - 40*(21*b^6*c^4 - 264*a*b^4*c^5 + 1104*a^2*b^2*c^6 - 2048*a^3*c^7)*d*e^2 + (231*b^7*c^3 - 2988*a*b^5*c^4 + 13200*a^2*b^3*c^5 - 20800*a^3*b*c^6)*e^3)*x^2 + 2*(2949120*a^2*b*c^7*d^3 - 120*(35*b^6*c^4 - 476*a*b^4*c^5 + 2256*a^2*b^2*c^6 - 6720*a^3*c^7)*d^2*e + 40*(105*b^7*c^3 - 1428*a*b^5*c^4 + 6768*a^2*b^3*c^5 - 11968*a^3*b*c^6)*d*e^2 - (1155*b^8*c^2 - 16128*a*b^6*c^3 + 80160*a^2*b^4*c^4 - 158720*a^3*b^2*c^5 + 80640*a^4*c^6)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^7, 1/13762560*(315*(40*(b^8*c^2 - 16*a*b^6*c^3 + 96*a^2*b^4*c^4 - 256*a^3*b^2*c^5 + 256*a^4*c^6)*d^2*e - 40*(b^9*c - 16*a*b^7*c^2 + 96*a^2*b^5*c^3 - 256*a^3*b^3*c^4 + 256*a^4*b*c^5)*d*e^2 + (11*b^10 - 180*a*b^8*c + 1120*a^2*b^6*c^2 - 3200*a^3*b^4*c^3 + 3840*a^4*b^2*c^4 - 1024*a^5*c^5)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(1376256*c^10*e^3*x^9 + 1966080*a^3*c^7*d^3 + 229376*(20*c^10*d*e^2 + 17*b*c^9*e^3)*x^8 + 14336*(360*c^10*d^2*e + 920*b*c^9*d*e^2 + (251*b^2*c^8 + 252*a*c^9)*e^3)*x^7 + 1024*(1920*c^10*d^3 + 14760*b*c^9*d^2*e + 40*(303*b^2*c^8 + 304*a*c^9)*d*e^2 + (1035*b^3*c^7 + 6268*a*b*c^8)*e^3)*x^6 + 256*(23040*b*c^9*d^3 + 120*(475*b^2*c^8 + 476*a*c^9)*d^2*e + 40*(367*b^3*c^7 + 2220*a*b*c^8)*d*e^2 - (5*b^4*c^6 - 10200*a*b^2*c^7 - 10416*a^2*c^8)*e^3)*x^5 + 128*(46080*(b^2*c^8 + a*c^9)*d^3 + 120*(299*b^3*c^7 + 1804*a*b*c^8)*d^2*e - 40*(b^4*c^6 - 1884*a*b^2*c^7 - 1920*a^2*c^8)*d*e^2 + (11*b^5*c^5 - 120*a*b^3*c^6 + 13680*a^2*b*c^7)*e^3)*x^4 + 120*(105*b^7*c^3 - 1540*a*b^5*c^4 + 8176*a^2*b^3*c^5 - 17856*a^3*b*c^6)*d^2*e - 40*(315*b^8*c^2 - 4620*a*b^6*c^3 + 24528*a^2*b^4*c^4 - 53568*a^3*b^2*c^5 + 32768*a^4*c^6)*d*e^2 + (3465*b^9*c - 52080*a*b^7*c^2 + 288288*a^2*b^5*c^3 - 687360*a^3*b^3*c^4 + 574720*a^4*b*c^5)*e^3 + 16*(122880*(b^3*c^7 + 6*a*b*c^8)*d^3 - 120*(3*b^4*c^6 - 6520*a*b^2*c^7 - 6608*a^2*c^8)*d^2*e + 40*(9*b^5*c^5 - 104*a*b^3*c^6 + 10896*a^2*b*c^7)*d*e^2 - (99*b^6*c^4 - 1180*a*b^4*c^5 + 4560*a^2*b^2*c^6 - 6720*a^3*c^7)*e^3)*x^3 + 8*(737280*(a*b^2*c^7 + a^2*c^8)*d^3 + 120*(7*b^5*c^5 - 88*a*b^3*c^6 + 10608*a^2*b*c^7)*d^2*e - 40*(21*b^6*c^4 - 264*a*b^4*c^5 + 1104*a^2*b^2*c^6 - 2048*a^3*c^7)*d*e^2 + (231*b^7*c^3 - 2988*a*b^5*c^4 + 13200*a^2*b^3*c^5 - 20800*a^3*b*c^6)*e^3)*x^2 + 2*(2949120*a^2*b*c^7*d^3 - 120*(35*b^6*c^4 - 476*a*b^4*c^5 + 2256*a^2*b^2*c^6 - 6720*a^3*c^7)*d^2*e + 40*(105*b^7*c^3 - 1428*a*b^5*c^4 + 6768*a^2*b^3*c^5 - 11968*a^3*b*c^6)*d*e^2 - (1155*b^8*c^2 - 16128*a*b^6*c^3 + 80160*a^2*b^4*c^4 - 158720*a^3*b^2*c^5 + 80640*a^4*c^6)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^7]","B",0
1566,1,1523,0,0.756220," ","integrate((2*c*x+b)*(e*x+d)^2*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(2 \, {\left(b^{8} c - 16 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} d e - {\left(b^{9} - 16 \, a b^{7} c + 96 \, a^{2} b^{5} c^{2} - 256 \, a^{3} b^{3} c^{3} + 256 \, a^{4} b c^{4}\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(114688 \, c^{9} e^{2} x^{8} + 147456 \, a^{3} c^{6} d^{2} + 14336 \, {\left(18 \, c^{9} d e + 23 \, b c^{8} e^{2}\right)} x^{7} + 1024 \, {\left(144 \, c^{9} d^{2} + 738 \, b c^{8} d e + {\left(303 \, b^{2} c^{7} + 304 \, a c^{8}\right)} e^{2}\right)} x^{6} + 256 \, {\left(1728 \, b c^{8} d^{2} + 6 \, {\left(475 \, b^{2} c^{7} + 476 \, a c^{8}\right)} d e + {\left(367 \, b^{3} c^{6} + 2220 \, a b c^{7}\right)} e^{2}\right)} x^{5} + 128 \, {\left(3456 \, {\left(b^{2} c^{7} + a c^{8}\right)} d^{2} + 6 \, {\left(299 \, b^{3} c^{6} + 1804 \, a b c^{7}\right)} d e - {\left(b^{4} c^{5} - 1884 \, a b^{2} c^{6} - 1920 \, a^{2} c^{7}\right)} e^{2}\right)} x^{4} + 16 \, {\left(9216 \, {\left(b^{3} c^{6} + 6 \, a b c^{7}\right)} d^{2} - 6 \, {\left(3 \, b^{4} c^{5} - 6520 \, a b^{2} c^{6} - 6608 \, a^{2} c^{7}\right)} d e + {\left(9 \, b^{5} c^{4} - 104 \, a b^{3} c^{5} + 10896 \, a^{2} b c^{6}\right)} e^{2}\right)} x^{3} + 6 \, {\left(105 \, b^{7} c^{2} - 1540 \, a b^{5} c^{3} + 8176 \, a^{2} b^{3} c^{4} - 17856 \, a^{3} b c^{5}\right)} d e - {\left(315 \, b^{8} c - 4620 \, a b^{6} c^{2} + 24528 \, a^{2} b^{4} c^{3} - 53568 \, a^{3} b^{2} c^{4} + 32768 \, a^{4} c^{5}\right)} e^{2} + 8 \, {\left(55296 \, {\left(a b^{2} c^{6} + a^{2} c^{7}\right)} d^{2} + 6 \, {\left(7 \, b^{5} c^{4} - 88 \, a b^{3} c^{5} + 10608 \, a^{2} b c^{6}\right)} d e - {\left(21 \, b^{6} c^{3} - 264 \, a b^{4} c^{4} + 1104 \, a^{2} b^{2} c^{5} - 2048 \, a^{3} c^{6}\right)} e^{2}\right)} x^{2} + 2 \, {\left(221184 \, a^{2} b c^{6} d^{2} - 6 \, {\left(35 \, b^{6} c^{3} - 476 \, a b^{4} c^{4} + 2256 \, a^{2} b^{2} c^{5} - 6720 \, a^{3} c^{6}\right)} d e + {\left(105 \, b^{7} c^{2} - 1428 \, a b^{5} c^{3} + 6768 \, a^{2} b^{3} c^{4} - 11968 \, a^{3} b c^{5}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2064384 \, c^{6}}, \frac{315 \, {\left(2 \, {\left(b^{8} c - 16 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} d e - {\left(b^{9} - 16 \, a b^{7} c + 96 \, a^{2} b^{5} c^{2} - 256 \, a^{3} b^{3} c^{3} + 256 \, a^{4} b c^{4}\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(114688 \, c^{9} e^{2} x^{8} + 147456 \, a^{3} c^{6} d^{2} + 14336 \, {\left(18 \, c^{9} d e + 23 \, b c^{8} e^{2}\right)} x^{7} + 1024 \, {\left(144 \, c^{9} d^{2} + 738 \, b c^{8} d e + {\left(303 \, b^{2} c^{7} + 304 \, a c^{8}\right)} e^{2}\right)} x^{6} + 256 \, {\left(1728 \, b c^{8} d^{2} + 6 \, {\left(475 \, b^{2} c^{7} + 476 \, a c^{8}\right)} d e + {\left(367 \, b^{3} c^{6} + 2220 \, a b c^{7}\right)} e^{2}\right)} x^{5} + 128 \, {\left(3456 \, {\left(b^{2} c^{7} + a c^{8}\right)} d^{2} + 6 \, {\left(299 \, b^{3} c^{6} + 1804 \, a b c^{7}\right)} d e - {\left(b^{4} c^{5} - 1884 \, a b^{2} c^{6} - 1920 \, a^{2} c^{7}\right)} e^{2}\right)} x^{4} + 16 \, {\left(9216 \, {\left(b^{3} c^{6} + 6 \, a b c^{7}\right)} d^{2} - 6 \, {\left(3 \, b^{4} c^{5} - 6520 \, a b^{2} c^{6} - 6608 \, a^{2} c^{7}\right)} d e + {\left(9 \, b^{5} c^{4} - 104 \, a b^{3} c^{5} + 10896 \, a^{2} b c^{6}\right)} e^{2}\right)} x^{3} + 6 \, {\left(105 \, b^{7} c^{2} - 1540 \, a b^{5} c^{3} + 8176 \, a^{2} b^{3} c^{4} - 17856 \, a^{3} b c^{5}\right)} d e - {\left(315 \, b^{8} c - 4620 \, a b^{6} c^{2} + 24528 \, a^{2} b^{4} c^{3} - 53568 \, a^{3} b^{2} c^{4} + 32768 \, a^{4} c^{5}\right)} e^{2} + 8 \, {\left(55296 \, {\left(a b^{2} c^{6} + a^{2} c^{7}\right)} d^{2} + 6 \, {\left(7 \, b^{5} c^{4} - 88 \, a b^{3} c^{5} + 10608 \, a^{2} b c^{6}\right)} d e - {\left(21 \, b^{6} c^{3} - 264 \, a b^{4} c^{4} + 1104 \, a^{2} b^{2} c^{5} - 2048 \, a^{3} c^{6}\right)} e^{2}\right)} x^{2} + 2 \, {\left(221184 \, a^{2} b c^{6} d^{2} - 6 \, {\left(35 \, b^{6} c^{3} - 476 \, a b^{4} c^{4} + 2256 \, a^{2} b^{2} c^{5} - 6720 \, a^{3} c^{6}\right)} d e + {\left(105 \, b^{7} c^{2} - 1428 \, a b^{5} c^{3} + 6768 \, a^{2} b^{3} c^{4} - 11968 \, a^{3} b c^{5}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1032192 \, c^{6}}\right]"," ",0,"[-1/2064384*(315*(2*(b^8*c - 16*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^3*b^2*c^4 + 256*a^4*c^5)*d*e - (b^9 - 16*a*b^7*c + 96*a^2*b^5*c^2 - 256*a^3*b^3*c^3 + 256*a^4*b*c^4)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(114688*c^9*e^2*x^8 + 147456*a^3*c^6*d^2 + 14336*(18*c^9*d*e + 23*b*c^8*e^2)*x^7 + 1024*(144*c^9*d^2 + 738*b*c^8*d*e + (303*b^2*c^7 + 304*a*c^8)*e^2)*x^6 + 256*(1728*b*c^8*d^2 + 6*(475*b^2*c^7 + 476*a*c^8)*d*e + (367*b^3*c^6 + 2220*a*b*c^7)*e^2)*x^5 + 128*(3456*(b^2*c^7 + a*c^8)*d^2 + 6*(299*b^3*c^6 + 1804*a*b*c^7)*d*e - (b^4*c^5 - 1884*a*b^2*c^6 - 1920*a^2*c^7)*e^2)*x^4 + 16*(9216*(b^3*c^6 + 6*a*b*c^7)*d^2 - 6*(3*b^4*c^5 - 6520*a*b^2*c^6 - 6608*a^2*c^7)*d*e + (9*b^5*c^4 - 104*a*b^3*c^5 + 10896*a^2*b*c^6)*e^2)*x^3 + 6*(105*b^7*c^2 - 1540*a*b^5*c^3 + 8176*a^2*b^3*c^4 - 17856*a^3*b*c^5)*d*e - (315*b^8*c - 4620*a*b^6*c^2 + 24528*a^2*b^4*c^3 - 53568*a^3*b^2*c^4 + 32768*a^4*c^5)*e^2 + 8*(55296*(a*b^2*c^6 + a^2*c^7)*d^2 + 6*(7*b^5*c^4 - 88*a*b^3*c^5 + 10608*a^2*b*c^6)*d*e - (21*b^6*c^3 - 264*a*b^4*c^4 + 1104*a^2*b^2*c^5 - 2048*a^3*c^6)*e^2)*x^2 + 2*(221184*a^2*b*c^6*d^2 - 6*(35*b^6*c^3 - 476*a*b^4*c^4 + 2256*a^2*b^2*c^5 - 6720*a^3*c^6)*d*e + (105*b^7*c^2 - 1428*a*b^5*c^3 + 6768*a^2*b^3*c^4 - 11968*a^3*b*c^5)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/1032192*(315*(2*(b^8*c - 16*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^3*b^2*c^4 + 256*a^4*c^5)*d*e - (b^9 - 16*a*b^7*c + 96*a^2*b^5*c^2 - 256*a^3*b^3*c^3 + 256*a^4*b*c^4)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(114688*c^9*e^2*x^8 + 147456*a^3*c^6*d^2 + 14336*(18*c^9*d*e + 23*b*c^8*e^2)*x^7 + 1024*(144*c^9*d^2 + 738*b*c^8*d*e + (303*b^2*c^7 + 304*a*c^8)*e^2)*x^6 + 256*(1728*b*c^8*d^2 + 6*(475*b^2*c^7 + 476*a*c^8)*d*e + (367*b^3*c^6 + 2220*a*b*c^7)*e^2)*x^5 + 128*(3456*(b^2*c^7 + a*c^8)*d^2 + 6*(299*b^3*c^6 + 1804*a*b*c^7)*d*e - (b^4*c^5 - 1884*a*b^2*c^6 - 1920*a^2*c^7)*e^2)*x^4 + 16*(9216*(b^3*c^6 + 6*a*b*c^7)*d^2 - 6*(3*b^4*c^5 - 6520*a*b^2*c^6 - 6608*a^2*c^7)*d*e + (9*b^5*c^4 - 104*a*b^3*c^5 + 10896*a^2*b*c^6)*e^2)*x^3 + 6*(105*b^7*c^2 - 1540*a*b^5*c^3 + 8176*a^2*b^3*c^4 - 17856*a^3*b*c^5)*d*e - (315*b^8*c - 4620*a*b^6*c^2 + 24528*a^2*b^4*c^3 - 53568*a^3*b^2*c^4 + 32768*a^4*c^5)*e^2 + 8*(55296*(a*b^2*c^6 + a^2*c^7)*d^2 + 6*(7*b^5*c^4 - 88*a*b^3*c^5 + 10608*a^2*b*c^6)*d*e - (21*b^6*c^3 - 264*a*b^4*c^4 + 1104*a^2*b^2*c^5 - 2048*a^3*c^6)*e^2)*x^2 + 2*(221184*a^2*b*c^6*d^2 - 6*(35*b^6*c^3 - 476*a*b^4*c^4 + 2256*a^2*b^2*c^5 - 6720*a^3*c^6)*d*e + (105*b^7*c^2 - 1428*a*b^5*c^3 + 6768*a^2*b^3*c^4 - 11968*a^3*b*c^5)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^6]","B",0
1567,1,841,0,0.525303," ","integrate((2*c*x+b)*(e*x+d)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{c} e \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(43008 \, c^{8} e x^{7} + 49152 \, a^{3} c^{5} d + 3072 \, {\left(16 \, c^{8} d + 41 \, b c^{7} e\right)} x^{6} + 256 \, {\left(576 \, b c^{7} d + {\left(475 \, b^{2} c^{6} + 476 \, a c^{7}\right)} e\right)} x^{5} + 128 \, {\left(1152 \, {\left(b^{2} c^{6} + a c^{7}\right)} d + {\left(299 \, b^{3} c^{5} + 1804 \, a b c^{6}\right)} e\right)} x^{4} + 16 \, {\left(3072 \, {\left(b^{3} c^{5} + 6 \, a b c^{6}\right)} d - {\left(3 \, b^{4} c^{4} - 6520 \, a b^{2} c^{5} - 6608 \, a^{2} c^{6}\right)} e\right)} x^{3} + 8 \, {\left(18432 \, {\left(a b^{2} c^{5} + a^{2} c^{6}\right)} d + {\left(7 \, b^{5} c^{3} - 88 \, a b^{3} c^{4} + 10608 \, a^{2} b c^{5}\right)} e\right)} x^{2} + {\left(105 \, b^{7} c - 1540 \, a b^{5} c^{2} + 8176 \, a^{2} b^{3} c^{3} - 17856 \, a^{3} b c^{4}\right)} e + 2 \, {\left(73728 \, a^{2} b c^{5} d - {\left(35 \, b^{6} c^{2} - 476 \, a b^{4} c^{3} + 2256 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{688128 \, c^{5}}, \frac{105 \, {\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{-c} e \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(43008 \, c^{8} e x^{7} + 49152 \, a^{3} c^{5} d + 3072 \, {\left(16 \, c^{8} d + 41 \, b c^{7} e\right)} x^{6} + 256 \, {\left(576 \, b c^{7} d + {\left(475 \, b^{2} c^{6} + 476 \, a c^{7}\right)} e\right)} x^{5} + 128 \, {\left(1152 \, {\left(b^{2} c^{6} + a c^{7}\right)} d + {\left(299 \, b^{3} c^{5} + 1804 \, a b c^{6}\right)} e\right)} x^{4} + 16 \, {\left(3072 \, {\left(b^{3} c^{5} + 6 \, a b c^{6}\right)} d - {\left(3 \, b^{4} c^{4} - 6520 \, a b^{2} c^{5} - 6608 \, a^{2} c^{6}\right)} e\right)} x^{3} + 8 \, {\left(18432 \, {\left(a b^{2} c^{5} + a^{2} c^{6}\right)} d + {\left(7 \, b^{5} c^{3} - 88 \, a b^{3} c^{4} + 10608 \, a^{2} b c^{5}\right)} e\right)} x^{2} + {\left(105 \, b^{7} c - 1540 \, a b^{5} c^{2} + 8176 \, a^{2} b^{3} c^{3} - 17856 \, a^{3} b c^{4}\right)} e + 2 \, {\left(73728 \, a^{2} b c^{5} d - {\left(35 \, b^{6} c^{2} - 476 \, a b^{4} c^{3} + 2256 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{344064 \, c^{5}}\right]"," ",0,"[1/688128*(105*(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(c)*e*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(43008*c^8*e*x^7 + 49152*a^3*c^5*d + 3072*(16*c^8*d + 41*b*c^7*e)*x^6 + 256*(576*b*c^7*d + (475*b^2*c^6 + 476*a*c^7)*e)*x^5 + 128*(1152*(b^2*c^6 + a*c^7)*d + (299*b^3*c^5 + 1804*a*b*c^6)*e)*x^4 + 16*(3072*(b^3*c^5 + 6*a*b*c^6)*d - (3*b^4*c^4 - 6520*a*b^2*c^5 - 6608*a^2*c^6)*e)*x^3 + 8*(18432*(a*b^2*c^5 + a^2*c^6)*d + (7*b^5*c^3 - 88*a*b^3*c^4 + 10608*a^2*b*c^5)*e)*x^2 + (105*b^7*c - 1540*a*b^5*c^2 + 8176*a^2*b^3*c^3 - 17856*a^3*b*c^4)*e + 2*(73728*a^2*b*c^5*d - (35*b^6*c^2 - 476*a*b^4*c^3 + 2256*a^2*b^2*c^4 - 6720*a^3*c^5)*e)*x)*sqrt(c*x^2 + b*x + a))/c^5, 1/344064*(105*(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(-c)*e*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(43008*c^8*e*x^7 + 49152*a^3*c^5*d + 3072*(16*c^8*d + 41*b*c^7*e)*x^6 + 256*(576*b*c^7*d + (475*b^2*c^6 + 476*a*c^7)*e)*x^5 + 128*(1152*(b^2*c^6 + a*c^7)*d + (299*b^3*c^5 + 1804*a*b*c^6)*e)*x^4 + 16*(3072*(b^3*c^5 + 6*a*b*c^6)*d - (3*b^4*c^4 - 6520*a*b^2*c^5 - 6608*a^2*c^6)*e)*x^3 + 8*(18432*(a*b^2*c^5 + a^2*c^6)*d + (7*b^5*c^3 - 88*a*b^3*c^4 + 10608*a^2*b*c^5)*e)*x^2 + (105*b^7*c - 1540*a*b^5*c^2 + 8176*a^2*b^3*c^3 - 17856*a^3*b*c^4)*e + 2*(73728*a^2*b*c^5*d - (35*b^6*c^2 - 476*a*b^4*c^3 + 2256*a^2*b^2*c^4 - 6720*a^3*c^5)*e)*x)*sqrt(c*x^2 + b*x + a))/c^5]","B",0
1568,1,86,0,0.441224," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2}{7} \, {\left(c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/7*(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2)*sqrt(c*x^2 + b*x + a)","B",0
1569,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1570,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1571,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1572,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1573,1,545,0,0.719384," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(16 \, c^{4} e^{3} x^{3} + 64 \, c^{4} d^{3} - 48 \, b c^{3} d^{2} e + 16 \, {\left(3 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d e^{2} - {\left(15 \, b^{3} c - 52 \, a b c^{2}\right)} e^{3} + 8 \, {\left(8 \, c^{4} d e^{2} - b c^{3} e^{3}\right)} x^{2} + 2 \, {\left(48 \, c^{4} d^{2} e - 16 \, b c^{3} d e^{2} + {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{128 \, c^{4}}, -\frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(16 \, c^{4} e^{3} x^{3} + 64 \, c^{4} d^{3} - 48 \, b c^{3} d^{2} e + 16 \, {\left(3 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d e^{2} - {\left(15 \, b^{3} c - 52 \, a b c^{2}\right)} e^{3} + 8 \, {\left(8 \, c^{4} d e^{2} - b c^{3} e^{3}\right)} x^{2} + 2 \, {\left(48 \, c^{4} d^{2} e - 16 \, b c^{3} d e^{2} + {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{64 \, c^{4}}\right]"," ",0,"[1/128*(3*(16*(b^2*c^2 - 4*a*c^3)*d^2*e - 16*(b^3*c - 4*a*b*c^2)*d*e^2 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(16*c^4*e^3*x^3 + 64*c^4*d^3 - 48*b*c^3*d^2*e + 16*(3*b^2*c^2 - 8*a*c^3)*d*e^2 - (15*b^3*c - 52*a*b*c^2)*e^3 + 8*(8*c^4*d*e^2 - b*c^3*e^3)*x^2 + 2*(48*c^4*d^2*e - 16*b*c^3*d*e^2 + (5*b^2*c^2 - 12*a*c^3)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^4, -1/64*(3*(16*(b^2*c^2 - 4*a*c^3)*d^2*e - 16*(b^3*c - 4*a*b*c^2)*d*e^2 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(16*c^4*e^3*x^3 + 64*c^4*d^3 - 48*b*c^3*d^2*e + 16*(3*b^2*c^2 - 8*a*c^3)*d*e^2 - (15*b^3*c - 52*a*b*c^2)*e^3 + 8*(8*c^4*d*e^2 - b*c^3*e^3)*x^2 + 2*(48*c^4*d^2*e - 16*b*c^3*d*e^2 + (5*b^2*c^2 - 12*a*c^3)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
1574,1,335,0,0.811273," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e - {\left(b^{3} - 4 \, a b c\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(4 \, c^{3} e^{2} x^{2} + 12 \, c^{3} d^{2} - 6 \, b c^{2} d e + {\left(3 \, b^{2} c - 8 \, a c^{2}\right)} e^{2} + 2 \, {\left(6 \, c^{3} d e - b c^{2} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{24 \, c^{3}}, -\frac{3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e - {\left(b^{3} - 4 \, a b c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(4 \, c^{3} e^{2} x^{2} + 12 \, c^{3} d^{2} - 6 \, b c^{2} d e + {\left(3 \, b^{2} c - 8 \, a c^{2}\right)} e^{2} + 2 \, {\left(6 \, c^{3} d e - b c^{2} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, c^{3}}\right]"," ",0,"[1/24*(3*(2*(b^2*c - 4*a*c^2)*d*e - (b^3 - 4*a*b*c)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(4*c^3*e^2*x^2 + 12*c^3*d^2 - 6*b*c^2*d*e + (3*b^2*c - 8*a*c^2)*e^2 + 2*(6*c^3*d*e - b*c^2*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^3, -1/12*(3*(2*(b^2*c - 4*a*c^2)*d*e - (b^3 - 4*a*b*c)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(4*c^3*e^2*x^2 + 12*c^3*d^2 - 6*b*c^2*d*e + (3*b^2*c - 8*a*c^2)*e^2 + 2*(6*c^3*d*e - b*c^2*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
1575,1,197,0,0.747286," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{c} e \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, c^{2} e x + 4 \, c^{2} d - b c e\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{2}}, -\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-c} e \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2 \, c^{2} e x + 4 \, c^{2} d - b c e\right)} \sqrt{c x^{2} + b x + a}}{4 \, c^{2}}\right]"," ",0,"[-1/8*((b^2 - 4*a*c)*sqrt(c)*e*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(2*c^2*e*x + 4*c^2*d - b*c*e)*sqrt(c*x^2 + b*x + a))/c^2, -1/4*((b^2 - 4*a*c)*sqrt(-c)*e*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2*c^2*e*x + 4*c^2*d - b*c*e)*sqrt(c*x^2 + b*x + a))/c^2]","A",0
1576,1,14,0,0.555199," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{c x^{2} + b x + a}"," ",0,"2*sqrt(c*x^2 + b*x + a)","A",0
1577,1,1048,0,2.621500," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - \sqrt{c d^{2} - b d e + a e^{2}} {\left(2 \, c d - b e\right)} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)}}, -\frac{\sqrt{-c d^{2} + b d e - a e^{2}} {\left(2 \, c d - b e\right)} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{c d^{2} e - b d e^{2} + a e^{3}}, -\frac{4 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + \sqrt{c d^{2} - b d e + a e^{2}} {\left(2 \, c d - b e\right)} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)}}, -\frac{\sqrt{-c d^{2} + b d e - a e^{2}} {\left(2 \, c d - b e\right)} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{c d^{2} e - b d e^{2} + a e^{3}}\right]"," ",0,"[1/2*(2*(c*d^2 - b*d*e + a*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - sqrt(c*d^2 - b*d*e + a*e^2)*(2*c*d - b*e)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c*d^2*e - b*d*e^2 + a*e^3), -(sqrt(-c*d^2 + b*d*e - a*e^2)*(2*c*d - b*e)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - (c*d^2 - b*d*e + a*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c))/(c*d^2*e - b*d*e^2 + a*e^3), -1/2*(4*(c*d^2 - b*d*e + a*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + sqrt(c*d^2 - b*d*e + a*e^2)*(2*c*d - b*e)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c*d^2*e - b*d*e^2 + a*e^3), -(sqrt(-c*d^2 + b*d*e - a*e^2)*(2*c*d - b*e)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(c*d^2 - b*d*e + a*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)))/(c*d^2*e - b*d*e^2 + a*e^3)]","B",0
1578,1,686,0,0.642431," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(b^{2} - 4 \, a c\right)} e^{2} x + {\left(b^{2} - 4 \, a c\right)} d e\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e - a b e^{3} + {\left(b^{2} + 2 \, a c\right)} d e^{2}\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e - 2 \, a b d^{2} e^{3} + a^{2} d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + a^{2} e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)}}, -\frac{{\left({\left(b^{2} - 4 \, a c\right)} e^{2} x + {\left(b^{2} - 4 \, a c\right)} d e\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e - a b e^{3} + {\left(b^{2} + 2 \, a c\right)} d e^{2}\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e - 2 \, a b d^{2} e^{3} + a^{2} d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + a^{2} e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/4*(((b^2 - 4*a*c)*e^2*x + (b^2 - 4*a*c)*d*e)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(2*c^2*d^3 - 3*b*c*d^2*e - a*b*e^3 + (b^2 + 2*a*c)*d*e^2)*sqrt(c*x^2 + b*x + a))/(c^2*d^5 - 2*b*c*d^4*e - 2*a*b*d^2*e^3 + a^2*d*e^4 + (b^2 + 2*a*c)*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + a^2*e^5 + (b^2 + 2*a*c)*d^2*e^3)*x), -1/2*(((b^2 - 4*a*c)*e^2*x + (b^2 - 4*a*c)*d*e)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(2*c^2*d^3 - 3*b*c*d^2*e - a*b*e^3 + (b^2 + 2*a*c)*d*e^2)*sqrt(c*x^2 + b*x + a))/(c^2*d^5 - 2*b*c*d^4*e - 2*a*b*d^2*e^3 + a^2*d*e^4 + (b^2 + 2*a*c)*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + a^2*e^5 + (b^2 + 2*a*c)*d^2*e^3)*x)]","B",0
1579,1,1500,0,1.310027," ","integrate((2*c*x+b)/(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} e - {\left(b^{3} - 4 \, a b c\right)} d^{2} e^{2} + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{3} - {\left(b^{3} - 4 \, a b c\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} - 4 \, a b c\right)} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(8 \, c^{3} d^{5} - 18 \, b c^{2} d^{4} e - 2 \, a^{2} b e^{5} + {\left(15 \, b^{2} c + 4 \, a c^{2}\right)} d^{3} e^{2} - {\left(5 \, b^{3} + 8 \, a b c\right)} d^{2} e^{3} + {\left(7 \, a b^{2} - 4 \, a^{2} c\right)} d e^{4} + {\left(4 \, c^{3} d^{4} e - 8 \, b c^{2} d^{3} e^{2} + {\left(7 \, b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{3} - 4 \, a b c\right)} d e^{4} + {\left(3 \, a b^{2} - 8 \, a^{2} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e - 3 \, a^{2} b d^{3} e^{5} + a^{3} d^{2} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} - 3 \, a^{2} b d e^{7} + a^{3} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} - 3 \, a^{2} b d^{2} e^{6} + a^{3} d e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)}}, -\frac{3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} e - {\left(b^{3} - 4 \, a b c\right)} d^{2} e^{2} + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{3} - {\left(b^{3} - 4 \, a b c\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} - 4 \, a b c\right)} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, c^{3} d^{5} - 18 \, b c^{2} d^{4} e - 2 \, a^{2} b e^{5} + {\left(15 \, b^{2} c + 4 \, a c^{2}\right)} d^{3} e^{2} - {\left(5 \, b^{3} + 8 \, a b c\right)} d^{2} e^{3} + {\left(7 \, a b^{2} - 4 \, a^{2} c\right)} d e^{4} + {\left(4 \, c^{3} d^{4} e - 8 \, b c^{2} d^{3} e^{2} + {\left(7 \, b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{3} - 4 \, a b c\right)} d e^{4} + {\left(3 \, a b^{2} - 8 \, a^{2} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e - 3 \, a^{2} b d^{3} e^{5} + a^{3} d^{2} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} - 3 \, a^{2} b d e^{7} + a^{3} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} - 3 \, a^{2} b d^{2} e^{6} + a^{3} d e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)}}\right]"," ",0,"[1/16*(3*(2*(b^2*c - 4*a*c^2)*d^3*e - (b^3 - 4*a*b*c)*d^2*e^2 + (2*(b^2*c - 4*a*c^2)*d*e^3 - (b^3 - 4*a*b*c)*e^4)*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^2*e^2 - (b^3 - 4*a*b*c)*d*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(8*c^3*d^5 - 18*b*c^2*d^4*e - 2*a^2*b*e^5 + (15*b^2*c + 4*a*c^2)*d^3*e^2 - (5*b^3 + 8*a*b*c)*d^2*e^3 + (7*a*b^2 - 4*a^2*c)*d*e^4 + (4*c^3*d^4*e - 8*b*c^2*d^3*e^2 + (7*b^2*c - 4*a*c^2)*d^2*e^3 - (3*b^3 - 4*a*b*c)*d*e^4 + (3*a*b^2 - 8*a^2*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^8 - 3*b*c^2*d^7*e - 3*a^2*b*d^3*e^5 + a^3*d^2*e^6 + 3*(b^2*c + a*c^2)*d^6*e^2 - (b^3 + 6*a*b*c)*d^5*e^3 + 3*(a*b^2 + a^2*c)*d^4*e^4 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 - 3*a^2*b*d*e^7 + a^3*e^8 + 3*(b^2*c + a*c^2)*d^4*e^4 - (b^3 + 6*a*b*c)*d^3*e^5 + 3*(a*b^2 + a^2*c)*d^2*e^6)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 - 3*a^2*b*d^2*e^6 + a^3*d*e^7 + 3*(b^2*c + a*c^2)*d^5*e^3 - (b^3 + 6*a*b*c)*d^4*e^4 + 3*(a*b^2 + a^2*c)*d^3*e^5)*x), -1/8*(3*(2*(b^2*c - 4*a*c^2)*d^3*e - (b^3 - 4*a*b*c)*d^2*e^2 + (2*(b^2*c - 4*a*c^2)*d*e^3 - (b^3 - 4*a*b*c)*e^4)*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^2*e^2 - (b^3 - 4*a*b*c)*d*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(8*c^3*d^5 - 18*b*c^2*d^4*e - 2*a^2*b*e^5 + (15*b^2*c + 4*a*c^2)*d^3*e^2 - (5*b^3 + 8*a*b*c)*d^2*e^3 + (7*a*b^2 - 4*a^2*c)*d*e^4 + (4*c^3*d^4*e - 8*b*c^2*d^3*e^2 + (7*b^2*c - 4*a*c^2)*d^2*e^3 - (3*b^3 - 4*a*b*c)*d*e^4 + (3*a*b^2 - 8*a^2*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^8 - 3*b*c^2*d^7*e - 3*a^2*b*d^3*e^5 + a^3*d^2*e^6 + 3*(b^2*c + a*c^2)*d^6*e^2 - (b^3 + 6*a*b*c)*d^5*e^3 + 3*(a*b^2 + a^2*c)*d^4*e^4 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 - 3*a^2*b*d*e^7 + a^3*e^8 + 3*(b^2*c + a*c^2)*d^4*e^4 - (b^3 + 6*a*b*c)*d^3*e^5 + 3*(a*b^2 + a^2*c)*d^2*e^6)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 - 3*a^2*b*d^2*e^6 + a^3*d*e^7 + 3*(b^2*c + a*c^2)*d^5*e^3 - (b^3 + 6*a*b*c)*d^4*e^4 + 3*(a*b^2 + a^2*c)*d^3*e^5)*x)]","B",0
1580,1,2998,0,5.894706," ","integrate((2*c*x+b)/(e*x+d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} e - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} e^{2} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} e^{3} + {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{4} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{6}\right)} x^{3} + 3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{3} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{4} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d e^{5}\right)} x^{2} + 3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e^{2} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{3} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(48 \, c^{4} d^{7} - 144 \, b c^{3} d^{6} e - 8 \, a^{3} b e^{7} + 32 \, {\left(6 \, b^{2} c^{2} - a c^{3}\right)} d^{5} e^{2} - {\left(129 \, b^{3} c + 4 \, a b c^{2}\right)} d^{4} e^{3} + 11 \, {\left(3 \, b^{4} + 10 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{4} - {\left(59 \, a b^{3} - 12 \, a^{2} b c\right)} d^{2} e^{5} + 2 \, {\left(17 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{6} + {\left(16 \, c^{4} d^{5} e^{2} - 40 \, b c^{3} d^{4} e^{3} + 2 \, {\left(31 \, b^{2} c^{2} - 44 \, a c^{3}\right)} d^{3} e^{4} - {\left(53 \, b^{3} c - 132 \, a b c^{2}\right)} d^{2} e^{5} + {\left(15 \, b^{4} - 14 \, a b^{2} c - 104 \, a^{2} c^{2}\right)} d e^{6} - {\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} e^{7}\right)} x^{2} + 2 \, {\left(24 \, c^{4} d^{6} e - 64 \, b c^{3} d^{5} e^{2} + 7 \, {\left(13 \, b^{2} c^{2} - 12 \, a c^{3}\right)} d^{4} e^{3} - {\left(71 \, b^{3} c - 124 \, a b c^{2}\right)} d^{3} e^{4} + 20 \, {\left(b^{4} - 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - {\left(25 \, a b^{3} - 68 \, a^{2} b c\right)} d e^{6} + {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(c^{4} d^{11} - 4 \, b c^{3} d^{10} e - 4 \, a^{3} b d^{4} e^{7} + a^{4} d^{3} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{6} + {\left(c^{4} d^{8} e^{3} - 4 \, b c^{3} d^{7} e^{4} - 4 \, a^{3} b d e^{10} + a^{4} e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{9}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} - 4 \, b c^{3} d^{8} e^{3} - 4 \, a^{3} b d^{2} e^{9} + a^{4} d e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{8}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e - 4 \, b c^{3} d^{9} e^{2} - 4 \, a^{3} b d^{3} e^{8} + a^{4} d^{2} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{7}\right)} x\right)}}, -\frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} e - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} e^{2} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} e^{3} + {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{4} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{6}\right)} x^{3} + 3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{3} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{4} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d e^{5}\right)} x^{2} + 3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e^{2} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{3} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, c^{4} d^{7} - 144 \, b c^{3} d^{6} e - 8 \, a^{3} b e^{7} + 32 \, {\left(6 \, b^{2} c^{2} - a c^{3}\right)} d^{5} e^{2} - {\left(129 \, b^{3} c + 4 \, a b c^{2}\right)} d^{4} e^{3} + 11 \, {\left(3 \, b^{4} + 10 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{4} - {\left(59 \, a b^{3} - 12 \, a^{2} b c\right)} d^{2} e^{5} + 2 \, {\left(17 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{6} + {\left(16 \, c^{4} d^{5} e^{2} - 40 \, b c^{3} d^{4} e^{3} + 2 \, {\left(31 \, b^{2} c^{2} - 44 \, a c^{3}\right)} d^{3} e^{4} - {\left(53 \, b^{3} c - 132 \, a b c^{2}\right)} d^{2} e^{5} + {\left(15 \, b^{4} - 14 \, a b^{2} c - 104 \, a^{2} c^{2}\right)} d e^{6} - {\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} e^{7}\right)} x^{2} + 2 \, {\left(24 \, c^{4} d^{6} e - 64 \, b c^{3} d^{5} e^{2} + 7 \, {\left(13 \, b^{2} c^{2} - 12 \, a c^{3}\right)} d^{4} e^{3} - {\left(71 \, b^{3} c - 124 \, a b c^{2}\right)} d^{3} e^{4} + 20 \, {\left(b^{4} - 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - {\left(25 \, a b^{3} - 68 \, a^{2} b c\right)} d e^{6} + {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(c^{4} d^{11} - 4 \, b c^{3} d^{10} e - 4 \, a^{3} b d^{4} e^{7} + a^{4} d^{3} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{6} + {\left(c^{4} d^{8} e^{3} - 4 \, b c^{3} d^{7} e^{4} - 4 \, a^{3} b d e^{10} + a^{4} e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{9}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} - 4 \, b c^{3} d^{8} e^{3} - 4 \, a^{3} b d^{2} e^{9} + a^{4} d e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{8}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e - 4 \, b c^{3} d^{9} e^{2} - 4 \, a^{3} b d^{3} e^{8} + a^{4} d^{2} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{7}\right)} x\right)}}\right]"," ",0,"[1/96*(3*(16*(b^2*c^2 - 4*a*c^3)*d^5*e - 16*(b^3*c - 4*a*b*c^2)*d^4*e^2 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^3*e^3 + (16*(b^2*c^2 - 4*a*c^3)*d^2*e^4 - 16*(b^3*c - 4*a*b*c^2)*d*e^5 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*e^6)*x^3 + 3*(16*(b^2*c^2 - 4*a*c^3)*d^3*e^3 - 16*(b^3*c - 4*a*b*c^2)*d^2*e^4 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d*e^5)*x^2 + 3*(16*(b^2*c^2 - 4*a*c^3)*d^4*e^2 - 16*(b^3*c - 4*a*b*c^2)*d^3*e^3 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^2*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(48*c^4*d^7 - 144*b*c^3*d^6*e - 8*a^3*b*e^7 + 32*(6*b^2*c^2 - a*c^3)*d^5*e^2 - (129*b^3*c + 4*a*b*c^2)*d^4*e^3 + 11*(3*b^4 + 10*a*b^2*c - 8*a^2*c^2)*d^3*e^4 - (59*a*b^3 - 12*a^2*b*c)*d^2*e^5 + 2*(17*a^2*b^2 - 4*a^3*c)*d*e^6 + (16*c^4*d^5*e^2 - 40*b*c^3*d^4*e^3 + 2*(31*b^2*c^2 - 44*a*c^3)*d^3*e^4 - (53*b^3*c - 132*a*b*c^2)*d^2*e^5 + (15*b^4 - 14*a*b^2*c - 104*a^2*c^2)*d*e^6 - (15*a*b^3 - 52*a^2*b*c)*e^7)*x^2 + 2*(24*c^4*d^6*e - 64*b*c^3*d^5*e^2 + 7*(13*b^2*c^2 - 12*a*c^3)*d^4*e^3 - (71*b^3*c - 124*a*b*c^2)*d^3*e^4 + 20*(b^4 - 6*a^2*c^2)*d^2*e^5 - (25*a*b^3 - 68*a^2*b*c)*d*e^6 + (5*a^2*b^2 - 12*a^3*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^11 - 4*b*c^3*d^10*e - 4*a^3*b*d^4*e^7 + a^4*d^3*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^6 + (c^4*d^8*e^3 - 4*b*c^3*d^7*e^4 - 4*a^3*b*d*e^10 + a^4*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^9)*x^3 + 3*(c^4*d^9*e^2 - 4*b*c^3*d^8*e^3 - 4*a^3*b*d^2*e^9 + a^4*d*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^8)*x^2 + 3*(c^4*d^10*e - 4*b*c^3*d^9*e^2 - 4*a^3*b*d^3*e^8 + a^4*d^2*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^7)*x), -1/48*(3*(16*(b^2*c^2 - 4*a*c^3)*d^5*e - 16*(b^3*c - 4*a*b*c^2)*d^4*e^2 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^3*e^3 + (16*(b^2*c^2 - 4*a*c^3)*d^2*e^4 - 16*(b^3*c - 4*a*b*c^2)*d*e^5 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*e^6)*x^3 + 3*(16*(b^2*c^2 - 4*a*c^3)*d^3*e^3 - 16*(b^3*c - 4*a*b*c^2)*d^2*e^4 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d*e^5)*x^2 + 3*(16*(b^2*c^2 - 4*a*c^3)*d^4*e^2 - 16*(b^3*c - 4*a*b*c^2)*d^3*e^3 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^2*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(48*c^4*d^7 - 144*b*c^3*d^6*e - 8*a^3*b*e^7 + 32*(6*b^2*c^2 - a*c^3)*d^5*e^2 - (129*b^3*c + 4*a*b*c^2)*d^4*e^3 + 11*(3*b^4 + 10*a*b^2*c - 8*a^2*c^2)*d^3*e^4 - (59*a*b^3 - 12*a^2*b*c)*d^2*e^5 + 2*(17*a^2*b^2 - 4*a^3*c)*d*e^6 + (16*c^4*d^5*e^2 - 40*b*c^3*d^4*e^3 + 2*(31*b^2*c^2 - 44*a*c^3)*d^3*e^4 - (53*b^3*c - 132*a*b*c^2)*d^2*e^5 + (15*b^4 - 14*a*b^2*c - 104*a^2*c^2)*d*e^6 - (15*a*b^3 - 52*a^2*b*c)*e^7)*x^2 + 2*(24*c^4*d^6*e - 64*b*c^3*d^5*e^2 + 7*(13*b^2*c^2 - 12*a*c^3)*d^4*e^3 - (71*b^3*c - 124*a*b*c^2)*d^3*e^4 + 20*(b^4 - 6*a^2*c^2)*d^2*e^5 - (25*a*b^3 - 68*a^2*b*c)*d*e^6 + (5*a^2*b^2 - 12*a^3*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^11 - 4*b*c^3*d^10*e - 4*a^3*b*d^4*e^7 + a^4*d^3*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^6 + (c^4*d^8*e^3 - 4*b*c^3*d^7*e^4 - 4*a^3*b*d*e^10 + a^4*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^9)*x^3 + 3*(c^4*d^9*e^2 - 4*b*c^3*d^8*e^3 - 4*a^3*b*d^2*e^9 + a^4*d*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^8)*x^2 + 3*(c^4*d^10*e - 4*b*c^3*d^9*e^2 - 4*a^3*b*d^3*e^8 + a^4*d^2*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^7)*x)]","B",0
1581,1,965,0,0.906786," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, a c^{3} d^{3} e - 24 \, a b c^{2} d^{2} e^{2} + 6 \, {\left(3 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{3} - {\left(5 \, a b^{3} - 12 \, a^{2} b c\right)} e^{4} + {\left(16 \, c^{4} d^{3} e - 24 \, b c^{3} d^{2} e^{2} + 6 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{3} - {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} e^{4}\right)} x^{2} + {\left(16 \, b c^{3} d^{3} e - 24 \, b^{2} c^{2} d^{2} e^{2} + 6 \, {\left(3 \, b^{3} c - 4 \, a b c^{2}\right)} d e^{3} - {\left(5 \, b^{4} - 12 \, a b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, c^{4} e^{4} x^{4} - 6 \, c^{4} d^{4} + 72 \, a c^{3} d^{2} e^{2} - 54 \, a b c^{2} d e^{3} + {\left(15 \, a b^{2} c - 16 \, a^{2} c^{2}\right)} e^{4} + 2 \, {\left(6 \, c^{4} d e^{3} - b c^{3} e^{4}\right)} x^{3} + {\left(36 \, c^{4} d^{2} e^{2} - 18 \, b c^{3} d e^{3} + {\left(5 \, b^{2} c^{2} - 8 \, a c^{3}\right)} e^{4}\right)} x^{2} - {\left(24 \, c^{4} d^{3} e - 72 \, b c^{3} d^{2} e^{2} + 18 \, {\left(3 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{3} - {\left(15 \, b^{3} c - 26 \, a b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left(c^{5} x^{2} + b c^{4} x + a c^{4}\right)}}, -\frac{3 \, {\left(16 \, a c^{3} d^{3} e - 24 \, a b c^{2} d^{2} e^{2} + 6 \, {\left(3 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{3} - {\left(5 \, a b^{3} - 12 \, a^{2} b c\right)} e^{4} + {\left(16 \, c^{4} d^{3} e - 24 \, b c^{3} d^{2} e^{2} + 6 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{3} - {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} e^{4}\right)} x^{2} + {\left(16 \, b c^{3} d^{3} e - 24 \, b^{2} c^{2} d^{2} e^{2} + 6 \, {\left(3 \, b^{3} c - 4 \, a b c^{2}\right)} d e^{3} - {\left(5 \, b^{4} - 12 \, a b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2 \, c^{4} e^{4} x^{4} - 6 \, c^{4} d^{4} + 72 \, a c^{3} d^{2} e^{2} - 54 \, a b c^{2} d e^{3} + {\left(15 \, a b^{2} c - 16 \, a^{2} c^{2}\right)} e^{4} + 2 \, {\left(6 \, c^{4} d e^{3} - b c^{3} e^{4}\right)} x^{3} + {\left(36 \, c^{4} d^{2} e^{2} - 18 \, b c^{3} d e^{3} + {\left(5 \, b^{2} c^{2} - 8 \, a c^{3}\right)} e^{4}\right)} x^{2} - {\left(24 \, c^{4} d^{3} e - 72 \, b c^{3} d^{2} e^{2} + 18 \, {\left(3 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{3} - {\left(15 \, b^{3} c - 26 \, a b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(c^{5} x^{2} + b c^{4} x + a c^{4}\right)}}\right]"," ",0,"[1/12*(3*(16*a*c^3*d^3*e - 24*a*b*c^2*d^2*e^2 + 6*(3*a*b^2*c - 4*a^2*c^2)*d*e^3 - (5*a*b^3 - 12*a^2*b*c)*e^4 + (16*c^4*d^3*e - 24*b*c^3*d^2*e^2 + 6*(3*b^2*c^2 - 4*a*c^3)*d*e^3 - (5*b^3*c - 12*a*b*c^2)*e^4)*x^2 + (16*b*c^3*d^3*e - 24*b^2*c^2*d^2*e^2 + 6*(3*b^3*c - 4*a*b*c^2)*d*e^3 - (5*b^4 - 12*a*b^2*c)*e^4)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(2*c^4*e^4*x^4 - 6*c^4*d^4 + 72*a*c^3*d^2*e^2 - 54*a*b*c^2*d*e^3 + (15*a*b^2*c - 16*a^2*c^2)*e^4 + 2*(6*c^4*d*e^3 - b*c^3*e^4)*x^3 + (36*c^4*d^2*e^2 - 18*b*c^3*d*e^3 + (5*b^2*c^2 - 8*a*c^3)*e^4)*x^2 - (24*c^4*d^3*e - 72*b*c^3*d^2*e^2 + 18*(3*b^2*c^2 - 2*a*c^3)*d*e^3 - (15*b^3*c - 26*a*b*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c^5*x^2 + b*c^4*x + a*c^4), -1/6*(3*(16*a*c^3*d^3*e - 24*a*b*c^2*d^2*e^2 + 6*(3*a*b^2*c - 4*a^2*c^2)*d*e^3 - (5*a*b^3 - 12*a^2*b*c)*e^4 + (16*c^4*d^3*e - 24*b*c^3*d^2*e^2 + 6*(3*b^2*c^2 - 4*a*c^3)*d*e^3 - (5*b^3*c - 12*a*b*c^2)*e^4)*x^2 + (16*b*c^3*d^3*e - 24*b^2*c^2*d^2*e^2 + 6*(3*b^3*c - 4*a*b*c^2)*d*e^3 - (5*b^4 - 12*a*b^2*c)*e^4)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2*c^4*e^4*x^4 - 6*c^4*d^4 + 72*a*c^3*d^2*e^2 - 54*a*b*c^2*d*e^3 + (15*a*b^2*c - 16*a^2*c^2)*e^4 + 2*(6*c^4*d*e^3 - b*c^3*e^4)*x^3 + (36*c^4*d^2*e^2 - 18*b*c^3*d*e^3 + (5*b^2*c^2 - 8*a*c^3)*e^4)*x^2 - (24*c^4*d^3*e - 72*b*c^3*d^2*e^2 + 18*(3*b^2*c^2 - 2*a*c^3)*d*e^3 - (15*b^3*c - 26*a*b*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c^5*x^2 + b*c^4*x + a*c^4)]","B",0
1582,1,615,0,0.771025," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, a c^{2} d^{2} e - 8 \, a b c d e^{2} + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} e^{3} + {\left(8 \, c^{3} d^{2} e - 8 \, b c^{2} d e^{2} + {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, b c^{2} d^{2} e - 8 \, b^{2} c d e^{2} + {\left(3 \, b^{3} - 4 \, a b c\right)} e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, c^{3} e^{3} x^{3} - 4 \, c^{3} d^{3} + 24 \, a c^{2} d e^{2} - 9 \, a b c e^{3} + 3 \, {\left(4 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} x^{2} - 3 \, {\left(4 \, c^{3} d^{2} e - 8 \, b c^{2} d e^{2} + {\left(3 \, b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(c^{4} x^{2} + b c^{3} x + a c^{3}\right)}}, -\frac{3 \, {\left(8 \, a c^{2} d^{2} e - 8 \, a b c d e^{2} + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} e^{3} + {\left(8 \, c^{3} d^{2} e - 8 \, b c^{2} d e^{2} + {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, b c^{2} d^{2} e - 8 \, b^{2} c d e^{2} + {\left(3 \, b^{3} - 4 \, a b c\right)} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2 \, c^{3} e^{3} x^{3} - 4 \, c^{3} d^{3} + 24 \, a c^{2} d e^{2} - 9 \, a b c e^{3} + 3 \, {\left(4 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} x^{2} - 3 \, {\left(4 \, c^{3} d^{2} e - 8 \, b c^{2} d e^{2} + {\left(3 \, b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(c^{4} x^{2} + b c^{3} x + a c^{3}\right)}}\right]"," ",0,"[-1/8*(3*(8*a*c^2*d^2*e - 8*a*b*c*d*e^2 + (3*a*b^2 - 4*a^2*c)*e^3 + (8*c^3*d^2*e - 8*b*c^2*d*e^2 + (3*b^2*c - 4*a*c^2)*e^3)*x^2 + (8*b*c^2*d^2*e - 8*b^2*c*d*e^2 + (3*b^3 - 4*a*b*c)*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(2*c^3*e^3*x^3 - 4*c^3*d^3 + 24*a*c^2*d*e^2 - 9*a*b*c*e^3 + 3*(4*c^3*d*e^2 - b*c^2*e^3)*x^2 - 3*(4*c^3*d^2*e - 8*b*c^2*d*e^2 + (3*b^2*c - 2*a*c^2)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(c^4*x^2 + b*c^3*x + a*c^3), -1/4*(3*(8*a*c^2*d^2*e - 8*a*b*c*d*e^2 + (3*a*b^2 - 4*a^2*c)*e^3 + (8*c^3*d^2*e - 8*b*c^2*d*e^2 + (3*b^2*c - 4*a*c^2)*e^3)*x^2 + (8*b*c^2*d^2*e - 8*b^2*c*d*e^2 + (3*b^3 - 4*a*b*c)*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2*c^3*e^3*x^3 - 4*c^3*d^3 + 24*a*c^2*d*e^2 - 9*a*b*c*e^3 + 3*(4*c^3*d*e^2 - b*c^2*e^3)*x^2 - 3*(4*c^3*d^2*e - 8*b*c^2*d*e^2 + (3*b^2*c - 2*a*c^2)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(c^4*x^2 + b*c^3*x + a*c^3)]","B",0
1583,1,363,0,0.661106," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a c d e - a b e^{2} + {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{2} + {\left(2 \, b c d e - b^{2} e^{2}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 2 \, {\left(c^{2} e^{2} x^{2} - c^{2} d^{2} + 2 \, a c e^{2} - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{c^{3} x^{2} + b c^{2} x + a c^{2}}, -\frac{2 \, {\left({\left(2 \, a c d e - a b e^{2} + {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{2} + {\left(2 \, b c d e - b^{2} e^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - {\left(c^{2} e^{2} x^{2} - c^{2} d^{2} + 2 \, a c e^{2} - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}\right)}}{c^{3} x^{2} + b c^{2} x + a c^{2}}\right]"," ",0,"[-((2*a*c*d*e - a*b*e^2 + (2*c^2*d*e - b*c*e^2)*x^2 + (2*b*c*d*e - b^2*e^2)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 2*(c^2*e^2*x^2 - c^2*d^2 + 2*a*c*e^2 - 2*(c^2*d*e - b*c*e^2)*x)*sqrt(c*x^2 + b*x + a))/(c^3*x^2 + b*c^2*x + a*c^2), -2*((2*a*c*d*e - a*b*e^2 + (2*c^2*d*e - b*c*e^2)*x^2 + (2*b*c*d*e - b^2*e^2)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - (c^2*e^2*x^2 - c^2*d^2 + 2*a*c*e^2 - 2*(c^2*d*e - b*c*e^2)*x)*sqrt(c*x^2 + b*x + a))/(c^3*x^2 + b*c^2*x + a*c^2)]","B",0
1584,1,211,0,0.571270," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(c e x^{2} + b e x + a e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 2 \, {\left(c e x + c d\right)} \sqrt{c x^{2} + b x + a}}{c^{2} x^{2} + b c x + a c}, -\frac{2 \, {\left({\left(c e x^{2} + b e x + a e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(c e x + c d\right)} \sqrt{c x^{2} + b x + a}\right)}}{c^{2} x^{2} + b c x + a c}\right]"," ",0,"[((c*e*x^2 + b*e*x + a*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 2*(c*e*x + c*d)*sqrt(c*x^2 + b*x + a))/(c^2*x^2 + b*c*x + a*c), -2*((c*e*x^2 + b*e*x + a*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + (c*e*x + c*d)*sqrt(c*x^2 + b*x + a))/(c^2*x^2 + b*c*x + a*c)]","B",0
1585,1,14,0,0.426841," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2}{\sqrt{c x^{2} + b x + a}}"," ",0,"-2/sqrt(c*x^2 + b*x + a)","A",0
1586,1,918,0,0.920140," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a c d e - a b e^{2} + {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{2} + {\left(2 \, b c d e - b^{2} e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(c^{2} d^{3} - 2 \, b c d^{2} e - a b e^{3} + {\left(b^{2} + a c\right)} d e^{2} - {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a c^{2} d^{4} - 2 \, a b c d^{3} e - 2 \, a^{2} b d e^{3} + a^{3} e^{4} + {\left(a b^{2} + 2 \, a^{2} c\right)} d^{2} e^{2} + {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e - 2 \, a b c d e^{3} + a^{2} c e^{4} + {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} e^{2}\right)} x^{2} + {\left(b c^{2} d^{4} - 2 \, b^{2} c d^{3} e - 2 \, a b^{2} d e^{3} + a^{2} b e^{4} + {\left(b^{3} + 2 \, a b c\right)} d^{2} e^{2}\right)} x\right)}}, -\frac{{\left(2 \, a c d e - a b e^{2} + {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{2} + {\left(2 \, b c d e - b^{2} e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(c^{2} d^{3} - 2 \, b c d^{2} e - a b e^{3} + {\left(b^{2} + a c\right)} d e^{2} - {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{a c^{2} d^{4} - 2 \, a b c d^{3} e - 2 \, a^{2} b d e^{3} + a^{3} e^{4} + {\left(a b^{2} + 2 \, a^{2} c\right)} d^{2} e^{2} + {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e - 2 \, a b c d e^{3} + a^{2} c e^{4} + {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} e^{2}\right)} x^{2} + {\left(b c^{2} d^{4} - 2 \, b^{2} c d^{3} e - 2 \, a b^{2} d e^{3} + a^{2} b e^{4} + {\left(b^{3} + 2 \, a b c\right)} d^{2} e^{2}\right)} x}\right]"," ",0,"[-1/2*((2*a*c*d*e - a*b*e^2 + (2*c^2*d*e - b*c*e^2)*x^2 + (2*b*c*d*e - b^2*e^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(c^2*d^3 - 2*b*c*d^2*e - a*b*e^3 + (b^2 + a*c)*d*e^2 - (c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a*c^2*d^4 - 2*a*b*c*d^3*e - 2*a^2*b*d*e^3 + a^3*e^4 + (a*b^2 + 2*a^2*c)*d^2*e^2 + (c^3*d^4 - 2*b*c^2*d^3*e - 2*a*b*c*d*e^3 + a^2*c*e^4 + (b^2*c + 2*a*c^2)*d^2*e^2)*x^2 + (b*c^2*d^4 - 2*b^2*c*d^3*e - 2*a*b^2*d*e^3 + a^2*b*e^4 + (b^3 + 2*a*b*c)*d^2*e^2)*x), -((2*a*c*d*e - a*b*e^2 + (2*c^2*d*e - b*c*e^2)*x^2 + (2*b*c*d*e - b^2*e^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(c^2*d^3 - 2*b*c*d^2*e - a*b*e^3 + (b^2 + a*c)*d*e^2 - (c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a*c^2*d^4 - 2*a*b*c*d^3*e - 2*a^2*b*d*e^3 + a^3*e^4 + (a*b^2 + 2*a^2*c)*d^2*e^2 + (c^3*d^4 - 2*b*c^2*d^3*e - 2*a*b*c*d*e^3 + a^2*c*e^4 + (b^2*c + 2*a*c^2)*d^2*e^2)*x^2 + (b*c^2*d^4 - 2*b^2*c*d^3*e - 2*a*b^2*d*e^3 + a^2*b*e^4 + (b^3 + 2*a*b*c)*d^2*e^2)*x)]","B",0
1587,1,2102,0,2.551254," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, a c^{2} d^{3} e - 8 \, a b c d^{2} e^{2} + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} d e^{3} + {\left(8 \, c^{3} d^{2} e^{2} - 8 \, b c^{2} d e^{3} + {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, c^{3} d^{3} e - {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3} + {\left(3 \, b^{3} - 4 \, a b c\right)} e^{4}\right)} x^{2} + {\left(8 \, b c^{2} d^{3} e - 8 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e^{2} + 3 \, {\left(b^{3} - 4 \, a b c\right)} d e^{3} + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(2 \, c^{3} d^{5} - 6 \, b c^{2} d^{4} e + a^{2} b e^{5} + 2 \, {\left(3 \, b^{2} c - a c^{2}\right)} d^{3} e^{2} - {\left(2 \, b^{3} - a b c\right)} d^{2} e^{3} + {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{4} - 3 \, {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} - a b c e^{5} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{4}\right)} x^{2} - {\left(2 \, c^{3} d^{4} e + 2 \, b c^{2} d^{3} e^{2} - {\left(7 \, b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{3} + {\left(3 \, b^{3} + 2 \, a b c\right)} d e^{4} - {\left(3 \, a b^{2} - 2 \, a^{2} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(a c^{3} d^{7} - 3 \, a b c^{2} d^{6} e - 3 \, a^{3} b d^{2} e^{5} + a^{4} d e^{6} + 3 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{5} e^{2} - {\left(a b^{3} + 6 \, a^{2} b c\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{2} + a^{3} c\right)} d^{3} e^{4} + {\left(c^{4} d^{6} e - 3 \, b c^{3} d^{5} e^{2} - 3 \, a^{2} b c d e^{6} + a^{3} c e^{7} + 3 \, {\left(b^{2} c^{2} + a c^{3}\right)} d^{4} e^{3} - {\left(b^{3} c + 6 \, a b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{2} e^{5}\right)} x^{3} + {\left(c^{4} d^{7} - 2 \, b c^{3} d^{6} e + 3 \, a c^{3} d^{5} e^{2} + 3 \, a b^{3} d^{2} e^{5} + a^{3} b e^{7} + {\left(2 \, b^{3} c - 3 \, a b c^{2}\right)} d^{4} e^{3} - {\left(b^{4} + 3 \, a b^{2} c - 3 \, a^{2} c^{2}\right)} d^{3} e^{4} - {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d e^{6}\right)} x^{2} + {\left(b c^{3} d^{7} + 3 \, b^{3} c d^{5} e^{2} + 3 \, a^{3} c d^{2} e^{5} - 2 \, a^{3} b d e^{6} + a^{4} e^{7} - {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{6} e - {\left(b^{4} + 3 \, a b^{2} c - 3 \, a^{2} c^{2}\right)} d^{4} e^{3} + {\left(2 \, a b^{3} - 3 \, a^{2} b c\right)} d^{3} e^{4}\right)} x\right)}}, -\frac{{\left(8 \, a c^{2} d^{3} e - 8 \, a b c d^{2} e^{2} + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} d e^{3} + {\left(8 \, c^{3} d^{2} e^{2} - 8 \, b c^{2} d e^{3} + {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, c^{3} d^{3} e - {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3} + {\left(3 \, b^{3} - 4 \, a b c\right)} e^{4}\right)} x^{2} + {\left(8 \, b c^{2} d^{3} e - 8 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e^{2} + 3 \, {\left(b^{3} - 4 \, a b c\right)} d e^{3} + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, c^{3} d^{5} - 6 \, b c^{2} d^{4} e + a^{2} b e^{5} + 2 \, {\left(3 \, b^{2} c - a c^{2}\right)} d^{3} e^{2} - {\left(2 \, b^{3} - a b c\right)} d^{2} e^{3} + {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{4} - 3 \, {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} - a b c e^{5} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{4}\right)} x^{2} - {\left(2 \, c^{3} d^{4} e + 2 \, b c^{2} d^{3} e^{2} - {\left(7 \, b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{3} + {\left(3 \, b^{3} + 2 \, a b c\right)} d e^{4} - {\left(3 \, a b^{2} - 2 \, a^{2} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a c^{3} d^{7} - 3 \, a b c^{2} d^{6} e - 3 \, a^{3} b d^{2} e^{5} + a^{4} d e^{6} + 3 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{5} e^{2} - {\left(a b^{3} + 6 \, a^{2} b c\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{2} + a^{3} c\right)} d^{3} e^{4} + {\left(c^{4} d^{6} e - 3 \, b c^{3} d^{5} e^{2} - 3 \, a^{2} b c d e^{6} + a^{3} c e^{7} + 3 \, {\left(b^{2} c^{2} + a c^{3}\right)} d^{4} e^{3} - {\left(b^{3} c + 6 \, a b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{2} e^{5}\right)} x^{3} + {\left(c^{4} d^{7} - 2 \, b c^{3} d^{6} e + 3 \, a c^{3} d^{5} e^{2} + 3 \, a b^{3} d^{2} e^{5} + a^{3} b e^{7} + {\left(2 \, b^{3} c - 3 \, a b c^{2}\right)} d^{4} e^{3} - {\left(b^{4} + 3 \, a b^{2} c - 3 \, a^{2} c^{2}\right)} d^{3} e^{4} - {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d e^{6}\right)} x^{2} + {\left(b c^{3} d^{7} + 3 \, b^{3} c d^{5} e^{2} + 3 \, a^{3} c d^{2} e^{5} - 2 \, a^{3} b d e^{6} + a^{4} e^{7} - {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{6} e - {\left(b^{4} + 3 \, a b^{2} c - 3 \, a^{2} c^{2}\right)} d^{4} e^{3} + {\left(2 \, a b^{3} - 3 \, a^{2} b c\right)} d^{3} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/4*((8*a*c^2*d^3*e - 8*a*b*c*d^2*e^2 + (3*a*b^2 - 4*a^2*c)*d*e^3 + (8*c^3*d^2*e^2 - 8*b*c^2*d*e^3 + (3*b^2*c - 4*a*c^2)*e^4)*x^3 + (8*c^3*d^3*e - (5*b^2*c + 4*a*c^2)*d*e^3 + (3*b^3 - 4*a*b*c)*e^4)*x^2 + (8*b*c^2*d^3*e - 8*(b^2*c - a*c^2)*d^2*e^2 + 3*(b^3 - 4*a*b*c)*d*e^3 + (3*a*b^2 - 4*a^2*c)*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(2*c^3*d^5 - 6*b*c^2*d^4*e + a^2*b*e^5 + 2*(3*b^2*c - a*c^2)*d^3*e^2 - (2*b^3 - a*b*c)*d^2*e^3 + (a*b^2 - 4*a^2*c)*d*e^4 - 3*(2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 - a*b*c*e^5 + (b^2*c + 2*a*c^2)*d*e^4)*x^2 - (2*c^3*d^4*e + 2*b*c^2*d^3*e^2 - (7*b^2*c - 4*a*c^2)*d^2*e^3 + (3*b^3 + 2*a*b*c)*d*e^4 - (3*a*b^2 - 2*a^2*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(a*c^3*d^7 - 3*a*b*c^2*d^6*e - 3*a^3*b*d^2*e^5 + a^4*d*e^6 + 3*(a*b^2*c + a^2*c^2)*d^5*e^2 - (a*b^3 + 6*a^2*b*c)*d^4*e^3 + 3*(a^2*b^2 + a^3*c)*d^3*e^4 + (c^4*d^6*e - 3*b*c^3*d^5*e^2 - 3*a^2*b*c*d*e^6 + a^3*c*e^7 + 3*(b^2*c^2 + a*c^3)*d^4*e^3 - (b^3*c + 6*a*b*c^2)*d^3*e^4 + 3*(a*b^2*c + a^2*c^2)*d^2*e^5)*x^3 + (c^4*d^7 - 2*b*c^3*d^6*e + 3*a*c^3*d^5*e^2 + 3*a*b^3*d^2*e^5 + a^3*b*e^7 + (2*b^3*c - 3*a*b*c^2)*d^4*e^3 - (b^4 + 3*a*b^2*c - 3*a^2*c^2)*d^3*e^4 - (3*a^2*b^2 - a^3*c)*d*e^6)*x^2 + (b*c^3*d^7 + 3*b^3*c*d^5*e^2 + 3*a^3*c*d^2*e^5 - 2*a^3*b*d*e^6 + a^4*e^7 - (3*b^2*c^2 - a*c^3)*d^6*e - (b^4 + 3*a*b^2*c - 3*a^2*c^2)*d^4*e^3 + (2*a*b^3 - 3*a^2*b*c)*d^3*e^4)*x), -1/2*((8*a*c^2*d^3*e - 8*a*b*c*d^2*e^2 + (3*a*b^2 - 4*a^2*c)*d*e^3 + (8*c^3*d^2*e^2 - 8*b*c^2*d*e^3 + (3*b^2*c - 4*a*c^2)*e^4)*x^3 + (8*c^3*d^3*e - (5*b^2*c + 4*a*c^2)*d*e^3 + (3*b^3 - 4*a*b*c)*e^4)*x^2 + (8*b*c^2*d^3*e - 8*(b^2*c - a*c^2)*d^2*e^2 + 3*(b^3 - 4*a*b*c)*d*e^3 + (3*a*b^2 - 4*a^2*c)*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(2*c^3*d^5 - 6*b*c^2*d^4*e + a^2*b*e^5 + 2*(3*b^2*c - a*c^2)*d^3*e^2 - (2*b^3 - a*b*c)*d^2*e^3 + (a*b^2 - 4*a^2*c)*d*e^4 - 3*(2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 - a*b*c*e^5 + (b^2*c + 2*a*c^2)*d*e^4)*x^2 - (2*c^3*d^4*e + 2*b*c^2*d^3*e^2 - (7*b^2*c - 4*a*c^2)*d^2*e^3 + (3*b^3 + 2*a*b*c)*d*e^4 - (3*a*b^2 - 2*a^2*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(a*c^3*d^7 - 3*a*b*c^2*d^6*e - 3*a^3*b*d^2*e^5 + a^4*d*e^6 + 3*(a*b^2*c + a^2*c^2)*d^5*e^2 - (a*b^3 + 6*a^2*b*c)*d^4*e^3 + 3*(a^2*b^2 + a^3*c)*d^3*e^4 + (c^4*d^6*e - 3*b*c^3*d^5*e^2 - 3*a^2*b*c*d*e^6 + a^3*c*e^7 + 3*(b^2*c^2 + a*c^3)*d^4*e^3 - (b^3*c + 6*a*b*c^2)*d^3*e^4 + 3*(a*b^2*c + a^2*c^2)*d^2*e^5)*x^3 + (c^4*d^7 - 2*b*c^3*d^6*e + 3*a*c^3*d^5*e^2 + 3*a*b^3*d^2*e^5 + a^3*b*e^7 + (2*b^3*c - 3*a*b*c^2)*d^4*e^3 - (b^4 + 3*a*b^2*c - 3*a^2*c^2)*d^3*e^4 - (3*a^2*b^2 - a^3*c)*d*e^6)*x^2 + (b*c^3*d^7 + 3*b^3*c*d^5*e^2 + 3*a^3*c*d^2*e^5 - 2*a^3*b*d*e^6 + a^4*e^7 - (3*b^2*c^2 - a*c^3)*d^6*e - (b^4 + 3*a*b^2*c - 3*a^2*c^2)*d^4*e^3 + (2*a*b^3 - 3*a^2*b*c)*d^3*e^4)*x)]","B",0
1588,1,1493,0,1.635039," ","integrate((2*c*x+b)*(e*x+d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(3 \, {\left(2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4} + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e^{4}\right)} x^{3} + {\left(2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + {\left(8 \, a b c^{3} d^{3} e - 48 \, a^{2} c^{3} d^{2} e^{2} + 24 \, a^{2} b c^{2} d e^{3} - 3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{4} x^{4} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 4 \, {\left(3 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} e^{4} + 4 \, {\left(4 \, c^{5} d^{3} e - 6 \, b c^{4} d^{2} e^{2} + {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} d e^{3} - 2 \, {\left(2 \, b^{3} c^{2} - 7 \, a b c^{3}\right)} e^{4}\right)} x^{3} + 6 \, {\left(4 \, b c^{4} d^{3} e - 3 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d^{2} e^{2} + 4 \, {\left(b^{3} c^{2} - a b c^{3}\right)} d e^{3} - 2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} + 12 \, {\left(b^{2} c^{3} d^{3} e - 6 \, a b c^{3} d^{2} e^{2} + 4 \, {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} d e^{3} - 2 \, {\left(a b^{3} c - 3 \, a^{2} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} + 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3} + {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} x^{2} + 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} x\right)}}, -\frac{2 \, {\left(6 \, {\left(2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4} + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e^{4}\right)} x^{3} + {\left(2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(8 \, a b c^{3} d^{3} e - 48 \, a^{2} c^{3} d^{2} e^{2} + 24 \, a^{2} b c^{2} d e^{3} - 3 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{4} x^{4} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 4 \, {\left(3 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} e^{4} + 4 \, {\left(4 \, c^{5} d^{3} e - 6 \, b c^{4} d^{2} e^{2} + {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} d e^{3} - 2 \, {\left(2 \, b^{3} c^{2} - 7 \, a b c^{3}\right)} e^{4}\right)} x^{3} + 6 \, {\left(4 \, b c^{4} d^{3} e - 3 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d^{2} e^{2} + 4 \, {\left(b^{3} c^{2} - a b c^{3}\right)} d e^{3} - 2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} + 12 \, {\left(b^{2} c^{3} d^{3} e - 6 \, a b c^{3} d^{2} e^{2} + 4 \, {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} d e^{3} - 2 \, {\left(a b^{3} c - 3 \, a^{2} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} + 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3} + {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} x^{2} + 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} x\right)}}\right]"," ",0,"[-2/3*(3*(2*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 - (a^2*b^3 - 4*a^3*b*c)*e^4 + (2*(b^2*c^3 - 4*a*c^4)*d*e^3 - (b^3*c^2 - 4*a*b*c^3)*e^4)*x^4 + 2*(2*(b^3*c^2 - 4*a*b*c^3)*d*e^3 - (b^4*c - 4*a*b^2*c^2)*e^4)*x^3 + (2*(b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d*e^3 - (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*e^4)*x^2 + 2*(2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 - (a*b^4 - 4*a^2*b^2*c)*e^4)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + (8*a*b*c^3*d^3*e - 48*a^2*c^3*d^2*e^2 + 24*a^2*b*c^2*d*e^3 - 3*(b^2*c^3 - 4*a*c^4)*e^4*x^4 + (b^2*c^3 - 4*a*c^4)*d^4 - 4*(3*a^2*b^2*c - 8*a^3*c^2)*e^4 + 4*(4*c^5*d^3*e - 6*b*c^4*d^2*e^2 + (7*b^2*c^3 - 16*a*c^4)*d*e^3 - 2*(2*b^3*c^2 - 7*a*b*c^3)*e^4)*x^3 + 6*(4*b*c^4*d^3*e - 3*(b^2*c^3 + 4*a*c^4)*d^2*e^2 + 4*(b^3*c^2 - a*b*c^3)*d*e^3 - 2*(b^4*c - 2*a*b^2*c^2 - 4*a^2*c^3)*e^4)*x^2 + 12*(b^2*c^3*d^3*e - 6*a*b*c^3*d^2*e^2 + 4*(a*b^2*c^2 - a^2*c^3)*d*e^3 - 2*(a*b^3*c - 3*a^2*b*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^2*c^3 - 4*a^3*c^4 + (b^2*c^5 - 4*a*c^6)*x^4 + 2*(b^3*c^4 - 4*a*b*c^5)*x^3 + (b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*x^2 + 2*(a*b^3*c^3 - 4*a^2*b*c^4)*x), -2/3*(6*(2*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 - (a^2*b^3 - 4*a^3*b*c)*e^4 + (2*(b^2*c^3 - 4*a*c^4)*d*e^3 - (b^3*c^2 - 4*a*b*c^3)*e^4)*x^4 + 2*(2*(b^3*c^2 - 4*a*b*c^3)*d*e^3 - (b^4*c - 4*a*b^2*c^2)*e^4)*x^3 + (2*(b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d*e^3 - (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*e^4)*x^2 + 2*(2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 - (a*b^4 - 4*a^2*b^2*c)*e^4)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + (8*a*b*c^3*d^3*e - 48*a^2*c^3*d^2*e^2 + 24*a^2*b*c^2*d*e^3 - 3*(b^2*c^3 - 4*a*c^4)*e^4*x^4 + (b^2*c^3 - 4*a*c^4)*d^4 - 4*(3*a^2*b^2*c - 8*a^3*c^2)*e^4 + 4*(4*c^5*d^3*e - 6*b*c^4*d^2*e^2 + (7*b^2*c^3 - 16*a*c^4)*d*e^3 - 2*(2*b^3*c^2 - 7*a*b*c^3)*e^4)*x^3 + 6*(4*b*c^4*d^3*e - 3*(b^2*c^3 + 4*a*c^4)*d^2*e^2 + 4*(b^3*c^2 - a*b*c^3)*d*e^3 - 2*(b^4*c - 2*a*b^2*c^2 - 4*a^2*c^3)*e^4)*x^2 + 12*(b^2*c^3*d^3*e - 6*a*b*c^3*d^2*e^2 + 4*(a*b^2*c^2 - a^2*c^3)*d*e^3 - 2*(a*b^3*c - 3*a^2*b*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^2*c^3 - 4*a^3*c^4 + (b^2*c^5 - 4*a*c^6)*x^4 + 2*(b^3*c^4 - 4*a*b*c^5)*x^3 + (b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*x^2 + 2*(a*b^3*c^3 - 4*a^2*b*c^4)*x)]","B",0
1589,1,958,0,1.412168," ","integrate((2*c*x+b)*(e*x+d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{3} x^{4} + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} e^{3} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} x + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 2 \, {\left(6 \, a b c^{2} d^{2} e - 24 \, a^{2} c^{2} d e^{2} + 6 \, a^{2} b c e^{3} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} + {\left(12 \, c^{4} d^{2} e - 12 \, b c^{3} d e^{2} + {\left(7 \, b^{2} c^{2} - 16 \, a c^{3}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, b c^{3} d^{2} e - 3 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d e^{2} + 2 \, {\left(b^{3} c - a b c^{2}\right)} e^{3}\right)} x^{2} + 3 \, {\left(3 \, b^{2} c^{2} d^{2} e - 12 \, a b c^{2} d e^{2} + 4 \, {\left(a b^{2} c - a^{2} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3} + {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} x\right)}}, -\frac{2 \, {\left(3 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{3} x^{4} + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} e^{3} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} x + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(6 \, a b c^{2} d^{2} e - 24 \, a^{2} c^{2} d e^{2} + 6 \, a^{2} b c e^{3} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} + {\left(12 \, c^{4} d^{2} e - 12 \, b c^{3} d e^{2} + {\left(7 \, b^{2} c^{2} - 16 \, a c^{3}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, b c^{3} d^{2} e - 3 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d e^{2} + 2 \, {\left(b^{3} c - a b c^{2}\right)} e^{3}\right)} x^{2} + 3 \, {\left(3 \, b^{2} c^{2} d^{2} e - 12 \, a b c^{2} d e^{2} + 4 \, {\left(a b^{2} c - a^{2} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3} + {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} x\right)}}\right]"," ",0,"[1/3*(3*((b^2*c^2 - 4*a*c^3)*e^3*x^4 + 2*(b^3*c - 4*a*b*c^2)*e^3*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*e^3*x^2 + 2*(a*b^3 - 4*a^2*b*c)*e^3*x + (a^2*b^2 - 4*a^3*c)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 2*(6*a*b*c^2*d^2*e - 24*a^2*c^2*d*e^2 + 6*a^2*b*c*e^3 + (b^2*c^2 - 4*a*c^3)*d^3 + (12*c^4*d^2*e - 12*b*c^3*d*e^2 + (7*b^2*c^2 - 16*a*c^3)*e^3)*x^3 + 3*(6*b*c^3*d^2*e - 3*(b^2*c^2 + 4*a*c^3)*d*e^2 + 2*(b^3*c - a*b*c^2)*e^3)*x^2 + 3*(3*b^2*c^2*d^2*e - 12*a*b*c^2*d*e^2 + 4*(a*b^2*c - a^2*c^2)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^2*c^2 - 4*a^3*c^3 + (b^2*c^4 - 4*a*c^5)*x^4 + 2*(b^3*c^3 - 4*a*b*c^4)*x^3 + (b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*x^2 + 2*(a*b^3*c^2 - 4*a^2*b*c^3)*x), -2/3*(3*((b^2*c^2 - 4*a*c^3)*e^3*x^4 + 2*(b^3*c - 4*a*b*c^2)*e^3*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*e^3*x^2 + 2*(a*b^3 - 4*a^2*b*c)*e^3*x + (a^2*b^2 - 4*a^3*c)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + (6*a*b*c^2*d^2*e - 24*a^2*c^2*d*e^2 + 6*a^2*b*c*e^3 + (b^2*c^2 - 4*a*c^3)*d^3 + (12*c^4*d^2*e - 12*b*c^3*d*e^2 + (7*b^2*c^2 - 16*a*c^3)*e^3)*x^3 + 3*(6*b*c^3*d^2*e - 3*(b^2*c^2 + 4*a*c^3)*d*e^2 + 2*(b^3*c - a*b*c^2)*e^3)*x^2 + 3*(3*b^2*c^2*d^2*e - 12*a*b*c^2*d*e^2 + 4*(a*b^2*c - a^2*c^2)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^2*c^2 - 4*a^3*c^3 + (b^2*c^4 - 4*a*c^5)*x^4 + 2*(b^3*c^3 - 4*a*b*c^4)*x^3 + (b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*x^2 + 2*(a*b^3*c^2 - 4*a^2*b*c^3)*x)]","B",0
1590,1,194,0,1.263558," ","integrate((2*c*x+b)*(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, a b d e - 8 \, a^{2} e^{2} + 4 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{3} + {\left(b^{2} - 4 \, a c\right)} d^{2} + 3 \, {\left(4 \, b c d e - {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 6 \, {\left(b^{2} d e - 2 \, a b e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}"," ",0,"-2/3*(4*a*b*d*e - 8*a^2*e^2 + 4*(2*c^2*d*e - b*c*e^2)*x^3 + (b^2 - 4*a*c)*d^2 + 3*(4*b*c*d*e - (b^2 + 4*a*c)*e^2)*x^2 + 6*(b^2*d*e - 2*a*b*e^2)*x)*sqrt(c*x^2 + b*x + a)/((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)","B",0
1591,1,145,0,1.155353," ","integrate((2*c*x+b)*(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, c^{2} e x^{3} + 6 \, b c e x^{2} + 3 \, b^{2} e x + 2 \, a b e + {\left(b^{2} - 4 \, a c\right)} d\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}"," ",0,"-2/3*(4*c^2*e*x^3 + 6*b*c*e*x^2 + 3*b^2*e*x + 2*a*b*e + (b^2 - 4*a*c)*d)*sqrt(c*x^2 + b*x + a)/((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)","B",0
1592,1,51,0,0.574169," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x + a}}{3 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-2/3*sqrt(c*x^2 + b*x + a)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1593,1,3858,0,2.785074," ","integrate((2*c*x+b)/(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4} + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e^{4}\right)} x^{3} + {\left(2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} d^{4} e + {\left(3 \, b^{4} c - 3 \, a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 8 \, a b^{3} c - 36 \, a^{2} b c^{2}\right)} d^{2} e^{3} + {\left(5 \, a b^{4} - 12 \, a^{2} b^{2} c - 16 \, a^{3} c^{2}\right)} d e^{4} - 2 \, {\left(2 \, a^{2} b^{3} - 7 \, a^{3} b c\right)} e^{5} - {\left(4 \, c^{5} d^{4} e - 8 \, b c^{4} d^{3} e^{2} + {\left(7 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{3} - {\left(3 \, b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{4} + {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e^{5}\right)} x^{3} - 3 \, {\left(2 \, b c^{4} d^{4} e - {\left(5 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} + {\left(5 \, b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{2} e^{3} - {\left(2 \, b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{4} + 2 \, {\left(a b^{3} c - 3 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} - 3 \, {\left(b^{2} c^{3} d^{4} e - {\left(3 \, b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{2} + {\left(3 \, b^{4} c - 5 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{3} - {\left(b^{5} - 8 \, a^{2} b c^{2}\right)} d e^{4} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left({\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{6} - 3 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{5} e + 3 \, {\left(a^{2} b^{4} c - 3 \, a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{4} e^{2} - {\left(a^{2} b^{5} + 2 \, a^{3} b^{3} c - 24 \, a^{4} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} b^{4} - 3 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{5} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{6} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{6} - 3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{5} e + 3 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} e^{2} - {\left(b^{5} c^{2} + 2 \, a b^{3} c^{3} - 24 \, a^{2} b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d e^{5} + {\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} e^{6}\right)} x^{4} + 2 \, {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} - 3 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{5} e + 3 \, {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e^{2} - {\left(b^{6} c + 2 \, a b^{4} c^{2} - 24 \, a^{2} b^{2} c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a b^{5} c - 3 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{4} c - 4 \, a^{3} b^{2} c^{2}\right)} d e^{5} + {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} e^{6}\right)} x^{3} + {\left({\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{6} - 3 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{5} e + 3 \, {\left(b^{6} c - a b^{4} c^{2} - 10 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{4} e^{2} - {\left(b^{7} + 4 \, a b^{5} c - 20 \, a^{2} b^{3} c^{2} - 48 \, a^{3} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a b^{6} - a^{2} b^{4} c - 10 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} d e^{5} + {\left(a^{3} b^{4} - 2 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{6} - 3 \, {\left(a b^{4} c^{2} - 4 \, a^{2} b^{2} c^{3}\right)} d^{5} e + 3 \, {\left(a b^{5} c - 3 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{4} e^{2} - {\left(a b^{6} + 2 \, a^{2} b^{4} c - 24 \, a^{3} b^{2} c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a^{2} b^{5} - 3 \, a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} d e^{5} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{6}\right)} x\right)}}, -\frac{3 \, {\left(2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4} + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e^{4}\right)} x^{3} + {\left(2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} d^{4} e + {\left(3 \, b^{4} c - 3 \, a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 8 \, a b^{3} c - 36 \, a^{2} b c^{2}\right)} d^{2} e^{3} + {\left(5 \, a b^{4} - 12 \, a^{2} b^{2} c - 16 \, a^{3} c^{2}\right)} d e^{4} - 2 \, {\left(2 \, a^{2} b^{3} - 7 \, a^{3} b c\right)} e^{5} - {\left(4 \, c^{5} d^{4} e - 8 \, b c^{4} d^{3} e^{2} + {\left(7 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{3} - {\left(3 \, b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{4} + {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e^{5}\right)} x^{3} - 3 \, {\left(2 \, b c^{4} d^{4} e - {\left(5 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} + {\left(5 \, b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{2} e^{3} - {\left(2 \, b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{4} + 2 \, {\left(a b^{3} c - 3 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} - 3 \, {\left(b^{2} c^{3} d^{4} e - {\left(3 \, b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{2} + {\left(3 \, b^{4} c - 5 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{3} - {\left(b^{5} - 8 \, a^{2} b c^{2}\right)} d e^{4} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left({\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{6} - 3 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{5} e + 3 \, {\left(a^{2} b^{4} c - 3 \, a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{4} e^{2} - {\left(a^{2} b^{5} + 2 \, a^{3} b^{3} c - 24 \, a^{4} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} b^{4} - 3 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{5} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{6} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{6} - 3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{5} e + 3 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} e^{2} - {\left(b^{5} c^{2} + 2 \, a b^{3} c^{3} - 24 \, a^{2} b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d e^{5} + {\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} e^{6}\right)} x^{4} + 2 \, {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} - 3 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{5} e + 3 \, {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e^{2} - {\left(b^{6} c + 2 \, a b^{4} c^{2} - 24 \, a^{2} b^{2} c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a b^{5} c - 3 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{4} c - 4 \, a^{3} b^{2} c^{2}\right)} d e^{5} + {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} e^{6}\right)} x^{3} + {\left({\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{6} - 3 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{5} e + 3 \, {\left(b^{6} c - a b^{4} c^{2} - 10 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{4} e^{2} - {\left(b^{7} + 4 \, a b^{5} c - 20 \, a^{2} b^{3} c^{2} - 48 \, a^{3} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a b^{6} - a^{2} b^{4} c - 10 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} d e^{5} + {\left(a^{3} b^{4} - 2 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{6} - 3 \, {\left(a b^{4} c^{2} - 4 \, a^{2} b^{2} c^{3}\right)} d^{5} e + 3 \, {\left(a b^{5} c - 3 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{4} e^{2} - {\left(a b^{6} + 2 \, a^{2} b^{4} c - 24 \, a^{3} b^{2} c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a^{2} b^{5} - 3 \, a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} d e^{5} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/6*(3*(2*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 - (a^2*b^3 - 4*a^3*b*c)*e^4 + (2*(b^2*c^3 - 4*a*c^4)*d*e^3 - (b^3*c^2 - 4*a*b*c^3)*e^4)*x^4 + 2*(2*(b^3*c^2 - 4*a*b*c^3)*d*e^3 - (b^4*c - 4*a*b^2*c^2)*e^4)*x^3 + (2*(b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d*e^3 - (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*e^4)*x^2 + 2*(2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 - (a*b^4 - 4*a^2*b^2*c)*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*((b^2*c^3 - 4*a*c^4)*d^5 - (3*b^3*c^2 - 10*a*b*c^3)*d^4*e + (3*b^4*c - 3*a*b^2*c^2 - 20*a^2*c^3)*d^3*e^2 - (b^5 + 8*a*b^3*c - 36*a^2*b*c^2)*d^2*e^3 + (5*a*b^4 - 12*a^2*b^2*c - 16*a^3*c^2)*d*e^4 - 2*(2*a^2*b^3 - 7*a^3*b*c)*e^5 - (4*c^5*d^4*e - 8*b*c^4*d^3*e^2 + (7*b^2*c^3 - 4*a*c^4)*d^2*e^3 - (3*b^3*c^2 - 4*a*b*c^3)*d*e^4 + (3*a*b^2*c^2 - 8*a^2*c^3)*e^5)*x^3 - 3*(2*b*c^4*d^4*e - (5*b^2*c^3 - 4*a*c^4)*d^3*e^2 + (5*b^3*c^2 - 8*a*b*c^3)*d^2*e^3 - (2*b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d*e^4 + 2*(a*b^3*c - 3*a^2*b*c^2)*e^5)*x^2 - 3*(b^2*c^3*d^4*e - (3*b^3*c^2 - 4*a*b*c^3)*d^3*e^2 + (3*b^4*c - 5*a*b^2*c^2 - 4*a^2*c^3)*d^2*e^3 - (b^5 - 8*a^2*b*c^2)*d*e^4 + (a*b^4 - 2*a^2*b^2*c - 4*a^3*c^2)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^2*c^3 - 4*a^3*c^4)*d^6 - 3*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^5*e + 3*(a^2*b^4*c - 3*a^3*b^2*c^2 - 4*a^4*c^3)*d^4*e^2 - (a^2*b^5 + 2*a^3*b^3*c - 24*a^4*b*c^2)*d^3*e^3 + 3*(a^3*b^4 - 3*a^4*b^2*c - 4*a^5*c^2)*d^2*e^4 - 3*(a^4*b^3 - 4*a^5*b*c)*d*e^5 + (a^5*b^2 - 4*a^6*c)*e^6 + ((b^2*c^5 - 4*a*c^6)*d^6 - 3*(b^3*c^4 - 4*a*b*c^5)*d^5*e + 3*(b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*d^4*e^2 - (b^5*c^2 + 2*a*b^3*c^3 - 24*a^2*b*c^4)*d^3*e^3 + 3*(a*b^4*c^2 - 3*a^2*b^2*c^3 - 4*a^3*c^4)*d^2*e^4 - 3*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d*e^5 + (a^3*b^2*c^2 - 4*a^4*c^3)*e^6)*x^4 + 2*((b^3*c^4 - 4*a*b*c^5)*d^6 - 3*(b^4*c^3 - 4*a*b^2*c^4)*d^5*e + 3*(b^5*c^2 - 3*a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e^2 - (b^6*c + 2*a*b^4*c^2 - 24*a^2*b^2*c^3)*d^3*e^3 + 3*(a*b^5*c - 3*a^2*b^3*c^2 - 4*a^3*b*c^3)*d^2*e^4 - 3*(a^2*b^4*c - 4*a^3*b^2*c^2)*d*e^5 + (a^3*b^3*c - 4*a^4*b*c^2)*e^6)*x^3 + ((b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^6 - 3*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^5*e + 3*(b^6*c - a*b^4*c^2 - 10*a^2*b^2*c^3 - 8*a^3*c^4)*d^4*e^2 - (b^7 + 4*a*b^5*c - 20*a^2*b^3*c^2 - 48*a^3*b*c^3)*d^3*e^3 + 3*(a*b^6 - a^2*b^4*c - 10*a^3*b^2*c^2 - 8*a^4*c^3)*d^2*e^4 - 3*(a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*d*e^5 + (a^3*b^4 - 2*a^4*b^2*c - 8*a^5*c^2)*e^6)*x^2 + 2*((a*b^3*c^3 - 4*a^2*b*c^4)*d^6 - 3*(a*b^4*c^2 - 4*a^2*b^2*c^3)*d^5*e + 3*(a*b^5*c - 3*a^2*b^3*c^2 - 4*a^3*b*c^3)*d^4*e^2 - (a*b^6 + 2*a^2*b^4*c - 24*a^3*b^2*c^2)*d^3*e^3 + 3*(a^2*b^5 - 3*a^3*b^3*c - 4*a^4*b*c^2)*d^2*e^4 - 3*(a^3*b^4 - 4*a^4*b^2*c)*d*e^5 + (a^4*b^3 - 4*a^5*b*c)*e^6)*x), -1/3*(3*(2*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 - (a^2*b^3 - 4*a^3*b*c)*e^4 + (2*(b^2*c^3 - 4*a*c^4)*d*e^3 - (b^3*c^2 - 4*a*b*c^3)*e^4)*x^4 + 2*(2*(b^3*c^2 - 4*a*b*c^3)*d*e^3 - (b^4*c - 4*a*b^2*c^2)*e^4)*x^3 + (2*(b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d*e^3 - (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*e^4)*x^2 + 2*(2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 - (a*b^4 - 4*a^2*b^2*c)*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*((b^2*c^3 - 4*a*c^4)*d^5 - (3*b^3*c^2 - 10*a*b*c^3)*d^4*e + (3*b^4*c - 3*a*b^2*c^2 - 20*a^2*c^3)*d^3*e^2 - (b^5 + 8*a*b^3*c - 36*a^2*b*c^2)*d^2*e^3 + (5*a*b^4 - 12*a^2*b^2*c - 16*a^3*c^2)*d*e^4 - 2*(2*a^2*b^3 - 7*a^3*b*c)*e^5 - (4*c^5*d^4*e - 8*b*c^4*d^3*e^2 + (7*b^2*c^3 - 4*a*c^4)*d^2*e^3 - (3*b^3*c^2 - 4*a*b*c^3)*d*e^4 + (3*a*b^2*c^2 - 8*a^2*c^3)*e^5)*x^3 - 3*(2*b*c^4*d^4*e - (5*b^2*c^3 - 4*a*c^4)*d^3*e^2 + (5*b^3*c^2 - 8*a*b*c^3)*d^2*e^3 - (2*b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d*e^4 + 2*(a*b^3*c - 3*a^2*b*c^2)*e^5)*x^2 - 3*(b^2*c^3*d^4*e - (3*b^3*c^2 - 4*a*b*c^3)*d^3*e^2 + (3*b^4*c - 5*a*b^2*c^2 - 4*a^2*c^3)*d^2*e^3 - (b^5 - 8*a^2*b*c^2)*d*e^4 + (a*b^4 - 2*a^2*b^2*c - 4*a^3*c^2)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^2*c^3 - 4*a^3*c^4)*d^6 - 3*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^5*e + 3*(a^2*b^4*c - 3*a^3*b^2*c^2 - 4*a^4*c^3)*d^4*e^2 - (a^2*b^5 + 2*a^3*b^3*c - 24*a^4*b*c^2)*d^3*e^3 + 3*(a^3*b^4 - 3*a^4*b^2*c - 4*a^5*c^2)*d^2*e^4 - 3*(a^4*b^3 - 4*a^5*b*c)*d*e^5 + (a^5*b^2 - 4*a^6*c)*e^6 + ((b^2*c^5 - 4*a*c^6)*d^6 - 3*(b^3*c^4 - 4*a*b*c^5)*d^5*e + 3*(b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*d^4*e^2 - (b^5*c^2 + 2*a*b^3*c^3 - 24*a^2*b*c^4)*d^3*e^3 + 3*(a*b^4*c^2 - 3*a^2*b^2*c^3 - 4*a^3*c^4)*d^2*e^4 - 3*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d*e^5 + (a^3*b^2*c^2 - 4*a^4*c^3)*e^6)*x^4 + 2*((b^3*c^4 - 4*a*b*c^5)*d^6 - 3*(b^4*c^3 - 4*a*b^2*c^4)*d^5*e + 3*(b^5*c^2 - 3*a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e^2 - (b^6*c + 2*a*b^4*c^2 - 24*a^2*b^2*c^3)*d^3*e^3 + 3*(a*b^5*c - 3*a^2*b^3*c^2 - 4*a^3*b*c^3)*d^2*e^4 - 3*(a^2*b^4*c - 4*a^3*b^2*c^2)*d*e^5 + (a^3*b^3*c - 4*a^4*b*c^2)*e^6)*x^3 + ((b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^6 - 3*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^5*e + 3*(b^6*c - a*b^4*c^2 - 10*a^2*b^2*c^3 - 8*a^3*c^4)*d^4*e^2 - (b^7 + 4*a*b^5*c - 20*a^2*b^3*c^2 - 48*a^3*b*c^3)*d^3*e^3 + 3*(a*b^6 - a^2*b^4*c - 10*a^3*b^2*c^2 - 8*a^4*c^3)*d^2*e^4 - 3*(a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*d*e^5 + (a^3*b^4 - 2*a^4*b^2*c - 8*a^5*c^2)*e^6)*x^2 + 2*((a*b^3*c^3 - 4*a^2*b*c^4)*d^6 - 3*(a*b^4*c^2 - 4*a^2*b^2*c^3)*d^5*e + 3*(a*b^5*c - 3*a^2*b^3*c^2 - 4*a^3*b*c^3)*d^4*e^2 - (a*b^6 + 2*a^2*b^4*c - 24*a^3*b^2*c^2)*d^3*e^3 + 3*(a^2*b^5 - 3*a^3*b^3*c - 4*a^4*b*c^2)*d^2*e^4 - 3*(a^3*b^4 - 4*a^4*b^2*c)*d*e^5 + (a^4*b^3 - 4*a^5*b*c)*e^6)*x)]","B",0
1594,1,7442,0,10.036685," ","integrate((2*c*x+b)/(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(16 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{3} - 16 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{4} - 24 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d e^{5} + {\left(16 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e^{4} - 16 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e^{5} + {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{6}\right)} x^{5} + {\left(16 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} e^{3} + 16 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e^{4} - {\left(27 \, b^{4} c^{2} - 104 \, a b^{2} c^{3} - 16 \, a^{2} c^{4}\right)} d e^{5} + 2 \, {\left(5 \, b^{5} c - 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6}\right)} x^{4} + {\left(32 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} - 16 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 2 \, {\left(3 \, b^{5} c + 8 \, a b^{3} c^{2} - 80 \, a^{2} b c^{3}\right)} d e^{5} + {\left(5 \, b^{6} - 14 \, a b^{4} c - 32 \, a^{2} b^{2} c^{2} + 32 \, a^{3} c^{3}\right)} e^{6}\right)} x^{3} + {\left(16 \, {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{3} e^{3} - 16 \, {\left(b^{5} c - 4 \, a b^{3} c^{2}\right)} d^{2} e^{4} + {\left(5 \, b^{6} - 46 \, a b^{4} c + 96 \, a^{2} b^{2} c^{2} + 32 \, a^{3} c^{3}\right)} d e^{5} + 2 \, {\left(5 \, a b^{5} - 24 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{6}\right)} x^{2} + {\left(32 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{3} - 16 \, {\left(2 \, a b^{4} c - 9 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{2} e^{4} + 2 \, {\left(5 \, a b^{5} - 32 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} d e^{5} + {\left(5 \, a^{2} b^{4} - 24 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{6}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} - 8 \, {\left(b^{3} c^{3} - 3 \, a b c^{4}\right)} d^{6} e + 4 \, {\left(3 \, b^{4} c^{2} - 2 \, a b^{2} c^{3} - 20 \, a^{2} c^{4}\right)} d^{5} e^{2} - 8 \, {\left(b^{5} c + 5 \, a b^{3} c^{2} - 26 \, a^{2} b c^{3}\right)} d^{4} e^{3} + 2 \, {\left(b^{6} + 24 \, a b^{4} c - 90 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{3} e^{4} - {\left(16 \, a b^{5} - 41 \, a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{5} + {\left(11 \, a^{2} b^{4} - 54 \, a^{3} b^{2} c + 56 \, a^{4} c^{2}\right)} d e^{6} + 3 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{7} - {\left(16 \, c^{6} d^{5} e^{2} - 40 \, b c^{5} d^{4} e^{3} + 2 \, {\left(31 \, b^{2} c^{4} - 44 \, a c^{5}\right)} d^{3} e^{4} - {\left(53 \, b^{3} c^{3} - 132 \, a b c^{4}\right)} d^{2} e^{5} + {\left(15 \, b^{4} c^{2} - 14 \, a b^{2} c^{3} - 104 \, a^{2} c^{4}\right)} d e^{6} - {\left(15 \, a b^{3} c^{2} - 52 \, a^{2} b c^{3}\right)} e^{7}\right)} x^{4} - 2 \, {\left(8 \, c^{6} d^{6} e - 8 \, b c^{5} d^{5} e^{2} - {\left(11 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{3} + 4 \, {\left(11 \, b^{3} c^{3} - 24 \, a b c^{4}\right)} d^{3} e^{4} - 2 \, {\left(24 \, b^{4} c^{2} - 73 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{5} + {\left(15 \, b^{5} c - 24 \, a b^{3} c^{2} - 88 \, a^{2} b c^{3}\right)} d e^{6} - 3 \, {\left(5 \, a b^{4} c - 19 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} e^{7}\right)} x^{3} - 3 \, {\left(8 \, b c^{5} d^{6} e - 2 \, {\left(11 \, b^{2} c^{4} - 12 \, a c^{5}\right)} d^{5} e^{2} + 8 \, {\left(3 \, b^{3} c^{3} - 7 \, a b c^{4}\right)} d^{4} e^{3} - 4 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} e^{4} - {\left(11 \, b^{5} c - 26 \, a b^{3} c^{2} - 32 \, a^{2} b c^{3}\right)} d^{2} e^{5} + {\left(5 \, b^{6} - 8 \, a b^{4} c - 18 \, a^{2} b^{2} c^{2} - 56 \, a^{3} c^{3}\right)} d e^{6} - {\left(5 \, a b^{5} - 14 \, a^{2} b^{3} c - 16 \, a^{3} b c^{2}\right)} e^{7}\right)} x^{2} - 2 \, {\left({\left(5 \, b^{2} c^{4} + 4 \, a c^{5}\right)} d^{6} e - 4 \, {\left(5 \, b^{3} c^{3} - 6 \, a b c^{4}\right)} d^{5} e^{2} + 2 \, {\left(15 \, b^{4} c^{2} - 34 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{3} - 4 \, {\left(5 \, b^{5} c - 17 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d^{3} e^{4} + {\left(5 \, b^{6} - 33 \, a b^{4} c + 69 \, a^{2} b^{2} c^{2} - 28 \, a^{3} c^{3}\right)} d^{2} e^{5} + {\left(5 \, a b^{5} - 4 \, a^{2} b^{3} c - 56 \, a^{3} b c^{2}\right)} d e^{6} - 2 \, {\left(5 \, a^{2} b^{4} - 21 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left({\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{9} - 4 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{8} e + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{7} e^{2} - 4 \, {\left(a^{2} b^{5} c - a^{3} b^{3} c^{2} - 12 \, a^{4} b c^{3}\right)} d^{6} e^{3} + {\left(a^{2} b^{6} + 8 \, a^{3} b^{4} c - 42 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d^{5} e^{4} - 4 \, {\left(a^{3} b^{5} - a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{4} e^{5} + 2 \, {\left(3 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{3} e^{6} - 4 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{2} e^{7} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d e^{8} + {\left({\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} e - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e^{2} + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{3} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{4} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{5} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{7} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{8} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{9}\right)} x^{5} + {\left({\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{9} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{8} e - 2 \, {\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} d^{7} e^{2} + 4 \, {\left(2 \, b^{5} c^{3} - 9 \, a b^{3} c^{4} + 4 \, a^{2} b c^{5}\right)} d^{6} e^{3} - {\left(7 \, b^{6} c^{2} - 16 \, a b^{4} c^{3} - 54 \, a^{2} b^{2} c^{4} + 24 \, a^{3} c^{5}\right)} d^{5} e^{4} + 2 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 40 \, a^{2} b^{3} c^{3}\right)} d^{4} e^{5} - 2 \, {\left(4 \, a b^{6} c - 7 \, a^{2} b^{4} c^{2} - 38 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4}\right)} d^{3} e^{6} + 4 \, {\left(3 \, a^{2} b^{5} c - 11 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{2} e^{7} - {\left(8 \, a^{3} b^{4} c - 33 \, a^{4} b^{2} c^{2} + 4 \, a^{5} c^{3}\right)} d e^{8} + 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} e^{9}\right)} x^{4} + {\left(2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{9} - {\left(7 \, b^{4} c^{4} - 30 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} d^{8} e + 8 \, {\left(b^{5} c^{3} - 4 \, a b^{3} c^{4}\right)} d^{7} e^{2} - 2 \, {\left(b^{6} c^{2} - 20 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{6} e^{3} - 2 \, {\left(b^{7} c - 6 \, a b^{5} c^{2} + 14 \, a^{2} b^{3} c^{3} - 24 \, a^{3} b c^{4}\right)} d^{5} e^{4} + {\left(b^{8} + 2 \, a b^{6} c - 18 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 48 \, a^{4} c^{4}\right)} d^{4} e^{5} - 4 \, {\left(a b^{7} - 2 \, a^{2} b^{5} c - 4 \, a^{3} b^{3} c^{2} - 16 \, a^{4} b c^{3}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{6} - 8 \, a^{3} b^{4} c - 12 \, a^{4} b^{2} c^{2} - 16 \, a^{5} c^{3}\right)} d^{2} e^{7} - 2 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d e^{8} + {\left(a^{4} b^{4} - 2 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} e^{9}\right)} x^{3} + {\left({\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{9} - 2 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{8} e + 2 \, {\left(3 \, b^{6} c^{2} - 8 \, a b^{4} c^{3} - 12 \, a^{2} b^{2} c^{4} - 16 \, a^{3} c^{5}\right)} d^{7} e^{2} - 4 \, {\left(b^{7} c - 2 \, a b^{5} c^{2} - 4 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b c^{4}\right)} d^{6} e^{3} + {\left(b^{8} + 2 \, a b^{6} c - 18 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 48 \, a^{4} c^{4}\right)} d^{5} e^{4} - 2 \, {\left(a b^{7} - 6 \, a^{2} b^{5} c + 14 \, a^{3} b^{3} c^{2} - 24 \, a^{4} b c^{3}\right)} d^{4} e^{5} - 2 \, {\left(a^{2} b^{6} - 20 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{3} e^{6} + 8 \, {\left(a^{3} b^{5} - 4 \, a^{4} b^{3} c\right)} d^{2} e^{7} - {\left(7 \, a^{4} b^{4} - 30 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d e^{8} + 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e^{9}\right)} x^{2} + {\left(2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{9} - {\left(8 \, a b^{4} c^{3} - 33 \, a^{2} b^{2} c^{4} + 4 \, a^{3} c^{5}\right)} d^{8} e + 4 \, {\left(3 \, a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{7} e^{2} - 2 \, {\left(4 \, a b^{6} c - 7 \, a^{2} b^{4} c^{2} - 38 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4}\right)} d^{6} e^{3} + 2 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 40 \, a^{3} b^{3} c^{2}\right)} d^{5} e^{4} - {\left(7 \, a^{2} b^{6} - 16 \, a^{3} b^{4} c - 54 \, a^{4} b^{2} c^{2} + 24 \, a^{5} c^{3}\right)} d^{4} e^{5} + 4 \, {\left(2 \, a^{3} b^{5} - 9 \, a^{4} b^{3} c + 4 \, a^{5} b c^{2}\right)} d^{3} e^{6} - 2 \, {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d^{2} e^{7} - 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{8} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{9}\right)} x\right)}}, -\frac{3 \, {\left(16 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{3} - 16 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{4} - 24 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d e^{5} + {\left(16 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e^{4} - 16 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e^{5} + {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{6}\right)} x^{5} + {\left(16 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} e^{3} + 16 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e^{4} - {\left(27 \, b^{4} c^{2} - 104 \, a b^{2} c^{3} - 16 \, a^{2} c^{4}\right)} d e^{5} + 2 \, {\left(5 \, b^{5} c - 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6}\right)} x^{4} + {\left(32 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} - 16 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 2 \, {\left(3 \, b^{5} c + 8 \, a b^{3} c^{2} - 80 \, a^{2} b c^{3}\right)} d e^{5} + {\left(5 \, b^{6} - 14 \, a b^{4} c - 32 \, a^{2} b^{2} c^{2} + 32 \, a^{3} c^{3}\right)} e^{6}\right)} x^{3} + {\left(16 \, {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{3} e^{3} - 16 \, {\left(b^{5} c - 4 \, a b^{3} c^{2}\right)} d^{2} e^{4} + {\left(5 \, b^{6} - 46 \, a b^{4} c + 96 \, a^{2} b^{2} c^{2} + 32 \, a^{3} c^{3}\right)} d e^{5} + 2 \, {\left(5 \, a b^{5} - 24 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{6}\right)} x^{2} + {\left(32 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{3} - 16 \, {\left(2 \, a b^{4} c - 9 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{2} e^{4} + 2 \, {\left(5 \, a b^{5} - 32 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} d e^{5} + {\left(5 \, a^{2} b^{4} - 24 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{6}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} - 8 \, {\left(b^{3} c^{3} - 3 \, a b c^{4}\right)} d^{6} e + 4 \, {\left(3 \, b^{4} c^{2} - 2 \, a b^{2} c^{3} - 20 \, a^{2} c^{4}\right)} d^{5} e^{2} - 8 \, {\left(b^{5} c + 5 \, a b^{3} c^{2} - 26 \, a^{2} b c^{3}\right)} d^{4} e^{3} + 2 \, {\left(b^{6} + 24 \, a b^{4} c - 90 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{3} e^{4} - {\left(16 \, a b^{5} - 41 \, a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{5} + {\left(11 \, a^{2} b^{4} - 54 \, a^{3} b^{2} c + 56 \, a^{4} c^{2}\right)} d e^{6} + 3 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{7} - {\left(16 \, c^{6} d^{5} e^{2} - 40 \, b c^{5} d^{4} e^{3} + 2 \, {\left(31 \, b^{2} c^{4} - 44 \, a c^{5}\right)} d^{3} e^{4} - {\left(53 \, b^{3} c^{3} - 132 \, a b c^{4}\right)} d^{2} e^{5} + {\left(15 \, b^{4} c^{2} - 14 \, a b^{2} c^{3} - 104 \, a^{2} c^{4}\right)} d e^{6} - {\left(15 \, a b^{3} c^{2} - 52 \, a^{2} b c^{3}\right)} e^{7}\right)} x^{4} - 2 \, {\left(8 \, c^{6} d^{6} e - 8 \, b c^{5} d^{5} e^{2} - {\left(11 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{3} + 4 \, {\left(11 \, b^{3} c^{3} - 24 \, a b c^{4}\right)} d^{3} e^{4} - 2 \, {\left(24 \, b^{4} c^{2} - 73 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{5} + {\left(15 \, b^{5} c - 24 \, a b^{3} c^{2} - 88 \, a^{2} b c^{3}\right)} d e^{6} - 3 \, {\left(5 \, a b^{4} c - 19 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} e^{7}\right)} x^{3} - 3 \, {\left(8 \, b c^{5} d^{6} e - 2 \, {\left(11 \, b^{2} c^{4} - 12 \, a c^{5}\right)} d^{5} e^{2} + 8 \, {\left(3 \, b^{3} c^{3} - 7 \, a b c^{4}\right)} d^{4} e^{3} - 4 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} e^{4} - {\left(11 \, b^{5} c - 26 \, a b^{3} c^{2} - 32 \, a^{2} b c^{3}\right)} d^{2} e^{5} + {\left(5 \, b^{6} - 8 \, a b^{4} c - 18 \, a^{2} b^{2} c^{2} - 56 \, a^{3} c^{3}\right)} d e^{6} - {\left(5 \, a b^{5} - 14 \, a^{2} b^{3} c - 16 \, a^{3} b c^{2}\right)} e^{7}\right)} x^{2} - 2 \, {\left({\left(5 \, b^{2} c^{4} + 4 \, a c^{5}\right)} d^{6} e - 4 \, {\left(5 \, b^{3} c^{3} - 6 \, a b c^{4}\right)} d^{5} e^{2} + 2 \, {\left(15 \, b^{4} c^{2} - 34 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{3} - 4 \, {\left(5 \, b^{5} c - 17 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d^{3} e^{4} + {\left(5 \, b^{6} - 33 \, a b^{4} c + 69 \, a^{2} b^{2} c^{2} - 28 \, a^{3} c^{3}\right)} d^{2} e^{5} + {\left(5 \, a b^{5} - 4 \, a^{2} b^{3} c - 56 \, a^{3} b c^{2}\right)} d e^{6} - 2 \, {\left(5 \, a^{2} b^{4} - 21 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left({\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{9} - 4 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{8} e + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{7} e^{2} - 4 \, {\left(a^{2} b^{5} c - a^{3} b^{3} c^{2} - 12 \, a^{4} b c^{3}\right)} d^{6} e^{3} + {\left(a^{2} b^{6} + 8 \, a^{3} b^{4} c - 42 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d^{5} e^{4} - 4 \, {\left(a^{3} b^{5} - a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{4} e^{5} + 2 \, {\left(3 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{3} e^{6} - 4 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{2} e^{7} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d e^{8} + {\left({\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} e - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e^{2} + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{3} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{4} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{5} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{7} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{8} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{9}\right)} x^{5} + {\left({\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{9} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{8} e - 2 \, {\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} d^{7} e^{2} + 4 \, {\left(2 \, b^{5} c^{3} - 9 \, a b^{3} c^{4} + 4 \, a^{2} b c^{5}\right)} d^{6} e^{3} - {\left(7 \, b^{6} c^{2} - 16 \, a b^{4} c^{3} - 54 \, a^{2} b^{2} c^{4} + 24 \, a^{3} c^{5}\right)} d^{5} e^{4} + 2 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 40 \, a^{2} b^{3} c^{3}\right)} d^{4} e^{5} - 2 \, {\left(4 \, a b^{6} c - 7 \, a^{2} b^{4} c^{2} - 38 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4}\right)} d^{3} e^{6} + 4 \, {\left(3 \, a^{2} b^{5} c - 11 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{2} e^{7} - {\left(8 \, a^{3} b^{4} c - 33 \, a^{4} b^{2} c^{2} + 4 \, a^{5} c^{3}\right)} d e^{8} + 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} e^{9}\right)} x^{4} + {\left(2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{9} - {\left(7 \, b^{4} c^{4} - 30 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} d^{8} e + 8 \, {\left(b^{5} c^{3} - 4 \, a b^{3} c^{4}\right)} d^{7} e^{2} - 2 \, {\left(b^{6} c^{2} - 20 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{6} e^{3} - 2 \, {\left(b^{7} c - 6 \, a b^{5} c^{2} + 14 \, a^{2} b^{3} c^{3} - 24 \, a^{3} b c^{4}\right)} d^{5} e^{4} + {\left(b^{8} + 2 \, a b^{6} c - 18 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 48 \, a^{4} c^{4}\right)} d^{4} e^{5} - 4 \, {\left(a b^{7} - 2 \, a^{2} b^{5} c - 4 \, a^{3} b^{3} c^{2} - 16 \, a^{4} b c^{3}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{6} - 8 \, a^{3} b^{4} c - 12 \, a^{4} b^{2} c^{2} - 16 \, a^{5} c^{3}\right)} d^{2} e^{7} - 2 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d e^{8} + {\left(a^{4} b^{4} - 2 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} e^{9}\right)} x^{3} + {\left({\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{9} - 2 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{8} e + 2 \, {\left(3 \, b^{6} c^{2} - 8 \, a b^{4} c^{3} - 12 \, a^{2} b^{2} c^{4} - 16 \, a^{3} c^{5}\right)} d^{7} e^{2} - 4 \, {\left(b^{7} c - 2 \, a b^{5} c^{2} - 4 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b c^{4}\right)} d^{6} e^{3} + {\left(b^{8} + 2 \, a b^{6} c - 18 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 48 \, a^{4} c^{4}\right)} d^{5} e^{4} - 2 \, {\left(a b^{7} - 6 \, a^{2} b^{5} c + 14 \, a^{3} b^{3} c^{2} - 24 \, a^{4} b c^{3}\right)} d^{4} e^{5} - 2 \, {\left(a^{2} b^{6} - 20 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{3} e^{6} + 8 \, {\left(a^{3} b^{5} - 4 \, a^{4} b^{3} c\right)} d^{2} e^{7} - {\left(7 \, a^{4} b^{4} - 30 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d e^{8} + 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e^{9}\right)} x^{2} + {\left(2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{9} - {\left(8 \, a b^{4} c^{3} - 33 \, a^{2} b^{2} c^{4} + 4 \, a^{3} c^{5}\right)} d^{8} e + 4 \, {\left(3 \, a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{7} e^{2} - 2 \, {\left(4 \, a b^{6} c - 7 \, a^{2} b^{4} c^{2} - 38 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4}\right)} d^{6} e^{3} + 2 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 40 \, a^{3} b^{3} c^{2}\right)} d^{5} e^{4} - {\left(7 \, a^{2} b^{6} - 16 \, a^{3} b^{4} c - 54 \, a^{4} b^{2} c^{2} + 24 \, a^{5} c^{3}\right)} d^{4} e^{5} + 4 \, {\left(2 \, a^{3} b^{5} - 9 \, a^{4} b^{3} c + 4 \, a^{5} b c^{2}\right)} d^{3} e^{6} - 2 \, {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d^{2} e^{7} - 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{8} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/12*(3*(16*(a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^3 - 16*(a^2*b^3*c - 4*a^3*b*c^2)*d^2*e^4 + (5*a^2*b^4 - 24*a^3*b^2*c + 16*a^4*c^2)*d*e^5 + (16*(b^2*c^4 - 4*a*c^5)*d^2*e^4 - 16*(b^3*c^3 - 4*a*b*c^4)*d*e^5 + (5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*e^6)*x^5 + (16*(b^2*c^4 - 4*a*c^5)*d^3*e^3 + 16*(b^3*c^3 - 4*a*b*c^4)*d^2*e^4 - (27*b^4*c^2 - 104*a*b^2*c^3 - 16*a^2*c^4)*d*e^5 + 2*(5*b^5*c - 24*a*b^3*c^2 + 16*a^2*b*c^3)*e^6)*x^4 + (32*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 - 16*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 2*(3*b^5*c + 8*a*b^3*c^2 - 80*a^2*b*c^3)*d*e^5 + (5*b^6 - 14*a*b^4*c - 32*a^2*b^2*c^2 + 32*a^3*c^3)*e^6)*x^3 + (16*(b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*d^3*e^3 - 16*(b^5*c - 4*a*b^3*c^2)*d^2*e^4 + (5*b^6 - 46*a*b^4*c + 96*a^2*b^2*c^2 + 32*a^3*c^3)*d*e^5 + 2*(5*a*b^5 - 24*a^2*b^3*c + 16*a^3*b*c^2)*e^6)*x^2 + (32*(a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^3 - 16*(2*a*b^4*c - 9*a^2*b^2*c^2 + 4*a^3*c^3)*d^2*e^4 + 2*(5*a*b^5 - 32*a^2*b^3*c + 48*a^3*b*c^2)*d*e^5 + (5*a^2*b^4 - 24*a^3*b^2*c + 16*a^4*c^2)*e^6)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(2*(b^2*c^4 - 4*a*c^5)*d^7 - 8*(b^3*c^3 - 3*a*b*c^4)*d^6*e + 4*(3*b^4*c^2 - 2*a*b^2*c^3 - 20*a^2*c^4)*d^5*e^2 - 8*(b^5*c + 5*a*b^3*c^2 - 26*a^2*b*c^3)*d^4*e^3 + 2*(b^6 + 24*a*b^4*c - 90*a^2*b^2*c^2 - 8*a^3*c^3)*d^3*e^4 - (16*a*b^5 - 41*a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^5 + (11*a^2*b^4 - 54*a^3*b^2*c + 56*a^4*c^2)*d*e^6 + 3*(a^3*b^3 - 4*a^4*b*c)*e^7 - (16*c^6*d^5*e^2 - 40*b*c^5*d^4*e^3 + 2*(31*b^2*c^4 - 44*a*c^5)*d^3*e^4 - (53*b^3*c^3 - 132*a*b*c^4)*d^2*e^5 + (15*b^4*c^2 - 14*a*b^2*c^3 - 104*a^2*c^4)*d*e^6 - (15*a*b^3*c^2 - 52*a^2*b*c^3)*e^7)*x^4 - 2*(8*c^6*d^6*e - 8*b*c^5*d^5*e^2 - (11*b^2*c^4 - 4*a*c^5)*d^4*e^3 + 4*(11*b^3*c^3 - 24*a*b*c^4)*d^3*e^4 - 2*(24*b^4*c^2 - 73*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^5 + (15*b^5*c - 24*a*b^3*c^2 - 88*a^2*b*c^3)*d*e^6 - 3*(5*a*b^4*c - 19*a^2*b^2*c^2 + 4*a^3*c^3)*e^7)*x^3 - 3*(8*b*c^5*d^6*e - 2*(11*b^2*c^4 - 12*a*c^5)*d^5*e^2 + 8*(3*b^3*c^3 - 7*a*b*c^4)*d^4*e^3 - 4*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*e^4 - (11*b^5*c - 26*a*b^3*c^2 - 32*a^2*b*c^3)*d^2*e^5 + (5*b^6 - 8*a*b^4*c - 18*a^2*b^2*c^2 - 56*a^3*c^3)*d*e^6 - (5*a*b^5 - 14*a^2*b^3*c - 16*a^3*b*c^2)*e^7)*x^2 - 2*((5*b^2*c^4 + 4*a*c^5)*d^6*e - 4*(5*b^3*c^3 - 6*a*b*c^4)*d^5*e^2 + 2*(15*b^4*c^2 - 34*a*b^2*c^3 - 4*a^2*c^4)*d^4*e^3 - 4*(5*b^5*c - 17*a*b^3*c^2 + 8*a^2*b*c^3)*d^3*e^4 + (5*b^6 - 33*a*b^4*c + 69*a^2*b^2*c^2 - 28*a^3*c^3)*d^2*e^5 + (5*a*b^5 - 4*a^2*b^3*c - 56*a^3*b*c^2)*d*e^6 - 2*(5*a^2*b^4 - 21*a^3*b^2*c + 8*a^4*c^2)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^2*c^4 - 4*a^3*c^5)*d^9 - 4*(a^2*b^3*c^3 - 4*a^3*b*c^4)*d^8*e + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^7*e^2 - 4*(a^2*b^5*c - a^3*b^3*c^2 - 12*a^4*b*c^3)*d^6*e^3 + (a^2*b^6 + 8*a^3*b^4*c - 42*a^4*b^2*c^2 - 24*a^5*c^3)*d^5*e^4 - 4*(a^3*b^5 - a^4*b^3*c - 12*a^5*b*c^2)*d^4*e^5 + 2*(3*a^4*b^4 - 10*a^5*b^2*c - 8*a^6*c^2)*d^3*e^6 - 4*(a^5*b^3 - 4*a^6*b*c)*d^2*e^7 + (a^6*b^2 - 4*a^7*c)*d*e^8 + ((b^2*c^6 - 4*a*c^7)*d^8*e - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e^2 + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^3 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^4 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^5 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^6 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^7 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^8 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^9)*x^5 + ((b^2*c^6 - 4*a*c^7)*d^9 - 2*(b^3*c^5 - 4*a*b*c^6)*d^8*e - 2*(b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*d^7*e^2 + 4*(2*b^5*c^3 - 9*a*b^3*c^4 + 4*a^2*b*c^5)*d^6*e^3 - (7*b^6*c^2 - 16*a*b^4*c^3 - 54*a^2*b^2*c^4 + 24*a^3*c^5)*d^5*e^4 + 2*(b^7*c + 6*a*b^5*c^2 - 40*a^2*b^3*c^3)*d^4*e^5 - 2*(4*a*b^6*c - 7*a^2*b^4*c^2 - 38*a^3*b^2*c^3 + 8*a^4*c^4)*d^3*e^6 + 4*(3*a^2*b^5*c - 11*a^3*b^3*c^2 - 4*a^4*b*c^3)*d^2*e^7 - (8*a^3*b^4*c - 33*a^4*b^2*c^2 + 4*a^5*c^3)*d*e^8 + 2*(a^4*b^3*c - 4*a^5*b*c^2)*e^9)*x^4 + (2*(b^3*c^5 - 4*a*b*c^6)*d^9 - (7*b^4*c^4 - 30*a*b^2*c^5 + 8*a^2*c^6)*d^8*e + 8*(b^5*c^3 - 4*a*b^3*c^4)*d^7*e^2 - 2*(b^6*c^2 - 20*a^2*b^2*c^4 + 16*a^3*c^5)*d^6*e^3 - 2*(b^7*c - 6*a*b^5*c^2 + 14*a^2*b^3*c^3 - 24*a^3*b*c^4)*d^5*e^4 + (b^8 + 2*a*b^6*c - 18*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 48*a^4*c^4)*d^4*e^5 - 4*(a*b^7 - 2*a^2*b^5*c - 4*a^3*b^3*c^2 - 16*a^4*b*c^3)*d^3*e^6 + 2*(3*a^2*b^6 - 8*a^3*b^4*c - 12*a^4*b^2*c^2 - 16*a^5*c^3)*d^2*e^7 - 2*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d*e^8 + (a^4*b^4 - 2*a^5*b^2*c - 8*a^6*c^2)*e^9)*x^3 + ((b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^9 - 2*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^8*e + 2*(3*b^6*c^2 - 8*a*b^4*c^3 - 12*a^2*b^2*c^4 - 16*a^3*c^5)*d^7*e^2 - 4*(b^7*c - 2*a*b^5*c^2 - 4*a^2*b^3*c^3 - 16*a^3*b*c^4)*d^6*e^3 + (b^8 + 2*a*b^6*c - 18*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 48*a^4*c^4)*d^5*e^4 - 2*(a*b^7 - 6*a^2*b^5*c + 14*a^3*b^3*c^2 - 24*a^4*b*c^3)*d^4*e^5 - 2*(a^2*b^6 - 20*a^4*b^2*c^2 + 16*a^5*c^3)*d^3*e^6 + 8*(a^3*b^5 - 4*a^4*b^3*c)*d^2*e^7 - (7*a^4*b^4 - 30*a^5*b^2*c + 8*a^6*c^2)*d*e^8 + 2*(a^5*b^3 - 4*a^6*b*c)*e^9)*x^2 + (2*(a*b^3*c^4 - 4*a^2*b*c^5)*d^9 - (8*a*b^4*c^3 - 33*a^2*b^2*c^4 + 4*a^3*c^5)*d^8*e + 4*(3*a*b^5*c^2 - 11*a^2*b^3*c^3 - 4*a^3*b*c^4)*d^7*e^2 - 2*(4*a*b^6*c - 7*a^2*b^4*c^2 - 38*a^3*b^2*c^3 + 8*a^4*c^4)*d^6*e^3 + 2*(a*b^7 + 6*a^2*b^5*c - 40*a^3*b^3*c^2)*d^5*e^4 - (7*a^2*b^6 - 16*a^3*b^4*c - 54*a^4*b^2*c^2 + 24*a^5*c^3)*d^4*e^5 + 4*(2*a^3*b^5 - 9*a^4*b^3*c + 4*a^5*b*c^2)*d^3*e^6 - 2*(a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d^2*e^7 - 2*(a^5*b^3 - 4*a^6*b*c)*d*e^8 + (a^6*b^2 - 4*a^7*c)*e^9)*x), -1/6*(3*(16*(a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^3 - 16*(a^2*b^3*c - 4*a^3*b*c^2)*d^2*e^4 + (5*a^2*b^4 - 24*a^3*b^2*c + 16*a^4*c^2)*d*e^5 + (16*(b^2*c^4 - 4*a*c^5)*d^2*e^4 - 16*(b^3*c^3 - 4*a*b*c^4)*d*e^5 + (5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*e^6)*x^5 + (16*(b^2*c^4 - 4*a*c^5)*d^3*e^3 + 16*(b^3*c^3 - 4*a*b*c^4)*d^2*e^4 - (27*b^4*c^2 - 104*a*b^2*c^3 - 16*a^2*c^4)*d*e^5 + 2*(5*b^5*c - 24*a*b^3*c^2 + 16*a^2*b*c^3)*e^6)*x^4 + (32*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 - 16*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 2*(3*b^5*c + 8*a*b^3*c^2 - 80*a^2*b*c^3)*d*e^5 + (5*b^6 - 14*a*b^4*c - 32*a^2*b^2*c^2 + 32*a^3*c^3)*e^6)*x^3 + (16*(b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*d^3*e^3 - 16*(b^5*c - 4*a*b^3*c^2)*d^2*e^4 + (5*b^6 - 46*a*b^4*c + 96*a^2*b^2*c^2 + 32*a^3*c^3)*d*e^5 + 2*(5*a*b^5 - 24*a^2*b^3*c + 16*a^3*b*c^2)*e^6)*x^2 + (32*(a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^3 - 16*(2*a*b^4*c - 9*a^2*b^2*c^2 + 4*a^3*c^3)*d^2*e^4 + 2*(5*a*b^5 - 32*a^2*b^3*c + 48*a^3*b*c^2)*d*e^5 + (5*a^2*b^4 - 24*a^3*b^2*c + 16*a^4*c^2)*e^6)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(2*(b^2*c^4 - 4*a*c^5)*d^7 - 8*(b^3*c^3 - 3*a*b*c^4)*d^6*e + 4*(3*b^4*c^2 - 2*a*b^2*c^3 - 20*a^2*c^4)*d^5*e^2 - 8*(b^5*c + 5*a*b^3*c^2 - 26*a^2*b*c^3)*d^4*e^3 + 2*(b^6 + 24*a*b^4*c - 90*a^2*b^2*c^2 - 8*a^3*c^3)*d^3*e^4 - (16*a*b^5 - 41*a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^5 + (11*a^2*b^4 - 54*a^3*b^2*c + 56*a^4*c^2)*d*e^6 + 3*(a^3*b^3 - 4*a^4*b*c)*e^7 - (16*c^6*d^5*e^2 - 40*b*c^5*d^4*e^3 + 2*(31*b^2*c^4 - 44*a*c^5)*d^3*e^4 - (53*b^3*c^3 - 132*a*b*c^4)*d^2*e^5 + (15*b^4*c^2 - 14*a*b^2*c^3 - 104*a^2*c^4)*d*e^6 - (15*a*b^3*c^2 - 52*a^2*b*c^3)*e^7)*x^4 - 2*(8*c^6*d^6*e - 8*b*c^5*d^5*e^2 - (11*b^2*c^4 - 4*a*c^5)*d^4*e^3 + 4*(11*b^3*c^3 - 24*a*b*c^4)*d^3*e^4 - 2*(24*b^4*c^2 - 73*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^5 + (15*b^5*c - 24*a*b^3*c^2 - 88*a^2*b*c^3)*d*e^6 - 3*(5*a*b^4*c - 19*a^2*b^2*c^2 + 4*a^3*c^3)*e^7)*x^3 - 3*(8*b*c^5*d^6*e - 2*(11*b^2*c^4 - 12*a*c^5)*d^5*e^2 + 8*(3*b^3*c^3 - 7*a*b*c^4)*d^4*e^3 - 4*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*e^4 - (11*b^5*c - 26*a*b^3*c^2 - 32*a^2*b*c^3)*d^2*e^5 + (5*b^6 - 8*a*b^4*c - 18*a^2*b^2*c^2 - 56*a^3*c^3)*d*e^6 - (5*a*b^5 - 14*a^2*b^3*c - 16*a^3*b*c^2)*e^7)*x^2 - 2*((5*b^2*c^4 + 4*a*c^5)*d^6*e - 4*(5*b^3*c^3 - 6*a*b*c^4)*d^5*e^2 + 2*(15*b^4*c^2 - 34*a*b^2*c^3 - 4*a^2*c^4)*d^4*e^3 - 4*(5*b^5*c - 17*a*b^3*c^2 + 8*a^2*b*c^3)*d^3*e^4 + (5*b^6 - 33*a*b^4*c + 69*a^2*b^2*c^2 - 28*a^3*c^3)*d^2*e^5 + (5*a*b^5 - 4*a^2*b^3*c - 56*a^3*b*c^2)*d*e^6 - 2*(5*a^2*b^4 - 21*a^3*b^2*c + 8*a^4*c^2)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^2*c^4 - 4*a^3*c^5)*d^9 - 4*(a^2*b^3*c^3 - 4*a^3*b*c^4)*d^8*e + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^7*e^2 - 4*(a^2*b^5*c - a^3*b^3*c^2 - 12*a^4*b*c^3)*d^6*e^3 + (a^2*b^6 + 8*a^3*b^4*c - 42*a^4*b^2*c^2 - 24*a^5*c^3)*d^5*e^4 - 4*(a^3*b^5 - a^4*b^3*c - 12*a^5*b*c^2)*d^4*e^5 + 2*(3*a^4*b^4 - 10*a^5*b^2*c - 8*a^6*c^2)*d^3*e^6 - 4*(a^5*b^3 - 4*a^6*b*c)*d^2*e^7 + (a^6*b^2 - 4*a^7*c)*d*e^8 + ((b^2*c^6 - 4*a*c^7)*d^8*e - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e^2 + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^3 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^4 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^5 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^6 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^7 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^8 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^9)*x^5 + ((b^2*c^6 - 4*a*c^7)*d^9 - 2*(b^3*c^5 - 4*a*b*c^6)*d^8*e - 2*(b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*d^7*e^2 + 4*(2*b^5*c^3 - 9*a*b^3*c^4 + 4*a^2*b*c^5)*d^6*e^3 - (7*b^6*c^2 - 16*a*b^4*c^3 - 54*a^2*b^2*c^4 + 24*a^3*c^5)*d^5*e^4 + 2*(b^7*c + 6*a*b^5*c^2 - 40*a^2*b^3*c^3)*d^4*e^5 - 2*(4*a*b^6*c - 7*a^2*b^4*c^2 - 38*a^3*b^2*c^3 + 8*a^4*c^4)*d^3*e^6 + 4*(3*a^2*b^5*c - 11*a^3*b^3*c^2 - 4*a^4*b*c^3)*d^2*e^7 - (8*a^3*b^4*c - 33*a^4*b^2*c^2 + 4*a^5*c^3)*d*e^8 + 2*(a^4*b^3*c - 4*a^5*b*c^2)*e^9)*x^4 + (2*(b^3*c^5 - 4*a*b*c^6)*d^9 - (7*b^4*c^4 - 30*a*b^2*c^5 + 8*a^2*c^6)*d^8*e + 8*(b^5*c^3 - 4*a*b^3*c^4)*d^7*e^2 - 2*(b^6*c^2 - 20*a^2*b^2*c^4 + 16*a^3*c^5)*d^6*e^3 - 2*(b^7*c - 6*a*b^5*c^2 + 14*a^2*b^3*c^3 - 24*a^3*b*c^4)*d^5*e^4 + (b^8 + 2*a*b^6*c - 18*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 48*a^4*c^4)*d^4*e^5 - 4*(a*b^7 - 2*a^2*b^5*c - 4*a^3*b^3*c^2 - 16*a^4*b*c^3)*d^3*e^6 + 2*(3*a^2*b^6 - 8*a^3*b^4*c - 12*a^4*b^2*c^2 - 16*a^5*c^3)*d^2*e^7 - 2*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d*e^8 + (a^4*b^4 - 2*a^5*b^2*c - 8*a^6*c^2)*e^9)*x^3 + ((b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^9 - 2*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^8*e + 2*(3*b^6*c^2 - 8*a*b^4*c^3 - 12*a^2*b^2*c^4 - 16*a^3*c^5)*d^7*e^2 - 4*(b^7*c - 2*a*b^5*c^2 - 4*a^2*b^3*c^3 - 16*a^3*b*c^4)*d^6*e^3 + (b^8 + 2*a*b^6*c - 18*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 48*a^4*c^4)*d^5*e^4 - 2*(a*b^7 - 6*a^2*b^5*c + 14*a^3*b^3*c^2 - 24*a^4*b*c^3)*d^4*e^5 - 2*(a^2*b^6 - 20*a^4*b^2*c^2 + 16*a^5*c^3)*d^3*e^6 + 8*(a^3*b^5 - 4*a^4*b^3*c)*d^2*e^7 - (7*a^4*b^4 - 30*a^5*b^2*c + 8*a^6*c^2)*d*e^8 + 2*(a^5*b^3 - 4*a^6*b*c)*e^9)*x^2 + (2*(a*b^3*c^4 - 4*a^2*b*c^5)*d^9 - (8*a*b^4*c^3 - 33*a^2*b^2*c^4 + 4*a^3*c^5)*d^8*e + 4*(3*a*b^5*c^2 - 11*a^2*b^3*c^3 - 4*a^3*b*c^4)*d^7*e^2 - 2*(4*a*b^6*c - 7*a^2*b^4*c^2 - 38*a^3*b^2*c^3 + 8*a^4*c^4)*d^6*e^3 + 2*(a*b^7 + 6*a^2*b^5*c - 40*a^3*b^3*c^2)*d^5*e^4 - (7*a^2*b^6 - 16*a^3*b^4*c - 54*a^4*b^2*c^2 + 24*a^5*c^3)*d^4*e^5 + 4*(2*a^3*b^5 - 9*a^4*b^3*c + 4*a^5*b*c^2)*d^3*e^6 - 2*(a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d^2*e^7 - 2*(a^5*b^3 - 4*a^6*b*c)*d*e^8 + (a^6*b^2 - 4*a^7*c)*e^9)*x)]","B",0
1595,1,272,0,0.398865," ","integrate((2*c*x+b)*(e*x+d)^(5/2)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(1386 \, c^{2} e^{6} x^{6} - 96 \, c^{2} d^{6} + 312 \, b c d^{5} e + 1287 \, a b d^{3} e^{3} - 286 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{2} + 189 \, {\left(18 \, c^{2} d e^{5} + 13 \, b c e^{6}\right)} x^{5} + 7 \, {\left(318 \, c^{2} d^{2} e^{4} + 897 \, b c d e^{5} + 143 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} x^{4} + {\left(30 \, c^{2} d^{3} e^{3} + 4407 \, b c d^{2} e^{4} + 1287 \, a b e^{6} + 2717 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} x^{3} - 3 \, {\left(12 \, c^{2} d^{4} e^{2} - 39 \, b c d^{3} e^{3} - 1287 \, a b d e^{5} - 715 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} x^{2} + {\left(48 \, c^{2} d^{5} e - 156 \, b c d^{4} e^{2} + 3861 \, a b d^{2} e^{4} + 143 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{9009 \, e^{4}}"," ",0,"2/9009*(1386*c^2*e^6*x^6 - 96*c^2*d^6 + 312*b*c*d^5*e + 1287*a*b*d^3*e^3 - 286*(b^2 + 2*a*c)*d^4*e^2 + 189*(18*c^2*d*e^5 + 13*b*c*e^6)*x^5 + 7*(318*c^2*d^2*e^4 + 897*b*c*d*e^5 + 143*(b^2 + 2*a*c)*e^6)*x^4 + (30*c^2*d^3*e^3 + 4407*b*c*d^2*e^4 + 1287*a*b*e^6 + 2717*(b^2 + 2*a*c)*d*e^5)*x^3 - 3*(12*c^2*d^4*e^2 - 39*b*c*d^3*e^3 - 1287*a*b*d*e^5 - 715*(b^2 + 2*a*c)*d^2*e^4)*x^2 + (48*c^2*d^5*e - 156*b*c*d^4*e^2 + 3861*a*b*d^2*e^4 + 143*(b^2 + 2*a*c)*d^3*e^3)*x)*sqrt(e*x + d)/e^4","B",0
1596,1,220,0,0.399941," ","integrate((2*c*x+b)*(e*x+d)^(3/2)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(210 \, c^{2} e^{5} x^{5} - 32 \, c^{2} d^{5} + 88 \, b c d^{4} e + 231 \, a b d^{2} e^{3} - 66 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + 35 \, {\left(8 \, c^{2} d e^{4} + 11 \, b c e^{5}\right)} x^{4} + 5 \, {\left(2 \, c^{2} d^{2} e^{3} + 110 \, b c d e^{4} + 33 \, {\left(b^{2} + 2 \, a c\right)} e^{5}\right)} x^{3} - 3 \, {\left(4 \, c^{2} d^{3} e^{2} - 11 \, b c d^{2} e^{3} - 77 \, a b e^{5} - 88 \, {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x^{2} + {\left(16 \, c^{2} d^{4} e - 44 \, b c d^{3} e^{2} + 462 \, a b d e^{4} + 33 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{1155 \, e^{4}}"," ",0,"2/1155*(210*c^2*e^5*x^5 - 32*c^2*d^5 + 88*b*c*d^4*e + 231*a*b*d^2*e^3 - 66*(b^2 + 2*a*c)*d^3*e^2 + 35*(8*c^2*d*e^4 + 11*b*c*e^5)*x^4 + 5*(2*c^2*d^2*e^3 + 110*b*c*d*e^4 + 33*(b^2 + 2*a*c)*e^5)*x^3 - 3*(4*c^2*d^3*e^2 - 11*b*c*d^2*e^3 - 77*a*b*e^5 - 88*(b^2 + 2*a*c)*d*e^4)*x^2 + (16*c^2*d^4*e - 44*b*c*d^3*e^2 + 462*a*b*d*e^4 + 33*(b^2 + 2*a*c)*d^2*e^3)*x)*sqrt(e*x + d)/e^4","A",0
1597,1,167,0,0.401805," ","integrate((2*c*x+b)*(c*x^2+b*x+a)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(70 \, c^{2} e^{4} x^{4} - 32 \, c^{2} d^{4} + 72 \, b c d^{3} e + 105 \, a b d e^{3} - 42 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + 5 \, {\left(2 \, c^{2} d e^{3} + 27 \, b c e^{4}\right)} x^{3} - 3 \, {\left(4 \, c^{2} d^{2} e^{2} - 9 \, b c d e^{3} - 21 \, {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} + {\left(16 \, c^{2} d^{3} e - 36 \, b c d^{2} e^{2} + 105 \, a b e^{4} + 21 \, {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{4}}"," ",0,"2/315*(70*c^2*e^4*x^4 - 32*c^2*d^4 + 72*b*c*d^3*e + 105*a*b*d*e^3 - 42*(b^2 + 2*a*c)*d^2*e^2 + 5*(2*c^2*d*e^3 + 27*b*c*e^4)*x^3 - 3*(4*c^2*d^2*e^2 - 9*b*c*d*e^3 - 21*(b^2 + 2*a*c)*e^4)*x^2 + (16*c^2*d^3*e - 36*b*c*d^2*e^2 + 105*a*b*e^4 + 21*(b^2 + 2*a*c)*d*e^3)*x)*sqrt(e*x + d)/e^4","A",0
1598,1,116,0,0.394439," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(30 \, c^{2} e^{3} x^{3} - 96 \, c^{2} d^{3} + 168 \, b c d^{2} e + 105 \, a b e^{3} - 70 \, {\left(b^{2} + 2 \, a c\right)} d e^{2} - 9 \, {\left(4 \, c^{2} d e^{2} - 7 \, b c e^{3}\right)} x^{2} + {\left(48 \, c^{2} d^{2} e - 84 \, b c d e^{2} + 35 \, {\left(b^{2} + 2 \, a c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{4}}"," ",0,"2/105*(30*c^2*e^3*x^3 - 96*c^2*d^3 + 168*b*c*d^2*e + 105*a*b*e^3 - 70*(b^2 + 2*a*c)*d*e^2 - 9*(4*c^2*d*e^2 - 7*b*c*e^3)*x^2 + (48*c^2*d^2*e - 84*b*c*d*e^2 + 35*(b^2 + 2*a*c)*e^3)*x)*sqrt(e*x + d)/e^4","A",0
1599,1,126,0,0.407985," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{2} e^{3} x^{3} + 32 \, c^{2} d^{3} - 40 \, b c d^{2} e - 5 \, a b e^{3} + 10 \, {\left(b^{2} + 2 \, a c\right)} d e^{2} - {\left(4 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} x^{2} + {\left(16 \, c^{2} d^{2} e - 20 \, b c d e^{2} + 5 \, {\left(b^{2} + 2 \, a c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{5 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"2/5*(2*c^2*e^3*x^3 + 32*c^2*d^3 - 40*b*c*d^2*e - 5*a*b*e^3 + 10*(b^2 + 2*a*c)*d*e^2 - (4*c^2*d*e^2 - 5*b*c*e^3)*x^2 + (16*c^2*d^2*e - 20*b*c*d*e^2 + 5*(b^2 + 2*a*c)*e^3)*x)*sqrt(e*x + d)/(e^5*x + d*e^4)","A",0
1600,1,137,0,0.411955," ","integrate((2*c*x+b)*(c*x^2+b*x+a)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{2} e^{3} x^{3} - 32 \, c^{2} d^{3} + 24 \, b c d^{2} e - a b e^{3} - 2 \, {\left(b^{2} + 2 \, a c\right)} d e^{2} - 3 \, {\left(4 \, c^{2} d e^{2} - 3 \, b c e^{3}\right)} x^{2} - 3 \, {\left(16 \, c^{2} d^{2} e - 12 \, b c d e^{2} + {\left(b^{2} + 2 \, a c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"2/3*(2*c^2*e^3*x^3 - 32*c^2*d^3 + 24*b*c*d^2*e - a*b*e^3 - 2*(b^2 + 2*a*c)*d*e^2 - 3*(4*c^2*d*e^2 - 3*b*c*e^3)*x^2 - 3*(16*c^2*d^2*e - 12*b*c*d*e^2 + (b^2 + 2*a*c)*e^3)*x)*sqrt(e*x + d)/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1601,1,590,0,0.411721," ","integrate((2*c*x+b)*(e*x+d)^(5/2)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(18018 \, c^{3} e^{8} x^{8} - 512 \, c^{3} d^{8} + 2176 \, b c^{2} d^{7} e + 21879 \, a^{2} b d^{3} e^{5} - 3264 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} + 1768 \, {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} - 9724 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + 3003 \, {\left(14 \, c^{3} d e^{7} + 17 \, b c^{2} e^{8}\right)} x^{7} + 231 \, {\left(110 \, c^{3} d^{2} e^{6} + 527 \, b c^{2} d e^{7} + 204 \, {\left(b^{2} c + a c^{2}\right)} e^{8}\right)} x^{6} + 63 \, {\left(2 \, c^{3} d^{3} e^{5} + 1207 \, b c^{2} d^{2} e^{6} + 1836 \, {\left(b^{2} c + a c^{2}\right)} d e^{7} + 221 \, {\left(b^{3} + 6 \, a b c\right)} e^{8}\right)} x^{5} - 7 \, {\left(20 \, c^{3} d^{4} e^{4} - 85 \, b c^{2} d^{3} e^{5} - 10812 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{6} - 5083 \, {\left(b^{3} + 6 \, a b c\right)} d e^{7} - 4862 \, {\left(a b^{2} + a^{2} c\right)} e^{8}\right)} x^{4} + {\left(160 \, c^{3} d^{5} e^{3} - 680 \, b c^{2} d^{4} e^{4} + 21879 \, a^{2} b e^{8} + 1020 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{5} + 24973 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{6} + 92378 \, {\left(a b^{2} + a^{2} c\right)} d e^{7}\right)} x^{3} - 3 \, {\left(64 \, c^{3} d^{6} e^{2} - 272 \, b c^{2} d^{5} e^{3} - 21879 \, a^{2} b d e^{7} + 408 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - 221 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} - 24310 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} + {\left(256 \, c^{3} d^{7} e - 1088 \, b c^{2} d^{6} e^{2} + 65637 \, a^{2} b d^{2} e^{6} + 1632 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - 884 \, {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 4862 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{153153 \, e^{6}}"," ",0,"2/153153*(18018*c^3*e^8*x^8 - 512*c^3*d^8 + 2176*b*c^2*d^7*e + 21879*a^2*b*d^3*e^5 - 3264*(b^2*c + a*c^2)*d^6*e^2 + 1768*(b^3 + 6*a*b*c)*d^5*e^3 - 9724*(a*b^2 + a^2*c)*d^4*e^4 + 3003*(14*c^3*d*e^7 + 17*b*c^2*e^8)*x^7 + 231*(110*c^3*d^2*e^6 + 527*b*c^2*d*e^7 + 204*(b^2*c + a*c^2)*e^8)*x^6 + 63*(2*c^3*d^3*e^5 + 1207*b*c^2*d^2*e^6 + 1836*(b^2*c + a*c^2)*d*e^7 + 221*(b^3 + 6*a*b*c)*e^8)*x^5 - 7*(20*c^3*d^4*e^4 - 85*b*c^2*d^3*e^5 - 10812*(b^2*c + a*c^2)*d^2*e^6 - 5083*(b^3 + 6*a*b*c)*d*e^7 - 4862*(a*b^2 + a^2*c)*e^8)*x^4 + (160*c^3*d^5*e^3 - 680*b*c^2*d^4*e^4 + 21879*a^2*b*e^8 + 1020*(b^2*c + a*c^2)*d^3*e^5 + 24973*(b^3 + 6*a*b*c)*d^2*e^6 + 92378*(a*b^2 + a^2*c)*d*e^7)*x^3 - 3*(64*c^3*d^6*e^2 - 272*b*c^2*d^5*e^3 - 21879*a^2*b*d*e^7 + 408*(b^2*c + a*c^2)*d^4*e^4 - 221*(b^3 + 6*a*b*c)*d^3*e^5 - 24310*(a*b^2 + a^2*c)*d^2*e^6)*x^2 + (256*c^3*d^7*e - 1088*b*c^2*d^6*e^2 + 65637*a^2*b*d^2*e^6 + 1632*(b^2*c + a*c^2)*d^5*e^3 - 884*(b^3 + 6*a*b*c)*d^4*e^4 + 4862*(a*b^2 + a^2*c)*d^3*e^5)*x)*sqrt(e*x + d)/e^6","B",0
1602,1,495,0,0.404357," ","integrate((2*c*x+b)*(e*x+d)^(3/2)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(6006 \, c^{3} e^{7} x^{7} - 512 \, c^{3} d^{7} + 1920 \, b c^{2} d^{6} e + 9009 \, a^{2} b d^{2} e^{5} - 2496 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{2} + 1144 \, {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{3} - 5148 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{4} + 231 \, {\left(32 \, c^{3} d e^{6} + 75 \, b c^{2} e^{7}\right)} x^{6} + 126 \, {\left(c^{3} d^{2} e^{5} + 175 \, b c^{2} d e^{6} + 130 \, {\left(b^{2} c + a c^{2}\right)} e^{7}\right)} x^{5} - 35 \, {\left(4 \, c^{3} d^{3} e^{4} - 15 \, b c^{2} d^{2} e^{5} - 624 \, {\left(b^{2} c + a c^{2}\right)} d e^{6} - 143 \, {\left(b^{3} + 6 \, a b c\right)} e^{7}\right)} x^{4} + 10 \, {\left(16 \, c^{3} d^{4} e^{3} - 60 \, b c^{2} d^{3} e^{4} + 78 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{5} + 715 \, {\left(b^{3} + 6 \, a b c\right)} d e^{6} + 1287 \, {\left(a b^{2} + a^{2} c\right)} e^{7}\right)} x^{3} - 3 \, {\left(64 \, c^{3} d^{5} e^{2} - 240 \, b c^{2} d^{4} e^{3} - 3003 \, a^{2} b e^{7} + 312 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{4} - 143 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{5} - 6864 \, {\left(a b^{2} + a^{2} c\right)} d e^{6}\right)} x^{2} + 2 \, {\left(128 \, c^{3} d^{6} e - 480 \, b c^{2} d^{5} e^{2} + 9009 \, a^{2} b d e^{6} + 624 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{3} - 286 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{4} + 1287 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{6}}"," ",0,"2/45045*(6006*c^3*e^7*x^7 - 512*c^3*d^7 + 1920*b*c^2*d^6*e + 9009*a^2*b*d^2*e^5 - 2496*(b^2*c + a*c^2)*d^5*e^2 + 1144*(b^3 + 6*a*b*c)*d^4*e^3 - 5148*(a*b^2 + a^2*c)*d^3*e^4 + 231*(32*c^3*d*e^6 + 75*b*c^2*e^7)*x^6 + 126*(c^3*d^2*e^5 + 175*b*c^2*d*e^6 + 130*(b^2*c + a*c^2)*e^7)*x^5 - 35*(4*c^3*d^3*e^4 - 15*b*c^2*d^2*e^5 - 624*(b^2*c + a*c^2)*d*e^6 - 143*(b^3 + 6*a*b*c)*e^7)*x^4 + 10*(16*c^3*d^4*e^3 - 60*b*c^2*d^3*e^4 + 78*(b^2*c + a*c^2)*d^2*e^5 + 715*(b^3 + 6*a*b*c)*d*e^6 + 1287*(a*b^2 + a^2*c)*e^7)*x^3 - 3*(64*c^3*d^5*e^2 - 240*b*c^2*d^4*e^3 - 3003*a^2*b*e^7 + 312*(b^2*c + a*c^2)*d^3*e^4 - 143*(b^3 + 6*a*b*c)*d^2*e^5 - 6864*(a*b^2 + a^2*c)*d*e^6)*x^2 + 2*(128*c^3*d^6*e - 480*b*c^2*d^5*e^2 + 9009*a^2*b*d*e^6 + 624*(b^2*c + a*c^2)*d^4*e^3 - 286*(b^3 + 6*a*b*c)*d^3*e^4 + 1287*(a*b^2 + a^2*c)*d^2*e^5)*x)*sqrt(e*x + d)/e^6","B",0
1603,1,399,0,0.393496," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6930 \, c^{3} e^{6} x^{6} - 2560 \, c^{3} d^{6} + 8320 \, b c^{2} d^{5} e + 15015 \, a^{2} b d e^{5} - 9152 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + 3432 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 12012 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} + 315 \, {\left(2 \, c^{3} d e^{5} + 65 \, b c^{2} e^{6}\right)} x^{5} - 35 \, {\left(20 \, c^{3} d^{2} e^{4} - 65 \, b c^{2} d e^{5} - 572 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} + 5 \, {\left(160 \, c^{3} d^{3} e^{3} - 520 \, b c^{2} d^{2} e^{4} + 572 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + 1287 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} - 3 \, {\left(320 \, c^{3} d^{4} e^{2} - 1040 \, b c^{2} d^{3} e^{3} + 1144 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - 429 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} - 6006 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} + {\left(1280 \, c^{3} d^{5} e - 4160 \, b c^{2} d^{4} e^{2} + 15015 \, a^{2} b e^{6} + 4576 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - 1716 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 6006 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{6}}"," ",0,"2/45045*(6930*c^3*e^6*x^6 - 2560*c^3*d^6 + 8320*b*c^2*d^5*e + 15015*a^2*b*d*e^5 - 9152*(b^2*c + a*c^2)*d^4*e^2 + 3432*(b^3 + 6*a*b*c)*d^3*e^3 - 12012*(a*b^2 + a^2*c)*d^2*e^4 + 315*(2*c^3*d*e^5 + 65*b*c^2*e^6)*x^5 - 35*(20*c^3*d^2*e^4 - 65*b*c^2*d*e^5 - 572*(b^2*c + a*c^2)*e^6)*x^4 + 5*(160*c^3*d^3*e^3 - 520*b*c^2*d^2*e^4 + 572*(b^2*c + a*c^2)*d*e^5 + 1287*(b^3 + 6*a*b*c)*e^6)*x^3 - 3*(320*c^3*d^4*e^2 - 1040*b*c^2*d^3*e^3 + 1144*(b^2*c + a*c^2)*d^2*e^4 - 429*(b^3 + 6*a*b*c)*d*e^5 - 6006*(a*b^2 + a^2*c)*e^6)*x^2 + (1280*c^3*d^5*e - 4160*b*c^2*d^4*e^2 + 15015*a^2*b*e^6 + 4576*(b^2*c + a*c^2)*d^3*e^3 - 1716*(b^3 + 6*a*b*c)*d^2*e^4 + 6006*(a*b^2 + a^2*c)*d*e^5)*x)*sqrt(e*x + d)/e^6","A",0
1604,1,306,0,0.407162," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(630 \, c^{3} e^{5} x^{5} - 2560 \, c^{3} d^{5} + 7040 \, b c^{2} d^{4} e + 3465 \, a^{2} b e^{5} - 6336 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} + 1848 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} - 4620 \, {\left(a b^{2} + a^{2} c\right)} d e^{4} - 175 \, {\left(4 \, c^{3} d e^{4} - 11 \, b c^{2} e^{5}\right)} x^{4} + 20 \, {\left(40 \, c^{3} d^{2} e^{3} - 110 \, b c^{2} d e^{4} + 99 \, {\left(b^{2} c + a c^{2}\right)} e^{5}\right)} x^{3} - 3 \, {\left(320 \, c^{3} d^{3} e^{2} - 880 \, b c^{2} d^{2} e^{3} + 792 \, {\left(b^{2} c + a c^{2}\right)} d e^{4} - 231 \, {\left(b^{3} + 6 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(640 \, c^{3} d^{4} e - 1760 \, b c^{2} d^{3} e^{2} + 1584 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} - 462 \, {\left(b^{3} + 6 \, a b c\right)} d e^{4} + 1155 \, {\left(a b^{2} + a^{2} c\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{6}}"," ",0,"2/3465*(630*c^3*e^5*x^5 - 2560*c^3*d^5 + 7040*b*c^2*d^4*e + 3465*a^2*b*e^5 - 6336*(b^2*c + a*c^2)*d^3*e^2 + 1848*(b^3 + 6*a*b*c)*d^2*e^3 - 4620*(a*b^2 + a^2*c)*d*e^4 - 175*(4*c^3*d*e^4 - 11*b*c^2*e^5)*x^4 + 20*(40*c^3*d^2*e^3 - 110*b*c^2*d*e^4 + 99*(b^2*c + a*c^2)*e^5)*x^3 - 3*(320*c^3*d^3*e^2 - 880*b*c^2*d^2*e^3 + 792*(b^2*c + a*c^2)*d*e^4 - 231*(b^3 + 6*a*b*c)*e^5)*x^2 + 2*(640*c^3*d^4*e - 1760*b*c^2*d^3*e^2 + 1584*(b^2*c + a*c^2)*d^2*e^3 - 462*(b^3 + 6*a*b*c)*d*e^4 + 1155*(a*b^2 + a^2*c)*e^5)*x)*sqrt(e*x + d)/e^6","A",0
1605,1,316,0,0.399784," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(70 \, c^{3} e^{5} x^{5} + 2560 \, c^{3} d^{5} - 5760 \, b c^{2} d^{4} e - 315 \, a^{2} b e^{5} + 4032 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} - 840 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} + 1260 \, {\left(a b^{2} + a^{2} c\right)} d e^{4} - 25 \, {\left(4 \, c^{3} d e^{4} - 9 \, b c^{2} e^{5}\right)} x^{4} + 4 \, {\left(40 \, c^{3} d^{2} e^{3} - 90 \, b c^{2} d e^{4} + 63 \, {\left(b^{2} c + a c^{2}\right)} e^{5}\right)} x^{3} - {\left(320 \, c^{3} d^{3} e^{2} - 720 \, b c^{2} d^{2} e^{3} + 504 \, {\left(b^{2} c + a c^{2}\right)} d e^{4} - 105 \, {\left(b^{3} + 6 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(640 \, c^{3} d^{4} e - 1440 \, b c^{2} d^{3} e^{2} + 1008 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} - 210 \, {\left(b^{3} + 6 \, a b c\right)} d e^{4} + 315 \, {\left(a b^{2} + a^{2} c\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"2/315*(70*c^3*e^5*x^5 + 2560*c^3*d^5 - 5760*b*c^2*d^4*e - 315*a^2*b*e^5 + 4032*(b^2*c + a*c^2)*d^3*e^2 - 840*(b^3 + 6*a*b*c)*d^2*e^3 + 1260*(a*b^2 + a^2*c)*d*e^4 - 25*(4*c^3*d*e^4 - 9*b*c^2*e^5)*x^4 + 4*(40*c^3*d^2*e^3 - 90*b*c^2*d*e^4 + 63*(b^2*c + a*c^2)*e^5)*x^3 - (320*c^3*d^3*e^2 - 720*b*c^2*d^2*e^3 + 504*(b^2*c + a*c^2)*d*e^4 - 105*(b^3 + 6*a*b*c)*e^5)*x^2 + 2*(640*c^3*d^4*e - 1440*b*c^2*d^3*e^2 + 1008*(b^2*c + a*c^2)*d^2*e^3 - 210*(b^3 + 6*a*b*c)*d*e^4 + 315*(a*b^2 + a^2*c)*e^5)*x)*sqrt(e*x + d)/(e^7*x + d*e^6)","A",0
1606,1,327,0,0.411246," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, c^{3} e^{5} x^{5} - 512 \, c^{3} d^{5} + 896 \, b c^{2} d^{4} e - 7 \, a^{2} b e^{5} - 448 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{2} + 56 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{3} - 28 \, {\left(a b^{2} + a^{2} c\right)} d e^{4} - 3 \, {\left(4 \, c^{3} d e^{4} - 7 \, b c^{2} e^{5}\right)} x^{4} + 4 \, {\left(8 \, c^{3} d^{2} e^{3} - 14 \, b c^{2} d e^{4} + 7 \, {\left(b^{2} c + a c^{2}\right)} e^{5}\right)} x^{3} - 3 \, {\left(64 \, c^{3} d^{3} e^{2} - 112 \, b c^{2} d^{2} e^{3} + 56 \, {\left(b^{2} c + a c^{2}\right)} d e^{4} - 7 \, {\left(b^{3} + 6 \, a b c\right)} e^{5}\right)} x^{2} - 6 \, {\left(128 \, c^{3} d^{4} e - 224 \, b c^{2} d^{3} e^{2} + 112 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{3} - 14 \, {\left(b^{3} + 6 \, a b c\right)} d e^{4} + 7 \, {\left(a b^{2} + a^{2} c\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{21 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"2/21*(6*c^3*e^5*x^5 - 512*c^3*d^5 + 896*b*c^2*d^4*e - 7*a^2*b*e^5 - 448*(b^2*c + a*c^2)*d^3*e^2 + 56*(b^3 + 6*a*b*c)*d^2*e^3 - 28*(a*b^2 + a^2*c)*d*e^4 - 3*(4*c^3*d*e^4 - 7*b*c^2*e^5)*x^4 + 4*(8*c^3*d^2*e^3 - 14*b*c^2*d*e^4 + 7*(b^2*c + a*c^2)*e^5)*x^3 - 3*(64*c^3*d^3*e^2 - 112*b*c^2*d^2*e^3 + 56*(b^2*c + a*c^2)*d*e^4 - 7*(b^3 + 6*a*b*c)*e^5)*x^2 - 6*(128*c^3*d^4*e - 224*b*c^2*d^3*e^2 + 112*(b^2*c + a*c^2)*d^2*e^3 - 14*(b^3 + 6*a*b*c)*d*e^4 + 7*(a*b^2 + a^2*c)*e^5)*x)*sqrt(e*x + d)/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","A",0
1607,1,1113,0,0.420711," ","integrate((2*c*x+b)*(e*x+d)^(5/2)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(277134 \, c^{4} e^{10} x^{10} - 4096 \, c^{4} d^{10} + 21504 \, b c^{3} d^{9} e + 415701 \, a^{3} b d^{3} e^{7} - 14592 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{2} + 41344 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{3} - 15504 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{4} + 100776 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{5} - 92378 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{6} + 7293 \, {\left(86 \, c^{4} d e^{9} + 147 \, b c^{3} e^{10}\right)} x^{9} + 3861 \, {\left(94 \, c^{4} d^{2} e^{8} + 637 \, b c^{3} d e^{9} + 133 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{10}\right)} x^{8} + 429 \, {\left(2 \, c^{4} d^{3} e^{7} + 3381 \, b c^{3} d^{2} e^{8} + 2793 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{9} + 2261 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{10}\right)} x^{7} - 231 \, {\left(4 \, c^{4} d^{4} e^{6} - 21 \, b c^{3} d^{3} e^{7} - 3135 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{8} - 10013 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{9} - 969 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{10}\right)} x^{6} + 63 \, {\left(16 \, c^{4} d^{5} e^{5} - 84 \, b c^{3} d^{4} e^{6} + 57 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{7} + 22933 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{8} + 8721 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{9} + 12597 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{10}\right)} x^{5} - 7 \, {\left(160 \, c^{4} d^{6} e^{4} - 840 \, b c^{3} d^{5} e^{5} + 570 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{6} - 1615 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{7} - 51357 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{8} - 289731 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{9} - 46189 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{10}\right)} x^{4} + {\left(1280 \, c^{4} d^{7} e^{3} - 6720 \, b c^{3} d^{6} e^{4} + 415701 \, a^{3} b e^{10} + 4560 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{5} - 12920 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{6} + 4845 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{7} + 1423461 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{8} + 877591 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{9}\right)} x^{3} - 3 \, {\left(512 \, c^{4} d^{8} e^{2} - 2688 \, b c^{3} d^{7} e^{3} - 415701 \, a^{3} b d e^{9} + 1824 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{4} - 5168 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{5} + 1938 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{6} - 12597 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{7} - 230945 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{8}\right)} x^{2} + {\left(2048 \, c^{4} d^{9} e - 10752 \, b c^{3} d^{8} e^{2} + 1247103 \, a^{3} b d^{2} e^{8} + 7296 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{3} - 20672 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{4} + 7752 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{5} - 50388 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{6} + 46189 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{2909907 \, e^{8}}"," ",0,"2/2909907*(277134*c^4*e^10*x^10 - 4096*c^4*d^10 + 21504*b*c^3*d^9*e + 415701*a^3*b*d^3*e^7 - 14592*(3*b^2*c^2 + 2*a*c^3)*d^8*e^2 + 41344*(b^3*c + 3*a*b*c^2)*d^7*e^3 - 15504*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^4 + 100776*(a*b^3 + 3*a^2*b*c)*d^5*e^5 - 92378*(3*a^2*b^2 + 2*a^3*c)*d^4*e^6 + 7293*(86*c^4*d*e^9 + 147*b*c^3*e^10)*x^9 + 3861*(94*c^4*d^2*e^8 + 637*b*c^3*d*e^9 + 133*(3*b^2*c^2 + 2*a*c^3)*e^10)*x^8 + 429*(2*c^4*d^3*e^7 + 3381*b*c^3*d^2*e^8 + 2793*(3*b^2*c^2 + 2*a*c^3)*d*e^9 + 2261*(b^3*c + 3*a*b*c^2)*e^10)*x^7 - 231*(4*c^4*d^4*e^6 - 21*b*c^3*d^3*e^7 - 3135*(3*b^2*c^2 + 2*a*c^3)*d^2*e^8 - 10013*(b^3*c + 3*a*b*c^2)*d*e^9 - 969*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^10)*x^6 + 63*(16*c^4*d^5*e^5 - 84*b*c^3*d^4*e^6 + 57*(3*b^2*c^2 + 2*a*c^3)*d^3*e^7 + 22933*(b^3*c + 3*a*b*c^2)*d^2*e^8 + 8721*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^9 + 12597*(a*b^3 + 3*a^2*b*c)*e^10)*x^5 - 7*(160*c^4*d^6*e^4 - 840*b*c^3*d^5*e^5 + 570*(3*b^2*c^2 + 2*a*c^3)*d^4*e^6 - 1615*(b^3*c + 3*a*b*c^2)*d^3*e^7 - 51357*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^8 - 289731*(a*b^3 + 3*a^2*b*c)*d*e^9 - 46189*(3*a^2*b^2 + 2*a^3*c)*e^10)*x^4 + (1280*c^4*d^7*e^3 - 6720*b*c^3*d^6*e^4 + 415701*a^3*b*e^10 + 4560*(3*b^2*c^2 + 2*a*c^3)*d^5*e^5 - 12920*(b^3*c + 3*a*b*c^2)*d^4*e^6 + 4845*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^7 + 1423461*(a*b^3 + 3*a^2*b*c)*d^2*e^8 + 877591*(3*a^2*b^2 + 2*a^3*c)*d*e^9)*x^3 - 3*(512*c^4*d^8*e^2 - 2688*b*c^3*d^7*e^3 - 415701*a^3*b*d*e^9 + 1824*(3*b^2*c^2 + 2*a*c^3)*d^6*e^4 - 5168*(b^3*c + 3*a*b*c^2)*d^5*e^5 + 1938*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^6 - 12597*(a*b^3 + 3*a^2*b*c)*d^3*e^7 - 230945*(3*a^2*b^2 + 2*a^3*c)*d^2*e^8)*x^2 + (2048*c^4*d^9*e - 10752*b*c^3*d^8*e^2 + 1247103*a^3*b*d^2*e^8 + 7296*(3*b^2*c^2 + 2*a*c^3)*d^7*e^3 - 20672*(b^3*c + 3*a*b*c^2)*d^6*e^4 + 7752*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^5 - 50388*(a*b^3 + 3*a^2*b*c)*d^4*e^6 + 46189*(3*a^2*b^2 + 2*a^3*c)*d^3*e^7)*x)*sqrt(e*x + d)/e^8","B",0
1608,1,958,0,0.422256," ","integrate((2*c*x+b)*(e*x+d)^(3/2)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(510510 \, c^{4} e^{9} x^{9} - 28672 \, c^{4} d^{9} + 136192 \, b c^{3} d^{8} e + 969969 \, a^{3} b d^{2} e^{7} - 82688 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{2} + 206720 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{3} - 67184 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{4} + 369512 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{5} - 277134 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{6} + 15015 \, {\left(40 \, c^{4} d e^{8} + 133 \, b c^{3} e^{9}\right)} x^{8} + 3003 \, {\left(2 \, c^{4} d^{2} e^{7} + 798 \, b c^{3} d e^{8} + 323 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9}\right)} x^{7} - 231 \, {\left(28 \, c^{4} d^{3} e^{6} - 133 \, b c^{3} d^{2} e^{7} - 5168 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{8} - 8075 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9}\right)} x^{6} + 21 \, {\left(336 \, c^{4} d^{4} e^{5} - 1596 \, b c^{3} d^{3} e^{6} + 969 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{7} + 113050 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{8} + 20995 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9}\right)} x^{5} - 35 \, {\left(224 \, c^{4} d^{5} e^{4} - 1064 \, b c^{3} d^{4} e^{5} + 646 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{6} - 1615 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{7} - 16796 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{8} - 46189 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9}\right)} x^{4} + 5 \, {\left(1792 \, c^{4} d^{6} e^{3} - 8512 \, b c^{3} d^{5} e^{4} + 5168 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{5} - 12920 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{6} + 4199 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{7} + 461890 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{8} + 138567 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9}\right)} x^{3} - 3 \, {\left(3584 \, c^{4} d^{7} e^{2} - 17024 \, b c^{3} d^{6} e^{3} - 323323 \, a^{3} b e^{9} + 10336 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{4} - 25840 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{5} + 8398 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{6} - 46189 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{7} - 369512 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{8}\right)} x^{2} + {\left(14336 \, c^{4} d^{8} e - 68096 \, b c^{3} d^{7} e^{2} + 1939938 \, a^{3} b d e^{8} + 41344 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{3} - 103360 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{4} + 33592 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{5} - 184756 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{6} + 138567 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{7}\right)} x\right)} \sqrt{e x + d}}{4849845 \, e^{8}}"," ",0,"2/4849845*(510510*c^4*e^9*x^9 - 28672*c^4*d^9 + 136192*b*c^3*d^8*e + 969969*a^3*b*d^2*e^7 - 82688*(3*b^2*c^2 + 2*a*c^3)*d^7*e^2 + 206720*(b^3*c + 3*a*b*c^2)*d^6*e^3 - 67184*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^4 + 369512*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 277134*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6 + 15015*(40*c^4*d*e^8 + 133*b*c^3*e^9)*x^8 + 3003*(2*c^4*d^2*e^7 + 798*b*c^3*d*e^8 + 323*(3*b^2*c^2 + 2*a*c^3)*e^9)*x^7 - 231*(28*c^4*d^3*e^6 - 133*b*c^3*d^2*e^7 - 5168*(3*b^2*c^2 + 2*a*c^3)*d*e^8 - 8075*(b^3*c + 3*a*b*c^2)*e^9)*x^6 + 21*(336*c^4*d^4*e^5 - 1596*b*c^3*d^3*e^6 + 969*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 + 113050*(b^3*c + 3*a*b*c^2)*d*e^8 + 20995*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*x^5 - 35*(224*c^4*d^5*e^4 - 1064*b*c^3*d^4*e^5 + 646*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 1615*(b^3*c + 3*a*b*c^2)*d^2*e^7 - 16796*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 - 46189*(a*b^3 + 3*a^2*b*c)*e^9)*x^4 + 5*(1792*c^4*d^6*e^3 - 8512*b*c^3*d^5*e^4 + 5168*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 - 12920*(b^3*c + 3*a*b*c^2)*d^3*e^6 + 4199*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 + 461890*(a*b^3 + 3*a^2*b*c)*d*e^8 + 138567*(3*a^2*b^2 + 2*a^3*c)*e^9)*x^3 - 3*(3584*c^4*d^7*e^2 - 17024*b*c^3*d^6*e^3 - 323323*a^3*b*e^9 + 10336*(3*b^2*c^2 + 2*a*c^3)*d^5*e^4 - 25840*(b^3*c + 3*a*b*c^2)*d^4*e^5 + 8398*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 46189*(a*b^3 + 3*a^2*b*c)*d^2*e^7 - 369512*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*x^2 + (14336*c^4*d^8*e - 68096*b*c^3*d^7*e^2 + 1939938*a^3*b*d*e^8 + 41344*(3*b^2*c^2 + 2*a*c^3)*d^6*e^3 - 103360*(b^3*c + 3*a*b*c^2)*d^5*e^4 + 33592*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 - 184756*(a*b^3 + 3*a^2*b*c)*d^3*e^6 + 138567*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*x)*sqrt(e*x + d)/e^8","B",0
1609,1,802,0,0.416101," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(90090 \, c^{4} e^{8} x^{8} - 28672 \, c^{4} d^{8} + 121856 \, b c^{3} d^{7} e + 255255 \, a^{3} b d e^{7} - 65280 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 141440 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - 38896 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 175032 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 102102 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} + 3003 \, {\left(2 \, c^{4} d e^{7} + 119 \, b c^{3} e^{8}\right)} x^{7} - 231 \, {\left(28 \, c^{4} d^{2} e^{6} - 119 \, b c^{3} d e^{7} - 765 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} + 63 \, {\left(112 \, c^{4} d^{3} e^{5} - 476 \, b c^{3} d^{2} e^{6} + 255 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 5525 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} - 35 \, {\left(224 \, c^{4} d^{4} e^{4} - 952 \, b c^{3} d^{3} e^{5} + 510 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 1105 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} - 2431 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} + 5 \, {\left(1792 \, c^{4} d^{5} e^{3} - 7616 \, b c^{3} d^{4} e^{4} + 4080 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 8840 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + 2431 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 65637 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} - 3 \, {\left(3584 \, c^{4} d^{6} e^{2} - 15232 \, b c^{3} d^{5} e^{3} + 8160 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 17680 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + 4862 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 21879 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} - 51051 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} + {\left(14336 \, c^{4} d^{7} e - 60928 \, b c^{3} d^{6} e^{2} + 255255 \, a^{3} b e^{8} + 32640 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 70720 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 19448 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 87516 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 51051 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x\right)} \sqrt{e x + d}}{765765 \, e^{8}}"," ",0,"2/765765*(90090*c^4*e^8*x^8 - 28672*c^4*d^8 + 121856*b*c^3*d^7*e + 255255*a^3*b*d*e^7 - 65280*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 141440*(b^3*c + 3*a*b*c^2)*d^5*e^3 - 38896*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 175032*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 102102*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 + 3003*(2*c^4*d*e^7 + 119*b*c^3*e^8)*x^7 - 231*(28*c^4*d^2*e^6 - 119*b*c^3*d*e^7 - 765*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 + 63*(112*c^4*d^3*e^5 - 476*b*c^3*d^2*e^6 + 255*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 5525*(b^3*c + 3*a*b*c^2)*e^8)*x^5 - 35*(224*c^4*d^4*e^4 - 952*b*c^3*d^3*e^5 + 510*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 1105*(b^3*c + 3*a*b*c^2)*d*e^7 - 2431*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 + 5*(1792*c^4*d^5*e^3 - 7616*b*c^3*d^4*e^4 + 4080*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 8840*(b^3*c + 3*a*b*c^2)*d^2*e^6 + 2431*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 65637*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 - 3*(3584*c^4*d^6*e^2 - 15232*b*c^3*d^5*e^3 + 8160*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 17680*(b^3*c + 3*a*b*c^2)*d^3*e^5 + 4862*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 21879*(a*b^3 + 3*a^2*b*c)*d*e^7 - 51051*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + (14336*c^4*d^7*e - 60928*b*c^3*d^6*e^2 + 255255*a^3*b*e^8 + 32640*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 70720*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 19448*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 87516*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 51051*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x)*sqrt(e*x + d)/e^8","B",0
1610,1,648,0,0.407073," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6006 \, c^{4} e^{7} x^{7} - 28672 \, c^{4} d^{7} + 107520 \, b c^{3} d^{6} e + 45045 \, a^{3} b e^{7} - 49920 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} + 91520 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} - 20592 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} + 72072 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} - 30030 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6} - 1617 \, {\left(4 \, c^{4} d e^{6} - 15 \, b c^{3} e^{7}\right)} x^{6} + 63 \, {\left(112 \, c^{4} d^{2} e^{5} - 420 \, b c^{3} d e^{6} + 195 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{7}\right)} x^{5} - 35 \, {\left(224 \, c^{4} d^{3} e^{4} - 840 \, b c^{3} d^{2} e^{5} + 390 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{6} - 715 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{7}\right)} x^{4} + 5 \, {\left(1792 \, c^{4} d^{4} e^{3} - 6720 \, b c^{3} d^{3} e^{4} + 3120 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} - 5720 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6} + 1287 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{7}\right)} x^{3} - 3 \, {\left(3584 \, c^{4} d^{5} e^{2} - 13440 \, b c^{3} d^{4} e^{3} + 6240 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - 11440 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} + 2574 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6} - 9009 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{7}\right)} x^{2} + {\left(14336 \, c^{4} d^{6} e - 53760 \, b c^{3} d^{5} e^{2} + 24960 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 45760 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + 10296 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - 36036 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6} + 15015 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{7}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{8}}"," ",0,"2/45045*(6006*c^4*e^7*x^7 - 28672*c^4*d^7 + 107520*b*c^3*d^6*e + 45045*a^3*b*e^7 - 49920*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 + 91520*(b^3*c + 3*a*b*c^2)*d^4*e^3 - 20592*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 + 72072*(a*b^3 + 3*a^2*b*c)*d^2*e^5 - 30030*(3*a^2*b^2 + 2*a^3*c)*d*e^6 - 1617*(4*c^4*d*e^6 - 15*b*c^3*e^7)*x^6 + 63*(112*c^4*d^2*e^5 - 420*b*c^3*d*e^6 + 195*(3*b^2*c^2 + 2*a*c^3)*e^7)*x^5 - 35*(224*c^4*d^3*e^4 - 840*b*c^3*d^2*e^5 + 390*(3*b^2*c^2 + 2*a*c^3)*d*e^6 - 715*(b^3*c + 3*a*b*c^2)*e^7)*x^4 + 5*(1792*c^4*d^4*e^3 - 6720*b*c^3*d^3*e^4 + 3120*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 - 5720*(b^3*c + 3*a*b*c^2)*d*e^6 + 1287*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^7)*x^3 - 3*(3584*c^4*d^5*e^2 - 13440*b*c^3*d^4*e^3 + 6240*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - 11440*(b^3*c + 3*a*b*c^2)*d^2*e^5 + 2574*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6 - 9009*(a*b^3 + 3*a^2*b*c)*e^7)*x^2 + (14336*c^4*d^6*e - 53760*b*c^3*d^5*e^2 + 24960*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 45760*(b^3*c + 3*a*b*c^2)*d^3*e^4 + 10296*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 - 36036*(a*b^3 + 3*a^2*b*c)*d*e^6 + 15015*(3*a^2*b^2 + 2*a^3*c)*e^7)*x)*sqrt(e*x + d)/e^8","A",0
1611,1,657,0,0.407417," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2310 \, c^{4} e^{7} x^{7} + 143360 \, c^{4} d^{7} - 465920 \, b c^{3} d^{6} e - 15015 \, a^{3} b e^{7} + 183040 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 274560 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + 48048 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 120120 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} + 30030 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6} - 735 \, {\left(4 \, c^{4} d e^{6} - 13 \, b c^{3} e^{7}\right)} x^{6} + 35 \, {\left(112 \, c^{4} d^{2} e^{5} - 364 \, b c^{3} d e^{6} + 143 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{7}\right)} x^{5} - 25 \, {\left(224 \, c^{4} d^{3} e^{4} - 728 \, b c^{3} d^{2} e^{5} + 286 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{6} - 429 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{7}\right)} x^{4} + {\left(8960 \, c^{4} d^{4} e^{3} - 29120 \, b c^{3} d^{3} e^{4} + 11440 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} - 17160 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6} + 3003 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{7}\right)} x^{3} - {\left(17920 \, c^{4} d^{5} e^{2} - 58240 \, b c^{3} d^{4} e^{3} + 22880 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - 34320 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} + 6006 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6} - 15015 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{7}\right)} x^{2} + {\left(71680 \, c^{4} d^{6} e - 232960 \, b c^{3} d^{5} e^{2} + 91520 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 137280 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + 24024 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - 60060 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6} + 15015 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{7}\right)} x\right)} \sqrt{e x + d}}{15015 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"2/15015*(2310*c^4*e^7*x^7 + 143360*c^4*d^7 - 465920*b*c^3*d^6*e - 15015*a^3*b*e^7 + 183040*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 274560*(b^3*c + 3*a*b*c^2)*d^4*e^3 + 48048*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 120120*(a*b^3 + 3*a^2*b*c)*d^2*e^5 + 30030*(3*a^2*b^2 + 2*a^3*c)*d*e^6 - 735*(4*c^4*d*e^6 - 13*b*c^3*e^7)*x^6 + 35*(112*c^4*d^2*e^5 - 364*b*c^3*d*e^6 + 143*(3*b^2*c^2 + 2*a*c^3)*e^7)*x^5 - 25*(224*c^4*d^3*e^4 - 728*b*c^3*d^2*e^5 + 286*(3*b^2*c^2 + 2*a*c^3)*d*e^6 - 429*(b^3*c + 3*a*b*c^2)*e^7)*x^4 + (8960*c^4*d^4*e^3 - 29120*b*c^3*d^3*e^4 + 11440*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 - 17160*(b^3*c + 3*a*b*c^2)*d*e^6 + 3003*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^7)*x^3 - (17920*c^4*d^5*e^2 - 58240*b*c^3*d^4*e^3 + 22880*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - 34320*(b^3*c + 3*a*b*c^2)*d^2*e^5 + 6006*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6 - 15015*(a*b^3 + 3*a^2*b*c)*e^7)*x^2 + (71680*c^4*d^6*e - 232960*b*c^3*d^5*e^2 + 91520*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 137280*(b^3*c + 3*a*b*c^2)*d^3*e^4 + 24024*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 - 60060*(a*b^3 + 3*a^2*b*c)*d*e^6 + 15015*(3*a^2*b^2 + 2*a^3*c)*e^7)*x)*sqrt(e*x + d)/(e^9*x + d*e^8)","A",0
1612,1,669,0,0.416960," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(126 \, c^{4} e^{7} x^{7} - 28672 \, c^{4} d^{7} + 78848 \, b c^{3} d^{6} e - 231 \, a^{3} b e^{7} - 25344 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} + 29568 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} - 3696 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} + 5544 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} - 462 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6} - 49 \, {\left(4 \, c^{4} d e^{6} - 11 \, b c^{3} e^{7}\right)} x^{6} + 3 \, {\left(112 \, c^{4} d^{2} e^{5} - 308 \, b c^{3} d e^{6} + 99 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{7}\right)} x^{5} - 3 \, {\left(224 \, c^{4} d^{3} e^{4} - 616 \, b c^{3} d^{2} e^{5} + 198 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{6} - 231 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{7}\right)} x^{4} + {\left(1792 \, c^{4} d^{4} e^{3} - 4928 \, b c^{3} d^{3} e^{4} + 1584 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{5} - 1848 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{6} + 231 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{7}\right)} x^{3} - 3 \, {\left(3584 \, c^{4} d^{5} e^{2} - 9856 \, b c^{3} d^{4} e^{3} + 3168 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{4} - 3696 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{5} + 462 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{6} - 693 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{7}\right)} x^{2} - 3 \, {\left(14336 \, c^{4} d^{6} e - 39424 \, b c^{3} d^{5} e^{2} + 12672 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{3} - 14784 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{4} + 1848 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{5} - 2772 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{6} + 231 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{7}\right)} x\right)} \sqrt{e x + d}}{693 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"2/693*(126*c^4*e^7*x^7 - 28672*c^4*d^7 + 78848*b*c^3*d^6*e - 231*a^3*b*e^7 - 25344*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 + 29568*(b^3*c + 3*a*b*c^2)*d^4*e^3 - 3696*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 + 5544*(a*b^3 + 3*a^2*b*c)*d^2*e^5 - 462*(3*a^2*b^2 + 2*a^3*c)*d*e^6 - 49*(4*c^4*d*e^6 - 11*b*c^3*e^7)*x^6 + 3*(112*c^4*d^2*e^5 - 308*b*c^3*d*e^6 + 99*(3*b^2*c^2 + 2*a*c^3)*e^7)*x^5 - 3*(224*c^4*d^3*e^4 - 616*b*c^3*d^2*e^5 + 198*(3*b^2*c^2 + 2*a*c^3)*d*e^6 - 231*(b^3*c + 3*a*b*c^2)*e^7)*x^4 + (1792*c^4*d^4*e^3 - 4928*b*c^3*d^3*e^4 + 1584*(3*b^2*c^2 + 2*a*c^3)*d^2*e^5 - 1848*(b^3*c + 3*a*b*c^2)*d*e^6 + 231*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^7)*x^3 - 3*(3584*c^4*d^5*e^2 - 9856*b*c^3*d^4*e^3 + 3168*(3*b^2*c^2 + 2*a*c^3)*d^3*e^4 - 3696*(b^3*c + 3*a*b*c^2)*d^2*e^5 + 462*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^6 - 693*(a*b^3 + 3*a^2*b*c)*e^7)*x^2 - 3*(14336*c^4*d^6*e - 39424*b*c^3*d^5*e^2 + 12672*(3*b^2*c^2 + 2*a*c^3)*d^4*e^3 - 14784*(b^3*c + 3*a*b*c^2)*d^3*e^4 + 1848*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^5 - 2772*(a*b^3 + 3*a^2*b*c)*d*e^6 + 231*(3*a^2*b^2 + 2*a^3*c)*e^7)*x)*sqrt(e*x + d)/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","A",0
1613,1,2909,0,0.535796," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}}{c^{3}}} \log\left(\sqrt{2} {\left(6 \, c^{3} d^{3} - 9 \, b c^{2} d^{2} e + {\left(5 \, b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - a b c\right)} e^{3} - c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}}{c^{3}}} - 4 \, {\left(3 \, c^{3} d^{4} - 6 \, b c^{2} d^{3} e + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} + 2 \, a b c\right)} d e^{3} + {\left(a b^{2} - a^{2} c\right)} e^{4}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}}{c^{3}}} \log\left(-\sqrt{2} {\left(6 \, c^{3} d^{3} - 9 \, b c^{2} d^{2} e + {\left(5 \, b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - a b c\right)} e^{3} - c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}}{c^{3}}} - 4 \, {\left(3 \, c^{3} d^{4} - 6 \, b c^{2} d^{3} e + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} + 2 \, a b c\right)} d e^{3} + {\left(a b^{2} - a^{2} c\right)} e^{4}\right)} \sqrt{e x + d}\right) + 3 \, \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}}{c^{3}}} \log\left(\sqrt{2} {\left(6 \, c^{3} d^{3} - 9 \, b c^{2} d^{2} e + {\left(5 \, b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - a b c\right)} e^{3} + c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}}{c^{3}}} - 4 \, {\left(3 \, c^{3} d^{4} - 6 \, b c^{2} d^{3} e + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} + 2 \, a b c\right)} d e^{3} + {\left(a b^{2} - a^{2} c\right)} e^{4}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}}{c^{3}}} \log\left(-\sqrt{2} {\left(6 \, c^{3} d^{3} - 9 \, b c^{2} d^{2} e + {\left(5 \, b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - a b c\right)} e^{3} + c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - c^{3} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6}}}}{c^{3}}} - 4 \, {\left(3 \, c^{3} d^{4} - 6 \, b c^{2} d^{3} e + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} + 2 \, a b c\right)} d e^{3} + {\left(a b^{2} - a^{2} c\right)} e^{4}\right)} \sqrt{e x + d}\right) + 4 \, {\left(2 \, c e x + 8 \, c d - 3 \, b e\right)} \sqrt{e x + d}}{6 \, c}"," ",0,"1/6*(3*sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))/c^3)*log(sqrt(2)*(6*c^3*d^3 - 9*b*c^2*d^2*e + (5*b^2*c - 2*a*c^2)*d*e^2 - (b^3 - a*b*c)*e^3 - c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))/c^3) - 4*(3*c^3*d^4 - 6*b*c^2*d^3*e + 2*(2*b^2*c + a*c^2)*d^2*e^2 - (b^3 + 2*a*b*c)*d*e^3 + (a*b^2 - a^2*c)*e^4)*sqrt(e*x + d)) - 3*sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))/c^3)*log(-sqrt(2)*(6*c^3*d^3 - 9*b*c^2*d^2*e + (5*b^2*c - 2*a*c^2)*d*e^2 - (b^3 - a*b*c)*e^3 - c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))/c^3) - 4*(3*c^3*d^4 - 6*b*c^2*d^3*e + 2*(2*b^2*c + a*c^2)*d^2*e^2 - (b^3 + 2*a*b*c)*d*e^3 + (a*b^2 - a^2*c)*e^4)*sqrt(e*x + d)) + 3*sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))/c^3)*log(sqrt(2)*(6*c^3*d^3 - 9*b*c^2*d^2*e + (5*b^2*c - 2*a*c^2)*d*e^2 - (b^3 - a*b*c)*e^3 + c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))/c^3) - 4*(3*c^3*d^4 - 6*b*c^2*d^3*e + 2*(2*b^2*c + a*c^2)*d^2*e^2 - (b^3 + 2*a*b*c)*d*e^3 + (a*b^2 - a^2*c)*e^4)*sqrt(e*x + d)) - 3*sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))/c^3)*log(-sqrt(2)*(6*c^3*d^3 - 9*b*c^2*d^2*e + (5*b^2*c - 2*a*c^2)*d*e^2 - (b^3 - a*b*c)*e^3 + c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - c^3*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/c^6))/c^3) - 4*(3*c^3*d^4 - 6*b*c^2*d^3*e + 2*(2*b^2*c + a*c^2)*d^2*e^2 - (b^3 + 2*a*b*c)*d*e^3 + (a*b^2 - a^2*c)*e^4)*sqrt(e*x + d)) + 4*(2*c*e*x + 8*c*d - 3*b*e)*sqrt(e*x + d))/c","B",0
1614,1,368,0,0.442743," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + c \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2}}}}{c}} \log\left(\sqrt{2} \sqrt{\frac{2 \, c d - b e + c \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2}}}}{c}} + 2 \, \sqrt{e x + d}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + c \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2}}}}{c}} \log\left(-\sqrt{2} \sqrt{\frac{2 \, c d - b e + c \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2}}}}{c}} + 2 \, \sqrt{e x + d}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - c \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2}}}}{c}} \log\left(\sqrt{2} \sqrt{\frac{2 \, c d - b e - c \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2}}}}{c}} + 2 \, \sqrt{e x + d}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - c \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2}}}}{c}} \log\left(-\sqrt{2} \sqrt{\frac{2 \, c d - b e - c \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2}}}}{c}} + 2 \, \sqrt{e x + d}\right) + 4 \, \sqrt{e x + d}"," ",0,"-1/2*sqrt(2)*sqrt((2*c*d - b*e + c*sqrt((b^2 - 4*a*c)*e^2/c^2))/c)*log(sqrt(2)*sqrt((2*c*d - b*e + c*sqrt((b^2 - 4*a*c)*e^2/c^2))/c) + 2*sqrt(e*x + d)) + 1/2*sqrt(2)*sqrt((2*c*d - b*e + c*sqrt((b^2 - 4*a*c)*e^2/c^2))/c)*log(-sqrt(2)*sqrt((2*c*d - b*e + c*sqrt((b^2 - 4*a*c)*e^2/c^2))/c) + 2*sqrt(e*x + d)) - 1/2*sqrt(2)*sqrt((2*c*d - b*e - c*sqrt((b^2 - 4*a*c)*e^2/c^2))/c)*log(sqrt(2)*sqrt((2*c*d - b*e - c*sqrt((b^2 - 4*a*c)*e^2/c^2))/c) + 2*sqrt(e*x + d)) + 1/2*sqrt(2)*sqrt((2*c*d - b*e - c*sqrt((b^2 - 4*a*c)*e^2/c^2))/c)*log(-sqrt(2)*sqrt((2*c*d - b*e - c*sqrt((b^2 - 4*a*c)*e^2/c^2))/c) + 2*sqrt(e*x + d)) + 4*sqrt(e*x + d)","A",0
1615,1,1317,0,0.442220," ","integrate((2*c*x+b)/(c*x^2+b*x+a)/(e*x+d)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}}{c d^{2} - b d e + a e^{2}}} \log\left(\sqrt{2} {\left(2 \, c d - b e - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}\right)} \sqrt{\frac{2 \, c d - b e + {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}}{c d^{2} - b d e + a e^{2}}} + 4 \, \sqrt{e x + d} c\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}}{c d^{2} - b d e + a e^{2}}} \log\left(-\sqrt{2} {\left(2 \, c d - b e - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}\right)} \sqrt{\frac{2 \, c d - b e + {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}}{c d^{2} - b d e + a e^{2}}} + 4 \, \sqrt{e x + d} c\right) - \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}}{c d^{2} - b d e + a e^{2}}} \log\left(\sqrt{2} {\left(2 \, c d - b e + {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}\right)} \sqrt{\frac{2 \, c d - b e - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}}{c d^{2} - b d e + a e^{2}}} + 4 \, \sqrt{e x + d} c\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}}{c d^{2} - b d e + a e^{2}}} \log\left(-\sqrt{2} {\left(2 \, c d - b e + {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}\right)} \sqrt{\frac{2 \, c d - b e - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{\frac{{\left(b^{2} - 4 \, a c\right)} e^{2}}{c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}}}}{c d^{2} - b d e + a e^{2}}} + 4 \, \sqrt{e x + d} c\right)"," ",0,"-1/2*sqrt(2)*sqrt((2*c*d - b*e + (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))/(c*d^2 - b*d*e + a*e^2))*log(sqrt(2)*(2*c*d - b*e - (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))*sqrt((2*c*d - b*e + (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))/(c*d^2 - b*d*e + a*e^2)) + 4*sqrt(e*x + d)*c) + 1/2*sqrt(2)*sqrt((2*c*d - b*e + (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))/(c*d^2 - b*d*e + a*e^2))*log(-sqrt(2)*(2*c*d - b*e - (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))*sqrt((2*c*d - b*e + (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))/(c*d^2 - b*d*e + a*e^2)) + 4*sqrt(e*x + d)*c) - 1/2*sqrt(2)*sqrt((2*c*d - b*e - (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))/(c*d^2 - b*d*e + a*e^2))*log(sqrt(2)*(2*c*d - b*e + (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))*sqrt((2*c*d - b*e - (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))/(c*d^2 - b*d*e + a*e^2)) + 4*sqrt(e*x + d)*c) + 1/2*sqrt(2)*sqrt((2*c*d - b*e - (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))/(c*d^2 - b*d*e + a*e^2))*log(-sqrt(2)*(2*c*d - b*e + (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))*sqrt((2*c*d - b*e - (c*d^2 - b*d*e + a*e^2)*sqrt((b^2 - 4*a*c)*e^2/(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)))/(c*d^2 - b*d*e + a*e^2)) + 4*sqrt(e*x + d)*c)","B",0
1616,1,8557,0,0.715349," ","integrate((2*c*x+b)/(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}}} \log\left(\sqrt{2} {\left(6 \, c^{4} d^{4} - 12 \, b c^{3} d^{3} e + {\left(11 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d^{2} e^{2} - {\left(5 \, b^{3} c - 8 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 3 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{4} - {\left(2 \, c^{4} d^{7} - 7 \, b c^{3} d^{6} e - a^{3} b e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}}} - 4 \, {\left(3 \, c^{4} d^{2} - 3 \, b c^{3} d e + {\left(b^{2} c^{2} - a c^{3}\right)} e^{2}\right)} \sqrt{e x + d}\right) - \sqrt{2} {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}}} \log\left(-\sqrt{2} {\left(6 \, c^{4} d^{4} - 12 \, b c^{3} d^{3} e + {\left(11 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d^{2} e^{2} - {\left(5 \, b^{3} c - 8 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 3 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{4} - {\left(2 \, c^{4} d^{7} - 7 \, b c^{3} d^{6} e - a^{3} b e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}}} - 4 \, {\left(3 \, c^{4} d^{2} - 3 \, b c^{3} d e + {\left(b^{2} c^{2} - a c^{3}\right)} e^{2}\right)} \sqrt{e x + d}\right) + \sqrt{2} {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}}} \log\left(\sqrt{2} {\left(6 \, c^{4} d^{4} - 12 \, b c^{3} d^{3} e + {\left(11 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d^{2} e^{2} - {\left(5 \, b^{3} c - 8 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 3 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{4} + {\left(2 \, c^{4} d^{7} - 7 \, b c^{3} d^{6} e - a^{3} b e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}}} - 4 \, {\left(3 \, c^{4} d^{2} - 3 \, b c^{3} d e + {\left(b^{2} c^{2} - a c^{3}\right)} e^{2}\right)} \sqrt{e x + d}\right) - \sqrt{2} {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}}} \log\left(-\sqrt{2} {\left(6 \, c^{4} d^{4} - 12 \, b c^{3} d^{3} e + {\left(11 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d^{2} e^{2} - {\left(5 \, b^{3} c - 8 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 3 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{4} + {\left(2 \, c^{4} d^{7} - 7 \, b c^{3} d^{6} e - a^{3} b e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{2} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{5} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{6}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} \sqrt{\frac{9 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{2} - 18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{4} - 6 \, {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d e^{5} + {\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{6}}{c^{6} d^{12} - 6 \, b c^{5} d^{11} e - 6 \, a^{5} b d e^{11} + a^{6} e^{12} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{9} e^{3} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{4} - 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{7} e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{6} e^{6} - 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{10}}}}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}}} - 4 \, {\left(3 \, c^{4} d^{2} - 3 \, b c^{3} d e + {\left(b^{2} c^{2} - a c^{3}\right)} e^{2}\right)} \sqrt{e x + d}\right) + 4 \, {\left(2 \, c d - b e\right)} \sqrt{e x + d}}{2 \, {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)}}"," ",0,"1/2*(sqrt(2)*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))/(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4))*log(sqrt(2)*(6*c^4*d^4 - 12*b*c^3*d^3*e + (11*b^2*c^2 - 8*a*c^3)*d^2*e^2 - (5*b^3*c - 8*a*b*c^2)*d*e^3 + (b^4 - 3*a*b^2*c + 2*a^2*c^2)*e^4 - (2*c^4*d^7 - 7*b*c^3*d^6*e - a^3*b*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 5*(b^3*c + 3*a*b*c^2)*d^4*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 3*(a*b^3 + 3*a^2*b*c)*d^2*e^5 + (3*a^2*b^2 + 2*a^3*c)*d*e^6)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))/(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)) - 4*(3*c^4*d^2 - 3*b*c^3*d*e + (b^2*c^2 - a*c^3)*e^2)*sqrt(e*x + d)) - sqrt(2)*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))/(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4))*log(-sqrt(2)*(6*c^4*d^4 - 12*b*c^3*d^3*e + (11*b^2*c^2 - 8*a*c^3)*d^2*e^2 - (5*b^3*c - 8*a*b*c^2)*d*e^3 + (b^4 - 3*a*b^2*c + 2*a^2*c^2)*e^4 - (2*c^4*d^7 - 7*b*c^3*d^6*e - a^3*b*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 5*(b^3*c + 3*a*b*c^2)*d^4*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 3*(a*b^3 + 3*a^2*b*c)*d^2*e^5 + (3*a^2*b^2 + 2*a^3*c)*d*e^6)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))/(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)) - 4*(3*c^4*d^2 - 3*b*c^3*d*e + (b^2*c^2 - a*c^3)*e^2)*sqrt(e*x + d)) + sqrt(2)*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))/(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4))*log(sqrt(2)*(6*c^4*d^4 - 12*b*c^3*d^3*e + (11*b^2*c^2 - 8*a*c^3)*d^2*e^2 - (5*b^3*c - 8*a*b*c^2)*d*e^3 + (b^4 - 3*a*b^2*c + 2*a^2*c^2)*e^4 + (2*c^4*d^7 - 7*b*c^3*d^6*e - a^3*b*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 5*(b^3*c + 3*a*b*c^2)*d^4*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 3*(a*b^3 + 3*a^2*b*c)*d^2*e^5 + (3*a^2*b^2 + 2*a^3*c)*d*e^6)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))/(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)) - 4*(3*c^4*d^2 - 3*b*c^3*d*e + (b^2*c^2 - a*c^3)*e^2)*sqrt(e*x + d)) - sqrt(2)*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))/(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4))*log(-sqrt(2)*(6*c^4*d^4 - 12*b*c^3*d^3*e + (11*b^2*c^2 - 8*a*c^3)*d^2*e^2 - (5*b^3*c - 8*a*b*c^2)*d*e^3 + (b^4 - 3*a*b^2*c + 2*a^2*c^2)*e^4 + (2*c^4*d^7 - 7*b*c^3*d^6*e - a^3*b*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*d^5*e^2 - 5*(b^3*c + 3*a*b*c^2)*d^4*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^4 - 3*(a*b^3 + 3*a^2*b*c)*d^2*e^5 + (3*a^2*b^2 + 2*a^3*c)*d*e^6)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*sqrt((9*(b^2*c^4 - 4*a*c^5)*d^4*e^2 - 18*(b^3*c^3 - 4*a*b*c^4)*d^3*e^3 + 3*(5*b^4*c^2 - 22*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^4 - 6*(b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d*e^5 + (b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 4*a^3*c^3)*e^6)/(c^6*d^12 - 6*b*c^5*d^11*e - 6*a^5*b*d*e^11 + a^6*e^12 + 3*(5*b^2*c^4 + 2*a*c^5)*d^10*e^2 - 10*(2*b^3*c^3 + 3*a*b*c^4)*d^9*e^3 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^4 - 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^7*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^6*e^6 - 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5*e^7 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e^8 - 10*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^9 + 3*(5*a^4*b^2 + 2*a^5*c)*d^2*e^10)))/(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)) - 4*(3*c^4*d^2 - 3*b*c^3*d*e + (b^2*c^2 - a*c^3)*e^2)*sqrt(e*x + d)) + 4*(2*c*d - b*e)*sqrt(e*x + d))/(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)","B",0
1617,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1618,1,2928,0,0.523183," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{5 \, \sqrt{\frac{1}{2}} {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(125 \, \sqrt{\frac{1}{2}} {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{4} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{6} - {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 250 \, {\left(3 \, c^{3} d^{4} e^{4} - 6 \, b c^{2} d^{3} e^{5} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{6} - {\left(b^{3} + 2 \, a b c\right)} d e^{7} + {\left(a b^{2} - a^{2} c\right)} e^{8}\right)} \sqrt{e x + d}\right) - 5 \, \sqrt{\frac{1}{2}} {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-125 \, \sqrt{\frac{1}{2}} {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{4} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{6} - {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 250 \, {\left(3 \, c^{3} d^{4} e^{4} - 6 \, b c^{2} d^{3} e^{5} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{6} - {\left(b^{3} + 2 \, a b c\right)} d e^{7} + {\left(a b^{2} - a^{2} c\right)} e^{8}\right)} \sqrt{e x + d}\right) + 5 \, \sqrt{\frac{1}{2}} {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(125 \, \sqrt{\frac{1}{2}} {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{4} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{6} + {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 250 \, {\left(3 \, c^{3} d^{4} e^{4} - 6 \, b c^{2} d^{3} e^{5} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{6} - {\left(b^{3} + 2 \, a b c\right)} d e^{7} + {\left(a b^{2} - a^{2} c\right)} e^{8}\right)} \sqrt{e x + d}\right) - 5 \, \sqrt{\frac{1}{2}} {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-125 \, \sqrt{\frac{1}{2}} {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{4} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{6} + {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 250 \, {\left(3 \, c^{3} d^{4} e^{4} - 6 \, b c^{2} d^{3} e^{5} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{6} - {\left(b^{3} + 2 \, a b c\right)} d e^{7} + {\left(a b^{2} - a^{2} c\right)} e^{8}\right)} \sqrt{e x + d}\right) - 2 \, {\left(4 \, c e^{2} x^{2} - c d^{2} + 5 \, a e^{2} - {\left(2 \, c d e - 5 \, b e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}"," ",0,"-1/2*(5*sqrt(1/2)*(c^2*x^2 + b*c*x + a*c)*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(125*sqrt(1/2)*(3*(b^2*c^2 - 4*a*c^3)*d^2*e^4 - 3*(b^3*c - 4*a*b*c^2)*d*e^5 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^6 - (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 250*(3*c^3*d^4*e^4 - 6*b*c^2*d^3*e^5 + 2*(2*b^2*c + a*c^2)*d^2*e^6 - (b^3 + 2*a*b*c)*d*e^7 + (a*b^2 - a^2*c)*e^8)*sqrt(e*x + d)) - 5*sqrt(1/2)*(c^2*x^2 + b*c*x + a*c)*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-125*sqrt(1/2)*(3*(b^2*c^2 - 4*a*c^3)*d^2*e^4 - 3*(b^3*c - 4*a*b*c^2)*d*e^5 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^6 - (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 250*(3*c^3*d^4*e^4 - 6*b*c^2*d^3*e^5 + 2*(2*b^2*c + a*c^2)*d^2*e^6 - (b^3 + 2*a*b*c)*d*e^7 + (a*b^2 - a^2*c)*e^8)*sqrt(e*x + d)) + 5*sqrt(1/2)*(c^2*x^2 + b*c*x + a*c)*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(125*sqrt(1/2)*(3*(b^2*c^2 - 4*a*c^3)*d^2*e^4 - 3*(b^3*c - 4*a*b*c^2)*d*e^5 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^6 + (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 250*(3*c^3*d^4*e^4 - 6*b*c^2*d^3*e^5 + 2*(2*b^2*c + a*c^2)*d^2*e^6 - (b^3 + 2*a*b*c)*d*e^7 + (a*b^2 - a^2*c)*e^8)*sqrt(e*x + d)) - 5*sqrt(1/2)*(c^2*x^2 + b*c*x + a*c)*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-125*sqrt(1/2)*(3*(b^2*c^2 - 4*a*c^3)*d^2*e^4 - 3*(b^3*c - 4*a*b*c^2)*d*e^5 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^6 + (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 250*(3*c^3*d^4*e^4 - 6*b*c^2*d^3*e^5 + 2*(2*b^2*c + a*c^2)*d^2*e^6 - (b^3 + 2*a*b*c)*d*e^7 + (a*b^2 - a^2*c)*e^8)*sqrt(e*x + d)) - 2*(4*c*e^2*x^2 - c*d^2 + 5*a*e^2 - (2*c*d*e - 5*b*e^2)*x)*sqrt(e*x + d))/(c^2*x^2 + b*c*x + a*c)","B",0
1619,1,828,0,0.447339," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{1}{2}} {\left(c x^{2} + b x + a\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} + \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)}}{b^{2} c - 4 \, a c^{2}}} \log\left(27 \, \sqrt{e x + d} e^{4} + 27 \, \sqrt{\frac{1}{2}} \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} + \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)}}{b^{2} c - 4 \, a c^{2}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(c x^{2} + b x + a\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} + \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)}}{b^{2} c - 4 \, a c^{2}}} \log\left(27 \, \sqrt{e x + d} e^{4} - 27 \, \sqrt{\frac{1}{2}} \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} + \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)}}{b^{2} c - 4 \, a c^{2}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(c x^{2} + b x + a\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} - \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)}}{b^{2} c - 4 \, a c^{2}}} \log\left(27 \, \sqrt{e x + d} e^{4} + 27 \, \sqrt{\frac{1}{2}} \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} - \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)}}{b^{2} c - 4 \, a c^{2}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left(c x^{2} + b x + a\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} - \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)}}{b^{2} c - 4 \, a c^{2}}} \log\left(27 \, \sqrt{e x + d} e^{4} - 27 \, \sqrt{\frac{1}{2}} \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} - \sqrt{\frac{e^{6}}{b^{2} c^{2} - 4 \, a c^{3}}} {\left(b^{2} c - 4 \, a c^{2}\right)}}{b^{2} c - 4 \, a c^{2}}}\right) + 2 \, {\left(e x + d\right)}^{\frac{3}{2}}}{2 \, {\left(c x^{2} + b x + a\right)}}"," ",0,"-1/2*(3*sqrt(1/2)*(c*x^2 + b*x + a)*sqrt((2*c*d*e^2 - b*e^3 + sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2))/(b^2*c - 4*a*c^2))*log(27*sqrt(e*x + d)*e^4 + 27*sqrt(1/2)*sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2)*sqrt((2*c*d*e^2 - b*e^3 + sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2))/(b^2*c - 4*a*c^2))) - 3*sqrt(1/2)*(c*x^2 + b*x + a)*sqrt((2*c*d*e^2 - b*e^3 + sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2))/(b^2*c - 4*a*c^2))*log(27*sqrt(e*x + d)*e^4 - 27*sqrt(1/2)*sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2)*sqrt((2*c*d*e^2 - b*e^3 + sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2))/(b^2*c - 4*a*c^2))) - 3*sqrt(1/2)*(c*x^2 + b*x + a)*sqrt((2*c*d*e^2 - b*e^3 - sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2))/(b^2*c - 4*a*c^2))*log(27*sqrt(e*x + d)*e^4 + 27*sqrt(1/2)*sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2)*sqrt((2*c*d*e^2 - b*e^3 - sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2))/(b^2*c - 4*a*c^2))) + 3*sqrt(1/2)*(c*x^2 + b*x + a)*sqrt((2*c*d*e^2 - b*e^3 - sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2))/(b^2*c - 4*a*c^2))*log(27*sqrt(e*x + d)*e^4 - 27*sqrt(1/2)*sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2)*sqrt((2*c*d*e^2 - b*e^3 - sqrt(e^6/(b^2*c^2 - 4*a*c^3))*(b^2*c - 4*a*c^2))/(b^2*c - 4*a*c^2))) + 2*(e*x + d)^(3/2))/(c*x^2 + b*x + a)","B",0
1620,1,2750,0,0.483011," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left(c x^{2} + b x + a\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} + \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(2 \, \sqrt{e x + d} c e^{4} + \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} e^{4} - \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3}\right)}\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} + \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left(c x^{2} + b x + a\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} + \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(2 \, \sqrt{e x + d} c e^{4} - \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} e^{4} - \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3}\right)}\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} + \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left(c x^{2} + b x + a\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} - \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(2 \, \sqrt{e x + d} c e^{4} + \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} e^{4} + \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3}\right)}\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} - \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left(c x^{2} + b x + a\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} - \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(2 \, \sqrt{e x + d} c e^{4} - \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} e^{4} + \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3}\right)}\right)} \sqrt{\frac{2 \, c d e^{2} - b e^{3} - \sqrt{\frac{e^{6}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}\right) + 2 \, \sqrt{e x + d}}{2 \, {\left(c x^{2} + b x + a\right)}}"," ",0,"-1/2*(sqrt(1/2)*(c*x^2 + b*x + a)*sqrt((2*c*d*e^2 - b*e^3 + sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(2*sqrt(e*x + d)*c*e^4 + sqrt(1/2)*((b^2 - 4*a*c)*e^4 - sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*(2*(b^2*c^2 - 4*a*c^3)*d^3 - 3*(b^3*c - 4*a*b*c^2)*d^2*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3))*sqrt((2*c*d*e^2 - b*e^3 + sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))) - sqrt(1/2)*(c*x^2 + b*x + a)*sqrt((2*c*d*e^2 - b*e^3 + sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(2*sqrt(e*x + d)*c*e^4 - sqrt(1/2)*((b^2 - 4*a*c)*e^4 - sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*(2*(b^2*c^2 - 4*a*c^3)*d^3 - 3*(b^3*c - 4*a*b*c^2)*d^2*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3))*sqrt((2*c*d*e^2 - b*e^3 + sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))) + sqrt(1/2)*(c*x^2 + b*x + a)*sqrt((2*c*d*e^2 - b*e^3 - sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(2*sqrt(e*x + d)*c*e^4 + sqrt(1/2)*((b^2 - 4*a*c)*e^4 + sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*(2*(b^2*c^2 - 4*a*c^3)*d^3 - 3*(b^3*c - 4*a*b*c^2)*d^2*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3))*sqrt((2*c*d*e^2 - b*e^3 - sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))) - sqrt(1/2)*(c*x^2 + b*x + a)*sqrt((2*c*d*e^2 - b*e^3 - sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(2*sqrt(e*x + d)*c*e^4 - sqrt(1/2)*((b^2 - 4*a*c)*e^4 + sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*(2*(b^2*c^2 - 4*a*c^3)*d^3 - 3*(b^3*c - 4*a*b*c^2)*d^2*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3))*sqrt((2*c*d*e^2 - b*e^3 - sqrt(e^6/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))) + 2*sqrt(e*x + d))/(c*x^2 + b*x + a)","B",0
1621,1,11482,0,0.714474," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} \log\left(\sqrt{\frac{1}{2}} {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{4} - 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{5} + {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{7} - {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e + {\left(13 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{6} e^{2} - {\left(11 \, b^{5} c^{2} - 32 \, a b^{3} c^{3} - 48 \, a^{2} b c^{4}\right)} d^{5} e^{3} + 5 \, {\left(b^{6} c - a b^{4} c^{2} - 12 \, a^{2} b^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{7} + 6 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2}\right)} d^{3} e^{5} + {\left(3 \, a b^{6} - 9 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{6} - {\left(3 \, a^{2} b^{5} - 16 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{7} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{8}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} - 2 \, {\left(3 \, c^{4} d^{2} e^{4} - 3 \, b c^{3} d e^{5} + {\left(b^{2} c^{2} - a c^{3}\right)} e^{6}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} \log\left(-\sqrt{\frac{1}{2}} {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{4} - 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{5} + {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{7} - {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e + {\left(13 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{6} e^{2} - {\left(11 \, b^{5} c^{2} - 32 \, a b^{3} c^{3} - 48 \, a^{2} b c^{4}\right)} d^{5} e^{3} + 5 \, {\left(b^{6} c - a b^{4} c^{2} - 12 \, a^{2} b^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{7} + 6 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2}\right)} d^{3} e^{5} + {\left(3 \, a b^{6} - 9 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{6} - {\left(3 \, a^{2} b^{5} - 16 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{7} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{8}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} - 2 \, {\left(3 \, c^{4} d^{2} e^{4} - 3 \, b c^{3} d e^{5} + {\left(b^{2} c^{2} - a c^{3}\right)} e^{6}\right)} \sqrt{e x + d}\right) + \sqrt{\frac{1}{2}} {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} \log\left(\sqrt{\frac{1}{2}} {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{4} - 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{5} + {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{7} + {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e + {\left(13 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{6} e^{2} - {\left(11 \, b^{5} c^{2} - 32 \, a b^{3} c^{3} - 48 \, a^{2} b c^{4}\right)} d^{5} e^{3} + 5 \, {\left(b^{6} c - a b^{4} c^{2} - 12 \, a^{2} b^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{7} + 6 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2}\right)} d^{3} e^{5} + {\left(3 \, a b^{6} - 9 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{6} - {\left(3 \, a^{2} b^{5} - 16 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{7} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{8}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} - 2 \, {\left(3 \, c^{4} d^{2} e^{4} - 3 \, b c^{3} d e^{5} + {\left(b^{2} c^{2} - a c^{3}\right)} e^{6}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} \log\left(-\sqrt{\frac{1}{2}} {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{4} - 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{5} + {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{7} + {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e + {\left(13 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{6} e^{2} - {\left(11 \, b^{5} c^{2} - 32 \, a b^{3} c^{3} - 48 \, a^{2} b c^{4}\right)} d^{5} e^{3} + 5 \, {\left(b^{6} c - a b^{4} c^{2} - 12 \, a^{2} b^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{7} + 6 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2}\right)} d^{3} e^{5} + {\left(3 \, a b^{6} - 9 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{6} - {\left(3 \, a^{2} b^{5} - 16 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{7} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{8}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5} - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{6} - 18 \, b c^{3} d^{3} e^{7} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{8} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{9} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{10}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} - 2 \, {\left(3 \, c^{4} d^{2} e^{4} - 3 \, b c^{3} d e^{5} + {\left(b^{2} c^{2} - a c^{3}\right)} e^{6}\right)} \sqrt{e x + d}\right) - 2 \, {\left(c e x - c d + b e\right)} \sqrt{e x + d}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}"," ",0,"-1/2*(sqrt(1/2)*(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 + ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6))*log(sqrt(1/2)*(6*(b^2*c^3 - 4*a*c^4)*d^3*e^4 - 9*(b^3*c^2 - 4*a*b*c^3)*d^2*e^5 + (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d*e^6 - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^7 - (2*(b^2*c^5 - 4*a*c^6)*d^8 - 8*(b^3*c^4 - 4*a*b*c^5)*d^7*e + (13*b^4*c^3 - 48*a*b^2*c^4 - 16*a^2*c^5)*d^6*e^2 - (11*b^5*c^2 - 32*a*b^3*c^3 - 48*a^2*b*c^4)*d^5*e^3 + 5*(b^6*c - a*b^4*c^2 - 12*a^2*b^2*c^3)*d^4*e^4 - (b^7 + 6*a*b^5*c - 40*a^2*b^3*c^2)*d^3*e^5 + (3*a*b^6 - 9*a^2*b^4*c - 16*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^6 - (3*a^2*b^5 - 16*a^3*b^3*c + 16*a^4*b*c^2)*d*e^7 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^8)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 + ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)) - 2*(3*c^4*d^2*e^4 - 3*b*c^3*d*e^5 + (b^2*c^2 - a*c^3)*e^6)*sqrt(e*x + d)) - sqrt(1/2)*(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 + ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6))*log(-sqrt(1/2)*(6*(b^2*c^3 - 4*a*c^4)*d^3*e^4 - 9*(b^3*c^2 - 4*a*b*c^3)*d^2*e^5 + (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d*e^6 - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^7 - (2*(b^2*c^5 - 4*a*c^6)*d^8 - 8*(b^3*c^4 - 4*a*b*c^5)*d^7*e + (13*b^4*c^3 - 48*a*b^2*c^4 - 16*a^2*c^5)*d^6*e^2 - (11*b^5*c^2 - 32*a*b^3*c^3 - 48*a^2*b*c^4)*d^5*e^3 + 5*(b^6*c - a*b^4*c^2 - 12*a^2*b^2*c^3)*d^4*e^4 - (b^7 + 6*a*b^5*c - 40*a^2*b^3*c^2)*d^3*e^5 + (3*a*b^6 - 9*a^2*b^4*c - 16*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^6 - (3*a^2*b^5 - 16*a^3*b^3*c + 16*a^4*b*c^2)*d*e^7 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^8)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 + ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)) - 2*(3*c^4*d^2*e^4 - 3*b*c^3*d*e^5 + (b^2*c^2 - a*c^3)*e^6)*sqrt(e*x + d)) + sqrt(1/2)*(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 - ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6))*log(sqrt(1/2)*(6*(b^2*c^3 - 4*a*c^4)*d^3*e^4 - 9*(b^3*c^2 - 4*a*b*c^3)*d^2*e^5 + (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d*e^6 - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^7 + (2*(b^2*c^5 - 4*a*c^6)*d^8 - 8*(b^3*c^4 - 4*a*b*c^5)*d^7*e + (13*b^4*c^3 - 48*a*b^2*c^4 - 16*a^2*c^5)*d^6*e^2 - (11*b^5*c^2 - 32*a*b^3*c^3 - 48*a^2*b*c^4)*d^5*e^3 + 5*(b^6*c - a*b^4*c^2 - 12*a^2*b^2*c^3)*d^4*e^4 - (b^7 + 6*a*b^5*c - 40*a^2*b^3*c^2)*d^3*e^5 + (3*a*b^6 - 9*a^2*b^4*c - 16*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^6 - (3*a^2*b^5 - 16*a^3*b^3*c + 16*a^4*b*c^2)*d*e^7 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^8)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 - ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)) - 2*(3*c^4*d^2*e^4 - 3*b*c^3*d*e^5 + (b^2*c^2 - a*c^3)*e^6)*sqrt(e*x + d)) - sqrt(1/2)*(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 - ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6))*log(-sqrt(1/2)*(6*(b^2*c^3 - 4*a*c^4)*d^3*e^4 - 9*(b^3*c^2 - 4*a*b*c^3)*d^2*e^5 + (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d*e^6 - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^7 + (2*(b^2*c^5 - 4*a*c^6)*d^8 - 8*(b^3*c^4 - 4*a*b*c^5)*d^7*e + (13*b^4*c^3 - 48*a*b^2*c^4 - 16*a^2*c^5)*d^6*e^2 - (11*b^5*c^2 - 32*a*b^3*c^3 - 48*a^2*b*c^4)*d^5*e^3 + 5*(b^6*c - a*b^4*c^2 - 12*a^2*b^2*c^3)*d^4*e^4 - (b^7 + 6*a*b^5*c - 40*a^2*b^3*c^2)*d^3*e^5 + (3*a*b^6 - 9*a^2*b^4*c - 16*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^6 - (3*a^2*b^5 - 16*a^3*b^3*c + 16*a^4*b*c^2)*d*e^7 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^8)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))*sqrt((2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5 - ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^6 - 18*b*c^3*d^3*e^7 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^8 - 6*(b^3*c - a*b*c^2)*d*e^9 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^10)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)) - 2*(3*c^4*d^2*e^4 - 3*b*c^3*d*e^5 + (b^2*c^2 - a*c^3)*e^6)*sqrt(e*x + d)) - 2*(c*e*x - c*d + b*e)*sqrt(e*x + d))/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)","B",0
1622,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1623,1,5701,0,0.886892," ","integrate((2*c*x+b)*(e*x+d)^(7/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{7 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{3} + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} x^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x\right)} \sqrt{\frac{32 \, c^{5} d^{5} e^{2} - 80 \, b c^{4} d^{4} e^{3} + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{4} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{5} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{7} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(\frac{343}{2} \, \sqrt{\frac{1}{2}} {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e^{6} - 15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{7} + 3 \, {\left(b^{6} c - 2 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 96 \, a^{3} c^{4}\right)} d e^{8} + {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3}\right)} e^{9} - {\left(8 \, {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} d^{2} - 8 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d e - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\frac{32 \, c^{5} d^{5} e^{2} - 80 \, b c^{4} d^{4} e^{3} + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{4} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{5} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{7} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} + 343 \, {\left(80 \, c^{5} d^{6} e^{6} - 240 \, b c^{4} d^{5} e^{7} + {\left(199 \, b^{2} c^{3} + 404 \, a c^{4}\right)} d^{4} e^{8} + 2 \, {\left(b^{3} c^{2} - 404 \, a b c^{3}\right)} d^{3} e^{9} - 6 \, {\left(6 \, b^{4} c - 47 \, a b^{2} c^{2} - 108 \, a^{2} c^{3}\right)} d^{2} e^{10} - {\left(5 \, b^{5} - 122 \, a b^{3} c + 648 \, a^{2} b c^{2}\right)} d e^{11} + {\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} e^{12}\right)} \sqrt{e x + d}\right) - 7 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{3} + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} x^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x\right)} \sqrt{\frac{32 \, c^{5} d^{5} e^{2} - 80 \, b c^{4} d^{4} e^{3} + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{4} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{5} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{7} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-\frac{343}{2} \, \sqrt{\frac{1}{2}} {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e^{6} - 15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{7} + 3 \, {\left(b^{6} c - 2 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 96 \, a^{3} c^{4}\right)} d e^{8} + {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3}\right)} e^{9} - {\left(8 \, {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} d^{2} - 8 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d e - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\frac{32 \, c^{5} d^{5} e^{2} - 80 \, b c^{4} d^{4} e^{3} + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{4} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{5} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{7} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} + 343 \, {\left(80 \, c^{5} d^{6} e^{6} - 240 \, b c^{4} d^{5} e^{7} + {\left(199 \, b^{2} c^{3} + 404 \, a c^{4}\right)} d^{4} e^{8} + 2 \, {\left(b^{3} c^{2} - 404 \, a b c^{3}\right)} d^{3} e^{9} - 6 \, {\left(6 \, b^{4} c - 47 \, a b^{2} c^{2} - 108 \, a^{2} c^{3}\right)} d^{2} e^{10} - {\left(5 \, b^{5} - 122 \, a b^{3} c + 648 \, a^{2} b c^{2}\right)} d e^{11} + {\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} e^{12}\right)} \sqrt{e x + d}\right) + 7 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{3} + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} x^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x\right)} \sqrt{\frac{32 \, c^{5} d^{5} e^{2} - 80 \, b c^{4} d^{4} e^{3} + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{4} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{5} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{7} - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(\frac{343}{2} \, \sqrt{\frac{1}{2}} {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e^{6} - 15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{7} + 3 \, {\left(b^{6} c - 2 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 96 \, a^{3} c^{4}\right)} d e^{8} + {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3}\right)} e^{9} + {\left(8 \, {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} d^{2} - 8 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d e - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\frac{32 \, c^{5} d^{5} e^{2} - 80 \, b c^{4} d^{4} e^{3} + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{4} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{5} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{7} - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} + 343 \, {\left(80 \, c^{5} d^{6} e^{6} - 240 \, b c^{4} d^{5} e^{7} + {\left(199 \, b^{2} c^{3} + 404 \, a c^{4}\right)} d^{4} e^{8} + 2 \, {\left(b^{3} c^{2} - 404 \, a b c^{3}\right)} d^{3} e^{9} - 6 \, {\left(6 \, b^{4} c - 47 \, a b^{2} c^{2} - 108 \, a^{2} c^{3}\right)} d^{2} e^{10} - {\left(5 \, b^{5} - 122 \, a b^{3} c + 648 \, a^{2} b c^{2}\right)} d e^{11} + {\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} e^{12}\right)} \sqrt{e x + d}\right) - 7 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{3} + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} x^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x\right)} \sqrt{\frac{32 \, c^{5} d^{5} e^{2} - 80 \, b c^{4} d^{4} e^{3} + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{4} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{5} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{7} - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-\frac{343}{2} \, \sqrt{\frac{1}{2}} {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e^{6} - 15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{7} + 3 \, {\left(b^{6} c - 2 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 96 \, a^{3} c^{4}\right)} d e^{8} + {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3}\right)} e^{9} + {\left(8 \, {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} d^{2} - 8 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d e - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\frac{32 \, c^{5} d^{5} e^{2} - 80 \, b c^{4} d^{4} e^{3} + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{4} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{5} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{7} - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{10} - 50 \, b c^{3} d^{3} e^{11} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{12} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{14}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} + 343 \, {\left(80 \, c^{5} d^{6} e^{6} - 240 \, b c^{4} d^{5} e^{7} + {\left(199 \, b^{2} c^{3} + 404 \, a c^{4}\right)} d^{4} e^{8} + 2 \, {\left(b^{3} c^{2} - 404 \, a b c^{3}\right)} d^{3} e^{9} - 6 \, {\left(6 \, b^{4} c - 47 \, a b^{2} c^{2} - 108 \, a^{2} c^{3}\right)} d^{2} e^{10} - {\left(5 \, b^{5} - 122 \, a b^{3} c + 648 \, a^{2} b c^{2}\right)} d e^{11} + {\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} e^{12}\right)} \sqrt{e x + d}\right) - 2 \, {\left(7 \, a b c d^{2} e - 28 \, a^{2} c d e^{2} + 7 \, a^{2} b e^{3} + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(14 \, c^{3} d^{2} e - 14 \, b c^{2} d e^{2} + {\left(9 \, b^{2} c - 22 \, a c^{2}\right)} e^{3}\right)} x^{3} + {\left(21 \, b c^{2} d^{2} e - 4 \, {\left(2 \, b^{2} c + 13 \, a c^{2}\right)} d e^{2} + 7 \, {\left(b^{3} - a b c\right)} e^{3}\right)} x^{2} - {\left(42 \, a b c d e^{2} - {\left(13 \, b^{2} c - 10 \, a c^{2}\right)} d^{2} e - 14 \, {\left(a b^{2} - a^{2} c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{3} + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} x^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x\right)}}"," ",0,"1/8*(7*sqrt(1/2)*(a^2*b^2*c - 4*a^3*c^2 + (b^2*c^3 - 4*a*c^4)*x^4 + 2*(b^3*c^2 - 4*a*b*c^3)*x^3 + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*x^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*x)*sqrt((32*c^5*d^5*e^2 - 80*b*c^4*d^4*e^3 + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^4 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^5 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^6 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^7 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(343/2*sqrt(1/2)*(10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e^6 - 15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^7 + 3*(b^6*c - 2*a*b^4*c^2 - 32*a^2*b^2*c^3 + 96*a^3*c^4)*d*e^8 + (b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3)*e^9 - (8*(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*d^2 - 8*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*d*e - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*e^2)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt((32*c^5*d^5*e^2 - 80*b*c^4*d^4*e^3 + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^4 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^5 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^6 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^7 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) + 343*(80*c^5*d^6*e^6 - 240*b*c^4*d^5*e^7 + (199*b^2*c^3 + 404*a*c^4)*d^4*e^8 + 2*(b^3*c^2 - 404*a*b*c^3)*d^3*e^9 - 6*(6*b^4*c - 47*a*b^2*c^2 - 108*a^2*c^3)*d^2*e^10 - (5*b^5 - 122*a*b^3*c + 648*a^2*b*c^2)*d*e^11 + (5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*e^12)*sqrt(e*x + d)) - 7*sqrt(1/2)*(a^2*b^2*c - 4*a^3*c^2 + (b^2*c^3 - 4*a*c^4)*x^4 + 2*(b^3*c^2 - 4*a*b*c^3)*x^3 + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*x^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*x)*sqrt((32*c^5*d^5*e^2 - 80*b*c^4*d^4*e^3 + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^4 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^5 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^6 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^7 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-343/2*sqrt(1/2)*(10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e^6 - 15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^7 + 3*(b^6*c - 2*a*b^4*c^2 - 32*a^2*b^2*c^3 + 96*a^3*c^4)*d*e^8 + (b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3)*e^9 - (8*(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*d^2 - 8*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*d*e - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*e^2)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt((32*c^5*d^5*e^2 - 80*b*c^4*d^4*e^3 + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^4 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^5 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^6 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^7 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) + 343*(80*c^5*d^6*e^6 - 240*b*c^4*d^5*e^7 + (199*b^2*c^3 + 404*a*c^4)*d^4*e^8 + 2*(b^3*c^2 - 404*a*b*c^3)*d^3*e^9 - 6*(6*b^4*c - 47*a*b^2*c^2 - 108*a^2*c^3)*d^2*e^10 - (5*b^5 - 122*a*b^3*c + 648*a^2*b*c^2)*d*e^11 + (5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*e^12)*sqrt(e*x + d)) + 7*sqrt(1/2)*(a^2*b^2*c - 4*a^3*c^2 + (b^2*c^3 - 4*a*c^4)*x^4 + 2*(b^3*c^2 - 4*a*b*c^3)*x^3 + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*x^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*x)*sqrt((32*c^5*d^5*e^2 - 80*b*c^4*d^4*e^3 + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^4 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^5 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^6 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^7 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(343/2*sqrt(1/2)*(10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e^6 - 15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^7 + 3*(b^6*c - 2*a*b^4*c^2 - 32*a^2*b^2*c^3 + 96*a^3*c^4)*d*e^8 + (b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3)*e^9 + (8*(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*d^2 - 8*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*d*e - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*e^2)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt((32*c^5*d^5*e^2 - 80*b*c^4*d^4*e^3 + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^4 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^5 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^6 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^7 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) + 343*(80*c^5*d^6*e^6 - 240*b*c^4*d^5*e^7 + (199*b^2*c^3 + 404*a*c^4)*d^4*e^8 + 2*(b^3*c^2 - 404*a*b*c^3)*d^3*e^9 - 6*(6*b^4*c - 47*a*b^2*c^2 - 108*a^2*c^3)*d^2*e^10 - (5*b^5 - 122*a*b^3*c + 648*a^2*b*c^2)*d*e^11 + (5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*e^12)*sqrt(e*x + d)) - 7*sqrt(1/2)*(a^2*b^2*c - 4*a^3*c^2 + (b^2*c^3 - 4*a*c^4)*x^4 + 2*(b^3*c^2 - 4*a*b*c^3)*x^3 + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*x^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*x)*sqrt((32*c^5*d^5*e^2 - 80*b*c^4*d^4*e^3 + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^4 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^5 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^6 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^7 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-343/2*sqrt(1/2)*(10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e^6 - 15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^7 + 3*(b^6*c - 2*a*b^4*c^2 - 32*a^2*b^2*c^3 + 96*a^3*c^4)*d*e^8 + (b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3)*e^9 + (8*(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*d^2 - 8*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*d*e - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*e^2)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt((32*c^5*d^5*e^2 - 80*b*c^4*d^4*e^3 + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^4 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^5 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^6 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^7 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^10 - 50*b*c^3*d^3*e^11 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^12 + 10*(b^3*c - 9*a*b*c^2)*d*e^13 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^14)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) + 343*(80*c^5*d^6*e^6 - 240*b*c^4*d^5*e^7 + (199*b^2*c^3 + 404*a*c^4)*d^4*e^8 + 2*(b^3*c^2 - 404*a*b*c^3)*d^3*e^9 - 6*(6*b^4*c - 47*a*b^2*c^2 - 108*a^2*c^3)*d^2*e^10 - (5*b^5 - 122*a*b^3*c + 648*a^2*b*c^2)*d*e^11 + (5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*e^12)*sqrt(e*x + d)) - 2*(7*a*b*c*d^2*e - 28*a^2*c*d*e^2 + 7*a^2*b*e^3 + 2*(b^2*c - 4*a*c^2)*d^3 + (14*c^3*d^2*e - 14*b*c^2*d*e^2 + (9*b^2*c - 22*a*c^2)*e^3)*x^3 + (21*b*c^2*d^2*e - 4*(2*b^2*c + 13*a*c^2)*d*e^2 + 7*(b^3 - a*b*c)*e^3)*x^2 - (42*a*b*c*d*e^2 - (13*b^2*c - 10*a*c^2)*d^2*e - 14*(a*b^2 - a^2*c)*e^3)*x)*sqrt(e*x + d))/(a^2*b^2*c - 4*a^3*c^2 + (b^2*c^3 - 4*a*c^4)*x^4 + 2*(b^3*c^2 - 4*a*b*c^3)*x^3 + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*x^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*x)","B",0
1624,1,2773,0,0.532295," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{5 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} + \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left(125 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{6} + 2 \, \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} + \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} + 125 \, {\left(16 \, c^{2} d^{2} e^{6} - 16 \, b c d e^{7} + {\left(3 \, b^{2} + 4 \, a c\right)} e^{8}\right)} \sqrt{e x + d}\right) - 5 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} + \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left(-125 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{6} + 2 \, \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} + \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} + 125 \, {\left(16 \, c^{2} d^{2} e^{6} - 16 \, b c d e^{7} + {\left(3 \, b^{2} + 4 \, a c\right)} e^{8}\right)} \sqrt{e x + d}\right) + 5 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} - \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left(125 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{6} - 2 \, \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} - \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} + 125 \, {\left(16 \, c^{2} d^{2} e^{6} - 16 \, b c d e^{7} + {\left(3 \, b^{2} + 4 \, a c\right)} e^{8}\right)} \sqrt{e x + d}\right) - 5 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} - \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left(-125 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{6} - 2 \, \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} - \sqrt{\frac{e^{10}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} + 125 \, {\left(16 \, c^{2} d^{2} e^{6} - 16 \, b c d e^{7} + {\left(3 \, b^{2} + 4 \, a c\right)} e^{8}\right)} \sqrt{e x + d}\right) - 2 \, {\left(5 \, a b d e - 10 \, a^{2} e^{2} + 5 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} d^{2} + 3 \, {\left(5 \, b c d e - {\left(b^{2} + 6 \, a c\right)} e^{2}\right)} x^{2} - 3 \, {\left(5 \, a b e^{2} - {\left(3 \, b^{2} - 2 \, a c\right)} d e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}"," ",0,"1/8*(5*sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 + sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log(125*sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^6 + 2*sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e))*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 + sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)) + 125*(16*c^2*d^2*e^6 - 16*b*c*d*e^7 + (3*b^2 + 4*a*c)*e^8)*sqrt(e*x + d)) - 5*sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 + sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log(-125*sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^6 + 2*sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e))*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 + sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)) + 125*(16*c^2*d^2*e^6 - 16*b*c*d*e^7 + (3*b^2 + 4*a*c)*e^8)*sqrt(e*x + d)) + 5*sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 - sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log(125*sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^6 - 2*sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e))*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 - sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)) + 125*(16*c^2*d^2*e^6 - 16*b*c*d*e^7 + (3*b^2 + 4*a*c)*e^8)*sqrt(e*x + d)) - 5*sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 - sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log(-125*sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^6 - 2*sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e))*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 - sqrt(e^10/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)) + 125*(16*c^2*d^2*e^6 - 16*b*c*d*e^7 + (3*b^2 + 4*a*c)*e^8)*sqrt(e*x + d)) - 2*(5*a*b*d*e - 10*a^2*e^2 + 5*(2*c^2*d*e - b*c*e^2)*x^3 + 2*(b^2 - 4*a*c)*d^2 + 3*(5*b*c*d*e - (b^2 + 6*a*c)*e^2)*x^2 - 3*(5*a*b*e^2 - (3*b^2 - 2*a*c)*d*e)*x)*sqrt(e*x + d))/((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)","B",0
1625,1,6728,0,0.649278," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} + \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{7} - \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} - 16 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} d^{3} e + 3 \, {\left(3 \, b^{8} c - 32 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{2} e^{2} - {\left(b^{9} - 96 \, a^{2} b^{5} c^{2} + 512 \, a^{3} b^{3} c^{3} - 768 \, a^{4} b c^{4}\right)} d e^{3} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{4}\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} + \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} + 27 \, {\left(16 \, c^{3} d^{2} e^{6} - 16 \, b c^{2} d e^{7} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{8}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} + \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{7} - \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} - 16 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} d^{3} e + 3 \, {\left(3 \, b^{8} c - 32 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{2} e^{2} - {\left(b^{9} - 96 \, a^{2} b^{5} c^{2} + 512 \, a^{3} b^{3} c^{3} - 768 \, a^{4} b c^{4}\right)} d e^{3} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{4}\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} + \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} + 27 \, {\left(16 \, c^{3} d^{2} e^{6} - 16 \, b c^{2} d e^{7} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{8}\right)} \sqrt{e x + d}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} - \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{7} + \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} - 16 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} d^{3} e + 3 \, {\left(3 \, b^{8} c - 32 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{2} e^{2} - {\left(b^{9} - 96 \, a^{2} b^{5} c^{2} + 512 \, a^{3} b^{3} c^{3} - 768 \, a^{4} b c^{4}\right)} d e^{3} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{4}\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} - \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} + 27 \, {\left(16 \, c^{3} d^{2} e^{6} - 16 \, b c^{2} d e^{7} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{8}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} - \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{6} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{7} + \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} - 16 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} d^{3} e + 3 \, {\left(3 \, b^{8} c - 32 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{2} e^{2} - {\left(b^{9} - 96 \, a^{2} b^{5} c^{2} + 512 \, a^{3} b^{3} c^{3} - 768 \, a^{4} b c^{4}\right)} d e^{3} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{4}\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5} - \sqrt{\frac{e^{10}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} + 27 \, {\left(16 \, c^{3} d^{2} e^{6} - 16 \, b c^{2} d e^{7} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{8}\right)} \sqrt{e x + d}\right) - 2 \, {\left(6 \, c^{2} e x^{3} + 9 \, b c e x^{2} + 3 \, a b e + {\left(5 \, b^{2} - 2 \, a c\right)} e x + 2 \, {\left(b^{2} - 4 \, a c\right)} d\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}"," ",0,"1/8*(3*sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 + sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log(27/2*sqrt(1/2)*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^6 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^7 - sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*(8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4 - 16*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3*e + 3*(3*b^8*c - 32*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^4*c^5)*d^2*e^2 - (b^9 - 96*a^2*b^5*c^2 + 512*a^3*b^3*c^3 - 768*a^4*b*c^4)*d*e^3 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^4))*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 + sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2)) + 27*(16*c^3*d^2*e^6 - 16*b*c^2*d*e^7 + (3*b^2*c + 4*a*c^2)*e^8)*sqrt(e*x + d)) - 3*sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 + sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log(-27/2*sqrt(1/2)*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^6 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^7 - sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*(8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4 - 16*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3*e + 3*(3*b^8*c - 32*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^4*c^5)*d^2*e^2 - (b^9 - 96*a^2*b^5*c^2 + 512*a^3*b^3*c^3 - 768*a^4*b*c^4)*d*e^3 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^4))*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 + sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2)) + 27*(16*c^3*d^2*e^6 - 16*b*c^2*d*e^7 + (3*b^2*c + 4*a*c^2)*e^8)*sqrt(e*x + d)) + 3*sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 - sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log(27/2*sqrt(1/2)*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^6 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^7 + sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*(8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4 - 16*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3*e + 3*(3*b^8*c - 32*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^4*c^5)*d^2*e^2 - (b^9 - 96*a^2*b^5*c^2 + 512*a^3*b^3*c^3 - 768*a^4*b*c^4)*d*e^3 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^4))*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 - sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2)) + 27*(16*c^3*d^2*e^6 - 16*b*c^2*d*e^7 + (3*b^2*c + 4*a*c^2)*e^8)*sqrt(e*x + d)) - 3*sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 - sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log(-27/2*sqrt(1/2)*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^6 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^7 + sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*(8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4 - 16*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3*e + 3*(3*b^8*c - 32*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^4*c^5)*d^2*e^2 - (b^9 - 96*a^2*b^5*c^2 + 512*a^3*b^3*c^3 - 768*a^4*b*c^4)*d*e^3 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^4))*sqrt((32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5 - sqrt(e^10/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2)) + 27*(16*c^3*d^2*e^6 - 16*b*c^2*d*e^7 + (3*b^2*c + 4*a*c^2)*e^8)*sqrt(e*x + d)) - 2*(6*c^2*e*x^3 + 9*b*c*e*x^2 + 3*a*b*e + (5*b^2 - 2*a*c)*e*x + 2*(b^2 - 4*a*c)*d)*sqrt(e*x + d))/((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)","B",0
1626,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1627,-1,0,0,0.000000," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1628,0,0,0,0.468630," ","integrate((2*c*x+b)*(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d), x)","F",0
1629,0,0,0,0.462267," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)}}{\sqrt{e x + d}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)/sqrt(e*x + d), x)","F",0
1630,0,0,0,0.477711," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
1631,0,0,0,0.465175," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
1632,0,0,0,0.458477," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
1633,0,0,0,0.465028," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c^{2} x^{3} + 3 \, b c x^{2} + a b + {\left(b^{2} + 2 \, a c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((2*c^2*x^3 + 3*b*c*x^2 + a*b + (b^2 + 2*a*c)*x)*sqrt(c*x^2 + b*x + a)/sqrt(e*x + d), x)","F",0
1634,0,0,0,0.448885," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c^{2} x^{3} + 3 \, b c x^{2} + a b + {\left(b^{2} + 2 \, a c\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((2*c^2*x^3 + 3*b*c*x^2 + a*b + (b^2 + 2*a*c)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
1635,0,0,0,0.460413," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c^{2} x^{3} + 3 \, b c x^{2} + a b + {\left(b^{2} + 2 \, a c\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((2*c^2*x^3 + 3*b*c*x^2 + a*b + (b^2 + 2*a*c)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
1636,0,0,0,0.484045," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c^{2} x^{3} + 3 \, b c x^{2} + a b + {\left(b^{2} + 2 \, a c\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((2*c^2*x^3 + 3*b*c*x^2 + a*b + (b^2 + 2*a*c)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
1637,0,0,0,0.467206," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c e^{2} x^{3} + b d^{2} + {\left(4 \, c d e + b e^{2}\right)} x^{2} + 2 \, {\left(c d^{2} + b d e\right)} x\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((2*c*e^2*x^3 + b*d^2 + (4*c*d*e + b*e^2)*x^2 + 2*(c*d^2 + b*d*e)*x)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
1638,0,0,0,0.460907," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c e x^{2} + b d + {\left(2 \, c d + b e\right)} x\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((2*c*e*x^2 + b*d + (2*c*d + b*e)*x)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
1639,0,0,0,0.472115," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c x + b\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((2*c*x + b)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
1640,0,0,0,0.459143," ","integrate((2*c*x+b)/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{c e x^{3} + {\left(c d + b e\right)} x^{2} + a d + {\left(b d + a e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(c*e*x^3 + (c*d + b*e)*x^2 + a*d + (b*d + a*e)*x), x)","F",0
1641,0,0,0,0.462206," ","integrate((2*c*x+b)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{c e^{2} x^{4} + {\left(2 \, c d e + b e^{2}\right)} x^{3} + a d^{2} + {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{2} + {\left(b d^{2} + 2 \, a d e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(c*e^2*x^4 + (2*c*d*e + b*e^2)*x^3 + a*d^2 + (c*d^2 + 2*b*d*e + a*e^2)*x^2 + (b*d^2 + 2*a*d*e)*x), x)","F",0
1642,0,0,0,0.463669," ","integrate((2*c*x+b)/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{c e^{3} x^{5} + {\left(3 \, c d e^{2} + b e^{3}\right)} x^{4} + a d^{3} + {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} x^{3} + {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} x^{2} + {\left(b d^{3} + 3 \, a d^{2} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(c*e^3*x^5 + (3*c*d*e^2 + b*e^3)*x^4 + a*d^3 + (3*c*d^2*e + 3*b*d*e^2 + a*e^3)*x^3 + (c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*x^2 + (b*d^3 + 3*a*d^2*e)*x), x)","F",0
1643,0,0,0,0.473530," ","integrate((2*c*x+b)*(e*x+d)^(7/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c e^{3} x^{4} + b d^{3} + {\left(6 \, c d e^{2} + b e^{3}\right)} x^{3} + 3 \, {\left(2 \, c d^{2} e + b d e^{2}\right)} x^{2} + {\left(2 \, c d^{3} + 3 \, b d^{2} e\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((2*c*e^3*x^4 + b*d^3 + (6*c*d*e^2 + b*e^3)*x^3 + 3*(2*c*d^2*e + b*d*e^2)*x^2 + (2*c*d^3 + 3*b*d^2*e)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1644,0,0,0,0.471615," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c e^{2} x^{3} + b d^{2} + {\left(4 \, c d e + b e^{2}\right)} x^{2} + 2 \, {\left(c d^{2} + b d e\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((2*c*e^2*x^3 + b*d^2 + (4*c*d*e + b*e^2)*x^2 + 2*(c*d^2 + b*d*e)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1645,0,0,0,0.463071," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c e x^{2} + b d + {\left(2 \, c d + b e\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((2*c*e*x^2 + b*d + (2*c*d + b*e)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1646,0,0,0,0.466175," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1647,0,0,0,0.455053," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{c^{2} e x^{5} + {\left(c^{2} d + 2 \, b c e\right)} x^{4} + {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} x^{3} + a^{2} d + {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} x^{2} + {\left(2 \, a b d + a^{2} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(c^2*e*x^5 + (c^2*d + 2*b*c*e)*x^4 + (2*b*c*d + (b^2 + 2*a*c)*e)*x^3 + a^2*d + (2*a*b*e + (b^2 + 2*a*c)*d)*x^2 + (2*a*b*d + a^2*e)*x), x)","F",0
1648,0,0,0,0.472494," ","integrate((2*c*x+b)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{c^{2} e^{2} x^{6} + 2 \, {\left(c^{2} d e + b c e^{2}\right)} x^{5} + {\left(c^{2} d^{2} + 4 \, b c d e + {\left(b^{2} + 2 \, a c\right)} e^{2}\right)} x^{4} + a^{2} d^{2} + 2 \, {\left(b c d^{2} + a b e^{2} + {\left(b^{2} + 2 \, a c\right)} d e\right)} x^{3} + {\left(4 \, a b d e + a^{2} e^{2} + {\left(b^{2} + 2 \, a c\right)} d^{2}\right)} x^{2} + 2 \, {\left(a b d^{2} + a^{2} d e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(c^2*e^2*x^6 + 2*(c^2*d*e + b*c*e^2)*x^5 + (c^2*d^2 + 4*b*c*d*e + (b^2 + 2*a*c)*e^2)*x^4 + a^2*d^2 + 2*(b*c*d^2 + a*b*e^2 + (b^2 + 2*a*c)*d*e)*x^3 + (4*a*b*d*e + a^2*e^2 + (b^2 + 2*a*c)*d^2)*x^2 + 2*(a*b*d^2 + a^2*d*e)*x), x)","F",0
1649,0,0,0,0.507756," ","integrate((2*c*x+b)*(e*x+d)^(7/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c e^{3} x^{4} + b d^{3} + {\left(6 \, c d e^{2} + b e^{3}\right)} x^{3} + 3 \, {\left(2 \, c d^{2} e + b d e^{2}\right)} x^{2} + {\left(2 \, c d^{3} + 3 \, b d^{2} e\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((2*c*e^3*x^4 + b*d^3 + (6*c*d*e^2 + b*e^3)*x^3 + 3*(2*c*d^2*e + b*d*e^2)*x^2 + (2*c*d^3 + 3*b*d^2*e)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1650,0,0,0,0.471303," ","integrate((2*c*x+b)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c e^{2} x^{3} + b d^{2} + {\left(4 \, c d e + b e^{2}\right)} x^{2} + 2 \, {\left(c d^{2} + b d e\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((2*c*e^2*x^3 + b*d^2 + (4*c*d*e + b*e^2)*x^2 + 2*(c*d^2 + b*d*e)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1651,0,0,0,0.456098," ","integrate((2*c*x+b)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c e x^{2} + b d + {\left(2 \, c d + b e\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((2*c*e*x^2 + b*d + (2*c*d + b*e)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1652,0,0,0,0.491394," ","integrate((2*c*x+b)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1653,0,0,0,0.513741," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{e x + d}}{c^{3} e x^{7} + {\left(c^{3} d + 3 \, b c^{2} e\right)} x^{6} + 3 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} x^{5} + {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} x^{4} + a^{3} d + {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} x^{3} + 3 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} x^{2} + {\left(3 \, a^{2} b d + a^{3} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(e*x + d)/(c^3*e*x^7 + (c^3*d + 3*b*c^2*e)*x^6 + 3*(b*c^2*d + (b^2*c + a*c^2)*e)*x^5 + (3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*x^4 + a^3*d + ((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*x^3 + 3*(a^2*b*e + (a*b^2 + a^2*c)*d)*x^2 + (3*a^2*b*d + a^3*e)*x), x)","F",0
1654,1,4607,0,0.540521," ","integrate((2*c*x+b)*(e*x+d)^m*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} b d e^{7} m^{7} - 10080 \, c^{4} d^{8} + 40320 \, b c^{3} d^{7} e + 40320 \, a^{3} b d e^{7} - 20160 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 40320 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - 10080 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 40320 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 20160 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} + 2 \, {\left(c^{4} e^{8} m^{7} + 28 \, c^{4} e^{8} m^{6} + 322 \, c^{4} e^{8} m^{5} + 1960 \, c^{4} e^{8} m^{4} + 6769 \, c^{4} e^{8} m^{3} + 13132 \, c^{4} e^{8} m^{2} + 13068 \, c^{4} e^{8} m + 5040 \, c^{4} e^{8}\right)} x^{8} + {\left(40320 \, b c^{3} e^{8} + {\left(2 \, c^{4} d e^{7} + 7 \, b c^{3} e^{8}\right)} m^{7} + 7 \, {\left(6 \, c^{4} d e^{7} + 29 \, b c^{3} e^{8}\right)} m^{6} + 7 \, {\left(50 \, c^{4} d e^{7} + 343 \, b c^{3} e^{8}\right)} m^{5} + 245 \, {\left(6 \, c^{4} d e^{7} + 61 \, b c^{3} e^{8}\right)} m^{4} + 112 \, {\left(29 \, c^{4} d e^{7} + 469 \, b c^{3} e^{8}\right)} m^{3} + 196 \, {\left(18 \, c^{4} d e^{7} + 527 \, b c^{3} e^{8}\right)} m^{2} + 144 \, {\left(10 \, c^{4} d e^{7} + 721 \, b c^{3} e^{8}\right)} m\right)} x^{7} + {\left(35 \, a^{3} b d e^{7} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6}\right)} m^{6} + {\left(20160 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8} + {\left(7 \, b c^{3} d e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} m^{7} - {\left(14 \, c^{4} d^{2} e^{6} - 161 \, b c^{3} d e^{7} - 90 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} m^{6} - {\left(210 \, c^{4} d^{2} e^{6} - 1435 \, b c^{3} d e^{7} - 1098 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} m^{5} - 5 \, {\left(238 \, c^{4} d^{2} e^{6} - 1267 \, b c^{3} d e^{7} - 1404 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} m^{4} - {\left(3150 \, c^{4} d^{2} e^{6} - 14518 \, b c^{3} d e^{7} - 25227 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} m^{3} - 2 \, {\left(1918 \, c^{4} d^{2} e^{6} - 8092 \, b c^{3} d e^{7} - 25245 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} m^{2} - 24 \, {\left(70 \, c^{4} d^{2} e^{6} - 280 \, b c^{3} d e^{7} - 2143 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} m\right)} x^{6} + {\left(511 \, a^{3} b d e^{7} + 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 33 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6}\right)} m^{5} + {\left(40320 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8} + {\left(3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} m^{7} - {\left(42 \, b c^{3} d^{2} e^{6} - 75 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} - 155 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} m^{6} + {\left(84 \, c^{4} d^{3} e^{5} - 756 \, b c^{3} d^{2} e^{6} + 723 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 1955 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} m^{5} + 5 \, {\left(168 \, c^{4} d^{3} e^{5} - 966 \, b c^{3} d^{2} e^{6} + 681 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 2581 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} m^{4} + 2 \, {\left(1470 \, c^{4} d^{3} e^{5} - 6930 \, b c^{3} d^{2} e^{6} + 4101 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 23860 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} m^{3} + 4 \, {\left(1050 \, c^{4} d^{3} e^{5} - 4452 \, b c^{3} d^{2} e^{6} + 2370 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 24455 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} m^{2} + 144 \, {\left(14 \, c^{4} d^{3} e^{5} - 56 \, b c^{3} d^{2} e^{6} + 28 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 705 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} m\right)} x^{5} + {\left(4025 \, a^{3} b d e^{7} - 6 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 180 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 445 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6}\right)} m^{4} + {\left(10080 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8} + {\left(5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} m^{7} - {\left(15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 135 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} - 32 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} m^{6} + {\left(210 \, b c^{3} d^{3} e^{5} - 315 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} + 1415 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + 418 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} m^{5} - {\left(420 \, c^{4} d^{4} e^{4} - 2940 \, b c^{3} d^{3} e^{5} + 2355 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 7245 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} - 2864 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} m^{4} - {\left(2520 \, c^{4} d^{4} e^{4} - 12390 \, b c^{3} d^{3} e^{5} + 7605 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 18740 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} - 10993 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} m^{3} - 2 \, {\left(2310 \, c^{4} d^{4} e^{4} - 9870 \, b c^{3} d^{3} e^{5} + 5295 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 11430 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} - 11656 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} m^{2} - 36 \, {\left(70 \, c^{4} d^{4} e^{4} - 280 \, b c^{3} d^{3} e^{5} + 140 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 280 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} - 691 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} m\right)} x^{4} + {\left(18424 \, a^{3} b d e^{7} + 120 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - 156 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 2130 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 3135 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6}\right)} m^{3} + {\left(40320 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8} + {\left({\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} m^{7} - {\left(20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} - 29 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} - 99 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} m^{6} + {\left(60 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 480 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + 331 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 1341 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} m^{5} - {\left(840 \, b c^{3} d^{4} e^{4} - 1080 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} + 4220 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} - 1871 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} - 9585 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} m^{4} + 4 \, {\left(420 \, c^{4} d^{5} e^{3} - 2310 \, b c^{3} d^{4} e^{4} + 1545 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 4080 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + 1345 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 9648 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} m^{3} + 4 \, {\left(1260 \, c^{4} d^{5} e^{3} - 5460 \, b c^{3} d^{4} e^{4} + 2970 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 6500 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + 1793 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 21519 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} m^{2} + 48 \, {\left(70 \, c^{4} d^{5} e^{3} - 280 \, b c^{3} d^{4} e^{4} + 140 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 280 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + 70 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 2003 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} m\right)} x^{3} + 2 \, {\left(24430 \, a^{3} b d e^{7} - 180 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 1260 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - 753 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 6210 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 6077 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6}\right)} m^{2} + {\left(20160 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8} + {\left(3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} m^{7} - {\left(3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 93 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} - 34 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} m^{6} + {\left(60 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} - 81 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} + 1155 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + 478 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} m^{5} - {\left(180 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 1320 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + 831 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 7275 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} - 3580 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} m^{4} + {\left(2520 \, b c^{3} d^{5} e^{3} - 2880 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} + 10020 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} - 3951 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} + 24042 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + 15289 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} m^{3} - 2 \, {\left(2520 \, c^{4} d^{6} e^{2} - 11340 \, b c^{3} d^{5} e^{3} + 6390 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 14460 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + 4119 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 18996 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} - 18353 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} m^{2} - 72 \, {\left(70 \, c^{4} d^{6} e^{2} - 280 \, b c^{3} d^{5} e^{3} + 140 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 280 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + 70 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 280 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} - 621 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} m\right)} x^{2} + 12 \, {\left(420 \, b c^{3} d^{7} e + 5772 \, a^{3} b d e^{7} - 450 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 1460 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - 533 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 2972 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 2046 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6}\right)} m + {\left(40320 \, a^{3} b e^{8} + {\left(a^{3} b e^{8} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} m^{7} + {\left(35 \, a^{3} b e^{8} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 33 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} m^{6} + {\left(511 \, a^{3} b e^{8} + 6 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 180 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 445 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} m^{5} + {\left(4025 \, a^{3} b e^{8} - 120 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 156 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 2130 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 3135 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} m^{4} + 2 \, {\left(9212 \, a^{3} b e^{8} + 180 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 1260 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 753 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 6210 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 6077 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} m^{3} - 4 \, {\left(1260 \, b c^{3} d^{6} e^{2} - 12215 \, a^{3} b e^{8} - 1350 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} + 4380 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} - 1599 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} + 8916 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} - 6138 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} m^{2} + 144 \, {\left(70 \, c^{4} d^{7} e - 280 \, b c^{3} d^{6} e^{2} + 481 \, a^{3} b e^{8} + 140 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 280 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 70 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 280 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 140 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{8} m^{8} + 36 \, e^{8} m^{7} + 546 \, e^{8} m^{6} + 4536 \, e^{8} m^{5} + 22449 \, e^{8} m^{4} + 67284 \, e^{8} m^{3} + 118124 \, e^{8} m^{2} + 109584 \, e^{8} m + 40320 \, e^{8}}"," ",0,"(a^3*b*d*e^7*m^7 - 10080*c^4*d^8 + 40320*b*c^3*d^7*e + 40320*a^3*b*d*e^7 - 20160*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 40320*(b^3*c + 3*a*b*c^2)*d^5*e^3 - 10080*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 40320*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 20160*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 + 2*(c^4*e^8*m^7 + 28*c^4*e^8*m^6 + 322*c^4*e^8*m^5 + 1960*c^4*e^8*m^4 + 6769*c^4*e^8*m^3 + 13132*c^4*e^8*m^2 + 13068*c^4*e^8*m + 5040*c^4*e^8)*x^8 + (40320*b*c^3*e^8 + (2*c^4*d*e^7 + 7*b*c^3*e^8)*m^7 + 7*(6*c^4*d*e^7 + 29*b*c^3*e^8)*m^6 + 7*(50*c^4*d*e^7 + 343*b*c^3*e^8)*m^5 + 245*(6*c^4*d*e^7 + 61*b*c^3*e^8)*m^4 + 112*(29*c^4*d*e^7 + 469*b*c^3*e^8)*m^3 + 196*(18*c^4*d*e^7 + 527*b*c^3*e^8)*m^2 + 144*(10*c^4*d*e^7 + 721*b*c^3*e^8)*m)*x^7 + (35*a^3*b*d*e^7 - (3*a^2*b^2 + 2*a^3*c)*d^2*e^6)*m^6 + (20160*(3*b^2*c^2 + 2*a*c^3)*e^8 + (7*b*c^3*d*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*e^8)*m^7 - (14*c^4*d^2*e^6 - 161*b*c^3*d*e^7 - 90*(3*b^2*c^2 + 2*a*c^3)*e^8)*m^6 - (210*c^4*d^2*e^6 - 1435*b*c^3*d*e^7 - 1098*(3*b^2*c^2 + 2*a*c^3)*e^8)*m^5 - 5*(238*c^4*d^2*e^6 - 1267*b*c^3*d*e^7 - 1404*(3*b^2*c^2 + 2*a*c^3)*e^8)*m^4 - (3150*c^4*d^2*e^6 - 14518*b*c^3*d*e^7 - 25227*(3*b^2*c^2 + 2*a*c^3)*e^8)*m^3 - 2*(1918*c^4*d^2*e^6 - 8092*b*c^3*d*e^7 - 25245*(3*b^2*c^2 + 2*a*c^3)*e^8)*m^2 - 24*(70*c^4*d^2*e^6 - 280*b*c^3*d*e^7 - 2143*(3*b^2*c^2 + 2*a*c^3)*e^8)*m)*x^6 + (511*a^3*b*d*e^7 + 6*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 33*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6)*m^5 + (40320*(b^3*c + 3*a*b*c^2)*e^8 + (3*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 5*(b^3*c + 3*a*b*c^2)*e^8)*m^7 - (42*b*c^3*d^2*e^6 - 75*(3*b^2*c^2 + 2*a*c^3)*d*e^7 - 155*(b^3*c + 3*a*b*c^2)*e^8)*m^6 + (84*c^4*d^3*e^5 - 756*b*c^3*d^2*e^6 + 723*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 1955*(b^3*c + 3*a*b*c^2)*e^8)*m^5 + 5*(168*c^4*d^3*e^5 - 966*b*c^3*d^2*e^6 + 681*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 2581*(b^3*c + 3*a*b*c^2)*e^8)*m^4 + 2*(1470*c^4*d^3*e^5 - 6930*b*c^3*d^2*e^6 + 4101*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 23860*(b^3*c + 3*a*b*c^2)*e^8)*m^3 + 4*(1050*c^4*d^3*e^5 - 4452*b*c^3*d^2*e^6 + 2370*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 24455*(b^3*c + 3*a*b*c^2)*e^8)*m^2 + 144*(14*c^4*d^3*e^5 - 56*b*c^3*d^2*e^6 + 28*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 705*(b^3*c + 3*a*b*c^2)*e^8)*m)*x^5 + (4025*a^3*b*d*e^7 - 6*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 180*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 445*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6)*m^4 + (10080*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8 + (5*(b^3*c + 3*a*b*c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*m^7 - (15*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 135*(b^3*c + 3*a*b*c^2)*d*e^7 - 32*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*m^6 + (210*b*c^3*d^3*e^5 - 315*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 + 1415*(b^3*c + 3*a*b*c^2)*d*e^7 + 418*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*m^5 - (420*c^4*d^4*e^4 - 2940*b*c^3*d^3*e^5 + 2355*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 7245*(b^3*c + 3*a*b*c^2)*d*e^7 - 2864*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*m^4 - (2520*c^4*d^4*e^4 - 12390*b*c^3*d^3*e^5 + 7605*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 18740*(b^3*c + 3*a*b*c^2)*d*e^7 - 10993*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*m^3 - 2*(2310*c^4*d^4*e^4 - 9870*b*c^3*d^3*e^5 + 5295*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 11430*(b^3*c + 3*a*b*c^2)*d*e^7 - 11656*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*m^2 - 36*(70*c^4*d^4*e^4 - 280*b*c^3*d^3*e^5 + 140*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 280*(b^3*c + 3*a*b*c^2)*d*e^7 - 691*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*m)*x^4 + (18424*a^3*b*d*e^7 + 120*(b^3*c + 3*a*b*c^2)*d^5*e^3 - 156*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 2130*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 3135*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6)*m^3 + (40320*(a*b^3 + 3*a^2*b*c)*e^8 + ((b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 3*(a*b^3 + 3*a^2*b*c)*e^8)*m^7 - (20*(b^3*c + 3*a*b*c^2)*d^2*e^6 - 29*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 - 99*(a*b^3 + 3*a^2*b*c)*e^8)*m^6 + (60*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 480*(b^3*c + 3*a*b*c^2)*d^2*e^6 + 331*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 1341*(a*b^3 + 3*a^2*b*c)*e^8)*m^5 - (840*b*c^3*d^4*e^4 - 1080*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 + 4220*(b^3*c + 3*a*b*c^2)*d^2*e^6 - 1871*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 - 9585*(a*b^3 + 3*a^2*b*c)*e^8)*m^4 + 4*(420*c^4*d^5*e^3 - 2310*b*c^3*d^4*e^4 + 1545*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 4080*(b^3*c + 3*a*b*c^2)*d^2*e^6 + 1345*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 9648*(a*b^3 + 3*a^2*b*c)*e^8)*m^3 + 4*(1260*c^4*d^5*e^3 - 5460*b*c^3*d^4*e^4 + 2970*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 6500*(b^3*c + 3*a*b*c^2)*d^2*e^6 + 1793*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 21519*(a*b^3 + 3*a^2*b*c)*e^8)*m^2 + 48*(70*c^4*d^5*e^3 - 280*b*c^3*d^4*e^4 + 140*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 280*(b^3*c + 3*a*b*c^2)*d^2*e^6 + 70*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 2003*(a*b^3 + 3*a^2*b*c)*e^8)*m)*x^3 + 2*(24430*a^3*b*d*e^7 - 180*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 1260*(b^3*c + 3*a*b*c^2)*d^5*e^3 - 753*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 6210*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 6077*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6)*m^2 + (20160*(3*a^2*b^2 + 2*a^3*c)*e^8 + (3*(a*b^3 + 3*a^2*b*c)*d*e^7 + (3*a^2*b^2 + 2*a^3*c)*e^8)*m^7 - (3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 93*(a*b^3 + 3*a^2*b*c)*d*e^7 - 34*(3*a^2*b^2 + 2*a^3*c)*e^8)*m^6 + (60*(b^3*c + 3*a*b*c^2)*d^3*e^5 - 81*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 + 1155*(a*b^3 + 3*a^2*b*c)*d*e^7 + 478*(3*a^2*b^2 + 2*a^3*c)*e^8)*m^5 - (180*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 1320*(b^3*c + 3*a*b*c^2)*d^3*e^5 + 831*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 7275*(a*b^3 + 3*a^2*b*c)*d*e^7 - 3580*(3*a^2*b^2 + 2*a^3*c)*e^8)*m^4 + (2520*b*c^3*d^5*e^3 - 2880*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 + 10020*(b^3*c + 3*a*b*c^2)*d^3*e^5 - 3951*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 + 24042*(a*b^3 + 3*a^2*b*c)*d*e^7 + 15289*(3*a^2*b^2 + 2*a^3*c)*e^8)*m^3 - 2*(2520*c^4*d^6*e^2 - 11340*b*c^3*d^5*e^3 + 6390*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 14460*(b^3*c + 3*a*b*c^2)*d^3*e^5 + 4119*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 18996*(a*b^3 + 3*a^2*b*c)*d*e^7 - 18353*(3*a^2*b^2 + 2*a^3*c)*e^8)*m^2 - 72*(70*c^4*d^6*e^2 - 280*b*c^3*d^5*e^3 + 140*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 280*(b^3*c + 3*a*b*c^2)*d^3*e^5 + 70*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 280*(a*b^3 + 3*a^2*b*c)*d*e^7 - 621*(3*a^2*b^2 + 2*a^3*c)*e^8)*m)*x^2 + 12*(420*b*c^3*d^7*e + 5772*a^3*b*d*e^7 - 450*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 1460*(b^3*c + 3*a*b*c^2)*d^5*e^3 - 533*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 2972*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 2046*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6)*m + (40320*a^3*b*e^8 + (a^3*b*e^8 + (3*a^2*b^2 + 2*a^3*c)*d*e^7)*m^7 + (35*a^3*b*e^8 - 6*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 33*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*m^6 + (511*a^3*b*e^8 + 6*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 180*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 445*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*m^5 + (4025*a^3*b*e^8 - 120*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 156*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 2130*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 3135*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*m^4 + 2*(9212*a^3*b*e^8 + 180*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 1260*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 753*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 6210*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 6077*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*m^3 - 4*(1260*b*c^3*d^6*e^2 - 12215*a^3*b*e^8 - 1350*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 + 4380*(b^3*c + 3*a*b*c^2)*d^4*e^4 - 1599*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 + 8916*(a*b^3 + 3*a^2*b*c)*d^2*e^6 - 6138*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*m^2 + 144*(70*c^4*d^7*e - 280*b*c^3*d^6*e^2 + 481*a^3*b*e^8 + 140*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 280*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 70*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 280*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 140*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*m)*x)*(e*x + d)^m/(e^8*m^8 + 36*e^8*m^7 + 546*e^8*m^6 + 4536*e^8*m^5 + 22449*e^8*m^4 + 67284*e^8*m^3 + 118124*e^8*m^2 + 109584*e^8*m + 40320*e^8)","B",0
1655,1,1750,0,0.497491," ","integrate((2*c*x+b)*(e*x+d)^m*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} b d e^{5} m^{5} - 240 \, c^{3} d^{6} + 720 \, b c^{2} d^{5} e + 720 \, a^{2} b d e^{5} - 720 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + 240 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 720 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} + 2 \, {\left(c^{3} e^{6} m^{5} + 15 \, c^{3} e^{6} m^{4} + 85 \, c^{3} e^{6} m^{3} + 225 \, c^{3} e^{6} m^{2} + 274 \, c^{3} e^{6} m + 120 \, c^{3} e^{6}\right)} x^{6} + {\left(720 \, b c^{2} e^{6} + {\left(2 \, c^{3} d e^{5} + 5 \, b c^{2} e^{6}\right)} m^{5} + 20 \, {\left(c^{3} d e^{5} + 4 \, b c^{2} e^{6}\right)} m^{4} + 5 \, {\left(14 \, c^{3} d e^{5} + 95 \, b c^{2} e^{6}\right)} m^{3} + 100 \, {\left(c^{3} d e^{5} + 13 \, b c^{2} e^{6}\right)} m^{2} + 12 \, {\left(4 \, c^{3} d e^{5} + 135 \, b c^{2} e^{6}\right)} m\right)} x^{5} + 2 \, {\left(10 \, a^{2} b d e^{5} - {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} m^{4} + {\left(720 \, {\left(b^{2} c + a c^{2}\right)} e^{6} + {\left(5 \, b c^{2} d e^{5} + 4 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} m^{5} - 2 \, {\left(5 \, c^{3} d^{2} e^{4} - 30 \, b c^{2} d e^{5} - 34 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} m^{4} - {\left(60 \, c^{3} d^{2} e^{4} - 235 \, b c^{2} d e^{5} - 428 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} m^{3} - 2 \, {\left(55 \, c^{3} d^{2} e^{4} - 180 \, b c^{2} d e^{5} - 614 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} m^{2} - 12 \, {\left(5 \, c^{3} d^{2} e^{4} - 15 \, b c^{2} d e^{5} - 132 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} m\right)} x^{4} + {\left(155 \, a^{2} b d e^{5} + 2 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 36 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} m^{3} + {\left(240 \, {\left(b^{3} + 6 \, a b c\right)} e^{6} + {\left(4 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} m^{5} - 2 \, {\left(10 \, b c^{2} d^{2} e^{4} - 28 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - 9 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} m^{4} + {\left(40 \, c^{3} d^{3} e^{3} - 180 \, b c^{2} d^{2} e^{4} + 260 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + 121 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} m^{3} + 4 \, {\left(30 \, c^{3} d^{3} e^{3} - 100 \, b c^{2} d^{2} e^{4} + 112 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + 93 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} m^{2} + 4 \, {\left(20 \, c^{3} d^{3} e^{3} - 60 \, b c^{2} d^{2} e^{4} + 60 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + 127 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} m\right)} x^{3} + 2 \, {\left(290 \, a^{2} b d e^{5} - 12 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + 15 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 119 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} m^{2} + {\left(720 \, {\left(a b^{2} + a^{2} c\right)} e^{6} + {\left({\left(b^{3} + 6 \, a b c\right)} d e^{5} + 2 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} m^{5} - 2 \, {\left(6 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - 8 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} - 19 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} m^{4} + {\left(60 \, b c^{2} d^{3} e^{3} - 144 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} + 89 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 274 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} m^{3} - 2 \, {\left(60 \, c^{3} d^{4} e^{2} - 210 \, b c^{2} d^{3} e^{3} + 246 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - 97 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} - 461 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} m^{2} - 12 \, {\left(10 \, c^{3} d^{4} e^{2} - 30 \, b c^{2} d^{3} e^{3} + 30 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - 10 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} - 117 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} m\right)} x^{2} + 4 \, {\left(30 \, b c^{2} d^{5} e + 261 \, a^{2} b d e^{5} - 66 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + 37 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 171 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} m + {\left(720 \, a^{2} b e^{6} + {\left(a^{2} b e^{6} + 2 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} m^{5} + 2 \, {\left(10 \, a^{2} b e^{6} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 18 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} m^{4} + {\left(155 \, a^{2} b e^{6} + 24 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - 30 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 238 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} m^{3} - 4 \, {\left(30 \, b c^{2} d^{4} e^{2} - 145 \, a^{2} b e^{6} - 66 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} + 37 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} - 171 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} m^{2} + 12 \, {\left(20 \, c^{3} d^{5} e - 60 \, b c^{2} d^{4} e^{2} + 87 \, a^{2} b e^{6} + 60 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - 20 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 60 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{6} m^{6} + 21 \, e^{6} m^{5} + 175 \, e^{6} m^{4} + 735 \, e^{6} m^{3} + 1624 \, e^{6} m^{2} + 1764 \, e^{6} m + 720 \, e^{6}}"," ",0,"(a^2*b*d*e^5*m^5 - 240*c^3*d^6 + 720*b*c^2*d^5*e + 720*a^2*b*d*e^5 - 720*(b^2*c + a*c^2)*d^4*e^2 + 240*(b^3 + 6*a*b*c)*d^3*e^3 - 720*(a*b^2 + a^2*c)*d^2*e^4 + 2*(c^3*e^6*m^5 + 15*c^3*e^6*m^4 + 85*c^3*e^6*m^3 + 225*c^3*e^6*m^2 + 274*c^3*e^6*m + 120*c^3*e^6)*x^6 + (720*b*c^2*e^6 + (2*c^3*d*e^5 + 5*b*c^2*e^6)*m^5 + 20*(c^3*d*e^5 + 4*b*c^2*e^6)*m^4 + 5*(14*c^3*d*e^5 + 95*b*c^2*e^6)*m^3 + 100*(c^3*d*e^5 + 13*b*c^2*e^6)*m^2 + 12*(4*c^3*d*e^5 + 135*b*c^2*e^6)*m)*x^5 + 2*(10*a^2*b*d*e^5 - (a*b^2 + a^2*c)*d^2*e^4)*m^4 + (720*(b^2*c + a*c^2)*e^6 + (5*b*c^2*d*e^5 + 4*(b^2*c + a*c^2)*e^6)*m^5 - 2*(5*c^3*d^2*e^4 - 30*b*c^2*d*e^5 - 34*(b^2*c + a*c^2)*e^6)*m^4 - (60*c^3*d^2*e^4 - 235*b*c^2*d*e^5 - 428*(b^2*c + a*c^2)*e^6)*m^3 - 2*(55*c^3*d^2*e^4 - 180*b*c^2*d*e^5 - 614*(b^2*c + a*c^2)*e^6)*m^2 - 12*(5*c^3*d^2*e^4 - 15*b*c^2*d*e^5 - 132*(b^2*c + a*c^2)*e^6)*m)*x^4 + (155*a^2*b*d*e^5 + 2*(b^3 + 6*a*b*c)*d^3*e^3 - 36*(a*b^2 + a^2*c)*d^2*e^4)*m^3 + (240*(b^3 + 6*a*b*c)*e^6 + (4*(b^2*c + a*c^2)*d*e^5 + (b^3 + 6*a*b*c)*e^6)*m^5 - 2*(10*b*c^2*d^2*e^4 - 28*(b^2*c + a*c^2)*d*e^5 - 9*(b^3 + 6*a*b*c)*e^6)*m^4 + (40*c^3*d^3*e^3 - 180*b*c^2*d^2*e^4 + 260*(b^2*c + a*c^2)*d*e^5 + 121*(b^3 + 6*a*b*c)*e^6)*m^3 + 4*(30*c^3*d^3*e^3 - 100*b*c^2*d^2*e^4 + 112*(b^2*c + a*c^2)*d*e^5 + 93*(b^3 + 6*a*b*c)*e^6)*m^2 + 4*(20*c^3*d^3*e^3 - 60*b*c^2*d^2*e^4 + 60*(b^2*c + a*c^2)*d*e^5 + 127*(b^3 + 6*a*b*c)*e^6)*m)*x^3 + 2*(290*a^2*b*d*e^5 - 12*(b^2*c + a*c^2)*d^4*e^2 + 15*(b^3 + 6*a*b*c)*d^3*e^3 - 119*(a*b^2 + a^2*c)*d^2*e^4)*m^2 + (720*(a*b^2 + a^2*c)*e^6 + ((b^3 + 6*a*b*c)*d*e^5 + 2*(a*b^2 + a^2*c)*e^6)*m^5 - 2*(6*(b^2*c + a*c^2)*d^2*e^4 - 8*(b^3 + 6*a*b*c)*d*e^5 - 19*(a*b^2 + a^2*c)*e^6)*m^4 + (60*b*c^2*d^3*e^3 - 144*(b^2*c + a*c^2)*d^2*e^4 + 89*(b^3 + 6*a*b*c)*d*e^5 + 274*(a*b^2 + a^2*c)*e^6)*m^3 - 2*(60*c^3*d^4*e^2 - 210*b*c^2*d^3*e^3 + 246*(b^2*c + a*c^2)*d^2*e^4 - 97*(b^3 + 6*a*b*c)*d*e^5 - 461*(a*b^2 + a^2*c)*e^6)*m^2 - 12*(10*c^3*d^4*e^2 - 30*b*c^2*d^3*e^3 + 30*(b^2*c + a*c^2)*d^2*e^4 - 10*(b^3 + 6*a*b*c)*d*e^5 - 117*(a*b^2 + a^2*c)*e^6)*m)*x^2 + 4*(30*b*c^2*d^5*e + 261*a^2*b*d*e^5 - 66*(b^2*c + a*c^2)*d^4*e^2 + 37*(b^3 + 6*a*b*c)*d^3*e^3 - 171*(a*b^2 + a^2*c)*d^2*e^4)*m + (720*a^2*b*e^6 + (a^2*b*e^6 + 2*(a*b^2 + a^2*c)*d*e^5)*m^5 + 2*(10*a^2*b*e^6 - (b^3 + 6*a*b*c)*d^2*e^4 + 18*(a*b^2 + a^2*c)*d*e^5)*m^4 + (155*a^2*b*e^6 + 24*(b^2*c + a*c^2)*d^3*e^3 - 30*(b^3 + 6*a*b*c)*d^2*e^4 + 238*(a*b^2 + a^2*c)*d*e^5)*m^3 - 4*(30*b*c^2*d^4*e^2 - 145*a^2*b*e^6 - 66*(b^2*c + a*c^2)*d^3*e^3 + 37*(b^3 + 6*a*b*c)*d^2*e^4 - 171*(a*b^2 + a^2*c)*d*e^5)*m^2 + 12*(20*c^3*d^5*e - 60*b*c^2*d^4*e^2 + 87*a^2*b*e^6 + 60*(b^2*c + a*c^2)*d^3*e^3 - 20*(b^3 + 6*a*b*c)*d^2*e^4 + 60*(a*b^2 + a^2*c)*d*e^5)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)","B",0
1656,1,511,0,0.438946," ","integrate((2*c*x+b)*(e*x+d)^m*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left(a b d e^{3} m^{3} - 12 \, c^{2} d^{4} + 24 \, b c d^{3} e + 24 \, a b d e^{3} - 12 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + 2 \, {\left(c^{2} e^{4} m^{3} + 6 \, c^{2} e^{4} m^{2} + 11 \, c^{2} e^{4} m + 6 \, c^{2} e^{4}\right)} x^{4} + {\left(24 \, b c e^{4} + {\left(2 \, c^{2} d e^{3} + 3 \, b c e^{4}\right)} m^{3} + 3 \, {\left(2 \, c^{2} d e^{3} + 7 \, b c e^{4}\right)} m^{2} + 2 \, {\left(2 \, c^{2} d e^{3} + 21 \, b c e^{4}\right)} m\right)} x^{3} + {\left(9 \, a b d e^{3} - {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}\right)} m^{2} + {\left(12 \, {\left(b^{2} + 2 \, a c\right)} e^{4} + {\left(3 \, b c d e^{3} + {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} m^{3} - {\left(6 \, c^{2} d^{2} e^{2} - 15 \, b c d e^{3} - 8 \, {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} m^{2} - {\left(6 \, c^{2} d^{2} e^{2} - 12 \, b c d e^{3} - 19 \, {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} m\right)} x^{2} + {\left(6 \, b c d^{3} e + 26 \, a b d e^{3} - 7 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}\right)} m + {\left(24 \, a b e^{4} + {\left(a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} m^{3} - {\left(6 \, b c d^{2} e^{2} - 9 \, a b e^{4} - 7 \, {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} m^{2} + 2 \, {\left(6 \, c^{2} d^{3} e - 12 \, b c d^{2} e^{2} + 13 \, a b e^{4} + 6 \, {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"(a*b*d*e^3*m^3 - 12*c^2*d^4 + 24*b*c*d^3*e + 24*a*b*d*e^3 - 12*(b^2 + 2*a*c)*d^2*e^2 + 2*(c^2*e^4*m^3 + 6*c^2*e^4*m^2 + 11*c^2*e^4*m + 6*c^2*e^4)*x^4 + (24*b*c*e^4 + (2*c^2*d*e^3 + 3*b*c*e^4)*m^3 + 3*(2*c^2*d*e^3 + 7*b*c*e^4)*m^2 + 2*(2*c^2*d*e^3 + 21*b*c*e^4)*m)*x^3 + (9*a*b*d*e^3 - (b^2 + 2*a*c)*d^2*e^2)*m^2 + (12*(b^2 + 2*a*c)*e^4 + (3*b*c*d*e^3 + (b^2 + 2*a*c)*e^4)*m^3 - (6*c^2*d^2*e^2 - 15*b*c*d*e^3 - 8*(b^2 + 2*a*c)*e^4)*m^2 - (6*c^2*d^2*e^2 - 12*b*c*d*e^3 - 19*(b^2 + 2*a*c)*e^4)*m)*x^2 + (6*b*c*d^3*e + 26*a*b*d*e^3 - 7*(b^2 + 2*a*c)*d^2*e^2)*m + (24*a*b*e^4 + (a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*m^3 - (6*b*c*d^2*e^2 - 9*a*b*e^4 - 7*(b^2 + 2*a*c)*d*e^3)*m^2 + 2*(6*c^2*d^3*e - 12*b*c*d^2*e^2 + 13*a*b*e^4 + 6*(b^2 + 2*a*c)*d*e^3)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
1657,0,0,0,0.436076," ","integrate((2*c*x+b)*(e*x+d)^m/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{m}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((2*c*x + b)*(e*x + d)^m/(c*x^2 + b*x + a), x)","F",0
1658,0,0,0,0.464799," ","integrate((2*c*x+b)*(e*x+d)^m/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c x + b\right)} {\left(e x + d\right)}^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((2*c*x + b)*(e*x + d)^m/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1659,1,463,0,0.356250," ","integrate((B*x+A)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{5} b^{2} B + \frac{5}{8} x^{8} e^{4} d b^{2} B + \frac{1}{4} x^{8} e^{5} b a B + \frac{1}{8} x^{8} e^{5} b^{2} A + \frac{10}{7} x^{7} e^{3} d^{2} b^{2} B + \frac{10}{7} x^{7} e^{4} d b a B + \frac{1}{7} x^{7} e^{5} a^{2} B + \frac{5}{7} x^{7} e^{4} d b^{2} A + \frac{2}{7} x^{7} e^{5} b a A + \frac{5}{3} x^{6} e^{2} d^{3} b^{2} B + \frac{10}{3} x^{6} e^{3} d^{2} b a B + \frac{5}{6} x^{6} e^{4} d a^{2} B + \frac{5}{3} x^{6} e^{3} d^{2} b^{2} A + \frac{5}{3} x^{6} e^{4} d b a A + \frac{1}{6} x^{6} e^{5} a^{2} A + x^{5} e d^{4} b^{2} B + 4 x^{5} e^{2} d^{3} b a B + 2 x^{5} e^{3} d^{2} a^{2} B + 2 x^{5} e^{2} d^{3} b^{2} A + 4 x^{5} e^{3} d^{2} b a A + x^{5} e^{4} d a^{2} A + \frac{1}{4} x^{4} d^{5} b^{2} B + \frac{5}{2} x^{4} e d^{4} b a B + \frac{5}{2} x^{4} e^{2} d^{3} a^{2} B + \frac{5}{4} x^{4} e d^{4} b^{2} A + 5 x^{4} e^{2} d^{3} b a A + \frac{5}{2} x^{4} e^{3} d^{2} a^{2} A + \frac{2}{3} x^{3} d^{5} b a B + \frac{5}{3} x^{3} e d^{4} a^{2} B + \frac{1}{3} x^{3} d^{5} b^{2} A + \frac{10}{3} x^{3} e d^{4} b a A + \frac{10}{3} x^{3} e^{2} d^{3} a^{2} A + \frac{1}{2} x^{2} d^{5} a^{2} B + x^{2} d^{5} b a A + \frac{5}{2} x^{2} e d^{4} a^{2} A + x d^{5} a^{2} A"," ",0,"1/9*x^9*e^5*b^2*B + 5/8*x^8*e^4*d*b^2*B + 1/4*x^8*e^5*b*a*B + 1/8*x^8*e^5*b^2*A + 10/7*x^7*e^3*d^2*b^2*B + 10/7*x^7*e^4*d*b*a*B + 1/7*x^7*e^5*a^2*B + 5/7*x^7*e^4*d*b^2*A + 2/7*x^7*e^5*b*a*A + 5/3*x^6*e^2*d^3*b^2*B + 10/3*x^6*e^3*d^2*b*a*B + 5/6*x^6*e^4*d*a^2*B + 5/3*x^6*e^3*d^2*b^2*A + 5/3*x^6*e^4*d*b*a*A + 1/6*x^6*e^5*a^2*A + x^5*e*d^4*b^2*B + 4*x^5*e^2*d^3*b*a*B + 2*x^5*e^3*d^2*a^2*B + 2*x^5*e^2*d^3*b^2*A + 4*x^5*e^3*d^2*b*a*A + x^5*e^4*d*a^2*A + 1/4*x^4*d^5*b^2*B + 5/2*x^4*e*d^4*b*a*B + 5/2*x^4*e^2*d^3*a^2*B + 5/4*x^4*e*d^4*b^2*A + 5*x^4*e^2*d^3*b*a*A + 5/2*x^4*e^3*d^2*a^2*A + 2/3*x^3*d^5*b*a*B + 5/3*x^3*e*d^4*a^2*B + 1/3*x^3*d^5*b^2*A + 10/3*x^3*e*d^4*b*a*A + 10/3*x^3*e^2*d^3*a^2*A + 1/2*x^2*d^5*a^2*B + x^2*d^5*b*a*A + 5/2*x^2*e*d^4*a^2*A + x*d^5*a^2*A","B",0
1660,1,374,0,0.369535," ","integrate((B*x+A)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{4} b^{2} B + \frac{4}{7} x^{7} e^{3} d b^{2} B + \frac{2}{7} x^{7} e^{4} b a B + \frac{1}{7} x^{7} e^{4} b^{2} A + x^{6} e^{2} d^{2} b^{2} B + \frac{4}{3} x^{6} e^{3} d b a B + \frac{1}{6} x^{6} e^{4} a^{2} B + \frac{2}{3} x^{6} e^{3} d b^{2} A + \frac{1}{3} x^{6} e^{4} b a A + \frac{4}{5} x^{5} e d^{3} b^{2} B + \frac{12}{5} x^{5} e^{2} d^{2} b a B + \frac{4}{5} x^{5} e^{3} d a^{2} B + \frac{6}{5} x^{5} e^{2} d^{2} b^{2} A + \frac{8}{5} x^{5} e^{3} d b a A + \frac{1}{5} x^{5} e^{4} a^{2} A + \frac{1}{4} x^{4} d^{4} b^{2} B + 2 x^{4} e d^{3} b a B + \frac{3}{2} x^{4} e^{2} d^{2} a^{2} B + x^{4} e d^{3} b^{2} A + 3 x^{4} e^{2} d^{2} b a A + x^{4} e^{3} d a^{2} A + \frac{2}{3} x^{3} d^{4} b a B + \frac{4}{3} x^{3} e d^{3} a^{2} B + \frac{1}{3} x^{3} d^{4} b^{2} A + \frac{8}{3} x^{3} e d^{3} b a A + 2 x^{3} e^{2} d^{2} a^{2} A + \frac{1}{2} x^{2} d^{4} a^{2} B + x^{2} d^{4} b a A + 2 x^{2} e d^{3} a^{2} A + x d^{4} a^{2} A"," ",0,"1/8*x^8*e^4*b^2*B + 4/7*x^7*e^3*d*b^2*B + 2/7*x^7*e^4*b*a*B + 1/7*x^7*e^4*b^2*A + x^6*e^2*d^2*b^2*B + 4/3*x^6*e^3*d*b*a*B + 1/6*x^6*e^4*a^2*B + 2/3*x^6*e^3*d*b^2*A + 1/3*x^6*e^4*b*a*A + 4/5*x^5*e*d^3*b^2*B + 12/5*x^5*e^2*d^2*b*a*B + 4/5*x^5*e^3*d*a^2*B + 6/5*x^5*e^2*d^2*b^2*A + 8/5*x^5*e^3*d*b*a*A + 1/5*x^5*e^4*a^2*A + 1/4*x^4*d^4*b^2*B + 2*x^4*e*d^3*b*a*B + 3/2*x^4*e^2*d^2*a^2*B + x^4*e*d^3*b^2*A + 3*x^4*e^2*d^2*b*a*A + x^4*e^3*d*a^2*A + 2/3*x^3*d^4*b*a*B + 4/3*x^3*e*d^3*a^2*B + 1/3*x^3*d^4*b^2*A + 8/3*x^3*e*d^3*b*a*A + 2*x^3*e^2*d^2*a^2*A + 1/2*x^2*d^4*a^2*B + x^2*d^4*b*a*A + 2*x^2*e*d^3*a^2*A + x*d^4*a^2*A","B",0
1661,1,287,0,0.367740," ","integrate((B*x+A)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{3} b^{2} B + \frac{1}{2} x^{6} e^{2} d b^{2} B + \frac{1}{3} x^{6} e^{3} b a B + \frac{1}{6} x^{6} e^{3} b^{2} A + \frac{3}{5} x^{5} e d^{2} b^{2} B + \frac{6}{5} x^{5} e^{2} d b a B + \frac{1}{5} x^{5} e^{3} a^{2} B + \frac{3}{5} x^{5} e^{2} d b^{2} A + \frac{2}{5} x^{5} e^{3} b a A + \frac{1}{4} x^{4} d^{3} b^{2} B + \frac{3}{2} x^{4} e d^{2} b a B + \frac{3}{4} x^{4} e^{2} d a^{2} B + \frac{3}{4} x^{4} e d^{2} b^{2} A + \frac{3}{2} x^{4} e^{2} d b a A + \frac{1}{4} x^{4} e^{3} a^{2} A + \frac{2}{3} x^{3} d^{3} b a B + x^{3} e d^{2} a^{2} B + \frac{1}{3} x^{3} d^{3} b^{2} A + 2 x^{3} e d^{2} b a A + x^{3} e^{2} d a^{2} A + \frac{1}{2} x^{2} d^{3} a^{2} B + x^{2} d^{3} b a A + \frac{3}{2} x^{2} e d^{2} a^{2} A + x d^{3} a^{2} A"," ",0,"1/7*x^7*e^3*b^2*B + 1/2*x^6*e^2*d*b^2*B + 1/3*x^6*e^3*b*a*B + 1/6*x^6*e^3*b^2*A + 3/5*x^5*e*d^2*b^2*B + 6/5*x^5*e^2*d*b*a*B + 1/5*x^5*e^3*a^2*B + 3/5*x^5*e^2*d*b^2*A + 2/5*x^5*e^3*b*a*A + 1/4*x^4*d^3*b^2*B + 3/2*x^4*e*d^2*b*a*B + 3/4*x^4*e^2*d*a^2*B + 3/4*x^4*e*d^2*b^2*A + 3/2*x^4*e^2*d*b*a*A + 1/4*x^4*e^3*a^2*A + 2/3*x^3*d^3*b*a*B + x^3*e*d^2*a^2*B + 1/3*x^3*d^3*b^2*A + 2*x^3*e*d^2*b*a*A + x^3*e^2*d*a^2*A + 1/2*x^2*d^3*a^2*B + x^2*d^3*b*a*A + 3/2*x^2*e*d^2*a^2*A + x*d^3*a^2*A","B",0
1662,1,199,0,0.356842," ","integrate((B*x+A)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{2} b^{2} B + \frac{2}{5} x^{5} e d b^{2} B + \frac{2}{5} x^{5} e^{2} b a B + \frac{1}{5} x^{5} e^{2} b^{2} A + \frac{1}{4} x^{4} d^{2} b^{2} B + x^{4} e d b a B + \frac{1}{4} x^{4} e^{2} a^{2} B + \frac{1}{2} x^{4} e d b^{2} A + \frac{1}{2} x^{4} e^{2} b a A + \frac{2}{3} x^{3} d^{2} b a B + \frac{2}{3} x^{3} e d a^{2} B + \frac{1}{3} x^{3} d^{2} b^{2} A + \frac{4}{3} x^{3} e d b a A + \frac{1}{3} x^{3} e^{2} a^{2} A + \frac{1}{2} x^{2} d^{2} a^{2} B + x^{2} d^{2} b a A + x^{2} e d a^{2} A + x d^{2} a^{2} A"," ",0,"1/6*x^6*e^2*b^2*B + 2/5*x^5*e*d*b^2*B + 2/5*x^5*e^2*b*a*B + 1/5*x^5*e^2*b^2*A + 1/4*x^4*d^2*b^2*B + x^4*e*d*b*a*B + 1/4*x^4*e^2*a^2*B + 1/2*x^4*e*d*b^2*A + 1/2*x^4*e^2*b*a*A + 2/3*x^3*d^2*b*a*B + 2/3*x^3*e*d*a^2*B + 1/3*x^3*d^2*b^2*A + 4/3*x^3*e*d*b*a*A + 1/3*x^3*e^2*a^2*A + 1/2*x^2*d^2*a^2*B + x^2*d^2*b*a*A + x^2*e*d*a^2*A + x*d^2*a^2*A","A",0
1663,1,113,0,0.356033," ","integrate((B*x+A)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e b^{2} B + \frac{1}{4} x^{4} d b^{2} B + \frac{1}{2} x^{4} e b a B + \frac{1}{4} x^{4} e b^{2} A + \frac{2}{3} x^{3} d b a B + \frac{1}{3} x^{3} e a^{2} B + \frac{1}{3} x^{3} d b^{2} A + \frac{2}{3} x^{3} e b a A + \frac{1}{2} x^{2} d a^{2} B + x^{2} d b a A + \frac{1}{2} x^{2} e a^{2} A + x d a^{2} A"," ",0,"1/5*x^5*e*b^2*B + 1/4*x^4*d*b^2*B + 1/2*x^4*e*b*a*B + 1/4*x^4*e*b^2*A + 2/3*x^3*d*b*a*B + 1/3*x^3*e*a^2*B + 1/3*x^3*d*b^2*A + 2/3*x^3*e*b*a*A + 1/2*x^2*d*a^2*B + x^2*d*b*a*A + 1/2*x^2*e*a^2*A + x*d*a^2*A","A",0
1664,1,49,0,0.360398," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{4} x^{4} b^{2} B + \frac{2}{3} x^{3} b a B + \frac{1}{3} x^{3} b^{2} A + \frac{1}{2} x^{2} a^{2} B + x^{2} b a A + x a^{2} A"," ",0,"1/4*x^4*b^2*B + 2/3*x^3*b*a*B + 1/3*x^3*b^2*A + 1/2*x^2*a^2*B + x^2*b*a*A + x*a^2*A","A",0
1665,1,153,0,0.418731," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d),x, algorithm=""fricas"")","\frac{2 \, B b^{2} e^{3} x^{3} - 3 \, {\left(B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 6 \, {\left(B b^{2} d^{2} e - {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x - 6 \, {\left(B b^{2} d^{3} - A a^{2} e^{3} - {\left(2 \, B a b + A b^{2}\right)} d^{2} e + {\left(B a^{2} + 2 \, A a b\right)} d e^{2}\right)} \log\left(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(2*B*b^2*e^3*x^3 - 3*(B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 + 6*(B*b^2*d^2*e - (2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x - 6*(B*b^2*d^3 - A*a^2*e^3 - (2*B*a*b + A*b^2)*d^2*e + (B*a^2 + 2*A*a*b)*d*e^2)*log(e*x + d))/e^4","A",0
1666,1,238,0,0.417996," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{B b^{2} e^{3} x^{3} + 2 \, B b^{2} d^{3} - 2 \, A a^{2} e^{3} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 2 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - {\left(3 \, B b^{2} d e^{2} - 2 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} - 2 \, {\left(2 \, B b^{2} d^{2} e - {\left(2 \, B a b + A b^{2}\right)} d e^{2}\right)} x + 2 \, {\left(3 \, B b^{2} d^{3} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + {\left(3 \, B b^{2} d^{2} e - 2 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(B*b^2*e^3*x^3 + 2*B*b^2*d^3 - 2*A*a^2*e^3 - 2*(2*B*a*b + A*b^2)*d^2*e + 2*(B*a^2 + 2*A*a*b)*d*e^2 - (3*B*b^2*d*e^2 - 2*(2*B*a*b + A*b^2)*e^3)*x^2 - 2*(2*B*b^2*d^2*e - (2*B*a*b + A*b^2)*d*e^2)*x + 2*(3*B*b^2*d^3 - 2*(2*B*a*b + A*b^2)*d^2*e + (B*a^2 + 2*A*a*b)*d*e^2 + (3*B*b^2*d^2*e - 2*(2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x)*log(e*x + d))/(e^5*x + d*e^4)","B",0
1667,1,247,0,0.397891," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{2} e^{3} x^{3} + 4 \, B b^{2} d e^{2} x^{2} - 5 \, B b^{2} d^{3} - A a^{2} e^{3} + 3 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - 2 \, {\left(2 \, B b^{2} d^{2} e - 2 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x - 2 \, {\left(3 \, B b^{2} d^{3} - {\left(2 \, B a b + A b^{2}\right)} d^{2} e + {\left(3 \, B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} d^{2} e - {\left(2 \, B a b + A b^{2}\right)} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(2*B*b^2*e^3*x^3 + 4*B*b^2*d*e^2*x^2 - 5*B*b^2*d^3 - A*a^2*e^3 + 3*(2*B*a*b + A*b^2)*d^2*e - (B*a^2 + 2*A*a*b)*d*e^2 - 2*(2*B*b^2*d^2*e - 2*(2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x - 2*(3*B*b^2*d^3 - (2*B*a*b + A*b^2)*d^2*e + (3*B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 + 2*(3*B*b^2*d^2*e - (2*B*a*b + A*b^2)*d*e^2)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","B",0
1668,1,221,0,0.413439," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{11 \, B b^{2} d^{3} - 2 \, A a^{2} e^{3} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 6 \, {\left(3 \, B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 3 \, {\left(9 \, B b^{2} d^{2} e - 2 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} - {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x + 6 \, {\left(B b^{2} e^{3} x^{3} + 3 \, B b^{2} d e^{2} x^{2} + 3 \, B b^{2} d^{2} e x + B b^{2} d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(11*B*b^2*d^3 - 2*A*a^2*e^3 - 2*(2*B*a*b + A*b^2)*d^2*e - (B*a^2 + 2*A*a*b)*d*e^2 + 6*(3*B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 + 3*(9*B*b^2*d^2*e - 2*(2*B*a*b + A*b^2)*d*e^2 - (B*a^2 + 2*A*a*b)*e^3)*x + 6*(B*b^2*e^3*x^3 + 3*B*b^2*d*e^2*x^2 + 3*B*b^2*d^2*e*x + B*b^2*d^3)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","B",0
1669,1,187,0,0.405474," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{12 \, B b^{2} e^{3} x^{3} + 3 \, B b^{2} d^{3} + 3 \, A a^{2} e^{3} + {\left(2 \, B a b + A b^{2}\right)} d^{2} e + {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 6 \, {\left(3 \, B b^{2} d e^{2} + {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 4 \, {\left(3 \, B b^{2} d^{2} e + {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x}{12 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-1/12*(12*B*b^2*e^3*x^3 + 3*B*b^2*d^3 + 3*A*a^2*e^3 + (2*B*a*b + A*b^2)*d^2*e + (B*a^2 + 2*A*a*b)*d*e^2 + 6*(3*B*b^2*d*e^2 + (2*B*a*b + A*b^2)*e^3)*x^2 + 4*(3*B*b^2*d^2*e + (2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","B",0
1670,1,203,0,0.400110," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{30 \, B b^{2} e^{3} x^{3} + 3 \, B b^{2} d^{3} + 12 \, A a^{2} e^{3} + 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 3 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 10 \, {\left(3 \, B b^{2} d e^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 5 \, {\left(3 \, B b^{2} d^{2} e + 2 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x}{60 \, {\left(e^{9} x^{5} + 5 \, d e^{8} x^{4} + 10 \, d^{2} e^{7} x^{3} + 10 \, d^{3} e^{6} x^{2} + 5 \, d^{4} e^{5} x + d^{5} e^{4}\right)}}"," ",0,"-1/60*(30*B*b^2*e^3*x^3 + 3*B*b^2*d^3 + 12*A*a^2*e^3 + 2*(2*B*a*b + A*b^2)*d^2*e + 3*(B*a^2 + 2*A*a*b)*d*e^2 + 10*(3*B*b^2*d*e^2 + 2*(2*B*a*b + A*b^2)*e^3)*x^2 + 5*(3*B*b^2*d^2*e + 2*(2*B*a*b + A*b^2)*d*e^2 + 3*(B*a^2 + 2*A*a*b)*e^3)*x)/(e^9*x^5 + 5*d*e^8*x^4 + 10*d^2*e^7*x^3 + 10*d^3*e^6*x^2 + 5*d^4*e^5*x + d^5*e^4)","A",0
1671,1,208,0,0.408358," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{20 \, B b^{2} e^{3} x^{3} + B b^{2} d^{3} + 10 \, A a^{2} e^{3} + {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 2 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 15 \, {\left(B b^{2} d e^{2} + {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 6 \, {\left(B b^{2} d^{2} e + {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x}{60 \, {\left(e^{10} x^{6} + 6 \, d e^{9} x^{5} + 15 \, d^{2} e^{8} x^{4} + 20 \, d^{3} e^{7} x^{3} + 15 \, d^{4} e^{6} x^{2} + 6 \, d^{5} e^{5} x + d^{6} e^{4}\right)}}"," ",0,"-1/60*(20*B*b^2*e^3*x^3 + B*b^2*d^3 + 10*A*a^2*e^3 + (2*B*a*b + A*b^2)*d^2*e + 2*(B*a^2 + 2*A*a*b)*d*e^2 + 15*(B*b^2*d*e^2 + (2*B*a*b + A*b^2)*e^3)*x^2 + 6*(B*b^2*d^2*e + (2*B*a*b + A*b^2)*d*e^2 + 2*(B*a^2 + 2*A*a*b)*e^3)*x)/(e^10*x^6 + 6*d*e^9*x^5 + 15*d^2*e^8*x^4 + 20*d^3*e^7*x^3 + 15*d^4*e^6*x^2 + 6*d^5*e^5*x + d^6*e^4)","A",0
1672,1,225,0,0.422915," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{105 \, B b^{2} e^{3} x^{3} + 3 \, B b^{2} d^{3} + 60 \, A a^{2} e^{3} + 4 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 10 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 21 \, {\left(3 \, B b^{2} d e^{2} + 4 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 7 \, {\left(3 \, B b^{2} d^{2} e + 4 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 10 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x}{420 \, {\left(e^{11} x^{7} + 7 \, d e^{10} x^{6} + 21 \, d^{2} e^{9} x^{5} + 35 \, d^{3} e^{8} x^{4} + 35 \, d^{4} e^{7} x^{3} + 21 \, d^{5} e^{6} x^{2} + 7 \, d^{6} e^{5} x + d^{7} e^{4}\right)}}"," ",0,"-1/420*(105*B*b^2*e^3*x^3 + 3*B*b^2*d^3 + 60*A*a^2*e^3 + 4*(2*B*a*b + A*b^2)*d^2*e + 10*(B*a^2 + 2*A*a*b)*d*e^2 + 21*(3*B*b^2*d*e^2 + 4*(2*B*a*b + A*b^2)*e^3)*x^2 + 7*(3*B*b^2*d^2*e + 4*(2*B*a*b + A*b^2)*d*e^2 + 10*(B*a^2 + 2*A*a*b)*e^3)*x)/(e^11*x^7 + 7*d*e^10*x^6 + 21*d^2*e^9*x^5 + 35*d^3*e^8*x^4 + 35*d^4*e^7*x^3 + 21*d^5*e^6*x^2 + 7*d^6*e^5*x + d^7*e^4)","B",0
1673,1,1175,0,0.361603," ","integrate((B*x+A)*(e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{7} b^{4} B + \frac{7}{12} x^{12} e^{6} d b^{4} B + \frac{1}{3} x^{12} e^{7} b^{3} a B + \frac{1}{12} x^{12} e^{7} b^{4} A + \frac{21}{11} x^{11} e^{5} d^{2} b^{4} B + \frac{28}{11} x^{11} e^{6} d b^{3} a B + \frac{6}{11} x^{11} e^{7} b^{2} a^{2} B + \frac{7}{11} x^{11} e^{6} d b^{4} A + \frac{4}{11} x^{11} e^{7} b^{3} a A + \frac{7}{2} x^{10} e^{4} d^{3} b^{4} B + \frac{42}{5} x^{10} e^{5} d^{2} b^{3} a B + \frac{21}{5} x^{10} e^{6} d b^{2} a^{2} B + \frac{2}{5} x^{10} e^{7} b a^{3} B + \frac{21}{10} x^{10} e^{5} d^{2} b^{4} A + \frac{14}{5} x^{10} e^{6} d b^{3} a A + \frac{3}{5} x^{10} e^{7} b^{2} a^{2} A + \frac{35}{9} x^{9} e^{3} d^{4} b^{4} B + \frac{140}{9} x^{9} e^{4} d^{3} b^{3} a B + 14 x^{9} e^{5} d^{2} b^{2} a^{2} B + \frac{28}{9} x^{9} e^{6} d b a^{3} B + \frac{1}{9} x^{9} e^{7} a^{4} B + \frac{35}{9} x^{9} e^{4} d^{3} b^{4} A + \frac{28}{3} x^{9} e^{5} d^{2} b^{3} a A + \frac{14}{3} x^{9} e^{6} d b^{2} a^{2} A + \frac{4}{9} x^{9} e^{7} b a^{3} A + \frac{21}{8} x^{8} e^{2} d^{5} b^{4} B + \frac{35}{2} x^{8} e^{3} d^{4} b^{3} a B + \frac{105}{4} x^{8} e^{4} d^{3} b^{2} a^{2} B + \frac{21}{2} x^{8} e^{5} d^{2} b a^{3} B + \frac{7}{8} x^{8} e^{6} d a^{4} B + \frac{35}{8} x^{8} e^{3} d^{4} b^{4} A + \frac{35}{2} x^{8} e^{4} d^{3} b^{3} a A + \frac{63}{4} x^{8} e^{5} d^{2} b^{2} a^{2} A + \frac{7}{2} x^{8} e^{6} d b a^{3} A + \frac{1}{8} x^{8} e^{7} a^{4} A + x^{7} e d^{6} b^{4} B + 12 x^{7} e^{2} d^{5} b^{3} a B + 30 x^{7} e^{3} d^{4} b^{2} a^{2} B + 20 x^{7} e^{4} d^{3} b a^{3} B + 3 x^{7} e^{5} d^{2} a^{4} B + 3 x^{7} e^{2} d^{5} b^{4} A + 20 x^{7} e^{3} d^{4} b^{3} a A + 30 x^{7} e^{4} d^{3} b^{2} a^{2} A + 12 x^{7} e^{5} d^{2} b a^{3} A + x^{7} e^{6} d a^{4} A + \frac{1}{6} x^{6} d^{7} b^{4} B + \frac{14}{3} x^{6} e d^{6} b^{3} a B + 21 x^{6} e^{2} d^{5} b^{2} a^{2} B + \frac{70}{3} x^{6} e^{3} d^{4} b a^{3} B + \frac{35}{6} x^{6} e^{4} d^{3} a^{4} B + \frac{7}{6} x^{6} e d^{6} b^{4} A + 14 x^{6} e^{2} d^{5} b^{3} a A + 35 x^{6} e^{3} d^{4} b^{2} a^{2} A + \frac{70}{3} x^{6} e^{4} d^{3} b a^{3} A + \frac{7}{2} x^{6} e^{5} d^{2} a^{4} A + \frac{4}{5} x^{5} d^{7} b^{3} a B + \frac{42}{5} x^{5} e d^{6} b^{2} a^{2} B + \frac{84}{5} x^{5} e^{2} d^{5} b a^{3} B + 7 x^{5} e^{3} d^{4} a^{4} B + \frac{1}{5} x^{5} d^{7} b^{4} A + \frac{28}{5} x^{5} e d^{6} b^{3} a A + \frac{126}{5} x^{5} e^{2} d^{5} b^{2} a^{2} A + 28 x^{5} e^{3} d^{4} b a^{3} A + 7 x^{5} e^{4} d^{3} a^{4} A + \frac{3}{2} x^{4} d^{7} b^{2} a^{2} B + 7 x^{4} e d^{6} b a^{3} B + \frac{21}{4} x^{4} e^{2} d^{5} a^{4} B + x^{4} d^{7} b^{3} a A + \frac{21}{2} x^{4} e d^{6} b^{2} a^{2} A + 21 x^{4} e^{2} d^{5} b a^{3} A + \frac{35}{4} x^{4} e^{3} d^{4} a^{4} A + \frac{4}{3} x^{3} d^{7} b a^{3} B + \frac{7}{3} x^{3} e d^{6} a^{4} B + 2 x^{3} d^{7} b^{2} a^{2} A + \frac{28}{3} x^{3} e d^{6} b a^{3} A + 7 x^{3} e^{2} d^{5} a^{4} A + \frac{1}{2} x^{2} d^{7} a^{4} B + 2 x^{2} d^{7} b a^{3} A + \frac{7}{2} x^{2} e d^{6} a^{4} A + x d^{7} a^{4} A"," ",0,"1/13*x^13*e^7*b^4*B + 7/12*x^12*e^6*d*b^4*B + 1/3*x^12*e^7*b^3*a*B + 1/12*x^12*e^7*b^4*A + 21/11*x^11*e^5*d^2*b^4*B + 28/11*x^11*e^6*d*b^3*a*B + 6/11*x^11*e^7*b^2*a^2*B + 7/11*x^11*e^6*d*b^4*A + 4/11*x^11*e^7*b^3*a*A + 7/2*x^10*e^4*d^3*b^4*B + 42/5*x^10*e^5*d^2*b^3*a*B + 21/5*x^10*e^6*d*b^2*a^2*B + 2/5*x^10*e^7*b*a^3*B + 21/10*x^10*e^5*d^2*b^4*A + 14/5*x^10*e^6*d*b^3*a*A + 3/5*x^10*e^7*b^2*a^2*A + 35/9*x^9*e^3*d^4*b^4*B + 140/9*x^9*e^4*d^3*b^3*a*B + 14*x^9*e^5*d^2*b^2*a^2*B + 28/9*x^9*e^6*d*b*a^3*B + 1/9*x^9*e^7*a^4*B + 35/9*x^9*e^4*d^3*b^4*A + 28/3*x^9*e^5*d^2*b^3*a*A + 14/3*x^9*e^6*d*b^2*a^2*A + 4/9*x^9*e^7*b*a^3*A + 21/8*x^8*e^2*d^5*b^4*B + 35/2*x^8*e^3*d^4*b^3*a*B + 105/4*x^8*e^4*d^3*b^2*a^2*B + 21/2*x^8*e^5*d^2*b*a^3*B + 7/8*x^8*e^6*d*a^4*B + 35/8*x^8*e^3*d^4*b^4*A + 35/2*x^8*e^4*d^3*b^3*a*A + 63/4*x^8*e^5*d^2*b^2*a^2*A + 7/2*x^8*e^6*d*b*a^3*A + 1/8*x^8*e^7*a^4*A + x^7*e*d^6*b^4*B + 12*x^7*e^2*d^5*b^3*a*B + 30*x^7*e^3*d^4*b^2*a^2*B + 20*x^7*e^4*d^3*b*a^3*B + 3*x^7*e^5*d^2*a^4*B + 3*x^7*e^2*d^5*b^4*A + 20*x^7*e^3*d^4*b^3*a*A + 30*x^7*e^4*d^3*b^2*a^2*A + 12*x^7*e^5*d^2*b*a^3*A + x^7*e^6*d*a^4*A + 1/6*x^6*d^7*b^4*B + 14/3*x^6*e*d^6*b^3*a*B + 21*x^6*e^2*d^5*b^2*a^2*B + 70/3*x^6*e^3*d^4*b*a^3*B + 35/6*x^6*e^4*d^3*a^4*B + 7/6*x^6*e*d^6*b^4*A + 14*x^6*e^2*d^5*b^3*a*A + 35*x^6*e^3*d^4*b^2*a^2*A + 70/3*x^6*e^4*d^3*b*a^3*A + 7/2*x^6*e^5*d^2*a^4*A + 4/5*x^5*d^7*b^3*a*B + 42/5*x^5*e*d^6*b^2*a^2*B + 84/5*x^5*e^2*d^5*b*a^3*B + 7*x^5*e^3*d^4*a^4*B + 1/5*x^5*d^7*b^4*A + 28/5*x^5*e*d^6*b^3*a*A + 126/5*x^5*e^2*d^5*b^2*a^2*A + 28*x^5*e^3*d^4*b*a^3*A + 7*x^5*e^4*d^3*a^4*A + 3/2*x^4*d^7*b^2*a^2*B + 7*x^4*e*d^6*b*a^3*B + 21/4*x^4*e^2*d^5*a^4*B + x^4*d^7*b^3*a*A + 21/2*x^4*e*d^6*b^2*a^2*A + 21*x^4*e^2*d^5*b*a^3*A + 35/4*x^4*e^3*d^4*a^4*A + 4/3*x^3*d^7*b*a^3*B + 7/3*x^3*e*d^6*a^4*B + 2*x^3*d^7*b^2*a^2*A + 28/3*x^3*e*d^6*b*a^3*A + 7*x^3*e^2*d^5*a^4*A + 1/2*x^2*d^7*a^4*B + 2*x^2*d^7*b*a^3*A + 7/2*x^2*e*d^6*a^4*A + x*d^7*a^4*A","B",0
1674,1,1015,0,0.379043," ","integrate((B*x+A)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{6} b^{4} B + \frac{6}{11} x^{11} e^{5} d b^{4} B + \frac{4}{11} x^{11} e^{6} b^{3} a B + \frac{1}{11} x^{11} e^{6} b^{4} A + \frac{3}{2} x^{10} e^{4} d^{2} b^{4} B + \frac{12}{5} x^{10} e^{5} d b^{3} a B + \frac{3}{5} x^{10} e^{6} b^{2} a^{2} B + \frac{3}{5} x^{10} e^{5} d b^{4} A + \frac{2}{5} x^{10} e^{6} b^{3} a A + \frac{20}{9} x^{9} e^{3} d^{3} b^{4} B + \frac{20}{3} x^{9} e^{4} d^{2} b^{3} a B + 4 x^{9} e^{5} d b^{2} a^{2} B + \frac{4}{9} x^{9} e^{6} b a^{3} B + \frac{5}{3} x^{9} e^{4} d^{2} b^{4} A + \frac{8}{3} x^{9} e^{5} d b^{3} a A + \frac{2}{3} x^{9} e^{6} b^{2} a^{2} A + \frac{15}{8} x^{8} e^{2} d^{4} b^{4} B + 10 x^{8} e^{3} d^{3} b^{3} a B + \frac{45}{4} x^{8} e^{4} d^{2} b^{2} a^{2} B + 3 x^{8} e^{5} d b a^{3} B + \frac{1}{8} x^{8} e^{6} a^{4} B + \frac{5}{2} x^{8} e^{3} d^{3} b^{4} A + \frac{15}{2} x^{8} e^{4} d^{2} b^{3} a A + \frac{9}{2} x^{8} e^{5} d b^{2} a^{2} A + \frac{1}{2} x^{8} e^{6} b a^{3} A + \frac{6}{7} x^{7} e d^{5} b^{4} B + \frac{60}{7} x^{7} e^{2} d^{4} b^{3} a B + \frac{120}{7} x^{7} e^{3} d^{3} b^{2} a^{2} B + \frac{60}{7} x^{7} e^{4} d^{2} b a^{3} B + \frac{6}{7} x^{7} e^{5} d a^{4} B + \frac{15}{7} x^{7} e^{2} d^{4} b^{4} A + \frac{80}{7} x^{7} e^{3} d^{3} b^{3} a A + \frac{90}{7} x^{7} e^{4} d^{2} b^{2} a^{2} A + \frac{24}{7} x^{7} e^{5} d b a^{3} A + \frac{1}{7} x^{7} e^{6} a^{4} A + \frac{1}{6} x^{6} d^{6} b^{4} B + 4 x^{6} e d^{5} b^{3} a B + 15 x^{6} e^{2} d^{4} b^{2} a^{2} B + \frac{40}{3} x^{6} e^{3} d^{3} b a^{3} B + \frac{5}{2} x^{6} e^{4} d^{2} a^{4} B + x^{6} e d^{5} b^{4} A + 10 x^{6} e^{2} d^{4} b^{3} a A + 20 x^{6} e^{3} d^{3} b^{2} a^{2} A + 10 x^{6} e^{4} d^{2} b a^{3} A + x^{6} e^{5} d a^{4} A + \frac{4}{5} x^{5} d^{6} b^{3} a B + \frac{36}{5} x^{5} e d^{5} b^{2} a^{2} B + 12 x^{5} e^{2} d^{4} b a^{3} B + 4 x^{5} e^{3} d^{3} a^{4} B + \frac{1}{5} x^{5} d^{6} b^{4} A + \frac{24}{5} x^{5} e d^{5} b^{3} a A + 18 x^{5} e^{2} d^{4} b^{2} a^{2} A + 16 x^{5} e^{3} d^{3} b a^{3} A + 3 x^{5} e^{4} d^{2} a^{4} A + \frac{3}{2} x^{4} d^{6} b^{2} a^{2} B + 6 x^{4} e d^{5} b a^{3} B + \frac{15}{4} x^{4} e^{2} d^{4} a^{4} B + x^{4} d^{6} b^{3} a A + 9 x^{4} e d^{5} b^{2} a^{2} A + 15 x^{4} e^{2} d^{4} b a^{3} A + 5 x^{4} e^{3} d^{3} a^{4} A + \frac{4}{3} x^{3} d^{6} b a^{3} B + 2 x^{3} e d^{5} a^{4} B + 2 x^{3} d^{6} b^{2} a^{2} A + 8 x^{3} e d^{5} b a^{3} A + 5 x^{3} e^{2} d^{4} a^{4} A + \frac{1}{2} x^{2} d^{6} a^{4} B + 2 x^{2} d^{6} b a^{3} A + 3 x^{2} e d^{5} a^{4} A + x d^{6} a^{4} A"," ",0,"1/12*x^12*e^6*b^4*B + 6/11*x^11*e^5*d*b^4*B + 4/11*x^11*e^6*b^3*a*B + 1/11*x^11*e^6*b^4*A + 3/2*x^10*e^4*d^2*b^4*B + 12/5*x^10*e^5*d*b^3*a*B + 3/5*x^10*e^6*b^2*a^2*B + 3/5*x^10*e^5*d*b^4*A + 2/5*x^10*e^6*b^3*a*A + 20/9*x^9*e^3*d^3*b^4*B + 20/3*x^9*e^4*d^2*b^3*a*B + 4*x^9*e^5*d*b^2*a^2*B + 4/9*x^9*e^6*b*a^3*B + 5/3*x^9*e^4*d^2*b^4*A + 8/3*x^9*e^5*d*b^3*a*A + 2/3*x^9*e^6*b^2*a^2*A + 15/8*x^8*e^2*d^4*b^4*B + 10*x^8*e^3*d^3*b^3*a*B + 45/4*x^8*e^4*d^2*b^2*a^2*B + 3*x^8*e^5*d*b*a^3*B + 1/8*x^8*e^6*a^4*B + 5/2*x^8*e^3*d^3*b^4*A + 15/2*x^8*e^4*d^2*b^3*a*A + 9/2*x^8*e^5*d*b^2*a^2*A + 1/2*x^8*e^6*b*a^3*A + 6/7*x^7*e*d^5*b^4*B + 60/7*x^7*e^2*d^4*b^3*a*B + 120/7*x^7*e^3*d^3*b^2*a^2*B + 60/7*x^7*e^4*d^2*b*a^3*B + 6/7*x^7*e^5*d*a^4*B + 15/7*x^7*e^2*d^4*b^4*A + 80/7*x^7*e^3*d^3*b^3*a*A + 90/7*x^7*e^4*d^2*b^2*a^2*A + 24/7*x^7*e^5*d*b*a^3*A + 1/7*x^7*e^6*a^4*A + 1/6*x^6*d^6*b^4*B + 4*x^6*e*d^5*b^3*a*B + 15*x^6*e^2*d^4*b^2*a^2*B + 40/3*x^6*e^3*d^3*b*a^3*B + 5/2*x^6*e^4*d^2*a^4*B + x^6*e*d^5*b^4*A + 10*x^6*e^2*d^4*b^3*a*A + 20*x^6*e^3*d^3*b^2*a^2*A + 10*x^6*e^4*d^2*b*a^3*A + x^6*e^5*d*a^4*A + 4/5*x^5*d^6*b^3*a*B + 36/5*x^5*e*d^5*b^2*a^2*B + 12*x^5*e^2*d^4*b*a^3*B + 4*x^5*e^3*d^3*a^4*B + 1/5*x^5*d^6*b^4*A + 24/5*x^5*e*d^5*b^3*a*A + 18*x^5*e^2*d^4*b^2*a^2*A + 16*x^5*e^3*d^3*b*a^3*A + 3*x^5*e^4*d^2*a^4*A + 3/2*x^4*d^6*b^2*a^2*B + 6*x^4*e*d^5*b*a^3*B + 15/4*x^4*e^2*d^4*a^4*B + x^4*d^6*b^3*a*A + 9*x^4*e*d^5*b^2*a^2*A + 15*x^4*e^2*d^4*b*a^3*A + 5*x^4*e^3*d^3*a^4*A + 4/3*x^3*d^6*b*a^3*B + 2*x^3*e*d^5*a^4*B + 2*x^3*d^6*b^2*a^2*A + 8*x^3*e*d^5*b*a^3*A + 5*x^3*e^2*d^4*a^4*A + 1/2*x^2*d^6*a^4*B + 2*x^2*d^6*b*a^3*A + 3*x^2*e*d^5*a^4*A + x*d^6*a^4*A","B",0
1675,1,856,0,0.366734," ","integrate((B*x+A)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{5} b^{4} B + \frac{1}{2} x^{10} e^{4} d b^{4} B + \frac{2}{5} x^{10} e^{5} b^{3} a B + \frac{1}{10} x^{10} e^{5} b^{4} A + \frac{10}{9} x^{9} e^{3} d^{2} b^{4} B + \frac{20}{9} x^{9} e^{4} d b^{3} a B + \frac{2}{3} x^{9} e^{5} b^{2} a^{2} B + \frac{5}{9} x^{9} e^{4} d b^{4} A + \frac{4}{9} x^{9} e^{5} b^{3} a A + \frac{5}{4} x^{8} e^{2} d^{3} b^{4} B + 5 x^{8} e^{3} d^{2} b^{3} a B + \frac{15}{4} x^{8} e^{4} d b^{2} a^{2} B + \frac{1}{2} x^{8} e^{5} b a^{3} B + \frac{5}{4} x^{8} e^{3} d^{2} b^{4} A + \frac{5}{2} x^{8} e^{4} d b^{3} a A + \frac{3}{4} x^{8} e^{5} b^{2} a^{2} A + \frac{5}{7} x^{7} e d^{4} b^{4} B + \frac{40}{7} x^{7} e^{2} d^{3} b^{3} a B + \frac{60}{7} x^{7} e^{3} d^{2} b^{2} a^{2} B + \frac{20}{7} x^{7} e^{4} d b a^{3} B + \frac{1}{7} x^{7} e^{5} a^{4} B + \frac{10}{7} x^{7} e^{2} d^{3} b^{4} A + \frac{40}{7} x^{7} e^{3} d^{2} b^{3} a A + \frac{30}{7} x^{7} e^{4} d b^{2} a^{2} A + \frac{4}{7} x^{7} e^{5} b a^{3} A + \frac{1}{6} x^{6} d^{5} b^{4} B + \frac{10}{3} x^{6} e d^{4} b^{3} a B + 10 x^{6} e^{2} d^{3} b^{2} a^{2} B + \frac{20}{3} x^{6} e^{3} d^{2} b a^{3} B + \frac{5}{6} x^{6} e^{4} d a^{4} B + \frac{5}{6} x^{6} e d^{4} b^{4} A + \frac{20}{3} x^{6} e^{2} d^{3} b^{3} a A + 10 x^{6} e^{3} d^{2} b^{2} a^{2} A + \frac{10}{3} x^{6} e^{4} d b a^{3} A + \frac{1}{6} x^{6} e^{5} a^{4} A + \frac{4}{5} x^{5} d^{5} b^{3} a B + 6 x^{5} e d^{4} b^{2} a^{2} B + 8 x^{5} e^{2} d^{3} b a^{3} B + 2 x^{5} e^{3} d^{2} a^{4} B + \frac{1}{5} x^{5} d^{5} b^{4} A + 4 x^{5} e d^{4} b^{3} a A + 12 x^{5} e^{2} d^{3} b^{2} a^{2} A + 8 x^{5} e^{3} d^{2} b a^{3} A + x^{5} e^{4} d a^{4} A + \frac{3}{2} x^{4} d^{5} b^{2} a^{2} B + 5 x^{4} e d^{4} b a^{3} B + \frac{5}{2} x^{4} e^{2} d^{3} a^{4} B + x^{4} d^{5} b^{3} a A + \frac{15}{2} x^{4} e d^{4} b^{2} a^{2} A + 10 x^{4} e^{2} d^{3} b a^{3} A + \frac{5}{2} x^{4} e^{3} d^{2} a^{4} A + \frac{4}{3} x^{3} d^{5} b a^{3} B + \frac{5}{3} x^{3} e d^{4} a^{4} B + 2 x^{3} d^{5} b^{2} a^{2} A + \frac{20}{3} x^{3} e d^{4} b a^{3} A + \frac{10}{3} x^{3} e^{2} d^{3} a^{4} A + \frac{1}{2} x^{2} d^{5} a^{4} B + 2 x^{2} d^{5} b a^{3} A + \frac{5}{2} x^{2} e d^{4} a^{4} A + x d^{5} a^{4} A"," ",0,"1/11*x^11*e^5*b^4*B + 1/2*x^10*e^4*d*b^4*B + 2/5*x^10*e^5*b^3*a*B + 1/10*x^10*e^5*b^4*A + 10/9*x^9*e^3*d^2*b^4*B + 20/9*x^9*e^4*d*b^3*a*B + 2/3*x^9*e^5*b^2*a^2*B + 5/9*x^9*e^4*d*b^4*A + 4/9*x^9*e^5*b^3*a*A + 5/4*x^8*e^2*d^3*b^4*B + 5*x^8*e^3*d^2*b^3*a*B + 15/4*x^8*e^4*d*b^2*a^2*B + 1/2*x^8*e^5*b*a^3*B + 5/4*x^8*e^3*d^2*b^4*A + 5/2*x^8*e^4*d*b^3*a*A + 3/4*x^8*e^5*b^2*a^2*A + 5/7*x^7*e*d^4*b^4*B + 40/7*x^7*e^2*d^3*b^3*a*B + 60/7*x^7*e^3*d^2*b^2*a^2*B + 20/7*x^7*e^4*d*b*a^3*B + 1/7*x^7*e^5*a^4*B + 10/7*x^7*e^2*d^3*b^4*A + 40/7*x^7*e^3*d^2*b^3*a*A + 30/7*x^7*e^4*d*b^2*a^2*A + 4/7*x^7*e^5*b*a^3*A + 1/6*x^6*d^5*b^4*B + 10/3*x^6*e*d^4*b^3*a*B + 10*x^6*e^2*d^3*b^2*a^2*B + 20/3*x^6*e^3*d^2*b*a^3*B + 5/6*x^6*e^4*d*a^4*B + 5/6*x^6*e*d^4*b^4*A + 20/3*x^6*e^2*d^3*b^3*a*A + 10*x^6*e^3*d^2*b^2*a^2*A + 10/3*x^6*e^4*d*b*a^3*A + 1/6*x^6*e^5*a^4*A + 4/5*x^5*d^5*b^3*a*B + 6*x^5*e*d^4*b^2*a^2*B + 8*x^5*e^2*d^3*b*a^3*B + 2*x^5*e^3*d^2*a^4*B + 1/5*x^5*d^5*b^4*A + 4*x^5*e*d^4*b^3*a*A + 12*x^5*e^2*d^3*b^2*a^2*A + 8*x^5*e^3*d^2*b*a^3*A + x^5*e^4*d*a^4*A + 3/2*x^4*d^5*b^2*a^2*B + 5*x^4*e*d^4*b*a^3*B + 5/2*x^4*e^2*d^3*a^4*B + x^4*d^5*b^3*a*A + 15/2*x^4*e*d^4*b^2*a^2*A + 10*x^4*e^2*d^3*b*a^3*A + 5/2*x^4*e^3*d^2*a^4*A + 4/3*x^3*d^5*b*a^3*B + 5/3*x^3*e*d^4*a^4*B + 2*x^3*d^5*b^2*a^2*A + 20/3*x^3*e*d^4*b*a^3*A + 10/3*x^3*e^2*d^3*a^4*A + 1/2*x^2*d^5*a^4*B + 2*x^2*d^5*b*a^3*A + 5/2*x^2*e*d^4*a^4*A + x*d^5*a^4*A","B",0
1676,1,696,0,0.365947," ","integrate((B*x+A)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{4} b^{4} B + \frac{4}{9} x^{9} e^{3} d b^{4} B + \frac{4}{9} x^{9} e^{4} b^{3} a B + \frac{1}{9} x^{9} e^{4} b^{4} A + \frac{3}{4} x^{8} e^{2} d^{2} b^{4} B + 2 x^{8} e^{3} d b^{3} a B + \frac{3}{4} x^{8} e^{4} b^{2} a^{2} B + \frac{1}{2} x^{8} e^{3} d b^{4} A + \frac{1}{2} x^{8} e^{4} b^{3} a A + \frac{4}{7} x^{7} e d^{3} b^{4} B + \frac{24}{7} x^{7} e^{2} d^{2} b^{3} a B + \frac{24}{7} x^{7} e^{3} d b^{2} a^{2} B + \frac{4}{7} x^{7} e^{4} b a^{3} B + \frac{6}{7} x^{7} e^{2} d^{2} b^{4} A + \frac{16}{7} x^{7} e^{3} d b^{3} a A + \frac{6}{7} x^{7} e^{4} b^{2} a^{2} A + \frac{1}{6} x^{6} d^{4} b^{4} B + \frac{8}{3} x^{6} e d^{3} b^{3} a B + 6 x^{6} e^{2} d^{2} b^{2} a^{2} B + \frac{8}{3} x^{6} e^{3} d b a^{3} B + \frac{1}{6} x^{6} e^{4} a^{4} B + \frac{2}{3} x^{6} e d^{3} b^{4} A + 4 x^{6} e^{2} d^{2} b^{3} a A + 4 x^{6} e^{3} d b^{2} a^{2} A + \frac{2}{3} x^{6} e^{4} b a^{3} A + \frac{4}{5} x^{5} d^{4} b^{3} a B + \frac{24}{5} x^{5} e d^{3} b^{2} a^{2} B + \frac{24}{5} x^{5} e^{2} d^{2} b a^{3} B + \frac{4}{5} x^{5} e^{3} d a^{4} B + \frac{1}{5} x^{5} d^{4} b^{4} A + \frac{16}{5} x^{5} e d^{3} b^{3} a A + \frac{36}{5} x^{5} e^{2} d^{2} b^{2} a^{2} A + \frac{16}{5} x^{5} e^{3} d b a^{3} A + \frac{1}{5} x^{5} e^{4} a^{4} A + \frac{3}{2} x^{4} d^{4} b^{2} a^{2} B + 4 x^{4} e d^{3} b a^{3} B + \frac{3}{2} x^{4} e^{2} d^{2} a^{4} B + x^{4} d^{4} b^{3} a A + 6 x^{4} e d^{3} b^{2} a^{2} A + 6 x^{4} e^{2} d^{2} b a^{3} A + x^{4} e^{3} d a^{4} A + \frac{4}{3} x^{3} d^{4} b a^{3} B + \frac{4}{3} x^{3} e d^{3} a^{4} B + 2 x^{3} d^{4} b^{2} a^{2} A + \frac{16}{3} x^{3} e d^{3} b a^{3} A + 2 x^{3} e^{2} d^{2} a^{4} A + \frac{1}{2} x^{2} d^{4} a^{4} B + 2 x^{2} d^{4} b a^{3} A + 2 x^{2} e d^{3} a^{4} A + x d^{4} a^{4} A"," ",0,"1/10*x^10*e^4*b^4*B + 4/9*x^9*e^3*d*b^4*B + 4/9*x^9*e^4*b^3*a*B + 1/9*x^9*e^4*b^4*A + 3/4*x^8*e^2*d^2*b^4*B + 2*x^8*e^3*d*b^3*a*B + 3/4*x^8*e^4*b^2*a^2*B + 1/2*x^8*e^3*d*b^4*A + 1/2*x^8*e^4*b^3*a*A + 4/7*x^7*e*d^3*b^4*B + 24/7*x^7*e^2*d^2*b^3*a*B + 24/7*x^7*e^3*d*b^2*a^2*B + 4/7*x^7*e^4*b*a^3*B + 6/7*x^7*e^2*d^2*b^4*A + 16/7*x^7*e^3*d*b^3*a*A + 6/7*x^7*e^4*b^2*a^2*A + 1/6*x^6*d^4*b^4*B + 8/3*x^6*e*d^3*b^3*a*B + 6*x^6*e^2*d^2*b^2*a^2*B + 8/3*x^6*e^3*d*b*a^3*B + 1/6*x^6*e^4*a^4*B + 2/3*x^6*e*d^3*b^4*A + 4*x^6*e^2*d^2*b^3*a*A + 4*x^6*e^3*d*b^2*a^2*A + 2/3*x^6*e^4*b*a^3*A + 4/5*x^5*d^4*b^3*a*B + 24/5*x^5*e*d^3*b^2*a^2*B + 24/5*x^5*e^2*d^2*b*a^3*B + 4/5*x^5*e^3*d*a^4*B + 1/5*x^5*d^4*b^4*A + 16/5*x^5*e*d^3*b^3*a*A + 36/5*x^5*e^2*d^2*b^2*a^2*A + 16/5*x^5*e^3*d*b*a^3*A + 1/5*x^5*e^4*a^4*A + 3/2*x^4*d^4*b^2*a^2*B + 4*x^4*e*d^3*b*a^3*B + 3/2*x^4*e^2*d^2*a^4*B + x^4*d^4*b^3*a*A + 6*x^4*e*d^3*b^2*a^2*A + 6*x^4*e^2*d^2*b*a^3*A + x^4*e^3*d*a^4*A + 4/3*x^3*d^4*b*a^3*B + 4/3*x^3*e*d^3*a^4*B + 2*x^3*d^4*b^2*a^2*A + 16/3*x^3*e*d^3*b*a^3*A + 2*x^3*e^2*d^2*a^4*A + 1/2*x^2*d^4*a^4*B + 2*x^2*d^4*b*a^3*A + 2*x^2*e*d^3*a^4*A + x*d^4*a^4*A","B",0
1677,1,534,0,0.374635," ","integrate((B*x+A)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{3} b^{4} B + \frac{3}{8} x^{8} e^{2} d b^{4} B + \frac{1}{2} x^{8} e^{3} b^{3} a B + \frac{1}{8} x^{8} e^{3} b^{4} A + \frac{3}{7} x^{7} e d^{2} b^{4} B + \frac{12}{7} x^{7} e^{2} d b^{3} a B + \frac{6}{7} x^{7} e^{3} b^{2} a^{2} B + \frac{3}{7} x^{7} e^{2} d b^{4} A + \frac{4}{7} x^{7} e^{3} b^{3} a A + \frac{1}{6} x^{6} d^{3} b^{4} B + 2 x^{6} e d^{2} b^{3} a B + 3 x^{6} e^{2} d b^{2} a^{2} B + \frac{2}{3} x^{6} e^{3} b a^{3} B + \frac{1}{2} x^{6} e d^{2} b^{4} A + 2 x^{6} e^{2} d b^{3} a A + x^{6} e^{3} b^{2} a^{2} A + \frac{4}{5} x^{5} d^{3} b^{3} a B + \frac{18}{5} x^{5} e d^{2} b^{2} a^{2} B + \frac{12}{5} x^{5} e^{2} d b a^{3} B + \frac{1}{5} x^{5} e^{3} a^{4} B + \frac{1}{5} x^{5} d^{3} b^{4} A + \frac{12}{5} x^{5} e d^{2} b^{3} a A + \frac{18}{5} x^{5} e^{2} d b^{2} a^{2} A + \frac{4}{5} x^{5} e^{3} b a^{3} A + \frac{3}{2} x^{4} d^{3} b^{2} a^{2} B + 3 x^{4} e d^{2} b a^{3} B + \frac{3}{4} x^{4} e^{2} d a^{4} B + x^{4} d^{3} b^{3} a A + \frac{9}{2} x^{4} e d^{2} b^{2} a^{2} A + 3 x^{4} e^{2} d b a^{3} A + \frac{1}{4} x^{4} e^{3} a^{4} A + \frac{4}{3} x^{3} d^{3} b a^{3} B + x^{3} e d^{2} a^{4} B + 2 x^{3} d^{3} b^{2} a^{2} A + 4 x^{3} e d^{2} b a^{3} A + x^{3} e^{2} d a^{4} A + \frac{1}{2} x^{2} d^{3} a^{4} B + 2 x^{2} d^{3} b a^{3} A + \frac{3}{2} x^{2} e d^{2} a^{4} A + x d^{3} a^{4} A"," ",0,"1/9*x^9*e^3*b^4*B + 3/8*x^8*e^2*d*b^4*B + 1/2*x^8*e^3*b^3*a*B + 1/8*x^8*e^3*b^4*A + 3/7*x^7*e*d^2*b^4*B + 12/7*x^7*e^2*d*b^3*a*B + 6/7*x^7*e^3*b^2*a^2*B + 3/7*x^7*e^2*d*b^4*A + 4/7*x^7*e^3*b^3*a*A + 1/6*x^6*d^3*b^4*B + 2*x^6*e*d^2*b^3*a*B + 3*x^6*e^2*d*b^2*a^2*B + 2/3*x^6*e^3*b*a^3*B + 1/2*x^6*e*d^2*b^4*A + 2*x^6*e^2*d*b^3*a*A + x^6*e^3*b^2*a^2*A + 4/5*x^5*d^3*b^3*a*B + 18/5*x^5*e*d^2*b^2*a^2*B + 12/5*x^5*e^2*d*b*a^3*B + 1/5*x^5*e^3*a^4*B + 1/5*x^5*d^3*b^4*A + 12/5*x^5*e*d^2*b^3*a*A + 18/5*x^5*e^2*d*b^2*a^2*A + 4/5*x^5*e^3*b*a^3*A + 3/2*x^4*d^3*b^2*a^2*B + 3*x^4*e*d^2*b*a^3*B + 3/4*x^4*e^2*d*a^4*B + x^4*d^3*b^3*a*A + 9/2*x^4*e*d^2*b^2*a^2*A + 3*x^4*e^2*d*b*a^3*A + 1/4*x^4*e^3*a^4*A + 4/3*x^3*d^3*b*a^3*B + x^3*e*d^2*a^4*B + 2*x^3*d^3*b^2*a^2*A + 4*x^3*e*d^2*b*a^3*A + x^3*e^2*d*a^4*A + 1/2*x^2*d^3*a^4*B + 2*x^2*d^3*b*a^3*A + 3/2*x^2*e*d^2*a^4*A + x*d^3*a^4*A","B",0
1678,1,374,0,0.373425," ","integrate((B*x+A)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{2} b^{4} B + \frac{2}{7} x^{7} e d b^{4} B + \frac{4}{7} x^{7} e^{2} b^{3} a B + \frac{1}{7} x^{7} e^{2} b^{4} A + \frac{1}{6} x^{6} d^{2} b^{4} B + \frac{4}{3} x^{6} e d b^{3} a B + x^{6} e^{2} b^{2} a^{2} B + \frac{1}{3} x^{6} e d b^{4} A + \frac{2}{3} x^{6} e^{2} b^{3} a A + \frac{4}{5} x^{5} d^{2} b^{3} a B + \frac{12}{5} x^{5} e d b^{2} a^{2} B + \frac{4}{5} x^{5} e^{2} b a^{3} B + \frac{1}{5} x^{5} d^{2} b^{4} A + \frac{8}{5} x^{5} e d b^{3} a A + \frac{6}{5} x^{5} e^{2} b^{2} a^{2} A + \frac{3}{2} x^{4} d^{2} b^{2} a^{2} B + 2 x^{4} e d b a^{3} B + \frac{1}{4} x^{4} e^{2} a^{4} B + x^{4} d^{2} b^{3} a A + 3 x^{4} e d b^{2} a^{2} A + x^{4} e^{2} b a^{3} A + \frac{4}{3} x^{3} d^{2} b a^{3} B + \frac{2}{3} x^{3} e d a^{4} B + 2 x^{3} d^{2} b^{2} a^{2} A + \frac{8}{3} x^{3} e d b a^{3} A + \frac{1}{3} x^{3} e^{2} a^{4} A + \frac{1}{2} x^{2} d^{2} a^{4} B + 2 x^{2} d^{2} b a^{3} A + x^{2} e d a^{4} A + x d^{2} a^{4} A"," ",0,"1/8*x^8*e^2*b^4*B + 2/7*x^7*e*d*b^4*B + 4/7*x^7*e^2*b^3*a*B + 1/7*x^7*e^2*b^4*A + 1/6*x^6*d^2*b^4*B + 4/3*x^6*e*d*b^3*a*B + x^6*e^2*b^2*a^2*B + 1/3*x^6*e*d*b^4*A + 2/3*x^6*e^2*b^3*a*A + 4/5*x^5*d^2*b^3*a*B + 12/5*x^5*e*d*b^2*a^2*B + 4/5*x^5*e^2*b*a^3*B + 1/5*x^5*d^2*b^4*A + 8/5*x^5*e*d*b^3*a*A + 6/5*x^5*e^2*b^2*a^2*A + 3/2*x^4*d^2*b^2*a^2*B + 2*x^4*e*d*b*a^3*B + 1/4*x^4*e^2*a^4*B + x^4*d^2*b^3*a*A + 3*x^4*e*d*b^2*a^2*A + x^4*e^2*b*a^3*A + 4/3*x^3*d^2*b*a^3*B + 2/3*x^3*e*d*a^4*B + 2*x^3*d^2*b^2*a^2*A + 8/3*x^3*e*d*b*a^3*A + 1/3*x^3*e^2*a^4*A + 1/2*x^2*d^2*a^4*B + 2*x^2*d^2*b*a^3*A + x^2*e*d*a^4*A + x*d^2*a^4*A","B",0
1679,1,216,0,0.361824," ","integrate((B*x+A)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e b^{4} B + \frac{1}{6} x^{6} d b^{4} B + \frac{2}{3} x^{6} e b^{3} a B + \frac{1}{6} x^{6} e b^{4} A + \frac{4}{5} x^{5} d b^{3} a B + \frac{6}{5} x^{5} e b^{2} a^{2} B + \frac{1}{5} x^{5} d b^{4} A + \frac{4}{5} x^{5} e b^{3} a A + \frac{3}{2} x^{4} d b^{2} a^{2} B + x^{4} e b a^{3} B + x^{4} d b^{3} a A + \frac{3}{2} x^{4} e b^{2} a^{2} A + \frac{4}{3} x^{3} d b a^{3} B + \frac{1}{3} x^{3} e a^{4} B + 2 x^{3} d b^{2} a^{2} A + \frac{4}{3} x^{3} e b a^{3} A + \frac{1}{2} x^{2} d a^{4} B + 2 x^{2} d b a^{3} A + \frac{1}{2} x^{2} e a^{4} A + x d a^{4} A"," ",0,"1/7*x^7*e*b^4*B + 1/6*x^6*d*b^4*B + 2/3*x^6*e*b^3*a*B + 1/6*x^6*e*b^4*A + 4/5*x^5*d*b^3*a*B + 6/5*x^5*e*b^2*a^2*B + 1/5*x^5*d*b^4*A + 4/5*x^5*e*b^3*a*A + 3/2*x^4*d*b^2*a^2*B + x^4*e*b*a^3*B + x^4*d*b^3*a*A + 3/2*x^4*e*b^2*a^2*A + 4/3*x^3*d*b*a^3*B + 1/3*x^3*e*a^4*B + 2*x^3*d*b^2*a^2*A + 4/3*x^3*e*b*a^3*A + 1/2*x^2*d*a^4*B + 2*x^2*d*b*a^3*A + 1/2*x^2*e*a^4*A + x*d*a^4*A","B",0
1680,1,97,0,0.346088," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} b^{4} B + \frac{4}{5} x^{5} b^{3} a B + \frac{1}{5} x^{5} b^{4} A + \frac{3}{2} x^{4} b^{2} a^{2} B + x^{4} b^{3} a A + \frac{4}{3} x^{3} b a^{3} B + 2 x^{3} b^{2} a^{2} A + \frac{1}{2} x^{2} a^{4} B + 2 x^{2} b a^{3} A + x a^{4} A"," ",0,"1/6*x^6*b^4*B + 4/5*x^5*b^3*a*B + 1/5*x^5*b^4*A + 3/2*x^4*b^2*a^2*B + x^4*b^3*a*A + 4/3*x^3*b*a^3*B + 2*x^3*b^2*a^2*A + 1/2*x^2*a^4*B + 2*x^2*b*a^3*A + x*a^4*A","B",0
1681,1,404,0,0.405364," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d),x, algorithm=""fricas"")","\frac{12 \, B b^{4} e^{5} x^{5} - 15 \, {\left(B b^{4} d e^{4} - {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 20 \, {\left(B b^{4} d^{2} e^{3} - {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} - 30 \, {\left(B b^{4} d^{3} e^{2} - {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} - 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 60 \, {\left(B b^{4} d^{4} e - {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x - 60 \, {\left(B b^{4} d^{5} - A a^{4} e^{5} - {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4}\right)} \log\left(e x + d\right)}{60 \, e^{6}}"," ",0,"1/60*(12*B*b^4*e^5*x^5 - 15*(B*b^4*d*e^4 - (4*B*a*b^3 + A*b^4)*e^5)*x^4 + 20*(B*b^4*d^2*e^3 - (4*B*a*b^3 + A*b^4)*d*e^4 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 - 30*(B*b^4*d^3*e^2 - (4*B*a*b^3 + A*b^4)*d^2*e^3 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 - 2*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 60*(B*b^4*d^4*e - (4*B*a*b^3 + A*b^4)*d^3*e^2 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - 2*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + (B*a^4 + 4*A*a^3*b)*e^5)*x - 60*(B*b^4*d^5 - A*a^4*e^5 - (4*B*a*b^3 + A*b^4)*d^4*e + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 - 2*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + (B*a^4 + 4*A*a^3*b)*d*e^4)*log(e*x + d))/e^6","B",0
1682,1,598,0,0.423544," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{3 \, B b^{4} e^{5} x^{5} + 12 \, B b^{4} d^{5} - 12 \, A a^{4} e^{5} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 24 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} - 24 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + 12 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} - {\left(5 \, B b^{4} d e^{4} - 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(5 \, B b^{4} d^{2} e^{3} - 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} - 6 \, {\left(5 \, B b^{4} d^{3} e^{2} - 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} - 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} - 12 \, {\left(4 \, B b^{4} d^{4} e - 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 4 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4}\right)} x + 12 \, {\left(5 \, B b^{4} d^{5} - 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} - 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} + {\left(5 \, B b^{4} d^{4} e - 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"1/12*(3*B*b^4*e^5*x^5 + 12*B*b^4*d^5 - 12*A*a^4*e^5 - 12*(4*B*a*b^3 + A*b^4)*d^4*e + 24*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 - 24*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + 12*(B*a^4 + 4*A*a^3*b)*d*e^4 - (5*B*b^4*d*e^4 - 4*(4*B*a*b^3 + A*b^4)*e^5)*x^4 + 2*(5*B*b^4*d^2*e^3 - 4*(4*B*a*b^3 + A*b^4)*d*e^4 + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 - 6*(5*B*b^4*d^3*e^2 - 4*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 - 4*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 - 12*(4*B*b^4*d^4*e - 3*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 4*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - 2*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4)*x + 12*(5*B*b^4*d^5 - 4*(4*B*a*b^3 + A*b^4)*d^4*e + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 - 4*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + (B*a^4 + 4*A*a^3*b)*d*e^4 + (5*B*b^4*d^4*e - 4*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - 4*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + (B*a^4 + 4*A*a^3*b)*e^5)*x)*log(e*x + d))/(e^7*x + d*e^6)","B",0
1683,1,652,0,0.413545," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{4} e^{5} x^{5} - 27 \, B b^{4} d^{5} - 3 \, A a^{4} e^{5} + 21 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e - 30 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + 18 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} - 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} - {\left(5 \, B b^{4} d e^{4} - 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 4 \, {\left(5 \, B b^{4} d^{2} e^{3} - 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 3 \, {\left(21 \, B b^{4} d^{3} e^{2} - 11 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 8 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4}\right)} x^{2} + 6 \, {\left(B b^{4} d^{4} e + {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} - 4 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} + 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} - {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x - 12 \, {\left(5 \, B b^{4} d^{5} - 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} - {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + {\left(5 \, B b^{4} d^{3} e^{2} - 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} - {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 2 \, {\left(5 \, B b^{4} d^{4} e - 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"1/6*(2*B*b^4*e^5*x^5 - 27*B*b^4*d^5 - 3*A*a^4*e^5 + 21*(4*B*a*b^3 + A*b^4)*d^4*e - 30*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + 18*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 - 3*(B*a^4 + 4*A*a^3*b)*d*e^4 - (5*B*b^4*d*e^4 - 3*(4*B*a*b^3 + A*b^4)*e^5)*x^4 + 4*(5*B*b^4*d^2*e^3 - 3*(4*B*a*b^3 + A*b^4)*d*e^4 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 3*(21*B*b^4*d^3*e^2 - 11*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 8*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4)*x^2 + 6*(B*b^4*d^4*e + (4*B*a*b^3 + A*b^4)*d^3*e^2 - 4*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 - (B*a^4 + 4*A*a^3*b)*e^5)*x - 12*(5*B*b^4*d^5 - 3*(4*B*a*b^3 + A*b^4)*d^4*e + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 - (2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + (5*B*b^4*d^3*e^2 - 3*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 - (2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 2*(5*B*b^4*d^4*e - 3*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - (2*B*a^3*b + 3*A*a^2*b^2)*d*e^4)*x)*log(e*x + d))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","B",0
1684,1,650,0,0.408659," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, B b^{4} e^{5} x^{5} + 47 \, B b^{4} d^{5} - 2 \, A a^{4} e^{5} - 26 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 22 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} - 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} - {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} - 3 \, {\left(5 \, B b^{4} d e^{4} - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} - 9 \, {\left(7 \, B b^{4} d^{2} e^{3} - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4}\right)} x^{3} - 3 \, {\left(3 \, B b^{4} d^{3} e^{2} + 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} - 12 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} + 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 3 \, {\left(27 \, B b^{4} d^{4} e - 18 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 18 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} - {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x + 12 \, {\left(5 \, B b^{4} d^{5} - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + {\left(5 \, B b^{4} d^{2} e^{3} - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 3 \, {\left(5 \, B b^{4} d^{3} e^{2} - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4}\right)} x^{2} + 3 \, {\left(5 \, B b^{4} d^{4} e - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"1/6*(3*B*b^4*e^5*x^5 + 47*B*b^4*d^5 - 2*A*a^4*e^5 - 26*(4*B*a*b^3 + A*b^4)*d^4*e + 22*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 - 4*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 - (B*a^4 + 4*A*a^3*b)*d*e^4 - 3*(5*B*b^4*d*e^4 - 2*(4*B*a*b^3 + A*b^4)*e^5)*x^4 - 9*(7*B*b^4*d^2*e^3 - 2*(4*B*a*b^3 + A*b^4)*d*e^4)*x^3 - 3*(3*B*b^4*d^3*e^2 + 6*(4*B*a*b^3 + A*b^4)*d^2*e^3 - 12*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 3*(27*B*b^4*d^4*e - 18*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 18*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - 4*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 - (B*a^4 + 4*A*a^3*b)*e^5)*x + 12*(5*B*b^4*d^5 - 2*(4*B*a*b^3 + A*b^4)*d^4*e + (3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + (5*B*b^4*d^2*e^3 - 2*(4*B*a*b^3 + A*b^4)*d*e^4 + (3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 3*(5*B*b^4*d^3*e^2 - 2*(4*B*a*b^3 + A*b^4)*d^2*e^3 + (3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4)*x^2 + 3*(5*B*b^4*d^4*e - 2*(4*B*a*b^3 + A*b^4)*d^3*e^2 + (3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3)*x)*log(e*x + d))/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","B",0
1685,1,602,0,0.410661," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{12 \, B b^{4} e^{5} x^{5} + 48 \, B b^{4} d e^{4} x^{4} - 77 \, B b^{4} d^{5} - 3 \, A a^{4} e^{5} + 25 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e - 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} - {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} - 24 \, {\left(2 \, B b^{4} d^{2} e^{3} - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} - 12 \, {\left(21 \, B b^{4} d^{3} e^{2} - 9 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} + {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} - 4 \, {\left(62 \, B b^{4} d^{4} e - 22 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} + 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x - 12 \, {\left(5 \, B b^{4} d^{5} - {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + {\left(5 \, B b^{4} d e^{4} - {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 4 \, {\left(5 \, B b^{4} d^{2} e^{3} - {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4}\right)} x^{3} + 6 \, {\left(5 \, B b^{4} d^{3} e^{2} - {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3}\right)} x^{2} + 4 \, {\left(5 \, B b^{4} d^{4} e - {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{10} x^{4} + 4 \, d e^{9} x^{3} + 6 \, d^{2} e^{8} x^{2} + 4 \, d^{3} e^{7} x + d^{4} e^{6}\right)}}"," ",0,"1/12*(12*B*b^4*e^5*x^5 + 48*B*b^4*d*e^4*x^4 - 77*B*b^4*d^5 - 3*A*a^4*e^5 + 25*(4*B*a*b^3 + A*b^4)*d^4*e - 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 - 2*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 - (B*a^4 + 4*A*a^3*b)*d*e^4 - 24*(2*B*b^4*d^2*e^3 - 2*(4*B*a*b^3 + A*b^4)*d*e^4 + (3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 - 12*(21*B*b^4*d^3*e^2 - 9*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 + (2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 - 4*(62*B*b^4*d^4*e - 22*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 + 2*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + (B*a^4 + 4*A*a^3*b)*e^5)*x - 12*(5*B*b^4*d^5 - (4*B*a*b^3 + A*b^4)*d^4*e + (5*B*b^4*d*e^4 - (4*B*a*b^3 + A*b^4)*e^5)*x^4 + 4*(5*B*b^4*d^2*e^3 - (4*B*a*b^3 + A*b^4)*d*e^4)*x^3 + 6*(5*B*b^4*d^3*e^2 - (4*B*a*b^3 + A*b^4)*d^2*e^3)*x^2 + 4*(5*B*b^4*d^4*e - (4*B*a*b^3 + A*b^4)*d^3*e^2)*x)*log(e*x + d))/(e^10*x^4 + 4*d*e^9*x^3 + 6*d^2*e^8*x^2 + 4*d^3*e^7*x + d^4*e^6)","B",0
1686,1,526,0,0.397752," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^6,x, algorithm=""fricas"")","\frac{137 \, B b^{4} d^{5} - 12 \, A a^{4} e^{5} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e - 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} - 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} - 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} + 60 \, {\left(5 \, B b^{4} d e^{4} - {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 60 \, {\left(15 \, B b^{4} d^{2} e^{3} - 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} - {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 20 \, {\left(55 \, B b^{4} d^{3} e^{2} - 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} - 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} - 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 5 \, {\left(125 \, B b^{4} d^{4} e - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} - 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} - 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x + 60 \, {\left(B b^{4} e^{5} x^{5} + 5 \, B b^{4} d e^{4} x^{4} + 10 \, B b^{4} d^{2} e^{3} x^{3} + 10 \, B b^{4} d^{3} e^{2} x^{2} + 5 \, B b^{4} d^{4} e x + B b^{4} d^{5}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{11} x^{5} + 5 \, d e^{10} x^{4} + 10 \, d^{2} e^{9} x^{3} + 10 \, d^{3} e^{8} x^{2} + 5 \, d^{4} e^{7} x + d^{5} e^{6}\right)}}"," ",0,"1/60*(137*B*b^4*d^5 - 12*A*a^4*e^5 - 12*(4*B*a*b^3 + A*b^4)*d^4*e - 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 - 4*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 - 3*(B*a^4 + 4*A*a^3*b)*d*e^4 + 60*(5*B*b^4*d*e^4 - (4*B*a*b^3 + A*b^4)*e^5)*x^4 + 60*(15*B*b^4*d^2*e^3 - 2*(4*B*a*b^3 + A*b^4)*d*e^4 - (3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 20*(55*B*b^4*d^3*e^2 - 6*(4*B*a*b^3 + A*b^4)*d^2*e^3 - 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 - 2*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 5*(125*B*b^4*d^4*e - 12*(4*B*a*b^3 + A*b^4)*d^3*e^2 - 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - 4*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 - 3*(B*a^4 + 4*A*a^3*b)*e^5)*x + 60*(B*b^4*e^5*x^5 + 5*B*b^4*d*e^4*x^4 + 10*B*b^4*d^2*e^3*x^3 + 10*B*b^4*d^3*e^2*x^2 + 5*B*b^4*d^4*e*x + B*b^4*d^5)*log(e*x + d))/(e^11*x^5 + 5*d*e^10*x^4 + 10*d^2*e^9*x^3 + 10*d^3*e^8*x^2 + 5*d^4*e^7*x + d^5*e^6)","B",0
1687,1,453,0,0.393239," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{30 \, B b^{4} e^{5} x^{5} + 5 \, B b^{4} d^{5} + 5 \, A a^{4} e^{5} + {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} + 15 \, {\left(5 \, B b^{4} d e^{4} + {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 20 \, {\left(5 \, B b^{4} d^{2} e^{3} + {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 15 \, {\left(5 \, B b^{4} d^{3} e^{2} + {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} + {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 6 \, {\left(5 \, B b^{4} d^{4} e + {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} + {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x}{30 \, {\left(e^{12} x^{6} + 6 \, d e^{11} x^{5} + 15 \, d^{2} e^{10} x^{4} + 20 \, d^{3} e^{9} x^{3} + 15 \, d^{4} e^{8} x^{2} + 6 \, d^{5} e^{7} x + d^{6} e^{6}\right)}}"," ",0,"-1/30*(30*B*b^4*e^5*x^5 + 5*B*b^4*d^5 + 5*A*a^4*e^5 + (4*B*a*b^3 + A*b^4)*d^4*e + (3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + (2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + (B*a^4 + 4*A*a^3*b)*d*e^4 + 15*(5*B*b^4*d*e^4 + (4*B*a*b^3 + A*b^4)*e^5)*x^4 + 20*(5*B*b^4*d^2*e^3 + (4*B*a*b^3 + A*b^4)*d*e^4 + (3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 15*(5*B*b^4*d^3*e^2 + (4*B*a*b^3 + A*b^4)*d^2*e^3 + (3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 + (2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 6*(5*B*b^4*d^4*e + (4*B*a*b^3 + A*b^4)*d^3*e^2 + (3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 + (2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + (B*a^4 + 4*A*a^3*b)*e^5)*x)/(e^12*x^6 + 6*d*e^11*x^5 + 15*d^2*e^10*x^4 + 20*d^3*e^9*x^3 + 15*d^4*e^8*x^2 + 6*d^5*e^7*x + d^6*e^6)","B",0
1688,1,478,0,0.395576," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{105 \, B b^{4} e^{5} x^{5} + 5 \, B b^{4} d^{5} + 30 \, A a^{4} e^{5} + 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + 5 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} + 35 \, {\left(5 \, B b^{4} d e^{4} + 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 35 \, {\left(5 \, B b^{4} d^{2} e^{3} + 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 21 \, {\left(5 \, B b^{4} d^{3} e^{2} + 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} + 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 7 \, {\left(5 \, B b^{4} d^{4} e + 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} + 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + 5 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x}{210 \, {\left(e^{13} x^{7} + 7 \, d e^{12} x^{6} + 21 \, d^{2} e^{11} x^{5} + 35 \, d^{3} e^{10} x^{4} + 35 \, d^{4} e^{9} x^{3} + 21 \, d^{5} e^{8} x^{2} + 7 \, d^{6} e^{7} x + d^{7} e^{6}\right)}}"," ",0,"-1/210*(105*B*b^4*e^5*x^5 + 5*B*b^4*d^5 + 30*A*a^4*e^5 + 2*(4*B*a*b^3 + A*b^4)*d^4*e + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + 5*(B*a^4 + 4*A*a^3*b)*d*e^4 + 35*(5*B*b^4*d*e^4 + 2*(4*B*a*b^3 + A*b^4)*e^5)*x^4 + 35*(5*B*b^4*d^2*e^3 + 2*(4*B*a*b^3 + A*b^4)*d*e^4 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 21*(5*B*b^4*d^3*e^2 + 2*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 7*(5*B*b^4*d^4*e + 2*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + 5*(B*a^4 + 4*A*a^3*b)*e^5)*x)/(e^13*x^7 + 7*d*e^12*x^6 + 21*d^2*e^11*x^5 + 35*d^3*e^10*x^4 + 35*d^4*e^9*x^3 + 21*d^5*e^8*x^2 + 7*d^6*e^7*x + d^7*e^6)","B",0
1689,1,489,0,0.403046," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{280 \, B b^{4} e^{5} x^{5} + 5 \, B b^{4} d^{5} + 105 \, A a^{4} e^{5} + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + 10 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + 15 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} + 70 \, {\left(5 \, B b^{4} d e^{4} + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 56 \, {\left(5 \, B b^{4} d^{2} e^{3} + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 28 \, {\left(5 \, B b^{4} d^{3} e^{2} + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} + 10 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 8 \, {\left(5 \, B b^{4} d^{4} e + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} + 10 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + 15 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x}{840 \, {\left(e^{14} x^{8} + 8 \, d e^{13} x^{7} + 28 \, d^{2} e^{12} x^{6} + 56 \, d^{3} e^{11} x^{5} + 70 \, d^{4} e^{10} x^{4} + 56 \, d^{5} e^{9} x^{3} + 28 \, d^{6} e^{8} x^{2} + 8 \, d^{7} e^{7} x + d^{8} e^{6}\right)}}"," ",0,"-1/840*(280*B*b^4*e^5*x^5 + 5*B*b^4*d^5 + 105*A*a^4*e^5 + 3*(4*B*a*b^3 + A*b^4)*d^4*e + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + 10*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + 15*(B*a^4 + 4*A*a^3*b)*d*e^4 + 70*(5*B*b^4*d*e^4 + 3*(4*B*a*b^3 + A*b^4)*e^5)*x^4 + 56*(5*B*b^4*d^2*e^3 + 3*(4*B*a*b^3 + A*b^4)*d*e^4 + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 28*(5*B*b^4*d^3*e^2 + 3*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 + 10*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 8*(5*B*b^4*d^4*e + 3*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 + 10*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + 15*(B*a^4 + 4*A*a^3*b)*e^5)*x)/(e^14*x^8 + 8*d*e^13*x^7 + 28*d^2*e^12*x^6 + 56*d^3*e^11*x^5 + 70*d^4*e^10*x^4 + 56*d^5*e^9*x^3 + 28*d^6*e^8*x^2 + 8*d^7*e^7*x + d^8*e^6)","B",0
1690,1,500,0,0.410242," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{630 \, B b^{4} e^{5} x^{5} + 5 \, B b^{4} d^{5} + 280 \, A a^{4} e^{5} + 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 10 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + 20 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + 35 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} + 126 \, {\left(5 \, B b^{4} d e^{4} + 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 84 \, {\left(5 \, B b^{4} d^{2} e^{3} + 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 10 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 36 \, {\left(5 \, B b^{4} d^{3} e^{2} + 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 10 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} + 20 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 9 \, {\left(5 \, B b^{4} d^{4} e + 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 10 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} + 20 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + 35 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x}{2520 \, {\left(e^{15} x^{9} + 9 \, d e^{14} x^{8} + 36 \, d^{2} e^{13} x^{7} + 84 \, d^{3} e^{12} x^{6} + 126 \, d^{4} e^{11} x^{5} + 126 \, d^{5} e^{10} x^{4} + 84 \, d^{6} e^{9} x^{3} + 36 \, d^{7} e^{8} x^{2} + 9 \, d^{8} e^{7} x + d^{9} e^{6}\right)}}"," ",0,"-1/2520*(630*B*b^4*e^5*x^5 + 5*B*b^4*d^5 + 280*A*a^4*e^5 + 4*(4*B*a*b^3 + A*b^4)*d^4*e + 10*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + 20*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + 35*(B*a^4 + 4*A*a^3*b)*d*e^4 + 126*(5*B*b^4*d*e^4 + 4*(4*B*a*b^3 + A*b^4)*e^5)*x^4 + 84*(5*B*b^4*d^2*e^3 + 4*(4*B*a*b^3 + A*b^4)*d*e^4 + 10*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 36*(5*B*b^4*d^3*e^2 + 4*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 10*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 + 20*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 9*(5*B*b^4*d^4*e + 4*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 10*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 + 20*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + 35*(B*a^4 + 4*A*a^3*b)*e^5)*x)/(e^15*x^9 + 9*d*e^14*x^8 + 36*d^2*e^13*x^7 + 84*d^3*e^12*x^6 + 126*d^4*e^11*x^5 + 126*d^5*e^10*x^4 + 84*d^6*e^9*x^3 + 36*d^7*e^8*x^2 + 9*d^8*e^7*x + d^9*e^6)","B",0
1691,1,501,0,0.403924," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{252 \, B b^{4} e^{5} x^{5} + B b^{4} d^{5} + 126 \, A a^{4} e^{5} + {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + 7 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + 14 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} + 210 \, {\left(B b^{4} d e^{4} + {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 120 \, {\left(B b^{4} d^{2} e^{3} + {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 45 \, {\left(B b^{4} d^{3} e^{2} + {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} + 7 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 10 \, {\left(B b^{4} d^{4} e + {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} + 7 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + 14 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x}{1260 \, {\left(e^{16} x^{10} + 10 \, d e^{15} x^{9} + 45 \, d^{2} e^{14} x^{8} + 120 \, d^{3} e^{13} x^{7} + 210 \, d^{4} e^{12} x^{6} + 252 \, d^{5} e^{11} x^{5} + 210 \, d^{6} e^{10} x^{4} + 120 \, d^{7} e^{9} x^{3} + 45 \, d^{8} e^{8} x^{2} + 10 \, d^{9} e^{7} x + d^{10} e^{6}\right)}}"," ",0,"-1/1260*(252*B*b^4*e^5*x^5 + B*b^4*d^5 + 126*A*a^4*e^5 + (4*B*a*b^3 + A*b^4)*d^4*e + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + 7*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + 14*(B*a^4 + 4*A*a^3*b)*d*e^4 + 210*(B*b^4*d*e^4 + (4*B*a*b^3 + A*b^4)*e^5)*x^4 + 120*(B*b^4*d^2*e^3 + (4*B*a*b^3 + A*b^4)*d*e^4 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 45*(B*b^4*d^3*e^2 + (4*B*a*b^3 + A*b^4)*d^2*e^3 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 + 7*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 10*(B*b^4*d^4*e + (4*B*a*b^3 + A*b^4)*d^3*e^2 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 + 7*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + 14*(B*a^4 + 4*A*a^3*b)*e^5)*x)/(e^16*x^10 + 10*d*e^15*x^9 + 45*d^2*e^14*x^8 + 120*d^3*e^13*x^7 + 210*d^4*e^12*x^6 + 252*d^5*e^11*x^5 + 210*d^6*e^10*x^4 + 120*d^7*e^9*x^3 + 45*d^8*e^8*x^2 + 10*d^9*e^7*x + d^10*e^6)","B",0
1692,1,522,0,0.398015," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{2310 \, B b^{4} e^{5} x^{5} + 5 \, B b^{4} d^{5} + 1260 \, A a^{4} e^{5} + 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 21 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + 56 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + 126 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} + 330 \, {\left(5 \, B b^{4} d e^{4} + 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 165 \, {\left(5 \, B b^{4} d^{2} e^{3} + 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 21 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 55 \, {\left(5 \, B b^{4} d^{3} e^{2} + 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 21 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} + 56 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 11 \, {\left(5 \, B b^{4} d^{4} e + 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 21 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} + 56 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + 126 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x}{13860 \, {\left(e^{17} x^{11} + 11 \, d e^{16} x^{10} + 55 \, d^{2} e^{15} x^{9} + 165 \, d^{3} e^{14} x^{8} + 330 \, d^{4} e^{13} x^{7} + 462 \, d^{5} e^{12} x^{6} + 462 \, d^{6} e^{11} x^{5} + 330 \, d^{7} e^{10} x^{4} + 165 \, d^{8} e^{9} x^{3} + 55 \, d^{9} e^{8} x^{2} + 11 \, d^{10} e^{7} x + d^{11} e^{6}\right)}}"," ",0,"-1/13860*(2310*B*b^4*e^5*x^5 + 5*B*b^4*d^5 + 1260*A*a^4*e^5 + 6*(4*B*a*b^3 + A*b^4)*d^4*e + 21*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + 56*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + 126*(B*a^4 + 4*A*a^3*b)*d*e^4 + 330*(5*B*b^4*d*e^4 + 6*(4*B*a*b^3 + A*b^4)*e^5)*x^4 + 165*(5*B*b^4*d^2*e^3 + 6*(4*B*a*b^3 + A*b^4)*d*e^4 + 21*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 55*(5*B*b^4*d^3*e^2 + 6*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 21*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 + 56*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 11*(5*B*b^4*d^4*e + 6*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 21*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 + 56*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + 126*(B*a^4 + 4*A*a^3*b)*e^5)*x)/(e^17*x^11 + 11*d*e^16*x^10 + 55*d^2*e^15*x^9 + 165*d^3*e^14*x^8 + 330*d^4*e^13*x^7 + 462*d^5*e^12*x^6 + 462*d^6*e^11*x^5 + 330*d^7*e^10*x^4 + 165*d^8*e^9*x^3 + 55*d^9*e^8*x^2 + 11*d^10*e^7*x + d^11*e^6)","B",0
1693,1,610,0,0.432518," ","integrate((B*x+A)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{3 \, B b^{5} e^{4} x^{5} + 12 \, {\left(B a b^{4} - A b^{5}\right)} d^{4} - 48 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d^{3} e + 72 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} d^{2} e^{2} - 48 \, {\left(B a^{4} b - A a^{3} b^{2}\right)} d e^{3} + 12 \, {\left(B a^{5} - A a^{4} b\right)} e^{4} + {\left(16 \, B b^{5} d e^{3} - {\left(5 \, B a b^{4} - 4 \, A b^{5}\right)} e^{4}\right)} x^{4} + 2 \, {\left(18 \, B b^{5} d^{2} e^{2} - 4 \, {\left(4 \, B a b^{4} - 3 \, A b^{5}\right)} d e^{3} + {\left(5 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B b^{5} d^{3} e - 6 \, {\left(3 \, B a b^{4} - 2 \, A b^{5}\right)} d^{2} e^{2} + 4 \, {\left(4 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} d e^{3} - {\left(5 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 12 \, {\left(4 \, B a b^{4} d^{3} e - 6 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} d^{2} e^{2} + 4 \, {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d e^{3} - {\left(4 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x + 12 \, {\left(B a b^{4} d^{4} - 4 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} d^{3} e + 6 \, {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d^{2} e^{2} - 4 \, {\left(4 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} d e^{3} + {\left(5 \, B a^{5} - 4 \, A a^{4} b\right)} e^{4} + {\left(B b^{5} d^{4} - 4 \, {\left(2 \, B a b^{4} - A b^{5}\right)} d^{3} e + 6 \, {\left(3 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} d^{2} e^{2} - 4 \, {\left(4 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} d e^{3} + {\left(5 \, B a^{4} b - 4 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{7} x + a b^{6}\right)}}"," ",0,"1/12*(3*B*b^5*e^4*x^5 + 12*(B*a*b^4 - A*b^5)*d^4 - 48*(B*a^2*b^3 - A*a*b^4)*d^3*e + 72*(B*a^3*b^2 - A*a^2*b^3)*d^2*e^2 - 48*(B*a^4*b - A*a^3*b^2)*d*e^3 + 12*(B*a^5 - A*a^4*b)*e^4 + (16*B*b^5*d*e^3 - (5*B*a*b^4 - 4*A*b^5)*e^4)*x^4 + 2*(18*B*b^5*d^2*e^2 - 4*(4*B*a*b^4 - 3*A*b^5)*d*e^3 + (5*B*a^2*b^3 - 4*A*a*b^4)*e^4)*x^3 + 6*(8*B*b^5*d^3*e - 6*(3*B*a*b^4 - 2*A*b^5)*d^2*e^2 + 4*(4*B*a^2*b^3 - 3*A*a*b^4)*d*e^3 - (5*B*a^3*b^2 - 4*A*a^2*b^3)*e^4)*x^2 + 12*(4*B*a*b^4*d^3*e - 6*(2*B*a^2*b^3 - A*a*b^4)*d^2*e^2 + 4*(3*B*a^3*b^2 - 2*A*a^2*b^3)*d*e^3 - (4*B*a^4*b - 3*A*a^3*b^2)*e^4)*x + 12*(B*a*b^4*d^4 - 4*(2*B*a^2*b^3 - A*a*b^4)*d^3*e + 6*(3*B*a^3*b^2 - 2*A*a^2*b^3)*d^2*e^2 - 4*(4*B*a^4*b - 3*A*a^3*b^2)*d*e^3 + (5*B*a^5 - 4*A*a^4*b)*e^4 + (B*b^5*d^4 - 4*(2*B*a*b^4 - A*b^5)*d^3*e + 6*(3*B*a^2*b^3 - 2*A*a*b^4)*d^2*e^2 - 4*(4*B*a^3*b^2 - 3*A*a^2*b^3)*d*e^3 + (5*B*a^4*b - 4*A*a^3*b^2)*e^4)*x)*log(b*x + a))/(b^7*x + a*b^6)","B",0
1694,1,417,0,0.427121," ","integrate((B*x+A)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, B b^{4} e^{3} x^{4} + 6 \, {\left(B a b^{3} - A b^{4}\right)} d^{3} - 18 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e + 18 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} d e^{2} - 6 \, {\left(B a^{4} - A a^{3} b\right)} e^{3} + {\left(9 \, B b^{4} d e^{2} - {\left(4 \, B a b^{3} - 3 \, A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, B b^{4} d^{2} e - 3 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} d e^{2} + {\left(4 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 6 \, {\left(3 \, B a b^{3} d^{2} e - 3 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} d e^{2} + {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{3}\right)} x + 6 \, {\left(B a b^{3} d^{3} - 3 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} d^{2} e + 3 \, {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{2} - {\left(4 \, B a^{4} - 3 \, A a^{3} b\right)} e^{3} + {\left(B b^{4} d^{3} - 3 \, {\left(2 \, B a b^{3} - A b^{4}\right)} d^{2} e + 3 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} d e^{2} - {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"1/6*(2*B*b^4*e^3*x^4 + 6*(B*a*b^3 - A*b^4)*d^3 - 18*(B*a^2*b^2 - A*a*b^3)*d^2*e + 18*(B*a^3*b - A*a^2*b^2)*d*e^2 - 6*(B*a^4 - A*a^3*b)*e^3 + (9*B*b^4*d*e^2 - (4*B*a*b^3 - 3*A*b^4)*e^3)*x^3 + 3*(6*B*b^4*d^2*e - 3*(3*B*a*b^3 - 2*A*b^4)*d*e^2 + (4*B*a^2*b^2 - 3*A*a*b^3)*e^3)*x^2 + 6*(3*B*a*b^3*d^2*e - 3*(2*B*a^2*b^2 - A*a*b^3)*d*e^2 + (3*B*a^3*b - 2*A*a^2*b^2)*e^3)*x + 6*(B*a*b^3*d^3 - 3*(2*B*a^2*b^2 - A*a*b^3)*d^2*e + 3*(3*B*a^3*b - 2*A*a^2*b^2)*d*e^2 - (4*B*a^4 - 3*A*a^3*b)*e^3 + (B*b^4*d^3 - 3*(2*B*a*b^3 - A*b^4)*d^2*e + 3*(3*B*a^2*b^2 - 2*A*a*b^3)*d*e^2 - (4*B*a^3*b - 3*A*a^2*b^2)*e^3)*x)*log(b*x + a))/(b^6*x + a*b^5)","B",0
1695,1,249,0,0.416451," ","integrate((B*x+A)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{B b^{3} e^{2} x^{3} + 2 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} - 4 \, {\left(B a^{2} b - A a b^{2}\right)} d e + 2 \, {\left(B a^{3} - A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(2 \, B a b^{2} d e - {\left(2 \, B a^{2} b - A a b^{2}\right)} e^{2}\right)} x + 2 \, {\left(B a b^{2} d^{2} - 2 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} d e + {\left(3 \, B a^{3} - 2 \, A a^{2} b\right)} e^{2} + {\left(B b^{3} d^{2} - 2 \, {\left(2 \, B a b^{2} - A b^{3}\right)} d e + {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} e^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(B*b^3*e^2*x^3 + 2*(B*a*b^2 - A*b^3)*d^2 - 4*(B*a^2*b - A*a*b^2)*d*e + 2*(B*a^3 - A*a^2*b)*e^2 + (4*B*b^3*d*e - (3*B*a*b^2 - 2*A*b^3)*e^2)*x^2 + 2*(2*B*a*b^2*d*e - (2*B*a^2*b - A*a*b^2)*e^2)*x + 2*(B*a*b^2*d^2 - 2*(2*B*a^2*b - A*a*b^2)*d*e + (3*B*a^3 - 2*A*a^2*b)*e^2 + (B*b^3*d^2 - 2*(2*B*a*b^2 - A*b^3)*d*e + (3*B*a^2*b - 2*A*a*b^2)*e^2)*x)*log(b*x + a))/(b^5*x + a*b^4)","B",0
1696,1,109,0,0.405540," ","integrate((B*x+A)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{B b^{2} e x^{2} + B a b e x + {\left(B a b - A b^{2}\right)} d - {\left(B a^{2} - A a b\right)} e + {\left(B a b d - {\left(2 \, B a^{2} - A a b\right)} e + {\left(B b^{2} d - {\left(2 \, B a b - A b^{2}\right)} e\right)} x\right)} \log\left(b x + a\right)}{b^{4} x + a b^{3}}"," ",0,"(B*b^2*e*x^2 + B*a*b*e*x + (B*a*b - A*b^2)*d - (B*a^2 - A*a*b)*e + (B*a*b*d - (2*B*a^2 - A*a*b)*e + (B*b^2*d - (2*B*a*b - A*b^2)*e)*x)*log(b*x + a))/(b^4*x + a*b^3)","A",0
1697,1,37,0,0.404384," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{B a - A b + {\left(B b x + B a\right)} \log\left(b x + a\right)}{b^{3} x + a b^{2}}"," ",0,"(B*a - A*b + (B*b*x + B*a)*log(b*x + a))/(b^3*x + a*b^2)","A",0
1698,1,157,0,0.423919," ","integrate((B*x+A)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{{\left(B a b - A b^{2}\right)} d - {\left(B a^{2} - A a b\right)} e + {\left(B a b d - A a b e + {\left(B b^{2} d - A b^{2} e\right)} x\right)} \log\left(b x + a\right) - {\left(B a b d - A a b e + {\left(B b^{2} d - A b^{2} e\right)} x\right)} \log\left(e x + d\right)}{a b^{3} d^{2} - 2 \, a^{2} b^{2} d e + a^{3} b e^{2} + {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} x}"," ",0,"((B*a*b - A*b^2)*d - (B*a^2 - A*a*b)*e + (B*a*b*d - A*a*b*e + (B*b^2*d - A*b^2*e)*x)*log(b*x + a) - (B*a*b*d - A*a*b*e + (B*b^2*d - A*b^2*e)*x)*log(e*x + d))/(a*b^3*d^2 - 2*a^2*b^2*d*e + a^3*b*e^2 + (b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*x)","A",0
1699,1,396,0,0.439541," ","integrate((B*x+A)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{2 \, B a^{2} d e - A a^{2} e^{2} - {\left(2 \, B a b - A b^{2}\right)} d^{2} - {\left(B b^{2} d^{2} - 2 \, A b^{2} d e - {\left(B a^{2} - 2 \, A a b\right)} e^{2}\right)} x - {\left(B a b d^{2} + {\left(B a^{2} - 2 \, A a b\right)} d e + {\left(B b^{2} d e + {\left(B a b - 2 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(B b^{2} d^{2} + 2 \, {\left(B a b - A b^{2}\right)} d e + {\left(B a^{2} - 2 \, A a b\right)} e^{2}\right)} x\right)} \log\left(b x + a\right) + {\left(B a b d^{2} + {\left(B a^{2} - 2 \, A a b\right)} d e + {\left(B b^{2} d e + {\left(B a b - 2 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(B b^{2} d^{2} + 2 \, {\left(B a b - A b^{2}\right)} d e + {\left(B a^{2} - 2 \, A a b\right)} e^{2}\right)} x\right)} \log\left(e x + d\right)}{a b^{3} d^{4} - 3 \, a^{2} b^{2} d^{3} e + 3 \, a^{3} b d^{2} e^{2} - a^{4} d e^{3} + {\left(b^{4} d^{3} e - 3 \, a b^{3} d^{2} e^{2} + 3 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x^{2} + {\left(b^{4} d^{4} - 2 \, a b^{3} d^{3} e + 2 \, a^{3} b d e^{3} - a^{4} e^{4}\right)} x}"," ",0,"-(2*B*a^2*d*e - A*a^2*e^2 - (2*B*a*b - A*b^2)*d^2 - (B*b^2*d^2 - 2*A*b^2*d*e - (B*a^2 - 2*A*a*b)*e^2)*x - (B*a*b*d^2 + (B*a^2 - 2*A*a*b)*d*e + (B*b^2*d*e + (B*a*b - 2*A*b^2)*e^2)*x^2 + (B*b^2*d^2 + 2*(B*a*b - A*b^2)*d*e + (B*a^2 - 2*A*a*b)*e^2)*x)*log(b*x + a) + (B*a*b*d^2 + (B*a^2 - 2*A*a*b)*d*e + (B*b^2*d*e + (B*a*b - 2*A*b^2)*e^2)*x^2 + (B*b^2*d^2 + 2*(B*a*b - A*b^2)*d*e + (B*a^2 - 2*A*a*b)*e^2)*x)*log(e*x + d))/(a*b^3*d^4 - 3*a^2*b^2*d^3*e + 3*a^3*b*d^2*e^2 - a^4*d*e^3 + (b^4*d^3*e - 3*a*b^3*d^2*e^2 + 3*a^2*b^2*d*e^3 - a^3*b*e^4)*x^2 + (b^4*d^4 - 2*a*b^3*d^3*e + 2*a^3*b*d*e^3 - a^4*e^4)*x)","B",0
1700,1,801,0,0.444359," ","integrate((B*x+A)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{A a^{3} e^{3} - {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} d^{3} + {\left(4 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{2} e + {\left(B a^{3} - 6 \, A a^{2} b\right)} d e^{2} - 2 \, {\left(B b^{3} d^{2} e + {\left(B a b^{2} - 3 \, A b^{3}\right)} d e^{2} - {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} - {\left(3 \, B b^{3} d^{3} + {\left(4 \, B a b^{2} - 9 \, A b^{3}\right)} d^{2} e - {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} d e^{2} - {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} e^{3}\right)} x - 2 \, {\left(B a b^{2} d^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d^{2} e + {\left(B b^{3} d e^{2} + {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(2 \, B b^{3} d^{2} e + {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} d e^{2} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(B b^{3} d^{3} + {\left(4 \, B a b^{2} - 3 \, A b^{3}\right)} d^{2} e + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d e^{2}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(B a b^{2} d^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d^{2} e + {\left(B b^{3} d e^{2} + {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(2 \, B b^{3} d^{2} e + {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} d e^{2} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(B b^{3} d^{3} + {\left(4 \, B a b^{2} - 3 \, A b^{3}\right)} d^{2} e + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a b^{4} d^{6} - 4 \, a^{2} b^{3} d^{5} e + 6 \, a^{3} b^{2} d^{4} e^{2} - 4 \, a^{4} b d^{3} e^{3} + a^{5} d^{2} e^{4} + {\left(b^{5} d^{4} e^{2} - 4 \, a b^{4} d^{3} e^{3} + 6 \, a^{2} b^{3} d^{2} e^{4} - 4 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{3} + {\left(2 \, b^{5} d^{5} e - 7 \, a b^{4} d^{4} e^{2} + 8 \, a^{2} b^{3} d^{3} e^{3} - 2 \, a^{3} b^{2} d^{2} e^{4} - 2 \, a^{4} b d e^{5} + a^{5} e^{6}\right)} x^{2} + {\left(b^{5} d^{6} - 2 \, a b^{4} d^{5} e - 2 \, a^{2} b^{3} d^{4} e^{2} + 8 \, a^{3} b^{2} d^{3} e^{3} - 7 \, a^{4} b d^{2} e^{4} + 2 \, a^{5} d e^{5}\right)} x\right)}}"," ",0,"-1/2*(A*a^3*e^3 - (5*B*a*b^2 - 2*A*b^3)*d^3 + (4*B*a^2*b + 3*A*a*b^2)*d^2*e + (B*a^3 - 6*A*a^2*b)*d*e^2 - 2*(B*b^3*d^2*e + (B*a*b^2 - 3*A*b^3)*d*e^2 - (2*B*a^2*b - 3*A*a*b^2)*e^3)*x^2 - (3*B*b^3*d^3 + (4*B*a*b^2 - 9*A*b^3)*d^2*e - (5*B*a^2*b - 6*A*a*b^2)*d*e^2 - (2*B*a^3 - 3*A*a^2*b)*e^3)*x - 2*(B*a*b^2*d^3 + (2*B*a^2*b - 3*A*a*b^2)*d^2*e + (B*b^3*d*e^2 + (2*B*a*b^2 - 3*A*b^3)*e^3)*x^3 + (2*B*b^3*d^2*e + (5*B*a*b^2 - 6*A*b^3)*d*e^2 + (2*B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (B*b^3*d^3 + (4*B*a*b^2 - 3*A*b^3)*d^2*e + 2*(2*B*a^2*b - 3*A*a*b^2)*d*e^2)*x)*log(b*x + a) + 2*(B*a*b^2*d^3 + (2*B*a^2*b - 3*A*a*b^2)*d^2*e + (B*b^3*d*e^2 + (2*B*a*b^2 - 3*A*b^3)*e^3)*x^3 + (2*B*b^3*d^2*e + (5*B*a*b^2 - 6*A*b^3)*d*e^2 + (2*B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (B*b^3*d^3 + (4*B*a*b^2 - 3*A*b^3)*d^2*e + 2*(2*B*a^2*b - 3*A*a*b^2)*d*e^2)*x)*log(e*x + d))/(a*b^4*d^6 - 4*a^2*b^3*d^5*e + 6*a^3*b^2*d^4*e^2 - 4*a^4*b*d^3*e^3 + a^5*d^2*e^4 + (b^5*d^4*e^2 - 4*a*b^4*d^3*e^3 + 6*a^2*b^3*d^2*e^4 - 4*a^3*b^2*d*e^5 + a^4*b*e^6)*x^3 + (2*b^5*d^5*e - 7*a*b^4*d^4*e^2 + 8*a^2*b^3*d^3*e^3 - 2*a^3*b^2*d^2*e^4 - 2*a^4*b*d*e^5 + a^5*e^6)*x^2 + (b^5*d^6 - 2*a*b^4*d^5*e - 2*a^2*b^3*d^4*e^2 + 8*a^3*b^2*d^3*e^3 - 7*a^4*b*d^2*e^4 + 2*a^5*d*e^5)*x)","B",0
1701,1,671,0,0.433795," ","integrate((B*x+A)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{3 \, B b^{5} e^{4} x^{5} - {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{4} - 4 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e + 6 \, {\left(11 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d^{2} e^{2} - 4 \, {\left(26 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d e^{3} + {\left(47 \, B a^{5} - 26 \, A a^{4} b\right)} e^{4} + 3 \, {\left(8 \, B b^{5} d e^{3} - {\left(5 \, B a b^{4} - 2 \, A b^{5}\right)} e^{4}\right)} x^{4} + 9 \, {\left(8 \, B a b^{4} d e^{3} - {\left(7 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} e^{4}\right)} x^{3} - 3 \, {\left(8 \, B b^{5} d^{3} e - 12 \, {\left(3 \, B a b^{4} - A b^{5}\right)} d^{2} e^{2} + 24 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d e^{3} + 3 \, {\left(B a^{3} b^{2} + 2 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - 3 \, {\left(B b^{5} d^{4} + 4 \, {\left(2 \, B a b^{4} + A b^{5}\right)} d^{3} e - 6 \, {\left(9 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} d^{2} e^{2} + 36 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} d e^{3} - 9 \, {\left(3 \, B a^{4} b - 2 \, A a^{3} b^{2}\right)} e^{4}\right)} x + 12 \, {\left(3 \, B a^{3} b^{2} d^{2} e^{2} - 2 \, {\left(4 \, B a^{4} b - A a^{3} b^{2}\right)} d e^{3} + {\left(5 \, B a^{5} - 2 \, A a^{4} b\right)} e^{4} + {\left(3 \, B b^{5} d^{2} e^{2} - 2 \, {\left(4 \, B a b^{4} - A b^{5}\right)} d e^{3} + {\left(5 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(3 \, B a b^{4} d^{2} e^{2} - 2 \, {\left(4 \, B a^{2} b^{3} - A a b^{4}\right)} d e^{3} + {\left(5 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 3 \, {\left(3 \, B a^{2} b^{3} d^{2} e^{2} - 2 \, {\left(4 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} d e^{3} + {\left(5 \, B a^{4} b - 2 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{9} x^{3} + 3 \, a b^{8} x^{2} + 3 \, a^{2} b^{7} x + a^{3} b^{6}\right)}}"," ",0,"1/6*(3*B*b^5*e^4*x^5 - (B*a*b^4 + 2*A*b^5)*d^4 - 4*(2*B*a^2*b^3 + A*a*b^4)*d^3*e + 6*(11*B*a^3*b^2 - 2*A*a^2*b^3)*d^2*e^2 - 4*(26*B*a^4*b - 11*A*a^3*b^2)*d*e^3 + (47*B*a^5 - 26*A*a^4*b)*e^4 + 3*(8*B*b^5*d*e^3 - (5*B*a*b^4 - 2*A*b^5)*e^4)*x^4 + 9*(8*B*a*b^4*d*e^3 - (7*B*a^2*b^3 - 2*A*a*b^4)*e^4)*x^3 - 3*(8*B*b^5*d^3*e - 12*(3*B*a*b^4 - A*b^5)*d^2*e^2 + 24*(B*a^2*b^3 - A*a*b^4)*d*e^3 + 3*(B*a^3*b^2 + 2*A*a^2*b^3)*e^4)*x^2 - 3*(B*b^5*d^4 + 4*(2*B*a*b^4 + A*b^5)*d^3*e - 6*(9*B*a^2*b^3 - 2*A*a*b^4)*d^2*e^2 + 36*(2*B*a^3*b^2 - A*a^2*b^3)*d*e^3 - 9*(3*B*a^4*b - 2*A*a^3*b^2)*e^4)*x + 12*(3*B*a^3*b^2*d^2*e^2 - 2*(4*B*a^4*b - A*a^3*b^2)*d*e^3 + (5*B*a^5 - 2*A*a^4*b)*e^4 + (3*B*b^5*d^2*e^2 - 2*(4*B*a*b^4 - A*b^5)*d*e^3 + (5*B*a^2*b^3 - 2*A*a*b^4)*e^4)*x^3 + 3*(3*B*a*b^4*d^2*e^2 - 2*(4*B*a^2*b^3 - A*a*b^4)*d*e^3 + (5*B*a^3*b^2 - 2*A*a^2*b^3)*e^4)*x^2 + 3*(3*B*a^2*b^3*d^2*e^2 - 2*(4*B*a^3*b^2 - A*a^2*b^3)*d*e^3 + (5*B*a^4*b - 2*A*a^3*b^2)*e^4)*x)*log(b*x + a))/(b^9*x^3 + 3*a*b^8*x^2 + 3*a^2*b^7*x + a^3*b^6)","B",0
1702,1,427,0,0.414471," ","integrate((B*x+A)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{6 \, B b^{4} e^{3} x^{4} + 18 \, B a b^{3} e^{3} x^{3} - {\left(B a b^{3} + 2 \, A b^{4}\right)} d^{3} - 3 \, {\left(2 \, B a^{2} b^{2} + A a b^{3}\right)} d^{2} e + 3 \, {\left(11 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{2} - {\left(26 \, B a^{4} - 11 \, A a^{3} b\right)} e^{3} - 18 \, {\left(B b^{4} d^{2} e - {\left(3 \, B a b^{3} - A b^{4}\right)} d e^{2} + {\left(B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} - 3 \, {\left(B b^{4} d^{3} + 3 \, {\left(2 \, B a b^{3} + A b^{4}\right)} d^{2} e - 3 \, {\left(9 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} d e^{2} + 9 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x + 6 \, {\left(3 \, B a^{3} b d e^{2} - {\left(4 \, B a^{4} - A a^{3} b\right)} e^{3} + {\left(3 \, B b^{4} d e^{2} - {\left(4 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(3 \, B a b^{3} d e^{2} - {\left(4 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(3 \, B a^{2} b^{2} d e^{2} - {\left(4 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}"," ",0,"1/6*(6*B*b^4*e^3*x^4 + 18*B*a*b^3*e^3*x^3 - (B*a*b^3 + 2*A*b^4)*d^3 - 3*(2*B*a^2*b^2 + A*a*b^3)*d^2*e + 3*(11*B*a^3*b - 2*A*a^2*b^2)*d*e^2 - (26*B*a^4 - 11*A*a^3*b)*e^3 - 18*(B*b^4*d^2*e - (3*B*a*b^3 - A*b^4)*d*e^2 + (B*a^2*b^2 - A*a*b^3)*e^3)*x^2 - 3*(B*b^4*d^3 + 3*(2*B*a*b^3 + A*b^4)*d^2*e - 3*(9*B*a^2*b^2 - 2*A*a*b^3)*d*e^2 + 9*(2*B*a^3*b - A*a^2*b^2)*e^3)*x + 6*(3*B*a^3*b*d*e^2 - (4*B*a^4 - A*a^3*b)*e^3 + (3*B*b^4*d*e^2 - (4*B*a*b^3 - A*b^4)*e^3)*x^3 + 3*(3*B*a*b^3*d*e^2 - (4*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 3*(3*B*a^2*b^2*d*e^2 - (4*B*a^3*b - A*a^2*b^2)*e^3)*x)*log(b*x + a))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5)","B",0
1703,1,226,0,0.417510," ","integrate((B*x+A)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{{\left(B a b^{2} + 2 \, A b^{3}\right)} d^{2} + 2 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} d e - {\left(11 \, B a^{3} - 2 \, A a^{2} b\right)} e^{2} + 6 \, {\left(2 \, B b^{3} d e - {\left(3 \, B a b^{2} - A b^{3}\right)} e^{2}\right)} x^{2} + 3 \, {\left(B b^{3} d^{2} + 2 \, {\left(2 \, B a b^{2} + A b^{3}\right)} d e - {\left(9 \, B a^{2} b - 2 \, A a b^{2}\right)} e^{2}\right)} x - 6 \, {\left(B b^{3} e^{2} x^{3} + 3 \, B a b^{2} e^{2} x^{2} + 3 \, B a^{2} b e^{2} x + B a^{3} e^{2}\right)} \log\left(b x + a\right)}{6 \, {\left(b^{7} x^{3} + 3 \, a b^{6} x^{2} + 3 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}"," ",0,"-1/6*((B*a*b^2 + 2*A*b^3)*d^2 + 2*(2*B*a^2*b + A*a*b^2)*d*e - (11*B*a^3 - 2*A*a^2*b)*e^2 + 6*(2*B*b^3*d*e - (3*B*a*b^2 - A*b^3)*e^2)*x^2 + 3*(B*b^3*d^2 + 2*(2*B*a*b^2 + A*b^3)*d*e - (9*B*a^2*b - 2*A*a*b^2)*e^2)*x - 6*(B*b^3*e^2*x^3 + 3*B*a*b^2*e^2*x^2 + 3*B*a^2*b*e^2*x + B*a^3*e^2)*log(b*x + a))/(b^7*x^3 + 3*a*b^6*x^2 + 3*a^2*b^5*x + a^3*b^4)","B",0
1704,1,97,0,0.415514," ","integrate((B*x+A)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{6 \, B b^{2} e x^{2} + {\left(B a b + 2 \, A b^{2}\right)} d + {\left(2 \, B a^{2} + A a b\right)} e + 3 \, {\left(B b^{2} d + {\left(2 \, B a b + A b^{2}\right)} e\right)} x}{6 \, {\left(b^{6} x^{3} + 3 \, a b^{5} x^{2} + 3 \, a^{2} b^{4} x + a^{3} b^{3}\right)}}"," ",0,"-1/6*(6*B*b^2*e*x^2 + (B*a*b + 2*A*b^2)*d + (2*B*a^2 + A*a*b)*e + 3*(B*b^2*d + (2*B*a*b + A*b^2)*e)*x)/(b^6*x^3 + 3*a*b^5*x^2 + 3*a^2*b^4*x + a^3*b^3)","A",0
1705,1,50,0,0.392709," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{3 \, B b x + B a + 2 \, A b}{6 \, {\left(b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x + a^{3} b^{2}\right)}}"," ",0,"-1/6*(3*B*b*x + B*a + 2*A*b)/(b^5*x^3 + 3*a*b^4*x^2 + 3*a^2*b^3*x + a^3*b^2)","A",0
1706,1,643,0,0.451586," ","integrate((B*x+A)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{{\left(B a b^{3} + 2 \, A b^{4}\right)} d^{3} - 3 \, {\left(2 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} d^{2} e + 3 \, {\left(B a^{3} b + 6 \, A a^{2} b^{2}\right)} d e^{2} + {\left(2 \, B a^{4} - 11 \, A a^{3} b\right)} e^{3} - 6 \, {\left(B b^{4} d^{2} e + A a b^{3} e^{3} - {\left(B a b^{3} + A b^{4}\right)} d e^{2}\right)} x^{2} + 3 \, {\left(B b^{4} d^{3} - 5 \, A a^{2} b^{2} e^{3} - {\left(6 \, B a b^{3} + A b^{4}\right)} d^{2} e + {\left(5 \, B a^{2} b^{2} + 6 \, A a b^{3}\right)} d e^{2}\right)} x - 6 \, {\left(B a^{3} b d e^{2} - A a^{3} b e^{3} + {\left(B b^{4} d e^{2} - A b^{4} e^{3}\right)} x^{3} + 3 \, {\left(B a b^{3} d e^{2} - A a b^{3} e^{3}\right)} x^{2} + 3 \, {\left(B a^{2} b^{2} d e^{2} - A a^{2} b^{2} e^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(B a^{3} b d e^{2} - A a^{3} b e^{3} + {\left(B b^{4} d e^{2} - A b^{4} e^{3}\right)} x^{3} + 3 \, {\left(B a b^{3} d e^{2} - A a b^{3} e^{3}\right)} x^{2} + 3 \, {\left(B a^{2} b^{2} d e^{2} - A a^{2} b^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(a^{3} b^{5} d^{4} - 4 \, a^{4} b^{4} d^{3} e + 6 \, a^{5} b^{3} d^{2} e^{2} - 4 \, a^{6} b^{2} d e^{3} + a^{7} b e^{4} + {\left(b^{8} d^{4} - 4 \, a b^{7} d^{3} e + 6 \, a^{2} b^{6} d^{2} e^{2} - 4 \, a^{3} b^{5} d e^{3} + a^{4} b^{4} e^{4}\right)} x^{3} + 3 \, {\left(a b^{7} d^{4} - 4 \, a^{2} b^{6} d^{3} e + 6 \, a^{3} b^{5} d^{2} e^{2} - 4 \, a^{4} b^{4} d e^{3} + a^{5} b^{3} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{4} - 4 \, a^{3} b^{5} d^{3} e + 6 \, a^{4} b^{4} d^{2} e^{2} - 4 \, a^{5} b^{3} d e^{3} + a^{6} b^{2} e^{4}\right)} x\right)}}"," ",0,"-1/6*((B*a*b^3 + 2*A*b^4)*d^3 - 3*(2*B*a^2*b^2 + 3*A*a*b^3)*d^2*e + 3*(B*a^3*b + 6*A*a^2*b^2)*d*e^2 + (2*B*a^4 - 11*A*a^3*b)*e^3 - 6*(B*b^4*d^2*e + A*a*b^3*e^3 - (B*a*b^3 + A*b^4)*d*e^2)*x^2 + 3*(B*b^4*d^3 - 5*A*a^2*b^2*e^3 - (6*B*a*b^3 + A*b^4)*d^2*e + (5*B*a^2*b^2 + 6*A*a*b^3)*d*e^2)*x - 6*(B*a^3*b*d*e^2 - A*a^3*b*e^3 + (B*b^4*d*e^2 - A*b^4*e^3)*x^3 + 3*(B*a*b^3*d*e^2 - A*a*b^3*e^3)*x^2 + 3*(B*a^2*b^2*d*e^2 - A*a^2*b^2*e^3)*x)*log(b*x + a) + 6*(B*a^3*b*d*e^2 - A*a^3*b*e^3 + (B*b^4*d*e^2 - A*b^4*e^3)*x^3 + 3*(B*a*b^3*d*e^2 - A*a*b^3*e^3)*x^2 + 3*(B*a^2*b^2*d*e^2 - A*a^2*b^2*e^3)*x)*log(e*x + d))/(a^3*b^5*d^4 - 4*a^4*b^4*d^3*e + 6*a^5*b^3*d^2*e^2 - 4*a^6*b^2*d*e^3 + a^7*b*e^4 + (b^8*d^4 - 4*a*b^7*d^3*e + 6*a^2*b^6*d^2*e^2 - 4*a^3*b^5*d*e^3 + a^4*b^4*e^4)*x^3 + 3*(a*b^7*d^4 - 4*a^2*b^6*d^3*e + 6*a^3*b^5*d^2*e^2 - 4*a^4*b^4*d*e^3 + a^5*b^3*e^4)*x^2 + 3*(a^2*b^6*d^4 - 4*a^3*b^5*d^3*e + 6*a^4*b^4*d^2*e^2 - 4*a^5*b^3*d*e^3 + a^6*b^2*e^4)*x)","B",0
1707,1,1228,0,0.438787," ","integrate((B*x+A)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{6 \, A a^{4} e^{4} - {\left(B a b^{3} + 2 \, A b^{4}\right)} d^{4} + 3 \, {\left(3 \, B a^{2} b^{2} + 4 \, A a b^{3}\right)} d^{3} e + 9 \, {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} d^{2} e^{2} - {\left(17 \, B a^{4} - 20 \, A a^{3} b\right)} d e^{3} + 6 \, {\left(3 \, B b^{4} d^{2} e^{2} - 2 \, {\left(B a b^{3} + 2 \, A b^{4}\right)} d e^{3} - {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(3 \, B b^{4} d^{3} e + {\left(13 \, B a b^{3} - 4 \, A b^{4}\right)} d^{2} e^{2} - {\left(11 \, B a^{2} b^{2} + 16 \, A a b^{3}\right)} d e^{3} - 5 \, {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - {\left(3 \, B b^{4} d^{4} - 2 \, {\left(13 \, B a b^{3} + 2 \, A b^{4}\right)} d^{3} e - 18 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} d^{2} e^{2} + 6 \, {\left(5 \, B a^{3} b + 2 \, A a^{2} b^{2}\right)} d e^{3} + 11 \, {\left(B a^{4} - 4 \, A a^{3} b\right)} e^{4}\right)} x + 6 \, {\left(3 \, B a^{3} b d^{2} e^{2} + {\left(B a^{4} - 4 \, A a^{3} b\right)} d e^{3} + {\left(3 \, B b^{4} d e^{3} + {\left(B a b^{3} - 4 \, A b^{4}\right)} e^{4}\right)} x^{4} + {\left(3 \, B b^{4} d^{2} e^{2} + 2 \, {\left(5 \, B a b^{3} - 2 \, A b^{4}\right)} d e^{3} + 3 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(3 \, B a b^{3} d^{2} e^{2} + 4 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{3} + {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + {\left(9 \, B a^{2} b^{2} d^{2} e^{2} + 6 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{3} + {\left(B a^{4} - 4 \, A a^{3} b\right)} e^{4}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(3 \, B a^{3} b d^{2} e^{2} + {\left(B a^{4} - 4 \, A a^{3} b\right)} d e^{3} + {\left(3 \, B b^{4} d e^{3} + {\left(B a b^{3} - 4 \, A b^{4}\right)} e^{4}\right)} x^{4} + {\left(3 \, B b^{4} d^{2} e^{2} + 2 \, {\left(5 \, B a b^{3} - 2 \, A b^{4}\right)} d e^{3} + 3 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(3 \, B a b^{3} d^{2} e^{2} + 4 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{3} + {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + {\left(9 \, B a^{2} b^{2} d^{2} e^{2} + 6 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{3} + {\left(B a^{4} - 4 \, A a^{3} b\right)} e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(a^{3} b^{5} d^{6} - 5 \, a^{4} b^{4} d^{5} e + 10 \, a^{5} b^{3} d^{4} e^{2} - 10 \, a^{6} b^{2} d^{3} e^{3} + 5 \, a^{7} b d^{2} e^{4} - a^{8} d e^{5} + {\left(b^{8} d^{5} e - 5 \, a b^{7} d^{4} e^{2} + 10 \, a^{2} b^{6} d^{3} e^{3} - 10 \, a^{3} b^{5} d^{2} e^{4} + 5 \, a^{4} b^{4} d e^{5} - a^{5} b^{3} e^{6}\right)} x^{4} + {\left(b^{8} d^{6} - 2 \, a b^{7} d^{5} e - 5 \, a^{2} b^{6} d^{4} e^{2} + 20 \, a^{3} b^{5} d^{3} e^{3} - 25 \, a^{4} b^{4} d^{2} e^{4} + 14 \, a^{5} b^{3} d e^{5} - 3 \, a^{6} b^{2} e^{6}\right)} x^{3} + 3 \, {\left(a b^{7} d^{6} - 4 \, a^{2} b^{6} d^{5} e + 5 \, a^{3} b^{5} d^{4} e^{2} - 5 \, a^{5} b^{3} d^{2} e^{4} + 4 \, a^{6} b^{2} d e^{5} - a^{7} b e^{6}\right)} x^{2} + {\left(3 \, a^{2} b^{6} d^{6} - 14 \, a^{3} b^{5} d^{5} e + 25 \, a^{4} b^{4} d^{4} e^{2} - 20 \, a^{5} b^{3} d^{3} e^{3} + 5 \, a^{6} b^{2} d^{2} e^{4} + 2 \, a^{7} b d e^{5} - a^{8} e^{6}\right)} x\right)}}"," ",0,"1/6*(6*A*a^4*e^4 - (B*a*b^3 + 2*A*b^4)*d^4 + 3*(3*B*a^2*b^2 + 4*A*a*b^3)*d^3*e + 9*(B*a^3*b - 4*A*a^2*b^2)*d^2*e^2 - (17*B*a^4 - 20*A*a^3*b)*d*e^3 + 6*(3*B*b^4*d^2*e^2 - 2*(B*a*b^3 + 2*A*b^4)*d*e^3 - (B*a^2*b^2 - 4*A*a*b^3)*e^4)*x^3 + 3*(3*B*b^4*d^3*e + (13*B*a*b^3 - 4*A*b^4)*d^2*e^2 - (11*B*a^2*b^2 + 16*A*a*b^3)*d*e^3 - 5*(B*a^3*b - 4*A*a^2*b^2)*e^4)*x^2 - (3*B*b^4*d^4 - 2*(13*B*a*b^3 + 2*A*b^4)*d^3*e - 18*(B*a^2*b^2 - 2*A*a*b^3)*d^2*e^2 + 6*(5*B*a^3*b + 2*A*a^2*b^2)*d*e^3 + 11*(B*a^4 - 4*A*a^3*b)*e^4)*x + 6*(3*B*a^3*b*d^2*e^2 + (B*a^4 - 4*A*a^3*b)*d*e^3 + (3*B*b^4*d*e^3 + (B*a*b^3 - 4*A*b^4)*e^4)*x^4 + (3*B*b^4*d^2*e^2 + 2*(5*B*a*b^3 - 2*A*b^4)*d*e^3 + 3*(B*a^2*b^2 - 4*A*a*b^3)*e^4)*x^3 + 3*(3*B*a*b^3*d^2*e^2 + 4*(B*a^2*b^2 - A*a*b^3)*d*e^3 + (B*a^3*b - 4*A*a^2*b^2)*e^4)*x^2 + (9*B*a^2*b^2*d^2*e^2 + 6*(B*a^3*b - 2*A*a^2*b^2)*d*e^3 + (B*a^4 - 4*A*a^3*b)*e^4)*x)*log(b*x + a) - 6*(3*B*a^3*b*d^2*e^2 + (B*a^4 - 4*A*a^3*b)*d*e^3 + (3*B*b^4*d*e^3 + (B*a*b^3 - 4*A*b^4)*e^4)*x^4 + (3*B*b^4*d^2*e^2 + 2*(5*B*a*b^3 - 2*A*b^4)*d*e^3 + 3*(B*a^2*b^2 - 4*A*a*b^3)*e^4)*x^3 + 3*(3*B*a*b^3*d^2*e^2 + 4*(B*a^2*b^2 - A*a*b^3)*d*e^3 + (B*a^3*b - 4*A*a^2*b^2)*e^4)*x^2 + (9*B*a^2*b^2*d^2*e^2 + 6*(B*a^3*b - 2*A*a^2*b^2)*d*e^3 + (B*a^4 - 4*A*a^3*b)*e^4)*x)*log(e*x + d))/(a^3*b^5*d^6 - 5*a^4*b^4*d^5*e + 10*a^5*b^3*d^4*e^2 - 10*a^6*b^2*d^3*e^3 + 5*a^7*b*d^2*e^4 - a^8*d*e^5 + (b^8*d^5*e - 5*a*b^7*d^4*e^2 + 10*a^2*b^6*d^3*e^3 - 10*a^3*b^5*d^2*e^4 + 5*a^4*b^4*d*e^5 - a^5*b^3*e^6)*x^4 + (b^8*d^6 - 2*a*b^7*d^5*e - 5*a^2*b^6*d^4*e^2 + 20*a^3*b^5*d^3*e^3 - 25*a^4*b^4*d^2*e^4 + 14*a^5*b^3*d*e^5 - 3*a^6*b^2*e^6)*x^3 + 3*(a*b^7*d^6 - 4*a^2*b^6*d^5*e + 5*a^3*b^5*d^4*e^2 - 5*a^5*b^3*d^2*e^4 + 4*a^6*b^2*d*e^5 - a^7*b*e^6)*x^2 + (3*a^2*b^6*d^6 - 14*a^3*b^5*d^5*e + 25*a^4*b^4*d^4*e^2 - 20*a^5*b^3*d^3*e^3 + 5*a^6*b^2*d^2*e^4 + 2*a^7*b*d*e^5 - a^8*e^6)*x)","B",0
1708,1,175,0,0.413221," ","integrate((B*x+A)*(e*x+d)^4*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{7} \, B b e^{4} x^{7} + A a d^{4} x + \frac{1}{6} \, {\left(4 \, B b d e^{3} + {\left(B a + A b\right)} e^{4}\right)} x^{6} + \frac{1}{5} \, {\left(6 \, B b d^{2} e^{2} + A a e^{4} + 4 \, {\left(B a + A b\right)} d e^{3}\right)} x^{5} + \frac{1}{2} \, {\left(2 \, B b d^{3} e + 2 \, A a d e^{3} + 3 \, {\left(B a + A b\right)} d^{2} e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(B b d^{4} + 6 \, A a d^{2} e^{2} + 4 \, {\left(B a + A b\right)} d^{3} e\right)} x^{3} + \frac{1}{2} \, {\left(4 \, A a d^{3} e + {\left(B a + A b\right)} d^{4}\right)} x^{2}"," ",0,"1/7*B*b*e^4*x^7 + A*a*d^4*x + 1/6*(4*B*b*d*e^3 + (B*a + A*b)*e^4)*x^6 + 1/5*(6*B*b*d^2*e^2 + A*a*e^4 + 4*(B*a + A*b)*d*e^3)*x^5 + 1/2*(2*B*b*d^3*e + 2*A*a*d*e^3 + 3*(B*a + A*b)*d^2*e^2)*x^4 + 1/3*(B*b*d^4 + 6*A*a*d^2*e^2 + 4*(B*a + A*b)*d^3*e)*x^3 + 1/2*(4*A*a*d^3*e + (B*a + A*b)*d^4)*x^2","A",0
1709,1,134,0,0.406443," ","integrate((B*x+A)*(e*x+d)^3*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, B b e^{3} x^{6} + A a d^{3} x + \frac{1}{5} \, {\left(3 \, B b d e^{2} + {\left(B a + A b\right)} e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(3 \, B b d^{2} e + A a e^{3} + 3 \, {\left(B a + A b\right)} d e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(B b d^{3} + 3 \, A a d e^{2} + 3 \, {\left(B a + A b\right)} d^{2} e\right)} x^{3} + \frac{1}{2} \, {\left(3 \, A a d^{2} e + {\left(B a + A b\right)} d^{3}\right)} x^{2}"," ",0,"1/6*B*b*e^3*x^6 + A*a*d^3*x + 1/5*(3*B*b*d*e^2 + (B*a + A*b)*e^3)*x^5 + 1/4*(3*B*b*d^2*e + A*a*e^3 + 3*(B*a + A*b)*d*e^2)*x^4 + 1/3*(B*b*d^3 + 3*A*a*d*e^2 + 3*(B*a + A*b)*d^2*e)*x^3 + 1/2*(3*A*a*d^2*e + (B*a + A*b)*d^3)*x^2","A",0
1710,1,93,0,0.409974," ","integrate((B*x+A)*(e*x+d)^2*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, B b e^{2} x^{5} + A a d^{2} x + \frac{1}{4} \, {\left(2 \, B b d e + {\left(B a + A b\right)} e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(B b d^{2} + A a e^{2} + 2 \, {\left(B a + A b\right)} d e\right)} x^{3} + \frac{1}{2} \, {\left(2 \, A a d e + {\left(B a + A b\right)} d^{2}\right)} x^{2}"," ",0,"1/5*B*b*e^2*x^5 + A*a*d^2*x + 1/4*(2*B*b*d*e + (B*a + A*b)*e^2)*x^4 + 1/3*(B*b*d^2 + A*a*e^2 + 2*(B*a + A*b)*d*e)*x^3 + 1/2*(2*A*a*d*e + (B*a + A*b)*d^2)*x^2","A",0
1711,1,52,0,0.413399," ","integrate((B*x+A)*(e*x+d)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, B b e x^{4} + A a d x + \frac{1}{3} \, {\left(B b d + {\left(B a + A b\right)} e\right)} x^{3} + \frac{1}{2} \, {\left(A a e + {\left(B a + A b\right)} d\right)} x^{2}"," ",0,"1/4*B*b*e*x^4 + A*a*d*x + 1/3*(B*b*d + (B*a + A*b)*e)*x^3 + 1/2*(A*a*e + (B*a + A*b)*d)*x^2","A",0
1712,1,24,0,0.415570," ","integrate((B*x+A)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, B b x^{3} + A a x + \frac{1}{2} \, {\left(B a + A b\right)} x^{2}"," ",0,"1/3*B*b*x^3 + A*a*x + 1/2*(B*a + A*b)*x^2","A",0
1713,1,68,0,0.424597," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\frac{B b e^{2} x^{2} - 2 \, {\left(B b d e - {\left(B a + A b\right)} e^{2}\right)} x + 2 \, {\left(B b d^{2} + A a e^{2} - {\left(B a + A b\right)} d e\right)} \log\left(e x + d\right)}{2 \, e^{3}}"," ",0,"1/2*(B*b*e^2*x^2 - 2*(B*b*d*e - (B*a + A*b)*e^2)*x + 2*(B*b*d^2 + A*a*e^2 - (B*a + A*b)*d*e)*log(e*x + d))/e^3","A",0
1714,1,102,0,0.422529," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{B b e^{2} x^{2} + B b d e x - B b d^{2} - A a e^{2} + {\left(B a + A b\right)} d e - {\left(2 \, B b d^{2} - {\left(B a + A b\right)} d e + {\left(2 \, B b d e - {\left(B a + A b\right)} e^{2}\right)} x\right)} \log\left(e x + d\right)}{e^{4} x + d e^{3}}"," ",0,"(B*b*e^2*x^2 + B*b*d*e*x - B*b*d^2 - A*a*e^2 + (B*a + A*b)*d*e - (2*B*b*d^2 - (B*a + A*b)*d*e + (2*B*b*d*e - (B*a + A*b)*e^2)*x)*log(e*x + d))/(e^4*x + d*e^3)","A",0
1715,1,105,0,0.438512," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{3 \, B b d^{2} - A a e^{2} - {\left(B a + A b\right)} d e + 2 \, {\left(2 \, B b d e - {\left(B a + A b\right)} e^{2}\right)} x + 2 \, {\left(B b e^{2} x^{2} + 2 \, B b d e x + B b d^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"1/2*(3*B*b*d^2 - A*a*e^2 - (B*a + A*b)*d*e + 2*(2*B*b*d*e - (B*a + A*b)*e^2)*x + 2*(B*b*e^2*x^2 + 2*B*b*d*e*x + B*b*d^2)*log(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
1716,1,93,0,0.412083," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{6 \, B b e^{2} x^{2} + 2 \, B b d^{2} + 2 \, A a e^{2} + {\left(B a + A b\right)} d e + 3 \, {\left(2 \, B b d e + {\left(B a + A b\right)} e^{2}\right)} x}{6 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/6*(6*B*b*e^2*x^2 + 2*B*b*d^2 + 2*A*a*e^2 + (B*a + A*b)*d*e + 3*(2*B*b*d*e + (B*a + A*b)*e^2)*x)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
1717,1,102,0,0.419032," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{6 \, B b e^{2} x^{2} + B b d^{2} + 3 \, A a e^{2} + {\left(B a + A b\right)} d e + 4 \, {\left(B b d e + {\left(B a + A b\right)} e^{2}\right)} x}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/12*(6*B*b*e^2*x^2 + B*b*d^2 + 3*A*a*e^2 + (B*a + A*b)*d*e + 4*(B*b*d*e + (B*a + A*b)*e^2)*x)/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","A",0
1718,1,117,0,0.417347," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{20 \, B b e^{2} x^{2} + 2 \, B b d^{2} + 12 \, A a e^{2} + 3 \, {\left(B a + A b\right)} d e + 5 \, {\left(2 \, B b d e + 3 \, {\left(B a + A b\right)} e^{2}\right)} x}{60 \, {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"-1/60*(20*B*b*e^2*x^2 + 2*B*b*d^2 + 12*A*a*e^2 + 3*(B*a + A*b)*d*e + 5*(2*B*b*d*e + 3*(B*a + A*b)*e^2)*x)/(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3)","A",0
1719,1,126,0,0.423772," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{15 \, B b e^{2} x^{2} + B b d^{2} + 10 \, A a e^{2} + 2 \, {\left(B a + A b\right)} d e + 6 \, {\left(B b d e + 2 \, {\left(B a + A b\right)} e^{2}\right)} x}{60 \, {\left(e^{9} x^{6} + 6 \, d e^{8} x^{5} + 15 \, d^{2} e^{7} x^{4} + 20 \, d^{3} e^{6} x^{3} + 15 \, d^{4} e^{5} x^{2} + 6 \, d^{5} e^{4} x + d^{6} e^{3}\right)}}"," ",0,"-1/60*(15*B*b*e^2*x^2 + B*b*d^2 + 10*A*a*e^2 + 2*(B*a + A*b)*d*e + 6*(B*b*d*e + 2*(B*a + A*b)*e^2)*x)/(e^9*x^6 + 6*d*e^8*x^5 + 15*d^2*e^7*x^4 + 20*d^3*e^6*x^3 + 15*d^4*e^5*x^2 + 6*d^5*e^4*x + d^6*e^3)","A",0
1720,1,518,0,0.438909," ","integrate((B*x+A)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{10} \, B b^{3} e^{5} x^{10} + A a^{3} d^{5} x + \frac{1}{9} \, {\left(5 \, B b^{3} d e^{4} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} x^{9} + \frac{1}{8} \, {\left(10 \, B b^{3} d^{2} e^{3} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} x^{8} + \frac{1}{7} \, {\left(10 \, B b^{3} d^{3} e^{2} + 10 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{3} + 15 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} x^{7} + \frac{1}{6} \, {\left(5 \, B b^{3} d^{4} e + A a^{3} e^{5} + 10 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{2} + 30 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{3} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} x^{6} + \frac{1}{5} \, {\left(B b^{3} d^{5} + 5 \, A a^{3} d e^{4} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e + 30 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{2} + 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(10 \, A a^{3} d^{2} e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{5} + 15 \, {\left(B a^{2} b + A a b^{2}\right)} d^{4} e + 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3} e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(10 \, A a^{3} d^{3} e^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{5} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{4} e\right)} x^{3} + \frac{1}{2} \, {\left(5 \, A a^{3} d^{4} e + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{5}\right)} x^{2}"," ",0,"1/10*B*b^3*e^5*x^10 + A*a^3*d^5*x + 1/9*(5*B*b^3*d*e^4 + (3*B*a*b^2 + A*b^3)*e^5)*x^9 + 1/8*(10*B*b^3*d^2*e^3 + 5*(3*B*a*b^2 + A*b^3)*d*e^4 + 3*(B*a^2*b + A*a*b^2)*e^5)*x^8 + 1/7*(10*B*b^3*d^3*e^2 + 10*(3*B*a*b^2 + A*b^3)*d^2*e^3 + 15*(B*a^2*b + A*a*b^2)*d*e^4 + (B*a^3 + 3*A*a^2*b)*e^5)*x^7 + 1/6*(5*B*b^3*d^4*e + A*a^3*e^5 + 10*(3*B*a*b^2 + A*b^3)*d^3*e^2 + 30*(B*a^2*b + A*a*b^2)*d^2*e^3 + 5*(B*a^3 + 3*A*a^2*b)*d*e^4)*x^6 + 1/5*(B*b^3*d^5 + 5*A*a^3*d*e^4 + 5*(3*B*a*b^2 + A*b^3)*d^4*e + 30*(B*a^2*b + A*a*b^2)*d^3*e^2 + 10*(B*a^3 + 3*A*a^2*b)*d^2*e^3)*x^5 + 1/4*(10*A*a^3*d^2*e^3 + (3*B*a*b^2 + A*b^3)*d^5 + 15*(B*a^2*b + A*a*b^2)*d^4*e + 10*(B*a^3 + 3*A*a^2*b)*d^3*e^2)*x^4 + 1/3*(10*A*a^3*d^3*e^2 + 3*(B*a^2*b + A*a*b^2)*d^5 + 5*(B*a^3 + 3*A*a^2*b)*d^4*e)*x^3 + 1/2*(5*A*a^3*d^4*e + (B*a^3 + 3*A*a^2*b)*d^5)*x^2","B",0
1721,1,425,0,0.420458," ","integrate((B*x+A)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{9} \, B b^{3} e^{4} x^{9} + A a^{3} d^{4} x + \frac{1}{8} \, {\left(4 \, B b^{3} d e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{8} + \frac{1}{7} \, {\left(6 \, B b^{3} d^{2} e^{2} + 4 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{7} + \frac{1}{6} \, {\left(4 \, B b^{3} d^{3} e + 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 12 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x^{6} + \frac{1}{5} \, {\left(B b^{3} d^{4} + A a^{3} e^{4} + 4 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 18 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 4 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(4 \, A a^{3} d e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} + 12 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e + 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(6 \, A a^{3} d^{2} e^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{4} + 4 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3} e\right)} x^{3} + \frac{1}{2} \, {\left(4 \, A a^{3} d^{3} e + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{4}\right)} x^{2}"," ",0,"1/9*B*b^3*e^4*x^9 + A*a^3*d^4*x + 1/8*(4*B*b^3*d*e^3 + (3*B*a*b^2 + A*b^3)*e^4)*x^8 + 1/7*(6*B*b^3*d^2*e^2 + 4*(3*B*a*b^2 + A*b^3)*d*e^3 + 3*(B*a^2*b + A*a*b^2)*e^4)*x^7 + 1/6*(4*B*b^3*d^3*e + 6*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 12*(B*a^2*b + A*a*b^2)*d*e^3 + (B*a^3 + 3*A*a^2*b)*e^4)*x^6 + 1/5*(B*b^3*d^4 + A*a^3*e^4 + 4*(3*B*a*b^2 + A*b^3)*d^3*e + 18*(B*a^2*b + A*a*b^2)*d^2*e^2 + 4*(B*a^3 + 3*A*a^2*b)*d*e^3)*x^5 + 1/4*(4*A*a^3*d*e^3 + (3*B*a*b^2 + A*b^3)*d^4 + 12*(B*a^2*b + A*a*b^2)*d^3*e + 6*(B*a^3 + 3*A*a^2*b)*d^2*e^2)*x^4 + 1/3*(6*A*a^3*d^2*e^2 + 3*(B*a^2*b + A*a*b^2)*d^4 + 4*(B*a^3 + 3*A*a^2*b)*d^3*e)*x^3 + 1/2*(4*A*a^3*d^3*e + (B*a^3 + 3*A*a^2*b)*d^4)*x^2","A",0
1722,1,325,0,0.430860," ","integrate((B*x+A)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{8} \, B b^{3} e^{3} x^{8} + A a^{3} d^{3} x + \frac{1}{7} \, {\left(3 \, B b^{3} d e^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{3}\right)} x^{7} + \frac{1}{2} \, {\left(B b^{3} d^{2} e + {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{2} + {\left(B a^{2} b + A a b^{2}\right)} e^{3}\right)} x^{6} + \frac{1}{5} \, {\left(B b^{3} d^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e + 9 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(A a^{3} e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} + 9 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{2}\right)} x^{4} + {\left(A a^{3} d e^{2} + {\left(B a^{2} b + A a b^{2}\right)} d^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e\right)} x^{3} + \frac{1}{2} \, {\left(3 \, A a^{3} d^{2} e + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3}\right)} x^{2}"," ",0,"1/8*B*b^3*e^3*x^8 + A*a^3*d^3*x + 1/7*(3*B*b^3*d*e^2 + (3*B*a*b^2 + A*b^3)*e^3)*x^7 + 1/2*(B*b^3*d^2*e + (3*B*a*b^2 + A*b^3)*d*e^2 + (B*a^2*b + A*a*b^2)*e^3)*x^6 + 1/5*(B*b^3*d^3 + 3*(3*B*a*b^2 + A*b^3)*d^2*e + 9*(B*a^2*b + A*a*b^2)*d*e^2 + (B*a^3 + 3*A*a^2*b)*e^3)*x^5 + 1/4*(A*a^3*e^3 + (3*B*a*b^2 + A*b^3)*d^3 + 9*(B*a^2*b + A*a*b^2)*d^2*e + 3*(B*a^3 + 3*A*a^2*b)*d*e^2)*x^4 + (A*a^3*d*e^2 + (B*a^2*b + A*a*b^2)*d^3 + (B*a^3 + 3*A*a^2*b)*d^2*e)*x^3 + 1/2*(3*A*a^3*d^2*e + (B*a^3 + 3*A*a^2*b)*d^3)*x^2","A",0
1723,1,239,0,0.409410," ","integrate((B*x+A)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{7} \, B b^{3} e^{2} x^{7} + A a^{3} d^{2} x + \frac{1}{6} \, {\left(2 \, B b^{3} d e + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{2}\right)} x^{6} + \frac{1}{5} \, {\left(B b^{3} d^{2} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{2}\right)} x^{5} + \frac{1}{4} \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d e + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(A a^{3} e^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e\right)} x^{3} + \frac{1}{2} \, {\left(2 \, A a^{3} d e + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2}\right)} x^{2}"," ",0,"1/7*B*b^3*e^2*x^7 + A*a^3*d^2*x + 1/6*(2*B*b^3*d*e + (3*B*a*b^2 + A*b^3)*e^2)*x^6 + 1/5*(B*b^3*d^2 + 2*(3*B*a*b^2 + A*b^3)*d*e + 3*(B*a^2*b + A*a*b^2)*e^2)*x^5 + 1/4*((3*B*a*b^2 + A*b^3)*d^2 + 6*(B*a^2*b + A*a*b^2)*d*e + (B*a^3 + 3*A*a^2*b)*e^2)*x^4 + 1/3*(A*a^3*e^2 + 3*(B*a^2*b + A*a*b^2)*d^2 + 2*(B*a^3 + 3*A*a^2*b)*d*e)*x^3 + 1/2*(2*A*a^3*d*e + (B*a^3 + 3*A*a^2*b)*d^2)*x^2","A",0
1724,1,146,0,0.412289," ","integrate((B*x+A)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{6} \, B b^{3} e x^{6} + A a^{3} d x + \frac{1}{5} \, {\left(B b^{3} d + {\left(3 \, B a b^{2} + A b^{3}\right)} e\right)} x^{5} + \frac{1}{4} \, {\left({\left(3 \, B a b^{2} + A b^{3}\right)} d + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e\right)} x^{4} + \frac{1}{3} \, {\left(3 \, {\left(B a^{2} b + A a b^{2}\right)} d + {\left(B a^{3} + 3 \, A a^{2} b\right)} e\right)} x^{3} + \frac{1}{2} \, {\left(A a^{3} e + {\left(B a^{3} + 3 \, A a^{2} b\right)} d\right)} x^{2}"," ",0,"1/6*B*b^3*e*x^6 + A*a^3*d*x + 1/5*(B*b^3*d + (3*B*a*b^2 + A*b^3)*e)*x^5 + 1/4*((3*B*a*b^2 + A*b^3)*d + 3*(B*a^2*b + A*a*b^2)*e)*x^4 + 1/3*(3*(B*a^2*b + A*a*b^2)*d + (B*a^3 + 3*A*a^2*b)*e)*x^3 + 1/2*(A*a^3*e + (B*a^3 + 3*A*a^2*b)*d)*x^2","A",0
1725,1,69,0,0.411786," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{5} \, B b^{3} x^{5} + A a^{3} x + \frac{1}{4} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{4} + {\left(B a^{2} b + A a b^{2}\right)} x^{3} + \frac{1}{2} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}"," ",0,"1/5*B*b^3*x^5 + A*a^3*x + 1/4*(3*B*a*b^2 + A*b^3)*x^4 + (B*a^2*b + A*a*b^2)*x^3 + 1/2*(B*a^3 + 3*A*a^2*b)*x^2","A",0
1726,1,260,0,0.427592," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\frac{3 \, B b^{3} e^{4} x^{4} - 4 \, {\left(B b^{3} d e^{3} - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 6 \, {\left(B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - 12 \, {\left(B b^{3} d^{3} e - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x + 12 \, {\left(B b^{3} d^{4} + A a^{3} e^{4} - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3}\right)} \log\left(e x + d\right)}{12 \, e^{5}}"," ",0,"1/12*(3*B*b^3*e^4*x^4 - 4*(B*b^3*d*e^3 - (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 6*(B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3 + 3*(B*a^2*b + A*a*b^2)*e^4)*x^2 - 12*(B*b^3*d^3*e - (3*B*a*b^2 + A*b^3)*d^2*e^2 + 3*(B*a^2*b + A*a*b^2)*d*e^3 - (B*a^3 + 3*A*a^2*b)*e^4)*x + 12*(B*b^3*d^4 + A*a^3*e^4 - (3*B*a*b^2 + A*b^3)*d^3*e + 3*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3)*log(e*x + d))/e^5","A",0
1727,1,396,0,0.421727," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{2 \, B b^{3} e^{4} x^{4} - 6 \, B b^{3} d^{4} - 6 \, A a^{3} e^{4} + 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 18 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - {\left(4 \, B b^{3} d e^{3} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(4 \, B b^{3} d^{2} e^{2} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 6 \, {\left(3 \, B b^{3} d^{3} e - 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3}\right)} x - 6 \, {\left(4 \, B b^{3} d^{4} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + {\left(4 \, B b^{3} d^{3} e - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"1/6*(2*B*b^3*e^4*x^4 - 6*B*b^3*d^4 - 6*A*a^3*e^4 + 6*(3*B*a*b^2 + A*b^3)*d^3*e - 18*(B*a^2*b + A*a*b^2)*d^2*e^2 + 6*(B*a^3 + 3*A*a^2*b)*d*e^3 - (4*B*b^3*d*e^3 - 3*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 3*(4*B*b^3*d^2*e^2 - 3*(3*B*a*b^2 + A*b^3)*d*e^3 + 6*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 6*(3*B*b^3*d^3*e - 2*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 3*(B*a^2*b + A*a*b^2)*d*e^3)*x - 6*(4*B*b^3*d^4 - 3*(3*B*a*b^2 + A*b^3)*d^3*e + 6*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3 + (4*B*b^3*d^3*e - 3*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 6*(B*a^2*b + A*a*b^2)*d*e^3 - (B*a^3 + 3*A*a^2*b)*e^4)*x)*log(e*x + d))/(e^6*x + d*e^5)","A",0
1728,1,420,0,0.429874," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{B b^{3} e^{4} x^{4} + 7 \, B b^{3} d^{4} - A a^{3} e^{4} - 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 9 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - 2 \, {\left(2 \, B b^{3} d e^{3} - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} - {\left(11 \, B b^{3} d^{2} e^{2} - 4 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3}\right)} x^{2} + 2 \, {\left(B b^{3} d^{3} e - 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x + 6 \, {\left(2 \, B b^{3} d^{4} - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + {\left(2 \, B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, B b^{3} d^{3} e - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + {\left(B a^{2} b + A a b^{2}\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"1/2*(B*b^3*e^4*x^4 + 7*B*b^3*d^4 - A*a^3*e^4 - 5*(3*B*a*b^2 + A*b^3)*d^3*e + 9*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3 - 2*(2*B*b^3*d*e^3 - (3*B*a*b^2 + A*b^3)*e^4)*x^3 - (11*B*b^3*d^2*e^2 - 4*(3*B*a*b^2 + A*b^3)*d*e^3)*x^2 + 2*(B*b^3*d^3*e - 2*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 6*(B*a^2*b + A*a*b^2)*d*e^3 - (B*a^3 + 3*A*a^2*b)*e^4)*x + 6*(2*B*b^3*d^4 - (3*B*a*b^2 + A*b^3)*d^3*e + (B*a^2*b + A*a*b^2)*d^2*e^2 + (2*B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3 + (B*a^2*b + A*a*b^2)*e^4)*x^2 + 2*(2*B*b^3*d^3*e - (3*B*a*b^2 + A*b^3)*d^2*e^2 + (B*a^2*b + A*a*b^2)*d*e^3)*x)*log(e*x + d))/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
1729,1,406,0,0.422822," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{6 \, B b^{3} e^{4} x^{4} + 18 \, B b^{3} d e^{3} x^{3} - 26 \, B b^{3} d^{4} - 2 \, A a^{3} e^{4} + 11 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 6 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - 18 \, {\left(B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - 3 \, {\left(18 \, B b^{3} d^{3} e - 9 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x - 6 \, {\left(4 \, B b^{3} d^{4} - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + {\left(4 \, B b^{3} d e^{3} - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(4 \, B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3}\right)} x^{2} + 3 \, {\left(4 \, B b^{3} d^{3} e - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"1/6*(6*B*b^3*e^4*x^4 + 18*B*b^3*d*e^3*x^3 - 26*B*b^3*d^4 - 2*A*a^3*e^4 + 11*(3*B*a*b^2 + A*b^3)*d^3*e - 6*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3 - 18*(B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3 + (B*a^2*b + A*a*b^2)*e^4)*x^2 - 3*(18*B*b^3*d^3*e - 9*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 6*(B*a^2*b + A*a*b^2)*d*e^3 + (B*a^3 + 3*A*a^2*b)*e^4)*x - 6*(4*B*b^3*d^4 - (3*B*a*b^2 + A*b^3)*d^3*e + (4*B*b^3*d*e^3 - (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 3*(4*B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3)*x^2 + 3*(4*B*b^3*d^3*e - (3*B*a*b^2 + A*b^3)*d^2*e^2)*x)*log(e*x + d))/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
1730,1,354,0,0.425717," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{25 \, B b^{3} d^{4} - 3 \, A a^{3} e^{4} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 12 \, {\left(4 \, B b^{3} d e^{3} - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 18 \, {\left(6 \, B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} - {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 4 \, {\left(22 \, B b^{3} d^{3} e - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} - 3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x + 12 \, {\left(B b^{3} e^{4} x^{4} + 4 \, B b^{3} d e^{3} x^{3} + 6 \, B b^{3} d^{2} e^{2} x^{2} + 4 \, B b^{3} d^{3} e x + B b^{3} d^{4}\right)} \log\left(e x + d\right)}{12 \, {\left(e^{9} x^{4} + 4 \, d e^{8} x^{3} + 6 \, d^{2} e^{7} x^{2} + 4 \, d^{3} e^{6} x + d^{4} e^{5}\right)}}"," ",0,"1/12*(25*B*b^3*d^4 - 3*A*a^3*e^4 - 3*(3*B*a*b^2 + A*b^3)*d^3*e - 3*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3 + 12*(4*B*b^3*d*e^3 - (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 18*(6*B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3 - (B*a^2*b + A*a*b^2)*e^4)*x^2 + 4*(22*B*b^3*d^3*e - 3*(3*B*a*b^2 + A*b^3)*d^2*e^2 - 3*(B*a^2*b + A*a*b^2)*d*e^3 - (B*a^3 + 3*A*a^2*b)*e^4)*x + 12*(B*b^3*e^4*x^4 + 4*B*b^3*d*e^3*x^3 + 6*B*b^3*d^2*e^2*x^2 + 4*B*b^3*d^3*e*x + B*b^3*d^4)*log(e*x + d))/(e^9*x^4 + 4*d*e^8*x^3 + 6*d^2*e^7*x^2 + 4*d^3*e^6*x + d^4*e^5)","A",0
1731,1,304,0,0.406527," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{20 \, B b^{3} e^{4} x^{4} + 4 \, B b^{3} d^{4} + 4 \, A a^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 2 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 10 \, {\left(4 \, B b^{3} d e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 10 \, {\left(4 \, B b^{3} d^{2} e^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 2 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 5 \, {\left(4 \, B b^{3} d^{3} e + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 2 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{20 \, {\left(e^{10} x^{5} + 5 \, d e^{9} x^{4} + 10 \, d^{2} e^{8} x^{3} + 10 \, d^{3} e^{7} x^{2} + 5 \, d^{4} e^{6} x + d^{5} e^{5}\right)}}"," ",0,"-1/20*(20*B*b^3*e^4*x^4 + 4*B*b^3*d^4 + 4*A*a^3*e^4 + (3*B*a*b^2 + A*b^3)*d^3*e + 2*(B*a^2*b + A*a*b^2)*d^2*e^2 + (B*a^3 + 3*A*a^2*b)*d*e^3 + 10*(4*B*b^3*d*e^3 + (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 10*(4*B*b^3*d^2*e^2 + (3*B*a*b^2 + A*b^3)*d*e^3 + 2*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 5*(4*B*b^3*d^3*e + (3*B*a*b^2 + A*b^3)*d^2*e^2 + 2*(B*a^2*b + A*a*b^2)*d*e^3 + (B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^10*x^5 + 5*d*e^9*x^4 + 10*d^2*e^8*x^3 + 10*d^3*e^7*x^2 + 5*d^4*e^6*x + d^5*e^5)","B",0
1732,1,317,0,0.422824," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{30 \, B b^{3} e^{4} x^{4} + 2 \, B b^{3} d^{4} + 10 \, A a^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 20 \, {\left(2 \, B b^{3} d e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 15 \, {\left(2 \, B b^{3} d^{2} e^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 6 \, {\left(2 \, B b^{3} d^{3} e + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{60 \, {\left(e^{11} x^{6} + 6 \, d e^{10} x^{5} + 15 \, d^{2} e^{9} x^{4} + 20 \, d^{3} e^{8} x^{3} + 15 \, d^{4} e^{7} x^{2} + 6 \, d^{5} e^{6} x + d^{6} e^{5}\right)}}"," ",0,"-1/60*(30*B*b^3*e^4*x^4 + 2*B*b^3*d^4 + 10*A*a^3*e^4 + (3*B*a*b^2 + A*b^3)*d^3*e + 3*(B*a^2*b + A*a*b^2)*d^2*e^2 + 2*(B*a^3 + 3*A*a^2*b)*d*e^3 + 20*(2*B*b^3*d*e^3 + (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 15*(2*B*b^3*d^2*e^2 + (3*B*a*b^2 + A*b^3)*d*e^3 + 3*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 6*(2*B*b^3*d^3*e + (3*B*a*b^2 + A*b^3)*d^2*e^2 + 3*(B*a^2*b + A*a*b^2)*d*e^3 + 2*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^11*x^6 + 6*d*e^10*x^5 + 15*d^2*e^9*x^4 + 20*d^3*e^8*x^3 + 15*d^4*e^7*x^2 + 6*d^5*e^6*x + d^6*e^5)","B",0
1733,1,332,0,0.411737," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{140 \, B b^{3} e^{4} x^{4} + 4 \, B b^{3} d^{4} + 60 \, A a^{3} e^{4} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 12 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 35 \, {\left(4 \, B b^{3} d e^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 21 \, {\left(4 \, B b^{3} d^{2} e^{2} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 12 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 7 \, {\left(4 \, B b^{3} d^{3} e + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 12 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{420 \, {\left(e^{12} x^{7} + 7 \, d e^{11} x^{6} + 21 \, d^{2} e^{10} x^{5} + 35 \, d^{3} e^{9} x^{4} + 35 \, d^{4} e^{8} x^{3} + 21 \, d^{5} e^{7} x^{2} + 7 \, d^{6} e^{6} x + d^{7} e^{5}\right)}}"," ",0,"-1/420*(140*B*b^3*e^4*x^4 + 4*B*b^3*d^4 + 60*A*a^3*e^4 + 3*(3*B*a*b^2 + A*b^3)*d^3*e + 12*(B*a^2*b + A*a*b^2)*d^2*e^2 + 10*(B*a^3 + 3*A*a^2*b)*d*e^3 + 35*(4*B*b^3*d*e^3 + 3*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 21*(4*B*b^3*d^2*e^2 + 3*(3*B*a*b^2 + A*b^3)*d*e^3 + 12*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 7*(4*B*b^3*d^3*e + 3*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 12*(B*a^2*b + A*a*b^2)*d*e^3 + 10*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^12*x^7 + 7*d*e^11*x^6 + 21*d^2*e^10*x^5 + 35*d^3*e^9*x^4 + 35*d^4*e^8*x^3 + 21*d^5*e^7*x^2 + 7*d^6*e^6*x + d^7*e^5)","A",0
1734,1,335,0,0.435182," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{70 \, B b^{3} e^{4} x^{4} + B b^{3} d^{4} + 35 \, A a^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 5 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 56 \, {\left(B b^{3} d e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 28 \, {\left(B b^{3} d^{2} e^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 5 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 8 \, {\left(B b^{3} d^{3} e + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 5 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{280 \, {\left(e^{13} x^{8} + 8 \, d e^{12} x^{7} + 28 \, d^{2} e^{11} x^{6} + 56 \, d^{3} e^{10} x^{5} + 70 \, d^{4} e^{9} x^{4} + 56 \, d^{5} e^{8} x^{3} + 28 \, d^{6} e^{7} x^{2} + 8 \, d^{7} e^{6} x + d^{8} e^{5}\right)}}"," ",0,"-1/280*(70*B*b^3*e^4*x^4 + B*b^3*d^4 + 35*A*a^3*e^4 + (3*B*a*b^2 + A*b^3)*d^3*e + 5*(B*a^2*b + A*a*b^2)*d^2*e^2 + 5*(B*a^3 + 3*A*a^2*b)*d*e^3 + 56*(B*b^3*d*e^3 + (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 28*(B*b^3*d^2*e^2 + (3*B*a*b^2 + A*b^3)*d*e^3 + 5*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 8*(B*b^3*d^3*e + (3*B*a*b^2 + A*b^3)*d^2*e^2 + 5*(B*a^2*b + A*a*b^2)*d*e^3 + 5*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^13*x^8 + 8*d*e^12*x^7 + 28*d^2*e^11*x^6 + 56*d^3*e^10*x^5 + 70*d^4*e^9*x^4 + 56*d^5*e^8*x^3 + 28*d^6*e^7*x^2 + 8*d^7*e^6*x + d^8*e^5)","A",0
1735,1,354,0,0.435327," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{504 \, B b^{3} e^{4} x^{4} + 4 \, B b^{3} d^{4} + 280 \, A a^{3} e^{4} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 30 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 84 \, {\left(4 \, B b^{3} d e^{3} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 36 \, {\left(4 \, B b^{3} d^{2} e^{2} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 30 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 9 \, {\left(4 \, B b^{3} d^{3} e + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 30 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{2520 \, {\left(e^{14} x^{9} + 9 \, d e^{13} x^{8} + 36 \, d^{2} e^{12} x^{7} + 84 \, d^{3} e^{11} x^{6} + 126 \, d^{4} e^{10} x^{5} + 126 \, d^{5} e^{9} x^{4} + 84 \, d^{6} e^{8} x^{3} + 36 \, d^{7} e^{7} x^{2} + 9 \, d^{8} e^{6} x + d^{9} e^{5}\right)}}"," ",0,"-1/2520*(504*B*b^3*e^4*x^4 + 4*B*b^3*d^4 + 280*A*a^3*e^4 + 5*(3*B*a*b^2 + A*b^3)*d^3*e + 30*(B*a^2*b + A*a*b^2)*d^2*e^2 + 35*(B*a^3 + 3*A*a^2*b)*d*e^3 + 84*(4*B*b^3*d*e^3 + 5*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 36*(4*B*b^3*d^2*e^2 + 5*(3*B*a*b^2 + A*b^3)*d*e^3 + 30*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 9*(4*B*b^3*d^3*e + 5*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 30*(B*a^2*b + A*a*b^2)*d*e^3 + 35*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^14*x^9 + 9*d*e^13*x^8 + 36*d^2*e^12*x^7 + 84*d^3*e^11*x^6 + 126*d^4*e^10*x^5 + 126*d^5*e^9*x^4 + 84*d^6*e^8*x^3 + 36*d^7*e^7*x^2 + 9*d^8*e^6*x + d^9*e^5)","A",0
1736,1,365,0,0.425828," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{420 \, B b^{3} e^{4} x^{4} + 2 \, B b^{3} d^{4} + 252 \, A a^{3} e^{4} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 21 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 28 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 120 \, {\left(2 \, B b^{3} d e^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 45 \, {\left(2 \, B b^{3} d^{2} e^{2} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 21 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 10 \, {\left(2 \, B b^{3} d^{3} e + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 21 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 28 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{2520 \, {\left(e^{15} x^{10} + 10 \, d e^{14} x^{9} + 45 \, d^{2} e^{13} x^{8} + 120 \, d^{3} e^{12} x^{7} + 210 \, d^{4} e^{11} x^{6} + 252 \, d^{5} e^{10} x^{5} + 210 \, d^{6} e^{9} x^{4} + 120 \, d^{7} e^{8} x^{3} + 45 \, d^{8} e^{7} x^{2} + 10 \, d^{9} e^{6} x + d^{10} e^{5}\right)}}"," ",0,"-1/2520*(420*B*b^3*e^4*x^4 + 2*B*b^3*d^4 + 252*A*a^3*e^4 + 3*(3*B*a*b^2 + A*b^3)*d^3*e + 21*(B*a^2*b + A*a*b^2)*d^2*e^2 + 28*(B*a^3 + 3*A*a^2*b)*d*e^3 + 120*(2*B*b^3*d*e^3 + 3*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 45*(2*B*b^3*d^2*e^2 + 3*(3*B*a*b^2 + A*b^3)*d*e^3 + 21*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 10*(2*B*b^3*d^3*e + 3*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 21*(B*a^2*b + A*a*b^2)*d*e^3 + 28*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^15*x^10 + 10*d*e^14*x^9 + 45*d^2*e^13*x^8 + 120*d^3*e^12*x^7 + 210*d^4*e^11*x^6 + 252*d^5*e^10*x^5 + 210*d^6*e^9*x^4 + 120*d^7*e^8*x^3 + 45*d^8*e^7*x^2 + 10*d^9*e^6*x + d^10*e^5)","A",0
1737,1,376,0,0.414608," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{1320 \, B b^{3} e^{4} x^{4} + 4 \, B b^{3} d^{4} + 840 \, A a^{3} e^{4} + 7 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 56 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 84 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 165 \, {\left(4 \, B b^{3} d e^{3} + 7 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 55 \, {\left(4 \, B b^{3} d^{2} e^{2} + 7 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 56 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 11 \, {\left(4 \, B b^{3} d^{3} e + 7 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 56 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 84 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{9240 \, {\left(e^{16} x^{11} + 11 \, d e^{15} x^{10} + 55 \, d^{2} e^{14} x^{9} + 165 \, d^{3} e^{13} x^{8} + 330 \, d^{4} e^{12} x^{7} + 462 \, d^{5} e^{11} x^{6} + 462 \, d^{6} e^{10} x^{5} + 330 \, d^{7} e^{9} x^{4} + 165 \, d^{8} e^{8} x^{3} + 55 \, d^{9} e^{7} x^{2} + 11 \, d^{10} e^{6} x + d^{11} e^{5}\right)}}"," ",0,"-1/9240*(1320*B*b^3*e^4*x^4 + 4*B*b^3*d^4 + 840*A*a^3*e^4 + 7*(3*B*a*b^2 + A*b^3)*d^3*e + 56*(B*a^2*b + A*a*b^2)*d^2*e^2 + 84*(B*a^3 + 3*A*a^2*b)*d*e^3 + 165*(4*B*b^3*d*e^3 + 7*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 55*(4*B*b^3*d^2*e^2 + 7*(3*B*a*b^2 + A*b^3)*d*e^3 + 56*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 11*(4*B*b^3*d^3*e + 7*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 56*(B*a^2*b + A*a*b^2)*d*e^3 + 84*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^16*x^11 + 11*d*e^15*x^10 + 55*d^2*e^14*x^9 + 165*d^3*e^13*x^8 + 330*d^4*e^12*x^7 + 462*d^5*e^11*x^6 + 462*d^6*e^10*x^5 + 330*d^7*e^9*x^4 + 165*d^8*e^8*x^3 + 55*d^9*e^7*x^2 + 11*d^10*e^6*x + d^11*e^5)","A",0
1738,1,964,0,0.430596," ","integrate((B*x+A)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{13} \, B b^{5} e^{6} x^{13} + A a^{5} d^{6} x + \frac{1}{12} \, {\left(6 \, B b^{5} d e^{5} + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{12} + \frac{1}{11} \, {\left(15 \, B b^{5} d^{2} e^{4} + 6 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{11} + \frac{1}{2} \, {\left(4 \, B b^{5} d^{3} e^{3} + 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 6 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + 2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{10} + \frac{5}{9} \, {\left(3 \, B b^{5} d^{4} e^{2} + 4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 15 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 12 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{9} + \frac{1}{8} \, {\left(6 \, B b^{5} d^{5} e + 15 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 100 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 150 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x^{8} + \frac{1}{7} \, {\left(B b^{5} d^{6} + A a^{5} e^{6} + 6 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 75 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 200 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 75 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + 6 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5}\right)} x^{7} + \frac{1}{6} \, {\left(6 \, A a^{5} d e^{5} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{6} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{5} e + 150 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e^{2} + 100 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{3} + 15 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{4}\right)} x^{6} + {\left(3 \, A a^{5} d^{2} e^{4} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{6} + 12 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{5} e + 15 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{4} e^{2} + 4 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{3} e^{3}\right)} x^{5} + \frac{5}{4} \, {\left(4 \, A a^{5} d^{3} e^{3} + 2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{6} + 6 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{5} e + 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{4} e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(15 \, A a^{5} d^{4} e^{2} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{6} + 6 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{5} e\right)} x^{3} + \frac{1}{2} \, {\left(6 \, A a^{5} d^{5} e + {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{6}\right)} x^{2}"," ",0,"1/13*B*b^5*e^6*x^13 + A*a^5*d^6*x + 1/12*(6*B*b^5*d*e^5 + (5*B*a*b^4 + A*b^5)*e^6)*x^12 + 1/11*(15*B*b^5*d^2*e^4 + 6*(5*B*a*b^4 + A*b^5)*d*e^5 + 5*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^11 + 1/2*(4*B*b^5*d^3*e^3 + 3*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 6*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + 2*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^10 + 5/9*(3*B*b^5*d^4*e^2 + 4*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 15*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 12*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + (B*a^4*b + 2*A*a^3*b^2)*e^6)*x^9 + 1/8*(6*B*b^5*d^5*e + 15*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 100*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 150*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 30*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + (B*a^5 + 5*A*a^4*b)*e^6)*x^8 + 1/7*(B*b^5*d^6 + A*a^5*e^6 + 6*(5*B*a*b^4 + A*b^5)*d^5*e + 75*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 200*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 75*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + 6*(B*a^5 + 5*A*a^4*b)*d*e^5)*x^7 + 1/6*(6*A*a^5*d*e^5 + (5*B*a*b^4 + A*b^5)*d^6 + 30*(2*B*a^2*b^3 + A*a*b^4)*d^5*e + 150*(B*a^3*b^2 + A*a^2*b^3)*d^4*e^2 + 100*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^3 + 15*(B*a^5 + 5*A*a^4*b)*d^2*e^4)*x^6 + (3*A*a^5*d^2*e^4 + (2*B*a^2*b^3 + A*a*b^4)*d^6 + 12*(B*a^3*b^2 + A*a^2*b^3)*d^5*e + 15*(B*a^4*b + 2*A*a^3*b^2)*d^4*e^2 + 4*(B*a^5 + 5*A*a^4*b)*d^3*e^3)*x^5 + 5/4*(4*A*a^5*d^3*e^3 + 2*(B*a^3*b^2 + A*a^2*b^3)*d^6 + 6*(B*a^4*b + 2*A*a^3*b^2)*d^5*e + 3*(B*a^5 + 5*A*a^4*b)*d^4*e^2)*x^4 + 1/3*(15*A*a^5*d^4*e^2 + 5*(B*a^4*b + 2*A*a^3*b^2)*d^6 + 6*(B*a^5 + 5*A*a^4*b)*d^5*e)*x^3 + 1/2*(6*A*a^5*d^5*e + (B*a^5 + 5*A*a^4*b)*d^6)*x^2","B",0
1739,1,813,0,0.424914," ","integrate((B*x+A)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{12} \, B b^{5} e^{5} x^{12} + A a^{5} d^{5} x + \frac{1}{11} \, {\left(5 \, B b^{5} d e^{4} + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{5}\right)} x^{11} + \frac{1}{2} \, {\left(2 \, B b^{5} d^{2} e^{3} + {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{4} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{5}\right)} x^{10} + \frac{5}{9} \, {\left(2 \, B b^{5} d^{3} e^{2} + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{3} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{4} + 2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{5}\right)} x^{9} + \frac{5}{8} \, {\left(B b^{5} d^{4} e + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{2} + 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{3} + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{4} + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{8} + \frac{1}{7} \, {\left(B b^{5} d^{5} + 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e + 50 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{2} + 100 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{3} + 25 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{4} + {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{5}\right)} x^{7} + \frac{1}{6} \, {\left(A a^{5} e^{5} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} + 25 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e + 100 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{2} + 50 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{3} + 5 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{4}\right)} x^{6} + {\left(A a^{5} d e^{4} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{5} + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{2} + 2 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{3}\right)} x^{5} + \frac{5}{4} \, {\left(2 \, A a^{5} d^{2} e^{3} + 2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{5} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{4} e + 2 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{3} e^{2}\right)} x^{4} + \frac{5}{3} \, {\left(2 \, A a^{5} d^{3} e^{2} + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{5} + {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{4} e\right)} x^{3} + \frac{1}{2} \, {\left(5 \, A a^{5} d^{4} e + {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{5}\right)} x^{2}"," ",0,"1/12*B*b^5*e^5*x^12 + A*a^5*d^5*x + 1/11*(5*B*b^5*d*e^4 + (5*B*a*b^4 + A*b^5)*e^5)*x^11 + 1/2*(2*B*b^5*d^2*e^3 + (5*B*a*b^4 + A*b^5)*d*e^4 + (2*B*a^2*b^3 + A*a*b^4)*e^5)*x^10 + 5/9*(2*B*b^5*d^3*e^2 + 2*(5*B*a*b^4 + A*b^5)*d^2*e^3 + 5*(2*B*a^2*b^3 + A*a*b^4)*d*e^4 + 2*(B*a^3*b^2 + A*a^2*b^3)*e^5)*x^9 + 5/8*(B*b^5*d^4*e + 2*(5*B*a*b^4 + A*b^5)*d^3*e^2 + 10*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^3 + 10*(B*a^3*b^2 + A*a^2*b^3)*d*e^4 + (B*a^4*b + 2*A*a^3*b^2)*e^5)*x^8 + 1/7*(B*b^5*d^5 + 5*(5*B*a*b^4 + A*b^5)*d^4*e + 50*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^2 + 100*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^3 + 25*(B*a^4*b + 2*A*a^3*b^2)*d*e^4 + (B*a^5 + 5*A*a^4*b)*e^5)*x^7 + 1/6*(A*a^5*e^5 + (5*B*a*b^4 + A*b^5)*d^5 + 25*(2*B*a^2*b^3 + A*a*b^4)*d^4*e + 100*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^2 + 50*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^3 + 5*(B*a^5 + 5*A*a^4*b)*d*e^4)*x^6 + (A*a^5*d*e^4 + (2*B*a^2*b^3 + A*a*b^4)*d^5 + 10*(B*a^3*b^2 + A*a^2*b^3)*d^4*e + 10*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^2 + 2*(B*a^5 + 5*A*a^4*b)*d^2*e^3)*x^5 + 5/4*(2*A*a^5*d^2*e^3 + 2*(B*a^3*b^2 + A*a^2*b^3)*d^5 + 5*(B*a^4*b + 2*A*a^3*b^2)*d^4*e + 2*(B*a^5 + 5*A*a^4*b)*d^3*e^2)*x^4 + 5/3*(2*A*a^5*d^3*e^2 + (B*a^4*b + 2*A*a^3*b^2)*d^5 + (B*a^5 + 5*A*a^4*b)*d^4*e)*x^3 + 1/2*(5*A*a^5*d^4*e + (B*a^5 + 5*A*a^4*b)*d^5)*x^2","B",0
1740,1,677,0,0.442265," ","integrate((B*x+A)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{11} \, B b^{5} e^{4} x^{11} + A a^{5} d^{4} x + \frac{1}{10} \, {\left(4 \, B b^{5} d e^{3} + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{4}\right)} x^{10} + \frac{1}{9} \, {\left(6 \, B b^{5} d^{2} e^{2} + 4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{3} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{4}\right)} x^{9} + \frac{1}{4} \, {\left(2 \, B b^{5} d^{3} e + 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{2} + 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{3} + 5 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{4}\right)} x^{8} + \frac{1}{7} \, {\left(B b^{5} d^{4} + 4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{2} + 40 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{3} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{4}\right)} x^{7} + \frac{1}{6} \, {\left({\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} + 20 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e + 60 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{2} + 20 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{3} + {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{4}\right)} x^{6} + \frac{1}{5} \, {\left(A a^{5} e^{4} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} + 40 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e + 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{2} + 4 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{3}\right)} x^{5} + \frac{1}{2} \, {\left(2 \, A a^{5} d e^{3} + 5 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e + 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(6 \, A a^{5} d^{2} e^{2} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{4} + 4 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{3} e\right)} x^{3} + \frac{1}{2} \, {\left(4 \, A a^{5} d^{3} e + {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{4}\right)} x^{2}"," ",0,"1/11*B*b^5*e^4*x^11 + A*a^5*d^4*x + 1/10*(4*B*b^5*d*e^3 + (5*B*a*b^4 + A*b^5)*e^4)*x^10 + 1/9*(6*B*b^5*d^2*e^2 + 4*(5*B*a*b^4 + A*b^5)*d*e^3 + 5*(2*B*a^2*b^3 + A*a*b^4)*e^4)*x^9 + 1/4*(2*B*b^5*d^3*e + 3*(5*B*a*b^4 + A*b^5)*d^2*e^2 + 10*(2*B*a^2*b^3 + A*a*b^4)*d*e^3 + 5*(B*a^3*b^2 + A*a^2*b^3)*e^4)*x^8 + 1/7*(B*b^5*d^4 + 4*(5*B*a*b^4 + A*b^5)*d^3*e + 30*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^2 + 40*(B*a^3*b^2 + A*a^2*b^3)*d*e^3 + 5*(B*a^4*b + 2*A*a^3*b^2)*e^4)*x^7 + 1/6*((5*B*a*b^4 + A*b^5)*d^4 + 20*(2*B*a^2*b^3 + A*a*b^4)*d^3*e + 60*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^2 + 20*(B*a^4*b + 2*A*a^3*b^2)*d*e^3 + (B*a^5 + 5*A*a^4*b)*e^4)*x^6 + 1/5*(A*a^5*e^4 + 5*(2*B*a^2*b^3 + A*a*b^4)*d^4 + 40*(B*a^3*b^2 + A*a^2*b^3)*d^3*e + 30*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^2 + 4*(B*a^5 + 5*A*a^4*b)*d*e^3)*x^5 + 1/2*(2*A*a^5*d*e^3 + 5*(B*a^3*b^2 + A*a^2*b^3)*d^4 + 10*(B*a^4*b + 2*A*a^3*b^2)*d^3*e + 3*(B*a^5 + 5*A*a^4*b)*d^2*e^2)*x^4 + 1/3*(6*A*a^5*d^2*e^2 + 5*(B*a^4*b + 2*A*a^3*b^2)*d^4 + 4*(B*a^5 + 5*A*a^4*b)*d^3*e)*x^3 + 1/2*(4*A*a^5*d^3*e + (B*a^5 + 5*A*a^4*b)*d^4)*x^2","B",0
1741,1,532,0,0.442057," ","integrate((B*x+A)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{10} \, B b^{5} e^{3} x^{10} + A a^{5} d^{3} x + \frac{1}{9} \, {\left(3 \, B b^{5} d e^{2} + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{3}\right)} x^{9} + \frac{1}{8} \, {\left(3 \, B b^{5} d^{2} e + 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{2} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{3}\right)} x^{8} + \frac{1}{7} \, {\left(B b^{5} d^{3} + 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e + 15 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{2} + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{3}\right)} x^{7} + \frac{1}{6} \, {\left({\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} + 15 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e + 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{2} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{3}\right)} x^{6} + \frac{1}{5} \, {\left(5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} + 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e + 15 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{2} + {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(A a^{5} e^{3} + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} + 15 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e + 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(3 \, A a^{5} d e^{2} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} + 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e\right)} x^{3} + \frac{1}{2} \, {\left(3 \, A a^{5} d^{2} e + {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{3}\right)} x^{2}"," ",0,"1/10*B*b^5*e^3*x^10 + A*a^5*d^3*x + 1/9*(3*B*b^5*d*e^2 + (5*B*a*b^4 + A*b^5)*e^3)*x^9 + 1/8*(3*B*b^5*d^2*e + 3*(5*B*a*b^4 + A*b^5)*d*e^2 + 5*(2*B*a^2*b^3 + A*a*b^4)*e^3)*x^8 + 1/7*(B*b^5*d^3 + 3*(5*B*a*b^4 + A*b^5)*d^2*e + 15*(2*B*a^2*b^3 + A*a*b^4)*d*e^2 + 10*(B*a^3*b^2 + A*a^2*b^3)*e^3)*x^7 + 1/6*((5*B*a*b^4 + A*b^5)*d^3 + 15*(2*B*a^2*b^3 + A*a*b^4)*d^2*e + 30*(B*a^3*b^2 + A*a^2*b^3)*d*e^2 + 5*(B*a^4*b + 2*A*a^3*b^2)*e^3)*x^6 + 1/5*(5*(2*B*a^2*b^3 + A*a*b^4)*d^3 + 30*(B*a^3*b^2 + A*a^2*b^3)*d^2*e + 15*(B*a^4*b + 2*A*a^3*b^2)*d*e^2 + (B*a^5 + 5*A*a^4*b)*e^3)*x^5 + 1/4*(A*a^5*e^3 + 10*(B*a^3*b^2 + A*a^2*b^3)*d^3 + 15*(B*a^4*b + 2*A*a^3*b^2)*d^2*e + 3*(B*a^5 + 5*A*a^4*b)*d*e^2)*x^4 + 1/3*(3*A*a^5*d*e^2 + 5*(B*a^4*b + 2*A*a^3*b^2)*d^3 + 3*(B*a^5 + 5*A*a^4*b)*d^2*e)*x^3 + 1/2*(3*A*a^5*d^2*e + (B*a^5 + 5*A*a^4*b)*d^3)*x^2","B",0
1742,1,384,0,0.414651," ","integrate((B*x+A)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{9} \, B b^{5} e^{2} x^{9} + A a^{5} d^{2} x + \frac{1}{8} \, {\left(2 \, B b^{5} d e + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{2}\right)} x^{8} + \frac{1}{7} \, {\left(B b^{5} d^{2} + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{2}\right)} x^{7} + \frac{1}{6} \, {\left({\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} + 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{2}\right)} x^{6} + {\left({\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} + 4 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{2}\right)} x^{5} + \frac{1}{4} \, {\left(10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e + {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(A a^{5} e^{2} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} + 2 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e\right)} x^{3} + \frac{1}{2} \, {\left(2 \, A a^{5} d e + {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2}\right)} x^{2}"," ",0,"1/9*B*b^5*e^2*x^9 + A*a^5*d^2*x + 1/8*(2*B*b^5*d*e + (5*B*a*b^4 + A*b^5)*e^2)*x^8 + 1/7*(B*b^5*d^2 + 2*(5*B*a*b^4 + A*b^5)*d*e + 5*(2*B*a^2*b^3 + A*a*b^4)*e^2)*x^7 + 1/6*((5*B*a*b^4 + A*b^5)*d^2 + 10*(2*B*a^2*b^3 + A*a*b^4)*d*e + 10*(B*a^3*b^2 + A*a^2*b^3)*e^2)*x^6 + ((2*B*a^2*b^3 + A*a*b^4)*d^2 + 4*(B*a^3*b^2 + A*a^2*b^3)*d*e + (B*a^4*b + 2*A*a^3*b^2)*e^2)*x^5 + 1/4*(10*(B*a^3*b^2 + A*a^2*b^3)*d^2 + 10*(B*a^4*b + 2*A*a^3*b^2)*d*e + (B*a^5 + 5*A*a^4*b)*e^2)*x^4 + 1/3*(A*a^5*e^2 + 5*(B*a^4*b + 2*A*a^3*b^2)*d^2 + 2*(B*a^5 + 5*A*a^4*b)*d*e)*x^3 + 1/2*(2*A*a^5*d*e + (B*a^5 + 5*A*a^4*b)*d^2)*x^2","B",0
1743,1,239,0,0.406461," ","integrate((B*x+A)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{8} \, B b^{5} e x^{8} + A a^{5} d x + \frac{1}{7} \, {\left(B b^{5} d + {\left(5 \, B a b^{4} + A b^{5}\right)} e\right)} x^{7} + \frac{1}{6} \, {\left({\left(5 \, B a b^{4} + A b^{5}\right)} d + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e\right)} x^{6} + {\left({\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d + 2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e\right)} x^{5} + \frac{5}{4} \, {\left(2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e\right)} x^{4} + \frac{1}{3} \, {\left(5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d + {\left(B a^{5} + 5 \, A a^{4} b\right)} e\right)} x^{3} + \frac{1}{2} \, {\left(A a^{5} e + {\left(B a^{5} + 5 \, A a^{4} b\right)} d\right)} x^{2}"," ",0,"1/8*B*b^5*e*x^8 + A*a^5*d*x + 1/7*(B*b^5*d + (5*B*a*b^4 + A*b^5)*e)*x^7 + 1/6*((5*B*a*b^4 + A*b^5)*d + 5*(2*B*a^2*b^3 + A*a*b^4)*e)*x^6 + ((2*B*a^2*b^3 + A*a*b^4)*d + 2*(B*a^3*b^2 + A*a^2*b^3)*e)*x^5 + 5/4*(2*(B*a^3*b^2 + A*a^2*b^3)*d + (B*a^4*b + 2*A*a^3*b^2)*e)*x^4 + 1/3*(5*(B*a^4*b + 2*A*a^3*b^2)*d + (B*a^5 + 5*A*a^4*b)*e)*x^3 + 1/2*(A*a^5*e + (B*a^5 + 5*A*a^4*b)*d)*x^2","B",0
1744,1,115,0,0.422829," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{7} \, B b^{5} x^{7} + A a^{5} x + \frac{1}{6} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{6} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{5} + \frac{5}{2} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{4} + \frac{5}{3} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{3} + \frac{1}{2} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}"," ",0,"1/7*B*b^5*x^7 + A*a^5*x + 1/6*(5*B*a*b^4 + A*b^5)*x^6 + (2*B*a^2*b^3 + A*a*b^4)*x^5 + 5/2*(B*a^3*b^2 + A*a^2*b^3)*x^4 + 5/3*(B*a^4*b + 2*A*a^3*b^2)*x^3 + 1/2*(B*a^5 + 5*A*a^4*b)*x^2","A",0
1745,1,555,0,0.418063," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\frac{10 \, B b^{5} e^{6} x^{6} - 12 \, {\left(B b^{5} d e^{5} - {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 15 \, {\left(B b^{5} d^{2} e^{4} - {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} - 20 \, {\left(B b^{5} d^{3} e^{3} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} - 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 30 \, {\left(B b^{5} d^{4} e^{2} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} - 60 \, {\left(B b^{5} d^{5} e - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} - {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x + 60 \, {\left(B b^{5} d^{6} + A a^{5} e^{6} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5}\right)} \log\left(e x + d\right)}{60 \, e^{7}}"," ",0,"1/60*(10*B*b^5*e^6*x^6 - 12*(B*b^5*d*e^5 - (5*B*a*b^4 + A*b^5)*e^6)*x^5 + 15*(B*b^5*d^2*e^4 - (5*B*a*b^4 + A*b^5)*d*e^5 + 5*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 - 20*(B*b^5*d^3*e^3 - (5*B*a*b^4 + A*b^5)*d^2*e^4 + 5*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 - 10*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 30*(B*b^5*d^4*e^2 - (5*B*a*b^4 + A*b^5)*d^3*e^3 + 5*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 10*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 5*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 - 60*(B*b^5*d^5*e - (5*B*a*b^4 + A*b^5)*d^4*e^2 + 5*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 10*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 5*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 - (B*a^5 + 5*A*a^4*b)*e^6)*x + 60*(B*b^5*d^6 + A*a^5*e^6 - (5*B*a*b^4 + A*b^5)*d^5*e + 5*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - 10*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 5*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - (B*a^5 + 5*A*a^4*b)*d*e^5)*log(e*x + d))/e^7","B",0
1746,1,797,0,0.435124," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{12 \, B b^{5} e^{6} x^{6} - 60 \, B b^{5} d^{6} - 60 \, A a^{5} e^{6} + 60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e - 300 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 600 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} - 300 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + 60 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} - 3 \, {\left(6 \, B b^{5} d e^{5} - 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 5 \, {\left(6 \, B b^{5} d^{2} e^{4} - 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 20 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} - 10 \, {\left(6 \, B b^{5} d^{3} e^{3} - 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 20 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} - 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 30 \, {\left(6 \, B b^{5} d^{4} e^{2} - 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 20 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 60 \, {\left(5 \, B b^{5} d^{5} e - 4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 15 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 20 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5}\right)} x - 60 \, {\left(6 \, B b^{5} d^{6} - 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 20 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} + {\left(6 \, B b^{5} d^{5} e - 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 20 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} - {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"1/60*(12*B*b^5*e^6*x^6 - 60*B*b^5*d^6 - 60*A*a^5*e^6 + 60*(5*B*a*b^4 + A*b^5)*d^5*e - 300*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 600*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 - 300*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + 60*(B*a^5 + 5*A*a^4*b)*d*e^5 - 3*(6*B*b^5*d*e^5 - 5*(5*B*a*b^4 + A*b^5)*e^6)*x^5 + 5*(6*B*b^5*d^2*e^4 - 5*(5*B*a*b^4 + A*b^5)*d*e^5 + 20*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 - 10*(6*B*b^5*d^3*e^3 - 5*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 20*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 - 30*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 30*(6*B*b^5*d^4*e^2 - 5*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 20*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 30*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 10*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 60*(5*B*b^5*d^5*e - 4*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 15*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 20*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 5*(B*a^4*b + 2*A*a^3*b^2)*d*e^5)*x - 60*(6*B*b^5*d^6 - 5*(5*B*a*b^4 + A*b^5)*d^5*e + 20*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - 30*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 10*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - (B*a^5 + 5*A*a^4*b)*d*e^5 + (6*B*b^5*d^5*e - 5*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 20*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 30*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 10*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 - (B*a^5 + 5*A*a^4*b)*e^6)*x)*log(e*x + d))/(e^8*x + d*e^7)","B",0
1747,1,871,0,0.446401," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{3 \, B b^{5} e^{6} x^{6} + 66 \, B b^{5} d^{6} - 6 \, A a^{5} e^{6} - 54 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 210 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 90 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - 6 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} - 2 \, {\left(3 \, B b^{5} d e^{5} - 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 5 \, {\left(3 \, B b^{5} d^{2} e^{4} - 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 6 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} - 20 \, {\left(3 \, B b^{5} d^{3} e^{3} - 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 6 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} - 6 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} - 6 \, {\left(34 \, B b^{5} d^{4} e^{2} - 21 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 55 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 40 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5}\right)} x^{2} - 12 \, {\left(4 \, B b^{5} d^{5} e - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} - 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 20 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} - 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x + 60 \, {\left(3 \, B b^{5} d^{6} - 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 6 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - 6 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + {\left(3 \, B b^{5} d^{4} e^{2} - 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 6 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 6 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 2 \, {\left(3 \, B b^{5} d^{5} e - 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 6 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 6 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"1/12*(3*B*b^5*e^6*x^6 + 66*B*b^5*d^6 - 6*A*a^5*e^6 - 54*(5*B*a*b^4 + A*b^5)*d^5*e + 210*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - 300*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 90*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - 6*(B*a^5 + 5*A*a^4*b)*d*e^5 - 2*(3*B*b^5*d*e^5 - 2*(5*B*a*b^4 + A*b^5)*e^6)*x^5 + 5*(3*B*b^5*d^2*e^4 - 2*(5*B*a*b^4 + A*b^5)*d*e^5 + 6*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 - 20*(3*B*b^5*d^3*e^3 - 2*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 6*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 - 6*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 - 6*(34*B*b^5*d^4*e^2 - 21*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 55*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 40*(B*a^3*b^2 + A*a^2*b^3)*d*e^5)*x^2 - 12*(4*B*b^5*d^5*e - (5*B*a*b^4 + A*b^5)*d^4*e^2 - 5*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 20*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 - 10*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + (B*a^5 + 5*A*a^4*b)*e^6)*x + 60*(3*B*b^5*d^6 - 2*(5*B*a*b^4 + A*b^5)*d^5*e + 6*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - 6*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + (B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + (3*B*b^5*d^4*e^2 - 2*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 6*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 6*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + (B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 2*(3*B*b^5*d^5*e - 2*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 6*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 6*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + (B*a^4*b + 2*A*a^3*b^2)*d*e^5)*x)*log(e*x + d))/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","B",0
1748,1,899,0,0.431811," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2 \, B b^{5} e^{6} x^{6} - 74 \, B b^{5} d^{6} - 2 \, A a^{5} e^{6} + 47 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e - 130 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 110 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} - 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} - 3 \, {\left(2 \, B b^{5} d e^{5} - {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 15 \, {\left(2 \, B b^{5} d^{2} e^{4} - {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + {\left(146 \, B b^{5} d^{3} e^{3} - 63 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 90 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5}\right)} x^{3} + 3 \, {\left(26 \, B b^{5} d^{4} e^{2} - 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} - 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 60 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} - 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} - 3 \, {\left(34 \, B b^{5} d^{5} e - 27 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 90 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 90 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x - 60 \, {\left(2 \, B b^{5} d^{6} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + {\left(2 \, B b^{5} d^{3} e^{3} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} - {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 3 \, {\left(2 \, B b^{5} d^{4} e^{2} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5}\right)} x^{2} + 3 \, {\left(2 \, B b^{5} d^{5} e - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"1/6*(2*B*b^5*e^6*x^6 - 74*B*b^5*d^6 - 2*A*a^5*e^6 + 47*(5*B*a*b^4 + A*b^5)*d^5*e - 130*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 110*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 - 10*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - (B*a^5 + 5*A*a^4*b)*d*e^5 - 3*(2*B*b^5*d*e^5 - (5*B*a*b^4 + A*b^5)*e^6)*x^5 + 15*(2*B*b^5*d^2*e^4 - (5*B*a*b^4 + A*b^5)*d*e^5 + 2*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + (146*B*b^5*d^3*e^3 - 63*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 90*(2*B*a^2*b^3 + A*a*b^4)*d*e^5)*x^3 + 3*(26*B*b^5*d^4*e^2 - 3*(5*B*a*b^4 + A*b^5)*d^3*e^3 - 30*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 60*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 - 10*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 - 3*(34*B*b^5*d^5*e - 27*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 90*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 90*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 10*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + (B*a^5 + 5*A*a^4*b)*e^6)*x - 60*(2*B*b^5*d^6 - (5*B*a*b^4 + A*b^5)*d^5*e + 2*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - (B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + (2*B*b^5*d^3*e^3 - (5*B*a*b^4 + A*b^5)*d^2*e^4 + 2*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 - (B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 3*(2*B*b^5*d^4*e^2 - (5*B*a*b^4 + A*b^5)*d^3*e^3 + 2*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - (B*a^3*b^2 + A*a^2*b^3)*d*e^5)*x^2 + 3*(2*B*b^5*d^5*e - (5*B*a*b^4 + A*b^5)*d^4*e^2 + 2*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - (B*a^3*b^2 + A*a^2*b^3)*d^2*e^4)*x)*log(e*x + d))/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","B",0
1749,1,871,0,0.461317," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{6 \, B b^{5} e^{6} x^{6} + 171 \, B b^{5} d^{6} - 3 \, A a^{5} e^{6} - 77 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 125 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} - 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} - 12 \, {\left(3 \, B b^{5} d e^{5} - {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} - 12 \, {\left(17 \, B b^{5} d^{2} e^{4} - 4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5}\right)} x^{4} - 24 \, {\left(4 \, B b^{5} d^{3} e^{3} + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} - 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + 5 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 6 \, {\left(66 \, B b^{5} d^{4} e^{2} - 42 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 90 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} - 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 4 \, {\left(126 \, B b^{5} d^{5} e - 62 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 110 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} - 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} - {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x + 60 \, {\left(3 \, B b^{5} d^{6} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + {\left(3 \, B b^{5} d^{2} e^{4} - {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + 4 \, {\left(3 \, B b^{5} d^{3} e^{3} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5}\right)} x^{3} + 6 \, {\left(3 \, B b^{5} d^{4} e^{2} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(3 \, B b^{5} d^{5} e - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{11} x^{4} + 4 \, d e^{10} x^{3} + 6 \, d^{2} e^{9} x^{2} + 4 \, d^{3} e^{8} x + d^{4} e^{7}\right)}}"," ",0,"1/12*(6*B*b^5*e^6*x^6 + 171*B*b^5*d^6 - 3*A*a^5*e^6 - 77*(5*B*a*b^4 + A*b^5)*d^5*e + 125*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - 30*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 - 5*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - (B*a^5 + 5*A*a^4*b)*d*e^5 - 12*(3*B*b^5*d*e^5 - (5*B*a*b^4 + A*b^5)*e^6)*x^5 - 12*(17*B*b^5*d^2*e^4 - 4*(5*B*a*b^4 + A*b^5)*d*e^5)*x^4 - 24*(4*B*b^5*d^3*e^3 + 2*(5*B*a*b^4 + A*b^5)*d^2*e^4 - 10*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + 5*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 6*(66*B*b^5*d^4*e^2 - 42*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 90*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 30*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 - 5*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 4*(126*B*b^5*d^5*e - 62*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 110*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 30*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 - 5*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 - (B*a^5 + 5*A*a^4*b)*e^6)*x + 60*(3*B*b^5*d^6 - (5*B*a*b^4 + A*b^5)*d^5*e + (2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + (3*B*b^5*d^2*e^4 - (5*B*a*b^4 + A*b^5)*d*e^5 + (2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + 4*(3*B*b^5*d^3*e^3 - (5*B*a*b^4 + A*b^5)*d^2*e^4 + (2*B*a^2*b^3 + A*a*b^4)*d*e^5)*x^3 + 6*(3*B*b^5*d^4*e^2 - (5*B*a*b^4 + A*b^5)*d^3*e^3 + (2*B*a^2*b^3 + A*a*b^4)*d^2*e^4)*x^2 + 4*(3*B*b^5*d^5*e - (5*B*a*b^4 + A*b^5)*d^4*e^2 + (2*B*a^2*b^3 + A*a*b^4)*d^3*e^3)*x)*log(e*x + d))/(e^11*x^4 + 4*d*e^10*x^3 + 6*d^2*e^9*x^2 + 4*d^3*e^8*x + d^4*e^7)","B",0
1750,1,802,0,0.435215," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^6,x, algorithm=""fricas"")","\frac{60 \, B b^{5} e^{6} x^{6} + 300 \, B b^{5} d e^{5} x^{5} - 522 \, B b^{5} d^{6} - 12 \, A a^{5} e^{6} + 137 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e - 60 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} - 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} - 300 \, {\left(B b^{5} d^{2} e^{4} - {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} - 300 \, {\left(8 \, B b^{5} d^{3} e^{3} - 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} - 100 \, {\left(36 \, B b^{5} d^{4} e^{2} - 11 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 6 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 3 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} - 5 \, {\left(450 \, B b^{5} d^{5} e - 125 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 60 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x - 60 \, {\left(6 \, B b^{5} d^{6} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + {\left(6 \, B b^{5} d e^{5} - {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 5 \, {\left(6 \, B b^{5} d^{2} e^{4} - {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5}\right)} x^{4} + 10 \, {\left(6 \, B b^{5} d^{3} e^{3} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4}\right)} x^{3} + 10 \, {\left(6 \, B b^{5} d^{4} e^{2} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3}\right)} x^{2} + 5 \, {\left(6 \, B b^{5} d^{5} e - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{12} x^{5} + 5 \, d e^{11} x^{4} + 10 \, d^{2} e^{10} x^{3} + 10 \, d^{3} e^{9} x^{2} + 5 \, d^{4} e^{8} x + d^{5} e^{7}\right)}}"," ",0,"1/60*(60*B*b^5*e^6*x^6 + 300*B*b^5*d*e^5*x^5 - 522*B*b^5*d^6 - 12*A*a^5*e^6 + 137*(5*B*a*b^4 + A*b^5)*d^5*e - 60*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - 30*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 - 10*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - 3*(B*a^5 + 5*A*a^4*b)*d*e^5 - 300*(B*b^5*d^2*e^4 - (5*B*a*b^4 + A*b^5)*d*e^5 + (2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 - 300*(8*B*b^5*d^3*e^3 - 3*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 2*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + (B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 - 100*(36*B*b^5*d^4*e^2 - 11*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 6*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 3*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + (B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 - 5*(450*B*b^5*d^5*e - 125*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 60*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 30*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 10*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + 3*(B*a^5 + 5*A*a^4*b)*e^6)*x - 60*(6*B*b^5*d^6 - (5*B*a*b^4 + A*b^5)*d^5*e + (6*B*b^5*d*e^5 - (5*B*a*b^4 + A*b^5)*e^6)*x^5 + 5*(6*B*b^5*d^2*e^4 - (5*B*a*b^4 + A*b^5)*d*e^5)*x^4 + 10*(6*B*b^5*d^3*e^3 - (5*B*a*b^4 + A*b^5)*d^2*e^4)*x^3 + 10*(6*B*b^5*d^4*e^2 - (5*B*a*b^4 + A*b^5)*d^3*e^3)*x^2 + 5*(6*B*b^5*d^5*e - (5*B*a*b^4 + A*b^5)*d^4*e^2)*x)*log(e*x + d))/(e^12*x^5 + 5*d*e^11*x^4 + 10*d^2*e^10*x^3 + 10*d^3*e^9*x^2 + 5*d^4*e^8*x + d^5*e^7)","B",0
1751,1,703,0,0.421573," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^7,x, algorithm=""fricas"")","\frac{147 \, B b^{5} d^{6} - 10 \, A a^{5} e^{6} - 10 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e - 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} - 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - 2 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} + 60 \, {\left(6 \, B b^{5} d e^{5} - {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 150 \, {\left(9 \, B b^{5} d^{2} e^{4} - {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} - {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + 200 \, {\left(11 \, B b^{5} d^{3} e^{3} - {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} - {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} - {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 75 \, {\left(25 \, B b^{5} d^{4} e^{2} - 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} - 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} - {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 6 \, {\left(137 \, B b^{5} d^{5} e - 10 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} - 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} - 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} - 2 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x + 60 \, {\left(B b^{5} e^{6} x^{6} + 6 \, B b^{5} d e^{5} x^{5} + 15 \, B b^{5} d^{2} e^{4} x^{4} + 20 \, B b^{5} d^{3} e^{3} x^{3} + 15 \, B b^{5} d^{4} e^{2} x^{2} + 6 \, B b^{5} d^{5} e x + B b^{5} d^{6}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{13} x^{6} + 6 \, d e^{12} x^{5} + 15 \, d^{2} e^{11} x^{4} + 20 \, d^{3} e^{10} x^{3} + 15 \, d^{4} e^{9} x^{2} + 6 \, d^{5} e^{8} x + d^{6} e^{7}\right)}}"," ",0,"1/60*(147*B*b^5*d^6 - 10*A*a^5*e^6 - 10*(5*B*a*b^4 + A*b^5)*d^5*e - 10*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - 10*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 - 5*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - 2*(B*a^5 + 5*A*a^4*b)*d*e^5 + 60*(6*B*b^5*d*e^5 - (5*B*a*b^4 + A*b^5)*e^6)*x^5 + 150*(9*B*b^5*d^2*e^4 - (5*B*a*b^4 + A*b^5)*d*e^5 - (2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + 200*(11*B*b^5*d^3*e^3 - (5*B*a*b^4 + A*b^5)*d^2*e^4 - (2*B*a^2*b^3 + A*a*b^4)*d*e^5 - (B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 75*(25*B*b^5*d^4*e^2 - 2*(5*B*a*b^4 + A*b^5)*d^3*e^3 - 2*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 2*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 - (B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 6*(137*B*b^5*d^5*e - 10*(5*B*a*b^4 + A*b^5)*d^4*e^2 - 10*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 10*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 - 5*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 - 2*(B*a^5 + 5*A*a^4*b)*e^6)*x + 60*(B*b^5*e^6*x^6 + 6*B*b^5*d*e^5*x^5 + 15*B*b^5*d^2*e^4*x^4 + 20*B*b^5*d^3*e^3*x^3 + 15*B*b^5*d^4*e^2*x^2 + 6*B*b^5*d^5*e*x + B*b^5*d^6)*log(e*x + d))/(e^13*x^6 + 6*d*e^12*x^5 + 15*d^2*e^11*x^4 + 20*d^3*e^10*x^3 + 15*d^4*e^9*x^2 + 6*d^5*e^8*x + d^6*e^7)","B",0
1752,1,621,0,0.431826," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{42 \, B b^{5} e^{6} x^{6} + 6 \, B b^{5} d^{6} + 6 \, A a^{5} e^{6} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 3 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 2 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} + 21 \, {\left(6 \, B b^{5} d e^{5} + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 35 \, {\left(6 \, B b^{5} d^{2} e^{4} + {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + 35 \, {\left(6 \, B b^{5} d^{3} e^{3} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + 3 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 21 \, {\left(6 \, B b^{5} d^{4} e^{2} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 3 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 2 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 7 \, {\left(6 \, B b^{5} d^{5} e + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 2 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 3 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 2 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x}{42 \, {\left(e^{14} x^{7} + 7 \, d e^{13} x^{6} + 21 \, d^{2} e^{12} x^{5} + 35 \, d^{3} e^{11} x^{4} + 35 \, d^{4} e^{10} x^{3} + 21 \, d^{5} e^{9} x^{2} + 7 \, d^{6} e^{8} x + d^{7} e^{7}\right)}}"," ",0,"-1/42*(42*B*b^5*e^6*x^6 + 6*B*b^5*d^6 + 6*A*a^5*e^6 + (5*B*a*b^4 + A*b^5)*d^5*e + 2*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 3*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 2*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + (B*a^5 + 5*A*a^4*b)*d*e^5 + 21*(6*B*b^5*d*e^5 + (5*B*a*b^4 + A*b^5)*e^6)*x^5 + 35*(6*B*b^5*d^2*e^4 + (5*B*a*b^4 + A*b^5)*d*e^5 + 2*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + 35*(6*B*b^5*d^3*e^3 + (5*B*a*b^4 + A*b^5)*d^2*e^4 + 2*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + 3*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 21*(6*B*b^5*d^4*e^2 + (5*B*a*b^4 + A*b^5)*d^3*e^3 + 2*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 3*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 2*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 7*(6*B*b^5*d^5*e + (5*B*a*b^4 + A*b^5)*d^4*e^2 + 2*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 3*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 2*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + (B*a^5 + 5*A*a^4*b)*e^6)*x)/(e^14*x^7 + 7*d*e^13*x^6 + 21*d^2*e^12*x^5 + 35*d^3*e^11*x^4 + 35*d^4*e^10*x^3 + 21*d^5*e^9*x^2 + 7*d^6*e^8*x + d^7*e^7)","B",0
1753,1,634,0,0.433077," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{84 \, B b^{5} e^{6} x^{6} + 3 \, B b^{5} d^{6} + 21 \, A a^{5} e^{6} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 3 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 6 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} + 56 \, {\left(3 \, B b^{5} d e^{5} + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 70 \, {\left(3 \, B b^{5} d^{2} e^{4} + {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 3 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + 56 \, {\left(3 \, B b^{5} d^{3} e^{3} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 3 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + 6 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 28 \, {\left(3 \, B b^{5} d^{4} e^{2} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 3 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 6 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 8 \, {\left(3 \, B b^{5} d^{5} e + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 3 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 6 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x}{168 \, {\left(e^{15} x^{8} + 8 \, d e^{14} x^{7} + 28 \, d^{2} e^{13} x^{6} + 56 \, d^{3} e^{12} x^{5} + 70 \, d^{4} e^{11} x^{4} + 56 \, d^{5} e^{10} x^{3} + 28 \, d^{6} e^{9} x^{2} + 8 \, d^{7} e^{8} x + d^{8} e^{7}\right)}}"," ",0,"-1/168*(84*B*b^5*e^6*x^6 + 3*B*b^5*d^6 + 21*A*a^5*e^6 + (5*B*a*b^4 + A*b^5)*d^5*e + 3*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 6*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 5*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + 3*(B*a^5 + 5*A*a^4*b)*d*e^5 + 56*(3*B*b^5*d*e^5 + (5*B*a*b^4 + A*b^5)*e^6)*x^5 + 70*(3*B*b^5*d^2*e^4 + (5*B*a*b^4 + A*b^5)*d*e^5 + 3*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + 56*(3*B*b^5*d^3*e^3 + (5*B*a*b^4 + A*b^5)*d^2*e^4 + 3*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + 6*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 28*(3*B*b^5*d^4*e^2 + (5*B*a*b^4 + A*b^5)*d^3*e^3 + 3*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 6*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 5*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 8*(3*B*b^5*d^5*e + (5*B*a*b^4 + A*b^5)*d^4*e^2 + 3*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 6*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 5*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + 3*(B*a^5 + 5*A*a^4*b)*e^6)*x)/(e^15*x^8 + 8*d*e^14*x^7 + 28*d^2*e^13*x^6 + 56*d^3*e^12*x^5 + 70*d^4*e^11*x^4 + 56*d^5*e^10*x^3 + 28*d^6*e^9*x^2 + 8*d^7*e^8*x + d^8*e^7)","B",0
1754,1,645,0,0.433006," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{168 \, B b^{5} e^{6} x^{6} + 2 \, B b^{5} d^{6} + 56 \, A a^{5} e^{6} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 4 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + 7 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} + 126 \, {\left(2 \, B b^{5} d e^{5} + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 126 \, {\left(2 \, B b^{5} d^{2} e^{4} + {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 4 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + 84 \, {\left(2 \, B b^{5} d^{3} e^{3} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 4 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 36 \, {\left(2 \, B b^{5} d^{4} e^{2} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 4 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 9 \, {\left(2 \, B b^{5} d^{5} e + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 4 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + 7 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x}{504 \, {\left(e^{16} x^{9} + 9 \, d e^{15} x^{8} + 36 \, d^{2} e^{14} x^{7} + 84 \, d^{3} e^{13} x^{6} + 126 \, d^{4} e^{12} x^{5} + 126 \, d^{5} e^{11} x^{4} + 84 \, d^{6} e^{10} x^{3} + 36 \, d^{7} e^{9} x^{2} + 9 \, d^{8} e^{8} x + d^{9} e^{7}\right)}}"," ",0,"-1/504*(168*B*b^5*e^6*x^6 + 2*B*b^5*d^6 + 56*A*a^5*e^6 + (5*B*a*b^4 + A*b^5)*d^5*e + 4*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 10*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 10*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + 7*(B*a^5 + 5*A*a^4*b)*d*e^5 + 126*(2*B*b^5*d*e^5 + (5*B*a*b^4 + A*b^5)*e^6)*x^5 + 126*(2*B*b^5*d^2*e^4 + (5*B*a*b^4 + A*b^5)*d*e^5 + 4*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + 84*(2*B*b^5*d^3*e^3 + (5*B*a*b^4 + A*b^5)*d^2*e^4 + 4*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + 10*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 36*(2*B*b^5*d^4*e^2 + (5*B*a*b^4 + A*b^5)*d^3*e^3 + 4*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 10*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 10*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 9*(2*B*b^5*d^5*e + (5*B*a*b^4 + A*b^5)*d^4*e^2 + 4*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 10*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 10*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + 7*(B*a^5 + 5*A*a^4*b)*e^6)*x)/(e^16*x^9 + 9*d*e^15*x^8 + 36*d^2*e^14*x^7 + 84*d^3*e^13*x^6 + 126*d^4*e^12*x^5 + 126*d^5*e^11*x^4 + 84*d^6*e^10*x^3 + 36*d^7*e^9*x^2 + 9*d^8*e^8*x + d^9*e^7)","B",0
1755,1,662,0,0.438051," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{630 \, B b^{5} e^{6} x^{6} + 3 \, B b^{5} d^{6} + 252 \, A a^{5} e^{6} + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 35 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + 28 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} + 252 \, {\left(3 \, B b^{5} d e^{5} + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 210 \, {\left(3 \, B b^{5} d^{2} e^{4} + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + 120 \, {\left(3 \, B b^{5} d^{3} e^{3} + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 45 \, {\left(3 \, B b^{5} d^{4} e^{2} + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 35 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 10 \, {\left(3 \, B b^{5} d^{5} e + 2 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 10 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 35 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + 28 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x}{2520 \, {\left(e^{17} x^{10} + 10 \, d e^{16} x^{9} + 45 \, d^{2} e^{15} x^{8} + 120 \, d^{3} e^{14} x^{7} + 210 \, d^{4} e^{13} x^{6} + 252 \, d^{5} e^{12} x^{5} + 210 \, d^{6} e^{11} x^{4} + 120 \, d^{7} e^{10} x^{3} + 45 \, d^{8} e^{9} x^{2} + 10 \, d^{9} e^{8} x + d^{10} e^{7}\right)}}"," ",0,"-1/2520*(630*B*b^5*e^6*x^6 + 3*B*b^5*d^6 + 252*A*a^5*e^6 + 2*(5*B*a*b^4 + A*b^5)*d^5*e + 10*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 30*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 35*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + 28*(B*a^5 + 5*A*a^4*b)*d*e^5 + 252*(3*B*b^5*d*e^5 + 2*(5*B*a*b^4 + A*b^5)*e^6)*x^5 + 210*(3*B*b^5*d^2*e^4 + 2*(5*B*a*b^4 + A*b^5)*d*e^5 + 10*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + 120*(3*B*b^5*d^3*e^3 + 2*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 10*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + 30*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 45*(3*B*b^5*d^4*e^2 + 2*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 10*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 30*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 35*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 10*(3*B*b^5*d^5*e + 2*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 10*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 30*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 35*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + 28*(B*a^5 + 5*A*a^4*b)*e^6)*x)/(e^17*x^10 + 10*d*e^16*x^9 + 45*d^2*e^15*x^8 + 120*d^3*e^14*x^7 + 210*d^4*e^13*x^6 + 252*d^5*e^12*x^5 + 210*d^6*e^11*x^4 + 120*d^7*e^10*x^3 + 45*d^8*e^9*x^2 + 10*d^9*e^8*x + d^10*e^7)","A",0
1756,1,673,0,0.445151," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{2772 \, B b^{5} e^{6} x^{6} + 6 \, B b^{5} d^{6} + 1260 \, A a^{5} e^{6} + 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 140 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + 126 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} + 462 \, {\left(6 \, B b^{5} d e^{5} + 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 330 \, {\left(6 \, B b^{5} d^{2} e^{4} + 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + 165 \, {\left(6 \, B b^{5} d^{3} e^{3} + 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 55 \, {\left(6 \, B b^{5} d^{4} e^{2} + 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 140 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 11 \, {\left(6 \, B b^{5} d^{5} e + 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 140 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + 126 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x}{13860 \, {\left(e^{18} x^{11} + 11 \, d e^{17} x^{10} + 55 \, d^{2} e^{16} x^{9} + 165 \, d^{3} e^{15} x^{8} + 330 \, d^{4} e^{14} x^{7} + 462 \, d^{5} e^{13} x^{6} + 462 \, d^{6} e^{12} x^{5} + 330 \, d^{7} e^{11} x^{4} + 165 \, d^{8} e^{10} x^{3} + 55 \, d^{9} e^{9} x^{2} + 11 \, d^{10} e^{8} x + d^{11} e^{7}\right)}}"," ",0,"-1/13860*(2772*B*b^5*e^6*x^6 + 6*B*b^5*d^6 + 1260*A*a^5*e^6 + 5*(5*B*a*b^4 + A*b^5)*d^5*e + 30*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 105*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 140*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + 126*(B*a^5 + 5*A*a^4*b)*d*e^5 + 462*(6*B*b^5*d*e^5 + 5*(5*B*a*b^4 + A*b^5)*e^6)*x^5 + 330*(6*B*b^5*d^2*e^4 + 5*(5*B*a*b^4 + A*b^5)*d*e^5 + 30*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + 165*(6*B*b^5*d^3*e^3 + 5*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 30*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + 105*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 55*(6*B*b^5*d^4*e^2 + 5*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 30*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 105*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 140*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 11*(6*B*b^5*d^5*e + 5*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 30*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 105*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 140*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + 126*(B*a^5 + 5*A*a^4*b)*e^6)*x)/(e^18*x^11 + 11*d*e^17*x^10 + 55*d^2*e^16*x^9 + 165*d^3*e^15*x^8 + 330*d^4*e^14*x^7 + 462*d^5*e^13*x^6 + 462*d^6*e^12*x^5 + 330*d^7*e^11*x^4 + 165*d^8*e^10*x^3 + 55*d^9*e^9*x^2 + 11*d^10*e^8*x + d^11*e^7)","A",0
1757,1,672,0,0.435111," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^13,x, algorithm=""fricas"")","-\frac{924 \, B b^{5} e^{6} x^{6} + B b^{5} d^{6} + 462 \, A a^{5} e^{6} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 7 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 28 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 42 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + 42 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} + 792 \, {\left(B b^{5} d e^{5} + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 495 \, {\left(B b^{5} d^{2} e^{4} + {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 7 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + 220 \, {\left(B b^{5} d^{3} e^{3} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 7 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + 28 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 66 \, {\left(B b^{5} d^{4} e^{2} + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 7 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 28 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 42 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 12 \, {\left(B b^{5} d^{5} e + {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 7 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 28 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 42 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + 42 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x}{5544 \, {\left(e^{19} x^{12} + 12 \, d e^{18} x^{11} + 66 \, d^{2} e^{17} x^{10} + 220 \, d^{3} e^{16} x^{9} + 495 \, d^{4} e^{15} x^{8} + 792 \, d^{5} e^{14} x^{7} + 924 \, d^{6} e^{13} x^{6} + 792 \, d^{7} e^{12} x^{5} + 495 \, d^{8} e^{11} x^{4} + 220 \, d^{9} e^{10} x^{3} + 66 \, d^{10} e^{9} x^{2} + 12 \, d^{11} e^{8} x + d^{12} e^{7}\right)}}"," ",0,"-1/5544*(924*B*b^5*e^6*x^6 + B*b^5*d^6 + 462*A*a^5*e^6 + (5*B*a*b^4 + A*b^5)*d^5*e + 7*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 28*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 42*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + 42*(B*a^5 + 5*A*a^4*b)*d*e^5 + 792*(B*b^5*d*e^5 + (5*B*a*b^4 + A*b^5)*e^6)*x^5 + 495*(B*b^5*d^2*e^4 + (5*B*a*b^4 + A*b^5)*d*e^5 + 7*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + 220*(B*b^5*d^3*e^3 + (5*B*a*b^4 + A*b^5)*d^2*e^4 + 7*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + 28*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 66*(B*b^5*d^4*e^2 + (5*B*a*b^4 + A*b^5)*d^3*e^3 + 7*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 28*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 42*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 12*(B*b^5*d^5*e + (5*B*a*b^4 + A*b^5)*d^4*e^2 + 7*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 28*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 42*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + 42*(B*a^5 + 5*A*a^4*b)*e^6)*x)/(e^19*x^12 + 12*d*e^18*x^11 + 66*d^2*e^17*x^10 + 220*d^3*e^16*x^9 + 495*d^4*e^15*x^8 + 792*d^5*e^14*x^7 + 924*d^6*e^13*x^6 + 792*d^7*e^12*x^5 + 495*d^8*e^11*x^4 + 220*d^9*e^10*x^3 + 66*d^10*e^9*x^2 + 12*d^11*e^8*x + d^12*e^7)","A",0
1758,1,695,0,0.445925," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^14,x, algorithm=""fricas"")","-\frac{10296 \, B b^{5} e^{6} x^{6} + 6 \, B b^{5} d^{6} + 5544 \, A a^{5} e^{6} + 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 56 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 252 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 420 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + 462 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} + 1287 \, {\left(6 \, B b^{5} d e^{5} + 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 715 \, {\left(6 \, B b^{5} d^{2} e^{4} + 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 56 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} + 286 \, {\left(6 \, B b^{5} d^{3} e^{3} + 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 56 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} + 252 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 78 \, {\left(6 \, B b^{5} d^{4} e^{2} + 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 56 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} + 252 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 420 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 13 \, {\left(6 \, B b^{5} d^{5} e + 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 56 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} + 252 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 420 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + 462 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x}{72072 \, {\left(e^{20} x^{13} + 13 \, d e^{19} x^{12} + 78 \, d^{2} e^{18} x^{11} + 286 \, d^{3} e^{17} x^{10} + 715 \, d^{4} e^{16} x^{9} + 1287 \, d^{5} e^{15} x^{8} + 1716 \, d^{6} e^{14} x^{7} + 1716 \, d^{7} e^{13} x^{6} + 1287 \, d^{8} e^{12} x^{5} + 715 \, d^{9} e^{11} x^{4} + 286 \, d^{10} e^{10} x^{3} + 78 \, d^{11} e^{9} x^{2} + 13 \, d^{12} e^{8} x + d^{13} e^{7}\right)}}"," ",0,"-1/72072*(10296*B*b^5*e^6*x^6 + 6*B*b^5*d^6 + 5544*A*a^5*e^6 + 7*(5*B*a*b^4 + A*b^5)*d^5*e + 56*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 252*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 420*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + 462*(B*a^5 + 5*A*a^4*b)*d*e^5 + 1287*(6*B*b^5*d*e^5 + 7*(5*B*a*b^4 + A*b^5)*e^6)*x^5 + 715*(6*B*b^5*d^2*e^4 + 7*(5*B*a*b^4 + A*b^5)*d*e^5 + 56*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 + 286*(6*B*b^5*d^3*e^3 + 7*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 56*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 + 252*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 78*(6*B*b^5*d^4*e^2 + 7*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 56*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 + 252*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 420*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 13*(6*B*b^5*d^5*e + 7*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 56*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 + 252*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 420*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + 462*(B*a^5 + 5*A*a^4*b)*e^6)*x)/(e^20*x^13 + 13*d*e^19*x^12 + 78*d^2*e^18*x^11 + 286*d^3*e^17*x^10 + 715*d^4*e^16*x^9 + 1287*d^5*e^15*x^8 + 1716*d^6*e^14*x^7 + 1716*d^7*e^13*x^6 + 1287*d^8*e^12*x^5 + 715*d^9*e^11*x^4 + 286*d^10*e^10*x^3 + 78*d^11*e^9*x^2 + 13*d^12*e^8*x + d^13*e^7)","B",0
1759,1,269,0,0.418341," ","integrate((B*x+A)*(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{3 \, B b^{4} e^{3} x^{4} + 4 \, {\left(3 \, B b^{4} d e^{2} - {\left(B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + 6 \, {\left(3 \, B b^{4} d^{2} e - 3 \, {\left(B a b^{3} - A b^{4}\right)} d e^{2} + {\left(B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 12 \, {\left(B b^{4} d^{3} - 3 \, {\left(B a b^{3} - A b^{4}\right)} d^{2} e + 3 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{2} - {\left(B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x - 12 \, {\left({\left(B a b^{3} - A b^{4}\right)} d^{3} - 3 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e + 3 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} d e^{2} - {\left(B a^{4} - A a^{3} b\right)} e^{3}\right)} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*B*b^4*e^3*x^4 + 4*(3*B*b^4*d*e^2 - (B*a*b^3 - A*b^4)*e^3)*x^3 + 6*(3*B*b^4*d^2*e - 3*(B*a*b^3 - A*b^4)*d*e^2 + (B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 12*(B*b^4*d^3 - 3*(B*a*b^3 - A*b^4)*d^2*e + 3*(B*a^2*b^2 - A*a*b^3)*d*e^2 - (B*a^3*b - A*a^2*b^2)*e^3)*x - 12*((B*a*b^3 - A*b^4)*d^3 - 3*(B*a^2*b^2 - A*a*b^3)*d^2*e + 3*(B*a^3*b - A*a^2*b^2)*d*e^2 - (B*a^4 - A*a^3*b)*e^3)*log(b*x + a))/b^5","A",0
1760,1,158,0,0.434401," ","integrate((B*x+A)*(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, B b^{3} e^{2} x^{3} + 3 \, {\left(2 \, B b^{3} d e - {\left(B a b^{2} - A b^{3}\right)} e^{2}\right)} x^{2} + 6 \, {\left(B b^{3} d^{2} - 2 \, {\left(B a b^{2} - A b^{3}\right)} d e + {\left(B a^{2} b - A a b^{2}\right)} e^{2}\right)} x - 6 \, {\left({\left(B a b^{2} - A b^{3}\right)} d^{2} - 2 \, {\left(B a^{2} b - A a b^{2}\right)} d e + {\left(B a^{3} - A a^{2} b\right)} e^{2}\right)} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*B*b^3*e^2*x^3 + 3*(2*B*b^3*d*e - (B*a*b^2 - A*b^3)*e^2)*x^2 + 6*(B*b^3*d^2 - 2*(B*a*b^2 - A*b^3)*d*e + (B*a^2*b - A*a*b^2)*e^2)*x - 6*((B*a*b^2 - A*b^3)*d^2 - 2*(B*a^2*b - A*a*b^2)*d*e + (B*a^3 - A*a^2*b)*e^2)*log(b*x + a))/b^4","A",0
1761,1,75,0,0.430592," ","integrate((B*x+A)*(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{B b^{2} e x^{2} + 2 \, {\left(B b^{2} d - {\left(B a b - A b^{2}\right)} e\right)} x - 2 \, {\left({\left(B a b - A b^{2}\right)} d - {\left(B a^{2} - A a b\right)} e\right)} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(B*b^2*e*x^2 + 2*(B*b^2*d - (B*a*b - A*b^2)*e)*x - 2*((B*a*b - A*b^2)*d - (B*a^2 - A*a*b)*e)*log(b*x + a))/b^3","A",0
1762,1,25,0,0.413841," ","integrate((B*x+A)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{B b x - {\left(B a - A b\right)} \log\left(b x + a\right)}{b^{2}}"," ",0,"(B*b*x - (B*a - A*b)*log(b*x + a))/b^2","A",0
1763,1,53,0,0.422286," ","integrate((B*x+A)/(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(B a - A b\right)} e \log\left(b x + a\right) - {\left(B b d - A b e\right)} \log\left(e x + d\right)}{b^{2} d e - a b e^{2}}"," ",0,"-((B*a - A*b)*e*log(b*x + a) - (B*b*d - A*b*e)*log(e*x + d))/(b^2*d*e - a*b*e^2)","A",0
1764,1,148,0,0.435103," ","integrate((B*x+A)/(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{B b d^{2} + A a e^{2} - {\left(B a + A b\right)} d e + {\left({\left(B a - A b\right)} e^{2} x + {\left(B a - A b\right)} d e\right)} \log\left(b x + a\right) - {\left({\left(B a - A b\right)} e^{2} x + {\left(B a - A b\right)} d e\right)} \log\left(e x + d\right)}{b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x}"," ",0,"-(B*b*d^2 + A*a*e^2 - (B*a + A*b)*d*e + ((B*a - A*b)*e^2*x + (B*a - A*b)*d*e)*log(b*x + a) - ((B*a - A*b)*e^2*x + (B*a - A*b)*d*e)*log(e*x + d))/(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x)","A",0
1765,1,343,0,0.435077," ","integrate((B*x+A)/(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{B b^{2} d^{3} - 3 \, A b^{2} d^{2} e - A a^{2} e^{3} - {\left(B a^{2} - 4 \, A a b\right)} d e^{2} + 2 \, {\left({\left(B a b - A b^{2}\right)} d e^{2} - {\left(B a^{2} - A a b\right)} e^{3}\right)} x + 2 \, {\left({\left(B a b - A b^{2}\right)} e^{3} x^{2} + 2 \, {\left(B a b - A b^{2}\right)} d e^{2} x + {\left(B a b - A b^{2}\right)} d^{2} e\right)} \log\left(b x + a\right) - 2 \, {\left({\left(B a b - A b^{2}\right)} e^{3} x^{2} + 2 \, {\left(B a b - A b^{2}\right)} d e^{2} x + {\left(B a b - A b^{2}\right)} d^{2} e\right)} \log\left(e x + d\right)}{2 \, {\left(b^{3} d^{5} e - 3 \, a b^{2} d^{4} e^{2} + 3 \, a^{2} b d^{3} e^{3} - a^{3} d^{2} e^{4} + {\left(b^{3} d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} b d e^{5} - a^{3} e^{6}\right)} x^{2} + 2 \, {\left(b^{3} d^{4} e^{2} - 3 \, a b^{2} d^{3} e^{3} + 3 \, a^{2} b d^{2} e^{4} - a^{3} d e^{5}\right)} x\right)}}"," ",0,"-1/2*(B*b^2*d^3 - 3*A*b^2*d^2*e - A*a^2*e^3 - (B*a^2 - 4*A*a*b)*d*e^2 + 2*((B*a*b - A*b^2)*d*e^2 - (B*a^2 - A*a*b)*e^3)*x + 2*((B*a*b - A*b^2)*e^3*x^2 + 2*(B*a*b - A*b^2)*d*e^2*x + (B*a*b - A*b^2)*d^2*e)*log(b*x + a) - 2*((B*a*b - A*b^2)*e^3*x^2 + 2*(B*a*b - A*b^2)*d*e^2*x + (B*a*b - A*b^2)*d^2*e)*log(e*x + d))/(b^3*d^5*e - 3*a*b^2*d^4*e^2 + 3*a^2*b*d^3*e^3 - a^3*d^2*e^4 + (b^3*d^3*e^3 - 3*a*b^2*d^2*e^4 + 3*a^2*b*d*e^5 - a^3*e^6)*x^2 + 2*(b^3*d^4*e^2 - 3*a*b^2*d^3*e^3 + 3*a^2*b*d^2*e^4 - a^3*d*e^5)*x)","B",0
1766,1,608,0,0.456553," ","integrate((B*x+A)/(e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, B b^{3} d^{4} + 2 \, A a^{3} e^{4} + {\left(3 \, B a b^{2} - 11 \, A b^{3}\right)} d^{3} e - 6 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} d^{2} e^{2} + {\left(B a^{3} - 9 \, A a^{2} b\right)} d e^{3} + 6 \, {\left({\left(B a b^{2} - A b^{3}\right)} d e^{3} - {\left(B a^{2} b - A a b^{2}\right)} e^{4}\right)} x^{2} + 3 \, {\left(5 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} - 6 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{3} + {\left(B a^{3} - A a^{2} b\right)} e^{4}\right)} x + 6 \, {\left({\left(B a b^{2} - A b^{3}\right)} e^{4} x^{3} + 3 \, {\left(B a b^{2} - A b^{3}\right)} d e^{3} x^{2} + 3 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} x + {\left(B a b^{2} - A b^{3}\right)} d^{3} e\right)} \log\left(b x + a\right) - 6 \, {\left({\left(B a b^{2} - A b^{3}\right)} e^{4} x^{3} + 3 \, {\left(B a b^{2} - A b^{3}\right)} d e^{3} x^{2} + 3 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} x + {\left(B a b^{2} - A b^{3}\right)} d^{3} e\right)} \log\left(e x + d\right)}{6 \, {\left(b^{4} d^{7} e - 4 \, a b^{3} d^{6} e^{2} + 6 \, a^{2} b^{2} d^{5} e^{3} - 4 \, a^{3} b d^{4} e^{4} + a^{4} d^{3} e^{5} + {\left(b^{4} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} x^{3} + 3 \, {\left(b^{4} d^{5} e^{3} - 4 \, a b^{3} d^{4} e^{4} + 6 \, a^{2} b^{2} d^{3} e^{5} - 4 \, a^{3} b d^{2} e^{6} + a^{4} d e^{7}\right)} x^{2} + 3 \, {\left(b^{4} d^{6} e^{2} - 4 \, a b^{3} d^{5} e^{3} + 6 \, a^{2} b^{2} d^{4} e^{4} - 4 \, a^{3} b d^{3} e^{5} + a^{4} d^{2} e^{6}\right)} x\right)}}"," ",0,"-1/6*(2*B*b^3*d^4 + 2*A*a^3*e^4 + (3*B*a*b^2 - 11*A*b^3)*d^3*e - 6*(B*a^2*b - 3*A*a*b^2)*d^2*e^2 + (B*a^3 - 9*A*a^2*b)*d*e^3 + 6*((B*a*b^2 - A*b^3)*d*e^3 - (B*a^2*b - A*a*b^2)*e^4)*x^2 + 3*(5*(B*a*b^2 - A*b^3)*d^2*e^2 - 6*(B*a^2*b - A*a*b^2)*d*e^3 + (B*a^3 - A*a^2*b)*e^4)*x + 6*((B*a*b^2 - A*b^3)*e^4*x^3 + 3*(B*a*b^2 - A*b^3)*d*e^3*x^2 + 3*(B*a*b^2 - A*b^3)*d^2*e^2*x + (B*a*b^2 - A*b^3)*d^3*e)*log(b*x + a) - 6*((B*a*b^2 - A*b^3)*e^4*x^3 + 3*(B*a*b^2 - A*b^3)*d*e^3*x^2 + 3*(B*a*b^2 - A*b^3)*d^2*e^2*x + (B*a*b^2 - A*b^3)*d^3*e)*log(e*x + d))/(b^4*d^7*e - 4*a*b^3*d^6*e^2 + 6*a^2*b^2*d^5*e^3 - 4*a^3*b*d^4*e^4 + a^4*d^3*e^5 + (b^4*d^4*e^4 - 4*a*b^3*d^3*e^5 + 6*a^2*b^2*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*x^3 + 3*(b^4*d^5*e^3 - 4*a*b^3*d^4*e^4 + 6*a^2*b^2*d^3*e^5 - 4*a^3*b*d^2*e^6 + a^4*d*e^7)*x^2 + 3*(b^4*d^6*e^2 - 4*a*b^3*d^5*e^3 + 6*a^2*b^2*d^4*e^4 - 4*a^3*b*d^3*e^5 + a^4*d^2*e^6)*x)","B",0
1767,1,668,0,0.434517," ","integrate((B*x+A)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, B b^{5} e^{4} x^{5} - 3 \, {\left(B a b^{4} + A b^{5}\right)} d^{4} + 12 \, {\left(3 \, B a^{2} b^{3} - A a b^{4}\right)} d^{3} e - 18 \, {\left(5 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} d^{2} e^{2} + 12 \, {\left(7 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} d e^{3} - 3 \, {\left(9 \, B a^{5} - 7 \, A a^{4} b\right)} e^{4} + {\left(12 \, B b^{5} d e^{3} - {\left(5 \, B a b^{4} - 3 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(9 \, B b^{5} d^{2} e^{2} - 6 \, {\left(2 \, B a b^{4} - A b^{5}\right)} d e^{3} + {\left(5 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(24 \, B a b^{4} d^{2} e^{2} - 4 \, {\left(11 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} d e^{3} + {\left(21 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - 6 \, {\left(B b^{5} d^{4} - 4 \, {\left(2 \, B a b^{4} - A b^{5}\right)} d^{3} e + 12 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d^{2} e^{2} - 4 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d e^{3} - {\left(B a^{4} b + A a^{3} b^{2}\right)} e^{4}\right)} x + 12 \, {\left(2 \, B a^{2} b^{3} d^{3} e - 3 \, {\left(3 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} d^{2} e^{2} + 6 \, {\left(2 \, B a^{4} b - A a^{3} b^{2}\right)} d e^{3} - {\left(5 \, B a^{5} - 3 \, A a^{4} b\right)} e^{4} + {\left(2 \, B b^{5} d^{3} e - 3 \, {\left(3 \, B a b^{4} - A b^{5}\right)} d^{2} e^{2} + 6 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} d e^{3} - {\left(5 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, B a b^{4} d^{3} e - 3 \, {\left(3 \, B a^{2} b^{3} - A a b^{4}\right)} d^{2} e^{2} + 6 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} d e^{3} - {\left(5 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{8} x^{2} + 2 \, a b^{7} x + a^{2} b^{6}\right)}}"," ",0,"1/6*(2*B*b^5*e^4*x^5 - 3*(B*a*b^4 + A*b^5)*d^4 + 12*(3*B*a^2*b^3 - A*a*b^4)*d^3*e - 18*(5*B*a^3*b^2 - 3*A*a^2*b^3)*d^2*e^2 + 12*(7*B*a^4*b - 5*A*a^3*b^2)*d*e^3 - 3*(9*B*a^5 - 7*A*a^4*b)*e^4 + (12*B*b^5*d*e^3 - (5*B*a*b^4 - 3*A*b^5)*e^4)*x^4 + 4*(9*B*b^5*d^2*e^2 - 6*(2*B*a*b^4 - A*b^5)*d*e^3 + (5*B*a^2*b^3 - 3*A*a*b^4)*e^4)*x^3 + 3*(24*B*a*b^4*d^2*e^2 - 4*(11*B*a^2*b^3 - 4*A*a*b^4)*d*e^3 + (21*B*a^3*b^2 - 11*A*a^2*b^3)*e^4)*x^2 - 6*(B*b^5*d^4 - 4*(2*B*a*b^4 - A*b^5)*d^3*e + 12*(B*a^2*b^3 - A*a*b^4)*d^2*e^2 - 4*(B*a^3*b^2 - 2*A*a^2*b^3)*d*e^3 - (B*a^4*b + A*a^3*b^2)*e^4)*x + 12*(2*B*a^2*b^3*d^3*e - 3*(3*B*a^3*b^2 - A*a^2*b^3)*d^2*e^2 + 6*(2*B*a^4*b - A*a^3*b^2)*d*e^3 - (5*B*a^5 - 3*A*a^4*b)*e^4 + (2*B*b^5*d^3*e - 3*(3*B*a*b^4 - A*b^5)*d^2*e^2 + 6*(2*B*a^2*b^3 - A*a*b^4)*d*e^3 - (5*B*a^3*b^2 - 3*A*a^2*b^3)*e^4)*x^2 + 2*(2*B*a*b^4*d^3*e - 3*(3*B*a^2*b^3 - A*a*b^4)*d^2*e^2 + 6*(2*B*a^3*b^2 - A*a^2*b^3)*d*e^3 - (5*B*a^4*b - 3*A*a^3*b^2)*e^4)*x)*log(b*x + a))/(b^8*x^2 + 2*a*b^7*x + a^2*b^6)","B",0
1768,1,442,0,0.432852," ","integrate((B*x+A)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{B b^{4} e^{3} x^{4} - {\left(B a b^{3} + A b^{4}\right)} d^{3} + 3 \, {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} d^{2} e - 3 \, {\left(5 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} d e^{2} + {\left(7 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + 2 \, {\left(3 \, B b^{4} d e^{2} - {\left(2 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + {\left(12 \, B a b^{3} d e^{2} - {\left(11 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{3}\right)} x^{2} - 2 \, {\left(B b^{4} d^{3} - 3 \, {\left(2 \, B a b^{3} - A b^{4}\right)} d^{2} e + 6 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{2} - {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{3}\right)} x + 6 \, {\left(B a^{2} b^{2} d^{2} e - {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} d e^{2} + {\left(2 \, B a^{4} - A a^{3} b\right)} e^{3} + {\left(B b^{4} d^{2} e - {\left(3 \, B a b^{3} - A b^{4}\right)} d e^{2} + {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(B a b^{3} d^{2} e - {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} d e^{2} + {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/2*(B*b^4*e^3*x^4 - (B*a*b^3 + A*b^4)*d^3 + 3*(3*B*a^2*b^2 - A*a*b^3)*d^2*e - 3*(5*B*a^3*b - 3*A*a^2*b^2)*d*e^2 + (7*B*a^4 - 5*A*a^3*b)*e^3 + 2*(3*B*b^4*d*e^2 - (2*B*a*b^3 - A*b^4)*e^3)*x^3 + (12*B*a*b^3*d*e^2 - (11*B*a^2*b^2 - 4*A*a*b^3)*e^3)*x^2 - 2*(B*b^4*d^3 - 3*(2*B*a*b^3 - A*b^4)*d^2*e + 6*(B*a^2*b^2 - A*a*b^3)*d*e^2 - (B*a^3*b - 2*A*a^2*b^2)*e^3)*x + 6*(B*a^2*b^2*d^2*e - (3*B*a^3*b - A*a^2*b^2)*d*e^2 + (2*B*a^4 - A*a^3*b)*e^3 + (B*b^4*d^2*e - (3*B*a*b^3 - A*b^4)*d*e^2 + (2*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 2*(B*a*b^3*d^2*e - (3*B*a^2*b^2 - A*a*b^3)*d*e^2 + (2*B*a^3*b - A*a^2*b^2)*e^3)*x)*log(b*x + a))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","B",0
1769,1,258,0,0.436710," ","integrate((B*x+A)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, B b^{3} e^{2} x^{3} + 4 \, B a b^{2} e^{2} x^{2} - {\left(B a b^{2} + A b^{3}\right)} d^{2} + 2 \, {\left(3 \, B a^{2} b - A a b^{2}\right)} d e - {\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} - 2 \, {\left(B b^{3} d^{2} - 2 \, {\left(2 \, B a b^{2} - A b^{3}\right)} d e + 2 \, {\left(B a^{2} b - A a b^{2}\right)} e^{2}\right)} x + 2 \, {\left(2 \, B a^{2} b d e - {\left(3 \, B a^{3} - A a^{2} b\right)} e^{2} + {\left(2 \, B b^{3} d e - {\left(3 \, B a b^{2} - A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(2 \, B a b^{2} d e - {\left(3 \, B a^{2} b - A a b^{2}\right)} e^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*B*b^3*e^2*x^3 + 4*B*a*b^2*e^2*x^2 - (B*a*b^2 + A*b^3)*d^2 + 2*(3*B*a^2*b - A*a*b^2)*d*e - (5*B*a^3 - 3*A*a^2*b)*e^2 - 2*(B*b^3*d^2 - 2*(2*B*a*b^2 - A*b^3)*d*e + 2*(B*a^2*b - A*a*b^2)*e^2)*x + 2*(2*B*a^2*b*d*e - (3*B*a^3 - A*a^2*b)*e^2 + (2*B*b^3*d*e - (3*B*a*b^2 - A*b^3)*e^2)*x^2 + 2*(2*B*a*b^2*d*e - (3*B*a^2*b - A*a*b^2)*e^2)*x)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","A",0
1770,1,110,0,0.432012," ","integrate((B*x+A)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(B a b + A b^{2}\right)} d - {\left(3 \, B a^{2} - A a b\right)} e + 2 \, {\left(B b^{2} d - {\left(2 \, B a b - A b^{2}\right)} e\right)} x - 2 \, {\left(B b^{2} e x^{2} + 2 \, B a b e x + B a^{2} e\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"-1/2*((B*a*b + A*b^2)*d - (3*B*a^2 - A*a*b)*e + 2*(B*b^2*d - (2*B*a*b - A*b^2)*e)*x - 2*(B*b^2*e*x^2 + 2*B*a*b*e*x + B*a^2*e)*log(b*x + a))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
1771,1,38,0,0.421492," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, B b x + B a + A b}{2 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*B*b*x + B*a + A*b)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
1772,1,361,0,0.429252," ","integrate((B*x+A)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{4 \, A a b^{2} d e - {\left(B a b^{2} + A b^{3}\right)} d^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} e^{2} - 2 \, {\left(B b^{3} d^{2} + A a b^{2} e^{2} - {\left(B a b^{2} + A b^{3}\right)} d e\right)} x - 2 \, {\left(B a^{2} b d e - A a^{2} b e^{2} + {\left(B b^{3} d e - A b^{3} e^{2}\right)} x^{2} + 2 \, {\left(B a b^{2} d e - A a b^{2} e^{2}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(B a^{2} b d e - A a^{2} b e^{2} + {\left(B b^{3} d e - A b^{3} e^{2}\right)} x^{2} + 2 \, {\left(B a b^{2} d e - A a b^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{4} d^{3} - 3 \, a^{3} b^{3} d^{2} e + 3 \, a^{4} b^{2} d e^{2} - a^{5} b e^{3} + {\left(b^{6} d^{3} - 3 \, a b^{5} d^{2} e + 3 \, a^{2} b^{4} d e^{2} - a^{3} b^{3} e^{3}\right)} x^{2} + 2 \, {\left(a b^{5} d^{3} - 3 \, a^{2} b^{4} d^{2} e + 3 \, a^{3} b^{3} d e^{2} - a^{4} b^{2} e^{3}\right)} x\right)}}"," ",0,"1/2*(4*A*a*b^2*d*e - (B*a*b^2 + A*b^3)*d^2 + (B*a^3 - 3*A*a^2*b)*e^2 - 2*(B*b^3*d^2 + A*a*b^2*e^2 - (B*a*b^2 + A*b^3)*d*e)*x - 2*(B*a^2*b*d*e - A*a^2*b*e^2 + (B*b^3*d*e - A*b^3*e^2)*x^2 + 2*(B*a*b^2*d*e - A*a*b^2*e^2)*x)*log(b*x + a) + 2*(B*a^2*b*d*e - A*a^2*b*e^2 + (B*b^3*d*e - A*b^3*e^2)*x^2 + 2*(B*a*b^2*d*e - A*a*b^2*e^2)*x)*log(e*x + d))/(a^2*b^4*d^3 - 3*a^3*b^3*d^2*e + 3*a^4*b^2*d*e^2 - a^5*b*e^3 + (b^6*d^3 - 3*a*b^5*d^2*e + 3*a^2*b^4*d*e^2 - a^3*b^3*e^3)*x^2 + 2*(a*b^5*d^3 - 3*a^2*b^4*d^2*e + 3*a^3*b^3*d*e^2 - a^4*b^2*e^3)*x)","B",0
1773,1,803,0,0.442275," ","integrate((B*x+A)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, A a^{3} e^{3} + {\left(B a b^{2} + A b^{3}\right)} d^{3} + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d^{2} e - {\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} d e^{2} + 2 \, {\left(2 \, B b^{3} d^{2} e - {\left(B a b^{2} + 3 \, A b^{3}\right)} d e^{2} - {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, B b^{3} d^{3} + {\left(5 \, B a b^{2} - 3 \, A b^{3}\right)} d^{2} e - 2 \, {\left(2 \, B a^{2} b + 3 \, A a b^{2}\right)} d e^{2} - 3 \, {\left(B a^{3} - 3 \, A a^{2} b\right)} e^{3}\right)} x + 2 \, {\left(2 \, B a^{2} b d^{2} e + {\left(B a^{3} - 3 \, A a^{2} b\right)} d e^{2} + {\left(2 \, B b^{3} d e^{2} + {\left(B a b^{2} - 3 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(2 \, B b^{3} d^{2} e + {\left(5 \, B a b^{2} - 3 \, A b^{3}\right)} d e^{2} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(4 \, B a b^{2} d^{2} e + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} e^{3}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(2 \, B a^{2} b d^{2} e + {\left(B a^{3} - 3 \, A a^{2} b\right)} d e^{2} + {\left(2 \, B b^{3} d e^{2} + {\left(B a b^{2} - 3 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(2 \, B b^{3} d^{2} e + {\left(5 \, B a b^{2} - 3 \, A b^{3}\right)} d e^{2} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(4 \, B a b^{2} d^{2} e + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{4} d^{5} - 4 \, a^{3} b^{3} d^{4} e + 6 \, a^{4} b^{2} d^{3} e^{2} - 4 \, a^{5} b d^{2} e^{3} + a^{6} d e^{4} + {\left(b^{6} d^{4} e - 4 \, a b^{5} d^{3} e^{2} + 6 \, a^{2} b^{4} d^{2} e^{3} - 4 \, a^{3} b^{3} d e^{4} + a^{4} b^{2} e^{5}\right)} x^{3} + {\left(b^{6} d^{5} - 2 \, a b^{5} d^{4} e - 2 \, a^{2} b^{4} d^{3} e^{2} + 8 \, a^{3} b^{3} d^{2} e^{3} - 7 \, a^{4} b^{2} d e^{4} + 2 \, a^{5} b e^{5}\right)} x^{2} + {\left(2 \, a b^{5} d^{5} - 7 \, a^{2} b^{4} d^{4} e + 8 \, a^{3} b^{3} d^{3} e^{2} - 2 \, a^{4} b^{2} d^{2} e^{3} - 2 \, a^{5} b d e^{4} + a^{6} e^{5}\right)} x\right)}}"," ",0,"-1/2*(2*A*a^3*e^3 + (B*a*b^2 + A*b^3)*d^3 + 2*(2*B*a^2*b - 3*A*a*b^2)*d^2*e - (5*B*a^3 - 3*A*a^2*b)*d*e^2 + 2*(2*B*b^3*d^2*e - (B*a*b^2 + 3*A*b^3)*d*e^2 - (B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (2*B*b^3*d^3 + (5*B*a*b^2 - 3*A*b^3)*d^2*e - 2*(2*B*a^2*b + 3*A*a*b^2)*d*e^2 - 3*(B*a^3 - 3*A*a^2*b)*e^3)*x + 2*(2*B*a^2*b*d^2*e + (B*a^3 - 3*A*a^2*b)*d*e^2 + (2*B*b^3*d*e^2 + (B*a*b^2 - 3*A*b^3)*e^3)*x^3 + (2*B*b^3*d^2*e + (5*B*a*b^2 - 3*A*b^3)*d*e^2 + 2*(B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (4*B*a*b^2*d^2*e + 2*(2*B*a^2*b - 3*A*a*b^2)*d*e^2 + (B*a^3 - 3*A*a^2*b)*e^3)*x)*log(b*x + a) - 2*(2*B*a^2*b*d^2*e + (B*a^3 - 3*A*a^2*b)*d*e^2 + (2*B*b^3*d*e^2 + (B*a*b^2 - 3*A*b^3)*e^3)*x^3 + (2*B*b^3*d^2*e + (5*B*a*b^2 - 3*A*b^3)*d*e^2 + 2*(B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (4*B*a*b^2*d^2*e + 2*(2*B*a^2*b - 3*A*a*b^2)*d*e^2 + (B*a^3 - 3*A*a^2*b)*e^3)*x)*log(e*x + d))/(a^2*b^4*d^5 - 4*a^3*b^3*d^4*e + 6*a^4*b^2*d^3*e^2 - 4*a^5*b*d^2*e^3 + a^6*d*e^4 + (b^6*d^4*e - 4*a*b^5*d^3*e^2 + 6*a^2*b^4*d^2*e^3 - 4*a^3*b^3*d*e^4 + a^4*b^2*e^5)*x^3 + (b^6*d^5 - 2*a*b^5*d^4*e - 2*a^2*b^4*d^3*e^2 + 8*a^3*b^3*d^2*e^3 - 7*a^4*b^2*d*e^4 + 2*a^5*b*e^5)*x^2 + (2*a*b^5*d^5 - 7*a^2*b^4*d^4*e + 8*a^3*b^3*d^3*e^2 - 2*a^4*b^2*d^2*e^3 - 2*a^5*b*d*e^4 + a^6*e^5)*x)","B",0
1774,1,1215,0,0.468054," ","integrate((B*x+A)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{9 \, B a^{3} b d^{2} e^{2} + A a^{4} e^{4} - {\left(B a b^{3} + A b^{4}\right)} d^{4} - {\left(9 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} d^{3} e + {\left(B a^{4} - 8 \, A a^{3} b\right)} d e^{3} - 6 \, {\left(B b^{4} d^{2} e^{2} - 2 \, A b^{4} d e^{3} - {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} e^{4}\right)} x^{3} - 9 \, {\left(B b^{4} d^{3} e - B a^{2} b^{2} d e^{3} + {\left(B a b^{3} - 2 \, A b^{4}\right)} d^{2} e^{2} - {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - 2 \, {\left(B b^{4} d^{4} - 12 \, A a b^{3} d^{2} e^{2} + {\left(7 \, B a b^{3} - 2 \, A b^{4}\right)} d^{3} e - {\left(7 \, B a^{3} b - 12 \, A a^{2} b^{2}\right)} d e^{3} - {\left(B a^{4} - 2 \, A a^{3} b\right)} e^{4}\right)} x - 6 \, {\left(B a^{2} b^{2} d^{3} e + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d^{2} e^{2} + {\left(B b^{4} d e^{3} + {\left(B a b^{3} - 2 \, A b^{4}\right)} e^{4}\right)} x^{4} + 2 \, {\left(B b^{4} d^{2} e^{2} + 2 \, {\left(B a b^{3} - A b^{4}\right)} d e^{3} + {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} e^{4}\right)} x^{3} + {\left(B b^{4} d^{3} e + {\left(5 \, B a b^{3} - 2 \, A b^{4}\right)} d^{2} e^{2} + {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} d e^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(B a b^{3} d^{3} e + 2 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e^{2} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(B a^{2} b^{2} d^{3} e + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d^{2} e^{2} + {\left(B b^{4} d e^{3} + {\left(B a b^{3} - 2 \, A b^{4}\right)} e^{4}\right)} x^{4} + 2 \, {\left(B b^{4} d^{2} e^{2} + 2 \, {\left(B a b^{3} - A b^{4}\right)} d e^{3} + {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} e^{4}\right)} x^{3} + {\left(B b^{4} d^{3} e + {\left(5 \, B a b^{3} - 2 \, A b^{4}\right)} d^{2} e^{2} + {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} d e^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(B a b^{3} d^{3} e + 2 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e^{2} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{5} d^{7} - 5 \, a^{3} b^{4} d^{6} e + 10 \, a^{4} b^{3} d^{5} e^{2} - 10 \, a^{5} b^{2} d^{4} e^{3} + 5 \, a^{6} b d^{3} e^{4} - a^{7} d^{2} e^{5} + {\left(b^{7} d^{5} e^{2} - 5 \, a b^{6} d^{4} e^{3} + 10 \, a^{2} b^{5} d^{3} e^{4} - 10 \, a^{3} b^{4} d^{2} e^{5} + 5 \, a^{4} b^{3} d e^{6} - a^{5} b^{2} e^{7}\right)} x^{4} + 2 \, {\left(b^{7} d^{6} e - 4 \, a b^{6} d^{5} e^{2} + 5 \, a^{2} b^{5} d^{4} e^{3} - 5 \, a^{4} b^{3} d^{2} e^{5} + 4 \, a^{5} b^{2} d e^{6} - a^{6} b e^{7}\right)} x^{3} + {\left(b^{7} d^{7} - a b^{6} d^{6} e - 9 \, a^{2} b^{5} d^{5} e^{2} + 25 \, a^{3} b^{4} d^{4} e^{3} - 25 \, a^{4} b^{3} d^{3} e^{4} + 9 \, a^{5} b^{2} d^{2} e^{5} + a^{6} b d e^{6} - a^{7} e^{7}\right)} x^{2} + 2 \, {\left(a b^{6} d^{7} - 4 \, a^{2} b^{5} d^{6} e + 5 \, a^{3} b^{4} d^{5} e^{2} - 5 \, a^{5} b^{2} d^{3} e^{4} + 4 \, a^{6} b d^{2} e^{5} - a^{7} d e^{6}\right)} x\right)}}"," ",0,"1/2*(9*B*a^3*b*d^2*e^2 + A*a^4*e^4 - (B*a*b^3 + A*b^4)*d^4 - (9*B*a^2*b^2 - 8*A*a*b^3)*d^3*e + (B*a^4 - 8*A*a^3*b)*d*e^3 - 6*(B*b^4*d^2*e^2 - 2*A*b^4*d*e^3 - (B*a^2*b^2 - 2*A*a*b^3)*e^4)*x^3 - 9*(B*b^4*d^3*e - B*a^2*b^2*d*e^3 + (B*a*b^3 - 2*A*b^4)*d^2*e^2 - (B*a^3*b - 2*A*a^2*b^2)*e^4)*x^2 - 2*(B*b^4*d^4 - 12*A*a*b^3*d^2*e^2 + (7*B*a*b^3 - 2*A*b^4)*d^3*e - (7*B*a^3*b - 12*A*a^2*b^2)*d*e^3 - (B*a^4 - 2*A*a^3*b)*e^4)*x - 6*(B*a^2*b^2*d^3*e + (B*a^3*b - 2*A*a^2*b^2)*d^2*e^2 + (B*b^4*d*e^3 + (B*a*b^3 - 2*A*b^4)*e^4)*x^4 + 2*(B*b^4*d^2*e^2 + 2*(B*a*b^3 - A*b^4)*d*e^3 + (B*a^2*b^2 - 2*A*a*b^3)*e^4)*x^3 + (B*b^4*d^3*e + (5*B*a*b^3 - 2*A*b^4)*d^2*e^2 + (5*B*a^2*b^2 - 8*A*a*b^3)*d*e^3 + (B*a^3*b - 2*A*a^2*b^2)*e^4)*x^2 + 2*(B*a*b^3*d^3*e + 2*(B*a^2*b^2 - A*a*b^3)*d^2*e^2 + (B*a^3*b - 2*A*a^2*b^2)*d*e^3)*x)*log(b*x + a) + 6*(B*a^2*b^2*d^3*e + (B*a^3*b - 2*A*a^2*b^2)*d^2*e^2 + (B*b^4*d*e^3 + (B*a*b^3 - 2*A*b^4)*e^4)*x^4 + 2*(B*b^4*d^2*e^2 + 2*(B*a*b^3 - A*b^4)*d*e^3 + (B*a^2*b^2 - 2*A*a*b^3)*e^4)*x^3 + (B*b^4*d^3*e + (5*B*a*b^3 - 2*A*b^4)*d^2*e^2 + (5*B*a^2*b^2 - 8*A*a*b^3)*d*e^3 + (B*a^3*b - 2*A*a^2*b^2)*e^4)*x^2 + 2*(B*a*b^3*d^3*e + 2*(B*a^2*b^2 - A*a*b^3)*d^2*e^2 + (B*a^3*b - 2*A*a^2*b^2)*d*e^3)*x)*log(e*x + d))/(a^2*b^5*d^7 - 5*a^3*b^4*d^6*e + 10*a^4*b^3*d^5*e^2 - 10*a^5*b^2*d^4*e^3 + 5*a^6*b*d^3*e^4 - a^7*d^2*e^5 + (b^7*d^5*e^2 - 5*a*b^6*d^4*e^3 + 10*a^2*b^5*d^3*e^4 - 10*a^3*b^4*d^2*e^5 + 5*a^4*b^3*d*e^6 - a^5*b^2*e^7)*x^4 + 2*(b^7*d^6*e - 4*a*b^6*d^5*e^2 + 5*a^2*b^5*d^4*e^3 - 5*a^4*b^3*d^2*e^5 + 4*a^5*b^2*d*e^6 - a^6*b*e^7)*x^3 + (b^7*d^7 - a*b^6*d^6*e - 9*a^2*b^5*d^5*e^2 + 25*a^3*b^4*d^4*e^3 - 25*a^4*b^3*d^3*e^4 + 9*a^5*b^2*d^2*e^5 + a^6*b*d*e^6 - a^7*e^7)*x^2 + 2*(a*b^6*d^7 - 4*a^2*b^5*d^6*e + 5*a^3*b^4*d^5*e^2 - 5*a^5*b^2*d^3*e^4 + 4*a^6*b*d^2*e^5 - a^7*d*e^6)*x)","B",0
1775,1,914,0,0.446254," ","integrate((B*x+A)*(e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{6 \, B b^{6} e^{5} x^{6} - {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{5} - 5 \, {\left(B a^{2} b^{4} + A a b^{5}\right)} d^{4} e - 10 \, {\left(3 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} d^{3} e^{2} + 10 \, {\left(25 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} d^{2} e^{3} - 5 \, {\left(77 \, B a^{5} b - 25 \, A a^{4} b^{2}\right)} d e^{4} + {\left(171 \, B a^{6} - 77 \, A a^{5} b\right)} e^{5} + 12 \, {\left(5 \, B b^{6} d e^{4} - {\left(3 \, B a b^{5} - A b^{6}\right)} e^{5}\right)} x^{5} + 12 \, {\left(20 \, B a b^{5} d e^{4} - {\left(17 \, B a^{2} b^{4} - 4 \, A a b^{5}\right)} e^{5}\right)} x^{4} - 24 \, {\left(5 \, B b^{6} d^{3} e^{2} - 5 \, {\left(4 \, B a b^{5} - A b^{6}\right)} d^{2} e^{3} + 10 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} d e^{4} + 2 \, {\left(2 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} e^{5}\right)} x^{3} - 6 \, {\left(5 \, B b^{6} d^{4} e + 10 \, {\left(3 \, B a b^{5} + A b^{6}\right)} d^{3} e^{2} - 30 \, {\left(6 \, B a^{2} b^{4} - A a b^{5}\right)} d^{2} e^{3} + 30 \, {\left(7 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} d e^{4} - 6 \, {\left(11 \, B a^{4} b^{2} - 7 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} - 4 \, {\left(B b^{6} d^{5} + 5 \, {\left(B a b^{5} + A b^{6}\right)} d^{4} e + 10 \, {\left(3 \, B a^{2} b^{4} + A a b^{5}\right)} d^{3} e^{2} - 10 \, {\left(22 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} d^{2} e^{3} + 10 \, {\left(31 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} d e^{4} - 2 \, {\left(63 \, B a^{5} b - 31 \, A a^{4} b^{2}\right)} e^{5}\right)} x + 60 \, {\left(2 \, B a^{4} b^{2} d^{2} e^{3} - {\left(5 \, B a^{5} b - A a^{4} b^{2}\right)} d e^{4} + {\left(3 \, B a^{6} - A a^{5} b\right)} e^{5} + {\left(2 \, B b^{6} d^{2} e^{3} - {\left(5 \, B a b^{5} - A b^{6}\right)} d e^{4} + {\left(3 \, B a^{2} b^{4} - A a b^{5}\right)} e^{5}\right)} x^{4} + 4 \, {\left(2 \, B a b^{5} d^{2} e^{3} - {\left(5 \, B a^{2} b^{4} - A a b^{5}\right)} d e^{4} + {\left(3 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 6 \, {\left(2 \, B a^{2} b^{4} d^{2} e^{3} - {\left(5 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} d e^{4} + {\left(3 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 4 \, {\left(2 \, B a^{3} b^{3} d^{2} e^{3} - {\left(5 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} d e^{4} + {\left(3 \, B a^{5} b - A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{11} x^{4} + 4 \, a b^{10} x^{3} + 6 \, a^{2} b^{9} x^{2} + 4 \, a^{3} b^{8} x + a^{4} b^{7}\right)}}"," ",0,"1/12*(6*B*b^6*e^5*x^6 - (B*a*b^5 + 3*A*b^6)*d^5 - 5*(B*a^2*b^4 + A*a*b^5)*d^4*e - 10*(3*B*a^3*b^3 + A*a^2*b^4)*d^3*e^2 + 10*(25*B*a^4*b^2 - 3*A*a^3*b^3)*d^2*e^3 - 5*(77*B*a^5*b - 25*A*a^4*b^2)*d*e^4 + (171*B*a^6 - 77*A*a^5*b)*e^5 + 12*(5*B*b^6*d*e^4 - (3*B*a*b^5 - A*b^6)*e^5)*x^5 + 12*(20*B*a*b^5*d*e^4 - (17*B*a^2*b^4 - 4*A*a*b^5)*e^5)*x^4 - 24*(5*B*b^6*d^3*e^2 - 5*(4*B*a*b^5 - A*b^6)*d^2*e^3 + 10*(B*a^2*b^4 - A*a*b^5)*d*e^4 + 2*(2*B*a^3*b^3 + A*a^2*b^4)*e^5)*x^3 - 6*(5*B*b^6*d^4*e + 10*(3*B*a*b^5 + A*b^6)*d^3*e^2 - 30*(6*B*a^2*b^4 - A*a*b^5)*d^2*e^3 + 30*(7*B*a^3*b^3 - 3*A*a^2*b^4)*d*e^4 - 6*(11*B*a^4*b^2 - 7*A*a^3*b^3)*e^5)*x^2 - 4*(B*b^6*d^5 + 5*(B*a*b^5 + A*b^6)*d^4*e + 10*(3*B*a^2*b^4 + A*a*b^5)*d^3*e^2 - 10*(22*B*a^3*b^3 - 3*A*a^2*b^4)*d^2*e^3 + 10*(31*B*a^4*b^2 - 11*A*a^3*b^3)*d*e^4 - 2*(63*B*a^5*b - 31*A*a^4*b^2)*e^5)*x + 60*(2*B*a^4*b^2*d^2*e^3 - (5*B*a^5*b - A*a^4*b^2)*d*e^4 + (3*B*a^6 - A*a^5*b)*e^5 + (2*B*b^6*d^2*e^3 - (5*B*a*b^5 - A*b^6)*d*e^4 + (3*B*a^2*b^4 - A*a*b^5)*e^5)*x^4 + 4*(2*B*a*b^5*d^2*e^3 - (5*B*a^2*b^4 - A*a*b^5)*d*e^4 + (3*B*a^3*b^3 - A*a^2*b^4)*e^5)*x^3 + 6*(2*B*a^2*b^4*d^2*e^3 - (5*B*a^3*b^3 - A*a^2*b^4)*d*e^4 + (3*B*a^4*b^2 - A*a^3*b^3)*e^5)*x^2 + 4*(2*B*a^3*b^3*d^2*e^3 - (5*B*a^4*b^2 - A*a^3*b^3)*d*e^4 + (3*B*a^5*b - A*a^4*b^2)*e^5)*x)*log(b*x + a))/(b^11*x^4 + 4*a*b^10*x^3 + 6*a^2*b^9*x^2 + 4*a^3*b^8*x + a^4*b^7)","B",0
1776,1,619,0,0.424523," ","integrate((B*x+A)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, B b^{5} e^{4} x^{5} + 48 \, B a b^{4} e^{4} x^{4} - {\left(B a b^{4} + 3 \, A b^{5}\right)} d^{4} - 4 \, {\left(B a^{2} b^{3} + A a b^{4}\right)} d^{3} e - 6 \, {\left(3 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{2} + 4 \, {\left(25 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} d e^{3} - {\left(77 \, B a^{5} - 25 \, A a^{4} b\right)} e^{4} - 24 \, {\left(3 \, B b^{5} d^{2} e^{2} - 2 \, {\left(4 \, B a b^{4} - A b^{5}\right)} d e^{3} + 2 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} e^{4}\right)} x^{3} - 12 \, {\left(2 \, B b^{5} d^{3} e + 3 \, {\left(3 \, B a b^{4} + A b^{5}\right)} d^{2} e^{2} - 6 \, {\left(6 \, B a^{2} b^{3} - A a b^{4}\right)} d e^{3} + 3 \, {\left(7 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - 4 \, {\left(B b^{5} d^{4} + 4 \, {\left(B a b^{4} + A b^{5}\right)} d^{3} e + 6 \, {\left(3 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{2} - 4 \, {\left(22 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} d e^{3} + 2 \, {\left(31 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{4}\right)} x + 12 \, {\left(4 \, B a^{4} b d e^{3} - {\left(5 \, B a^{5} - A a^{4} b\right)} e^{4} + {\left(4 \, B b^{5} d e^{3} - {\left(5 \, B a b^{4} - A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(4 \, B a b^{4} d e^{3} - {\left(5 \, B a^{2} b^{3} - A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(4 \, B a^{2} b^{3} d e^{3} - {\left(5 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(4 \, B a^{3} b^{2} d e^{3} - {\left(5 \, B a^{4} b - A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}"," ",0,"1/12*(12*B*b^5*e^4*x^5 + 48*B*a*b^4*e^4*x^4 - (B*a*b^4 + 3*A*b^5)*d^4 - 4*(B*a^2*b^3 + A*a*b^4)*d^3*e - 6*(3*B*a^3*b^2 + A*a^2*b^3)*d^2*e^2 + 4*(25*B*a^4*b - 3*A*a^3*b^2)*d*e^3 - (77*B*a^5 - 25*A*a^4*b)*e^4 - 24*(3*B*b^5*d^2*e^2 - 2*(4*B*a*b^4 - A*b^5)*d*e^3 + 2*(B*a^2*b^3 - A*a*b^4)*e^4)*x^3 - 12*(2*B*b^5*d^3*e + 3*(3*B*a*b^4 + A*b^5)*d^2*e^2 - 6*(6*B*a^2*b^3 - A*a*b^4)*d*e^3 + 3*(7*B*a^3*b^2 - 3*A*a^2*b^3)*e^4)*x^2 - 4*(B*b^5*d^4 + 4*(B*a*b^4 + A*b^5)*d^3*e + 6*(3*B*a^2*b^3 + A*a*b^4)*d^2*e^2 - 4*(22*B*a^3*b^2 - 3*A*a^2*b^3)*d*e^3 + 2*(31*B*a^4*b - 11*A*a^3*b^2)*e^4)*x + 12*(4*B*a^4*b*d*e^3 - (5*B*a^5 - A*a^4*b)*e^4 + (4*B*b^5*d*e^3 - (5*B*a*b^4 - A*b^5)*e^4)*x^4 + 4*(4*B*a*b^4*d*e^3 - (5*B*a^2*b^3 - A*a*b^4)*e^4)*x^3 + 6*(4*B*a^2*b^3*d*e^3 - (5*B*a^3*b^2 - A*a^2*b^3)*e^4)*x^2 + 4*(4*B*a^3*b^2*d*e^3 - (5*B*a^4*b - A*a^3*b^2)*e^4)*x)*log(b*x + a))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6)","B",0
1777,1,359,0,0.423395," ","integrate((B*x+A)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(B a b^{3} + 3 \, A b^{4}\right)} d^{3} + 3 \, {\left(B a^{2} b^{2} + A a b^{3}\right)} d^{2} e + 3 \, {\left(3 \, B a^{3} b + A a^{2} b^{2}\right)} d e^{2} - {\left(25 \, B a^{4} - 3 \, A a^{3} b\right)} e^{3} + 12 \, {\left(3 \, B b^{4} d e^{2} - {\left(4 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + 18 \, {\left(B b^{4} d^{2} e + {\left(3 \, B a b^{3} + A b^{4}\right)} d e^{2} - {\left(6 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 4 \, {\left(B b^{4} d^{3} + 3 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} e + 3 \, {\left(3 \, B a^{2} b^{2} + A a b^{3}\right)} d e^{2} - {\left(22 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} e^{3}\right)} x - 12 \, {\left(B b^{4} e^{3} x^{4} + 4 \, B a b^{3} e^{3} x^{3} + 6 \, B a^{2} b^{2} e^{3} x^{2} + 4 \, B a^{3} b e^{3} x + B a^{4} e^{3}\right)} \log\left(b x + a\right)}{12 \, {\left(b^{9} x^{4} + 4 \, a b^{8} x^{3} + 6 \, a^{2} b^{7} x^{2} + 4 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}"," ",0,"-1/12*((B*a*b^3 + 3*A*b^4)*d^3 + 3*(B*a^2*b^2 + A*a*b^3)*d^2*e + 3*(3*B*a^3*b + A*a^2*b^2)*d*e^2 - (25*B*a^4 - 3*A*a^3*b)*e^3 + 12*(3*B*b^4*d*e^2 - (4*B*a*b^3 - A*b^4)*e^3)*x^3 + 18*(B*b^4*d^2*e + (3*B*a*b^3 + A*b^4)*d*e^2 - (6*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 4*(B*b^4*d^3 + 3*(B*a*b^3 + A*b^4)*d^2*e + 3*(3*B*a^2*b^2 + A*a*b^3)*d*e^2 - (22*B*a^3*b - 3*A*a^2*b^2)*e^3)*x - 12*(B*b^4*e^3*x^4 + 4*B*a*b^3*e^3*x^3 + 6*B*a^2*b^2*e^3*x^2 + 4*B*a^3*b*e^3*x + B*a^4*e^3)*log(b*x + a))/(b^9*x^4 + 4*a*b^8*x^3 + 6*a^2*b^7*x^2 + 4*a^3*b^6*x + a^4*b^5)","B",0
1778,1,189,0,0.461240," ","integrate((B*x+A)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{12 \, B b^{3} e^{2} x^{3} + {\left(B a b^{2} + 3 \, A b^{3}\right)} d^{2} + 2 \, {\left(B a^{2} b + A a b^{2}\right)} d e + {\left(3 \, B a^{3} + A a^{2} b\right)} e^{2} + 6 \, {\left(2 \, B b^{3} d e + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{2}\right)} x^{2} + 4 \, {\left(B b^{3} d^{2} + 2 \, {\left(B a b^{2} + A b^{3}\right)} d e + {\left(3 \, B a^{2} b + A a b^{2}\right)} e^{2}\right)} x}{12 \, {\left(b^{8} x^{4} + 4 \, a b^{7} x^{3} + 6 \, a^{2} b^{6} x^{2} + 4 \, a^{3} b^{5} x + a^{4} b^{4}\right)}}"," ",0,"-1/12*(12*B*b^3*e^2*x^3 + (B*a*b^2 + 3*A*b^3)*d^2 + 2*(B*a^2*b + A*a*b^2)*d*e + (3*B*a^3 + A*a^2*b)*e^2 + 6*(2*B*b^3*d*e + (3*B*a*b^2 + A*b^3)*e^2)*x^2 + 4*(B*b^3*d^2 + 2*(B*a*b^2 + A*b^3)*d*e + (3*B*a^2*b + A*a*b^2)*e^2)*x)/(b^8*x^4 + 4*a*b^7*x^3 + 6*a^2*b^6*x^2 + 4*a^3*b^5*x + a^4*b^4)","B",0
1779,1,106,0,0.439261," ","integrate((B*x+A)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{6 \, B b^{2} e x^{2} + {\left(B a b + 3 \, A b^{2}\right)} d + {\left(B a^{2} + A a b\right)} e + 4 \, {\left(B b^{2} d + {\left(B a b + A b^{2}\right)} e\right)} x}{12 \, {\left(b^{7} x^{4} + 4 \, a b^{6} x^{3} + 6 \, a^{2} b^{5} x^{2} + 4 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}"," ",0,"-1/12*(6*B*b^2*e*x^2 + (B*a*b + 3*A*b^2)*d + (B*a^2 + A*a*b)*e + 4*(B*b^2*d + (B*a*b + A*b^2)*e)*x)/(b^7*x^4 + 4*a*b^6*x^3 + 6*a^2*b^5*x^2 + 4*a^3*b^4*x + a^4*b^3)","A",0
1780,1,61,0,0.428687," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, B b x + B a + 3 \, A b}{12 \, {\left(b^{6} x^{4} + 4 \, a b^{5} x^{3} + 6 \, a^{2} b^{4} x^{2} + 4 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}"," ",0,"-1/12*(4*B*b*x + B*a + 3*A*b)/(b^6*x^4 + 4*a*b^5*x^3 + 6*a^2*b^4*x^2 + 4*a^3*b^3*x + a^4*b^2)","A",0
1781,1,969,0,0.447635," ","integrate((B*x+A)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(B a b^{4} + 3 \, A b^{5}\right)} d^{4} - 2 \, {\left(3 \, B a^{2} b^{3} + 8 \, A a b^{4}\right)} d^{3} e + 18 \, {\left(B a^{3} b^{2} + 2 \, A a^{2} b^{3}\right)} d^{2} e^{2} - 2 \, {\left(5 \, B a^{4} b + 24 \, A a^{3} b^{2}\right)} d e^{3} - {\left(3 \, B a^{5} - 25 \, A a^{4} b\right)} e^{4} + 12 \, {\left(B b^{5} d^{2} e^{2} + A a b^{4} e^{4} - {\left(B a b^{4} + A b^{5}\right)} d e^{3}\right)} x^{3} - 6 \, {\left(B b^{5} d^{3} e - 7 \, A a^{2} b^{3} e^{4} - {\left(8 \, B a b^{4} + A b^{5}\right)} d^{2} e^{2} + {\left(7 \, B a^{2} b^{3} + 8 \, A a b^{4}\right)} d e^{3}\right)} x^{2} + 4 \, {\left(B b^{5} d^{4} + 13 \, A a^{3} b^{2} e^{4} - {\left(6 \, B a b^{4} + A b^{5}\right)} d^{3} e + 6 \, {\left(3 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{2} - {\left(13 \, B a^{3} b^{2} + 18 \, A a^{2} b^{3}\right)} d e^{3}\right)} x + 12 \, {\left(B a^{4} b d e^{3} - A a^{4} b e^{4} + {\left(B b^{5} d e^{3} - A b^{5} e^{4}\right)} x^{4} + 4 \, {\left(B a b^{4} d e^{3} - A a b^{4} e^{4}\right)} x^{3} + 6 \, {\left(B a^{2} b^{3} d e^{3} - A a^{2} b^{3} e^{4}\right)} x^{2} + 4 \, {\left(B a^{3} b^{2} d e^{3} - A a^{3} b^{2} e^{4}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(B a^{4} b d e^{3} - A a^{4} b e^{4} + {\left(B b^{5} d e^{3} - A b^{5} e^{4}\right)} x^{4} + 4 \, {\left(B a b^{4} d e^{3} - A a b^{4} e^{4}\right)} x^{3} + 6 \, {\left(B a^{2} b^{3} d e^{3} - A a^{2} b^{3} e^{4}\right)} x^{2} + 4 \, {\left(B a^{3} b^{2} d e^{3} - A a^{3} b^{2} e^{4}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(a^{4} b^{6} d^{5} - 5 \, a^{5} b^{5} d^{4} e + 10 \, a^{6} b^{4} d^{3} e^{2} - 10 \, a^{7} b^{3} d^{2} e^{3} + 5 \, a^{8} b^{2} d e^{4} - a^{9} b e^{5} + {\left(b^{10} d^{5} - 5 \, a b^{9} d^{4} e + 10 \, a^{2} b^{8} d^{3} e^{2} - 10 \, a^{3} b^{7} d^{2} e^{3} + 5 \, a^{4} b^{6} d e^{4} - a^{5} b^{5} e^{5}\right)} x^{4} + 4 \, {\left(a b^{9} d^{5} - 5 \, a^{2} b^{8} d^{4} e + 10 \, a^{3} b^{7} d^{3} e^{2} - 10 \, a^{4} b^{6} d^{2} e^{3} + 5 \, a^{5} b^{5} d e^{4} - a^{6} b^{4} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{5} - 5 \, a^{3} b^{7} d^{4} e + 10 \, a^{4} b^{6} d^{3} e^{2} - 10 \, a^{5} b^{5} d^{2} e^{3} + 5 \, a^{6} b^{4} d e^{4} - a^{7} b^{3} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{5} - 5 \, a^{4} b^{6} d^{4} e + 10 \, a^{5} b^{5} d^{3} e^{2} - 10 \, a^{6} b^{4} d^{2} e^{3} + 5 \, a^{7} b^{3} d e^{4} - a^{8} b^{2} e^{5}\right)} x\right)}}"," ",0,"-1/12*((B*a*b^4 + 3*A*b^5)*d^4 - 2*(3*B*a^2*b^3 + 8*A*a*b^4)*d^3*e + 18*(B*a^3*b^2 + 2*A*a^2*b^3)*d^2*e^2 - 2*(5*B*a^4*b + 24*A*a^3*b^2)*d*e^3 - (3*B*a^5 - 25*A*a^4*b)*e^4 + 12*(B*b^5*d^2*e^2 + A*a*b^4*e^4 - (B*a*b^4 + A*b^5)*d*e^3)*x^3 - 6*(B*b^5*d^3*e - 7*A*a^2*b^3*e^4 - (8*B*a*b^4 + A*b^5)*d^2*e^2 + (7*B*a^2*b^3 + 8*A*a*b^4)*d*e^3)*x^2 + 4*(B*b^5*d^4 + 13*A*a^3*b^2*e^4 - (6*B*a*b^4 + A*b^5)*d^3*e + 6*(3*B*a^2*b^3 + A*a*b^4)*d^2*e^2 - (13*B*a^3*b^2 + 18*A*a^2*b^3)*d*e^3)*x + 12*(B*a^4*b*d*e^3 - A*a^4*b*e^4 + (B*b^5*d*e^3 - A*b^5*e^4)*x^4 + 4*(B*a*b^4*d*e^3 - A*a*b^4*e^4)*x^3 + 6*(B*a^2*b^3*d*e^3 - A*a^2*b^3*e^4)*x^2 + 4*(B*a^3*b^2*d*e^3 - A*a^3*b^2*e^4)*x)*log(b*x + a) - 12*(B*a^4*b*d*e^3 - A*a^4*b*e^4 + (B*b^5*d*e^3 - A*b^5*e^4)*x^4 + 4*(B*a*b^4*d*e^3 - A*a*b^4*e^4)*x^3 + 6*(B*a^2*b^3*d*e^3 - A*a^2*b^3*e^4)*x^2 + 4*(B*a^3*b^2*d*e^3 - A*a^3*b^2*e^4)*x)*log(e*x + d))/(a^4*b^6*d^5 - 5*a^5*b^5*d^4*e + 10*a^6*b^4*d^3*e^2 - 10*a^7*b^3*d^2*e^3 + 5*a^8*b^2*d*e^4 - a^9*b*e^5 + (b^10*d^5 - 5*a*b^9*d^4*e + 10*a^2*b^8*d^3*e^2 - 10*a^3*b^7*d^2*e^3 + 5*a^4*b^6*d*e^4 - a^5*b^5*e^5)*x^4 + 4*(a*b^9*d^5 - 5*a^2*b^8*d^4*e + 10*a^3*b^7*d^3*e^2 - 10*a^4*b^6*d^2*e^3 + 5*a^5*b^5*d*e^4 - a^6*b^4*e^5)*x^3 + 6*(a^2*b^8*d^5 - 5*a^3*b^7*d^4*e + 10*a^4*b^6*d^3*e^2 - 10*a^5*b^5*d^2*e^3 + 5*a^6*b^4*d*e^4 - a^7*b^3*e^5)*x^2 + 4*(a^3*b^7*d^5 - 5*a^4*b^6*d^4*e + 10*a^5*b^5*d^3*e^2 - 10*a^6*b^4*d^2*e^3 + 5*a^7*b^3*d*e^4 - a^8*b^2*e^5)*x)","B",0
1782,1,1724,0,0.464480," ","integrate((B*x+A)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{12 \, A a^{5} e^{5} + {\left(B a b^{4} + 3 \, A b^{5}\right)} d^{5} - 4 \, {\left(2 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} d^{4} e + 12 \, {\left(3 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} d^{3} e^{2} + 8 \, {\left(B a^{4} b - 15 \, A a^{3} b^{2}\right)} d^{2} e^{3} - {\left(37 \, B a^{5} - 65 \, A a^{4} b\right)} d e^{4} + 12 \, {\left(4 \, B b^{5} d^{2} e^{3} - {\left(3 \, B a b^{4} + 5 \, A b^{5}\right)} d e^{4} - {\left(B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 6 \, {\left(4 \, B b^{5} d^{3} e^{2} + 5 \, {\left(5 \, B a b^{4} - A b^{5}\right)} d^{2} e^{3} - 2 \, {\left(11 \, B a^{2} b^{3} + 15 \, A a b^{4}\right)} d e^{4} - 7 \, {\left(B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} - 2 \, {\left(4 \, B b^{5} d^{4} e - {\left(47 \, B a b^{4} + 5 \, A b^{5}\right)} d^{3} e^{2} - 12 \, {\left(6 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{2} e^{3} + {\left(89 \, B a^{3} b^{2} + 75 \, A a^{2} b^{3}\right)} d e^{4} + 26 \, {\left(B a^{4} b - 5 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(4 \, B b^{5} d^{5} - {\left(31 \, B a b^{4} + 5 \, A b^{5}\right)} d^{4} e + 8 \, {\left(17 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} d^{3} e^{2} + 20 \, {\left(B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} d^{2} e^{3} - 4 \, {\left(26 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} d e^{4} - 25 \, {\left(B a^{5} - 5 \, A a^{4} b\right)} e^{5}\right)} x + 12 \, {\left(4 \, B a^{4} b d^{2} e^{3} + {\left(B a^{5} - 5 \, A a^{4} b\right)} d e^{4} + {\left(4 \, B b^{5} d e^{4} + {\left(B a b^{4} - 5 \, A b^{5}\right)} e^{5}\right)} x^{5} + {\left(4 \, B b^{5} d^{2} e^{3} + {\left(17 \, B a b^{4} - 5 \, A b^{5}\right)} d e^{4} + 4 \, {\left(B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(8 \, B a b^{4} d^{2} e^{3} + 2 \, {\left(7 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d e^{4} + 3 \, {\left(B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} + 2 \, {\left(12 \, B a^{2} b^{3} d^{2} e^{3} + {\left(11 \, B a^{3} b^{2} - 15 \, A a^{2} b^{3}\right)} d e^{4} + 2 \, {\left(B a^{4} b - 5 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(16 \, B a^{3} b^{2} d^{2} e^{3} + 4 \, {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} d e^{4} + {\left(B a^{5} - 5 \, A a^{4} b\right)} e^{5}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(4 \, B a^{4} b d^{2} e^{3} + {\left(B a^{5} - 5 \, A a^{4} b\right)} d e^{4} + {\left(4 \, B b^{5} d e^{4} + {\left(B a b^{4} - 5 \, A b^{5}\right)} e^{5}\right)} x^{5} + {\left(4 \, B b^{5} d^{2} e^{3} + {\left(17 \, B a b^{4} - 5 \, A b^{5}\right)} d e^{4} + 4 \, {\left(B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(8 \, B a b^{4} d^{2} e^{3} + 2 \, {\left(7 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d e^{4} + 3 \, {\left(B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} + 2 \, {\left(12 \, B a^{2} b^{3} d^{2} e^{3} + {\left(11 \, B a^{3} b^{2} - 15 \, A a^{2} b^{3}\right)} d e^{4} + 2 \, {\left(B a^{4} b - 5 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(16 \, B a^{3} b^{2} d^{2} e^{3} + 4 \, {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} d e^{4} + {\left(B a^{5} - 5 \, A a^{4} b\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(a^{4} b^{6} d^{7} - 6 \, a^{5} b^{5} d^{6} e + 15 \, a^{6} b^{4} d^{5} e^{2} - 20 \, a^{7} b^{3} d^{4} e^{3} + 15 \, a^{8} b^{2} d^{3} e^{4} - 6 \, a^{9} b d^{2} e^{5} + a^{10} d e^{6} + {\left(b^{10} d^{6} e - 6 \, a b^{9} d^{5} e^{2} + 15 \, a^{2} b^{8} d^{4} e^{3} - 20 \, a^{3} b^{7} d^{3} e^{4} + 15 \, a^{4} b^{6} d^{2} e^{5} - 6 \, a^{5} b^{5} d e^{6} + a^{6} b^{4} e^{7}\right)} x^{5} + {\left(b^{10} d^{7} - 2 \, a b^{9} d^{6} e - 9 \, a^{2} b^{8} d^{5} e^{2} + 40 \, a^{3} b^{7} d^{4} e^{3} - 65 \, a^{4} b^{6} d^{3} e^{4} + 54 \, a^{5} b^{5} d^{2} e^{5} - 23 \, a^{6} b^{4} d e^{6} + 4 \, a^{7} b^{3} e^{7}\right)} x^{4} + 2 \, {\left(2 \, a b^{9} d^{7} - 9 \, a^{2} b^{8} d^{6} e + 12 \, a^{3} b^{7} d^{5} e^{2} + 5 \, a^{4} b^{6} d^{4} e^{3} - 30 \, a^{5} b^{5} d^{3} e^{4} + 33 \, a^{6} b^{4} d^{2} e^{5} - 16 \, a^{7} b^{3} d e^{6} + 3 \, a^{8} b^{2} e^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{8} d^{7} - 16 \, a^{3} b^{7} d^{6} e + 33 \, a^{4} b^{6} d^{5} e^{2} - 30 \, a^{5} b^{5} d^{4} e^{3} + 5 \, a^{6} b^{4} d^{3} e^{4} + 12 \, a^{7} b^{3} d^{2} e^{5} - 9 \, a^{8} b^{2} d e^{6} + 2 \, a^{9} b e^{7}\right)} x^{2} + {\left(4 \, a^{3} b^{7} d^{7} - 23 \, a^{4} b^{6} d^{6} e + 54 \, a^{5} b^{5} d^{5} e^{2} - 65 \, a^{6} b^{4} d^{4} e^{3} + 40 \, a^{7} b^{3} d^{3} e^{4} - 9 \, a^{8} b^{2} d^{2} e^{5} - 2 \, a^{9} b d e^{6} + a^{10} e^{7}\right)} x\right)}}"," ",0,"-1/12*(12*A*a^5*e^5 + (B*a*b^4 + 3*A*b^5)*d^5 - 4*(2*B*a^2*b^3 + 5*A*a*b^4)*d^4*e + 12*(3*B*a^3*b^2 + 5*A*a^2*b^3)*d^3*e^2 + 8*(B*a^4*b - 15*A*a^3*b^2)*d^2*e^3 - (37*B*a^5 - 65*A*a^4*b)*d*e^4 + 12*(4*B*b^5*d^2*e^3 - (3*B*a*b^4 + 5*A*b^5)*d*e^4 - (B*a^2*b^3 - 5*A*a*b^4)*e^5)*x^4 + 6*(4*B*b^5*d^3*e^2 + 5*(5*B*a*b^4 - A*b^5)*d^2*e^3 - 2*(11*B*a^2*b^3 + 15*A*a*b^4)*d*e^4 - 7*(B*a^3*b^2 - 5*A*a^2*b^3)*e^5)*x^3 - 2*(4*B*b^5*d^4*e - (47*B*a*b^4 + 5*A*b^5)*d^3*e^2 - 12*(6*B*a^2*b^3 - 5*A*a*b^4)*d^2*e^3 + (89*B*a^3*b^2 + 75*A*a^2*b^3)*d*e^4 + 26*(B*a^4*b - 5*A*a^3*b^2)*e^5)*x^2 + (4*B*b^5*d^5 - (31*B*a*b^4 + 5*A*b^5)*d^4*e + 8*(17*B*a^2*b^3 + 5*A*a*b^4)*d^3*e^2 + 20*(B*a^3*b^2 - 9*A*a^2*b^3)*d^2*e^3 - 4*(26*B*a^4*b - 5*A*a^3*b^2)*d*e^4 - 25*(B*a^5 - 5*A*a^4*b)*e^5)*x + 12*(4*B*a^4*b*d^2*e^3 + (B*a^5 - 5*A*a^4*b)*d*e^4 + (4*B*b^5*d*e^4 + (B*a*b^4 - 5*A*b^5)*e^5)*x^5 + (4*B*b^5*d^2*e^3 + (17*B*a*b^4 - 5*A*b^5)*d*e^4 + 4*(B*a^2*b^3 - 5*A*a*b^4)*e^5)*x^4 + 2*(8*B*a*b^4*d^2*e^3 + 2*(7*B*a^2*b^3 - 5*A*a*b^4)*d*e^4 + 3*(B*a^3*b^2 - 5*A*a^2*b^3)*e^5)*x^3 + 2*(12*B*a^2*b^3*d^2*e^3 + (11*B*a^3*b^2 - 15*A*a^2*b^3)*d*e^4 + 2*(B*a^4*b - 5*A*a^3*b^2)*e^5)*x^2 + (16*B*a^3*b^2*d^2*e^3 + 4*(2*B*a^4*b - 5*A*a^3*b^2)*d*e^4 + (B*a^5 - 5*A*a^4*b)*e^5)*x)*log(b*x + a) - 12*(4*B*a^4*b*d^2*e^3 + (B*a^5 - 5*A*a^4*b)*d*e^4 + (4*B*b^5*d*e^4 + (B*a*b^4 - 5*A*b^5)*e^5)*x^5 + (4*B*b^5*d^2*e^3 + (17*B*a*b^4 - 5*A*b^5)*d*e^4 + 4*(B*a^2*b^3 - 5*A*a*b^4)*e^5)*x^4 + 2*(8*B*a*b^4*d^2*e^3 + 2*(7*B*a^2*b^3 - 5*A*a*b^4)*d*e^4 + 3*(B*a^3*b^2 - 5*A*a^2*b^3)*e^5)*x^3 + 2*(12*B*a^2*b^3*d^2*e^3 + (11*B*a^3*b^2 - 15*A*a^2*b^3)*d*e^4 + 2*(B*a^4*b - 5*A*a^3*b^2)*e^5)*x^2 + (16*B*a^3*b^2*d^2*e^3 + 4*(2*B*a^4*b - 5*A*a^3*b^2)*d*e^4 + (B*a^5 - 5*A*a^4*b)*e^5)*x)*log(e*x + d))/(a^4*b^6*d^7 - 6*a^5*b^5*d^6*e + 15*a^6*b^4*d^5*e^2 - 20*a^7*b^3*d^4*e^3 + 15*a^8*b^2*d^3*e^4 - 6*a^9*b*d^2*e^5 + a^10*d*e^6 + (b^10*d^6*e - 6*a*b^9*d^5*e^2 + 15*a^2*b^8*d^4*e^3 - 20*a^3*b^7*d^3*e^4 + 15*a^4*b^6*d^2*e^5 - 6*a^5*b^5*d*e^6 + a^6*b^4*e^7)*x^5 + (b^10*d^7 - 2*a*b^9*d^6*e - 9*a^2*b^8*d^5*e^2 + 40*a^3*b^7*d^4*e^3 - 65*a^4*b^6*d^3*e^4 + 54*a^5*b^5*d^2*e^5 - 23*a^6*b^4*d*e^6 + 4*a^7*b^3*e^7)*x^4 + 2*(2*a*b^9*d^7 - 9*a^2*b^8*d^6*e + 12*a^3*b^7*d^5*e^2 + 5*a^4*b^6*d^4*e^3 - 30*a^5*b^5*d^3*e^4 + 33*a^6*b^4*d^2*e^5 - 16*a^7*b^3*d*e^6 + 3*a^8*b^2*e^7)*x^3 + 2*(3*a^2*b^8*d^7 - 16*a^3*b^7*d^6*e + 33*a^4*b^6*d^5*e^2 - 30*a^5*b^5*d^4*e^3 + 5*a^6*b^4*d^3*e^4 + 12*a^7*b^3*d^2*e^5 - 9*a^8*b^2*d*e^6 + 2*a^9*b*e^7)*x^2 + (4*a^3*b^7*d^7 - 23*a^4*b^6*d^6*e + 54*a^5*b^5*d^5*e^2 - 65*a^6*b^4*d^4*e^3 + 40*a^7*b^3*d^3*e^4 - 9*a^8*b^2*d^2*e^5 - 2*a^9*b*d*e^6 + a^10*e^7)*x)","B",0
1783,1,2466,0,0.523612," ","integrate((B*x+A)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{6 \, A a^{6} e^{6} - {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{6} + 2 \, {\left(5 \, B a^{2} b^{4} + 12 \, A a b^{5}\right)} d^{5} e - 30 \, {\left(2 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{2} - 80 \, {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} d^{3} e^{3} + 5 \, {\left(25 \, B a^{5} b - 21 \, A a^{4} b^{2}\right)} d^{2} e^{4} + 6 \, {\left(B a^{6} - 12 \, A a^{5} b\right)} d e^{5} - 60 \, {\left(2 \, B b^{6} d^{2} e^{4} - {\left(B a b^{5} + 3 \, A b^{6}\right)} d e^{5} - {\left(B a^{2} b^{4} - 3 \, A a b^{5}\right)} e^{6}\right)} x^{5} - 30 \, {\left(6 \, B b^{6} d^{3} e^{3} + {\left(11 \, B a b^{5} - 9 \, A b^{6}\right)} d^{2} e^{4} - 2 \, {\left(5 \, B a^{2} b^{4} + 6 \, A a b^{5}\right)} d e^{5} - 7 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{4} - 20 \, {\left(2 \, B b^{6} d^{4} e^{2} + {\left(31 \, B a b^{5} - 3 \, A b^{6}\right)} d^{3} e^{3} + 9 \, {\left(B a^{2} b^{4} - 5 \, A a b^{5}\right)} d^{2} e^{4} - {\left(29 \, B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} d e^{5} - 13 \, {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} e^{6}\right)} x^{3} + 5 \, {\left(2 \, B b^{6} d^{5} e - {\left(31 \, B a b^{5} + 3 \, A b^{6}\right)} d^{4} e^{2} - 4 \, {\left(37 \, B a^{2} b^{4} - 12 \, A a b^{5}\right)} d^{3} e^{3} + 2 \, {\left(23 \, B a^{3} b^{3} + 99 \, A a^{2} b^{4}\right)} d^{2} e^{4} + 2 \, {\left(53 \, B a^{4} b^{2} - 84 \, A a^{3} b^{3}\right)} d e^{5} + 25 \, {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} e^{6}\right)} x^{2} - 2 \, {\left(2 \, B b^{6} d^{6} - {\left(19 \, B a b^{5} + 3 \, A b^{6}\right)} d^{5} e + 10 \, {\left(11 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} d^{4} e^{2} + 20 \, {\left(8 \, B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} d^{3} e^{3} - 10 \, {\left(14 \, B a^{4} b^{2} + 15 \, A a^{3} b^{3}\right)} d^{2} e^{4} - {\left(107 \, B a^{5} b - 285 \, A a^{4} b^{2}\right)} d e^{5} - 6 \, {\left(B a^{6} - 3 \, A a^{5} b\right)} e^{6}\right)} x - 60 \, {\left(2 \, B a^{4} b^{2} d^{3} e^{3} + {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} d^{2} e^{4} + {\left(2 \, B b^{6} d e^{5} + {\left(B a b^{5} - 3 \, A b^{6}\right)} e^{6}\right)} x^{6} + 2 \, {\left(2 \, B b^{6} d^{2} e^{4} + {\left(5 \, B a b^{5} - 3 \, A b^{6}\right)} d e^{5} + 2 \, {\left(B a^{2} b^{4} - 3 \, A a b^{5}\right)} e^{6}\right)} x^{5} + {\left(2 \, B b^{6} d^{3} e^{3} + {\left(17 \, B a b^{5} - 3 \, A b^{6}\right)} d^{2} e^{4} + 4 \, {\left(5 \, B a^{2} b^{4} - 6 \, A a b^{5}\right)} d e^{5} + 6 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{4} + 4 \, {\left(2 \, B a b^{5} d^{3} e^{3} + {\left(7 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} d^{2} e^{4} + {\left(5 \, B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} d e^{5} + {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} e^{6}\right)} x^{3} + {\left(12 \, B a^{2} b^{4} d^{3} e^{3} + 2 \, {\left(11 \, B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} d^{2} e^{4} + 2 \, {\left(5 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} d e^{5} + {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} e^{6}\right)} x^{2} + 2 \, {\left(4 \, B a^{3} b^{3} d^{3} e^{3} + 2 \, {\left(2 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} d^{2} e^{4} + {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} d e^{5}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(2 \, B a^{4} b^{2} d^{3} e^{3} + {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} d^{2} e^{4} + {\left(2 \, B b^{6} d e^{5} + {\left(B a b^{5} - 3 \, A b^{6}\right)} e^{6}\right)} x^{6} + 2 \, {\left(2 \, B b^{6} d^{2} e^{4} + {\left(5 \, B a b^{5} - 3 \, A b^{6}\right)} d e^{5} + 2 \, {\left(B a^{2} b^{4} - 3 \, A a b^{5}\right)} e^{6}\right)} x^{5} + {\left(2 \, B b^{6} d^{3} e^{3} + {\left(17 \, B a b^{5} - 3 \, A b^{6}\right)} d^{2} e^{4} + 4 \, {\left(5 \, B a^{2} b^{4} - 6 \, A a b^{5}\right)} d e^{5} + 6 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{4} + 4 \, {\left(2 \, B a b^{5} d^{3} e^{3} + {\left(7 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} d^{2} e^{4} + {\left(5 \, B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} d e^{5} + {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} e^{6}\right)} x^{3} + {\left(12 \, B a^{2} b^{4} d^{3} e^{3} + 2 \, {\left(11 \, B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} d^{2} e^{4} + 2 \, {\left(5 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} d e^{5} + {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} e^{6}\right)} x^{2} + 2 \, {\left(4 \, B a^{3} b^{3} d^{3} e^{3} + 2 \, {\left(2 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} d^{2} e^{4} + {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(a^{4} b^{7} d^{9} - 7 \, a^{5} b^{6} d^{8} e + 21 \, a^{6} b^{5} d^{7} e^{2} - 35 \, a^{7} b^{4} d^{6} e^{3} + 35 \, a^{8} b^{3} d^{5} e^{4} - 21 \, a^{9} b^{2} d^{4} e^{5} + 7 \, a^{10} b d^{3} e^{6} - a^{11} d^{2} e^{7} + {\left(b^{11} d^{7} e^{2} - 7 \, a b^{10} d^{6} e^{3} + 21 \, a^{2} b^{9} d^{5} e^{4} - 35 \, a^{3} b^{8} d^{4} e^{5} + 35 \, a^{4} b^{7} d^{3} e^{6} - 21 \, a^{5} b^{6} d^{2} e^{7} + 7 \, a^{6} b^{5} d e^{8} - a^{7} b^{4} e^{9}\right)} x^{6} + 2 \, {\left(b^{11} d^{8} e - 5 \, a b^{10} d^{7} e^{2} + 7 \, a^{2} b^{9} d^{6} e^{3} + 7 \, a^{3} b^{8} d^{5} e^{4} - 35 \, a^{4} b^{7} d^{4} e^{5} + 49 \, a^{5} b^{6} d^{3} e^{6} - 35 \, a^{6} b^{5} d^{2} e^{7} + 13 \, a^{7} b^{4} d e^{8} - 2 \, a^{8} b^{3} e^{9}\right)} x^{5} + {\left(b^{11} d^{9} + a b^{10} d^{8} e - 29 \, a^{2} b^{9} d^{7} e^{2} + 91 \, a^{3} b^{8} d^{6} e^{3} - 119 \, a^{4} b^{7} d^{5} e^{4} + 49 \, a^{5} b^{6} d^{4} e^{5} + 49 \, a^{6} b^{5} d^{3} e^{6} - 71 \, a^{7} b^{4} d^{2} e^{7} + 34 \, a^{8} b^{3} d e^{8} - 6 \, a^{9} b^{2} e^{9}\right)} x^{4} + 4 \, {\left(a b^{10} d^{9} - 4 \, a^{2} b^{9} d^{8} e + a^{3} b^{8} d^{7} e^{2} + 21 \, a^{4} b^{7} d^{6} e^{3} - 49 \, a^{5} b^{6} d^{5} e^{4} + 49 \, a^{6} b^{5} d^{4} e^{5} - 21 \, a^{7} b^{4} d^{3} e^{6} - a^{8} b^{3} d^{2} e^{7} + 4 \, a^{9} b^{2} d e^{8} - a^{10} b e^{9}\right)} x^{3} + {\left(6 \, a^{2} b^{9} d^{9} - 34 \, a^{3} b^{8} d^{8} e + 71 \, a^{4} b^{7} d^{7} e^{2} - 49 \, a^{5} b^{6} d^{6} e^{3} - 49 \, a^{6} b^{5} d^{5} e^{4} + 119 \, a^{7} b^{4} d^{4} e^{5} - 91 \, a^{8} b^{3} d^{3} e^{6} + 29 \, a^{9} b^{2} d^{2} e^{7} - a^{10} b d e^{8} - a^{11} e^{9}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{8} d^{9} - 13 \, a^{4} b^{7} d^{8} e + 35 \, a^{5} b^{6} d^{7} e^{2} - 49 \, a^{6} b^{5} d^{6} e^{3} + 35 \, a^{7} b^{4} d^{5} e^{4} - 7 \, a^{8} b^{3} d^{4} e^{5} - 7 \, a^{9} b^{2} d^{3} e^{6} + 5 \, a^{10} b d^{2} e^{7} - a^{11} d e^{8}\right)} x\right)}}"," ",0,"1/12*(6*A*a^6*e^6 - (B*a*b^5 + 3*A*b^6)*d^6 + 2*(5*B*a^2*b^4 + 12*A*a*b^5)*d^5*e - 30*(2*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^2 - 80*(B*a^4*b^2 - 3*A*a^3*b^3)*d^3*e^3 + 5*(25*B*a^5*b - 21*A*a^4*b^2)*d^2*e^4 + 6*(B*a^6 - 12*A*a^5*b)*d*e^5 - 60*(2*B*b^6*d^2*e^4 - (B*a*b^5 + 3*A*b^6)*d*e^5 - (B*a^2*b^4 - 3*A*a*b^5)*e^6)*x^5 - 30*(6*B*b^6*d^3*e^3 + (11*B*a*b^5 - 9*A*b^6)*d^2*e^4 - 2*(5*B*a^2*b^4 + 6*A*a*b^5)*d*e^5 - 7*(B*a^3*b^3 - 3*A*a^2*b^4)*e^6)*x^4 - 20*(2*B*b^6*d^4*e^2 + (31*B*a*b^5 - 3*A*b^6)*d^3*e^3 + 9*(B*a^2*b^4 - 5*A*a*b^5)*d^2*e^4 - (29*B*a^3*b^3 - 9*A*a^2*b^4)*d*e^5 - 13*(B*a^4*b^2 - 3*A*a^3*b^3)*e^6)*x^3 + 5*(2*B*b^6*d^5*e - (31*B*a*b^5 + 3*A*b^6)*d^4*e^2 - 4*(37*B*a^2*b^4 - 12*A*a*b^5)*d^3*e^3 + 2*(23*B*a^3*b^3 + 99*A*a^2*b^4)*d^2*e^4 + 2*(53*B*a^4*b^2 - 84*A*a^3*b^3)*d*e^5 + 25*(B*a^5*b - 3*A*a^4*b^2)*e^6)*x^2 - 2*(2*B*b^6*d^6 - (19*B*a*b^5 + 3*A*b^6)*d^5*e + 10*(11*B*a^2*b^4 + 3*A*a*b^5)*d^4*e^2 + 20*(8*B*a^3*b^3 - 9*A*a^2*b^4)*d^3*e^3 - 10*(14*B*a^4*b^2 + 15*A*a^3*b^3)*d^2*e^4 - (107*B*a^5*b - 285*A*a^4*b^2)*d*e^5 - 6*(B*a^6 - 3*A*a^5*b)*e^6)*x - 60*(2*B*a^4*b^2*d^3*e^3 + (B*a^5*b - 3*A*a^4*b^2)*d^2*e^4 + (2*B*b^6*d*e^5 + (B*a*b^5 - 3*A*b^6)*e^6)*x^6 + 2*(2*B*b^6*d^2*e^4 + (5*B*a*b^5 - 3*A*b^6)*d*e^5 + 2*(B*a^2*b^4 - 3*A*a*b^5)*e^6)*x^5 + (2*B*b^6*d^3*e^3 + (17*B*a*b^5 - 3*A*b^6)*d^2*e^4 + 4*(5*B*a^2*b^4 - 6*A*a*b^5)*d*e^5 + 6*(B*a^3*b^3 - 3*A*a^2*b^4)*e^6)*x^4 + 4*(2*B*a*b^5*d^3*e^3 + (7*B*a^2*b^4 - 3*A*a*b^5)*d^2*e^4 + (5*B*a^3*b^3 - 9*A*a^2*b^4)*d*e^5 + (B*a^4*b^2 - 3*A*a^3*b^3)*e^6)*x^3 + (12*B*a^2*b^4*d^3*e^3 + 2*(11*B*a^3*b^3 - 9*A*a^2*b^4)*d^2*e^4 + 2*(5*B*a^4*b^2 - 12*A*a^3*b^3)*d*e^5 + (B*a^5*b - 3*A*a^4*b^2)*e^6)*x^2 + 2*(4*B*a^3*b^3*d^3*e^3 + 2*(2*B*a^4*b^2 - 3*A*a^3*b^3)*d^2*e^4 + (B*a^5*b - 3*A*a^4*b^2)*d*e^5)*x)*log(b*x + a) + 60*(2*B*a^4*b^2*d^3*e^3 + (B*a^5*b - 3*A*a^4*b^2)*d^2*e^4 + (2*B*b^6*d*e^5 + (B*a*b^5 - 3*A*b^6)*e^6)*x^6 + 2*(2*B*b^6*d^2*e^4 + (5*B*a*b^5 - 3*A*b^6)*d*e^5 + 2*(B*a^2*b^4 - 3*A*a*b^5)*e^6)*x^5 + (2*B*b^6*d^3*e^3 + (17*B*a*b^5 - 3*A*b^6)*d^2*e^4 + 4*(5*B*a^2*b^4 - 6*A*a*b^5)*d*e^5 + 6*(B*a^3*b^3 - 3*A*a^2*b^4)*e^6)*x^4 + 4*(2*B*a*b^5*d^3*e^3 + (7*B*a^2*b^4 - 3*A*a*b^5)*d^2*e^4 + (5*B*a^3*b^3 - 9*A*a^2*b^4)*d*e^5 + (B*a^4*b^2 - 3*A*a^3*b^3)*e^6)*x^3 + (12*B*a^2*b^4*d^3*e^3 + 2*(11*B*a^3*b^3 - 9*A*a^2*b^4)*d^2*e^4 + 2*(5*B*a^4*b^2 - 12*A*a^3*b^3)*d*e^5 + (B*a^5*b - 3*A*a^4*b^2)*e^6)*x^2 + 2*(4*B*a^3*b^3*d^3*e^3 + 2*(2*B*a^4*b^2 - 3*A*a^3*b^3)*d^2*e^4 + (B*a^5*b - 3*A*a^4*b^2)*d*e^5)*x)*log(e*x + d))/(a^4*b^7*d^9 - 7*a^5*b^6*d^8*e + 21*a^6*b^5*d^7*e^2 - 35*a^7*b^4*d^6*e^3 + 35*a^8*b^3*d^5*e^4 - 21*a^9*b^2*d^4*e^5 + 7*a^10*b*d^3*e^6 - a^11*d^2*e^7 + (b^11*d^7*e^2 - 7*a*b^10*d^6*e^3 + 21*a^2*b^9*d^5*e^4 - 35*a^3*b^8*d^4*e^5 + 35*a^4*b^7*d^3*e^6 - 21*a^5*b^6*d^2*e^7 + 7*a^6*b^5*d*e^8 - a^7*b^4*e^9)*x^6 + 2*(b^11*d^8*e - 5*a*b^10*d^7*e^2 + 7*a^2*b^9*d^6*e^3 + 7*a^3*b^8*d^5*e^4 - 35*a^4*b^7*d^4*e^5 + 49*a^5*b^6*d^3*e^6 - 35*a^6*b^5*d^2*e^7 + 13*a^7*b^4*d*e^8 - 2*a^8*b^3*e^9)*x^5 + (b^11*d^9 + a*b^10*d^8*e - 29*a^2*b^9*d^7*e^2 + 91*a^3*b^8*d^6*e^3 - 119*a^4*b^7*d^5*e^4 + 49*a^5*b^6*d^4*e^5 + 49*a^6*b^5*d^3*e^6 - 71*a^7*b^4*d^2*e^7 + 34*a^8*b^3*d*e^8 - 6*a^9*b^2*e^9)*x^4 + 4*(a*b^10*d^9 - 4*a^2*b^9*d^8*e + a^3*b^8*d^7*e^2 + 21*a^4*b^7*d^6*e^3 - 49*a^5*b^6*d^5*e^4 + 49*a^6*b^5*d^4*e^5 - 21*a^7*b^4*d^3*e^6 - a^8*b^3*d^2*e^7 + 4*a^9*b^2*d*e^8 - a^10*b*e^9)*x^3 + (6*a^2*b^9*d^9 - 34*a^3*b^8*d^8*e + 71*a^4*b^7*d^7*e^2 - 49*a^5*b^6*d^6*e^3 - 49*a^6*b^5*d^5*e^4 + 119*a^7*b^4*d^4*e^5 - 91*a^8*b^3*d^3*e^6 + 29*a^9*b^2*d^2*e^7 - a^10*b*d*e^8 - a^11*e^9)*x^2 + 2*(2*a^3*b^8*d^9 - 13*a^4*b^7*d^8*e + 35*a^5*b^6*d^7*e^2 - 49*a^6*b^5*d^6*e^3 + 35*a^7*b^4*d^5*e^4 - 7*a^8*b^3*d^4*e^5 - 7*a^9*b^2*d^3*e^6 + 5*a^10*b*d^2*e^7 - a^11*d*e^8)*x)","B",0
1784,1,424,0,0.428447," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, {\left(429 \, B b^{2} e^{7} x^{7} - 16 \, B b^{2} d^{7} + 715 \, A a^{2} d^{4} e^{3} + 40 \, {\left(2 \, B a b + A b^{2}\right)} d^{6} e - 130 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5} e^{2} + 33 \, {\left(46 \, B b^{2} d e^{6} + 15 \, {\left(2 \, B a b + A b^{2}\right)} e^{7}\right)} x^{6} + 9 \, {\left(206 \, B b^{2} d^{2} e^{5} + 200 \, {\left(2 \, B a b + A b^{2}\right)} d e^{6} + 65 \, {\left(B a^{2} + 2 \, A a b\right)} e^{7}\right)} x^{5} + 5 \, {\left(160 \, B b^{2} d^{3} e^{4} + 143 \, A a^{2} e^{7} + 458 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{5} + 442 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{6}\right)} x^{4} + 5 \, {\left(B b^{2} d^{4} e^{3} + 572 \, A a^{2} d e^{6} + 212 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e^{4} + 598 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{5}\right)} x^{3} - 3 \, {\left(2 \, B b^{2} d^{5} e^{2} - 1430 \, A a^{2} d^{2} e^{5} - 5 \, {\left(2 \, B a b + A b^{2}\right)} d^{4} e^{3} - 520 \, {\left(B a^{2} + 2 \, A a b\right)} d^{3} e^{4}\right)} x^{2} + {\left(8 \, B b^{2} d^{6} e + 2860 \, A a^{2} d^{3} e^{4} - 20 \, {\left(2 \, B a b + A b^{2}\right)} d^{5} e^{2} + 65 \, {\left(B a^{2} + 2 \, A a b\right)} d^{4} e^{3}\right)} x\right)} \sqrt{e x + d}}{6435 \, e^{4}}"," ",0,"2/6435*(429*B*b^2*e^7*x^7 - 16*B*b^2*d^7 + 715*A*a^2*d^4*e^3 + 40*(2*B*a*b + A*b^2)*d^6*e - 130*(B*a^2 + 2*A*a*b)*d^5*e^2 + 33*(46*B*b^2*d*e^6 + 15*(2*B*a*b + A*b^2)*e^7)*x^6 + 9*(206*B*b^2*d^2*e^5 + 200*(2*B*a*b + A*b^2)*d*e^6 + 65*(B*a^2 + 2*A*a*b)*e^7)*x^5 + 5*(160*B*b^2*d^3*e^4 + 143*A*a^2*e^7 + 458*(2*B*a*b + A*b^2)*d^2*e^5 + 442*(B*a^2 + 2*A*a*b)*d*e^6)*x^4 + 5*(B*b^2*d^4*e^3 + 572*A*a^2*d*e^6 + 212*(2*B*a*b + A*b^2)*d^3*e^4 + 598*(B*a^2 + 2*A*a*b)*d^2*e^5)*x^3 - 3*(2*B*b^2*d^5*e^2 - 1430*A*a^2*d^2*e^5 - 5*(2*B*a*b + A*b^2)*d^4*e^3 - 520*(B*a^2 + 2*A*a*b)*d^3*e^4)*x^2 + (8*B*b^2*d^6*e + 2860*A*a^2*d^3*e^4 - 20*(2*B*a*b + A*b^2)*d^5*e^2 + 65*(B*a^2 + 2*A*a*b)*d^4*e^3)*x)*sqrt(e*x + d)/e^4","B",0
1785,1,356,0,0.434489," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, B b^{2} e^{6} x^{6} - 48 \, B b^{2} d^{6} + 1287 \, A a^{2} d^{3} e^{3} + 104 \, {\left(2 \, B a b + A b^{2}\right)} d^{5} e - 286 \, {\left(B a^{2} + 2 \, A a b\right)} d^{4} e^{2} + 63 \, {\left(27 \, B b^{2} d e^{5} + 13 \, {\left(2 \, B a b + A b^{2}\right)} e^{6}\right)} x^{5} + 7 \, {\left(159 \, B b^{2} d^{2} e^{4} + 299 \, {\left(2 \, B a b + A b^{2}\right)} d e^{5} + 143 \, {\left(B a^{2} + 2 \, A a b\right)} e^{6}\right)} x^{4} + {\left(15 \, B b^{2} d^{3} e^{3} + 1287 \, A a^{2} e^{6} + 1469 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{4} + 2717 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{5}\right)} x^{3} - 3 \, {\left(6 \, B b^{2} d^{4} e^{2} - 1287 \, A a^{2} d e^{5} - 13 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e^{3} - 715 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{4}\right)} x^{2} + {\left(24 \, B b^{2} d^{5} e + 3861 \, A a^{2} d^{2} e^{4} - 52 \, {\left(2 \, B a b + A b^{2}\right)} d^{4} e^{2} + 143 \, {\left(B a^{2} + 2 \, A a b\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{9009 \, e^{4}}"," ",0,"2/9009*(693*B*b^2*e^6*x^6 - 48*B*b^2*d^6 + 1287*A*a^2*d^3*e^3 + 104*(2*B*a*b + A*b^2)*d^5*e - 286*(B*a^2 + 2*A*a*b)*d^4*e^2 + 63*(27*B*b^2*d*e^5 + 13*(2*B*a*b + A*b^2)*e^6)*x^5 + 7*(159*B*b^2*d^2*e^4 + 299*(2*B*a*b + A*b^2)*d*e^5 + 143*(B*a^2 + 2*A*a*b)*e^6)*x^4 + (15*B*b^2*d^3*e^3 + 1287*A*a^2*e^6 + 1469*(2*B*a*b + A*b^2)*d^2*e^4 + 2717*(B*a^2 + 2*A*a*b)*d*e^5)*x^3 - 3*(6*B*b^2*d^4*e^2 - 1287*A*a^2*d*e^5 - 13*(2*B*a*b + A*b^2)*d^3*e^3 - 715*(B*a^2 + 2*A*a*b)*d^2*e^4)*x^2 + (24*B*b^2*d^5*e + 3861*A*a^2*d^2*e^4 - 52*(2*B*a*b + A*b^2)*d^4*e^2 + 143*(B*a^2 + 2*A*a*b)*d^3*e^3)*x)*sqrt(e*x + d)/e^4","B",0
1786,1,289,0,0.399538," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B b^{2} e^{5} x^{5} - 48 \, B b^{2} d^{5} + 693 \, A a^{2} d^{2} e^{3} + 88 \, {\left(2 \, B a b + A b^{2}\right)} d^{4} e - 198 \, {\left(B a^{2} + 2 \, A a b\right)} d^{3} e^{2} + 35 \, {\left(12 \, B b^{2} d e^{4} + 11 \, {\left(2 \, B a b + A b^{2}\right)} e^{5}\right)} x^{4} + 5 \, {\left(3 \, B b^{2} d^{2} e^{3} + 110 \, {\left(2 \, B a b + A b^{2}\right)} d e^{4} + 99 \, {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x^{3} - 3 \, {\left(6 \, B b^{2} d^{3} e^{2} - 231 \, A a^{2} e^{5} - 11 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{3} - 264 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{4}\right)} x^{2} + {\left(24 \, B b^{2} d^{4} e + 1386 \, A a^{2} d e^{4} - 44 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e^{2} + 99 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{4}}"," ",0,"2/3465*(315*B*b^2*e^5*x^5 - 48*B*b^2*d^5 + 693*A*a^2*d^2*e^3 + 88*(2*B*a*b + A*b^2)*d^4*e - 198*(B*a^2 + 2*A*a*b)*d^3*e^2 + 35*(12*B*b^2*d*e^4 + 11*(2*B*a*b + A*b^2)*e^5)*x^4 + 5*(3*B*b^2*d^2*e^3 + 110*(2*B*a*b + A*b^2)*d*e^4 + 99*(B*a^2 + 2*A*a*b)*e^5)*x^3 - 3*(6*B*b^2*d^3*e^2 - 231*A*a^2*e^5 - 11*(2*B*a*b + A*b^2)*d^2*e^3 - 264*(B*a^2 + 2*A*a*b)*d*e^4)*x^2 + (24*B*b^2*d^4*e + 1386*A*a^2*d*e^4 - 44*(2*B*a*b + A*b^2)*d^3*e^2 + 99*(B*a^2 + 2*A*a*b)*d^2*e^3)*x)*sqrt(e*x + d)/e^4","B",0
1787,1,220,0,0.414057," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{2} e^{4} x^{4} - 16 \, B b^{2} d^{4} + 105 \, A a^{2} d e^{3} + 24 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e - 42 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{2} + 5 \, {\left(B b^{2} d e^{3} + 9 \, {\left(2 \, B a b + A b^{2}\right)} e^{4}\right)} x^{3} - 3 \, {\left(2 \, B b^{2} d^{2} e^{2} - 3 \, {\left(2 \, B a b + A b^{2}\right)} d e^{3} - 21 \, {\left(B a^{2} + 2 \, A a b\right)} e^{4}\right)} x^{2} + {\left(8 \, B b^{2} d^{3} e + 105 \, A a^{2} e^{4} - 12 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{2} + 21 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{4}}"," ",0,"2/315*(35*B*b^2*e^4*x^4 - 16*B*b^2*d^4 + 105*A*a^2*d*e^3 + 24*(2*B*a*b + A*b^2)*d^3*e - 42*(B*a^2 + 2*A*a*b)*d^2*e^2 + 5*(B*b^2*d*e^3 + 9*(2*B*a*b + A*b^2)*e^4)*x^3 - 3*(2*B*b^2*d^2*e^2 - 3*(2*B*a*b + A*b^2)*d*e^3 - 21*(B*a^2 + 2*A*a*b)*e^4)*x^2 + (8*B*b^2*d^3*e + 105*A*a^2*e^4 - 12*(2*B*a*b + A*b^2)*d^2*e^2 + 21*(B*a^2 + 2*A*a*b)*d*e^3)*x)*sqrt(e*x + d)/e^4","A",0
1788,1,155,0,0.420920," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{2} e^{3} x^{3} - 48 \, B b^{2} d^{3} + 105 \, A a^{2} e^{3} + 56 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - 70 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - 3 \, {\left(6 \, B b^{2} d e^{2} - 7 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + {\left(24 \, B b^{2} d^{2} e - 28 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 35 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{4}}"," ",0,"2/105*(15*B*b^2*e^3*x^3 - 48*B*b^2*d^3 + 105*A*a^2*e^3 + 56*(2*B*a*b + A*b^2)*d^2*e - 70*(B*a^2 + 2*A*a*b)*d*e^2 - 3*(6*B*b^2*d*e^2 - 7*(2*B*a*b + A*b^2)*e^3)*x^2 + (24*B*b^2*d^2*e - 28*(2*B*a*b + A*b^2)*d*e^2 + 35*(B*a^2 + 2*A*a*b)*e^3)*x)*sqrt(e*x + d)/e^4","A",0
1789,1,165,0,0.409108," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} e^{3} x^{3} + 48 \, B b^{2} d^{3} - 15 \, A a^{2} e^{3} - 40 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 30 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - {\left(6 \, B b^{2} d e^{2} - 5 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + {\left(24 \, B b^{2} d^{2} e - 20 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"2/15*(3*B*b^2*e^3*x^3 + 48*B*b^2*d^3 - 15*A*a^2*e^3 - 40*(2*B*a*b + A*b^2)*d^2*e + 30*(B*a^2 + 2*A*a*b)*d*e^2 - (6*B*b^2*d*e^2 - 5*(2*B*a*b + A*b^2)*e^3)*x^2 + (24*B*b^2*d^2*e - 20*(2*B*a*b + A*b^2)*d*e^2 + 15*(B*a^2 + 2*A*a*b)*e^3)*x)*sqrt(e*x + d)/(e^5*x + d*e^4)","A",0
1790,1,175,0,0.413831," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{2} e^{3} x^{3} - 16 \, B b^{2} d^{3} - A a^{2} e^{3} + 8 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - 2 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - 3 \, {\left(2 \, B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} - 3 \, {\left(8 \, B b^{2} d^{2} e - 4 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"2/3*(B*b^2*e^3*x^3 - 16*B*b^2*d^3 - A*a^2*e^3 + 8*(2*B*a*b + A*b^2)*d^2*e - 2*(B*a^2 + 2*A*a*b)*d*e^2 - 3*(2*B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 - 3*(8*B*b^2*d^2*e - 4*(2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x)*sqrt(e*x + d)/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1791,1,188,0,0.403014," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{2} e^{3} x^{3} + 48 \, B b^{2} d^{3} - 3 \, A a^{2} e^{3} - 8 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - 2 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 15 \, {\left(6 \, B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 5 \, {\left(24 \, B b^{2} d^{2} e - 4 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} - {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"2/15*(15*B*b^2*e^3*x^3 + 48*B*b^2*d^3 - 3*A*a^2*e^3 - 8*(2*B*a*b + A*b^2)*d^2*e - 2*(B*a^2 + 2*A*a*b)*d*e^2 + 15*(6*B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 + 5*(24*B*b^2*d^2*e - 4*(2*B*a*b + A*b^2)*d*e^2 - (B*a^2 + 2*A*a*b)*e^3)*x)*sqrt(e*x + d)/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1792,1,894,0,0.421676," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(109395 \, B b^{4} e^{9} x^{9} - 1280 \, B b^{4} d^{9} + 230945 \, A a^{4} d^{4} e^{5} + 2432 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{8} e - 10336 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{7} e^{2} + 25840 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{6} e^{3} - 41990 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{5} e^{4} + 6435 \, {\left(58 \, B b^{4} d e^{8} + 19 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{9}\right)} x^{8} + 858 \, {\left(505 \, B b^{4} d^{2} e^{7} + 494 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{8} + 323 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{9}\right)} x^{7} + 66 \, {\left(2620 \, B b^{4} d^{3} e^{6} + 7619 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{7} + 14858 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{8} + 4845 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{9}\right)} x^{6} + 9 \, {\left(35 \, B b^{4} d^{4} e^{5} + 23028 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{6} + 133076 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{7} + 129200 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{8} + 20995 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{9}\right)} x^{5} - 5 \, {\left(70 \, B b^{4} d^{5} e^{4} - 46189 \, A a^{4} e^{9} - 133 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e^{5} - 103360 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{6} - 295868 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{7} - 142766 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{8}\right)} x^{4} + 10 \, {\left(40 \, B b^{4} d^{6} e^{3} + 92378 \, A a^{4} d e^{8} - 76 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{5} e^{4} + 323 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{5} + 68476 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{6} + 96577 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{7}\right)} x^{3} - 6 \, {\left(80 \, B b^{4} d^{7} e^{2} - 230945 \, A a^{4} d^{2} e^{7} - 152 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{6} e^{3} + 646 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{5} e^{4} - 1615 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{4} e^{5} - 83980 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{3} e^{6}\right)} x^{2} + {\left(640 \, B b^{4} d^{8} e + 923780 \, A a^{4} d^{3} e^{6} - 1216 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{7} e^{2} + 5168 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{6} e^{3} - 12920 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{5} e^{4} + 20995 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{4} e^{5}\right)} x\right)} \sqrt{e x + d}}{2078505 \, e^{6}}"," ",0,"2/2078505*(109395*B*b^4*e^9*x^9 - 1280*B*b^4*d^9 + 230945*A*a^4*d^4*e^5 + 2432*(4*B*a*b^3 + A*b^4)*d^8*e - 10336*(3*B*a^2*b^2 + 2*A*a*b^3)*d^7*e^2 + 25840*(2*B*a^3*b + 3*A*a^2*b^2)*d^6*e^3 - 41990*(B*a^4 + 4*A*a^3*b)*d^5*e^4 + 6435*(58*B*b^4*d*e^8 + 19*(4*B*a*b^3 + A*b^4)*e^9)*x^8 + 858*(505*B*b^4*d^2*e^7 + 494*(4*B*a*b^3 + A*b^4)*d*e^8 + 323*(3*B*a^2*b^2 + 2*A*a*b^3)*e^9)*x^7 + 66*(2620*B*b^4*d^3*e^6 + 7619*(4*B*a*b^3 + A*b^4)*d^2*e^7 + 14858*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^8 + 4845*(2*B*a^3*b + 3*A*a^2*b^2)*e^9)*x^6 + 9*(35*B*b^4*d^4*e^5 + 23028*(4*B*a*b^3 + A*b^4)*d^3*e^6 + 133076*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^7 + 129200*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^8 + 20995*(B*a^4 + 4*A*a^3*b)*e^9)*x^5 - 5*(70*B*b^4*d^5*e^4 - 46189*A*a^4*e^9 - 133*(4*B*a*b^3 + A*b^4)*d^4*e^5 - 103360*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^6 - 295868*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^7 - 142766*(B*a^4 + 4*A*a^3*b)*d*e^8)*x^4 + 10*(40*B*b^4*d^6*e^3 + 92378*A*a^4*d*e^8 - 76*(4*B*a*b^3 + A*b^4)*d^5*e^4 + 323*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^5 + 68476*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^6 + 96577*(B*a^4 + 4*A*a^3*b)*d^2*e^7)*x^3 - 6*(80*B*b^4*d^7*e^2 - 230945*A*a^4*d^2*e^7 - 152*(4*B*a*b^3 + A*b^4)*d^6*e^3 + 646*(3*B*a^2*b^2 + 2*A*a*b^3)*d^5*e^4 - 1615*(2*B*a^3*b + 3*A*a^2*b^2)*d^4*e^5 - 83980*(B*a^4 + 4*A*a^3*b)*d^3*e^6)*x^2 + (640*B*b^4*d^8*e + 923780*A*a^4*d^3*e^6 - 1216*(4*B*a*b^3 + A*b^4)*d^7*e^2 + 5168*(3*B*a^2*b^2 + 2*A*a*b^3)*d^6*e^3 - 12920*(2*B*a^3*b + 3*A*a^2*b^2)*d^5*e^4 + 20995*(B*a^4 + 4*A*a^3*b)*d^4*e^5)*x)*sqrt(e*x + d)/e^6","B",0
1793,1,772,0,0.430806," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(45045 \, B b^{4} e^{8} x^{8} - 1280 \, B b^{4} d^{8} + 109395 \, A a^{4} d^{3} e^{5} + 2176 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{7} e - 8160 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{6} e^{2} + 17680 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{5} e^{3} - 24310 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{4} e^{4} + 3003 \, {\left(35 \, B b^{4} d e^{7} + 17 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{8}\right)} x^{7} + 231 \, {\left(275 \, B b^{4} d^{2} e^{6} + 527 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{7} + 510 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{8}\right)} x^{6} + 63 \, {\left(5 \, B b^{4} d^{3} e^{5} + 1207 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{6} + 4590 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{7} + 2210 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{8}\right)} x^{5} - 35 \, {\left(10 \, B b^{4} d^{4} e^{4} - 17 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{5} - 5406 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{6} - 10166 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{7} - 2431 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{8}\right)} x^{4} + 5 \, {\left(80 \, B b^{4} d^{5} e^{3} + 21879 \, A a^{4} e^{8} - 136 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e^{4} + 510 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{5} + 49946 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{6} + 46189 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{7}\right)} x^{3} - 3 \, {\left(160 \, B b^{4} d^{6} e^{2} - 109395 \, A a^{4} d e^{7} - 272 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{5} e^{3} + 1020 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{4} - 2210 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{5} - 60775 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{6}\right)} x^{2} + {\left(640 \, B b^{4} d^{7} e + 328185 \, A a^{4} d^{2} e^{6} - 1088 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{6} e^{2} + 4080 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{5} e^{3} - 8840 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{4} e^{4} + 12155 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{765765 \, e^{6}}"," ",0,"2/765765*(45045*B*b^4*e^8*x^8 - 1280*B*b^4*d^8 + 109395*A*a^4*d^3*e^5 + 2176*(4*B*a*b^3 + A*b^4)*d^7*e - 8160*(3*B*a^2*b^2 + 2*A*a*b^3)*d^6*e^2 + 17680*(2*B*a^3*b + 3*A*a^2*b^2)*d^5*e^3 - 24310*(B*a^4 + 4*A*a^3*b)*d^4*e^4 + 3003*(35*B*b^4*d*e^7 + 17*(4*B*a*b^3 + A*b^4)*e^8)*x^7 + 231*(275*B*b^4*d^2*e^6 + 527*(4*B*a*b^3 + A*b^4)*d*e^7 + 510*(3*B*a^2*b^2 + 2*A*a*b^3)*e^8)*x^6 + 63*(5*B*b^4*d^3*e^5 + 1207*(4*B*a*b^3 + A*b^4)*d^2*e^6 + 4590*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^7 + 2210*(2*B*a^3*b + 3*A*a^2*b^2)*e^8)*x^5 - 35*(10*B*b^4*d^4*e^4 - 17*(4*B*a*b^3 + A*b^4)*d^3*e^5 - 5406*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^6 - 10166*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^7 - 2431*(B*a^4 + 4*A*a^3*b)*e^8)*x^4 + 5*(80*B*b^4*d^5*e^3 + 21879*A*a^4*e^8 - 136*(4*B*a*b^3 + A*b^4)*d^4*e^4 + 510*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^5 + 49946*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^6 + 46189*(B*a^4 + 4*A*a^3*b)*d*e^7)*x^3 - 3*(160*B*b^4*d^6*e^2 - 109395*A*a^4*d*e^7 - 272*(4*B*a*b^3 + A*b^4)*d^5*e^3 + 1020*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^4 - 2210*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^5 - 60775*(B*a^4 + 4*A*a^3*b)*d^2*e^6)*x^2 + (640*B*b^4*d^7*e + 328185*A*a^4*d^2*e^6 - 1088*(4*B*a*b^3 + A*b^4)*d^6*e^2 + 4080*(3*B*a^2*b^2 + 2*A*a*b^3)*d^5*e^3 - 8840*(2*B*a^3*b + 3*A*a^2*b^2)*d^4*e^4 + 12155*(B*a^4 + 4*A*a^3*b)*d^3*e^5)*x)*sqrt(e*x + d)/e^6","B",0
1794,1,649,0,0.421941," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B b^{4} e^{7} x^{7} - 256 \, B b^{4} d^{7} + 9009 \, A a^{4} d^{2} e^{5} + 384 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{6} e - 1248 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{5} e^{2} + 2288 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{4} e^{3} - 2574 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{3} e^{4} + 231 \, {\left(16 \, B b^{4} d e^{6} + 15 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{7}\right)} x^{6} + 63 \, {\left(B b^{4} d^{2} e^{5} + 70 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{6} + 130 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{7}\right)} x^{5} - 35 \, {\left(2 \, B b^{4} d^{3} e^{4} - 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{5} - 312 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{6} - 286 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{7}\right)} x^{4} + 5 \, {\left(16 \, B b^{4} d^{4} e^{3} - 24 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{4} + 78 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{5} + 2860 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{6} + 1287 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{7}\right)} x^{3} - 3 \, {\left(32 \, B b^{4} d^{5} e^{2} - 3003 \, A a^{4} e^{7} - 48 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e^{3} + 156 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{4} - 286 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{5} - 3432 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{6}\right)} x^{2} + {\left(128 \, B b^{4} d^{6} e + 18018 \, A a^{4} d e^{6} - 192 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{5} e^{2} + 624 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{3} - 1144 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{4} + 1287 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{6}}"," ",0,"2/45045*(3003*B*b^4*e^7*x^7 - 256*B*b^4*d^7 + 9009*A*a^4*d^2*e^5 + 384*(4*B*a*b^3 + A*b^4)*d^6*e - 1248*(3*B*a^2*b^2 + 2*A*a*b^3)*d^5*e^2 + 2288*(2*B*a^3*b + 3*A*a^2*b^2)*d^4*e^3 - 2574*(B*a^4 + 4*A*a^3*b)*d^3*e^4 + 231*(16*B*b^4*d*e^6 + 15*(4*B*a*b^3 + A*b^4)*e^7)*x^6 + 63*(B*b^4*d^2*e^5 + 70*(4*B*a*b^3 + A*b^4)*d*e^6 + 130*(3*B*a^2*b^2 + 2*A*a*b^3)*e^7)*x^5 - 35*(2*B*b^4*d^3*e^4 - 3*(4*B*a*b^3 + A*b^4)*d^2*e^5 - 312*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^6 - 286*(2*B*a^3*b + 3*A*a^2*b^2)*e^7)*x^4 + 5*(16*B*b^4*d^4*e^3 - 24*(4*B*a*b^3 + A*b^4)*d^3*e^4 + 78*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^5 + 2860*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^6 + 1287*(B*a^4 + 4*A*a^3*b)*e^7)*x^3 - 3*(32*B*b^4*d^5*e^2 - 3003*A*a^4*e^7 - 48*(4*B*a*b^3 + A*b^4)*d^4*e^3 + 156*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^4 - 286*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^5 - 3432*(B*a^4 + 4*A*a^3*b)*d*e^6)*x^2 + (128*B*b^4*d^6*e + 18018*A*a^4*d*e^6 - 192*(4*B*a*b^3 + A*b^4)*d^5*e^2 + 624*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^3 - 1144*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^4 + 1287*(B*a^4 + 4*A*a^3*b)*d^2*e^5)*x)*sqrt(e*x + d)/e^6","B",0
1795,1,527,0,0.410320," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, B b^{4} e^{6} x^{6} - 1280 \, B b^{4} d^{6} + 15015 \, A a^{4} d e^{5} + 1664 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{5} e - 4576 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{2} + 6864 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{3} - 6006 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4} + 315 \, {\left(B b^{4} d e^{5} + 13 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} x^{5} - 35 \, {\left(10 \, B b^{4} d^{2} e^{4} - 13 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} - 286 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} x^{4} + 10 \, {\left(40 \, B b^{4} d^{3} e^{3} - 52 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{4} + 143 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} + 1287 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} x^{3} - 3 \, {\left(160 \, B b^{4} d^{4} e^{2} - 208 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{3} + 572 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{4} - 858 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} - 3003 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} x^{2} + {\left(640 \, B b^{4} d^{5} e + 15015 \, A a^{4} e^{6} - 832 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e^{2} + 2288 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{3} - 3432 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{4} + 3003 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{6}}"," ",0,"2/45045*(3465*B*b^4*e^6*x^6 - 1280*B*b^4*d^6 + 15015*A*a^4*d*e^5 + 1664*(4*B*a*b^3 + A*b^4)*d^5*e - 4576*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^2 + 6864*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 6006*(B*a^4 + 4*A*a^3*b)*d^2*e^4 + 315*(B*b^4*d*e^5 + 13*(4*B*a*b^3 + A*b^4)*e^6)*x^5 - 35*(10*B*b^4*d^2*e^4 - 13*(4*B*a*b^3 + A*b^4)*d*e^5 - 286*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*x^4 + 10*(40*B*b^4*d^3*e^3 - 52*(4*B*a*b^3 + A*b^4)*d^2*e^4 + 143*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + 1287*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*x^3 - 3*(160*B*b^4*d^4*e^2 - 208*(4*B*a*b^3 + A*b^4)*d^3*e^3 + 572*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 - 858*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 3003*(B*a^4 + 4*A*a^3*b)*e^6)*x^2 + (640*B*b^4*d^5*e + 15015*A*a^4*e^6 - 832*(4*B*a*b^3 + A*b^4)*d^4*e^2 + 2288*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^3 - 3432*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 3003*(B*a^4 + 4*A*a^3*b)*d*e^5)*x)*sqrt(e*x + d)/e^6","B",0
1796,1,408,0,0.412312," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B b^{4} e^{5} x^{5} - 1280 \, B b^{4} d^{5} + 3465 \, A a^{4} e^{5} + 1408 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e - 3168 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + 3696 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} - 2310 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} - 35 \, {\left(10 \, B b^{4} d e^{4} - 11 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 10 \, {\left(40 \, B b^{4} d^{2} e^{3} - 44 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 99 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} - 6 \, {\left(80 \, B b^{4} d^{3} e^{2} - 88 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 198 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} - 231 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + {\left(640 \, B b^{4} d^{4} e - 704 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 1584 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - 1848 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + 1155 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{6}}"," ",0,"2/3465*(315*B*b^4*e^5*x^5 - 1280*B*b^4*d^5 + 3465*A*a^4*e^5 + 1408*(4*B*a*b^3 + A*b^4)*d^4*e - 3168*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + 3696*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 - 2310*(B*a^4 + 4*A*a^3*b)*d*e^4 - 35*(10*B*b^4*d*e^4 - 11*(4*B*a*b^3 + A*b^4)*e^5)*x^4 + 10*(40*B*b^4*d^2*e^3 - 44*(4*B*a*b^3 + A*b^4)*d*e^4 + 99*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 - 6*(80*B*b^4*d^3*e^2 - 88*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 198*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 - 231*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + (640*B*b^4*d^4*e - 704*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 1584*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - 1848*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + 1155*(B*a^4 + 4*A*a^3*b)*e^5)*x)*sqrt(e*x + d)/e^6","B",0
1797,1,418,0,0.409981," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{4} e^{5} x^{5} + 1280 \, B b^{4} d^{5} - 315 \, A a^{4} e^{5} - 1152 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 2016 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} - 1680 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} + 630 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} - 5 \, {\left(10 \, B b^{4} d e^{4} - 9 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(40 \, B b^{4} d^{2} e^{3} - 36 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 63 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} - 2 \, {\left(80 \, B b^{4} d^{3} e^{2} - 72 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 126 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} - 105 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + {\left(640 \, B b^{4} d^{4} e - 576 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 1008 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - 840 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + 315 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"2/315*(35*B*b^4*e^5*x^5 + 1280*B*b^4*d^5 - 315*A*a^4*e^5 - 1152*(4*B*a*b^3 + A*b^4)*d^4*e + 2016*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 - 1680*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 + 630*(B*a^4 + 4*A*a^3*b)*d*e^4 - 5*(10*B*b^4*d*e^4 - 9*(4*B*a*b^3 + A*b^4)*e^5)*x^4 + 2*(40*B*b^4*d^2*e^3 - 36*(4*B*a*b^3 + A*b^4)*d*e^4 + 63*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 - 2*(80*B*b^4*d^3*e^2 - 72*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 126*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 - 105*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + (640*B*b^4*d^4*e - 576*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 1008*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - 840*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + 315*(B*a^4 + 4*A*a^3*b)*e^5)*x)*sqrt(e*x + d)/(e^7*x + d*e^6)","B",0
1798,1,430,0,0.407293," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{4} e^{5} x^{5} - 1280 \, B b^{4} d^{5} - 35 \, A a^{4} e^{5} + 896 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e - 1120 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} + 560 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} - 70 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} - 3 \, {\left(10 \, B b^{4} d e^{4} - 7 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(40 \, B b^{4} d^{2} e^{3} - 28 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 35 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} - 6 \, {\left(80 \, B b^{4} d^{3} e^{2} - 56 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 70 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} - 35 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} - 3 \, {\left(640 \, B b^{4} d^{4} e - 448 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 560 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - 280 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} + 35 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"2/105*(15*B*b^4*e^5*x^5 - 1280*B*b^4*d^5 - 35*A*a^4*e^5 + 896*(4*B*a*b^3 + A*b^4)*d^4*e - 1120*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 + 560*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 - 70*(B*a^4 + 4*A*a^3*b)*d*e^4 - 3*(10*B*b^4*d*e^4 - 7*(4*B*a*b^3 + A*b^4)*e^5)*x^4 + 2*(40*B*b^4*d^2*e^3 - 28*(4*B*a*b^3 + A*b^4)*d*e^4 + 35*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 - 6*(80*B*b^4*d^3*e^2 - 56*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 70*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 - 35*(2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 - 3*(640*B*b^4*d^4*e - 448*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 560*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - 280*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 + 35*(B*a^4 + 4*A*a^3*b)*e^5)*x)*sqrt(e*x + d)/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","B",0
1799,1,441,0,0.411597," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{4} e^{5} x^{5} + 256 \, B b^{4} d^{5} - 3 \, A a^{4} e^{5} - 128 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e + 96 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{2} - 16 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{3} - 2 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{4} - 5 \, {\left(2 \, B b^{4} d e^{4} - {\left(4 \, B a b^{3} + A b^{4}\right)} e^{5}\right)} x^{4} + 10 \, {\left(8 \, B b^{4} d^{2} e^{3} - 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{4} + 3 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{5}\right)} x^{3} + 30 \, {\left(16 \, B b^{4} d^{3} e^{2} - 8 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{3} + 6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{4} - {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 5 \, {\left(128 \, B b^{4} d^{4} e - 64 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{2} + 48 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{3} - 8 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{4} - {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"2/15*(3*B*b^4*e^5*x^5 + 256*B*b^4*d^5 - 3*A*a^4*e^5 - 128*(4*B*a*b^3 + A*b^4)*d^4*e + 96*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^2 - 16*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^3 - 2*(B*a^4 + 4*A*a^3*b)*d*e^4 - 5*(2*B*b^4*d*e^4 - (4*B*a*b^3 + A*b^4)*e^5)*x^4 + 10*(8*B*b^4*d^2*e^3 - 4*(4*B*a*b^3 + A*b^4)*d*e^4 + 3*(3*B*a^2*b^2 + 2*A*a*b^3)*e^5)*x^3 + 30*(16*B*b^4*d^3*e^2 - 8*(4*B*a*b^3 + A*b^4)*d^2*e^3 + 6*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^4 - (2*B*a^3*b + 3*A*a^2*b^2)*e^5)*x^2 + 5*(128*B*b^4*d^4*e - 64*(4*B*a*b^3 + A*b^4)*d^3*e^2 + 48*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^3 - 8*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^4 - (B*a^4 + 4*A*a^3*b)*e^5)*x)*sqrt(e*x + d)/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","B",0
1800,1,1470,0,0.435203," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2909907 \, B b^{6} e^{11} x^{11} - 14336 \, B b^{6} d^{11} + 7436429 \, A a^{6} d^{4} e^{7} + 23552 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{10} e - 123648 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{9} e^{2} + 391552 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{8} e^{3} - 832048 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{7} e^{4} + 1248072 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{6} e^{5} - 1352078 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{5} e^{6} + 138567 \, {\left(70 \, B b^{6} d e^{10} + 23 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{11}\right)} x^{10} + 7293 \, {\left(1498 \, B b^{6} d^{2} e^{9} + 1472 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{10} + 1449 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{11}\right)} x^{9} + 1287 \, {\left(3248 \, B b^{6} d^{3} e^{8} + 9522 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{9} + 28014 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{10} + 15295 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{11}\right)} x^{8} + 429 \, {\left(7 \, B b^{6} d^{4} e^{7} + 11132 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{8} + 97566 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{9} + 159068 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{10} + 52003 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{11}\right)} x^{7} - 231 \, {\left(14 \, B b^{6} d^{5} e^{6} - 23 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{7} - 72312 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{8} - 350474 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{9} - 341734 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{10} - 66861 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{11}\right)} x^{6} + 63 \, {\left(56 \, B b^{6} d^{6} e^{5} - 92 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{6} + 483 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{7} + 529644 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{8} + 1530374 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{9} + 891480 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{10} + 96577 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{11}\right)} x^{5} - 7 \, {\left(560 \, B b^{6} d^{7} e^{4} - 1062347 \, A a^{6} e^{11} - 920 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e^{5} + 4830 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{6} - 15295 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{7} - 5943200 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{8} - 10207446 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{9} - 3283618 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{10}\right)} x^{4} + {\left(4480 \, B b^{6} d^{8} e^{3} + 29745716 \, A a^{6} d e^{10} - 7360 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{7} e^{4} + 38640 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{6} e^{5} - 122360 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{5} e^{6} + 260015 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{4} e^{7} + 33073908 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{3} e^{8} + 31097794 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{2} e^{9}\right)} x^{3} - 3 \, {\left(1792 \, B b^{6} d^{9} e^{2} - 14872858 \, A a^{6} d^{2} e^{9} - 2944 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{8} e^{3} + 15456 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{7} e^{4} - 48944 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{6} e^{5} + 104006 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{5} e^{6} - 156009 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{4} e^{7} - 5408312 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{3} e^{8}\right)} x^{2} + {\left(7168 \, B b^{6} d^{10} e + 29745716 \, A a^{6} d^{3} e^{8} - 11776 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{9} e^{2} + 61824 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{8} e^{3} - 195776 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{7} e^{4} + 416024 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{6} e^{5} - 624036 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{5} e^{6} + 676039 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{4} e^{7}\right)} x\right)} \sqrt{e x + d}}{66927861 \, e^{8}}"," ",0,"2/66927861*(2909907*B*b^6*e^11*x^11 - 14336*B*b^6*d^11 + 7436429*A*a^6*d^4*e^7 + 23552*(6*B*a*b^5 + A*b^6)*d^10*e - 123648*(5*B*a^2*b^4 + 2*A*a*b^5)*d^9*e^2 + 391552*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^8*e^3 - 832048*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^7*e^4 + 1248072*(2*B*a^5*b + 5*A*a^4*b^2)*d^6*e^5 - 1352078*(B*a^6 + 6*A*a^5*b)*d^5*e^6 + 138567*(70*B*b^6*d*e^10 + 23*(6*B*a*b^5 + A*b^6)*e^11)*x^10 + 7293*(1498*B*b^6*d^2*e^9 + 1472*(6*B*a*b^5 + A*b^6)*d*e^10 + 1449*(5*B*a^2*b^4 + 2*A*a*b^5)*e^11)*x^9 + 1287*(3248*B*b^6*d^3*e^8 + 9522*(6*B*a*b^5 + A*b^6)*d^2*e^9 + 28014*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^10 + 15295*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^11)*x^8 + 429*(7*B*b^6*d^4*e^7 + 11132*(6*B*a*b^5 + A*b^6)*d^3*e^8 + 97566*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^9 + 159068*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^10 + 52003*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^11)*x^7 - 231*(14*B*b^6*d^5*e^6 - 23*(6*B*a*b^5 + A*b^6)*d^4*e^7 - 72312*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^8 - 350474*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^9 - 341734*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^10 - 66861*(2*B*a^5*b + 5*A*a^4*b^2)*e^11)*x^6 + 63*(56*B*b^6*d^6*e^5 - 92*(6*B*a*b^5 + A*b^6)*d^5*e^6 + 483*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^7 + 529644*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^8 + 1530374*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^9 + 891480*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^10 + 96577*(B*a^6 + 6*A*a^5*b)*e^11)*x^5 - 7*(560*B*b^6*d^7*e^4 - 1062347*A*a^6*e^11 - 920*(6*B*a*b^5 + A*b^6)*d^6*e^5 + 4830*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^6 - 15295*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^7 - 5943200*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^8 - 10207446*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^9 - 3283618*(B*a^6 + 6*A*a^5*b)*d*e^10)*x^4 + (4480*B*b^6*d^8*e^3 + 29745716*A*a^6*d*e^10 - 7360*(6*B*a*b^5 + A*b^6)*d^7*e^4 + 38640*(5*B*a^2*b^4 + 2*A*a*b^5)*d^6*e^5 - 122360*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^5*e^6 + 260015*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^4*e^7 + 33073908*(2*B*a^5*b + 5*A*a^4*b^2)*d^3*e^8 + 31097794*(B*a^6 + 6*A*a^5*b)*d^2*e^9)*x^3 - 3*(1792*B*b^6*d^9*e^2 - 14872858*A*a^6*d^2*e^9 - 2944*(6*B*a*b^5 + A*b^6)*d^8*e^3 + 15456*(5*B*a^2*b^4 + 2*A*a*b^5)*d^7*e^4 - 48944*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^6*e^5 + 104006*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^5*e^6 - 156009*(2*B*a^5*b + 5*A*a^4*b^2)*d^4*e^7 - 5408312*(B*a^6 + 6*A*a^5*b)*d^3*e^8)*x^2 + (7168*B*b^6*d^10*e + 29745716*A*a^6*d^3*e^8 - 11776*(6*B*a*b^5 + A*b^6)*d^9*e^2 + 61824*(5*B*a^2*b^4 + 2*A*a*b^5)*d^8*e^3 - 195776*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^7*e^4 + 416024*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^6*e^5 - 624036*(2*B*a^5*b + 5*A*a^4*b^2)*d^5*e^6 + 676039*(B*a^6 + 6*A*a^5*b)*d^4*e^7)*x)*sqrt(e*x + d)/e^8","B",0
1801,1,1293,0,0.432795," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(138567 \, B b^{6} e^{10} x^{10} - 2048 \, B b^{6} d^{10} + 415701 \, A a^{6} d^{3} e^{7} + 3072 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{9} e - 14592 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{8} e^{2} + 41344 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{7} e^{3} - 77520 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{6} e^{4} + 100776 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{5} e^{5} - 92378 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{4} e^{6} + 7293 \, {\left(43 \, B b^{6} d e^{9} + 21 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{10}\right)} x^{9} + 3861 \, {\left(47 \, B b^{6} d^{2} e^{8} + 91 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{9} + 133 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{10}\right)} x^{8} + 429 \, {\left(B b^{6} d^{3} e^{7} + 483 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{8} + 2793 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{9} + 2261 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{10}\right)} x^{7} - 231 \, {\left(2 \, B b^{6} d^{4} e^{6} - 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{7} - 3135 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{8} - 10013 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{9} - 4845 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{10}\right)} x^{6} + 63 \, {\left(8 \, B b^{6} d^{5} e^{5} - 12 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{6} + 57 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{7} + 22933 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{8} + 43605 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{9} + 12597 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{10}\right)} x^{5} - 7 \, {\left(80 \, B b^{6} d^{6} e^{4} - 120 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{5} + 570 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{6} - 1615 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{7} - 256785 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{8} - 289731 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{9} - 46189 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{10}\right)} x^{4} + {\left(640 \, B b^{6} d^{7} e^{3} + 415701 \, A a^{6} e^{10} - 960 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e^{4} + 4560 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{5} - 12920 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{6} + 24225 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{7} + 1423461 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{8} + 877591 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{9}\right)} x^{3} - 3 \, {\left(256 \, B b^{6} d^{8} e^{2} - 415701 \, A a^{6} d e^{9} - 384 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{7} e^{3} + 1824 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{6} e^{4} - 5168 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{5} e^{5} + 9690 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{4} e^{6} - 12597 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{3} e^{7} - 230945 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{2} e^{8}\right)} x^{2} + {\left(1024 \, B b^{6} d^{9} e + 1247103 \, A a^{6} d^{2} e^{8} - 1536 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{8} e^{2} + 7296 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{7} e^{3} - 20672 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{6} e^{4} + 38760 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{5} e^{5} - 50388 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{4} e^{6} + 46189 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{2909907 \, e^{8}}"," ",0,"2/2909907*(138567*B*b^6*e^10*x^10 - 2048*B*b^6*d^10 + 415701*A*a^6*d^3*e^7 + 3072*(6*B*a*b^5 + A*b^6)*d^9*e - 14592*(5*B*a^2*b^4 + 2*A*a*b^5)*d^8*e^2 + 41344*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^7*e^3 - 77520*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^6*e^4 + 100776*(2*B*a^5*b + 5*A*a^4*b^2)*d^5*e^5 - 92378*(B*a^6 + 6*A*a^5*b)*d^4*e^6 + 7293*(43*B*b^6*d*e^9 + 21*(6*B*a*b^5 + A*b^6)*e^10)*x^9 + 3861*(47*B*b^6*d^2*e^8 + 91*(6*B*a*b^5 + A*b^6)*d*e^9 + 133*(5*B*a^2*b^4 + 2*A*a*b^5)*e^10)*x^8 + 429*(B*b^6*d^3*e^7 + 483*(6*B*a*b^5 + A*b^6)*d^2*e^8 + 2793*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^9 + 2261*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^10)*x^7 - 231*(2*B*b^6*d^4*e^6 - 3*(6*B*a*b^5 + A*b^6)*d^3*e^7 - 3135*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^8 - 10013*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^9 - 4845*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^10)*x^6 + 63*(8*B*b^6*d^5*e^5 - 12*(6*B*a*b^5 + A*b^6)*d^4*e^6 + 57*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^7 + 22933*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^8 + 43605*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^9 + 12597*(2*B*a^5*b + 5*A*a^4*b^2)*e^10)*x^5 - 7*(80*B*b^6*d^6*e^4 - 120*(6*B*a*b^5 + A*b^6)*d^5*e^5 + 570*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^6 - 1615*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^7 - 256785*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^8 - 289731*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^9 - 46189*(B*a^6 + 6*A*a^5*b)*e^10)*x^4 + (640*B*b^6*d^7*e^3 + 415701*A*a^6*e^10 - 960*(6*B*a*b^5 + A*b^6)*d^6*e^4 + 4560*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^5 - 12920*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^6 + 24225*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^7 + 1423461*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^8 + 877591*(B*a^6 + 6*A*a^5*b)*d*e^9)*x^3 - 3*(256*B*b^6*d^8*e^2 - 415701*A*a^6*d*e^9 - 384*(6*B*a*b^5 + A*b^6)*d^7*e^3 + 1824*(5*B*a^2*b^4 + 2*A*a*b^5)*d^6*e^4 - 5168*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^5*e^5 + 9690*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^4*e^6 - 12597*(2*B*a^5*b + 5*A*a^4*b^2)*d^3*e^7 - 230945*(B*a^6 + 6*A*a^5*b)*d^2*e^8)*x^2 + (1024*B*b^6*d^9*e + 1247103*A*a^6*d^2*e^8 - 1536*(6*B*a*b^5 + A*b^6)*d^8*e^2 + 7296*(5*B*a^2*b^4 + 2*A*a*b^5)*d^7*e^3 - 20672*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^6*e^4 + 38760*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^5*e^5 - 50388*(2*B*a^5*b + 5*A*a^4*b^2)*d^4*e^6 + 46189*(B*a^6 + 6*A*a^5*b)*d^3*e^7)*x)*sqrt(e*x + d)/e^8","B",0
1802,1,1118,0,0.450175," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(255255 \, B b^{6} e^{9} x^{9} - 14336 \, B b^{6} d^{9} + 969969 \, A a^{6} d^{2} e^{7} + 19456 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{8} e - 82688 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{7} e^{2} + 206720 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{6} e^{3} - 335920 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{5} e^{4} + 369512 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{4} e^{5} - 277134 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{3} e^{6} + 15015 \, {\left(20 \, B b^{6} d e^{8} + 19 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{9}\right)} x^{8} + 3003 \, {\left(B b^{6} d^{2} e^{7} + 114 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{8} + 323 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{9}\right)} x^{7} - 231 \, {\left(14 \, B b^{6} d^{3} e^{6} - 19 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{7} - 5168 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{8} - 8075 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{9}\right)} x^{6} + 21 \, {\left(168 \, B b^{6} d^{4} e^{5} - 228 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{6} + 969 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{7} + 113050 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{8} + 104975 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{9}\right)} x^{5} - 35 \, {\left(112 \, B b^{6} d^{5} e^{4} - 152 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{5} + 646 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{6} - 1615 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{7} - 83980 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{8} - 46189 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{9}\right)} x^{4} + 5 \, {\left(896 \, B b^{6} d^{6} e^{3} - 1216 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{4} + 5168 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{5} - 12920 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{6} + 20995 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{7} + 461890 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{8} + 138567 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{9}\right)} x^{3} - 3 \, {\left(1792 \, B b^{6} d^{7} e^{2} - 323323 \, A a^{6} e^{9} - 2432 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e^{3} + 10336 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{4} - 25840 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{5} + 41990 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{6} - 46189 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{7} - 369512 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{8}\right)} x^{2} + {\left(7168 \, B b^{6} d^{8} e + 1939938 \, A a^{6} d e^{8} - 9728 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{7} e^{2} + 41344 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{6} e^{3} - 103360 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{5} e^{4} + 167960 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{4} e^{5} - 184756 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{3} e^{6} + 138567 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{2} e^{7}\right)} x\right)} \sqrt{e x + d}}{4849845 \, e^{8}}"," ",0,"2/4849845*(255255*B*b^6*e^9*x^9 - 14336*B*b^6*d^9 + 969969*A*a^6*d^2*e^7 + 19456*(6*B*a*b^5 + A*b^6)*d^8*e - 82688*(5*B*a^2*b^4 + 2*A*a*b^5)*d^7*e^2 + 206720*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^6*e^3 - 335920*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^5*e^4 + 369512*(2*B*a^5*b + 5*A*a^4*b^2)*d^4*e^5 - 277134*(B*a^6 + 6*A*a^5*b)*d^3*e^6 + 15015*(20*B*b^6*d*e^8 + 19*(6*B*a*b^5 + A*b^6)*e^9)*x^8 + 3003*(B*b^6*d^2*e^7 + 114*(6*B*a*b^5 + A*b^6)*d*e^8 + 323*(5*B*a^2*b^4 + 2*A*a*b^5)*e^9)*x^7 - 231*(14*B*b^6*d^3*e^6 - 19*(6*B*a*b^5 + A*b^6)*d^2*e^7 - 5168*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^8 - 8075*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^9)*x^6 + 21*(168*B*b^6*d^4*e^5 - 228*(6*B*a*b^5 + A*b^6)*d^3*e^6 + 969*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^7 + 113050*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^8 + 104975*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^9)*x^5 - 35*(112*B*b^6*d^5*e^4 - 152*(6*B*a*b^5 + A*b^6)*d^4*e^5 + 646*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^6 - 1615*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^7 - 83980*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^8 - 46189*(2*B*a^5*b + 5*A*a^4*b^2)*e^9)*x^4 + 5*(896*B*b^6*d^6*e^3 - 1216*(6*B*a*b^5 + A*b^6)*d^5*e^4 + 5168*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^5 - 12920*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^6 + 20995*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^7 + 461890*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^8 + 138567*(B*a^6 + 6*A*a^5*b)*e^9)*x^3 - 3*(1792*B*b^6*d^7*e^2 - 323323*A*a^6*e^9 - 2432*(6*B*a*b^5 + A*b^6)*d^6*e^3 + 10336*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^4 - 25840*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^5 + 41990*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^6 - 46189*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^7 - 369512*(B*a^6 + 6*A*a^5*b)*d*e^8)*x^2 + (7168*B*b^6*d^8*e + 1939938*A*a^6*d*e^8 - 9728*(6*B*a*b^5 + A*b^6)*d^7*e^2 + 41344*(5*B*a^2*b^4 + 2*A*a*b^5)*d^6*e^3 - 103360*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^5*e^4 + 167960*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^4*e^5 - 184756*(2*B*a^5*b + 5*A*a^4*b^2)*d^3*e^6 + 138567*(B*a^6 + 6*A*a^5*b)*d^2*e^7)*x)*sqrt(e*x + d)/e^8","B",0
1803,1,942,0,0.428598," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(45045 \, B b^{6} e^{8} x^{8} - 14336 \, B b^{6} d^{8} + 255255 \, A a^{6} d e^{7} + 17408 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{7} e - 65280 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{6} e^{2} + 141440 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{5} e^{3} - 194480 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{4} e^{4} + 175032 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{3} e^{5} - 102102 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d^{2} e^{6} + 3003 \, {\left(B b^{6} d e^{7} + 17 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{8}\right)} x^{7} - 231 \, {\left(14 \, B b^{6} d^{2} e^{6} - 17 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{7} - 765 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{8}\right)} x^{6} + 63 \, {\left(56 \, B b^{6} d^{3} e^{5} - 68 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{6} + 255 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{7} + 5525 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{8}\right)} x^{5} - 35 \, {\left(112 \, B b^{6} d^{4} e^{4} - 136 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{5} + 510 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{6} - 1105 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{7} - 12155 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{8}\right)} x^{4} + 5 \, {\left(896 \, B b^{6} d^{5} e^{3} - 1088 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{4} + 4080 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{5} - 8840 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{6} + 12155 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{7} + 65637 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{8}\right)} x^{3} - 3 \, {\left(1792 \, B b^{6} d^{6} e^{2} - 2176 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{3} + 8160 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{4} - 17680 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{5} + 24310 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{6} - 21879 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{7} - 51051 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{8}\right)} x^{2} + {\left(7168 \, B b^{6} d^{7} e + 255255 \, A a^{6} e^{8} - 8704 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e^{2} + 32640 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{3} - 70720 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{4} + 97240 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{5} - 87516 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{6} + 51051 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{7}\right)} x\right)} \sqrt{e x + d}}{765765 \, e^{8}}"," ",0,"2/765765*(45045*B*b^6*e^8*x^8 - 14336*B*b^6*d^8 + 255255*A*a^6*d*e^7 + 17408*(6*B*a*b^5 + A*b^6)*d^7*e - 65280*(5*B*a^2*b^4 + 2*A*a*b^5)*d^6*e^2 + 141440*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^5*e^3 - 194480*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^4*e^4 + 175032*(2*B*a^5*b + 5*A*a^4*b^2)*d^3*e^5 - 102102*(B*a^6 + 6*A*a^5*b)*d^2*e^6 + 3003*(B*b^6*d*e^7 + 17*(6*B*a*b^5 + A*b^6)*e^8)*x^7 - 231*(14*B*b^6*d^2*e^6 - 17*(6*B*a*b^5 + A*b^6)*d*e^7 - 765*(5*B*a^2*b^4 + 2*A*a*b^5)*e^8)*x^6 + 63*(56*B*b^6*d^3*e^5 - 68*(6*B*a*b^5 + A*b^6)*d^2*e^6 + 255*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^7 + 5525*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^8)*x^5 - 35*(112*B*b^6*d^4*e^4 - 136*(6*B*a*b^5 + A*b^6)*d^3*e^5 + 510*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^6 - 1105*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^7 - 12155*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^8)*x^4 + 5*(896*B*b^6*d^5*e^3 - 1088*(6*B*a*b^5 + A*b^6)*d^4*e^4 + 4080*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^5 - 8840*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^6 + 12155*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^7 + 65637*(2*B*a^5*b + 5*A*a^4*b^2)*e^8)*x^3 - 3*(1792*B*b^6*d^6*e^2 - 2176*(6*B*a*b^5 + A*b^6)*d^5*e^3 + 8160*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^4 - 17680*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^5 + 24310*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^6 - 21879*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^7 - 51051*(B*a^6 + 6*A*a^5*b)*e^8)*x^2 + (7168*B*b^6*d^7*e + 255255*A*a^6*e^8 - 8704*(6*B*a*b^5 + A*b^6)*d^6*e^2 + 32640*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^3 - 70720*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^4 + 97240*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^5 - 87516*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^6 + 51051*(B*a^6 + 6*A*a^5*b)*d*e^7)*x)*sqrt(e*x + d)/e^8","B",0
1804,1,769,0,0.481568," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B b^{6} e^{7} x^{7} - 14336 \, B b^{6} d^{7} + 45045 \, A a^{6} e^{7} + 15360 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e - 49920 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 91520 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} - 102960 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 72072 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} - 30030 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - 231 \, {\left(14 \, B b^{6} d e^{6} - 15 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 63 \, {\left(56 \, B b^{6} d^{2} e^{5} - 60 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 195 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} - 35 \, {\left(112 \, B b^{6} d^{3} e^{4} - 120 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 390 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - 715 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 5 \, {\left(896 \, B b^{6} d^{4} e^{3} - 960 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 3120 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 5720 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 6435 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} - 3 \, {\left(1792 \, B b^{6} d^{5} e^{2} - 1920 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 6240 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 11440 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 12870 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} - 9009 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + {\left(7168 \, B b^{6} d^{6} e - 7680 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 24960 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 45760 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 51480 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 36036 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 15015 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{8}}"," ",0,"2/45045*(3003*B*b^6*e^7*x^7 - 14336*B*b^6*d^7 + 45045*A*a^6*e^7 + 15360*(6*B*a*b^5 + A*b^6)*d^6*e - 49920*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 91520*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 - 102960*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 72072*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 - 30030*(B*a^6 + 6*A*a^5*b)*d*e^6 - 231*(14*B*b^6*d*e^6 - 15*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 63*(56*B*b^6*d^2*e^5 - 60*(6*B*a*b^5 + A*b^6)*d*e^6 + 195*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 - 35*(112*B*b^6*d^3*e^4 - 120*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 390*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - 715*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 5*(896*B*b^6*d^4*e^3 - 960*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 3120*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 5720*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 6435*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 - 3*(1792*B*b^6*d^5*e^2 - 1920*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 6240*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 11440*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 12870*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 - 9009*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + (7168*B*b^6*d^6*e - 7680*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 24960*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 45760*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 51480*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 36036*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 15015*(B*a^6 + 6*A*a^5*b)*e^7)*x)*sqrt(e*x + d)/e^8","B",0
1805,1,778,0,0.491137," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, B b^{6} e^{7} x^{7} + 14336 \, B b^{6} d^{7} - 3003 \, A a^{6} e^{7} - 13312 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 36608 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 54912 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 48048 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 24024 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 6006 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - 21 \, {\left(14 \, B b^{6} d e^{6} - 13 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 7 \, {\left(56 \, B b^{6} d^{2} e^{5} - 52 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 143 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} - 5 \, {\left(112 \, B b^{6} d^{3} e^{4} - 104 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 286 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - 429 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + {\left(896 \, B b^{6} d^{4} e^{3} - 832 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 2288 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 3432 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 3003 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} - {\left(1792 \, B b^{6} d^{5} e^{2} - 1664 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 4576 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 6864 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 6006 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} - 3003 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + {\left(7168 \, B b^{6} d^{6} e - 6656 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 18304 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 27456 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 24024 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 12012 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 3003 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x\right)} \sqrt{e x + d}}{3003 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"2/3003*(231*B*b^6*e^7*x^7 + 14336*B*b^6*d^7 - 3003*A*a^6*e^7 - 13312*(6*B*a*b^5 + A*b^6)*d^6*e + 36608*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 54912*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 48048*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 24024*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 6006*(B*a^6 + 6*A*a^5*b)*d*e^6 - 21*(14*B*b^6*d*e^6 - 13*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 7*(56*B*b^6*d^2*e^5 - 52*(6*B*a*b^5 + A*b^6)*d*e^6 + 143*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 - 5*(112*B*b^6*d^3*e^4 - 104*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 286*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - 429*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + (896*B*b^6*d^4*e^3 - 832*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 2288*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 3432*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 3003*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 - (1792*B*b^6*d^5*e^2 - 1664*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 4576*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 6864*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 6006*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 - 3003*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + (7168*B*b^6*d^6*e - 6656*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 18304*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 27456*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 24024*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 12012*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 3003*(B*a^6 + 6*A*a^5*b)*e^7)*x)*sqrt(e*x + d)/(e^9*x + d*e^8)","B",0
1806,1,790,0,0.446644," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B b^{6} e^{7} x^{7} - 14336 \, B b^{6} d^{7} - 231 \, A a^{6} e^{7} + 11264 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e - 25344 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 29568 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} - 18480 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 5544 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} - 462 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - 7 \, {\left(14 \, B b^{6} d e^{6} - 11 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 3 \, {\left(56 \, B b^{6} d^{2} e^{5} - 44 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 99 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} - 3 \, {\left(112 \, B b^{6} d^{3} e^{4} - 88 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 198 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - 231 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + {\left(896 \, B b^{6} d^{4} e^{3} - 704 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 1584 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 1848 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 1155 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} - 3 \, {\left(1792 \, B b^{6} d^{5} e^{2} - 1408 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 3168 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 3696 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 2310 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} - 693 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} - 3 \, {\left(7168 \, B b^{6} d^{6} e - 5632 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 12672 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 14784 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 9240 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 2772 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 231 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x\right)} \sqrt{e x + d}}{693 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"2/693*(63*B*b^6*e^7*x^7 - 14336*B*b^6*d^7 - 231*A*a^6*e^7 + 11264*(6*B*a*b^5 + A*b^6)*d^6*e - 25344*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 29568*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 - 18480*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 5544*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 - 462*(B*a^6 + 6*A*a^5*b)*d*e^6 - 7*(14*B*b^6*d*e^6 - 11*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 3*(56*B*b^6*d^2*e^5 - 44*(6*B*a*b^5 + A*b^6)*d*e^6 + 99*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 - 3*(112*B*b^6*d^3*e^4 - 88*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 198*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - 231*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + (896*B*b^6*d^4*e^3 - 704*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 1584*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 1848*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 1155*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 - 3*(1792*B*b^6*d^5*e^2 - 1408*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 3168*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 3696*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 2310*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 - 693*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 - 3*(7168*B*b^6*d^6*e - 5632*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 12672*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 14784*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 9240*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 2772*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 231*(B*a^6 + 6*A*a^5*b)*e^7)*x)*sqrt(e*x + d)/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","B",0
1807,1,802,0,0.439846," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{6} e^{7} x^{7} + 14336 \, B b^{6} d^{7} - 63 \, A a^{6} e^{7} - 9216 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 16128 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 13440 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 5040 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 504 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} - 42 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - 5 \, {\left(14 \, B b^{6} d e^{6} - 9 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 3 \, {\left(56 \, B b^{6} d^{2} e^{5} - 36 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 63 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} - 5 \, {\left(112 \, B b^{6} d^{3} e^{4} - 72 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 126 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - 105 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 5 \, {\left(896 \, B b^{6} d^{4} e^{3} - 576 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 1008 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 840 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 315 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 15 \, {\left(1792 \, B b^{6} d^{5} e^{2} - 1152 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 2016 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 1680 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 630 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} - 63 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 5 \, {\left(7168 \, B b^{6} d^{6} e - 4608 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 8064 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 6720 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 2520 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 252 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} - 21 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right)}}"," ",0,"2/315*(35*B*b^6*e^7*x^7 + 14336*B*b^6*d^7 - 63*A*a^6*e^7 - 9216*(6*B*a*b^5 + A*b^6)*d^6*e + 16128*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 13440*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 5040*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 504*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 - 42*(B*a^6 + 6*A*a^5*b)*d*e^6 - 5*(14*B*b^6*d*e^6 - 9*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 3*(56*B*b^6*d^2*e^5 - 36*(6*B*a*b^5 + A*b^6)*d*e^6 + 63*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 - 5*(112*B*b^6*d^3*e^4 - 72*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 126*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - 105*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 5*(896*B*b^6*d^4*e^3 - 576*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 1008*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 840*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 315*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 15*(1792*B*b^6*d^5*e^2 - 1152*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 2016*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 1680*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 630*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 - 63*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 5*(7168*B*b^6*d^6*e - 4608*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 8064*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 6720*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 2520*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 252*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 - 21*(B*a^6 + 6*A*a^5*b)*e^7)*x)*sqrt(e*x + d)/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8)","B",0
1808,1,1006,0,0.467573," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(2 \, B a b^{3} d^{3} - {\left(13 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d^{2} e + 2 \, {\left(10 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} d e^{2} - {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} e^{3} + {\left(2 \, B b^{4} d^{3} - {\left(13 \, B a b^{3} - 7 \, A b^{4}\right)} d^{2} e + 2 \, {\left(10 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d e^{2} - {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(30 \, B b^{4} e^{3} x^{4} + {\left(457 \, B a b^{3} - 105 \, A b^{4}\right)} d^{3} - 7 \, {\left(277 \, B a^{2} b^{2} - 161 \, A a b^{3}\right)} d^{2} e + 35 \, {\left(69 \, B a^{3} b - 49 \, A a^{2} b^{2}\right)} d e^{2} - 105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} e^{3} + 6 \, {\left(22 \, B b^{4} d e^{2} - {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} e^{3}\right)} x^{3} + 2 \, {\left(122 \, B b^{4} d^{2} e - 2 \, {\left(79 \, B a b^{3} - 56 \, A b^{4}\right)} d e^{2} + 7 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(176 \, B b^{4} d^{3} - 2 \, {\left(345 \, B a b^{3} - 203 \, A b^{4}\right)} d^{2} e + 14 \, {\left(59 \, B a^{2} b^{2} - 42 \, A a b^{3}\right)} d e^{2} - 35 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{210 \, {\left(b^{6} x + a b^{5}\right)}}, -\frac{105 \, {\left(2 \, B a b^{3} d^{3} - {\left(13 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d^{2} e + 2 \, {\left(10 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} d e^{2} - {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} e^{3} + {\left(2 \, B b^{4} d^{3} - {\left(13 \, B a b^{3} - 7 \, A b^{4}\right)} d^{2} e + 2 \, {\left(10 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d e^{2} - {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(30 \, B b^{4} e^{3} x^{4} + {\left(457 \, B a b^{3} - 105 \, A b^{4}\right)} d^{3} - 7 \, {\left(277 \, B a^{2} b^{2} - 161 \, A a b^{3}\right)} d^{2} e + 35 \, {\left(69 \, B a^{3} b - 49 \, A a^{2} b^{2}\right)} d e^{2} - 105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} e^{3} + 6 \, {\left(22 \, B b^{4} d e^{2} - {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} e^{3}\right)} x^{3} + 2 \, {\left(122 \, B b^{4} d^{2} e - 2 \, {\left(79 \, B a b^{3} - 56 \, A b^{4}\right)} d e^{2} + 7 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(176 \, B b^{4} d^{3} - 2 \, {\left(345 \, B a b^{3} - 203 \, A b^{4}\right)} d^{2} e + 14 \, {\left(59 \, B a^{2} b^{2} - 42 \, A a b^{3}\right)} d e^{2} - 35 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(b^{6} x + a b^{5}\right)}}\right]"," ",0,"[1/210*(105*(2*B*a*b^3*d^3 - (13*B*a^2*b^2 - 7*A*a*b^3)*d^2*e + 2*(10*B*a^3*b - 7*A*a^2*b^2)*d*e^2 - (9*B*a^4 - 7*A*a^3*b)*e^3 + (2*B*b^4*d^3 - (13*B*a*b^3 - 7*A*b^4)*d^2*e + 2*(10*B*a^2*b^2 - 7*A*a*b^3)*d*e^2 - (9*B*a^3*b - 7*A*a^2*b^2)*e^3)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(30*B*b^4*e^3*x^4 + (457*B*a*b^3 - 105*A*b^4)*d^3 - 7*(277*B*a^2*b^2 - 161*A*a*b^3)*d^2*e + 35*(69*B*a^3*b - 49*A*a^2*b^2)*d*e^2 - 105*(9*B*a^4 - 7*A*a^3*b)*e^3 + 6*(22*B*b^4*d*e^2 - (9*B*a*b^3 - 7*A*b^4)*e^3)*x^3 + 2*(122*B*b^4*d^2*e - 2*(79*B*a*b^3 - 56*A*b^4)*d*e^2 + 7*(9*B*a^2*b^2 - 7*A*a*b^3)*e^3)*x^2 + 2*(176*B*b^4*d^3 - 2*(345*B*a*b^3 - 203*A*b^4)*d^2*e + 14*(59*B*a^2*b^2 - 42*A*a*b^3)*d*e^2 - 35*(9*B*a^3*b - 7*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^6*x + a*b^5), -1/105*(105*(2*B*a*b^3*d^3 - (13*B*a^2*b^2 - 7*A*a*b^3)*d^2*e + 2*(10*B*a^3*b - 7*A*a^2*b^2)*d*e^2 - (9*B*a^4 - 7*A*a^3*b)*e^3 + (2*B*b^4*d^3 - (13*B*a*b^3 - 7*A*b^4)*d^2*e + 2*(10*B*a^2*b^2 - 7*A*a*b^3)*d*e^2 - (9*B*a^3*b - 7*A*a^2*b^2)*e^3)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (30*B*b^4*e^3*x^4 + (457*B*a*b^3 - 105*A*b^4)*d^3 - 7*(277*B*a^2*b^2 - 161*A*a*b^3)*d^2*e + 35*(69*B*a^3*b - 49*A*a^2*b^2)*d*e^2 - 105*(9*B*a^4 - 7*A*a^3*b)*e^3 + 6*(22*B*b^4*d*e^2 - (9*B*a*b^3 - 7*A*b^4)*e^3)*x^3 + 2*(122*B*b^4*d^2*e - 2*(79*B*a*b^3 - 56*A*b^4)*d*e^2 + 7*(9*B*a^2*b^2 - 7*A*a*b^3)*e^3)*x^2 + 2*(176*B*b^4*d^3 - 2*(345*B*a*b^3 - 203*A*b^4)*d^2*e + 14*(59*B*a^2*b^2 - 42*A*a*b^3)*d*e^2 - 35*(9*B*a^3*b - 7*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^6*x + a*b^5)]","B",0
1809,1,666,0,0.476420," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, B a b^{2} d^{2} - {\left(9 \, B a^{2} b - 5 \, A a b^{2}\right)} d e + {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} e^{2} + {\left(2 \, B b^{3} d^{2} - {\left(9 \, B a b^{2} - 5 \, A b^{3}\right)} d e + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(6 \, B b^{3} e^{2} x^{3} + {\left(61 \, B a b^{2} - 15 \, A b^{3}\right)} d^{2} - 10 \, {\left(17 \, B a^{2} b - 10 \, A a b^{2}\right)} d e + 15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} e^{2} + 2 \, {\left(11 \, B b^{3} d e - {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(23 \, B b^{3} d^{2} - {\left(59 \, B a b^{2} - 35 \, A b^{3}\right)} d e + 5 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{15 \, {\left(2 \, B a b^{2} d^{2} - {\left(9 \, B a^{2} b - 5 \, A a b^{2}\right)} d e + {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} e^{2} + {\left(2 \, B b^{3} d^{2} - {\left(9 \, B a b^{2} - 5 \, A b^{3}\right)} d e + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(6 \, B b^{3} e^{2} x^{3} + {\left(61 \, B a b^{2} - 15 \, A b^{3}\right)} d^{2} - 10 \, {\left(17 \, B a^{2} b - 10 \, A a b^{2}\right)} d e + 15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} e^{2} + 2 \, {\left(11 \, B b^{3} d e - {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(23 \, B b^{3} d^{2} - {\left(59 \, B a b^{2} - 35 \, A b^{3}\right)} d e + 5 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[-1/30*(15*(2*B*a*b^2*d^2 - (9*B*a^2*b - 5*A*a*b^2)*d*e + (7*B*a^3 - 5*A*a^2*b)*e^2 + (2*B*b^3*d^2 - (9*B*a*b^2 - 5*A*b^3)*d*e + (7*B*a^2*b - 5*A*a*b^2)*e^2)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(6*B*b^3*e^2*x^3 + (61*B*a*b^2 - 15*A*b^3)*d^2 - 10*(17*B*a^2*b - 10*A*a*b^2)*d*e + 15*(7*B*a^3 - 5*A*a^2*b)*e^2 + 2*(11*B*b^3*d*e - (7*B*a*b^2 - 5*A*b^3)*e^2)*x^2 + 2*(23*B*b^3*d^2 - (59*B*a*b^2 - 35*A*b^3)*d*e + 5*(7*B*a^2*b - 5*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(b^5*x + a*b^4), -1/15*(15*(2*B*a*b^2*d^2 - (9*B*a^2*b - 5*A*a*b^2)*d*e + (7*B*a^3 - 5*A*a^2*b)*e^2 + (2*B*b^3*d^2 - (9*B*a*b^2 - 5*A*b^3)*d*e + (7*B*a^2*b - 5*A*a*b^2)*e^2)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (6*B*b^3*e^2*x^3 + (61*B*a*b^2 - 15*A*b^3)*d^2 - 10*(17*B*a^2*b - 10*A*a*b^2)*d*e + 15*(7*B*a^3 - 5*A*a^2*b)*e^2 + 2*(11*B*b^3*d*e - (7*B*a*b^2 - 5*A*b^3)*e^2)*x^2 + 2*(23*B*b^3*d^2 - (59*B*a*b^2 - 35*A*b^3)*d*e + 5*(7*B*a^2*b - 5*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(b^5*x + a*b^4)]","A",0
1810,1,392,0,0.440428," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a b d - {\left(5 \, B a^{2} - 3 \, A a b\right)} e + {\left(2 \, B b^{2} d - {\left(5 \, B a b - 3 \, A b^{2}\right)} e\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(2 \, B b^{2} e x^{2} + {\left(11 \, B a b - 3 \, A b^{2}\right)} d - 3 \, {\left(5 \, B a^{2} - 3 \, A a b\right)} e + 2 \, {\left(4 \, B b^{2} d - {\left(5 \, B a b - 3 \, A b^{2}\right)} e\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{4} x + a b^{3}\right)}}, -\frac{3 \, {\left(2 \, B a b d - {\left(5 \, B a^{2} - 3 \, A a b\right)} e + {\left(2 \, B b^{2} d - {\left(5 \, B a b - 3 \, A b^{2}\right)} e\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(2 \, B b^{2} e x^{2} + {\left(11 \, B a b - 3 \, A b^{2}\right)} d - 3 \, {\left(5 \, B a^{2} - 3 \, A a b\right)} e + 2 \, {\left(4 \, B b^{2} d - {\left(5 \, B a b - 3 \, A b^{2}\right)} e\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b^{4} x + a b^{3}\right)}}\right]"," ",0,"[1/6*(3*(2*B*a*b*d - (5*B*a^2 - 3*A*a*b)*e + (2*B*b^2*d - (5*B*a*b - 3*A*b^2)*e)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(2*B*b^2*e*x^2 + (11*B*a*b - 3*A*b^2)*d - 3*(5*B*a^2 - 3*A*a*b)*e + 2*(4*B*b^2*d - (5*B*a*b - 3*A*b^2)*e)*x)*sqrt(e*x + d))/(b^4*x + a*b^3), -1/3*(3*(2*B*a*b*d - (5*B*a^2 - 3*A*a*b)*e + (2*B*b^2*d - (5*B*a*b - 3*A*b^2)*e)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (2*B*b^2*e*x^2 + (11*B*a*b - 3*A*b^2)*d - 3*(5*B*a^2 - 3*A*a*b)*e + 2*(4*B*b^2*d - (5*B*a*b - 3*A*b^2)*e)*x)*sqrt(e*x + d))/(b^4*x + a*b^3)]","A",0
1811,1,393,0,0.453050," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a b d - {\left(3 \, B a^{2} - A a b\right)} e + {\left(2 \, B b^{2} d - {\left(3 \, B a b - A b^{2}\right)} e\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left({\left(3 \, B a b^{2} - A b^{3}\right)} d - {\left(3 \, B a^{2} b - A a b^{2}\right)} e + 2 \, {\left(B b^{3} d - B a b^{2} e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(a b^{4} d - a^{2} b^{3} e + {\left(b^{5} d - a b^{4} e\right)} x\right)}}, \frac{{\left(2 \, B a b d - {\left(3 \, B a^{2} - A a b\right)} e + {\left(2 \, B b^{2} d - {\left(3 \, B a b - A b^{2}\right)} e\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left({\left(3 \, B a b^{2} - A b^{3}\right)} d - {\left(3 \, B a^{2} b - A a b^{2}\right)} e + 2 \, {\left(B b^{3} d - B a b^{2} e\right)} x\right)} \sqrt{e x + d}}{a b^{4} d - a^{2} b^{3} e + {\left(b^{5} d - a b^{4} e\right)} x}\right]"," ",0,"[1/2*((2*B*a*b*d - (3*B*a^2 - A*a*b)*e + (2*B*b^2*d - (3*B*a*b - A*b^2)*e)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*((3*B*a*b^2 - A*b^3)*d - (3*B*a^2*b - A*a*b^2)*e + 2*(B*b^3*d - B*a*b^2*e)*x)*sqrt(e*x + d))/(a*b^4*d - a^2*b^3*e + (b^5*d - a*b^4*e)*x), ((2*B*a*b*d - (3*B*a^2 - A*a*b)*e + (2*B*b^2*d - (3*B*a*b - A*b^2)*e)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + ((3*B*a*b^2 - A*b^3)*d - (3*B*a^2*b - A*a*b^2)*e + 2*(B*b^3*d - B*a*b^2*e)*x)*sqrt(e*x + d))/(a*b^4*d - a^2*b^3*e + (b^5*d - a*b^4*e)*x)]","A",0
1812,1,397,0,0.431430," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a b d - {\left(B a^{2} + A a b\right)} e + {\left(2 \, B b^{2} d - {\left(B a b + A b^{2}\right)} e\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left({\left(B a b^{2} - A b^{3}\right)} d - {\left(B a^{2} b - A a b^{2}\right)} e\right)} \sqrt{e x + d}}{2 \, {\left(a b^{4} d^{2} - 2 \, a^{2} b^{3} d e + a^{3} b^{2} e^{2} + {\left(b^{5} d^{2} - 2 \, a b^{4} d e + a^{2} b^{3} e^{2}\right)} x\right)}}, \frac{{\left(2 \, B a b d - {\left(B a^{2} + A a b\right)} e + {\left(2 \, B b^{2} d - {\left(B a b + A b^{2}\right)} e\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left({\left(B a b^{2} - A b^{3}\right)} d - {\left(B a^{2} b - A a b^{2}\right)} e\right)} \sqrt{e x + d}}{a b^{4} d^{2} - 2 \, a^{2} b^{3} d e + a^{3} b^{2} e^{2} + {\left(b^{5} d^{2} - 2 \, a b^{4} d e + a^{2} b^{3} e^{2}\right)} x}\right]"," ",0,"[1/2*((2*B*a*b*d - (B*a^2 + A*a*b)*e + (2*B*b^2*d - (B*a*b + A*b^2)*e)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*((B*a*b^2 - A*b^3)*d - (B*a^2*b - A*a*b^2)*e)*sqrt(e*x + d))/(a*b^4*d^2 - 2*a^2*b^3*d*e + a^3*b^2*e^2 + (b^5*d^2 - 2*a*b^4*d*e + a^2*b^3*e^2)*x), ((2*B*a*b*d - (B*a^2 + A*a*b)*e + (2*B*b^2*d - (B*a*b + A*b^2)*e)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + ((B*a*b^2 - A*b^3)*d - (B*a^2*b - A*a*b^2)*e)*sqrt(e*x + d))/(a*b^4*d^2 - 2*a^2*b^3*d*e + a^3*b^2*e^2 + (b^5*d^2 - 2*a*b^4*d*e + a^2*b^3*e^2)*x)]","B",0
1813,1,775,0,0.453691," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a b d^{2} + {\left(B a^{2} - 3 \, A a b\right)} d e + {\left(2 \, B b^{2} d e + {\left(B a b - 3 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(2 \, B b^{2} d^{2} + 3 \, {\left(B a b - A b^{2}\right)} d e + {\left(B a^{2} - 3 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, A a^{2} b e^{2} + {\left(3 \, B a b^{2} - A b^{3}\right)} d^{2} - {\left(3 \, B a^{2} b + A a b^{2}\right)} d e + {\left(2 \, B b^{3} d^{2} - {\left(B a b^{2} + 3 \, A b^{3}\right)} d e - {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(a b^{4} d^{4} - 3 \, a^{2} b^{3} d^{3} e + 3 \, a^{3} b^{2} d^{2} e^{2} - a^{4} b d e^{3} + {\left(b^{5} d^{3} e - 3 \, a b^{4} d^{2} e^{2} + 3 \, a^{2} b^{3} d e^{3} - a^{3} b^{2} e^{4}\right)} x^{2} + {\left(b^{5} d^{4} - 2 \, a b^{4} d^{3} e + 2 \, a^{3} b^{2} d e^{3} - a^{4} b e^{4}\right)} x\right)}}, \frac{{\left(2 \, B a b d^{2} + {\left(B a^{2} - 3 \, A a b\right)} d e + {\left(2 \, B b^{2} d e + {\left(B a b - 3 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(2 \, B b^{2} d^{2} + 3 \, {\left(B a b - A b^{2}\right)} d e + {\left(B a^{2} - 3 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(2 \, A a^{2} b e^{2} + {\left(3 \, B a b^{2} - A b^{3}\right)} d^{2} - {\left(3 \, B a^{2} b + A a b^{2}\right)} d e + {\left(2 \, B b^{3} d^{2} - {\left(B a b^{2} + 3 \, A b^{3}\right)} d e - {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{a b^{4} d^{4} - 3 \, a^{2} b^{3} d^{3} e + 3 \, a^{3} b^{2} d^{2} e^{2} - a^{4} b d e^{3} + {\left(b^{5} d^{3} e - 3 \, a b^{4} d^{2} e^{2} + 3 \, a^{2} b^{3} d e^{3} - a^{3} b^{2} e^{4}\right)} x^{2} + {\left(b^{5} d^{4} - 2 \, a b^{4} d^{3} e + 2 \, a^{3} b^{2} d e^{3} - a^{4} b e^{4}\right)} x}\right]"," ",0,"[-1/2*((2*B*a*b*d^2 + (B*a^2 - 3*A*a*b)*d*e + (2*B*b^2*d*e + (B*a*b - 3*A*b^2)*e^2)*x^2 + (2*B*b^2*d^2 + 3*(B*a*b - A*b^2)*d*e + (B*a^2 - 3*A*a*b)*e^2)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e + 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*A*a^2*b*e^2 + (3*B*a*b^2 - A*b^3)*d^2 - (3*B*a^2*b + A*a*b^2)*d*e + (2*B*b^3*d^2 - (B*a*b^2 + 3*A*b^3)*d*e - (B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(a*b^4*d^4 - 3*a^2*b^3*d^3*e + 3*a^3*b^2*d^2*e^2 - a^4*b*d*e^3 + (b^5*d^3*e - 3*a*b^4*d^2*e^2 + 3*a^2*b^3*d*e^3 - a^3*b^2*e^4)*x^2 + (b^5*d^4 - 2*a*b^4*d^3*e + 2*a^3*b^2*d*e^3 - a^4*b*e^4)*x), ((2*B*a*b*d^2 + (B*a^2 - 3*A*a*b)*d*e + (2*B*b^2*d*e + (B*a*b - 3*A*b^2)*e^2)*x^2 + (2*B*b^2*d^2 + 3*(B*a*b - A*b^2)*d*e + (B*a^2 - 3*A*a*b)*e^2)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (2*A*a^2*b*e^2 + (3*B*a*b^2 - A*b^3)*d^2 - (3*B*a^2*b + A*a*b^2)*d*e + (2*B*b^3*d^2 - (B*a*b^2 + 3*A*b^3)*d*e - (B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(a*b^4*d^4 - 3*a^2*b^3*d^3*e + 3*a^3*b^2*d^2*e^2 - a^4*b*d*e^3 + (b^5*d^3*e - 3*a*b^4*d^2*e^2 + 3*a^2*b^3*d*e^3 - a^3*b^2*e^4)*x^2 + (b^5*d^4 - 2*a*b^4*d^3*e + 2*a^3*b^2*d*e^3 - a^4*b*e^4)*x)]","B",0
1814,1,1106,0,0.459693," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a b d^{3} + {\left(3 \, B a^{2} - 5 \, A a b\right)} d^{2} e + {\left(2 \, B b^{2} d e^{2} + {\left(3 \, B a b - 5 \, A b^{2}\right)} e^{3}\right)} x^{3} + {\left(4 \, B b^{2} d^{2} e + 2 \, {\left(4 \, B a b - 5 \, A b^{2}\right)} d e^{2} + {\left(3 \, B a^{2} - 5 \, A a b\right)} e^{3}\right)} x^{2} + {\left(2 \, B b^{2} d^{3} + {\left(7 \, B a b - 5 \, A b^{2}\right)} d^{2} e + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} d e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(2 \, A a^{2} e^{2} + {\left(11 \, B a b - 3 \, A b^{2}\right)} d^{2} + 2 \, {\left(2 \, B a^{2} - 7 \, A a b\right)} d e + 3 \, {\left(2 \, B b^{2} d e + {\left(3 \, B a b - 5 \, A b^{2}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B b^{2} d^{2} + 2 \, {\left(4 \, B a b - 5 \, A b^{2}\right)} d e + {\left(3 \, B a^{2} - 5 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(a b^{3} d^{5} - 3 \, a^{2} b^{2} d^{4} e + 3 \, a^{3} b d^{3} e^{2} - a^{4} d^{2} e^{3} + {\left(b^{4} d^{3} e^{2} - 3 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4} - a^{3} b e^{5}\right)} x^{3} + {\left(2 \, b^{4} d^{4} e - 5 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3} + a^{3} b d e^{4} - a^{4} e^{5}\right)} x^{2} + {\left(b^{4} d^{5} - a b^{3} d^{4} e - 3 \, a^{2} b^{2} d^{3} e^{2} + 5 \, a^{3} b d^{2} e^{3} - 2 \, a^{4} d e^{4}\right)} x\right)}}, -\frac{3 \, {\left(2 \, B a b d^{3} + {\left(3 \, B a^{2} - 5 \, A a b\right)} d^{2} e + {\left(2 \, B b^{2} d e^{2} + {\left(3 \, B a b - 5 \, A b^{2}\right)} e^{3}\right)} x^{3} + {\left(4 \, B b^{2} d^{2} e + 2 \, {\left(4 \, B a b - 5 \, A b^{2}\right)} d e^{2} + {\left(3 \, B a^{2} - 5 \, A a b\right)} e^{3}\right)} x^{2} + {\left(2 \, B b^{2} d^{3} + {\left(7 \, B a b - 5 \, A b^{2}\right)} d^{2} e + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} d e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(2 \, A a^{2} e^{2} + {\left(11 \, B a b - 3 \, A b^{2}\right)} d^{2} + 2 \, {\left(2 \, B a^{2} - 7 \, A a b\right)} d e + 3 \, {\left(2 \, B b^{2} d e + {\left(3 \, B a b - 5 \, A b^{2}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B b^{2} d^{2} + 2 \, {\left(4 \, B a b - 5 \, A b^{2}\right)} d e + {\left(3 \, B a^{2} - 5 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(a b^{3} d^{5} - 3 \, a^{2} b^{2} d^{4} e + 3 \, a^{3} b d^{3} e^{2} - a^{4} d^{2} e^{3} + {\left(b^{4} d^{3} e^{2} - 3 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4} - a^{3} b e^{5}\right)} x^{3} + {\left(2 \, b^{4} d^{4} e - 5 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3} + a^{3} b d e^{4} - a^{4} e^{5}\right)} x^{2} + {\left(b^{4} d^{5} - a b^{3} d^{4} e - 3 \, a^{2} b^{2} d^{3} e^{2} + 5 \, a^{3} b d^{2} e^{3} - 2 \, a^{4} d e^{4}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(2*B*a*b*d^3 + (3*B*a^2 - 5*A*a*b)*d^2*e + (2*B*b^2*d*e^2 + (3*B*a*b - 5*A*b^2)*e^3)*x^3 + (4*B*b^2*d^2*e + 2*(4*B*a*b - 5*A*b^2)*d*e^2 + (3*B*a^2 - 5*A*a*b)*e^3)*x^2 + (2*B*b^2*d^3 + (7*B*a*b - 5*A*b^2)*d^2*e + 2*(3*B*a^2 - 5*A*a*b)*d*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(2*A*a^2*e^2 + (11*B*a*b - 3*A*b^2)*d^2 + 2*(2*B*a^2 - 7*A*a*b)*d*e + 3*(2*B*b^2*d*e + (3*B*a*b - 5*A*b^2)*e^2)*x^2 + 2*(4*B*b^2*d^2 + 2*(4*B*a*b - 5*A*b^2)*d*e + (3*B*a^2 - 5*A*a*b)*e^2)*x)*sqrt(e*x + d))/(a*b^3*d^5 - 3*a^2*b^2*d^4*e + 3*a^3*b*d^3*e^2 - a^4*d^2*e^3 + (b^4*d^3*e^2 - 3*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4 - a^3*b*e^5)*x^3 + (2*b^4*d^4*e - 5*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3 + a^3*b*d*e^4 - a^4*e^5)*x^2 + (b^4*d^5 - a*b^3*d^4*e - 3*a^2*b^2*d^3*e^2 + 5*a^3*b*d^2*e^3 - 2*a^4*d*e^4)*x), -1/3*(3*(2*B*a*b*d^3 + (3*B*a^2 - 5*A*a*b)*d^2*e + (2*B*b^2*d*e^2 + (3*B*a*b - 5*A*b^2)*e^3)*x^3 + (4*B*b^2*d^2*e + 2*(4*B*a*b - 5*A*b^2)*d*e^2 + (3*B*a^2 - 5*A*a*b)*e^3)*x^2 + (2*B*b^2*d^3 + (7*B*a*b - 5*A*b^2)*d^2*e + 2*(3*B*a^2 - 5*A*a*b)*d*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (2*A*a^2*e^2 + (11*B*a*b - 3*A*b^2)*d^2 + 2*(2*B*a^2 - 7*A*a*b)*d*e + 3*(2*B*b^2*d*e + (3*B*a*b - 5*A*b^2)*e^2)*x^2 + 2*(4*B*b^2*d^2 + 2*(4*B*a*b - 5*A*b^2)*d*e + (3*B*a^2 - 5*A*a*b)*e^2)*x)*sqrt(e*x + d))/(a*b^3*d^5 - 3*a^2*b^2*d^4*e + 3*a^3*b*d^3*e^2 - a^4*d^2*e^3 + (b^4*d^3*e^2 - 3*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4 - a^3*b*e^5)*x^3 + (2*b^4*d^4*e - 5*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3 + a^3*b*d*e^4 - a^4*e^5)*x^2 + (b^4*d^5 - a*b^3*d^4*e - 3*a^2*b^2*d^3*e^2 + 5*a^3*b*d^2*e^3 - 2*a^4*d*e^4)*x)]","B",0
1815,1,1749,0,0.471874," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, B a b^{2} d^{4} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d^{3} e + {\left(2 \, B b^{3} d e^{3} + {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} e^{4}\right)} x^{4} + {\left(6 \, B b^{3} d^{2} e^{2} + {\left(17 \, B a b^{2} - 21 \, A b^{3}\right)} d e^{3} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{4}\right)} x^{3} + 3 \, {\left(2 \, B b^{3} d^{3} e + 7 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d e^{3}\right)} x^{2} + {\left(2 \, B b^{3} d^{4} + {\left(11 \, B a b^{2} - 7 \, A b^{3}\right)} d^{3} e + 3 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d^{2} e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(6 \, A a^{3} e^{3} - {\left(61 \, B a b^{2} - 15 \, A b^{3}\right)} d^{3} - 4 \, {\left(12 \, B a^{2} b - 29 \, A a b^{2}\right)} d^{2} e + 4 \, {\left(B a^{3} - 8 \, A a^{2} b\right)} d e^{2} - 15 \, {\left(2 \, B b^{3} d e^{2} + {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} e^{3}\right)} x^{3} - 5 \, {\left(14 \, B b^{3} d^{2} e + {\left(39 \, B a b^{2} - 49 \, A b^{3}\right)} d e^{2} + 2 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{3}\right)} x^{2} - {\left(46 \, B b^{3} d^{3} + {\left(163 \, B a b^{2} - 161 \, A b^{3}\right)} d^{2} e + 4 \, {\left(29 \, B a^{2} b - 42 \, A a b^{2}\right)} d e^{2} - 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(a b^{4} d^{7} - 4 \, a^{2} b^{3} d^{6} e + 6 \, a^{3} b^{2} d^{5} e^{2} - 4 \, a^{4} b d^{4} e^{3} + a^{5} d^{3} e^{4} + {\left(b^{5} d^{4} e^{3} - 4 \, a b^{4} d^{3} e^{4} + 6 \, a^{2} b^{3} d^{2} e^{5} - 4 \, a^{3} b^{2} d e^{6} + a^{4} b e^{7}\right)} x^{4} + {\left(3 \, b^{5} d^{5} e^{2} - 11 \, a b^{4} d^{4} e^{3} + 14 \, a^{2} b^{3} d^{3} e^{4} - 6 \, a^{3} b^{2} d^{2} e^{5} - a^{4} b d e^{6} + a^{5} e^{7}\right)} x^{3} + 3 \, {\left(b^{5} d^{6} e - 3 \, a b^{4} d^{5} e^{2} + 2 \, a^{2} b^{3} d^{4} e^{3} + 2 \, a^{3} b^{2} d^{3} e^{4} - 3 \, a^{4} b d^{2} e^{5} + a^{5} d e^{6}\right)} x^{2} + {\left(b^{5} d^{7} - a b^{4} d^{6} e - 6 \, a^{2} b^{3} d^{5} e^{2} + 14 \, a^{3} b^{2} d^{4} e^{3} - 11 \, a^{4} b d^{3} e^{4} + 3 \, a^{5} d^{2} e^{5}\right)} x\right)}}, -\frac{15 \, {\left(2 \, B a b^{2} d^{4} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d^{3} e + {\left(2 \, B b^{3} d e^{3} + {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} e^{4}\right)} x^{4} + {\left(6 \, B b^{3} d^{2} e^{2} + {\left(17 \, B a b^{2} - 21 \, A b^{3}\right)} d e^{3} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{4}\right)} x^{3} + 3 \, {\left(2 \, B b^{3} d^{3} e + 7 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d e^{3}\right)} x^{2} + {\left(2 \, B b^{3} d^{4} + {\left(11 \, B a b^{2} - 7 \, A b^{3}\right)} d^{3} e + 3 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) + {\left(6 \, A a^{3} e^{3} - {\left(61 \, B a b^{2} - 15 \, A b^{3}\right)} d^{3} - 4 \, {\left(12 \, B a^{2} b - 29 \, A a b^{2}\right)} d^{2} e + 4 \, {\left(B a^{3} - 8 \, A a^{2} b\right)} d e^{2} - 15 \, {\left(2 \, B b^{3} d e^{2} + {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} e^{3}\right)} x^{3} - 5 \, {\left(14 \, B b^{3} d^{2} e + {\left(39 \, B a b^{2} - 49 \, A b^{3}\right)} d e^{2} + 2 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{3}\right)} x^{2} - {\left(46 \, B b^{3} d^{3} + {\left(163 \, B a b^{2} - 161 \, A b^{3}\right)} d^{2} e + 4 \, {\left(29 \, B a^{2} b - 42 \, A a b^{2}\right)} d e^{2} - 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(a b^{4} d^{7} - 4 \, a^{2} b^{3} d^{6} e + 6 \, a^{3} b^{2} d^{5} e^{2} - 4 \, a^{4} b d^{4} e^{3} + a^{5} d^{3} e^{4} + {\left(b^{5} d^{4} e^{3} - 4 \, a b^{4} d^{3} e^{4} + 6 \, a^{2} b^{3} d^{2} e^{5} - 4 \, a^{3} b^{2} d e^{6} + a^{4} b e^{7}\right)} x^{4} + {\left(3 \, b^{5} d^{5} e^{2} - 11 \, a b^{4} d^{4} e^{3} + 14 \, a^{2} b^{3} d^{3} e^{4} - 6 \, a^{3} b^{2} d^{2} e^{5} - a^{4} b d e^{6} + a^{5} e^{7}\right)} x^{3} + 3 \, {\left(b^{5} d^{6} e - 3 \, a b^{4} d^{5} e^{2} + 2 \, a^{2} b^{3} d^{4} e^{3} + 2 \, a^{3} b^{2} d^{3} e^{4} - 3 \, a^{4} b d^{2} e^{5} + a^{5} d e^{6}\right)} x^{2} + {\left(b^{5} d^{7} - a b^{4} d^{6} e - 6 \, a^{2} b^{3} d^{5} e^{2} + 14 \, a^{3} b^{2} d^{4} e^{3} - 11 \, a^{4} b d^{3} e^{4} + 3 \, a^{5} d^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/30*(15*(2*B*a*b^2*d^4 + (5*B*a^2*b - 7*A*a*b^2)*d^3*e + (2*B*b^3*d*e^3 + (5*B*a*b^2 - 7*A*b^3)*e^4)*x^4 + (6*B*b^3*d^2*e^2 + (17*B*a*b^2 - 21*A*b^3)*d*e^3 + (5*B*a^2*b - 7*A*a*b^2)*e^4)*x^3 + 3*(2*B*b^3*d^3*e + 7*(B*a*b^2 - A*b^3)*d^2*e^2 + (5*B*a^2*b - 7*A*a*b^2)*d*e^3)*x^2 + (2*B*b^3*d^4 + (11*B*a*b^2 - 7*A*b^3)*d^3*e + 3*(5*B*a^2*b - 7*A*a*b^2)*d^2*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(6*A*a^3*e^3 - (61*B*a*b^2 - 15*A*b^3)*d^3 - 4*(12*B*a^2*b - 29*A*a*b^2)*d^2*e + 4*(B*a^3 - 8*A*a^2*b)*d*e^2 - 15*(2*B*b^3*d*e^2 + (5*B*a*b^2 - 7*A*b^3)*e^3)*x^3 - 5*(14*B*b^3*d^2*e + (39*B*a*b^2 - 49*A*b^3)*d*e^2 + 2*(5*B*a^2*b - 7*A*a*b^2)*e^3)*x^2 - (46*B*b^3*d^3 + (163*B*a*b^2 - 161*A*b^3)*d^2*e + 4*(29*B*a^2*b - 42*A*a*b^2)*d*e^2 - 2*(5*B*a^3 - 7*A*a^2*b)*e^3)*x)*sqrt(e*x + d))/(a*b^4*d^7 - 4*a^2*b^3*d^6*e + 6*a^3*b^2*d^5*e^2 - 4*a^4*b*d^4*e^3 + a^5*d^3*e^4 + (b^5*d^4*e^3 - 4*a*b^4*d^3*e^4 + 6*a^2*b^3*d^2*e^5 - 4*a^3*b^2*d*e^6 + a^4*b*e^7)*x^4 + (3*b^5*d^5*e^2 - 11*a*b^4*d^4*e^3 + 14*a^2*b^3*d^3*e^4 - 6*a^3*b^2*d^2*e^5 - a^4*b*d*e^6 + a^5*e^7)*x^3 + 3*(b^5*d^6*e - 3*a*b^4*d^5*e^2 + 2*a^2*b^3*d^4*e^3 + 2*a^3*b^2*d^3*e^4 - 3*a^4*b*d^2*e^5 + a^5*d*e^6)*x^2 + (b^5*d^7 - a*b^4*d^6*e - 6*a^2*b^3*d^5*e^2 + 14*a^3*b^2*d^4*e^3 - 11*a^4*b*d^3*e^4 + 3*a^5*d^2*e^5)*x), -1/15*(15*(2*B*a*b^2*d^4 + (5*B*a^2*b - 7*A*a*b^2)*d^3*e + (2*B*b^3*d*e^3 + (5*B*a*b^2 - 7*A*b^3)*e^4)*x^4 + (6*B*b^3*d^2*e^2 + (17*B*a*b^2 - 21*A*b^3)*d*e^3 + (5*B*a^2*b - 7*A*a*b^2)*e^4)*x^3 + 3*(2*B*b^3*d^3*e + 7*(B*a*b^2 - A*b^3)*d^2*e^2 + (5*B*a^2*b - 7*A*a*b^2)*d*e^3)*x^2 + (2*B*b^3*d^4 + (11*B*a*b^2 - 7*A*b^3)*d^3*e + 3*(5*B*a^2*b - 7*A*a*b^2)*d^2*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) + (6*A*a^3*e^3 - (61*B*a*b^2 - 15*A*b^3)*d^3 - 4*(12*B*a^2*b - 29*A*a*b^2)*d^2*e + 4*(B*a^3 - 8*A*a^2*b)*d*e^2 - 15*(2*B*b^3*d*e^2 + (5*B*a*b^2 - 7*A*b^3)*e^3)*x^3 - 5*(14*B*b^3*d^2*e + (39*B*a*b^2 - 49*A*b^3)*d*e^2 + 2*(5*B*a^2*b - 7*A*a*b^2)*e^3)*x^2 - (46*B*b^3*d^3 + (163*B*a*b^2 - 161*A*b^3)*d^2*e + 4*(29*B*a^2*b - 42*A*a*b^2)*d*e^2 - 2*(5*B*a^3 - 7*A*a^2*b)*e^3)*x)*sqrt(e*x + d))/(a*b^4*d^7 - 4*a^2*b^3*d^6*e + 6*a^3*b^2*d^5*e^2 - 4*a^4*b*d^4*e^3 + a^5*d^3*e^4 + (b^5*d^4*e^3 - 4*a*b^4*d^3*e^4 + 6*a^2*b^3*d^2*e^5 - 4*a^3*b^2*d*e^6 + a^4*b*e^7)*x^4 + (3*b^5*d^5*e^2 - 11*a*b^4*d^4*e^3 + 14*a^2*b^3*d^3*e^4 - 6*a^3*b^2*d^2*e^5 - a^4*b*d*e^6 + a^5*e^7)*x^3 + 3*(b^5*d^6*e - 3*a*b^4*d^5*e^2 + 2*a^2*b^3*d^4*e^3 + 2*a^3*b^2*d^3*e^4 - 3*a^4*b*d^2*e^5 + a^5*d*e^6)*x^2 + (b^5*d^7 - a*b^4*d^6*e - 6*a^2*b^3*d^5*e^2 + 14*a^3*b^2*d^4*e^3 - 11*a^4*b*d^3*e^4 + 3*a^5*d^2*e^5)*x)]","B",0
1816,1,1514,0,0.459656," ","integrate((B*x+A)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(6 \, B a^{3} b^{2} d^{2} e^{2} - {\left(17 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} d e^{3} + {\left(11 \, B a^{5} - 5 \, A a^{4} b\right)} e^{4} + {\left(6 \, B b^{5} d^{2} e^{2} - {\left(17 \, B a b^{4} - 5 \, A b^{5}\right)} d e^{3} + {\left(11 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(6 \, B a b^{4} d^{2} e^{2} - {\left(17 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d e^{3} + {\left(11 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{3} d^{2} e^{2} - {\left(17 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d e^{3} + {\left(11 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(48 \, B b^{5} e^{4} x^{5} - 20 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{4} - 90 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e + 63 \, {\left(51 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d^{2} e^{2} - 210 \, {\left(31 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} d e^{3} + 315 \, {\left(11 \, B a^{5} - 5 \, A a^{4} b\right)} e^{4} + 16 \, {\left(21 \, B b^{5} d e^{3} - {\left(11 \, B a b^{4} - 5 \, A b^{5}\right)} e^{4}\right)} x^{4} + 16 \, {\left(108 \, B b^{5} d^{2} e^{2} - {\left(197 \, B a b^{4} - 65 \, A b^{5}\right)} d e^{3} + 9 \, {\left(11 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{4}\right)} x^{3} - 3 \, {\left(170 \, B b^{5} d^{3} e - {\left(2513 \, B a b^{4} - 275 \, A b^{5}\right)} d^{2} e^{2} + 6 \, {\left(814 \, B a^{2} b^{3} - 265 \, A a b^{4}\right)} d e^{3} - 231 \, {\left(11 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - 2 \, {\left(30 \, B b^{5} d^{4} + 5 \, {\left(53 \, B a b^{4} + 25 \, A b^{5}\right)} d^{3} e - 18 \, {\left(244 \, B a^{2} b^{3} - 25 \, A a b^{4}\right)} d^{2} e^{2} + 63 \, {\left(139 \, B a^{3} b^{2} - 45 \, A a^{2} b^{3}\right)} d e^{3} - 420 \, {\left(11 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{240 \, {\left(b^{9} x^{3} + 3 \, a b^{8} x^{2} + 3 \, a^{2} b^{7} x + a^{3} b^{6}\right)}}, -\frac{315 \, {\left(6 \, B a^{3} b^{2} d^{2} e^{2} - {\left(17 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} d e^{3} + {\left(11 \, B a^{5} - 5 \, A a^{4} b\right)} e^{4} + {\left(6 \, B b^{5} d^{2} e^{2} - {\left(17 \, B a b^{4} - 5 \, A b^{5}\right)} d e^{3} + {\left(11 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(6 \, B a b^{4} d^{2} e^{2} - {\left(17 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d e^{3} + {\left(11 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{3} d^{2} e^{2} - {\left(17 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d e^{3} + {\left(11 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(48 \, B b^{5} e^{4} x^{5} - 20 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{4} - 90 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e + 63 \, {\left(51 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d^{2} e^{2} - 210 \, {\left(31 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} d e^{3} + 315 \, {\left(11 \, B a^{5} - 5 \, A a^{4} b\right)} e^{4} + 16 \, {\left(21 \, B b^{5} d e^{3} - {\left(11 \, B a b^{4} - 5 \, A b^{5}\right)} e^{4}\right)} x^{4} + 16 \, {\left(108 \, B b^{5} d^{2} e^{2} - {\left(197 \, B a b^{4} - 65 \, A b^{5}\right)} d e^{3} + 9 \, {\left(11 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{4}\right)} x^{3} - 3 \, {\left(170 \, B b^{5} d^{3} e - {\left(2513 \, B a b^{4} - 275 \, A b^{5}\right)} d^{2} e^{2} + 6 \, {\left(814 \, B a^{2} b^{3} - 265 \, A a b^{4}\right)} d e^{3} - 231 \, {\left(11 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - 2 \, {\left(30 \, B b^{5} d^{4} + 5 \, {\left(53 \, B a b^{4} + 25 \, A b^{5}\right)} d^{3} e - 18 \, {\left(244 \, B a^{2} b^{3} - 25 \, A a b^{4}\right)} d^{2} e^{2} + 63 \, {\left(139 \, B a^{3} b^{2} - 45 \, A a^{2} b^{3}\right)} d e^{3} - 420 \, {\left(11 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{120 \, {\left(b^{9} x^{3} + 3 \, a b^{8} x^{2} + 3 \, a^{2} b^{7} x + a^{3} b^{6}\right)}}\right]"," ",0,"[1/240*(315*(6*B*a^3*b^2*d^2*e^2 - (17*B*a^4*b - 5*A*a^3*b^2)*d*e^3 + (11*B*a^5 - 5*A*a^4*b)*e^4 + (6*B*b^5*d^2*e^2 - (17*B*a*b^4 - 5*A*b^5)*d*e^3 + (11*B*a^2*b^3 - 5*A*a*b^4)*e^4)*x^3 + 3*(6*B*a*b^4*d^2*e^2 - (17*B*a^2*b^3 - 5*A*a*b^4)*d*e^3 + (11*B*a^3*b^2 - 5*A*a^2*b^3)*e^4)*x^2 + 3*(6*B*a^2*b^3*d^2*e^2 - (17*B*a^3*b^2 - 5*A*a^2*b^3)*d*e^3 + (11*B*a^4*b - 5*A*a^3*b^2)*e^4)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(48*B*b^5*e^4*x^5 - 20*(B*a*b^4 + 2*A*b^5)*d^4 - 90*(2*B*a^2*b^3 + A*a*b^4)*d^3*e + 63*(51*B*a^3*b^2 - 5*A*a^2*b^3)*d^2*e^2 - 210*(31*B*a^4*b - 10*A*a^3*b^2)*d*e^3 + 315*(11*B*a^5 - 5*A*a^4*b)*e^4 + 16*(21*B*b^5*d*e^3 - (11*B*a*b^4 - 5*A*b^5)*e^4)*x^4 + 16*(108*B*b^5*d^2*e^2 - (197*B*a*b^4 - 65*A*b^5)*d*e^3 + 9*(11*B*a^2*b^3 - 5*A*a*b^4)*e^4)*x^3 - 3*(170*B*b^5*d^3*e - (2513*B*a*b^4 - 275*A*b^5)*d^2*e^2 + 6*(814*B*a^2*b^3 - 265*A*a*b^4)*d*e^3 - 231*(11*B*a^3*b^2 - 5*A*a^2*b^3)*e^4)*x^2 - 2*(30*B*b^5*d^4 + 5*(53*B*a*b^4 + 25*A*b^5)*d^3*e - 18*(244*B*a^2*b^3 - 25*A*a*b^4)*d^2*e^2 + 63*(139*B*a^3*b^2 - 45*A*a^2*b^3)*d*e^3 - 420*(11*B*a^4*b - 5*A*a^3*b^2)*e^4)*x)*sqrt(e*x + d))/(b^9*x^3 + 3*a*b^8*x^2 + 3*a^2*b^7*x + a^3*b^6), -1/120*(315*(6*B*a^3*b^2*d^2*e^2 - (17*B*a^4*b - 5*A*a^3*b^2)*d*e^3 + (11*B*a^5 - 5*A*a^4*b)*e^4 + (6*B*b^5*d^2*e^2 - (17*B*a*b^4 - 5*A*b^5)*d*e^3 + (11*B*a^2*b^3 - 5*A*a*b^4)*e^4)*x^3 + 3*(6*B*a*b^4*d^2*e^2 - (17*B*a^2*b^3 - 5*A*a*b^4)*d*e^3 + (11*B*a^3*b^2 - 5*A*a^2*b^3)*e^4)*x^2 + 3*(6*B*a^2*b^3*d^2*e^2 - (17*B*a^3*b^2 - 5*A*a^2*b^3)*d*e^3 + (11*B*a^4*b - 5*A*a^3*b^2)*e^4)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (48*B*b^5*e^4*x^5 - 20*(B*a*b^4 + 2*A*b^5)*d^4 - 90*(2*B*a^2*b^3 + A*a*b^4)*d^3*e + 63*(51*B*a^3*b^2 - 5*A*a^2*b^3)*d^2*e^2 - 210*(31*B*a^4*b - 10*A*a^3*b^2)*d*e^3 + 315*(11*B*a^5 - 5*A*a^4*b)*e^4 + 16*(21*B*b^5*d*e^3 - (11*B*a*b^4 - 5*A*b^5)*e^4)*x^4 + 16*(108*B*b^5*d^2*e^2 - (197*B*a*b^4 - 65*A*b^5)*d*e^3 + 9*(11*B*a^2*b^3 - 5*A*a*b^4)*e^4)*x^3 - 3*(170*B*b^5*d^3*e - (2513*B*a*b^4 - 275*A*b^5)*d^2*e^2 + 6*(814*B*a^2*b^3 - 265*A*a*b^4)*d*e^3 - 231*(11*B*a^3*b^2 - 5*A*a^2*b^3)*e^4)*x^2 - 2*(30*B*b^5*d^4 + 5*(53*B*a*b^4 + 25*A*b^5)*d^3*e - 18*(244*B*a^2*b^3 - 25*A*a*b^4)*d^2*e^2 + 63*(139*B*a^3*b^2 - 45*A*a^2*b^3)*d*e^3 - 420*(11*B*a^4*b - 5*A*a^3*b^2)*e^4)*x)*sqrt(e*x + d))/(b^9*x^3 + 3*a*b^8*x^2 + 3*a^2*b^7*x + a^3*b^6)]","B",0
1817,1,1026,0,0.461868," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(2 \, B a^{3} b d e^{2} - {\left(3 \, B a^{4} - A a^{3} b\right)} e^{3} + {\left(2 \, B b^{4} d e^{2} - {\left(3 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(2 \, B a b^{3} d e^{2} - {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(2 \, B a^{2} b^{2} d e^{2} - {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(16 \, B b^{4} e^{3} x^{4} - 4 \, {\left(B a b^{3} + 2 \, A b^{4}\right)} d^{3} - 14 \, {\left(2 \, B a^{2} b^{2} + A a b^{3}\right)} d^{2} e + 35 \, {\left(9 \, B a^{3} b - A a^{2} b^{2}\right)} d e^{2} - 105 \, {\left(3 \, B a^{4} - A a^{3} b\right)} e^{3} + 16 \, {\left(10 \, B b^{4} d e^{2} - 3 \, {\left(3 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} - 3 \, {\left(26 \, B b^{4} d^{2} e - {\left(241 \, B a b^{3} - 29 \, A b^{4}\right)} d e^{2} + 77 \, {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} - 2 \, {\left(6 \, B b^{4} d^{3} + {\left(41 \, B a b^{3} + 19 \, A b^{4}\right)} d^{2} e - 7 \, {\left(61 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d e^{2} + 140 \, {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}, -\frac{105 \, {\left(2 \, B a^{3} b d e^{2} - {\left(3 \, B a^{4} - A a^{3} b\right)} e^{3} + {\left(2 \, B b^{4} d e^{2} - {\left(3 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(2 \, B a b^{3} d e^{2} - {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(2 \, B a^{2} b^{2} d e^{2} - {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(16 \, B b^{4} e^{3} x^{4} - 4 \, {\left(B a b^{3} + 2 \, A b^{4}\right)} d^{3} - 14 \, {\left(2 \, B a^{2} b^{2} + A a b^{3}\right)} d^{2} e + 35 \, {\left(9 \, B a^{3} b - A a^{2} b^{2}\right)} d e^{2} - 105 \, {\left(3 \, B a^{4} - A a^{3} b\right)} e^{3} + 16 \, {\left(10 \, B b^{4} d e^{2} - 3 \, {\left(3 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} - 3 \, {\left(26 \, B b^{4} d^{2} e - {\left(241 \, B a b^{3} - 29 \, A b^{4}\right)} d e^{2} + 77 \, {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} - 2 \, {\left(6 \, B b^{4} d^{3} + {\left(41 \, B a b^{3} + 19 \, A b^{4}\right)} d^{2} e - 7 \, {\left(61 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d e^{2} + 140 \, {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}\right]"," ",0,"[-1/48*(105*(2*B*a^3*b*d*e^2 - (3*B*a^4 - A*a^3*b)*e^3 + (2*B*b^4*d*e^2 - (3*B*a*b^3 - A*b^4)*e^3)*x^3 + 3*(2*B*a*b^3*d*e^2 - (3*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 3*(2*B*a^2*b^2*d*e^2 - (3*B*a^3*b - A*a^2*b^2)*e^3)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(16*B*b^4*e^3*x^4 - 4*(B*a*b^3 + 2*A*b^4)*d^3 - 14*(2*B*a^2*b^2 + A*a*b^3)*d^2*e + 35*(9*B*a^3*b - A*a^2*b^2)*d*e^2 - 105*(3*B*a^4 - A*a^3*b)*e^3 + 16*(10*B*b^4*d*e^2 - 3*(3*B*a*b^3 - A*b^4)*e^3)*x^3 - 3*(26*B*b^4*d^2*e - (241*B*a*b^3 - 29*A*b^4)*d*e^2 + 77*(3*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 - 2*(6*B*b^4*d^3 + (41*B*a*b^3 + 19*A*b^4)*d^2*e - 7*(61*B*a^2*b^2 - 7*A*a*b^3)*d*e^2 + 140*(3*B*a^3*b - A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5), -1/24*(105*(2*B*a^3*b*d*e^2 - (3*B*a^4 - A*a^3*b)*e^3 + (2*B*b^4*d*e^2 - (3*B*a*b^3 - A*b^4)*e^3)*x^3 + 3*(2*B*a*b^3*d*e^2 - (3*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 3*(2*B*a^2*b^2*d*e^2 - (3*B*a^3*b - A*a^2*b^2)*e^3)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (16*B*b^4*e^3*x^4 - 4*(B*a*b^3 + 2*A*b^4)*d^3 - 14*(2*B*a^2*b^2 + A*a*b^3)*d^2*e + 35*(9*B*a^3*b - A*a^2*b^2)*d*e^2 - 105*(3*B*a^4 - A*a^3*b)*e^3 + 16*(10*B*b^4*d*e^2 - 3*(3*B*a*b^3 - A*b^4)*e^3)*x^3 - 3*(26*B*b^4*d^2*e - (241*B*a*b^3 - 29*A*b^4)*d*e^2 + 77*(3*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 - 2*(6*B*b^4*d^3 + (41*B*a*b^3 + 19*A*b^4)*d^2*e - 7*(61*B*a^2*b^2 - 7*A*a*b^3)*d*e^2 + 140*(3*B*a^3*b - A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5)]","B",0
1818,1,1075,0,0.464211," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(6 \, B a^{3} b d e^{2} - {\left(7 \, B a^{4} - A a^{3} b\right)} e^{3} + {\left(6 \, B b^{4} d e^{2} - {\left(7 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, B a b^{3} d e^{2} - {\left(7 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{2} d e^{2} - {\left(7 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{3} + 2 \, {\left(8 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e - 5 \, {\left(25 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} d e^{2} + 15 \, {\left(7 \, B a^{4} b - A a^{3} b^{2}\right)} e^{3} - 48 \, {\left(B b^{5} d e^{2} - B a b^{4} e^{3}\right)} x^{3} + 3 \, {\left(18 \, B b^{5} d^{2} e - {\left(95 \, B a b^{4} - 11 \, A b^{5}\right)} d e^{2} + 11 \, {\left(7 \, B a^{2} b^{3} - A a b^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(6 \, B b^{5} d^{3} + {\left(23 \, B a b^{4} + 13 \, A b^{5}\right)} d^{2} e - {\left(169 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} d e^{2} + 20 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{6} d - a^{4} b^{5} e + {\left(b^{9} d - a b^{8} e\right)} x^{3} + 3 \, {\left(a b^{8} d - a^{2} b^{7} e\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d - a^{3} b^{6} e\right)} x\right)}}, \frac{15 \, {\left(6 \, B a^{3} b d e^{2} - {\left(7 \, B a^{4} - A a^{3} b\right)} e^{3} + {\left(6 \, B b^{4} d e^{2} - {\left(7 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, B a b^{3} d e^{2} - {\left(7 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{2} d e^{2} - {\left(7 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{3} + 2 \, {\left(8 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e - 5 \, {\left(25 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} d e^{2} + 15 \, {\left(7 \, B a^{4} b - A a^{3} b^{2}\right)} e^{3} - 48 \, {\left(B b^{5} d e^{2} - B a b^{4} e^{3}\right)} x^{3} + 3 \, {\left(18 \, B b^{5} d^{2} e - {\left(95 \, B a b^{4} - 11 \, A b^{5}\right)} d e^{2} + 11 \, {\left(7 \, B a^{2} b^{3} - A a b^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(6 \, B b^{5} d^{3} + {\left(23 \, B a b^{4} + 13 \, A b^{5}\right)} d^{2} e - {\left(169 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} d e^{2} + 20 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{6} d - a^{4} b^{5} e + {\left(b^{9} d - a b^{8} e\right)} x^{3} + 3 \, {\left(a b^{8} d - a^{2} b^{7} e\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d - a^{3} b^{6} e\right)} x\right)}}\right]"," ",0,"[1/48*(15*(6*B*a^3*b*d*e^2 - (7*B*a^4 - A*a^3*b)*e^3 + (6*B*b^4*d*e^2 - (7*B*a*b^3 - A*b^4)*e^3)*x^3 + 3*(6*B*a*b^3*d*e^2 - (7*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 3*(6*B*a^2*b^2*d*e^2 - (7*B*a^3*b - A*a^2*b^2)*e^3)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(4*(B*a*b^4 + 2*A*b^5)*d^3 + 2*(8*B*a^2*b^3 + A*a*b^4)*d^2*e - 5*(25*B*a^3*b^2 - A*a^2*b^3)*d*e^2 + 15*(7*B*a^4*b - A*a^3*b^2)*e^3 - 48*(B*b^5*d*e^2 - B*a*b^4*e^3)*x^3 + 3*(18*B*b^5*d^2*e - (95*B*a*b^4 - 11*A*b^5)*d*e^2 + 11*(7*B*a^2*b^3 - A*a*b^4)*e^3)*x^2 + 2*(6*B*b^5*d^3 + (23*B*a*b^4 + 13*A*b^5)*d^2*e - (169*B*a^2*b^3 - 7*A*a*b^4)*d*e^2 + 20*(7*B*a^3*b^2 - A*a^2*b^3)*e^3)*x)*sqrt(e*x + d))/(a^3*b^6*d - a^4*b^5*e + (b^9*d - a*b^8*e)*x^3 + 3*(a*b^8*d - a^2*b^7*e)*x^2 + 3*(a^2*b^7*d - a^3*b^6*e)*x), 1/24*(15*(6*B*a^3*b*d*e^2 - (7*B*a^4 - A*a^3*b)*e^3 + (6*B*b^4*d*e^2 - (7*B*a*b^3 - A*b^4)*e^3)*x^3 + 3*(6*B*a*b^3*d*e^2 - (7*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 3*(6*B*a^2*b^2*d*e^2 - (7*B*a^3*b - A*a^2*b^2)*e^3)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (4*(B*a*b^4 + 2*A*b^5)*d^3 + 2*(8*B*a^2*b^3 + A*a*b^4)*d^2*e - 5*(25*B*a^3*b^2 - A*a^2*b^3)*d*e^2 + 15*(7*B*a^4*b - A*a^3*b^2)*e^3 - 48*(B*b^5*d*e^2 - B*a*b^4*e^3)*x^3 + 3*(18*B*b^5*d^2*e - (95*B*a*b^4 - 11*A*b^5)*d*e^2 + 11*(7*B*a^2*b^3 - A*a*b^4)*e^3)*x^2 + 2*(6*B*b^5*d^3 + (23*B*a*b^4 + 13*A*b^5)*d^2*e - (169*B*a^2*b^3 - 7*A*a*b^4)*d*e^2 + 20*(7*B*a^3*b^2 - A*a^2*b^3)*e^3)*x)*sqrt(e*x + d))/(a^3*b^6*d - a^4*b^5*e + (b^9*d - a*b^8*e)*x^3 + 3*(a*b^8*d - a^2*b^7*e)*x^2 + 3*(a^2*b^7*d - a^3*b^6*e)*x)]","B",0
1819,1,1115,0,0.491312," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(6 \, B a^{3} b d e^{2} - {\left(5 \, B a^{4} + A a^{3} b\right)} e^{3} + {\left(6 \, B b^{4} d e^{2} - {\left(5 \, B a b^{3} + A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, B a b^{3} d e^{2} - {\left(5 \, B a^{2} b^{2} + A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{2} d e^{2} - {\left(5 \, B a^{3} b + A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{3} + 2 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{2} e - {\left(23 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{2} + 3 \, {\left(5 \, B a^{4} b + A a^{3} b^{2}\right)} e^{3} + 3 \, {\left(10 \, B b^{5} d^{2} e - {\left(21 \, B a b^{4} - A b^{5}\right)} d e^{2} + {\left(11 \, B a^{2} b^{3} - A a b^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(6 \, B b^{5} d^{3} + {\left(5 \, B a b^{4} + 7 \, A b^{5}\right)} d^{2} e - {\left(31 \, B a^{2} b^{3} + 11 \, A a b^{4}\right)} d e^{2} + 4 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{6} d^{2} - 2 \, a^{4} b^{5} d e + a^{5} b^{4} e^{2} + {\left(b^{9} d^{2} - 2 \, a b^{8} d e + a^{2} b^{7} e^{2}\right)} x^{3} + 3 \, {\left(a b^{8} d^{2} - 2 \, a^{2} b^{7} d e + a^{3} b^{6} e^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{2} - 2 \, a^{3} b^{6} d e + a^{4} b^{5} e^{2}\right)} x\right)}}, \frac{3 \, {\left(6 \, B a^{3} b d e^{2} - {\left(5 \, B a^{4} + A a^{3} b\right)} e^{3} + {\left(6 \, B b^{4} d e^{2} - {\left(5 \, B a b^{3} + A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, B a b^{3} d e^{2} - {\left(5 \, B a^{2} b^{2} + A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{2} d e^{2} - {\left(5 \, B a^{3} b + A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{3} + 2 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{2} e - {\left(23 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{2} + 3 \, {\left(5 \, B a^{4} b + A a^{3} b^{2}\right)} e^{3} + 3 \, {\left(10 \, B b^{5} d^{2} e - {\left(21 \, B a b^{4} - A b^{5}\right)} d e^{2} + {\left(11 \, B a^{2} b^{3} - A a b^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(6 \, B b^{5} d^{3} + {\left(5 \, B a b^{4} + 7 \, A b^{5}\right)} d^{2} e - {\left(31 \, B a^{2} b^{3} + 11 \, A a b^{4}\right)} d e^{2} + 4 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{6} d^{2} - 2 \, a^{4} b^{5} d e + a^{5} b^{4} e^{2} + {\left(b^{9} d^{2} - 2 \, a b^{8} d e + a^{2} b^{7} e^{2}\right)} x^{3} + 3 \, {\left(a b^{8} d^{2} - 2 \, a^{2} b^{7} d e + a^{3} b^{6} e^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{2} - 2 \, a^{3} b^{6} d e + a^{4} b^{5} e^{2}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(6*B*a^3*b*d*e^2 - (5*B*a^4 + A*a^3*b)*e^3 + (6*B*b^4*d*e^2 - (5*B*a*b^3 + A*b^4)*e^3)*x^3 + 3*(6*B*a*b^3*d*e^2 - (5*B*a^2*b^2 + A*a*b^3)*e^3)*x^2 + 3*(6*B*a^2*b^2*d*e^2 - (5*B*a^3*b + A*a^2*b^2)*e^3)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(4*(B*a*b^4 + 2*A*b^5)*d^3 + 2*(2*B*a^2*b^3 - 5*A*a*b^4)*d^2*e - (23*B*a^3*b^2 + A*a^2*b^3)*d*e^2 + 3*(5*B*a^4*b + A*a^3*b^2)*e^3 + 3*(10*B*b^5*d^2*e - (21*B*a*b^4 - A*b^5)*d*e^2 + (11*B*a^2*b^3 - A*a*b^4)*e^3)*x^2 + 2*(6*B*b^5*d^3 + (5*B*a*b^4 + 7*A*b^5)*d^2*e - (31*B*a^2*b^3 + 11*A*a*b^4)*d*e^2 + 4*(5*B*a^3*b^2 + A*a^2*b^3)*e^3)*x)*sqrt(e*x + d))/(a^3*b^6*d^2 - 2*a^4*b^5*d*e + a^5*b^4*e^2 + (b^9*d^2 - 2*a*b^8*d*e + a^2*b^7*e^2)*x^3 + 3*(a*b^8*d^2 - 2*a^2*b^7*d*e + a^3*b^6*e^2)*x^2 + 3*(a^2*b^7*d^2 - 2*a^3*b^6*d*e + a^4*b^5*e^2)*x), 1/24*(3*(6*B*a^3*b*d*e^2 - (5*B*a^4 + A*a^3*b)*e^3 + (6*B*b^4*d*e^2 - (5*B*a*b^3 + A*b^4)*e^3)*x^3 + 3*(6*B*a*b^3*d*e^2 - (5*B*a^2*b^2 + A*a*b^3)*e^3)*x^2 + 3*(6*B*a^2*b^2*d*e^2 - (5*B*a^3*b + A*a^2*b^2)*e^3)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (4*(B*a*b^4 + 2*A*b^5)*d^3 + 2*(2*B*a^2*b^3 - 5*A*a*b^4)*d^2*e - (23*B*a^3*b^2 + A*a^2*b^3)*d*e^2 + 3*(5*B*a^4*b + A*a^3*b^2)*e^3 + 3*(10*B*b^5*d^2*e - (21*B*a*b^4 - A*b^5)*d*e^2 + (11*B*a^2*b^3 - A*a*b^4)*e^3)*x^2 + 2*(6*B*b^5*d^3 + (5*B*a*b^4 + 7*A*b^5)*d^2*e - (31*B*a^2*b^3 + 11*A*a*b^4)*d*e^2 + 4*(5*B*a^3*b^2 + A*a^2*b^3)*e^3)*x)*sqrt(e*x + d))/(a^3*b^6*d^2 - 2*a^4*b^5*d*e + a^5*b^4*e^2 + (b^9*d^2 - 2*a*b^8*d*e + a^2*b^7*e^2)*x^3 + 3*(a*b^8*d^2 - 2*a^2*b^7*d*e + a^3*b^6*e^2)*x^2 + 3*(a^2*b^7*d^2 - 2*a^3*b^6*d*e + a^4*b^5*e^2)*x)]","B",0
1820,1,1218,0,0.474106," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, B a^{3} b d e^{2} - {\left(B a^{4} + A a^{3} b\right)} e^{3} + {\left(2 \, B b^{4} d e^{2} - {\left(B a b^{3} + A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(2 \, B a b^{3} d e^{2} - {\left(B a^{2} b^{2} + A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(2 \, B a^{2} b^{2} d e^{2} - {\left(B a^{3} b + A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{3} - 2 \, {\left(4 \, B a^{2} b^{3} + 11 \, A a b^{4}\right)} d^{2} e + {\left(7 \, B a^{3} b^{2} + 17 \, A a^{2} b^{3}\right)} d e^{2} - 3 \, {\left(B a^{4} b + A a^{3} b^{2}\right)} e^{3} + 3 \, {\left(2 \, B b^{5} d^{2} e - {\left(3 \, B a b^{4} + A b^{5}\right)} d e^{2} + {\left(B a^{2} b^{3} + A a b^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(6 \, B b^{5} d^{3} - {\left(13 \, B a b^{4} - A b^{5}\right)} d^{2} e + {\left(11 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d e^{2} - 4 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{6} d^{3} - 3 \, a^{4} b^{5} d^{2} e + 3 \, a^{5} b^{4} d e^{2} - a^{6} b^{3} e^{3} + {\left(b^{9} d^{3} - 3 \, a b^{8} d^{2} e + 3 \, a^{2} b^{7} d e^{2} - a^{3} b^{6} e^{3}\right)} x^{3} + 3 \, {\left(a b^{8} d^{3} - 3 \, a^{2} b^{7} d^{2} e + 3 \, a^{3} b^{6} d e^{2} - a^{4} b^{5} e^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{3} - 3 \, a^{3} b^{6} d^{2} e + 3 \, a^{4} b^{5} d e^{2} - a^{5} b^{4} e^{3}\right)} x\right)}}, -\frac{3 \, {\left(2 \, B a^{3} b d e^{2} - {\left(B a^{4} + A a^{3} b\right)} e^{3} + {\left(2 \, B b^{4} d e^{2} - {\left(B a b^{3} + A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(2 \, B a b^{3} d e^{2} - {\left(B a^{2} b^{2} + A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(2 \, B a^{2} b^{2} d e^{2} - {\left(B a^{3} b + A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{3} - 2 \, {\left(4 \, B a^{2} b^{3} + 11 \, A a b^{4}\right)} d^{2} e + {\left(7 \, B a^{3} b^{2} + 17 \, A a^{2} b^{3}\right)} d e^{2} - 3 \, {\left(B a^{4} b + A a^{3} b^{2}\right)} e^{3} + 3 \, {\left(2 \, B b^{5} d^{2} e - {\left(3 \, B a b^{4} + A b^{5}\right)} d e^{2} + {\left(B a^{2} b^{3} + A a b^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(6 \, B b^{5} d^{3} - {\left(13 \, B a b^{4} - A b^{5}\right)} d^{2} e + {\left(11 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d e^{2} - 4 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{6} d^{3} - 3 \, a^{4} b^{5} d^{2} e + 3 \, a^{5} b^{4} d e^{2} - a^{6} b^{3} e^{3} + {\left(b^{9} d^{3} - 3 \, a b^{8} d^{2} e + 3 \, a^{2} b^{7} d e^{2} - a^{3} b^{6} e^{3}\right)} x^{3} + 3 \, {\left(a b^{8} d^{3} - 3 \, a^{2} b^{7} d^{2} e + 3 \, a^{3} b^{6} d e^{2} - a^{4} b^{5} e^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{3} - 3 \, a^{3} b^{6} d^{2} e + 3 \, a^{4} b^{5} d e^{2} - a^{5} b^{4} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(2*B*a^3*b*d*e^2 - (B*a^4 + A*a^3*b)*e^3 + (2*B*b^4*d*e^2 - (B*a*b^3 + A*b^4)*e^3)*x^3 + 3*(2*B*a*b^3*d*e^2 - (B*a^2*b^2 + A*a*b^3)*e^3)*x^2 + 3*(2*B*a^2*b^2*d*e^2 - (B*a^3*b + A*a^2*b^2)*e^3)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(4*(B*a*b^4 + 2*A*b^5)*d^3 - 2*(4*B*a^2*b^3 + 11*A*a*b^4)*d^2*e + (7*B*a^3*b^2 + 17*A*a^2*b^3)*d*e^2 - 3*(B*a^4*b + A*a^3*b^2)*e^3 + 3*(2*B*b^5*d^2*e - (3*B*a*b^4 + A*b^5)*d*e^2 + (B*a^2*b^3 + A*a*b^4)*e^3)*x^2 + 2*(6*B*b^5*d^3 - (13*B*a*b^4 - A*b^5)*d^2*e + (11*B*a^2*b^3 - 5*A*a*b^4)*d*e^2 - 4*(B*a^3*b^2 - A*a^2*b^3)*e^3)*x)*sqrt(e*x + d))/(a^3*b^6*d^3 - 3*a^4*b^5*d^2*e + 3*a^5*b^4*d*e^2 - a^6*b^3*e^3 + (b^9*d^3 - 3*a*b^8*d^2*e + 3*a^2*b^7*d*e^2 - a^3*b^6*e^3)*x^3 + 3*(a*b^8*d^3 - 3*a^2*b^7*d^2*e + 3*a^3*b^6*d*e^2 - a^4*b^5*e^3)*x^2 + 3*(a^2*b^7*d^3 - 3*a^3*b^6*d^2*e + 3*a^4*b^5*d*e^2 - a^5*b^4*e^3)*x), -1/24*(3*(2*B*a^3*b*d*e^2 - (B*a^4 + A*a^3*b)*e^3 + (2*B*b^4*d*e^2 - (B*a*b^3 + A*b^4)*e^3)*x^3 + 3*(2*B*a*b^3*d*e^2 - (B*a^2*b^2 + A*a*b^3)*e^3)*x^2 + 3*(2*B*a^2*b^2*d*e^2 - (B*a^3*b + A*a^2*b^2)*e^3)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (4*(B*a*b^4 + 2*A*b^5)*d^3 - 2*(4*B*a^2*b^3 + 11*A*a*b^4)*d^2*e + (7*B*a^3*b^2 + 17*A*a^2*b^3)*d*e^2 - 3*(B*a^4*b + A*a^3*b^2)*e^3 + 3*(2*B*b^5*d^2*e - (3*B*a*b^4 + A*b^5)*d*e^2 + (B*a^2*b^3 + A*a*b^4)*e^3)*x^2 + 2*(6*B*b^5*d^3 - (13*B*a*b^4 - A*b^5)*d^2*e + (11*B*a^2*b^3 - 5*A*a*b^4)*d*e^2 - 4*(B*a^3*b^2 - A*a^2*b^3)*e^3)*x)*sqrt(e*x + d))/(a^3*b^6*d^3 - 3*a^4*b^5*d^2*e + 3*a^5*b^4*d*e^2 - a^6*b^3*e^3 + (b^9*d^3 - 3*a*b^8*d^2*e + 3*a^2*b^7*d*e^2 - a^3*b^6*e^3)*x^3 + 3*(a*b^8*d^3 - 3*a^2*b^7*d^2*e + 3*a^3*b^6*d*e^2 - a^4*b^5*e^3)*x^2 + 3*(a^2*b^7*d^3 - 3*a^3*b^6*d^2*e + 3*a^4*b^5*d*e^2 - a^5*b^4*e^3)*x)]","B",0
1821,1,1337,0,0.476777," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(6 \, B a^{3} b d e^{2} - {\left(B a^{4} + 5 \, A a^{3} b\right)} e^{3} + {\left(6 \, B b^{4} d e^{2} - {\left(B a b^{3} + 5 \, A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, B a b^{3} d e^{2} - {\left(B a^{2} b^{2} + 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{2} d e^{2} - {\left(B a^{3} b + 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{3} - 2 \, {\left(10 \, B a^{2} b^{3} + 17 \, A a b^{4}\right)} d^{2} e + {\left(13 \, B a^{3} b^{2} + 59 \, A a^{2} b^{3}\right)} d e^{2} + 3 \, {\left(B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{3} - 3 \, {\left(6 \, B b^{5} d^{2} e - {\left(7 \, B a b^{4} + 5 \, A b^{5}\right)} d e^{2} + {\left(B a^{2} b^{3} + 5 \, A a b^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(6 \, B b^{5} d^{3} - {\left(31 \, B a b^{4} + 5 \, A b^{5}\right)} d^{2} e + {\left(29 \, B a^{2} b^{3} + 25 \, A a b^{4}\right)} d e^{2} - 4 \, {\left(B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{6} d^{4} - 4 \, a^{4} b^{5} d^{3} e + 6 \, a^{5} b^{4} d^{2} e^{2} - 4 \, a^{6} b^{3} d e^{3} + a^{7} b^{2} e^{4} + {\left(b^{9} d^{4} - 4 \, a b^{8} d^{3} e + 6 \, a^{2} b^{7} d^{2} e^{2} - 4 \, a^{3} b^{6} d e^{3} + a^{4} b^{5} e^{4}\right)} x^{3} + 3 \, {\left(a b^{8} d^{4} - 4 \, a^{2} b^{7} d^{3} e + 6 \, a^{3} b^{6} d^{2} e^{2} - 4 \, a^{4} b^{5} d e^{3} + a^{5} b^{4} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{4} - 4 \, a^{3} b^{6} d^{3} e + 6 \, a^{4} b^{5} d^{2} e^{2} - 4 \, a^{5} b^{4} d e^{3} + a^{6} b^{3} e^{4}\right)} x\right)}}, \frac{3 \, {\left(6 \, B a^{3} b d e^{2} - {\left(B a^{4} + 5 \, A a^{3} b\right)} e^{3} + {\left(6 \, B b^{4} d e^{2} - {\left(B a b^{3} + 5 \, A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, B a b^{3} d e^{2} - {\left(B a^{2} b^{2} + 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{2} d e^{2} - {\left(B a^{3} b + 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{3} - 2 \, {\left(10 \, B a^{2} b^{3} + 17 \, A a b^{4}\right)} d^{2} e + {\left(13 \, B a^{3} b^{2} + 59 \, A a^{2} b^{3}\right)} d e^{2} + 3 \, {\left(B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{3} - 3 \, {\left(6 \, B b^{5} d^{2} e - {\left(7 \, B a b^{4} + 5 \, A b^{5}\right)} d e^{2} + {\left(B a^{2} b^{3} + 5 \, A a b^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(6 \, B b^{5} d^{3} - {\left(31 \, B a b^{4} + 5 \, A b^{5}\right)} d^{2} e + {\left(29 \, B a^{2} b^{3} + 25 \, A a b^{4}\right)} d e^{2} - 4 \, {\left(B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{6} d^{4} - 4 \, a^{4} b^{5} d^{3} e + 6 \, a^{5} b^{4} d^{2} e^{2} - 4 \, a^{6} b^{3} d e^{3} + a^{7} b^{2} e^{4} + {\left(b^{9} d^{4} - 4 \, a b^{8} d^{3} e + 6 \, a^{2} b^{7} d^{2} e^{2} - 4 \, a^{3} b^{6} d e^{3} + a^{4} b^{5} e^{4}\right)} x^{3} + 3 \, {\left(a b^{8} d^{4} - 4 \, a^{2} b^{7} d^{3} e + 6 \, a^{3} b^{6} d^{2} e^{2} - 4 \, a^{4} b^{5} d e^{3} + a^{5} b^{4} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{4} - 4 \, a^{3} b^{6} d^{3} e + 6 \, a^{4} b^{5} d^{2} e^{2} - 4 \, a^{5} b^{4} d e^{3} + a^{6} b^{3} e^{4}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(6*B*a^3*b*d*e^2 - (B*a^4 + 5*A*a^3*b)*e^3 + (6*B*b^4*d*e^2 - (B*a*b^3 + 5*A*b^4)*e^3)*x^3 + 3*(6*B*a*b^3*d*e^2 - (B*a^2*b^2 + 5*A*a*b^3)*e^3)*x^2 + 3*(6*B*a^2*b^2*d*e^2 - (B*a^3*b + 5*A*a^2*b^2)*e^3)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(4*(B*a*b^4 + 2*A*b^5)*d^3 - 2*(10*B*a^2*b^3 + 17*A*a*b^4)*d^2*e + (13*B*a^3*b^2 + 59*A*a^2*b^3)*d*e^2 + 3*(B*a^4*b - 11*A*a^3*b^2)*e^3 - 3*(6*B*b^5*d^2*e - (7*B*a*b^4 + 5*A*b^5)*d*e^2 + (B*a^2*b^3 + 5*A*a*b^4)*e^3)*x^2 + 2*(6*B*b^5*d^3 - (31*B*a*b^4 + 5*A*b^5)*d^2*e + (29*B*a^2*b^3 + 25*A*a*b^4)*d*e^2 - 4*(B*a^3*b^2 + 5*A*a^2*b^3)*e^3)*x)*sqrt(e*x + d))/(a^3*b^6*d^4 - 4*a^4*b^5*d^3*e + 6*a^5*b^4*d^2*e^2 - 4*a^6*b^3*d*e^3 + a^7*b^2*e^4 + (b^9*d^4 - 4*a*b^8*d^3*e + 6*a^2*b^7*d^2*e^2 - 4*a^3*b^6*d*e^3 + a^4*b^5*e^4)*x^3 + 3*(a*b^8*d^4 - 4*a^2*b^7*d^3*e + 6*a^3*b^6*d^2*e^2 - 4*a^4*b^5*d*e^3 + a^5*b^4*e^4)*x^2 + 3*(a^2*b^7*d^4 - 4*a^3*b^6*d^3*e + 6*a^4*b^5*d^2*e^2 - 4*a^5*b^4*d*e^3 + a^6*b^3*e^4)*x), 1/24*(3*(6*B*a^3*b*d*e^2 - (B*a^4 + 5*A*a^3*b)*e^3 + (6*B*b^4*d*e^2 - (B*a*b^3 + 5*A*b^4)*e^3)*x^3 + 3*(6*B*a*b^3*d*e^2 - (B*a^2*b^2 + 5*A*a*b^3)*e^3)*x^2 + 3*(6*B*a^2*b^2*d*e^2 - (B*a^3*b + 5*A*a^2*b^2)*e^3)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (4*(B*a*b^4 + 2*A*b^5)*d^3 - 2*(10*B*a^2*b^3 + 17*A*a*b^4)*d^2*e + (13*B*a^3*b^2 + 59*A*a^2*b^3)*d*e^2 + 3*(B*a^4*b - 11*A*a^3*b^2)*e^3 - 3*(6*B*b^5*d^2*e - (7*B*a*b^4 + 5*A*b^5)*d*e^2 + (B*a^2*b^3 + 5*A*a*b^4)*e^3)*x^2 + 2*(6*B*b^5*d^3 - (31*B*a*b^4 + 5*A*b^5)*d^2*e + (29*B*a^2*b^3 + 25*A*a*b^4)*d*e^2 - 4*(B*a^3*b^2 + 5*A*a^2*b^3)*e^3)*x)*sqrt(e*x + d))/(a^3*b^6*d^4 - 4*a^4*b^5*d^3*e + 6*a^5*b^4*d^2*e^2 - 4*a^6*b^3*d*e^3 + a^7*b^2*e^4 + (b^9*d^4 - 4*a*b^8*d^3*e + 6*a^2*b^7*d^2*e^2 - 4*a^3*b^6*d*e^3 + a^4*b^5*e^4)*x^3 + 3*(a*b^8*d^4 - 4*a^2*b^7*d^3*e + 6*a^3*b^6*d^2*e^2 - 4*a^4*b^5*d*e^3 + a^5*b^4*e^4)*x^2 + 3*(a^2*b^7*d^4 - 4*a^3*b^6*d^3*e + 6*a^4*b^5*d^2*e^2 - 4*a^5*b^4*d*e^3 + a^6*b^3*e^4)*x)]","B",0
1822,1,2114,0,0.492449," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(6 \, B a^{3} b d^{2} e^{2} + {\left(B a^{4} - 7 \, A a^{3} b\right)} d e^{3} + {\left(6 \, B b^{4} d e^{3} + {\left(B a b^{3} - 7 \, A b^{4}\right)} e^{4}\right)} x^{4} + {\left(6 \, B b^{4} d^{2} e^{2} + {\left(19 \, B a b^{3} - 7 \, A b^{4}\right)} d e^{3} + 3 \, {\left(B a^{2} b^{2} - 7 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(6 \, B a b^{3} d^{2} e^{2} + 7 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{3} + {\left(B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + {\left(18 \, B a^{2} b^{2} d^{2} e^{2} + 3 \, {\left(3 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} d e^{3} + {\left(B a^{4} - 7 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(48 \, A a^{4} b e^{4} - 4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{4} + 2 \, {\left(16 \, B a^{2} b^{3} + 23 \, A a b^{4}\right)} d^{3} e + {\left(53 \, B a^{3} b^{2} - 125 \, A a^{2} b^{3}\right)} d^{2} e^{2} - 3 \, {\left(27 \, B a^{4} b - 13 \, A a^{3} b^{2}\right)} d e^{3} + 15 \, {\left(6 \, B b^{5} d^{2} e^{2} - {\left(5 \, B a b^{4} + 7 \, A b^{5}\right)} d e^{3} - {\left(B a^{2} b^{3} - 7 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 5 \, {\left(6 \, B b^{5} d^{3} e + {\left(43 \, B a b^{4} - 7 \, A b^{5}\right)} d^{2} e^{2} - {\left(41 \, B a^{2} b^{3} + 49 \, A a b^{4}\right)} d e^{3} - 8 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - {\left(12 \, B b^{5} d^{4} - 2 \, {\left(47 \, B a b^{4} + 7 \, A b^{5}\right)} d^{3} e - 2 \, {\left(65 \, B a^{2} b^{3} - 56 \, A a b^{4}\right)} d^{2} e^{2} + {\left(179 \, B a^{3} b^{2} + 133 \, A a^{2} b^{3}\right)} d e^{3} + 33 \, {\left(B a^{4} b - 7 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{6} d^{6} - 5 \, a^{4} b^{5} d^{5} e + 10 \, a^{5} b^{4} d^{4} e^{2} - 10 \, a^{6} b^{3} d^{3} e^{3} + 5 \, a^{7} b^{2} d^{2} e^{4} - a^{8} b d e^{5} + {\left(b^{9} d^{5} e - 5 \, a b^{8} d^{4} e^{2} + 10 \, a^{2} b^{7} d^{3} e^{3} - 10 \, a^{3} b^{6} d^{2} e^{4} + 5 \, a^{4} b^{5} d e^{5} - a^{5} b^{4} e^{6}\right)} x^{4} + {\left(b^{9} d^{6} - 2 \, a b^{8} d^{5} e - 5 \, a^{2} b^{7} d^{4} e^{2} + 20 \, a^{3} b^{6} d^{3} e^{3} - 25 \, a^{4} b^{5} d^{2} e^{4} + 14 \, a^{5} b^{4} d e^{5} - 3 \, a^{6} b^{3} e^{6}\right)} x^{3} + 3 \, {\left(a b^{8} d^{6} - 4 \, a^{2} b^{7} d^{5} e + 5 \, a^{3} b^{6} d^{4} e^{2} - 5 \, a^{5} b^{4} d^{2} e^{4} + 4 \, a^{6} b^{3} d e^{5} - a^{7} b^{2} e^{6}\right)} x^{2} + {\left(3 \, a^{2} b^{7} d^{6} - 14 \, a^{3} b^{6} d^{5} e + 25 \, a^{4} b^{5} d^{4} e^{2} - 20 \, a^{5} b^{4} d^{3} e^{3} + 5 \, a^{6} b^{3} d^{2} e^{4} + 2 \, a^{7} b^{2} d e^{5} - a^{8} b e^{6}\right)} x\right)}}, \frac{15 \, {\left(6 \, B a^{3} b d^{2} e^{2} + {\left(B a^{4} - 7 \, A a^{3} b\right)} d e^{3} + {\left(6 \, B b^{4} d e^{3} + {\left(B a b^{3} - 7 \, A b^{4}\right)} e^{4}\right)} x^{4} + {\left(6 \, B b^{4} d^{2} e^{2} + {\left(19 \, B a b^{3} - 7 \, A b^{4}\right)} d e^{3} + 3 \, {\left(B a^{2} b^{2} - 7 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(6 \, B a b^{3} d^{2} e^{2} + 7 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{3} + {\left(B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + {\left(18 \, B a^{2} b^{2} d^{2} e^{2} + 3 \, {\left(3 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} d e^{3} + {\left(B a^{4} - 7 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(48 \, A a^{4} b e^{4} - 4 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{4} + 2 \, {\left(16 \, B a^{2} b^{3} + 23 \, A a b^{4}\right)} d^{3} e + {\left(53 \, B a^{3} b^{2} - 125 \, A a^{2} b^{3}\right)} d^{2} e^{2} - 3 \, {\left(27 \, B a^{4} b - 13 \, A a^{3} b^{2}\right)} d e^{3} + 15 \, {\left(6 \, B b^{5} d^{2} e^{2} - {\left(5 \, B a b^{4} + 7 \, A b^{5}\right)} d e^{3} - {\left(B a^{2} b^{3} - 7 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 5 \, {\left(6 \, B b^{5} d^{3} e + {\left(43 \, B a b^{4} - 7 \, A b^{5}\right)} d^{2} e^{2} - {\left(41 \, B a^{2} b^{3} + 49 \, A a b^{4}\right)} d e^{3} - 8 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - {\left(12 \, B b^{5} d^{4} - 2 \, {\left(47 \, B a b^{4} + 7 \, A b^{5}\right)} d^{3} e - 2 \, {\left(65 \, B a^{2} b^{3} - 56 \, A a b^{4}\right)} d^{2} e^{2} + {\left(179 \, B a^{3} b^{2} + 133 \, A a^{2} b^{3}\right)} d e^{3} + 33 \, {\left(B a^{4} b - 7 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{6} d^{6} - 5 \, a^{4} b^{5} d^{5} e + 10 \, a^{5} b^{4} d^{4} e^{2} - 10 \, a^{6} b^{3} d^{3} e^{3} + 5 \, a^{7} b^{2} d^{2} e^{4} - a^{8} b d e^{5} + {\left(b^{9} d^{5} e - 5 \, a b^{8} d^{4} e^{2} + 10 \, a^{2} b^{7} d^{3} e^{3} - 10 \, a^{3} b^{6} d^{2} e^{4} + 5 \, a^{4} b^{5} d e^{5} - a^{5} b^{4} e^{6}\right)} x^{4} + {\left(b^{9} d^{6} - 2 \, a b^{8} d^{5} e - 5 \, a^{2} b^{7} d^{4} e^{2} + 20 \, a^{3} b^{6} d^{3} e^{3} - 25 \, a^{4} b^{5} d^{2} e^{4} + 14 \, a^{5} b^{4} d e^{5} - 3 \, a^{6} b^{3} e^{6}\right)} x^{3} + 3 \, {\left(a b^{8} d^{6} - 4 \, a^{2} b^{7} d^{5} e + 5 \, a^{3} b^{6} d^{4} e^{2} - 5 \, a^{5} b^{4} d^{2} e^{4} + 4 \, a^{6} b^{3} d e^{5} - a^{7} b^{2} e^{6}\right)} x^{2} + {\left(3 \, a^{2} b^{7} d^{6} - 14 \, a^{3} b^{6} d^{5} e + 25 \, a^{4} b^{5} d^{4} e^{2} - 20 \, a^{5} b^{4} d^{3} e^{3} + 5 \, a^{6} b^{3} d^{2} e^{4} + 2 \, a^{7} b^{2} d e^{5} - a^{8} b e^{6}\right)} x\right)}}\right]"," ",0,"[-1/48*(15*(6*B*a^3*b*d^2*e^2 + (B*a^4 - 7*A*a^3*b)*d*e^3 + (6*B*b^4*d*e^3 + (B*a*b^3 - 7*A*b^4)*e^4)*x^4 + (6*B*b^4*d^2*e^2 + (19*B*a*b^3 - 7*A*b^4)*d*e^3 + 3*(B*a^2*b^2 - 7*A*a*b^3)*e^4)*x^3 + 3*(6*B*a*b^3*d^2*e^2 + 7*(B*a^2*b^2 - A*a*b^3)*d*e^3 + (B*a^3*b - 7*A*a^2*b^2)*e^4)*x^2 + (18*B*a^2*b^2*d^2*e^2 + 3*(3*B*a^3*b - 7*A*a^2*b^2)*d*e^3 + (B*a^4 - 7*A*a^3*b)*e^4)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e + 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(48*A*a^4*b*e^4 - 4*(B*a*b^4 + 2*A*b^5)*d^4 + 2*(16*B*a^2*b^3 + 23*A*a*b^4)*d^3*e + (53*B*a^3*b^2 - 125*A*a^2*b^3)*d^2*e^2 - 3*(27*B*a^4*b - 13*A*a^3*b^2)*d*e^3 + 15*(6*B*b^5*d^2*e^2 - (5*B*a*b^4 + 7*A*b^5)*d*e^3 - (B*a^2*b^3 - 7*A*a*b^4)*e^4)*x^3 + 5*(6*B*b^5*d^3*e + (43*B*a*b^4 - 7*A*b^5)*d^2*e^2 - (41*B*a^2*b^3 + 49*A*a*b^4)*d*e^3 - 8*(B*a^3*b^2 - 7*A*a^2*b^3)*e^4)*x^2 - (12*B*b^5*d^4 - 2*(47*B*a*b^4 + 7*A*b^5)*d^3*e - 2*(65*B*a^2*b^3 - 56*A*a*b^4)*d^2*e^2 + (179*B*a^3*b^2 + 133*A*a^2*b^3)*d*e^3 + 33*(B*a^4*b - 7*A*a^3*b^2)*e^4)*x)*sqrt(e*x + d))/(a^3*b^6*d^6 - 5*a^4*b^5*d^5*e + 10*a^5*b^4*d^4*e^2 - 10*a^6*b^3*d^3*e^3 + 5*a^7*b^2*d^2*e^4 - a^8*b*d*e^5 + (b^9*d^5*e - 5*a*b^8*d^4*e^2 + 10*a^2*b^7*d^3*e^3 - 10*a^3*b^6*d^2*e^4 + 5*a^4*b^5*d*e^5 - a^5*b^4*e^6)*x^4 + (b^9*d^6 - 2*a*b^8*d^5*e - 5*a^2*b^7*d^4*e^2 + 20*a^3*b^6*d^3*e^3 - 25*a^4*b^5*d^2*e^4 + 14*a^5*b^4*d*e^5 - 3*a^6*b^3*e^6)*x^3 + 3*(a*b^8*d^6 - 4*a^2*b^7*d^5*e + 5*a^3*b^6*d^4*e^2 - 5*a^5*b^4*d^2*e^4 + 4*a^6*b^3*d*e^5 - a^7*b^2*e^6)*x^2 + (3*a^2*b^7*d^6 - 14*a^3*b^6*d^5*e + 25*a^4*b^5*d^4*e^2 - 20*a^5*b^4*d^3*e^3 + 5*a^6*b^3*d^2*e^4 + 2*a^7*b^2*d*e^5 - a^8*b*e^6)*x), 1/24*(15*(6*B*a^3*b*d^2*e^2 + (B*a^4 - 7*A*a^3*b)*d*e^3 + (6*B*b^4*d*e^3 + (B*a*b^3 - 7*A*b^4)*e^4)*x^4 + (6*B*b^4*d^2*e^2 + (19*B*a*b^3 - 7*A*b^4)*d*e^3 + 3*(B*a^2*b^2 - 7*A*a*b^3)*e^4)*x^3 + 3*(6*B*a*b^3*d^2*e^2 + 7*(B*a^2*b^2 - A*a*b^3)*d*e^3 + (B*a^3*b - 7*A*a^2*b^2)*e^4)*x^2 + (18*B*a^2*b^2*d^2*e^2 + 3*(3*B*a^3*b - 7*A*a^2*b^2)*d*e^3 + (B*a^4 - 7*A*a^3*b)*e^4)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (48*A*a^4*b*e^4 - 4*(B*a*b^4 + 2*A*b^5)*d^4 + 2*(16*B*a^2*b^3 + 23*A*a*b^4)*d^3*e + (53*B*a^3*b^2 - 125*A*a^2*b^3)*d^2*e^2 - 3*(27*B*a^4*b - 13*A*a^3*b^2)*d*e^3 + 15*(6*B*b^5*d^2*e^2 - (5*B*a*b^4 + 7*A*b^5)*d*e^3 - (B*a^2*b^3 - 7*A*a*b^4)*e^4)*x^3 + 5*(6*B*b^5*d^3*e + (43*B*a*b^4 - 7*A*b^5)*d^2*e^2 - (41*B*a^2*b^3 + 49*A*a*b^4)*d*e^3 - 8*(B*a^3*b^2 - 7*A*a^2*b^3)*e^4)*x^2 - (12*B*b^5*d^4 - 2*(47*B*a*b^4 + 7*A*b^5)*d^3*e - 2*(65*B*a^2*b^3 - 56*A*a*b^4)*d^2*e^2 + (179*B*a^3*b^2 + 133*A*a^2*b^3)*d*e^3 + 33*(B*a^4*b - 7*A*a^3*b^2)*e^4)*x)*sqrt(e*x + d))/(a^3*b^6*d^6 - 5*a^4*b^5*d^5*e + 10*a^5*b^4*d^4*e^2 - 10*a^6*b^3*d^3*e^3 + 5*a^7*b^2*d^2*e^4 - a^8*b*d*e^5 + (b^9*d^5*e - 5*a*b^8*d^4*e^2 + 10*a^2*b^7*d^3*e^3 - 10*a^3*b^6*d^2*e^4 + 5*a^4*b^5*d*e^5 - a^5*b^4*e^6)*x^4 + (b^9*d^6 - 2*a*b^8*d^5*e - 5*a^2*b^7*d^4*e^2 + 20*a^3*b^6*d^3*e^3 - 25*a^4*b^5*d^2*e^4 + 14*a^5*b^4*d*e^5 - 3*a^6*b^3*e^6)*x^3 + 3*(a*b^8*d^6 - 4*a^2*b^7*d^5*e + 5*a^3*b^6*d^4*e^2 - 5*a^5*b^4*d^2*e^4 + 4*a^6*b^3*d*e^5 - a^7*b^2*e^6)*x^2 + (3*a^2*b^7*d^6 - 14*a^3*b^6*d^5*e + 25*a^4*b^5*d^4*e^2 - 20*a^5*b^4*d^3*e^3 + 5*a^6*b^3*d^2*e^4 + 2*a^7*b^2*d*e^5 - a^8*b*e^6)*x)]","B",0
1823,1,2648,0,0.500394," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(2 \, B a^{3} b d^{3} e^{2} + {\left(B a^{4} - 3 \, A a^{3} b\right)} d^{2} e^{3} + {\left(2 \, B b^{4} d e^{4} + {\left(B a b^{3} - 3 \, A b^{4}\right)} e^{5}\right)} x^{5} + {\left(4 \, B b^{4} d^{2} e^{3} + 2 \, {\left(4 \, B a b^{3} - 3 \, A b^{4}\right)} d e^{4} + 3 \, {\left(B a^{2} b^{2} - 3 \, A a b^{3}\right)} e^{5}\right)} x^{4} + {\left(2 \, B b^{4} d^{3} e^{2} + {\left(13 \, B a b^{3} - 3 \, A b^{4}\right)} d^{2} e^{3} + 6 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} d e^{4} + 3 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{3} + {\left(6 \, B a b^{3} d^{3} e^{2} + 3 \, {\left(5 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} d^{2} e^{3} + 2 \, {\left(4 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d e^{4} + {\left(B a^{4} - 3 \, A a^{3} b\right)} e^{5}\right)} x^{2} + {\left(6 \, B a^{2} b^{2} d^{3} e^{2} + {\left(7 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{2} e^{3} + 2 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} d e^{4}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(16 \, A a^{4} e^{4} - 4 \, {\left(B a b^{3} + 2 \, A b^{4}\right)} d^{4} + 10 \, {\left(4 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} d^{3} e + {\left(247 \, B a^{3} b - 165 \, A a^{2} b^{2}\right)} d^{2} e^{2} + 16 \, {\left(2 \, B a^{4} - 13 \, A a^{3} b\right)} d e^{3} + 105 \, {\left(2 \, B b^{4} d e^{3} + {\left(B a b^{3} - 3 \, A b^{4}\right)} e^{4}\right)} x^{4} + 140 \, {\left(2 \, B b^{4} d^{2} e^{2} + {\left(5 \, B a b^{3} - 3 \, A b^{4}\right)} d e^{3} + 2 \, {\left(B a^{2} b^{2} - 3 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 21 \, {\left(2 \, B b^{4} d^{3} e + {\left(37 \, B a b^{3} - 3 \, A b^{4}\right)} d^{2} e^{2} + 2 \, {\left(20 \, B a^{2} b^{2} - 27 \, A a b^{3}\right)} d e^{3} + 11 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - 6 \, {\left(2 \, B b^{4} d^{4} - {\left(19 \, B a b^{3} + 3 \, A b^{4}\right)} d^{3} e - 2 \, {\left(58 \, B a^{2} b^{2} - 15 \, A a b^{3}\right)} d^{2} e^{2} - 3 \, {\left(23 \, B a^{3} b - 53 \, A a^{2} b^{2}\right)} d e^{3} - 8 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d^{7} - 5 \, a^{4} b^{4} d^{6} e + 10 \, a^{5} b^{3} d^{5} e^{2} - 10 \, a^{6} b^{2} d^{4} e^{3} + 5 \, a^{7} b d^{3} e^{4} - a^{8} d^{2} e^{5} + {\left(b^{8} d^{5} e^{2} - 5 \, a b^{7} d^{4} e^{3} + 10 \, a^{2} b^{6} d^{3} e^{4} - 10 \, a^{3} b^{5} d^{2} e^{5} + 5 \, a^{4} b^{4} d e^{6} - a^{5} b^{3} e^{7}\right)} x^{5} + {\left(2 \, b^{8} d^{6} e - 7 \, a b^{7} d^{5} e^{2} + 5 \, a^{2} b^{6} d^{4} e^{3} + 10 \, a^{3} b^{5} d^{3} e^{4} - 20 \, a^{4} b^{4} d^{2} e^{5} + 13 \, a^{5} b^{3} d e^{6} - 3 \, a^{6} b^{2} e^{7}\right)} x^{4} + {\left(b^{8} d^{7} + a b^{7} d^{6} e - 17 \, a^{2} b^{6} d^{5} e^{2} + 35 \, a^{3} b^{5} d^{4} e^{3} - 25 \, a^{4} b^{4} d^{3} e^{4} - a^{5} b^{3} d^{2} e^{5} + 9 \, a^{6} b^{2} d e^{6} - 3 \, a^{7} b e^{7}\right)} x^{3} + {\left(3 \, a b^{7} d^{7} - 9 \, a^{2} b^{6} d^{6} e + a^{3} b^{5} d^{5} e^{2} + 25 \, a^{4} b^{4} d^{4} e^{3} - 35 \, a^{5} b^{3} d^{3} e^{4} + 17 \, a^{6} b^{2} d^{2} e^{5} - a^{7} b d e^{6} - a^{8} e^{7}\right)} x^{2} + {\left(3 \, a^{2} b^{6} d^{7} - 13 \, a^{3} b^{5} d^{6} e + 20 \, a^{4} b^{4} d^{5} e^{2} - 10 \, a^{5} b^{3} d^{4} e^{3} - 5 \, a^{6} b^{2} d^{3} e^{4} + 7 \, a^{7} b d^{2} e^{5} - 2 \, a^{8} d e^{6}\right)} x\right)}}, -\frac{105 \, {\left(2 \, B a^{3} b d^{3} e^{2} + {\left(B a^{4} - 3 \, A a^{3} b\right)} d^{2} e^{3} + {\left(2 \, B b^{4} d e^{4} + {\left(B a b^{3} - 3 \, A b^{4}\right)} e^{5}\right)} x^{5} + {\left(4 \, B b^{4} d^{2} e^{3} + 2 \, {\left(4 \, B a b^{3} - 3 \, A b^{4}\right)} d e^{4} + 3 \, {\left(B a^{2} b^{2} - 3 \, A a b^{3}\right)} e^{5}\right)} x^{4} + {\left(2 \, B b^{4} d^{3} e^{2} + {\left(13 \, B a b^{3} - 3 \, A b^{4}\right)} d^{2} e^{3} + 6 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} d e^{4} + 3 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{3} + {\left(6 \, B a b^{3} d^{3} e^{2} + 3 \, {\left(5 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} d^{2} e^{3} + 2 \, {\left(4 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d e^{4} + {\left(B a^{4} - 3 \, A a^{3} b\right)} e^{5}\right)} x^{2} + {\left(6 \, B a^{2} b^{2} d^{3} e^{2} + {\left(7 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{2} e^{3} + 2 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} d e^{4}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(16 \, A a^{4} e^{4} - 4 \, {\left(B a b^{3} + 2 \, A b^{4}\right)} d^{4} + 10 \, {\left(4 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} d^{3} e + {\left(247 \, B a^{3} b - 165 \, A a^{2} b^{2}\right)} d^{2} e^{2} + 16 \, {\left(2 \, B a^{4} - 13 \, A a^{3} b\right)} d e^{3} + 105 \, {\left(2 \, B b^{4} d e^{3} + {\left(B a b^{3} - 3 \, A b^{4}\right)} e^{4}\right)} x^{4} + 140 \, {\left(2 \, B b^{4} d^{2} e^{2} + {\left(5 \, B a b^{3} - 3 \, A b^{4}\right)} d e^{3} + 2 \, {\left(B a^{2} b^{2} - 3 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 21 \, {\left(2 \, B b^{4} d^{3} e + {\left(37 \, B a b^{3} - 3 \, A b^{4}\right)} d^{2} e^{2} + 2 \, {\left(20 \, B a^{2} b^{2} - 27 \, A a b^{3}\right)} d e^{3} + 11 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - 6 \, {\left(2 \, B b^{4} d^{4} - {\left(19 \, B a b^{3} + 3 \, A b^{4}\right)} d^{3} e - 2 \, {\left(58 \, B a^{2} b^{2} - 15 \, A a b^{3}\right)} d^{2} e^{2} - 3 \, {\left(23 \, B a^{3} b - 53 \, A a^{2} b^{2}\right)} d e^{3} - 8 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d^{7} - 5 \, a^{4} b^{4} d^{6} e + 10 \, a^{5} b^{3} d^{5} e^{2} - 10 \, a^{6} b^{2} d^{4} e^{3} + 5 \, a^{7} b d^{3} e^{4} - a^{8} d^{2} e^{5} + {\left(b^{8} d^{5} e^{2} - 5 \, a b^{7} d^{4} e^{3} + 10 \, a^{2} b^{6} d^{3} e^{4} - 10 \, a^{3} b^{5} d^{2} e^{5} + 5 \, a^{4} b^{4} d e^{6} - a^{5} b^{3} e^{7}\right)} x^{5} + {\left(2 \, b^{8} d^{6} e - 7 \, a b^{7} d^{5} e^{2} + 5 \, a^{2} b^{6} d^{4} e^{3} + 10 \, a^{3} b^{5} d^{3} e^{4} - 20 \, a^{4} b^{4} d^{2} e^{5} + 13 \, a^{5} b^{3} d e^{6} - 3 \, a^{6} b^{2} e^{7}\right)} x^{4} + {\left(b^{8} d^{7} + a b^{7} d^{6} e - 17 \, a^{2} b^{6} d^{5} e^{2} + 35 \, a^{3} b^{5} d^{4} e^{3} - 25 \, a^{4} b^{4} d^{3} e^{4} - a^{5} b^{3} d^{2} e^{5} + 9 \, a^{6} b^{2} d e^{6} - 3 \, a^{7} b e^{7}\right)} x^{3} + {\left(3 \, a b^{7} d^{7} - 9 \, a^{2} b^{6} d^{6} e + a^{3} b^{5} d^{5} e^{2} + 25 \, a^{4} b^{4} d^{4} e^{3} - 35 \, a^{5} b^{3} d^{3} e^{4} + 17 \, a^{6} b^{2} d^{2} e^{5} - a^{7} b d e^{6} - a^{8} e^{7}\right)} x^{2} + {\left(3 \, a^{2} b^{6} d^{7} - 13 \, a^{3} b^{5} d^{6} e + 20 \, a^{4} b^{4} d^{5} e^{2} - 10 \, a^{5} b^{3} d^{4} e^{3} - 5 \, a^{6} b^{2} d^{3} e^{4} + 7 \, a^{7} b d^{2} e^{5} - 2 \, a^{8} d e^{6}\right)} x\right)}}\right]"," ",0,"[1/48*(105*(2*B*a^3*b*d^3*e^2 + (B*a^4 - 3*A*a^3*b)*d^2*e^3 + (2*B*b^4*d*e^4 + (B*a*b^3 - 3*A*b^4)*e^5)*x^5 + (4*B*b^4*d^2*e^3 + 2*(4*B*a*b^3 - 3*A*b^4)*d*e^4 + 3*(B*a^2*b^2 - 3*A*a*b^3)*e^5)*x^4 + (2*B*b^4*d^3*e^2 + (13*B*a*b^3 - 3*A*b^4)*d^2*e^3 + 6*(2*B*a^2*b^2 - 3*A*a*b^3)*d*e^4 + 3*(B*a^3*b - 3*A*a^2*b^2)*e^5)*x^3 + (6*B*a*b^3*d^3*e^2 + 3*(5*B*a^2*b^2 - 3*A*a*b^3)*d^2*e^3 + 2*(4*B*a^3*b - 9*A*a^2*b^2)*d*e^4 + (B*a^4 - 3*A*a^3*b)*e^5)*x^2 + (6*B*a^2*b^2*d^3*e^2 + (7*B*a^3*b - 9*A*a^2*b^2)*d^2*e^3 + 2*(B*a^4 - 3*A*a^3*b)*d*e^4)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(16*A*a^4*e^4 - 4*(B*a*b^3 + 2*A*b^4)*d^4 + 10*(4*B*a^2*b^2 + 5*A*a*b^3)*d^3*e + (247*B*a^3*b - 165*A*a^2*b^2)*d^2*e^2 + 16*(2*B*a^4 - 13*A*a^3*b)*d*e^3 + 105*(2*B*b^4*d*e^3 + (B*a*b^3 - 3*A*b^4)*e^4)*x^4 + 140*(2*B*b^4*d^2*e^2 + (5*B*a*b^3 - 3*A*b^4)*d*e^3 + 2*(B*a^2*b^2 - 3*A*a*b^3)*e^4)*x^3 + 21*(2*B*b^4*d^3*e + (37*B*a*b^3 - 3*A*b^4)*d^2*e^2 + 2*(20*B*a^2*b^2 - 27*A*a*b^3)*d*e^3 + 11*(B*a^3*b - 3*A*a^2*b^2)*e^4)*x^2 - 6*(2*B*b^4*d^4 - (19*B*a*b^3 + 3*A*b^4)*d^3*e - 2*(58*B*a^2*b^2 - 15*A*a*b^3)*d^2*e^2 - 3*(23*B*a^3*b - 53*A*a^2*b^2)*d*e^3 - 8*(B*a^4 - 3*A*a^3*b)*e^4)*x)*sqrt(e*x + d))/(a^3*b^5*d^7 - 5*a^4*b^4*d^6*e + 10*a^5*b^3*d^5*e^2 - 10*a^6*b^2*d^4*e^3 + 5*a^7*b*d^3*e^4 - a^8*d^2*e^5 + (b^8*d^5*e^2 - 5*a*b^7*d^4*e^3 + 10*a^2*b^6*d^3*e^4 - 10*a^3*b^5*d^2*e^5 + 5*a^4*b^4*d*e^6 - a^5*b^3*e^7)*x^5 + (2*b^8*d^6*e - 7*a*b^7*d^5*e^2 + 5*a^2*b^6*d^4*e^3 + 10*a^3*b^5*d^3*e^4 - 20*a^4*b^4*d^2*e^5 + 13*a^5*b^3*d*e^6 - 3*a^6*b^2*e^7)*x^4 + (b^8*d^7 + a*b^7*d^6*e - 17*a^2*b^6*d^5*e^2 + 35*a^3*b^5*d^4*e^3 - 25*a^4*b^4*d^3*e^4 - a^5*b^3*d^2*e^5 + 9*a^6*b^2*d*e^6 - 3*a^7*b*e^7)*x^3 + (3*a*b^7*d^7 - 9*a^2*b^6*d^6*e + a^3*b^5*d^5*e^2 + 25*a^4*b^4*d^4*e^3 - 35*a^5*b^3*d^3*e^4 + 17*a^6*b^2*d^2*e^5 - a^7*b*d*e^6 - a^8*e^7)*x^2 + (3*a^2*b^6*d^7 - 13*a^3*b^5*d^6*e + 20*a^4*b^4*d^5*e^2 - 10*a^5*b^3*d^4*e^3 - 5*a^6*b^2*d^3*e^4 + 7*a^7*b*d^2*e^5 - 2*a^8*d*e^6)*x), -1/24*(105*(2*B*a^3*b*d^3*e^2 + (B*a^4 - 3*A*a^3*b)*d^2*e^3 + (2*B*b^4*d*e^4 + (B*a*b^3 - 3*A*b^4)*e^5)*x^5 + (4*B*b^4*d^2*e^3 + 2*(4*B*a*b^3 - 3*A*b^4)*d*e^4 + 3*(B*a^2*b^2 - 3*A*a*b^3)*e^5)*x^4 + (2*B*b^4*d^3*e^2 + (13*B*a*b^3 - 3*A*b^4)*d^2*e^3 + 6*(2*B*a^2*b^2 - 3*A*a*b^3)*d*e^4 + 3*(B*a^3*b - 3*A*a^2*b^2)*e^5)*x^3 + (6*B*a*b^3*d^3*e^2 + 3*(5*B*a^2*b^2 - 3*A*a*b^3)*d^2*e^3 + 2*(4*B*a^3*b - 9*A*a^2*b^2)*d*e^4 + (B*a^4 - 3*A*a^3*b)*e^5)*x^2 + (6*B*a^2*b^2*d^3*e^2 + (7*B*a^3*b - 9*A*a^2*b^2)*d^2*e^3 + 2*(B*a^4 - 3*A*a^3*b)*d*e^4)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (16*A*a^4*e^4 - 4*(B*a*b^3 + 2*A*b^4)*d^4 + 10*(4*B*a^2*b^2 + 5*A*a*b^3)*d^3*e + (247*B*a^3*b - 165*A*a^2*b^2)*d^2*e^2 + 16*(2*B*a^4 - 13*A*a^3*b)*d*e^3 + 105*(2*B*b^4*d*e^3 + (B*a*b^3 - 3*A*b^4)*e^4)*x^4 + 140*(2*B*b^4*d^2*e^2 + (5*B*a*b^3 - 3*A*b^4)*d*e^3 + 2*(B*a^2*b^2 - 3*A*a*b^3)*e^4)*x^3 + 21*(2*B*b^4*d^3*e + (37*B*a*b^3 - 3*A*b^4)*d^2*e^2 + 2*(20*B*a^2*b^2 - 27*A*a*b^3)*d*e^3 + 11*(B*a^3*b - 3*A*a^2*b^2)*e^4)*x^2 - 6*(2*B*b^4*d^4 - (19*B*a*b^3 + 3*A*b^4)*d^3*e - 2*(58*B*a^2*b^2 - 15*A*a*b^3)*d^2*e^2 - 3*(23*B*a^3*b - 53*A*a^2*b^2)*d*e^3 - 8*(B*a^4 - 3*A*a^3*b)*e^4)*x)*sqrt(e*x + d))/(a^3*b^5*d^7 - 5*a^4*b^4*d^6*e + 10*a^5*b^3*d^5*e^2 - 10*a^6*b^2*d^4*e^3 + 5*a^7*b*d^3*e^4 - a^8*d^2*e^5 + (b^8*d^5*e^2 - 5*a*b^7*d^4*e^3 + 10*a^2*b^6*d^3*e^4 - 10*a^3*b^5*d^2*e^5 + 5*a^4*b^4*d*e^6 - a^5*b^3*e^7)*x^5 + (2*b^8*d^6*e - 7*a*b^7*d^5*e^2 + 5*a^2*b^6*d^4*e^3 + 10*a^3*b^5*d^3*e^4 - 20*a^4*b^4*d^2*e^5 + 13*a^5*b^3*d*e^6 - 3*a^6*b^2*e^7)*x^4 + (b^8*d^7 + a*b^7*d^6*e - 17*a^2*b^6*d^5*e^2 + 35*a^3*b^5*d^4*e^3 - 25*a^4*b^4*d^3*e^4 - a^5*b^3*d^2*e^5 + 9*a^6*b^2*d*e^6 - 3*a^7*b*e^7)*x^3 + (3*a*b^7*d^7 - 9*a^2*b^6*d^6*e + a^3*b^5*d^5*e^2 + 25*a^4*b^4*d^4*e^3 - 35*a^5*b^3*d^3*e^4 + 17*a^6*b^2*d^2*e^5 - a^7*b*d*e^6 - a^8*e^7)*x^2 + (3*a^2*b^6*d^7 - 13*a^3*b^5*d^6*e + 20*a^4*b^4*d^5*e^2 - 10*a^5*b^3*d^4*e^3 - 5*a^6*b^2*d^3*e^4 + 7*a^7*b*d^2*e^5 - 2*a^8*d*e^6)*x)]","B",0
1824,1,3685,0,0.509205," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(6 \, B a^{3} b^{2} d^{4} e^{2} + {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d^{3} e^{3} + {\left(6 \, B b^{5} d e^{5} + {\left(5 \, B a b^{4} - 11 \, A b^{5}\right)} e^{6}\right)} x^{6} + 3 \, {\left(6 \, B b^{5} d^{2} e^{4} + 11 \, {\left(B a b^{4} - A b^{5}\right)} d e^{5} + {\left(5 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} e^{6}\right)} x^{5} + 3 \, {\left(6 \, B b^{5} d^{3} e^{3} + {\left(23 \, B a b^{4} - 11 \, A b^{5}\right)} d^{2} e^{4} + 3 \, {\left(7 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} d e^{5} + {\left(5 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{6}\right)} x^{4} + {\left(6 \, B b^{5} d^{4} e^{2} + {\left(59 \, B a b^{4} - 11 \, A b^{5}\right)} d^{3} e^{3} + 99 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d^{2} e^{4} + 3 \, {\left(17 \, B a^{3} b^{2} - 33 \, A a^{2} b^{3}\right)} d e^{5} + {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{3} + 3 \, {\left(6 \, B a b^{4} d^{4} e^{2} + {\left(23 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} d^{3} e^{3} + 3 \, {\left(7 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} d^{2} e^{4} + {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d e^{5}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{3} d^{4} e^{2} + 11 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} d^{3} e^{3} + {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d^{2} e^{4}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(48 \, A a^{5} e^{5} + 20 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{5} - 10 \, {\left(26 \, B a^{2} b^{3} + 31 \, A a b^{4}\right)} d^{4} e - 3 \, {\left(851 \, B a^{3} b^{2} - 445 \, A a^{2} b^{3}\right)} d^{3} e^{2} - 16 \, {\left(44 \, B a^{4} b - 173 \, A a^{3} b^{2}\right)} d^{2} e^{3} + 32 \, {\left(B a^{5} - 13 \, A a^{4} b\right)} d e^{4} - 315 \, {\left(6 \, B b^{5} d e^{4} + {\left(5 \, B a b^{4} - 11 \, A b^{5}\right)} e^{5}\right)} x^{5} - 105 \, {\left(42 \, B b^{5} d^{2} e^{3} + {\left(83 \, B a b^{4} - 77 \, A b^{5}\right)} d e^{4} + 8 \, {\left(5 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} e^{5}\right)} x^{4} - 21 \, {\left(138 \, B b^{5} d^{3} e^{2} + {\left(679 \, B a b^{4} - 253 \, A b^{5}\right)} d^{2} e^{3} + 2 \, {\left(334 \, B a^{2} b^{3} - 517 \, A a b^{4}\right)} d e^{4} + 33 \, {\left(5 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} - 9 \, {\left(30 \, B b^{5} d^{4} e + {\left(901 \, B a b^{4} - 55 \, A b^{5}\right)} d^{3} e^{2} + 2 \, {\left(914 \, B a^{2} b^{3} - 803 \, A a b^{4}\right)} d^{2} e^{3} + 3 \, {\left(337 \, B a^{3} b^{2} - 671 \, A a^{2} b^{3}\right)} d e^{4} + 16 \, {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(60 \, B b^{5} d^{5} - 10 \, {\left(73 \, B a b^{4} + 11 \, A b^{5}\right)} d^{4} e - 2 \, {\left(3682 \, B a^{2} b^{3} - 715 \, A a b^{4}\right)} d^{3} e^{2} - 3 \, {\left(2569 \, B a^{3} b^{2} - 4103 \, A a^{2} b^{3}\right)} d^{2} e^{3} - 32 \, {\left(52 \, B a^{4} b - 121 \, A a^{3} b^{2}\right)} d e^{4} + 16 \, {\left(5 \, B a^{5} - 11 \, A a^{4} b\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{240 \, {\left(a^{3} b^{6} d^{9} - 6 \, a^{4} b^{5} d^{8} e + 15 \, a^{5} b^{4} d^{7} e^{2} - 20 \, a^{6} b^{3} d^{6} e^{3} + 15 \, a^{7} b^{2} d^{5} e^{4} - 6 \, a^{8} b d^{4} e^{5} + a^{9} d^{3} e^{6} + {\left(b^{9} d^{6} e^{3} - 6 \, a b^{8} d^{5} e^{4} + 15 \, a^{2} b^{7} d^{4} e^{5} - 20 \, a^{3} b^{6} d^{3} e^{6} + 15 \, a^{4} b^{5} d^{2} e^{7} - 6 \, a^{5} b^{4} d e^{8} + a^{6} b^{3} e^{9}\right)} x^{6} + 3 \, {\left(b^{9} d^{7} e^{2} - 5 \, a b^{8} d^{6} e^{3} + 9 \, a^{2} b^{7} d^{5} e^{4} - 5 \, a^{3} b^{6} d^{4} e^{5} - 5 \, a^{4} b^{5} d^{3} e^{6} + 9 \, a^{5} b^{4} d^{2} e^{7} - 5 \, a^{6} b^{3} d e^{8} + a^{7} b^{2} e^{9}\right)} x^{5} + 3 \, {\left(b^{9} d^{8} e - 3 \, a b^{8} d^{7} e^{2} - 2 \, a^{2} b^{7} d^{6} e^{3} + 19 \, a^{3} b^{6} d^{5} e^{4} - 30 \, a^{4} b^{5} d^{4} e^{5} + 19 \, a^{5} b^{4} d^{3} e^{6} - 2 \, a^{6} b^{3} d^{2} e^{7} - 3 \, a^{7} b^{2} d e^{8} + a^{8} b e^{9}\right)} x^{4} + {\left(b^{9} d^{9} + 3 \, a b^{8} d^{8} e - 30 \, a^{2} b^{7} d^{7} e^{2} + 62 \, a^{3} b^{6} d^{6} e^{3} - 36 \, a^{4} b^{5} d^{5} e^{4} - 36 \, a^{5} b^{4} d^{4} e^{5} + 62 \, a^{6} b^{3} d^{3} e^{6} - 30 \, a^{7} b^{2} d^{2} e^{7} + 3 \, a^{8} b d e^{8} + a^{9} e^{9}\right)} x^{3} + 3 \, {\left(a b^{8} d^{9} - 3 \, a^{2} b^{7} d^{8} e - 2 \, a^{3} b^{6} d^{7} e^{2} + 19 \, a^{4} b^{5} d^{6} e^{3} - 30 \, a^{5} b^{4} d^{5} e^{4} + 19 \, a^{6} b^{3} d^{4} e^{5} - 2 \, a^{7} b^{2} d^{3} e^{6} - 3 \, a^{8} b d^{2} e^{7} + a^{9} d e^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{9} - 5 \, a^{3} b^{6} d^{8} e + 9 \, a^{4} b^{5} d^{7} e^{2} - 5 \, a^{5} b^{4} d^{6} e^{3} - 5 \, a^{6} b^{3} d^{5} e^{4} + 9 \, a^{7} b^{2} d^{4} e^{5} - 5 \, a^{8} b d^{3} e^{6} + a^{9} d^{2} e^{7}\right)} x\right)}}, -\frac{315 \, {\left(6 \, B a^{3} b^{2} d^{4} e^{2} + {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d^{3} e^{3} + {\left(6 \, B b^{5} d e^{5} + {\left(5 \, B a b^{4} - 11 \, A b^{5}\right)} e^{6}\right)} x^{6} + 3 \, {\left(6 \, B b^{5} d^{2} e^{4} + 11 \, {\left(B a b^{4} - A b^{5}\right)} d e^{5} + {\left(5 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} e^{6}\right)} x^{5} + 3 \, {\left(6 \, B b^{5} d^{3} e^{3} + {\left(23 \, B a b^{4} - 11 \, A b^{5}\right)} d^{2} e^{4} + 3 \, {\left(7 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} d e^{5} + {\left(5 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{6}\right)} x^{4} + {\left(6 \, B b^{5} d^{4} e^{2} + {\left(59 \, B a b^{4} - 11 \, A b^{5}\right)} d^{3} e^{3} + 99 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d^{2} e^{4} + 3 \, {\left(17 \, B a^{3} b^{2} - 33 \, A a^{2} b^{3}\right)} d e^{5} + {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{3} + 3 \, {\left(6 \, B a b^{4} d^{4} e^{2} + {\left(23 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} d^{3} e^{3} + 3 \, {\left(7 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} d^{2} e^{4} + {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d e^{5}\right)} x^{2} + 3 \, {\left(6 \, B a^{2} b^{3} d^{4} e^{2} + 11 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} d^{3} e^{3} + {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d^{2} e^{4}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) + {\left(48 \, A a^{5} e^{5} + 20 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{5} - 10 \, {\left(26 \, B a^{2} b^{3} + 31 \, A a b^{4}\right)} d^{4} e - 3 \, {\left(851 \, B a^{3} b^{2} - 445 \, A a^{2} b^{3}\right)} d^{3} e^{2} - 16 \, {\left(44 \, B a^{4} b - 173 \, A a^{3} b^{2}\right)} d^{2} e^{3} + 32 \, {\left(B a^{5} - 13 \, A a^{4} b\right)} d e^{4} - 315 \, {\left(6 \, B b^{5} d e^{4} + {\left(5 \, B a b^{4} - 11 \, A b^{5}\right)} e^{5}\right)} x^{5} - 105 \, {\left(42 \, B b^{5} d^{2} e^{3} + {\left(83 \, B a b^{4} - 77 \, A b^{5}\right)} d e^{4} + 8 \, {\left(5 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} e^{5}\right)} x^{4} - 21 \, {\left(138 \, B b^{5} d^{3} e^{2} + {\left(679 \, B a b^{4} - 253 \, A b^{5}\right)} d^{2} e^{3} + 2 \, {\left(334 \, B a^{2} b^{3} - 517 \, A a b^{4}\right)} d e^{4} + 33 \, {\left(5 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} - 9 \, {\left(30 \, B b^{5} d^{4} e + {\left(901 \, B a b^{4} - 55 \, A b^{5}\right)} d^{3} e^{2} + 2 \, {\left(914 \, B a^{2} b^{3} - 803 \, A a b^{4}\right)} d^{2} e^{3} + 3 \, {\left(337 \, B a^{3} b^{2} - 671 \, A a^{2} b^{3}\right)} d e^{4} + 16 \, {\left(5 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(60 \, B b^{5} d^{5} - 10 \, {\left(73 \, B a b^{4} + 11 \, A b^{5}\right)} d^{4} e - 2 \, {\left(3682 \, B a^{2} b^{3} - 715 \, A a b^{4}\right)} d^{3} e^{2} - 3 \, {\left(2569 \, B a^{3} b^{2} - 4103 \, A a^{2} b^{3}\right)} d^{2} e^{3} - 32 \, {\left(52 \, B a^{4} b - 121 \, A a^{3} b^{2}\right)} d e^{4} + 16 \, {\left(5 \, B a^{5} - 11 \, A a^{4} b\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{120 \, {\left(a^{3} b^{6} d^{9} - 6 \, a^{4} b^{5} d^{8} e + 15 \, a^{5} b^{4} d^{7} e^{2} - 20 \, a^{6} b^{3} d^{6} e^{3} + 15 \, a^{7} b^{2} d^{5} e^{4} - 6 \, a^{8} b d^{4} e^{5} + a^{9} d^{3} e^{6} + {\left(b^{9} d^{6} e^{3} - 6 \, a b^{8} d^{5} e^{4} + 15 \, a^{2} b^{7} d^{4} e^{5} - 20 \, a^{3} b^{6} d^{3} e^{6} + 15 \, a^{4} b^{5} d^{2} e^{7} - 6 \, a^{5} b^{4} d e^{8} + a^{6} b^{3} e^{9}\right)} x^{6} + 3 \, {\left(b^{9} d^{7} e^{2} - 5 \, a b^{8} d^{6} e^{3} + 9 \, a^{2} b^{7} d^{5} e^{4} - 5 \, a^{3} b^{6} d^{4} e^{5} - 5 \, a^{4} b^{5} d^{3} e^{6} + 9 \, a^{5} b^{4} d^{2} e^{7} - 5 \, a^{6} b^{3} d e^{8} + a^{7} b^{2} e^{9}\right)} x^{5} + 3 \, {\left(b^{9} d^{8} e - 3 \, a b^{8} d^{7} e^{2} - 2 \, a^{2} b^{7} d^{6} e^{3} + 19 \, a^{3} b^{6} d^{5} e^{4} - 30 \, a^{4} b^{5} d^{4} e^{5} + 19 \, a^{5} b^{4} d^{3} e^{6} - 2 \, a^{6} b^{3} d^{2} e^{7} - 3 \, a^{7} b^{2} d e^{8} + a^{8} b e^{9}\right)} x^{4} + {\left(b^{9} d^{9} + 3 \, a b^{8} d^{8} e - 30 \, a^{2} b^{7} d^{7} e^{2} + 62 \, a^{3} b^{6} d^{6} e^{3} - 36 \, a^{4} b^{5} d^{5} e^{4} - 36 \, a^{5} b^{4} d^{4} e^{5} + 62 \, a^{6} b^{3} d^{3} e^{6} - 30 \, a^{7} b^{2} d^{2} e^{7} + 3 \, a^{8} b d e^{8} + a^{9} e^{9}\right)} x^{3} + 3 \, {\left(a b^{8} d^{9} - 3 \, a^{2} b^{7} d^{8} e - 2 \, a^{3} b^{6} d^{7} e^{2} + 19 \, a^{4} b^{5} d^{6} e^{3} - 30 \, a^{5} b^{4} d^{5} e^{4} + 19 \, a^{6} b^{3} d^{4} e^{5} - 2 \, a^{7} b^{2} d^{3} e^{6} - 3 \, a^{8} b d^{2} e^{7} + a^{9} d e^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{9} - 5 \, a^{3} b^{6} d^{8} e + 9 \, a^{4} b^{5} d^{7} e^{2} - 5 \, a^{5} b^{4} d^{6} e^{3} - 5 \, a^{6} b^{3} d^{5} e^{4} + 9 \, a^{7} b^{2} d^{4} e^{5} - 5 \, a^{8} b d^{3} e^{6} + a^{9} d^{2} e^{7}\right)} x\right)}}\right]"," ",0,"[-1/240*(315*(6*B*a^3*b^2*d^4*e^2 + (5*B*a^4*b - 11*A*a^3*b^2)*d^3*e^3 + (6*B*b^5*d*e^5 + (5*B*a*b^4 - 11*A*b^5)*e^6)*x^6 + 3*(6*B*b^5*d^2*e^4 + 11*(B*a*b^4 - A*b^5)*d*e^5 + (5*B*a^2*b^3 - 11*A*a*b^4)*e^6)*x^5 + 3*(6*B*b^5*d^3*e^3 + (23*B*a*b^4 - 11*A*b^5)*d^2*e^4 + 3*(7*B*a^2*b^3 - 11*A*a*b^4)*d*e^5 + (5*B*a^3*b^2 - 11*A*a^2*b^3)*e^6)*x^4 + (6*B*b^5*d^4*e^2 + (59*B*a*b^4 - 11*A*b^5)*d^3*e^3 + 99*(B*a^2*b^3 - A*a*b^4)*d^2*e^4 + 3*(17*B*a^3*b^2 - 33*A*a^2*b^3)*d*e^5 + (5*B*a^4*b - 11*A*a^3*b^2)*e^6)*x^3 + 3*(6*B*a*b^4*d^4*e^2 + (23*B*a^2*b^3 - 11*A*a*b^4)*d^3*e^3 + 3*(7*B*a^3*b^2 - 11*A*a^2*b^3)*d^2*e^4 + (5*B*a^4*b - 11*A*a^3*b^2)*d*e^5)*x^2 + 3*(6*B*a^2*b^3*d^4*e^2 + 11*(B*a^3*b^2 - A*a^2*b^3)*d^3*e^3 + (5*B*a^4*b - 11*A*a^3*b^2)*d^2*e^4)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(48*A*a^5*e^5 + 20*(B*a*b^4 + 2*A*b^5)*d^5 - 10*(26*B*a^2*b^3 + 31*A*a*b^4)*d^4*e - 3*(851*B*a^3*b^2 - 445*A*a^2*b^3)*d^3*e^2 - 16*(44*B*a^4*b - 173*A*a^3*b^2)*d^2*e^3 + 32*(B*a^5 - 13*A*a^4*b)*d*e^4 - 315*(6*B*b^5*d*e^4 + (5*B*a*b^4 - 11*A*b^5)*e^5)*x^5 - 105*(42*B*b^5*d^2*e^3 + (83*B*a*b^4 - 77*A*b^5)*d*e^4 + 8*(5*B*a^2*b^3 - 11*A*a*b^4)*e^5)*x^4 - 21*(138*B*b^5*d^3*e^2 + (679*B*a*b^4 - 253*A*b^5)*d^2*e^3 + 2*(334*B*a^2*b^3 - 517*A*a*b^4)*d*e^4 + 33*(5*B*a^3*b^2 - 11*A*a^2*b^3)*e^5)*x^3 - 9*(30*B*b^5*d^4*e + (901*B*a*b^4 - 55*A*b^5)*d^3*e^2 + 2*(914*B*a^2*b^3 - 803*A*a*b^4)*d^2*e^3 + 3*(337*B*a^3*b^2 - 671*A*a^2*b^3)*d*e^4 + 16*(5*B*a^4*b - 11*A*a^3*b^2)*e^5)*x^2 + (60*B*b^5*d^5 - 10*(73*B*a*b^4 + 11*A*b^5)*d^4*e - 2*(3682*B*a^2*b^3 - 715*A*a*b^4)*d^3*e^2 - 3*(2569*B*a^3*b^2 - 4103*A*a^2*b^3)*d^2*e^3 - 32*(52*B*a^4*b - 121*A*a^3*b^2)*d*e^4 + 16*(5*B*a^5 - 11*A*a^4*b)*e^5)*x)*sqrt(e*x + d))/(a^3*b^6*d^9 - 6*a^4*b^5*d^8*e + 15*a^5*b^4*d^7*e^2 - 20*a^6*b^3*d^6*e^3 + 15*a^7*b^2*d^5*e^4 - 6*a^8*b*d^4*e^5 + a^9*d^3*e^6 + (b^9*d^6*e^3 - 6*a*b^8*d^5*e^4 + 15*a^2*b^7*d^4*e^5 - 20*a^3*b^6*d^3*e^6 + 15*a^4*b^5*d^2*e^7 - 6*a^5*b^4*d*e^8 + a^6*b^3*e^9)*x^6 + 3*(b^9*d^7*e^2 - 5*a*b^8*d^6*e^3 + 9*a^2*b^7*d^5*e^4 - 5*a^3*b^6*d^4*e^5 - 5*a^4*b^5*d^3*e^6 + 9*a^5*b^4*d^2*e^7 - 5*a^6*b^3*d*e^8 + a^7*b^2*e^9)*x^5 + 3*(b^9*d^8*e - 3*a*b^8*d^7*e^2 - 2*a^2*b^7*d^6*e^3 + 19*a^3*b^6*d^5*e^4 - 30*a^4*b^5*d^4*e^5 + 19*a^5*b^4*d^3*e^6 - 2*a^6*b^3*d^2*e^7 - 3*a^7*b^2*d*e^8 + a^8*b*e^9)*x^4 + (b^9*d^9 + 3*a*b^8*d^8*e - 30*a^2*b^7*d^7*e^2 + 62*a^3*b^6*d^6*e^3 - 36*a^4*b^5*d^5*e^4 - 36*a^5*b^4*d^4*e^5 + 62*a^6*b^3*d^3*e^6 - 30*a^7*b^2*d^2*e^7 + 3*a^8*b*d*e^8 + a^9*e^9)*x^3 + 3*(a*b^8*d^9 - 3*a^2*b^7*d^8*e - 2*a^3*b^6*d^7*e^2 + 19*a^4*b^5*d^6*e^3 - 30*a^5*b^4*d^5*e^4 + 19*a^6*b^3*d^4*e^5 - 2*a^7*b^2*d^3*e^6 - 3*a^8*b*d^2*e^7 + a^9*d*e^8)*x^2 + 3*(a^2*b^7*d^9 - 5*a^3*b^6*d^8*e + 9*a^4*b^5*d^7*e^2 - 5*a^5*b^4*d^6*e^3 - 5*a^6*b^3*d^5*e^4 + 9*a^7*b^2*d^4*e^5 - 5*a^8*b*d^3*e^6 + a^9*d^2*e^7)*x), -1/120*(315*(6*B*a^3*b^2*d^4*e^2 + (5*B*a^4*b - 11*A*a^3*b^2)*d^3*e^3 + (6*B*b^5*d*e^5 + (5*B*a*b^4 - 11*A*b^5)*e^6)*x^6 + 3*(6*B*b^5*d^2*e^4 + 11*(B*a*b^4 - A*b^5)*d*e^5 + (5*B*a^2*b^3 - 11*A*a*b^4)*e^6)*x^5 + 3*(6*B*b^5*d^3*e^3 + (23*B*a*b^4 - 11*A*b^5)*d^2*e^4 + 3*(7*B*a^2*b^3 - 11*A*a*b^4)*d*e^5 + (5*B*a^3*b^2 - 11*A*a^2*b^3)*e^6)*x^4 + (6*B*b^5*d^4*e^2 + (59*B*a*b^4 - 11*A*b^5)*d^3*e^3 + 99*(B*a^2*b^3 - A*a*b^4)*d^2*e^4 + 3*(17*B*a^3*b^2 - 33*A*a^2*b^3)*d*e^5 + (5*B*a^4*b - 11*A*a^3*b^2)*e^6)*x^3 + 3*(6*B*a*b^4*d^4*e^2 + (23*B*a^2*b^3 - 11*A*a*b^4)*d^3*e^3 + 3*(7*B*a^3*b^2 - 11*A*a^2*b^3)*d^2*e^4 + (5*B*a^4*b - 11*A*a^3*b^2)*d*e^5)*x^2 + 3*(6*B*a^2*b^3*d^4*e^2 + 11*(B*a^3*b^2 - A*a^2*b^3)*d^3*e^3 + (5*B*a^4*b - 11*A*a^3*b^2)*d^2*e^4)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) + (48*A*a^5*e^5 + 20*(B*a*b^4 + 2*A*b^5)*d^5 - 10*(26*B*a^2*b^3 + 31*A*a*b^4)*d^4*e - 3*(851*B*a^3*b^2 - 445*A*a^2*b^3)*d^3*e^2 - 16*(44*B*a^4*b - 173*A*a^3*b^2)*d^2*e^3 + 32*(B*a^5 - 13*A*a^4*b)*d*e^4 - 315*(6*B*b^5*d*e^4 + (5*B*a*b^4 - 11*A*b^5)*e^5)*x^5 - 105*(42*B*b^5*d^2*e^3 + (83*B*a*b^4 - 77*A*b^5)*d*e^4 + 8*(5*B*a^2*b^3 - 11*A*a*b^4)*e^5)*x^4 - 21*(138*B*b^5*d^3*e^2 + (679*B*a*b^4 - 253*A*b^5)*d^2*e^3 + 2*(334*B*a^2*b^3 - 517*A*a*b^4)*d*e^4 + 33*(5*B*a^3*b^2 - 11*A*a^2*b^3)*e^5)*x^3 - 9*(30*B*b^5*d^4*e + (901*B*a*b^4 - 55*A*b^5)*d^3*e^2 + 2*(914*B*a^2*b^3 - 803*A*a*b^4)*d^2*e^3 + 3*(337*B*a^3*b^2 - 671*A*a^2*b^3)*d*e^4 + 16*(5*B*a^4*b - 11*A*a^3*b^2)*e^5)*x^2 + (60*B*b^5*d^5 - 10*(73*B*a*b^4 + 11*A*b^5)*d^4*e - 2*(3682*B*a^2*b^3 - 715*A*a*b^4)*d^3*e^2 - 3*(2569*B*a^3*b^2 - 4103*A*a^2*b^3)*d^2*e^3 - 32*(52*B*a^4*b - 121*A*a^3*b^2)*d*e^4 + 16*(5*B*a^5 - 11*A*a^4*b)*e^5)*x)*sqrt(e*x + d))/(a^3*b^6*d^9 - 6*a^4*b^5*d^8*e + 15*a^5*b^4*d^7*e^2 - 20*a^6*b^3*d^6*e^3 + 15*a^7*b^2*d^5*e^4 - 6*a^8*b*d^4*e^5 + a^9*d^3*e^6 + (b^9*d^6*e^3 - 6*a*b^8*d^5*e^4 + 15*a^2*b^7*d^4*e^5 - 20*a^3*b^6*d^3*e^6 + 15*a^4*b^5*d^2*e^7 - 6*a^5*b^4*d*e^8 + a^6*b^3*e^9)*x^6 + 3*(b^9*d^7*e^2 - 5*a*b^8*d^6*e^3 + 9*a^2*b^7*d^5*e^4 - 5*a^3*b^6*d^4*e^5 - 5*a^4*b^5*d^3*e^6 + 9*a^5*b^4*d^2*e^7 - 5*a^6*b^3*d*e^8 + a^7*b^2*e^9)*x^5 + 3*(b^9*d^8*e - 3*a*b^8*d^7*e^2 - 2*a^2*b^7*d^6*e^3 + 19*a^3*b^6*d^5*e^4 - 30*a^4*b^5*d^4*e^5 + 19*a^5*b^4*d^3*e^6 - 2*a^6*b^3*d^2*e^7 - 3*a^7*b^2*d*e^8 + a^8*b*e^9)*x^4 + (b^9*d^9 + 3*a*b^8*d^8*e - 30*a^2*b^7*d^7*e^2 + 62*a^3*b^6*d^6*e^3 - 36*a^4*b^5*d^5*e^4 - 36*a^5*b^4*d^4*e^5 + 62*a^6*b^3*d^3*e^6 - 30*a^7*b^2*d^2*e^7 + 3*a^8*b*d*e^8 + a^9*e^9)*x^3 + 3*(a*b^8*d^9 - 3*a^2*b^7*d^8*e - 2*a^3*b^6*d^7*e^2 + 19*a^4*b^5*d^6*e^3 - 30*a^5*b^4*d^5*e^4 + 19*a^6*b^3*d^4*e^5 - 2*a^7*b^2*d^3*e^6 - 3*a^8*b*d^2*e^7 + a^9*d*e^8)*x^2 + 3*(a^2*b^7*d^9 - 5*a^3*b^6*d^8*e + 9*a^4*b^5*d^7*e^2 - 5*a^5*b^4*d^6*e^3 - 5*a^6*b^3*d^5*e^4 + 9*a^7*b^2*d^4*e^5 - 5*a^8*b*d^3*e^6 + a^9*d^2*e^7)*x)]","B",0
1825,1,1862,0,0.487149," ","integrate((B*x+A)*(e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left(10 \, B a^{5} b d e^{4} - {\left(13 \, B a^{6} - 3 \, A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(13 \, B a b^{5} - 3 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(13 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(13 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(13 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(13 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(1280 \, B b^{6} e^{5} x^{6} - 96 \, {\left(B a b^{5} + 4 \, A b^{6}\right)} d^{5} - 176 \, {\left(2 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} d^{4} e - 396 \, {\left(3 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4}\right)} d^{3} e^{2} - 1386 \, {\left(4 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} d^{2} e^{3} + 1155 \, {\left(43 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} d e^{4} - 3465 \, {\left(13 \, B a^{6} - 3 \, A a^{5} b\right)} e^{5} + 1280 \, {\left(16 \, B b^{6} d e^{4} - {\left(13 \, B a b^{5} - 3 \, A b^{6}\right)} e^{5}\right)} x^{5} - 5 \, {\left(4590 \, B b^{6} d^{2} e^{3} - {\left(32189 \, B a b^{5} - 2529 \, A b^{6}\right)} d e^{4} + 2123 \, {\left(13 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} e^{5}\right)} x^{4} - 10 \, {\left(1030 \, B b^{6} d^{3} e^{2} + 3 \, {\left(1671 \, B a b^{5} + 359 \, A b^{6}\right)} d^{2} e^{3} - 22 \, {\left(1757 \, B a^{2} b^{4} - 132 \, A a b^{5}\right)} d e^{4} + 2607 \, {\left(13 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} - 2 \, {\left(1640 \, B b^{6} d^{4} e + 2 \, {\left(2759 \, B a b^{5} + 1686 \, A b^{6}\right)} d^{3} e^{2} + 33 \, {\left(797 \, B a^{2} b^{4} + 183 \, A a b^{5}\right)} d^{2} e^{3} - 33 \, {\left(6547 \, B a^{3} b^{3} - 477 \, A a^{2} b^{4}\right)} d e^{4} + 14784 \, {\left(13 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} - 2 \, {\left(240 \, B b^{6} d^{5} + 8 \, {\left(107 \, B a b^{5} + 153 \, A b^{6}\right)} d^{4} e + 22 \, {\left(131 \, B a^{2} b^{4} + 84 \, A a b^{5}\right)} d^{3} e^{2} + 99 \, {\left(137 \, B a^{3} b^{3} + 33 \, A a^{2} b^{4}\right)} d^{2} e^{3} - 462 \, {\left(253 \, B a^{4} b^{2} - 18 \, A a^{3} b^{3}\right)} d e^{4} + 8085 \, {\left(13 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(b^{12} x^{5} + 5 \, a b^{11} x^{4} + 10 \, a^{2} b^{10} x^{3} + 10 \, a^{3} b^{9} x^{2} + 5 \, a^{4} b^{8} x + a^{5} b^{7}\right)}}, -\frac{3465 \, {\left(10 \, B a^{5} b d e^{4} - {\left(13 \, B a^{6} - 3 \, A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(13 \, B a b^{5} - 3 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(13 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(13 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(13 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(13 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(1280 \, B b^{6} e^{5} x^{6} - 96 \, {\left(B a b^{5} + 4 \, A b^{6}\right)} d^{5} - 176 \, {\left(2 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} d^{4} e - 396 \, {\left(3 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4}\right)} d^{3} e^{2} - 1386 \, {\left(4 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} d^{2} e^{3} + 1155 \, {\left(43 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} d e^{4} - 3465 \, {\left(13 \, B a^{6} - 3 \, A a^{5} b\right)} e^{5} + 1280 \, {\left(16 \, B b^{6} d e^{4} - {\left(13 \, B a b^{5} - 3 \, A b^{6}\right)} e^{5}\right)} x^{5} - 5 \, {\left(4590 \, B b^{6} d^{2} e^{3} - {\left(32189 \, B a b^{5} - 2529 \, A b^{6}\right)} d e^{4} + 2123 \, {\left(13 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} e^{5}\right)} x^{4} - 10 \, {\left(1030 \, B b^{6} d^{3} e^{2} + 3 \, {\left(1671 \, B a b^{5} + 359 \, A b^{6}\right)} d^{2} e^{3} - 22 \, {\left(1757 \, B a^{2} b^{4} - 132 \, A a b^{5}\right)} d e^{4} + 2607 \, {\left(13 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} - 2 \, {\left(1640 \, B b^{6} d^{4} e + 2 \, {\left(2759 \, B a b^{5} + 1686 \, A b^{6}\right)} d^{3} e^{2} + 33 \, {\left(797 \, B a^{2} b^{4} + 183 \, A a b^{5}\right)} d^{2} e^{3} - 33 \, {\left(6547 \, B a^{3} b^{3} - 477 \, A a^{2} b^{4}\right)} d e^{4} + 14784 \, {\left(13 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} - 2 \, {\left(240 \, B b^{6} d^{5} + 8 \, {\left(107 \, B a b^{5} + 153 \, A b^{6}\right)} d^{4} e + 22 \, {\left(131 \, B a^{2} b^{4} + 84 \, A a b^{5}\right)} d^{3} e^{2} + 99 \, {\left(137 \, B a^{3} b^{3} + 33 \, A a^{2} b^{4}\right)} d^{2} e^{3} - 462 \, {\left(253 \, B a^{4} b^{2} - 18 \, A a^{3} b^{3}\right)} d e^{4} + 8085 \, {\left(13 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(b^{12} x^{5} + 5 \, a b^{11} x^{4} + 10 \, a^{2} b^{10} x^{3} + 10 \, a^{3} b^{9} x^{2} + 5 \, a^{4} b^{8} x + a^{5} b^{7}\right)}}\right]"," ",0,"[-1/3840*(3465*(10*B*a^5*b*d*e^4 - (13*B*a^6 - 3*A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (13*B*a*b^5 - 3*A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (13*B*a^2*b^4 - 3*A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (13*B*a^3*b^3 - 3*A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (13*B*a^4*b^2 - 3*A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (13*B*a^5*b - 3*A*a^4*b^2)*e^5)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(1280*B*b^6*e^5*x^6 - 96*(B*a*b^5 + 4*A*b^6)*d^5 - 176*(2*B*a^2*b^4 + 3*A*a*b^5)*d^4*e - 396*(3*B*a^3*b^3 + 2*A*a^2*b^4)*d^3*e^2 - 1386*(4*B*a^4*b^2 + A*a^3*b^3)*d^2*e^3 + 1155*(43*B*a^5*b - 3*A*a^4*b^2)*d*e^4 - 3465*(13*B*a^6 - 3*A*a^5*b)*e^5 + 1280*(16*B*b^6*d*e^4 - (13*B*a*b^5 - 3*A*b^6)*e^5)*x^5 - 5*(4590*B*b^6*d^2*e^3 - (32189*B*a*b^5 - 2529*A*b^6)*d*e^4 + 2123*(13*B*a^2*b^4 - 3*A*a*b^5)*e^5)*x^4 - 10*(1030*B*b^6*d^3*e^2 + 3*(1671*B*a*b^5 + 359*A*b^6)*d^2*e^3 - 22*(1757*B*a^2*b^4 - 132*A*a*b^5)*d*e^4 + 2607*(13*B*a^3*b^3 - 3*A*a^2*b^4)*e^5)*x^3 - 2*(1640*B*b^6*d^4*e + 2*(2759*B*a*b^5 + 1686*A*b^6)*d^3*e^2 + 33*(797*B*a^2*b^4 + 183*A*a*b^5)*d^2*e^3 - 33*(6547*B*a^3*b^3 - 477*A*a^2*b^4)*d*e^4 + 14784*(13*B*a^4*b^2 - 3*A*a^3*b^3)*e^5)*x^2 - 2*(240*B*b^6*d^5 + 8*(107*B*a*b^5 + 153*A*b^6)*d^4*e + 22*(131*B*a^2*b^4 + 84*A*a*b^5)*d^3*e^2 + 99*(137*B*a^3*b^3 + 33*A*a^2*b^4)*d^2*e^3 - 462*(253*B*a^4*b^2 - 18*A*a^3*b^3)*d*e^4 + 8085*(13*B*a^5*b - 3*A*a^4*b^2)*e^5)*x)*sqrt(e*x + d))/(b^12*x^5 + 5*a*b^11*x^4 + 10*a^2*b^10*x^3 + 10*a^3*b^9*x^2 + 5*a^4*b^8*x + a^5*b^7), -1/1920*(3465*(10*B*a^5*b*d*e^4 - (13*B*a^6 - 3*A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (13*B*a*b^5 - 3*A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (13*B*a^2*b^4 - 3*A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (13*B*a^3*b^3 - 3*A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (13*B*a^4*b^2 - 3*A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (13*B*a^5*b - 3*A*a^4*b^2)*e^5)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (1280*B*b^6*e^5*x^6 - 96*(B*a*b^5 + 4*A*b^6)*d^5 - 176*(2*B*a^2*b^4 + 3*A*a*b^5)*d^4*e - 396*(3*B*a^3*b^3 + 2*A*a^2*b^4)*d^3*e^2 - 1386*(4*B*a^4*b^2 + A*a^3*b^3)*d^2*e^3 + 1155*(43*B*a^5*b - 3*A*a^4*b^2)*d*e^4 - 3465*(13*B*a^6 - 3*A*a^5*b)*e^5 + 1280*(16*B*b^6*d*e^4 - (13*B*a*b^5 - 3*A*b^6)*e^5)*x^5 - 5*(4590*B*b^6*d^2*e^3 - (32189*B*a*b^5 - 2529*A*b^6)*d*e^4 + 2123*(13*B*a^2*b^4 - 3*A*a*b^5)*e^5)*x^4 - 10*(1030*B*b^6*d^3*e^2 + 3*(1671*B*a*b^5 + 359*A*b^6)*d^2*e^3 - 22*(1757*B*a^2*b^4 - 132*A*a*b^5)*d*e^4 + 2607*(13*B*a^3*b^3 - 3*A*a^2*b^4)*e^5)*x^3 - 2*(1640*B*b^6*d^4*e + 2*(2759*B*a*b^5 + 1686*A*b^6)*d^3*e^2 + 33*(797*B*a^2*b^4 + 183*A*a*b^5)*d^2*e^3 - 33*(6547*B*a^3*b^3 - 477*A*a^2*b^4)*d*e^4 + 14784*(13*B*a^4*b^2 - 3*A*a^3*b^3)*e^5)*x^2 - 2*(240*B*b^6*d^5 + 8*(107*B*a*b^5 + 153*A*b^6)*d^4*e + 22*(131*B*a^2*b^4 + 84*A*a*b^5)*d^3*e^2 + 99*(137*B*a^3*b^3 + 33*A*a^2*b^4)*d^2*e^3 - 462*(253*B*a^4*b^2 - 18*A*a^3*b^3)*d*e^4 + 8085*(13*B*a^5*b - 3*A*a^4*b^2)*e^5)*x)*sqrt(e*x + d))/(b^12*x^5 + 5*a*b^11*x^4 + 10*a^2*b^10*x^3 + 10*a^3*b^9*x^2 + 5*a^4*b^8*x + a^5*b^7)]","B",0
1826,1,1955,0,0.493752," ","integrate((B*x+A)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(10 \, B a^{5} b d e^{4} - {\left(11 \, B a^{6} - A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(11 \, B a b^{5} - A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(11 \, B a^{2} b^{4} - A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(11 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(11 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(11 \, B a^{5} b - A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(32 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} + 16 \, {\left(4 \, B a^{2} b^{5} + A a b^{6}\right)} d^{4} e + 12 \, {\left(13 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5}\right)} d^{3} e^{2} + 42 \, {\left(14 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} d^{2} e^{3} - 105 \, {\left(41 \, B a^{5} b^{2} - A a^{4} b^{3}\right)} d e^{4} + 315 \, {\left(11 \, B a^{6} b - A a^{5} b^{2}\right)} e^{5} - 1280 \, {\left(B b^{7} d e^{4} - B a b^{6} e^{5}\right)} x^{5} + 5 \, {\left(650 \, B b^{7} d^{2} e^{3} - {\left(2773 \, B a b^{6} - 193 \, A b^{7}\right)} d e^{4} + 193 \, {\left(11 \, B a^{2} b^{5} - A a b^{6}\right)} e^{5}\right)} x^{4} + 10 \, {\left(210 \, B b^{7} d^{3} e^{2} + {\left(521 \, B a b^{6} + 149 \, A b^{7}\right)} d^{2} e^{3} - 2 \, {\left(1669 \, B a^{2} b^{5} - 44 \, A a b^{6}\right)} d e^{4} + 237 \, {\left(11 \, B a^{3} b^{4} - A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(440 \, B b^{7} d^{4} e + 2 \, {\left(353 \, B a b^{6} + 342 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(919 \, B a^{2} b^{5} + 61 \, A a b^{6}\right)} d^{2} e^{3} - 3 \, {\left(6229 \, B a^{3} b^{4} - 159 \, A a^{2} b^{5}\right)} d e^{4} + 1344 \, {\left(11 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(80 \, B b^{7} d^{5} + 8 \, {\left(19 \, B a b^{6} + 41 \, A b^{7}\right)} d^{4} e + 2 \, {\left(187 \, B a^{2} b^{5} + 28 \, A a b^{6}\right)} d^{3} e^{2} + 9 \, {\left(159 \, B a^{3} b^{4} + 11 \, A a^{2} b^{5}\right)} d^{2} e^{3} - 42 \, {\left(241 \, B a^{4} b^{3} - 6 \, A a^{3} b^{4}\right)} d e^{4} + 735 \, {\left(11 \, B a^{5} b^{2} - A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(a^{5} b^{8} d - a^{6} b^{7} e + {\left(b^{13} d - a b^{12} e\right)} x^{5} + 5 \, {\left(a b^{12} d - a^{2} b^{11} e\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d - a^{3} b^{10} e\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d - a^{4} b^{9} e\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d - a^{5} b^{8} e\right)} x\right)}}, \frac{315 \, {\left(10 \, B a^{5} b d e^{4} - {\left(11 \, B a^{6} - A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(11 \, B a b^{5} - A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(11 \, B a^{2} b^{4} - A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(11 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(11 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(11 \, B a^{5} b - A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(32 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} + 16 \, {\left(4 \, B a^{2} b^{5} + A a b^{6}\right)} d^{4} e + 12 \, {\left(13 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5}\right)} d^{3} e^{2} + 42 \, {\left(14 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} d^{2} e^{3} - 105 \, {\left(41 \, B a^{5} b^{2} - A a^{4} b^{3}\right)} d e^{4} + 315 \, {\left(11 \, B a^{6} b - A a^{5} b^{2}\right)} e^{5} - 1280 \, {\left(B b^{7} d e^{4} - B a b^{6} e^{5}\right)} x^{5} + 5 \, {\left(650 \, B b^{7} d^{2} e^{3} - {\left(2773 \, B a b^{6} - 193 \, A b^{7}\right)} d e^{4} + 193 \, {\left(11 \, B a^{2} b^{5} - A a b^{6}\right)} e^{5}\right)} x^{4} + 10 \, {\left(210 \, B b^{7} d^{3} e^{2} + {\left(521 \, B a b^{6} + 149 \, A b^{7}\right)} d^{2} e^{3} - 2 \, {\left(1669 \, B a^{2} b^{5} - 44 \, A a b^{6}\right)} d e^{4} + 237 \, {\left(11 \, B a^{3} b^{4} - A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(440 \, B b^{7} d^{4} e + 2 \, {\left(353 \, B a b^{6} + 342 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(919 \, B a^{2} b^{5} + 61 \, A a b^{6}\right)} d^{2} e^{3} - 3 \, {\left(6229 \, B a^{3} b^{4} - 159 \, A a^{2} b^{5}\right)} d e^{4} + 1344 \, {\left(11 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(80 \, B b^{7} d^{5} + 8 \, {\left(19 \, B a b^{6} + 41 \, A b^{7}\right)} d^{4} e + 2 \, {\left(187 \, B a^{2} b^{5} + 28 \, A a b^{6}\right)} d^{3} e^{2} + 9 \, {\left(159 \, B a^{3} b^{4} + 11 \, A a^{2} b^{5}\right)} d^{2} e^{3} - 42 \, {\left(241 \, B a^{4} b^{3} - 6 \, A a^{3} b^{4}\right)} d e^{4} + 735 \, {\left(11 \, B a^{5} b^{2} - A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(a^{5} b^{8} d - a^{6} b^{7} e + {\left(b^{13} d - a b^{12} e\right)} x^{5} + 5 \, {\left(a b^{12} d - a^{2} b^{11} e\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d - a^{3} b^{10} e\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d - a^{4} b^{9} e\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d - a^{5} b^{8} e\right)} x\right)}}\right]"," ",0,"[1/1280*(315*(10*B*a^5*b*d*e^4 - (11*B*a^6 - A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (11*B*a*b^5 - A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (11*B*a^2*b^4 - A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (11*B*a^3*b^3 - A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (11*B*a^4*b^2 - A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (11*B*a^5*b - A*a^4*b^2)*e^5)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(32*(B*a*b^6 + 4*A*b^7)*d^5 + 16*(4*B*a^2*b^5 + A*a*b^6)*d^4*e + 12*(13*B*a^3*b^4 + 2*A*a^2*b^5)*d^3*e^2 + 42*(14*B*a^4*b^3 + A*a^3*b^4)*d^2*e^3 - 105*(41*B*a^5*b^2 - A*a^4*b^3)*d*e^4 + 315*(11*B*a^6*b - A*a^5*b^2)*e^5 - 1280*(B*b^7*d*e^4 - B*a*b^6*e^5)*x^5 + 5*(650*B*b^7*d^2*e^3 - (2773*B*a*b^6 - 193*A*b^7)*d*e^4 + 193*(11*B*a^2*b^5 - A*a*b^6)*e^5)*x^4 + 10*(210*B*b^7*d^3*e^2 + (521*B*a*b^6 + 149*A*b^7)*d^2*e^3 - 2*(1669*B*a^2*b^5 - 44*A*a*b^6)*d*e^4 + 237*(11*B*a^3*b^4 - A*a^2*b^5)*e^5)*x^3 + 2*(440*B*b^7*d^4*e + 2*(353*B*a*b^6 + 342*A*b^7)*d^3*e^2 + 3*(919*B*a^2*b^5 + 61*A*a*b^6)*d^2*e^3 - 3*(6229*B*a^3*b^4 - 159*A*a^2*b^5)*d*e^4 + 1344*(11*B*a^4*b^3 - A*a^3*b^4)*e^5)*x^2 + 2*(80*B*b^7*d^5 + 8*(19*B*a*b^6 + 41*A*b^7)*d^4*e + 2*(187*B*a^2*b^5 + 28*A*a*b^6)*d^3*e^2 + 9*(159*B*a^3*b^4 + 11*A*a^2*b^5)*d^2*e^3 - 42*(241*B*a^4*b^3 - 6*A*a^3*b^4)*d*e^4 + 735*(11*B*a^5*b^2 - A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d - a^6*b^7*e + (b^13*d - a*b^12*e)*x^5 + 5*(a*b^12*d - a^2*b^11*e)*x^4 + 10*(a^2*b^11*d - a^3*b^10*e)*x^3 + 10*(a^3*b^10*d - a^4*b^9*e)*x^2 + 5*(a^4*b^9*d - a^5*b^8*e)*x), 1/640*(315*(10*B*a^5*b*d*e^4 - (11*B*a^6 - A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (11*B*a*b^5 - A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (11*B*a^2*b^4 - A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (11*B*a^3*b^3 - A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (11*B*a^4*b^2 - A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (11*B*a^5*b - A*a^4*b^2)*e^5)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (32*(B*a*b^6 + 4*A*b^7)*d^5 + 16*(4*B*a^2*b^5 + A*a*b^6)*d^4*e + 12*(13*B*a^3*b^4 + 2*A*a^2*b^5)*d^3*e^2 + 42*(14*B*a^4*b^3 + A*a^3*b^4)*d^2*e^3 - 105*(41*B*a^5*b^2 - A*a^4*b^3)*d*e^4 + 315*(11*B*a^6*b - A*a^5*b^2)*e^5 - 1280*(B*b^7*d*e^4 - B*a*b^6*e^5)*x^5 + 5*(650*B*b^7*d^2*e^3 - (2773*B*a*b^6 - 193*A*b^7)*d*e^4 + 193*(11*B*a^2*b^5 - A*a*b^6)*e^5)*x^4 + 10*(210*B*b^7*d^3*e^2 + (521*B*a*b^6 + 149*A*b^7)*d^2*e^3 - 2*(1669*B*a^2*b^5 - 44*A*a*b^6)*d*e^4 + 237*(11*B*a^3*b^4 - A*a^2*b^5)*e^5)*x^3 + 2*(440*B*b^7*d^4*e + 2*(353*B*a*b^6 + 342*A*b^7)*d^3*e^2 + 3*(919*B*a^2*b^5 + 61*A*a*b^6)*d^2*e^3 - 3*(6229*B*a^3*b^4 - 159*A*a^2*b^5)*d*e^4 + 1344*(11*B*a^4*b^3 - A*a^3*b^4)*e^5)*x^2 + 2*(80*B*b^7*d^5 + 8*(19*B*a*b^6 + 41*A*b^7)*d^4*e + 2*(187*B*a^2*b^5 + 28*A*a*b^6)*d^3*e^2 + 9*(159*B*a^3*b^4 + 11*A*a^2*b^5)*d^2*e^3 - 42*(241*B*a^4*b^3 - 6*A*a^3*b^4)*d*e^4 + 735*(11*B*a^5*b^2 - A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d - a^6*b^7*e + (b^13*d - a*b^12*e)*x^5 + 5*(a*b^12*d - a^2*b^11*e)*x^4 + 10*(a^2*b^11*d - a^3*b^10*e)*x^3 + 10*(a^3*b^10*d - a^4*b^9*e)*x^2 + 5*(a^4*b^9*d - a^5*b^8*e)*x)]","B",0
1827,1,2041,0,0.487612," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(10 \, B a^{5} b d e^{4} - {\left(9 \, B a^{6} + A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(9 \, B a b^{5} + A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(9 \, B a^{2} b^{4} + A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(9 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(9 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(9 \, B a^{5} b + A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} + 16 \, {\left(2 \, B a^{2} b^{5} - 27 \, A a b^{6}\right)} d^{4} e + 4 \, {\left(17 \, B a^{3} b^{4} - 2 \, A a^{2} b^{5}\right)} d^{3} e^{2} + 14 \, {\left(16 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} d^{2} e^{3} - 35 \, {\left(39 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} d e^{4} + 105 \, {\left(9 \, B a^{6} b + A a^{5} b^{2}\right)} e^{5} + 15 \, {\left(186 \, B b^{7} d^{2} e^{3} - {\left(379 \, B a b^{6} - 7 \, A b^{7}\right)} d e^{4} + {\left(193 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} e^{5}\right)} x^{4} + 10 \, {\left(326 \, B b^{7} d^{3} e^{2} + {\left(17 \, B a b^{6} + 121 \, A b^{7}\right)} d^{2} e^{3} - 2 \, {\left(527 \, B a^{2} b^{5} + 100 \, A a b^{6}\right)} d e^{4} + 79 \, {\left(9 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(1000 \, B b^{7} d^{4} e - 2 \, {\left(81 \, B a b^{6} - 526 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(347 \, B a^{2} b^{5} - 447 \, A a b^{6}\right)} d^{2} e^{3} - {\left(5911 \, B a^{3} b^{4} + 159 \, A a^{2} b^{5}\right)} d e^{4} + 448 \, {\left(9 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(240 \, B b^{7} d^{5} + 8 \, {\left(7 \, B a b^{6} + 93 \, A b^{7}\right)} d^{4} e + 2 \, {\left(81 \, B a^{2} b^{5} - 436 \, A a b^{6}\right)} d^{3} e^{2} + 3 \, {\left(181 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5}\right)} d^{2} e^{3} - 14 \, {\left(229 \, B a^{4} b^{3} + 6 \, A a^{3} b^{4}\right)} d e^{4} + 245 \, {\left(9 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(a^{5} b^{8} d^{2} - 2 \, a^{6} b^{7} d e + a^{7} b^{6} e^{2} + {\left(b^{13} d^{2} - 2 \, a b^{12} d e + a^{2} b^{11} e^{2}\right)} x^{5} + 5 \, {\left(a b^{12} d^{2} - 2 \, a^{2} b^{11} d e + a^{3} b^{10} e^{2}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{2} - 2 \, a^{3} b^{10} d e + a^{4} b^{9} e^{2}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{2} - 2 \, a^{4} b^{9} d e + a^{5} b^{8} e^{2}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{2} - 2 \, a^{5} b^{8} d e + a^{6} b^{7} e^{2}\right)} x\right)}}, \frac{105 \, {\left(10 \, B a^{5} b d e^{4} - {\left(9 \, B a^{6} + A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(9 \, B a b^{5} + A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(9 \, B a^{2} b^{4} + A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(9 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(9 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(9 \, B a^{5} b + A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} + 16 \, {\left(2 \, B a^{2} b^{5} - 27 \, A a b^{6}\right)} d^{4} e + 4 \, {\left(17 \, B a^{3} b^{4} - 2 \, A a^{2} b^{5}\right)} d^{3} e^{2} + 14 \, {\left(16 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} d^{2} e^{3} - 35 \, {\left(39 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} d e^{4} + 105 \, {\left(9 \, B a^{6} b + A a^{5} b^{2}\right)} e^{5} + 15 \, {\left(186 \, B b^{7} d^{2} e^{3} - {\left(379 \, B a b^{6} - 7 \, A b^{7}\right)} d e^{4} + {\left(193 \, B a^{2} b^{5} - 7 \, A a b^{6}\right)} e^{5}\right)} x^{4} + 10 \, {\left(326 \, B b^{7} d^{3} e^{2} + {\left(17 \, B a b^{6} + 121 \, A b^{7}\right)} d^{2} e^{3} - 2 \, {\left(527 \, B a^{2} b^{5} + 100 \, A a b^{6}\right)} d e^{4} + 79 \, {\left(9 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(1000 \, B b^{7} d^{4} e - 2 \, {\left(81 \, B a b^{6} - 526 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(347 \, B a^{2} b^{5} - 447 \, A a b^{6}\right)} d^{2} e^{3} - {\left(5911 \, B a^{3} b^{4} + 159 \, A a^{2} b^{5}\right)} d e^{4} + 448 \, {\left(9 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(240 \, B b^{7} d^{5} + 8 \, {\left(7 \, B a b^{6} + 93 \, A b^{7}\right)} d^{4} e + 2 \, {\left(81 \, B a^{2} b^{5} - 436 \, A a b^{6}\right)} d^{3} e^{2} + 3 \, {\left(181 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5}\right)} d^{2} e^{3} - 14 \, {\left(229 \, B a^{4} b^{3} + 6 \, A a^{3} b^{4}\right)} d e^{4} + 245 \, {\left(9 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{5} b^{8} d^{2} - 2 \, a^{6} b^{7} d e + a^{7} b^{6} e^{2} + {\left(b^{13} d^{2} - 2 \, a b^{12} d e + a^{2} b^{11} e^{2}\right)} x^{5} + 5 \, {\left(a b^{12} d^{2} - 2 \, a^{2} b^{11} d e + a^{3} b^{10} e^{2}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{2} - 2 \, a^{3} b^{10} d e + a^{4} b^{9} e^{2}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{2} - 2 \, a^{4} b^{9} d e + a^{5} b^{8} e^{2}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{2} - 2 \, a^{5} b^{8} d e + a^{6} b^{7} e^{2}\right)} x\right)}}\right]"," ",0,"[1/3840*(105*(10*B*a^5*b*d*e^4 - (9*B*a^6 + A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (9*B*a*b^5 + A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (9*B*a^2*b^4 + A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (9*B*a^3*b^3 + A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (9*B*a^4*b^2 + A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (9*B*a^5*b + A*a^4*b^2)*e^5)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(96*(B*a*b^6 + 4*A*b^7)*d^5 + 16*(2*B*a^2*b^5 - 27*A*a*b^6)*d^4*e + 4*(17*B*a^3*b^4 - 2*A*a^2*b^5)*d^3*e^2 + 14*(16*B*a^4*b^3 - A*a^3*b^4)*d^2*e^3 - 35*(39*B*a^5*b^2 + A*a^4*b^3)*d*e^4 + 105*(9*B*a^6*b + A*a^5*b^2)*e^5 + 15*(186*B*b^7*d^2*e^3 - (379*B*a*b^6 - 7*A*b^7)*d*e^4 + (193*B*a^2*b^5 - 7*A*a*b^6)*e^5)*x^4 + 10*(326*B*b^7*d^3*e^2 + (17*B*a*b^6 + 121*A*b^7)*d^2*e^3 - 2*(527*B*a^2*b^5 + 100*A*a*b^6)*d*e^4 + 79*(9*B*a^3*b^4 + A*a^2*b^5)*e^5)*x^3 + 2*(1000*B*b^7*d^4*e - 2*(81*B*a*b^6 - 526*A*b^7)*d^3*e^2 + 3*(347*B*a^2*b^5 - 447*A*a*b^6)*d^2*e^3 - (5911*B*a^3*b^4 + 159*A*a^2*b^5)*d*e^4 + 448*(9*B*a^4*b^3 + A*a^3*b^4)*e^5)*x^2 + 2*(240*B*b^7*d^5 + 8*(7*B*a*b^6 + 93*A*b^7)*d^4*e + 2*(81*B*a^2*b^5 - 436*A*a*b^6)*d^3*e^2 + 3*(181*B*a^3*b^4 - 11*A*a^2*b^5)*d^2*e^3 - 14*(229*B*a^4*b^3 + 6*A*a^3*b^4)*d*e^4 + 245*(9*B*a^5*b^2 + A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^2 - 2*a^6*b^7*d*e + a^7*b^6*e^2 + (b^13*d^2 - 2*a*b^12*d*e + a^2*b^11*e^2)*x^5 + 5*(a*b^12*d^2 - 2*a^2*b^11*d*e + a^3*b^10*e^2)*x^4 + 10*(a^2*b^11*d^2 - 2*a^3*b^10*d*e + a^4*b^9*e^2)*x^3 + 10*(a^3*b^10*d^2 - 2*a^4*b^9*d*e + a^5*b^8*e^2)*x^2 + 5*(a^4*b^9*d^2 - 2*a^5*b^8*d*e + a^6*b^7*e^2)*x), 1/1920*(105*(10*B*a^5*b*d*e^4 - (9*B*a^6 + A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (9*B*a*b^5 + A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (9*B*a^2*b^4 + A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (9*B*a^3*b^3 + A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (9*B*a^4*b^2 + A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (9*B*a^5*b + A*a^4*b^2)*e^5)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (96*(B*a*b^6 + 4*A*b^7)*d^5 + 16*(2*B*a^2*b^5 - 27*A*a*b^6)*d^4*e + 4*(17*B*a^3*b^4 - 2*A*a^2*b^5)*d^3*e^2 + 14*(16*B*a^4*b^3 - A*a^3*b^4)*d^2*e^3 - 35*(39*B*a^5*b^2 + A*a^4*b^3)*d*e^4 + 105*(9*B*a^6*b + A*a^5*b^2)*e^5 + 15*(186*B*b^7*d^2*e^3 - (379*B*a*b^6 - 7*A*b^7)*d*e^4 + (193*B*a^2*b^5 - 7*A*a*b^6)*e^5)*x^4 + 10*(326*B*b^7*d^3*e^2 + (17*B*a*b^6 + 121*A*b^7)*d^2*e^3 - 2*(527*B*a^2*b^5 + 100*A*a*b^6)*d*e^4 + 79*(9*B*a^3*b^4 + A*a^2*b^5)*e^5)*x^3 + 2*(1000*B*b^7*d^4*e - 2*(81*B*a*b^6 - 526*A*b^7)*d^3*e^2 + 3*(347*B*a^2*b^5 - 447*A*a*b^6)*d^2*e^3 - (5911*B*a^3*b^4 + 159*A*a^2*b^5)*d*e^4 + 448*(9*B*a^4*b^3 + A*a^3*b^4)*e^5)*x^2 + 2*(240*B*b^7*d^5 + 8*(7*B*a*b^6 + 93*A*b^7)*d^4*e + 2*(81*B*a^2*b^5 - 436*A*a*b^6)*d^3*e^2 + 3*(181*B*a^3*b^4 - 11*A*a^2*b^5)*d^2*e^3 - 14*(229*B*a^4*b^3 + 6*A*a^3*b^4)*d*e^4 + 245*(9*B*a^5*b^2 + A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^2 - 2*a^6*b^7*d*e + a^7*b^6*e^2 + (b^13*d^2 - 2*a*b^12*d*e + a^2*b^11*e^2)*x^5 + 5*(a*b^12*d^2 - 2*a^2*b^11*d*e + a^3*b^10*e^2)*x^4 + 10*(a^2*b^11*d^2 - 2*a^3*b^10*d*e + a^4*b^9*e^2)*x^3 + 10*(a^3*b^10*d^2 - 2*a^4*b^9*d*e + a^5*b^8*e^2)*x^2 + 5*(a^4*b^9*d^2 - 2*a^5*b^8*d*e + a^6*b^7*e^2)*x)]","B",0
1828,1,2238,0,0.503804," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(10 \, B a^{5} b d e^{4} - {\left(7 \, B a^{6} + 3 \, A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(7 \, B a b^{5} + 3 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(7 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(7 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(7 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(7 \, B a^{5} b + 3 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} - 16 \, {\left(8 \, B a^{2} b^{5} + 57 \, A a b^{6}\right)} d^{4} e - 12 \, {\left(B a^{3} b^{4} - 46 \, A a^{2} b^{5}\right)} d^{3} e^{2} - 6 \, {\left(6 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} d^{2} e^{3} + 5 \, {\left(37 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3}\right)} d e^{4} - 15 \, {\left(7 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} e^{5} + 15 \, {\left(10 \, B b^{7} d^{2} e^{3} - {\left(17 \, B a b^{6} + 3 \, A b^{7}\right)} d e^{4} + {\left(7 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} e^{5}\right)} x^{4} + 10 \, {\left(118 \, B b^{7} d^{3} e^{2} - 3 \, {\left(99 \, B a b^{6} - A b^{7}\right)} d^{2} e^{3} + 6 \, {\left(43 \, B a^{2} b^{5} - 4 \, A a b^{6}\right)} d e^{4} - {\left(79 \, B a^{3} b^{4} - 21 \, A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(680 \, B b^{7} d^{4} e - 2 \, {\left(661 \, B a b^{6} - 186 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(97 \, B a^{2} b^{5} - 357 \, A a b^{6}\right)} d^{2} e^{3} + {\left(799 \, B a^{3} b^{4} + 891 \, A a^{2} b^{5}\right)} d e^{4} - 64 \, {\left(7 \, B a^{4} b^{3} + 3 \, A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(240 \, B b^{7} d^{5} - 8 \, {\left(43 \, B a b^{6} - 63 \, A b^{7}\right)} d^{4} e + 2 \, {\left(B a^{2} b^{5} - 636 \, A a b^{6}\right)} d^{3} e^{2} - 3 \, {\left(29 \, B a^{3} b^{4} - 279 \, A a^{2} b^{5}\right)} d^{2} e^{3} + 2 \, {\left(217 \, B a^{4} b^{3} + 18 \, A a^{3} b^{4}\right)} d e^{4} - 35 \, {\left(7 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(a^{5} b^{8} d^{3} - 3 \, a^{6} b^{7} d^{2} e + 3 \, a^{7} b^{6} d e^{2} - a^{8} b^{5} e^{3} + {\left(b^{13} d^{3} - 3 \, a b^{12} d^{2} e + 3 \, a^{2} b^{11} d e^{2} - a^{3} b^{10} e^{3}\right)} x^{5} + 5 \, {\left(a b^{12} d^{3} - 3 \, a^{2} b^{11} d^{2} e + 3 \, a^{3} b^{10} d e^{2} - a^{4} b^{9} e^{3}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{3} - 3 \, a^{3} b^{10} d^{2} e + 3 \, a^{4} b^{9} d e^{2} - a^{5} b^{8} e^{3}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{3} - 3 \, a^{4} b^{9} d^{2} e + 3 \, a^{5} b^{8} d e^{2} - a^{6} b^{7} e^{3}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{3} - 3 \, a^{5} b^{8} d^{2} e + 3 \, a^{6} b^{7} d e^{2} - a^{7} b^{6} e^{3}\right)} x\right)}}, -\frac{15 \, {\left(10 \, B a^{5} b d e^{4} - {\left(7 \, B a^{6} + 3 \, A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(7 \, B a b^{5} + 3 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(7 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(7 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(7 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(7 \, B a^{5} b + 3 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} - 16 \, {\left(8 \, B a^{2} b^{5} + 57 \, A a b^{6}\right)} d^{4} e - 12 \, {\left(B a^{3} b^{4} - 46 \, A a^{2} b^{5}\right)} d^{3} e^{2} - 6 \, {\left(6 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} d^{2} e^{3} + 5 \, {\left(37 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3}\right)} d e^{4} - 15 \, {\left(7 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} e^{5} + 15 \, {\left(10 \, B b^{7} d^{2} e^{3} - {\left(17 \, B a b^{6} + 3 \, A b^{7}\right)} d e^{4} + {\left(7 \, B a^{2} b^{5} + 3 \, A a b^{6}\right)} e^{5}\right)} x^{4} + 10 \, {\left(118 \, B b^{7} d^{3} e^{2} - 3 \, {\left(99 \, B a b^{6} - A b^{7}\right)} d^{2} e^{3} + 6 \, {\left(43 \, B a^{2} b^{5} - 4 \, A a b^{6}\right)} d e^{4} - {\left(79 \, B a^{3} b^{4} - 21 \, A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(680 \, B b^{7} d^{4} e - 2 \, {\left(661 \, B a b^{6} - 186 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(97 \, B a^{2} b^{5} - 357 \, A a b^{6}\right)} d^{2} e^{3} + {\left(799 \, B a^{3} b^{4} + 891 \, A a^{2} b^{5}\right)} d e^{4} - 64 \, {\left(7 \, B a^{4} b^{3} + 3 \, A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(240 \, B b^{7} d^{5} - 8 \, {\left(43 \, B a b^{6} - 63 \, A b^{7}\right)} d^{4} e + 2 \, {\left(B a^{2} b^{5} - 636 \, A a b^{6}\right)} d^{3} e^{2} - 3 \, {\left(29 \, B a^{3} b^{4} - 279 \, A a^{2} b^{5}\right)} d^{2} e^{3} + 2 \, {\left(217 \, B a^{4} b^{3} + 18 \, A a^{3} b^{4}\right)} d e^{4} - 35 \, {\left(7 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{5} b^{8} d^{3} - 3 \, a^{6} b^{7} d^{2} e + 3 \, a^{7} b^{6} d e^{2} - a^{8} b^{5} e^{3} + {\left(b^{13} d^{3} - 3 \, a b^{12} d^{2} e + 3 \, a^{2} b^{11} d e^{2} - a^{3} b^{10} e^{3}\right)} x^{5} + 5 \, {\left(a b^{12} d^{3} - 3 \, a^{2} b^{11} d^{2} e + 3 \, a^{3} b^{10} d e^{2} - a^{4} b^{9} e^{3}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{3} - 3 \, a^{3} b^{10} d^{2} e + 3 \, a^{4} b^{9} d e^{2} - a^{5} b^{8} e^{3}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{3} - 3 \, a^{4} b^{9} d^{2} e + 3 \, a^{5} b^{8} d e^{2} - a^{6} b^{7} e^{3}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{3} - 3 \, a^{5} b^{8} d^{2} e + 3 \, a^{6} b^{7} d e^{2} - a^{7} b^{6} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/3840*(15*(10*B*a^5*b*d*e^4 - (7*B*a^6 + 3*A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (7*B*a*b^5 + 3*A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (7*B*a^2*b^4 + 3*A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (7*B*a^3*b^3 + 3*A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (7*B*a^4*b^2 + 3*A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (7*B*a^5*b + 3*A*a^4*b^2)*e^5)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(96*(B*a*b^6 + 4*A*b^7)*d^5 - 16*(8*B*a^2*b^5 + 57*A*a*b^6)*d^4*e - 12*(B*a^3*b^4 - 46*A*a^2*b^5)*d^3*e^2 - 6*(6*B*a^4*b^3 - A*a^3*b^4)*d^2*e^3 + 5*(37*B*a^5*b^2 + 3*A*a^4*b^3)*d*e^4 - 15*(7*B*a^6*b + 3*A*a^5*b^2)*e^5 + 15*(10*B*b^7*d^2*e^3 - (17*B*a*b^6 + 3*A*b^7)*d*e^4 + (7*B*a^2*b^5 + 3*A*a*b^6)*e^5)*x^4 + 10*(118*B*b^7*d^3*e^2 - 3*(99*B*a*b^6 - A*b^7)*d^2*e^3 + 6*(43*B*a^2*b^5 - 4*A*a*b^6)*d*e^4 - (79*B*a^3*b^4 - 21*A*a^2*b^5)*e^5)*x^3 + 2*(680*B*b^7*d^4*e - 2*(661*B*a*b^6 - 186*A*b^7)*d^3*e^2 + 3*(97*B*a^2*b^5 - 357*A*a*b^6)*d^2*e^3 + (799*B*a^3*b^4 + 891*A*a^2*b^5)*d*e^4 - 64*(7*B*a^4*b^3 + 3*A*a^3*b^4)*e^5)*x^2 + 2*(240*B*b^7*d^5 - 8*(43*B*a*b^6 - 63*A*b^7)*d^4*e + 2*(B*a^2*b^5 - 636*A*a*b^6)*d^3*e^2 - 3*(29*B*a^3*b^4 - 279*A*a^2*b^5)*d^2*e^3 + 2*(217*B*a^4*b^3 + 18*A*a^3*b^4)*d*e^4 - 35*(7*B*a^5*b^2 + 3*A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^3 - 3*a^6*b^7*d^2*e + 3*a^7*b^6*d*e^2 - a^8*b^5*e^3 + (b^13*d^3 - 3*a*b^12*d^2*e + 3*a^2*b^11*d*e^2 - a^3*b^10*e^3)*x^5 + 5*(a*b^12*d^3 - 3*a^2*b^11*d^2*e + 3*a^3*b^10*d*e^2 - a^4*b^9*e^3)*x^4 + 10*(a^2*b^11*d^3 - 3*a^3*b^10*d^2*e + 3*a^4*b^9*d*e^2 - a^5*b^8*e^3)*x^3 + 10*(a^3*b^10*d^3 - 3*a^4*b^9*d^2*e + 3*a^5*b^8*d*e^2 - a^6*b^7*e^3)*x^2 + 5*(a^4*b^9*d^3 - 3*a^5*b^8*d^2*e + 3*a^6*b^7*d*e^2 - a^7*b^6*e^3)*x), -1/1920*(15*(10*B*a^5*b*d*e^4 - (7*B*a^6 + 3*A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (7*B*a*b^5 + 3*A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (7*B*a^2*b^4 + 3*A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (7*B*a^3*b^3 + 3*A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (7*B*a^4*b^2 + 3*A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (7*B*a^5*b + 3*A*a^4*b^2)*e^5)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (96*(B*a*b^6 + 4*A*b^7)*d^5 - 16*(8*B*a^2*b^5 + 57*A*a*b^6)*d^4*e - 12*(B*a^3*b^4 - 46*A*a^2*b^5)*d^3*e^2 - 6*(6*B*a^4*b^3 - A*a^3*b^4)*d^2*e^3 + 5*(37*B*a^5*b^2 + 3*A*a^4*b^3)*d*e^4 - 15*(7*B*a^6*b + 3*A*a^5*b^2)*e^5 + 15*(10*B*b^7*d^2*e^3 - (17*B*a*b^6 + 3*A*b^7)*d*e^4 + (7*B*a^2*b^5 + 3*A*a*b^6)*e^5)*x^4 + 10*(118*B*b^7*d^3*e^2 - 3*(99*B*a*b^6 - A*b^7)*d^2*e^3 + 6*(43*B*a^2*b^5 - 4*A*a*b^6)*d*e^4 - (79*B*a^3*b^4 - 21*A*a^2*b^5)*e^5)*x^3 + 2*(680*B*b^7*d^4*e - 2*(661*B*a*b^6 - 186*A*b^7)*d^3*e^2 + 3*(97*B*a^2*b^5 - 357*A*a*b^6)*d^2*e^3 + (799*B*a^3*b^4 + 891*A*a^2*b^5)*d*e^4 - 64*(7*B*a^4*b^3 + 3*A*a^3*b^4)*e^5)*x^2 + 2*(240*B*b^7*d^5 - 8*(43*B*a*b^6 - 63*A*b^7)*d^4*e + 2*(B*a^2*b^5 - 636*A*a*b^6)*d^3*e^2 - 3*(29*B*a^3*b^4 - 279*A*a^2*b^5)*d^2*e^3 + 2*(217*B*a^4*b^3 + 18*A*a^3*b^4)*d*e^4 - 35*(7*B*a^5*b^2 + 3*A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^3 - 3*a^6*b^7*d^2*e + 3*a^7*b^6*d*e^2 - a^8*b^5*e^3 + (b^13*d^3 - 3*a*b^12*d^2*e + 3*a^2*b^11*d*e^2 - a^3*b^10*e^3)*x^5 + 5*(a*b^12*d^3 - 3*a^2*b^11*d^2*e + 3*a^3*b^10*d*e^2 - a^4*b^9*e^3)*x^4 + 10*(a^2*b^11*d^3 - 3*a^3*b^10*d^2*e + 3*a^4*b^9*d*e^2 - a^5*b^8*e^3)*x^3 + 10*(a^3*b^10*d^3 - 3*a^4*b^9*d^2*e + 3*a^5*b^8*d*e^2 - a^6*b^7*e^3)*x^2 + 5*(a^4*b^9*d^3 - 3*a^5*b^8*d^2*e + 3*a^6*b^7*d*e^2 - a^7*b^6*e^3)*x)]","B",0
1829,1,2349,0,0.506749," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(2 \, B a^{5} b d e^{4} - {\left(B a^{6} + A a^{5} b\right)} e^{5} + {\left(2 \, B b^{6} d e^{4} - {\left(B a b^{5} + A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(2 \, B a b^{5} d e^{4} - {\left(B a^{2} b^{4} + A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(2 \, B a^{2} b^{4} d e^{4} - {\left(B a^{3} b^{3} + A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(2 \, B a^{3} b^{3} d e^{4} - {\left(B a^{4} b^{2} + A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(2 \, B a^{4} b^{2} d e^{4} - {\left(B a^{5} b + A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(32 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} - 16 \, {\left(6 \, B a^{2} b^{5} + 29 \, A a b^{6}\right)} d^{4} e + 4 \, {\left(19 \, B a^{3} b^{4} + 146 \, A a^{2} b^{5}\right)} d^{3} e^{2} + 2 \, {\left(4 \, B a^{4} b^{3} - 129 \, A a^{3} b^{4}\right)} d^{2} e^{3} - 5 \, {\left(7 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} d e^{4} + 15 \, {\left(B a^{6} b + A a^{5} b^{2}\right)} e^{5} - 15 \, {\left(2 \, B b^{7} d^{2} e^{3} - {\left(3 \, B a b^{6} + A b^{7}\right)} d e^{4} + {\left(B a^{2} b^{5} + A a b^{6}\right)} e^{5}\right)} x^{4} + 10 \, {\left(2 \, B b^{7} d^{3} e^{2} - {\left(17 \, B a b^{6} + A b^{7}\right)} d^{2} e^{3} + 2 \, {\left(11 \, B a^{2} b^{5} + 4 \, A a b^{6}\right)} d e^{4} - 7 \, {\left(B a^{3} b^{4} + A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(120 \, B b^{7} d^{4} e - 2 \, {\left(227 \, B a b^{6} - 2 \, A b^{7}\right)} d^{3} e^{2} + 27 \, {\left(21 \, B a^{2} b^{5} - A a b^{6}\right)} d^{2} e^{3} - 3 \, {\left(99 \, B a^{3} b^{4} - 29 \, A a^{2} b^{5}\right)} d e^{4} + 64 \, {\left(B a^{4} b^{3} - A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(80 \, B b^{7} d^{5} - 8 \, {\left(31 \, B a b^{6} - 11 \, A b^{7}\right)} d^{4} e + 2 \, {\left(107 \, B a^{2} b^{5} - 172 \, A a b^{6}\right)} d^{3} e^{2} + {\left(B a^{3} b^{4} + 489 \, A a^{2} b^{5}\right)} d^{2} e^{3} - 2 \, {\left(41 \, B a^{4} b^{3} + 134 \, A a^{3} b^{4}\right)} d e^{4} + 35 \, {\left(B a^{5} b^{2} + A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(a^{5} b^{8} d^{4} - 4 \, a^{6} b^{7} d^{3} e + 6 \, a^{7} b^{6} d^{2} e^{2} - 4 \, a^{8} b^{5} d e^{3} + a^{9} b^{4} e^{4} + {\left(b^{13} d^{4} - 4 \, a b^{12} d^{3} e + 6 \, a^{2} b^{11} d^{2} e^{2} - 4 \, a^{3} b^{10} d e^{3} + a^{4} b^{9} e^{4}\right)} x^{5} + 5 \, {\left(a b^{12} d^{4} - 4 \, a^{2} b^{11} d^{3} e + 6 \, a^{3} b^{10} d^{2} e^{2} - 4 \, a^{4} b^{9} d e^{3} + a^{5} b^{8} e^{4}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{4} - 4 \, a^{3} b^{10} d^{3} e + 6 \, a^{4} b^{9} d^{2} e^{2} - 4 \, a^{5} b^{8} d e^{3} + a^{6} b^{7} e^{4}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{4} - 4 \, a^{4} b^{9} d^{3} e + 6 \, a^{5} b^{8} d^{2} e^{2} - 4 \, a^{6} b^{7} d e^{3} + a^{7} b^{6} e^{4}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{4} - 4 \, a^{5} b^{8} d^{3} e + 6 \, a^{6} b^{7} d^{2} e^{2} - 4 \, a^{7} b^{6} d e^{3} + a^{8} b^{5} e^{4}\right)} x\right)}}, \frac{15 \, {\left(2 \, B a^{5} b d e^{4} - {\left(B a^{6} + A a^{5} b\right)} e^{5} + {\left(2 \, B b^{6} d e^{4} - {\left(B a b^{5} + A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(2 \, B a b^{5} d e^{4} - {\left(B a^{2} b^{4} + A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(2 \, B a^{2} b^{4} d e^{4} - {\left(B a^{3} b^{3} + A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(2 \, B a^{3} b^{3} d e^{4} - {\left(B a^{4} b^{2} + A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(2 \, B a^{4} b^{2} d e^{4} - {\left(B a^{5} b + A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(32 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} - 16 \, {\left(6 \, B a^{2} b^{5} + 29 \, A a b^{6}\right)} d^{4} e + 4 \, {\left(19 \, B a^{3} b^{4} + 146 \, A a^{2} b^{5}\right)} d^{3} e^{2} + 2 \, {\left(4 \, B a^{4} b^{3} - 129 \, A a^{3} b^{4}\right)} d^{2} e^{3} - 5 \, {\left(7 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} d e^{4} + 15 \, {\left(B a^{6} b + A a^{5} b^{2}\right)} e^{5} - 15 \, {\left(2 \, B b^{7} d^{2} e^{3} - {\left(3 \, B a b^{6} + A b^{7}\right)} d e^{4} + {\left(B a^{2} b^{5} + A a b^{6}\right)} e^{5}\right)} x^{4} + 10 \, {\left(2 \, B b^{7} d^{3} e^{2} - {\left(17 \, B a b^{6} + A b^{7}\right)} d^{2} e^{3} + 2 \, {\left(11 \, B a^{2} b^{5} + 4 \, A a b^{6}\right)} d e^{4} - 7 \, {\left(B a^{3} b^{4} + A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(120 \, B b^{7} d^{4} e - 2 \, {\left(227 \, B a b^{6} - 2 \, A b^{7}\right)} d^{3} e^{2} + 27 \, {\left(21 \, B a^{2} b^{5} - A a b^{6}\right)} d^{2} e^{3} - 3 \, {\left(99 \, B a^{3} b^{4} - 29 \, A a^{2} b^{5}\right)} d e^{4} + 64 \, {\left(B a^{4} b^{3} - A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(80 \, B b^{7} d^{5} - 8 \, {\left(31 \, B a b^{6} - 11 \, A b^{7}\right)} d^{4} e + 2 \, {\left(107 \, B a^{2} b^{5} - 172 \, A a b^{6}\right)} d^{3} e^{2} + {\left(B a^{3} b^{4} + 489 \, A a^{2} b^{5}\right)} d^{2} e^{3} - 2 \, {\left(41 \, B a^{4} b^{3} + 134 \, A a^{3} b^{4}\right)} d e^{4} + 35 \, {\left(B a^{5} b^{2} + A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(a^{5} b^{8} d^{4} - 4 \, a^{6} b^{7} d^{3} e + 6 \, a^{7} b^{6} d^{2} e^{2} - 4 \, a^{8} b^{5} d e^{3} + a^{9} b^{4} e^{4} + {\left(b^{13} d^{4} - 4 \, a b^{12} d^{3} e + 6 \, a^{2} b^{11} d^{2} e^{2} - 4 \, a^{3} b^{10} d e^{3} + a^{4} b^{9} e^{4}\right)} x^{5} + 5 \, {\left(a b^{12} d^{4} - 4 \, a^{2} b^{11} d^{3} e + 6 \, a^{3} b^{10} d^{2} e^{2} - 4 \, a^{4} b^{9} d e^{3} + a^{5} b^{8} e^{4}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{4} - 4 \, a^{3} b^{10} d^{3} e + 6 \, a^{4} b^{9} d^{2} e^{2} - 4 \, a^{5} b^{8} d e^{3} + a^{6} b^{7} e^{4}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{4} - 4 \, a^{4} b^{9} d^{3} e + 6 \, a^{5} b^{8} d^{2} e^{2} - 4 \, a^{6} b^{7} d e^{3} + a^{7} b^{6} e^{4}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{4} - 4 \, a^{5} b^{8} d^{3} e + 6 \, a^{6} b^{7} d^{2} e^{2} - 4 \, a^{7} b^{6} d e^{3} + a^{8} b^{5} e^{4}\right)} x\right)}}\right]"," ",0,"[1/1280*(15*(2*B*a^5*b*d*e^4 - (B*a^6 + A*a^5*b)*e^5 + (2*B*b^6*d*e^4 - (B*a*b^5 + A*b^6)*e^5)*x^5 + 5*(2*B*a*b^5*d*e^4 - (B*a^2*b^4 + A*a*b^5)*e^5)*x^4 + 10*(2*B*a^2*b^4*d*e^4 - (B*a^3*b^3 + A*a^2*b^4)*e^5)*x^3 + 10*(2*B*a^3*b^3*d*e^4 - (B*a^4*b^2 + A*a^3*b^3)*e^5)*x^2 + 5*(2*B*a^4*b^2*d*e^4 - (B*a^5*b + A*a^4*b^2)*e^5)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(32*(B*a*b^6 + 4*A*b^7)*d^5 - 16*(6*B*a^2*b^5 + 29*A*a*b^6)*d^4*e + 4*(19*B*a^3*b^4 + 146*A*a^2*b^5)*d^3*e^2 + 2*(4*B*a^4*b^3 - 129*A*a^3*b^4)*d^2*e^3 - 5*(7*B*a^5*b^2 + A*a^4*b^3)*d*e^4 + 15*(B*a^6*b + A*a^5*b^2)*e^5 - 15*(2*B*b^7*d^2*e^3 - (3*B*a*b^6 + A*b^7)*d*e^4 + (B*a^2*b^5 + A*a*b^6)*e^5)*x^4 + 10*(2*B*b^7*d^3*e^2 - (17*B*a*b^6 + A*b^7)*d^2*e^3 + 2*(11*B*a^2*b^5 + 4*A*a*b^6)*d*e^4 - 7*(B*a^3*b^4 + A*a^2*b^5)*e^5)*x^3 + 2*(120*B*b^7*d^4*e - 2*(227*B*a*b^6 - 2*A*b^7)*d^3*e^2 + 27*(21*B*a^2*b^5 - A*a*b^6)*d^2*e^3 - 3*(99*B*a^3*b^4 - 29*A*a^2*b^5)*d*e^4 + 64*(B*a^4*b^3 - A*a^3*b^4)*e^5)*x^2 + 2*(80*B*b^7*d^5 - 8*(31*B*a*b^6 - 11*A*b^7)*d^4*e + 2*(107*B*a^2*b^5 - 172*A*a*b^6)*d^3*e^2 + (B*a^3*b^4 + 489*A*a^2*b^5)*d^2*e^3 - 2*(41*B*a^4*b^3 + 134*A*a^3*b^4)*d*e^4 + 35*(B*a^5*b^2 + A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^4 - 4*a^6*b^7*d^3*e + 6*a^7*b^6*d^2*e^2 - 4*a^8*b^5*d*e^3 + a^9*b^4*e^4 + (b^13*d^4 - 4*a*b^12*d^3*e + 6*a^2*b^11*d^2*e^2 - 4*a^3*b^10*d*e^3 + a^4*b^9*e^4)*x^5 + 5*(a*b^12*d^4 - 4*a^2*b^11*d^3*e + 6*a^3*b^10*d^2*e^2 - 4*a^4*b^9*d*e^3 + a^5*b^8*e^4)*x^4 + 10*(a^2*b^11*d^4 - 4*a^3*b^10*d^3*e + 6*a^4*b^9*d^2*e^2 - 4*a^5*b^8*d*e^3 + a^6*b^7*e^4)*x^3 + 10*(a^3*b^10*d^4 - 4*a^4*b^9*d^3*e + 6*a^5*b^8*d^2*e^2 - 4*a^6*b^7*d*e^3 + a^7*b^6*e^4)*x^2 + 5*(a^4*b^9*d^4 - 4*a^5*b^8*d^3*e + 6*a^6*b^7*d^2*e^2 - 4*a^7*b^6*d*e^3 + a^8*b^5*e^4)*x), 1/640*(15*(2*B*a^5*b*d*e^4 - (B*a^6 + A*a^5*b)*e^5 + (2*B*b^6*d*e^4 - (B*a*b^5 + A*b^6)*e^5)*x^5 + 5*(2*B*a*b^5*d*e^4 - (B*a^2*b^4 + A*a*b^5)*e^5)*x^4 + 10*(2*B*a^2*b^4*d*e^4 - (B*a^3*b^3 + A*a^2*b^4)*e^5)*x^3 + 10*(2*B*a^3*b^3*d*e^4 - (B*a^4*b^2 + A*a^3*b^3)*e^5)*x^2 + 5*(2*B*a^4*b^2*d*e^4 - (B*a^5*b + A*a^4*b^2)*e^5)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (32*(B*a*b^6 + 4*A*b^7)*d^5 - 16*(6*B*a^2*b^5 + 29*A*a*b^6)*d^4*e + 4*(19*B*a^3*b^4 + 146*A*a^2*b^5)*d^3*e^2 + 2*(4*B*a^4*b^3 - 129*A*a^3*b^4)*d^2*e^3 - 5*(7*B*a^5*b^2 + A*a^4*b^3)*d*e^4 + 15*(B*a^6*b + A*a^5*b^2)*e^5 - 15*(2*B*b^7*d^2*e^3 - (3*B*a*b^6 + A*b^7)*d*e^4 + (B*a^2*b^5 + A*a*b^6)*e^5)*x^4 + 10*(2*B*b^7*d^3*e^2 - (17*B*a*b^6 + A*b^7)*d^2*e^3 + 2*(11*B*a^2*b^5 + 4*A*a*b^6)*d*e^4 - 7*(B*a^3*b^4 + A*a^2*b^5)*e^5)*x^3 + 2*(120*B*b^7*d^4*e - 2*(227*B*a*b^6 - 2*A*b^7)*d^3*e^2 + 27*(21*B*a^2*b^5 - A*a*b^6)*d^2*e^3 - 3*(99*B*a^3*b^4 - 29*A*a^2*b^5)*d*e^4 + 64*(B*a^4*b^3 - A*a^3*b^4)*e^5)*x^2 + 2*(80*B*b^7*d^5 - 8*(31*B*a*b^6 - 11*A*b^7)*d^4*e + 2*(107*B*a^2*b^5 - 172*A*a*b^6)*d^3*e^2 + (B*a^3*b^4 + 489*A*a^2*b^5)*d^2*e^3 - 2*(41*B*a^4*b^3 + 134*A*a^3*b^4)*d*e^4 + 35*(B*a^5*b^2 + A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^4 - 4*a^6*b^7*d^3*e + 6*a^7*b^6*d^2*e^2 - 4*a^8*b^5*d*e^3 + a^9*b^4*e^4 + (b^13*d^4 - 4*a*b^12*d^3*e + 6*a^2*b^11*d^2*e^2 - 4*a^3*b^10*d*e^3 + a^4*b^9*e^4)*x^5 + 5*(a*b^12*d^4 - 4*a^2*b^11*d^3*e + 6*a^3*b^10*d^2*e^2 - 4*a^4*b^9*d*e^3 + a^5*b^8*e^4)*x^4 + 10*(a^2*b^11*d^4 - 4*a^3*b^10*d^3*e + 6*a^4*b^9*d^2*e^2 - 4*a^5*b^8*d*e^3 + a^6*b^7*e^4)*x^3 + 10*(a^3*b^10*d^4 - 4*a^4*b^9*d^3*e + 6*a^5*b^8*d^2*e^2 - 4*a^6*b^7*d*e^3 + a^7*b^6*e^4)*x^2 + 5*(a^4*b^9*d^4 - 4*a^5*b^8*d^3*e + 6*a^6*b^7*d^2*e^2 - 4*a^7*b^6*d*e^3 + a^8*b^5*e^4)*x)]","B",0
1830,1,2580,0,0.496618," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(10 \, B a^{5} b d e^{4} - {\left(3 \, B a^{6} + 7 \, A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(3 \, B a b^{5} + 7 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(3 \, B a^{2} b^{4} + 7 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(3 \, B a^{3} b^{3} + 7 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(3 \, B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(3 \, B a^{5} b + 7 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} - 16 \, {\left(28 \, B a^{2} b^{5} + 117 \, A a b^{6}\right)} d^{4} e + 4 \, {\left(197 \, B a^{3} b^{4} + 898 \, A a^{2} b^{5}\right)} d^{3} e^{2} - 2 \, {\left(278 \, B a^{4} b^{3} + 1657 \, A a^{3} b^{4}\right)} d^{2} e^{3} + 5 \, {\left(33 \, B a^{5} b^{2} + 263 \, A a^{4} b^{3}\right)} d e^{4} - 15 \, {\left(3 \, B a^{6} b + 7 \, A a^{5} b^{2}\right)} e^{5} + 15 \, {\left(10 \, B b^{7} d^{2} e^{3} - {\left(13 \, B a b^{6} + 7 \, A b^{7}\right)} d e^{4} + {\left(3 \, B a^{2} b^{5} + 7 \, A a b^{6}\right)} e^{5}\right)} x^{4} - 10 \, {\left(10 \, B b^{7} d^{3} e^{2} - {\left(83 \, B a b^{6} + 7 \, A b^{7}\right)} d^{2} e^{3} + 2 \, {\left(47 \, B a^{2} b^{5} + 28 \, A a b^{6}\right)} d e^{4} - 7 \, {\left(3 \, B a^{3} b^{4} + 7 \, A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(40 \, B b^{7} d^{4} e - 2 \, {\left(141 \, B a b^{6} + 14 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(317 \, B a^{2} b^{5} + 63 \, A a b^{6}\right)} d^{2} e^{3} - {\left(901 \, B a^{3} b^{4} + 609 \, A a^{2} b^{5}\right)} d e^{4} + 64 \, {\left(3 \, B a^{4} b^{3} + 7 \, A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(240 \, B b^{7} d^{5} - 8 \, {\left(143 \, B a b^{6} - 3 \, A b^{7}\right)} d^{4} e + 2 \, {\left(1041 \, B a^{2} b^{5} - 76 \, A a b^{6}\right)} d^{3} e^{2} - 3 \, {\left(529 \, B a^{3} b^{4} - 139 \, A a^{2} b^{5}\right)} d^{2} e^{3} + 2 \, {\left(257 \, B a^{4} b^{3} - 342 \, A a^{3} b^{4}\right)} d e^{4} - 5 \, {\left(21 \, B a^{5} b^{2} - 79 \, A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(a^{5} b^{8} d^{5} - 5 \, a^{6} b^{7} d^{4} e + 10 \, a^{7} b^{6} d^{3} e^{2} - 10 \, a^{8} b^{5} d^{2} e^{3} + 5 \, a^{9} b^{4} d e^{4} - a^{10} b^{3} e^{5} + {\left(b^{13} d^{5} - 5 \, a b^{12} d^{4} e + 10 \, a^{2} b^{11} d^{3} e^{2} - 10 \, a^{3} b^{10} d^{2} e^{3} + 5 \, a^{4} b^{9} d e^{4} - a^{5} b^{8} e^{5}\right)} x^{5} + 5 \, {\left(a b^{12} d^{5} - 5 \, a^{2} b^{11} d^{4} e + 10 \, a^{3} b^{10} d^{3} e^{2} - 10 \, a^{4} b^{9} d^{2} e^{3} + 5 \, a^{5} b^{8} d e^{4} - a^{6} b^{7} e^{5}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{5} - 5 \, a^{3} b^{10} d^{4} e + 10 \, a^{4} b^{9} d^{3} e^{2} - 10 \, a^{5} b^{8} d^{2} e^{3} + 5 \, a^{6} b^{7} d e^{4} - a^{7} b^{6} e^{5}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{5} - 5 \, a^{4} b^{9} d^{4} e + 10 \, a^{5} b^{8} d^{3} e^{2} - 10 \, a^{6} b^{7} d^{2} e^{3} + 5 \, a^{7} b^{6} d e^{4} - a^{8} b^{5} e^{5}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{5} - 5 \, a^{5} b^{8} d^{4} e + 10 \, a^{6} b^{7} d^{3} e^{2} - 10 \, a^{7} b^{6} d^{2} e^{3} + 5 \, a^{8} b^{5} d e^{4} - a^{9} b^{4} e^{5}\right)} x\right)}}, -\frac{15 \, {\left(10 \, B a^{5} b d e^{4} - {\left(3 \, B a^{6} + 7 \, A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(3 \, B a b^{5} + 7 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(3 \, B a^{2} b^{4} + 7 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(3 \, B a^{3} b^{3} + 7 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(3 \, B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(3 \, B a^{5} b + 7 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} - 16 \, {\left(28 \, B a^{2} b^{5} + 117 \, A a b^{6}\right)} d^{4} e + 4 \, {\left(197 \, B a^{3} b^{4} + 898 \, A a^{2} b^{5}\right)} d^{3} e^{2} - 2 \, {\left(278 \, B a^{4} b^{3} + 1657 \, A a^{3} b^{4}\right)} d^{2} e^{3} + 5 \, {\left(33 \, B a^{5} b^{2} + 263 \, A a^{4} b^{3}\right)} d e^{4} - 15 \, {\left(3 \, B a^{6} b + 7 \, A a^{5} b^{2}\right)} e^{5} + 15 \, {\left(10 \, B b^{7} d^{2} e^{3} - {\left(13 \, B a b^{6} + 7 \, A b^{7}\right)} d e^{4} + {\left(3 \, B a^{2} b^{5} + 7 \, A a b^{6}\right)} e^{5}\right)} x^{4} - 10 \, {\left(10 \, B b^{7} d^{3} e^{2} - {\left(83 \, B a b^{6} + 7 \, A b^{7}\right)} d^{2} e^{3} + 2 \, {\left(47 \, B a^{2} b^{5} + 28 \, A a b^{6}\right)} d e^{4} - 7 \, {\left(3 \, B a^{3} b^{4} + 7 \, A a^{2} b^{5}\right)} e^{5}\right)} x^{3} + 2 \, {\left(40 \, B b^{7} d^{4} e - 2 \, {\left(141 \, B a b^{6} + 14 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(317 \, B a^{2} b^{5} + 63 \, A a b^{6}\right)} d^{2} e^{3} - {\left(901 \, B a^{3} b^{4} + 609 \, A a^{2} b^{5}\right)} d e^{4} + 64 \, {\left(3 \, B a^{4} b^{3} + 7 \, A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(240 \, B b^{7} d^{5} - 8 \, {\left(143 \, B a b^{6} - 3 \, A b^{7}\right)} d^{4} e + 2 \, {\left(1041 \, B a^{2} b^{5} - 76 \, A a b^{6}\right)} d^{3} e^{2} - 3 \, {\left(529 \, B a^{3} b^{4} - 139 \, A a^{2} b^{5}\right)} d^{2} e^{3} + 2 \, {\left(257 \, B a^{4} b^{3} - 342 \, A a^{3} b^{4}\right)} d e^{4} - 5 \, {\left(21 \, B a^{5} b^{2} - 79 \, A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{5} b^{8} d^{5} - 5 \, a^{6} b^{7} d^{4} e + 10 \, a^{7} b^{6} d^{3} e^{2} - 10 \, a^{8} b^{5} d^{2} e^{3} + 5 \, a^{9} b^{4} d e^{4} - a^{10} b^{3} e^{5} + {\left(b^{13} d^{5} - 5 \, a b^{12} d^{4} e + 10 \, a^{2} b^{11} d^{3} e^{2} - 10 \, a^{3} b^{10} d^{2} e^{3} + 5 \, a^{4} b^{9} d e^{4} - a^{5} b^{8} e^{5}\right)} x^{5} + 5 \, {\left(a b^{12} d^{5} - 5 \, a^{2} b^{11} d^{4} e + 10 \, a^{3} b^{10} d^{3} e^{2} - 10 \, a^{4} b^{9} d^{2} e^{3} + 5 \, a^{5} b^{8} d e^{4} - a^{6} b^{7} e^{5}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{5} - 5 \, a^{3} b^{10} d^{4} e + 10 \, a^{4} b^{9} d^{3} e^{2} - 10 \, a^{5} b^{8} d^{2} e^{3} + 5 \, a^{6} b^{7} d e^{4} - a^{7} b^{6} e^{5}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{5} - 5 \, a^{4} b^{9} d^{4} e + 10 \, a^{5} b^{8} d^{3} e^{2} - 10 \, a^{6} b^{7} d^{2} e^{3} + 5 \, a^{7} b^{6} d e^{4} - a^{8} b^{5} e^{5}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{5} - 5 \, a^{5} b^{8} d^{4} e + 10 \, a^{6} b^{7} d^{3} e^{2} - 10 \, a^{7} b^{6} d^{2} e^{3} + 5 \, a^{8} b^{5} d e^{4} - a^{9} b^{4} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/3840*(15*(10*B*a^5*b*d*e^4 - (3*B*a^6 + 7*A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (3*B*a*b^5 + 7*A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (3*B*a^2*b^4 + 7*A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (3*B*a^3*b^3 + 7*A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (3*B*a^4*b^2 + 7*A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (3*B*a^5*b + 7*A*a^4*b^2)*e^5)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(96*(B*a*b^6 + 4*A*b^7)*d^5 - 16*(28*B*a^2*b^5 + 117*A*a*b^6)*d^4*e + 4*(197*B*a^3*b^4 + 898*A*a^2*b^5)*d^3*e^2 - 2*(278*B*a^4*b^3 + 1657*A*a^3*b^4)*d^2*e^3 + 5*(33*B*a^5*b^2 + 263*A*a^4*b^3)*d*e^4 - 15*(3*B*a^6*b + 7*A*a^5*b^2)*e^5 + 15*(10*B*b^7*d^2*e^3 - (13*B*a*b^6 + 7*A*b^7)*d*e^4 + (3*B*a^2*b^5 + 7*A*a*b^6)*e^5)*x^4 - 10*(10*B*b^7*d^3*e^2 - (83*B*a*b^6 + 7*A*b^7)*d^2*e^3 + 2*(47*B*a^2*b^5 + 28*A*a*b^6)*d*e^4 - 7*(3*B*a^3*b^4 + 7*A*a^2*b^5)*e^5)*x^3 + 2*(40*B*b^7*d^4*e - 2*(141*B*a*b^6 + 14*A*b^7)*d^3*e^2 + 3*(317*B*a^2*b^5 + 63*A*a*b^6)*d^2*e^3 - (901*B*a^3*b^4 + 609*A*a^2*b^5)*d*e^4 + 64*(3*B*a^4*b^3 + 7*A*a^3*b^4)*e^5)*x^2 + 2*(240*B*b^7*d^5 - 8*(143*B*a*b^6 - 3*A*b^7)*d^4*e + 2*(1041*B*a^2*b^5 - 76*A*a*b^6)*d^3*e^2 - 3*(529*B*a^3*b^4 - 139*A*a^2*b^5)*d^2*e^3 + 2*(257*B*a^4*b^3 - 342*A*a^3*b^4)*d*e^4 - 5*(21*B*a^5*b^2 - 79*A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^5 - 5*a^6*b^7*d^4*e + 10*a^7*b^6*d^3*e^2 - 10*a^8*b^5*d^2*e^3 + 5*a^9*b^4*d*e^4 - a^10*b^3*e^5 + (b^13*d^5 - 5*a*b^12*d^4*e + 10*a^2*b^11*d^3*e^2 - 10*a^3*b^10*d^2*e^3 + 5*a^4*b^9*d*e^4 - a^5*b^8*e^5)*x^5 + 5*(a*b^12*d^5 - 5*a^2*b^11*d^4*e + 10*a^3*b^10*d^3*e^2 - 10*a^4*b^9*d^2*e^3 + 5*a^5*b^8*d*e^4 - a^6*b^7*e^5)*x^4 + 10*(a^2*b^11*d^5 - 5*a^3*b^10*d^4*e + 10*a^4*b^9*d^3*e^2 - 10*a^5*b^8*d^2*e^3 + 5*a^6*b^7*d*e^4 - a^7*b^6*e^5)*x^3 + 10*(a^3*b^10*d^5 - 5*a^4*b^9*d^4*e + 10*a^5*b^8*d^3*e^2 - 10*a^6*b^7*d^2*e^3 + 5*a^7*b^6*d*e^4 - a^8*b^5*e^5)*x^2 + 5*(a^4*b^9*d^5 - 5*a^5*b^8*d^4*e + 10*a^6*b^7*d^3*e^2 - 10*a^7*b^6*d^2*e^3 + 5*a^8*b^5*d*e^4 - a^9*b^4*e^5)*x), -1/1920*(15*(10*B*a^5*b*d*e^4 - (3*B*a^6 + 7*A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (3*B*a*b^5 + 7*A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (3*B*a^2*b^4 + 7*A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (3*B*a^3*b^3 + 7*A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (3*B*a^4*b^2 + 7*A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (3*B*a^5*b + 7*A*a^4*b^2)*e^5)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (96*(B*a*b^6 + 4*A*b^7)*d^5 - 16*(28*B*a^2*b^5 + 117*A*a*b^6)*d^4*e + 4*(197*B*a^3*b^4 + 898*A*a^2*b^5)*d^3*e^2 - 2*(278*B*a^4*b^3 + 1657*A*a^3*b^4)*d^2*e^3 + 5*(33*B*a^5*b^2 + 263*A*a^4*b^3)*d*e^4 - 15*(3*B*a^6*b + 7*A*a^5*b^2)*e^5 + 15*(10*B*b^7*d^2*e^3 - (13*B*a*b^6 + 7*A*b^7)*d*e^4 + (3*B*a^2*b^5 + 7*A*a*b^6)*e^5)*x^4 - 10*(10*B*b^7*d^3*e^2 - (83*B*a*b^6 + 7*A*b^7)*d^2*e^3 + 2*(47*B*a^2*b^5 + 28*A*a*b^6)*d*e^4 - 7*(3*B*a^3*b^4 + 7*A*a^2*b^5)*e^5)*x^3 + 2*(40*B*b^7*d^4*e - 2*(141*B*a*b^6 + 14*A*b^7)*d^3*e^2 + 3*(317*B*a^2*b^5 + 63*A*a*b^6)*d^2*e^3 - (901*B*a^3*b^4 + 609*A*a^2*b^5)*d*e^4 + 64*(3*B*a^4*b^3 + 7*A*a^3*b^4)*e^5)*x^2 + 2*(240*B*b^7*d^5 - 8*(143*B*a*b^6 - 3*A*b^7)*d^4*e + 2*(1041*B*a^2*b^5 - 76*A*a*b^6)*d^3*e^2 - 3*(529*B*a^3*b^4 - 139*A*a^2*b^5)*d^2*e^3 + 2*(257*B*a^4*b^3 - 342*A*a^3*b^4)*d*e^4 - 5*(21*B*a^5*b^2 - 79*A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^5 - 5*a^6*b^7*d^4*e + 10*a^7*b^6*d^3*e^2 - 10*a^8*b^5*d^2*e^3 + 5*a^9*b^4*d*e^4 - a^10*b^3*e^5 + (b^13*d^5 - 5*a*b^12*d^4*e + 10*a^2*b^11*d^3*e^2 - 10*a^3*b^10*d^2*e^3 + 5*a^4*b^9*d*e^4 - a^5*b^8*e^5)*x^5 + 5*(a*b^12*d^5 - 5*a^2*b^11*d^4*e + 10*a^3*b^10*d^3*e^2 - 10*a^4*b^9*d^2*e^3 + 5*a^5*b^8*d*e^4 - a^6*b^7*e^5)*x^4 + 10*(a^2*b^11*d^5 - 5*a^3*b^10*d^4*e + 10*a^4*b^9*d^3*e^2 - 10*a^5*b^8*d^2*e^3 + 5*a^6*b^7*d*e^4 - a^7*b^6*e^5)*x^3 + 10*(a^3*b^10*d^5 - 5*a^4*b^9*d^4*e + 10*a^5*b^8*d^3*e^2 - 10*a^6*b^7*d^2*e^3 + 5*a^7*b^6*d*e^4 - a^8*b^5*e^5)*x^2 + 5*(a^4*b^9*d^5 - 5*a^5*b^8*d^4*e + 10*a^6*b^7*d^3*e^2 - 10*a^7*b^6*d^2*e^3 + 5*a^8*b^5*d*e^4 - a^9*b^4*e^5)*x)]","B",0
1831,1,2715,0,0.519143," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(10 \, B a^{5} b d e^{4} - {\left(B a^{6} + 9 \, A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(B a b^{5} + 9 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(B a^{2} b^{4} + 9 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(B a^{3} b^{3} + 9 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(B a^{4} b^{2} + 9 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(B a^{5} b + 9 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} - 16 \, {\left(38 \, B a^{2} b^{5} + 147 \, A a b^{6}\right)} d^{4} e + 12 \, {\left(139 \, B a^{3} b^{4} + 506 \, A a^{2} b^{5}\right)} d^{3} e^{2} - 6 \, {\left(456 \, B a^{4} b^{3} + 1429 \, A a^{3} b^{4}\right)} d^{2} e^{3} + 5 \, {\left(295 \, B a^{5} b^{2} + 1473 \, A a^{4} b^{3}\right)} d e^{4} + 15 \, {\left(7 \, B a^{6} b - 193 \, A a^{5} b^{2}\right)} e^{5} - 105 \, {\left(10 \, B b^{7} d^{2} e^{3} - {\left(11 \, B a b^{6} + 9 \, A b^{7}\right)} d e^{4} + {\left(B a^{2} b^{5} + 9 \, A a b^{6}\right)} e^{5}\right)} x^{4} + 70 \, {\left(10 \, B b^{7} d^{3} e^{2} - 9 \, {\left(9 \, B a b^{6} + A b^{7}\right)} d^{2} e^{3} + 6 \, {\left(13 \, B a^{2} b^{5} + 12 \, A a b^{6}\right)} d e^{4} - 7 \, {\left(B a^{3} b^{4} + 9 \, A a^{2} b^{5}\right)} e^{5}\right)} x^{3} - 14 \, {\left(40 \, B b^{7} d^{4} e - 2 \, {\left(137 \, B a b^{6} + 18 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(299 \, B a^{2} b^{5} + 81 \, A a b^{6}\right)} d^{2} e^{3} - {\left(727 \, B a^{3} b^{4} + 783 \, A a^{2} b^{5}\right)} d e^{4} + 64 \, {\left(B a^{4} b^{3} + 9 \, A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(240 \, B b^{7} d^{5} - 8 \, {\left(193 \, B a b^{6} + 27 \, A b^{7}\right)} d^{4} e + 2 \, {\left(2161 \, B a^{2} b^{5} + 684 \, A a b^{6}\right)} d^{3} e^{2} - 3 \, {\left(2419 \, B a^{3} b^{4} + 1251 \, A a^{2} b^{5}\right)} d^{2} e^{3} + 2 \, {\left(2317 \, B a^{4} b^{3} + 3078 \, A a^{3} b^{4}\right)} d e^{4} - 395 \, {\left(B a^{5} b^{2} + 9 \, A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(a^{5} b^{8} d^{6} - 6 \, a^{6} b^{7} d^{5} e + 15 \, a^{7} b^{6} d^{4} e^{2} - 20 \, a^{8} b^{5} d^{3} e^{3} + 15 \, a^{9} b^{4} d^{2} e^{4} - 6 \, a^{10} b^{3} d e^{5} + a^{11} b^{2} e^{6} + {\left(b^{13} d^{6} - 6 \, a b^{12} d^{5} e + 15 \, a^{2} b^{11} d^{4} e^{2} - 20 \, a^{3} b^{10} d^{3} e^{3} + 15 \, a^{4} b^{9} d^{2} e^{4} - 6 \, a^{5} b^{8} d e^{5} + a^{6} b^{7} e^{6}\right)} x^{5} + 5 \, {\left(a b^{12} d^{6} - 6 \, a^{2} b^{11} d^{5} e + 15 \, a^{3} b^{10} d^{4} e^{2} - 20 \, a^{4} b^{9} d^{3} e^{3} + 15 \, a^{5} b^{8} d^{2} e^{4} - 6 \, a^{6} b^{7} d e^{5} + a^{7} b^{6} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{6} - 6 \, a^{3} b^{10} d^{5} e + 15 \, a^{4} b^{9} d^{4} e^{2} - 20 \, a^{5} b^{8} d^{3} e^{3} + 15 \, a^{6} b^{7} d^{2} e^{4} - 6 \, a^{7} b^{6} d e^{5} + a^{8} b^{5} e^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{6} - 6 \, a^{4} b^{9} d^{5} e + 15 \, a^{5} b^{8} d^{4} e^{2} - 20 \, a^{6} b^{7} d^{3} e^{3} + 15 \, a^{7} b^{6} d^{2} e^{4} - 6 \, a^{8} b^{5} d e^{5} + a^{9} b^{4} e^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{6} - 6 \, a^{5} b^{8} d^{5} e + 15 \, a^{6} b^{7} d^{4} e^{2} - 20 \, a^{7} b^{6} d^{3} e^{3} + 15 \, a^{8} b^{5} d^{2} e^{4} - 6 \, a^{9} b^{4} d e^{5} + a^{10} b^{3} e^{6}\right)} x\right)}}, \frac{105 \, {\left(10 \, B a^{5} b d e^{4} - {\left(B a^{6} + 9 \, A a^{5} b\right)} e^{5} + {\left(10 \, B b^{6} d e^{4} - {\left(B a b^{5} + 9 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d e^{4} - {\left(B a^{2} b^{4} + 9 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d e^{4} - {\left(B a^{3} b^{3} + 9 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 10 \, {\left(10 \, B a^{3} b^{3} d e^{4} - {\left(B a^{4} b^{2} + 9 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 5 \, {\left(10 \, B a^{4} b^{2} d e^{4} - {\left(B a^{5} b + 9 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{5} - 16 \, {\left(38 \, B a^{2} b^{5} + 147 \, A a b^{6}\right)} d^{4} e + 12 \, {\left(139 \, B a^{3} b^{4} + 506 \, A a^{2} b^{5}\right)} d^{3} e^{2} - 6 \, {\left(456 \, B a^{4} b^{3} + 1429 \, A a^{3} b^{4}\right)} d^{2} e^{3} + 5 \, {\left(295 \, B a^{5} b^{2} + 1473 \, A a^{4} b^{3}\right)} d e^{4} + 15 \, {\left(7 \, B a^{6} b - 193 \, A a^{5} b^{2}\right)} e^{5} - 105 \, {\left(10 \, B b^{7} d^{2} e^{3} - {\left(11 \, B a b^{6} + 9 \, A b^{7}\right)} d e^{4} + {\left(B a^{2} b^{5} + 9 \, A a b^{6}\right)} e^{5}\right)} x^{4} + 70 \, {\left(10 \, B b^{7} d^{3} e^{2} - 9 \, {\left(9 \, B a b^{6} + A b^{7}\right)} d^{2} e^{3} + 6 \, {\left(13 \, B a^{2} b^{5} + 12 \, A a b^{6}\right)} d e^{4} - 7 \, {\left(B a^{3} b^{4} + 9 \, A a^{2} b^{5}\right)} e^{5}\right)} x^{3} - 14 \, {\left(40 \, B b^{7} d^{4} e - 2 \, {\left(137 \, B a b^{6} + 18 \, A b^{7}\right)} d^{3} e^{2} + 3 \, {\left(299 \, B a^{2} b^{5} + 81 \, A a b^{6}\right)} d^{2} e^{3} - {\left(727 \, B a^{3} b^{4} + 783 \, A a^{2} b^{5}\right)} d e^{4} + 64 \, {\left(B a^{4} b^{3} + 9 \, A a^{3} b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(240 \, B b^{7} d^{5} - 8 \, {\left(193 \, B a b^{6} + 27 \, A b^{7}\right)} d^{4} e + 2 \, {\left(2161 \, B a^{2} b^{5} + 684 \, A a b^{6}\right)} d^{3} e^{2} - 3 \, {\left(2419 \, B a^{3} b^{4} + 1251 \, A a^{2} b^{5}\right)} d^{2} e^{3} + 2 \, {\left(2317 \, B a^{4} b^{3} + 3078 \, A a^{3} b^{4}\right)} d e^{4} - 395 \, {\left(B a^{5} b^{2} + 9 \, A a^{4} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{5} b^{8} d^{6} - 6 \, a^{6} b^{7} d^{5} e + 15 \, a^{7} b^{6} d^{4} e^{2} - 20 \, a^{8} b^{5} d^{3} e^{3} + 15 \, a^{9} b^{4} d^{2} e^{4} - 6 \, a^{10} b^{3} d e^{5} + a^{11} b^{2} e^{6} + {\left(b^{13} d^{6} - 6 \, a b^{12} d^{5} e + 15 \, a^{2} b^{11} d^{4} e^{2} - 20 \, a^{3} b^{10} d^{3} e^{3} + 15 \, a^{4} b^{9} d^{2} e^{4} - 6 \, a^{5} b^{8} d e^{5} + a^{6} b^{7} e^{6}\right)} x^{5} + 5 \, {\left(a b^{12} d^{6} - 6 \, a^{2} b^{11} d^{5} e + 15 \, a^{3} b^{10} d^{4} e^{2} - 20 \, a^{4} b^{9} d^{3} e^{3} + 15 \, a^{5} b^{8} d^{2} e^{4} - 6 \, a^{6} b^{7} d e^{5} + a^{7} b^{6} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{6} - 6 \, a^{3} b^{10} d^{5} e + 15 \, a^{4} b^{9} d^{4} e^{2} - 20 \, a^{5} b^{8} d^{3} e^{3} + 15 \, a^{6} b^{7} d^{2} e^{4} - 6 \, a^{7} b^{6} d e^{5} + a^{8} b^{5} e^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} d^{6} - 6 \, a^{4} b^{9} d^{5} e + 15 \, a^{5} b^{8} d^{4} e^{2} - 20 \, a^{6} b^{7} d^{3} e^{3} + 15 \, a^{7} b^{6} d^{2} e^{4} - 6 \, a^{8} b^{5} d e^{5} + a^{9} b^{4} e^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} d^{6} - 6 \, a^{5} b^{8} d^{5} e + 15 \, a^{6} b^{7} d^{4} e^{2} - 20 \, a^{7} b^{6} d^{3} e^{3} + 15 \, a^{8} b^{5} d^{2} e^{4} - 6 \, a^{9} b^{4} d e^{5} + a^{10} b^{3} e^{6}\right)} x\right)}}\right]"," ",0,"[1/3840*(105*(10*B*a^5*b*d*e^4 - (B*a^6 + 9*A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (B*a*b^5 + 9*A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (B*a^2*b^4 + 9*A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (B*a^3*b^3 + 9*A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (B*a^4*b^2 + 9*A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (B*a^5*b + 9*A*a^4*b^2)*e^5)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(96*(B*a*b^6 + 4*A*b^7)*d^5 - 16*(38*B*a^2*b^5 + 147*A*a*b^6)*d^4*e + 12*(139*B*a^3*b^4 + 506*A*a^2*b^5)*d^3*e^2 - 6*(456*B*a^4*b^3 + 1429*A*a^3*b^4)*d^2*e^3 + 5*(295*B*a^5*b^2 + 1473*A*a^4*b^3)*d*e^4 + 15*(7*B*a^6*b - 193*A*a^5*b^2)*e^5 - 105*(10*B*b^7*d^2*e^3 - (11*B*a*b^6 + 9*A*b^7)*d*e^4 + (B*a^2*b^5 + 9*A*a*b^6)*e^5)*x^4 + 70*(10*B*b^7*d^3*e^2 - 9*(9*B*a*b^6 + A*b^7)*d^2*e^3 + 6*(13*B*a^2*b^5 + 12*A*a*b^6)*d*e^4 - 7*(B*a^3*b^4 + 9*A*a^2*b^5)*e^5)*x^3 - 14*(40*B*b^7*d^4*e - 2*(137*B*a*b^6 + 18*A*b^7)*d^3*e^2 + 3*(299*B*a^2*b^5 + 81*A*a*b^6)*d^2*e^3 - (727*B*a^3*b^4 + 783*A*a^2*b^5)*d*e^4 + 64*(B*a^4*b^3 + 9*A*a^3*b^4)*e^5)*x^2 + 2*(240*B*b^7*d^5 - 8*(193*B*a*b^6 + 27*A*b^7)*d^4*e + 2*(2161*B*a^2*b^5 + 684*A*a*b^6)*d^3*e^2 - 3*(2419*B*a^3*b^4 + 1251*A*a^2*b^5)*d^2*e^3 + 2*(2317*B*a^4*b^3 + 3078*A*a^3*b^4)*d*e^4 - 395*(B*a^5*b^2 + 9*A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^6 - 6*a^6*b^7*d^5*e + 15*a^7*b^6*d^4*e^2 - 20*a^8*b^5*d^3*e^3 + 15*a^9*b^4*d^2*e^4 - 6*a^10*b^3*d*e^5 + a^11*b^2*e^6 + (b^13*d^6 - 6*a*b^12*d^5*e + 15*a^2*b^11*d^4*e^2 - 20*a^3*b^10*d^3*e^3 + 15*a^4*b^9*d^2*e^4 - 6*a^5*b^8*d*e^5 + a^6*b^7*e^6)*x^5 + 5*(a*b^12*d^6 - 6*a^2*b^11*d^5*e + 15*a^3*b^10*d^4*e^2 - 20*a^4*b^9*d^3*e^3 + 15*a^5*b^8*d^2*e^4 - 6*a^6*b^7*d*e^5 + a^7*b^6*e^6)*x^4 + 10*(a^2*b^11*d^6 - 6*a^3*b^10*d^5*e + 15*a^4*b^9*d^4*e^2 - 20*a^5*b^8*d^3*e^3 + 15*a^6*b^7*d^2*e^4 - 6*a^7*b^6*d*e^5 + a^8*b^5*e^6)*x^3 + 10*(a^3*b^10*d^6 - 6*a^4*b^9*d^5*e + 15*a^5*b^8*d^4*e^2 - 20*a^6*b^7*d^3*e^3 + 15*a^7*b^6*d^2*e^4 - 6*a^8*b^5*d*e^5 + a^9*b^4*e^6)*x^2 + 5*(a^4*b^9*d^6 - 6*a^5*b^8*d^5*e + 15*a^6*b^7*d^4*e^2 - 20*a^7*b^6*d^3*e^3 + 15*a^8*b^5*d^2*e^4 - 6*a^9*b^4*d*e^5 + a^10*b^3*e^6)*x), 1/1920*(105*(10*B*a^5*b*d*e^4 - (B*a^6 + 9*A*a^5*b)*e^5 + (10*B*b^6*d*e^4 - (B*a*b^5 + 9*A*b^6)*e^5)*x^5 + 5*(10*B*a*b^5*d*e^4 - (B*a^2*b^4 + 9*A*a*b^5)*e^5)*x^4 + 10*(10*B*a^2*b^4*d*e^4 - (B*a^3*b^3 + 9*A*a^2*b^4)*e^5)*x^3 + 10*(10*B*a^3*b^3*d*e^4 - (B*a^4*b^2 + 9*A*a^3*b^3)*e^5)*x^2 + 5*(10*B*a^4*b^2*d*e^4 - (B*a^5*b + 9*A*a^4*b^2)*e^5)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (96*(B*a*b^6 + 4*A*b^7)*d^5 - 16*(38*B*a^2*b^5 + 147*A*a*b^6)*d^4*e + 12*(139*B*a^3*b^4 + 506*A*a^2*b^5)*d^3*e^2 - 6*(456*B*a^4*b^3 + 1429*A*a^3*b^4)*d^2*e^3 + 5*(295*B*a^5*b^2 + 1473*A*a^4*b^3)*d*e^4 + 15*(7*B*a^6*b - 193*A*a^5*b^2)*e^5 - 105*(10*B*b^7*d^2*e^3 - (11*B*a*b^6 + 9*A*b^7)*d*e^4 + (B*a^2*b^5 + 9*A*a*b^6)*e^5)*x^4 + 70*(10*B*b^7*d^3*e^2 - 9*(9*B*a*b^6 + A*b^7)*d^2*e^3 + 6*(13*B*a^2*b^5 + 12*A*a*b^6)*d*e^4 - 7*(B*a^3*b^4 + 9*A*a^2*b^5)*e^5)*x^3 - 14*(40*B*b^7*d^4*e - 2*(137*B*a*b^6 + 18*A*b^7)*d^3*e^2 + 3*(299*B*a^2*b^5 + 81*A*a*b^6)*d^2*e^3 - (727*B*a^3*b^4 + 783*A*a^2*b^5)*d*e^4 + 64*(B*a^4*b^3 + 9*A*a^3*b^4)*e^5)*x^2 + 2*(240*B*b^7*d^5 - 8*(193*B*a*b^6 + 27*A*b^7)*d^4*e + 2*(2161*B*a^2*b^5 + 684*A*a*b^6)*d^3*e^2 - 3*(2419*B*a^3*b^4 + 1251*A*a^2*b^5)*d^2*e^3 + 2*(2317*B*a^4*b^3 + 3078*A*a^3*b^4)*d*e^4 - 395*(B*a^5*b^2 + 9*A*a^4*b^3)*e^5)*x)*sqrt(e*x + d))/(a^5*b^8*d^6 - 6*a^6*b^7*d^5*e + 15*a^7*b^6*d^4*e^2 - 20*a^8*b^5*d^3*e^3 + 15*a^9*b^4*d^2*e^4 - 6*a^10*b^3*d*e^5 + a^11*b^2*e^6 + (b^13*d^6 - 6*a*b^12*d^5*e + 15*a^2*b^11*d^4*e^2 - 20*a^3*b^10*d^3*e^3 + 15*a^4*b^9*d^2*e^4 - 6*a^5*b^8*d*e^5 + a^6*b^7*e^6)*x^5 + 5*(a*b^12*d^6 - 6*a^2*b^11*d^5*e + 15*a^3*b^10*d^4*e^2 - 20*a^4*b^9*d^3*e^3 + 15*a^5*b^8*d^2*e^4 - 6*a^6*b^7*d*e^5 + a^7*b^6*e^6)*x^4 + 10*(a^2*b^11*d^6 - 6*a^3*b^10*d^5*e + 15*a^4*b^9*d^4*e^2 - 20*a^5*b^8*d^3*e^3 + 15*a^6*b^7*d^2*e^4 - 6*a^7*b^6*d*e^5 + a^8*b^5*e^6)*x^3 + 10*(a^3*b^10*d^6 - 6*a^4*b^9*d^5*e + 15*a^5*b^8*d^4*e^2 - 20*a^6*b^7*d^3*e^3 + 15*a^7*b^6*d^2*e^4 - 6*a^8*b^5*d*e^5 + a^9*b^4*e^6)*x^2 + 5*(a^4*b^9*d^6 - 6*a^5*b^8*d^5*e + 15*a^6*b^7*d^4*e^2 - 20*a^7*b^6*d^3*e^3 + 15*a^8*b^5*d^2*e^4 - 6*a^9*b^4*d*e^5 + a^10*b^3*e^6)*x)]","B",0
1832,1,3876,0,0.547844," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(10 \, B a^{5} b d^{2} e^{4} + {\left(B a^{6} - 11 \, A a^{5} b\right)} d e^{5} + {\left(10 \, B b^{6} d e^{5} + {\left(B a b^{5} - 11 \, A b^{6}\right)} e^{6}\right)} x^{6} + {\left(10 \, B b^{6} d^{2} e^{4} + {\left(51 \, B a b^{5} - 11 \, A b^{6}\right)} d e^{5} + 5 \, {\left(B a^{2} b^{4} - 11 \, A a b^{5}\right)} e^{6}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d^{2} e^{4} + {\left(21 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} d e^{5} + 2 \, {\left(B a^{3} b^{3} - 11 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d^{2} e^{4} + 11 \, {\left(B a^{3} b^{3} - A a^{2} b^{4}\right)} d e^{5} + {\left(B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} e^{6}\right)} x^{3} + 5 \, {\left(20 \, B a^{3} b^{3} d^{2} e^{4} + 2 \, {\left(6 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} d e^{5} + {\left(B a^{5} b - 11 \, A a^{4} b^{2}\right)} e^{6}\right)} x^{2} + {\left(50 \, B a^{4} b^{2} d^{2} e^{4} + 5 \, {\left(3 \, B a^{5} b - 11 \, A a^{4} b^{2}\right)} d e^{5} + {\left(B a^{6} - 11 \, A a^{5} b\right)} e^{6}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(1280 \, A a^{6} b e^{6} - 32 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{6} + 16 \, {\left(16 \, B a^{2} b^{5} + 59 \, A a b^{6}\right)} d^{5} e - 4 \, {\left(239 \, B a^{3} b^{4} + 766 \, A a^{2} b^{5}\right)} d^{4} e^{2} + 14 \, {\left(178 \, B a^{4} b^{3} + 417 \, A a^{3} b^{4}\right)} d^{3} e^{3} + 5 \, {\left(97 \, B a^{5} b^{2} - 1561 \, A a^{4} b^{3}\right)} d^{2} e^{4} - 5 \, {\left(449 \, B a^{6} b - 587 \, A a^{5} b^{2}\right)} d e^{5} + 315 \, {\left(10 \, B b^{7} d^{2} e^{4} - {\left(9 \, B a b^{6} + 11 \, A b^{7}\right)} d e^{5} - {\left(B a^{2} b^{5} - 11 \, A a b^{6}\right)} e^{6}\right)} x^{5} + 105 \, {\left(10 \, B b^{7} d^{3} e^{3} + {\left(131 \, B a b^{6} - 11 \, A b^{7}\right)} d^{2} e^{4} - {\left(127 \, B a^{2} b^{5} + 143 \, A a b^{6}\right)} d e^{5} - 14 \, {\left(B a^{3} b^{4} - 11 \, A a^{2} b^{5}\right)} e^{6}\right)} x^{4} - 42 \, {\left(10 \, B b^{7} d^{4} e^{2} - {\left(129 \, B a b^{6} + 11 \, A b^{7}\right)} d^{3} e^{3} - 13 \, {\left(41 \, B a^{2} b^{5} - 11 \, A a b^{6}\right)} d^{2} e^{4} + 4 \, {\left(147 \, B a^{3} b^{4} + 143 \, A a^{2} b^{5}\right)} d e^{5} + 64 \, {\left(B a^{4} b^{3} - 11 \, A a^{3} b^{4}\right)} e^{6}\right)} x^{3} + 6 \, {\left(40 \, B b^{7} d^{5} e - 2 \, {\left(183 \, B a b^{6} + 22 \, A b^{7}\right)} d^{4} e^{2} + {\left(1883 \, B a^{2} b^{5} + 407 \, A a b^{6}\right)} d^{3} e^{3} + 88 \, {\left(29 \, B a^{3} b^{4} - 24 \, A a^{2} b^{5}\right)} d^{2} e^{4} - 2 \, {\left(1857 \, B a^{4} b^{3} + 1298 \, A a^{3} b^{4}\right)} d e^{5} - 395 \, {\left(B a^{5} b^{2} - 11 \, A a^{4} b^{3}\right)} e^{6}\right)} x^{2} - {\left(160 \, B b^{7} d^{6} - 16 \, {\left(79 \, B a b^{6} + 11 \, A b^{7}\right)} d^{5} e + 4 \, {\left(1163 \, B a^{2} b^{5} + 352 \, A a b^{6}\right)} d^{4} e^{2} - 2 \, {\left(5991 \, B a^{3} b^{4} + 2629 \, A a^{2} b^{5}\right)} d^{3} e^{3} - 2 \, {\left(1048 \, B a^{4} b^{3} - 6853 \, A a^{3} b^{4}\right)} d^{2} e^{4} + 5 \, {\left(1913 \, B a^{5} b^{2} + 187 \, A a^{4} b^{3}\right)} d e^{5} + 965 \, {\left(B a^{6} b - 11 \, A a^{5} b^{2}\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(a^{5} b^{8} d^{8} - 7 \, a^{6} b^{7} d^{7} e + 21 \, a^{7} b^{6} d^{6} e^{2} - 35 \, a^{8} b^{5} d^{5} e^{3} + 35 \, a^{9} b^{4} d^{4} e^{4} - 21 \, a^{10} b^{3} d^{3} e^{5} + 7 \, a^{11} b^{2} d^{2} e^{6} - a^{12} b d e^{7} + {\left(b^{13} d^{7} e - 7 \, a b^{12} d^{6} e^{2} + 21 \, a^{2} b^{11} d^{5} e^{3} - 35 \, a^{3} b^{10} d^{4} e^{4} + 35 \, a^{4} b^{9} d^{3} e^{5} - 21 \, a^{5} b^{8} d^{2} e^{6} + 7 \, a^{6} b^{7} d e^{7} - a^{7} b^{6} e^{8}\right)} x^{6} + {\left(b^{13} d^{8} - 2 \, a b^{12} d^{7} e - 14 \, a^{2} b^{11} d^{6} e^{2} + 70 \, a^{3} b^{10} d^{5} e^{3} - 140 \, a^{4} b^{9} d^{4} e^{4} + 154 \, a^{5} b^{8} d^{3} e^{5} - 98 \, a^{6} b^{7} d^{2} e^{6} + 34 \, a^{7} b^{6} d e^{7} - 5 \, a^{8} b^{5} e^{8}\right)} x^{5} + 5 \, {\left(a b^{12} d^{8} - 5 \, a^{2} b^{11} d^{7} e + 7 \, a^{3} b^{10} d^{6} e^{2} + 7 \, a^{4} b^{9} d^{5} e^{3} - 35 \, a^{5} b^{8} d^{4} e^{4} + 49 \, a^{6} b^{7} d^{3} e^{5} - 35 \, a^{7} b^{6} d^{2} e^{6} + 13 \, a^{8} b^{5} d e^{7} - 2 \, a^{9} b^{4} e^{8}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{8} - 6 \, a^{3} b^{10} d^{7} e + 14 \, a^{4} b^{9} d^{6} e^{2} - 14 \, a^{5} b^{8} d^{5} e^{3} + 14 \, a^{7} b^{6} d^{3} e^{5} - 14 \, a^{8} b^{5} d^{2} e^{6} + 6 \, a^{9} b^{4} d e^{7} - a^{10} b^{3} e^{8}\right)} x^{3} + 5 \, {\left(2 \, a^{3} b^{10} d^{8} - 13 \, a^{4} b^{9} d^{7} e + 35 \, a^{5} b^{8} d^{6} e^{2} - 49 \, a^{6} b^{7} d^{5} e^{3} + 35 \, a^{7} b^{6} d^{4} e^{4} - 7 \, a^{8} b^{5} d^{3} e^{5} - 7 \, a^{9} b^{4} d^{2} e^{6} + 5 \, a^{10} b^{3} d e^{7} - a^{11} b^{2} e^{8}\right)} x^{2} + {\left(5 \, a^{4} b^{9} d^{8} - 34 \, a^{5} b^{8} d^{7} e + 98 \, a^{6} b^{7} d^{6} e^{2} - 154 \, a^{7} b^{6} d^{5} e^{3} + 140 \, a^{8} b^{5} d^{4} e^{4} - 70 \, a^{9} b^{4} d^{3} e^{5} + 14 \, a^{10} b^{3} d^{2} e^{6} + 2 \, a^{11} b^{2} d e^{7} - a^{12} b e^{8}\right)} x\right)}}, \frac{315 \, {\left(10 \, B a^{5} b d^{2} e^{4} + {\left(B a^{6} - 11 \, A a^{5} b\right)} d e^{5} + {\left(10 \, B b^{6} d e^{5} + {\left(B a b^{5} - 11 \, A b^{6}\right)} e^{6}\right)} x^{6} + {\left(10 \, B b^{6} d^{2} e^{4} + {\left(51 \, B a b^{5} - 11 \, A b^{6}\right)} d e^{5} + 5 \, {\left(B a^{2} b^{4} - 11 \, A a b^{5}\right)} e^{6}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d^{2} e^{4} + {\left(21 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} d e^{5} + 2 \, {\left(B a^{3} b^{3} - 11 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{4} + 10 \, {\left(10 \, B a^{2} b^{4} d^{2} e^{4} + 11 \, {\left(B a^{3} b^{3} - A a^{2} b^{4}\right)} d e^{5} + {\left(B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} e^{6}\right)} x^{3} + 5 \, {\left(20 \, B a^{3} b^{3} d^{2} e^{4} + 2 \, {\left(6 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} d e^{5} + {\left(B a^{5} b - 11 \, A a^{4} b^{2}\right)} e^{6}\right)} x^{2} + {\left(50 \, B a^{4} b^{2} d^{2} e^{4} + 5 \, {\left(3 \, B a^{5} b - 11 \, A a^{4} b^{2}\right)} d e^{5} + {\left(B a^{6} - 11 \, A a^{5} b\right)} e^{6}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(1280 \, A a^{6} b e^{6} - 32 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{6} + 16 \, {\left(16 \, B a^{2} b^{5} + 59 \, A a b^{6}\right)} d^{5} e - 4 \, {\left(239 \, B a^{3} b^{4} + 766 \, A a^{2} b^{5}\right)} d^{4} e^{2} + 14 \, {\left(178 \, B a^{4} b^{3} + 417 \, A a^{3} b^{4}\right)} d^{3} e^{3} + 5 \, {\left(97 \, B a^{5} b^{2} - 1561 \, A a^{4} b^{3}\right)} d^{2} e^{4} - 5 \, {\left(449 \, B a^{6} b - 587 \, A a^{5} b^{2}\right)} d e^{5} + 315 \, {\left(10 \, B b^{7} d^{2} e^{4} - {\left(9 \, B a b^{6} + 11 \, A b^{7}\right)} d e^{5} - {\left(B a^{2} b^{5} - 11 \, A a b^{6}\right)} e^{6}\right)} x^{5} + 105 \, {\left(10 \, B b^{7} d^{3} e^{3} + {\left(131 \, B a b^{6} - 11 \, A b^{7}\right)} d^{2} e^{4} - {\left(127 \, B a^{2} b^{5} + 143 \, A a b^{6}\right)} d e^{5} - 14 \, {\left(B a^{3} b^{4} - 11 \, A a^{2} b^{5}\right)} e^{6}\right)} x^{4} - 42 \, {\left(10 \, B b^{7} d^{4} e^{2} - {\left(129 \, B a b^{6} + 11 \, A b^{7}\right)} d^{3} e^{3} - 13 \, {\left(41 \, B a^{2} b^{5} - 11 \, A a b^{6}\right)} d^{2} e^{4} + 4 \, {\left(147 \, B a^{3} b^{4} + 143 \, A a^{2} b^{5}\right)} d e^{5} + 64 \, {\left(B a^{4} b^{3} - 11 \, A a^{3} b^{4}\right)} e^{6}\right)} x^{3} + 6 \, {\left(40 \, B b^{7} d^{5} e - 2 \, {\left(183 \, B a b^{6} + 22 \, A b^{7}\right)} d^{4} e^{2} + {\left(1883 \, B a^{2} b^{5} + 407 \, A a b^{6}\right)} d^{3} e^{3} + 88 \, {\left(29 \, B a^{3} b^{4} - 24 \, A a^{2} b^{5}\right)} d^{2} e^{4} - 2 \, {\left(1857 \, B a^{4} b^{3} + 1298 \, A a^{3} b^{4}\right)} d e^{5} - 395 \, {\left(B a^{5} b^{2} - 11 \, A a^{4} b^{3}\right)} e^{6}\right)} x^{2} - {\left(160 \, B b^{7} d^{6} - 16 \, {\left(79 \, B a b^{6} + 11 \, A b^{7}\right)} d^{5} e + 4 \, {\left(1163 \, B a^{2} b^{5} + 352 \, A a b^{6}\right)} d^{4} e^{2} - 2 \, {\left(5991 \, B a^{3} b^{4} + 2629 \, A a^{2} b^{5}\right)} d^{3} e^{3} - 2 \, {\left(1048 \, B a^{4} b^{3} - 6853 \, A a^{3} b^{4}\right)} d^{2} e^{4} + 5 \, {\left(1913 \, B a^{5} b^{2} + 187 \, A a^{4} b^{3}\right)} d e^{5} + 965 \, {\left(B a^{6} b - 11 \, A a^{5} b^{2}\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(a^{5} b^{8} d^{8} - 7 \, a^{6} b^{7} d^{7} e + 21 \, a^{7} b^{6} d^{6} e^{2} - 35 \, a^{8} b^{5} d^{5} e^{3} + 35 \, a^{9} b^{4} d^{4} e^{4} - 21 \, a^{10} b^{3} d^{3} e^{5} + 7 \, a^{11} b^{2} d^{2} e^{6} - a^{12} b d e^{7} + {\left(b^{13} d^{7} e - 7 \, a b^{12} d^{6} e^{2} + 21 \, a^{2} b^{11} d^{5} e^{3} - 35 \, a^{3} b^{10} d^{4} e^{4} + 35 \, a^{4} b^{9} d^{3} e^{5} - 21 \, a^{5} b^{8} d^{2} e^{6} + 7 \, a^{6} b^{7} d e^{7} - a^{7} b^{6} e^{8}\right)} x^{6} + {\left(b^{13} d^{8} - 2 \, a b^{12} d^{7} e - 14 \, a^{2} b^{11} d^{6} e^{2} + 70 \, a^{3} b^{10} d^{5} e^{3} - 140 \, a^{4} b^{9} d^{4} e^{4} + 154 \, a^{5} b^{8} d^{3} e^{5} - 98 \, a^{6} b^{7} d^{2} e^{6} + 34 \, a^{7} b^{6} d e^{7} - 5 \, a^{8} b^{5} e^{8}\right)} x^{5} + 5 \, {\left(a b^{12} d^{8} - 5 \, a^{2} b^{11} d^{7} e + 7 \, a^{3} b^{10} d^{6} e^{2} + 7 \, a^{4} b^{9} d^{5} e^{3} - 35 \, a^{5} b^{8} d^{4} e^{4} + 49 \, a^{6} b^{7} d^{3} e^{5} - 35 \, a^{7} b^{6} d^{2} e^{6} + 13 \, a^{8} b^{5} d e^{7} - 2 \, a^{9} b^{4} e^{8}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} d^{8} - 6 \, a^{3} b^{10} d^{7} e + 14 \, a^{4} b^{9} d^{6} e^{2} - 14 \, a^{5} b^{8} d^{5} e^{3} + 14 \, a^{7} b^{6} d^{3} e^{5} - 14 \, a^{8} b^{5} d^{2} e^{6} + 6 \, a^{9} b^{4} d e^{7} - a^{10} b^{3} e^{8}\right)} x^{3} + 5 \, {\left(2 \, a^{3} b^{10} d^{8} - 13 \, a^{4} b^{9} d^{7} e + 35 \, a^{5} b^{8} d^{6} e^{2} - 49 \, a^{6} b^{7} d^{5} e^{3} + 35 \, a^{7} b^{6} d^{4} e^{4} - 7 \, a^{8} b^{5} d^{3} e^{5} - 7 \, a^{9} b^{4} d^{2} e^{6} + 5 \, a^{10} b^{3} d e^{7} - a^{11} b^{2} e^{8}\right)} x^{2} + {\left(5 \, a^{4} b^{9} d^{8} - 34 \, a^{5} b^{8} d^{7} e + 98 \, a^{6} b^{7} d^{6} e^{2} - 154 \, a^{7} b^{6} d^{5} e^{3} + 140 \, a^{8} b^{5} d^{4} e^{4} - 70 \, a^{9} b^{4} d^{3} e^{5} + 14 \, a^{10} b^{3} d^{2} e^{6} + 2 \, a^{11} b^{2} d e^{7} - a^{12} b e^{8}\right)} x\right)}}\right]"," ",0,"[-1/1280*(315*(10*B*a^5*b*d^2*e^4 + (B*a^6 - 11*A*a^5*b)*d*e^5 + (10*B*b^6*d*e^5 + (B*a*b^5 - 11*A*b^6)*e^6)*x^6 + (10*B*b^6*d^2*e^4 + (51*B*a*b^5 - 11*A*b^6)*d*e^5 + 5*(B*a^2*b^4 - 11*A*a*b^5)*e^6)*x^5 + 5*(10*B*a*b^5*d^2*e^4 + (21*B*a^2*b^4 - 11*A*a*b^5)*d*e^5 + 2*(B*a^3*b^3 - 11*A*a^2*b^4)*e^6)*x^4 + 10*(10*B*a^2*b^4*d^2*e^4 + 11*(B*a^3*b^3 - A*a^2*b^4)*d*e^5 + (B*a^4*b^2 - 11*A*a^3*b^3)*e^6)*x^3 + 5*(20*B*a^3*b^3*d^2*e^4 + 2*(6*B*a^4*b^2 - 11*A*a^3*b^3)*d*e^5 + (B*a^5*b - 11*A*a^4*b^2)*e^6)*x^2 + (50*B*a^4*b^2*d^2*e^4 + 5*(3*B*a^5*b - 11*A*a^4*b^2)*d*e^5 + (B*a^6 - 11*A*a^5*b)*e^6)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e + 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(1280*A*a^6*b*e^6 - 32*(B*a*b^6 + 4*A*b^7)*d^6 + 16*(16*B*a^2*b^5 + 59*A*a*b^6)*d^5*e - 4*(239*B*a^3*b^4 + 766*A*a^2*b^5)*d^4*e^2 + 14*(178*B*a^4*b^3 + 417*A*a^3*b^4)*d^3*e^3 + 5*(97*B*a^5*b^2 - 1561*A*a^4*b^3)*d^2*e^4 - 5*(449*B*a^6*b - 587*A*a^5*b^2)*d*e^5 + 315*(10*B*b^7*d^2*e^4 - (9*B*a*b^6 + 11*A*b^7)*d*e^5 - (B*a^2*b^5 - 11*A*a*b^6)*e^6)*x^5 + 105*(10*B*b^7*d^3*e^3 + (131*B*a*b^6 - 11*A*b^7)*d^2*e^4 - (127*B*a^2*b^5 + 143*A*a*b^6)*d*e^5 - 14*(B*a^3*b^4 - 11*A*a^2*b^5)*e^6)*x^4 - 42*(10*B*b^7*d^4*e^2 - (129*B*a*b^6 + 11*A*b^7)*d^3*e^3 - 13*(41*B*a^2*b^5 - 11*A*a*b^6)*d^2*e^4 + 4*(147*B*a^3*b^4 + 143*A*a^2*b^5)*d*e^5 + 64*(B*a^4*b^3 - 11*A*a^3*b^4)*e^6)*x^3 + 6*(40*B*b^7*d^5*e - 2*(183*B*a*b^6 + 22*A*b^7)*d^4*e^2 + (1883*B*a^2*b^5 + 407*A*a*b^6)*d^3*e^3 + 88*(29*B*a^3*b^4 - 24*A*a^2*b^5)*d^2*e^4 - 2*(1857*B*a^4*b^3 + 1298*A*a^3*b^4)*d*e^5 - 395*(B*a^5*b^2 - 11*A*a^4*b^3)*e^6)*x^2 - (160*B*b^7*d^6 - 16*(79*B*a*b^6 + 11*A*b^7)*d^5*e + 4*(1163*B*a^2*b^5 + 352*A*a*b^6)*d^4*e^2 - 2*(5991*B*a^3*b^4 + 2629*A*a^2*b^5)*d^3*e^3 - 2*(1048*B*a^4*b^3 - 6853*A*a^3*b^4)*d^2*e^4 + 5*(1913*B*a^5*b^2 + 187*A*a^4*b^3)*d*e^5 + 965*(B*a^6*b - 11*A*a^5*b^2)*e^6)*x)*sqrt(e*x + d))/(a^5*b^8*d^8 - 7*a^6*b^7*d^7*e + 21*a^7*b^6*d^6*e^2 - 35*a^8*b^5*d^5*e^3 + 35*a^9*b^4*d^4*e^4 - 21*a^10*b^3*d^3*e^5 + 7*a^11*b^2*d^2*e^6 - a^12*b*d*e^7 + (b^13*d^7*e - 7*a*b^12*d^6*e^2 + 21*a^2*b^11*d^5*e^3 - 35*a^3*b^10*d^4*e^4 + 35*a^4*b^9*d^3*e^5 - 21*a^5*b^8*d^2*e^6 + 7*a^6*b^7*d*e^7 - a^7*b^6*e^8)*x^6 + (b^13*d^8 - 2*a*b^12*d^7*e - 14*a^2*b^11*d^6*e^2 + 70*a^3*b^10*d^5*e^3 - 140*a^4*b^9*d^4*e^4 + 154*a^5*b^8*d^3*e^5 - 98*a^6*b^7*d^2*e^6 + 34*a^7*b^6*d*e^7 - 5*a^8*b^5*e^8)*x^5 + 5*(a*b^12*d^8 - 5*a^2*b^11*d^7*e + 7*a^3*b^10*d^6*e^2 + 7*a^4*b^9*d^5*e^3 - 35*a^5*b^8*d^4*e^4 + 49*a^6*b^7*d^3*e^5 - 35*a^7*b^6*d^2*e^6 + 13*a^8*b^5*d*e^7 - 2*a^9*b^4*e^8)*x^4 + 10*(a^2*b^11*d^8 - 6*a^3*b^10*d^7*e + 14*a^4*b^9*d^6*e^2 - 14*a^5*b^8*d^5*e^3 + 14*a^7*b^6*d^3*e^5 - 14*a^8*b^5*d^2*e^6 + 6*a^9*b^4*d*e^7 - a^10*b^3*e^8)*x^3 + 5*(2*a^3*b^10*d^8 - 13*a^4*b^9*d^7*e + 35*a^5*b^8*d^6*e^2 - 49*a^6*b^7*d^5*e^3 + 35*a^7*b^6*d^4*e^4 - 7*a^8*b^5*d^3*e^5 - 7*a^9*b^4*d^2*e^6 + 5*a^10*b^3*d*e^7 - a^11*b^2*e^8)*x^2 + (5*a^4*b^9*d^8 - 34*a^5*b^8*d^7*e + 98*a^6*b^7*d^6*e^2 - 154*a^7*b^6*d^5*e^3 + 140*a^8*b^5*d^4*e^4 - 70*a^9*b^4*d^3*e^5 + 14*a^10*b^3*d^2*e^6 + 2*a^11*b^2*d*e^7 - a^12*b*e^8)*x), 1/640*(315*(10*B*a^5*b*d^2*e^4 + (B*a^6 - 11*A*a^5*b)*d*e^5 + (10*B*b^6*d*e^5 + (B*a*b^5 - 11*A*b^6)*e^6)*x^6 + (10*B*b^6*d^2*e^4 + (51*B*a*b^5 - 11*A*b^6)*d*e^5 + 5*(B*a^2*b^4 - 11*A*a*b^5)*e^6)*x^5 + 5*(10*B*a*b^5*d^2*e^4 + (21*B*a^2*b^4 - 11*A*a*b^5)*d*e^5 + 2*(B*a^3*b^3 - 11*A*a^2*b^4)*e^6)*x^4 + 10*(10*B*a^2*b^4*d^2*e^4 + 11*(B*a^3*b^3 - A*a^2*b^4)*d*e^5 + (B*a^4*b^2 - 11*A*a^3*b^3)*e^6)*x^3 + 5*(20*B*a^3*b^3*d^2*e^4 + 2*(6*B*a^4*b^2 - 11*A*a^3*b^3)*d*e^5 + (B*a^5*b - 11*A*a^4*b^2)*e^6)*x^2 + (50*B*a^4*b^2*d^2*e^4 + 5*(3*B*a^5*b - 11*A*a^4*b^2)*d*e^5 + (B*a^6 - 11*A*a^5*b)*e^6)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (1280*A*a^6*b*e^6 - 32*(B*a*b^6 + 4*A*b^7)*d^6 + 16*(16*B*a^2*b^5 + 59*A*a*b^6)*d^5*e - 4*(239*B*a^3*b^4 + 766*A*a^2*b^5)*d^4*e^2 + 14*(178*B*a^4*b^3 + 417*A*a^3*b^4)*d^3*e^3 + 5*(97*B*a^5*b^2 - 1561*A*a^4*b^3)*d^2*e^4 - 5*(449*B*a^6*b - 587*A*a^5*b^2)*d*e^5 + 315*(10*B*b^7*d^2*e^4 - (9*B*a*b^6 + 11*A*b^7)*d*e^5 - (B*a^2*b^5 - 11*A*a*b^6)*e^6)*x^5 + 105*(10*B*b^7*d^3*e^3 + (131*B*a*b^6 - 11*A*b^7)*d^2*e^4 - (127*B*a^2*b^5 + 143*A*a*b^6)*d*e^5 - 14*(B*a^3*b^4 - 11*A*a^2*b^5)*e^6)*x^4 - 42*(10*B*b^7*d^4*e^2 - (129*B*a*b^6 + 11*A*b^7)*d^3*e^3 - 13*(41*B*a^2*b^5 - 11*A*a*b^6)*d^2*e^4 + 4*(147*B*a^3*b^4 + 143*A*a^2*b^5)*d*e^5 + 64*(B*a^4*b^3 - 11*A*a^3*b^4)*e^6)*x^3 + 6*(40*B*b^7*d^5*e - 2*(183*B*a*b^6 + 22*A*b^7)*d^4*e^2 + (1883*B*a^2*b^5 + 407*A*a*b^6)*d^3*e^3 + 88*(29*B*a^3*b^4 - 24*A*a^2*b^5)*d^2*e^4 - 2*(1857*B*a^4*b^3 + 1298*A*a^3*b^4)*d*e^5 - 395*(B*a^5*b^2 - 11*A*a^4*b^3)*e^6)*x^2 - (160*B*b^7*d^6 - 16*(79*B*a*b^6 + 11*A*b^7)*d^5*e + 4*(1163*B*a^2*b^5 + 352*A*a*b^6)*d^4*e^2 - 2*(5991*B*a^3*b^4 + 2629*A*a^2*b^5)*d^3*e^3 - 2*(1048*B*a^4*b^3 - 6853*A*a^3*b^4)*d^2*e^4 + 5*(1913*B*a^5*b^2 + 187*A*a^4*b^3)*d*e^5 + 965*(B*a^6*b - 11*A*a^5*b^2)*e^6)*x)*sqrt(e*x + d))/(a^5*b^8*d^8 - 7*a^6*b^7*d^7*e + 21*a^7*b^6*d^6*e^2 - 35*a^8*b^5*d^5*e^3 + 35*a^9*b^4*d^4*e^4 - 21*a^10*b^3*d^3*e^5 + 7*a^11*b^2*d^2*e^6 - a^12*b*d*e^7 + (b^13*d^7*e - 7*a*b^12*d^6*e^2 + 21*a^2*b^11*d^5*e^3 - 35*a^3*b^10*d^4*e^4 + 35*a^4*b^9*d^3*e^5 - 21*a^5*b^8*d^2*e^6 + 7*a^6*b^7*d*e^7 - a^7*b^6*e^8)*x^6 + (b^13*d^8 - 2*a*b^12*d^7*e - 14*a^2*b^11*d^6*e^2 + 70*a^3*b^10*d^5*e^3 - 140*a^4*b^9*d^4*e^4 + 154*a^5*b^8*d^3*e^5 - 98*a^6*b^7*d^2*e^6 + 34*a^7*b^6*d*e^7 - 5*a^8*b^5*e^8)*x^5 + 5*(a*b^12*d^8 - 5*a^2*b^11*d^7*e + 7*a^3*b^10*d^6*e^2 + 7*a^4*b^9*d^5*e^3 - 35*a^5*b^8*d^4*e^4 + 49*a^6*b^7*d^3*e^5 - 35*a^7*b^6*d^2*e^6 + 13*a^8*b^5*d*e^7 - 2*a^9*b^4*e^8)*x^4 + 10*(a^2*b^11*d^8 - 6*a^3*b^10*d^7*e + 14*a^4*b^9*d^6*e^2 - 14*a^5*b^8*d^5*e^3 + 14*a^7*b^6*d^3*e^5 - 14*a^8*b^5*d^2*e^6 + 6*a^9*b^4*d*e^7 - a^10*b^3*e^8)*x^3 + 5*(2*a^3*b^10*d^8 - 13*a^4*b^9*d^7*e + 35*a^5*b^8*d^6*e^2 - 49*a^6*b^7*d^5*e^3 + 35*a^7*b^6*d^4*e^4 - 7*a^8*b^5*d^3*e^5 - 7*a^9*b^4*d^2*e^6 + 5*a^10*b^3*d*e^7 - a^11*b^2*e^8)*x^2 + (5*a^4*b^9*d^8 - 34*a^5*b^8*d^7*e + 98*a^6*b^7*d^6*e^2 - 154*a^7*b^6*d^5*e^3 + 140*a^8*b^5*d^4*e^4 - 70*a^9*b^4*d^3*e^5 + 14*a^10*b^3*d^2*e^6 + 2*a^11*b^2*d*e^7 - a^12*b*e^8)*x)]","B",0
1833,1,4664,0,0.573769," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(10 \, B a^{5} b d^{3} e^{4} + {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} d^{2} e^{5} + {\left(10 \, B b^{6} d e^{6} + {\left(3 \, B a b^{5} - 13 \, A b^{6}\right)} e^{7}\right)} x^{7} + {\left(20 \, B b^{6} d^{2} e^{5} + 2 \, {\left(28 \, B a b^{5} - 13 \, A b^{6}\right)} d e^{6} + 5 \, {\left(3 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} e^{7}\right)} x^{6} + {\left(10 \, B b^{6} d^{3} e^{4} + {\left(103 \, B a b^{5} - 13 \, A b^{6}\right)} d^{2} e^{5} + 130 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} d e^{6} + 10 \, {\left(3 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d^{3} e^{4} + {\left(43 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d^{2} e^{5} + 4 \, {\left(8 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} d e^{6} + 2 \, {\left(3 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{4} + 5 \, {\left(20 \, B a^{2} b^{4} d^{3} e^{4} + 2 \, {\left(23 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 2 \, {\left(11 \, B a^{4} b^{2} - 26 \, A a^{3} b^{3}\right)} d e^{6} + {\left(3 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{3} + {\left(100 \, B a^{3} b^{3} d^{3} e^{4} + 130 \, {\left(B a^{4} b^{2} - A a^{3} b^{3}\right)} d^{2} e^{5} + 10 \, {\left(4 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d e^{6} + {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} e^{7}\right)} x^{2} + {\left(50 \, B a^{4} b^{2} d^{3} e^{4} + 5 \, {\left(7 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 2 \, {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} d e^{6}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(1280 \, A a^{6} e^{6} - 96 \, {\left(B a b^{5} + 4 \, A b^{6}\right)} d^{6} + 16 \, {\left(52 \, B a^{2} b^{4} + 183 \, A a b^{5}\right)} d^{5} e - 28 \, {\left(127 \, B a^{3} b^{3} + 358 \, A a^{2} b^{4}\right)} d^{4} e^{2} + 70 \, {\left(174 \, B a^{4} b^{2} + 301 \, A a^{3} b^{3}\right)} d^{3} e^{3} + 5 \, {\left(6625 \, B a^{5} b - 7119 \, A a^{4} b^{2}\right)} d^{2} e^{4} + 1280 \, {\left(2 \, B a^{6} - 19 \, A a^{5} b\right)} d e^{5} + 3465 \, {\left(10 \, B b^{6} d e^{5} + {\left(3 \, B a b^{5} - 13 \, A b^{6}\right)} e^{6}\right)} x^{6} + 2310 \, {\left(20 \, B b^{6} d^{2} e^{4} + 2 \, {\left(38 \, B a b^{5} - 13 \, A b^{6}\right)} d e^{5} + 7 \, {\left(3 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} e^{6}\right)} x^{5} + 231 \, {\left(30 \, B b^{6} d^{3} e^{3} + 13 \, {\left(73 \, B a b^{5} - 3 \, A b^{6}\right)} d^{2} e^{4} + 2 \, {\left(781 \, B a^{2} b^{4} - 611 \, A a b^{5}\right)} d e^{5} + 128 \, {\left(3 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{4} - 66 \, {\left(30 \, B b^{6} d^{4} e^{2} - 3 \, {\left(167 \, B a b^{5} + 13 \, A b^{6}\right)} d^{3} e^{3} - {\left(6223 \, B a^{2} b^{4} - 663 \, A a b^{5}\right)} d^{2} e^{4} - {\left(5771 \, B a^{3} b^{3} - 7891 \, A a^{2} b^{4}\right)} d e^{5} - 395 \, {\left(3 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} e^{6}\right)} x^{3} + 11 \, {\left(80 \, B b^{6} d^{5} e - 4 \, {\left(209 \, B a b^{5} + 26 \, A b^{6}\right)} d^{4} e^{2} + 2 \, {\left(2811 \, B a^{2} b^{4} + 559 \, A a b^{5}\right)} d^{3} e^{3} + 4 \, {\left(8566 \, B a^{3} b^{3} - 1911 \, A a^{2} b^{4}\right)} d^{2} e^{4} + 50 \, {\left(388 \, B a^{4} b^{2} - 845 \, A a^{3} b^{3}\right)} d e^{5} + 965 \, {\left(3 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} e^{6}\right)} x^{2} - 2 \, {\left(240 \, B b^{6} d^{6} - 8 \, {\left(251 \, B a b^{5} + 39 \, A b^{6}\right)} d^{5} e + 2 \, {\left(4133 \, B a^{2} b^{4} + 1352 \, A a b^{5}\right)} d^{4} e^{2} - 7 \, {\left(3969 \, B a^{3} b^{3} + 1651 \, A a^{2} b^{4}\right)} d^{3} e^{3} - 5 \, {\left(16657 \, B a^{4} b^{2} - 7917 \, A a^{3} b^{3}\right)} d^{2} e^{4} - 5 \, {\left(5729 \, B a^{5} b - 19279 \, A a^{4} b^{2}\right)} d e^{5} - 640 \, {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(a^{5} b^{7} d^{9} - 7 \, a^{6} b^{6} d^{8} e + 21 \, a^{7} b^{5} d^{7} e^{2} - 35 \, a^{8} b^{4} d^{6} e^{3} + 35 \, a^{9} b^{3} d^{5} e^{4} - 21 \, a^{10} b^{2} d^{4} e^{5} + 7 \, a^{11} b d^{3} e^{6} - a^{12} d^{2} e^{7} + {\left(b^{12} d^{7} e^{2} - 7 \, a b^{11} d^{6} e^{3} + 21 \, a^{2} b^{10} d^{5} e^{4} - 35 \, a^{3} b^{9} d^{4} e^{5} + 35 \, a^{4} b^{8} d^{3} e^{6} - 21 \, a^{5} b^{7} d^{2} e^{7} + 7 \, a^{6} b^{6} d e^{8} - a^{7} b^{5} e^{9}\right)} x^{7} + {\left(2 \, b^{12} d^{8} e - 9 \, a b^{11} d^{7} e^{2} + 7 \, a^{2} b^{10} d^{6} e^{3} + 35 \, a^{3} b^{9} d^{5} e^{4} - 105 \, a^{4} b^{8} d^{4} e^{5} + 133 \, a^{5} b^{7} d^{3} e^{6} - 91 \, a^{6} b^{6} d^{2} e^{7} + 33 \, a^{7} b^{5} d e^{8} - 5 \, a^{8} b^{4} e^{9}\right)} x^{6} + {\left(b^{12} d^{9} + 3 \, a b^{11} d^{8} e - 39 \, a^{2} b^{10} d^{7} e^{2} + 105 \, a^{3} b^{9} d^{6} e^{3} - 105 \, a^{4} b^{8} d^{5} e^{4} - 21 \, a^{5} b^{7} d^{4} e^{5} + 147 \, a^{6} b^{6} d^{3} e^{6} - 141 \, a^{7} b^{5} d^{2} e^{7} + 60 \, a^{8} b^{4} d e^{8} - 10 \, a^{9} b^{3} e^{9}\right)} x^{5} + 5 \, {\left(a b^{11} d^{9} - 3 \, a^{2} b^{10} d^{8} e - 5 \, a^{3} b^{9} d^{7} e^{2} + 35 \, a^{4} b^{8} d^{6} e^{3} - 63 \, a^{5} b^{7} d^{5} e^{4} + 49 \, a^{6} b^{6} d^{4} e^{5} - 7 \, a^{7} b^{5} d^{3} e^{6} - 15 \, a^{8} b^{4} d^{2} e^{7} + 10 \, a^{9} b^{3} d e^{8} - 2 \, a^{10} b^{2} e^{9}\right)} x^{4} + 5 \, {\left(2 \, a^{2} b^{10} d^{9} - 10 \, a^{3} b^{9} d^{8} e + 15 \, a^{4} b^{8} d^{7} e^{2} + 7 \, a^{5} b^{7} d^{6} e^{3} - 49 \, a^{6} b^{6} d^{5} e^{4} + 63 \, a^{7} b^{5} d^{4} e^{5} - 35 \, a^{8} b^{4} d^{3} e^{6} + 5 \, a^{9} b^{3} d^{2} e^{7} + 3 \, a^{10} b^{2} d e^{8} - a^{11} b e^{9}\right)} x^{3} + {\left(10 \, a^{3} b^{9} d^{9} - 60 \, a^{4} b^{8} d^{8} e + 141 \, a^{5} b^{7} d^{7} e^{2} - 147 \, a^{6} b^{6} d^{6} e^{3} + 21 \, a^{7} b^{5} d^{5} e^{4} + 105 \, a^{8} b^{4} d^{4} e^{5} - 105 \, a^{9} b^{3} d^{3} e^{6} + 39 \, a^{10} b^{2} d^{2} e^{7} - 3 \, a^{11} b d e^{8} - a^{12} e^{9}\right)} x^{2} + {\left(5 \, a^{4} b^{8} d^{9} - 33 \, a^{5} b^{7} d^{8} e + 91 \, a^{6} b^{6} d^{7} e^{2} - 133 \, a^{7} b^{5} d^{6} e^{3} + 105 \, a^{8} b^{4} d^{5} e^{4} - 35 \, a^{9} b^{3} d^{4} e^{5} - 7 \, a^{10} b^{2} d^{3} e^{6} + 9 \, a^{11} b d^{2} e^{7} - 2 \, a^{12} d e^{8}\right)} x\right)}}, -\frac{3465 \, {\left(10 \, B a^{5} b d^{3} e^{4} + {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} d^{2} e^{5} + {\left(10 \, B b^{6} d e^{6} + {\left(3 \, B a b^{5} - 13 \, A b^{6}\right)} e^{7}\right)} x^{7} + {\left(20 \, B b^{6} d^{2} e^{5} + 2 \, {\left(28 \, B a b^{5} - 13 \, A b^{6}\right)} d e^{6} + 5 \, {\left(3 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} e^{7}\right)} x^{6} + {\left(10 \, B b^{6} d^{3} e^{4} + {\left(103 \, B a b^{5} - 13 \, A b^{6}\right)} d^{2} e^{5} + 130 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} d e^{6} + 10 \, {\left(3 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{5} + 5 \, {\left(10 \, B a b^{5} d^{3} e^{4} + {\left(43 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d^{2} e^{5} + 4 \, {\left(8 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} d e^{6} + 2 \, {\left(3 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{4} + 5 \, {\left(20 \, B a^{2} b^{4} d^{3} e^{4} + 2 \, {\left(23 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 2 \, {\left(11 \, B a^{4} b^{2} - 26 \, A a^{3} b^{3}\right)} d e^{6} + {\left(3 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{3} + {\left(100 \, B a^{3} b^{3} d^{3} e^{4} + 130 \, {\left(B a^{4} b^{2} - A a^{3} b^{3}\right)} d^{2} e^{5} + 10 \, {\left(4 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d e^{6} + {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} e^{7}\right)} x^{2} + {\left(50 \, B a^{4} b^{2} d^{3} e^{4} + 5 \, {\left(7 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 2 \, {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} d e^{6}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(1280 \, A a^{6} e^{6} - 96 \, {\left(B a b^{5} + 4 \, A b^{6}\right)} d^{6} + 16 \, {\left(52 \, B a^{2} b^{4} + 183 \, A a b^{5}\right)} d^{5} e - 28 \, {\left(127 \, B a^{3} b^{3} + 358 \, A a^{2} b^{4}\right)} d^{4} e^{2} + 70 \, {\left(174 \, B a^{4} b^{2} + 301 \, A a^{3} b^{3}\right)} d^{3} e^{3} + 5 \, {\left(6625 \, B a^{5} b - 7119 \, A a^{4} b^{2}\right)} d^{2} e^{4} + 1280 \, {\left(2 \, B a^{6} - 19 \, A a^{5} b\right)} d e^{5} + 3465 \, {\left(10 \, B b^{6} d e^{5} + {\left(3 \, B a b^{5} - 13 \, A b^{6}\right)} e^{6}\right)} x^{6} + 2310 \, {\left(20 \, B b^{6} d^{2} e^{4} + 2 \, {\left(38 \, B a b^{5} - 13 \, A b^{6}\right)} d e^{5} + 7 \, {\left(3 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} e^{6}\right)} x^{5} + 231 \, {\left(30 \, B b^{6} d^{3} e^{3} + 13 \, {\left(73 \, B a b^{5} - 3 \, A b^{6}\right)} d^{2} e^{4} + 2 \, {\left(781 \, B a^{2} b^{4} - 611 \, A a b^{5}\right)} d e^{5} + 128 \, {\left(3 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{4} - 66 \, {\left(30 \, B b^{6} d^{4} e^{2} - 3 \, {\left(167 \, B a b^{5} + 13 \, A b^{6}\right)} d^{3} e^{3} - {\left(6223 \, B a^{2} b^{4} - 663 \, A a b^{5}\right)} d^{2} e^{4} - {\left(5771 \, B a^{3} b^{3} - 7891 \, A a^{2} b^{4}\right)} d e^{5} - 395 \, {\left(3 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} e^{6}\right)} x^{3} + 11 \, {\left(80 \, B b^{6} d^{5} e - 4 \, {\left(209 \, B a b^{5} + 26 \, A b^{6}\right)} d^{4} e^{2} + 2 \, {\left(2811 \, B a^{2} b^{4} + 559 \, A a b^{5}\right)} d^{3} e^{3} + 4 \, {\left(8566 \, B a^{3} b^{3} - 1911 \, A a^{2} b^{4}\right)} d^{2} e^{4} + 50 \, {\left(388 \, B a^{4} b^{2} - 845 \, A a^{3} b^{3}\right)} d e^{5} + 965 \, {\left(3 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} e^{6}\right)} x^{2} - 2 \, {\left(240 \, B b^{6} d^{6} - 8 \, {\left(251 \, B a b^{5} + 39 \, A b^{6}\right)} d^{5} e + 2 \, {\left(4133 \, B a^{2} b^{4} + 1352 \, A a b^{5}\right)} d^{4} e^{2} - 7 \, {\left(3969 \, B a^{3} b^{3} + 1651 \, A a^{2} b^{4}\right)} d^{3} e^{3} - 5 \, {\left(16657 \, B a^{4} b^{2} - 7917 \, A a^{3} b^{3}\right)} d^{2} e^{4} - 5 \, {\left(5729 \, B a^{5} b - 19279 \, A a^{4} b^{2}\right)} d e^{5} - 640 \, {\left(3 \, B a^{6} - 13 \, A a^{5} b\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{5} b^{7} d^{9} - 7 \, a^{6} b^{6} d^{8} e + 21 \, a^{7} b^{5} d^{7} e^{2} - 35 \, a^{8} b^{4} d^{6} e^{3} + 35 \, a^{9} b^{3} d^{5} e^{4} - 21 \, a^{10} b^{2} d^{4} e^{5} + 7 \, a^{11} b d^{3} e^{6} - a^{12} d^{2} e^{7} + {\left(b^{12} d^{7} e^{2} - 7 \, a b^{11} d^{6} e^{3} + 21 \, a^{2} b^{10} d^{5} e^{4} - 35 \, a^{3} b^{9} d^{4} e^{5} + 35 \, a^{4} b^{8} d^{3} e^{6} - 21 \, a^{5} b^{7} d^{2} e^{7} + 7 \, a^{6} b^{6} d e^{8} - a^{7} b^{5} e^{9}\right)} x^{7} + {\left(2 \, b^{12} d^{8} e - 9 \, a b^{11} d^{7} e^{2} + 7 \, a^{2} b^{10} d^{6} e^{3} + 35 \, a^{3} b^{9} d^{5} e^{4} - 105 \, a^{4} b^{8} d^{4} e^{5} + 133 \, a^{5} b^{7} d^{3} e^{6} - 91 \, a^{6} b^{6} d^{2} e^{7} + 33 \, a^{7} b^{5} d e^{8} - 5 \, a^{8} b^{4} e^{9}\right)} x^{6} + {\left(b^{12} d^{9} + 3 \, a b^{11} d^{8} e - 39 \, a^{2} b^{10} d^{7} e^{2} + 105 \, a^{3} b^{9} d^{6} e^{3} - 105 \, a^{4} b^{8} d^{5} e^{4} - 21 \, a^{5} b^{7} d^{4} e^{5} + 147 \, a^{6} b^{6} d^{3} e^{6} - 141 \, a^{7} b^{5} d^{2} e^{7} + 60 \, a^{8} b^{4} d e^{8} - 10 \, a^{9} b^{3} e^{9}\right)} x^{5} + 5 \, {\left(a b^{11} d^{9} - 3 \, a^{2} b^{10} d^{8} e - 5 \, a^{3} b^{9} d^{7} e^{2} + 35 \, a^{4} b^{8} d^{6} e^{3} - 63 \, a^{5} b^{7} d^{5} e^{4} + 49 \, a^{6} b^{6} d^{4} e^{5} - 7 \, a^{7} b^{5} d^{3} e^{6} - 15 \, a^{8} b^{4} d^{2} e^{7} + 10 \, a^{9} b^{3} d e^{8} - 2 \, a^{10} b^{2} e^{9}\right)} x^{4} + 5 \, {\left(2 \, a^{2} b^{10} d^{9} - 10 \, a^{3} b^{9} d^{8} e + 15 \, a^{4} b^{8} d^{7} e^{2} + 7 \, a^{5} b^{7} d^{6} e^{3} - 49 \, a^{6} b^{6} d^{5} e^{4} + 63 \, a^{7} b^{5} d^{4} e^{5} - 35 \, a^{8} b^{4} d^{3} e^{6} + 5 \, a^{9} b^{3} d^{2} e^{7} + 3 \, a^{10} b^{2} d e^{8} - a^{11} b e^{9}\right)} x^{3} + {\left(10 \, a^{3} b^{9} d^{9} - 60 \, a^{4} b^{8} d^{8} e + 141 \, a^{5} b^{7} d^{7} e^{2} - 147 \, a^{6} b^{6} d^{6} e^{3} + 21 \, a^{7} b^{5} d^{5} e^{4} + 105 \, a^{8} b^{4} d^{4} e^{5} - 105 \, a^{9} b^{3} d^{3} e^{6} + 39 \, a^{10} b^{2} d^{2} e^{7} - 3 \, a^{11} b d e^{8} - a^{12} e^{9}\right)} x^{2} + {\left(5 \, a^{4} b^{8} d^{9} - 33 \, a^{5} b^{7} d^{8} e + 91 \, a^{6} b^{6} d^{7} e^{2} - 133 \, a^{7} b^{5} d^{6} e^{3} + 105 \, a^{8} b^{4} d^{5} e^{4} - 35 \, a^{9} b^{3} d^{4} e^{5} - 7 \, a^{10} b^{2} d^{3} e^{6} + 9 \, a^{11} b d^{2} e^{7} - 2 \, a^{12} d e^{8}\right)} x\right)}}\right]"," ",0,"[1/3840*(3465*(10*B*a^5*b*d^3*e^4 + (3*B*a^6 - 13*A*a^5*b)*d^2*e^5 + (10*B*b^6*d*e^6 + (3*B*a*b^5 - 13*A*b^6)*e^7)*x^7 + (20*B*b^6*d^2*e^5 + 2*(28*B*a*b^5 - 13*A*b^6)*d*e^6 + 5*(3*B*a^2*b^4 - 13*A*a*b^5)*e^7)*x^6 + (10*B*b^6*d^3*e^4 + (103*B*a*b^5 - 13*A*b^6)*d^2*e^5 + 130*(B*a^2*b^4 - A*a*b^5)*d*e^6 + 10*(3*B*a^3*b^3 - 13*A*a^2*b^4)*e^7)*x^5 + 5*(10*B*a*b^5*d^3*e^4 + (43*B*a^2*b^4 - 13*A*a*b^5)*d^2*e^5 + 4*(8*B*a^3*b^3 - 13*A*a^2*b^4)*d*e^6 + 2*(3*B*a^4*b^2 - 13*A*a^3*b^3)*e^7)*x^4 + 5*(20*B*a^2*b^4*d^3*e^4 + 2*(23*B*a^3*b^3 - 13*A*a^2*b^4)*d^2*e^5 + 2*(11*B*a^4*b^2 - 26*A*a^3*b^3)*d*e^6 + (3*B*a^5*b - 13*A*a^4*b^2)*e^7)*x^3 + (100*B*a^3*b^3*d^3*e^4 + 130*(B*a^4*b^2 - A*a^3*b^3)*d^2*e^5 + 10*(4*B*a^5*b - 13*A*a^4*b^2)*d*e^6 + (3*B*a^6 - 13*A*a^5*b)*e^7)*x^2 + (50*B*a^4*b^2*d^3*e^4 + 5*(7*B*a^5*b - 13*A*a^4*b^2)*d^2*e^5 + 2*(3*B*a^6 - 13*A*a^5*b)*d*e^6)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(1280*A*a^6*e^6 - 96*(B*a*b^5 + 4*A*b^6)*d^6 + 16*(52*B*a^2*b^4 + 183*A*a*b^5)*d^5*e - 28*(127*B*a^3*b^3 + 358*A*a^2*b^4)*d^4*e^2 + 70*(174*B*a^4*b^2 + 301*A*a^3*b^3)*d^3*e^3 + 5*(6625*B*a^5*b - 7119*A*a^4*b^2)*d^2*e^4 + 1280*(2*B*a^6 - 19*A*a^5*b)*d*e^5 + 3465*(10*B*b^6*d*e^5 + (3*B*a*b^5 - 13*A*b^6)*e^6)*x^6 + 2310*(20*B*b^6*d^2*e^4 + 2*(38*B*a*b^5 - 13*A*b^6)*d*e^5 + 7*(3*B*a^2*b^4 - 13*A*a*b^5)*e^6)*x^5 + 231*(30*B*b^6*d^3*e^3 + 13*(73*B*a*b^5 - 3*A*b^6)*d^2*e^4 + 2*(781*B*a^2*b^4 - 611*A*a*b^5)*d*e^5 + 128*(3*B*a^3*b^3 - 13*A*a^2*b^4)*e^6)*x^4 - 66*(30*B*b^6*d^4*e^2 - 3*(167*B*a*b^5 + 13*A*b^6)*d^3*e^3 - (6223*B*a^2*b^4 - 663*A*a*b^5)*d^2*e^4 - (5771*B*a^3*b^3 - 7891*A*a^2*b^4)*d*e^5 - 395*(3*B*a^4*b^2 - 13*A*a^3*b^3)*e^6)*x^3 + 11*(80*B*b^6*d^5*e - 4*(209*B*a*b^5 + 26*A*b^6)*d^4*e^2 + 2*(2811*B*a^2*b^4 + 559*A*a*b^5)*d^3*e^3 + 4*(8566*B*a^3*b^3 - 1911*A*a^2*b^4)*d^2*e^4 + 50*(388*B*a^4*b^2 - 845*A*a^3*b^3)*d*e^5 + 965*(3*B*a^5*b - 13*A*a^4*b^2)*e^6)*x^2 - 2*(240*B*b^6*d^6 - 8*(251*B*a*b^5 + 39*A*b^6)*d^5*e + 2*(4133*B*a^2*b^4 + 1352*A*a*b^5)*d^4*e^2 - 7*(3969*B*a^3*b^3 + 1651*A*a^2*b^4)*d^3*e^3 - 5*(16657*B*a^4*b^2 - 7917*A*a^3*b^3)*d^2*e^4 - 5*(5729*B*a^5*b - 19279*A*a^4*b^2)*d*e^5 - 640*(3*B*a^6 - 13*A*a^5*b)*e^6)*x)*sqrt(e*x + d))/(a^5*b^7*d^9 - 7*a^6*b^6*d^8*e + 21*a^7*b^5*d^7*e^2 - 35*a^8*b^4*d^6*e^3 + 35*a^9*b^3*d^5*e^4 - 21*a^10*b^2*d^4*e^5 + 7*a^11*b*d^3*e^6 - a^12*d^2*e^7 + (b^12*d^7*e^2 - 7*a*b^11*d^6*e^3 + 21*a^2*b^10*d^5*e^4 - 35*a^3*b^9*d^4*e^5 + 35*a^4*b^8*d^3*e^6 - 21*a^5*b^7*d^2*e^7 + 7*a^6*b^6*d*e^8 - a^7*b^5*e^9)*x^7 + (2*b^12*d^8*e - 9*a*b^11*d^7*e^2 + 7*a^2*b^10*d^6*e^3 + 35*a^3*b^9*d^5*e^4 - 105*a^4*b^8*d^4*e^5 + 133*a^5*b^7*d^3*e^6 - 91*a^6*b^6*d^2*e^7 + 33*a^7*b^5*d*e^8 - 5*a^8*b^4*e^9)*x^6 + (b^12*d^9 + 3*a*b^11*d^8*e - 39*a^2*b^10*d^7*e^2 + 105*a^3*b^9*d^6*e^3 - 105*a^4*b^8*d^5*e^4 - 21*a^5*b^7*d^4*e^5 + 147*a^6*b^6*d^3*e^6 - 141*a^7*b^5*d^2*e^7 + 60*a^8*b^4*d*e^8 - 10*a^9*b^3*e^9)*x^5 + 5*(a*b^11*d^9 - 3*a^2*b^10*d^8*e - 5*a^3*b^9*d^7*e^2 + 35*a^4*b^8*d^6*e^3 - 63*a^5*b^7*d^5*e^4 + 49*a^6*b^6*d^4*e^5 - 7*a^7*b^5*d^3*e^6 - 15*a^8*b^4*d^2*e^7 + 10*a^9*b^3*d*e^8 - 2*a^10*b^2*e^9)*x^4 + 5*(2*a^2*b^10*d^9 - 10*a^3*b^9*d^8*e + 15*a^4*b^8*d^7*e^2 + 7*a^5*b^7*d^6*e^3 - 49*a^6*b^6*d^5*e^4 + 63*a^7*b^5*d^4*e^5 - 35*a^8*b^4*d^3*e^6 + 5*a^9*b^3*d^2*e^7 + 3*a^10*b^2*d*e^8 - a^11*b*e^9)*x^3 + (10*a^3*b^9*d^9 - 60*a^4*b^8*d^8*e + 141*a^5*b^7*d^7*e^2 - 147*a^6*b^6*d^6*e^3 + 21*a^7*b^5*d^5*e^4 + 105*a^8*b^4*d^4*e^5 - 105*a^9*b^3*d^3*e^6 + 39*a^10*b^2*d^2*e^7 - 3*a^11*b*d*e^8 - a^12*e^9)*x^2 + (5*a^4*b^8*d^9 - 33*a^5*b^7*d^8*e + 91*a^6*b^6*d^7*e^2 - 133*a^7*b^5*d^6*e^3 + 105*a^8*b^4*d^5*e^4 - 35*a^9*b^3*d^4*e^5 - 7*a^10*b^2*d^3*e^6 + 9*a^11*b*d^2*e^7 - 2*a^12*d*e^8)*x), -1/1920*(3465*(10*B*a^5*b*d^3*e^4 + (3*B*a^6 - 13*A*a^5*b)*d^2*e^5 + (10*B*b^6*d*e^6 + (3*B*a*b^5 - 13*A*b^6)*e^7)*x^7 + (20*B*b^6*d^2*e^5 + 2*(28*B*a*b^5 - 13*A*b^6)*d*e^6 + 5*(3*B*a^2*b^4 - 13*A*a*b^5)*e^7)*x^6 + (10*B*b^6*d^3*e^4 + (103*B*a*b^5 - 13*A*b^6)*d^2*e^5 + 130*(B*a^2*b^4 - A*a*b^5)*d*e^6 + 10*(3*B*a^3*b^3 - 13*A*a^2*b^4)*e^7)*x^5 + 5*(10*B*a*b^5*d^3*e^4 + (43*B*a^2*b^4 - 13*A*a*b^5)*d^2*e^5 + 4*(8*B*a^3*b^3 - 13*A*a^2*b^4)*d*e^6 + 2*(3*B*a^4*b^2 - 13*A*a^3*b^3)*e^7)*x^4 + 5*(20*B*a^2*b^4*d^3*e^4 + 2*(23*B*a^3*b^3 - 13*A*a^2*b^4)*d^2*e^5 + 2*(11*B*a^4*b^2 - 26*A*a^3*b^3)*d*e^6 + (3*B*a^5*b - 13*A*a^4*b^2)*e^7)*x^3 + (100*B*a^3*b^3*d^3*e^4 + 130*(B*a^4*b^2 - A*a^3*b^3)*d^2*e^5 + 10*(4*B*a^5*b - 13*A*a^4*b^2)*d*e^6 + (3*B*a^6 - 13*A*a^5*b)*e^7)*x^2 + (50*B*a^4*b^2*d^3*e^4 + 5*(7*B*a^5*b - 13*A*a^4*b^2)*d^2*e^5 + 2*(3*B*a^6 - 13*A*a^5*b)*d*e^6)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (1280*A*a^6*e^6 - 96*(B*a*b^5 + 4*A*b^6)*d^6 + 16*(52*B*a^2*b^4 + 183*A*a*b^5)*d^5*e - 28*(127*B*a^3*b^3 + 358*A*a^2*b^4)*d^4*e^2 + 70*(174*B*a^4*b^2 + 301*A*a^3*b^3)*d^3*e^3 + 5*(6625*B*a^5*b - 7119*A*a^4*b^2)*d^2*e^4 + 1280*(2*B*a^6 - 19*A*a^5*b)*d*e^5 + 3465*(10*B*b^6*d*e^5 + (3*B*a*b^5 - 13*A*b^6)*e^6)*x^6 + 2310*(20*B*b^6*d^2*e^4 + 2*(38*B*a*b^5 - 13*A*b^6)*d*e^5 + 7*(3*B*a^2*b^4 - 13*A*a*b^5)*e^6)*x^5 + 231*(30*B*b^6*d^3*e^3 + 13*(73*B*a*b^5 - 3*A*b^6)*d^2*e^4 + 2*(781*B*a^2*b^4 - 611*A*a*b^5)*d*e^5 + 128*(3*B*a^3*b^3 - 13*A*a^2*b^4)*e^6)*x^4 - 66*(30*B*b^6*d^4*e^2 - 3*(167*B*a*b^5 + 13*A*b^6)*d^3*e^3 - (6223*B*a^2*b^4 - 663*A*a*b^5)*d^2*e^4 - (5771*B*a^3*b^3 - 7891*A*a^2*b^4)*d*e^5 - 395*(3*B*a^4*b^2 - 13*A*a^3*b^3)*e^6)*x^3 + 11*(80*B*b^6*d^5*e - 4*(209*B*a*b^5 + 26*A*b^6)*d^4*e^2 + 2*(2811*B*a^2*b^4 + 559*A*a*b^5)*d^3*e^3 + 4*(8566*B*a^3*b^3 - 1911*A*a^2*b^4)*d^2*e^4 + 50*(388*B*a^4*b^2 - 845*A*a^3*b^3)*d*e^5 + 965*(3*B*a^5*b - 13*A*a^4*b^2)*e^6)*x^2 - 2*(240*B*b^6*d^6 - 8*(251*B*a*b^5 + 39*A*b^6)*d^5*e + 2*(4133*B*a^2*b^4 + 1352*A*a*b^5)*d^4*e^2 - 7*(3969*B*a^3*b^3 + 1651*A*a^2*b^4)*d^3*e^3 - 5*(16657*B*a^4*b^2 - 7917*A*a^3*b^3)*d^2*e^4 - 5*(5729*B*a^5*b - 19279*A*a^4*b^2)*d*e^5 - 640*(3*B*a^6 - 13*A*a^5*b)*e^6)*x)*sqrt(e*x + d))/(a^5*b^7*d^9 - 7*a^6*b^6*d^8*e + 21*a^7*b^5*d^7*e^2 - 35*a^8*b^4*d^6*e^3 + 35*a^9*b^3*d^5*e^4 - 21*a^10*b^2*d^4*e^5 + 7*a^11*b*d^3*e^6 - a^12*d^2*e^7 + (b^12*d^7*e^2 - 7*a*b^11*d^6*e^3 + 21*a^2*b^10*d^5*e^4 - 35*a^3*b^9*d^4*e^5 + 35*a^4*b^8*d^3*e^6 - 21*a^5*b^7*d^2*e^7 + 7*a^6*b^6*d*e^8 - a^7*b^5*e^9)*x^7 + (2*b^12*d^8*e - 9*a*b^11*d^7*e^2 + 7*a^2*b^10*d^6*e^3 + 35*a^3*b^9*d^5*e^4 - 105*a^4*b^8*d^4*e^5 + 133*a^5*b^7*d^3*e^6 - 91*a^6*b^6*d^2*e^7 + 33*a^7*b^5*d*e^8 - 5*a^8*b^4*e^9)*x^6 + (b^12*d^9 + 3*a*b^11*d^8*e - 39*a^2*b^10*d^7*e^2 + 105*a^3*b^9*d^6*e^3 - 105*a^4*b^8*d^5*e^4 - 21*a^5*b^7*d^4*e^5 + 147*a^6*b^6*d^3*e^6 - 141*a^7*b^5*d^2*e^7 + 60*a^8*b^4*d*e^8 - 10*a^9*b^3*e^9)*x^5 + 5*(a*b^11*d^9 - 3*a^2*b^10*d^8*e - 5*a^3*b^9*d^7*e^2 + 35*a^4*b^8*d^6*e^3 - 63*a^5*b^7*d^5*e^4 + 49*a^6*b^6*d^4*e^5 - 7*a^7*b^5*d^3*e^6 - 15*a^8*b^4*d^2*e^7 + 10*a^9*b^3*d*e^8 - 2*a^10*b^2*e^9)*x^4 + 5*(2*a^2*b^10*d^9 - 10*a^3*b^9*d^8*e + 15*a^4*b^8*d^7*e^2 + 7*a^5*b^7*d^6*e^3 - 49*a^6*b^6*d^5*e^4 + 63*a^7*b^5*d^4*e^5 - 35*a^8*b^4*d^3*e^6 + 5*a^9*b^3*d^2*e^7 + 3*a^10*b^2*d*e^8 - a^11*b*e^9)*x^3 + (10*a^3*b^9*d^9 - 60*a^4*b^8*d^8*e + 141*a^5*b^7*d^7*e^2 - 147*a^6*b^6*d^6*e^3 + 21*a^7*b^5*d^5*e^4 + 105*a^8*b^4*d^4*e^5 - 105*a^9*b^3*d^3*e^6 + 39*a^10*b^2*d^2*e^7 - 3*a^11*b*d*e^8 - a^12*e^9)*x^2 + (5*a^4*b^8*d^9 - 33*a^5*b^7*d^8*e + 91*a^6*b^6*d^7*e^2 - 133*a^7*b^5*d^6*e^3 + 105*a^8*b^4*d^5*e^4 - 35*a^9*b^3*d^4*e^5 - 7*a^10*b^2*d^3*e^6 + 9*a^11*b*d^2*e^7 - 2*a^12*d*e^8)*x)]","B",0
1834,1,6033,0,0.609616," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{45045 \, {\left(2 \, B a^{5} b^{2} d^{4} e^{4} + {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} d^{3} e^{5} + {\left(2 \, B b^{7} d e^{7} + {\left(B a b^{6} - 3 \, A b^{7}\right)} e^{8}\right)} x^{8} + {\left(6 \, B b^{7} d^{2} e^{6} + {\left(13 \, B a b^{6} - 9 \, A b^{7}\right)} d e^{7} + 5 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} e^{8}\right)} x^{7} + {\left(6 \, B b^{7} d^{3} e^{5} + 3 \, {\left(11 \, B a b^{6} - 3 \, A b^{7}\right)} d^{2} e^{6} + 5 \, {\left(7 \, B a^{2} b^{5} - 9 \, A a b^{6}\right)} d e^{7} + 10 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} e^{8}\right)} x^{6} + {\left(2 \, B b^{7} d^{4} e^{4} + {\left(31 \, B a b^{6} - 3 \, A b^{7}\right)} d^{3} e^{5} + 15 \, {\left(5 \, B a^{2} b^{5} - 3 \, A a b^{6}\right)} d^{2} e^{6} + 10 \, {\left(5 \, B a^{3} b^{4} - 9 \, A a^{2} b^{5}\right)} d e^{7} + 10 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} e^{8}\right)} x^{5} + 5 \, {\left(2 \, B a b^{6} d^{4} e^{4} + {\left(13 \, B a^{2} b^{5} - 3 \, A a b^{6}\right)} d^{3} e^{5} + 18 \, {\left(B a^{3} b^{4} - A a^{2} b^{5}\right)} d^{2} e^{6} + 2 \, {\left(4 \, B a^{4} b^{3} - 9 \, A a^{3} b^{4}\right)} d e^{7} + {\left(B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)} e^{8}\right)} x^{4} + {\left(20 \, B a^{2} b^{5} d^{4} e^{4} + 10 \, {\left(7 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} d^{3} e^{5} + 30 \, {\left(2 \, B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} d^{2} e^{6} + {\left(17 \, B a^{5} b^{2} - 45 \, A a^{4} b^{3}\right)} d e^{7} + {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} e^{8}\right)} x^{3} + {\left(20 \, B a^{3} b^{4} d^{4} e^{4} + 10 \, {\left(4 \, B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} d^{3} e^{5} + 3 \, {\left(7 \, B a^{5} b^{2} - 15 \, A a^{4} b^{3}\right)} d^{2} e^{6} + 3 \, {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} d e^{7}\right)} x^{2} + {\left(10 \, B a^{4} b^{3} d^{4} e^{4} + {\left(11 \, B a^{5} b^{2} - 15 \, A a^{4} b^{3}\right)} d^{3} e^{5} + 3 \, {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} d^{2} e^{6}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(768 \, A a^{7} e^{7} + 96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{7} - 16 \, {\left(62 \, B a^{2} b^{5} + 213 \, A a b^{6}\right)} d^{6} e + 28 \, {\left(187 \, B a^{3} b^{4} + 498 \, A a^{2} b^{5}\right)} d^{5} e^{2} - 70 \, {\left(332 \, B a^{4} b^{3} + 519 \, A a^{3} b^{4}\right)} d^{4} e^{3} - {\left(100363 \, B a^{5} b^{2} - 79905 \, A a^{4} b^{3}\right)} d^{3} e^{4} - 1024 \, {\left(16 \, B a^{6} b - 87 \, A a^{5} b^{2}\right)} d^{2} e^{5} + 512 \, {\left(B a^{7} - 18 \, A a^{6} b\right)} d e^{6} - 45045 \, {\left(2 \, B b^{7} d e^{6} + {\left(B a b^{6} - 3 \, A b^{7}\right)} e^{7}\right)} x^{7} - 105105 \, {\left(2 \, B b^{7} d^{2} e^{5} + {\left(5 \, B a b^{6} - 3 \, A b^{7}\right)} d e^{6} + 2 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} e^{7}\right)} x^{6} - 3003 \, {\left(46 \, B b^{7} d^{3} e^{4} + 3 \, {\left(117 \, B a b^{6} - 23 \, A b^{7}\right)} d^{2} e^{5} + 12 \, {\left(35 \, B a^{2} b^{5} - 41 \, A a b^{6}\right)} d e^{6} + 128 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} e^{7}\right)} x^{5} - 2145 \, {\left(6 \, B b^{7} d^{4} e^{3} + {\left(307 \, B a b^{6} - 9 \, A b^{7}\right)} d^{3} e^{4} + 12 \, {\left(83 \, B a^{2} b^{5} - 38 \, A a b^{6}\right)} d^{2} e^{5} + 6 \, {\left(123 \, B a^{3} b^{4} - 211 \, A a^{2} b^{5}\right)} d e^{6} + 158 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} e^{7}\right)} x^{4} + 715 \, {\left(4 \, B b^{7} d^{5} e^{2} - 2 \, {\left(43 \, B a b^{6} + 3 \, A b^{7}\right)} d^{4} e^{3} - 4 \, {\left(434 \, B a^{2} b^{5} - 33 \, A a b^{6}\right)} d^{3} e^{4} - 2 \, {\left(1547 \, B a^{3} b^{4} - 1269 \, A a^{2} b^{5}\right)} d^{2} e^{5} - 2 \, {\left(755 \, B a^{4} b^{3} - 1686 \, A a^{3} b^{4}\right)} d e^{6} - 193 \, {\left(B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)} e^{7}\right)} x^{3} - 65 \, {\left(16 \, B b^{7} d^{6} e - 12 \, {\left(17 \, B a b^{6} + 2 \, A b^{7}\right)} d^{5} e^{2} + 6 \, {\left(295 \, B a^{2} b^{5} + 53 \, A a b^{6}\right)} d^{4} e^{3} + 2 \, {\left(8837 \, B a^{3} b^{4} - 1407 \, A a^{2} b^{5}\right)} d^{3} e^{4} + 6 \, {\left(3091 \, B a^{4} b^{3} - 4184 \, A a^{3} b^{4}\right)} d^{2} e^{5} + 3 \, {\left(1867 \, B a^{5} b^{2} - 5089 \, A a^{4} b^{3}\right)} d e^{6} + 256 \, {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} e^{7}\right)} x^{2} + 5 \, {\left(96 \, B b^{7} d^{7} - 16 \, {\left(59 \, B a b^{6} + 9 \, A b^{7}\right)} d^{6} e + 12 \, {\left(395 \, B a^{2} b^{5} + 124 \, A a b^{6}\right)} d^{5} e^{2} - 42 \, {\left(491 \, B a^{3} b^{4} + 187 \, A a^{2} b^{5}\right)} d^{4} e^{3} - 2 \, {\left(51487 \, B a^{4} b^{3} - 17430 \, A a^{3} b^{4}\right)} d^{3} e^{4} - 3 \, {\left(20687 \, B a^{5} b^{2} - 45677 \, A a^{4} b^{3}\right)} d^{2} e^{5} - 1536 \, {\left(5 \, B a^{6} b - 16 \, A a^{5} b^{2}\right)} d e^{6} + 256 \, {\left(B a^{7} - 3 \, A a^{6} b\right)} e^{7}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(a^{5} b^{8} d^{11} - 8 \, a^{6} b^{7} d^{10} e + 28 \, a^{7} b^{6} d^{9} e^{2} - 56 \, a^{8} b^{5} d^{8} e^{3} + 70 \, a^{9} b^{4} d^{7} e^{4} - 56 \, a^{10} b^{3} d^{6} e^{5} + 28 \, a^{11} b^{2} d^{5} e^{6} - 8 \, a^{12} b d^{4} e^{7} + a^{13} d^{3} e^{8} + {\left(b^{13} d^{8} e^{3} - 8 \, a b^{12} d^{7} e^{4} + 28 \, a^{2} b^{11} d^{6} e^{5} - 56 \, a^{3} b^{10} d^{5} e^{6} + 70 \, a^{4} b^{9} d^{4} e^{7} - 56 \, a^{5} b^{8} d^{3} e^{8} + 28 \, a^{6} b^{7} d^{2} e^{9} - 8 \, a^{7} b^{6} d e^{10} + a^{8} b^{5} e^{11}\right)} x^{8} + {\left(3 \, b^{13} d^{9} e^{2} - 19 \, a b^{12} d^{8} e^{3} + 44 \, a^{2} b^{11} d^{7} e^{4} - 28 \, a^{3} b^{10} d^{6} e^{5} - 70 \, a^{4} b^{9} d^{5} e^{6} + 182 \, a^{5} b^{8} d^{4} e^{7} - 196 \, a^{6} b^{7} d^{3} e^{8} + 116 \, a^{7} b^{6} d^{2} e^{9} - 37 \, a^{8} b^{5} d e^{10} + 5 \, a^{9} b^{4} e^{11}\right)} x^{7} + {\left(3 \, b^{13} d^{10} e - 9 \, a b^{12} d^{9} e^{2} - 26 \, a^{2} b^{11} d^{8} e^{3} + 172 \, a^{3} b^{10} d^{7} e^{4} - 350 \, a^{4} b^{9} d^{6} e^{5} + 322 \, a^{5} b^{8} d^{5} e^{6} - 56 \, a^{6} b^{7} d^{4} e^{7} - 164 \, a^{7} b^{6} d^{3} e^{8} + 163 \, a^{8} b^{5} d^{2} e^{9} - 65 \, a^{9} b^{4} d e^{10} + 10 \, a^{10} b^{3} e^{11}\right)} x^{6} + {\left(b^{13} d^{11} + 7 \, a b^{12} d^{10} e - 62 \, a^{2} b^{11} d^{9} e^{2} + 134 \, a^{3} b^{10} d^{8} e^{3} - 10 \, a^{4} b^{9} d^{7} e^{4} - 406 \, a^{5} b^{8} d^{6} e^{5} + 728 \, a^{6} b^{7} d^{5} e^{6} - 568 \, a^{7} b^{6} d^{4} e^{7} + 161 \, a^{8} b^{5} d^{3} e^{8} + 55 \, a^{9} b^{4} d^{2} e^{9} - 50 \, a^{10} b^{3} d e^{10} + 10 \, a^{11} b^{2} e^{11}\right)} x^{5} + 5 \, {\left(a b^{12} d^{11} - 2 \, a^{2} b^{11} d^{10} e - 14 \, a^{3} b^{10} d^{9} e^{2} + 65 \, a^{4} b^{9} d^{8} e^{3} - 106 \, a^{5} b^{8} d^{7} e^{4} + 56 \, a^{6} b^{7} d^{6} e^{5} + 56 \, a^{7} b^{6} d^{5} e^{6} - 106 \, a^{8} b^{5} d^{4} e^{7} + 65 \, a^{9} b^{4} d^{3} e^{8} - 14 \, a^{10} b^{3} d^{2} e^{9} - 2 \, a^{11} b^{2} d e^{10} + a^{12} b e^{11}\right)} x^{4} + {\left(10 \, a^{2} b^{11} d^{11} - 50 \, a^{3} b^{10} d^{10} e + 55 \, a^{4} b^{9} d^{9} e^{2} + 161 \, a^{5} b^{8} d^{8} e^{3} - 568 \, a^{6} b^{7} d^{7} e^{4} + 728 \, a^{7} b^{6} d^{6} e^{5} - 406 \, a^{8} b^{5} d^{5} e^{6} - 10 \, a^{9} b^{4} d^{4} e^{7} + 134 \, a^{10} b^{3} d^{3} e^{8} - 62 \, a^{11} b^{2} d^{2} e^{9} + 7 \, a^{12} b d e^{10} + a^{13} e^{11}\right)} x^{3} + {\left(10 \, a^{3} b^{10} d^{11} - 65 \, a^{4} b^{9} d^{10} e + 163 \, a^{5} b^{8} d^{9} e^{2} - 164 \, a^{6} b^{7} d^{8} e^{3} - 56 \, a^{7} b^{6} d^{7} e^{4} + 322 \, a^{8} b^{5} d^{6} e^{5} - 350 \, a^{9} b^{4} d^{5} e^{6} + 172 \, a^{10} b^{3} d^{4} e^{7} - 26 \, a^{11} b^{2} d^{3} e^{8} - 9 \, a^{12} b d^{2} e^{9} + 3 \, a^{13} d e^{10}\right)} x^{2} + {\left(5 \, a^{4} b^{9} d^{11} - 37 \, a^{5} b^{8} d^{10} e + 116 \, a^{6} b^{7} d^{9} e^{2} - 196 \, a^{7} b^{6} d^{8} e^{3} + 182 \, a^{8} b^{5} d^{7} e^{4} - 70 \, a^{9} b^{4} d^{6} e^{5} - 28 \, a^{10} b^{3} d^{5} e^{6} + 44 \, a^{11} b^{2} d^{4} e^{7} - 19 \, a^{12} b d^{3} e^{8} + 3 \, a^{13} d^{2} e^{9}\right)} x\right)}}, -\frac{45045 \, {\left(2 \, B a^{5} b^{2} d^{4} e^{4} + {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} d^{3} e^{5} + {\left(2 \, B b^{7} d e^{7} + {\left(B a b^{6} - 3 \, A b^{7}\right)} e^{8}\right)} x^{8} + {\left(6 \, B b^{7} d^{2} e^{6} + {\left(13 \, B a b^{6} - 9 \, A b^{7}\right)} d e^{7} + 5 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} e^{8}\right)} x^{7} + {\left(6 \, B b^{7} d^{3} e^{5} + 3 \, {\left(11 \, B a b^{6} - 3 \, A b^{7}\right)} d^{2} e^{6} + 5 \, {\left(7 \, B a^{2} b^{5} - 9 \, A a b^{6}\right)} d e^{7} + 10 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} e^{8}\right)} x^{6} + {\left(2 \, B b^{7} d^{4} e^{4} + {\left(31 \, B a b^{6} - 3 \, A b^{7}\right)} d^{3} e^{5} + 15 \, {\left(5 \, B a^{2} b^{5} - 3 \, A a b^{6}\right)} d^{2} e^{6} + 10 \, {\left(5 \, B a^{3} b^{4} - 9 \, A a^{2} b^{5}\right)} d e^{7} + 10 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} e^{8}\right)} x^{5} + 5 \, {\left(2 \, B a b^{6} d^{4} e^{4} + {\left(13 \, B a^{2} b^{5} - 3 \, A a b^{6}\right)} d^{3} e^{5} + 18 \, {\left(B a^{3} b^{4} - A a^{2} b^{5}\right)} d^{2} e^{6} + 2 \, {\left(4 \, B a^{4} b^{3} - 9 \, A a^{3} b^{4}\right)} d e^{7} + {\left(B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)} e^{8}\right)} x^{4} + {\left(20 \, B a^{2} b^{5} d^{4} e^{4} + 10 \, {\left(7 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} d^{3} e^{5} + 30 \, {\left(2 \, B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} d^{2} e^{6} + {\left(17 \, B a^{5} b^{2} - 45 \, A a^{4} b^{3}\right)} d e^{7} + {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} e^{8}\right)} x^{3} + {\left(20 \, B a^{3} b^{4} d^{4} e^{4} + 10 \, {\left(4 \, B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} d^{3} e^{5} + 3 \, {\left(7 \, B a^{5} b^{2} - 15 \, A a^{4} b^{3}\right)} d^{2} e^{6} + 3 \, {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} d e^{7}\right)} x^{2} + {\left(10 \, B a^{4} b^{3} d^{4} e^{4} + {\left(11 \, B a^{5} b^{2} - 15 \, A a^{4} b^{3}\right)} d^{3} e^{5} + 3 \, {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} d^{2} e^{6}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) + {\left(768 \, A a^{7} e^{7} + 96 \, {\left(B a b^{6} + 4 \, A b^{7}\right)} d^{7} - 16 \, {\left(62 \, B a^{2} b^{5} + 213 \, A a b^{6}\right)} d^{6} e + 28 \, {\left(187 \, B a^{3} b^{4} + 498 \, A a^{2} b^{5}\right)} d^{5} e^{2} - 70 \, {\left(332 \, B a^{4} b^{3} + 519 \, A a^{3} b^{4}\right)} d^{4} e^{3} - {\left(100363 \, B a^{5} b^{2} - 79905 \, A a^{4} b^{3}\right)} d^{3} e^{4} - 1024 \, {\left(16 \, B a^{6} b - 87 \, A a^{5} b^{2}\right)} d^{2} e^{5} + 512 \, {\left(B a^{7} - 18 \, A a^{6} b\right)} d e^{6} - 45045 \, {\left(2 \, B b^{7} d e^{6} + {\left(B a b^{6} - 3 \, A b^{7}\right)} e^{7}\right)} x^{7} - 105105 \, {\left(2 \, B b^{7} d^{2} e^{5} + {\left(5 \, B a b^{6} - 3 \, A b^{7}\right)} d e^{6} + 2 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} e^{7}\right)} x^{6} - 3003 \, {\left(46 \, B b^{7} d^{3} e^{4} + 3 \, {\left(117 \, B a b^{6} - 23 \, A b^{7}\right)} d^{2} e^{5} + 12 \, {\left(35 \, B a^{2} b^{5} - 41 \, A a b^{6}\right)} d e^{6} + 128 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} e^{7}\right)} x^{5} - 2145 \, {\left(6 \, B b^{7} d^{4} e^{3} + {\left(307 \, B a b^{6} - 9 \, A b^{7}\right)} d^{3} e^{4} + 12 \, {\left(83 \, B a^{2} b^{5} - 38 \, A a b^{6}\right)} d^{2} e^{5} + 6 \, {\left(123 \, B a^{3} b^{4} - 211 \, A a^{2} b^{5}\right)} d e^{6} + 158 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} e^{7}\right)} x^{4} + 715 \, {\left(4 \, B b^{7} d^{5} e^{2} - 2 \, {\left(43 \, B a b^{6} + 3 \, A b^{7}\right)} d^{4} e^{3} - 4 \, {\left(434 \, B a^{2} b^{5} - 33 \, A a b^{6}\right)} d^{3} e^{4} - 2 \, {\left(1547 \, B a^{3} b^{4} - 1269 \, A a^{2} b^{5}\right)} d^{2} e^{5} - 2 \, {\left(755 \, B a^{4} b^{3} - 1686 \, A a^{3} b^{4}\right)} d e^{6} - 193 \, {\left(B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)} e^{7}\right)} x^{3} - 65 \, {\left(16 \, B b^{7} d^{6} e - 12 \, {\left(17 \, B a b^{6} + 2 \, A b^{7}\right)} d^{5} e^{2} + 6 \, {\left(295 \, B a^{2} b^{5} + 53 \, A a b^{6}\right)} d^{4} e^{3} + 2 \, {\left(8837 \, B a^{3} b^{4} - 1407 \, A a^{2} b^{5}\right)} d^{3} e^{4} + 6 \, {\left(3091 \, B a^{4} b^{3} - 4184 \, A a^{3} b^{4}\right)} d^{2} e^{5} + 3 \, {\left(1867 \, B a^{5} b^{2} - 5089 \, A a^{4} b^{3}\right)} d e^{6} + 256 \, {\left(B a^{6} b - 3 \, A a^{5} b^{2}\right)} e^{7}\right)} x^{2} + 5 \, {\left(96 \, B b^{7} d^{7} - 16 \, {\left(59 \, B a b^{6} + 9 \, A b^{7}\right)} d^{6} e + 12 \, {\left(395 \, B a^{2} b^{5} + 124 \, A a b^{6}\right)} d^{5} e^{2} - 42 \, {\left(491 \, B a^{3} b^{4} + 187 \, A a^{2} b^{5}\right)} d^{4} e^{3} - 2 \, {\left(51487 \, B a^{4} b^{3} - 17430 \, A a^{3} b^{4}\right)} d^{3} e^{4} - 3 \, {\left(20687 \, B a^{5} b^{2} - 45677 \, A a^{4} b^{3}\right)} d^{2} e^{5} - 1536 \, {\left(5 \, B a^{6} b - 16 \, A a^{5} b^{2}\right)} d e^{6} + 256 \, {\left(B a^{7} - 3 \, A a^{6} b\right)} e^{7}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{5} b^{8} d^{11} - 8 \, a^{6} b^{7} d^{10} e + 28 \, a^{7} b^{6} d^{9} e^{2} - 56 \, a^{8} b^{5} d^{8} e^{3} + 70 \, a^{9} b^{4} d^{7} e^{4} - 56 \, a^{10} b^{3} d^{6} e^{5} + 28 \, a^{11} b^{2} d^{5} e^{6} - 8 \, a^{12} b d^{4} e^{7} + a^{13} d^{3} e^{8} + {\left(b^{13} d^{8} e^{3} - 8 \, a b^{12} d^{7} e^{4} + 28 \, a^{2} b^{11} d^{6} e^{5} - 56 \, a^{3} b^{10} d^{5} e^{6} + 70 \, a^{4} b^{9} d^{4} e^{7} - 56 \, a^{5} b^{8} d^{3} e^{8} + 28 \, a^{6} b^{7} d^{2} e^{9} - 8 \, a^{7} b^{6} d e^{10} + a^{8} b^{5} e^{11}\right)} x^{8} + {\left(3 \, b^{13} d^{9} e^{2} - 19 \, a b^{12} d^{8} e^{3} + 44 \, a^{2} b^{11} d^{7} e^{4} - 28 \, a^{3} b^{10} d^{6} e^{5} - 70 \, a^{4} b^{9} d^{5} e^{6} + 182 \, a^{5} b^{8} d^{4} e^{7} - 196 \, a^{6} b^{7} d^{3} e^{8} + 116 \, a^{7} b^{6} d^{2} e^{9} - 37 \, a^{8} b^{5} d e^{10} + 5 \, a^{9} b^{4} e^{11}\right)} x^{7} + {\left(3 \, b^{13} d^{10} e - 9 \, a b^{12} d^{9} e^{2} - 26 \, a^{2} b^{11} d^{8} e^{3} + 172 \, a^{3} b^{10} d^{7} e^{4} - 350 \, a^{4} b^{9} d^{6} e^{5} + 322 \, a^{5} b^{8} d^{5} e^{6} - 56 \, a^{6} b^{7} d^{4} e^{7} - 164 \, a^{7} b^{6} d^{3} e^{8} + 163 \, a^{8} b^{5} d^{2} e^{9} - 65 \, a^{9} b^{4} d e^{10} + 10 \, a^{10} b^{3} e^{11}\right)} x^{6} + {\left(b^{13} d^{11} + 7 \, a b^{12} d^{10} e - 62 \, a^{2} b^{11} d^{9} e^{2} + 134 \, a^{3} b^{10} d^{8} e^{3} - 10 \, a^{4} b^{9} d^{7} e^{4} - 406 \, a^{5} b^{8} d^{6} e^{5} + 728 \, a^{6} b^{7} d^{5} e^{6} - 568 \, a^{7} b^{6} d^{4} e^{7} + 161 \, a^{8} b^{5} d^{3} e^{8} + 55 \, a^{9} b^{4} d^{2} e^{9} - 50 \, a^{10} b^{3} d e^{10} + 10 \, a^{11} b^{2} e^{11}\right)} x^{5} + 5 \, {\left(a b^{12} d^{11} - 2 \, a^{2} b^{11} d^{10} e - 14 \, a^{3} b^{10} d^{9} e^{2} + 65 \, a^{4} b^{9} d^{8} e^{3} - 106 \, a^{5} b^{8} d^{7} e^{4} + 56 \, a^{6} b^{7} d^{6} e^{5} + 56 \, a^{7} b^{6} d^{5} e^{6} - 106 \, a^{8} b^{5} d^{4} e^{7} + 65 \, a^{9} b^{4} d^{3} e^{8} - 14 \, a^{10} b^{3} d^{2} e^{9} - 2 \, a^{11} b^{2} d e^{10} + a^{12} b e^{11}\right)} x^{4} + {\left(10 \, a^{2} b^{11} d^{11} - 50 \, a^{3} b^{10} d^{10} e + 55 \, a^{4} b^{9} d^{9} e^{2} + 161 \, a^{5} b^{8} d^{8} e^{3} - 568 \, a^{6} b^{7} d^{7} e^{4} + 728 \, a^{7} b^{6} d^{6} e^{5} - 406 \, a^{8} b^{5} d^{5} e^{6} - 10 \, a^{9} b^{4} d^{4} e^{7} + 134 \, a^{10} b^{3} d^{3} e^{8} - 62 \, a^{11} b^{2} d^{2} e^{9} + 7 \, a^{12} b d e^{10} + a^{13} e^{11}\right)} x^{3} + {\left(10 \, a^{3} b^{10} d^{11} - 65 \, a^{4} b^{9} d^{10} e + 163 \, a^{5} b^{8} d^{9} e^{2} - 164 \, a^{6} b^{7} d^{8} e^{3} - 56 \, a^{7} b^{6} d^{7} e^{4} + 322 \, a^{8} b^{5} d^{6} e^{5} - 350 \, a^{9} b^{4} d^{5} e^{6} + 172 \, a^{10} b^{3} d^{4} e^{7} - 26 \, a^{11} b^{2} d^{3} e^{8} - 9 \, a^{12} b d^{2} e^{9} + 3 \, a^{13} d e^{10}\right)} x^{2} + {\left(5 \, a^{4} b^{9} d^{11} - 37 \, a^{5} b^{8} d^{10} e + 116 \, a^{6} b^{7} d^{9} e^{2} - 196 \, a^{7} b^{6} d^{8} e^{3} + 182 \, a^{8} b^{5} d^{7} e^{4} - 70 \, a^{9} b^{4} d^{6} e^{5} - 28 \, a^{10} b^{3} d^{5} e^{6} + 44 \, a^{11} b^{2} d^{4} e^{7} - 19 \, a^{12} b d^{3} e^{8} + 3 \, a^{13} d^{2} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/3840*(45045*(2*B*a^5*b^2*d^4*e^4 + (B*a^6*b - 3*A*a^5*b^2)*d^3*e^5 + (2*B*b^7*d*e^7 + (B*a*b^6 - 3*A*b^7)*e^8)*x^8 + (6*B*b^7*d^2*e^6 + (13*B*a*b^6 - 9*A*b^7)*d*e^7 + 5*(B*a^2*b^5 - 3*A*a*b^6)*e^8)*x^7 + (6*B*b^7*d^3*e^5 + 3*(11*B*a*b^6 - 3*A*b^7)*d^2*e^6 + 5*(7*B*a^2*b^5 - 9*A*a*b^6)*d*e^7 + 10*(B*a^3*b^4 - 3*A*a^2*b^5)*e^8)*x^6 + (2*B*b^7*d^4*e^4 + (31*B*a*b^6 - 3*A*b^7)*d^3*e^5 + 15*(5*B*a^2*b^5 - 3*A*a*b^6)*d^2*e^6 + 10*(5*B*a^3*b^4 - 9*A*a^2*b^5)*d*e^7 + 10*(B*a^4*b^3 - 3*A*a^3*b^4)*e^8)*x^5 + 5*(2*B*a*b^6*d^4*e^4 + (13*B*a^2*b^5 - 3*A*a*b^6)*d^3*e^5 + 18*(B*a^3*b^4 - A*a^2*b^5)*d^2*e^6 + 2*(4*B*a^4*b^3 - 9*A*a^3*b^4)*d*e^7 + (B*a^5*b^2 - 3*A*a^4*b^3)*e^8)*x^4 + (20*B*a^2*b^5*d^4*e^4 + 10*(7*B*a^3*b^4 - 3*A*a^2*b^5)*d^3*e^5 + 30*(2*B*a^4*b^3 - 3*A*a^3*b^4)*d^2*e^6 + (17*B*a^5*b^2 - 45*A*a^4*b^3)*d*e^7 + (B*a^6*b - 3*A*a^5*b^2)*e^8)*x^3 + (20*B*a^3*b^4*d^4*e^4 + 10*(4*B*a^4*b^3 - 3*A*a^3*b^4)*d^3*e^5 + 3*(7*B*a^5*b^2 - 15*A*a^4*b^3)*d^2*e^6 + 3*(B*a^6*b - 3*A*a^5*b^2)*d*e^7)*x^2 + (10*B*a^4*b^3*d^4*e^4 + (11*B*a^5*b^2 - 15*A*a^4*b^3)*d^3*e^5 + 3*(B*a^6*b - 3*A*a^5*b^2)*d^2*e^6)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(768*A*a^7*e^7 + 96*(B*a*b^6 + 4*A*b^7)*d^7 - 16*(62*B*a^2*b^5 + 213*A*a*b^6)*d^6*e + 28*(187*B*a^3*b^4 + 498*A*a^2*b^5)*d^5*e^2 - 70*(332*B*a^4*b^3 + 519*A*a^3*b^4)*d^4*e^3 - (100363*B*a^5*b^2 - 79905*A*a^4*b^3)*d^3*e^4 - 1024*(16*B*a^6*b - 87*A*a^5*b^2)*d^2*e^5 + 512*(B*a^7 - 18*A*a^6*b)*d*e^6 - 45045*(2*B*b^7*d*e^6 + (B*a*b^6 - 3*A*b^7)*e^7)*x^7 - 105105*(2*B*b^7*d^2*e^5 + (5*B*a*b^6 - 3*A*b^7)*d*e^6 + 2*(B*a^2*b^5 - 3*A*a*b^6)*e^7)*x^6 - 3003*(46*B*b^7*d^3*e^4 + 3*(117*B*a*b^6 - 23*A*b^7)*d^2*e^5 + 12*(35*B*a^2*b^5 - 41*A*a*b^6)*d*e^6 + 128*(B*a^3*b^4 - 3*A*a^2*b^5)*e^7)*x^5 - 2145*(6*B*b^7*d^4*e^3 + (307*B*a*b^6 - 9*A*b^7)*d^3*e^4 + 12*(83*B*a^2*b^5 - 38*A*a*b^6)*d^2*e^5 + 6*(123*B*a^3*b^4 - 211*A*a^2*b^5)*d*e^6 + 158*(B*a^4*b^3 - 3*A*a^3*b^4)*e^7)*x^4 + 715*(4*B*b^7*d^5*e^2 - 2*(43*B*a*b^6 + 3*A*b^7)*d^4*e^3 - 4*(434*B*a^2*b^5 - 33*A*a*b^6)*d^3*e^4 - 2*(1547*B*a^3*b^4 - 1269*A*a^2*b^5)*d^2*e^5 - 2*(755*B*a^4*b^3 - 1686*A*a^3*b^4)*d*e^6 - 193*(B*a^5*b^2 - 3*A*a^4*b^3)*e^7)*x^3 - 65*(16*B*b^7*d^6*e - 12*(17*B*a*b^6 + 2*A*b^7)*d^5*e^2 + 6*(295*B*a^2*b^5 + 53*A*a*b^6)*d^4*e^3 + 2*(8837*B*a^3*b^4 - 1407*A*a^2*b^5)*d^3*e^4 + 6*(3091*B*a^4*b^3 - 4184*A*a^3*b^4)*d^2*e^5 + 3*(1867*B*a^5*b^2 - 5089*A*a^4*b^3)*d*e^6 + 256*(B*a^6*b - 3*A*a^5*b^2)*e^7)*x^2 + 5*(96*B*b^7*d^7 - 16*(59*B*a*b^6 + 9*A*b^7)*d^6*e + 12*(395*B*a^2*b^5 + 124*A*a*b^6)*d^5*e^2 - 42*(491*B*a^3*b^4 + 187*A*a^2*b^5)*d^4*e^3 - 2*(51487*B*a^4*b^3 - 17430*A*a^3*b^4)*d^3*e^4 - 3*(20687*B*a^5*b^2 - 45677*A*a^4*b^3)*d^2*e^5 - 1536*(5*B*a^6*b - 16*A*a^5*b^2)*d*e^6 + 256*(B*a^7 - 3*A*a^6*b)*e^7)*x)*sqrt(e*x + d))/(a^5*b^8*d^11 - 8*a^6*b^7*d^10*e + 28*a^7*b^6*d^9*e^2 - 56*a^8*b^5*d^8*e^3 + 70*a^9*b^4*d^7*e^4 - 56*a^10*b^3*d^6*e^5 + 28*a^11*b^2*d^5*e^6 - 8*a^12*b*d^4*e^7 + a^13*d^3*e^8 + (b^13*d^8*e^3 - 8*a*b^12*d^7*e^4 + 28*a^2*b^11*d^6*e^5 - 56*a^3*b^10*d^5*e^6 + 70*a^4*b^9*d^4*e^7 - 56*a^5*b^8*d^3*e^8 + 28*a^6*b^7*d^2*e^9 - 8*a^7*b^6*d*e^10 + a^8*b^5*e^11)*x^8 + (3*b^13*d^9*e^2 - 19*a*b^12*d^8*e^3 + 44*a^2*b^11*d^7*e^4 - 28*a^3*b^10*d^6*e^5 - 70*a^4*b^9*d^5*e^6 + 182*a^5*b^8*d^4*e^7 - 196*a^6*b^7*d^3*e^8 + 116*a^7*b^6*d^2*e^9 - 37*a^8*b^5*d*e^10 + 5*a^9*b^4*e^11)*x^7 + (3*b^13*d^10*e - 9*a*b^12*d^9*e^2 - 26*a^2*b^11*d^8*e^3 + 172*a^3*b^10*d^7*e^4 - 350*a^4*b^9*d^6*e^5 + 322*a^5*b^8*d^5*e^6 - 56*a^6*b^7*d^4*e^7 - 164*a^7*b^6*d^3*e^8 + 163*a^8*b^5*d^2*e^9 - 65*a^9*b^4*d*e^10 + 10*a^10*b^3*e^11)*x^6 + (b^13*d^11 + 7*a*b^12*d^10*e - 62*a^2*b^11*d^9*e^2 + 134*a^3*b^10*d^8*e^3 - 10*a^4*b^9*d^7*e^4 - 406*a^5*b^8*d^6*e^5 + 728*a^6*b^7*d^5*e^6 - 568*a^7*b^6*d^4*e^7 + 161*a^8*b^5*d^3*e^8 + 55*a^9*b^4*d^2*e^9 - 50*a^10*b^3*d*e^10 + 10*a^11*b^2*e^11)*x^5 + 5*(a*b^12*d^11 - 2*a^2*b^11*d^10*e - 14*a^3*b^10*d^9*e^2 + 65*a^4*b^9*d^8*e^3 - 106*a^5*b^8*d^7*e^4 + 56*a^6*b^7*d^6*e^5 + 56*a^7*b^6*d^5*e^6 - 106*a^8*b^5*d^4*e^7 + 65*a^9*b^4*d^3*e^8 - 14*a^10*b^3*d^2*e^9 - 2*a^11*b^2*d*e^10 + a^12*b*e^11)*x^4 + (10*a^2*b^11*d^11 - 50*a^3*b^10*d^10*e + 55*a^4*b^9*d^9*e^2 + 161*a^5*b^8*d^8*e^3 - 568*a^6*b^7*d^7*e^4 + 728*a^7*b^6*d^6*e^5 - 406*a^8*b^5*d^5*e^6 - 10*a^9*b^4*d^4*e^7 + 134*a^10*b^3*d^3*e^8 - 62*a^11*b^2*d^2*e^9 + 7*a^12*b*d*e^10 + a^13*e^11)*x^3 + (10*a^3*b^10*d^11 - 65*a^4*b^9*d^10*e + 163*a^5*b^8*d^9*e^2 - 164*a^6*b^7*d^8*e^3 - 56*a^7*b^6*d^7*e^4 + 322*a^8*b^5*d^6*e^5 - 350*a^9*b^4*d^5*e^6 + 172*a^10*b^3*d^4*e^7 - 26*a^11*b^2*d^3*e^8 - 9*a^12*b*d^2*e^9 + 3*a^13*d*e^10)*x^2 + (5*a^4*b^9*d^11 - 37*a^5*b^8*d^10*e + 116*a^6*b^7*d^9*e^2 - 196*a^7*b^6*d^8*e^3 + 182*a^8*b^5*d^7*e^4 - 70*a^9*b^4*d^6*e^5 - 28*a^10*b^3*d^5*e^6 + 44*a^11*b^2*d^4*e^7 - 19*a^12*b*d^3*e^8 + 3*a^13*d^2*e^9)*x), -1/1920*(45045*(2*B*a^5*b^2*d^4*e^4 + (B*a^6*b - 3*A*a^5*b^2)*d^3*e^5 + (2*B*b^7*d*e^7 + (B*a*b^6 - 3*A*b^7)*e^8)*x^8 + (6*B*b^7*d^2*e^6 + (13*B*a*b^6 - 9*A*b^7)*d*e^7 + 5*(B*a^2*b^5 - 3*A*a*b^6)*e^8)*x^7 + (6*B*b^7*d^3*e^5 + 3*(11*B*a*b^6 - 3*A*b^7)*d^2*e^6 + 5*(7*B*a^2*b^5 - 9*A*a*b^6)*d*e^7 + 10*(B*a^3*b^4 - 3*A*a^2*b^5)*e^8)*x^6 + (2*B*b^7*d^4*e^4 + (31*B*a*b^6 - 3*A*b^7)*d^3*e^5 + 15*(5*B*a^2*b^5 - 3*A*a*b^6)*d^2*e^6 + 10*(5*B*a^3*b^4 - 9*A*a^2*b^5)*d*e^7 + 10*(B*a^4*b^3 - 3*A*a^3*b^4)*e^8)*x^5 + 5*(2*B*a*b^6*d^4*e^4 + (13*B*a^2*b^5 - 3*A*a*b^6)*d^3*e^5 + 18*(B*a^3*b^4 - A*a^2*b^5)*d^2*e^6 + 2*(4*B*a^4*b^3 - 9*A*a^3*b^4)*d*e^7 + (B*a^5*b^2 - 3*A*a^4*b^3)*e^8)*x^4 + (20*B*a^2*b^5*d^4*e^4 + 10*(7*B*a^3*b^4 - 3*A*a^2*b^5)*d^3*e^5 + 30*(2*B*a^4*b^3 - 3*A*a^3*b^4)*d^2*e^6 + (17*B*a^5*b^2 - 45*A*a^4*b^3)*d*e^7 + (B*a^6*b - 3*A*a^5*b^2)*e^8)*x^3 + (20*B*a^3*b^4*d^4*e^4 + 10*(4*B*a^4*b^3 - 3*A*a^3*b^4)*d^3*e^5 + 3*(7*B*a^5*b^2 - 15*A*a^4*b^3)*d^2*e^6 + 3*(B*a^6*b - 3*A*a^5*b^2)*d*e^7)*x^2 + (10*B*a^4*b^3*d^4*e^4 + (11*B*a^5*b^2 - 15*A*a^4*b^3)*d^3*e^5 + 3*(B*a^6*b - 3*A*a^5*b^2)*d^2*e^6)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) + (768*A*a^7*e^7 + 96*(B*a*b^6 + 4*A*b^7)*d^7 - 16*(62*B*a^2*b^5 + 213*A*a*b^6)*d^6*e + 28*(187*B*a^3*b^4 + 498*A*a^2*b^5)*d^5*e^2 - 70*(332*B*a^4*b^3 + 519*A*a^3*b^4)*d^4*e^3 - (100363*B*a^5*b^2 - 79905*A*a^4*b^3)*d^3*e^4 - 1024*(16*B*a^6*b - 87*A*a^5*b^2)*d^2*e^5 + 512*(B*a^7 - 18*A*a^6*b)*d*e^6 - 45045*(2*B*b^7*d*e^6 + (B*a*b^6 - 3*A*b^7)*e^7)*x^7 - 105105*(2*B*b^7*d^2*e^5 + (5*B*a*b^6 - 3*A*b^7)*d*e^6 + 2*(B*a^2*b^5 - 3*A*a*b^6)*e^7)*x^6 - 3003*(46*B*b^7*d^3*e^4 + 3*(117*B*a*b^6 - 23*A*b^7)*d^2*e^5 + 12*(35*B*a^2*b^5 - 41*A*a*b^6)*d*e^6 + 128*(B*a^3*b^4 - 3*A*a^2*b^5)*e^7)*x^5 - 2145*(6*B*b^7*d^4*e^3 + (307*B*a*b^6 - 9*A*b^7)*d^3*e^4 + 12*(83*B*a^2*b^5 - 38*A*a*b^6)*d^2*e^5 + 6*(123*B*a^3*b^4 - 211*A*a^2*b^5)*d*e^6 + 158*(B*a^4*b^3 - 3*A*a^3*b^4)*e^7)*x^4 + 715*(4*B*b^7*d^5*e^2 - 2*(43*B*a*b^6 + 3*A*b^7)*d^4*e^3 - 4*(434*B*a^2*b^5 - 33*A*a*b^6)*d^3*e^4 - 2*(1547*B*a^3*b^4 - 1269*A*a^2*b^5)*d^2*e^5 - 2*(755*B*a^4*b^3 - 1686*A*a^3*b^4)*d*e^6 - 193*(B*a^5*b^2 - 3*A*a^4*b^3)*e^7)*x^3 - 65*(16*B*b^7*d^6*e - 12*(17*B*a*b^6 + 2*A*b^7)*d^5*e^2 + 6*(295*B*a^2*b^5 + 53*A*a*b^6)*d^4*e^3 + 2*(8837*B*a^3*b^4 - 1407*A*a^2*b^5)*d^3*e^4 + 6*(3091*B*a^4*b^3 - 4184*A*a^3*b^4)*d^2*e^5 + 3*(1867*B*a^5*b^2 - 5089*A*a^4*b^3)*d*e^6 + 256*(B*a^6*b - 3*A*a^5*b^2)*e^7)*x^2 + 5*(96*B*b^7*d^7 - 16*(59*B*a*b^6 + 9*A*b^7)*d^6*e + 12*(395*B*a^2*b^5 + 124*A*a*b^6)*d^5*e^2 - 42*(491*B*a^3*b^4 + 187*A*a^2*b^5)*d^4*e^3 - 2*(51487*B*a^4*b^3 - 17430*A*a^3*b^4)*d^3*e^4 - 3*(20687*B*a^5*b^2 - 45677*A*a^4*b^3)*d^2*e^5 - 1536*(5*B*a^6*b - 16*A*a^5*b^2)*d*e^6 + 256*(B*a^7 - 3*A*a^6*b)*e^7)*x)*sqrt(e*x + d))/(a^5*b^8*d^11 - 8*a^6*b^7*d^10*e + 28*a^7*b^6*d^9*e^2 - 56*a^8*b^5*d^8*e^3 + 70*a^9*b^4*d^7*e^4 - 56*a^10*b^3*d^6*e^5 + 28*a^11*b^2*d^5*e^6 - 8*a^12*b*d^4*e^7 + a^13*d^3*e^8 + (b^13*d^8*e^3 - 8*a*b^12*d^7*e^4 + 28*a^2*b^11*d^6*e^5 - 56*a^3*b^10*d^5*e^6 + 70*a^4*b^9*d^4*e^7 - 56*a^5*b^8*d^3*e^8 + 28*a^6*b^7*d^2*e^9 - 8*a^7*b^6*d*e^10 + a^8*b^5*e^11)*x^8 + (3*b^13*d^9*e^2 - 19*a*b^12*d^8*e^3 + 44*a^2*b^11*d^7*e^4 - 28*a^3*b^10*d^6*e^5 - 70*a^4*b^9*d^5*e^6 + 182*a^5*b^8*d^4*e^7 - 196*a^6*b^7*d^3*e^8 + 116*a^7*b^6*d^2*e^9 - 37*a^8*b^5*d*e^10 + 5*a^9*b^4*e^11)*x^7 + (3*b^13*d^10*e - 9*a*b^12*d^9*e^2 - 26*a^2*b^11*d^8*e^3 + 172*a^3*b^10*d^7*e^4 - 350*a^4*b^9*d^6*e^5 + 322*a^5*b^8*d^5*e^6 - 56*a^6*b^7*d^4*e^7 - 164*a^7*b^6*d^3*e^8 + 163*a^8*b^5*d^2*e^9 - 65*a^9*b^4*d*e^10 + 10*a^10*b^3*e^11)*x^6 + (b^13*d^11 + 7*a*b^12*d^10*e - 62*a^2*b^11*d^9*e^2 + 134*a^3*b^10*d^8*e^3 - 10*a^4*b^9*d^7*e^4 - 406*a^5*b^8*d^6*e^5 + 728*a^6*b^7*d^5*e^6 - 568*a^7*b^6*d^4*e^7 + 161*a^8*b^5*d^3*e^8 + 55*a^9*b^4*d^2*e^9 - 50*a^10*b^3*d*e^10 + 10*a^11*b^2*e^11)*x^5 + 5*(a*b^12*d^11 - 2*a^2*b^11*d^10*e - 14*a^3*b^10*d^9*e^2 + 65*a^4*b^9*d^8*e^3 - 106*a^5*b^8*d^7*e^4 + 56*a^6*b^7*d^6*e^5 + 56*a^7*b^6*d^5*e^6 - 106*a^8*b^5*d^4*e^7 + 65*a^9*b^4*d^3*e^8 - 14*a^10*b^3*d^2*e^9 - 2*a^11*b^2*d*e^10 + a^12*b*e^11)*x^4 + (10*a^2*b^11*d^11 - 50*a^3*b^10*d^10*e + 55*a^4*b^9*d^9*e^2 + 161*a^5*b^8*d^8*e^3 - 568*a^6*b^7*d^7*e^4 + 728*a^7*b^6*d^6*e^5 - 406*a^8*b^5*d^5*e^6 - 10*a^9*b^4*d^4*e^7 + 134*a^10*b^3*d^3*e^8 - 62*a^11*b^2*d^2*e^9 + 7*a^12*b*d*e^10 + a^13*e^11)*x^3 + (10*a^3*b^10*d^11 - 65*a^4*b^9*d^10*e + 163*a^5*b^8*d^9*e^2 - 164*a^6*b^7*d^8*e^3 - 56*a^7*b^6*d^7*e^4 + 322*a^8*b^5*d^6*e^5 - 350*a^9*b^4*d^5*e^6 + 172*a^10*b^3*d^4*e^7 - 26*a^11*b^2*d^3*e^8 - 9*a^12*b*d^2*e^9 + 3*a^13*d*e^10)*x^2 + (5*a^4*b^9*d^11 - 37*a^5*b^8*d^10*e + 116*a^6*b^7*d^9*e^2 - 196*a^7*b^6*d^8*e^3 + 182*a^8*b^5*d^7*e^4 - 70*a^9*b^4*d^6*e^5 - 28*a^10*b^3*d^5*e^6 + 44*a^11*b^2*d^4*e^7 - 19*a^12*b*d^3*e^8 + 3*a^13*d^2*e^9)*x)]","B",0
1835,1,230,0,0.426132," ","integrate((B*x+A)*(e*x+d)^(7/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(99 \, B b e^{6} x^{6} + 8 \, B b d^{6} + 143 \, A a d^{4} e^{2} - 26 \, {\left(B a + A b\right)} d^{5} e + 9 \, {\left(40 \, B b d e^{5} + 13 \, {\left(B a + A b\right)} e^{6}\right)} x^{5} + {\left(458 \, B b d^{2} e^{4} + 143 \, A a e^{6} + 442 \, {\left(B a + A b\right)} d e^{5}\right)} x^{4} + 2 \, {\left(106 \, B b d^{3} e^{3} + 286 \, A a d e^{5} + 299 \, {\left(B a + A b\right)} d^{2} e^{4}\right)} x^{3} + 3 \, {\left(B b d^{4} e^{2} + 286 \, A a d^{2} e^{4} + 104 \, {\left(B a + A b\right)} d^{3} e^{3}\right)} x^{2} - {\left(4 \, B b d^{5} e - 572 \, A a d^{3} e^{3} - 13 \, {\left(B a + A b\right)} d^{4} e^{2}\right)} x\right)} \sqrt{e x + d}}{1287 \, e^{3}}"," ",0,"2/1287*(99*B*b*e^6*x^6 + 8*B*b*d^6 + 143*A*a*d^4*e^2 - 26*(B*a + A*b)*d^5*e + 9*(40*B*b*d*e^5 + 13*(B*a + A*b)*e^6)*x^5 + (458*B*b*d^2*e^4 + 143*A*a*e^6 + 442*(B*a + A*b)*d*e^5)*x^4 + 2*(106*B*b*d^3*e^3 + 286*A*a*d*e^5 + 299*(B*a + A*b)*d^2*e^4)*x^3 + 3*(B*b*d^4*e^2 + 286*A*a*d^2*e^4 + 104*(B*a + A*b)*d^3*e^3)*x^2 - (4*B*b*d^5*e - 572*A*a*d^3*e^3 - 13*(B*a + A*b)*d^4*e^2)*x)*sqrt(e*x + d)/e^3","A",0
1836,1,189,0,0.424490," ","integrate((B*x+A)*(e*x+d)^(5/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B b e^{5} x^{5} + 8 \, B b d^{5} + 99 \, A a d^{3} e^{2} - 22 \, {\left(B a + A b\right)} d^{4} e + 7 \, {\left(23 \, B b d e^{4} + 11 \, {\left(B a + A b\right)} e^{5}\right)} x^{4} + {\left(113 \, B b d^{2} e^{3} + 99 \, A a e^{5} + 209 \, {\left(B a + A b\right)} d e^{4}\right)} x^{3} + 3 \, {\left(B b d^{3} e^{2} + 99 \, A a d e^{4} + 55 \, {\left(B a + A b\right)} d^{2} e^{3}\right)} x^{2} - {\left(4 \, B b d^{4} e - 297 \, A a d^{2} e^{3} - 11 \, {\left(B a + A b\right)} d^{3} e^{2}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{3}}"," ",0,"2/693*(63*B*b*e^5*x^5 + 8*B*b*d^5 + 99*A*a*d^3*e^2 - 22*(B*a + A*b)*d^4*e + 7*(23*B*b*d*e^4 + 11*(B*a + A*b)*e^5)*x^4 + (113*B*b*d^2*e^3 + 99*A*a*e^5 + 209*(B*a + A*b)*d*e^4)*x^3 + 3*(B*b*d^3*e^2 + 99*A*a*d*e^4 + 55*(B*a + A*b)*d^2*e^3)*x^2 - (4*B*b*d^4*e - 297*A*a*d^2*e^3 - 11*(B*a + A*b)*d^3*e^2)*x)*sqrt(e*x + d)/e^3","A",0
1837,1,149,0,0.424643," ","integrate((B*x+A)*(e*x+d)^(3/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b e^{4} x^{4} + 8 \, B b d^{4} + 63 \, A a d^{2} e^{2} - 18 \, {\left(B a + A b\right)} d^{3} e + 5 \, {\left(10 \, B b d e^{3} + 9 \, {\left(B a + A b\right)} e^{4}\right)} x^{3} + 3 \, {\left(B b d^{2} e^{2} + 21 \, A a e^{4} + 24 \, {\left(B a + A b\right)} d e^{3}\right)} x^{2} - {\left(4 \, B b d^{3} e - 126 \, A a d e^{3} - 9 \, {\left(B a + A b\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{3}}"," ",0,"2/315*(35*B*b*e^4*x^4 + 8*B*b*d^4 + 63*A*a*d^2*e^2 - 18*(B*a + A*b)*d^3*e + 5*(10*B*b*d*e^3 + 9*(B*a + A*b)*e^4)*x^3 + 3*(B*b*d^2*e^2 + 21*A*a*e^4 + 24*(B*a + A*b)*d*e^3)*x^2 - (4*B*b*d^3*e - 126*A*a*d*e^3 - 9*(B*a + A*b)*d^2*e^2)*x)*sqrt(e*x + d)/e^3","A",0
1838,1,108,0,0.423848," ","integrate((B*x+A)*(e*x+d)^(1/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b e^{3} x^{3} + 8 \, B b d^{3} + 35 \, A a d e^{2} - 14 \, {\left(B a + A b\right)} d^{2} e + 3 \, {\left(B b d e^{2} + 7 \, {\left(B a + A b\right)} e^{3}\right)} x^{2} - {\left(4 \, B b d^{2} e - 35 \, A a e^{3} - 7 \, {\left(B a + A b\right)} d e^{2}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{3}}"," ",0,"2/105*(15*B*b*e^3*x^3 + 8*B*b*d^3 + 35*A*a*d*e^2 - 14*(B*a + A*b)*d^2*e + 3*(B*b*d*e^2 + 7*(B*a + A*b)*e^3)*x^2 - (4*B*b*d^2*e - 35*A*a*e^3 - 7*(B*a + A*b)*d*e^2)*x)*sqrt(e*x + d)/e^3","A",0
1839,1,70,0,0.422623," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b e^{2} x^{2} + 8 \, B b d^{2} + 15 \, A a e^{2} - 10 \, {\left(B a + A b\right)} d e - {\left(4 \, B b d e - 5 \, {\left(B a + A b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, e^{3}}"," ",0,"2/15*(3*B*b*e^2*x^2 + 8*B*b*d^2 + 15*A*a*e^2 - 10*(B*a + A*b)*d*e - (4*B*b*d*e - 5*(B*a + A*b)*e^2)*x)*sqrt(e*x + d)/e^3","A",0
1840,1,79,0,0.423973," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b e^{2} x^{2} - 8 \, B b d^{2} - 3 \, A a e^{2} + 6 \, {\left(B a + A b\right)} d e - {\left(4 \, B b d e - 3 \, {\left(B a + A b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"2/3*(B*b*e^2*x^2 - 8*B*b*d^2 - 3*A*a*e^2 + 6*(B*a + A*b)*d*e - (4*B*b*d*e - 3*(B*a + A*b)*e^2)*x)*sqrt(e*x + d)/(e^4*x + d*e^3)","A",0
1841,1,91,0,0.413714," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b e^{2} x^{2} + 8 \, B b d^{2} - A a e^{2} - 2 \, {\left(B a + A b\right)} d e + 3 \, {\left(4 \, B b d e - {\left(B a + A b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"2/3*(3*B*b*e^2*x^2 + 8*B*b*d^2 - A*a*e^2 - 2*(B*a + A*b)*d*e + 3*(4*B*b*d*e - (B*a + A*b)*e^2)*x)*sqrt(e*x + d)/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
1842,1,101,0,0.438200," ","integrate((B*x+A)*((b*x+a)^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, B b e^{2} x^{2} + 8 \, B b d^{2} + 3 \, A a e^{2} + 2 \, {\left(B a + A b\right)} d e + 5 \, {\left(4 \, B b d e + {\left(B a + A b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-2/15*(15*B*b*e^2*x^2 + 8*B*b*d^2 + 3*A*a*e^2 + 2*(B*a + A*b)*d*e + 5*(4*B*b*d*e + (B*a + A*b)*e^2)*x)*sqrt(e*x + d)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
1843,1,633,0,0.444071," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6435 \, B b^{3} e^{8} x^{8} + 128 \, B b^{3} d^{8} + 12155 \, A a^{3} d^{4} e^{4} - 272 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{7} e + 2040 \, {\left(B a^{2} b + A a b^{2}\right)} d^{6} e^{2} - 2210 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{5} e^{3} + 429 \, {\left(52 \, B b^{3} d e^{7} + 17 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{8}\right)} x^{7} + 33 \, {\left(802 \, B b^{3} d^{2} e^{6} + 782 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{7} + 765 \, {\left(B a^{2} b + A a b^{2}\right)} e^{8}\right)} x^{6} + 9 \, {\left(1212 \, B b^{3} d^{3} e^{5} + 3502 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{6} + 10200 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{7} + 1105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8}\right)} x^{5} + 5 \, {\left(7 \, B b^{3} d^{4} e^{4} + 2431 \, A a^{3} e^{8} + 2720 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{5} + 23358 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{6} + 7514 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{7}\right)} x^{4} - 5 \, {\left(8 \, B b^{3} d^{5} e^{3} - 9724 \, A a^{3} d e^{7} - 17 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e^{4} - 10812 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{5} - 10166 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{6}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{6} e^{2} + 24310 \, A a^{3} d^{2} e^{6} - 34 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{5} e^{3} + 255 \, {\left(B a^{2} b + A a b^{2}\right)} d^{4} e^{4} + 8840 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3} e^{5}\right)} x^{2} - {\left(64 \, B b^{3} d^{7} e - 48620 \, A a^{3} d^{3} e^{5} - 136 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{6} e^{2} + 1020 \, {\left(B a^{2} b + A a b^{2}\right)} d^{5} e^{3} - 1105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{4} e^{4}\right)} x\right)} \sqrt{e x + d}}{109395 \, e^{5}}"," ",0,"2/109395*(6435*B*b^3*e^8*x^8 + 128*B*b^3*d^8 + 12155*A*a^3*d^4*e^4 - 272*(3*B*a*b^2 + A*b^3)*d^7*e + 2040*(B*a^2*b + A*a*b^2)*d^6*e^2 - 2210*(B*a^3 + 3*A*a^2*b)*d^5*e^3 + 429*(52*B*b^3*d*e^7 + 17*(3*B*a*b^2 + A*b^3)*e^8)*x^7 + 33*(802*B*b^3*d^2*e^6 + 782*(3*B*a*b^2 + A*b^3)*d*e^7 + 765*(B*a^2*b + A*a*b^2)*e^8)*x^6 + 9*(1212*B*b^3*d^3*e^5 + 3502*(3*B*a*b^2 + A*b^3)*d^2*e^6 + 10200*(B*a^2*b + A*a*b^2)*d*e^7 + 1105*(B*a^3 + 3*A*a^2*b)*e^8)*x^5 + 5*(7*B*b^3*d^4*e^4 + 2431*A*a^3*e^8 + 2720*(3*B*a*b^2 + A*b^3)*d^3*e^5 + 23358*(B*a^2*b + A*a*b^2)*d^2*e^6 + 7514*(B*a^3 + 3*A*a^2*b)*d*e^7)*x^4 - 5*(8*B*b^3*d^5*e^3 - 9724*A*a^3*d*e^7 - 17*(3*B*a*b^2 + A*b^3)*d^4*e^4 - 10812*(B*a^2*b + A*a*b^2)*d^3*e^5 - 10166*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*x^3 + 3*(16*B*b^3*d^6*e^2 + 24310*A*a^3*d^2*e^6 - 34*(3*B*a*b^2 + A*b^3)*d^5*e^3 + 255*(B*a^2*b + A*a*b^2)*d^4*e^4 + 8840*(B*a^3 + 3*A*a^2*b)*d^3*e^5)*x^2 - (64*B*b^3*d^7*e - 48620*A*a^3*d^3*e^5 - 136*(3*B*a*b^2 + A*b^3)*d^6*e^2 + 1020*(B*a^2*b + A*a*b^2)*d^5*e^3 - 1105*(B*a^3 + 3*A*a^2*b)*d^4*e^4)*x)*sqrt(e*x + d)/e^5","B",0
1844,1,539,0,0.424737," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B b^{3} e^{7} x^{7} + 128 \, B b^{3} d^{7} + 6435 \, A a^{3} d^{3} e^{4} - 240 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{6} e + 1560 \, {\left(B a^{2} b + A a b^{2}\right)} d^{5} e^{2} - 1430 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{4} e^{3} + 231 \, {\left(31 \, B b^{3} d e^{6} + 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{7}\right)} x^{6} + 63 \, {\left(71 \, B b^{3} d^{2} e^{5} + 135 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{6} + 195 \, {\left(B a^{2} b + A a b^{2}\right)} e^{7}\right)} x^{5} + 35 \, {\left(B b^{3} d^{3} e^{4} + 159 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{5} + 897 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{6} + 143 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x^{4} - 5 \, {\left(8 \, B b^{3} d^{4} e^{3} - 1287 \, A a^{3} e^{7} - 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{4} - 4407 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{5} - 2717 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{5} e^{2} + 6435 \, A a^{3} d e^{6} - 30 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e^{3} + 195 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{4} + 3575 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{5}\right)} x^{2} - {\left(64 \, B b^{3} d^{6} e - 19305 \, A a^{3} d^{2} e^{5} - 120 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{5} e^{2} + 780 \, {\left(B a^{2} b + A a b^{2}\right)} d^{4} e^{3} - 715 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3} e^{4}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3003*B*b^3*e^7*x^7 + 128*B*b^3*d^7 + 6435*A*a^3*d^3*e^4 - 240*(3*B*a*b^2 + A*b^3)*d^6*e + 1560*(B*a^2*b + A*a*b^2)*d^5*e^2 - 1430*(B*a^3 + 3*A*a^2*b)*d^4*e^3 + 231*(31*B*b^3*d*e^6 + 15*(3*B*a*b^2 + A*b^3)*e^7)*x^6 + 63*(71*B*b^3*d^2*e^5 + 135*(3*B*a*b^2 + A*b^3)*d*e^6 + 195*(B*a^2*b + A*a*b^2)*e^7)*x^5 + 35*(B*b^3*d^3*e^4 + 159*(3*B*a*b^2 + A*b^3)*d^2*e^5 + 897*(B*a^2*b + A*a*b^2)*d*e^6 + 143*(B*a^3 + 3*A*a^2*b)*e^7)*x^4 - 5*(8*B*b^3*d^4*e^3 - 1287*A*a^3*e^7 - 15*(3*B*a*b^2 + A*b^3)*d^3*e^4 - 4407*(B*a^2*b + A*a*b^2)*d^2*e^5 - 2717*(B*a^3 + 3*A*a^2*b)*d*e^6)*x^3 + 3*(16*B*b^3*d^5*e^2 + 6435*A*a^3*d*e^6 - 30*(3*B*a*b^2 + A*b^3)*d^4*e^3 + 195*(B*a^2*b + A*a*b^2)*d^3*e^4 + 3575*(B*a^3 + 3*A*a^2*b)*d^2*e^5)*x^2 - (64*B*b^3*d^6*e - 19305*A*a^3*d^2*e^5 - 120*(3*B*a*b^2 + A*b^3)*d^5*e^2 + 780*(B*a^2*b + A*a*b^2)*d^4*e^3 - 715*(B*a^3 + 3*A*a^2*b)*d^3*e^4)*x)*sqrt(e*x + d)/e^5","B",0
1845,1,446,0,0.429568," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, B b^{3} e^{6} x^{6} + 128 \, B b^{3} d^{6} + 3003 \, A a^{3} d^{2} e^{4} - 208 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{5} e + 1144 \, {\left(B a^{2} b + A a b^{2}\right)} d^{4} e^{2} - 858 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3} e^{3} + 105 \, {\left(14 \, B b^{3} d e^{5} + 13 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{6}\right)} x^{5} + 35 \, {\left(B b^{3} d^{2} e^{4} + 52 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{5} + 143 \, {\left(B a^{2} b + A a b^{2}\right)} e^{6}\right)} x^{4} - 5 \, {\left(8 \, B b^{3} d^{3} e^{3} - 13 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{4} - 1430 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{5} - 429 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{6}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{4} e^{2} + 1001 \, A a^{3} e^{6} - 26 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{3} + 143 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{4} + 1144 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{5}\right)} x^{2} - {\left(64 \, B b^{3} d^{5} e - 6006 \, A a^{3} d e^{5} - 104 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e^{2} + 572 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{3} - 429 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{15015 \, e^{5}}"," ",0,"2/15015*(1155*B*b^3*e^6*x^6 + 128*B*b^3*d^6 + 3003*A*a^3*d^2*e^4 - 208*(3*B*a*b^2 + A*b^3)*d^5*e + 1144*(B*a^2*b + A*a*b^2)*d^4*e^2 - 858*(B*a^3 + 3*A*a^2*b)*d^3*e^3 + 105*(14*B*b^3*d*e^5 + 13*(3*B*a*b^2 + A*b^3)*e^6)*x^5 + 35*(B*b^3*d^2*e^4 + 52*(3*B*a*b^2 + A*b^3)*d*e^5 + 143*(B*a^2*b + A*a*b^2)*e^6)*x^4 - 5*(8*B*b^3*d^3*e^3 - 13*(3*B*a*b^2 + A*b^3)*d^2*e^4 - 1430*(B*a^2*b + A*a*b^2)*d*e^5 - 429*(B*a^3 + 3*A*a^2*b)*e^6)*x^3 + 3*(16*B*b^3*d^4*e^2 + 1001*A*a^3*e^6 - 26*(3*B*a*b^2 + A*b^3)*d^3*e^3 + 143*(B*a^2*b + A*a*b^2)*d^2*e^4 + 1144*(B*a^3 + 3*A*a^2*b)*d*e^5)*x^2 - (64*B*b^3*d^5*e - 6006*A*a^3*d*e^5 - 104*(3*B*a*b^2 + A*b^3)*d^4*e^2 + 572*(B*a^2*b + A*a*b^2)*d^3*e^3 - 429*(B*a^3 + 3*A*a^2*b)*d^2*e^4)*x)*sqrt(e*x + d)/e^5","A",0
1846,1,353,0,0.436718," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B b^{3} e^{5} x^{5} + 128 \, B b^{3} d^{5} + 1155 \, A a^{3} d e^{4} - 176 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e + 792 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{2} - 462 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3} + 35 \, {\left(B b^{3} d e^{4} + 11 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} x^{4} - 5 \, {\left(8 \, B b^{3} d^{2} e^{3} - 11 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} - 297 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{3} e^{2} - 22 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{3} + 99 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} + 231 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} x^{2} - {\left(64 \, B b^{3} d^{4} e - 1155 \, A a^{3} e^{5} - 88 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{2} + 396 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{3} - 231 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{5}}"," ",0,"2/3465*(315*B*b^3*e^5*x^5 + 128*B*b^3*d^5 + 1155*A*a^3*d*e^4 - 176*(3*B*a*b^2 + A*b^3)*d^4*e + 792*(B*a^2*b + A*a*b^2)*d^3*e^2 - 462*(B*a^3 + 3*A*a^2*b)*d^2*e^3 + 35*(B*b^3*d*e^4 + 11*(3*B*a*b^2 + A*b^3)*e^5)*x^4 - 5*(8*B*b^3*d^2*e^3 - 11*(3*B*a*b^2 + A*b^3)*d*e^4 - 297*(B*a^2*b + A*a*b^2)*e^5)*x^3 + 3*(16*B*b^3*d^3*e^2 - 22*(3*B*a*b^2 + A*b^3)*d^2*e^3 + 99*(B*a^2*b + A*a*b^2)*d*e^4 + 231*(B*a^3 + 3*A*a^2*b)*e^5)*x^2 - (64*B*b^3*d^4*e - 1155*A*a^3*e^5 - 88*(3*B*a*b^2 + A*b^3)*d^3*e^2 + 396*(B*a^2*b + A*a*b^2)*d^2*e^3 - 231*(B*a^3 + 3*A*a^2*b)*d*e^4)*x)*sqrt(e*x + d)/e^5","A",0
1847,1,263,0,0.432997," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{3} e^{4} x^{4} + 128 \, B b^{3} d^{4} + 315 \, A a^{3} e^{4} - 144 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 504 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - 210 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - 5 \, {\left(8 \, B b^{3} d e^{3} - 9 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{2} e^{2} - 18 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 63 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - {\left(64 \, B b^{3} d^{3} e - 72 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 252 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - 105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{5}}"," ",0,"2/315*(35*B*b^3*e^4*x^4 + 128*B*b^3*d^4 + 315*A*a^3*e^4 - 144*(3*B*a*b^2 + A*b^3)*d^3*e + 504*(B*a^2*b + A*a*b^2)*d^2*e^2 - 210*(B*a^3 + 3*A*a^2*b)*d*e^3 - 5*(8*B*b^3*d*e^3 - 9*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 3*(16*B*b^3*d^2*e^2 - 18*(3*B*a*b^2 + A*b^3)*d*e^3 + 63*(B*a^2*b + A*a*b^2)*e^4)*x^2 - (64*B*b^3*d^3*e - 72*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 252*(B*a^2*b + A*a*b^2)*d*e^3 - 105*(B*a^3 + 3*A*a^2*b)*e^4)*x)*sqrt(e*x + d)/e^5","A",0
1848,1,272,0,0.430883," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} e^{4} x^{4} - 128 \, B b^{3} d^{4} - 35 \, A a^{3} e^{4} + 112 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 280 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 70 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - {\left(8 \, B b^{3} d e^{3} - 7 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + {\left(16 \, B b^{3} d^{2} e^{2} - 14 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 35 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - {\left(64 \, B b^{3} d^{3} e - 56 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 140 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"2/35*(5*B*b^3*e^4*x^4 - 128*B*b^3*d^4 - 35*A*a^3*e^4 + 112*(3*B*a*b^2 + A*b^3)*d^3*e - 280*(B*a^2*b + A*a*b^2)*d^2*e^2 + 70*(B*a^3 + 3*A*a^2*b)*d*e^3 - (8*B*b^3*d*e^3 - 7*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + (16*B*b^3*d^2*e^2 - 14*(3*B*a*b^2 + A*b^3)*d*e^3 + 35*(B*a^2*b + A*a*b^2)*e^4)*x^2 - (64*B*b^3*d^3*e - 56*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 140*(B*a^2*b + A*a*b^2)*d*e^3 - 35*(B*a^3 + 3*A*a^2*b)*e^4)*x)*sqrt(e*x + d)/(e^6*x + d*e^5)","A",0
1849,1,284,0,0.425158," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{3} e^{4} x^{4} + 128 \, B b^{3} d^{4} - 5 \, A a^{3} e^{4} - 80 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 120 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - {\left(8 \, B b^{3} d e^{3} - 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{2} e^{2} - 10 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 15 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 3 \, {\left(64 \, B b^{3} d^{3} e - 40 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 60 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"2/15*(3*B*b^3*e^4*x^4 + 128*B*b^3*d^4 - 5*A*a^3*e^4 - 80*(3*B*a*b^2 + A*b^3)*d^3*e + 120*(B*a^2*b + A*a*b^2)*d^2*e^2 - 10*(B*a^3 + 3*A*a^2*b)*d*e^3 - (8*B*b^3*d*e^3 - 5*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 3*(16*B*b^3*d^2*e^2 - 10*(3*B*a*b^2 + A*b^3)*d*e^3 + 15*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 3*(64*B*b^3*d^3*e - 40*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 60*(B*a^2*b + A*a*b^2)*d*e^3 - 5*(B*a^3 + 3*A*a^2*b)*e^4)*x)*sqrt(e*x + d)/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
1850,1,294,0,0.447015," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} e^{4} x^{4} - 128 \, B b^{3} d^{4} - 3 \, A a^{3} e^{4} + 48 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 24 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - 5 \, {\left(8 \, B b^{3} d e^{3} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} - 15 \, {\left(16 \, B b^{3} d^{2} e^{2} - 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - 5 \, {\left(64 \, B b^{3} d^{3} e - 24 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 12 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"2/15*(5*B*b^3*e^4*x^4 - 128*B*b^3*d^4 - 3*A*a^3*e^4 + 48*(3*B*a*b^2 + A*b^3)*d^3*e - 24*(B*a^2*b + A*a*b^2)*d^2*e^2 - 2*(B*a^3 + 3*A*a^2*b)*d*e^3 - 5*(8*B*b^3*d*e^3 - 3*(3*B*a*b^2 + A*b^3)*e^4)*x^3 - 15*(16*B*b^3*d^2*e^2 - 6*(3*B*a*b^2 + A*b^3)*d*e^3 + 3*(B*a^2*b + A*a*b^2)*e^4)*x^2 - 5*(64*B*b^3*d^3*e - 24*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 12*(B*a^2*b + A*a*b^2)*d*e^3 + (B*a^3 + 3*A*a^2*b)*e^4)*x)*sqrt(e*x + d)/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
1851,1,1137,0,0.465771," ","integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(138567 \, B b^{5} e^{10} x^{10} + 1024 \, B b^{5} d^{10} + 323323 \, A a^{5} d^{4} e^{6} - 1792 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{9} e + 17024 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{8} e^{2} - 72352 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{7} e^{3} + 90440 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{6} e^{4} - 58786 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{5} e^{5} + 7293 \, {\left(64 \, B b^{5} d e^{9} + 21 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{10}\right)} x^{9} + 1287 \, {\left(414 \, B b^{5} d^{2} e^{8} + 406 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{9} + 665 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{10}\right)} x^{8} + 858 \, {\left(242 \, B b^{5} d^{3} e^{7} + 707 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{8} + 3458 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{9} + 2261 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{10}\right)} x^{7} + 231 \, {\left(B b^{5} d^{4} e^{6} + 1048 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{7} + 15238 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{8} + 29716 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{9} + 4845 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{10}\right)} x^{6} - 63 \, {\left(4 \, B b^{5} d^{5} e^{5} - 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{6} - 23028 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{7} - 133076 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{8} - 64600 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{9} - 4199 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{10}\right)} x^{5} + 7 \, {\left(40 \, B b^{5} d^{6} e^{4} + 46189 \, A a^{5} e^{10} - 70 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e^{5} + 665 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{6} + 516800 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{7} + 739670 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{8} + 142766 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{9}\right)} x^{4} - 2 \, {\left(160 \, B b^{5} d^{7} e^{3} - 646646 \, A a^{5} d e^{9} - 280 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{6} e^{4} + 2660 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{5} e^{5} - 11305 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e^{6} - 1198330 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{7} - 676039 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{8}\right)} x^{3} + 3 \, {\left(128 \, B b^{5} d^{8} e^{2} + 646646 \, A a^{5} d^{2} e^{8} - 224 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{7} e^{3} + 2128 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{6} e^{4} - 9044 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{5} e^{5} + 11305 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{4} e^{6} + 235144 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{3} e^{7}\right)} x^{2} - {\left(512 \, B b^{5} d^{9} e - 1293292 \, A a^{5} d^{3} e^{7} - 896 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{8} e^{2} + 8512 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{7} e^{3} - 36176 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{6} e^{4} + 45220 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{5} e^{5} - 29393 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{4} e^{6}\right)} x\right)} \sqrt{e x + d}}{2909907 \, e^{7}}"," ",0,"2/2909907*(138567*B*b^5*e^10*x^10 + 1024*B*b^5*d^10 + 323323*A*a^5*d^4*e^6 - 1792*(5*B*a*b^4 + A*b^5)*d^9*e + 17024*(2*B*a^2*b^3 + A*a*b^4)*d^8*e^2 - 72352*(B*a^3*b^2 + A*a^2*b^3)*d^7*e^3 + 90440*(B*a^4*b + 2*A*a^3*b^2)*d^6*e^4 - 58786*(B*a^5 + 5*A*a^4*b)*d^5*e^5 + 7293*(64*B*b^5*d*e^9 + 21*(5*B*a*b^4 + A*b^5)*e^10)*x^9 + 1287*(414*B*b^5*d^2*e^8 + 406*(5*B*a*b^4 + A*b^5)*d*e^9 + 665*(2*B*a^2*b^3 + A*a*b^4)*e^10)*x^8 + 858*(242*B*b^5*d^3*e^7 + 707*(5*B*a*b^4 + A*b^5)*d^2*e^8 + 3458*(2*B*a^2*b^3 + A*a*b^4)*d*e^9 + 2261*(B*a^3*b^2 + A*a^2*b^3)*e^10)*x^7 + 231*(B*b^5*d^4*e^6 + 1048*(5*B*a*b^4 + A*b^5)*d^3*e^7 + 15238*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^8 + 29716*(B*a^3*b^2 + A*a^2*b^3)*d*e^9 + 4845*(B*a^4*b + 2*A*a^3*b^2)*e^10)*x^6 - 63*(4*B*b^5*d^5*e^5 - 7*(5*B*a*b^4 + A*b^5)*d^4*e^6 - 23028*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^7 - 133076*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^8 - 64600*(B*a^4*b + 2*A*a^3*b^2)*d*e^9 - 4199*(B*a^5 + 5*A*a^4*b)*e^10)*x^5 + 7*(40*B*b^5*d^6*e^4 + 46189*A*a^5*e^10 - 70*(5*B*a*b^4 + A*b^5)*d^5*e^5 + 665*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^6 + 516800*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^7 + 739670*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^8 + 142766*(B*a^5 + 5*A*a^4*b)*d*e^9)*x^4 - 2*(160*B*b^5*d^7*e^3 - 646646*A*a^5*d*e^9 - 280*(5*B*a*b^4 + A*b^5)*d^6*e^4 + 2660*(2*B*a^2*b^3 + A*a*b^4)*d^5*e^5 - 11305*(B*a^3*b^2 + A*a^2*b^3)*d^4*e^6 - 1198330*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^7 - 676039*(B*a^5 + 5*A*a^4*b)*d^2*e^8)*x^3 + 3*(128*B*b^5*d^8*e^2 + 646646*A*a^5*d^2*e^8 - 224*(5*B*a*b^4 + A*b^5)*d^7*e^3 + 2128*(2*B*a^2*b^3 + A*a*b^4)*d^6*e^4 - 9044*(B*a^3*b^2 + A*a^2*b^3)*d^5*e^5 + 11305*(B*a^4*b + 2*A*a^3*b^2)*d^4*e^6 + 235144*(B*a^5 + 5*A*a^4*b)*d^3*e^7)*x^2 - (512*B*b^5*d^9*e - 1293292*A*a^5*d^3*e^7 - 896*(5*B*a*b^4 + A*b^5)*d^8*e^2 + 8512*(2*B*a^2*b^3 + A*a*b^4)*d^7*e^3 - 36176*(B*a^3*b^2 + A*a^2*b^3)*d^6*e^4 + 45220*(B*a^4*b + 2*A*a^3*b^2)*d^5*e^5 - 29393*(B*a^5 + 5*A*a^4*b)*d^4*e^6)*x)*sqrt(e*x + d)/e^7","B",0
1852,1,993,0,0.451234," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(153153 \, B b^{5} e^{9} x^{9} + 3072 \, B b^{5} d^{9} + 415701 \, A a^{5} d^{3} e^{6} - 4864 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{8} e + 41344 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{7} e^{2} - 155040 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{6} e^{3} + 167960 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{5} e^{4} - 92378 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{4} e^{5} + 9009 \, {\left(39 \, B b^{5} d e^{8} + 19 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{9}\right)} x^{8} + 3003 \, {\left(69 \, B b^{5} d^{2} e^{7} + 133 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{8} + 323 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{9}\right)} x^{7} + 231 \, {\left(3 \, B b^{5} d^{3} e^{6} + 1045 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{7} + 10013 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{8} + 9690 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{9}\right)} x^{6} - 63 \, {\left(12 \, B b^{5} d^{4} e^{5} - 19 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{6} - 22933 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{7} - 87210 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{8} - 20995 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{9}\right)} x^{5} + 7 \, {\left(120 \, B b^{5} d^{5} e^{4} - 190 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{5} + 1615 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{6} + 513570 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{7} + 482885 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{8} + 46189 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{9}\right)} x^{4} - {\left(960 \, B b^{5} d^{6} e^{3} - 415701 \, A a^{5} e^{9} - 1520 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e^{4} + 12920 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{5} - 48450 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{6} - 2372435 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{7} - 877591 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{8}\right)} x^{3} + 3 \, {\left(384 \, B b^{5} d^{7} e^{2} + 415701 \, A a^{5} d e^{8} - 608 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{6} e^{3} + 5168 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{5} e^{4} - 19380 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e^{5} + 20995 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{6} + 230945 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{7}\right)} x^{2} - {\left(1536 \, B b^{5} d^{8} e - 1247103 \, A a^{5} d^{2} e^{7} - 2432 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{7} e^{2} + 20672 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{6} e^{3} - 77520 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{5} e^{4} + 83980 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{4} e^{5} - 46189 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{3} e^{6}\right)} x\right)} \sqrt{e x + d}}{2909907 \, e^{7}}"," ",0,"2/2909907*(153153*B*b^5*e^9*x^9 + 3072*B*b^5*d^9 + 415701*A*a^5*d^3*e^6 - 4864*(5*B*a*b^4 + A*b^5)*d^8*e + 41344*(2*B*a^2*b^3 + A*a*b^4)*d^7*e^2 - 155040*(B*a^3*b^2 + A*a^2*b^3)*d^6*e^3 + 167960*(B*a^4*b + 2*A*a^3*b^2)*d^5*e^4 - 92378*(B*a^5 + 5*A*a^4*b)*d^4*e^5 + 9009*(39*B*b^5*d*e^8 + 19*(5*B*a*b^4 + A*b^5)*e^9)*x^8 + 3003*(69*B*b^5*d^2*e^7 + 133*(5*B*a*b^4 + A*b^5)*d*e^8 + 323*(2*B*a^2*b^3 + A*a*b^4)*e^9)*x^7 + 231*(3*B*b^5*d^3*e^6 + 1045*(5*B*a*b^4 + A*b^5)*d^2*e^7 + 10013*(2*B*a^2*b^3 + A*a*b^4)*d*e^8 + 9690*(B*a^3*b^2 + A*a^2*b^3)*e^9)*x^6 - 63*(12*B*b^5*d^4*e^5 - 19*(5*B*a*b^4 + A*b^5)*d^3*e^6 - 22933*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^7 - 87210*(B*a^3*b^2 + A*a^2*b^3)*d*e^8 - 20995*(B*a^4*b + 2*A*a^3*b^2)*e^9)*x^5 + 7*(120*B*b^5*d^5*e^4 - 190*(5*B*a*b^4 + A*b^5)*d^4*e^5 + 1615*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^6 + 513570*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^7 + 482885*(B*a^4*b + 2*A*a^3*b^2)*d*e^8 + 46189*(B*a^5 + 5*A*a^4*b)*e^9)*x^4 - (960*B*b^5*d^6*e^3 - 415701*A*a^5*e^9 - 1520*(5*B*a*b^4 + A*b^5)*d^5*e^4 + 12920*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^5 - 48450*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^6 - 2372435*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^7 - 877591*(B*a^5 + 5*A*a^4*b)*d*e^8)*x^3 + 3*(384*B*b^5*d^7*e^2 + 415701*A*a^5*d*e^8 - 608*(5*B*a*b^4 + A*b^5)*d^6*e^3 + 5168*(2*B*a^2*b^3 + A*a*b^4)*d^5*e^4 - 19380*(B*a^3*b^2 + A*a^2*b^3)*d^4*e^5 + 20995*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^6 + 230945*(B*a^5 + 5*A*a^4*b)*d^2*e^7)*x^2 - (1536*B*b^5*d^8*e - 1247103*A*a^5*d^2*e^7 - 2432*(5*B*a*b^4 + A*b^5)*d^7*e^2 + 20672*(2*B*a^2*b^3 + A*a*b^4)*d^6*e^3 - 77520*(B*a^3*b^2 + A*a^2*b^3)*d^5*e^4 + 83980*(B*a^4*b + 2*A*a^3*b^2)*d^4*e^5 - 46189*(B*a^5 + 5*A*a^4*b)*d^3*e^6)*x)*sqrt(e*x + d)/e^7","B",0
1853,1,848,0,0.437907," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(45045 \, B b^{5} e^{8} x^{8} + 3072 \, B b^{5} d^{8} + 153153 \, A a^{5} d^{2} e^{6} - 4352 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{7} e + 32640 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{6} e^{2} - 106080 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{5} e^{3} + 97240 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{4} e^{4} - 43758 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{3} e^{5} + 3003 \, {\left(18 \, B b^{5} d e^{7} + 17 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{8}\right)} x^{7} + 231 \, {\left(3 \, B b^{5} d^{2} e^{6} + 272 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{7} + 1275 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{8}\right)} x^{6} - 63 \, {\left(12 \, B b^{5} d^{3} e^{5} - 17 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{6} - 5950 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{7} - 11050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{8}\right)} x^{5} + 35 \, {\left(24 \, B b^{5} d^{4} e^{4} - 34 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{5} + 255 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{6} + 26520 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{7} + 12155 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{8}\right)} x^{4} - 5 \, {\left(192 \, B b^{5} d^{5} e^{3} - 272 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{4} + 2040 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{5} - 6630 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{6} - 121550 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{7} - 21879 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{8}\right)} x^{3} + 3 \, {\left(384 \, B b^{5} d^{6} e^{2} + 51051 \, A a^{5} e^{8} - 544 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e^{3} + 4080 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{4} - 13260 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{5} + 12155 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{6} + 58344 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{7}\right)} x^{2} - {\left(1536 \, B b^{5} d^{7} e - 306306 \, A a^{5} d e^{7} - 2176 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{6} e^{2} + 16320 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{5} e^{3} - 53040 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e^{4} + 48620 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{5} - 21879 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{6}\right)} x\right)} \sqrt{e x + d}}{765765 \, e^{7}}"," ",0,"2/765765*(45045*B*b^5*e^8*x^8 + 3072*B*b^5*d^8 + 153153*A*a^5*d^2*e^6 - 4352*(5*B*a*b^4 + A*b^5)*d^7*e + 32640*(2*B*a^2*b^3 + A*a*b^4)*d^6*e^2 - 106080*(B*a^3*b^2 + A*a^2*b^3)*d^5*e^3 + 97240*(B*a^4*b + 2*A*a^3*b^2)*d^4*e^4 - 43758*(B*a^5 + 5*A*a^4*b)*d^3*e^5 + 3003*(18*B*b^5*d*e^7 + 17*(5*B*a*b^4 + A*b^5)*e^8)*x^7 + 231*(3*B*b^5*d^2*e^6 + 272*(5*B*a*b^4 + A*b^5)*d*e^7 + 1275*(2*B*a^2*b^3 + A*a*b^4)*e^8)*x^6 - 63*(12*B*b^5*d^3*e^5 - 17*(5*B*a*b^4 + A*b^5)*d^2*e^6 - 5950*(2*B*a^2*b^3 + A*a*b^4)*d*e^7 - 11050*(B*a^3*b^2 + A*a^2*b^3)*e^8)*x^5 + 35*(24*B*b^5*d^4*e^4 - 34*(5*B*a*b^4 + A*b^5)*d^3*e^5 + 255*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^6 + 26520*(B*a^3*b^2 + A*a^2*b^3)*d*e^7 + 12155*(B*a^4*b + 2*A*a^3*b^2)*e^8)*x^4 - 5*(192*B*b^5*d^5*e^3 - 272*(5*B*a*b^4 + A*b^5)*d^4*e^4 + 2040*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^5 - 6630*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^6 - 121550*(B*a^4*b + 2*A*a^3*b^2)*d*e^7 - 21879*(B*a^5 + 5*A*a^4*b)*e^8)*x^3 + 3*(384*B*b^5*d^6*e^2 + 51051*A*a^5*e^8 - 544*(5*B*a*b^4 + A*b^5)*d^5*e^3 + 4080*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^4 - 13260*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^5 + 12155*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^6 + 58344*(B*a^5 + 5*A*a^4*b)*d*e^7)*x^2 - (1536*B*b^5*d^7*e - 306306*A*a^5*d*e^7 - 2176*(5*B*a*b^4 + A*b^5)*d^6*e^2 + 16320*(2*B*a^2*b^3 + A*a*b^4)*d^5*e^3 - 53040*(B*a^3*b^2 + A*a^2*b^3)*d^4*e^4 + 48620*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^5 - 21879*(B*a^5 + 5*A*a^4*b)*d^2*e^6)*x)*sqrt(e*x + d)/e^7","B",0
1854,1,702,0,0.433872," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B b^{5} e^{7} x^{7} + 1024 \, B b^{5} d^{7} + 15015 \, A a^{5} d e^{6} - 1280 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{6} e + 8320 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{5} e^{2} - 22880 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e^{3} + 17160 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{4} - 6006 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{5} + 231 \, {\left(B b^{5} d e^{6} + 15 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{7}\right)} x^{6} - 63 \, {\left(4 \, B b^{5} d^{2} e^{5} - 5 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{6} - 325 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{7}\right)} x^{5} + 35 \, {\left(8 \, B b^{5} d^{3} e^{4} - 10 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{5} + 65 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{6} + 1430 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{7}\right)} x^{4} - 5 \, {\left(64 \, B b^{5} d^{4} e^{3} - 80 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{4} + 520 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{5} - 1430 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{6} - 6435 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{7}\right)} x^{3} + 3 \, {\left(128 \, B b^{5} d^{5} e^{2} - 160 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{3} + 1040 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{4} - 2860 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{5} + 2145 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{6} + 3003 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{7}\right)} x^{2} - {\left(512 \, B b^{5} d^{6} e - 15015 \, A a^{5} e^{7} - 640 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e^{2} + 4160 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{3} - 11440 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{4} + 8580 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{5} - 3003 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{6}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{7}}"," ",0,"2/45045*(3003*B*b^5*e^7*x^7 + 1024*B*b^5*d^7 + 15015*A*a^5*d*e^6 - 1280*(5*B*a*b^4 + A*b^5)*d^6*e + 8320*(2*B*a^2*b^3 + A*a*b^4)*d^5*e^2 - 22880*(B*a^3*b^2 + A*a^2*b^3)*d^4*e^3 + 17160*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^4 - 6006*(B*a^5 + 5*A*a^4*b)*d^2*e^5 + 231*(B*b^5*d*e^6 + 15*(5*B*a*b^4 + A*b^5)*e^7)*x^6 - 63*(4*B*b^5*d^2*e^5 - 5*(5*B*a*b^4 + A*b^5)*d*e^6 - 325*(2*B*a^2*b^3 + A*a*b^4)*e^7)*x^5 + 35*(8*B*b^5*d^3*e^4 - 10*(5*B*a*b^4 + A*b^5)*d^2*e^5 + 65*(2*B*a^2*b^3 + A*a*b^4)*d*e^6 + 1430*(B*a^3*b^2 + A*a^2*b^3)*e^7)*x^4 - 5*(64*B*b^5*d^4*e^3 - 80*(5*B*a*b^4 + A*b^5)*d^3*e^4 + 520*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^5 - 1430*(B*a^3*b^2 + A*a^2*b^3)*d*e^6 - 6435*(B*a^4*b + 2*A*a^3*b^2)*e^7)*x^3 + 3*(128*B*b^5*d^5*e^2 - 160*(5*B*a*b^4 + A*b^5)*d^4*e^3 + 1040*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^4 - 2860*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^5 + 2145*(B*a^4*b + 2*A*a^3*b^2)*d*e^6 + 3003*(B*a^5 + 5*A*a^4*b)*e^7)*x^2 - (512*B*b^5*d^6*e - 15015*A*a^5*e^7 - 640*(5*B*a*b^4 + A*b^5)*d^5*e^2 + 4160*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^3 - 11440*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^4 + 8580*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^5 - 3003*(B*a^5 + 5*A*a^4*b)*d*e^6)*x)*sqrt(e*x + d)/e^7","B",0
1855,1,560,0,0.435570," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, B b^{5} e^{6} x^{6} + 3072 \, B b^{5} d^{6} + 9009 \, A a^{5} e^{6} - 3328 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 18304 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - 41184 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 24024 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - 6006 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} - 63 \, {\left(12 \, B b^{5} d e^{5} - 13 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 35 \, {\left(24 \, B b^{5} d^{2} e^{4} - 26 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 143 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} - 10 \, {\left(96 \, B b^{5} d^{3} e^{3} - 104 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 572 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} - 1287 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 3 \, {\left(384 \, B b^{5} d^{4} e^{2} - 416 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 2288 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 5148 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 3003 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} - {\left(1536 \, B b^{5} d^{5} e - 1664 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 9152 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 20592 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 12012 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} - 3003 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{9009 \, e^{7}}"," ",0,"2/9009*(693*B*b^5*e^6*x^6 + 3072*B*b^5*d^6 + 9009*A*a^5*e^6 - 3328*(5*B*a*b^4 + A*b^5)*d^5*e + 18304*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - 41184*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 24024*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - 6006*(B*a^5 + 5*A*a^4*b)*d*e^5 - 63*(12*B*b^5*d*e^5 - 13*(5*B*a*b^4 + A*b^5)*e^6)*x^5 + 35*(24*B*b^5*d^2*e^4 - 26*(5*B*a*b^4 + A*b^5)*d*e^5 + 143*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 - 10*(96*B*b^5*d^3*e^3 - 104*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 572*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 - 1287*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 3*(384*B*b^5*d^4*e^2 - 416*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 2288*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 5148*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 3003*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 - (1536*B*b^5*d^5*e - 1664*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 9152*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 20592*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 12012*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 - 3003*(B*a^5 + 5*A*a^4*b)*e^6)*x)*sqrt(e*x + d)/e^7","A",0
1856,1,569,0,0.425844," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B b^{5} e^{6} x^{6} - 3072 \, B b^{5} d^{6} - 693 \, A a^{5} e^{6} + 2816 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e - 12672 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 22176 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} - 9240 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} + 1386 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} - 7 \, {\left(12 \, B b^{5} d e^{5} - 11 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 5 \, {\left(24 \, B b^{5} d^{2} e^{4} - 22 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 99 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} - 2 \, {\left(96 \, B b^{5} d^{3} e^{3} - 88 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 396 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} - 693 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + {\left(384 \, B b^{5} d^{4} e^{2} - 352 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 1584 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 2772 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 1155 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} - {\left(1536 \, B b^{5} d^{5} e - 1408 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 6336 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 11088 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 4620 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} - 693 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{693 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"2/693*(63*B*b^5*e^6*x^6 - 3072*B*b^5*d^6 - 693*A*a^5*e^6 + 2816*(5*B*a*b^4 + A*b^5)*d^5*e - 12672*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 22176*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 - 9240*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 + 1386*(B*a^5 + 5*A*a^4*b)*d*e^5 - 7*(12*B*b^5*d*e^5 - 11*(5*B*a*b^4 + A*b^5)*e^6)*x^5 + 5*(24*B*b^5*d^2*e^4 - 22*(5*B*a*b^4 + A*b^5)*d*e^5 + 99*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 - 2*(96*B*b^5*d^3*e^3 - 88*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 396*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 - 693*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + (384*B*b^5*d^4*e^2 - 352*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 1584*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 2772*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 1155*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 - (1536*B*b^5*d^5*e - 1408*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 6336*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 11088*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 4620*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 - 693*(B*a^5 + 5*A*a^4*b)*e^6)*x)*sqrt(e*x + d)/(e^8*x + d*e^7)","A",0
1857,1,581,0,0.422713," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, B b^{5} e^{6} x^{6} + 1024 \, B b^{5} d^{6} - 21 \, A a^{5} e^{6} - 768 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e + 2688 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} - 3360 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} + 840 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - 42 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} - 3 \, {\left(4 \, B b^{5} d e^{5} - 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 3 \, {\left(8 \, B b^{5} d^{2} e^{4} - 6 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 21 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} - 2 \, {\left(32 \, B b^{5} d^{3} e^{3} - 24 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 84 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} - 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} + 3 \, {\left(128 \, B b^{5} d^{4} e^{2} - 96 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 336 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 420 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 105 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} + 3 \, {\left(512 \, B b^{5} d^{5} e - 384 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 1344 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 1680 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 420 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} - 21 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{63 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"2/63*(7*B*b^5*e^6*x^6 + 1024*B*b^5*d^6 - 21*A*a^5*e^6 - 768*(5*B*a*b^4 + A*b^5)*d^5*e + 2688*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 - 3360*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 + 840*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - 42*(B*a^5 + 5*A*a^4*b)*d*e^5 - 3*(4*B*b^5*d*e^5 - 3*(5*B*a*b^4 + A*b^5)*e^6)*x^5 + 3*(8*B*b^5*d^2*e^4 - 6*(5*B*a*b^4 + A*b^5)*d*e^5 + 21*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 - 2*(32*B*b^5*d^3*e^3 - 24*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 84*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 - 105*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 + 3*(128*B*b^5*d^4*e^2 - 96*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 336*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 420*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 105*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 + 3*(512*B*b^5*d^5*e - 384*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 1344*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 1680*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 420*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 - 21*(B*a^5 + 5*A*a^4*b)*e^6)*x)*sqrt(e*x + d)/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","A",0
1858,1,592,0,0.428505," ","integrate((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{5} e^{6} x^{6} - 3072 \, B b^{5} d^{6} - 21 \, A a^{5} e^{6} + 1792 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e - 4480 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{2} + 3360 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{3} - 280 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{4} - 14 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{5} - 3 \, {\left(12 \, B b^{5} d e^{5} - 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{6}\right)} x^{5} + 5 \, {\left(24 \, B b^{5} d^{2} e^{4} - 14 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{5} + 35 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{6}\right)} x^{4} - 10 \, {\left(96 \, B b^{5} d^{3} e^{3} - 56 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{4} + 140 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{5} - 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{6}\right)} x^{3} - 15 \, {\left(384 \, B b^{5} d^{4} e^{2} - 224 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{3} + 560 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{4} - 420 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{5} + 35 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{2} - 5 \, {\left(1536 \, B b^{5} d^{5} e - 896 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{2} + 2240 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{3} - 1680 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{4} + 140 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{5} + 7 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"2/105*(15*B*b^5*e^6*x^6 - 3072*B*b^5*d^6 - 21*A*a^5*e^6 + 1792*(5*B*a*b^4 + A*b^5)*d^5*e - 4480*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^2 + 3360*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^3 - 280*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^4 - 14*(B*a^5 + 5*A*a^4*b)*d*e^5 - 3*(12*B*b^5*d*e^5 - 7*(5*B*a*b^4 + A*b^5)*e^6)*x^5 + 5*(24*B*b^5*d^2*e^4 - 14*(5*B*a*b^4 + A*b^5)*d*e^5 + 35*(2*B*a^2*b^3 + A*a*b^4)*e^6)*x^4 - 10*(96*B*b^5*d^3*e^3 - 56*(5*B*a*b^4 + A*b^5)*d^2*e^4 + 140*(2*B*a^2*b^3 + A*a*b^4)*d*e^5 - 105*(B*a^3*b^2 + A*a^2*b^3)*e^6)*x^3 - 15*(384*B*b^5*d^4*e^2 - 224*(5*B*a*b^4 + A*b^5)*d^3*e^3 + 560*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^4 - 420*(B*a^3*b^2 + A*a^2*b^3)*d*e^5 + 35*(B*a^4*b + 2*A*a^3*b^2)*e^6)*x^2 - 5*(1536*B*b^5*d^5*e - 896*(5*B*a*b^4 + A*b^5)*d^4*e^2 + 2240*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^3 - 1680*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^4 + 140*(B*a^4*b + 2*A*a^3*b^2)*d*e^5 + 7*(B*a^5 + 5*A*a^4*b)*e^6)*x)*sqrt(e*x + d)/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","A",0
1859,1,591,0,0.457980," ","integrate((B*x+A)*(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(B a b^{2} - A b^{3}\right)} d^{2} e - 2 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{2} + {\left(B a^{3} - A a^{2} b\right)} e^{3}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(15 \, B b^{3} e^{3} x^{3} + 15 \, B b^{3} d^{3} - 161 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e + 245 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{2} - 105 \, {\left(B a^{3} - A a^{2} b\right)} e^{3} + 3 \, {\left(15 \, B b^{3} d e^{2} - 7 \, {\left(B a b^{2} - A b^{3}\right)} e^{3}\right)} x^{2} + {\left(45 \, B b^{3} d^{2} e - 77 \, {\left(B a b^{2} - A b^{3}\right)} d e^{2} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, b^{4} e}, \frac{2 \, {\left(105 \, {\left({\left(B a b^{2} - A b^{3}\right)} d^{2} e - 2 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{2} + {\left(B a^{3} - A a^{2} b\right)} e^{3}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) + {\left(15 \, B b^{3} e^{3} x^{3} + 15 \, B b^{3} d^{3} - 161 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e + 245 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{2} - 105 \, {\left(B a^{3} - A a^{2} b\right)} e^{3} + 3 \, {\left(15 \, B b^{3} d e^{2} - 7 \, {\left(B a b^{2} - A b^{3}\right)} e^{3}\right)} x^{2} + {\left(45 \, B b^{3} d^{2} e - 77 \, {\left(B a b^{2} - A b^{3}\right)} d e^{2} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{105 \, b^{4} e}\right]"," ",0,"[1/105*(105*((B*a*b^2 - A*b^3)*d^2*e - 2*(B*a^2*b - A*a*b^2)*d*e^2 + (B*a^3 - A*a^2*b)*e^3)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(15*B*b^3*e^3*x^3 + 15*B*b^3*d^3 - 161*(B*a*b^2 - A*b^3)*d^2*e + 245*(B*a^2*b - A*a*b^2)*d*e^2 - 105*(B*a^3 - A*a^2*b)*e^3 + 3*(15*B*b^3*d*e^2 - 7*(B*a*b^2 - A*b^3)*e^3)*x^2 + (45*B*b^3*d^2*e - 77*(B*a*b^2 - A*b^3)*d*e^2 + 35*(B*a^2*b - A*a*b^2)*e^3)*x)*sqrt(e*x + d))/(b^4*e), 2/105*(105*((B*a*b^2 - A*b^3)*d^2*e - 2*(B*a^2*b - A*a*b^2)*d*e^2 + (B*a^3 - A*a^2*b)*e^3)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) + (15*B*b^3*e^3*x^3 + 15*B*b^3*d^3 - 161*(B*a*b^2 - A*b^3)*d^2*e + 245*(B*a^2*b - A*a*b^2)*d*e^2 - 105*(B*a^3 - A*a^2*b)*e^3 + 3*(15*B*b^3*d*e^2 - 7*(B*a*b^2 - A*b^3)*e^3)*x^2 + (45*B*b^3*d^2*e - 77*(B*a*b^2 - A*b^3)*d*e^2 + 35*(B*a^2*b - A*a*b^2)*e^3)*x)*sqrt(e*x + d))/(b^4*e)]","A",0
1860,1,373,0,0.428884," ","integrate((B*x+A)*(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(B a b - A b^{2}\right)} d e - {\left(B a^{2} - A a b\right)} e^{2}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(3 \, B b^{2} e^{2} x^{2} + 3 \, B b^{2} d^{2} - 20 \, {\left(B a b - A b^{2}\right)} d e + 15 \, {\left(B a^{2} - A a b\right)} e^{2} + {\left(6 \, B b^{2} d e - 5 \, {\left(B a b - A b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, b^{3} e}, \frac{2 \, {\left(15 \, {\left({\left(B a b - A b^{2}\right)} d e - {\left(B a^{2} - A a b\right)} e^{2}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) + {\left(3 \, B b^{2} e^{2} x^{2} + 3 \, B b^{2} d^{2} - 20 \, {\left(B a b - A b^{2}\right)} d e + 15 \, {\left(B a^{2} - A a b\right)} e^{2} + {\left(6 \, B b^{2} d e - 5 \, {\left(B a b - A b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, b^{3} e}\right]"," ",0,"[-1/15*(15*((B*a*b - A*b^2)*d*e - (B*a^2 - A*a*b)*e^2)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(3*B*b^2*e^2*x^2 + 3*B*b^2*d^2 - 20*(B*a*b - A*b^2)*d*e + 15*(B*a^2 - A*a*b)*e^2 + (6*B*b^2*d*e - 5*(B*a*b - A*b^2)*e^2)*x)*sqrt(e*x + d))/(b^3*e), 2/15*(15*((B*a*b - A*b^2)*d*e - (B*a^2 - A*a*b)*e^2)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) + (3*B*b^2*e^2*x^2 + 3*B*b^2*d^2 - 20*(B*a*b - A*b^2)*d*e + 15*(B*a^2 - A*a*b)*e^2 + (6*B*b^2*d*e - 5*(B*a*b - A*b^2)*e^2)*x)*sqrt(e*x + d))/(b^3*e)]","A",0
1861,1,211,0,0.429348," ","integrate((B*x+A)*(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a - A b\right)} e \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(B b e x + B b d - 3 \, {\left(B a - A b\right)} e\right)} \sqrt{e x + d}}{3 \, b^{2} e}, \frac{2 \, {\left(3 \, {\left(B a - A b\right)} e \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) + {\left(B b e x + B b d - 3 \, {\left(B a - A b\right)} e\right)} \sqrt{e x + d}\right)}}{3 \, b^{2} e}\right]"," ",0,"[-1/3*(3*(B*a - A*b)*e*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(B*b*e*x + B*b*d - 3*(B*a - A*b)*e)*sqrt(e*x + d))/(b^2*e), 2/3*(3*(B*a - A*b)*e*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) + (B*b*e*x + B*b*d - 3*(B*a - A*b)*e)*sqrt(e*x + d))/(b^2*e)]","A",0
1862,1,209,0,0.451607," ","integrate((B*x+A)/(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{b^{2} d - a b e} {\left(B a - A b\right)} e \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(B b^{2} d - B a b e\right)} \sqrt{e x + d}}{b^{3} d e - a b^{2} e^{2}}, -\frac{2 \, {\left(\sqrt{-b^{2} d + a b e} {\left(B a - A b\right)} e \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(B b^{2} d - B a b e\right)} \sqrt{e x + d}\right)}}{b^{3} d e - a b^{2} e^{2}}\right]"," ",0,"[-(sqrt(b^2*d - a*b*e)*(B*a - A*b)*e*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(B*b^2*d - B*a*b*e)*sqrt(e*x + d))/(b^3*d*e - a*b^2*e^2), -2*(sqrt(-b^2*d + a*b*e)*(B*a - A*b)*e*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (B*b^2*d - B*a*b*e)*sqrt(e*x + d))/(b^3*d*e - a*b^2*e^2)]","A",0
1863,1,363,0,0.433835," ","integrate((B*x+A)/(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(B a - A b\right)} e^{2} x + {\left(B a - A b\right)} d e\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(B b^{2} d^{2} + A a b e^{2} - {\left(B a b + A b^{2}\right)} d e\right)} \sqrt{e x + d}}{b^{3} d^{3} e - 2 \, a b^{2} d^{2} e^{2} + a^{2} b d e^{3} + {\left(b^{3} d^{2} e^{2} - 2 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)} x}, -\frac{2 \, {\left({\left({\left(B a - A b\right)} e^{2} x + {\left(B a - A b\right)} d e\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(B b^{2} d^{2} + A a b e^{2} - {\left(B a b + A b^{2}\right)} d e\right)} \sqrt{e x + d}\right)}}{b^{3} d^{3} e - 2 \, a b^{2} d^{2} e^{2} + a^{2} b d e^{3} + {\left(b^{3} d^{2} e^{2} - 2 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)} x}\right]"," ",0,"[(((B*a - A*b)*e^2*x + (B*a - A*b)*d*e)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e + 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(B*b^2*d^2 + A*a*b*e^2 - (B*a*b + A*b^2)*d*e)*sqrt(e*x + d))/(b^3*d^3*e - 2*a*b^2*d^2*e^2 + a^2*b*d*e^3 + (b^3*d^2*e^2 - 2*a*b^2*d*e^3 + a^2*b*e^4)*x), -2*(((B*a - A*b)*e^2*x + (B*a - A*b)*d*e)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (B*b^2*d^2 + A*a*b*e^2 - (B*a*b + A*b^2)*d*e)*sqrt(e*x + d))/(b^3*d^3*e - 2*a*b^2*d^2*e^2 + a^2*b*d*e^3 + (b^3*d^2*e^2 - 2*a*b^2*d*e^3 + a^2*b*e^4)*x)]","A",0
1864,1,506,0,0.437988," ","integrate((B*x+A)/(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(B a - A b\right)} e^{3} x^{2} + 2 \, {\left(B a - A b\right)} d e^{2} x + {\left(B a - A b\right)} d^{2} e\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(B b d^{2} + A a e^{2} + 3 \, {\left(B a - A b\right)} e^{2} x + 2 \, {\left(B a - 2 \, A b\right)} d e\right)} \sqrt{e x + d}}{3 \, {\left(b^{2} d^{4} e - 2 \, a b d^{3} e^{2} + a^{2} d^{2} e^{3} + {\left(b^{2} d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e^{2} - 2 \, a b d^{2} e^{3} + a^{2} d e^{4}\right)} x\right)}}, \frac{2 \, {\left(3 \, {\left({\left(B a - A b\right)} e^{3} x^{2} + 2 \, {\left(B a - A b\right)} d e^{2} x + {\left(B a - A b\right)} d^{2} e\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(B b d^{2} + A a e^{2} + 3 \, {\left(B a - A b\right)} e^{2} x + 2 \, {\left(B a - 2 \, A b\right)} d e\right)} \sqrt{e x + d}\right)}}{3 \, {\left(b^{2} d^{4} e - 2 \, a b d^{3} e^{2} + a^{2} d^{2} e^{3} + {\left(b^{2} d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e^{2} - 2 \, a b d^{2} e^{3} + a^{2} d e^{4}\right)} x\right)}}\right]"," ",0,"[-1/3*(3*((B*a - A*b)*e^3*x^2 + 2*(B*a - A*b)*d*e^2*x + (B*a - A*b)*d^2*e)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(B*b*d^2 + A*a*e^2 + 3*(B*a - A*b)*e^2*x + 2*(B*a - 2*A*b)*d*e)*sqrt(e*x + d))/(b^2*d^4*e - 2*a*b*d^3*e^2 + a^2*d^2*e^3 + (b^2*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*x^2 + 2*(b^2*d^3*e^2 - 2*a*b*d^2*e^3 + a^2*d*e^4)*x), 2/3*(3*((B*a - A*b)*e^3*x^2 + 2*(B*a - A*b)*d*e^2*x + (B*a - A*b)*d^2*e)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (B*b*d^2 + A*a*e^2 + 3*(B*a - A*b)*e^2*x + 2*(B*a - 2*A*b)*d*e)*sqrt(e*x + d))/(b^2*d^4*e - 2*a*b*d^3*e^2 + a^2*d^2*e^3 + (b^2*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*x^2 + 2*(b^2*d^3*e^2 - 2*a*b*d^2*e^3 + a^2*d*e^4)*x)]","A",0
1865,1,902,0,0.489551," ","integrate((B*x+A)/(e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(B a b - A b^{2}\right)} e^{4} x^{3} + 3 \, {\left(B a b - A b^{2}\right)} d e^{3} x^{2} + 3 \, {\left(B a b - A b^{2}\right)} d^{2} e^{2} x + {\left(B a b - A b^{2}\right)} d^{3} e\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(3 \, B b^{2} d^{3} - 3 \, A a^{2} e^{3} + 15 \, {\left(B a b - A b^{2}\right)} e^{3} x^{2} + {\left(14 \, B a b - 23 \, A b^{2}\right)} d^{2} e - {\left(2 \, B a^{2} - 11 \, A a b\right)} d e^{2} + 5 \, {\left(7 \, {\left(B a b - A b^{2}\right)} d e^{2} - {\left(B a^{2} - A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b^{3} d^{6} e - 3 \, a b^{2} d^{5} e^{2} + 3 \, a^{2} b d^{4} e^{3} - a^{3} d^{3} e^{4} + {\left(b^{3} d^{3} e^{4} - 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} b d e^{6} - a^{3} e^{7}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{3} - 3 \, a b^{2} d^{3} e^{4} + 3 \, a^{2} b d^{2} e^{5} - a^{3} d e^{6}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e^{2} - 3 \, a b^{2} d^{4} e^{3} + 3 \, a^{2} b d^{3} e^{4} - a^{3} d^{2} e^{5}\right)} x\right)}}, \frac{2 \, {\left(15 \, {\left({\left(B a b - A b^{2}\right)} e^{4} x^{3} + 3 \, {\left(B a b - A b^{2}\right)} d e^{3} x^{2} + 3 \, {\left(B a b - A b^{2}\right)} d^{2} e^{2} x + {\left(B a b - A b^{2}\right)} d^{3} e\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3 \, B b^{2} d^{3} - 3 \, A a^{2} e^{3} + 15 \, {\left(B a b - A b^{2}\right)} e^{3} x^{2} + {\left(14 \, B a b - 23 \, A b^{2}\right)} d^{2} e - {\left(2 \, B a^{2} - 11 \, A a b\right)} d e^{2} + 5 \, {\left(7 \, {\left(B a b - A b^{2}\right)} d e^{2} - {\left(B a^{2} - A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, {\left(b^{3} d^{6} e - 3 \, a b^{2} d^{5} e^{2} + 3 \, a^{2} b d^{4} e^{3} - a^{3} d^{3} e^{4} + {\left(b^{3} d^{3} e^{4} - 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} b d e^{6} - a^{3} e^{7}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{3} - 3 \, a b^{2} d^{3} e^{4} + 3 \, a^{2} b d^{2} e^{5} - a^{3} d e^{6}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e^{2} - 3 \, a b^{2} d^{4} e^{3} + 3 \, a^{2} b d^{3} e^{4} - a^{3} d^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[1/15*(15*((B*a*b - A*b^2)*e^4*x^3 + 3*(B*a*b - A*b^2)*d*e^3*x^2 + 3*(B*a*b - A*b^2)*d^2*e^2*x + (B*a*b - A*b^2)*d^3*e)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(3*B*b^2*d^3 - 3*A*a^2*e^3 + 15*(B*a*b - A*b^2)*e^3*x^2 + (14*B*a*b - 23*A*b^2)*d^2*e - (2*B*a^2 - 11*A*a*b)*d*e^2 + 5*(7*(B*a*b - A*b^2)*d*e^2 - (B*a^2 - A*a*b)*e^3)*x)*sqrt(e*x + d))/(b^3*d^6*e - 3*a*b^2*d^5*e^2 + 3*a^2*b*d^4*e^3 - a^3*d^3*e^4 + (b^3*d^3*e^4 - 3*a*b^2*d^2*e^5 + 3*a^2*b*d*e^6 - a^3*e^7)*x^3 + 3*(b^3*d^4*e^3 - 3*a*b^2*d^3*e^4 + 3*a^2*b*d^2*e^5 - a^3*d*e^6)*x^2 + 3*(b^3*d^5*e^2 - 3*a*b^2*d^4*e^3 + 3*a^2*b*d^3*e^4 - a^3*d^2*e^5)*x), 2/15*(15*((B*a*b - A*b^2)*e^4*x^3 + 3*(B*a*b - A*b^2)*d*e^3*x^2 + 3*(B*a*b - A*b^2)*d^2*e^2*x + (B*a*b - A*b^2)*d^3*e)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3*B*b^2*d^3 - 3*A*a^2*e^3 + 15*(B*a*b - A*b^2)*e^3*x^2 + (14*B*a*b - 23*A*b^2)*d^2*e - (2*B*a^2 - 11*A*a*b)*d*e^2 + 5*(7*(B*a*b - A*b^2)*d*e^2 - (B*a^2 - A*a*b)*e^3)*x)*sqrt(e*x + d))/(b^3*d^6*e - 3*a*b^2*d^5*e^2 + 3*a^2*b*d^4*e^3 - a^3*d^3*e^4 + (b^3*d^3*e^4 - 3*a*b^2*d^2*e^5 + 3*a^2*b*d*e^6 - a^3*e^7)*x^3 + 3*(b^3*d^4*e^3 - 3*a*b^2*d^3*e^4 + 3*a^2*b*d^2*e^5 - a^3*d*e^6)*x^2 + 3*(b^3*d^5*e^2 - 3*a*b^2*d^4*e^3 + 3*a^2*b*d^3*e^4 - a^3*d^2*e^5)*x)]","B",0
1866,1,1060,0,0.470050," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(4 \, B a^{2} b^{2} d^{2} e - {\left(13 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + {\left(4 \, B b^{4} d^{2} e - {\left(13 \, B a b^{3} - 5 \, A b^{4}\right)} d e^{2} + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(4 \, B a b^{3} d^{2} e - {\left(13 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} d e^{2} + {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(24 \, B b^{4} e^{3} x^{4} - 30 \, {\left(B a b^{3} + A b^{4}\right)} d^{3} + 7 \, {\left(107 \, B a^{2} b^{2} - 15 \, A a b^{3}\right)} d^{2} e - 140 \, {\left(12 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + 105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + 8 \, {\left(16 \, B b^{4} d e^{2} - {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} e^{3}\right)} x^{3} + 8 \, {\left(58 \, B b^{4} d^{2} e - 2 \, {\left(59 \, B a b^{3} - 25 \, A b^{4}\right)} d e^{2} + 7 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} - {\left(60 \, B b^{4} d^{3} - {\left(1303 \, B a b^{3} - 195 \, A b^{4}\right)} d^{2} e + 14 \, {\left(203 \, B a^{2} b^{2} - 85 \, A a b^{3}\right)} d e^{2} - 175 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{120 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{105 \, {\left(4 \, B a^{2} b^{2} d^{2} e - {\left(13 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + {\left(4 \, B b^{4} d^{2} e - {\left(13 \, B a b^{3} - 5 \, A b^{4}\right)} d e^{2} + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(4 \, B a b^{3} d^{2} e - {\left(13 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} d e^{2} + {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(24 \, B b^{4} e^{3} x^{4} - 30 \, {\left(B a b^{3} + A b^{4}\right)} d^{3} + 7 \, {\left(107 \, B a^{2} b^{2} - 15 \, A a b^{3}\right)} d^{2} e - 140 \, {\left(12 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + 105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + 8 \, {\left(16 \, B b^{4} d e^{2} - {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} e^{3}\right)} x^{3} + 8 \, {\left(58 \, B b^{4} d^{2} e - 2 \, {\left(59 \, B a b^{3} - 25 \, A b^{4}\right)} d e^{2} + 7 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} - {\left(60 \, B b^{4} d^{3} - {\left(1303 \, B a b^{3} - 195 \, A b^{4}\right)} d^{2} e + 14 \, {\left(203 \, B a^{2} b^{2} - 85 \, A a b^{3}\right)} d e^{2} - 175 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{60 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[1/120*(105*(4*B*a^2*b^2*d^2*e - (13*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + (9*B*a^4 - 5*A*a^3*b)*e^3 + (4*B*b^4*d^2*e - (13*B*a*b^3 - 5*A*b^4)*d*e^2 + (9*B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 + 2*(4*B*a*b^3*d^2*e - (13*B*a^2*b^2 - 5*A*a*b^3)*d*e^2 + (9*B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(24*B*b^4*e^3*x^4 - 30*(B*a*b^3 + A*b^4)*d^3 + 7*(107*B*a^2*b^2 - 15*A*a*b^3)*d^2*e - 140*(12*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + 105*(9*B*a^4 - 5*A*a^3*b)*e^3 + 8*(16*B*b^4*d*e^2 - (9*B*a*b^3 - 5*A*b^4)*e^3)*x^3 + 8*(58*B*b^4*d^2*e - 2*(59*B*a*b^3 - 25*A*b^4)*d*e^2 + 7*(9*B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 - (60*B*b^4*d^3 - (1303*B*a*b^3 - 195*A*b^4)*d^2*e + 14*(203*B*a^2*b^2 - 85*A*a*b^3)*d*e^2 - 175*(9*B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/60*(105*(4*B*a^2*b^2*d^2*e - (13*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + (9*B*a^4 - 5*A*a^3*b)*e^3 + (4*B*b^4*d^2*e - (13*B*a*b^3 - 5*A*b^4)*d*e^2 + (9*B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 + 2*(4*B*a*b^3*d^2*e - (13*B*a^2*b^2 - 5*A*a*b^3)*d*e^2 + (9*B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (24*B*b^4*e^3*x^4 - 30*(B*a*b^3 + A*b^4)*d^3 + 7*(107*B*a^2*b^2 - 15*A*a*b^3)*d^2*e - 140*(12*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + 105*(9*B*a^4 - 5*A*a^3*b)*e^3 + 8*(16*B*b^4*d*e^2 - (9*B*a*b^3 - 5*A*b^4)*e^3)*x^3 + 8*(58*B*b^4*d^2*e - 2*(59*B*a*b^3 - 25*A*b^4)*d*e^2 + 7*(9*B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 - (60*B*b^4*d^3 - (1303*B*a*b^3 - 195*A*b^4)*d^2*e + 14*(203*B*a^2*b^2 - 85*A*a*b^3)*d*e^2 - 175*(9*B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","A",0
1867,1,680,0,0.463794," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(4 \, B a^{2} b d e - {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(8 \, B b^{3} e^{2} x^{3} - 6 \, {\left(B a b^{2} + A b^{3}\right)} d^{2} + 5 \, {\left(19 \, B a^{2} b - 3 \, A a b^{2}\right)} d e - 15 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} + 8 \, {\left(7 \, B b^{3} d e - {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} e^{2}\right)} x^{2} - {\left(12 \, B b^{3} d^{2} - {\left(163 \, B a b^{2} - 27 \, A b^{3}\right)} d e + 25 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, -\frac{15 \, {\left(4 \, B a^{2} b d e - {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(8 \, B b^{3} e^{2} x^{3} - 6 \, {\left(B a b^{2} + A b^{3}\right)} d^{2} + 5 \, {\left(19 \, B a^{2} b - 3 \, A a b^{2}\right)} d e - 15 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} + 8 \, {\left(7 \, B b^{3} d e - {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} e^{2}\right)} x^{2} - {\left(12 \, B b^{3} d^{2} - {\left(163 \, B a b^{2} - 27 \, A b^{3}\right)} d e + 25 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[-1/24*(15*(4*B*a^2*b*d*e - (7*B*a^3 - 3*A*a^2*b)*e^2 + (4*B*b^3*d*e - (7*B*a*b^2 - 3*A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (7*B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(8*B*b^3*e^2*x^3 - 6*(B*a*b^2 + A*b^3)*d^2 + 5*(19*B*a^2*b - 3*A*a*b^2)*d*e - 15*(7*B*a^3 - 3*A*a^2*b)*e^2 + 8*(7*B*b^3*d*e - (7*B*a*b^2 - 3*A*b^3)*e^2)*x^2 - (12*B*b^3*d^2 - (163*B*a*b^2 - 27*A*b^3)*d*e + 25*(7*B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), -1/12*(15*(4*B*a^2*b*d*e - (7*B*a^3 - 3*A*a^2*b)*e^2 + (4*B*b^3*d*e - (7*B*a*b^2 - 3*A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (7*B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (8*B*b^3*e^2*x^3 - 6*(B*a*b^2 + A*b^3)*d^2 + 5*(19*B*a^2*b - 3*A*a*b^2)*d*e - 15*(7*B*a^3 - 3*A*a^2*b)*e^2 + 8*(7*B*b^3*d*e - (7*B*a*b^2 - 3*A*b^3)*e^2)*x^2 - (12*B*b^3*d^2 - (163*B*a*b^2 - 27*A*b^3)*d*e + 25*(7*B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
1868,1,703,0,0.443670," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, B a^{2} b d e - {\left(5 \, B a^{3} - A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(5 \, B a b^{2} - A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(5 \, B a^{2} b - A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(17 \, B a^{2} b^{2} - A a b^{3}\right)} d e + 3 \, {\left(5 \, B a^{3} b - A a^{2} b^{2}\right)} e^{2} - 8 \, {\left(B b^{4} d e - B a b^{3} e^{2}\right)} x^{2} + {\left(4 \, B b^{4} d^{2} - {\left(29 \, B a b^{3} - 5 \, A b^{4}\right)} d e + 5 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{5} d - a^{3} b^{4} e + {\left(b^{7} d - a b^{6} e\right)} x^{2} + 2 \, {\left(a b^{6} d - a^{2} b^{5} e\right)} x\right)}}, \frac{3 \, {\left(4 \, B a^{2} b d e - {\left(5 \, B a^{3} - A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(5 \, B a b^{2} - A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(5 \, B a^{2} b - A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(17 \, B a^{2} b^{2} - A a b^{3}\right)} d e + 3 \, {\left(5 \, B a^{3} b - A a^{2} b^{2}\right)} e^{2} - 8 \, {\left(B b^{4} d e - B a b^{3} e^{2}\right)} x^{2} + {\left(4 \, B b^{4} d^{2} - {\left(29 \, B a b^{3} - 5 \, A b^{4}\right)} d e + 5 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{5} d - a^{3} b^{4} e + {\left(b^{7} d - a b^{6} e\right)} x^{2} + 2 \, {\left(a b^{6} d - a^{2} b^{5} e\right)} x\right)}}\right]"," ",0,"[1/8*(3*(4*B*a^2*b*d*e - (5*B*a^3 - A*a^2*b)*e^2 + (4*B*b^3*d*e - (5*B*a*b^2 - A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (5*B*a^2*b - A*a*b^2)*e^2)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*(B*a*b^3 + A*b^4)*d^2 - (17*B*a^2*b^2 - A*a*b^3)*d*e + 3*(5*B*a^3*b - A*a^2*b^2)*e^2 - 8*(B*b^4*d*e - B*a*b^3*e^2)*x^2 + (4*B*b^4*d^2 - (29*B*a*b^3 - 5*A*b^4)*d*e + 5*(5*B*a^2*b^2 - A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d - a^3*b^4*e + (b^7*d - a*b^6*e)*x^2 + 2*(a*b^6*d - a^2*b^5*e)*x), 1/4*(3*(4*B*a^2*b*d*e - (5*B*a^3 - A*a^2*b)*e^2 + (4*B*b^3*d*e - (5*B*a*b^2 - A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (5*B*a^2*b - A*a*b^2)*e^2)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (2*(B*a*b^3 + A*b^4)*d^2 - (17*B*a^2*b^2 - A*a*b^3)*d*e + 3*(5*B*a^3*b - A*a^2*b^2)*e^2 - 8*(B*b^4*d*e - B*a*b^3*e^2)*x^2 + (4*B*b^4*d^2 - (29*B*a*b^3 - 5*A*b^4)*d*e + 5*(5*B*a^2*b^2 - A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d - a^3*b^4*e + (b^7*d - a*b^6*e)*x^2 + 2*(a*b^6*d - a^2*b^5*e)*x)]","A",0
1869,1,721,0,0.461533," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, B a^{2} b d e - {\left(3 \, B a^{3} + A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(3 \, B a^{2} b + A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(5 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} d e + {\left(3 \, B a^{3} b + A a^{2} b^{2}\right)} e^{2} + {\left(4 \, B b^{4} d^{2} - {\left(9 \, B a b^{3} - A b^{4}\right)} d e + {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{5} d^{2} - 2 \, a^{3} b^{4} d e + a^{4} b^{3} e^{2} + {\left(b^{7} d^{2} - 2 \, a b^{6} d e + a^{2} b^{5} e^{2}\right)} x^{2} + 2 \, {\left(a b^{6} d^{2} - 2 \, a^{2} b^{5} d e + a^{3} b^{4} e^{2}\right)} x\right)}}, \frac{{\left(4 \, B a^{2} b d e - {\left(3 \, B a^{3} + A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(3 \, B a^{2} b + A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(5 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} d e + {\left(3 \, B a^{3} b + A a^{2} b^{2}\right)} e^{2} + {\left(4 \, B b^{4} d^{2} - {\left(9 \, B a b^{3} - A b^{4}\right)} d e + {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{5} d^{2} - 2 \, a^{3} b^{4} d e + a^{4} b^{3} e^{2} + {\left(b^{7} d^{2} - 2 \, a b^{6} d e + a^{2} b^{5} e^{2}\right)} x^{2} + 2 \, {\left(a b^{6} d^{2} - 2 \, a^{2} b^{5} d e + a^{3} b^{4} e^{2}\right)} x\right)}}\right]"," ",0,"[1/8*((4*B*a^2*b*d*e - (3*B*a^3 + A*a^2*b)*e^2 + (4*B*b^3*d*e - (3*B*a*b^2 + A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (3*B*a^2*b + A*a*b^2)*e^2)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*(B*a*b^3 + A*b^4)*d^2 - (5*B*a^2*b^2 + 3*A*a*b^3)*d*e + (3*B*a^3*b + A*a^2*b^2)*e^2 + (4*B*b^4*d^2 - (9*B*a*b^3 - A*b^4)*d*e + (5*B*a^2*b^2 - A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d^2 - 2*a^3*b^4*d*e + a^4*b^3*e^2 + (b^7*d^2 - 2*a*b^6*d*e + a^2*b^5*e^2)*x^2 + 2*(a*b^6*d^2 - 2*a^2*b^5*d*e + a^3*b^4*e^2)*x), 1/4*((4*B*a^2*b*d*e - (3*B*a^3 + A*a^2*b)*e^2 + (4*B*b^3*d*e - (3*B*a*b^2 + A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (3*B*a^2*b + A*a*b^2)*e^2)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (2*(B*a*b^3 + A*b^4)*d^2 - (5*B*a^2*b^2 + 3*A*a*b^3)*d*e + (3*B*a^3*b + A*a^2*b^2)*e^2 + (4*B*b^4*d^2 - (9*B*a*b^3 - A*b^4)*d*e + (5*B*a^2*b^2 - A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d^2 - 2*a^3*b^4*d*e + a^4*b^3*e^2 + (b^7*d^2 - 2*a*b^6*d*e + a^2*b^5*e^2)*x^2 + 2*(a*b^6*d^2 - 2*a^2*b^5*d*e + a^3*b^4*e^2)*x)]","B",0
1870,1,808,0,0.548672," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B a^{2} b d e - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(B a b^{2} + 3 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(B a^{2} b + 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(B a^{2} b^{2} + 7 \, A a b^{3}\right)} d e - {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{2} + {\left(4 \, B b^{4} d^{2} - {\left(5 \, B a b^{3} + 3 \, A b^{4}\right)} d e + {\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{5} d^{3} - 3 \, a^{3} b^{4} d^{2} e + 3 \, a^{4} b^{3} d e^{2} - a^{5} b^{2} e^{3} + {\left(b^{7} d^{3} - 3 \, a b^{6} d^{2} e + 3 \, a^{2} b^{5} d e^{2} - a^{3} b^{4} e^{3}\right)} x^{2} + 2 \, {\left(a b^{6} d^{3} - 3 \, a^{2} b^{5} d^{2} e + 3 \, a^{3} b^{4} d e^{2} - a^{4} b^{3} e^{3}\right)} x\right)}}, -\frac{{\left(4 \, B a^{2} b d e - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(B a b^{2} + 3 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(B a^{2} b + 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(B a^{2} b^{2} + 7 \, A a b^{3}\right)} d e - {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{2} + {\left(4 \, B b^{4} d^{2} - {\left(5 \, B a b^{3} + 3 \, A b^{4}\right)} d e + {\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{5} d^{3} - 3 \, a^{3} b^{4} d^{2} e + 3 \, a^{4} b^{3} d e^{2} - a^{5} b^{2} e^{3} + {\left(b^{7} d^{3} - 3 \, a b^{6} d^{2} e + 3 \, a^{2} b^{5} d e^{2} - a^{3} b^{4} e^{3}\right)} x^{2} + 2 \, {\left(a b^{6} d^{3} - 3 \, a^{2} b^{5} d^{2} e + 3 \, a^{3} b^{4} d e^{2} - a^{4} b^{3} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/8*((4*B*a^2*b*d*e - (B*a^3 + 3*A*a^2*b)*e^2 + (4*B*b^3*d*e - (B*a*b^2 + 3*A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (B*a^2*b + 3*A*a*b^2)*e^2)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(2*(B*a*b^3 + A*b^4)*d^2 - (B*a^2*b^2 + 7*A*a*b^3)*d*e - (B*a^3*b - 5*A*a^2*b^2)*e^2 + (4*B*b^4*d^2 - (5*B*a*b^3 + 3*A*b^4)*d*e + (B*a^2*b^2 + 3*A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d^3 - 3*a^3*b^4*d^2*e + 3*a^4*b^3*d*e^2 - a^5*b^2*e^3 + (b^7*d^3 - 3*a*b^6*d^2*e + 3*a^2*b^5*d*e^2 - a^3*b^4*e^3)*x^2 + 2*(a*b^6*d^3 - 3*a^2*b^5*d^2*e + 3*a^3*b^4*d*e^2 - a^4*b^3*e^3)*x), -1/4*((4*B*a^2*b*d*e - (B*a^3 + 3*A*a^2*b)*e^2 + (4*B*b^3*d*e - (B*a*b^2 + 3*A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (B*a^2*b + 3*A*a*b^2)*e^2)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (2*(B*a*b^3 + A*b^4)*d^2 - (B*a^2*b^2 + 7*A*a*b^3)*d*e - (B*a^3*b - 5*A*a^2*b^2)*e^2 + (4*B*b^4*d^2 - (5*B*a*b^3 + 3*A*b^4)*d*e + (B*a^2*b^2 + 3*A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d^3 - 3*a^3*b^4*d^2*e + 3*a^4*b^3*d*e^2 - a^5*b^2*e^3 + (b^7*d^3 - 3*a*b^6*d^2*e + 3*a^2*b^5*d*e^2 - a^3*b^4*e^3)*x^2 + 2*(a*b^6*d^3 - 3*a^2*b^5*d^2*e + 3*a^3*b^4*d*e^2 - a^4*b^3*e^3)*x)]","B",0
1871,1,1410,0,0.547920," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, B a^{2} b d^{2} e + {\left(B a^{3} - 5 \, A a^{2} b\right)} d e^{2} + {\left(4 \, B b^{3} d e^{2} + {\left(B a b^{2} - 5 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(4 \, B b^{3} d^{2} e + {\left(9 \, B a b^{2} - 5 \, A b^{3}\right)} d e^{2} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, B a b^{2} d^{2} e + 2 \, {\left(3 \, B a^{2} b - 5 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 5 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(8 \, A a^{3} b e^{3} + 2 \, {\left(B a b^{3} + A b^{4}\right)} d^{3} + 11 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e - {\left(13 \, B a^{3} b - A a^{2} b^{2}\right)} d e^{2} + 3 \, {\left(4 \, B b^{4} d^{2} e - {\left(3 \, B a b^{3} + 5 \, A b^{4}\right)} d e^{2} - {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + {\left(4 \, B b^{4} d^{3} + {\left(17 \, B a b^{3} - 5 \, A b^{4}\right)} d^{2} e - 4 \, {\left(4 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} d e^{2} - 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{5} d^{5} - 4 \, a^{3} b^{4} d^{4} e + 6 \, a^{4} b^{3} d^{3} e^{2} - 4 \, a^{5} b^{2} d^{2} e^{3} + a^{6} b d e^{4} + {\left(b^{7} d^{4} e - 4 \, a b^{6} d^{3} e^{2} + 6 \, a^{2} b^{5} d^{2} e^{3} - 4 \, a^{3} b^{4} d e^{4} + a^{4} b^{3} e^{5}\right)} x^{3} + {\left(b^{7} d^{5} - 2 \, a b^{6} d^{4} e - 2 \, a^{2} b^{5} d^{3} e^{2} + 8 \, a^{3} b^{4} d^{2} e^{3} - 7 \, a^{4} b^{3} d e^{4} + 2 \, a^{5} b^{2} e^{5}\right)} x^{2} + {\left(2 \, a b^{6} d^{5} - 7 \, a^{2} b^{5} d^{4} e + 8 \, a^{3} b^{4} d^{3} e^{2} - 2 \, a^{4} b^{3} d^{2} e^{3} - 2 \, a^{5} b^{2} d e^{4} + a^{6} b e^{5}\right)} x\right)}}, -\frac{3 \, {\left(4 \, B a^{2} b d^{2} e + {\left(B a^{3} - 5 \, A a^{2} b\right)} d e^{2} + {\left(4 \, B b^{3} d e^{2} + {\left(B a b^{2} - 5 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(4 \, B b^{3} d^{2} e + {\left(9 \, B a b^{2} - 5 \, A b^{3}\right)} d e^{2} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, B a b^{2} d^{2} e + 2 \, {\left(3 \, B a^{2} b - 5 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 5 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(8 \, A a^{3} b e^{3} + 2 \, {\left(B a b^{3} + A b^{4}\right)} d^{3} + 11 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e - {\left(13 \, B a^{3} b - A a^{2} b^{2}\right)} d e^{2} + 3 \, {\left(4 \, B b^{4} d^{2} e - {\left(3 \, B a b^{3} + 5 \, A b^{4}\right)} d e^{2} - {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + {\left(4 \, B b^{4} d^{3} + {\left(17 \, B a b^{3} - 5 \, A b^{4}\right)} d^{2} e - 4 \, {\left(4 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} d e^{2} - 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{5} d^{5} - 4 \, a^{3} b^{4} d^{4} e + 6 \, a^{4} b^{3} d^{3} e^{2} - 4 \, a^{5} b^{2} d^{2} e^{3} + a^{6} b d e^{4} + {\left(b^{7} d^{4} e - 4 \, a b^{6} d^{3} e^{2} + 6 \, a^{2} b^{5} d^{2} e^{3} - 4 \, a^{3} b^{4} d e^{4} + a^{4} b^{3} e^{5}\right)} x^{3} + {\left(b^{7} d^{5} - 2 \, a b^{6} d^{4} e - 2 \, a^{2} b^{5} d^{3} e^{2} + 8 \, a^{3} b^{4} d^{2} e^{3} - 7 \, a^{4} b^{3} d e^{4} + 2 \, a^{5} b^{2} e^{5}\right)} x^{2} + {\left(2 \, a b^{6} d^{5} - 7 \, a^{2} b^{5} d^{4} e + 8 \, a^{3} b^{4} d^{3} e^{2} - 2 \, a^{4} b^{3} d^{2} e^{3} - 2 \, a^{5} b^{2} d e^{4} + a^{6} b e^{5}\right)} x\right)}}\right]"," ",0,"[1/8*(3*(4*B*a^2*b*d^2*e + (B*a^3 - 5*A*a^2*b)*d*e^2 + (4*B*b^3*d*e^2 + (B*a*b^2 - 5*A*b^3)*e^3)*x^3 + (4*B*b^3*d^2*e + (9*B*a*b^2 - 5*A*b^3)*d*e^2 + 2*(B*a^2*b - 5*A*a*b^2)*e^3)*x^2 + (8*B*a*b^2*d^2*e + 2*(3*B*a^2*b - 5*A*a*b^2)*d*e^2 + (B*a^3 - 5*A*a^2*b)*e^3)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e + 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(8*A*a^3*b*e^3 + 2*(B*a*b^3 + A*b^4)*d^3 + 11*(B*a^2*b^2 - A*a*b^3)*d^2*e - (13*B*a^3*b - A*a^2*b^2)*d*e^2 + 3*(4*B*b^4*d^2*e - (3*B*a*b^3 + 5*A*b^4)*d*e^2 - (B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 + (4*B*b^4*d^3 + (17*B*a*b^3 - 5*A*b^4)*d^2*e - 4*(4*B*a^2*b^2 + 5*A*a*b^3)*d*e^2 - 5*(B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(a^2*b^5*d^5 - 4*a^3*b^4*d^4*e + 6*a^4*b^3*d^3*e^2 - 4*a^5*b^2*d^2*e^3 + a^6*b*d*e^4 + (b^7*d^4*e - 4*a*b^6*d^3*e^2 + 6*a^2*b^5*d^2*e^3 - 4*a^3*b^4*d*e^4 + a^4*b^3*e^5)*x^3 + (b^7*d^5 - 2*a*b^6*d^4*e - 2*a^2*b^5*d^3*e^2 + 8*a^3*b^4*d^2*e^3 - 7*a^4*b^3*d*e^4 + 2*a^5*b^2*e^5)*x^2 + (2*a*b^6*d^5 - 7*a^2*b^5*d^4*e + 8*a^3*b^4*d^3*e^2 - 2*a^4*b^3*d^2*e^3 - 2*a^5*b^2*d*e^4 + a^6*b*e^5)*x), -1/4*(3*(4*B*a^2*b*d^2*e + (B*a^3 - 5*A*a^2*b)*d*e^2 + (4*B*b^3*d*e^2 + (B*a*b^2 - 5*A*b^3)*e^3)*x^3 + (4*B*b^3*d^2*e + (9*B*a*b^2 - 5*A*b^3)*d*e^2 + 2*(B*a^2*b - 5*A*a*b^2)*e^3)*x^2 + (8*B*a*b^2*d^2*e + 2*(3*B*a^2*b - 5*A*a*b^2)*d*e^2 + (B*a^3 - 5*A*a^2*b)*e^3)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (8*A*a^3*b*e^3 + 2*(B*a*b^3 + A*b^4)*d^3 + 11*(B*a^2*b^2 - A*a*b^3)*d^2*e - (13*B*a^3*b - A*a^2*b^2)*d*e^2 + 3*(4*B*b^4*d^2*e - (3*B*a*b^3 + 5*A*b^4)*d*e^2 - (B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 + (4*B*b^4*d^3 + (17*B*a*b^3 - 5*A*b^4)*d^2*e - 4*(4*B*a^2*b^2 + 5*A*a*b^3)*d*e^2 - 5*(B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(a^2*b^5*d^5 - 4*a^3*b^4*d^4*e + 6*a^4*b^3*d^3*e^2 - 4*a^5*b^2*d^2*e^3 + a^6*b*d*e^4 + (b^7*d^4*e - 4*a*b^6*d^3*e^2 + 6*a^2*b^5*d^2*e^3 - 4*a^3*b^4*d*e^4 + a^4*b^3*e^5)*x^3 + (b^7*d^5 - 2*a*b^6*d^4*e - 2*a^2*b^5*d^3*e^2 + 8*a^3*b^4*d^2*e^3 - 7*a^4*b^3*d*e^4 + 2*a^5*b^2*e^5)*x^2 + (2*a*b^6*d^5 - 7*a^2*b^5*d^4*e + 8*a^3*b^4*d^3*e^2 - 2*a^4*b^3*d^2*e^3 - 2*a^5*b^2*d*e^4 + a^6*b*e^5)*x)]","B",0
1872,1,1776,0,0.550526," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(4 \, B a^{2} b d^{3} e + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} d^{2} e^{2} + {\left(4 \, B b^{3} d e^{3} + {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(4 \, B b^{3} d^{2} e^{2} + 7 \, {\left(B a b^{2} - A b^{3}\right)} d e^{3} + {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{4}\right)} x^{3} + {\left(4 \, B b^{3} d^{3} e + {\left(19 \, B a b^{2} - 7 \, A b^{3}\right)} d^{2} e^{2} + 4 \, {\left(4 \, B a^{2} b - 7 \, A a b^{2}\right)} d e^{3} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} e^{4}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d^{3} e + 7 \, {\left(B a^{2} b - A a b^{2}\right)} d^{2} e^{2} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} d e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(8 \, A a^{3} e^{3} + 6 \, {\left(B a b^{2} + A b^{3}\right)} d^{3} + {\left(83 \, B a^{2} b - 39 \, A a b^{2}\right)} d^{2} e + 16 \, {\left(B a^{3} - 5 \, A a^{2} b\right)} d e^{2} + 15 \, {\left(4 \, B b^{3} d e^{2} + {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} e^{3}\right)} x^{3} + 5 \, {\left(16 \, B b^{3} d^{2} e + 4 \, {\left(8 \, B a b^{2} - 7 \, A b^{3}\right)} d e^{2} + 5 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(12 \, B b^{3} d^{3} + {\left(145 \, B a b^{2} - 21 \, A b^{3}\right)} d^{2} e + 2 \, {\left(67 \, B a^{2} b - 119 \, A a b^{2}\right)} d e^{2} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{2} b^{4} d^{6} - 4 \, a^{3} b^{3} d^{5} e + 6 \, a^{4} b^{2} d^{4} e^{2} - 4 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4} + {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 2 \, a^{2} b^{4} d^{3} e^{3} + 2 \, a^{3} b^{3} d^{2} e^{4} - 3 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{3} + {\left(b^{6} d^{6} - 9 \, a^{2} b^{4} d^{4} e^{2} + 16 \, a^{3} b^{3} d^{3} e^{3} - 9 \, a^{4} b^{2} d^{2} e^{4} + a^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} d^{6} - 3 \, a^{2} b^{4} d^{5} e + 2 \, a^{3} b^{3} d^{4} e^{2} + 2 \, a^{4} b^{2} d^{3} e^{3} - 3 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x\right)}}, \frac{15 \, {\left(4 \, B a^{2} b d^{3} e + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} d^{2} e^{2} + {\left(4 \, B b^{3} d e^{3} + {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(4 \, B b^{3} d^{2} e^{2} + 7 \, {\left(B a b^{2} - A b^{3}\right)} d e^{3} + {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{4}\right)} x^{3} + {\left(4 \, B b^{3} d^{3} e + {\left(19 \, B a b^{2} - 7 \, A b^{3}\right)} d^{2} e^{2} + 4 \, {\left(4 \, B a^{2} b - 7 \, A a b^{2}\right)} d e^{3} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} e^{4}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d^{3} e + 7 \, {\left(B a^{2} b - A a b^{2}\right)} d^{2} e^{2} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} d e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(8 \, A a^{3} e^{3} + 6 \, {\left(B a b^{2} + A b^{3}\right)} d^{3} + {\left(83 \, B a^{2} b - 39 \, A a b^{2}\right)} d^{2} e + 16 \, {\left(B a^{3} - 5 \, A a^{2} b\right)} d e^{2} + 15 \, {\left(4 \, B b^{3} d e^{2} + {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} e^{3}\right)} x^{3} + 5 \, {\left(16 \, B b^{3} d^{2} e + 4 \, {\left(8 \, B a b^{2} - 7 \, A b^{3}\right)} d e^{2} + 5 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(12 \, B b^{3} d^{3} + {\left(145 \, B a b^{2} - 21 \, A b^{3}\right)} d^{2} e + 2 \, {\left(67 \, B a^{2} b - 119 \, A a b^{2}\right)} d e^{2} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(a^{2} b^{4} d^{6} - 4 \, a^{3} b^{3} d^{5} e + 6 \, a^{4} b^{2} d^{4} e^{2} - 4 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4} + {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 2 \, a^{2} b^{4} d^{3} e^{3} + 2 \, a^{3} b^{3} d^{2} e^{4} - 3 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{3} + {\left(b^{6} d^{6} - 9 \, a^{2} b^{4} d^{4} e^{2} + 16 \, a^{3} b^{3} d^{3} e^{3} - 9 \, a^{4} b^{2} d^{2} e^{4} + a^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} d^{6} - 3 \, a^{2} b^{4} d^{5} e + 2 \, a^{3} b^{3} d^{4} e^{2} + 2 \, a^{4} b^{2} d^{3} e^{3} - 3 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x\right)}}\right]"," ",0,"[-1/24*(15*(4*B*a^2*b*d^3*e + (3*B*a^3 - 7*A*a^2*b)*d^2*e^2 + (4*B*b^3*d*e^3 + (3*B*a*b^2 - 7*A*b^3)*e^4)*x^4 + 2*(4*B*b^3*d^2*e^2 + 7*(B*a*b^2 - A*b^3)*d*e^3 + (3*B*a^2*b - 7*A*a*b^2)*e^4)*x^3 + (4*B*b^3*d^3*e + (19*B*a*b^2 - 7*A*b^3)*d^2*e^2 + 4*(4*B*a^2*b - 7*A*a*b^2)*d*e^3 + (3*B*a^3 - 7*A*a^2*b)*e^4)*x^2 + 2*(4*B*a*b^2*d^3*e + 7*(B*a^2*b - A*a*b^2)*d^2*e^2 + (3*B*a^3 - 7*A*a^2*b)*d*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(8*A*a^3*e^3 + 6*(B*a*b^2 + A*b^3)*d^3 + (83*B*a^2*b - 39*A*a*b^2)*d^2*e + 16*(B*a^3 - 5*A*a^2*b)*d*e^2 + 15*(4*B*b^3*d*e^2 + (3*B*a*b^2 - 7*A*b^3)*e^3)*x^3 + 5*(16*B*b^3*d^2*e + 4*(8*B*a*b^2 - 7*A*b^3)*d*e^2 + 5*(3*B*a^2*b - 7*A*a*b^2)*e^3)*x^2 + (12*B*b^3*d^3 + (145*B*a*b^2 - 21*A*b^3)*d^2*e + 2*(67*B*a^2*b - 119*A*a*b^2)*d*e^2 + 8*(3*B*a^3 - 7*A*a^2*b)*e^3)*x)*sqrt(e*x + d))/(a^2*b^4*d^6 - 4*a^3*b^3*d^5*e + 6*a^4*b^2*d^4*e^2 - 4*a^5*b*d^3*e^3 + a^6*d^2*e^4 + (b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^4 + 2*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 2*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4 - 3*a^4*b^2*d*e^5 + a^5*b*e^6)*x^3 + (b^6*d^6 - 9*a^2*b^4*d^4*e^2 + 16*a^3*b^3*d^3*e^3 - 9*a^4*b^2*d^2*e^4 + a^6*e^6)*x^2 + 2*(a*b^5*d^6 - 3*a^2*b^4*d^5*e + 2*a^3*b^3*d^4*e^2 + 2*a^4*b^2*d^3*e^3 - 3*a^5*b*d^2*e^4 + a^6*d*e^5)*x), 1/12*(15*(4*B*a^2*b*d^3*e + (3*B*a^3 - 7*A*a^2*b)*d^2*e^2 + (4*B*b^3*d*e^3 + (3*B*a*b^2 - 7*A*b^3)*e^4)*x^4 + 2*(4*B*b^3*d^2*e^2 + 7*(B*a*b^2 - A*b^3)*d*e^3 + (3*B*a^2*b - 7*A*a*b^2)*e^4)*x^3 + (4*B*b^3*d^3*e + (19*B*a*b^2 - 7*A*b^3)*d^2*e^2 + 4*(4*B*a^2*b - 7*A*a*b^2)*d*e^3 + (3*B*a^3 - 7*A*a^2*b)*e^4)*x^2 + 2*(4*B*a*b^2*d^3*e + 7*(B*a^2*b - A*a*b^2)*d^2*e^2 + (3*B*a^3 - 7*A*a^2*b)*d*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (8*A*a^3*e^3 + 6*(B*a*b^2 + A*b^3)*d^3 + (83*B*a^2*b - 39*A*a*b^2)*d^2*e + 16*(B*a^3 - 5*A*a^2*b)*d*e^2 + 15*(4*B*b^3*d*e^2 + (3*B*a*b^2 - 7*A*b^3)*e^3)*x^3 + 5*(16*B*b^3*d^2*e + 4*(8*B*a*b^2 - 7*A*b^3)*d*e^2 + 5*(3*B*a^2*b - 7*A*a*b^2)*e^3)*x^2 + (12*B*b^3*d^3 + (145*B*a*b^2 - 21*A*b^3)*d^2*e + 2*(67*B*a^2*b - 119*A*a*b^2)*d*e^2 + 8*(3*B*a^3 - 7*A*a^2*b)*e^3)*x)*sqrt(e*x + d))/(a^2*b^4*d^6 - 4*a^3*b^3*d^5*e + 6*a^4*b^2*d^4*e^2 - 4*a^5*b*d^3*e^3 + a^6*d^2*e^4 + (b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^4 + 2*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 2*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4 - 3*a^4*b^2*d*e^5 + a^5*b*e^6)*x^3 + (b^6*d^6 - 9*a^2*b^4*d^4*e^2 + 16*a^3*b^3*d^3*e^3 - 9*a^4*b^2*d^2*e^4 + a^6*e^6)*x^2 + 2*(a*b^5*d^6 - 3*a^2*b^4*d^5*e + 2*a^3*b^3*d^4*e^2 + 2*a^4*b^2*d^3*e^3 - 3*a^5*b*d^2*e^4 + a^6*d*e^5)*x)]","B",0
1873,1,2675,0,0.490913," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(4 \, B a^{2} b^{2} d^{4} e + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{3} e^{2} + {\left(4 \, B b^{4} d e^{4} + {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} e^{5}\right)} x^{5} + {\left(12 \, B b^{4} d^{2} e^{3} + {\left(23 \, B a b^{3} - 27 \, A b^{4}\right)} d e^{4} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} e^{5}\right)} x^{4} + {\left(12 \, B b^{4} d^{3} e^{2} + 3 \, {\left(13 \, B a b^{3} - 9 \, A b^{4}\right)} d^{2} e^{3} + 2 \, {\left(17 \, B a^{2} b^{2} - 27 \, A a b^{3}\right)} d e^{4} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{3} + {\left(4 \, B b^{4} d^{4} e + {\left(29 \, B a b^{3} - 9 \, A b^{4}\right)} d^{3} e^{2} + 6 \, {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} d^{2} e^{3} + 3 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d e^{4}\right)} x^{2} + {\left(8 \, B a b^{3} d^{4} e + 2 \, {\left(11 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} d^{3} e^{2} + 3 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(24 \, A a^{4} e^{4} - 30 \, {\left(B a b^{3} + A b^{4}\right)} d^{4} - {\left(659 \, B a^{2} b^{2} - 255 \, A a b^{3}\right)} d^{3} e - 16 \, {\left(17 \, B a^{3} b - 54 \, A a^{2} b^{2}\right)} d^{2} e^{2} + 8 \, {\left(2 \, B a^{4} - 21 \, A a^{3} b\right)} d e^{3} - 105 \, {\left(4 \, B b^{4} d e^{3} + {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} e^{4}\right)} x^{4} - 35 \, {\left(28 \, B b^{4} d^{2} e^{2} + {\left(55 \, B a b^{3} - 63 \, A b^{4}\right)} d e^{3} + 5 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} e^{4}\right)} x^{3} - 7 \, {\left(92 \, B b^{4} d^{3} e + 9 \, {\left(39 \, B a b^{3} - 23 \, A b^{4}\right)} d^{2} e^{2} + 3 \, {\left(109 \, B a^{2} b^{2} - 177 \, A a b^{3}\right)} d e^{3} + 8 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - {\left(60 \, B b^{4} d^{4} + {\left(1183 \, B a b^{3} - 135 \, A b^{4}\right)} d^{3} e + 3 \, {\left(643 \, B a^{2} b^{2} - 831 \, A a b^{3}\right)} d^{2} e^{2} + 72 \, {\left(9 \, B a^{3} b - 17 \, A a^{2} b^{2}\right)} d e^{3} - 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{120 \, {\left(a^{2} b^{5} d^{8} - 5 \, a^{3} b^{4} d^{7} e + 10 \, a^{4} b^{3} d^{6} e^{2} - 10 \, a^{5} b^{2} d^{5} e^{3} + 5 \, a^{6} b d^{4} e^{4} - a^{7} d^{3} e^{5} + {\left(b^{7} d^{5} e^{3} - 5 \, a b^{6} d^{4} e^{4} + 10 \, a^{2} b^{5} d^{3} e^{5} - 10 \, a^{3} b^{4} d^{2} e^{6} + 5 \, a^{4} b^{3} d e^{7} - a^{5} b^{2} e^{8}\right)} x^{5} + {\left(3 \, b^{7} d^{6} e^{2} - 13 \, a b^{6} d^{5} e^{3} + 20 \, a^{2} b^{5} d^{4} e^{4} - 10 \, a^{3} b^{4} d^{3} e^{5} - 5 \, a^{4} b^{3} d^{2} e^{6} + 7 \, a^{5} b^{2} d e^{7} - 2 \, a^{6} b e^{8}\right)} x^{4} + {\left(3 \, b^{7} d^{7} e - 9 \, a b^{6} d^{6} e^{2} + a^{2} b^{5} d^{5} e^{3} + 25 \, a^{3} b^{4} d^{4} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{5} + 17 \, a^{5} b^{2} d^{2} e^{6} - a^{6} b d e^{7} - a^{7} e^{8}\right)} x^{3} + {\left(b^{7} d^{8} + a b^{6} d^{7} e - 17 \, a^{2} b^{5} d^{6} e^{2} + 35 \, a^{3} b^{4} d^{5} e^{3} - 25 \, a^{4} b^{3} d^{4} e^{4} - a^{5} b^{2} d^{3} e^{5} + 9 \, a^{6} b d^{2} e^{6} - 3 \, a^{7} d e^{7}\right)} x^{2} + {\left(2 \, a b^{6} d^{8} - 7 \, a^{2} b^{5} d^{7} e + 5 \, a^{3} b^{4} d^{6} e^{2} + 10 \, a^{4} b^{3} d^{5} e^{3} - 20 \, a^{5} b^{2} d^{4} e^{4} + 13 \, a^{6} b d^{3} e^{5} - 3 \, a^{7} d^{2} e^{6}\right)} x\right)}}, \frac{105 \, {\left(4 \, B a^{2} b^{2} d^{4} e + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{3} e^{2} + {\left(4 \, B b^{4} d e^{4} + {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} e^{5}\right)} x^{5} + {\left(12 \, B b^{4} d^{2} e^{3} + {\left(23 \, B a b^{3} - 27 \, A b^{4}\right)} d e^{4} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} e^{5}\right)} x^{4} + {\left(12 \, B b^{4} d^{3} e^{2} + 3 \, {\left(13 \, B a b^{3} - 9 \, A b^{4}\right)} d^{2} e^{3} + 2 \, {\left(17 \, B a^{2} b^{2} - 27 \, A a b^{3}\right)} d e^{4} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{3} + {\left(4 \, B b^{4} d^{4} e + {\left(29 \, B a b^{3} - 9 \, A b^{4}\right)} d^{3} e^{2} + 6 \, {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} d^{2} e^{3} + 3 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d e^{4}\right)} x^{2} + {\left(8 \, B a b^{3} d^{4} e + 2 \, {\left(11 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} d^{3} e^{2} + 3 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) + {\left(24 \, A a^{4} e^{4} - 30 \, {\left(B a b^{3} + A b^{4}\right)} d^{4} - {\left(659 \, B a^{2} b^{2} - 255 \, A a b^{3}\right)} d^{3} e - 16 \, {\left(17 \, B a^{3} b - 54 \, A a^{2} b^{2}\right)} d^{2} e^{2} + 8 \, {\left(2 \, B a^{4} - 21 \, A a^{3} b\right)} d e^{3} - 105 \, {\left(4 \, B b^{4} d e^{3} + {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} e^{4}\right)} x^{4} - 35 \, {\left(28 \, B b^{4} d^{2} e^{2} + {\left(55 \, B a b^{3} - 63 \, A b^{4}\right)} d e^{3} + 5 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} e^{4}\right)} x^{3} - 7 \, {\left(92 \, B b^{4} d^{3} e + 9 \, {\left(39 \, B a b^{3} - 23 \, A b^{4}\right)} d^{2} e^{2} + 3 \, {\left(109 \, B a^{2} b^{2} - 177 \, A a b^{3}\right)} d e^{3} + 8 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - {\left(60 \, B b^{4} d^{4} + {\left(1183 \, B a b^{3} - 135 \, A b^{4}\right)} d^{3} e + 3 \, {\left(643 \, B a^{2} b^{2} - 831 \, A a b^{3}\right)} d^{2} e^{2} + 72 \, {\left(9 \, B a^{3} b - 17 \, A a^{2} b^{2}\right)} d e^{3} - 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{60 \, {\left(a^{2} b^{5} d^{8} - 5 \, a^{3} b^{4} d^{7} e + 10 \, a^{4} b^{3} d^{6} e^{2} - 10 \, a^{5} b^{2} d^{5} e^{3} + 5 \, a^{6} b d^{4} e^{4} - a^{7} d^{3} e^{5} + {\left(b^{7} d^{5} e^{3} - 5 \, a b^{6} d^{4} e^{4} + 10 \, a^{2} b^{5} d^{3} e^{5} - 10 \, a^{3} b^{4} d^{2} e^{6} + 5 \, a^{4} b^{3} d e^{7} - a^{5} b^{2} e^{8}\right)} x^{5} + {\left(3 \, b^{7} d^{6} e^{2} - 13 \, a b^{6} d^{5} e^{3} + 20 \, a^{2} b^{5} d^{4} e^{4} - 10 \, a^{3} b^{4} d^{3} e^{5} - 5 \, a^{4} b^{3} d^{2} e^{6} + 7 \, a^{5} b^{2} d e^{7} - 2 \, a^{6} b e^{8}\right)} x^{4} + {\left(3 \, b^{7} d^{7} e - 9 \, a b^{6} d^{6} e^{2} + a^{2} b^{5} d^{5} e^{3} + 25 \, a^{3} b^{4} d^{4} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{5} + 17 \, a^{5} b^{2} d^{2} e^{6} - a^{6} b d e^{7} - a^{7} e^{8}\right)} x^{3} + {\left(b^{7} d^{8} + a b^{6} d^{7} e - 17 \, a^{2} b^{5} d^{6} e^{2} + 35 \, a^{3} b^{4} d^{5} e^{3} - 25 \, a^{4} b^{3} d^{4} e^{4} - a^{5} b^{2} d^{3} e^{5} + 9 \, a^{6} b d^{2} e^{6} - 3 \, a^{7} d e^{7}\right)} x^{2} + {\left(2 \, a b^{6} d^{8} - 7 \, a^{2} b^{5} d^{7} e + 5 \, a^{3} b^{4} d^{6} e^{2} + 10 \, a^{4} b^{3} d^{5} e^{3} - 20 \, a^{5} b^{2} d^{4} e^{4} + 13 \, a^{6} b d^{3} e^{5} - 3 \, a^{7} d^{2} e^{6}\right)} x\right)}}\right]"," ",0,"[1/120*(105*(4*B*a^2*b^2*d^4*e + (5*B*a^3*b - 9*A*a^2*b^2)*d^3*e^2 + (4*B*b^4*d*e^4 + (5*B*a*b^3 - 9*A*b^4)*e^5)*x^5 + (12*B*b^4*d^2*e^3 + (23*B*a*b^3 - 27*A*b^4)*d*e^4 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*e^5)*x^4 + (12*B*b^4*d^3*e^2 + 3*(13*B*a*b^3 - 9*A*b^4)*d^2*e^3 + 2*(17*B*a^2*b^2 - 27*A*a*b^3)*d*e^4 + (5*B*a^3*b - 9*A*a^2*b^2)*e^5)*x^3 + (4*B*b^4*d^4*e + (29*B*a*b^3 - 9*A*b^4)*d^3*e^2 + 6*(7*B*a^2*b^2 - 9*A*a*b^3)*d^2*e^3 + 3*(5*B*a^3*b - 9*A*a^2*b^2)*d*e^4)*x^2 + (8*B*a*b^3*d^4*e + 2*(11*B*a^2*b^2 - 9*A*a*b^3)*d^3*e^2 + 3*(5*B*a^3*b - 9*A*a^2*b^2)*d^2*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(24*A*a^4*e^4 - 30*(B*a*b^3 + A*b^4)*d^4 - (659*B*a^2*b^2 - 255*A*a*b^3)*d^3*e - 16*(17*B*a^3*b - 54*A*a^2*b^2)*d^2*e^2 + 8*(2*B*a^4 - 21*A*a^3*b)*d*e^3 - 105*(4*B*b^4*d*e^3 + (5*B*a*b^3 - 9*A*b^4)*e^4)*x^4 - 35*(28*B*b^4*d^2*e^2 + (55*B*a*b^3 - 63*A*b^4)*d*e^3 + 5*(5*B*a^2*b^2 - 9*A*a*b^3)*e^4)*x^3 - 7*(92*B*b^4*d^3*e + 9*(39*B*a*b^3 - 23*A*b^4)*d^2*e^2 + 3*(109*B*a^2*b^2 - 177*A*a*b^3)*d*e^3 + 8*(5*B*a^3*b - 9*A*a^2*b^2)*e^4)*x^2 - (60*B*b^4*d^4 + (1183*B*a*b^3 - 135*A*b^4)*d^3*e + 3*(643*B*a^2*b^2 - 831*A*a*b^3)*d^2*e^2 + 72*(9*B*a^3*b - 17*A*a^2*b^2)*d*e^3 - 8*(5*B*a^4 - 9*A*a^3*b)*e^4)*x)*sqrt(e*x + d))/(a^2*b^5*d^8 - 5*a^3*b^4*d^7*e + 10*a^4*b^3*d^6*e^2 - 10*a^5*b^2*d^5*e^3 + 5*a^6*b*d^4*e^4 - a^7*d^3*e^5 + (b^7*d^5*e^3 - 5*a*b^6*d^4*e^4 + 10*a^2*b^5*d^3*e^5 - 10*a^3*b^4*d^2*e^6 + 5*a^4*b^3*d*e^7 - a^5*b^2*e^8)*x^5 + (3*b^7*d^6*e^2 - 13*a*b^6*d^5*e^3 + 20*a^2*b^5*d^4*e^4 - 10*a^3*b^4*d^3*e^5 - 5*a^4*b^3*d^2*e^6 + 7*a^5*b^2*d*e^7 - 2*a^6*b*e^8)*x^4 + (3*b^7*d^7*e - 9*a*b^6*d^6*e^2 + a^2*b^5*d^5*e^3 + 25*a^3*b^4*d^4*e^4 - 35*a^4*b^3*d^3*e^5 + 17*a^5*b^2*d^2*e^6 - a^6*b*d*e^7 - a^7*e^8)*x^3 + (b^7*d^8 + a*b^6*d^7*e - 17*a^2*b^5*d^6*e^2 + 35*a^3*b^4*d^5*e^3 - 25*a^4*b^3*d^4*e^4 - a^5*b^2*d^3*e^5 + 9*a^6*b*d^2*e^6 - 3*a^7*d*e^7)*x^2 + (2*a*b^6*d^8 - 7*a^2*b^5*d^7*e + 5*a^3*b^4*d^6*e^2 + 10*a^4*b^3*d^5*e^3 - 20*a^5*b^2*d^4*e^4 + 13*a^6*b*d^3*e^5 - 3*a^7*d^2*e^6)*x), 1/60*(105*(4*B*a^2*b^2*d^4*e + (5*B*a^3*b - 9*A*a^2*b^2)*d^3*e^2 + (4*B*b^4*d*e^4 + (5*B*a*b^3 - 9*A*b^4)*e^5)*x^5 + (12*B*b^4*d^2*e^3 + (23*B*a*b^3 - 27*A*b^4)*d*e^4 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*e^5)*x^4 + (12*B*b^4*d^3*e^2 + 3*(13*B*a*b^3 - 9*A*b^4)*d^2*e^3 + 2*(17*B*a^2*b^2 - 27*A*a*b^3)*d*e^4 + (5*B*a^3*b - 9*A*a^2*b^2)*e^5)*x^3 + (4*B*b^4*d^4*e + (29*B*a*b^3 - 9*A*b^4)*d^3*e^2 + 6*(7*B*a^2*b^2 - 9*A*a*b^3)*d^2*e^3 + 3*(5*B*a^3*b - 9*A*a^2*b^2)*d*e^4)*x^2 + (8*B*a*b^3*d^4*e + 2*(11*B*a^2*b^2 - 9*A*a*b^3)*d^3*e^2 + 3*(5*B*a^3*b - 9*A*a^2*b^2)*d^2*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) + (24*A*a^4*e^4 - 30*(B*a*b^3 + A*b^4)*d^4 - (659*B*a^2*b^2 - 255*A*a*b^3)*d^3*e - 16*(17*B*a^3*b - 54*A*a^2*b^2)*d^2*e^2 + 8*(2*B*a^4 - 21*A*a^3*b)*d*e^3 - 105*(4*B*b^4*d*e^3 + (5*B*a*b^3 - 9*A*b^4)*e^4)*x^4 - 35*(28*B*b^4*d^2*e^2 + (55*B*a*b^3 - 63*A*b^4)*d*e^3 + 5*(5*B*a^2*b^2 - 9*A*a*b^3)*e^4)*x^3 - 7*(92*B*b^4*d^3*e + 9*(39*B*a*b^3 - 23*A*b^4)*d^2*e^2 + 3*(109*B*a^2*b^2 - 177*A*a*b^3)*d*e^3 + 8*(5*B*a^3*b - 9*A*a^2*b^2)*e^4)*x^2 - (60*B*b^4*d^4 + (1183*B*a*b^3 - 135*A*b^4)*d^3*e + 3*(643*B*a^2*b^2 - 831*A*a*b^3)*d^2*e^2 + 72*(9*B*a^3*b - 17*A*a^2*b^2)*d*e^3 - 8*(5*B*a^4 - 9*A*a^3*b)*e^4)*x)*sqrt(e*x + d))/(a^2*b^5*d^8 - 5*a^3*b^4*d^7*e + 10*a^4*b^3*d^6*e^2 - 10*a^5*b^2*d^5*e^3 + 5*a^6*b*d^4*e^4 - a^7*d^3*e^5 + (b^7*d^5*e^3 - 5*a*b^6*d^4*e^4 + 10*a^2*b^5*d^3*e^5 - 10*a^3*b^4*d^2*e^6 + 5*a^4*b^3*d*e^7 - a^5*b^2*e^8)*x^5 + (3*b^7*d^6*e^2 - 13*a*b^6*d^5*e^3 + 20*a^2*b^5*d^4*e^4 - 10*a^3*b^4*d^3*e^5 - 5*a^4*b^3*d^2*e^6 + 7*a^5*b^2*d*e^7 - 2*a^6*b*e^8)*x^4 + (3*b^7*d^7*e - 9*a*b^6*d^6*e^2 + a^2*b^5*d^5*e^3 + 25*a^3*b^4*d^4*e^4 - 35*a^4*b^3*d^3*e^5 + 17*a^5*b^2*d^2*e^6 - a^6*b*d*e^7 - a^7*e^8)*x^3 + (b^7*d^8 + a*b^6*d^7*e - 17*a^2*b^5*d^6*e^2 + 35*a^3*b^4*d^5*e^3 - 25*a^4*b^3*d^4*e^4 - a^5*b^2*d^3*e^5 + 9*a^6*b*d^2*e^6 - 3*a^7*d*e^7)*x^2 + (2*a*b^6*d^8 - 7*a^2*b^5*d^7*e + 5*a^3*b^4*d^6*e^2 + 10*a^4*b^3*d^5*e^3 - 20*a^5*b^2*d^4*e^4 + 13*a^6*b*d^3*e^5 - 3*a^7*d^2*e^6)*x)]","B",0
1874,1,2006,0,0.473192," ","integrate((B*x+A)*(e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(8 \, B a^{4} b^{2} d^{2} e^{3} - {\left(21 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} d e^{4} + {\left(13 \, B a^{6} - 5 \, A a^{5} b\right)} e^{5} + {\left(8 \, B b^{6} d^{2} e^{3} - {\left(21 \, B a b^{5} - 5 \, A b^{6}\right)} d e^{4} + {\left(13 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 4 \, {\left(8 \, B a b^{5} d^{2} e^{3} - {\left(21 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} d e^{4} + {\left(13 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{4} d^{2} e^{3} - {\left(21 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} d e^{4} + {\left(13 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{3} d^{2} e^{3} - {\left(21 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} d e^{4} + {\left(13 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(384 \, B b^{6} e^{5} x^{6} - 80 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{5} - 440 \, {\left(B a^{2} b^{4} + A a b^{5}\right)} d^{4} e - 990 \, {\left(3 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} d^{3} e^{2} + 231 \, {\left(199 \, B a^{4} b^{2} - 15 \, A a^{3} b^{3}\right)} d^{2} e^{3} - 4620 \, {\left(19 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} d e^{4} + 3465 \, {\left(13 \, B a^{6} - 5 \, A a^{5} b\right)} e^{5} + 128 \, {\left(26 \, B b^{6} d e^{4} - {\left(13 \, B a b^{5} - 5 \, A b^{6}\right)} e^{5}\right)} x^{5} + 128 \, {\left(173 \, B b^{6} d^{2} e^{3} - 8 \, {\left(37 \, B a b^{5} - 10 \, A b^{6}\right)} d e^{4} + 11 \, {\left(13 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} e^{5}\right)} x^{4} - {\left(10680 \, B b^{6} d^{3} e^{2} - {\left(132091 \, B a b^{5} - 11475 \, A b^{6}\right)} d^{2} e^{3} + 22 \, {\left(10901 \, B a^{2} b^{4} - 2905 \, A a b^{5}\right)} d e^{4} - 9207 \, {\left(13 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} - {\left(2480 \, B b^{6} d^{4} e + 10 \, {\left(1697 \, B a b^{5} + 515 \, A b^{6}\right)} d^{3} e^{2} - 33 \, {\left(7063 \, B a^{2} b^{4} - 575 \, A a b^{5}\right)} d^{2} e^{3} + 264 \, {\left(1642 \, B a^{3} b^{3} - 435 \, A a^{2} b^{4}\right)} d e^{4} - 16863 \, {\left(13 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} - {\left(320 \, B b^{6} d^{5} + 40 \, {\left(43 \, B a b^{5} + 41 \, A b^{6}\right)} d^{4} e + 220 \, {\left(53 \, B a^{2} b^{4} + 17 \, A a b^{5}\right)} d^{3} e^{2} - 33 \, {\left(5197 \, B a^{3} b^{3} - 405 \, A a^{2} b^{4}\right)} d^{2} e^{3} + 462 \, {\left(701 \, B a^{4} b^{2} - 185 \, A a^{3} b^{3}\right)} d e^{4} - 12705 \, {\left(13 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(b^{11} x^{4} + 4 \, a b^{10} x^{3} + 6 \, a^{2} b^{9} x^{2} + 4 \, a^{3} b^{8} x + a^{4} b^{7}\right)}}, -\frac{3465 \, {\left(8 \, B a^{4} b^{2} d^{2} e^{3} - {\left(21 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} d e^{4} + {\left(13 \, B a^{6} - 5 \, A a^{5} b\right)} e^{5} + {\left(8 \, B b^{6} d^{2} e^{3} - {\left(21 \, B a b^{5} - 5 \, A b^{6}\right)} d e^{4} + {\left(13 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 4 \, {\left(8 \, B a b^{5} d^{2} e^{3} - {\left(21 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} d e^{4} + {\left(13 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{4} d^{2} e^{3} - {\left(21 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} d e^{4} + {\left(13 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{3} d^{2} e^{3} - {\left(21 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} d e^{4} + {\left(13 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(384 \, B b^{6} e^{5} x^{6} - 80 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{5} - 440 \, {\left(B a^{2} b^{4} + A a b^{5}\right)} d^{4} e - 990 \, {\left(3 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} d^{3} e^{2} + 231 \, {\left(199 \, B a^{4} b^{2} - 15 \, A a^{3} b^{3}\right)} d^{2} e^{3} - 4620 \, {\left(19 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} d e^{4} + 3465 \, {\left(13 \, B a^{6} - 5 \, A a^{5} b\right)} e^{5} + 128 \, {\left(26 \, B b^{6} d e^{4} - {\left(13 \, B a b^{5} - 5 \, A b^{6}\right)} e^{5}\right)} x^{5} + 128 \, {\left(173 \, B b^{6} d^{2} e^{3} - 8 \, {\left(37 \, B a b^{5} - 10 \, A b^{6}\right)} d e^{4} + 11 \, {\left(13 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} e^{5}\right)} x^{4} - {\left(10680 \, B b^{6} d^{3} e^{2} - {\left(132091 \, B a b^{5} - 11475 \, A b^{6}\right)} d^{2} e^{3} + 22 \, {\left(10901 \, B a^{2} b^{4} - 2905 \, A a b^{5}\right)} d e^{4} - 9207 \, {\left(13 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} - {\left(2480 \, B b^{6} d^{4} e + 10 \, {\left(1697 \, B a b^{5} + 515 \, A b^{6}\right)} d^{3} e^{2} - 33 \, {\left(7063 \, B a^{2} b^{4} - 575 \, A a b^{5}\right)} d^{2} e^{3} + 264 \, {\left(1642 \, B a^{3} b^{3} - 435 \, A a^{2} b^{4}\right)} d e^{4} - 16863 \, {\left(13 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} - {\left(320 \, B b^{6} d^{5} + 40 \, {\left(43 \, B a b^{5} + 41 \, A b^{6}\right)} d^{4} e + 220 \, {\left(53 \, B a^{2} b^{4} + 17 \, A a b^{5}\right)} d^{3} e^{2} - 33 \, {\left(5197 \, B a^{3} b^{3} - 405 \, A a^{2} b^{4}\right)} d^{2} e^{3} + 462 \, {\left(701 \, B a^{4} b^{2} - 185 \, A a^{3} b^{3}\right)} d e^{4} - 12705 \, {\left(13 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{960 \, {\left(b^{11} x^{4} + 4 \, a b^{10} x^{3} + 6 \, a^{2} b^{9} x^{2} + 4 \, a^{3} b^{8} x + a^{4} b^{7}\right)}}\right]"," ",0,"[1/1920*(3465*(8*B*a^4*b^2*d^2*e^3 - (21*B*a^5*b - 5*A*a^4*b^2)*d*e^4 + (13*B*a^6 - 5*A*a^5*b)*e^5 + (8*B*b^6*d^2*e^3 - (21*B*a*b^5 - 5*A*b^6)*d*e^4 + (13*B*a^2*b^4 - 5*A*a*b^5)*e^5)*x^4 + 4*(8*B*a*b^5*d^2*e^3 - (21*B*a^2*b^4 - 5*A*a*b^5)*d*e^4 + (13*B*a^3*b^3 - 5*A*a^2*b^4)*e^5)*x^3 + 6*(8*B*a^2*b^4*d^2*e^3 - (21*B*a^3*b^3 - 5*A*a^2*b^4)*d*e^4 + (13*B*a^4*b^2 - 5*A*a^3*b^3)*e^5)*x^2 + 4*(8*B*a^3*b^3*d^2*e^3 - (21*B*a^4*b^2 - 5*A*a^3*b^3)*d*e^4 + (13*B*a^5*b - 5*A*a^4*b^2)*e^5)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(384*B*b^6*e^5*x^6 - 80*(B*a*b^5 + 3*A*b^6)*d^5 - 440*(B*a^2*b^4 + A*a*b^5)*d^4*e - 990*(3*B*a^3*b^3 + A*a^2*b^4)*d^3*e^2 + 231*(199*B*a^4*b^2 - 15*A*a^3*b^3)*d^2*e^3 - 4620*(19*B*a^5*b - 5*A*a^4*b^2)*d*e^4 + 3465*(13*B*a^6 - 5*A*a^5*b)*e^5 + 128*(26*B*b^6*d*e^4 - (13*B*a*b^5 - 5*A*b^6)*e^5)*x^5 + 128*(173*B*b^6*d^2*e^3 - 8*(37*B*a*b^5 - 10*A*b^6)*d*e^4 + 11*(13*B*a^2*b^4 - 5*A*a*b^5)*e^5)*x^4 - (10680*B*b^6*d^3*e^2 - (132091*B*a*b^5 - 11475*A*b^6)*d^2*e^3 + 22*(10901*B*a^2*b^4 - 2905*A*a*b^5)*d*e^4 - 9207*(13*B*a^3*b^3 - 5*A*a^2*b^4)*e^5)*x^3 - (2480*B*b^6*d^4*e + 10*(1697*B*a*b^5 + 515*A*b^6)*d^3*e^2 - 33*(7063*B*a^2*b^4 - 575*A*a*b^5)*d^2*e^3 + 264*(1642*B*a^3*b^3 - 435*A*a^2*b^4)*d*e^4 - 16863*(13*B*a^4*b^2 - 5*A*a^3*b^3)*e^5)*x^2 - (320*B*b^6*d^5 + 40*(43*B*a*b^5 + 41*A*b^6)*d^4*e + 220*(53*B*a^2*b^4 + 17*A*a*b^5)*d^3*e^2 - 33*(5197*B*a^3*b^3 - 405*A*a^2*b^4)*d^2*e^3 + 462*(701*B*a^4*b^2 - 185*A*a^3*b^3)*d*e^4 - 12705*(13*B*a^5*b - 5*A*a^4*b^2)*e^5)*x)*sqrt(e*x + d))/(b^11*x^4 + 4*a*b^10*x^3 + 6*a^2*b^9*x^2 + 4*a^3*b^8*x + a^4*b^7), -1/960*(3465*(8*B*a^4*b^2*d^2*e^3 - (21*B*a^5*b - 5*A*a^4*b^2)*d*e^4 + (13*B*a^6 - 5*A*a^5*b)*e^5 + (8*B*b^6*d^2*e^3 - (21*B*a*b^5 - 5*A*b^6)*d*e^4 + (13*B*a^2*b^4 - 5*A*a*b^5)*e^5)*x^4 + 4*(8*B*a*b^5*d^2*e^3 - (21*B*a^2*b^4 - 5*A*a*b^5)*d*e^4 + (13*B*a^3*b^3 - 5*A*a^2*b^4)*e^5)*x^3 + 6*(8*B*a^2*b^4*d^2*e^3 - (21*B*a^3*b^3 - 5*A*a^2*b^4)*d*e^4 + (13*B*a^4*b^2 - 5*A*a^3*b^3)*e^5)*x^2 + 4*(8*B*a^3*b^3*d^2*e^3 - (21*B*a^4*b^2 - 5*A*a^3*b^3)*d*e^4 + (13*B*a^5*b - 5*A*a^4*b^2)*e^5)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (384*B*b^6*e^5*x^6 - 80*(B*a*b^5 + 3*A*b^6)*d^5 - 440*(B*a^2*b^4 + A*a*b^5)*d^4*e - 990*(3*B*a^3*b^3 + A*a^2*b^4)*d^3*e^2 + 231*(199*B*a^4*b^2 - 15*A*a^3*b^3)*d^2*e^3 - 4620*(19*B*a^5*b - 5*A*a^4*b^2)*d*e^4 + 3465*(13*B*a^6 - 5*A*a^5*b)*e^5 + 128*(26*B*b^6*d*e^4 - (13*B*a*b^5 - 5*A*b^6)*e^5)*x^5 + 128*(173*B*b^6*d^2*e^3 - 8*(37*B*a*b^5 - 10*A*b^6)*d*e^4 + 11*(13*B*a^2*b^4 - 5*A*a*b^5)*e^5)*x^4 - (10680*B*b^6*d^3*e^2 - (132091*B*a*b^5 - 11475*A*b^6)*d^2*e^3 + 22*(10901*B*a^2*b^4 - 2905*A*a*b^5)*d*e^4 - 9207*(13*B*a^3*b^3 - 5*A*a^2*b^4)*e^5)*x^3 - (2480*B*b^6*d^4*e + 10*(1697*B*a*b^5 + 515*A*b^6)*d^3*e^2 - 33*(7063*B*a^2*b^4 - 575*A*a*b^5)*d^2*e^3 + 264*(1642*B*a^3*b^3 - 435*A*a^2*b^4)*d*e^4 - 16863*(13*B*a^4*b^2 - 5*A*a^3*b^3)*e^5)*x^2 - (320*B*b^6*d^5 + 40*(43*B*a*b^5 + 41*A*b^6)*d^4*e + 220*(53*B*a^2*b^4 + 17*A*a*b^5)*d^3*e^2 - 33*(5197*B*a^3*b^3 - 405*A*a^2*b^4)*d^2*e^3 + 462*(701*B*a^4*b^2 - 185*A*a^3*b^3)*d*e^4 - 12705*(13*B*a^5*b - 5*A*a^4*b^2)*e^5)*x)*sqrt(e*x + d))/(b^11*x^4 + 4*a*b^10*x^3 + 6*a^2*b^9*x^2 + 4*a^3*b^8*x + a^4*b^7)]","B",0
1875,1,1414,0,0.455184," ","integrate((B*x+A)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(8 \, B a^{4} b d e^{3} - {\left(11 \, B a^{5} - 3 \, A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(11 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(11 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(11 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(128 \, B b^{5} e^{4} x^{5} - 16 \, {\left(B a b^{4} + 3 \, A b^{5}\right)} d^{4} - 72 \, {\left(B a^{2} b^{3} + A a b^{4}\right)} d^{3} e - 126 \, {\left(3 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{2} + 105 \, {\left(35 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} d e^{3} - 315 \, {\left(11 \, B a^{5} - 3 \, A a^{4} b\right)} e^{4} + 128 \, {\left(13 \, B b^{5} d e^{3} - {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} e^{4}\right)} x^{4} - {\left(1320 \, B b^{5} d^{2} e^{2} - {\left(10271 \, B a b^{4} - 975 \, A b^{5}\right)} d e^{3} + 837 \, {\left(11 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} e^{4}\right)} x^{3} - {\left(400 \, B b^{5} d^{3} e + 30 \, {\left(71 \, B a b^{4} + 21 \, A b^{5}\right)} d^{2} e^{2} - 9 \, {\left(2041 \, B a^{2} b^{3} - 185 \, A a b^{4}\right)} d e^{3} + 1533 \, {\left(11 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - {\left(64 \, B b^{5} d^{4} + 8 \, {\left(35 \, B a b^{4} + 33 \, A b^{5}\right)} d^{3} e + 36 \, {\left(41 \, B a^{2} b^{3} + 13 \, A a b^{4}\right)} d^{2} e^{2} - 21 \, {\left(649 \, B a^{3} b^{2} - 57 \, A a^{2} b^{3}\right)} d e^{3} + 1155 \, {\left(11 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}, -\frac{315 \, {\left(8 \, B a^{4} b d e^{3} - {\left(11 \, B a^{5} - 3 \, A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(11 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(11 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(11 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(128 \, B b^{5} e^{4} x^{5} - 16 \, {\left(B a b^{4} + 3 \, A b^{5}\right)} d^{4} - 72 \, {\left(B a^{2} b^{3} + A a b^{4}\right)} d^{3} e - 126 \, {\left(3 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{2} + 105 \, {\left(35 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} d e^{3} - 315 \, {\left(11 \, B a^{5} - 3 \, A a^{4} b\right)} e^{4} + 128 \, {\left(13 \, B b^{5} d e^{3} - {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} e^{4}\right)} x^{4} - {\left(1320 \, B b^{5} d^{2} e^{2} - {\left(10271 \, B a b^{4} - 975 \, A b^{5}\right)} d e^{3} + 837 \, {\left(11 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} e^{4}\right)} x^{3} - {\left(400 \, B b^{5} d^{3} e + 30 \, {\left(71 \, B a b^{4} + 21 \, A b^{5}\right)} d^{2} e^{2} - 9 \, {\left(2041 \, B a^{2} b^{3} - 185 \, A a b^{4}\right)} d e^{3} + 1533 \, {\left(11 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - {\left(64 \, B b^{5} d^{4} + 8 \, {\left(35 \, B a b^{4} + 33 \, A b^{5}\right)} d^{3} e + 36 \, {\left(41 \, B a^{2} b^{3} + 13 \, A a b^{4}\right)} d^{2} e^{2} - 21 \, {\left(649 \, B a^{3} b^{2} - 57 \, A a^{2} b^{3}\right)} d e^{3} + 1155 \, {\left(11 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}\right]"," ",0,"[-1/384*(315*(8*B*a^4*b*d*e^3 - (11*B*a^5 - 3*A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (11*B*a*b^4 - 3*A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (11*B*a^2*b^3 - 3*A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (11*B*a^3*b^2 - 3*A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (11*B*a^4*b - 3*A*a^3*b^2)*e^4)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(128*B*b^5*e^4*x^5 - 16*(B*a*b^4 + 3*A*b^5)*d^4 - 72*(B*a^2*b^3 + A*a*b^4)*d^3*e - 126*(3*B*a^3*b^2 + A*a^2*b^3)*d^2*e^2 + 105*(35*B*a^4*b - 3*A*a^3*b^2)*d*e^3 - 315*(11*B*a^5 - 3*A*a^4*b)*e^4 + 128*(13*B*b^5*d*e^3 - (11*B*a*b^4 - 3*A*b^5)*e^4)*x^4 - (1320*B*b^5*d^2*e^2 - (10271*B*a*b^4 - 975*A*b^5)*d*e^3 + 837*(11*B*a^2*b^3 - 3*A*a*b^4)*e^4)*x^3 - (400*B*b^5*d^3*e + 30*(71*B*a*b^4 + 21*A*b^5)*d^2*e^2 - 9*(2041*B*a^2*b^3 - 185*A*a*b^4)*d*e^3 + 1533*(11*B*a^3*b^2 - 3*A*a^2*b^3)*e^4)*x^2 - (64*B*b^5*d^4 + 8*(35*B*a*b^4 + 33*A*b^5)*d^3*e + 36*(41*B*a^2*b^3 + 13*A*a*b^4)*d^2*e^2 - 21*(649*B*a^3*b^2 - 57*A*a^2*b^3)*d*e^3 + 1155*(11*B*a^4*b - 3*A*a^3*b^2)*e^4)*x)*sqrt(e*x + d))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6), -1/192*(315*(8*B*a^4*b*d*e^3 - (11*B*a^5 - 3*A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (11*B*a*b^4 - 3*A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (11*B*a^2*b^3 - 3*A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (11*B*a^3*b^2 - 3*A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (11*B*a^4*b - 3*A*a^3*b^2)*e^4)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (128*B*b^5*e^4*x^5 - 16*(B*a*b^4 + 3*A*b^5)*d^4 - 72*(B*a^2*b^3 + A*a*b^4)*d^3*e - 126*(3*B*a^3*b^2 + A*a^2*b^3)*d^2*e^2 + 105*(35*B*a^4*b - 3*A*a^3*b^2)*d*e^3 - 315*(11*B*a^5 - 3*A*a^4*b)*e^4 + 128*(13*B*b^5*d*e^3 - (11*B*a*b^4 - 3*A*b^5)*e^4)*x^4 - (1320*B*b^5*d^2*e^2 - (10271*B*a*b^4 - 975*A*b^5)*d*e^3 + 837*(11*B*a^2*b^3 - 3*A*a*b^4)*e^4)*x^3 - (400*B*b^5*d^3*e + 30*(71*B*a*b^4 + 21*A*b^5)*d^2*e^2 - 9*(2041*B*a^2*b^3 - 185*A*a*b^4)*d*e^3 + 1533*(11*B*a^3*b^2 - 3*A*a^2*b^3)*e^4)*x^2 - (64*B*b^5*d^4 + 8*(35*B*a*b^4 + 33*A*b^5)*d^3*e + 36*(41*B*a^2*b^3 + 13*A*a*b^4)*d^2*e^2 - 21*(649*B*a^3*b^2 - 57*A*a^2*b^3)*d*e^3 + 1155*(11*B*a^4*b - 3*A*a^3*b^2)*e^4)*x)*sqrt(e*x + d))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6)]","A",0
1876,1,1485,0,0.471896," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(8 \, B a^{4} b d e^{3} - {\left(9 \, B a^{5} - A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(9 \, B a b^{4} - A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(9 \, B a^{2} b^{3} - A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(9 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(9 \, B a^{4} b - A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} + 8 \, {\left(5 \, B a^{2} b^{4} + A a b^{5}\right)} d^{3} e + 14 \, {\left(11 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} d^{2} e^{2} - 35 \, {\left(33 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} d e^{3} + 105 \, {\left(9 \, B a^{5} b - A a^{4} b^{2}\right)} e^{4} - 384 \, {\left(B b^{6} d e^{3} - B a b^{5} e^{4}\right)} x^{4} + 3 \, {\left(232 \, B b^{6} d^{2} e^{2} - {\left(1069 \, B a b^{5} - 93 \, A b^{6}\right)} d e^{3} + 93 \, {\left(9 \, B a^{2} b^{4} - A a b^{5}\right)} e^{4}\right)} x^{3} + {\left(304 \, B b^{6} d^{3} e + 2 \, {\left(425 \, B a b^{5} + 163 \, A b^{6}\right)} d^{2} e^{2} - {\left(5753 \, B a^{2} b^{4} - 185 \, A a b^{5}\right)} d e^{3} + 511 \, {\left(9 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} + 8 \, {\left(19 \, B a b^{5} + 25 \, A b^{6}\right)} d^{3} e + 4 \, {\left(149 \, B a^{2} b^{4} + 13 \, A a b^{5}\right)} d^{2} e^{2} - 7 \, {\left(611 \, B a^{3} b^{3} - 19 \, A a^{2} b^{4}\right)} d e^{3} + 385 \, {\left(9 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{7} d - a^{5} b^{6} e + {\left(b^{11} d - a b^{10} e\right)} x^{4} + 4 \, {\left(a b^{10} d - a^{2} b^{9} e\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d - a^{3} b^{8} e\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d - a^{4} b^{7} e\right)} x\right)}}, \frac{105 \, {\left(8 \, B a^{4} b d e^{3} - {\left(9 \, B a^{5} - A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(9 \, B a b^{4} - A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(9 \, B a^{2} b^{3} - A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(9 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(9 \, B a^{4} b - A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} + 8 \, {\left(5 \, B a^{2} b^{4} + A a b^{5}\right)} d^{3} e + 14 \, {\left(11 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} d^{2} e^{2} - 35 \, {\left(33 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} d e^{3} + 105 \, {\left(9 \, B a^{5} b - A a^{4} b^{2}\right)} e^{4} - 384 \, {\left(B b^{6} d e^{3} - B a b^{5} e^{4}\right)} x^{4} + 3 \, {\left(232 \, B b^{6} d^{2} e^{2} - {\left(1069 \, B a b^{5} - 93 \, A b^{6}\right)} d e^{3} + 93 \, {\left(9 \, B a^{2} b^{4} - A a b^{5}\right)} e^{4}\right)} x^{3} + {\left(304 \, B b^{6} d^{3} e + 2 \, {\left(425 \, B a b^{5} + 163 \, A b^{6}\right)} d^{2} e^{2} - {\left(5753 \, B a^{2} b^{4} - 185 \, A a b^{5}\right)} d e^{3} + 511 \, {\left(9 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} + 8 \, {\left(19 \, B a b^{5} + 25 \, A b^{6}\right)} d^{3} e + 4 \, {\left(149 \, B a^{2} b^{4} + 13 \, A a b^{5}\right)} d^{2} e^{2} - 7 \, {\left(611 \, B a^{3} b^{3} - 19 \, A a^{2} b^{4}\right)} d e^{3} + 385 \, {\left(9 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{7} d - a^{5} b^{6} e + {\left(b^{11} d - a b^{10} e\right)} x^{4} + 4 \, {\left(a b^{10} d - a^{2} b^{9} e\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d - a^{3} b^{8} e\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d - a^{4} b^{7} e\right)} x\right)}}\right]"," ",0,"[1/384*(105*(8*B*a^4*b*d*e^3 - (9*B*a^5 - A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (9*B*a*b^4 - A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (9*B*a^2*b^3 - A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (9*B*a^3*b^2 - A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (9*B*a^4*b - A*a^3*b^2)*e^4)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(16*(B*a*b^5 + 3*A*b^6)*d^4 + 8*(5*B*a^2*b^4 + A*a*b^5)*d^3*e + 14*(11*B*a^3*b^3 + A*a^2*b^4)*d^2*e^2 - 35*(33*B*a^4*b^2 - A*a^3*b^3)*d*e^3 + 105*(9*B*a^5*b - A*a^4*b^2)*e^4 - 384*(B*b^6*d*e^3 - B*a*b^5*e^4)*x^4 + 3*(232*B*b^6*d^2*e^2 - (1069*B*a*b^5 - 93*A*b^6)*d*e^3 + 93*(9*B*a^2*b^4 - A*a*b^5)*e^4)*x^3 + (304*B*b^6*d^3*e + 2*(425*B*a*b^5 + 163*A*b^6)*d^2*e^2 - (5753*B*a^2*b^4 - 185*A*a*b^5)*d*e^3 + 511*(9*B*a^3*b^3 - A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 + 8*(19*B*a*b^5 + 25*A*b^6)*d^3*e + 4*(149*B*a^2*b^4 + 13*A*a*b^5)*d^2*e^2 - 7*(611*B*a^3*b^3 - 19*A*a^2*b^4)*d*e^3 + 385*(9*B*a^4*b^2 - A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d - a^5*b^6*e + (b^11*d - a*b^10*e)*x^4 + 4*(a*b^10*d - a^2*b^9*e)*x^3 + 6*(a^2*b^9*d - a^3*b^8*e)*x^2 + 4*(a^3*b^8*d - a^4*b^7*e)*x), 1/192*(105*(8*B*a^4*b*d*e^3 - (9*B*a^5 - A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (9*B*a*b^4 - A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (9*B*a^2*b^3 - A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (9*B*a^3*b^2 - A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (9*B*a^4*b - A*a^3*b^2)*e^4)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (16*(B*a*b^5 + 3*A*b^6)*d^4 + 8*(5*B*a^2*b^4 + A*a*b^5)*d^3*e + 14*(11*B*a^3*b^3 + A*a^2*b^4)*d^2*e^2 - 35*(33*B*a^4*b^2 - A*a^3*b^3)*d*e^3 + 105*(9*B*a^5*b - A*a^4*b^2)*e^4 - 384*(B*b^6*d*e^3 - B*a*b^5*e^4)*x^4 + 3*(232*B*b^6*d^2*e^2 - (1069*B*a*b^5 - 93*A*b^6)*d*e^3 + 93*(9*B*a^2*b^4 - A*a*b^5)*e^4)*x^3 + (304*B*b^6*d^3*e + 2*(425*B*a*b^5 + 163*A*b^6)*d^2*e^2 - (5753*B*a^2*b^4 - 185*A*a*b^5)*d*e^3 + 511*(9*B*a^3*b^3 - A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 + 8*(19*B*a*b^5 + 25*A*b^6)*d^3*e + 4*(149*B*a^2*b^4 + 13*A*a*b^5)*d^2*e^2 - 7*(611*B*a^3*b^3 - 19*A*a^2*b^4)*d*e^3 + 385*(9*B*a^4*b^2 - A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d - a^5*b^6*e + (b^11*d - a*b^10*e)*x^4 + 4*(a*b^10*d - a^2*b^9*e)*x^3 + 6*(a^2*b^9*d - a^3*b^8*e)*x^2 + 4*(a^3*b^8*d - a^4*b^7*e)*x)]","B",0
1877,1,1547,0,0.480603," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(8 \, B a^{4} b d e^{3} - {\left(7 \, B a^{5} + A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(7 \, B a b^{4} + A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(7 \, B a^{2} b^{3} + A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(7 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(7 \, B a^{4} b + A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} + 8 \, {\left(B a^{2} b^{4} - 7 \, A a b^{5}\right)} d^{3} e + 2 \, {\left(13 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} d^{2} e^{2} - 5 \, {\left(31 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} d e^{3} + 15 \, {\left(7 \, B a^{5} b + A a^{4} b^{2}\right)} e^{4} + 3 \, {\left(88 \, B b^{6} d^{2} e^{2} - {\left(181 \, B a b^{5} - 5 \, A b^{6}\right)} d e^{3} + {\left(93 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} e^{4}\right)} x^{3} + {\left(208 \, B b^{6} d^{3} e + 2 \, {\left(25 \, B a b^{5} + 59 \, A b^{6}\right)} d^{2} e^{2} - {\left(769 \, B a^{2} b^{4} + 191 \, A a b^{5}\right)} d e^{3} + 73 \, {\left(7 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} + 8 \, {\left(3 \, B a b^{5} + 17 \, A b^{6}\right)} d^{3} e + 4 \, {\left(25 \, B a^{2} b^{4} - 43 \, A a b^{5}\right)} d^{2} e^{2} - {\left(573 \, B a^{3} b^{3} + 19 \, A a^{2} b^{4}\right)} d e^{3} + 55 \, {\left(7 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{7} d^{2} - 2 \, a^{5} b^{6} d e + a^{6} b^{5} e^{2} + {\left(b^{11} d^{2} - 2 \, a b^{10} d e + a^{2} b^{9} e^{2}\right)} x^{4} + 4 \, {\left(a b^{10} d^{2} - 2 \, a^{2} b^{9} d e + a^{3} b^{8} e^{2}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d^{2} - 2 \, a^{3} b^{8} d e + a^{4} b^{7} e^{2}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d^{2} - 2 \, a^{4} b^{7} d e + a^{5} b^{6} e^{2}\right)} x\right)}}, \frac{15 \, {\left(8 \, B a^{4} b d e^{3} - {\left(7 \, B a^{5} + A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(7 \, B a b^{4} + A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(7 \, B a^{2} b^{3} + A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(7 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(7 \, B a^{4} b + A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} + 8 \, {\left(B a^{2} b^{4} - 7 \, A a b^{5}\right)} d^{3} e + 2 \, {\left(13 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} d^{2} e^{2} - 5 \, {\left(31 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} d e^{3} + 15 \, {\left(7 \, B a^{5} b + A a^{4} b^{2}\right)} e^{4} + 3 \, {\left(88 \, B b^{6} d^{2} e^{2} - {\left(181 \, B a b^{5} - 5 \, A b^{6}\right)} d e^{3} + {\left(93 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} e^{4}\right)} x^{3} + {\left(208 \, B b^{6} d^{3} e + 2 \, {\left(25 \, B a b^{5} + 59 \, A b^{6}\right)} d^{2} e^{2} - {\left(769 \, B a^{2} b^{4} + 191 \, A a b^{5}\right)} d e^{3} + 73 \, {\left(7 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} + 8 \, {\left(3 \, B a b^{5} + 17 \, A b^{6}\right)} d^{3} e + 4 \, {\left(25 \, B a^{2} b^{4} - 43 \, A a b^{5}\right)} d^{2} e^{2} - {\left(573 \, B a^{3} b^{3} + 19 \, A a^{2} b^{4}\right)} d e^{3} + 55 \, {\left(7 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{7} d^{2} - 2 \, a^{5} b^{6} d e + a^{6} b^{5} e^{2} + {\left(b^{11} d^{2} - 2 \, a b^{10} d e + a^{2} b^{9} e^{2}\right)} x^{4} + 4 \, {\left(a b^{10} d^{2} - 2 \, a^{2} b^{9} d e + a^{3} b^{8} e^{2}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d^{2} - 2 \, a^{3} b^{8} d e + a^{4} b^{7} e^{2}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d^{2} - 2 \, a^{4} b^{7} d e + a^{5} b^{6} e^{2}\right)} x\right)}}\right]"," ",0,"[1/384*(15*(8*B*a^4*b*d*e^3 - (7*B*a^5 + A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (7*B*a*b^4 + A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (7*B*a^2*b^3 + A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (7*B*a^3*b^2 + A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (7*B*a^4*b + A*a^3*b^2)*e^4)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(16*(B*a*b^5 + 3*A*b^6)*d^4 + 8*(B*a^2*b^4 - 7*A*a*b^5)*d^3*e + 2*(13*B*a^3*b^3 - A*a^2*b^4)*d^2*e^2 - 5*(31*B*a^4*b^2 + A*a^3*b^3)*d*e^3 + 15*(7*B*a^5*b + A*a^4*b^2)*e^4 + 3*(88*B*b^6*d^2*e^2 - (181*B*a*b^5 - 5*A*b^6)*d*e^3 + (93*B*a^2*b^4 - 5*A*a*b^5)*e^4)*x^3 + (208*B*b^6*d^3*e + 2*(25*B*a*b^5 + 59*A*b^6)*d^2*e^2 - (769*B*a^2*b^4 + 191*A*a*b^5)*d*e^3 + 73*(7*B*a^3*b^3 + A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 + 8*(3*B*a*b^5 + 17*A*b^6)*d^3*e + 4*(25*B*a^2*b^4 - 43*A*a*b^5)*d^2*e^2 - (573*B*a^3*b^3 + 19*A*a^2*b^4)*d*e^3 + 55*(7*B*a^4*b^2 + A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d^2 - 2*a^5*b^6*d*e + a^6*b^5*e^2 + (b^11*d^2 - 2*a*b^10*d*e + a^2*b^9*e^2)*x^4 + 4*(a*b^10*d^2 - 2*a^2*b^9*d*e + a^3*b^8*e^2)*x^3 + 6*(a^2*b^9*d^2 - 2*a^3*b^8*d*e + a^4*b^7*e^2)*x^2 + 4*(a^3*b^8*d^2 - 2*a^4*b^7*d*e + a^5*b^6*e^2)*x), 1/192*(15*(8*B*a^4*b*d*e^3 - (7*B*a^5 + A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (7*B*a*b^4 + A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (7*B*a^2*b^3 + A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (7*B*a^3*b^2 + A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (7*B*a^4*b + A*a^3*b^2)*e^4)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (16*(B*a*b^5 + 3*A*b^6)*d^4 + 8*(B*a^2*b^4 - 7*A*a*b^5)*d^3*e + 2*(13*B*a^3*b^3 - A*a^2*b^4)*d^2*e^2 - 5*(31*B*a^4*b^2 + A*a^3*b^3)*d*e^3 + 15*(7*B*a^5*b + A*a^4*b^2)*e^4 + 3*(88*B*b^6*d^2*e^2 - (181*B*a*b^5 - 5*A*b^6)*d*e^3 + (93*B*a^2*b^4 - 5*A*a*b^5)*e^4)*x^3 + (208*B*b^6*d^3*e + 2*(25*B*a*b^5 + 59*A*b^6)*d^2*e^2 - (769*B*a^2*b^4 + 191*A*a*b^5)*d*e^3 + 73*(7*B*a^3*b^3 + A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 + 8*(3*B*a*b^5 + 17*A*b^6)*d^3*e + 4*(25*B*a^2*b^4 - 43*A*a*b^5)*d^2*e^2 - (573*B*a^3*b^3 + 19*A*a^2*b^4)*d*e^3 + 55*(7*B*a^4*b^2 + A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d^2 - 2*a^5*b^6*d*e + a^6*b^5*e^2 + (b^11*d^2 - 2*a*b^10*d*e + a^2*b^9*e^2)*x^4 + 4*(a*b^10*d^2 - 2*a^2*b^9*d*e + a^3*b^8*e^2)*x^3 + 6*(a^2*b^9*d^2 - 2*a^3*b^8*d*e + a^4*b^7*e^2)*x^2 + 4*(a^3*b^8*d^2 - 2*a^4*b^7*d*e + a^5*b^6*e^2)*x)]","B",0
1878,1,1706,0,0.463713," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, B a^{4} b d e^{3} - {\left(5 \, B a^{5} + 3 \, A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(5 \, B a b^{4} + 3 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(5 \, B a^{2} b^{3} + 3 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(5 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(5 \, B a^{4} b + 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} - 24 \, {\left(B a^{2} b^{4} + 5 \, A a b^{5}\right)} d^{3} e - 6 \, {\left(B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} d^{2} e^{2} + {\left(29 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} d e^{3} - 3 \, {\left(5 \, B a^{5} b + 3 \, A a^{4} b^{2}\right)} e^{4} + 3 \, {\left(8 \, B b^{6} d^{2} e^{2} - {\left(13 \, B a b^{5} + 3 \, A b^{6}\right)} d e^{3} + {\left(5 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} e^{4}\right)} x^{3} + {\left(112 \, B b^{6} d^{3} e - 6 \, {\left(45 \, B a b^{5} - A b^{6}\right)} d^{2} e^{2} + 3 \, {\left(77 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d e^{3} - {\left(73 \, B a^{3} b^{3} - 33 \, A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} - 8 \, {\left(13 \, B a b^{5} - 9 \, A b^{6}\right)} d^{3} e - 12 \, {\left(B a^{2} b^{4} + 17 \, A a b^{5}\right)} d^{2} e^{2} + {\left(107 \, B a^{3} b^{3} + 165 \, A a^{2} b^{4}\right)} d e^{3} - 11 \, {\left(5 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{7} d^{3} - 3 \, a^{5} b^{6} d^{2} e + 3 \, a^{6} b^{5} d e^{2} - a^{7} b^{4} e^{3} + {\left(b^{11} d^{3} - 3 \, a b^{10} d^{2} e + 3 \, a^{2} b^{9} d e^{2} - a^{3} b^{8} e^{3}\right)} x^{4} + 4 \, {\left(a b^{10} d^{3} - 3 \, a^{2} b^{9} d^{2} e + 3 \, a^{3} b^{8} d e^{2} - a^{4} b^{7} e^{3}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d^{3} - 3 \, a^{3} b^{8} d^{2} e + 3 \, a^{4} b^{7} d e^{2} - a^{5} b^{6} e^{3}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d^{3} - 3 \, a^{4} b^{7} d^{2} e + 3 \, a^{5} b^{6} d e^{2} - a^{6} b^{5} e^{3}\right)} x\right)}}, -\frac{3 \, {\left(8 \, B a^{4} b d e^{3} - {\left(5 \, B a^{5} + 3 \, A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(5 \, B a b^{4} + 3 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(5 \, B a^{2} b^{3} + 3 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(5 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(5 \, B a^{4} b + 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} - 24 \, {\left(B a^{2} b^{4} + 5 \, A a b^{5}\right)} d^{3} e - 6 \, {\left(B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} d^{2} e^{2} + {\left(29 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} d e^{3} - 3 \, {\left(5 \, B a^{5} b + 3 \, A a^{4} b^{2}\right)} e^{4} + 3 \, {\left(8 \, B b^{6} d^{2} e^{2} - {\left(13 \, B a b^{5} + 3 \, A b^{6}\right)} d e^{3} + {\left(5 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} e^{4}\right)} x^{3} + {\left(112 \, B b^{6} d^{3} e - 6 \, {\left(45 \, B a b^{5} - A b^{6}\right)} d^{2} e^{2} + 3 \, {\left(77 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d e^{3} - {\left(73 \, B a^{3} b^{3} - 33 \, A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} - 8 \, {\left(13 \, B a b^{5} - 9 \, A b^{6}\right)} d^{3} e - 12 \, {\left(B a^{2} b^{4} + 17 \, A a b^{5}\right)} d^{2} e^{2} + {\left(107 \, B a^{3} b^{3} + 165 \, A a^{2} b^{4}\right)} d e^{3} - 11 \, {\left(5 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{7} d^{3} - 3 \, a^{5} b^{6} d^{2} e + 3 \, a^{6} b^{5} d e^{2} - a^{7} b^{4} e^{3} + {\left(b^{11} d^{3} - 3 \, a b^{10} d^{2} e + 3 \, a^{2} b^{9} d e^{2} - a^{3} b^{8} e^{3}\right)} x^{4} + 4 \, {\left(a b^{10} d^{3} - 3 \, a^{2} b^{9} d^{2} e + 3 \, a^{3} b^{8} d e^{2} - a^{4} b^{7} e^{3}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d^{3} - 3 \, a^{3} b^{8} d^{2} e + 3 \, a^{4} b^{7} d e^{2} - a^{5} b^{6} e^{3}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d^{3} - 3 \, a^{4} b^{7} d^{2} e + 3 \, a^{5} b^{6} d e^{2} - a^{6} b^{5} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/384*(3*(8*B*a^4*b*d*e^3 - (5*B*a^5 + 3*A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (5*B*a*b^4 + 3*A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (5*B*a^2*b^3 + 3*A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (5*B*a^3*b^2 + 3*A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (5*B*a^4*b + 3*A*a^3*b^2)*e^4)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(16*(B*a*b^5 + 3*A*b^6)*d^4 - 24*(B*a^2*b^4 + 5*A*a*b^5)*d^3*e - 6*(B*a^3*b^3 - 13*A*a^2*b^4)*d^2*e^2 + (29*B*a^4*b^2 + 3*A*a^3*b^3)*d*e^3 - 3*(5*B*a^5*b + 3*A*a^4*b^2)*e^4 + 3*(8*B*b^6*d^2*e^2 - (13*B*a*b^5 + 3*A*b^6)*d*e^3 + (5*B*a^2*b^4 + 3*A*a*b^5)*e^4)*x^3 + (112*B*b^6*d^3*e - 6*(45*B*a*b^5 - A*b^6)*d^2*e^2 + 3*(77*B*a^2*b^4 - 13*A*a*b^5)*d*e^3 - (73*B*a^3*b^3 - 33*A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 - 8*(13*B*a*b^5 - 9*A*b^6)*d^3*e - 12*(B*a^2*b^4 + 17*A*a*b^5)*d^2*e^2 + (107*B*a^3*b^3 + 165*A*a^2*b^4)*d*e^3 - 11*(5*B*a^4*b^2 + 3*A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d^3 - 3*a^5*b^6*d^2*e + 3*a^6*b^5*d*e^2 - a^7*b^4*e^3 + (b^11*d^3 - 3*a*b^10*d^2*e + 3*a^2*b^9*d*e^2 - a^3*b^8*e^3)*x^4 + 4*(a*b^10*d^3 - 3*a^2*b^9*d^2*e + 3*a^3*b^8*d*e^2 - a^4*b^7*e^3)*x^3 + 6*(a^2*b^9*d^3 - 3*a^3*b^8*d^2*e + 3*a^4*b^7*d*e^2 - a^5*b^6*e^3)*x^2 + 4*(a^3*b^8*d^3 - 3*a^4*b^7*d^2*e + 3*a^5*b^6*d*e^2 - a^6*b^5*e^3)*x), -1/192*(3*(8*B*a^4*b*d*e^3 - (5*B*a^5 + 3*A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (5*B*a*b^4 + 3*A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (5*B*a^2*b^3 + 3*A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (5*B*a^3*b^2 + 3*A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (5*B*a^4*b + 3*A*a^3*b^2)*e^4)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (16*(B*a*b^5 + 3*A*b^6)*d^4 - 24*(B*a^2*b^4 + 5*A*a*b^5)*d^3*e - 6*(B*a^3*b^3 - 13*A*a^2*b^4)*d^2*e^2 + (29*B*a^4*b^2 + 3*A*a^3*b^3)*d*e^3 - 3*(5*B*a^5*b + 3*A*a^4*b^2)*e^4 + 3*(8*B*b^6*d^2*e^2 - (13*B*a*b^5 + 3*A*b^6)*d*e^3 + (5*B*a^2*b^4 + 3*A*a*b^5)*e^4)*x^3 + (112*B*b^6*d^3*e - 6*(45*B*a*b^5 - A*b^6)*d^2*e^2 + 3*(77*B*a^2*b^4 - 13*A*a*b^5)*d*e^3 - (73*B*a^3*b^3 - 33*A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 - 8*(13*B*a*b^5 - 9*A*b^6)*d^3*e - 12*(B*a^2*b^4 + 17*A*a*b^5)*d^2*e^2 + (107*B*a^3*b^3 + 165*A*a^2*b^4)*d*e^3 - 11*(5*B*a^4*b^2 + 3*A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d^3 - 3*a^5*b^6*d^2*e + 3*a^6*b^5*d*e^2 - a^7*b^4*e^3 + (b^11*d^3 - 3*a*b^10*d^2*e + 3*a^2*b^9*d*e^2 - a^3*b^8*e^3)*x^4 + 4*(a*b^10*d^3 - 3*a^2*b^9*d^2*e + 3*a^3*b^8*d*e^2 - a^4*b^7*e^3)*x^3 + 6*(a^2*b^9*d^3 - 3*a^3*b^8*d^2*e + 3*a^4*b^7*d*e^2 - a^5*b^6*e^3)*x^2 + 4*(a^3*b^8*d^3 - 3*a^4*b^7*d^2*e + 3*a^5*b^6*d*e^2 - a^6*b^5*e^3)*x)]","B",0
1879,1,1841,0,0.492208," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, B a^{4} b d e^{3} - {\left(3 \, B a^{5} + 5 \, A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(3 \, B a b^{4} + 5 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(3 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(3 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(3 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} - 8 \, {\left(7 \, B a^{2} b^{4} + 23 \, A a b^{5}\right)} d^{3} e + 2 \, {\left(29 \, B a^{3} b^{3} + 127 \, A a^{2} b^{4}\right)} d^{2} e^{2} - {\left(27 \, B a^{4} b^{2} + 133 \, A a^{3} b^{3}\right)} d e^{3} + 3 \, {\left(3 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{4} - 3 \, {\left(8 \, B b^{6} d^{2} e^{2} - {\left(11 \, B a b^{5} + 5 \, A b^{6}\right)} d e^{3} + {\left(3 \, B a^{2} b^{4} + 5 \, A a b^{5}\right)} e^{4}\right)} x^{3} + {\left(16 \, B b^{6} d^{3} e - 10 \, {\left(11 \, B a b^{5} + A b^{6}\right)} d^{2} e^{2} + {\left(127 \, B a^{2} b^{4} + 65 \, A a b^{5}\right)} d e^{3} - 11 \, {\left(3 \, B a^{3} b^{3} + 5 \, A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} - 8 \, {\left(29 \, B a b^{5} - A b^{6}\right)} d^{3} e + 4 \, {\left(65 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} d^{2} e^{2} - {\left(125 \, B a^{3} b^{3} - 109 \, A a^{2} b^{4}\right)} d e^{3} + {\left(33 \, B a^{4} b^{2} - 73 \, A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{7} d^{4} - 4 \, a^{5} b^{6} d^{3} e + 6 \, a^{6} b^{5} d^{2} e^{2} - 4 \, a^{7} b^{4} d e^{3} + a^{8} b^{3} e^{4} + {\left(b^{11} d^{4} - 4 \, a b^{10} d^{3} e + 6 \, a^{2} b^{9} d^{2} e^{2} - 4 \, a^{3} b^{8} d e^{3} + a^{4} b^{7} e^{4}\right)} x^{4} + 4 \, {\left(a b^{10} d^{4} - 4 \, a^{2} b^{9} d^{3} e + 6 \, a^{3} b^{8} d^{2} e^{2} - 4 \, a^{4} b^{7} d e^{3} + a^{5} b^{6} e^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d^{4} - 4 \, a^{3} b^{8} d^{3} e + 6 \, a^{4} b^{7} d^{2} e^{2} - 4 \, a^{5} b^{6} d e^{3} + a^{6} b^{5} e^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d^{4} - 4 \, a^{4} b^{7} d^{3} e + 6 \, a^{5} b^{6} d^{2} e^{2} - 4 \, a^{6} b^{5} d e^{3} + a^{7} b^{4} e^{4}\right)} x\right)}}, \frac{3 \, {\left(8 \, B a^{4} b d e^{3} - {\left(3 \, B a^{5} + 5 \, A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(3 \, B a b^{4} + 5 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(3 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(3 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(3 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} - 8 \, {\left(7 \, B a^{2} b^{4} + 23 \, A a b^{5}\right)} d^{3} e + 2 \, {\left(29 \, B a^{3} b^{3} + 127 \, A a^{2} b^{4}\right)} d^{2} e^{2} - {\left(27 \, B a^{4} b^{2} + 133 \, A a^{3} b^{3}\right)} d e^{3} + 3 \, {\left(3 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{4} - 3 \, {\left(8 \, B b^{6} d^{2} e^{2} - {\left(11 \, B a b^{5} + 5 \, A b^{6}\right)} d e^{3} + {\left(3 \, B a^{2} b^{4} + 5 \, A a b^{5}\right)} e^{4}\right)} x^{3} + {\left(16 \, B b^{6} d^{3} e - 10 \, {\left(11 \, B a b^{5} + A b^{6}\right)} d^{2} e^{2} + {\left(127 \, B a^{2} b^{4} + 65 \, A a b^{5}\right)} d e^{3} - 11 \, {\left(3 \, B a^{3} b^{3} + 5 \, A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} - 8 \, {\left(29 \, B a b^{5} - A b^{6}\right)} d^{3} e + 4 \, {\left(65 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} d^{2} e^{2} - {\left(125 \, B a^{3} b^{3} - 109 \, A a^{2} b^{4}\right)} d e^{3} + {\left(33 \, B a^{4} b^{2} - 73 \, A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{7} d^{4} - 4 \, a^{5} b^{6} d^{3} e + 6 \, a^{6} b^{5} d^{2} e^{2} - 4 \, a^{7} b^{4} d e^{3} + a^{8} b^{3} e^{4} + {\left(b^{11} d^{4} - 4 \, a b^{10} d^{3} e + 6 \, a^{2} b^{9} d^{2} e^{2} - 4 \, a^{3} b^{8} d e^{3} + a^{4} b^{7} e^{4}\right)} x^{4} + 4 \, {\left(a b^{10} d^{4} - 4 \, a^{2} b^{9} d^{3} e + 6 \, a^{3} b^{8} d^{2} e^{2} - 4 \, a^{4} b^{7} d e^{3} + a^{5} b^{6} e^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d^{4} - 4 \, a^{3} b^{8} d^{3} e + 6 \, a^{4} b^{7} d^{2} e^{2} - 4 \, a^{5} b^{6} d e^{3} + a^{6} b^{5} e^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d^{4} - 4 \, a^{4} b^{7} d^{3} e + 6 \, a^{5} b^{6} d^{2} e^{2} - 4 \, a^{6} b^{5} d e^{3} + a^{7} b^{4} e^{4}\right)} x\right)}}\right]"," ",0,"[1/384*(3*(8*B*a^4*b*d*e^3 - (3*B*a^5 + 5*A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (3*B*a*b^4 + 5*A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (3*B*a^2*b^3 + 5*A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (3*B*a^3*b^2 + 5*A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (3*B*a^4*b + 5*A*a^3*b^2)*e^4)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(16*(B*a*b^5 + 3*A*b^6)*d^4 - 8*(7*B*a^2*b^4 + 23*A*a*b^5)*d^3*e + 2*(29*B*a^3*b^3 + 127*A*a^2*b^4)*d^2*e^2 - (27*B*a^4*b^2 + 133*A*a^3*b^3)*d*e^3 + 3*(3*B*a^5*b + 5*A*a^4*b^2)*e^4 - 3*(8*B*b^6*d^2*e^2 - (11*B*a*b^5 + 5*A*b^6)*d*e^3 + (3*B*a^2*b^4 + 5*A*a*b^5)*e^4)*x^3 + (16*B*b^6*d^3*e - 10*(11*B*a*b^5 + A*b^6)*d^2*e^2 + (127*B*a^2*b^4 + 65*A*a*b^5)*d*e^3 - 11*(3*B*a^3*b^3 + 5*A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 - 8*(29*B*a*b^5 - A*b^6)*d^3*e + 4*(65*B*a^2*b^4 - 11*A*a*b^5)*d^2*e^2 - (125*B*a^3*b^3 - 109*A*a^2*b^4)*d*e^3 + (33*B*a^4*b^2 - 73*A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d^4 - 4*a^5*b^6*d^3*e + 6*a^6*b^5*d^2*e^2 - 4*a^7*b^4*d*e^3 + a^8*b^3*e^4 + (b^11*d^4 - 4*a*b^10*d^3*e + 6*a^2*b^9*d^2*e^2 - 4*a^3*b^8*d*e^3 + a^4*b^7*e^4)*x^4 + 4*(a*b^10*d^4 - 4*a^2*b^9*d^3*e + 6*a^3*b^8*d^2*e^2 - 4*a^4*b^7*d*e^3 + a^5*b^6*e^4)*x^3 + 6*(a^2*b^9*d^4 - 4*a^3*b^8*d^3*e + 6*a^4*b^7*d^2*e^2 - 4*a^5*b^6*d*e^3 + a^6*b^5*e^4)*x^2 + 4*(a^3*b^8*d^4 - 4*a^4*b^7*d^3*e + 6*a^5*b^6*d^2*e^2 - 4*a^6*b^5*d*e^3 + a^7*b^4*e^4)*x), 1/192*(3*(8*B*a^4*b*d*e^3 - (3*B*a^5 + 5*A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (3*B*a*b^4 + 5*A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (3*B*a^2*b^3 + 5*A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (3*B*a^3*b^2 + 5*A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (3*B*a^4*b + 5*A*a^3*b^2)*e^4)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (16*(B*a*b^5 + 3*A*b^6)*d^4 - 8*(7*B*a^2*b^4 + 23*A*a*b^5)*d^3*e + 2*(29*B*a^3*b^3 + 127*A*a^2*b^4)*d^2*e^2 - (27*B*a^4*b^2 + 133*A*a^3*b^3)*d*e^3 + 3*(3*B*a^5*b + 5*A*a^4*b^2)*e^4 - 3*(8*B*b^6*d^2*e^2 - (11*B*a*b^5 + 5*A*b^6)*d*e^3 + (3*B*a^2*b^4 + 5*A*a*b^5)*e^4)*x^3 + (16*B*b^6*d^3*e - 10*(11*B*a*b^5 + A*b^6)*d^2*e^2 + (127*B*a^2*b^4 + 65*A*a*b^5)*d*e^3 - 11*(3*B*a^3*b^3 + 5*A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 - 8*(29*B*a*b^5 - A*b^6)*d^3*e + 4*(65*B*a^2*b^4 - 11*A*a*b^5)*d^2*e^2 - (125*B*a^3*b^3 - 109*A*a^2*b^4)*d*e^3 + (33*B*a^4*b^2 - 73*A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d^4 - 4*a^5*b^6*d^3*e + 6*a^6*b^5*d^2*e^2 - 4*a^7*b^4*d*e^3 + a^8*b^3*e^4 + (b^11*d^4 - 4*a*b^10*d^3*e + 6*a^2*b^9*d^2*e^2 - 4*a^3*b^8*d*e^3 + a^4*b^7*e^4)*x^4 + 4*(a*b^10*d^4 - 4*a^2*b^9*d^3*e + 6*a^3*b^8*d^2*e^2 - 4*a^4*b^7*d*e^3 + a^5*b^6*e^4)*x^3 + 6*(a^2*b^9*d^4 - 4*a^3*b^8*d^3*e + 6*a^4*b^7*d^2*e^2 - 4*a^5*b^6*d*e^3 + a^6*b^5*e^4)*x^2 + 4*(a^3*b^8*d^4 - 4*a^4*b^7*d^3*e + 6*a^5*b^6*d^2*e^2 - 4*a^6*b^5*d*e^3 + a^7*b^4*e^4)*x)]","B",0
1880,1,1980,0,0.490887," ","integrate((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(8 \, B a^{4} b d e^{3} - {\left(B a^{5} + 7 \, A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(B a b^{4} + 7 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(B a^{2} b^{3} + 7 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(B a^{3} b^{2} + 7 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(B a^{4} b + 7 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} - 8 \, {\left(11 \, B a^{2} b^{4} + 31 \, A a b^{5}\right)} d^{3} e + 2 \, {\left(109 \, B a^{3} b^{3} + 263 \, A a^{2} b^{4}\right)} d^{2} e^{2} - {\left(131 \, B a^{4} b^{2} + 605 \, A a^{3} b^{3}\right)} d e^{3} - 3 \, {\left(5 \, B a^{5} b - 93 \, A a^{4} b^{2}\right)} e^{4} + 15 \, {\left(8 \, B b^{6} d^{2} e^{2} - {\left(9 \, B a b^{5} + 7 \, A b^{6}\right)} d e^{3} + {\left(B a^{2} b^{4} + 7 \, A a b^{5}\right)} e^{4}\right)} x^{3} - 5 \, {\left(16 \, B b^{6} d^{3} e - 2 \, {\left(53 \, B a b^{5} + 7 \, A b^{6}\right)} d^{2} e^{2} + {\left(101 \, B a^{2} b^{4} + 91 \, A a b^{5}\right)} d e^{3} - 11 \, {\left(B a^{3} b^{3} + 7 \, A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} - 8 \, {\left(45 \, B a b^{5} + 7 \, A b^{6}\right)} d^{3} e + 4 \, {\left(229 \, B a^{2} b^{4} + 77 \, A a b^{5}\right)} d^{2} e^{2} - 7 \, {\left(99 \, B a^{3} b^{3} + 109 \, A a^{2} b^{4}\right)} d e^{3} + 73 \, {\left(B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{7} d^{5} - 5 \, a^{5} b^{6} d^{4} e + 10 \, a^{6} b^{5} d^{3} e^{2} - 10 \, a^{7} b^{4} d^{2} e^{3} + 5 \, a^{8} b^{3} d e^{4} - a^{9} b^{2} e^{5} + {\left(b^{11} d^{5} - 5 \, a b^{10} d^{4} e + 10 \, a^{2} b^{9} d^{3} e^{2} - 10 \, a^{3} b^{8} d^{2} e^{3} + 5 \, a^{4} b^{7} d e^{4} - a^{5} b^{6} e^{5}\right)} x^{4} + 4 \, {\left(a b^{10} d^{5} - 5 \, a^{2} b^{9} d^{4} e + 10 \, a^{3} b^{8} d^{3} e^{2} - 10 \, a^{4} b^{7} d^{2} e^{3} + 5 \, a^{5} b^{6} d e^{4} - a^{6} b^{5} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d^{5} - 5 \, a^{3} b^{8} d^{4} e + 10 \, a^{4} b^{7} d^{3} e^{2} - 10 \, a^{5} b^{6} d^{2} e^{3} + 5 \, a^{6} b^{5} d e^{4} - a^{7} b^{4} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d^{5} - 5 \, a^{4} b^{7} d^{4} e + 10 \, a^{5} b^{6} d^{3} e^{2} - 10 \, a^{6} b^{5} d^{2} e^{3} + 5 \, a^{7} b^{4} d e^{4} - a^{8} b^{3} e^{5}\right)} x\right)}}, -\frac{15 \, {\left(8 \, B a^{4} b d e^{3} - {\left(B a^{5} + 7 \, A a^{4} b\right)} e^{4} + {\left(8 \, B b^{5} d e^{3} - {\left(B a b^{4} + 7 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d e^{3} - {\left(B a^{2} b^{3} + 7 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{3} d e^{3} - {\left(B a^{3} b^{2} + 7 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(8 \, B a^{3} b^{2} d e^{3} - {\left(B a^{4} b + 7 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{4} - 8 \, {\left(11 \, B a^{2} b^{4} + 31 \, A a b^{5}\right)} d^{3} e + 2 \, {\left(109 \, B a^{3} b^{3} + 263 \, A a^{2} b^{4}\right)} d^{2} e^{2} - {\left(131 \, B a^{4} b^{2} + 605 \, A a^{3} b^{3}\right)} d e^{3} - 3 \, {\left(5 \, B a^{5} b - 93 \, A a^{4} b^{2}\right)} e^{4} + 15 \, {\left(8 \, B b^{6} d^{2} e^{2} - {\left(9 \, B a b^{5} + 7 \, A b^{6}\right)} d e^{3} + {\left(B a^{2} b^{4} + 7 \, A a b^{5}\right)} e^{4}\right)} x^{3} - 5 \, {\left(16 \, B b^{6} d^{3} e - 2 \, {\left(53 \, B a b^{5} + 7 \, A b^{6}\right)} d^{2} e^{2} + {\left(101 \, B a^{2} b^{4} + 91 \, A a b^{5}\right)} d e^{3} - 11 \, {\left(B a^{3} b^{3} + 7 \, A a^{2} b^{4}\right)} e^{4}\right)} x^{2} + {\left(64 \, B b^{6} d^{4} - 8 \, {\left(45 \, B a b^{5} + 7 \, A b^{6}\right)} d^{3} e + 4 \, {\left(229 \, B a^{2} b^{4} + 77 \, A a b^{5}\right)} d^{2} e^{2} - 7 \, {\left(99 \, B a^{3} b^{3} + 109 \, A a^{2} b^{4}\right)} d e^{3} + 73 \, {\left(B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{7} d^{5} - 5 \, a^{5} b^{6} d^{4} e + 10 \, a^{6} b^{5} d^{3} e^{2} - 10 \, a^{7} b^{4} d^{2} e^{3} + 5 \, a^{8} b^{3} d e^{4} - a^{9} b^{2} e^{5} + {\left(b^{11} d^{5} - 5 \, a b^{10} d^{4} e + 10 \, a^{2} b^{9} d^{3} e^{2} - 10 \, a^{3} b^{8} d^{2} e^{3} + 5 \, a^{4} b^{7} d e^{4} - a^{5} b^{6} e^{5}\right)} x^{4} + 4 \, {\left(a b^{10} d^{5} - 5 \, a^{2} b^{9} d^{4} e + 10 \, a^{3} b^{8} d^{3} e^{2} - 10 \, a^{4} b^{7} d^{2} e^{3} + 5 \, a^{5} b^{6} d e^{4} - a^{6} b^{5} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} d^{5} - 5 \, a^{3} b^{8} d^{4} e + 10 \, a^{4} b^{7} d^{3} e^{2} - 10 \, a^{5} b^{6} d^{2} e^{3} + 5 \, a^{6} b^{5} d e^{4} - a^{7} b^{4} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} d^{5} - 5 \, a^{4} b^{7} d^{4} e + 10 \, a^{5} b^{6} d^{3} e^{2} - 10 \, a^{6} b^{5} d^{2} e^{3} + 5 \, a^{7} b^{4} d e^{4} - a^{8} b^{3} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/384*(15*(8*B*a^4*b*d*e^3 - (B*a^5 + 7*A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (B*a*b^4 + 7*A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (B*a^2*b^3 + 7*A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (B*a^3*b^2 + 7*A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (B*a^4*b + 7*A*a^3*b^2)*e^4)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(16*(B*a*b^5 + 3*A*b^6)*d^4 - 8*(11*B*a^2*b^4 + 31*A*a*b^5)*d^3*e + 2*(109*B*a^3*b^3 + 263*A*a^2*b^4)*d^2*e^2 - (131*B*a^4*b^2 + 605*A*a^3*b^3)*d*e^3 - 3*(5*B*a^5*b - 93*A*a^4*b^2)*e^4 + 15*(8*B*b^6*d^2*e^2 - (9*B*a*b^5 + 7*A*b^6)*d*e^3 + (B*a^2*b^4 + 7*A*a*b^5)*e^4)*x^3 - 5*(16*B*b^6*d^3*e - 2*(53*B*a*b^5 + 7*A*b^6)*d^2*e^2 + (101*B*a^2*b^4 + 91*A*a*b^5)*d*e^3 - 11*(B*a^3*b^3 + 7*A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 - 8*(45*B*a*b^5 + 7*A*b^6)*d^3*e + 4*(229*B*a^2*b^4 + 77*A*a*b^5)*d^2*e^2 - 7*(99*B*a^3*b^3 + 109*A*a^2*b^4)*d*e^3 + 73*(B*a^4*b^2 + 7*A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d^5 - 5*a^5*b^6*d^4*e + 10*a^6*b^5*d^3*e^2 - 10*a^7*b^4*d^2*e^3 + 5*a^8*b^3*d*e^4 - a^9*b^2*e^5 + (b^11*d^5 - 5*a*b^10*d^4*e + 10*a^2*b^9*d^3*e^2 - 10*a^3*b^8*d^2*e^3 + 5*a^4*b^7*d*e^4 - a^5*b^6*e^5)*x^4 + 4*(a*b^10*d^5 - 5*a^2*b^9*d^4*e + 10*a^3*b^8*d^3*e^2 - 10*a^4*b^7*d^2*e^3 + 5*a^5*b^6*d*e^4 - a^6*b^5*e^5)*x^3 + 6*(a^2*b^9*d^5 - 5*a^3*b^8*d^4*e + 10*a^4*b^7*d^3*e^2 - 10*a^5*b^6*d^2*e^3 + 5*a^6*b^5*d*e^4 - a^7*b^4*e^5)*x^2 + 4*(a^3*b^8*d^5 - 5*a^4*b^7*d^4*e + 10*a^5*b^6*d^3*e^2 - 10*a^6*b^5*d^2*e^3 + 5*a^7*b^4*d*e^4 - a^8*b^3*e^5)*x), -1/192*(15*(8*B*a^4*b*d*e^3 - (B*a^5 + 7*A*a^4*b)*e^4 + (8*B*b^5*d*e^3 - (B*a*b^4 + 7*A*b^5)*e^4)*x^4 + 4*(8*B*a*b^4*d*e^3 - (B*a^2*b^3 + 7*A*a*b^4)*e^4)*x^3 + 6*(8*B*a^2*b^3*d*e^3 - (B*a^3*b^2 + 7*A*a^2*b^3)*e^4)*x^2 + 4*(8*B*a^3*b^2*d*e^3 - (B*a^4*b + 7*A*a^3*b^2)*e^4)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (16*(B*a*b^5 + 3*A*b^6)*d^4 - 8*(11*B*a^2*b^4 + 31*A*a*b^5)*d^3*e + 2*(109*B*a^3*b^3 + 263*A*a^2*b^4)*d^2*e^2 - (131*B*a^4*b^2 + 605*A*a^3*b^3)*d*e^3 - 3*(5*B*a^5*b - 93*A*a^4*b^2)*e^4 + 15*(8*B*b^6*d^2*e^2 - (9*B*a*b^5 + 7*A*b^6)*d*e^3 + (B*a^2*b^4 + 7*A*a*b^5)*e^4)*x^3 - 5*(16*B*b^6*d^3*e - 2*(53*B*a*b^5 + 7*A*b^6)*d^2*e^2 + (101*B*a^2*b^4 + 91*A*a*b^5)*d*e^3 - 11*(B*a^3*b^3 + 7*A*a^2*b^4)*e^4)*x^2 + (64*B*b^6*d^4 - 8*(45*B*a*b^5 + 7*A*b^6)*d^3*e + 4*(229*B*a^2*b^4 + 77*A*a*b^5)*d^2*e^2 - 7*(99*B*a^3*b^3 + 109*A*a^2*b^4)*d*e^3 + 73*(B*a^4*b^2 + 7*A*a^3*b^3)*e^4)*x)*sqrt(e*x + d))/(a^4*b^7*d^5 - 5*a^5*b^6*d^4*e + 10*a^6*b^5*d^3*e^2 - 10*a^7*b^4*d^2*e^3 + 5*a^8*b^3*d*e^4 - a^9*b^2*e^5 + (b^11*d^5 - 5*a*b^10*d^4*e + 10*a^2*b^9*d^3*e^2 - 10*a^3*b^8*d^2*e^3 + 5*a^4*b^7*d*e^4 - a^5*b^6*e^5)*x^4 + 4*(a*b^10*d^5 - 5*a^2*b^9*d^4*e + 10*a^3*b^8*d^3*e^2 - 10*a^4*b^7*d^2*e^3 + 5*a^5*b^6*d*e^4 - a^6*b^5*e^5)*x^3 + 6*(a^2*b^9*d^5 - 5*a^3*b^8*d^4*e + 10*a^4*b^7*d^3*e^2 - 10*a^5*b^6*d^2*e^3 + 5*a^6*b^5*d*e^4 - a^7*b^4*e^5)*x^2 + 4*(a^3*b^8*d^5 - 5*a^4*b^7*d^4*e + 10*a^5*b^6*d^3*e^2 - 10*a^6*b^5*d^2*e^3 + 5*a^7*b^4*d*e^4 - a^8*b^3*e^5)*x)]","B",0
1881,1,2968,0,0.504461," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(8 \, B a^{4} b d^{2} e^{3} + {\left(B a^{5} - 9 \, A a^{4} b\right)} d e^{4} + {\left(8 \, B b^{5} d e^{4} + {\left(B a b^{4} - 9 \, A b^{5}\right)} e^{5}\right)} x^{5} + {\left(8 \, B b^{5} d^{2} e^{3} + 3 \, {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} d e^{4} + 4 \, {\left(B a^{2} b^{3} - 9 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(16 \, B a b^{4} d^{2} e^{3} + 2 \, {\left(13 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} d e^{4} + 3 \, {\left(B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} + 2 \, {\left(24 \, B a^{2} b^{3} d^{2} e^{3} + {\left(19 \, B a^{3} b^{2} - 27 \, A a^{2} b^{3}\right)} d e^{4} + 2 \, {\left(B a^{4} b - 9 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(32 \, B a^{3} b^{2} d^{2} e^{3} + 12 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2}\right)} d e^{4} + {\left(B a^{5} - 9 \, A a^{4} b\right)} e^{5}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(384 \, A a^{5} b e^{5} + 16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{5} - 24 \, {\left(5 \, B a^{2} b^{4} + 13 \, A a b^{5}\right)} d^{4} e + 6 \, {\left(79 \, B a^{3} b^{3} + 149 \, A a^{2} b^{4}\right)} d^{3} e^{2} + {\left(293 \, B a^{4} b^{2} - 1605 \, A a^{3} b^{3}\right)} d^{2} e^{3} - 3 \, {\left(221 \, B a^{5} b - 197 \, A a^{4} b^{2}\right)} d e^{4} + 105 \, {\left(8 \, B b^{6} d^{2} e^{3} - {\left(7 \, B a b^{5} + 9 \, A b^{6}\right)} d e^{4} - {\left(B a^{2} b^{4} - 9 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 35 \, {\left(8 \, B b^{6} d^{3} e^{2} + 9 \, {\left(9 \, B a b^{5} - A b^{6}\right)} d^{2} e^{3} - 6 \, {\left(13 \, B a^{2} b^{4} + 15 \, A a b^{5}\right)} d e^{4} - 11 \, {\left(B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} - 7 \, {\left(16 \, B b^{6} d^{4} e - 2 \, {\left(83 \, B a b^{5} + 9 \, A b^{6}\right)} d^{3} e^{2} - 3 \, {\left(151 \, B a^{2} b^{4} - 63 \, A a b^{5}\right)} d^{2} e^{3} + 2 \, {\left(265 \, B a^{3} b^{3} + 243 \, A a^{2} b^{4}\right)} d e^{4} + 73 \, {\left(B a^{4} b^{2} - 9 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + {\left(64 \, B b^{6} d^{5} - 8 \, {\left(59 \, B a b^{5} + 9 \, A b^{6}\right)} d^{4} e + 108 \, {\left(17 \, B a^{2} b^{4} + 5 \, A a b^{5}\right)} d^{3} e^{2} + {\left(989 \, B a^{3} b^{3} - 2133 \, A a^{2} b^{4}\right)} d^{2} e^{3} - 2 \, {\left(1069 \, B a^{4} b^{2} + 423 \, A a^{3} b^{3}\right)} d e^{4} - 279 \, {\left(B a^{5} b - 9 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{7} d^{7} - 6 \, a^{5} b^{6} d^{6} e + 15 \, a^{6} b^{5} d^{5} e^{2} - 20 \, a^{7} b^{4} d^{4} e^{3} + 15 \, a^{8} b^{3} d^{3} e^{4} - 6 \, a^{9} b^{2} d^{2} e^{5} + a^{10} b d e^{6} + {\left(b^{11} d^{6} e - 6 \, a b^{10} d^{5} e^{2} + 15 \, a^{2} b^{9} d^{4} e^{3} - 20 \, a^{3} b^{8} d^{3} e^{4} + 15 \, a^{4} b^{7} d^{2} e^{5} - 6 \, a^{5} b^{6} d e^{6} + a^{6} b^{5} e^{7}\right)} x^{5} + {\left(b^{11} d^{7} - 2 \, a b^{10} d^{6} e - 9 \, a^{2} b^{9} d^{5} e^{2} + 40 \, a^{3} b^{8} d^{4} e^{3} - 65 \, a^{4} b^{7} d^{3} e^{4} + 54 \, a^{5} b^{6} d^{2} e^{5} - 23 \, a^{6} b^{5} d e^{6} + 4 \, a^{7} b^{4} e^{7}\right)} x^{4} + 2 \, {\left(2 \, a b^{10} d^{7} - 9 \, a^{2} b^{9} d^{6} e + 12 \, a^{3} b^{8} d^{5} e^{2} + 5 \, a^{4} b^{7} d^{4} e^{3} - 30 \, a^{5} b^{6} d^{3} e^{4} + 33 \, a^{6} b^{5} d^{2} e^{5} - 16 \, a^{7} b^{4} d e^{6} + 3 \, a^{8} b^{3} e^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{9} d^{7} - 16 \, a^{3} b^{8} d^{6} e + 33 \, a^{4} b^{7} d^{5} e^{2} - 30 \, a^{5} b^{6} d^{4} e^{3} + 5 \, a^{6} b^{5} d^{3} e^{4} + 12 \, a^{7} b^{4} d^{2} e^{5} - 9 \, a^{8} b^{3} d e^{6} + 2 \, a^{9} b^{2} e^{7}\right)} x^{2} + {\left(4 \, a^{3} b^{8} d^{7} - 23 \, a^{4} b^{7} d^{6} e + 54 \, a^{5} b^{6} d^{5} e^{2} - 65 \, a^{6} b^{5} d^{4} e^{3} + 40 \, a^{7} b^{4} d^{3} e^{4} - 9 \, a^{8} b^{3} d^{2} e^{5} - 2 \, a^{9} b^{2} d e^{6} + a^{10} b e^{7}\right)} x\right)}}, -\frac{105 \, {\left(8 \, B a^{4} b d^{2} e^{3} + {\left(B a^{5} - 9 \, A a^{4} b\right)} d e^{4} + {\left(8 \, B b^{5} d e^{4} + {\left(B a b^{4} - 9 \, A b^{5}\right)} e^{5}\right)} x^{5} + {\left(8 \, B b^{5} d^{2} e^{3} + 3 \, {\left(11 \, B a b^{4} - 3 \, A b^{5}\right)} d e^{4} + 4 \, {\left(B a^{2} b^{3} - 9 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(16 \, B a b^{4} d^{2} e^{3} + 2 \, {\left(13 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} d e^{4} + 3 \, {\left(B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} + 2 \, {\left(24 \, B a^{2} b^{3} d^{2} e^{3} + {\left(19 \, B a^{3} b^{2} - 27 \, A a^{2} b^{3}\right)} d e^{4} + 2 \, {\left(B a^{4} b - 9 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(32 \, B a^{3} b^{2} d^{2} e^{3} + 12 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2}\right)} d e^{4} + {\left(B a^{5} - 9 \, A a^{4} b\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(384 \, A a^{5} b e^{5} + 16 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{5} - 24 \, {\left(5 \, B a^{2} b^{4} + 13 \, A a b^{5}\right)} d^{4} e + 6 \, {\left(79 \, B a^{3} b^{3} + 149 \, A a^{2} b^{4}\right)} d^{3} e^{2} + {\left(293 \, B a^{4} b^{2} - 1605 \, A a^{3} b^{3}\right)} d^{2} e^{3} - 3 \, {\left(221 \, B a^{5} b - 197 \, A a^{4} b^{2}\right)} d e^{4} + 105 \, {\left(8 \, B b^{6} d^{2} e^{3} - {\left(7 \, B a b^{5} + 9 \, A b^{6}\right)} d e^{4} - {\left(B a^{2} b^{4} - 9 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 35 \, {\left(8 \, B b^{6} d^{3} e^{2} + 9 \, {\left(9 \, B a b^{5} - A b^{6}\right)} d^{2} e^{3} - 6 \, {\left(13 \, B a^{2} b^{4} + 15 \, A a b^{5}\right)} d e^{4} - 11 \, {\left(B a^{3} b^{3} - 9 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} - 7 \, {\left(16 \, B b^{6} d^{4} e - 2 \, {\left(83 \, B a b^{5} + 9 \, A b^{6}\right)} d^{3} e^{2} - 3 \, {\left(151 \, B a^{2} b^{4} - 63 \, A a b^{5}\right)} d^{2} e^{3} + 2 \, {\left(265 \, B a^{3} b^{3} + 243 \, A a^{2} b^{4}\right)} d e^{4} + 73 \, {\left(B a^{4} b^{2} - 9 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + {\left(64 \, B b^{6} d^{5} - 8 \, {\left(59 \, B a b^{5} + 9 \, A b^{6}\right)} d^{4} e + 108 \, {\left(17 \, B a^{2} b^{4} + 5 \, A a b^{5}\right)} d^{3} e^{2} + {\left(989 \, B a^{3} b^{3} - 2133 \, A a^{2} b^{4}\right)} d^{2} e^{3} - 2 \, {\left(1069 \, B a^{4} b^{2} + 423 \, A a^{3} b^{3}\right)} d e^{4} - 279 \, {\left(B a^{5} b - 9 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{7} d^{7} - 6 \, a^{5} b^{6} d^{6} e + 15 \, a^{6} b^{5} d^{5} e^{2} - 20 \, a^{7} b^{4} d^{4} e^{3} + 15 \, a^{8} b^{3} d^{3} e^{4} - 6 \, a^{9} b^{2} d^{2} e^{5} + a^{10} b d e^{6} + {\left(b^{11} d^{6} e - 6 \, a b^{10} d^{5} e^{2} + 15 \, a^{2} b^{9} d^{4} e^{3} - 20 \, a^{3} b^{8} d^{3} e^{4} + 15 \, a^{4} b^{7} d^{2} e^{5} - 6 \, a^{5} b^{6} d e^{6} + a^{6} b^{5} e^{7}\right)} x^{5} + {\left(b^{11} d^{7} - 2 \, a b^{10} d^{6} e - 9 \, a^{2} b^{9} d^{5} e^{2} + 40 \, a^{3} b^{8} d^{4} e^{3} - 65 \, a^{4} b^{7} d^{3} e^{4} + 54 \, a^{5} b^{6} d^{2} e^{5} - 23 \, a^{6} b^{5} d e^{6} + 4 \, a^{7} b^{4} e^{7}\right)} x^{4} + 2 \, {\left(2 \, a b^{10} d^{7} - 9 \, a^{2} b^{9} d^{6} e + 12 \, a^{3} b^{8} d^{5} e^{2} + 5 \, a^{4} b^{7} d^{4} e^{3} - 30 \, a^{5} b^{6} d^{3} e^{4} + 33 \, a^{6} b^{5} d^{2} e^{5} - 16 \, a^{7} b^{4} d e^{6} + 3 \, a^{8} b^{3} e^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{9} d^{7} - 16 \, a^{3} b^{8} d^{6} e + 33 \, a^{4} b^{7} d^{5} e^{2} - 30 \, a^{5} b^{6} d^{4} e^{3} + 5 \, a^{6} b^{5} d^{3} e^{4} + 12 \, a^{7} b^{4} d^{2} e^{5} - 9 \, a^{8} b^{3} d e^{6} + 2 \, a^{9} b^{2} e^{7}\right)} x^{2} + {\left(4 \, a^{3} b^{8} d^{7} - 23 \, a^{4} b^{7} d^{6} e + 54 \, a^{5} b^{6} d^{5} e^{2} - 65 \, a^{6} b^{5} d^{4} e^{3} + 40 \, a^{7} b^{4} d^{3} e^{4} - 9 \, a^{8} b^{3} d^{2} e^{5} - 2 \, a^{9} b^{2} d e^{6} + a^{10} b e^{7}\right)} x\right)}}\right]"," ",0,"[1/384*(105*(8*B*a^4*b*d^2*e^3 + (B*a^5 - 9*A*a^4*b)*d*e^4 + (8*B*b^5*d*e^4 + (B*a*b^4 - 9*A*b^5)*e^5)*x^5 + (8*B*b^5*d^2*e^3 + 3*(11*B*a*b^4 - 3*A*b^5)*d*e^4 + 4*(B*a^2*b^3 - 9*A*a*b^4)*e^5)*x^4 + 2*(16*B*a*b^4*d^2*e^3 + 2*(13*B*a^2*b^3 - 9*A*a*b^4)*d*e^4 + 3*(B*a^3*b^2 - 9*A*a^2*b^3)*e^5)*x^3 + 2*(24*B*a^2*b^3*d^2*e^3 + (19*B*a^3*b^2 - 27*A*a^2*b^3)*d*e^4 + 2*(B*a^4*b - 9*A*a^3*b^2)*e^5)*x^2 + (32*B*a^3*b^2*d^2*e^3 + 12*(B*a^4*b - 3*A*a^3*b^2)*d*e^4 + (B*a^5 - 9*A*a^4*b)*e^5)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e + 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(384*A*a^5*b*e^5 + 16*(B*a*b^5 + 3*A*b^6)*d^5 - 24*(5*B*a^2*b^4 + 13*A*a*b^5)*d^4*e + 6*(79*B*a^3*b^3 + 149*A*a^2*b^4)*d^3*e^2 + (293*B*a^4*b^2 - 1605*A*a^3*b^3)*d^2*e^3 - 3*(221*B*a^5*b - 197*A*a^4*b^2)*d*e^4 + 105*(8*B*b^6*d^2*e^3 - (7*B*a*b^5 + 9*A*b^6)*d*e^4 - (B*a^2*b^4 - 9*A*a*b^5)*e^5)*x^4 + 35*(8*B*b^6*d^3*e^2 + 9*(9*B*a*b^5 - A*b^6)*d^2*e^3 - 6*(13*B*a^2*b^4 + 15*A*a*b^5)*d*e^4 - 11*(B*a^3*b^3 - 9*A*a^2*b^4)*e^5)*x^3 - 7*(16*B*b^6*d^4*e - 2*(83*B*a*b^5 + 9*A*b^6)*d^3*e^2 - 3*(151*B*a^2*b^4 - 63*A*a*b^5)*d^2*e^3 + 2*(265*B*a^3*b^3 + 243*A*a^2*b^4)*d*e^4 + 73*(B*a^4*b^2 - 9*A*a^3*b^3)*e^5)*x^2 + (64*B*b^6*d^5 - 8*(59*B*a*b^5 + 9*A*b^6)*d^4*e + 108*(17*B*a^2*b^4 + 5*A*a*b^5)*d^3*e^2 + (989*B*a^3*b^3 - 2133*A*a^2*b^4)*d^2*e^3 - 2*(1069*B*a^4*b^2 + 423*A*a^3*b^3)*d*e^4 - 279*(B*a^5*b - 9*A*a^4*b^2)*e^5)*x)*sqrt(e*x + d))/(a^4*b^7*d^7 - 6*a^5*b^6*d^6*e + 15*a^6*b^5*d^5*e^2 - 20*a^7*b^4*d^4*e^3 + 15*a^8*b^3*d^3*e^4 - 6*a^9*b^2*d^2*e^5 + a^10*b*d*e^6 + (b^11*d^6*e - 6*a*b^10*d^5*e^2 + 15*a^2*b^9*d^4*e^3 - 20*a^3*b^8*d^3*e^4 + 15*a^4*b^7*d^2*e^5 - 6*a^5*b^6*d*e^6 + a^6*b^5*e^7)*x^5 + (b^11*d^7 - 2*a*b^10*d^6*e - 9*a^2*b^9*d^5*e^2 + 40*a^3*b^8*d^4*e^3 - 65*a^4*b^7*d^3*e^4 + 54*a^5*b^6*d^2*e^5 - 23*a^6*b^5*d*e^6 + 4*a^7*b^4*e^7)*x^4 + 2*(2*a*b^10*d^7 - 9*a^2*b^9*d^6*e + 12*a^3*b^8*d^5*e^2 + 5*a^4*b^7*d^4*e^3 - 30*a^5*b^6*d^3*e^4 + 33*a^6*b^5*d^2*e^5 - 16*a^7*b^4*d*e^6 + 3*a^8*b^3*e^7)*x^3 + 2*(3*a^2*b^9*d^7 - 16*a^3*b^8*d^6*e + 33*a^4*b^7*d^5*e^2 - 30*a^5*b^6*d^4*e^3 + 5*a^6*b^5*d^3*e^4 + 12*a^7*b^4*d^2*e^5 - 9*a^8*b^3*d*e^6 + 2*a^9*b^2*e^7)*x^2 + (4*a^3*b^8*d^7 - 23*a^4*b^7*d^6*e + 54*a^5*b^6*d^5*e^2 - 65*a^6*b^5*d^4*e^3 + 40*a^7*b^4*d^3*e^4 - 9*a^8*b^3*d^2*e^5 - 2*a^9*b^2*d*e^6 + a^10*b*e^7)*x), -1/192*(105*(8*B*a^4*b*d^2*e^3 + (B*a^5 - 9*A*a^4*b)*d*e^4 + (8*B*b^5*d*e^4 + (B*a*b^4 - 9*A*b^5)*e^5)*x^5 + (8*B*b^5*d^2*e^3 + 3*(11*B*a*b^4 - 3*A*b^5)*d*e^4 + 4*(B*a^2*b^3 - 9*A*a*b^4)*e^5)*x^4 + 2*(16*B*a*b^4*d^2*e^3 + 2*(13*B*a^2*b^3 - 9*A*a*b^4)*d*e^4 + 3*(B*a^3*b^2 - 9*A*a^2*b^3)*e^5)*x^3 + 2*(24*B*a^2*b^3*d^2*e^3 + (19*B*a^3*b^2 - 27*A*a^2*b^3)*d*e^4 + 2*(B*a^4*b - 9*A*a^3*b^2)*e^5)*x^2 + (32*B*a^3*b^2*d^2*e^3 + 12*(B*a^4*b - 3*A*a^3*b^2)*d*e^4 + (B*a^5 - 9*A*a^4*b)*e^5)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (384*A*a^5*b*e^5 + 16*(B*a*b^5 + 3*A*b^6)*d^5 - 24*(5*B*a^2*b^4 + 13*A*a*b^5)*d^4*e + 6*(79*B*a^3*b^3 + 149*A*a^2*b^4)*d^3*e^2 + (293*B*a^4*b^2 - 1605*A*a^3*b^3)*d^2*e^3 - 3*(221*B*a^5*b - 197*A*a^4*b^2)*d*e^4 + 105*(8*B*b^6*d^2*e^3 - (7*B*a*b^5 + 9*A*b^6)*d*e^4 - (B*a^2*b^4 - 9*A*a*b^5)*e^5)*x^4 + 35*(8*B*b^6*d^3*e^2 + 9*(9*B*a*b^5 - A*b^6)*d^2*e^3 - 6*(13*B*a^2*b^4 + 15*A*a*b^5)*d*e^4 - 11*(B*a^3*b^3 - 9*A*a^2*b^4)*e^5)*x^3 - 7*(16*B*b^6*d^4*e - 2*(83*B*a*b^5 + 9*A*b^6)*d^3*e^2 - 3*(151*B*a^2*b^4 - 63*A*a*b^5)*d^2*e^3 + 2*(265*B*a^3*b^3 + 243*A*a^2*b^4)*d*e^4 + 73*(B*a^4*b^2 - 9*A*a^3*b^3)*e^5)*x^2 + (64*B*b^6*d^5 - 8*(59*B*a*b^5 + 9*A*b^6)*d^4*e + 108*(17*B*a^2*b^4 + 5*A*a*b^5)*d^3*e^2 + (989*B*a^3*b^3 - 2133*A*a^2*b^4)*d^2*e^3 - 2*(1069*B*a^4*b^2 + 423*A*a^3*b^3)*d*e^4 - 279*(B*a^5*b - 9*A*a^4*b^2)*e^5)*x)*sqrt(e*x + d))/(a^4*b^7*d^7 - 6*a^5*b^6*d^6*e + 15*a^6*b^5*d^5*e^2 - 20*a^7*b^4*d^4*e^3 + 15*a^8*b^3*d^3*e^4 - 6*a^9*b^2*d^2*e^5 + a^10*b*d*e^6 + (b^11*d^6*e - 6*a*b^10*d^5*e^2 + 15*a^2*b^9*d^4*e^3 - 20*a^3*b^8*d^3*e^4 + 15*a^4*b^7*d^2*e^5 - 6*a^5*b^6*d*e^6 + a^6*b^5*e^7)*x^5 + (b^11*d^7 - 2*a*b^10*d^6*e - 9*a^2*b^9*d^5*e^2 + 40*a^3*b^8*d^4*e^3 - 65*a^4*b^7*d^3*e^4 + 54*a^5*b^6*d^2*e^5 - 23*a^6*b^5*d*e^6 + 4*a^7*b^4*e^7)*x^4 + 2*(2*a*b^10*d^7 - 9*a^2*b^9*d^6*e + 12*a^3*b^8*d^5*e^2 + 5*a^4*b^7*d^4*e^3 - 30*a^5*b^6*d^3*e^4 + 33*a^6*b^5*d^2*e^5 - 16*a^7*b^4*d*e^6 + 3*a^8*b^3*e^7)*x^3 + 2*(3*a^2*b^9*d^7 - 16*a^3*b^8*d^6*e + 33*a^4*b^7*d^5*e^2 - 30*a^5*b^6*d^4*e^3 + 5*a^6*b^5*d^3*e^4 + 12*a^7*b^4*d^2*e^5 - 9*a^8*b^3*d*e^6 + 2*a^9*b^2*e^7)*x^2 + (4*a^3*b^8*d^7 - 23*a^4*b^7*d^6*e + 54*a^5*b^6*d^5*e^2 - 65*a^6*b^5*d^4*e^3 + 40*a^7*b^4*d^3*e^4 - 9*a^8*b^3*d^2*e^5 - 2*a^9*b^2*d*e^6 + a^10*b*e^7)*x)]","B",0
1882,1,3596,0,0.536684," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(8 \, B a^{4} b d^{3} e^{3} + {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} d^{2} e^{4} + {\left(8 \, B b^{5} d e^{5} + {\left(3 \, B a b^{4} - 11 \, A b^{5}\right)} e^{6}\right)} x^{6} + 2 \, {\left(8 \, B b^{5} d^{2} e^{4} + {\left(19 \, B a b^{4} - 11 \, A b^{5}\right)} d e^{5} + 2 \, {\left(3 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} e^{6}\right)} x^{5} + {\left(8 \, B b^{5} d^{3} e^{3} + {\left(67 \, B a b^{4} - 11 \, A b^{5}\right)} d^{2} e^{4} + 8 \, {\left(9 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} d e^{5} + 6 \, {\left(3 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{6}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d^{3} e^{3} + {\left(27 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} d^{2} e^{4} + {\left(17 \, B a^{3} b^{2} - 33 \, A a^{2} b^{3}\right)} d e^{5} + {\left(3 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{3} + {\left(48 \, B a^{2} b^{3} d^{3} e^{3} + 2 \, {\left(41 \, B a^{3} b^{2} - 33 \, A a^{2} b^{3}\right)} d^{2} e^{4} + 8 \, {\left(4 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d e^{5} + {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} e^{6}\right)} x^{2} + 2 \, {\left(16 \, B a^{3} b^{2} d^{3} e^{3} + 2 \, {\left(7 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d^{2} e^{4} + {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} d e^{5}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(128 \, A a^{5} e^{5} + 16 \, {\left(B a b^{4} + 3 \, A b^{5}\right)} d^{5} - 8 \, {\left(17 \, B a^{2} b^{3} + 41 \, A a b^{4}\right)} d^{4} e + 10 \, {\left(69 \, B a^{3} b^{2} + 103 \, A a^{2} b^{3}\right)} d^{3} e^{2} + {\left(2639 \, B a^{4} b - 2295 \, A a^{3} b^{2}\right)} d^{2} e^{3} + 256 \, {\left(B a^{5} - 8 \, A a^{4} b\right)} d e^{4} + 315 \, {\left(8 \, B b^{5} d e^{4} + {\left(3 \, B a b^{4} - 11 \, A b^{5}\right)} e^{5}\right)} x^{5} + 105 \, {\left(32 \, B b^{5} d^{2} e^{3} + 4 \, {\left(25 \, B a b^{4} - 11 \, A b^{5}\right)} d e^{4} + 11 \, {\left(3 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 21 \, {\left(24 \, B b^{5} d^{3} e^{2} + {\left(601 \, B a b^{4} - 33 \, A b^{5}\right)} d^{2} e^{3} + 2 \, {\left(403 \, B a^{2} b^{3} - 407 \, A a b^{4}\right)} d e^{4} + 73 \, {\left(3 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} - 9 \, {\left(16 \, B b^{5} d^{4} e - 2 \, {\left(105 \, B a b^{4} + 11 \, A b^{5}\right)} d^{3} e^{2} - {\left(1937 \, B a^{2} b^{3} - 297 \, A a b^{4}\right)} d^{2} e^{3} - 8 \, {\left(180 \, B a^{3} b^{2} - 319 \, A a^{2} b^{3}\right)} d e^{4} - 93 \, {\left(3 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(64 \, B b^{5} d^{5} - 8 \, {\left(65 \, B a b^{4} + 11 \, A b^{5}\right)} d^{4} e + 4 \, {\left(639 \, B a^{2} b^{3} + 187 \, A a b^{4}\right)} d^{3} e^{2} + {\left(10331 \, B a^{3} b^{2} - 3795 \, A a^{2} b^{3}\right)} d^{2} e^{3} + 22 \, {\left(205 \, B a^{4} b - 581 \, A a^{3} b^{2}\right)} d e^{4} + 128 \, {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d^{8} - 6 \, a^{5} b^{5} d^{7} e + 15 \, a^{6} b^{4} d^{6} e^{2} - 20 \, a^{7} b^{3} d^{5} e^{3} + 15 \, a^{8} b^{2} d^{4} e^{4} - 6 \, a^{9} b d^{3} e^{5} + a^{10} d^{2} e^{6} + {\left(b^{10} d^{6} e^{2} - 6 \, a b^{9} d^{5} e^{3} + 15 \, a^{2} b^{8} d^{4} e^{4} - 20 \, a^{3} b^{7} d^{3} e^{5} + 15 \, a^{4} b^{6} d^{2} e^{6} - 6 \, a^{5} b^{5} d e^{7} + a^{6} b^{4} e^{8}\right)} x^{6} + 2 \, {\left(b^{10} d^{7} e - 4 \, a b^{9} d^{6} e^{2} + 3 \, a^{2} b^{8} d^{5} e^{3} + 10 \, a^{3} b^{7} d^{4} e^{4} - 25 \, a^{4} b^{6} d^{3} e^{5} + 24 \, a^{5} b^{5} d^{2} e^{6} - 11 \, a^{6} b^{4} d e^{7} + 2 \, a^{7} b^{3} e^{8}\right)} x^{5} + {\left(b^{10} d^{8} + 2 \, a b^{9} d^{7} e - 27 \, a^{2} b^{8} d^{6} e^{2} + 64 \, a^{3} b^{7} d^{5} e^{3} - 55 \, a^{4} b^{6} d^{4} e^{4} - 6 \, a^{5} b^{5} d^{3} e^{5} + 43 \, a^{6} b^{4} d^{2} e^{6} - 28 \, a^{7} b^{3} d e^{7} + 6 \, a^{8} b^{2} e^{8}\right)} x^{4} + 4 \, {\left(a b^{9} d^{8} - 3 \, a^{2} b^{8} d^{7} e - 2 \, a^{3} b^{7} d^{6} e^{2} + 19 \, a^{4} b^{6} d^{5} e^{3} - 30 \, a^{5} b^{5} d^{4} e^{4} + 19 \, a^{6} b^{4} d^{3} e^{5} - 2 \, a^{7} b^{3} d^{2} e^{6} - 3 \, a^{8} b^{2} d e^{7} + a^{9} b e^{8}\right)} x^{3} + {\left(6 \, a^{2} b^{8} d^{8} - 28 \, a^{3} b^{7} d^{7} e + 43 \, a^{4} b^{6} d^{6} e^{2} - 6 \, a^{5} b^{5} d^{5} e^{3} - 55 \, a^{6} b^{4} d^{4} e^{4} + 64 \, a^{7} b^{3} d^{3} e^{5} - 27 \, a^{8} b^{2} d^{2} e^{6} + 2 \, a^{9} b d e^{7} + a^{10} e^{8}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{7} d^{8} - 11 \, a^{4} b^{6} d^{7} e + 24 \, a^{5} b^{5} d^{6} e^{2} - 25 \, a^{6} b^{4} d^{5} e^{3} + 10 \, a^{7} b^{3} d^{4} e^{4} + 3 \, a^{8} b^{2} d^{3} e^{5} - 4 \, a^{9} b d^{2} e^{6} + a^{10} d e^{7}\right)} x\right)}}, \frac{315 \, {\left(8 \, B a^{4} b d^{3} e^{3} + {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} d^{2} e^{4} + {\left(8 \, B b^{5} d e^{5} + {\left(3 \, B a b^{4} - 11 \, A b^{5}\right)} e^{6}\right)} x^{6} + 2 \, {\left(8 \, B b^{5} d^{2} e^{4} + {\left(19 \, B a b^{4} - 11 \, A b^{5}\right)} d e^{5} + 2 \, {\left(3 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} e^{6}\right)} x^{5} + {\left(8 \, B b^{5} d^{3} e^{3} + {\left(67 \, B a b^{4} - 11 \, A b^{5}\right)} d^{2} e^{4} + 8 \, {\left(9 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} d e^{5} + 6 \, {\left(3 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{6}\right)} x^{4} + 4 \, {\left(8 \, B a b^{4} d^{3} e^{3} + {\left(27 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} d^{2} e^{4} + {\left(17 \, B a^{3} b^{2} - 33 \, A a^{2} b^{3}\right)} d e^{5} + {\left(3 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{6}\right)} x^{3} + {\left(48 \, B a^{2} b^{3} d^{3} e^{3} + 2 \, {\left(41 \, B a^{3} b^{2} - 33 \, A a^{2} b^{3}\right)} d^{2} e^{4} + 8 \, {\left(4 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d e^{5} + {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} e^{6}\right)} x^{2} + 2 \, {\left(16 \, B a^{3} b^{2} d^{3} e^{3} + 2 \, {\left(7 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} d^{2} e^{4} + {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} d e^{5}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(128 \, A a^{5} e^{5} + 16 \, {\left(B a b^{4} + 3 \, A b^{5}\right)} d^{5} - 8 \, {\left(17 \, B a^{2} b^{3} + 41 \, A a b^{4}\right)} d^{4} e + 10 \, {\left(69 \, B a^{3} b^{2} + 103 \, A a^{2} b^{3}\right)} d^{3} e^{2} + {\left(2639 \, B a^{4} b - 2295 \, A a^{3} b^{2}\right)} d^{2} e^{3} + 256 \, {\left(B a^{5} - 8 \, A a^{4} b\right)} d e^{4} + 315 \, {\left(8 \, B b^{5} d e^{4} + {\left(3 \, B a b^{4} - 11 \, A b^{5}\right)} e^{5}\right)} x^{5} + 105 \, {\left(32 \, B b^{5} d^{2} e^{3} + 4 \, {\left(25 \, B a b^{4} - 11 \, A b^{5}\right)} d e^{4} + 11 \, {\left(3 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 21 \, {\left(24 \, B b^{5} d^{3} e^{2} + {\left(601 \, B a b^{4} - 33 \, A b^{5}\right)} d^{2} e^{3} + 2 \, {\left(403 \, B a^{2} b^{3} - 407 \, A a b^{4}\right)} d e^{4} + 73 \, {\left(3 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} - 9 \, {\left(16 \, B b^{5} d^{4} e - 2 \, {\left(105 \, B a b^{4} + 11 \, A b^{5}\right)} d^{3} e^{2} - {\left(1937 \, B a^{2} b^{3} - 297 \, A a b^{4}\right)} d^{2} e^{3} - 8 \, {\left(180 \, B a^{3} b^{2} - 319 \, A a^{2} b^{3}\right)} d e^{4} - 93 \, {\left(3 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(64 \, B b^{5} d^{5} - 8 \, {\left(65 \, B a b^{4} + 11 \, A b^{5}\right)} d^{4} e + 4 \, {\left(639 \, B a^{2} b^{3} + 187 \, A a b^{4}\right)} d^{3} e^{2} + {\left(10331 \, B a^{3} b^{2} - 3795 \, A a^{2} b^{3}\right)} d^{2} e^{3} + 22 \, {\left(205 \, B a^{4} b - 581 \, A a^{3} b^{2}\right)} d e^{4} + 128 \, {\left(3 \, B a^{5} - 11 \, A a^{4} b\right)} e^{5}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d^{8} - 6 \, a^{5} b^{5} d^{7} e + 15 \, a^{6} b^{4} d^{6} e^{2} - 20 \, a^{7} b^{3} d^{5} e^{3} + 15 \, a^{8} b^{2} d^{4} e^{4} - 6 \, a^{9} b d^{3} e^{5} + a^{10} d^{2} e^{6} + {\left(b^{10} d^{6} e^{2} - 6 \, a b^{9} d^{5} e^{3} + 15 \, a^{2} b^{8} d^{4} e^{4} - 20 \, a^{3} b^{7} d^{3} e^{5} + 15 \, a^{4} b^{6} d^{2} e^{6} - 6 \, a^{5} b^{5} d e^{7} + a^{6} b^{4} e^{8}\right)} x^{6} + 2 \, {\left(b^{10} d^{7} e - 4 \, a b^{9} d^{6} e^{2} + 3 \, a^{2} b^{8} d^{5} e^{3} + 10 \, a^{3} b^{7} d^{4} e^{4} - 25 \, a^{4} b^{6} d^{3} e^{5} + 24 \, a^{5} b^{5} d^{2} e^{6} - 11 \, a^{6} b^{4} d e^{7} + 2 \, a^{7} b^{3} e^{8}\right)} x^{5} + {\left(b^{10} d^{8} + 2 \, a b^{9} d^{7} e - 27 \, a^{2} b^{8} d^{6} e^{2} + 64 \, a^{3} b^{7} d^{5} e^{3} - 55 \, a^{4} b^{6} d^{4} e^{4} - 6 \, a^{5} b^{5} d^{3} e^{5} + 43 \, a^{6} b^{4} d^{2} e^{6} - 28 \, a^{7} b^{3} d e^{7} + 6 \, a^{8} b^{2} e^{8}\right)} x^{4} + 4 \, {\left(a b^{9} d^{8} - 3 \, a^{2} b^{8} d^{7} e - 2 \, a^{3} b^{7} d^{6} e^{2} + 19 \, a^{4} b^{6} d^{5} e^{3} - 30 \, a^{5} b^{5} d^{4} e^{4} + 19 \, a^{6} b^{4} d^{3} e^{5} - 2 \, a^{7} b^{3} d^{2} e^{6} - 3 \, a^{8} b^{2} d e^{7} + a^{9} b e^{8}\right)} x^{3} + {\left(6 \, a^{2} b^{8} d^{8} - 28 \, a^{3} b^{7} d^{7} e + 43 \, a^{4} b^{6} d^{6} e^{2} - 6 \, a^{5} b^{5} d^{5} e^{3} - 55 \, a^{6} b^{4} d^{4} e^{4} + 64 \, a^{7} b^{3} d^{3} e^{5} - 27 \, a^{8} b^{2} d^{2} e^{6} + 2 \, a^{9} b d e^{7} + a^{10} e^{8}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{7} d^{8} - 11 \, a^{4} b^{6} d^{7} e + 24 \, a^{5} b^{5} d^{6} e^{2} - 25 \, a^{6} b^{4} d^{5} e^{3} + 10 \, a^{7} b^{3} d^{4} e^{4} + 3 \, a^{8} b^{2} d^{3} e^{5} - 4 \, a^{9} b d^{2} e^{6} + a^{10} d e^{7}\right)} x\right)}}\right]"," ",0,"[-1/384*(315*(8*B*a^4*b*d^3*e^3 + (3*B*a^5 - 11*A*a^4*b)*d^2*e^4 + (8*B*b^5*d*e^5 + (3*B*a*b^4 - 11*A*b^5)*e^6)*x^6 + 2*(8*B*b^5*d^2*e^4 + (19*B*a*b^4 - 11*A*b^5)*d*e^5 + 2*(3*B*a^2*b^3 - 11*A*a*b^4)*e^6)*x^5 + (8*B*b^5*d^3*e^3 + (67*B*a*b^4 - 11*A*b^5)*d^2*e^4 + 8*(9*B*a^2*b^3 - 11*A*a*b^4)*d*e^5 + 6*(3*B*a^3*b^2 - 11*A*a^2*b^3)*e^6)*x^4 + 4*(8*B*a*b^4*d^3*e^3 + (27*B*a^2*b^3 - 11*A*a*b^4)*d^2*e^4 + (17*B*a^3*b^2 - 33*A*a^2*b^3)*d*e^5 + (3*B*a^4*b - 11*A*a^3*b^2)*e^6)*x^3 + (48*B*a^2*b^3*d^3*e^3 + 2*(41*B*a^3*b^2 - 33*A*a^2*b^3)*d^2*e^4 + 8*(4*B*a^4*b - 11*A*a^3*b^2)*d*e^5 + (3*B*a^5 - 11*A*a^4*b)*e^6)*x^2 + 2*(16*B*a^3*b^2*d^3*e^3 + 2*(7*B*a^4*b - 11*A*a^3*b^2)*d^2*e^4 + (3*B*a^5 - 11*A*a^4*b)*d*e^5)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(128*A*a^5*e^5 + 16*(B*a*b^4 + 3*A*b^5)*d^5 - 8*(17*B*a^2*b^3 + 41*A*a*b^4)*d^4*e + 10*(69*B*a^3*b^2 + 103*A*a^2*b^3)*d^3*e^2 + (2639*B*a^4*b - 2295*A*a^3*b^2)*d^2*e^3 + 256*(B*a^5 - 8*A*a^4*b)*d*e^4 + 315*(8*B*b^5*d*e^4 + (3*B*a*b^4 - 11*A*b^5)*e^5)*x^5 + 105*(32*B*b^5*d^2*e^3 + 4*(25*B*a*b^4 - 11*A*b^5)*d*e^4 + 11*(3*B*a^2*b^3 - 11*A*a*b^4)*e^5)*x^4 + 21*(24*B*b^5*d^3*e^2 + (601*B*a*b^4 - 33*A*b^5)*d^2*e^3 + 2*(403*B*a^2*b^3 - 407*A*a*b^4)*d*e^4 + 73*(3*B*a^3*b^2 - 11*A*a^2*b^3)*e^5)*x^3 - 9*(16*B*b^5*d^4*e - 2*(105*B*a*b^4 + 11*A*b^5)*d^3*e^2 - (1937*B*a^2*b^3 - 297*A*a*b^4)*d^2*e^3 - 8*(180*B*a^3*b^2 - 319*A*a^2*b^3)*d*e^4 - 93*(3*B*a^4*b - 11*A*a^3*b^2)*e^5)*x^2 + (64*B*b^5*d^5 - 8*(65*B*a*b^4 + 11*A*b^5)*d^4*e + 4*(639*B*a^2*b^3 + 187*A*a*b^4)*d^3*e^2 + (10331*B*a^3*b^2 - 3795*A*a^2*b^3)*d^2*e^3 + 22*(205*B*a^4*b - 581*A*a^3*b^2)*d*e^4 + 128*(3*B*a^5 - 11*A*a^4*b)*e^5)*x)*sqrt(e*x + d))/(a^4*b^6*d^8 - 6*a^5*b^5*d^7*e + 15*a^6*b^4*d^6*e^2 - 20*a^7*b^3*d^5*e^3 + 15*a^8*b^2*d^4*e^4 - 6*a^9*b*d^3*e^5 + a^10*d^2*e^6 + (b^10*d^6*e^2 - 6*a*b^9*d^5*e^3 + 15*a^2*b^8*d^4*e^4 - 20*a^3*b^7*d^3*e^5 + 15*a^4*b^6*d^2*e^6 - 6*a^5*b^5*d*e^7 + a^6*b^4*e^8)*x^6 + 2*(b^10*d^7*e - 4*a*b^9*d^6*e^2 + 3*a^2*b^8*d^5*e^3 + 10*a^3*b^7*d^4*e^4 - 25*a^4*b^6*d^3*e^5 + 24*a^5*b^5*d^2*e^6 - 11*a^6*b^4*d*e^7 + 2*a^7*b^3*e^8)*x^5 + (b^10*d^8 + 2*a*b^9*d^7*e - 27*a^2*b^8*d^6*e^2 + 64*a^3*b^7*d^5*e^3 - 55*a^4*b^6*d^4*e^4 - 6*a^5*b^5*d^3*e^5 + 43*a^6*b^4*d^2*e^6 - 28*a^7*b^3*d*e^7 + 6*a^8*b^2*e^8)*x^4 + 4*(a*b^9*d^8 - 3*a^2*b^8*d^7*e - 2*a^3*b^7*d^6*e^2 + 19*a^4*b^6*d^5*e^3 - 30*a^5*b^5*d^4*e^4 + 19*a^6*b^4*d^3*e^5 - 2*a^7*b^3*d^2*e^6 - 3*a^8*b^2*d*e^7 + a^9*b*e^8)*x^3 + (6*a^2*b^8*d^8 - 28*a^3*b^7*d^7*e + 43*a^4*b^6*d^6*e^2 - 6*a^5*b^5*d^5*e^3 - 55*a^6*b^4*d^4*e^4 + 64*a^7*b^3*d^3*e^5 - 27*a^8*b^2*d^2*e^6 + 2*a^9*b*d*e^7 + a^10*e^8)*x^2 + 2*(2*a^3*b^7*d^8 - 11*a^4*b^6*d^7*e + 24*a^5*b^5*d^6*e^2 - 25*a^6*b^4*d^5*e^3 + 10*a^7*b^3*d^4*e^4 + 3*a^8*b^2*d^3*e^5 - 4*a^9*b*d^2*e^6 + a^10*d*e^7)*x), 1/192*(315*(8*B*a^4*b*d^3*e^3 + (3*B*a^5 - 11*A*a^4*b)*d^2*e^4 + (8*B*b^5*d*e^5 + (3*B*a*b^4 - 11*A*b^5)*e^6)*x^6 + 2*(8*B*b^5*d^2*e^4 + (19*B*a*b^4 - 11*A*b^5)*d*e^5 + 2*(3*B*a^2*b^3 - 11*A*a*b^4)*e^6)*x^5 + (8*B*b^5*d^3*e^3 + (67*B*a*b^4 - 11*A*b^5)*d^2*e^4 + 8*(9*B*a^2*b^3 - 11*A*a*b^4)*d*e^5 + 6*(3*B*a^3*b^2 - 11*A*a^2*b^3)*e^6)*x^4 + 4*(8*B*a*b^4*d^3*e^3 + (27*B*a^2*b^3 - 11*A*a*b^4)*d^2*e^4 + (17*B*a^3*b^2 - 33*A*a^2*b^3)*d*e^5 + (3*B*a^4*b - 11*A*a^3*b^2)*e^6)*x^3 + (48*B*a^2*b^3*d^3*e^3 + 2*(41*B*a^3*b^2 - 33*A*a^2*b^3)*d^2*e^4 + 8*(4*B*a^4*b - 11*A*a^3*b^2)*d*e^5 + (3*B*a^5 - 11*A*a^4*b)*e^6)*x^2 + 2*(16*B*a^3*b^2*d^3*e^3 + 2*(7*B*a^4*b - 11*A*a^3*b^2)*d^2*e^4 + (3*B*a^5 - 11*A*a^4*b)*d*e^5)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (128*A*a^5*e^5 + 16*(B*a*b^4 + 3*A*b^5)*d^5 - 8*(17*B*a^2*b^3 + 41*A*a*b^4)*d^4*e + 10*(69*B*a^3*b^2 + 103*A*a^2*b^3)*d^3*e^2 + (2639*B*a^4*b - 2295*A*a^3*b^2)*d^2*e^3 + 256*(B*a^5 - 8*A*a^4*b)*d*e^4 + 315*(8*B*b^5*d*e^4 + (3*B*a*b^4 - 11*A*b^5)*e^5)*x^5 + 105*(32*B*b^5*d^2*e^3 + 4*(25*B*a*b^4 - 11*A*b^5)*d*e^4 + 11*(3*B*a^2*b^3 - 11*A*a*b^4)*e^5)*x^4 + 21*(24*B*b^5*d^3*e^2 + (601*B*a*b^4 - 33*A*b^5)*d^2*e^3 + 2*(403*B*a^2*b^3 - 407*A*a*b^4)*d*e^4 + 73*(3*B*a^3*b^2 - 11*A*a^2*b^3)*e^5)*x^3 - 9*(16*B*b^5*d^4*e - 2*(105*B*a*b^4 + 11*A*b^5)*d^3*e^2 - (1937*B*a^2*b^3 - 297*A*a*b^4)*d^2*e^3 - 8*(180*B*a^3*b^2 - 319*A*a^2*b^3)*d*e^4 - 93*(3*B*a^4*b - 11*A*a^3*b^2)*e^5)*x^2 + (64*B*b^5*d^5 - 8*(65*B*a*b^4 + 11*A*b^5)*d^4*e + 4*(639*B*a^2*b^3 + 187*A*a*b^4)*d^3*e^2 + (10331*B*a^3*b^2 - 3795*A*a^2*b^3)*d^2*e^3 + 22*(205*B*a^4*b - 581*A*a^3*b^2)*d*e^4 + 128*(3*B*a^5 - 11*A*a^4*b)*e^5)*x)*sqrt(e*x + d))/(a^4*b^6*d^8 - 6*a^5*b^5*d^7*e + 15*a^6*b^4*d^6*e^2 - 20*a^7*b^3*d^5*e^3 + 15*a^8*b^2*d^4*e^4 - 6*a^9*b*d^3*e^5 + a^10*d^2*e^6 + (b^10*d^6*e^2 - 6*a*b^9*d^5*e^3 + 15*a^2*b^8*d^4*e^4 - 20*a^3*b^7*d^3*e^5 + 15*a^4*b^6*d^2*e^6 - 6*a^5*b^5*d*e^7 + a^6*b^4*e^8)*x^6 + 2*(b^10*d^7*e - 4*a*b^9*d^6*e^2 + 3*a^2*b^8*d^5*e^3 + 10*a^3*b^7*d^4*e^4 - 25*a^4*b^6*d^3*e^5 + 24*a^5*b^5*d^2*e^6 - 11*a^6*b^4*d*e^7 + 2*a^7*b^3*e^8)*x^5 + (b^10*d^8 + 2*a*b^9*d^7*e - 27*a^2*b^8*d^6*e^2 + 64*a^3*b^7*d^5*e^3 - 55*a^4*b^6*d^4*e^4 - 6*a^5*b^5*d^3*e^5 + 43*a^6*b^4*d^2*e^6 - 28*a^7*b^3*d*e^7 + 6*a^8*b^2*e^8)*x^4 + 4*(a*b^9*d^8 - 3*a^2*b^8*d^7*e - 2*a^3*b^7*d^6*e^2 + 19*a^4*b^6*d^5*e^3 - 30*a^5*b^5*d^4*e^4 + 19*a^6*b^4*d^3*e^5 - 2*a^7*b^3*d^2*e^6 - 3*a^8*b^2*d*e^7 + a^9*b*e^8)*x^3 + (6*a^2*b^8*d^8 - 28*a^3*b^7*d^7*e + 43*a^4*b^6*d^6*e^2 - 6*a^5*b^5*d^5*e^3 - 55*a^6*b^4*d^4*e^4 + 64*a^7*b^3*d^3*e^5 - 27*a^8*b^2*d^2*e^6 + 2*a^9*b*d*e^7 + a^10*e^8)*x^2 + 2*(2*a^3*b^7*d^8 - 11*a^4*b^6*d^7*e + 24*a^5*b^5*d^6*e^2 - 25*a^6*b^4*d^5*e^3 + 10*a^7*b^3*d^4*e^4 + 3*a^8*b^2*d^3*e^5 - 4*a^9*b*d^2*e^6 + a^10*d*e^7)*x)]","B",0
1883,1,4833,0,0.559422," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(8 \, B a^{4} b^{2} d^{4} e^{3} + {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d^{3} e^{4} + {\left(8 \, B b^{6} d e^{6} + {\left(5 \, B a b^{5} - 13 \, A b^{6}\right)} e^{7}\right)} x^{7} + {\left(24 \, B b^{6} d^{2} e^{5} + {\left(47 \, B a b^{5} - 39 \, A b^{6}\right)} d e^{6} + 4 \, {\left(5 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} e^{7}\right)} x^{6} + 3 \, {\left(8 \, B b^{6} d^{3} e^{4} + {\left(37 \, B a b^{5} - 13 \, A b^{6}\right)} d^{2} e^{5} + 4 \, {\left(9 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d e^{6} + 2 \, {\left(5 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{5} + {\left(8 \, B b^{6} d^{4} e^{3} + {\left(101 \, B a b^{5} - 13 \, A b^{6}\right)} d^{3} e^{4} + 12 \, {\left(17 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d^{2} e^{5} + 2 \, {\left(61 \, B a^{3} b^{3} - 117 \, A a^{2} b^{4}\right)} d e^{6} + 4 \, {\left(5 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{4} + {\left(32 \, B a b^{5} d^{4} e^{3} + 4 \, {\left(41 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d^{3} e^{4} + 6 \, {\left(31 \, B a^{3} b^{3} - 39 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 4 \, {\left(17 \, B a^{4} b^{2} - 39 \, A a^{3} b^{3}\right)} d e^{6} + {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{3} + 3 \, {\left(16 \, B a^{2} b^{4} d^{4} e^{3} + 2 \, {\left(21 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 4 \, {\left(7 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} d^{2} e^{5} + {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d e^{6}\right)} x^{2} + {\left(32 \, B a^{3} b^{3} d^{4} e^{3} + 4 \, {\left(11 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 3 \, {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d^{2} e^{5}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(384 \, A a^{6} e^{6} - 80 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{6} + 280 \, {\left(3 \, B a^{2} b^{4} + 7 \, A a b^{5}\right)} d^{5} e - 70 \, {\left(79 \, B a^{3} b^{3} + 109 \, A a^{2} b^{4}\right)} d^{4} e^{2} - {\left(33619 \, B a^{4} b^{2} - 22155 \, A a^{3} b^{3}\right)} d^{3} e^{3} - 128 \, {\left(54 \, B a^{5} b - 253 \, A a^{4} b^{2}\right)} d^{2} e^{4} + 128 \, {\left(2 \, B a^{6} - 31 \, A a^{5} b\right)} d e^{5} - 3465 \, {\left(8 \, B b^{6} d e^{5} + {\left(5 \, B a b^{5} - 13 \, A b^{6}\right)} e^{6}\right)} x^{6} - 1155 \, {\left(56 \, B b^{6} d^{2} e^{4} + {\left(123 \, B a b^{5} - 91 \, A b^{6}\right)} d e^{5} + 11 \, {\left(5 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} e^{6}\right)} x^{5} - 231 \, {\left(184 \, B b^{6} d^{3} e^{3} + {\left(1147 \, B a b^{5} - 299 \, A b^{6}\right)} d^{2} e^{4} + {\left(1229 \, B a^{2} b^{4} - 1677 \, A a b^{5}\right)} d e^{5} + 73 \, {\left(5 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{4} - 33 \, {\left(120 \, B b^{6} d^{4} e^{2} + {\left(4867 \, B a b^{5} - 195 \, A b^{6}\right)} d^{3} e^{3} + {\left(12651 \, B a^{2} b^{4} - 7787 \, A a b^{5}\right)} d^{2} e^{4} + {\left(8267 \, B a^{3} b^{3} - 15691 \, A a^{2} b^{4}\right)} d e^{5} + 279 \, {\left(5 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} e^{6}\right)} x^{3} + 11 \, {\left(80 \, B b^{6} d^{5} e - 10 \, {\left(135 \, B a b^{5} + 13 \, A b^{6}\right)} d^{4} e^{2} - {\left(20339 \, B a^{2} b^{4} - 2275 \, A a b^{5}\right)} d^{3} e^{3} - {\left(28157 \, B a^{3} b^{3} - 31629 \, A a^{2} b^{4}\right)} d^{2} e^{4} - {\left(11019 \, B a^{4} b^{2} - 25987 \, A a^{3} b^{3}\right)} d e^{5} - 128 \, {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} e^{6}\right)} x^{2} - {\left(320 \, B b^{6} d^{6} - 40 \, {\left(79 \, B a b^{5} + 13 \, A b^{6}\right)} d^{5} e + 1820 \, {\left(11 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} d^{4} e^{2} + {\left(134441 \, B a^{3} b^{3} - 35945 \, A a^{2} b^{4}\right)} d^{3} e^{3} + {\left(103033 \, B a^{4} b^{2} - 196001 \, A a^{3} b^{3}\right)} d^{2} e^{4} + 128 \, {\left(127 \, B a^{5} b - 351 \, A a^{4} b^{2}\right)} d e^{5} - 128 \, {\left(5 \, B a^{6} - 13 \, A a^{5} b\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{4} b^{7} d^{10} - 7 \, a^{5} b^{6} d^{9} e + 21 \, a^{6} b^{5} d^{8} e^{2} - 35 \, a^{7} b^{4} d^{7} e^{3} + 35 \, a^{8} b^{3} d^{6} e^{4} - 21 \, a^{9} b^{2} d^{5} e^{5} + 7 \, a^{10} b d^{4} e^{6} - a^{11} d^{3} e^{7} + {\left(b^{11} d^{7} e^{3} - 7 \, a b^{10} d^{6} e^{4} + 21 \, a^{2} b^{9} d^{5} e^{5} - 35 \, a^{3} b^{8} d^{4} e^{6} + 35 \, a^{4} b^{7} d^{3} e^{7} - 21 \, a^{5} b^{6} d^{2} e^{8} + 7 \, a^{6} b^{5} d e^{9} - a^{7} b^{4} e^{10}\right)} x^{7} + {\left(3 \, b^{11} d^{8} e^{2} - 17 \, a b^{10} d^{7} e^{3} + 35 \, a^{2} b^{9} d^{6} e^{4} - 21 \, a^{3} b^{8} d^{5} e^{5} - 35 \, a^{4} b^{7} d^{4} e^{6} + 77 \, a^{5} b^{6} d^{3} e^{7} - 63 \, a^{6} b^{5} d^{2} e^{8} + 25 \, a^{7} b^{4} d e^{9} - 4 \, a^{8} b^{3} e^{10}\right)} x^{6} + 3 \, {\left(b^{11} d^{9} e - 3 \, a b^{10} d^{8} e^{2} - 5 \, a^{2} b^{9} d^{7} e^{3} + 35 \, a^{3} b^{8} d^{6} e^{4} - 63 \, a^{4} b^{7} d^{5} e^{5} + 49 \, a^{5} b^{6} d^{4} e^{6} - 7 \, a^{6} b^{5} d^{3} e^{7} - 15 \, a^{7} b^{4} d^{2} e^{8} + 10 \, a^{8} b^{3} d e^{9} - 2 \, a^{9} b^{2} e^{10}\right)} x^{5} + {\left(b^{11} d^{10} + 5 \, a b^{10} d^{9} e - 45 \, a^{2} b^{9} d^{8} e^{2} + 95 \, a^{3} b^{8} d^{7} e^{3} - 35 \, a^{4} b^{7} d^{6} e^{4} - 147 \, a^{5} b^{6} d^{5} e^{5} + 245 \, a^{6} b^{5} d^{4} e^{6} - 155 \, a^{7} b^{4} d^{3} e^{7} + 30 \, a^{8} b^{3} d^{2} e^{8} + 10 \, a^{9} b^{2} d e^{9} - 4 \, a^{10} b e^{10}\right)} x^{4} + {\left(4 \, a b^{10} d^{10} - 10 \, a^{2} b^{9} d^{9} e - 30 \, a^{3} b^{8} d^{8} e^{2} + 155 \, a^{4} b^{7} d^{7} e^{3} - 245 \, a^{5} b^{6} d^{6} e^{4} + 147 \, a^{6} b^{5} d^{5} e^{5} + 35 \, a^{7} b^{4} d^{4} e^{6} - 95 \, a^{8} b^{3} d^{3} e^{7} + 45 \, a^{9} b^{2} d^{2} e^{8} - 5 \, a^{10} b d e^{9} - a^{11} e^{10}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{9} d^{10} - 10 \, a^{3} b^{8} d^{9} e + 15 \, a^{4} b^{7} d^{8} e^{2} + 7 \, a^{5} b^{6} d^{7} e^{3} - 49 \, a^{6} b^{5} d^{6} e^{4} + 63 \, a^{7} b^{4} d^{5} e^{5} - 35 \, a^{8} b^{3} d^{4} e^{6} + 5 \, a^{9} b^{2} d^{3} e^{7} + 3 \, a^{10} b d^{2} e^{8} - a^{11} d e^{9}\right)} x^{2} + {\left(4 \, a^{3} b^{8} d^{10} - 25 \, a^{4} b^{7} d^{9} e + 63 \, a^{5} b^{6} d^{8} e^{2} - 77 \, a^{6} b^{5} d^{7} e^{3} + 35 \, a^{7} b^{4} d^{6} e^{4} + 21 \, a^{8} b^{3} d^{5} e^{5} - 35 \, a^{9} b^{2} d^{4} e^{6} + 17 \, a^{10} b d^{3} e^{7} - 3 \, a^{11} d^{2} e^{8}\right)} x\right)}}, \frac{3465 \, {\left(8 \, B a^{4} b^{2} d^{4} e^{3} + {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d^{3} e^{4} + {\left(8 \, B b^{6} d e^{6} + {\left(5 \, B a b^{5} - 13 \, A b^{6}\right)} e^{7}\right)} x^{7} + {\left(24 \, B b^{6} d^{2} e^{5} + {\left(47 \, B a b^{5} - 39 \, A b^{6}\right)} d e^{6} + 4 \, {\left(5 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} e^{7}\right)} x^{6} + 3 \, {\left(8 \, B b^{6} d^{3} e^{4} + {\left(37 \, B a b^{5} - 13 \, A b^{6}\right)} d^{2} e^{5} + 4 \, {\left(9 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d e^{6} + 2 \, {\left(5 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{5} + {\left(8 \, B b^{6} d^{4} e^{3} + {\left(101 \, B a b^{5} - 13 \, A b^{6}\right)} d^{3} e^{4} + 12 \, {\left(17 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d^{2} e^{5} + 2 \, {\left(61 \, B a^{3} b^{3} - 117 \, A a^{2} b^{4}\right)} d e^{6} + 4 \, {\left(5 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{4} + {\left(32 \, B a b^{5} d^{4} e^{3} + 4 \, {\left(41 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} d^{3} e^{4} + 6 \, {\left(31 \, B a^{3} b^{3} - 39 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 4 \, {\left(17 \, B a^{4} b^{2} - 39 \, A a^{3} b^{3}\right)} d e^{6} + {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{3} + 3 \, {\left(16 \, B a^{2} b^{4} d^{4} e^{3} + 2 \, {\left(21 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 4 \, {\left(7 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} d^{2} e^{5} + {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d e^{6}\right)} x^{2} + {\left(32 \, B a^{3} b^{3} d^{4} e^{3} + 4 \, {\left(11 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 3 \, {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} d^{2} e^{5}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) + {\left(384 \, A a^{6} e^{6} - 80 \, {\left(B a b^{5} + 3 \, A b^{6}\right)} d^{6} + 280 \, {\left(3 \, B a^{2} b^{4} + 7 \, A a b^{5}\right)} d^{5} e - 70 \, {\left(79 \, B a^{3} b^{3} + 109 \, A a^{2} b^{4}\right)} d^{4} e^{2} - {\left(33619 \, B a^{4} b^{2} - 22155 \, A a^{3} b^{3}\right)} d^{3} e^{3} - 128 \, {\left(54 \, B a^{5} b - 253 \, A a^{4} b^{2}\right)} d^{2} e^{4} + 128 \, {\left(2 \, B a^{6} - 31 \, A a^{5} b\right)} d e^{5} - 3465 \, {\left(8 \, B b^{6} d e^{5} + {\left(5 \, B a b^{5} - 13 \, A b^{6}\right)} e^{6}\right)} x^{6} - 1155 \, {\left(56 \, B b^{6} d^{2} e^{4} + {\left(123 \, B a b^{5} - 91 \, A b^{6}\right)} d e^{5} + 11 \, {\left(5 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} e^{6}\right)} x^{5} - 231 \, {\left(184 \, B b^{6} d^{3} e^{3} + {\left(1147 \, B a b^{5} - 299 \, A b^{6}\right)} d^{2} e^{4} + {\left(1229 \, B a^{2} b^{4} - 1677 \, A a b^{5}\right)} d e^{5} + 73 \, {\left(5 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{4} - 33 \, {\left(120 \, B b^{6} d^{4} e^{2} + {\left(4867 \, B a b^{5} - 195 \, A b^{6}\right)} d^{3} e^{3} + {\left(12651 \, B a^{2} b^{4} - 7787 \, A a b^{5}\right)} d^{2} e^{4} + {\left(8267 \, B a^{3} b^{3} - 15691 \, A a^{2} b^{4}\right)} d e^{5} + 279 \, {\left(5 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} e^{6}\right)} x^{3} + 11 \, {\left(80 \, B b^{6} d^{5} e - 10 \, {\left(135 \, B a b^{5} + 13 \, A b^{6}\right)} d^{4} e^{2} - {\left(20339 \, B a^{2} b^{4} - 2275 \, A a b^{5}\right)} d^{3} e^{3} - {\left(28157 \, B a^{3} b^{3} - 31629 \, A a^{2} b^{4}\right)} d^{2} e^{4} - {\left(11019 \, B a^{4} b^{2} - 25987 \, A a^{3} b^{3}\right)} d e^{5} - 128 \, {\left(5 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} e^{6}\right)} x^{2} - {\left(320 \, B b^{6} d^{6} - 40 \, {\left(79 \, B a b^{5} + 13 \, A b^{6}\right)} d^{5} e + 1820 \, {\left(11 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} d^{4} e^{2} + {\left(134441 \, B a^{3} b^{3} - 35945 \, A a^{2} b^{4}\right)} d^{3} e^{3} + {\left(103033 \, B a^{4} b^{2} - 196001 \, A a^{3} b^{3}\right)} d^{2} e^{4} + 128 \, {\left(127 \, B a^{5} b - 351 \, A a^{4} b^{2}\right)} d e^{5} - 128 \, {\left(5 \, B a^{6} - 13 \, A a^{5} b\right)} e^{6}\right)} x\right)} \sqrt{e x + d}}{960 \, {\left(a^{4} b^{7} d^{10} - 7 \, a^{5} b^{6} d^{9} e + 21 \, a^{6} b^{5} d^{8} e^{2} - 35 \, a^{7} b^{4} d^{7} e^{3} + 35 \, a^{8} b^{3} d^{6} e^{4} - 21 \, a^{9} b^{2} d^{5} e^{5} + 7 \, a^{10} b d^{4} e^{6} - a^{11} d^{3} e^{7} + {\left(b^{11} d^{7} e^{3} - 7 \, a b^{10} d^{6} e^{4} + 21 \, a^{2} b^{9} d^{5} e^{5} - 35 \, a^{3} b^{8} d^{4} e^{6} + 35 \, a^{4} b^{7} d^{3} e^{7} - 21 \, a^{5} b^{6} d^{2} e^{8} + 7 \, a^{6} b^{5} d e^{9} - a^{7} b^{4} e^{10}\right)} x^{7} + {\left(3 \, b^{11} d^{8} e^{2} - 17 \, a b^{10} d^{7} e^{3} + 35 \, a^{2} b^{9} d^{6} e^{4} - 21 \, a^{3} b^{8} d^{5} e^{5} - 35 \, a^{4} b^{7} d^{4} e^{6} + 77 \, a^{5} b^{6} d^{3} e^{7} - 63 \, a^{6} b^{5} d^{2} e^{8} + 25 \, a^{7} b^{4} d e^{9} - 4 \, a^{8} b^{3} e^{10}\right)} x^{6} + 3 \, {\left(b^{11} d^{9} e - 3 \, a b^{10} d^{8} e^{2} - 5 \, a^{2} b^{9} d^{7} e^{3} + 35 \, a^{3} b^{8} d^{6} e^{4} - 63 \, a^{4} b^{7} d^{5} e^{5} + 49 \, a^{5} b^{6} d^{4} e^{6} - 7 \, a^{6} b^{5} d^{3} e^{7} - 15 \, a^{7} b^{4} d^{2} e^{8} + 10 \, a^{8} b^{3} d e^{9} - 2 \, a^{9} b^{2} e^{10}\right)} x^{5} + {\left(b^{11} d^{10} + 5 \, a b^{10} d^{9} e - 45 \, a^{2} b^{9} d^{8} e^{2} + 95 \, a^{3} b^{8} d^{7} e^{3} - 35 \, a^{4} b^{7} d^{6} e^{4} - 147 \, a^{5} b^{6} d^{5} e^{5} + 245 \, a^{6} b^{5} d^{4} e^{6} - 155 \, a^{7} b^{4} d^{3} e^{7} + 30 \, a^{8} b^{3} d^{2} e^{8} + 10 \, a^{9} b^{2} d e^{9} - 4 \, a^{10} b e^{10}\right)} x^{4} + {\left(4 \, a b^{10} d^{10} - 10 \, a^{2} b^{9} d^{9} e - 30 \, a^{3} b^{8} d^{8} e^{2} + 155 \, a^{4} b^{7} d^{7} e^{3} - 245 \, a^{5} b^{6} d^{6} e^{4} + 147 \, a^{6} b^{5} d^{5} e^{5} + 35 \, a^{7} b^{4} d^{4} e^{6} - 95 \, a^{8} b^{3} d^{3} e^{7} + 45 \, a^{9} b^{2} d^{2} e^{8} - 5 \, a^{10} b d e^{9} - a^{11} e^{10}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{9} d^{10} - 10 \, a^{3} b^{8} d^{9} e + 15 \, a^{4} b^{7} d^{8} e^{2} + 7 \, a^{5} b^{6} d^{7} e^{3} - 49 \, a^{6} b^{5} d^{6} e^{4} + 63 \, a^{7} b^{4} d^{5} e^{5} - 35 \, a^{8} b^{3} d^{4} e^{6} + 5 \, a^{9} b^{2} d^{3} e^{7} + 3 \, a^{10} b d^{2} e^{8} - a^{11} d e^{9}\right)} x^{2} + {\left(4 \, a^{3} b^{8} d^{10} - 25 \, a^{4} b^{7} d^{9} e + 63 \, a^{5} b^{6} d^{8} e^{2} - 77 \, a^{6} b^{5} d^{7} e^{3} + 35 \, a^{7} b^{4} d^{6} e^{4} + 21 \, a^{8} b^{3} d^{5} e^{5} - 35 \, a^{9} b^{2} d^{4} e^{6} + 17 \, a^{10} b d^{3} e^{7} - 3 \, a^{11} d^{2} e^{8}\right)} x\right)}}\right]"," ",0,"[1/1920*(3465*(8*B*a^4*b^2*d^4*e^3 + (5*B*a^5*b - 13*A*a^4*b^2)*d^3*e^4 + (8*B*b^6*d*e^6 + (5*B*a*b^5 - 13*A*b^6)*e^7)*x^7 + (24*B*b^6*d^2*e^5 + (47*B*a*b^5 - 39*A*b^6)*d*e^6 + 4*(5*B*a^2*b^4 - 13*A*a*b^5)*e^7)*x^6 + 3*(8*B*b^6*d^3*e^4 + (37*B*a*b^5 - 13*A*b^6)*d^2*e^5 + 4*(9*B*a^2*b^4 - 13*A*a*b^5)*d*e^6 + 2*(5*B*a^3*b^3 - 13*A*a^2*b^4)*e^7)*x^5 + (8*B*b^6*d^4*e^3 + (101*B*a*b^5 - 13*A*b^6)*d^3*e^4 + 12*(17*B*a^2*b^4 - 13*A*a*b^5)*d^2*e^5 + 2*(61*B*a^3*b^3 - 117*A*a^2*b^4)*d*e^6 + 4*(5*B*a^4*b^2 - 13*A*a^3*b^3)*e^7)*x^4 + (32*B*a*b^5*d^4*e^3 + 4*(41*B*a^2*b^4 - 13*A*a*b^5)*d^3*e^4 + 6*(31*B*a^3*b^3 - 39*A*a^2*b^4)*d^2*e^5 + 4*(17*B*a^4*b^2 - 39*A*a^3*b^3)*d*e^6 + (5*B*a^5*b - 13*A*a^4*b^2)*e^7)*x^3 + 3*(16*B*a^2*b^4*d^4*e^3 + 2*(21*B*a^3*b^3 - 13*A*a^2*b^4)*d^3*e^4 + 4*(7*B*a^4*b^2 - 13*A*a^3*b^3)*d^2*e^5 + (5*B*a^5*b - 13*A*a^4*b^2)*d*e^6)*x^2 + (32*B*a^3*b^3*d^4*e^3 + 4*(11*B*a^4*b^2 - 13*A*a^3*b^3)*d^3*e^4 + 3*(5*B*a^5*b - 13*A*a^4*b^2)*d^2*e^5)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(384*A*a^6*e^6 - 80*(B*a*b^5 + 3*A*b^6)*d^6 + 280*(3*B*a^2*b^4 + 7*A*a*b^5)*d^5*e - 70*(79*B*a^3*b^3 + 109*A*a^2*b^4)*d^4*e^2 - (33619*B*a^4*b^2 - 22155*A*a^3*b^3)*d^3*e^3 - 128*(54*B*a^5*b - 253*A*a^4*b^2)*d^2*e^4 + 128*(2*B*a^6 - 31*A*a^5*b)*d*e^5 - 3465*(8*B*b^6*d*e^5 + (5*B*a*b^5 - 13*A*b^6)*e^6)*x^6 - 1155*(56*B*b^6*d^2*e^4 + (123*B*a*b^5 - 91*A*b^6)*d*e^5 + 11*(5*B*a^2*b^4 - 13*A*a*b^5)*e^6)*x^5 - 231*(184*B*b^6*d^3*e^3 + (1147*B*a*b^5 - 299*A*b^6)*d^2*e^4 + (1229*B*a^2*b^4 - 1677*A*a*b^5)*d*e^5 + 73*(5*B*a^3*b^3 - 13*A*a^2*b^4)*e^6)*x^4 - 33*(120*B*b^6*d^4*e^2 + (4867*B*a*b^5 - 195*A*b^6)*d^3*e^3 + (12651*B*a^2*b^4 - 7787*A*a*b^5)*d^2*e^4 + (8267*B*a^3*b^3 - 15691*A*a^2*b^4)*d*e^5 + 279*(5*B*a^4*b^2 - 13*A*a^3*b^3)*e^6)*x^3 + 11*(80*B*b^6*d^5*e - 10*(135*B*a*b^5 + 13*A*b^6)*d^4*e^2 - (20339*B*a^2*b^4 - 2275*A*a*b^5)*d^3*e^3 - (28157*B*a^3*b^3 - 31629*A*a^2*b^4)*d^2*e^4 - (11019*B*a^4*b^2 - 25987*A*a^3*b^3)*d*e^5 - 128*(5*B*a^5*b - 13*A*a^4*b^2)*e^6)*x^2 - (320*B*b^6*d^6 - 40*(79*B*a*b^5 + 13*A*b^6)*d^5*e + 1820*(11*B*a^2*b^4 + 3*A*a*b^5)*d^4*e^2 + (134441*B*a^3*b^3 - 35945*A*a^2*b^4)*d^3*e^3 + (103033*B*a^4*b^2 - 196001*A*a^3*b^3)*d^2*e^4 + 128*(127*B*a^5*b - 351*A*a^4*b^2)*d*e^5 - 128*(5*B*a^6 - 13*A*a^5*b)*e^6)*x)*sqrt(e*x + d))/(a^4*b^7*d^10 - 7*a^5*b^6*d^9*e + 21*a^6*b^5*d^8*e^2 - 35*a^7*b^4*d^7*e^3 + 35*a^8*b^3*d^6*e^4 - 21*a^9*b^2*d^5*e^5 + 7*a^10*b*d^4*e^6 - a^11*d^3*e^7 + (b^11*d^7*e^3 - 7*a*b^10*d^6*e^4 + 21*a^2*b^9*d^5*e^5 - 35*a^3*b^8*d^4*e^6 + 35*a^4*b^7*d^3*e^7 - 21*a^5*b^6*d^2*e^8 + 7*a^6*b^5*d*e^9 - a^7*b^4*e^10)*x^7 + (3*b^11*d^8*e^2 - 17*a*b^10*d^7*e^3 + 35*a^2*b^9*d^6*e^4 - 21*a^3*b^8*d^5*e^5 - 35*a^4*b^7*d^4*e^6 + 77*a^5*b^6*d^3*e^7 - 63*a^6*b^5*d^2*e^8 + 25*a^7*b^4*d*e^9 - 4*a^8*b^3*e^10)*x^6 + 3*(b^11*d^9*e - 3*a*b^10*d^8*e^2 - 5*a^2*b^9*d^7*e^3 + 35*a^3*b^8*d^6*e^4 - 63*a^4*b^7*d^5*e^5 + 49*a^5*b^6*d^4*e^6 - 7*a^6*b^5*d^3*e^7 - 15*a^7*b^4*d^2*e^8 + 10*a^8*b^3*d*e^9 - 2*a^9*b^2*e^10)*x^5 + (b^11*d^10 + 5*a*b^10*d^9*e - 45*a^2*b^9*d^8*e^2 + 95*a^3*b^8*d^7*e^3 - 35*a^4*b^7*d^6*e^4 - 147*a^5*b^6*d^5*e^5 + 245*a^6*b^5*d^4*e^6 - 155*a^7*b^4*d^3*e^7 + 30*a^8*b^3*d^2*e^8 + 10*a^9*b^2*d*e^9 - 4*a^10*b*e^10)*x^4 + (4*a*b^10*d^10 - 10*a^2*b^9*d^9*e - 30*a^3*b^8*d^8*e^2 + 155*a^4*b^7*d^7*e^3 - 245*a^5*b^6*d^6*e^4 + 147*a^6*b^5*d^5*e^5 + 35*a^7*b^4*d^4*e^6 - 95*a^8*b^3*d^3*e^7 + 45*a^9*b^2*d^2*e^8 - 5*a^10*b*d*e^9 - a^11*e^10)*x^3 + 3*(2*a^2*b^9*d^10 - 10*a^3*b^8*d^9*e + 15*a^4*b^7*d^8*e^2 + 7*a^5*b^6*d^7*e^3 - 49*a^6*b^5*d^6*e^4 + 63*a^7*b^4*d^5*e^5 - 35*a^8*b^3*d^4*e^6 + 5*a^9*b^2*d^3*e^7 + 3*a^10*b*d^2*e^8 - a^11*d*e^9)*x^2 + (4*a^3*b^8*d^10 - 25*a^4*b^7*d^9*e + 63*a^5*b^6*d^8*e^2 - 77*a^6*b^5*d^7*e^3 + 35*a^7*b^4*d^6*e^4 + 21*a^8*b^3*d^5*e^5 - 35*a^9*b^2*d^4*e^6 + 17*a^10*b*d^3*e^7 - 3*a^11*d^2*e^8)*x), 1/960*(3465*(8*B*a^4*b^2*d^4*e^3 + (5*B*a^5*b - 13*A*a^4*b^2)*d^3*e^4 + (8*B*b^6*d*e^6 + (5*B*a*b^5 - 13*A*b^6)*e^7)*x^7 + (24*B*b^6*d^2*e^5 + (47*B*a*b^5 - 39*A*b^6)*d*e^6 + 4*(5*B*a^2*b^4 - 13*A*a*b^5)*e^7)*x^6 + 3*(8*B*b^6*d^3*e^4 + (37*B*a*b^5 - 13*A*b^6)*d^2*e^5 + 4*(9*B*a^2*b^4 - 13*A*a*b^5)*d*e^6 + 2*(5*B*a^3*b^3 - 13*A*a^2*b^4)*e^7)*x^5 + (8*B*b^6*d^4*e^3 + (101*B*a*b^5 - 13*A*b^6)*d^3*e^4 + 12*(17*B*a^2*b^4 - 13*A*a*b^5)*d^2*e^5 + 2*(61*B*a^3*b^3 - 117*A*a^2*b^4)*d*e^6 + 4*(5*B*a^4*b^2 - 13*A*a^3*b^3)*e^7)*x^4 + (32*B*a*b^5*d^4*e^3 + 4*(41*B*a^2*b^4 - 13*A*a*b^5)*d^3*e^4 + 6*(31*B*a^3*b^3 - 39*A*a^2*b^4)*d^2*e^5 + 4*(17*B*a^4*b^2 - 39*A*a^3*b^3)*d*e^6 + (5*B*a^5*b - 13*A*a^4*b^2)*e^7)*x^3 + 3*(16*B*a^2*b^4*d^4*e^3 + 2*(21*B*a^3*b^3 - 13*A*a^2*b^4)*d^3*e^4 + 4*(7*B*a^4*b^2 - 13*A*a^3*b^3)*d^2*e^5 + (5*B*a^5*b - 13*A*a^4*b^2)*d*e^6)*x^2 + (32*B*a^3*b^3*d^4*e^3 + 4*(11*B*a^4*b^2 - 13*A*a^3*b^3)*d^3*e^4 + 3*(5*B*a^5*b - 13*A*a^4*b^2)*d^2*e^5)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) + (384*A*a^6*e^6 - 80*(B*a*b^5 + 3*A*b^6)*d^6 + 280*(3*B*a^2*b^4 + 7*A*a*b^5)*d^5*e - 70*(79*B*a^3*b^3 + 109*A*a^2*b^4)*d^4*e^2 - (33619*B*a^4*b^2 - 22155*A*a^3*b^3)*d^3*e^3 - 128*(54*B*a^5*b - 253*A*a^4*b^2)*d^2*e^4 + 128*(2*B*a^6 - 31*A*a^5*b)*d*e^5 - 3465*(8*B*b^6*d*e^5 + (5*B*a*b^5 - 13*A*b^6)*e^6)*x^6 - 1155*(56*B*b^6*d^2*e^4 + (123*B*a*b^5 - 91*A*b^6)*d*e^5 + 11*(5*B*a^2*b^4 - 13*A*a*b^5)*e^6)*x^5 - 231*(184*B*b^6*d^3*e^3 + (1147*B*a*b^5 - 299*A*b^6)*d^2*e^4 + (1229*B*a^2*b^4 - 1677*A*a*b^5)*d*e^5 + 73*(5*B*a^3*b^3 - 13*A*a^2*b^4)*e^6)*x^4 - 33*(120*B*b^6*d^4*e^2 + (4867*B*a*b^5 - 195*A*b^6)*d^3*e^3 + (12651*B*a^2*b^4 - 7787*A*a*b^5)*d^2*e^4 + (8267*B*a^3*b^3 - 15691*A*a^2*b^4)*d*e^5 + 279*(5*B*a^4*b^2 - 13*A*a^3*b^3)*e^6)*x^3 + 11*(80*B*b^6*d^5*e - 10*(135*B*a*b^5 + 13*A*b^6)*d^4*e^2 - (20339*B*a^2*b^4 - 2275*A*a*b^5)*d^3*e^3 - (28157*B*a^3*b^3 - 31629*A*a^2*b^4)*d^2*e^4 - (11019*B*a^4*b^2 - 25987*A*a^3*b^3)*d*e^5 - 128*(5*B*a^5*b - 13*A*a^4*b^2)*e^6)*x^2 - (320*B*b^6*d^6 - 40*(79*B*a*b^5 + 13*A*b^6)*d^5*e + 1820*(11*B*a^2*b^4 + 3*A*a*b^5)*d^4*e^2 + (134441*B*a^3*b^3 - 35945*A*a^2*b^4)*d^3*e^3 + (103033*B*a^4*b^2 - 196001*A*a^3*b^3)*d^2*e^4 + 128*(127*B*a^5*b - 351*A*a^4*b^2)*d*e^5 - 128*(5*B*a^6 - 13*A*a^5*b)*e^6)*x)*sqrt(e*x + d))/(a^4*b^7*d^10 - 7*a^5*b^6*d^9*e + 21*a^6*b^5*d^8*e^2 - 35*a^7*b^4*d^7*e^3 + 35*a^8*b^3*d^6*e^4 - 21*a^9*b^2*d^5*e^5 + 7*a^10*b*d^4*e^6 - a^11*d^3*e^7 + (b^11*d^7*e^3 - 7*a*b^10*d^6*e^4 + 21*a^2*b^9*d^5*e^5 - 35*a^3*b^8*d^4*e^6 + 35*a^4*b^7*d^3*e^7 - 21*a^5*b^6*d^2*e^8 + 7*a^6*b^5*d*e^9 - a^7*b^4*e^10)*x^7 + (3*b^11*d^8*e^2 - 17*a*b^10*d^7*e^3 + 35*a^2*b^9*d^6*e^4 - 21*a^3*b^8*d^5*e^5 - 35*a^4*b^7*d^4*e^6 + 77*a^5*b^6*d^3*e^7 - 63*a^6*b^5*d^2*e^8 + 25*a^7*b^4*d*e^9 - 4*a^8*b^3*e^10)*x^6 + 3*(b^11*d^9*e - 3*a*b^10*d^8*e^2 - 5*a^2*b^9*d^7*e^3 + 35*a^3*b^8*d^6*e^4 - 63*a^4*b^7*d^5*e^5 + 49*a^5*b^6*d^4*e^6 - 7*a^6*b^5*d^3*e^7 - 15*a^7*b^4*d^2*e^8 + 10*a^8*b^3*d*e^9 - 2*a^9*b^2*e^10)*x^5 + (b^11*d^10 + 5*a*b^10*d^9*e - 45*a^2*b^9*d^8*e^2 + 95*a^3*b^8*d^7*e^3 - 35*a^4*b^7*d^6*e^4 - 147*a^5*b^6*d^5*e^5 + 245*a^6*b^5*d^4*e^6 - 155*a^7*b^4*d^3*e^7 + 30*a^8*b^3*d^2*e^8 + 10*a^9*b^2*d*e^9 - 4*a^10*b*e^10)*x^4 + (4*a*b^10*d^10 - 10*a^2*b^9*d^9*e - 30*a^3*b^8*d^8*e^2 + 155*a^4*b^7*d^7*e^3 - 245*a^5*b^6*d^6*e^4 + 147*a^6*b^5*d^5*e^5 + 35*a^7*b^4*d^4*e^6 - 95*a^8*b^3*d^3*e^7 + 45*a^9*b^2*d^2*e^8 - 5*a^10*b*d*e^9 - a^11*e^10)*x^3 + 3*(2*a^2*b^9*d^10 - 10*a^3*b^8*d^9*e + 15*a^4*b^7*d^8*e^2 + 7*a^5*b^6*d^7*e^3 - 49*a^6*b^5*d^6*e^4 + 63*a^7*b^4*d^5*e^5 - 35*a^8*b^3*d^4*e^6 + 5*a^9*b^2*d^3*e^7 + 3*a^10*b*d^2*e^8 - a^11*d*e^9)*x^2 + (4*a^3*b^8*d^10 - 25*a^4*b^7*d^9*e + 63*a^5*b^6*d^8*e^2 - 77*a^6*b^5*d^7*e^3 + 35*a^7*b^4*d^6*e^4 + 21*a^8*b^3*d^5*e^5 - 35*a^9*b^2*d^4*e^6 + 17*a^10*b*d^3*e^7 - 3*a^11*d^2*e^8)*x)]","B",0
1884,1,2274,0,0.477246," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{{\left(A a^{4} d e^{5} m^{5} - 120 \, B b^{4} d^{6} + 720 \, A a^{4} d e^{5} + 144 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{5} e - 360 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{2} + 480 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{3} - 360 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4} + {\left(B b^{4} e^{6} m^{5} + 15 \, B b^{4} e^{6} m^{4} + 85 \, B b^{4} e^{6} m^{3} + 225 \, B b^{4} e^{6} m^{2} + 274 \, B b^{4} e^{6} m + 120 \, B b^{4} e^{6}\right)} x^{6} + {\left(144 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6} + {\left(B b^{4} d e^{5} + {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m^{5} + 2 \, {\left(5 \, B b^{4} d e^{5} + 8 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m^{4} + 5 \, {\left(7 \, B b^{4} d e^{5} + 19 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m^{3} + 10 \, {\left(5 \, B b^{4} d e^{5} + 26 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m^{2} + 12 \, {\left(2 \, B b^{4} d e^{5} + 27 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m\right)} x^{5} + {\left(20 \, A a^{4} d e^{5} - {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4}\right)} m^{4} + {\left(360 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6} + {\left({\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m^{5} - {\left(5 \, B b^{4} d^{2} e^{4} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} - 34 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m^{4} - {\left(30 \, B b^{4} d^{2} e^{4} - 47 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} - 214 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m^{3} - {\left(55 \, B b^{4} d^{2} e^{4} - 72 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} - 614 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m^{2} - 6 \, {\left(5 \, B b^{4} d^{2} e^{4} - 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} - 132 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m\right)} x^{4} + {\left(155 \, A a^{4} d e^{5} + 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{3} - 18 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4}\right)} m^{3} + 2 \, {\left(240 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6} + {\left({\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} + {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m^{5} - 2 \, {\left({\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{4} - 7 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} - 9 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m^{4} + {\left(10 \, B b^{4} d^{3} e^{3} - 18 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{4} + 65 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} + 121 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m^{3} + 2 \, {\left(15 \, B b^{4} d^{3} e^{3} - 20 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{4} + 56 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} + 186 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m^{2} + 4 \, {\left(5 \, B b^{4} d^{3} e^{3} - 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{4} + 15 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} + 127 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m\right)} x^{3} + {\left(580 \, A a^{4} d e^{5} - 12 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{2} + 60 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{3} - 119 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4}\right)} m^{2} + {\left(360 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6} + {\left(2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} + {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m^{5} - {\left(6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{4} - 32 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} - 19 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m^{4} + {\left(12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{3} - 72 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{4} + 178 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} + 137 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m^{3} - {\left(60 \, B b^{4} d^{4} e^{2} - 84 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{3} + 246 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{4} - 388 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} - 461 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m^{2} - 6 \, {\left(10 \, B b^{4} d^{4} e^{2} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{3} + 30 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{4} - 40 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} - 117 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m\right)} x^{2} + 2 \, {\left(522 \, A a^{4} d e^{5} + 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{5} e - 66 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{2} + 148 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{3} - 171 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4}\right)} m + {\left(720 \, A a^{4} e^{6} + {\left(A a^{4} e^{6} + {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m^{5} + 2 \, {\left(10 \, A a^{4} e^{6} - 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{4} + 9 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m^{4} + {\left(155 \, A a^{4} e^{6} + 12 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{3} - 60 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{4} + 119 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m^{3} + 2 \, {\left(290 \, A a^{4} e^{6} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e^{2} + 66 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{3} - 148 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{4} + 171 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m^{2} + 12 \, {\left(10 \, B b^{4} d^{5} e + 87 \, A a^{4} e^{6} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e^{2} + 30 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{3} - 40 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{4} + 30 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{6} m^{6} + 21 \, e^{6} m^{5} + 175 \, e^{6} m^{4} + 735 \, e^{6} m^{3} + 1624 \, e^{6} m^{2} + 1764 \, e^{6} m + 720 \, e^{6}}"," ",0,"(A*a^4*d*e^5*m^5 - 120*B*b^4*d^6 + 720*A*a^4*d*e^5 + 144*(4*B*a*b^3 + A*b^4)*d^5*e - 360*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^2 + 480*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 360*(B*a^4 + 4*A*a^3*b)*d^2*e^4 + (B*b^4*e^6*m^5 + 15*B*b^4*e^6*m^4 + 85*B*b^4*e^6*m^3 + 225*B*b^4*e^6*m^2 + 274*B*b^4*e^6*m + 120*B*b^4*e^6)*x^6 + (144*(4*B*a*b^3 + A*b^4)*e^6 + (B*b^4*d*e^5 + (4*B*a*b^3 + A*b^4)*e^6)*m^5 + 2*(5*B*b^4*d*e^5 + 8*(4*B*a*b^3 + A*b^4)*e^6)*m^4 + 5*(7*B*b^4*d*e^5 + 19*(4*B*a*b^3 + A*b^4)*e^6)*m^3 + 10*(5*B*b^4*d*e^5 + 26*(4*B*a*b^3 + A*b^4)*e^6)*m^2 + 12*(2*B*b^4*d*e^5 + 27*(4*B*a*b^3 + A*b^4)*e^6)*m)*x^5 + (20*A*a^4*d*e^5 - (B*a^4 + 4*A*a^3*b)*d^2*e^4)*m^4 + (360*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6 + ((4*B*a*b^3 + A*b^4)*d*e^5 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^5 - (5*B*b^4*d^2*e^4 - 12*(4*B*a*b^3 + A*b^4)*d*e^5 - 34*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^4 - (30*B*b^4*d^2*e^4 - 47*(4*B*a*b^3 + A*b^4)*d*e^5 - 214*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^3 - (55*B*b^4*d^2*e^4 - 72*(4*B*a*b^3 + A*b^4)*d*e^5 - 614*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^2 - 6*(5*B*b^4*d^2*e^4 - 6*(4*B*a*b^3 + A*b^4)*d*e^5 - 132*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m)*x^4 + (155*A*a^4*d*e^5 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 18*(B*a^4 + 4*A*a^3*b)*d^2*e^4)*m^3 + 2*(240*(2*B*a^3*b + 3*A*a^2*b^2)*e^6 + ((3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + (2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^5 - 2*((4*B*a*b^3 + A*b^4)*d^2*e^4 - 7*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 - 9*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^4 + (10*B*b^4*d^3*e^3 - 18*(4*B*a*b^3 + A*b^4)*d^2*e^4 + 65*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + 121*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^3 + 2*(15*B*b^4*d^3*e^3 - 20*(4*B*a*b^3 + A*b^4)*d^2*e^4 + 56*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + 186*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^2 + 4*(5*B*b^4*d^3*e^3 - 6*(4*B*a*b^3 + A*b^4)*d^2*e^4 + 15*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + 127*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m)*x^3 + (580*A*a^4*d*e^5 - 12*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^2 + 60*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 119*(B*a^4 + 4*A*a^3*b)*d^2*e^4)*m^2 + (360*(B*a^4 + 4*A*a^3*b)*e^6 + (2*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 + (B*a^4 + 4*A*a^3*b)*e^6)*m^5 - (6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 - 32*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 19*(B*a^4 + 4*A*a^3*b)*e^6)*m^4 + (12*(4*B*a*b^3 + A*b^4)*d^3*e^3 - 72*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 + 178*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 + 137*(B*a^4 + 4*A*a^3*b)*e^6)*m^3 - (60*B*b^4*d^4*e^2 - 84*(4*B*a*b^3 + A*b^4)*d^3*e^3 + 246*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 - 388*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 461*(B*a^4 + 4*A*a^3*b)*e^6)*m^2 - 6*(10*B*b^4*d^4*e^2 - 12*(4*B*a*b^3 + A*b^4)*d^3*e^3 + 30*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 - 40*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 117*(B*a^4 + 4*A*a^3*b)*e^6)*m)*x^2 + 2*(522*A*a^4*d*e^5 + 12*(4*B*a*b^3 + A*b^4)*d^5*e - 66*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^2 + 148*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 171*(B*a^4 + 4*A*a^3*b)*d^2*e^4)*m + (720*A*a^4*e^6 + (A*a^4*e^6 + (B*a^4 + 4*A*a^3*b)*d*e^5)*m^5 + 2*(10*A*a^4*e^6 - 2*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 9*(B*a^4 + 4*A*a^3*b)*d*e^5)*m^4 + (155*A*a^4*e^6 + 12*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^3 - 60*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 119*(B*a^4 + 4*A*a^3*b)*d*e^5)*m^3 + 2*(290*A*a^4*e^6 - 12*(4*B*a*b^3 + A*b^4)*d^4*e^2 + 66*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^3 - 148*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 171*(B*a^4 + 4*A*a^3*b)*d*e^5)*m^2 + 12*(10*B*b^4*d^5*e + 87*A*a^4*e^6 - 12*(4*B*a*b^3 + A*b^4)*d^4*e^2 + 30*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^3 - 40*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 30*(B*a^4 + 4*A*a^3*b)*d*e^5)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)","B",0
1885,1,660,0,0.475885," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{{\left(A a^{2} d e^{3} m^{3} - 6 \, B b^{2} d^{4} + 24 \, A a^{2} d e^{3} + 8 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e - 12 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{2} + {\left(B b^{2} e^{4} m^{3} + 6 \, B b^{2} e^{4} m^{2} + 11 \, B b^{2} e^{4} m + 6 \, B b^{2} e^{4}\right)} x^{4} + {\left(8 \, {\left(2 \, B a b + A b^{2}\right)} e^{4} + {\left(B b^{2} d e^{3} + {\left(2 \, B a b + A b^{2}\right)} e^{4}\right)} m^{3} + {\left(3 \, B b^{2} d e^{3} + 7 \, {\left(2 \, B a b + A b^{2}\right)} e^{4}\right)} m^{2} + 2 \, {\left(B b^{2} d e^{3} + 7 \, {\left(2 \, B a b + A b^{2}\right)} e^{4}\right)} m\right)} x^{3} + {\left(9 \, A a^{2} d e^{3} - {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{2}\right)} m^{2} + {\left(12 \, {\left(B a^{2} + 2 \, A a b\right)} e^{4} + {\left({\left(2 \, B a b + A b^{2}\right)} d e^{3} + {\left(B a^{2} + 2 \, A a b\right)} e^{4}\right)} m^{3} - {\left(3 \, B b^{2} d^{2} e^{2} - 5 \, {\left(2 \, B a b + A b^{2}\right)} d e^{3} - 8 \, {\left(B a^{2} + 2 \, A a b\right)} e^{4}\right)} m^{2} - {\left(3 \, B b^{2} d^{2} e^{2} - 4 \, {\left(2 \, B a b + A b^{2}\right)} d e^{3} - 19 \, {\left(B a^{2} + 2 \, A a b\right)} e^{4}\right)} m\right)} x^{2} + {\left(26 \, A a^{2} d e^{3} + 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e - 7 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{2}\right)} m + {\left(24 \, A a^{2} e^{4} + {\left(A a^{2} e^{4} + {\left(B a^{2} + 2 \, A a b\right)} d e^{3}\right)} m^{3} + {\left(9 \, A a^{2} e^{4} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{2} + 7 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{3}\right)} m^{2} + 2 \, {\left(3 \, B b^{2} d^{3} e + 13 \, A a^{2} e^{4} - 4 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{2} + 6 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"(A*a^2*d*e^3*m^3 - 6*B*b^2*d^4 + 24*A*a^2*d*e^3 + 8*(2*B*a*b + A*b^2)*d^3*e - 12*(B*a^2 + 2*A*a*b)*d^2*e^2 + (B*b^2*e^4*m^3 + 6*B*b^2*e^4*m^2 + 11*B*b^2*e^4*m + 6*B*b^2*e^4)*x^4 + (8*(2*B*a*b + A*b^2)*e^4 + (B*b^2*d*e^3 + (2*B*a*b + A*b^2)*e^4)*m^3 + (3*B*b^2*d*e^3 + 7*(2*B*a*b + A*b^2)*e^4)*m^2 + 2*(B*b^2*d*e^3 + 7*(2*B*a*b + A*b^2)*e^4)*m)*x^3 + (9*A*a^2*d*e^3 - (B*a^2 + 2*A*a*b)*d^2*e^2)*m^2 + (12*(B*a^2 + 2*A*a*b)*e^4 + ((2*B*a*b + A*b^2)*d*e^3 + (B*a^2 + 2*A*a*b)*e^4)*m^3 - (3*B*b^2*d^2*e^2 - 5*(2*B*a*b + A*b^2)*d*e^3 - 8*(B*a^2 + 2*A*a*b)*e^4)*m^2 - (3*B*b^2*d^2*e^2 - 4*(2*B*a*b + A*b^2)*d*e^3 - 19*(B*a^2 + 2*A*a*b)*e^4)*m)*x^2 + (26*A*a^2*d*e^3 + 2*(2*B*a*b + A*b^2)*d^3*e - 7*(B*a^2 + 2*A*a*b)*d^2*e^2)*m + (24*A*a^2*e^4 + (A*a^2*e^4 + (B*a^2 + 2*A*a*b)*d*e^3)*m^3 + (9*A*a^2*e^4 - 2*(2*B*a*b + A*b^2)*d^2*e^2 + 7*(B*a^2 + 2*A*a*b)*d*e^3)*m^2 + 2*(3*B*b^2*d^3*e + 13*A*a^2*e^4 - 4*(2*B*a*b + A*b^2)*d^2*e^2 + 6*(B*a^2 + 2*A*a*b)*d*e^3)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
1886,0,0,0,0.445745," ","integrate((B*x+A)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
1887,0,0,0,0.461418," ","integrate((B*x+A)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^m/(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4), x)","F",0
1888,1,3485,0,0.512549," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(A a^{5} d e^{6} m^{6} + 720 \, B b^{5} d^{7} + 5040 \, A a^{5} d e^{6} - 840 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{6} e + 5040 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{5} e^{2} - 12600 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e^{3} + 8400 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{4} - 2520 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{5} + {\left(B b^{5} e^{7} m^{6} + 21 \, B b^{5} e^{7} m^{5} + 175 \, B b^{5} e^{7} m^{4} + 735 \, B b^{5} e^{7} m^{3} + 1624 \, B b^{5} e^{7} m^{2} + 1764 \, B b^{5} e^{7} m + 720 \, B b^{5} e^{7}\right)} x^{7} + {\left(840 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{7} + {\left(B b^{5} d e^{6} + {\left(5 \, B a b^{4} + A b^{5}\right)} e^{7}\right)} m^{6} + {\left(15 \, B b^{5} d e^{6} + 22 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{7}\right)} m^{5} + 5 \, {\left(17 \, B b^{5} d e^{6} + 38 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{7}\right)} m^{4} + 5 \, {\left(45 \, B b^{5} d e^{6} + 164 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{7}\right)} m^{3} + {\left(274 \, B b^{5} d e^{6} + 1849 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{7}\right)} m^{2} + 2 \, {\left(60 \, B b^{5} d e^{6} + 1019 \, {\left(5 \, B a b^{4} + A b^{5}\right)} e^{7}\right)} m\right)} x^{6} + {\left(27 \, A a^{5} d e^{6} - {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{5}\right)} m^{5} + {\left(5040 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{7} + {\left({\left(5 \, B a b^{4} + A b^{5}\right)} d e^{6} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{7}\right)} m^{6} - {\left(6 \, B b^{5} d^{2} e^{5} - 17 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{6} - 115 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{7}\right)} m^{5} - 15 \, {\left(4 \, B b^{5} d^{2} e^{5} - 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{6} - 69 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{7}\right)} m^{4} - 5 \, {\left(42 \, B b^{5} d^{2} e^{5} - 59 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{6} - 925 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{7}\right)} m^{3} - 2 \, {\left(150 \, B b^{5} d^{2} e^{5} - 187 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{6} - 5360 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{7}\right)} m^{2} - 12 \, {\left(12 \, B b^{5} d^{2} e^{5} - 14 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d e^{6} - 1005 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} e^{7}\right)} m\right)} x^{5} + 5 \, {\left(59 \, A a^{5} d e^{6} + 2 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{4} - 5 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{5}\right)} m^{4} + 5 \, {\left(2520 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{7} + {\left({\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{6} + 2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{7}\right)} m^{6} - {\left({\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{5} - 19 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{6} - 48 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{7}\right)} m^{5} + {\left(6 \, B b^{5} d^{3} e^{4} - 13 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{5} + 131 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{6} + 452 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{7}\right)} m^{4} + {\left(36 \, B b^{5} d^{3} e^{4} - 53 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{5} + 401 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{6} + 2112 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{7}\right)} m^{3} + {\left(66 \, B b^{5} d^{3} e^{4} - 83 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{5} + 540 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{6} + 5090 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{7}\right)} m^{2} + 6 \, {\left(6 \, B b^{5} d^{3} e^{4} - 7 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{2} e^{5} + 42 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d e^{6} + 984 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} e^{7}\right)} m\right)} x^{4} + 5 \, {\left(333 \, A a^{5} d e^{6} - 12 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e^{3} + 44 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{4} - 49 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{5}\right)} m^{3} + 5 \, {\left(1680 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{7} + {\left(2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{6} + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{7}\right)} m^{6} - {\left(4 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{5} - 42 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{6} - 25 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{7}\right)} m^{5} + {\left(4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{4} - 64 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{5} + 326 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{6} + 247 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{7}\right)} m^{4} - {\left(24 \, B b^{5} d^{4} e^{3} - 40 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{4} + 332 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{5} - 1134 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{6} - 1219 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{7}\right)} m^{3} - 4 \, {\left(18 \, B b^{5} d^{4} e^{3} - 23 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{4} + 152 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{5} - 422 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{6} - 778 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{7}\right)} m^{2} - 4 \, {\left(12 \, B b^{5} d^{4} e^{3} - 14 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{3} e^{4} + 84 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{2} e^{5} - 210 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d e^{6} - 949 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} e^{7}\right)} m\right)} x^{3} + {\left(5104 \, A a^{5} d e^{6} + 120 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{5} e^{2} - 1080 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e^{3} + 1790 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{4} - 1175 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{5}\right)} m^{2} + {\left(2520 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{7} + {\left(5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{6} + {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{7}\right)} m^{6} - {\left(30 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{5} - 115 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{6} - 26 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{7}\right)} m^{5} + 15 \, {\left(4 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{4} - 38 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{5} + 67 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{6} + 18 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{7}\right)} m^{4} - 5 \, {\left(12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{3} - 168 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{4} + 750 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{5} - 817 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{6} - 284 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{7}\right)} m^{3} + {\left(360 \, B b^{5} d^{5} e^{2} - 480 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{3} + 3300 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{4} - 9510 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{5} + 7390 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{6} + 3929 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{7}\right)} m^{2} + 6 \, {\left(60 \, B b^{5} d^{5} e^{2} - 70 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{4} e^{3} + 420 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{4} - 1050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{2} e^{5} + 700 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d e^{6} + 879 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} e^{7}\right)} m\right)} x^{2} + 2 \, {\left(4014 \, A a^{5} d e^{6} - 60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{6} e + 780 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{5} e^{2} - 3210 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{4} e^{3} + 3190 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{3} e^{4} - 1377 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d^{2} e^{5}\right)} m + {\left(5040 \, A a^{5} e^{7} + {\left(A a^{5} e^{7} + {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{6}\right)} m^{6} + {\left(27 \, A a^{5} e^{7} - 10 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{5} + 25 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{6}\right)} m^{5} + 5 \, {\left(59 \, A a^{5} e^{7} + 12 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{4} - 44 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{5} + 49 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{6}\right)} m^{4} + 5 \, {\left(333 \, A a^{5} e^{7} - 24 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{3} + 216 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{4} - 358 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{5} + 235 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{6}\right)} m^{3} + 2 \, {\left(2552 \, A a^{5} e^{7} + 60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e^{2} - 780 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{3} + 3210 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{4} - 3190 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{5} + 1377 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{6}\right)} m^{2} - 12 \, {\left(60 \, B b^{5} d^{6} e - 669 \, A a^{5} e^{7} - 70 \, {\left(5 \, B a b^{4} + A b^{5}\right)} d^{5} e^{2} + 420 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} d^{4} e^{3} - 1050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} d^{3} e^{4} + 700 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} d^{2} e^{5} - 210 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} d e^{6}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{7} m^{7} + 28 \, e^{7} m^{6} + 322 \, e^{7} m^{5} + 1960 \, e^{7} m^{4} + 6769 \, e^{7} m^{3} + 13132 \, e^{7} m^{2} + 13068 \, e^{7} m + 5040 \, e^{7}}"," ",0,"(A*a^5*d*e^6*m^6 + 720*B*b^5*d^7 + 5040*A*a^5*d*e^6 - 840*(5*B*a*b^4 + A*b^5)*d^6*e + 5040*(2*B*a^2*b^3 + A*a*b^4)*d^5*e^2 - 12600*(B*a^3*b^2 + A*a^2*b^3)*d^4*e^3 + 8400*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^4 - 2520*(B*a^5 + 5*A*a^4*b)*d^2*e^5 + (B*b^5*e^7*m^6 + 21*B*b^5*e^7*m^5 + 175*B*b^5*e^7*m^4 + 735*B*b^5*e^7*m^3 + 1624*B*b^5*e^7*m^2 + 1764*B*b^5*e^7*m + 720*B*b^5*e^7)*x^7 + (840*(5*B*a*b^4 + A*b^5)*e^7 + (B*b^5*d*e^6 + (5*B*a*b^4 + A*b^5)*e^7)*m^6 + (15*B*b^5*d*e^6 + 22*(5*B*a*b^4 + A*b^5)*e^7)*m^5 + 5*(17*B*b^5*d*e^6 + 38*(5*B*a*b^4 + A*b^5)*e^7)*m^4 + 5*(45*B*b^5*d*e^6 + 164*(5*B*a*b^4 + A*b^5)*e^7)*m^3 + (274*B*b^5*d*e^6 + 1849*(5*B*a*b^4 + A*b^5)*e^7)*m^2 + 2*(60*B*b^5*d*e^6 + 1019*(5*B*a*b^4 + A*b^5)*e^7)*m)*x^6 + (27*A*a^5*d*e^6 - (B*a^5 + 5*A*a^4*b)*d^2*e^5)*m^5 + (5040*(2*B*a^2*b^3 + A*a*b^4)*e^7 + ((5*B*a*b^4 + A*b^5)*d*e^6 + 5*(2*B*a^2*b^3 + A*a*b^4)*e^7)*m^6 - (6*B*b^5*d^2*e^5 - 17*(5*B*a*b^4 + A*b^5)*d*e^6 - 115*(2*B*a^2*b^3 + A*a*b^4)*e^7)*m^5 - 15*(4*B*b^5*d^2*e^5 - 7*(5*B*a*b^4 + A*b^5)*d*e^6 - 69*(2*B*a^2*b^3 + A*a*b^4)*e^7)*m^4 - 5*(42*B*b^5*d^2*e^5 - 59*(5*B*a*b^4 + A*b^5)*d*e^6 - 925*(2*B*a^2*b^3 + A*a*b^4)*e^7)*m^3 - 2*(150*B*b^5*d^2*e^5 - 187*(5*B*a*b^4 + A*b^5)*d*e^6 - 5360*(2*B*a^2*b^3 + A*a*b^4)*e^7)*m^2 - 12*(12*B*b^5*d^2*e^5 - 14*(5*B*a*b^4 + A*b^5)*d*e^6 - 1005*(2*B*a^2*b^3 + A*a*b^4)*e^7)*m)*x^5 + 5*(59*A*a^5*d*e^6 + 2*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^4 - 5*(B*a^5 + 5*A*a^4*b)*d^2*e^5)*m^4 + 5*(2520*(B*a^3*b^2 + A*a^2*b^3)*e^7 + ((2*B*a^2*b^3 + A*a*b^4)*d*e^6 + 2*(B*a^3*b^2 + A*a^2*b^3)*e^7)*m^6 - ((5*B*a*b^4 + A*b^5)*d^2*e^5 - 19*(2*B*a^2*b^3 + A*a*b^4)*d*e^6 - 48*(B*a^3*b^2 + A*a^2*b^3)*e^7)*m^5 + (6*B*b^5*d^3*e^4 - 13*(5*B*a*b^4 + A*b^5)*d^2*e^5 + 131*(2*B*a^2*b^3 + A*a*b^4)*d*e^6 + 452*(B*a^3*b^2 + A*a^2*b^3)*e^7)*m^4 + (36*B*b^5*d^3*e^4 - 53*(5*B*a*b^4 + A*b^5)*d^2*e^5 + 401*(2*B*a^2*b^3 + A*a*b^4)*d*e^6 + 2112*(B*a^3*b^2 + A*a^2*b^3)*e^7)*m^3 + (66*B*b^5*d^3*e^4 - 83*(5*B*a*b^4 + A*b^5)*d^2*e^5 + 540*(2*B*a^2*b^3 + A*a*b^4)*d*e^6 + 5090*(B*a^3*b^2 + A*a^2*b^3)*e^7)*m^2 + 6*(6*B*b^5*d^3*e^4 - 7*(5*B*a*b^4 + A*b^5)*d^2*e^5 + 42*(2*B*a^2*b^3 + A*a*b^4)*d*e^6 + 984*(B*a^3*b^2 + A*a^2*b^3)*e^7)*m)*x^4 + 5*(333*A*a^5*d*e^6 - 12*(B*a^3*b^2 + A*a^2*b^3)*d^4*e^3 + 44*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^4 - 49*(B*a^5 + 5*A*a^4*b)*d^2*e^5)*m^3 + 5*(1680*(B*a^4*b + 2*A*a^3*b^2)*e^7 + (2*(B*a^3*b^2 + A*a^2*b^3)*d*e^6 + (B*a^4*b + 2*A*a^3*b^2)*e^7)*m^6 - (4*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^5 - 42*(B*a^3*b^2 + A*a^2*b^3)*d*e^6 - 25*(B*a^4*b + 2*A*a^3*b^2)*e^7)*m^5 + (4*(5*B*a*b^4 + A*b^5)*d^3*e^4 - 64*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^5 + 326*(B*a^3*b^2 + A*a^2*b^3)*d*e^6 + 247*(B*a^4*b + 2*A*a^3*b^2)*e^7)*m^4 - (24*B*b^5*d^4*e^3 - 40*(5*B*a*b^4 + A*b^5)*d^3*e^4 + 332*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^5 - 1134*(B*a^3*b^2 + A*a^2*b^3)*d*e^6 - 1219*(B*a^4*b + 2*A*a^3*b^2)*e^7)*m^3 - 4*(18*B*b^5*d^4*e^3 - 23*(5*B*a*b^4 + A*b^5)*d^3*e^4 + 152*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^5 - 422*(B*a^3*b^2 + A*a^2*b^3)*d*e^6 - 778*(B*a^4*b + 2*A*a^3*b^2)*e^7)*m^2 - 4*(12*B*b^5*d^4*e^3 - 14*(5*B*a*b^4 + A*b^5)*d^3*e^4 + 84*(2*B*a^2*b^3 + A*a*b^4)*d^2*e^5 - 210*(B*a^3*b^2 + A*a^2*b^3)*d*e^6 - 949*(B*a^4*b + 2*A*a^3*b^2)*e^7)*m)*x^3 + (5104*A*a^5*d*e^6 + 120*(2*B*a^2*b^3 + A*a*b^4)*d^5*e^2 - 1080*(B*a^3*b^2 + A*a^2*b^3)*d^4*e^3 + 1790*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^4 - 1175*(B*a^5 + 5*A*a^4*b)*d^2*e^5)*m^2 + (2520*(B*a^5 + 5*A*a^4*b)*e^7 + (5*(B*a^4*b + 2*A*a^3*b^2)*d*e^6 + (B*a^5 + 5*A*a^4*b)*e^7)*m^6 - (30*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^5 - 115*(B*a^4*b + 2*A*a^3*b^2)*d*e^6 - 26*(B*a^5 + 5*A*a^4*b)*e^7)*m^5 + 15*(4*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^4 - 38*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^5 + 67*(B*a^4*b + 2*A*a^3*b^2)*d*e^6 + 18*(B*a^5 + 5*A*a^4*b)*e^7)*m^4 - 5*(12*(5*B*a*b^4 + A*b^5)*d^4*e^3 - 168*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^4 + 750*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^5 - 817*(B*a^4*b + 2*A*a^3*b^2)*d*e^6 - 284*(B*a^5 + 5*A*a^4*b)*e^7)*m^3 + (360*B*b^5*d^5*e^2 - 480*(5*B*a*b^4 + A*b^5)*d^4*e^3 + 3300*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^4 - 9510*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^5 + 7390*(B*a^4*b + 2*A*a^3*b^2)*d*e^6 + 3929*(B*a^5 + 5*A*a^4*b)*e^7)*m^2 + 6*(60*B*b^5*d^5*e^2 - 70*(5*B*a*b^4 + A*b^5)*d^4*e^3 + 420*(2*B*a^2*b^3 + A*a*b^4)*d^3*e^4 - 1050*(B*a^3*b^2 + A*a^2*b^3)*d^2*e^5 + 700*(B*a^4*b + 2*A*a^3*b^2)*d*e^6 + 879*(B*a^5 + 5*A*a^4*b)*e^7)*m)*x^2 + 2*(4014*A*a^5*d*e^6 - 60*(5*B*a*b^4 + A*b^5)*d^6*e + 780*(2*B*a^2*b^3 + A*a*b^4)*d^5*e^2 - 3210*(B*a^3*b^2 + A*a^2*b^3)*d^4*e^3 + 3190*(B*a^4*b + 2*A*a^3*b^2)*d^3*e^4 - 1377*(B*a^5 + 5*A*a^4*b)*d^2*e^5)*m + (5040*A*a^5*e^7 + (A*a^5*e^7 + (B*a^5 + 5*A*a^4*b)*d*e^6)*m^6 + (27*A*a^5*e^7 - 10*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^5 + 25*(B*a^5 + 5*A*a^4*b)*d*e^6)*m^5 + 5*(59*A*a^5*e^7 + 12*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^4 - 44*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^5 + 49*(B*a^5 + 5*A*a^4*b)*d*e^6)*m^4 + 5*(333*A*a^5*e^7 - 24*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^3 + 216*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^4 - 358*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^5 + 235*(B*a^5 + 5*A*a^4*b)*d*e^6)*m^3 + 2*(2552*A*a^5*e^7 + 60*(5*B*a*b^4 + A*b^5)*d^5*e^2 - 780*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^3 + 3210*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^4 - 3190*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^5 + 1377*(B*a^5 + 5*A*a^4*b)*d*e^6)*m^2 - 12*(60*B*b^5*d^6*e - 669*A*a^5*e^7 - 70*(5*B*a*b^4 + A*b^5)*d^5*e^2 + 420*(2*B*a^2*b^3 + A*a*b^4)*d^4*e^3 - 1050*(B*a^3*b^2 + A*a^2*b^3)*d^3*e^4 + 700*(B*a^4*b + 2*A*a^3*b^2)*d^2*e^5 - 210*(B*a^5 + 5*A*a^4*b)*d*e^6)*m)*x)*(e*x + d)^m/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m^4 + 6769*e^7*m^3 + 13132*e^7*m^2 + 13068*e^7*m + 5040*e^7)","B",0
1889,1,1282,0,0.468533," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(A a^{3} d e^{4} m^{4} + 24 \, B b^{3} d^{5} + 120 \, A a^{3} d e^{4} - 30 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e + 120 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{2} - 60 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3} + {\left(B b^{3} e^{5} m^{4} + 10 \, B b^{3} e^{5} m^{3} + 35 \, B b^{3} e^{5} m^{2} + 50 \, B b^{3} e^{5} m + 24 \, B b^{3} e^{5}\right)} x^{5} + {\left(30 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5} + {\left(B b^{3} d e^{4} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} m^{4} + {\left(6 \, B b^{3} d e^{4} + 11 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} m^{3} + {\left(11 \, B b^{3} d e^{4} + 41 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} m^{2} + {\left(6 \, B b^{3} d e^{4} + 61 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} m\right)} x^{4} + {\left(14 \, A a^{3} d e^{4} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3}\right)} m^{3} + {\left(120 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5} + {\left({\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} m^{4} - 4 \, {\left(B b^{3} d^{2} e^{3} - 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} - 9 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} m^{3} - {\left(12 \, B b^{3} d^{2} e^{3} - 17 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} - 147 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} m^{2} - 2 \, {\left(4 \, B b^{3} d^{2} e^{3} - 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} - 117 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} m\right)} x^{3} + {\left(71 \, A a^{3} d e^{4} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{2} - 12 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3}\right)} m^{2} + {\left(60 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5} + {\left(3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} m^{4} - {\left(3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{3} - 30 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} - 13 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} m^{3} + {\left(12 \, B b^{3} d^{3} e^{2} - 18 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{3} + 87 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} + 59 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} m^{2} + {\left(12 \, B b^{3} d^{3} e^{2} - 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{3} + 60 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} + 107 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} m\right)} x^{2} + {\left(154 \, A a^{3} d e^{4} - 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e + 54 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{2} - 47 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3}\right)} m + {\left(120 \, A a^{3} e^{5} + {\left(A a^{3} e^{5} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} m^{4} + 2 \, {\left(7 \, A a^{3} e^{5} - 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{3} + 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} m^{3} + {\left(71 \, A a^{3} e^{5} + 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{2} - 54 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{3} + 47 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} m^{2} - 2 \, {\left(12 \, B b^{3} d^{4} e - 77 \, A a^{3} e^{5} - 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{2} + 60 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{3} - 30 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{5} m^{5} + 15 \, e^{5} m^{4} + 85 \, e^{5} m^{3} + 225 \, e^{5} m^{2} + 274 \, e^{5} m + 120 \, e^{5}}"," ",0,"(A*a^3*d*e^4*m^4 + 24*B*b^3*d^5 + 120*A*a^3*d*e^4 - 30*(3*B*a*b^2 + A*b^3)*d^4*e + 120*(B*a^2*b + A*a*b^2)*d^3*e^2 - 60*(B*a^3 + 3*A*a^2*b)*d^2*e^3 + (B*b^3*e^5*m^4 + 10*B*b^3*e^5*m^3 + 35*B*b^3*e^5*m^2 + 50*B*b^3*e^5*m + 24*B*b^3*e^5)*x^5 + (30*(3*B*a*b^2 + A*b^3)*e^5 + (B*b^3*d*e^4 + (3*B*a*b^2 + A*b^3)*e^5)*m^4 + (6*B*b^3*d*e^4 + 11*(3*B*a*b^2 + A*b^3)*e^5)*m^3 + (11*B*b^3*d*e^4 + 41*(3*B*a*b^2 + A*b^3)*e^5)*m^2 + (6*B*b^3*d*e^4 + 61*(3*B*a*b^2 + A*b^3)*e^5)*m)*x^4 + (14*A*a^3*d*e^4 - (B*a^3 + 3*A*a^2*b)*d^2*e^3)*m^3 + (120*(B*a^2*b + A*a*b^2)*e^5 + ((3*B*a*b^2 + A*b^3)*d*e^4 + 3*(B*a^2*b + A*a*b^2)*e^5)*m^4 - 4*(B*b^3*d^2*e^3 - 2*(3*B*a*b^2 + A*b^3)*d*e^4 - 9*(B*a^2*b + A*a*b^2)*e^5)*m^3 - (12*B*b^3*d^2*e^3 - 17*(3*B*a*b^2 + A*b^3)*d*e^4 - 147*(B*a^2*b + A*a*b^2)*e^5)*m^2 - 2*(4*B*b^3*d^2*e^3 - 5*(3*B*a*b^2 + A*b^3)*d*e^4 - 117*(B*a^2*b + A*a*b^2)*e^5)*m)*x^3 + (71*A*a^3*d*e^4 + 6*(B*a^2*b + A*a*b^2)*d^3*e^2 - 12*(B*a^3 + 3*A*a^2*b)*d^2*e^3)*m^2 + (60*(B*a^3 + 3*A*a^2*b)*e^5 + (3*(B*a^2*b + A*a*b^2)*d*e^4 + (B*a^3 + 3*A*a^2*b)*e^5)*m^4 - (3*(3*B*a*b^2 + A*b^3)*d^2*e^3 - 30*(B*a^2*b + A*a*b^2)*d*e^4 - 13*(B*a^3 + 3*A*a^2*b)*e^5)*m^3 + (12*B*b^3*d^3*e^2 - 18*(3*B*a*b^2 + A*b^3)*d^2*e^3 + 87*(B*a^2*b + A*a*b^2)*d*e^4 + 59*(B*a^3 + 3*A*a^2*b)*e^5)*m^2 + (12*B*b^3*d^3*e^2 - 15*(3*B*a*b^2 + A*b^3)*d^2*e^3 + 60*(B*a^2*b + A*a*b^2)*d*e^4 + 107*(B*a^3 + 3*A*a^2*b)*e^5)*m)*x^2 + (154*A*a^3*d*e^4 - 6*(3*B*a*b^2 + A*b^3)*d^4*e + 54*(B*a^2*b + A*a*b^2)*d^3*e^2 - 47*(B*a^3 + 3*A*a^2*b)*d^2*e^3)*m + (120*A*a^3*e^5 + (A*a^3*e^5 + (B*a^3 + 3*A*a^2*b)*d*e^4)*m^4 + 2*(7*A*a^3*e^5 - 3*(B*a^2*b + A*a*b^2)*d^2*e^3 + 6*(B*a^3 + 3*A*a^2*b)*d*e^4)*m^3 + (71*A*a^3*e^5 + 6*(3*B*a*b^2 + A*b^3)*d^3*e^2 - 54*(B*a^2*b + A*a*b^2)*d^2*e^3 + 47*(B*a^3 + 3*A*a^2*b)*d*e^4)*m^2 - 2*(12*B*b^3*d^4*e - 77*A*a^3*e^5 - 15*(3*B*a*b^2 + A*b^3)*d^3*e^2 + 60*(B*a^2*b + A*a*b^2)*d^2*e^3 - 30*(B*a^3 + 3*A*a^2*b)*d*e^4)*m)*x)*(e*x + d)^m/(e^5*m^5 + 15*e^5*m^4 + 85*e^5*m^3 + 225*e^5*m^2 + 274*e^5*m + 120*e^5)","B",0
1890,1,256,0,0.435942," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(A a d e^{2} m^{2} + 2 \, B b d^{3} + 6 \, A a d e^{2} - 3 \, {\left(B a + A b\right)} d^{2} e + {\left(B b e^{3} m^{2} + 3 \, B b e^{3} m + 2 \, B b e^{3}\right)} x^{3} + {\left(3 \, {\left(B a + A b\right)} e^{3} + {\left(B b d e^{2} + {\left(B a + A b\right)} e^{3}\right)} m^{2} + {\left(B b d e^{2} + 4 \, {\left(B a + A b\right)} e^{3}\right)} m\right)} x^{2} + {\left(5 \, A a d e^{2} - {\left(B a + A b\right)} d^{2} e\right)} m + {\left(6 \, A a e^{3} + {\left(A a e^{3} + {\left(B a + A b\right)} d e^{2}\right)} m^{2} - {\left(2 \, B b d^{2} e - 5 \, A a e^{3} - 3 \, {\left(B a + A b\right)} d e^{2}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{3} m^{3} + 6 \, e^{3} m^{2} + 11 \, e^{3} m + 6 \, e^{3}}"," ",0,"(A*a*d*e^2*m^2 + 2*B*b*d^3 + 6*A*a*d*e^2 - 3*(B*a + A*b)*d^2*e + (B*b*e^3*m^2 + 3*B*b*e^3*m + 2*B*b*e^3)*x^3 + (3*(B*a + A*b)*e^3 + (B*b*d*e^2 + (B*a + A*b)*e^3)*m^2 + (B*b*d*e^2 + 4*(B*a + A*b)*e^3)*m)*x^2 + (5*A*a*d*e^2 - (B*a + A*b)*d^2*e)*m + (6*A*a*e^3 + (A*a*e^3 + (B*a + A*b)*d*e^2)*m^2 - (2*B*b*d^2*e - 5*A*a*e^3 - 3*(B*a + A*b)*d*e^2)*m)*x)*(e*x + d)^m/(e^3*m^3 + 6*e^3*m^2 + 11*e^3*m + 6*e^3)","A",0
1891,0,0,0,0.445693," ","integrate((B*x+A)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^m/sqrt(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
1892,0,0,0,0.454621," ","integrate((B*x+A)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}} {\left(B x + A\right)} {\left(e x + d\right)}^{m}}{b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}}, x\right)"," ",0,"integral(sqrt(b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)*(e*x + d)^m/(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4), x)","F",0
1893,0,0,0,0.437758," ","integrate((B*x+A)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((B*x + A)*(b^2*x^2 + 2*a*b*x + a^2)^p*(e*x + d)^m, x)","F",0
1894,1,348,0,0.451901," ","integrate((e*x+d)^(-3-2*p)*(g*x+f)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","-\frac{{\left(a^{2} d^{2} g - {\left(b^{2} e^{2} f + 2 \, {\left(b^{2} d e - a b e^{2}\right)} g p + {\left(b^{2} d e - 2 \, a b e^{2}\right)} g\right)} x^{3} - 2 \, {\left(a b d^{2} - a^{2} d e\right)} f p - {\left(3 \, b^{2} d e f + {\left(b^{2} d^{2} - 2 \, a b d e - 2 \, a^{2} e^{2}\right)} g + 2 \, {\left({\left(b^{2} d e - a b e^{2}\right)} f + {\left(b^{2} d^{2} - a^{2} e^{2}\right)} g\right)} p\right)} x^{2} - {\left(2 \, a b d^{2} - a^{2} d e\right)} f + {\left(3 \, a^{2} d e g - {\left(2 \, b^{2} d^{2} + 2 \, a b d e - a^{2} e^{2}\right)} f - 2 \, {\left({\left(b^{2} d^{2} - a^{2} e^{2}\right)} f + {\left(a b d^{2} - a^{2} d e\right)} g\right)} p\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}}{2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2} + 2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} p^{2} + 3 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} p\right)}}"," ",0,"-1/2*(a^2*d^2*g - (b^2*e^2*f + 2*(b^2*d*e - a*b*e^2)*g*p + (b^2*d*e - 2*a*b*e^2)*g)*x^3 - 2*(a*b*d^2 - a^2*d*e)*f*p - (3*b^2*d*e*f + (b^2*d^2 - 2*a*b*d*e - 2*a^2*e^2)*g + 2*((b^2*d*e - a*b*e^2)*f + (b^2*d^2 - a^2*e^2)*g)*p)*x^2 - (2*a*b*d^2 - a^2*d*e)*f + (3*a^2*d*e*g - (2*b^2*d^2 + 2*a*b*d*e - a^2*e^2)*f - 2*((b^2*d^2 - a^2*e^2)*f + (a*b*d^2 - a^2*d*e)*g)*p)*x)*(b^2*x^2 + 2*a*b*x + a^2)^p*(e*x + d)^(-2*p - 3)/(b^2*d^2 - 2*a*b*d*e + a^2*e^2 + 2*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*p^2 + 3*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*p)","B",0
1895,1,303,0,0.403872," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{5} b^{3} + \frac{5}{8} x^{8} e^{4} d b^{3} + \frac{3}{8} x^{8} e^{5} b^{2} a + \frac{10}{7} x^{7} e^{3} d^{2} b^{3} + \frac{15}{7} x^{7} e^{4} d b^{2} a + \frac{3}{7} x^{7} e^{5} b a^{2} + \frac{5}{3} x^{6} e^{2} d^{3} b^{3} + 5 x^{6} e^{3} d^{2} b^{2} a + \frac{5}{2} x^{6} e^{4} d b a^{2} + \frac{1}{6} x^{6} e^{5} a^{3} + x^{5} e d^{4} b^{3} + 6 x^{5} e^{2} d^{3} b^{2} a + 6 x^{5} e^{3} d^{2} b a^{2} + x^{5} e^{4} d a^{3} + \frac{1}{4} x^{4} d^{5} b^{3} + \frac{15}{4} x^{4} e d^{4} b^{2} a + \frac{15}{2} x^{4} e^{2} d^{3} b a^{2} + \frac{5}{2} x^{4} e^{3} d^{2} a^{3} + x^{3} d^{5} b^{2} a + 5 x^{3} e d^{4} b a^{2} + \frac{10}{3} x^{3} e^{2} d^{3} a^{3} + \frac{3}{2} x^{2} d^{5} b a^{2} + \frac{5}{2} x^{2} e d^{4} a^{3} + x d^{5} a^{3}"," ",0,"1/9*x^9*e^5*b^3 + 5/8*x^8*e^4*d*b^3 + 3/8*x^8*e^5*b^2*a + 10/7*x^7*e^3*d^2*b^3 + 15/7*x^7*e^4*d*b^2*a + 3/7*x^7*e^5*b*a^2 + 5/3*x^6*e^2*d^3*b^3 + 5*x^6*e^3*d^2*b^2*a + 5/2*x^6*e^4*d*b*a^2 + 1/6*x^6*e^5*a^3 + x^5*e*d^4*b^3 + 6*x^5*e^2*d^3*b^2*a + 6*x^5*e^3*d^2*b*a^2 + x^5*e^4*d*a^3 + 1/4*x^4*d^5*b^3 + 15/4*x^4*e*d^4*b^2*a + 15/2*x^4*e^2*d^3*b*a^2 + 5/2*x^4*e^3*d^2*a^3 + x^3*d^5*b^2*a + 5*x^3*e*d^4*b*a^2 + 10/3*x^3*e^2*d^3*a^3 + 3/2*x^2*d^5*b*a^2 + 5/2*x^2*e*d^4*a^3 + x*d^5*a^3","B",0
1896,1,245,0,0.363937," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{4} b^{3} + \frac{4}{7} x^{7} e^{3} d b^{3} + \frac{3}{7} x^{7} e^{4} b^{2} a + x^{6} e^{2} d^{2} b^{3} + 2 x^{6} e^{3} d b^{2} a + \frac{1}{2} x^{6} e^{4} b a^{2} + \frac{4}{5} x^{5} e d^{3} b^{3} + \frac{18}{5} x^{5} e^{2} d^{2} b^{2} a + \frac{12}{5} x^{5} e^{3} d b a^{2} + \frac{1}{5} x^{5} e^{4} a^{3} + \frac{1}{4} x^{4} d^{4} b^{3} + 3 x^{4} e d^{3} b^{2} a + \frac{9}{2} x^{4} e^{2} d^{2} b a^{2} + x^{4} e^{3} d a^{3} + x^{3} d^{4} b^{2} a + 4 x^{3} e d^{3} b a^{2} + 2 x^{3} e^{2} d^{2} a^{3} + \frac{3}{2} x^{2} d^{4} b a^{2} + 2 x^{2} e d^{3} a^{3} + x d^{4} a^{3}"," ",0,"1/8*x^8*e^4*b^3 + 4/7*x^7*e^3*d*b^3 + 3/7*x^7*e^4*b^2*a + x^6*e^2*d^2*b^3 + 2*x^6*e^3*d*b^2*a + 1/2*x^6*e^4*b*a^2 + 4/5*x^5*e*d^3*b^3 + 18/5*x^5*e^2*d^2*b^2*a + 12/5*x^5*e^3*d*b*a^2 + 1/5*x^5*e^4*a^3 + 1/4*x^4*d^4*b^3 + 3*x^4*e*d^3*b^2*a + 9/2*x^4*e^2*d^2*b*a^2 + x^4*e^3*d*a^3 + x^3*d^4*b^2*a + 4*x^3*e*d^3*b*a^2 + 2*x^3*e^2*d^2*a^3 + 3/2*x^2*d^4*b*a^2 + 2*x^2*e*d^3*a^3 + x*d^4*a^3","B",0
1897,1,188,0,0.393668," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{3} b^{3} + \frac{1}{2} x^{6} e^{2} d b^{3} + \frac{1}{2} x^{6} e^{3} b^{2} a + \frac{3}{5} x^{5} e d^{2} b^{3} + \frac{9}{5} x^{5} e^{2} d b^{2} a + \frac{3}{5} x^{5} e^{3} b a^{2} + \frac{1}{4} x^{4} d^{3} b^{3} + \frac{9}{4} x^{4} e d^{2} b^{2} a + \frac{9}{4} x^{4} e^{2} d b a^{2} + \frac{1}{4} x^{4} e^{3} a^{3} + x^{3} d^{3} b^{2} a + 3 x^{3} e d^{2} b a^{2} + x^{3} e^{2} d a^{3} + \frac{3}{2} x^{2} d^{3} b a^{2} + \frac{3}{2} x^{2} e d^{2} a^{3} + x d^{3} a^{3}"," ",0,"1/7*x^7*e^3*b^3 + 1/2*x^6*e^2*d*b^3 + 1/2*x^6*e^3*b^2*a + 3/5*x^5*e*d^2*b^3 + 9/5*x^5*e^2*d*b^2*a + 3/5*x^5*e^3*b*a^2 + 1/4*x^4*d^3*b^3 + 9/4*x^4*e*d^2*b^2*a + 9/4*x^4*e^2*d*b*a^2 + 1/4*x^4*e^3*a^3 + x^3*d^3*b^2*a + 3*x^3*e*d^2*b*a^2 + x^3*e^2*d*a^3 + 3/2*x^2*d^3*b*a^2 + 3/2*x^2*e*d^2*a^3 + x*d^3*a^3","B",0
1898,1,130,0,0.385591," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{2} b^{3} + \frac{2}{5} x^{5} e d b^{3} + \frac{3}{5} x^{5} e^{2} b^{2} a + \frac{1}{4} x^{4} d^{2} b^{3} + \frac{3}{2} x^{4} e d b^{2} a + \frac{3}{4} x^{4} e^{2} b a^{2} + x^{3} d^{2} b^{2} a + 2 x^{3} e d b a^{2} + \frac{1}{3} x^{3} e^{2} a^{3} + \frac{3}{2} x^{2} d^{2} b a^{2} + x^{2} e d a^{3} + x d^{2} a^{3}"," ",0,"1/6*x^6*e^2*b^3 + 2/5*x^5*e*d*b^3 + 3/5*x^5*e^2*b^2*a + 1/4*x^4*d^2*b^3 + 3/2*x^4*e*d*b^2*a + 3/4*x^4*e^2*b*a^2 + x^3*d^2*b^2*a + 2*x^3*e*d*b*a^2 + 1/3*x^3*e^2*a^3 + 3/2*x^2*d^2*b*a^2 + x^2*e*d*a^3 + x*d^2*a^3","B",0
1899,1,72,0,0.351715," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e b^{3} + \frac{1}{4} x^{4} d b^{3} + \frac{3}{4} x^{4} e b^{2} a + x^{3} d b^{2} a + x^{3} e b a^{2} + \frac{3}{2} x^{2} d b a^{2} + \frac{1}{2} x^{2} e a^{3} + x d a^{3}"," ",0,"1/5*x^5*e*b^3 + 1/4*x^4*d*b^3 + 3/4*x^4*e*b^2*a + x^3*d*b^2*a + x^3*e*b*a^2 + 3/2*x^2*d*b*a^2 + 1/2*x^2*e*a^3 + x*d*a^3","B",0
1900,1,31,0,0.371446," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{4} x^{4} b^{3} + x^{3} b^{2} a + \frac{3}{2} x^{2} b a^{2} + x a^{3}"," ",0,"1/4*x^4*b^3 + x^3*b^2*a + 3/2*x^2*b*a^2 + x*a^3","B",0
1901,1,115,0,0.407191," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d),x, algorithm=""fricas"")","\frac{2 \, b^{3} e^{3} x^{3} - 3 \, {\left(b^{3} d e^{2} - 3 \, a b^{2} e^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{2} e - 3 \, a b^{2} d e^{2} + 3 \, a^{2} b e^{3}\right)} x - 6 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \log\left(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(2*b^3*e^3*x^3 - 3*(b^3*d*e^2 - 3*a*b^2*e^3)*x^2 + 6*(b^3*d^2*e - 3*a*b^2*d*e^2 + 3*a^2*b*e^3)*x - 6*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*log(e*x + d))/e^4","A",0
1902,1,172,0,0.418465," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{b^{3} e^{3} x^{3} + 2 \, b^{3} d^{3} - 6 \, a b^{2} d^{2} e + 6 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} - 3 \, {\left(b^{3} d e^{2} - 2 \, a b^{2} e^{3}\right)} x^{2} - 2 \, {\left(2 \, b^{3} d^{2} e - 3 \, a b^{2} d e^{2}\right)} x + 6 \, {\left(b^{3} d^{3} - 2 \, a b^{2} d^{2} e + a^{2} b d e^{2} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(b^3*e^3*x^3 + 2*b^3*d^3 - 6*a*b^2*d^2*e + 6*a^2*b*d*e^2 - 2*a^3*e^3 - 3*(b^3*d*e^2 - 2*a*b^2*e^3)*x^2 - 2*(2*b^3*d^2*e - 3*a*b^2*d*e^2)*x + 6*(b^3*d^3 - 2*a*b^2*d^2*e + a^2*b*d*e^2 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)*log(e*x + d))/(e^5*x + d*e^4)","B",0
1903,1,188,0,0.401450," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} e^{3} x^{3} + 4 \, b^{3} d e^{2} x^{2} - 5 \, b^{3} d^{3} + 9 \, a b^{2} d^{2} e - 3 \, a^{2} b d e^{2} - a^{3} e^{3} - 2 \, {\left(2 \, b^{3} d^{2} e - 6 \, a b^{2} d e^{2} + 3 \, a^{2} b e^{3}\right)} x - 6 \, {\left(b^{3} d^{3} - a b^{2} d^{2} e + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(b^{3} d^{2} e - a b^{2} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(2*b^3*e^3*x^3 + 4*b^3*d*e^2*x^2 - 5*b^3*d^3 + 9*a*b^2*d^2*e - 3*a^2*b*d*e^2 - a^3*e^3 - 2*(2*b^3*d^2*e - 6*a*b^2*d*e^2 + 3*a^2*b*e^3)*x - 6*(b^3*d^3 - a*b^2*d^2*e + (b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(b^3*d^2*e - a*b^2*d*e^2)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","B",0
1904,1,177,0,0.421990," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{11 \, b^{3} d^{3} - 6 \, a b^{2} d^{2} e - 3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + 18 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 9 \, {\left(3 \, b^{3} d^{2} e - 2 \, a b^{2} d e^{2} - a^{2} b e^{3}\right)} x + 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, b^{3} d e^{2} x^{2} + 3 \, b^{3} d^{2} e x + b^{3} d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(11*b^3*d^3 - 6*a*b^2*d^2*e - 3*a^2*b*d*e^2 - 2*a^3*e^3 + 18*(b^3*d*e^2 - a*b^2*e^3)*x^2 + 9*(3*b^3*d^2*e - 2*a*b^2*d*e^2 - a^2*b*e^3)*x + 6*(b^3*e^3*x^3 + 3*b^3*d*e^2*x^2 + 3*b^3*d^2*e*x + b^3*d^3)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","B",0
1905,1,579,0,0.380178," ","integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{6} b^{5} + \frac{6}{11} x^{11} e^{5} d b^{5} + \frac{5}{11} x^{11} e^{6} b^{4} a + \frac{3}{2} x^{10} e^{4} d^{2} b^{5} + 3 x^{10} e^{5} d b^{4} a + x^{10} e^{6} b^{3} a^{2} + \frac{20}{9} x^{9} e^{3} d^{3} b^{5} + \frac{25}{3} x^{9} e^{4} d^{2} b^{4} a + \frac{20}{3} x^{9} e^{5} d b^{3} a^{2} + \frac{10}{9} x^{9} e^{6} b^{2} a^{3} + \frac{15}{8} x^{8} e^{2} d^{4} b^{5} + \frac{25}{2} x^{8} e^{3} d^{3} b^{4} a + \frac{75}{4} x^{8} e^{4} d^{2} b^{3} a^{2} + \frac{15}{2} x^{8} e^{5} d b^{2} a^{3} + \frac{5}{8} x^{8} e^{6} b a^{4} + \frac{6}{7} x^{7} e d^{5} b^{5} + \frac{75}{7} x^{7} e^{2} d^{4} b^{4} a + \frac{200}{7} x^{7} e^{3} d^{3} b^{3} a^{2} + \frac{150}{7} x^{7} e^{4} d^{2} b^{2} a^{3} + \frac{30}{7} x^{7} e^{5} d b a^{4} + \frac{1}{7} x^{7} e^{6} a^{5} + \frac{1}{6} x^{6} d^{6} b^{5} + 5 x^{6} e d^{5} b^{4} a + 25 x^{6} e^{2} d^{4} b^{3} a^{2} + \frac{100}{3} x^{6} e^{3} d^{3} b^{2} a^{3} + \frac{25}{2} x^{6} e^{4} d^{2} b a^{4} + x^{6} e^{5} d a^{5} + x^{5} d^{6} b^{4} a + 12 x^{5} e d^{5} b^{3} a^{2} + 30 x^{5} e^{2} d^{4} b^{2} a^{3} + 20 x^{5} e^{3} d^{3} b a^{4} + 3 x^{5} e^{4} d^{2} a^{5} + \frac{5}{2} x^{4} d^{6} b^{3} a^{2} + 15 x^{4} e d^{5} b^{2} a^{3} + \frac{75}{4} x^{4} e^{2} d^{4} b a^{4} + 5 x^{4} e^{3} d^{3} a^{5} + \frac{10}{3} x^{3} d^{6} b^{2} a^{3} + 10 x^{3} e d^{5} b a^{4} + 5 x^{3} e^{2} d^{4} a^{5} + \frac{5}{2} x^{2} d^{6} b a^{4} + 3 x^{2} e d^{5} a^{5} + x d^{6} a^{5}"," ",0,"1/12*x^12*e^6*b^5 + 6/11*x^11*e^5*d*b^5 + 5/11*x^11*e^6*b^4*a + 3/2*x^10*e^4*d^2*b^5 + 3*x^10*e^5*d*b^4*a + x^10*e^6*b^3*a^2 + 20/9*x^9*e^3*d^3*b^5 + 25/3*x^9*e^4*d^2*b^4*a + 20/3*x^9*e^5*d*b^3*a^2 + 10/9*x^9*e^6*b^2*a^3 + 15/8*x^8*e^2*d^4*b^5 + 25/2*x^8*e^3*d^3*b^4*a + 75/4*x^8*e^4*d^2*b^3*a^2 + 15/2*x^8*e^5*d*b^2*a^3 + 5/8*x^8*e^6*b*a^4 + 6/7*x^7*e*d^5*b^5 + 75/7*x^7*e^2*d^4*b^4*a + 200/7*x^7*e^3*d^3*b^3*a^2 + 150/7*x^7*e^4*d^2*b^2*a^3 + 30/7*x^7*e^5*d*b*a^4 + 1/7*x^7*e^6*a^5 + 1/6*x^6*d^6*b^5 + 5*x^6*e*d^5*b^4*a + 25*x^6*e^2*d^4*b^3*a^2 + 100/3*x^6*e^3*d^3*b^2*a^3 + 25/2*x^6*e^4*d^2*b*a^4 + x^6*e^5*d*a^5 + x^5*d^6*b^4*a + 12*x^5*e*d^5*b^3*a^2 + 30*x^5*e^2*d^4*b^2*a^3 + 20*x^5*e^3*d^3*b*a^4 + 3*x^5*e^4*d^2*a^5 + 5/2*x^4*d^6*b^3*a^2 + 15*x^4*e*d^5*b^2*a^3 + 75/4*x^4*e^2*d^4*b*a^4 + 5*x^4*e^3*d^3*a^5 + 10/3*x^3*d^6*b^2*a^3 + 10*x^3*e*d^5*b*a^4 + 5*x^3*e^2*d^4*a^5 + 5/2*x^2*d^6*b*a^4 + 3*x^2*e*d^5*a^5 + x*d^6*a^5","B",0
1906,1,488,0,0.366245," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{5} b^{5} + \frac{1}{2} x^{10} e^{4} d b^{5} + \frac{1}{2} x^{10} e^{5} b^{4} a + \frac{10}{9} x^{9} e^{3} d^{2} b^{5} + \frac{25}{9} x^{9} e^{4} d b^{4} a + \frac{10}{9} x^{9} e^{5} b^{3} a^{2} + \frac{5}{4} x^{8} e^{2} d^{3} b^{5} + \frac{25}{4} x^{8} e^{3} d^{2} b^{4} a + \frac{25}{4} x^{8} e^{4} d b^{3} a^{2} + \frac{5}{4} x^{8} e^{5} b^{2} a^{3} + \frac{5}{7} x^{7} e d^{4} b^{5} + \frac{50}{7} x^{7} e^{2} d^{3} b^{4} a + \frac{100}{7} x^{7} e^{3} d^{2} b^{3} a^{2} + \frac{50}{7} x^{7} e^{4} d b^{2} a^{3} + \frac{5}{7} x^{7} e^{5} b a^{4} + \frac{1}{6} x^{6} d^{5} b^{5} + \frac{25}{6} x^{6} e d^{4} b^{4} a + \frac{50}{3} x^{6} e^{2} d^{3} b^{3} a^{2} + \frac{50}{3} x^{6} e^{3} d^{2} b^{2} a^{3} + \frac{25}{6} x^{6} e^{4} d b a^{4} + \frac{1}{6} x^{6} e^{5} a^{5} + x^{5} d^{5} b^{4} a + 10 x^{5} e d^{4} b^{3} a^{2} + 20 x^{5} e^{2} d^{3} b^{2} a^{3} + 10 x^{5} e^{3} d^{2} b a^{4} + x^{5} e^{4} d a^{5} + \frac{5}{2} x^{4} d^{5} b^{3} a^{2} + \frac{25}{2} x^{4} e d^{4} b^{2} a^{3} + \frac{25}{2} x^{4} e^{2} d^{3} b a^{4} + \frac{5}{2} x^{4} e^{3} d^{2} a^{5} + \frac{10}{3} x^{3} d^{5} b^{2} a^{3} + \frac{25}{3} x^{3} e d^{4} b a^{4} + \frac{10}{3} x^{3} e^{2} d^{3} a^{5} + \frac{5}{2} x^{2} d^{5} b a^{4} + \frac{5}{2} x^{2} e d^{4} a^{5} + x d^{5} a^{5}"," ",0,"1/11*x^11*e^5*b^5 + 1/2*x^10*e^4*d*b^5 + 1/2*x^10*e^5*b^4*a + 10/9*x^9*e^3*d^2*b^5 + 25/9*x^9*e^4*d*b^4*a + 10/9*x^9*e^5*b^3*a^2 + 5/4*x^8*e^2*d^3*b^5 + 25/4*x^8*e^3*d^2*b^4*a + 25/4*x^8*e^4*d*b^3*a^2 + 5/4*x^8*e^5*b^2*a^3 + 5/7*x^7*e*d^4*b^5 + 50/7*x^7*e^2*d^3*b^4*a + 100/7*x^7*e^3*d^2*b^3*a^2 + 50/7*x^7*e^4*d*b^2*a^3 + 5/7*x^7*e^5*b*a^4 + 1/6*x^6*d^5*b^5 + 25/6*x^6*e*d^4*b^4*a + 50/3*x^6*e^2*d^3*b^3*a^2 + 50/3*x^6*e^3*d^2*b^2*a^3 + 25/6*x^6*e^4*d*b*a^4 + 1/6*x^6*e^5*a^5 + x^5*d^5*b^4*a + 10*x^5*e*d^4*b^3*a^2 + 20*x^5*e^2*d^3*b^2*a^3 + 10*x^5*e^3*d^2*b*a^4 + x^5*e^4*d*a^5 + 5/2*x^4*d^5*b^3*a^2 + 25/2*x^4*e*d^4*b^2*a^3 + 25/2*x^4*e^2*d^3*b*a^4 + 5/2*x^4*e^3*d^2*a^5 + 10/3*x^3*d^5*b^2*a^3 + 25/3*x^3*e*d^4*b*a^4 + 10/3*x^3*e^2*d^3*a^5 + 5/2*x^2*d^5*b*a^4 + 5/2*x^2*e*d^4*a^5 + x*d^5*a^5","B",0
1907,1,396,0,0.494227," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{4} b^{5} + \frac{4}{9} x^{9} e^{3} d b^{5} + \frac{5}{9} x^{9} e^{4} b^{4} a + \frac{3}{4} x^{8} e^{2} d^{2} b^{5} + \frac{5}{2} x^{8} e^{3} d b^{4} a + \frac{5}{4} x^{8} e^{4} b^{3} a^{2} + \frac{4}{7} x^{7} e d^{3} b^{5} + \frac{30}{7} x^{7} e^{2} d^{2} b^{4} a + \frac{40}{7} x^{7} e^{3} d b^{3} a^{2} + \frac{10}{7} x^{7} e^{4} b^{2} a^{3} + \frac{1}{6} x^{6} d^{4} b^{5} + \frac{10}{3} x^{6} e d^{3} b^{4} a + 10 x^{6} e^{2} d^{2} b^{3} a^{2} + \frac{20}{3} x^{6} e^{3} d b^{2} a^{3} + \frac{5}{6} x^{6} e^{4} b a^{4} + x^{5} d^{4} b^{4} a + 8 x^{5} e d^{3} b^{3} a^{2} + 12 x^{5} e^{2} d^{2} b^{2} a^{3} + 4 x^{5} e^{3} d b a^{4} + \frac{1}{5} x^{5} e^{4} a^{5} + \frac{5}{2} x^{4} d^{4} b^{3} a^{2} + 10 x^{4} e d^{3} b^{2} a^{3} + \frac{15}{2} x^{4} e^{2} d^{2} b a^{4} + x^{4} e^{3} d a^{5} + \frac{10}{3} x^{3} d^{4} b^{2} a^{3} + \frac{20}{3} x^{3} e d^{3} b a^{4} + 2 x^{3} e^{2} d^{2} a^{5} + \frac{5}{2} x^{2} d^{4} b a^{4} + 2 x^{2} e d^{3} a^{5} + x d^{4} a^{5}"," ",0,"1/10*x^10*e^4*b^5 + 4/9*x^9*e^3*d*b^5 + 5/9*x^9*e^4*b^4*a + 3/4*x^8*e^2*d^2*b^5 + 5/2*x^8*e^3*d*b^4*a + 5/4*x^8*e^4*b^3*a^2 + 4/7*x^7*e*d^3*b^5 + 30/7*x^7*e^2*d^2*b^4*a + 40/7*x^7*e^3*d*b^3*a^2 + 10/7*x^7*e^4*b^2*a^3 + 1/6*x^6*d^4*b^5 + 10/3*x^6*e*d^3*b^4*a + 10*x^6*e^2*d^2*b^3*a^2 + 20/3*x^6*e^3*d*b^2*a^3 + 5/6*x^6*e^4*b*a^4 + x^5*d^4*b^4*a + 8*x^5*e*d^3*b^3*a^2 + 12*x^5*e^2*d^2*b^2*a^3 + 4*x^5*e^3*d*b*a^4 + 1/5*x^5*e^4*a^5 + 5/2*x^4*d^4*b^3*a^2 + 10*x^4*e*d^3*b^2*a^3 + 15/2*x^4*e^2*d^2*b*a^4 + x^4*e^3*d*a^5 + 10/3*x^3*d^4*b^2*a^3 + 20/3*x^3*e*d^3*b*a^4 + 2*x^3*e^2*d^2*a^5 + 5/2*x^2*d^4*b*a^4 + 2*x^2*e*d^3*a^5 + x*d^4*a^5","B",0
1908,1,303,0,0.372858," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{3} b^{5} + \frac{3}{8} x^{8} e^{2} d b^{5} + \frac{5}{8} x^{8} e^{3} b^{4} a + \frac{3}{7} x^{7} e d^{2} b^{5} + \frac{15}{7} x^{7} e^{2} d b^{4} a + \frac{10}{7} x^{7} e^{3} b^{3} a^{2} + \frac{1}{6} x^{6} d^{3} b^{5} + \frac{5}{2} x^{6} e d^{2} b^{4} a + 5 x^{6} e^{2} d b^{3} a^{2} + \frac{5}{3} x^{6} e^{3} b^{2} a^{3} + x^{5} d^{3} b^{4} a + 6 x^{5} e d^{2} b^{3} a^{2} + 6 x^{5} e^{2} d b^{2} a^{3} + x^{5} e^{3} b a^{4} + \frac{5}{2} x^{4} d^{3} b^{3} a^{2} + \frac{15}{2} x^{4} e d^{2} b^{2} a^{3} + \frac{15}{4} x^{4} e^{2} d b a^{4} + \frac{1}{4} x^{4} e^{3} a^{5} + \frac{10}{3} x^{3} d^{3} b^{2} a^{3} + 5 x^{3} e d^{2} b a^{4} + x^{3} e^{2} d a^{5} + \frac{5}{2} x^{2} d^{3} b a^{4} + \frac{3}{2} x^{2} e d^{2} a^{5} + x d^{3} a^{5}"," ",0,"1/9*x^9*e^3*b^5 + 3/8*x^8*e^2*d*b^5 + 5/8*x^8*e^3*b^4*a + 3/7*x^7*e*d^2*b^5 + 15/7*x^7*e^2*d*b^4*a + 10/7*x^7*e^3*b^3*a^2 + 1/6*x^6*d^3*b^5 + 5/2*x^6*e*d^2*b^4*a + 5*x^6*e^2*d*b^3*a^2 + 5/3*x^6*e^3*b^2*a^3 + x^5*d^3*b^4*a + 6*x^5*e*d^2*b^3*a^2 + 6*x^5*e^2*d*b^2*a^3 + x^5*e^3*b*a^4 + 5/2*x^4*d^3*b^3*a^2 + 15/2*x^4*e*d^2*b^2*a^3 + 15/4*x^4*e^2*d*b*a^4 + 1/4*x^4*e^3*a^5 + 10/3*x^3*d^3*b^2*a^3 + 5*x^3*e*d^2*b*a^4 + x^3*e^2*d*a^5 + 5/2*x^2*d^3*b*a^4 + 3/2*x^2*e*d^2*a^5 + x*d^3*a^5","B",0
1909,1,212,0,0.358528," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{2} b^{5} + \frac{2}{7} x^{7} e d b^{5} + \frac{5}{7} x^{7} e^{2} b^{4} a + \frac{1}{6} x^{6} d^{2} b^{5} + \frac{5}{3} x^{6} e d b^{4} a + \frac{5}{3} x^{6} e^{2} b^{3} a^{2} + x^{5} d^{2} b^{4} a + 4 x^{5} e d b^{3} a^{2} + 2 x^{5} e^{2} b^{2} a^{3} + \frac{5}{2} x^{4} d^{2} b^{3} a^{2} + 5 x^{4} e d b^{2} a^{3} + \frac{5}{4} x^{4} e^{2} b a^{4} + \frac{10}{3} x^{3} d^{2} b^{2} a^{3} + \frac{10}{3} x^{3} e d b a^{4} + \frac{1}{3} x^{3} e^{2} a^{5} + \frac{5}{2} x^{2} d^{2} b a^{4} + x^{2} e d a^{5} + x d^{2} a^{5}"," ",0,"1/8*x^8*e^2*b^5 + 2/7*x^7*e*d*b^5 + 5/7*x^7*e^2*b^4*a + 1/6*x^6*d^2*b^5 + 5/3*x^6*e*d*b^4*a + 5/3*x^6*e^2*b^3*a^2 + x^5*d^2*b^4*a + 4*x^5*e*d*b^3*a^2 + 2*x^5*e^2*b^2*a^3 + 5/2*x^4*d^2*b^3*a^2 + 5*x^4*e*d*b^2*a^3 + 5/4*x^4*e^2*b*a^4 + 10/3*x^3*d^2*b^2*a^3 + 10/3*x^3*e*d*b*a^4 + 1/3*x^3*e^2*a^5 + 5/2*x^2*d^2*b*a^4 + x^2*e*d*a^5 + x*d^2*a^5","B",0
1910,1,121,0,0.361730," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e b^{5} + \frac{1}{6} x^{6} d b^{5} + \frac{5}{6} x^{6} e b^{4} a + x^{5} d b^{4} a + 2 x^{5} e b^{3} a^{2} + \frac{5}{2} x^{4} d b^{3} a^{2} + \frac{5}{2} x^{4} e b^{2} a^{3} + \frac{10}{3} x^{3} d b^{2} a^{3} + \frac{5}{3} x^{3} e b a^{4} + \frac{5}{2} x^{2} d b a^{4} + \frac{1}{2} x^{2} e a^{5} + x d a^{5}"," ",0,"1/7*x^7*e*b^5 + 1/6*x^6*d*b^5 + 5/6*x^6*e*b^4*a + x^5*d*b^4*a + 2*x^5*e*b^3*a^2 + 5/2*x^4*d*b^3*a^2 + 5/2*x^4*e*b^2*a^3 + 10/3*x^3*d*b^2*a^3 + 5/3*x^3*e*b*a^4 + 5/2*x^2*d*b*a^4 + 1/2*x^2*e*a^5 + x*d*a^5","B",0
1911,1,53,0,0.383599," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} b^{5} + x^{5} b^{4} a + \frac{5}{2} x^{4} b^{3} a^{2} + \frac{10}{3} x^{3} b^{2} a^{3} + \frac{5}{2} x^{2} b a^{4} + x a^{5}"," ",0,"1/6*x^6*b^5 + x^5*b^4*a + 5/2*x^4*b^3*a^2 + 10/3*x^3*b^2*a^3 + 5/2*x^2*b*a^4 + x*a^5","B",0
1912,1,259,0,0.394591," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d),x, algorithm=""fricas"")","\frac{12 \, b^{5} e^{5} x^{5} - 15 \, {\left(b^{5} d e^{4} - 5 \, a b^{4} e^{5}\right)} x^{4} + 20 \, {\left(b^{5} d^{2} e^{3} - 5 \, a b^{4} d e^{4} + 10 \, a^{2} b^{3} e^{5}\right)} x^{3} - 30 \, {\left(b^{5} d^{3} e^{2} - 5 \, a b^{4} d^{2} e^{3} + 10 \, a^{2} b^{3} d e^{4} - 10 \, a^{3} b^{2} e^{5}\right)} x^{2} + 60 \, {\left(b^{5} d^{4} e - 5 \, a b^{4} d^{3} e^{2} + 10 \, a^{2} b^{3} d^{2} e^{3} - 10 \, a^{3} b^{2} d e^{4} + 5 \, a^{4} b e^{5}\right)} x - 60 \, {\left(b^{5} d^{5} - 5 \, a b^{4} d^{4} e + 10 \, a^{2} b^{3} d^{3} e^{2} - 10 \, a^{3} b^{2} d^{2} e^{3} + 5 \, a^{4} b d e^{4} - a^{5} e^{5}\right)} \log\left(e x + d\right)}{60 \, e^{6}}"," ",0,"1/60*(12*b^5*e^5*x^5 - 15*(b^5*d*e^4 - 5*a*b^4*e^5)*x^4 + 20*(b^5*d^2*e^3 - 5*a*b^4*d*e^4 + 10*a^2*b^3*e^5)*x^3 - 30*(b^5*d^3*e^2 - 5*a*b^4*d^2*e^3 + 10*a^2*b^3*d*e^4 - 10*a^3*b^2*e^5)*x^2 + 60*(b^5*d^4*e - 5*a*b^4*d^3*e^2 + 10*a^2*b^3*d^2*e^3 - 10*a^3*b^2*d*e^4 + 5*a^4*b*e^5)*x - 60*(b^5*d^5 - 5*a*b^4*d^4*e + 10*a^2*b^3*d^3*e^2 - 10*a^3*b^2*d^2*e^3 + 5*a^4*b*d*e^4 - a^5*e^5)*log(e*x + d))/e^6","B",0
1913,1,373,0,0.400978," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{3 \, b^{5} e^{5} x^{5} + 12 \, b^{5} d^{5} - 60 \, a b^{4} d^{4} e + 120 \, a^{2} b^{3} d^{3} e^{2} - 120 \, a^{3} b^{2} d^{2} e^{3} + 60 \, a^{4} b d e^{4} - 12 \, a^{5} e^{5} - 5 \, {\left(b^{5} d e^{4} - 4 \, a b^{4} e^{5}\right)} x^{4} + 10 \, {\left(b^{5} d^{2} e^{3} - 4 \, a b^{4} d e^{4} + 6 \, a^{2} b^{3} e^{5}\right)} x^{3} - 30 \, {\left(b^{5} d^{3} e^{2} - 4 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} - 4 \, a^{3} b^{2} e^{5}\right)} x^{2} - 12 \, {\left(4 \, b^{5} d^{4} e - 15 \, a b^{4} d^{3} e^{2} + 20 \, a^{2} b^{3} d^{2} e^{3} - 10 \, a^{3} b^{2} d e^{4}\right)} x + 60 \, {\left(b^{5} d^{5} - 4 \, a b^{4} d^{4} e + 6 \, a^{2} b^{3} d^{3} e^{2} - 4 \, a^{3} b^{2} d^{2} e^{3} + a^{4} b d e^{4} + {\left(b^{5} d^{4} e - 4 \, a b^{4} d^{3} e^{2} + 6 \, a^{2} b^{3} d^{2} e^{3} - 4 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"1/12*(3*b^5*e^5*x^5 + 12*b^5*d^5 - 60*a*b^4*d^4*e + 120*a^2*b^3*d^3*e^2 - 120*a^3*b^2*d^2*e^3 + 60*a^4*b*d*e^4 - 12*a^5*e^5 - 5*(b^5*d*e^4 - 4*a*b^4*e^5)*x^4 + 10*(b^5*d^2*e^3 - 4*a*b^4*d*e^4 + 6*a^2*b^3*e^5)*x^3 - 30*(b^5*d^3*e^2 - 4*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 - 4*a^3*b^2*e^5)*x^2 - 12*(4*b^5*d^4*e - 15*a*b^4*d^3*e^2 + 20*a^2*b^3*d^2*e^3 - 10*a^3*b^2*d*e^4)*x + 60*(b^5*d^5 - 4*a*b^4*d^4*e + 6*a^2*b^3*d^3*e^2 - 4*a^3*b^2*d^2*e^3 + a^4*b*d*e^4 + (b^5*d^4*e - 4*a*b^4*d^3*e^2 + 6*a^2*b^3*d^2*e^3 - 4*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*log(e*x + d))/(e^7*x + d*e^6)","B",0
1914,1,416,0,0.418441," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, b^{5} e^{5} x^{5} - 27 \, b^{5} d^{5} + 105 \, a b^{4} d^{4} e - 150 \, a^{2} b^{3} d^{3} e^{2} + 90 \, a^{3} b^{2} d^{2} e^{3} - 15 \, a^{4} b d e^{4} - 3 \, a^{5} e^{5} - 5 \, {\left(b^{5} d e^{4} - 3 \, a b^{4} e^{5}\right)} x^{4} + 20 \, {\left(b^{5} d^{2} e^{3} - 3 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + 3 \, {\left(21 \, b^{5} d^{3} e^{2} - 55 \, a b^{4} d^{2} e^{3} + 40 \, a^{2} b^{3} d e^{4}\right)} x^{2} + 6 \, {\left(b^{5} d^{4} e + 5 \, a b^{4} d^{3} e^{2} - 20 \, a^{2} b^{3} d^{2} e^{3} + 20 \, a^{3} b^{2} d e^{4} - 5 \, a^{4} b e^{5}\right)} x - 60 \, {\left(b^{5} d^{5} - 3 \, a b^{4} d^{4} e + 3 \, a^{2} b^{3} d^{3} e^{2} - a^{3} b^{2} d^{2} e^{3} + {\left(b^{5} d^{3} e^{2} - 3 \, a b^{4} d^{2} e^{3} + 3 \, a^{2} b^{3} d e^{4} - a^{3} b^{2} e^{5}\right)} x^{2} + 2 \, {\left(b^{5} d^{4} e - 3 \, a b^{4} d^{3} e^{2} + 3 \, a^{2} b^{3} d^{2} e^{3} - a^{3} b^{2} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"1/6*(2*b^5*e^5*x^5 - 27*b^5*d^5 + 105*a*b^4*d^4*e - 150*a^2*b^3*d^3*e^2 + 90*a^3*b^2*d^2*e^3 - 15*a^4*b*d*e^4 - 3*a^5*e^5 - 5*(b^5*d*e^4 - 3*a*b^4*e^5)*x^4 + 20*(b^5*d^2*e^3 - 3*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + 3*(21*b^5*d^3*e^2 - 55*a*b^4*d^2*e^3 + 40*a^2*b^3*d*e^4)*x^2 + 6*(b^5*d^4*e + 5*a*b^4*d^3*e^2 - 20*a^2*b^3*d^2*e^3 + 20*a^3*b^2*d*e^4 - 5*a^4*b*e^5)*x - 60*(b^5*d^5 - 3*a*b^4*d^4*e + 3*a^2*b^3*d^3*e^2 - a^3*b^2*d^2*e^3 + (b^5*d^3*e^2 - 3*a*b^4*d^2*e^3 + 3*a^2*b^3*d*e^4 - a^3*b^2*e^5)*x^2 + 2*(b^5*d^4*e - 3*a*b^4*d^3*e^2 + 3*a^2*b^3*d^2*e^3 - a^3*b^2*d*e^4)*x)*log(e*x + d))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","B",0
1915,1,425,0,0.402229," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, b^{5} e^{5} x^{5} + 47 \, b^{5} d^{5} - 130 \, a b^{4} d^{4} e + 110 \, a^{2} b^{3} d^{3} e^{2} - 20 \, a^{3} b^{2} d^{2} e^{3} - 5 \, a^{4} b d e^{4} - 2 \, a^{5} e^{5} - 15 \, {\left(b^{5} d e^{4} - 2 \, a b^{4} e^{5}\right)} x^{4} - 9 \, {\left(7 \, b^{5} d^{2} e^{3} - 10 \, a b^{4} d e^{4}\right)} x^{3} - 3 \, {\left(3 \, b^{5} d^{3} e^{2} + 30 \, a b^{4} d^{2} e^{3} - 60 \, a^{2} b^{3} d e^{4} + 20 \, a^{3} b^{2} e^{5}\right)} x^{2} + 3 \, {\left(27 \, b^{5} d^{4} e - 90 \, a b^{4} d^{3} e^{2} + 90 \, a^{2} b^{3} d^{2} e^{3} - 20 \, a^{3} b^{2} d e^{4} - 5 \, a^{4} b e^{5}\right)} x + 60 \, {\left(b^{5} d^{5} - 2 \, a b^{4} d^{4} e + a^{2} b^{3} d^{3} e^{2} + {\left(b^{5} d^{2} e^{3} - 2 \, a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + 3 \, {\left(b^{5} d^{3} e^{2} - 2 \, a b^{4} d^{2} e^{3} + a^{2} b^{3} d e^{4}\right)} x^{2} + 3 \, {\left(b^{5} d^{4} e - 2 \, a b^{4} d^{3} e^{2} + a^{2} b^{3} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"1/6*(3*b^5*e^5*x^5 + 47*b^5*d^5 - 130*a*b^4*d^4*e + 110*a^2*b^3*d^3*e^2 - 20*a^3*b^2*d^2*e^3 - 5*a^4*b*d*e^4 - 2*a^5*e^5 - 15*(b^5*d*e^4 - 2*a*b^4*e^5)*x^4 - 9*(7*b^5*d^2*e^3 - 10*a*b^4*d*e^4)*x^3 - 3*(3*b^5*d^3*e^2 + 30*a*b^4*d^2*e^3 - 60*a^2*b^3*d*e^4 + 20*a^3*b^2*e^5)*x^2 + 3*(27*b^5*d^4*e - 90*a*b^4*d^3*e^2 + 90*a^2*b^3*d^2*e^3 - 20*a^3*b^2*d*e^4 - 5*a^4*b*e^5)*x + 60*(b^5*d^5 - 2*a*b^4*d^4*e + a^2*b^3*d^3*e^2 + (b^5*d^2*e^3 - 2*a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + 3*(b^5*d^3*e^2 - 2*a*b^4*d^2*e^3 + a^2*b^3*d*e^4)*x^2 + 3*(b^5*d^4*e - 2*a*b^4*d^3*e^2 + a^2*b^3*d^2*e^3)*x)*log(e*x + d))/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","B",0
1916,1,798,0,0.365960," ","integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{14} x^{14} e^{6} b^{7} + \frac{6}{13} x^{13} e^{5} d b^{7} + \frac{7}{13} x^{13} e^{6} b^{6} a + \frac{5}{4} x^{12} e^{4} d^{2} b^{7} + \frac{7}{2} x^{12} e^{5} d b^{6} a + \frac{7}{4} x^{12} e^{6} b^{5} a^{2} + \frac{20}{11} x^{11} e^{3} d^{3} b^{7} + \frac{105}{11} x^{11} e^{4} d^{2} b^{6} a + \frac{126}{11} x^{11} e^{5} d b^{5} a^{2} + \frac{35}{11} x^{11} e^{6} b^{4} a^{3} + \frac{3}{2} x^{10} e^{2} d^{4} b^{7} + 14 x^{10} e^{3} d^{3} b^{6} a + \frac{63}{2} x^{10} e^{4} d^{2} b^{5} a^{2} + 21 x^{10} e^{5} d b^{4} a^{3} + \frac{7}{2} x^{10} e^{6} b^{3} a^{4} + \frac{2}{3} x^{9} e d^{5} b^{7} + \frac{35}{3} x^{9} e^{2} d^{4} b^{6} a + \frac{140}{3} x^{9} e^{3} d^{3} b^{5} a^{2} + \frac{175}{3} x^{9} e^{4} d^{2} b^{4} a^{3} + \frac{70}{3} x^{9} e^{5} d b^{3} a^{4} + \frac{7}{3} x^{9} e^{6} b^{2} a^{5} + \frac{1}{8} x^{8} d^{6} b^{7} + \frac{21}{4} x^{8} e d^{5} b^{6} a + \frac{315}{8} x^{8} e^{2} d^{4} b^{5} a^{2} + \frac{175}{2} x^{8} e^{3} d^{3} b^{4} a^{3} + \frac{525}{8} x^{8} e^{4} d^{2} b^{3} a^{4} + \frac{63}{4} x^{8} e^{5} d b^{2} a^{5} + \frac{7}{8} x^{8} e^{6} b a^{6} + x^{7} d^{6} b^{6} a + 18 x^{7} e d^{5} b^{5} a^{2} + 75 x^{7} e^{2} d^{4} b^{4} a^{3} + 100 x^{7} e^{3} d^{3} b^{3} a^{4} + 45 x^{7} e^{4} d^{2} b^{2} a^{5} + 6 x^{7} e^{5} d b a^{6} + \frac{1}{7} x^{7} e^{6} a^{7} + \frac{7}{2} x^{6} d^{6} b^{5} a^{2} + 35 x^{6} e d^{5} b^{4} a^{3} + \frac{175}{2} x^{6} e^{2} d^{4} b^{3} a^{4} + 70 x^{6} e^{3} d^{3} b^{2} a^{5} + \frac{35}{2} x^{6} e^{4} d^{2} b a^{6} + x^{6} e^{5} d a^{7} + 7 x^{5} d^{6} b^{4} a^{3} + 42 x^{5} e d^{5} b^{3} a^{4} + 63 x^{5} e^{2} d^{4} b^{2} a^{5} + 28 x^{5} e^{3} d^{3} b a^{6} + 3 x^{5} e^{4} d^{2} a^{7} + \frac{35}{4} x^{4} d^{6} b^{3} a^{4} + \frac{63}{2} x^{4} e d^{5} b^{2} a^{5} + \frac{105}{4} x^{4} e^{2} d^{4} b a^{6} + 5 x^{4} e^{3} d^{3} a^{7} + 7 x^{3} d^{6} b^{2} a^{5} + 14 x^{3} e d^{5} b a^{6} + 5 x^{3} e^{2} d^{4} a^{7} + \frac{7}{2} x^{2} d^{6} b a^{6} + 3 x^{2} e d^{5} a^{7} + x d^{6} a^{7}"," ",0,"1/14*x^14*e^6*b^7 + 6/13*x^13*e^5*d*b^7 + 7/13*x^13*e^6*b^6*a + 5/4*x^12*e^4*d^2*b^7 + 7/2*x^12*e^5*d*b^6*a + 7/4*x^12*e^6*b^5*a^2 + 20/11*x^11*e^3*d^3*b^7 + 105/11*x^11*e^4*d^2*b^6*a + 126/11*x^11*e^5*d*b^5*a^2 + 35/11*x^11*e^6*b^4*a^3 + 3/2*x^10*e^2*d^4*b^7 + 14*x^10*e^3*d^3*b^6*a + 63/2*x^10*e^4*d^2*b^5*a^2 + 21*x^10*e^5*d*b^4*a^3 + 7/2*x^10*e^6*b^3*a^4 + 2/3*x^9*e*d^5*b^7 + 35/3*x^9*e^2*d^4*b^6*a + 140/3*x^9*e^3*d^3*b^5*a^2 + 175/3*x^9*e^4*d^2*b^4*a^3 + 70/3*x^9*e^5*d*b^3*a^4 + 7/3*x^9*e^6*b^2*a^5 + 1/8*x^8*d^6*b^7 + 21/4*x^8*e*d^5*b^6*a + 315/8*x^8*e^2*d^4*b^5*a^2 + 175/2*x^8*e^3*d^3*b^4*a^3 + 525/8*x^8*e^4*d^2*b^3*a^4 + 63/4*x^8*e^5*d*b^2*a^5 + 7/8*x^8*e^6*b*a^6 + x^7*d^6*b^6*a + 18*x^7*e*d^5*b^5*a^2 + 75*x^7*e^2*d^4*b^4*a^3 + 100*x^7*e^3*d^3*b^3*a^4 + 45*x^7*e^4*d^2*b^2*a^5 + 6*x^7*e^5*d*b*a^6 + 1/7*x^7*e^6*a^7 + 7/2*x^6*d^6*b^5*a^2 + 35*x^6*e*d^5*b^4*a^3 + 175/2*x^6*e^2*d^4*b^3*a^4 + 70*x^6*e^3*d^3*b^2*a^5 + 35/2*x^6*e^4*d^2*b*a^6 + x^6*e^5*d*a^7 + 7*x^5*d^6*b^4*a^3 + 42*x^5*e*d^5*b^3*a^4 + 63*x^5*e^2*d^4*b^2*a^5 + 28*x^5*e^3*d^3*b*a^6 + 3*x^5*e^4*d^2*a^7 + 35/4*x^4*d^6*b^3*a^4 + 63/2*x^4*e*d^5*b^2*a^5 + 105/4*x^4*e^2*d^4*b*a^6 + 5*x^4*e^3*d^3*a^7 + 7*x^3*d^6*b^2*a^5 + 14*x^3*e*d^5*b*a^6 + 5*x^3*e^2*d^4*a^7 + 7/2*x^2*d^6*b*a^6 + 3*x^2*e*d^5*a^7 + x*d^6*a^7","B",0
1917,1,670,0,0.385813," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{5} b^{7} + \frac{5}{12} x^{12} e^{4} d b^{7} + \frac{7}{12} x^{12} e^{5} b^{6} a + \frac{10}{11} x^{11} e^{3} d^{2} b^{7} + \frac{35}{11} x^{11} e^{4} d b^{6} a + \frac{21}{11} x^{11} e^{5} b^{5} a^{2} + x^{10} e^{2} d^{3} b^{7} + 7 x^{10} e^{3} d^{2} b^{6} a + \frac{21}{2} x^{10} e^{4} d b^{5} a^{2} + \frac{7}{2} x^{10} e^{5} b^{4} a^{3} + \frac{5}{9} x^{9} e d^{4} b^{7} + \frac{70}{9} x^{9} e^{2} d^{3} b^{6} a + \frac{70}{3} x^{9} e^{3} d^{2} b^{5} a^{2} + \frac{175}{9} x^{9} e^{4} d b^{4} a^{3} + \frac{35}{9} x^{9} e^{5} b^{3} a^{4} + \frac{1}{8} x^{8} d^{5} b^{7} + \frac{35}{8} x^{8} e d^{4} b^{6} a + \frac{105}{4} x^{8} e^{2} d^{3} b^{5} a^{2} + \frac{175}{4} x^{8} e^{3} d^{2} b^{4} a^{3} + \frac{175}{8} x^{8} e^{4} d b^{3} a^{4} + \frac{21}{8} x^{8} e^{5} b^{2} a^{5} + x^{7} d^{5} b^{6} a + 15 x^{7} e d^{4} b^{5} a^{2} + 50 x^{7} e^{2} d^{3} b^{4} a^{3} + 50 x^{7} e^{3} d^{2} b^{3} a^{4} + 15 x^{7} e^{4} d b^{2} a^{5} + x^{7} e^{5} b a^{6} + \frac{7}{2} x^{6} d^{5} b^{5} a^{2} + \frac{175}{6} x^{6} e d^{4} b^{4} a^{3} + \frac{175}{3} x^{6} e^{2} d^{3} b^{3} a^{4} + 35 x^{6} e^{3} d^{2} b^{2} a^{5} + \frac{35}{6} x^{6} e^{4} d b a^{6} + \frac{1}{6} x^{6} e^{5} a^{7} + 7 x^{5} d^{5} b^{4} a^{3} + 35 x^{5} e d^{4} b^{3} a^{4} + 42 x^{5} e^{2} d^{3} b^{2} a^{5} + 14 x^{5} e^{3} d^{2} b a^{6} + x^{5} e^{4} d a^{7} + \frac{35}{4} x^{4} d^{5} b^{3} a^{4} + \frac{105}{4} x^{4} e d^{4} b^{2} a^{5} + \frac{35}{2} x^{4} e^{2} d^{3} b a^{6} + \frac{5}{2} x^{4} e^{3} d^{2} a^{7} + 7 x^{3} d^{5} b^{2} a^{5} + \frac{35}{3} x^{3} e d^{4} b a^{6} + \frac{10}{3} x^{3} e^{2} d^{3} a^{7} + \frac{7}{2} x^{2} d^{5} b a^{6} + \frac{5}{2} x^{2} e d^{4} a^{7} + x d^{5} a^{7}"," ",0,"1/13*x^13*e^5*b^7 + 5/12*x^12*e^4*d*b^7 + 7/12*x^12*e^5*b^6*a + 10/11*x^11*e^3*d^2*b^7 + 35/11*x^11*e^4*d*b^6*a + 21/11*x^11*e^5*b^5*a^2 + x^10*e^2*d^3*b^7 + 7*x^10*e^3*d^2*b^6*a + 21/2*x^10*e^4*d*b^5*a^2 + 7/2*x^10*e^5*b^4*a^3 + 5/9*x^9*e*d^4*b^7 + 70/9*x^9*e^2*d^3*b^6*a + 70/3*x^9*e^3*d^2*b^5*a^2 + 175/9*x^9*e^4*d*b^4*a^3 + 35/9*x^9*e^5*b^3*a^4 + 1/8*x^8*d^5*b^7 + 35/8*x^8*e*d^4*b^6*a + 105/4*x^8*e^2*d^3*b^5*a^2 + 175/4*x^8*e^3*d^2*b^4*a^3 + 175/8*x^8*e^4*d*b^3*a^4 + 21/8*x^8*e^5*b^2*a^5 + x^7*d^5*b^6*a + 15*x^7*e*d^4*b^5*a^2 + 50*x^7*e^2*d^3*b^4*a^3 + 50*x^7*e^3*d^2*b^3*a^4 + 15*x^7*e^4*d*b^2*a^5 + x^7*e^5*b*a^6 + 7/2*x^6*d^5*b^5*a^2 + 175/6*x^6*e*d^4*b^4*a^3 + 175/3*x^6*e^2*d^3*b^3*a^4 + 35*x^6*e^3*d^2*b^2*a^5 + 35/6*x^6*e^4*d*b*a^6 + 1/6*x^6*e^5*a^7 + 7*x^5*d^5*b^4*a^3 + 35*x^5*e*d^4*b^3*a^4 + 42*x^5*e^2*d^3*b^2*a^5 + 14*x^5*e^3*d^2*b*a^6 + x^5*e^4*d*a^7 + 35/4*x^4*d^5*b^3*a^4 + 105/4*x^4*e*d^4*b^2*a^5 + 35/2*x^4*e^2*d^3*b*a^6 + 5/2*x^4*e^3*d^2*a^7 + 7*x^3*d^5*b^2*a^5 + 35/3*x^3*e*d^4*b*a^6 + 10/3*x^3*e^2*d^3*a^7 + 7/2*x^2*d^5*b*a^6 + 5/2*x^2*e*d^4*a^7 + x*d^5*a^7","B",0
1918,1,546,0,0.370323," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{4} b^{7} + \frac{4}{11} x^{11} e^{3} d b^{7} + \frac{7}{11} x^{11} e^{4} b^{6} a + \frac{3}{5} x^{10} e^{2} d^{2} b^{7} + \frac{14}{5} x^{10} e^{3} d b^{6} a + \frac{21}{10} x^{10} e^{4} b^{5} a^{2} + \frac{4}{9} x^{9} e d^{3} b^{7} + \frac{14}{3} x^{9} e^{2} d^{2} b^{6} a + \frac{28}{3} x^{9} e^{3} d b^{5} a^{2} + \frac{35}{9} x^{9} e^{4} b^{4} a^{3} + \frac{1}{8} x^{8} d^{4} b^{7} + \frac{7}{2} x^{8} e d^{3} b^{6} a + \frac{63}{4} x^{8} e^{2} d^{2} b^{5} a^{2} + \frac{35}{2} x^{8} e^{3} d b^{4} a^{3} + \frac{35}{8} x^{8} e^{4} b^{3} a^{4} + x^{7} d^{4} b^{6} a + 12 x^{7} e d^{3} b^{5} a^{2} + 30 x^{7} e^{2} d^{2} b^{4} a^{3} + 20 x^{7} e^{3} d b^{3} a^{4} + 3 x^{7} e^{4} b^{2} a^{5} + \frac{7}{2} x^{6} d^{4} b^{5} a^{2} + \frac{70}{3} x^{6} e d^{3} b^{4} a^{3} + 35 x^{6} e^{2} d^{2} b^{3} a^{4} + 14 x^{6} e^{3} d b^{2} a^{5} + \frac{7}{6} x^{6} e^{4} b a^{6} + 7 x^{5} d^{4} b^{4} a^{3} + 28 x^{5} e d^{3} b^{3} a^{4} + \frac{126}{5} x^{5} e^{2} d^{2} b^{2} a^{5} + \frac{28}{5} x^{5} e^{3} d b a^{6} + \frac{1}{5} x^{5} e^{4} a^{7} + \frac{35}{4} x^{4} d^{4} b^{3} a^{4} + 21 x^{4} e d^{3} b^{2} a^{5} + \frac{21}{2} x^{4} e^{2} d^{2} b a^{6} + x^{4} e^{3} d a^{7} + 7 x^{3} d^{4} b^{2} a^{5} + \frac{28}{3} x^{3} e d^{3} b a^{6} + 2 x^{3} e^{2} d^{2} a^{7} + \frac{7}{2} x^{2} d^{4} b a^{6} + 2 x^{2} e d^{3} a^{7} + x d^{4} a^{7}"," ",0,"1/12*x^12*e^4*b^7 + 4/11*x^11*e^3*d*b^7 + 7/11*x^11*e^4*b^6*a + 3/5*x^10*e^2*d^2*b^7 + 14/5*x^10*e^3*d*b^6*a + 21/10*x^10*e^4*b^5*a^2 + 4/9*x^9*e*d^3*b^7 + 14/3*x^9*e^2*d^2*b^6*a + 28/3*x^9*e^3*d*b^5*a^2 + 35/9*x^9*e^4*b^4*a^3 + 1/8*x^8*d^4*b^7 + 7/2*x^8*e*d^3*b^6*a + 63/4*x^8*e^2*d^2*b^5*a^2 + 35/2*x^8*e^3*d*b^4*a^3 + 35/8*x^8*e^4*b^3*a^4 + x^7*d^4*b^6*a + 12*x^7*e*d^3*b^5*a^2 + 30*x^7*e^2*d^2*b^4*a^3 + 20*x^7*e^3*d*b^3*a^4 + 3*x^7*e^4*b^2*a^5 + 7/2*x^6*d^4*b^5*a^2 + 70/3*x^6*e*d^3*b^4*a^3 + 35*x^6*e^2*d^2*b^3*a^4 + 14*x^6*e^3*d*b^2*a^5 + 7/6*x^6*e^4*b*a^6 + 7*x^5*d^4*b^4*a^3 + 28*x^5*e*d^3*b^3*a^4 + 126/5*x^5*e^2*d^2*b^2*a^5 + 28/5*x^5*e^3*d*b*a^6 + 1/5*x^5*e^4*a^7 + 35/4*x^4*d^4*b^3*a^4 + 21*x^4*e*d^3*b^2*a^5 + 21/2*x^4*e^2*d^2*b*a^6 + x^4*e^3*d*a^7 + 7*x^3*d^4*b^2*a^5 + 28/3*x^3*e*d^3*b*a^6 + 2*x^3*e^2*d^2*a^7 + 7/2*x^2*d^4*b*a^6 + 2*x^2*e*d^3*a^7 + x*d^4*a^7","B",0
1919,1,420,0,0.436565," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{3} b^{7} + \frac{3}{10} x^{10} e^{2} d b^{7} + \frac{7}{10} x^{10} e^{3} b^{6} a + \frac{1}{3} x^{9} e d^{2} b^{7} + \frac{7}{3} x^{9} e^{2} d b^{6} a + \frac{7}{3} x^{9} e^{3} b^{5} a^{2} + \frac{1}{8} x^{8} d^{3} b^{7} + \frac{21}{8} x^{8} e d^{2} b^{6} a + \frac{63}{8} x^{8} e^{2} d b^{5} a^{2} + \frac{35}{8} x^{8} e^{3} b^{4} a^{3} + x^{7} d^{3} b^{6} a + 9 x^{7} e d^{2} b^{5} a^{2} + 15 x^{7} e^{2} d b^{4} a^{3} + 5 x^{7} e^{3} b^{3} a^{4} + \frac{7}{2} x^{6} d^{3} b^{5} a^{2} + \frac{35}{2} x^{6} e d^{2} b^{4} a^{3} + \frac{35}{2} x^{6} e^{2} d b^{3} a^{4} + \frac{7}{2} x^{6} e^{3} b^{2} a^{5} + 7 x^{5} d^{3} b^{4} a^{3} + 21 x^{5} e d^{2} b^{3} a^{4} + \frac{63}{5} x^{5} e^{2} d b^{2} a^{5} + \frac{7}{5} x^{5} e^{3} b a^{6} + \frac{35}{4} x^{4} d^{3} b^{3} a^{4} + \frac{63}{4} x^{4} e d^{2} b^{2} a^{5} + \frac{21}{4} x^{4} e^{2} d b a^{6} + \frac{1}{4} x^{4} e^{3} a^{7} + 7 x^{3} d^{3} b^{2} a^{5} + 7 x^{3} e d^{2} b a^{6} + x^{3} e^{2} d a^{7} + \frac{7}{2} x^{2} d^{3} b a^{6} + \frac{3}{2} x^{2} e d^{2} a^{7} + x d^{3} a^{7}"," ",0,"1/11*x^11*e^3*b^7 + 3/10*x^10*e^2*d*b^7 + 7/10*x^10*e^3*b^6*a + 1/3*x^9*e*d^2*b^7 + 7/3*x^9*e^2*d*b^6*a + 7/3*x^9*e^3*b^5*a^2 + 1/8*x^8*d^3*b^7 + 21/8*x^8*e*d^2*b^6*a + 63/8*x^8*e^2*d*b^5*a^2 + 35/8*x^8*e^3*b^4*a^3 + x^7*d^3*b^6*a + 9*x^7*e*d^2*b^5*a^2 + 15*x^7*e^2*d*b^4*a^3 + 5*x^7*e^3*b^3*a^4 + 7/2*x^6*d^3*b^5*a^2 + 35/2*x^6*e*d^2*b^4*a^3 + 35/2*x^6*e^2*d*b^3*a^4 + 7/2*x^6*e^3*b^2*a^5 + 7*x^5*d^3*b^4*a^3 + 21*x^5*e*d^2*b^3*a^4 + 63/5*x^5*e^2*d*b^2*a^5 + 7/5*x^5*e^3*b*a^6 + 35/4*x^4*d^3*b^3*a^4 + 63/4*x^4*e*d^2*b^2*a^5 + 21/4*x^4*e^2*d*b*a^6 + 1/4*x^4*e^3*a^7 + 7*x^3*d^3*b^2*a^5 + 7*x^3*e*d^2*b*a^6 + x^3*e^2*d*a^7 + 7/2*x^2*d^3*b*a^6 + 3/2*x^2*e*d^2*a^7 + x*d^3*a^7","B",0
1920,1,294,0,0.395971," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{2} b^{7} + \frac{2}{9} x^{9} e d b^{7} + \frac{7}{9} x^{9} e^{2} b^{6} a + \frac{1}{8} x^{8} d^{2} b^{7} + \frac{7}{4} x^{8} e d b^{6} a + \frac{21}{8} x^{8} e^{2} b^{5} a^{2} + x^{7} d^{2} b^{6} a + 6 x^{7} e d b^{5} a^{2} + 5 x^{7} e^{2} b^{4} a^{3} + \frac{7}{2} x^{6} d^{2} b^{5} a^{2} + \frac{35}{3} x^{6} e d b^{4} a^{3} + \frac{35}{6} x^{6} e^{2} b^{3} a^{4} + 7 x^{5} d^{2} b^{4} a^{3} + 14 x^{5} e d b^{3} a^{4} + \frac{21}{5} x^{5} e^{2} b^{2} a^{5} + \frac{35}{4} x^{4} d^{2} b^{3} a^{4} + \frac{21}{2} x^{4} e d b^{2} a^{5} + \frac{7}{4} x^{4} e^{2} b a^{6} + 7 x^{3} d^{2} b^{2} a^{5} + \frac{14}{3} x^{3} e d b a^{6} + \frac{1}{3} x^{3} e^{2} a^{7} + \frac{7}{2} x^{2} d^{2} b a^{6} + x^{2} e d a^{7} + x d^{2} a^{7}"," ",0,"1/10*x^10*e^2*b^7 + 2/9*x^9*e*d*b^7 + 7/9*x^9*e^2*b^6*a + 1/8*x^8*d^2*b^7 + 7/4*x^8*e*d*b^6*a + 21/8*x^8*e^2*b^5*a^2 + x^7*d^2*b^6*a + 6*x^7*e*d*b^5*a^2 + 5*x^7*e^2*b^4*a^3 + 7/2*x^6*d^2*b^5*a^2 + 35/3*x^6*e*d*b^4*a^3 + 35/6*x^6*e^2*b^3*a^4 + 7*x^5*d^2*b^4*a^3 + 14*x^5*e*d*b^3*a^4 + 21/5*x^5*e^2*b^2*a^5 + 35/4*x^4*d^2*b^3*a^4 + 21/2*x^4*e*d*b^2*a^5 + 7/4*x^4*e^2*b*a^6 + 7*x^3*d^2*b^2*a^5 + 14/3*x^3*e*d*b*a^6 + 1/3*x^3*e^2*a^7 + 7/2*x^2*d^2*b*a^6 + x^2*e*d*a^7 + x*d^2*a^7","B",0
1921,1,169,0,0.380155," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e b^{7} + \frac{1}{8} x^{8} d b^{7} + \frac{7}{8} x^{8} e b^{6} a + x^{7} d b^{6} a + 3 x^{7} e b^{5} a^{2} + \frac{7}{2} x^{6} d b^{5} a^{2} + \frac{35}{6} x^{6} e b^{4} a^{3} + 7 x^{5} d b^{4} a^{3} + 7 x^{5} e b^{3} a^{4} + \frac{35}{4} x^{4} d b^{3} a^{4} + \frac{21}{4} x^{4} e b^{2} a^{5} + 7 x^{3} d b^{2} a^{5} + \frac{7}{3} x^{3} e b a^{6} + \frac{7}{2} x^{2} d b a^{6} + \frac{1}{2} x^{2} e a^{7} + x d a^{7}"," ",0,"1/9*x^9*e*b^7 + 1/8*x^8*d*b^7 + 7/8*x^8*e*b^6*a + x^7*d*b^6*a + 3*x^7*e*b^5*a^2 + 7/2*x^6*d*b^5*a^2 + 35/6*x^6*e*b^4*a^3 + 7*x^5*d*b^4*a^3 + 7*x^5*e*b^3*a^4 + 35/4*x^4*d*b^3*a^4 + 21/4*x^4*e*b^2*a^5 + 7*x^3*d*b^2*a^5 + 7/3*x^3*e*b*a^6 + 7/2*x^2*d*b*a^6 + 1/2*x^2*e*a^7 + x*d*a^7","B",0
1922,1,75,0,0.376015," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{7} + x^{7} b^{6} a + \frac{7}{2} x^{6} b^{5} a^{2} + 7 x^{5} b^{4} a^{3} + \frac{35}{4} x^{4} b^{3} a^{4} + 7 x^{3} b^{2} a^{5} + \frac{7}{2} x^{2} b a^{6} + x a^{7}"," ",0,"1/8*x^8*b^7 + x^7*b^6*a + 7/2*x^6*b^5*a^2 + 7*x^5*b^4*a^3 + 35/4*x^4*b^3*a^4 + 7*x^3*b^2*a^5 + 7/2*x^2*b*a^6 + x*a^7","B",0
1923,1,459,0,0.455206," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d),x, algorithm=""fricas"")","\frac{60 \, b^{7} e^{7} x^{7} - 70 \, {\left(b^{7} d e^{6} - 7 \, a b^{6} e^{7}\right)} x^{6} + 84 \, {\left(b^{7} d^{2} e^{5} - 7 \, a b^{6} d e^{6} + 21 \, a^{2} b^{5} e^{7}\right)} x^{5} - 105 \, {\left(b^{7} d^{3} e^{4} - 7 \, a b^{6} d^{2} e^{5} + 21 \, a^{2} b^{5} d e^{6} - 35 \, a^{3} b^{4} e^{7}\right)} x^{4} + 140 \, {\left(b^{7} d^{4} e^{3} - 7 \, a b^{6} d^{3} e^{4} + 21 \, a^{2} b^{5} d^{2} e^{5} - 35 \, a^{3} b^{4} d e^{6} + 35 \, a^{4} b^{3} e^{7}\right)} x^{3} - 210 \, {\left(b^{7} d^{5} e^{2} - 7 \, a b^{6} d^{4} e^{3} + 21 \, a^{2} b^{5} d^{3} e^{4} - 35 \, a^{3} b^{4} d^{2} e^{5} + 35 \, a^{4} b^{3} d e^{6} - 21 \, a^{5} b^{2} e^{7}\right)} x^{2} + 420 \, {\left(b^{7} d^{6} e - 7 \, a b^{6} d^{5} e^{2} + 21 \, a^{2} b^{5} d^{4} e^{3} - 35 \, a^{3} b^{4} d^{3} e^{4} + 35 \, a^{4} b^{3} d^{2} e^{5} - 21 \, a^{5} b^{2} d e^{6} + 7 \, a^{6} b e^{7}\right)} x - 420 \, {\left(b^{7} d^{7} - 7 \, a b^{6} d^{6} e + 21 \, a^{2} b^{5} d^{5} e^{2} - 35 \, a^{3} b^{4} d^{4} e^{3} + 35 \, a^{4} b^{3} d^{3} e^{4} - 21 \, a^{5} b^{2} d^{2} e^{5} + 7 \, a^{6} b d e^{6} - a^{7} e^{7}\right)} \log\left(e x + d\right)}{420 \, e^{8}}"," ",0,"1/420*(60*b^7*e^7*x^7 - 70*(b^7*d*e^6 - 7*a*b^6*e^7)*x^6 + 84*(b^7*d^2*e^5 - 7*a*b^6*d*e^6 + 21*a^2*b^5*e^7)*x^5 - 105*(b^7*d^3*e^4 - 7*a*b^6*d^2*e^5 + 21*a^2*b^5*d*e^6 - 35*a^3*b^4*e^7)*x^4 + 140*(b^7*d^4*e^3 - 7*a*b^6*d^3*e^4 + 21*a^2*b^5*d^2*e^5 - 35*a^3*b^4*d*e^6 + 35*a^4*b^3*e^7)*x^3 - 210*(b^7*d^5*e^2 - 7*a*b^6*d^4*e^3 + 21*a^2*b^5*d^3*e^4 - 35*a^3*b^4*d^2*e^5 + 35*a^4*b^3*d*e^6 - 21*a^5*b^2*e^7)*x^2 + 420*(b^7*d^6*e - 7*a*b^6*d^5*e^2 + 21*a^2*b^5*d^4*e^3 - 35*a^3*b^4*d^3*e^4 + 35*a^4*b^3*d^2*e^5 - 21*a^5*b^2*d*e^6 + 7*a^6*b*e^7)*x - 420*(b^7*d^7 - 7*a*b^6*d^6*e + 21*a^2*b^5*d^5*e^2 - 35*a^3*b^4*d^4*e^3 + 35*a^4*b^3*d^3*e^4 - 21*a^5*b^2*d^2*e^5 + 7*a^6*b*d*e^6 - a^7*e^7)*log(e*x + d))/e^8","B",0
1924,1,629,0,0.441003," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{10 \, b^{7} e^{7} x^{7} + 60 \, b^{7} d^{7} - 420 \, a b^{6} d^{6} e + 1260 \, a^{2} b^{5} d^{5} e^{2} - 2100 \, a^{3} b^{4} d^{4} e^{3} + 2100 \, a^{4} b^{3} d^{3} e^{4} - 1260 \, a^{5} b^{2} d^{2} e^{5} + 420 \, a^{6} b d e^{6} - 60 \, a^{7} e^{7} - 14 \, {\left(b^{7} d e^{6} - 6 \, a b^{6} e^{7}\right)} x^{6} + 21 \, {\left(b^{7} d^{2} e^{5} - 6 \, a b^{6} d e^{6} + 15 \, a^{2} b^{5} e^{7}\right)} x^{5} - 35 \, {\left(b^{7} d^{3} e^{4} - 6 \, a b^{6} d^{2} e^{5} + 15 \, a^{2} b^{5} d e^{6} - 20 \, a^{3} b^{4} e^{7}\right)} x^{4} + 70 \, {\left(b^{7} d^{4} e^{3} - 6 \, a b^{6} d^{3} e^{4} + 15 \, a^{2} b^{5} d^{2} e^{5} - 20 \, a^{3} b^{4} d e^{6} + 15 \, a^{4} b^{3} e^{7}\right)} x^{3} - 210 \, {\left(b^{7} d^{5} e^{2} - 6 \, a b^{6} d^{4} e^{3} + 15 \, a^{2} b^{5} d^{3} e^{4} - 20 \, a^{3} b^{4} d^{2} e^{5} + 15 \, a^{4} b^{3} d e^{6} - 6 \, a^{5} b^{2} e^{7}\right)} x^{2} - 60 \, {\left(6 \, b^{7} d^{6} e - 35 \, a b^{6} d^{5} e^{2} + 84 \, a^{2} b^{5} d^{4} e^{3} - 105 \, a^{3} b^{4} d^{3} e^{4} + 70 \, a^{4} b^{3} d^{2} e^{5} - 21 \, a^{5} b^{2} d e^{6}\right)} x + 420 \, {\left(b^{7} d^{7} - 6 \, a b^{6} d^{6} e + 15 \, a^{2} b^{5} d^{5} e^{2} - 20 \, a^{3} b^{4} d^{4} e^{3} + 15 \, a^{4} b^{3} d^{3} e^{4} - 6 \, a^{5} b^{2} d^{2} e^{5} + a^{6} b d e^{6} + {\left(b^{7} d^{6} e - 6 \, a b^{6} d^{5} e^{2} + 15 \, a^{2} b^{5} d^{4} e^{3} - 20 \, a^{3} b^{4} d^{3} e^{4} + 15 \, a^{4} b^{3} d^{2} e^{5} - 6 \, a^{5} b^{2} d e^{6} + a^{6} b e^{7}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"1/60*(10*b^7*e^7*x^7 + 60*b^7*d^7 - 420*a*b^6*d^6*e + 1260*a^2*b^5*d^5*e^2 - 2100*a^3*b^4*d^4*e^3 + 2100*a^4*b^3*d^3*e^4 - 1260*a^5*b^2*d^2*e^5 + 420*a^6*b*d*e^6 - 60*a^7*e^7 - 14*(b^7*d*e^6 - 6*a*b^6*e^7)*x^6 + 21*(b^7*d^2*e^5 - 6*a*b^6*d*e^6 + 15*a^2*b^5*e^7)*x^5 - 35*(b^7*d^3*e^4 - 6*a*b^6*d^2*e^5 + 15*a^2*b^5*d*e^6 - 20*a^3*b^4*e^7)*x^4 + 70*(b^7*d^4*e^3 - 6*a*b^6*d^3*e^4 + 15*a^2*b^5*d^2*e^5 - 20*a^3*b^4*d*e^6 + 15*a^4*b^3*e^7)*x^3 - 210*(b^7*d^5*e^2 - 6*a*b^6*d^4*e^3 + 15*a^2*b^5*d^3*e^4 - 20*a^3*b^4*d^2*e^5 + 15*a^4*b^3*d*e^6 - 6*a^5*b^2*e^7)*x^2 - 60*(6*b^7*d^6*e - 35*a*b^6*d^5*e^2 + 84*a^2*b^5*d^4*e^3 - 105*a^3*b^4*d^3*e^4 + 70*a^4*b^3*d^2*e^5 - 21*a^5*b^2*d*e^6)*x + 420*(b^7*d^7 - 6*a*b^6*d^6*e + 15*a^2*b^5*d^5*e^2 - 20*a^3*b^4*d^4*e^3 + 15*a^4*b^3*d^3*e^4 - 6*a^5*b^2*d^2*e^5 + a^6*b*d*e^6 + (b^7*d^6*e - 6*a*b^6*d^5*e^2 + 15*a^2*b^5*d^4*e^3 - 20*a^3*b^4*d^3*e^4 + 15*a^4*b^3*d^2*e^5 - 6*a^5*b^2*d*e^6 + a^6*b*e^7)*x)*log(e*x + d))/(e^9*x + d*e^8)","B",0
1925,1,701,0,0.437193," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{4 \, b^{7} e^{7} x^{7} - 130 \, b^{7} d^{7} + 770 \, a b^{6} d^{6} e - 1890 \, a^{2} b^{5} d^{5} e^{2} + 2450 \, a^{3} b^{4} d^{4} e^{3} - 1750 \, a^{4} b^{3} d^{3} e^{4} + 630 \, a^{5} b^{2} d^{2} e^{5} - 70 \, a^{6} b d e^{6} - 10 \, a^{7} e^{7} - 7 \, {\left(b^{7} d e^{6} - 5 \, a b^{6} e^{7}\right)} x^{6} + 14 \, {\left(b^{7} d^{2} e^{5} - 5 \, a b^{6} d e^{6} + 10 \, a^{2} b^{5} e^{7}\right)} x^{5} - 35 \, {\left(b^{7} d^{3} e^{4} - 5 \, a b^{6} d^{2} e^{5} + 10 \, a^{2} b^{5} d e^{6} - 10 \, a^{3} b^{4} e^{7}\right)} x^{4} + 140 \, {\left(b^{7} d^{4} e^{3} - 5 \, a b^{6} d^{3} e^{4} + 10 \, a^{2} b^{5} d^{2} e^{5} - 10 \, a^{3} b^{4} d e^{6} + 5 \, a^{4} b^{3} e^{7}\right)} x^{3} + 10 \, {\left(50 \, b^{7} d^{5} e^{2} - 238 \, a b^{6} d^{4} e^{3} + 441 \, a^{2} b^{5} d^{3} e^{4} - 385 \, a^{3} b^{4} d^{2} e^{5} + 140 \, a^{4} b^{3} d e^{6}\right)} x^{2} + 20 \, {\left(8 \, b^{7} d^{6} e - 28 \, a b^{6} d^{5} e^{2} + 21 \, a^{2} b^{5} d^{4} e^{3} + 35 \, a^{3} b^{4} d^{3} e^{4} - 70 \, a^{4} b^{3} d^{2} e^{5} + 42 \, a^{5} b^{2} d e^{6} - 7 \, a^{6} b e^{7}\right)} x - 420 \, {\left(b^{7} d^{7} - 5 \, a b^{6} d^{6} e + 10 \, a^{2} b^{5} d^{5} e^{2} - 10 \, a^{3} b^{4} d^{4} e^{3} + 5 \, a^{4} b^{3} d^{3} e^{4} - a^{5} b^{2} d^{2} e^{5} + {\left(b^{7} d^{5} e^{2} - 5 \, a b^{6} d^{4} e^{3} + 10 \, a^{2} b^{5} d^{3} e^{4} - 10 \, a^{3} b^{4} d^{2} e^{5} + 5 \, a^{4} b^{3} d e^{6} - a^{5} b^{2} e^{7}\right)} x^{2} + 2 \, {\left(b^{7} d^{6} e - 5 \, a b^{6} d^{5} e^{2} + 10 \, a^{2} b^{5} d^{4} e^{3} - 10 \, a^{3} b^{4} d^{3} e^{4} + 5 \, a^{4} b^{3} d^{2} e^{5} - a^{5} b^{2} d e^{6}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"1/20*(4*b^7*e^7*x^7 - 130*b^7*d^7 + 770*a*b^6*d^6*e - 1890*a^2*b^5*d^5*e^2 + 2450*a^3*b^4*d^4*e^3 - 1750*a^4*b^3*d^3*e^4 + 630*a^5*b^2*d^2*e^5 - 70*a^6*b*d*e^6 - 10*a^7*e^7 - 7*(b^7*d*e^6 - 5*a*b^6*e^7)*x^6 + 14*(b^7*d^2*e^5 - 5*a*b^6*d*e^6 + 10*a^2*b^5*e^7)*x^5 - 35*(b^7*d^3*e^4 - 5*a*b^6*d^2*e^5 + 10*a^2*b^5*d*e^6 - 10*a^3*b^4*e^7)*x^4 + 140*(b^7*d^4*e^3 - 5*a*b^6*d^3*e^4 + 10*a^2*b^5*d^2*e^5 - 10*a^3*b^4*d*e^6 + 5*a^4*b^3*e^7)*x^3 + 10*(50*b^7*d^5*e^2 - 238*a*b^6*d^4*e^3 + 441*a^2*b^5*d^3*e^4 - 385*a^3*b^4*d^2*e^5 + 140*a^4*b^3*d*e^6)*x^2 + 20*(8*b^7*d^6*e - 28*a*b^6*d^5*e^2 + 21*a^2*b^5*d^4*e^3 + 35*a^3*b^4*d^3*e^4 - 70*a^4*b^3*d^2*e^5 + 42*a^5*b^2*d*e^6 - 7*a^6*b*e^7)*x - 420*(b^7*d^7 - 5*a*b^6*d^6*e + 10*a^2*b^5*d^5*e^2 - 10*a^3*b^4*d^4*e^3 + 5*a^4*b^3*d^3*e^4 - a^5*b^2*d^2*e^5 + (b^7*d^5*e^2 - 5*a*b^6*d^4*e^3 + 10*a^2*b^5*d^3*e^4 - 10*a^3*b^4*d^2*e^5 + 5*a^4*b^3*d*e^6 - a^5*b^2*e^7)*x^2 + 2*(b^7*d^6*e - 5*a*b^6*d^5*e^2 + 10*a^2*b^5*d^4*e^3 - 10*a^3*b^4*d^3*e^4 + 5*a^4*b^3*d^2*e^5 - a^5*b^2*d*e^6)*x)*log(e*x + d))/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","B",0
1926,1,737,0,0.434983," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, b^{7} e^{7} x^{7} + 214 \, b^{7} d^{7} - 1036 \, a b^{6} d^{6} e + 1974 \, a^{2} b^{5} d^{5} e^{2} - 1820 \, a^{3} b^{4} d^{4} e^{3} + 770 \, a^{4} b^{3} d^{3} e^{4} - 84 \, a^{5} b^{2} d^{2} e^{5} - 14 \, a^{6} b d e^{6} - 4 \, a^{7} e^{7} - 7 \, {\left(b^{7} d e^{6} - 4 \, a b^{6} e^{7}\right)} x^{6} + 21 \, {\left(b^{7} d^{2} e^{5} - 4 \, a b^{6} d e^{6} + 6 \, a^{2} b^{5} e^{7}\right)} x^{5} - 105 \, {\left(b^{7} d^{3} e^{4} - 4 \, a b^{6} d^{2} e^{5} + 6 \, a^{2} b^{5} d e^{6} - 4 \, a^{3} b^{4} e^{7}\right)} x^{4} - 2 \, {\left(278 \, b^{7} d^{4} e^{3} - 1022 \, a b^{6} d^{3} e^{4} + 1323 \, a^{2} b^{5} d^{2} e^{5} - 630 \, a^{3} b^{4} d e^{6}\right)} x^{3} - 6 \, {\left(68 \, b^{7} d^{5} e^{2} - 182 \, a b^{6} d^{4} e^{3} + 63 \, a^{2} b^{5} d^{3} e^{4} + 210 \, a^{3} b^{4} d^{2} e^{5} - 210 \, a^{4} b^{3} d e^{6} + 42 \, a^{5} b^{2} e^{7}\right)} x^{2} + 6 \, {\left(37 \, b^{7} d^{6} e - 238 \, a b^{6} d^{5} e^{2} + 567 \, a^{2} b^{5} d^{4} e^{3} - 630 \, a^{3} b^{4} d^{3} e^{4} + 315 \, a^{4} b^{3} d^{2} e^{5} - 42 \, a^{5} b^{2} d e^{6} - 7 \, a^{6} b e^{7}\right)} x + 420 \, {\left(b^{7} d^{7} - 4 \, a b^{6} d^{6} e + 6 \, a^{2} b^{5} d^{5} e^{2} - 4 \, a^{3} b^{4} d^{4} e^{3} + a^{4} b^{3} d^{3} e^{4} + {\left(b^{7} d^{4} e^{3} - 4 \, a b^{6} d^{3} e^{4} + 6 \, a^{2} b^{5} d^{2} e^{5} - 4 \, a^{3} b^{4} d e^{6} + a^{4} b^{3} e^{7}\right)} x^{3} + 3 \, {\left(b^{7} d^{5} e^{2} - 4 \, a b^{6} d^{4} e^{3} + 6 \, a^{2} b^{5} d^{3} e^{4} - 4 \, a^{3} b^{4} d^{2} e^{5} + a^{4} b^{3} d e^{6}\right)} x^{2} + 3 \, {\left(b^{7} d^{6} e - 4 \, a b^{6} d^{5} e^{2} + 6 \, a^{2} b^{5} d^{4} e^{3} - 4 \, a^{3} b^{4} d^{3} e^{4} + a^{4} b^{3} d^{2} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right)}}"," ",0,"1/12*(3*b^7*e^7*x^7 + 214*b^7*d^7 - 1036*a*b^6*d^6*e + 1974*a^2*b^5*d^5*e^2 - 1820*a^3*b^4*d^4*e^3 + 770*a^4*b^3*d^3*e^4 - 84*a^5*b^2*d^2*e^5 - 14*a^6*b*d*e^6 - 4*a^7*e^7 - 7*(b^7*d*e^6 - 4*a*b^6*e^7)*x^6 + 21*(b^7*d^2*e^5 - 4*a*b^6*d*e^6 + 6*a^2*b^5*e^7)*x^5 - 105*(b^7*d^3*e^4 - 4*a*b^6*d^2*e^5 + 6*a^2*b^5*d*e^6 - 4*a^3*b^4*e^7)*x^4 - 2*(278*b^7*d^4*e^3 - 1022*a*b^6*d^3*e^4 + 1323*a^2*b^5*d^2*e^5 - 630*a^3*b^4*d*e^6)*x^3 - 6*(68*b^7*d^5*e^2 - 182*a*b^6*d^4*e^3 + 63*a^2*b^5*d^3*e^4 + 210*a^3*b^4*d^2*e^5 - 210*a^4*b^3*d*e^6 + 42*a^5*b^2*e^7)*x^2 + 6*(37*b^7*d^6*e - 238*a*b^6*d^5*e^2 + 567*a^2*b^5*d^4*e^3 - 630*a^3*b^4*d^3*e^4 + 315*a^4*b^3*d^2*e^5 - 42*a^5*b^2*d*e^6 - 7*a^6*b*e^7)*x + 420*(b^7*d^7 - 4*a*b^6*d^6*e + 6*a^2*b^5*d^5*e^2 - 4*a^3*b^4*d^4*e^3 + a^4*b^3*d^3*e^4 + (b^7*d^4*e^3 - 4*a*b^6*d^3*e^4 + 6*a^2*b^5*d^2*e^5 - 4*a^3*b^4*d*e^6 + a^4*b^3*e^7)*x^3 + 3*(b^7*d^5*e^2 - 4*a*b^6*d^4*e^3 + 6*a^2*b^5*d^3*e^4 - 4*a^3*b^4*d^2*e^5 + a^4*b^3*d*e^6)*x^2 + 3*(b^7*d^6*e - 4*a*b^6*d^5*e^2 + 6*a^2*b^5*d^4*e^3 - 4*a^3*b^4*d^3*e^4 + a^4*b^3*d^2*e^5)*x)*log(e*x + d))/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8)","B",0
1927,1,181,0,0.393331," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{3 \, b^{4} e^{4} x^{4} + 4 \, {\left(4 \, b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(6 \, b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 12 \, {\left(4 \, b^{4} d^{3} e - 6 \, a b^{3} d^{2} e^{2} + 4 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x + 12 \, {\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*b^4*e^4*x^4 + 4*(4*b^4*d*e^3 - a*b^3*e^4)*x^3 + 6*(6*b^4*d^2*e^2 - 4*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 12*(4*b^4*d^3*e - 6*a*b^3*d^2*e^2 + 4*a^2*b^2*d*e^3 - a^3*b*e^4)*x + 12*(b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*log(b*x + a))/b^5","A",0
1928,1,116,0,0.383549," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, b^{3} e^{3} x^{3} + 3 \, {\left(3 \, b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 6 \, {\left(3 \, b^{3} d^{2} e - 3 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x + 6 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*b^3*e^3*x^3 + 3*(3*b^3*d*e^2 - a*b^2*e^3)*x^2 + 6*(3*b^3*d^2*e - 3*a*b^2*d*e^2 + a^2*b*e^3)*x + 6*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*log(b*x + a))/b^4","A",0
1929,1,63,0,0.385686," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{b^{2} e^{2} x^{2} + 2 \, {\left(2 \, b^{2} d e - a b e^{2}\right)} x + 2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(b^2*e^2*x^2 + 2*(2*b^2*d*e - a*b*e^2)*x + 2*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*log(b*x + a))/b^3","A",0
1930,1,24,0,0.379334," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{b e x + {\left(b d - a e\right)} \log\left(b x + a\right)}{b^{2}}"," ",0,"(b*e*x + (b*d - a*e)*log(b*x + a))/b^2","A",0
1931,1,10,0,0.391114," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{\log\left(b x + a\right)}{b}"," ",0,"log(b*x + a)/b","A",0
1932,1,26,0,0.403380," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{\log\left(b x + a\right) - \log\left(e x + d\right)}{b d - a e}"," ",0,"(log(b*x + a) - log(e*x + d))/(b*d - a*e)","A",0
1933,1,92,0,0.421927," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{b d - a e + {\left(b e x + b d\right)} \log\left(b x + a\right) - {\left(b e x + b d\right)} \log\left(e x + d\right)}{b^{2} d^{3} - 2 \, a b d^{2} e + a^{2} d e^{2} + {\left(b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}\right)} x}"," ",0,"(b*d - a*e + (b*e*x + b*d)*log(b*x + a) - (b*e*x + b*d)*log(e*x + d))/(b^2*d^3 - 2*a*b*d^2*e + a^2*d*e^2 + (b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3)*x)","A",0
1934,1,242,0,0.406548," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{3 \, b^{2} d^{2} - 4 \, a b d e + a^{2} e^{2} + 2 \, {\left(b^{2} d e - a b e^{2}\right)} x + 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, b^{2} d e x + b^{2} d^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, b^{2} d e x + b^{2} d^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(b^{3} d^{5} - 3 \, a b^{2} d^{4} e + 3 \, a^{2} b d^{3} e^{2} - a^{3} d^{2} e^{3} + {\left(b^{3} d^{3} e^{2} - 3 \, a b^{2} d^{2} e^{3} + 3 \, a^{2} b d e^{4} - a^{3} e^{5}\right)} x^{2} + 2 \, {\left(b^{3} d^{4} e - 3 \, a b^{2} d^{3} e^{2} + 3 \, a^{2} b d^{2} e^{3} - a^{3} d e^{4}\right)} x\right)}}"," ",0,"1/2*(3*b^2*d^2 - 4*a*b*d*e + a^2*e^2 + 2*(b^2*d*e - a*b*e^2)*x + 2*(b^2*e^2*x^2 + 2*b^2*d*e*x + b^2*d^2)*log(b*x + a) - 2*(b^2*e^2*x^2 + 2*b^2*d*e*x + b^2*d^2)*log(e*x + d))/(b^3*d^5 - 3*a*b^2*d^4*e + 3*a^2*b*d^3*e^2 - a^3*d^2*e^3 + (b^3*d^3*e^2 - 3*a*b^2*d^2*e^3 + 3*a^2*b*d*e^4 - a^3*e^5)*x^2 + 2*(b^3*d^4*e - 3*a*b^2*d^3*e^2 + 3*a^2*b*d^2*e^3 - a^3*d*e^4)*x)","B",0
1935,1,425,0,0.401326," ","integrate((b*x+a)/(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{11 \, b^{3} d^{3} - 18 \, a b^{2} d^{2} e + 9 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + 6 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 3 \, {\left(5 \, b^{3} d^{2} e - 6 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x + 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, b^{3} d e^{2} x^{2} + 3 \, b^{3} d^{2} e x + b^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, b^{3} d e^{2} x^{2} + 3 \, b^{3} d^{2} e x + b^{3} d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(b^{4} d^{7} - 4 \, a b^{3} d^{6} e + 6 \, a^{2} b^{2} d^{5} e^{2} - 4 \, a^{3} b d^{4} e^{3} + a^{4} d^{3} e^{4} + {\left(b^{4} d^{4} e^{3} - 4 \, a b^{3} d^{3} e^{4} + 6 \, a^{2} b^{2} d^{2} e^{5} - 4 \, a^{3} b d e^{6} + a^{4} e^{7}\right)} x^{3} + 3 \, {\left(b^{4} d^{5} e^{2} - 4 \, a b^{3} d^{4} e^{3} + 6 \, a^{2} b^{2} d^{3} e^{4} - 4 \, a^{3} b d^{2} e^{5} + a^{4} d e^{6}\right)} x^{2} + 3 \, {\left(b^{4} d^{6} e - 4 \, a b^{3} d^{5} e^{2} + 6 \, a^{2} b^{2} d^{4} e^{3} - 4 \, a^{3} b d^{3} e^{4} + a^{4} d^{2} e^{5}\right)} x\right)}}"," ",0,"1/6*(11*b^3*d^3 - 18*a*b^2*d^2*e + 9*a^2*b*d*e^2 - 2*a^3*e^3 + 6*(b^3*d*e^2 - a*b^2*e^3)*x^2 + 3*(5*b^3*d^2*e - 6*a*b^2*d*e^2 + a^2*b*e^3)*x + 6*(b^3*e^3*x^3 + 3*b^3*d*e^2*x^2 + 3*b^3*d^2*e*x + b^3*d^3)*log(b*x + a) - 6*(b^3*e^3*x^3 + 3*b^3*d*e^2*x^2 + 3*b^3*d^2*e*x + b^3*d^3)*log(e*x + d))/(b^4*d^7 - 4*a*b^3*d^6*e + 6*a^2*b^2*d^5*e^2 - 4*a^3*b*d^4*e^3 + a^4*d^3*e^4 + (b^4*d^4*e^3 - 4*a*b^3*d^3*e^4 + 6*a^2*b^2*d^2*e^5 - 4*a^3*b*d*e^6 + a^4*e^7)*x^3 + 3*(b^4*d^5*e^2 - 4*a*b^3*d^4*e^3 + 6*a^2*b^2*d^3*e^4 - 4*a^3*b*d^2*e^5 + a^4*d*e^6)*x^2 + 3*(b^4*d^6*e - 4*a*b^3*d^5*e^2 + 6*a^2*b^2*d^4*e^3 - 4*a^3*b*d^3*e^4 + a^4*d^2*e^5)*x)","B",0
1936,1,292,0,0.410952," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{b^{4} e^{4} x^{4} - b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 18 \, a^{2} b^{2} d^{2} e^{2} - 20 \, a^{3} b d e^{3} + 7 \, a^{4} e^{4} + 4 \, {\left(2 \, b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + {\left(16 \, a b^{3} d e^{3} - 11 \, a^{2} b^{2} e^{4}\right)} x^{2} - 2 \, {\left(4 \, b^{4} d^{3} e - 12 \, a b^{3} d^{2} e^{2} + 8 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x + 12 \, {\left(a^{2} b^{2} d^{2} e^{2} - 2 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} - 2 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/2*(b^4*e^4*x^4 - b^4*d^4 - 4*a*b^3*d^3*e + 18*a^2*b^2*d^2*e^2 - 20*a^3*b*d*e^3 + 7*a^4*e^4 + 4*(2*b^4*d*e^3 - a*b^3*e^4)*x^3 + (16*a*b^3*d*e^3 - 11*a^2*b^2*e^4)*x^2 - 2*(4*b^4*d^3*e - 12*a*b^3*d^2*e^2 + 8*a^2*b^2*d*e^3 - a^3*b*e^4)*x + 12*(a^2*b^2*d^2*e^2 - 2*a^3*b*d*e^3 + a^4*e^4 + (b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 - 2*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*log(b*x + a))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","B",0
1937,1,188,0,0.404728," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, b^{3} e^{3} x^{3} + 4 \, a b^{2} e^{3} x^{2} - b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 9 \, a^{2} b d e^{2} - 5 \, a^{3} e^{3} - 2 \, {\left(3 \, b^{3} d^{2} e - 6 \, a b^{2} d e^{2} + 2 \, a^{2} b e^{3}\right)} x + 6 \, {\left(a^{2} b d e^{2} - a^{3} e^{3} + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(a b^{2} d e^{2} - a^{2} b e^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*b^3*e^3*x^3 + 4*a*b^2*e^3*x^2 - b^3*d^3 - 3*a*b^2*d^2*e + 9*a^2*b*d*e^2 - 5*a^3*e^3 - 2*(3*b^3*d^2*e - 6*a*b^2*d*e^2 + 2*a^2*b*e^3)*x + 6*(a^2*b*d*e^2 - a^3*e^3 + (b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(a*b^2*d*e^2 - a^2*b*e^3)*x)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","B",0
1938,1,99,0,0.407299," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{b^{2} d^{2} + 2 \, a b d e - 3 \, a^{2} e^{2} + 4 \, {\left(b^{2} d e - a b e^{2}\right)} x - 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"-1/2*(b^2*d^2 + 2*a*b*d*e - 3*a^2*e^2 + 4*(b^2*d*e - a*b*e^2)*x - 2*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*log(b*x + a))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
1939,1,38,0,0.392962," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{2 \, b e x + b d + a e}{2 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*b*e*x + b*d + a*e)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
1940,1,24,0,0.388347," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"-1/2/(b^3*x^2 + 2*a*b^2*x + a^2*b)","A",0
1941,1,242,0,0.408923," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{b^{2} d^{2} - 4 \, a b d e + 3 \, a^{2} e^{2} - 2 \, {\left(b^{2} d e - a b e^{2}\right)} x - 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{3} d^{3} - 3 \, a^{3} b^{2} d^{2} e + 3 \, a^{4} b d e^{2} - a^{5} e^{3} + {\left(b^{5} d^{3} - 3 \, a b^{4} d^{2} e + 3 \, a^{2} b^{3} d e^{2} - a^{3} b^{2} e^{3}\right)} x^{2} + 2 \, {\left(a b^{4} d^{3} - 3 \, a^{2} b^{3} d^{2} e + 3 \, a^{3} b^{2} d e^{2} - a^{4} b e^{3}\right)} x\right)}}"," ",0,"-1/2*(b^2*d^2 - 4*a*b*d*e + 3*a^2*e^2 - 2*(b^2*d*e - a*b*e^2)*x - 2*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*log(b*x + a) + 2*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*log(e*x + d))/(a^2*b^3*d^3 - 3*a^3*b^2*d^2*e + 3*a^4*b*d*e^2 - a^5*e^3 + (b^5*d^3 - 3*a*b^4*d^2*e + 3*a^2*b^3*d*e^2 - a^3*b^2*e^3)*x^2 + 2*(a*b^4*d^3 - 3*a^2*b^3*d^2*e + 3*a^3*b^2*d*e^2 - a^4*b*e^3)*x)","B",0
1942,1,494,0,0.441936," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{b^{3} d^{3} - 6 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} + 2 \, a^{3} e^{3} - 6 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} - 3 \, {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2} - 3 \, a^{2} b e^{3}\right)} x - 6 \, {\left(b^{3} e^{3} x^{3} + a^{2} b d e^{2} + {\left(b^{3} d e^{2} + 2 \, a b^{2} e^{3}\right)} x^{2} + {\left(2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} e^{3} x^{3} + a^{2} b d e^{2} + {\left(b^{3} d e^{2} + 2 \, a b^{2} e^{3}\right)} x^{2} + {\left(2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{4} d^{5} - 4 \, a^{3} b^{3} d^{4} e + 6 \, a^{4} b^{2} d^{3} e^{2} - 4 \, a^{5} b d^{2} e^{3} + a^{6} d e^{4} + {\left(b^{6} d^{4} e - 4 \, a b^{5} d^{3} e^{2} + 6 \, a^{2} b^{4} d^{2} e^{3} - 4 \, a^{3} b^{3} d e^{4} + a^{4} b^{2} e^{5}\right)} x^{3} + {\left(b^{6} d^{5} - 2 \, a b^{5} d^{4} e - 2 \, a^{2} b^{4} d^{3} e^{2} + 8 \, a^{3} b^{3} d^{2} e^{3} - 7 \, a^{4} b^{2} d e^{4} + 2 \, a^{5} b e^{5}\right)} x^{2} + {\left(2 \, a b^{5} d^{5} - 7 \, a^{2} b^{4} d^{4} e + 8 \, a^{3} b^{3} d^{3} e^{2} - 2 \, a^{4} b^{2} d^{2} e^{3} - 2 \, a^{5} b d e^{4} + a^{6} e^{5}\right)} x\right)}}"," ",0,"-1/2*(b^3*d^3 - 6*a*b^2*d^2*e + 3*a^2*b*d*e^2 + 2*a^3*e^3 - 6*(b^3*d*e^2 - a*b^2*e^3)*x^2 - 3*(b^3*d^2*e + 2*a*b^2*d*e^2 - 3*a^2*b*e^3)*x - 6*(b^3*e^3*x^3 + a^2*b*d*e^2 + (b^3*d*e^2 + 2*a*b^2*e^3)*x^2 + (2*a*b^2*d*e^2 + a^2*b*e^3)*x)*log(b*x + a) + 6*(b^3*e^3*x^3 + a^2*b*d*e^2 + (b^3*d*e^2 + 2*a*b^2*e^3)*x^2 + (2*a*b^2*d*e^2 + a^2*b*e^3)*x)*log(e*x + d))/(a^2*b^4*d^5 - 4*a^3*b^3*d^4*e + 6*a^4*b^2*d^3*e^2 - 4*a^5*b*d^2*e^3 + a^6*d*e^4 + (b^6*d^4*e - 4*a*b^5*d^3*e^2 + 6*a^2*b^4*d^2*e^3 - 4*a^3*b^3*d*e^4 + a^4*b^2*e^5)*x^3 + (b^6*d^5 - 2*a*b^5*d^4*e - 2*a^2*b^4*d^3*e^2 + 8*a^3*b^3*d^2*e^3 - 7*a^4*b^2*d*e^4 + 2*a^5*b*e^5)*x^2 + (2*a*b^5*d^5 - 7*a^2*b^4*d^4*e + 8*a^3*b^3*d^3*e^2 - 2*a^4*b^2*d^2*e^3 - 2*a^5*b*d*e^4 + a^6*e^5)*x)","B",0
1943,1,760,0,0.426549," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{b^{4} d^{4} - 8 \, a b^{3} d^{3} e + 8 \, a^{3} b d e^{3} - a^{4} e^{4} - 12 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} - 18 \, {\left(b^{4} d^{2} e^{2} - a^{2} b^{2} e^{4}\right)} x^{2} - 4 \, {\left(b^{4} d^{3} e + 6 \, a b^{3} d^{2} e^{2} - 6 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x - 12 \, {\left(b^{4} e^{4} x^{4} + a^{2} b^{2} d^{2} e^{2} + 2 \, {\left(b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + {\left(b^{4} d^{2} e^{2} + 4 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} + a^{2} b^{2} d e^{3}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} e^{4} x^{4} + a^{2} b^{2} d^{2} e^{2} + 2 \, {\left(b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + {\left(b^{4} d^{2} e^{2} + 4 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} + a^{2} b^{2} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{5} d^{7} - 5 \, a^{3} b^{4} d^{6} e + 10 \, a^{4} b^{3} d^{5} e^{2} - 10 \, a^{5} b^{2} d^{4} e^{3} + 5 \, a^{6} b d^{3} e^{4} - a^{7} d^{2} e^{5} + {\left(b^{7} d^{5} e^{2} - 5 \, a b^{6} d^{4} e^{3} + 10 \, a^{2} b^{5} d^{3} e^{4} - 10 \, a^{3} b^{4} d^{2} e^{5} + 5 \, a^{4} b^{3} d e^{6} - a^{5} b^{2} e^{7}\right)} x^{4} + 2 \, {\left(b^{7} d^{6} e - 4 \, a b^{6} d^{5} e^{2} + 5 \, a^{2} b^{5} d^{4} e^{3} - 5 \, a^{4} b^{3} d^{2} e^{5} + 4 \, a^{5} b^{2} d e^{6} - a^{6} b e^{7}\right)} x^{3} + {\left(b^{7} d^{7} - a b^{6} d^{6} e - 9 \, a^{2} b^{5} d^{5} e^{2} + 25 \, a^{3} b^{4} d^{4} e^{3} - 25 \, a^{4} b^{3} d^{3} e^{4} + 9 \, a^{5} b^{2} d^{2} e^{5} + a^{6} b d e^{6} - a^{7} e^{7}\right)} x^{2} + 2 \, {\left(a b^{6} d^{7} - 4 \, a^{2} b^{5} d^{6} e + 5 \, a^{3} b^{4} d^{5} e^{2} - 5 \, a^{5} b^{2} d^{3} e^{4} + 4 \, a^{6} b d^{2} e^{5} - a^{7} d e^{6}\right)} x\right)}}"," ",0,"-1/2*(b^4*d^4 - 8*a*b^3*d^3*e + 8*a^3*b*d*e^3 - a^4*e^4 - 12*(b^4*d*e^3 - a*b^3*e^4)*x^3 - 18*(b^4*d^2*e^2 - a^2*b^2*e^4)*x^2 - 4*(b^4*d^3*e + 6*a*b^3*d^2*e^2 - 6*a^2*b^2*d*e^3 - a^3*b*e^4)*x - 12*(b^4*e^4*x^4 + a^2*b^2*d^2*e^2 + 2*(b^4*d*e^3 + a*b^3*e^4)*x^3 + (b^4*d^2*e^2 + 4*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 + a^2*b^2*d*e^3)*x)*log(b*x + a) + 12*(b^4*e^4*x^4 + a^2*b^2*d^2*e^2 + 2*(b^4*d*e^3 + a*b^3*e^4)*x^3 + (b^4*d^2*e^2 + 4*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 + a^2*b^2*d*e^3)*x)*log(e*x + d))/(a^2*b^5*d^7 - 5*a^3*b^4*d^6*e + 10*a^4*b^3*d^5*e^2 - 10*a^5*b^2*d^4*e^3 + 5*a^6*b*d^3*e^4 - a^7*d^2*e^5 + (b^7*d^5*e^2 - 5*a*b^6*d^4*e^3 + 10*a^2*b^5*d^3*e^4 - 10*a^3*b^4*d^2*e^5 + 5*a^4*b^3*d*e^6 - a^5*b^2*e^7)*x^4 + 2*(b^7*d^6*e - 4*a*b^6*d^5*e^2 + 5*a^2*b^5*d^4*e^3 - 5*a^4*b^3*d^2*e^5 + 4*a^5*b^2*d*e^6 - a^6*b*e^7)*x^3 + (b^7*d^7 - a*b^6*d^6*e - 9*a^2*b^5*d^5*e^2 + 25*a^3*b^4*d^4*e^3 - 25*a^4*b^3*d^3*e^4 + 9*a^5*b^2*d^2*e^5 + a^6*b*d*e^6 - a^7*e^7)*x^2 + 2*(a*b^6*d^7 - 4*a^2*b^5*d^6*e + 5*a^3*b^4*d^5*e^2 - 5*a^5*b^2*d^3*e^4 + 4*a^6*b*d^2*e^5 - a^7*d*e^6)*x)","B",0
1944,1,1151,0,0.433905," ","integrate((b*x+a)/(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{3 \, b^{5} d^{5} - 30 \, a b^{4} d^{4} e - 20 \, a^{2} b^{3} d^{3} e^{2} + 60 \, a^{3} b^{2} d^{2} e^{3} - 15 \, a^{4} b d e^{4} + 2 \, a^{5} e^{5} - 60 \, {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} - 30 \, {\left(5 \, b^{5} d^{2} e^{3} - 2 \, a b^{4} d e^{4} - 3 \, a^{2} b^{3} e^{5}\right)} x^{3} - 10 \, {\left(11 \, b^{5} d^{3} e^{2} + 12 \, a b^{4} d^{2} e^{3} - 21 \, a^{2} b^{3} d e^{4} - 2 \, a^{3} b^{2} e^{5}\right)} x^{2} - 5 \, {\left(3 \, b^{5} d^{4} e + 32 \, a b^{4} d^{3} e^{2} - 24 \, a^{2} b^{3} d^{2} e^{3} - 12 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x - 60 \, {\left(b^{5} e^{5} x^{5} + a^{2} b^{3} d^{3} e^{2} + {\left(3 \, b^{5} d e^{4} + 2 \, a b^{4} e^{5}\right)} x^{4} + {\left(3 \, b^{5} d^{2} e^{3} + 6 \, a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + {\left(b^{5} d^{3} e^{2} + 6 \, a b^{4} d^{2} e^{3} + 3 \, a^{2} b^{3} d e^{4}\right)} x^{2} + {\left(2 \, a b^{4} d^{3} e^{2} + 3 \, a^{2} b^{3} d^{2} e^{3}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(b^{5} e^{5} x^{5} + a^{2} b^{3} d^{3} e^{2} + {\left(3 \, b^{5} d e^{4} + 2 \, a b^{4} e^{5}\right)} x^{4} + {\left(3 \, b^{5} d^{2} e^{3} + 6 \, a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + {\left(b^{5} d^{3} e^{2} + 6 \, a b^{4} d^{2} e^{3} + 3 \, a^{2} b^{3} d e^{4}\right)} x^{2} + {\left(2 \, a b^{4} d^{3} e^{2} + 3 \, a^{2} b^{3} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(a^{2} b^{6} d^{9} - 6 \, a^{3} b^{5} d^{8} e + 15 \, a^{4} b^{4} d^{7} e^{2} - 20 \, a^{5} b^{3} d^{6} e^{3} + 15 \, a^{6} b^{2} d^{5} e^{4} - 6 \, a^{7} b d^{4} e^{5} + a^{8} d^{3} e^{6} + {\left(b^{8} d^{6} e^{3} - 6 \, a b^{7} d^{5} e^{4} + 15 \, a^{2} b^{6} d^{4} e^{5} - 20 \, a^{3} b^{5} d^{3} e^{6} + 15 \, a^{4} b^{4} d^{2} e^{7} - 6 \, a^{5} b^{3} d e^{8} + a^{6} b^{2} e^{9}\right)} x^{5} + {\left(3 \, b^{8} d^{7} e^{2} - 16 \, a b^{7} d^{6} e^{3} + 33 \, a^{2} b^{6} d^{5} e^{4} - 30 \, a^{3} b^{5} d^{4} e^{5} + 5 \, a^{4} b^{4} d^{3} e^{6} + 12 \, a^{5} b^{3} d^{2} e^{7} - 9 \, a^{6} b^{2} d e^{8} + 2 \, a^{7} b e^{9}\right)} x^{4} + {\left(3 \, b^{8} d^{8} e - 12 \, a b^{7} d^{7} e^{2} + 10 \, a^{2} b^{6} d^{6} e^{3} + 24 \, a^{3} b^{5} d^{5} e^{4} - 60 \, a^{4} b^{4} d^{4} e^{5} + 52 \, a^{5} b^{3} d^{3} e^{6} - 18 \, a^{6} b^{2} d^{2} e^{7} + a^{8} e^{9}\right)} x^{3} + {\left(b^{8} d^{9} - 18 \, a^{2} b^{6} d^{7} e^{2} + 52 \, a^{3} b^{5} d^{6} e^{3} - 60 \, a^{4} b^{4} d^{5} e^{4} + 24 \, a^{5} b^{3} d^{4} e^{5} + 10 \, a^{6} b^{2} d^{3} e^{6} - 12 \, a^{7} b d^{2} e^{7} + 3 \, a^{8} d e^{8}\right)} x^{2} + {\left(2 \, a b^{7} d^{9} - 9 \, a^{2} b^{6} d^{8} e + 12 \, a^{3} b^{5} d^{7} e^{2} + 5 \, a^{4} b^{4} d^{6} e^{3} - 30 \, a^{5} b^{3} d^{5} e^{4} + 33 \, a^{6} b^{2} d^{4} e^{5} - 16 \, a^{7} b d^{3} e^{6} + 3 \, a^{8} d^{2} e^{7}\right)} x\right)}}"," ",0,"-1/6*(3*b^5*d^5 - 30*a*b^4*d^4*e - 20*a^2*b^3*d^3*e^2 + 60*a^3*b^2*d^2*e^3 - 15*a^4*b*d*e^4 + 2*a^5*e^5 - 60*(b^5*d*e^4 - a*b^4*e^5)*x^4 - 30*(5*b^5*d^2*e^3 - 2*a*b^4*d*e^4 - 3*a^2*b^3*e^5)*x^3 - 10*(11*b^5*d^3*e^2 + 12*a*b^4*d^2*e^3 - 21*a^2*b^3*d*e^4 - 2*a^3*b^2*e^5)*x^2 - 5*(3*b^5*d^4*e + 32*a*b^4*d^3*e^2 - 24*a^2*b^3*d^2*e^3 - 12*a^3*b^2*d*e^4 + a^4*b*e^5)*x - 60*(b^5*e^5*x^5 + a^2*b^3*d^3*e^2 + (3*b^5*d*e^4 + 2*a*b^4*e^5)*x^4 + (3*b^5*d^2*e^3 + 6*a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + (b^5*d^3*e^2 + 6*a*b^4*d^2*e^3 + 3*a^2*b^3*d*e^4)*x^2 + (2*a*b^4*d^3*e^2 + 3*a^2*b^3*d^2*e^3)*x)*log(b*x + a) + 60*(b^5*e^5*x^5 + a^2*b^3*d^3*e^2 + (3*b^5*d*e^4 + 2*a*b^4*e^5)*x^4 + (3*b^5*d^2*e^3 + 6*a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + (b^5*d^3*e^2 + 6*a*b^4*d^2*e^3 + 3*a^2*b^3*d*e^4)*x^2 + (2*a*b^4*d^3*e^2 + 3*a^2*b^3*d^2*e^3)*x)*log(e*x + d))/(a^2*b^6*d^9 - 6*a^3*b^5*d^8*e + 15*a^4*b^4*d^7*e^2 - 20*a^5*b^3*d^6*e^3 + 15*a^6*b^2*d^5*e^4 - 6*a^7*b*d^4*e^5 + a^8*d^3*e^6 + (b^8*d^6*e^3 - 6*a*b^7*d^5*e^4 + 15*a^2*b^6*d^4*e^5 - 20*a^3*b^5*d^3*e^6 + 15*a^4*b^4*d^2*e^7 - 6*a^5*b^3*d*e^8 + a^6*b^2*e^9)*x^5 + (3*b^8*d^7*e^2 - 16*a*b^7*d^6*e^3 + 33*a^2*b^6*d^5*e^4 - 30*a^3*b^5*d^4*e^5 + 5*a^4*b^4*d^3*e^6 + 12*a^5*b^3*d^2*e^7 - 9*a^6*b^2*d*e^8 + 2*a^7*b*e^9)*x^4 + (3*b^8*d^8*e - 12*a*b^7*d^7*e^2 + 10*a^2*b^6*d^6*e^3 + 24*a^3*b^5*d^5*e^4 - 60*a^4*b^4*d^4*e^5 + 52*a^5*b^3*d^3*e^6 - 18*a^6*b^2*d^2*e^7 + a^8*e^9)*x^3 + (b^8*d^9 - 18*a^2*b^6*d^7*e^2 + 52*a^3*b^5*d^6*e^3 - 60*a^4*b^4*d^5*e^4 + 24*a^5*b^3*d^4*e^5 + 10*a^6*b^2*d^3*e^6 - 12*a^7*b*d^2*e^7 + 3*a^8*d*e^8)*x^2 + (2*a*b^7*d^9 - 9*a^2*b^6*d^8*e + 12*a^3*b^5*d^7*e^2 + 5*a^4*b^4*d^6*e^3 - 30*a^5*b^3*d^5*e^4 + 33*a^6*b^2*d^4*e^5 - 16*a^7*b*d^3*e^6 + 3*a^8*d^2*e^7)*x)","B",0
1945,1,267,0,0.405397," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{3 \, b^{4} d^{4} + 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} + 12 \, a^{3} b d e^{3} - 25 \, a^{4} e^{4} + 48 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 36 \, {\left(b^{4} d^{2} e^{2} + 2 \, a b^{3} d e^{3} - 3 \, a^{2} b^{2} e^{4}\right)} x^{2} + 8 \, {\left(2 \, b^{4} d^{3} e + 3 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} - 11 \, a^{3} b e^{4}\right)} x - 12 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \log\left(b x + a\right)}{12 \, {\left(b^{9} x^{4} + 4 \, a b^{8} x^{3} + 6 \, a^{2} b^{7} x^{2} + 4 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}"," ",0,"-1/12*(3*b^4*d^4 + 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 + 12*a^3*b*d*e^3 - 25*a^4*e^4 + 48*(b^4*d*e^3 - a*b^3*e^4)*x^3 + 36*(b^4*d^2*e^2 + 2*a*b^3*d*e^3 - 3*a^2*b^2*e^4)*x^2 + 8*(2*b^4*d^3*e + 3*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 - 11*a^3*b*e^4)*x - 12*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*log(b*x + a))/(b^9*x^4 + 4*a*b^8*x^3 + 6*a^2*b^7*x^2 + 4*a^3*b^6*x + a^4*b^5)","B",0
1946,1,143,0,0.393229," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{4 \, b^{3} e^{3} x^{3} + b^{3} d^{3} + a b^{2} d^{2} e + a^{2} b d e^{2} + a^{3} e^{3} + 6 \, {\left(b^{3} d e^{2} + a b^{2} e^{3}\right)} x^{2} + 4 \, {\left(b^{3} d^{2} e + a b^{2} d e^{2} + a^{2} b e^{3}\right)} x}{4 \, {\left(b^{8} x^{4} + 4 \, a b^{7} x^{3} + 6 \, a^{2} b^{6} x^{2} + 4 \, a^{3} b^{5} x + a^{4} b^{4}\right)}}"," ",0,"-1/4*(4*b^3*e^3*x^3 + b^3*d^3 + a*b^2*d^2*e + a^2*b*d*e^2 + a^3*e^3 + 6*(b^3*d*e^2 + a*b^2*e^3)*x^2 + 4*(b^3*d^2*e + a*b^2*d*e^2 + a^2*b*e^3)*x)/(b^8*x^4 + 4*a*b^7*x^3 + 6*a^2*b^6*x^2 + 4*a^3*b^5*x + a^4*b^4)","B",0
1947,1,98,0,0.398341," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{6 \, b^{2} e^{2} x^{2} + 3 \, b^{2} d^{2} + 2 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b^{2} d e + a b e^{2}\right)} x}{12 \, {\left(b^{7} x^{4} + 4 \, a b^{6} x^{3} + 6 \, a^{2} b^{5} x^{2} + 4 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}"," ",0,"-1/12*(6*b^2*e^2*x^2 + 3*b^2*d^2 + 2*a*b*d*e + a^2*e^2 + 4*(2*b^2*d*e + a*b*e^2)*x)/(b^7*x^4 + 4*a*b^6*x^3 + 6*a^2*b^5*x^2 + 4*a^3*b^4*x + a^4*b^3)","A",0
1948,1,61,0,0.390753," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{4 \, b e x + 3 \, b d + a e}{12 \, {\left(b^{6} x^{4} + 4 \, a b^{5} x^{3} + 6 \, a^{2} b^{4} x^{2} + 4 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}"," ",0,"-1/12*(4*b*e*x + 3*b*d + a*e)/(b^6*x^4 + 4*a*b^5*x^3 + 6*a^2*b^4*x^2 + 4*a^3*b^3*x + a^4*b^2)","A",0
1949,1,46,0,0.382368," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}}"," ",0,"-1/4/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b)","B",0
1950,1,657,0,0.408432," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{3 \, b^{4} d^{4} - 16 \, a b^{3} d^{3} e + 36 \, a^{2} b^{2} d^{2} e^{2} - 48 \, a^{3} b d e^{3} + 25 \, a^{4} e^{4} - 12 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(b^{4} d^{2} e^{2} - 8 \, a b^{3} d e^{3} + 7 \, a^{2} b^{2} e^{4}\right)} x^{2} - 4 \, {\left(b^{4} d^{3} e - 6 \, a b^{3} d^{2} e^{2} + 18 \, a^{2} b^{2} d e^{3} - 13 \, a^{3} b e^{4}\right)} x - 12 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \log\left(e x + d\right)}{12 \, {\left(a^{4} b^{5} d^{5} - 5 \, a^{5} b^{4} d^{4} e + 10 \, a^{6} b^{3} d^{3} e^{2} - 10 \, a^{7} b^{2} d^{2} e^{3} + 5 \, a^{8} b d e^{4} - a^{9} e^{5} + {\left(b^{9} d^{5} - 5 \, a b^{8} d^{4} e + 10 \, a^{2} b^{7} d^{3} e^{2} - 10 \, a^{3} b^{6} d^{2} e^{3} + 5 \, a^{4} b^{5} d e^{4} - a^{5} b^{4} e^{5}\right)} x^{4} + 4 \, {\left(a b^{8} d^{5} - 5 \, a^{2} b^{7} d^{4} e + 10 \, a^{3} b^{6} d^{3} e^{2} - 10 \, a^{4} b^{5} d^{2} e^{3} + 5 \, a^{5} b^{4} d e^{4} - a^{6} b^{3} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} d^{5} - 5 \, a^{3} b^{6} d^{4} e + 10 \, a^{4} b^{5} d^{3} e^{2} - 10 \, a^{5} b^{4} d^{2} e^{3} + 5 \, a^{6} b^{3} d e^{4} - a^{7} b^{2} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} d^{5} - 5 \, a^{4} b^{5} d^{4} e + 10 \, a^{5} b^{4} d^{3} e^{2} - 10 \, a^{6} b^{3} d^{2} e^{3} + 5 \, a^{7} b^{2} d e^{4} - a^{8} b e^{5}\right)} x\right)}}"," ",0,"-1/12*(3*b^4*d^4 - 16*a*b^3*d^3*e + 36*a^2*b^2*d^2*e^2 - 48*a^3*b*d*e^3 + 25*a^4*e^4 - 12*(b^4*d*e^3 - a*b^3*e^4)*x^3 + 6*(b^4*d^2*e^2 - 8*a*b^3*d*e^3 + 7*a^2*b^2*e^4)*x^2 - 4*(b^4*d^3*e - 6*a*b^3*d^2*e^2 + 18*a^2*b^2*d*e^3 - 13*a^3*b*e^4)*x - 12*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*log(b*x + a) + 12*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*log(e*x + d))/(a^4*b^5*d^5 - 5*a^5*b^4*d^4*e + 10*a^6*b^3*d^3*e^2 - 10*a^7*b^2*d^2*e^3 + 5*a^8*b*d*e^4 - a^9*e^5 + (b^9*d^5 - 5*a*b^8*d^4*e + 10*a^2*b^7*d^3*e^2 - 10*a^3*b^6*d^2*e^3 + 5*a^4*b^5*d*e^4 - a^5*b^4*e^5)*x^4 + 4*(a*b^8*d^5 - 5*a^2*b^7*d^4*e + 10*a^3*b^6*d^3*e^2 - 10*a^4*b^5*d^2*e^3 + 5*a^5*b^4*d*e^4 - a^6*b^3*e^5)*x^3 + 6*(a^2*b^7*d^5 - 5*a^3*b^6*d^4*e + 10*a^4*b^5*d^3*e^2 - 10*a^5*b^4*d^2*e^3 + 5*a^6*b^3*d*e^4 - a^7*b^2*e^5)*x^2 + 4*(a^3*b^6*d^5 - 5*a^4*b^5*d^4*e + 10*a^5*b^4*d^3*e^2 - 10*a^6*b^3*d^2*e^3 + 5*a^7*b^2*d*e^4 - a^8*b*e^5)*x)","B",0
1951,1,1083,0,0.430220," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{3 \, b^{5} d^{5} - 20 \, a b^{4} d^{4} e + 60 \, a^{2} b^{3} d^{3} e^{2} - 120 \, a^{3} b^{2} d^{2} e^{3} + 65 \, a^{4} b d e^{4} + 12 \, a^{5} e^{5} - 60 \, {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} - 30 \, {\left(b^{5} d^{2} e^{3} + 6 \, a b^{4} d e^{4} - 7 \, a^{2} b^{3} e^{5}\right)} x^{3} + 10 \, {\left(b^{5} d^{3} e^{2} - 12 \, a b^{4} d^{2} e^{3} - 15 \, a^{2} b^{3} d e^{4} + 26 \, a^{3} b^{2} e^{5}\right)} x^{2} - 5 \, {\left(b^{5} d^{4} e - 8 \, a b^{4} d^{3} e^{2} + 36 \, a^{2} b^{3} d^{2} e^{3} - 4 \, a^{3} b^{2} d e^{4} - 25 \, a^{4} b e^{5}\right)} x - 60 \, {\left(b^{5} e^{5} x^{5} + a^{4} b d e^{4} + {\left(b^{5} d e^{4} + 4 \, a b^{4} e^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{3} d e^{4} + 2 \, a^{3} b^{2} e^{5}\right)} x^{2} + {\left(4 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(b^{5} e^{5} x^{5} + a^{4} b d e^{4} + {\left(b^{5} d e^{4} + 4 \, a b^{4} e^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{3} d e^{4} + 2 \, a^{3} b^{2} e^{5}\right)} x^{2} + {\left(4 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(a^{4} b^{6} d^{7} - 6 \, a^{5} b^{5} d^{6} e + 15 \, a^{6} b^{4} d^{5} e^{2} - 20 \, a^{7} b^{3} d^{4} e^{3} + 15 \, a^{8} b^{2} d^{3} e^{4} - 6 \, a^{9} b d^{2} e^{5} + a^{10} d e^{6} + {\left(b^{10} d^{6} e - 6 \, a b^{9} d^{5} e^{2} + 15 \, a^{2} b^{8} d^{4} e^{3} - 20 \, a^{3} b^{7} d^{3} e^{4} + 15 \, a^{4} b^{6} d^{2} e^{5} - 6 \, a^{5} b^{5} d e^{6} + a^{6} b^{4} e^{7}\right)} x^{5} + {\left(b^{10} d^{7} - 2 \, a b^{9} d^{6} e - 9 \, a^{2} b^{8} d^{5} e^{2} + 40 \, a^{3} b^{7} d^{4} e^{3} - 65 \, a^{4} b^{6} d^{3} e^{4} + 54 \, a^{5} b^{5} d^{2} e^{5} - 23 \, a^{6} b^{4} d e^{6} + 4 \, a^{7} b^{3} e^{7}\right)} x^{4} + 2 \, {\left(2 \, a b^{9} d^{7} - 9 \, a^{2} b^{8} d^{6} e + 12 \, a^{3} b^{7} d^{5} e^{2} + 5 \, a^{4} b^{6} d^{4} e^{3} - 30 \, a^{5} b^{5} d^{3} e^{4} + 33 \, a^{6} b^{4} d^{2} e^{5} - 16 \, a^{7} b^{3} d e^{6} + 3 \, a^{8} b^{2} e^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{8} d^{7} - 16 \, a^{3} b^{7} d^{6} e + 33 \, a^{4} b^{6} d^{5} e^{2} - 30 \, a^{5} b^{5} d^{4} e^{3} + 5 \, a^{6} b^{4} d^{3} e^{4} + 12 \, a^{7} b^{3} d^{2} e^{5} - 9 \, a^{8} b^{2} d e^{6} + 2 \, a^{9} b e^{7}\right)} x^{2} + {\left(4 \, a^{3} b^{7} d^{7} - 23 \, a^{4} b^{6} d^{6} e + 54 \, a^{5} b^{5} d^{5} e^{2} - 65 \, a^{6} b^{4} d^{4} e^{3} + 40 \, a^{7} b^{3} d^{3} e^{4} - 9 \, a^{8} b^{2} d^{2} e^{5} - 2 \, a^{9} b d e^{6} + a^{10} e^{7}\right)} x\right)}}"," ",0,"-1/12*(3*b^5*d^5 - 20*a*b^4*d^4*e + 60*a^2*b^3*d^3*e^2 - 120*a^3*b^2*d^2*e^3 + 65*a^4*b*d*e^4 + 12*a^5*e^5 - 60*(b^5*d*e^4 - a*b^4*e^5)*x^4 - 30*(b^5*d^2*e^3 + 6*a*b^4*d*e^4 - 7*a^2*b^3*e^5)*x^3 + 10*(b^5*d^3*e^2 - 12*a*b^4*d^2*e^3 - 15*a^2*b^3*d*e^4 + 26*a^3*b^2*e^5)*x^2 - 5*(b^5*d^4*e - 8*a*b^4*d^3*e^2 + 36*a^2*b^3*d^2*e^3 - 4*a^3*b^2*d*e^4 - 25*a^4*b*e^5)*x - 60*(b^5*e^5*x^5 + a^4*b*d*e^4 + (b^5*d*e^4 + 4*a*b^4*e^5)*x^4 + 2*(2*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + 2*(3*a^2*b^3*d*e^4 + 2*a^3*b^2*e^5)*x^2 + (4*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*log(b*x + a) + 60*(b^5*e^5*x^5 + a^4*b*d*e^4 + (b^5*d*e^4 + 4*a*b^4*e^5)*x^4 + 2*(2*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + 2*(3*a^2*b^3*d*e^4 + 2*a^3*b^2*e^5)*x^2 + (4*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*log(e*x + d))/(a^4*b^6*d^7 - 6*a^5*b^5*d^6*e + 15*a^6*b^4*d^5*e^2 - 20*a^7*b^3*d^4*e^3 + 15*a^8*b^2*d^3*e^4 - 6*a^9*b*d^2*e^5 + a^10*d*e^6 + (b^10*d^6*e - 6*a*b^9*d^5*e^2 + 15*a^2*b^8*d^4*e^3 - 20*a^3*b^7*d^3*e^4 + 15*a^4*b^6*d^2*e^5 - 6*a^5*b^5*d*e^6 + a^6*b^4*e^7)*x^5 + (b^10*d^7 - 2*a*b^9*d^6*e - 9*a^2*b^8*d^5*e^2 + 40*a^3*b^7*d^4*e^3 - 65*a^4*b^6*d^3*e^4 + 54*a^5*b^5*d^2*e^5 - 23*a^6*b^4*d*e^6 + 4*a^7*b^3*e^7)*x^4 + 2*(2*a*b^9*d^7 - 9*a^2*b^8*d^6*e + 12*a^3*b^7*d^5*e^2 + 5*a^4*b^6*d^4*e^3 - 30*a^5*b^5*d^3*e^4 + 33*a^6*b^4*d^2*e^5 - 16*a^7*b^3*d*e^6 + 3*a^8*b^2*e^7)*x^3 + 2*(3*a^2*b^8*d^7 - 16*a^3*b^7*d^6*e + 33*a^4*b^6*d^5*e^2 - 30*a^5*b^5*d^4*e^3 + 5*a^6*b^4*d^3*e^4 + 12*a^7*b^3*d^2*e^5 - 9*a^8*b^2*d*e^6 + 2*a^9*b*e^7)*x^2 + (4*a^3*b^7*d^7 - 23*a^4*b^6*d^6*e + 54*a^5*b^5*d^5*e^2 - 65*a^6*b^4*d^4*e^3 + 40*a^7*b^3*d^3*e^4 - 9*a^8*b^2*d^2*e^5 - 2*a^9*b*d*e^6 + a^10*e^7)*x)","B",0
1952,1,1565,0,0.452529," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{b^{6} d^{6} - 8 \, a b^{5} d^{5} e + 30 \, a^{2} b^{4} d^{4} e^{2} - 80 \, a^{3} b^{3} d^{3} e^{3} + 35 \, a^{4} b^{2} d^{2} e^{4} + 24 \, a^{5} b d e^{5} - 2 \, a^{6} e^{6} - 60 \, {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} - 30 \, {\left(3 \, b^{6} d^{2} e^{4} + 4 \, a b^{5} d e^{5} - 7 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(b^{6} d^{3} e^{3} + 15 \, a b^{5} d^{2} e^{4} - 3 \, a^{2} b^{4} d e^{5} - 13 \, a^{3} b^{3} e^{6}\right)} x^{3} + 5 \, {\left(b^{6} d^{4} e^{2} - 16 \, a b^{5} d^{3} e^{3} - 66 \, a^{2} b^{4} d^{2} e^{4} + 56 \, a^{3} b^{3} d e^{5} + 25 \, a^{4} b^{2} e^{6}\right)} x^{2} - 2 \, {\left(b^{6} d^{5} e - 10 \, a b^{5} d^{4} e^{2} + 60 \, a^{2} b^{4} d^{3} e^{3} + 50 \, a^{3} b^{3} d^{2} e^{4} - 95 \, a^{4} b^{2} d e^{5} - 6 \, a^{5} b e^{6}\right)} x - 60 \, {\left(b^{6} e^{6} x^{6} + a^{4} b^{2} d^{2} e^{4} + 2 \, {\left(b^{6} d e^{5} + 2 \, a b^{5} e^{6}\right)} x^{5} + {\left(b^{6} d^{2} e^{4} + 8 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right)} x^{4} + 4 \, {\left(a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + {\left(6 \, a^{2} b^{4} d^{2} e^{4} + 8 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{3} d^{2} e^{4} + a^{4} b^{2} d e^{5}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(b^{6} e^{6} x^{6} + a^{4} b^{2} d^{2} e^{4} + 2 \, {\left(b^{6} d e^{5} + 2 \, a b^{5} e^{6}\right)} x^{5} + {\left(b^{6} d^{2} e^{4} + 8 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right)} x^{4} + 4 \, {\left(a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + {\left(6 \, a^{2} b^{4} d^{2} e^{4} + 8 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{3} d^{2} e^{4} + a^{4} b^{2} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(a^{4} b^{7} d^{9} - 7 \, a^{5} b^{6} d^{8} e + 21 \, a^{6} b^{5} d^{7} e^{2} - 35 \, a^{7} b^{4} d^{6} e^{3} + 35 \, a^{8} b^{3} d^{5} e^{4} - 21 \, a^{9} b^{2} d^{4} e^{5} + 7 \, a^{10} b d^{3} e^{6} - a^{11} d^{2} e^{7} + {\left(b^{11} d^{7} e^{2} - 7 \, a b^{10} d^{6} e^{3} + 21 \, a^{2} b^{9} d^{5} e^{4} - 35 \, a^{3} b^{8} d^{4} e^{5} + 35 \, a^{4} b^{7} d^{3} e^{6} - 21 \, a^{5} b^{6} d^{2} e^{7} + 7 \, a^{6} b^{5} d e^{8} - a^{7} b^{4} e^{9}\right)} x^{6} + 2 \, {\left(b^{11} d^{8} e - 5 \, a b^{10} d^{7} e^{2} + 7 \, a^{2} b^{9} d^{6} e^{3} + 7 \, a^{3} b^{8} d^{5} e^{4} - 35 \, a^{4} b^{7} d^{4} e^{5} + 49 \, a^{5} b^{6} d^{3} e^{6} - 35 \, a^{6} b^{5} d^{2} e^{7} + 13 \, a^{7} b^{4} d e^{8} - 2 \, a^{8} b^{3} e^{9}\right)} x^{5} + {\left(b^{11} d^{9} + a b^{10} d^{8} e - 29 \, a^{2} b^{9} d^{7} e^{2} + 91 \, a^{3} b^{8} d^{6} e^{3} - 119 \, a^{4} b^{7} d^{5} e^{4} + 49 \, a^{5} b^{6} d^{4} e^{5} + 49 \, a^{6} b^{5} d^{3} e^{6} - 71 \, a^{7} b^{4} d^{2} e^{7} + 34 \, a^{8} b^{3} d e^{8} - 6 \, a^{9} b^{2} e^{9}\right)} x^{4} + 4 \, {\left(a b^{10} d^{9} - 4 \, a^{2} b^{9} d^{8} e + a^{3} b^{8} d^{7} e^{2} + 21 \, a^{4} b^{7} d^{6} e^{3} - 49 \, a^{5} b^{6} d^{5} e^{4} + 49 \, a^{6} b^{5} d^{4} e^{5} - 21 \, a^{7} b^{4} d^{3} e^{6} - a^{8} b^{3} d^{2} e^{7} + 4 \, a^{9} b^{2} d e^{8} - a^{10} b e^{9}\right)} x^{3} + {\left(6 \, a^{2} b^{9} d^{9} - 34 \, a^{3} b^{8} d^{8} e + 71 \, a^{4} b^{7} d^{7} e^{2} - 49 \, a^{5} b^{6} d^{6} e^{3} - 49 \, a^{6} b^{5} d^{5} e^{4} + 119 \, a^{7} b^{4} d^{4} e^{5} - 91 \, a^{8} b^{3} d^{3} e^{6} + 29 \, a^{9} b^{2} d^{2} e^{7} - a^{10} b d e^{8} - a^{11} e^{9}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{8} d^{9} - 13 \, a^{4} b^{7} d^{8} e + 35 \, a^{5} b^{6} d^{7} e^{2} - 49 \, a^{6} b^{5} d^{6} e^{3} + 35 \, a^{7} b^{4} d^{5} e^{4} - 7 \, a^{8} b^{3} d^{4} e^{5} - 7 \, a^{9} b^{2} d^{3} e^{6} + 5 \, a^{10} b d^{2} e^{7} - a^{11} d e^{8}\right)} x\right)}}"," ",0,"-1/4*(b^6*d^6 - 8*a*b^5*d^5*e + 30*a^2*b^4*d^4*e^2 - 80*a^3*b^3*d^3*e^3 + 35*a^4*b^2*d^2*e^4 + 24*a^5*b*d*e^5 - 2*a^6*e^6 - 60*(b^6*d*e^5 - a*b^5*e^6)*x^5 - 30*(3*b^6*d^2*e^4 + 4*a*b^5*d*e^5 - 7*a^2*b^4*e^6)*x^4 - 20*(b^6*d^3*e^3 + 15*a*b^5*d^2*e^4 - 3*a^2*b^4*d*e^5 - 13*a^3*b^3*e^6)*x^3 + 5*(b^6*d^4*e^2 - 16*a*b^5*d^3*e^3 - 66*a^2*b^4*d^2*e^4 + 56*a^3*b^3*d*e^5 + 25*a^4*b^2*e^6)*x^2 - 2*(b^6*d^5*e - 10*a*b^5*d^4*e^2 + 60*a^2*b^4*d^3*e^3 + 50*a^3*b^3*d^2*e^4 - 95*a^4*b^2*d*e^5 - 6*a^5*b*e^6)*x - 60*(b^6*e^6*x^6 + a^4*b^2*d^2*e^4 + 2*(b^6*d*e^5 + 2*a*b^5*e^6)*x^5 + (b^6*d^2*e^4 + 8*a*b^5*d*e^5 + 6*a^2*b^4*e^6)*x^4 + 4*(a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 + (6*a^2*b^4*d^2*e^4 + 8*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 2*(2*a^3*b^3*d^2*e^4 + a^4*b^2*d*e^5)*x)*log(b*x + a) + 60*(b^6*e^6*x^6 + a^4*b^2*d^2*e^4 + 2*(b^6*d*e^5 + 2*a*b^5*e^6)*x^5 + (b^6*d^2*e^4 + 8*a*b^5*d*e^5 + 6*a^2*b^4*e^6)*x^4 + 4*(a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 + (6*a^2*b^4*d^2*e^4 + 8*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 2*(2*a^3*b^3*d^2*e^4 + a^4*b^2*d*e^5)*x)*log(e*x + d))/(a^4*b^7*d^9 - 7*a^5*b^6*d^8*e + 21*a^6*b^5*d^7*e^2 - 35*a^7*b^4*d^6*e^3 + 35*a^8*b^3*d^5*e^4 - 21*a^9*b^2*d^4*e^5 + 7*a^10*b*d^3*e^6 - a^11*d^2*e^7 + (b^11*d^7*e^2 - 7*a*b^10*d^6*e^3 + 21*a^2*b^9*d^5*e^4 - 35*a^3*b^8*d^4*e^5 + 35*a^4*b^7*d^3*e^6 - 21*a^5*b^6*d^2*e^7 + 7*a^6*b^5*d*e^8 - a^7*b^4*e^9)*x^6 + 2*(b^11*d^8*e - 5*a*b^10*d^7*e^2 + 7*a^2*b^9*d^6*e^3 + 7*a^3*b^8*d^5*e^4 - 35*a^4*b^7*d^4*e^5 + 49*a^5*b^6*d^3*e^6 - 35*a^6*b^5*d^2*e^7 + 13*a^7*b^4*d*e^8 - 2*a^8*b^3*e^9)*x^5 + (b^11*d^9 + a*b^10*d^8*e - 29*a^2*b^9*d^7*e^2 + 91*a^3*b^8*d^6*e^3 - 119*a^4*b^7*d^5*e^4 + 49*a^5*b^6*d^4*e^5 + 49*a^6*b^5*d^3*e^6 - 71*a^7*b^4*d^2*e^7 + 34*a^8*b^3*d*e^8 - 6*a^9*b^2*e^9)*x^4 + 4*(a*b^10*d^9 - 4*a^2*b^9*d^8*e + a^3*b^8*d^7*e^2 + 21*a^4*b^7*d^6*e^3 - 49*a^5*b^6*d^5*e^4 + 49*a^6*b^5*d^4*e^5 - 21*a^7*b^4*d^3*e^6 - a^8*b^3*d^2*e^7 + 4*a^9*b^2*d*e^8 - a^10*b*e^9)*x^3 + (6*a^2*b^9*d^9 - 34*a^3*b^8*d^8*e + 71*a^4*b^7*d^7*e^2 - 49*a^5*b^6*d^6*e^3 - 49*a^6*b^5*d^5*e^4 + 119*a^7*b^4*d^4*e^5 - 91*a^8*b^3*d^3*e^6 + 29*a^9*b^2*d^2*e^7 - a^10*b*d*e^8 - a^11*e^9)*x^2 + 2*(2*a^3*b^8*d^9 - 13*a^4*b^7*d^8*e + 35*a^5*b^6*d^7*e^2 - 49*a^6*b^5*d^6*e^3 + 35*a^7*b^4*d^5*e^4 - 7*a^8*b^3*d^4*e^5 - 7*a^9*b^2*d^3*e^6 + 5*a^10*b*d^2*e^7 - a^11*d*e^8)*x)","B",0
1953,1,2090,0,0.488282," ","integrate((b*x+a)/(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{3 \, b^{7} d^{7} - 28 \, a b^{6} d^{6} e + 126 \, a^{2} b^{5} d^{5} e^{2} - 420 \, a^{3} b^{4} d^{4} e^{3} + 105 \, a^{4} b^{3} d^{3} e^{4} + 252 \, a^{5} b^{2} d^{2} e^{5} - 42 \, a^{6} b d e^{6} + 4 \, a^{7} e^{7} - 420 \, {\left(b^{7} d e^{6} - a b^{6} e^{7}\right)} x^{6} - 210 \, {\left(5 \, b^{7} d^{2} e^{5} + 2 \, a b^{6} d e^{6} - 7 \, a^{2} b^{5} e^{7}\right)} x^{5} - 70 \, {\left(11 \, b^{7} d^{3} e^{4} + 42 \, a b^{6} d^{2} e^{5} - 27 \, a^{2} b^{5} d e^{6} - 26 \, a^{3} b^{4} e^{7}\right)} x^{4} - 35 \, {\left(3 \, b^{7} d^{4} e^{3} + 76 \, a b^{6} d^{3} e^{4} + 54 \, a^{2} b^{5} d^{2} e^{5} - 108 \, a^{3} b^{4} d e^{6} - 25 \, a^{4} b^{3} e^{7}\right)} x^{3} + 21 \, {\left(b^{7} d^{5} e^{2} - 20 \, a b^{6} d^{4} e^{3} - 150 \, a^{2} b^{5} d^{3} e^{4} + 60 \, a^{3} b^{4} d^{2} e^{5} + 105 \, a^{4} b^{3} d e^{6} + 4 \, a^{5} b^{2} e^{7}\right)} x^{2} - 7 \, {\left(b^{7} d^{6} e - 12 \, a b^{6} d^{5} e^{2} + 90 \, a^{2} b^{5} d^{4} e^{3} + 180 \, a^{3} b^{4} d^{3} e^{4} - 225 \, a^{4} b^{3} d^{2} e^{5} - 36 \, a^{5} b^{2} d e^{6} + 2 \, a^{6} b e^{7}\right)} x - 420 \, {\left(b^{7} e^{7} x^{7} + a^{4} b^{3} d^{3} e^{4} + {\left(3 \, b^{7} d e^{6} + 4 \, a b^{6} e^{7}\right)} x^{6} + 3 \, {\left(b^{7} d^{2} e^{5} + 4 \, a b^{6} d e^{6} + 2 \, a^{2} b^{5} e^{7}\right)} x^{5} + {\left(b^{7} d^{3} e^{4} + 12 \, a b^{6} d^{2} e^{5} + 18 \, a^{2} b^{5} d e^{6} + 4 \, a^{3} b^{4} e^{7}\right)} x^{4} + {\left(4 \, a b^{6} d^{3} e^{4} + 18 \, a^{2} b^{5} d^{2} e^{5} + 12 \, a^{3} b^{4} d e^{6} + a^{4} b^{3} e^{7}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{5} d^{3} e^{4} + 4 \, a^{3} b^{4} d^{2} e^{5} + a^{4} b^{3} d e^{6}\right)} x^{2} + {\left(4 \, a^{3} b^{4} d^{3} e^{4} + 3 \, a^{4} b^{3} d^{2} e^{5}\right)} x\right)} \log\left(b x + a\right) + 420 \, {\left(b^{7} e^{7} x^{7} + a^{4} b^{3} d^{3} e^{4} + {\left(3 \, b^{7} d e^{6} + 4 \, a b^{6} e^{7}\right)} x^{6} + 3 \, {\left(b^{7} d^{2} e^{5} + 4 \, a b^{6} d e^{6} + 2 \, a^{2} b^{5} e^{7}\right)} x^{5} + {\left(b^{7} d^{3} e^{4} + 12 \, a b^{6} d^{2} e^{5} + 18 \, a^{2} b^{5} d e^{6} + 4 \, a^{3} b^{4} e^{7}\right)} x^{4} + {\left(4 \, a b^{6} d^{3} e^{4} + 18 \, a^{2} b^{5} d^{2} e^{5} + 12 \, a^{3} b^{4} d e^{6} + a^{4} b^{3} e^{7}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{5} d^{3} e^{4} + 4 \, a^{3} b^{4} d^{2} e^{5} + a^{4} b^{3} d e^{6}\right)} x^{2} + {\left(4 \, a^{3} b^{4} d^{3} e^{4} + 3 \, a^{4} b^{3} d^{2} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(a^{4} b^{8} d^{11} - 8 \, a^{5} b^{7} d^{10} e + 28 \, a^{6} b^{6} d^{9} e^{2} - 56 \, a^{7} b^{5} d^{8} e^{3} + 70 \, a^{8} b^{4} d^{7} e^{4} - 56 \, a^{9} b^{3} d^{6} e^{5} + 28 \, a^{10} b^{2} d^{5} e^{6} - 8 \, a^{11} b d^{4} e^{7} + a^{12} d^{3} e^{8} + {\left(b^{12} d^{8} e^{3} - 8 \, a b^{11} d^{7} e^{4} + 28 \, a^{2} b^{10} d^{6} e^{5} - 56 \, a^{3} b^{9} d^{5} e^{6} + 70 \, a^{4} b^{8} d^{4} e^{7} - 56 \, a^{5} b^{7} d^{3} e^{8} + 28 \, a^{6} b^{6} d^{2} e^{9} - 8 \, a^{7} b^{5} d e^{10} + a^{8} b^{4} e^{11}\right)} x^{7} + {\left(3 \, b^{12} d^{9} e^{2} - 20 \, a b^{11} d^{8} e^{3} + 52 \, a^{2} b^{10} d^{7} e^{4} - 56 \, a^{3} b^{9} d^{6} e^{5} - 14 \, a^{4} b^{8} d^{5} e^{6} + 112 \, a^{5} b^{7} d^{4} e^{7} - 140 \, a^{6} b^{6} d^{3} e^{8} + 88 \, a^{7} b^{5} d^{2} e^{9} - 29 \, a^{8} b^{4} d e^{10} + 4 \, a^{9} b^{3} e^{11}\right)} x^{6} + 3 \, {\left(b^{12} d^{10} e - 4 \, a b^{11} d^{9} e^{2} - 2 \, a^{2} b^{10} d^{8} e^{3} + 40 \, a^{3} b^{9} d^{7} e^{4} - 98 \, a^{4} b^{8} d^{6} e^{5} + 112 \, a^{5} b^{7} d^{5} e^{6} - 56 \, a^{6} b^{6} d^{4} e^{7} - 8 \, a^{7} b^{5} d^{3} e^{8} + 25 \, a^{8} b^{4} d^{2} e^{9} - 12 \, a^{9} b^{3} d e^{10} + 2 \, a^{10} b^{2} e^{11}\right)} x^{5} + {\left(b^{12} d^{11} + 4 \, a b^{11} d^{10} e - 50 \, a^{2} b^{10} d^{9} e^{2} + 140 \, a^{3} b^{9} d^{8} e^{3} - 130 \, a^{4} b^{8} d^{7} e^{4} - 112 \, a^{5} b^{7} d^{6} e^{5} + 392 \, a^{6} b^{6} d^{5} e^{6} - 400 \, a^{7} b^{5} d^{4} e^{7} + 185 \, a^{8} b^{4} d^{3} e^{8} - 20 \, a^{9} b^{3} d^{2} e^{9} - 14 \, a^{10} b^{2} d e^{10} + 4 \, a^{11} b e^{11}\right)} x^{4} + {\left(4 \, a b^{11} d^{11} - 14 \, a^{2} b^{10} d^{10} e - 20 \, a^{3} b^{9} d^{9} e^{2} + 185 \, a^{4} b^{8} d^{8} e^{3} - 400 \, a^{5} b^{7} d^{7} e^{4} + 392 \, a^{6} b^{6} d^{6} e^{5} - 112 \, a^{7} b^{5} d^{5} e^{6} - 130 \, a^{8} b^{4} d^{4} e^{7} + 140 \, a^{9} b^{3} d^{3} e^{8} - 50 \, a^{10} b^{2} d^{2} e^{9} + 4 \, a^{11} b d e^{10} + a^{12} e^{11}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{10} d^{11} - 12 \, a^{3} b^{9} d^{10} e + 25 \, a^{4} b^{8} d^{9} e^{2} - 8 \, a^{5} b^{7} d^{8} e^{3} - 56 \, a^{6} b^{6} d^{7} e^{4} + 112 \, a^{7} b^{5} d^{6} e^{5} - 98 \, a^{8} b^{4} d^{5} e^{6} + 40 \, a^{9} b^{3} d^{4} e^{7} - 2 \, a^{10} b^{2} d^{3} e^{8} - 4 \, a^{11} b d^{2} e^{9} + a^{12} d e^{10}\right)} x^{2} + {\left(4 \, a^{3} b^{9} d^{11} - 29 \, a^{4} b^{8} d^{10} e + 88 \, a^{5} b^{7} d^{9} e^{2} - 140 \, a^{6} b^{6} d^{8} e^{3} + 112 \, a^{7} b^{5} d^{7} e^{4} - 14 \, a^{8} b^{4} d^{6} e^{5} - 56 \, a^{9} b^{3} d^{5} e^{6} + 52 \, a^{10} b^{2} d^{4} e^{7} - 20 \, a^{11} b d^{3} e^{8} + 3 \, a^{12} d^{2} e^{9}\right)} x\right)}}"," ",0,"-1/12*(3*b^7*d^7 - 28*a*b^6*d^6*e + 126*a^2*b^5*d^5*e^2 - 420*a^3*b^4*d^4*e^3 + 105*a^4*b^3*d^3*e^4 + 252*a^5*b^2*d^2*e^5 - 42*a^6*b*d*e^6 + 4*a^7*e^7 - 420*(b^7*d*e^6 - a*b^6*e^7)*x^6 - 210*(5*b^7*d^2*e^5 + 2*a*b^6*d*e^6 - 7*a^2*b^5*e^7)*x^5 - 70*(11*b^7*d^3*e^4 + 42*a*b^6*d^2*e^5 - 27*a^2*b^5*d*e^6 - 26*a^3*b^4*e^7)*x^4 - 35*(3*b^7*d^4*e^3 + 76*a*b^6*d^3*e^4 + 54*a^2*b^5*d^2*e^5 - 108*a^3*b^4*d*e^6 - 25*a^4*b^3*e^7)*x^3 + 21*(b^7*d^5*e^2 - 20*a*b^6*d^4*e^3 - 150*a^2*b^5*d^3*e^4 + 60*a^3*b^4*d^2*e^5 + 105*a^4*b^3*d*e^6 + 4*a^5*b^2*e^7)*x^2 - 7*(b^7*d^6*e - 12*a*b^6*d^5*e^2 + 90*a^2*b^5*d^4*e^3 + 180*a^3*b^4*d^3*e^4 - 225*a^4*b^3*d^2*e^5 - 36*a^5*b^2*d*e^6 + 2*a^6*b*e^7)*x - 420*(b^7*e^7*x^7 + a^4*b^3*d^3*e^4 + (3*b^7*d*e^6 + 4*a*b^6*e^7)*x^6 + 3*(b^7*d^2*e^5 + 4*a*b^6*d*e^6 + 2*a^2*b^5*e^7)*x^5 + (b^7*d^3*e^4 + 12*a*b^6*d^2*e^5 + 18*a^2*b^5*d*e^6 + 4*a^3*b^4*e^7)*x^4 + (4*a*b^6*d^3*e^4 + 18*a^2*b^5*d^2*e^5 + 12*a^3*b^4*d*e^6 + a^4*b^3*e^7)*x^3 + 3*(2*a^2*b^5*d^3*e^4 + 4*a^3*b^4*d^2*e^5 + a^4*b^3*d*e^6)*x^2 + (4*a^3*b^4*d^3*e^4 + 3*a^4*b^3*d^2*e^5)*x)*log(b*x + a) + 420*(b^7*e^7*x^7 + a^4*b^3*d^3*e^4 + (3*b^7*d*e^6 + 4*a*b^6*e^7)*x^6 + 3*(b^7*d^2*e^5 + 4*a*b^6*d*e^6 + 2*a^2*b^5*e^7)*x^5 + (b^7*d^3*e^4 + 12*a*b^6*d^2*e^5 + 18*a^2*b^5*d*e^6 + 4*a^3*b^4*e^7)*x^4 + (4*a*b^6*d^3*e^4 + 18*a^2*b^5*d^2*e^5 + 12*a^3*b^4*d*e^6 + a^4*b^3*e^7)*x^3 + 3*(2*a^2*b^5*d^3*e^4 + 4*a^3*b^4*d^2*e^5 + a^4*b^3*d*e^6)*x^2 + (4*a^3*b^4*d^3*e^4 + 3*a^4*b^3*d^2*e^5)*x)*log(e*x + d))/(a^4*b^8*d^11 - 8*a^5*b^7*d^10*e + 28*a^6*b^6*d^9*e^2 - 56*a^7*b^5*d^8*e^3 + 70*a^8*b^4*d^7*e^4 - 56*a^9*b^3*d^6*e^5 + 28*a^10*b^2*d^5*e^6 - 8*a^11*b*d^4*e^7 + a^12*d^3*e^8 + (b^12*d^8*e^3 - 8*a*b^11*d^7*e^4 + 28*a^2*b^10*d^6*e^5 - 56*a^3*b^9*d^5*e^6 + 70*a^4*b^8*d^4*e^7 - 56*a^5*b^7*d^3*e^8 + 28*a^6*b^6*d^2*e^9 - 8*a^7*b^5*d*e^10 + a^8*b^4*e^11)*x^7 + (3*b^12*d^9*e^2 - 20*a*b^11*d^8*e^3 + 52*a^2*b^10*d^7*e^4 - 56*a^3*b^9*d^6*e^5 - 14*a^4*b^8*d^5*e^6 + 112*a^5*b^7*d^4*e^7 - 140*a^6*b^6*d^3*e^8 + 88*a^7*b^5*d^2*e^9 - 29*a^8*b^4*d*e^10 + 4*a^9*b^3*e^11)*x^6 + 3*(b^12*d^10*e - 4*a*b^11*d^9*e^2 - 2*a^2*b^10*d^8*e^3 + 40*a^3*b^9*d^7*e^4 - 98*a^4*b^8*d^6*e^5 + 112*a^5*b^7*d^5*e^6 - 56*a^6*b^6*d^4*e^7 - 8*a^7*b^5*d^3*e^8 + 25*a^8*b^4*d^2*e^9 - 12*a^9*b^3*d*e^10 + 2*a^10*b^2*e^11)*x^5 + (b^12*d^11 + 4*a*b^11*d^10*e - 50*a^2*b^10*d^9*e^2 + 140*a^3*b^9*d^8*e^3 - 130*a^4*b^8*d^7*e^4 - 112*a^5*b^7*d^6*e^5 + 392*a^6*b^6*d^5*e^6 - 400*a^7*b^5*d^4*e^7 + 185*a^8*b^4*d^3*e^8 - 20*a^9*b^3*d^2*e^9 - 14*a^10*b^2*d*e^10 + 4*a^11*b*e^11)*x^4 + (4*a*b^11*d^11 - 14*a^2*b^10*d^10*e - 20*a^3*b^9*d^9*e^2 + 185*a^4*b^8*d^8*e^3 - 400*a^5*b^7*d^7*e^4 + 392*a^6*b^6*d^6*e^5 - 112*a^7*b^5*d^5*e^6 - 130*a^8*b^4*d^4*e^7 + 140*a^9*b^3*d^3*e^8 - 50*a^10*b^2*d^2*e^9 + 4*a^11*b*d*e^10 + a^12*e^11)*x^3 + 3*(2*a^2*b^10*d^11 - 12*a^3*b^9*d^10*e + 25*a^4*b^8*d^9*e^2 - 8*a^5*b^7*d^8*e^3 - 56*a^6*b^6*d^7*e^4 + 112*a^7*b^5*d^6*e^5 - 98*a^8*b^4*d^5*e^6 + 40*a^9*b^3*d^4*e^7 - 2*a^10*b^2*d^3*e^8 - 4*a^11*b*d^2*e^9 + a^12*d*e^10)*x^2 + (4*a^3*b^9*d^11 - 29*a^4*b^8*d^10*e + 88*a^5*b^7*d^9*e^2 - 140*a^6*b^6*d^8*e^3 + 112*a^7*b^5*d^7*e^4 - 14*a^8*b^4*d^6*e^5 - 56*a^9*b^3*d^5*e^6 + 52*a^10*b^2*d^4*e^7 - 20*a^11*b*d^3*e^8 + 3*a^12*d^2*e^9)*x)","B",0
1954,1,197,0,0.405474," ","integrate((b*x+a)*(e*x+d)^5*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, b^{2} e^{5} x^{8} + a^{2} d^{5} x + \frac{1}{7} \, {\left(5 \, b^{2} d e^{4} + 2 \, a b e^{5}\right)} x^{7} + \frac{1}{6} \, {\left(10 \, b^{2} d^{2} e^{3} + 10 \, a b d e^{4} + a^{2} e^{5}\right)} x^{6} + {\left(2 \, b^{2} d^{3} e^{2} + 4 \, a b d^{2} e^{3} + a^{2} d e^{4}\right)} x^{5} + \frac{5}{4} \, {\left(b^{2} d^{4} e + 4 \, a b d^{3} e^{2} + 2 \, a^{2} d^{2} e^{3}\right)} x^{4} + \frac{1}{3} \, {\left(b^{2} d^{5} + 10 \, a b d^{4} e + 10 \, a^{2} d^{3} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(2 \, a b d^{5} + 5 \, a^{2} d^{4} e\right)} x^{2}"," ",0,"1/8*b^2*e^5*x^8 + a^2*d^5*x + 1/7*(5*b^2*d*e^4 + 2*a*b*e^5)*x^7 + 1/6*(10*b^2*d^2*e^3 + 10*a*b*d*e^4 + a^2*e^5)*x^6 + (2*b^2*d^3*e^2 + 4*a*b*d^2*e^3 + a^2*d*e^4)*x^5 + 5/4*(b^2*d^4*e + 4*a*b*d^3*e^2 + 2*a^2*d^2*e^3)*x^4 + 1/3*(b^2*d^5 + 10*a*b*d^4*e + 10*a^2*d^3*e^2)*x^3 + 1/2*(2*a*b*d^5 + 5*a^2*d^4*e)*x^2","A",0
1955,1,156,0,0.393119," ","integrate((b*x+a)*(e*x+d)^4*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{7} \, b^{2} e^{4} x^{7} + a^{2} d^{4} x + \frac{1}{3} \, {\left(2 \, b^{2} d e^{3} + a b e^{4}\right)} x^{6} + \frac{1}{5} \, {\left(6 \, b^{2} d^{2} e^{2} + 8 \, a b d e^{3} + a^{2} e^{4}\right)} x^{5} + {\left(b^{2} d^{3} e + 3 \, a b d^{2} e^{2} + a^{2} d e^{3}\right)} x^{4} + \frac{1}{3} \, {\left(b^{2} d^{4} + 8 \, a b d^{3} e + 6 \, a^{2} d^{2} e^{2}\right)} x^{3} + {\left(a b d^{4} + 2 \, a^{2} d^{3} e\right)} x^{2}"," ",0,"1/7*b^2*e^4*x^7 + a^2*d^4*x + 1/3*(2*b^2*d*e^3 + a*b*e^4)*x^6 + 1/5*(6*b^2*d^2*e^2 + 8*a*b*d*e^3 + a^2*e^4)*x^5 + (b^2*d^3*e + 3*a*b*d^2*e^2 + a^2*d*e^3)*x^4 + 1/3*(b^2*d^4 + 8*a*b*d^3*e + 6*a^2*d^2*e^2)*x^3 + (a*b*d^4 + 2*a^2*d^3*e)*x^2","A",0
1956,1,124,0,0.397784," ","integrate((b*x+a)*(e*x+d)^3*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, b^{2} e^{3} x^{6} + a^{2} d^{3} x + \frac{1}{5} \, {\left(3 \, b^{2} d e^{2} + 2 \, a b e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(3 \, b^{2} d^{2} e + 6 \, a b d e^{2} + a^{2} e^{3}\right)} x^{4} + \frac{1}{3} \, {\left(b^{2} d^{3} + 6 \, a b d^{2} e + 3 \, a^{2} d e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(2 \, a b d^{3} + 3 \, a^{2} d^{2} e\right)} x^{2}"," ",0,"1/6*b^2*e^3*x^6 + a^2*d^3*x + 1/5*(3*b^2*d*e^2 + 2*a*b*e^3)*x^5 + 1/4*(3*b^2*d^2*e + 6*a*b*d*e^2 + a^2*e^3)*x^4 + 1/3*(b^2*d^3 + 6*a*b*d^2*e + 3*a^2*d*e^2)*x^3 + 1/2*(2*a*b*d^3 + 3*a^2*d^2*e)*x^2","A",0
1957,1,81,0,0.395232," ","integrate((b*x+a)*(e*x+d)^2*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, b^{2} e^{2} x^{5} + a^{2} d^{2} x + \frac{1}{2} \, {\left(b^{2} d e + a b e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(b^{2} d^{2} + 4 \, a b d e + a^{2} e^{2}\right)} x^{3} + {\left(a b d^{2} + a^{2} d e\right)} x^{2}"," ",0,"1/5*b^2*e^2*x^5 + a^2*d^2*x + 1/2*(b^2*d*e + a*b*e^2)*x^4 + 1/3*(b^2*d^2 + 4*a*b*d*e + a^2*e^2)*x^3 + (a*b*d^2 + a^2*d*e)*x^2","A",0
1958,1,48,0,0.404909," ","integrate((b*x+a)*(e*x+d)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, b^{2} e x^{4} + a^{2} d x + \frac{1}{3} \, {\left(b^{2} d + 2 \, a b e\right)} x^{3} + \frac{1}{2} \, {\left(2 \, a b d + a^{2} e\right)} x^{2}"," ",0,"1/4*b^2*e*x^4 + a^2*d*x + 1/3*(b^2*d + 2*a*b*e)*x^3 + 1/2*(2*a*b*d + a^2*e)*x^2","A",0
1959,1,20,0,0.422027," ","integrate((b*x+a)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x"," ",0,"1/3*b^2*x^3 + a*b*x^2 + a^2*x","A",0
1960,1,62,0,0.418854," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\frac{b^{2} e^{2} x^{2} - 2 \, {\left(b^{2} d e - 2 \, a b e^{2}\right)} x + 2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \log\left(e x + d\right)}{2 \, e^{3}}"," ",0,"1/2*(b^2*e^2*x^2 - 2*(b^2*d*e - 2*a*b*e^2)*x + 2*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*log(e*x + d))/e^3","A",0
1961,1,92,0,0.423344," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{b^{2} e^{2} x^{2} + b^{2} d e x - b^{2} d^{2} + 2 \, a b d e - a^{2} e^{2} - 2 \, {\left(b^{2} d^{2} - a b d e + {\left(b^{2} d e - a b e^{2}\right)} x\right)} \log\left(e x + d\right)}{e^{4} x + d e^{3}}"," ",0,"(b^2*e^2*x^2 + b^2*d*e*x - b^2*d^2 + 2*a*b*d*e - a^2*e^2 - 2*(b^2*d^2 - a*b*d*e + (b^2*d*e - a*b*e^2)*x)*log(e*x + d))/(e^4*x + d*e^3)","A",0
1962,1,100,0,0.426821," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{3 \, b^{2} d^{2} - 2 \, a b d e - a^{2} e^{2} + 4 \, {\left(b^{2} d e - a b e^{2}\right)} x + 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, b^{2} d e x + b^{2} d^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"1/2*(3*b^2*d^2 - 2*a*b*d*e - a^2*e^2 + 4*(b^2*d*e - a*b*e^2)*x + 2*(b^2*e^2*x^2 + 2*b^2*d*e*x + b^2*d^2)*log(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
1963,1,84,0,0.408196," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{3 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + a b d e + a^{2} e^{2} + 3 \, {\left(b^{2} d e + a b e^{2}\right)} x}{3 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/3*(3*b^2*e^2*x^2 + b^2*d^2 + a*b*d*e + a^2*e^2 + 3*(b^2*d*e + a*b*e^2)*x)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","B",0
1964,1,98,0,0.395745," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{6 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 2 \, a b d e + 3 \, a^{2} e^{2} + 4 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} x}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/12*(6*b^2*e^2*x^2 + b^2*d^2 + 2*a*b*d*e + 3*a^2*e^2 + 4*(b^2*d*e + 2*a*b*e^2)*x)/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","A",0
1965,1,109,0,0.417016," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{10 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 3 \, a b d e + 6 \, a^{2} e^{2} + 5 \, {\left(b^{2} d e + 3 \, a b e^{2}\right)} x}{30 \, {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"-1/30*(10*b^2*e^2*x^2 + b^2*d^2 + 3*a*b*d*e + 6*a^2*e^2 + 5*(b^2*d*e + 3*a*b*e^2)*x)/(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3)","A",0
1966,1,120,0,0.403364," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{15 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 4 \, a b d e + 10 \, a^{2} e^{2} + 6 \, {\left(b^{2} d e + 4 \, a b e^{2}\right)} x}{60 \, {\left(e^{9} x^{6} + 6 \, d e^{8} x^{5} + 15 \, d^{2} e^{7} x^{4} + 20 \, d^{3} e^{6} x^{3} + 15 \, d^{4} e^{5} x^{2} + 6 \, d^{5} e^{4} x + d^{6} e^{3}\right)}}"," ",0,"-1/60*(15*b^2*e^2*x^2 + b^2*d^2 + 4*a*b*d*e + 10*a^2*e^2 + 6*(b^2*d*e + 4*a*b*e^2)*x)/(e^9*x^6 + 6*d*e^8*x^5 + 15*d^2*e^7*x^4 + 20*d^3*e^6*x^3 + 15*d^4*e^5*x^2 + 6*d^5*e^4*x + d^6*e^3)","A",0
1967,1,131,0,0.401863," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{21 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 5 \, a b d e + 15 \, a^{2} e^{2} + 7 \, {\left(b^{2} d e + 5 \, a b e^{2}\right)} x}{105 \, {\left(e^{10} x^{7} + 7 \, d e^{9} x^{6} + 21 \, d^{2} e^{8} x^{5} + 35 \, d^{3} e^{7} x^{4} + 35 \, d^{4} e^{6} x^{3} + 21 \, d^{5} e^{5} x^{2} + 7 \, d^{6} e^{4} x + d^{7} e^{3}\right)}}"," ",0,"-1/105*(21*b^2*e^2*x^2 + b^2*d^2 + 5*a*b*d*e + 15*a^2*e^2 + 7*(b^2*d*e + 5*a*b*e^2)*x)/(e^10*x^7 + 7*d*e^9*x^6 + 21*d^2*e^8*x^5 + 35*d^3*e^7*x^4 + 35*d^4*e^6*x^3 + 21*d^5*e^5*x^2 + 7*d^6*e^4*x + d^7*e^3)","A",0
1968,1,489,0,0.399465," ","integrate((b*x+a)*(e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{12} \, b^{4} e^{7} x^{12} + a^{4} d^{7} x + \frac{1}{11} \, {\left(7 \, b^{4} d e^{6} + 4 \, a b^{3} e^{7}\right)} x^{11} + \frac{1}{10} \, {\left(21 \, b^{4} d^{2} e^{5} + 28 \, a b^{3} d e^{6} + 6 \, a^{2} b^{2} e^{7}\right)} x^{10} + \frac{1}{9} \, {\left(35 \, b^{4} d^{3} e^{4} + 84 \, a b^{3} d^{2} e^{5} + 42 \, a^{2} b^{2} d e^{6} + 4 \, a^{3} b e^{7}\right)} x^{9} + \frac{1}{8} \, {\left(35 \, b^{4} d^{4} e^{3} + 140 \, a b^{3} d^{3} e^{4} + 126 \, a^{2} b^{2} d^{2} e^{5} + 28 \, a^{3} b d e^{6} + a^{4} e^{7}\right)} x^{8} + {\left(3 \, b^{4} d^{5} e^{2} + 20 \, a b^{3} d^{4} e^{3} + 30 \, a^{2} b^{2} d^{3} e^{4} + 12 \, a^{3} b d^{2} e^{5} + a^{4} d e^{6}\right)} x^{7} + \frac{7}{6} \, {\left(b^{4} d^{6} e + 12 \, a b^{3} d^{5} e^{2} + 30 \, a^{2} b^{2} d^{4} e^{3} + 20 \, a^{3} b d^{3} e^{4} + 3 \, a^{4} d^{2} e^{5}\right)} x^{6} + \frac{1}{5} \, {\left(b^{4} d^{7} + 28 \, a b^{3} d^{6} e + 126 \, a^{2} b^{2} d^{5} e^{2} + 140 \, a^{3} b d^{4} e^{3} + 35 \, a^{4} d^{3} e^{4}\right)} x^{5} + \frac{1}{4} \, {\left(4 \, a b^{3} d^{7} + 42 \, a^{2} b^{2} d^{6} e + 84 \, a^{3} b d^{5} e^{2} + 35 \, a^{4} d^{4} e^{3}\right)} x^{4} + \frac{1}{3} \, {\left(6 \, a^{2} b^{2} d^{7} + 28 \, a^{3} b d^{6} e + 21 \, a^{4} d^{5} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(4 \, a^{3} b d^{7} + 7 \, a^{4} d^{6} e\right)} x^{2}"," ",0,"1/12*b^4*e^7*x^12 + a^4*d^7*x + 1/11*(7*b^4*d*e^6 + 4*a*b^3*e^7)*x^11 + 1/10*(21*b^4*d^2*e^5 + 28*a*b^3*d*e^6 + 6*a^2*b^2*e^7)*x^10 + 1/9*(35*b^4*d^3*e^4 + 84*a*b^3*d^2*e^5 + 42*a^2*b^2*d*e^6 + 4*a^3*b*e^7)*x^9 + 1/8*(35*b^4*d^4*e^3 + 140*a*b^3*d^3*e^4 + 126*a^2*b^2*d^2*e^5 + 28*a^3*b*d*e^6 + a^4*e^7)*x^8 + (3*b^4*d^5*e^2 + 20*a*b^3*d^4*e^3 + 30*a^2*b^2*d^3*e^4 + 12*a^3*b*d^2*e^5 + a^4*d*e^6)*x^7 + 7/6*(b^4*d^6*e + 12*a*b^3*d^5*e^2 + 30*a^2*b^2*d^4*e^3 + 20*a^3*b*d^3*e^4 + 3*a^4*d^2*e^5)*x^6 + 1/5*(b^4*d^7 + 28*a*b^3*d^6*e + 126*a^2*b^2*d^5*e^2 + 140*a^3*b*d^4*e^3 + 35*a^4*d^3*e^4)*x^5 + 1/4*(4*a*b^3*d^7 + 42*a^2*b^2*d^6*e + 84*a^3*b*d^5*e^2 + 35*a^4*d^4*e^3)*x^4 + 1/3*(6*a^2*b^2*d^7 + 28*a^3*b*d^6*e + 21*a^4*d^5*e^2)*x^3 + 1/2*(4*a^3*b*d^7 + 7*a^4*d^6*e)*x^2","B",0
1969,1,418,0,0.426927," ","integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{11} \, b^{4} e^{6} x^{11} + a^{4} d^{6} x + \frac{1}{5} \, {\left(3 \, b^{4} d e^{5} + 2 \, a b^{3} e^{6}\right)} x^{10} + \frac{1}{3} \, {\left(5 \, b^{4} d^{2} e^{4} + 8 \, a b^{3} d e^{5} + 2 \, a^{2} b^{2} e^{6}\right)} x^{9} + \frac{1}{2} \, {\left(5 \, b^{4} d^{3} e^{3} + 15 \, a b^{3} d^{2} e^{4} + 9 \, a^{2} b^{2} d e^{5} + a^{3} b e^{6}\right)} x^{8} + \frac{1}{7} \, {\left(15 \, b^{4} d^{4} e^{2} + 80 \, a b^{3} d^{3} e^{3} + 90 \, a^{2} b^{2} d^{2} e^{4} + 24 \, a^{3} b d e^{5} + a^{4} e^{6}\right)} x^{7} + {\left(b^{4} d^{5} e + 10 \, a b^{3} d^{4} e^{2} + 20 \, a^{2} b^{2} d^{3} e^{3} + 10 \, a^{3} b d^{2} e^{4} + a^{4} d e^{5}\right)} x^{6} + \frac{1}{5} \, {\left(b^{4} d^{6} + 24 \, a b^{3} d^{5} e + 90 \, a^{2} b^{2} d^{4} e^{2} + 80 \, a^{3} b d^{3} e^{3} + 15 \, a^{4} d^{2} e^{4}\right)} x^{5} + {\left(a b^{3} d^{6} + 9 \, a^{2} b^{2} d^{5} e + 15 \, a^{3} b d^{4} e^{2} + 5 \, a^{4} d^{3} e^{3}\right)} x^{4} + {\left(2 \, a^{2} b^{2} d^{6} + 8 \, a^{3} b d^{5} e + 5 \, a^{4} d^{4} e^{2}\right)} x^{3} + {\left(2 \, a^{3} b d^{6} + 3 \, a^{4} d^{5} e\right)} x^{2}"," ",0,"1/11*b^4*e^6*x^11 + a^4*d^6*x + 1/5*(3*b^4*d*e^5 + 2*a*b^3*e^6)*x^10 + 1/3*(5*b^4*d^2*e^4 + 8*a*b^3*d*e^5 + 2*a^2*b^2*e^6)*x^9 + 1/2*(5*b^4*d^3*e^3 + 15*a*b^3*d^2*e^4 + 9*a^2*b^2*d*e^5 + a^3*b*e^6)*x^8 + 1/7*(15*b^4*d^4*e^2 + 80*a*b^3*d^3*e^3 + 90*a^2*b^2*d^2*e^4 + 24*a^3*b*d*e^5 + a^4*e^6)*x^7 + (b^4*d^5*e + 10*a*b^3*d^4*e^2 + 20*a^2*b^2*d^3*e^3 + 10*a^3*b*d^2*e^4 + a^4*d*e^5)*x^6 + 1/5*(b^4*d^6 + 24*a*b^3*d^5*e + 90*a^2*b^2*d^4*e^2 + 80*a^3*b*d^3*e^3 + 15*a^4*d^2*e^4)*x^5 + (a*b^3*d^6 + 9*a^2*b^2*d^5*e + 15*a^3*b*d^4*e^2 + 5*a^4*d^3*e^3)*x^4 + (2*a^2*b^2*d^6 + 8*a^3*b*d^5*e + 5*a^4*d^4*e^2)*x^3 + (2*a^3*b*d^6 + 3*a^4*d^5*e)*x^2","B",0
1970,1,360,0,0.410954," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{10} \, b^{4} e^{5} x^{10} + a^{4} d^{5} x + \frac{1}{9} \, {\left(5 \, b^{4} d e^{4} + 4 \, a b^{3} e^{5}\right)} x^{9} + \frac{1}{4} \, {\left(5 \, b^{4} d^{2} e^{3} + 10 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} x^{8} + \frac{2}{7} \, {\left(5 \, b^{4} d^{3} e^{2} + 20 \, a b^{3} d^{2} e^{3} + 15 \, a^{2} b^{2} d e^{4} + 2 \, a^{3} b e^{5}\right)} x^{7} + \frac{1}{6} \, {\left(5 \, b^{4} d^{4} e + 40 \, a b^{3} d^{3} e^{2} + 60 \, a^{2} b^{2} d^{2} e^{3} + 20 \, a^{3} b d e^{4} + a^{4} e^{5}\right)} x^{6} + \frac{1}{5} \, {\left(b^{4} d^{5} + 20 \, a b^{3} d^{4} e + 60 \, a^{2} b^{2} d^{3} e^{2} + 40 \, a^{3} b d^{2} e^{3} + 5 \, a^{4} d e^{4}\right)} x^{5} + \frac{1}{2} \, {\left(2 \, a b^{3} d^{5} + 15 \, a^{2} b^{2} d^{4} e + 20 \, a^{3} b d^{3} e^{2} + 5 \, a^{4} d^{2} e^{3}\right)} x^{4} + \frac{2}{3} \, {\left(3 \, a^{2} b^{2} d^{5} + 10 \, a^{3} b d^{4} e + 5 \, a^{4} d^{3} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(4 \, a^{3} b d^{5} + 5 \, a^{4} d^{4} e\right)} x^{2}"," ",0,"1/10*b^4*e^5*x^10 + a^4*d^5*x + 1/9*(5*b^4*d*e^4 + 4*a*b^3*e^5)*x^9 + 1/4*(5*b^4*d^2*e^3 + 10*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*x^8 + 2/7*(5*b^4*d^3*e^2 + 20*a*b^3*d^2*e^3 + 15*a^2*b^2*d*e^4 + 2*a^3*b*e^5)*x^7 + 1/6*(5*b^4*d^4*e + 40*a*b^3*d^3*e^2 + 60*a^2*b^2*d^2*e^3 + 20*a^3*b*d*e^4 + a^4*e^5)*x^6 + 1/5*(b^4*d^5 + 20*a*b^3*d^4*e + 60*a^2*b^2*d^3*e^2 + 40*a^3*b*d^2*e^3 + 5*a^4*d*e^4)*x^5 + 1/2*(2*a*b^3*d^5 + 15*a^2*b^2*d^4*e + 20*a^3*b*d^3*e^2 + 5*a^4*d^2*e^3)*x^4 + 2/3*(3*a^2*b^2*d^5 + 10*a^3*b*d^4*e + 5*a^4*d^3*e^2)*x^3 + 1/2*(4*a^3*b*d^5 + 5*a^4*d^4*e)*x^2","A",0
1971,1,285,0,0.423994," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{9} \, b^{4} e^{4} x^{9} + a^{4} d^{4} x + \frac{1}{2} \, {\left(b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{8} + \frac{2}{7} \, {\left(3 \, b^{4} d^{2} e^{2} + 8 \, a b^{3} d e^{3} + 3 \, a^{2} b^{2} e^{4}\right)} x^{7} + \frac{2}{3} \, {\left(b^{4} d^{3} e + 6 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x^{6} + \frac{1}{5} \, {\left(b^{4} d^{4} + 16 \, a b^{3} d^{3} e + 36 \, a^{2} b^{2} d^{2} e^{2} + 16 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} x^{5} + {\left(a b^{3} d^{4} + 6 \, a^{2} b^{2} d^{3} e + 6 \, a^{3} b d^{2} e^{2} + a^{4} d e^{3}\right)} x^{4} + \frac{2}{3} \, {\left(3 \, a^{2} b^{2} d^{4} + 8 \, a^{3} b d^{3} e + 3 \, a^{4} d^{2} e^{2}\right)} x^{3} + 2 \, {\left(a^{3} b d^{4} + a^{4} d^{3} e\right)} x^{2}"," ",0,"1/9*b^4*e^4*x^9 + a^4*d^4*x + 1/2*(b^4*d*e^3 + a*b^3*e^4)*x^8 + 2/7*(3*b^4*d^2*e^2 + 8*a*b^3*d*e^3 + 3*a^2*b^2*e^4)*x^7 + 2/3*(b^4*d^3*e + 6*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 + a^3*b*e^4)*x^6 + 1/5*(b^4*d^4 + 16*a*b^3*d^3*e + 36*a^2*b^2*d^2*e^2 + 16*a^3*b*d*e^3 + a^4*e^4)*x^5 + (a*b^3*d^4 + 6*a^2*b^2*d^3*e + 6*a^3*b*d^2*e^2 + a^4*d*e^3)*x^4 + 2/3*(3*a^2*b^2*d^4 + 8*a^3*b*d^3*e + 3*a^4*d^2*e^2)*x^3 + 2*(a^3*b*d^4 + a^4*d^3*e)*x^2","A",0
1972,1,225,0,0.411744," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{8} \, b^{4} e^{3} x^{8} + a^{4} d^{3} x + \frac{1}{7} \, {\left(3 \, b^{4} d e^{2} + 4 \, a b^{3} e^{3}\right)} x^{7} + \frac{1}{2} \, {\left(b^{4} d^{2} e + 4 \, a b^{3} d e^{2} + 2 \, a^{2} b^{2} e^{3}\right)} x^{6} + \frac{1}{5} \, {\left(b^{4} d^{3} + 12 \, a b^{3} d^{2} e + 18 \, a^{2} b^{2} d e^{2} + 4 \, a^{3} b e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(4 \, a b^{3} d^{3} + 18 \, a^{2} b^{2} d^{2} e + 12 \, a^{3} b d e^{2} + a^{4} e^{3}\right)} x^{4} + {\left(2 \, a^{2} b^{2} d^{3} + 4 \, a^{3} b d^{2} e + a^{4} d e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(4 \, a^{3} b d^{3} + 3 \, a^{4} d^{2} e\right)} x^{2}"," ",0,"1/8*b^4*e^3*x^8 + a^4*d^3*x + 1/7*(3*b^4*d*e^2 + 4*a*b^3*e^3)*x^7 + 1/2*(b^4*d^2*e + 4*a*b^3*d*e^2 + 2*a^2*b^2*e^3)*x^6 + 1/5*(b^4*d^3 + 12*a*b^3*d^2*e + 18*a^2*b^2*d*e^2 + 4*a^3*b*e^3)*x^5 + 1/4*(4*a*b^3*d^3 + 18*a^2*b^2*d^2*e + 12*a^3*b*d*e^2 + a^4*e^3)*x^4 + (2*a^2*b^2*d^3 + 4*a^3*b*d^2*e + a^4*d*e^2)*x^3 + 1/2*(4*a^3*b*d^3 + 3*a^4*d^2*e)*x^2","A",0
1973,1,156,0,0.413413," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{7} \, b^{4} e^{2} x^{7} + a^{4} d^{2} x + \frac{1}{3} \, {\left(b^{4} d e + 2 \, a b^{3} e^{2}\right)} x^{6} + \frac{1}{5} \, {\left(b^{4} d^{2} + 8 \, a b^{3} d e + 6 \, a^{2} b^{2} e^{2}\right)} x^{5} + {\left(a b^{3} d^{2} + 3 \, a^{2} b^{2} d e + a^{3} b e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(6 \, a^{2} b^{2} d^{2} + 8 \, a^{3} b d e + a^{4} e^{2}\right)} x^{3} + {\left(2 \, a^{3} b d^{2} + a^{4} d e\right)} x^{2}"," ",0,"1/7*b^4*e^2*x^7 + a^4*d^2*x + 1/3*(b^4*d*e + 2*a*b^3*e^2)*x^6 + 1/5*(b^4*d^2 + 8*a*b^3*d*e + 6*a^2*b^2*e^2)*x^5 + (a*b^3*d^2 + 3*a^2*b^2*d*e + a^3*b*e^2)*x^4 + 1/3*(6*a^2*b^2*d^2 + 8*a^3*b*d*e + a^4*e^2)*x^3 + (2*a^3*b*d^2 + a^4*d*e)*x^2","A",0
1974,1,96,0,0.393437," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{6} \, b^{4} e x^{6} + a^{4} d x + \frac{1}{5} \, {\left(b^{4} d + 4 \, a b^{3} e\right)} x^{5} + \frac{1}{2} \, {\left(2 \, a b^{3} d + 3 \, a^{2} b^{2} e\right)} x^{4} + \frac{2}{3} \, {\left(3 \, a^{2} b^{2} d + 2 \, a^{3} b e\right)} x^{3} + \frac{1}{2} \, {\left(4 \, a^{3} b d + a^{4} e\right)} x^{2}"," ",0,"1/6*b^4*e*x^6 + a^4*d*x + 1/5*(b^4*d + 4*a*b^3*e)*x^5 + 1/2*(2*a*b^3*d + 3*a^2*b^2*e)*x^4 + 2/3*(3*a^2*b^2*d + 2*a^3*b*e)*x^3 + 1/2*(4*a^3*b*d + a^4*e)*x^2","A",0
1975,1,42,0,0.405816," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{5} \, b^{4} x^{5} + a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{3} + 2 \, a^{3} b x^{2} + a^{4} x"," ",0,"1/5*b^4*x^5 + a*b^3*x^4 + 2*a^2*b^2*x^3 + 2*a^3*b*x^2 + a^4*x","A",0
1976,1,179,0,0.414152," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\frac{3 \, b^{4} e^{4} x^{4} - 4 \, {\left(b^{4} d e^{3} - 4 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} + 6 \, a^{2} b^{2} e^{4}\right)} x^{2} - 12 \, {\left(b^{4} d^{3} e - 4 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} - 4 \, a^{3} b e^{4}\right)} x + 12 \, {\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} \log\left(e x + d\right)}{12 \, e^{5}}"," ",0,"1/12*(3*b^4*e^4*x^4 - 4*(b^4*d*e^3 - 4*a*b^3*e^4)*x^3 + 6*(b^4*d^2*e^2 - 4*a*b^3*d*e^3 + 6*a^2*b^2*e^4)*x^2 - 12*(b^4*d^3*e - 4*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 - 4*a^3*b*e^4)*x + 12*(b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*log(e*x + d))/e^5","A",0
1977,1,267,0,0.410831," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{b^{4} e^{4} x^{4} - 3 \, b^{4} d^{4} + 12 \, a b^{3} d^{3} e - 18 \, a^{2} b^{2} d^{2} e^{2} + 12 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} - 2 \, {\left(b^{4} d e^{3} - 3 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(b^{4} d^{2} e^{2} - 3 \, a b^{3} d e^{3} + 3 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(3 \, b^{4} d^{3} e - 8 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3}\right)} x - 12 \, {\left(b^{4} d^{4} - 3 \, a b^{3} d^{3} e + 3 \, a^{2} b^{2} d^{2} e^{2} - a^{3} b d e^{3} + {\left(b^{4} d^{3} e - 3 \, a b^{3} d^{2} e^{2} + 3 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"1/3*(b^4*e^4*x^4 - 3*b^4*d^4 + 12*a*b^3*d^3*e - 18*a^2*b^2*d^2*e^2 + 12*a^3*b*d*e^3 - 3*a^4*e^4 - 2*(b^4*d*e^3 - 3*a*b^3*e^4)*x^3 + 6*(b^4*d^2*e^2 - 3*a*b^3*d*e^3 + 3*a^2*b^2*e^4)*x^2 + 3*(3*b^4*d^3*e - 8*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3)*x - 12*(b^4*d^4 - 3*a*b^3*d^3*e + 3*a^2*b^2*d^2*e^2 - a^3*b*d*e^3 + (b^4*d^3*e - 3*a*b^3*d^2*e^2 + 3*a^2*b^2*d*e^3 - a^3*b*e^4)*x)*log(e*x + d))/(e^6*x + d*e^5)","A",0
1978,1,291,0,0.438563," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{b^{4} e^{4} x^{4} + 7 \, b^{4} d^{4} - 20 \, a b^{3} d^{3} e + 18 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} - a^{4} e^{4} - 4 \, {\left(b^{4} d e^{3} - 2 \, a b^{3} e^{4}\right)} x^{3} - {\left(11 \, b^{4} d^{2} e^{2} - 16 \, a b^{3} d e^{3}\right)} x^{2} + 2 \, {\left(b^{4} d^{3} e - 8 \, a b^{3} d^{2} e^{2} + 12 \, a^{2} b^{2} d e^{3} - 4 \, a^{3} b e^{4}\right)} x + 12 \, {\left(b^{4} d^{4} - 2 \, a b^{3} d^{3} e + a^{2} b^{2} d^{2} e^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{4} d^{3} e - 2 \, a b^{3} d^{2} e^{2} + a^{2} b^{2} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"1/2*(b^4*e^4*x^4 + 7*b^4*d^4 - 20*a*b^3*d^3*e + 18*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 - a^4*e^4 - 4*(b^4*d*e^3 - 2*a*b^3*e^4)*x^3 - (11*b^4*d^2*e^2 - 16*a*b^3*d*e^3)*x^2 + 2*(b^4*d^3*e - 8*a*b^3*d^2*e^2 + 12*a^2*b^2*d*e^3 - 4*a^3*b*e^4)*x + 12*(b^4*d^4 - 2*a*b^3*d^3*e + a^2*b^2*d^2*e^2 + (b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(b^4*d^3*e - 2*a*b^3*d^2*e^2 + a^2*b^2*d*e^3)*x)*log(e*x + d))/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
1979,1,292,0,0.462624," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, b^{4} e^{4} x^{4} + 9 \, b^{4} d e^{3} x^{3} - 13 \, b^{4} d^{4} + 22 \, a b^{3} d^{3} e - 6 \, a^{2} b^{2} d^{2} e^{2} - 2 \, a^{3} b d e^{3} - a^{4} e^{4} - 9 \, {\left(b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} + 2 \, a^{2} b^{2} e^{4}\right)} x^{2} - 3 \, {\left(9 \, b^{4} d^{3} e - 18 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} + 2 \, a^{3} b e^{4}\right)} x - 12 \, {\left(b^{4} d^{4} - a b^{3} d^{3} e + {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(b^{4} d^{2} e^{2} - a b^{3} d e^{3}\right)} x^{2} + 3 \, {\left(b^{4} d^{3} e - a b^{3} d^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"1/3*(3*b^4*e^4*x^4 + 9*b^4*d*e^3*x^3 - 13*b^4*d^4 + 22*a*b^3*d^3*e - 6*a^2*b^2*d^2*e^2 - 2*a^3*b*d*e^3 - a^4*e^4 - 9*(b^4*d^2*e^2 - 4*a*b^3*d*e^3 + 2*a^2*b^2*e^4)*x^2 - 3*(9*b^4*d^3*e - 18*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 + 2*a^3*b*e^4)*x - 12*(b^4*d^4 - a*b^3*d^3*e + (b^4*d*e^3 - a*b^3*e^4)*x^3 + 3*(b^4*d^2*e^2 - a*b^3*d*e^3)*x^2 + 3*(b^4*d^3*e - a*b^3*d^2*e^2)*x)*log(e*x + d))/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
1980,1,268,0,0.427626," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{25 \, b^{4} d^{4} - 12 \, a b^{3} d^{3} e - 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} + 48 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 36 \, {\left(3 \, b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} - a^{2} b^{2} e^{4}\right)} x^{2} + 8 \, {\left(11 \, b^{4} d^{3} e - 6 \, a b^{3} d^{2} e^{2} - 3 \, a^{2} b^{2} d e^{3} - 2 \, a^{3} b e^{4}\right)} x + 12 \, {\left(b^{4} e^{4} x^{4} + 4 \, b^{4} d e^{3} x^{3} + 6 \, b^{4} d^{2} e^{2} x^{2} + 4 \, b^{4} d^{3} e x + b^{4} d^{4}\right)} \log\left(e x + d\right)}{12 \, {\left(e^{9} x^{4} + 4 \, d e^{8} x^{3} + 6 \, d^{2} e^{7} x^{2} + 4 \, d^{3} e^{6} x + d^{4} e^{5}\right)}}"," ",0,"1/12*(25*b^4*d^4 - 12*a*b^3*d^3*e - 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 - 3*a^4*e^4 + 48*(b^4*d*e^3 - a*b^3*e^4)*x^3 + 36*(3*b^4*d^2*e^2 - 2*a*b^3*d*e^3 - a^2*b^2*e^4)*x^2 + 8*(11*b^4*d^3*e - 6*a*b^3*d^2*e^2 - 3*a^2*b^2*d*e^3 - 2*a^3*b*e^4)*x + 12*(b^4*e^4*x^4 + 4*b^4*d*e^3*x^3 + 6*b^4*d^2*e^2*x^2 + 4*b^4*d^3*e*x + b^4*d^4)*log(e*x + d))/(e^9*x^4 + 4*d*e^8*x^3 + 6*d^2*e^7*x^2 + 4*d^3*e^6*x + d^4*e^5)","A",0
1981,1,215,0,0.445067," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{5 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + a b^{3} d^{3} e + a^{2} b^{2} d^{2} e^{2} + a^{3} b d e^{3} + a^{4} e^{4} + 10 \, {\left(b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + 10 \, {\left(b^{4} d^{2} e^{2} + a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 5 \, {\left(b^{4} d^{3} e + a b^{3} d^{2} e^{2} + a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x}{5 \, {\left(e^{10} x^{5} + 5 \, d e^{9} x^{4} + 10 \, d^{2} e^{8} x^{3} + 10 \, d^{3} e^{7} x^{2} + 5 \, d^{4} e^{6} x + d^{5} e^{5}\right)}}"," ",0,"-1/5*(5*b^4*e^4*x^4 + b^4*d^4 + a*b^3*d^3*e + a^2*b^2*d^2*e^2 + a^3*b*d*e^3 + a^4*e^4 + 10*(b^4*d*e^3 + a*b^3*e^4)*x^3 + 10*(b^4*d^2*e^2 + a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 5*(b^4*d^3*e + a*b^3*d^2*e^2 + a^2*b^2*d*e^3 + a^3*b*e^4)*x)/(e^10*x^5 + 5*d*e^9*x^4 + 10*d^2*e^8*x^3 + 10*d^3*e^7*x^2 + 5*d^4*e^6*x + d^5*e^5)","B",0
1982,1,236,0,0.423629," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{15 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 2 \, a b^{3} d^{3} e + 3 \, a^{2} b^{2} d^{2} e^{2} + 4 \, a^{3} b d e^{3} + 5 \, a^{4} e^{4} + 20 \, {\left(b^{4} d e^{3} + 2 \, a b^{3} e^{4}\right)} x^{3} + 15 \, {\left(b^{4} d^{2} e^{2} + 2 \, a b^{3} d e^{3} + 3 \, a^{2} b^{2} e^{4}\right)} x^{2} + 6 \, {\left(b^{4} d^{3} e + 2 \, a b^{3} d^{2} e^{2} + 3 \, a^{2} b^{2} d e^{3} + 4 \, a^{3} b e^{4}\right)} x}{30 \, {\left(e^{11} x^{6} + 6 \, d e^{10} x^{5} + 15 \, d^{2} e^{9} x^{4} + 20 \, d^{3} e^{8} x^{3} + 15 \, d^{4} e^{7} x^{2} + 6 \, d^{5} e^{6} x + d^{6} e^{5}\right)}}"," ",0,"-1/30*(15*b^4*e^4*x^4 + b^4*d^4 + 2*a*b^3*d^3*e + 3*a^2*b^2*d^2*e^2 + 4*a^3*b*d*e^3 + 5*a^4*e^4 + 20*(b^4*d*e^3 + 2*a*b^3*e^4)*x^3 + 15*(b^4*d^2*e^2 + 2*a*b^3*d*e^3 + 3*a^2*b^2*e^4)*x^2 + 6*(b^4*d^3*e + 2*a*b^3*d^2*e^2 + 3*a^2*b^2*d*e^3 + 4*a^3*b*e^4)*x)/(e^11*x^6 + 6*d*e^10*x^5 + 15*d^2*e^9*x^4 + 20*d^3*e^8*x^3 + 15*d^4*e^7*x^2 + 6*d^5*e^6*x + d^6*e^5)","B",0
1983,1,247,0,0.451550," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{35 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 3 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} + 10 \, a^{3} b d e^{3} + 15 \, a^{4} e^{4} + 35 \, {\left(b^{4} d e^{3} + 3 \, a b^{3} e^{4}\right)} x^{3} + 21 \, {\left(b^{4} d^{2} e^{2} + 3 \, a b^{3} d e^{3} + 6 \, a^{2} b^{2} e^{4}\right)} x^{2} + 7 \, {\left(b^{4} d^{3} e + 3 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} + 10 \, a^{3} b e^{4}\right)} x}{105 \, {\left(e^{12} x^{7} + 7 \, d e^{11} x^{6} + 21 \, d^{2} e^{10} x^{5} + 35 \, d^{3} e^{9} x^{4} + 35 \, d^{4} e^{8} x^{3} + 21 \, d^{5} e^{7} x^{2} + 7 \, d^{6} e^{6} x + d^{7} e^{5}\right)}}"," ",0,"-1/105*(35*b^4*e^4*x^4 + b^4*d^4 + 3*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 + 15*a^4*e^4 + 35*(b^4*d*e^3 + 3*a*b^3*e^4)*x^3 + 21*(b^4*d^2*e^2 + 3*a*b^3*d*e^3 + 6*a^2*b^2*e^4)*x^2 + 7*(b^4*d^3*e + 3*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 + 10*a^3*b*e^4)*x)/(e^12*x^7 + 7*d*e^11*x^6 + 21*d^2*e^10*x^5 + 35*d^3*e^9*x^4 + 35*d^4*e^8*x^3 + 21*d^5*e^7*x^2 + 7*d^6*e^6*x + d^7*e^5)","B",0
1984,1,258,0,0.426395," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{70 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 4 \, a b^{3} d^{3} e + 10 \, a^{2} b^{2} d^{2} e^{2} + 20 \, a^{3} b d e^{3} + 35 \, a^{4} e^{4} + 56 \, {\left(b^{4} d e^{3} + 4 \, a b^{3} e^{4}\right)} x^{3} + 28 \, {\left(b^{4} d^{2} e^{2} + 4 \, a b^{3} d e^{3} + 10 \, a^{2} b^{2} e^{4}\right)} x^{2} + 8 \, {\left(b^{4} d^{3} e + 4 \, a b^{3} d^{2} e^{2} + 10 \, a^{2} b^{2} d e^{3} + 20 \, a^{3} b e^{4}\right)} x}{280 \, {\left(e^{13} x^{8} + 8 \, d e^{12} x^{7} + 28 \, d^{2} e^{11} x^{6} + 56 \, d^{3} e^{10} x^{5} + 70 \, d^{4} e^{9} x^{4} + 56 \, d^{5} e^{8} x^{3} + 28 \, d^{6} e^{7} x^{2} + 8 \, d^{7} e^{6} x + d^{8} e^{5}\right)}}"," ",0,"-1/280*(70*b^4*e^4*x^4 + b^4*d^4 + 4*a*b^3*d^3*e + 10*a^2*b^2*d^2*e^2 + 20*a^3*b*d*e^3 + 35*a^4*e^4 + 56*(b^4*d*e^3 + 4*a*b^3*e^4)*x^3 + 28*(b^4*d^2*e^2 + 4*a*b^3*d*e^3 + 10*a^2*b^2*e^4)*x^2 + 8*(b^4*d^3*e + 4*a*b^3*d^2*e^2 + 10*a^2*b^2*d*e^3 + 20*a^3*b*e^4)*x)/(e^13*x^8 + 8*d*e^12*x^7 + 28*d^2*e^11*x^6 + 56*d^3*e^10*x^5 + 70*d^4*e^9*x^4 + 56*d^5*e^8*x^3 + 28*d^6*e^7*x^2 + 8*d^7*e^6*x + d^8*e^5)","A",0
1985,1,269,0,0.475867," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{126 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 5 \, a b^{3} d^{3} e + 15 \, a^{2} b^{2} d^{2} e^{2} + 35 \, a^{3} b d e^{3} + 70 \, a^{4} e^{4} + 84 \, {\left(b^{4} d e^{3} + 5 \, a b^{3} e^{4}\right)} x^{3} + 36 \, {\left(b^{4} d^{2} e^{2} + 5 \, a b^{3} d e^{3} + 15 \, a^{2} b^{2} e^{4}\right)} x^{2} + 9 \, {\left(b^{4} d^{3} e + 5 \, a b^{3} d^{2} e^{2} + 15 \, a^{2} b^{2} d e^{3} + 35 \, a^{3} b e^{4}\right)} x}{630 \, {\left(e^{14} x^{9} + 9 \, d e^{13} x^{8} + 36 \, d^{2} e^{12} x^{7} + 84 \, d^{3} e^{11} x^{6} + 126 \, d^{4} e^{10} x^{5} + 126 \, d^{5} e^{9} x^{4} + 84 \, d^{6} e^{8} x^{3} + 36 \, d^{7} e^{7} x^{2} + 9 \, d^{8} e^{6} x + d^{9} e^{5}\right)}}"," ",0,"-1/630*(126*b^4*e^4*x^4 + b^4*d^4 + 5*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^2 + 35*a^3*b*d*e^3 + 70*a^4*e^4 + 84*(b^4*d*e^3 + 5*a*b^3*e^4)*x^3 + 36*(b^4*d^2*e^2 + 5*a*b^3*d*e^3 + 15*a^2*b^2*e^4)*x^2 + 9*(b^4*d^3*e + 5*a*b^3*d^2*e^2 + 15*a^2*b^2*d*e^3 + 35*a^3*b*e^4)*x)/(e^14*x^9 + 9*d*e^13*x^8 + 36*d^2*e^12*x^7 + 84*d^3*e^11*x^6 + 126*d^4*e^10*x^5 + 126*d^5*e^9*x^4 + 84*d^6*e^8*x^3 + 36*d^7*e^7*x^2 + 9*d^8*e^6*x + d^9*e^5)","A",0
1986,1,280,0,0.433015," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{210 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 6 \, a b^{3} d^{3} e + 21 \, a^{2} b^{2} d^{2} e^{2} + 56 \, a^{3} b d e^{3} + 126 \, a^{4} e^{4} + 120 \, {\left(b^{4} d e^{3} + 6 \, a b^{3} e^{4}\right)} x^{3} + 45 \, {\left(b^{4} d^{2} e^{2} + 6 \, a b^{3} d e^{3} + 21 \, a^{2} b^{2} e^{4}\right)} x^{2} + 10 \, {\left(b^{4} d^{3} e + 6 \, a b^{3} d^{2} e^{2} + 21 \, a^{2} b^{2} d e^{3} + 56 \, a^{3} b e^{4}\right)} x}{1260 \, {\left(e^{15} x^{10} + 10 \, d e^{14} x^{9} + 45 \, d^{2} e^{13} x^{8} + 120 \, d^{3} e^{12} x^{7} + 210 \, d^{4} e^{11} x^{6} + 252 \, d^{5} e^{10} x^{5} + 210 \, d^{6} e^{9} x^{4} + 120 \, d^{7} e^{8} x^{3} + 45 \, d^{8} e^{7} x^{2} + 10 \, d^{9} e^{6} x + d^{10} e^{5}\right)}}"," ",0,"-1/1260*(210*b^4*e^4*x^4 + b^4*d^4 + 6*a*b^3*d^3*e + 21*a^2*b^2*d^2*e^2 + 56*a^3*b*d*e^3 + 126*a^4*e^4 + 120*(b^4*d*e^3 + 6*a*b^3*e^4)*x^3 + 45*(b^4*d^2*e^2 + 6*a*b^3*d*e^3 + 21*a^2*b^2*e^4)*x^2 + 10*(b^4*d^3*e + 6*a*b^3*d^2*e^2 + 21*a^2*b^2*d*e^3 + 56*a^3*b*e^4)*x)/(e^15*x^10 + 10*d*e^14*x^9 + 45*d^2*e^13*x^8 + 120*d^3*e^12*x^7 + 210*d^4*e^11*x^6 + 252*d^5*e^10*x^5 + 210*d^6*e^9*x^4 + 120*d^7*e^8*x^3 + 45*d^8*e^7*x^2 + 10*d^9*e^6*x + d^10*e^5)","A",0
1987,1,291,0,0.439048," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{330 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 7 \, a b^{3} d^{3} e + 28 \, a^{2} b^{2} d^{2} e^{2} + 84 \, a^{3} b d e^{3} + 210 \, a^{4} e^{4} + 165 \, {\left(b^{4} d e^{3} + 7 \, a b^{3} e^{4}\right)} x^{3} + 55 \, {\left(b^{4} d^{2} e^{2} + 7 \, a b^{3} d e^{3} + 28 \, a^{2} b^{2} e^{4}\right)} x^{2} + 11 \, {\left(b^{4} d^{3} e + 7 \, a b^{3} d^{2} e^{2} + 28 \, a^{2} b^{2} d e^{3} + 84 \, a^{3} b e^{4}\right)} x}{2310 \, {\left(e^{16} x^{11} + 11 \, d e^{15} x^{10} + 55 \, d^{2} e^{14} x^{9} + 165 \, d^{3} e^{13} x^{8} + 330 \, d^{4} e^{12} x^{7} + 462 \, d^{5} e^{11} x^{6} + 462 \, d^{6} e^{10} x^{5} + 330 \, d^{7} e^{9} x^{4} + 165 \, d^{8} e^{8} x^{3} + 55 \, d^{9} e^{7} x^{2} + 11 \, d^{10} e^{6} x + d^{11} e^{5}\right)}}"," ",0,"-1/2310*(330*b^4*e^4*x^4 + b^4*d^4 + 7*a*b^3*d^3*e + 28*a^2*b^2*d^2*e^2 + 84*a^3*b*d*e^3 + 210*a^4*e^4 + 165*(b^4*d*e^3 + 7*a*b^3*e^4)*x^3 + 55*(b^4*d^2*e^2 + 7*a*b^3*d*e^3 + 28*a^2*b^2*e^4)*x^2 + 11*(b^4*d^3*e + 7*a*b^3*d^2*e^2 + 28*a^2*b^2*d*e^3 + 84*a^3*b*e^4)*x)/(e^16*x^11 + 11*d*e^15*x^10 + 55*d^2*e^14*x^9 + 165*d^3*e^13*x^8 + 330*d^4*e^12*x^7 + 462*d^5*e^11*x^6 + 462*d^6*e^10*x^5 + 330*d^7*e^9*x^4 + 165*d^8*e^8*x^3 + 55*d^9*e^7*x^2 + 11*d^10*e^6*x + d^11*e^5)","A",0
1988,1,892,0,0.475601," ","integrate((b*x+a)*(e*x+d)^9*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{16} \, b^{6} e^{9} x^{16} + a^{6} d^{9} x + \frac{1}{5} \, {\left(3 \, b^{6} d e^{8} + 2 \, a b^{5} e^{9}\right)} x^{15} + \frac{3}{14} \, {\left(12 \, b^{6} d^{2} e^{7} + 18 \, a b^{5} d e^{8} + 5 \, a^{2} b^{4} e^{9}\right)} x^{14} + \frac{1}{13} \, {\left(84 \, b^{6} d^{3} e^{6} + 216 \, a b^{5} d^{2} e^{7} + 135 \, a^{2} b^{4} d e^{8} + 20 \, a^{3} b^{3} e^{9}\right)} x^{13} + \frac{1}{4} \, {\left(42 \, b^{6} d^{4} e^{5} + 168 \, a b^{5} d^{3} e^{6} + 180 \, a^{2} b^{4} d^{2} e^{7} + 60 \, a^{3} b^{3} d e^{8} + 5 \, a^{4} b^{2} e^{9}\right)} x^{12} + \frac{3}{11} \, {\left(42 \, b^{6} d^{5} e^{4} + 252 \, a b^{5} d^{4} e^{5} + 420 \, a^{2} b^{4} d^{3} e^{6} + 240 \, a^{3} b^{3} d^{2} e^{7} + 45 \, a^{4} b^{2} d e^{8} + 2 \, a^{5} b e^{9}\right)} x^{11} + \frac{1}{10} \, {\left(84 \, b^{6} d^{6} e^{3} + 756 \, a b^{5} d^{5} e^{4} + 1890 \, a^{2} b^{4} d^{4} e^{5} + 1680 \, a^{3} b^{3} d^{3} e^{6} + 540 \, a^{4} b^{2} d^{2} e^{7} + 54 \, a^{5} b d e^{8} + a^{6} e^{9}\right)} x^{10} + {\left(4 \, b^{6} d^{7} e^{2} + 56 \, a b^{5} d^{6} e^{3} + 210 \, a^{2} b^{4} d^{5} e^{4} + 280 \, a^{3} b^{3} d^{4} e^{5} + 140 \, a^{4} b^{2} d^{3} e^{6} + 24 \, a^{5} b d^{2} e^{7} + a^{6} d e^{8}\right)} x^{9} + \frac{9}{8} \, {\left(b^{6} d^{8} e + 24 \, a b^{5} d^{7} e^{2} + 140 \, a^{2} b^{4} d^{6} e^{3} + 280 \, a^{3} b^{3} d^{5} e^{4} + 210 \, a^{4} b^{2} d^{4} e^{5} + 56 \, a^{5} b d^{3} e^{6} + 4 \, a^{6} d^{2} e^{7}\right)} x^{8} + \frac{1}{7} \, {\left(b^{6} d^{9} + 54 \, a b^{5} d^{8} e + 540 \, a^{2} b^{4} d^{7} e^{2} + 1680 \, a^{3} b^{3} d^{6} e^{3} + 1890 \, a^{4} b^{2} d^{5} e^{4} + 756 \, a^{5} b d^{4} e^{5} + 84 \, a^{6} d^{3} e^{6}\right)} x^{7} + \frac{1}{2} \, {\left(2 \, a b^{5} d^{9} + 45 \, a^{2} b^{4} d^{8} e + 240 \, a^{3} b^{3} d^{7} e^{2} + 420 \, a^{4} b^{2} d^{6} e^{3} + 252 \, a^{5} b d^{5} e^{4} + 42 \, a^{6} d^{4} e^{5}\right)} x^{6} + \frac{3}{5} \, {\left(5 \, a^{2} b^{4} d^{9} + 60 \, a^{3} b^{3} d^{8} e + 180 \, a^{4} b^{2} d^{7} e^{2} + 168 \, a^{5} b d^{6} e^{3} + 42 \, a^{6} d^{5} e^{4}\right)} x^{5} + \frac{1}{4} \, {\left(20 \, a^{3} b^{3} d^{9} + 135 \, a^{4} b^{2} d^{8} e + 216 \, a^{5} b d^{7} e^{2} + 84 \, a^{6} d^{6} e^{3}\right)} x^{4} + {\left(5 \, a^{4} b^{2} d^{9} + 18 \, a^{5} b d^{8} e + 12 \, a^{6} d^{7} e^{2}\right)} x^{3} + \frac{3}{2} \, {\left(2 \, a^{5} b d^{9} + 3 \, a^{6} d^{8} e\right)} x^{2}"," ",0,"1/16*b^6*e^9*x^16 + a^6*d^9*x + 1/5*(3*b^6*d*e^8 + 2*a*b^5*e^9)*x^15 + 3/14*(12*b^6*d^2*e^7 + 18*a*b^5*d*e^8 + 5*a^2*b^4*e^9)*x^14 + 1/13*(84*b^6*d^3*e^6 + 216*a*b^5*d^2*e^7 + 135*a^2*b^4*d*e^8 + 20*a^3*b^3*e^9)*x^13 + 1/4*(42*b^6*d^4*e^5 + 168*a*b^5*d^3*e^6 + 180*a^2*b^4*d^2*e^7 + 60*a^3*b^3*d*e^8 + 5*a^4*b^2*e^9)*x^12 + 3/11*(42*b^6*d^5*e^4 + 252*a*b^5*d^4*e^5 + 420*a^2*b^4*d^3*e^6 + 240*a^3*b^3*d^2*e^7 + 45*a^4*b^2*d*e^8 + 2*a^5*b*e^9)*x^11 + 1/10*(84*b^6*d^6*e^3 + 756*a*b^5*d^5*e^4 + 1890*a^2*b^4*d^4*e^5 + 1680*a^3*b^3*d^3*e^6 + 540*a^4*b^2*d^2*e^7 + 54*a^5*b*d*e^8 + a^6*e^9)*x^10 + (4*b^6*d^7*e^2 + 56*a*b^5*d^6*e^3 + 210*a^2*b^4*d^5*e^4 + 280*a^3*b^3*d^4*e^5 + 140*a^4*b^2*d^3*e^6 + 24*a^5*b*d^2*e^7 + a^6*d*e^8)*x^9 + 9/8*(b^6*d^8*e + 24*a*b^5*d^7*e^2 + 140*a^2*b^4*d^6*e^3 + 280*a^3*b^3*d^5*e^4 + 210*a^4*b^2*d^4*e^5 + 56*a^5*b*d^3*e^6 + 4*a^6*d^2*e^7)*x^8 + 1/7*(b^6*d^9 + 54*a*b^5*d^8*e + 540*a^2*b^4*d^7*e^2 + 1680*a^3*b^3*d^6*e^3 + 1890*a^4*b^2*d^5*e^4 + 756*a^5*b*d^4*e^5 + 84*a^6*d^3*e^6)*x^7 + 1/2*(2*a*b^5*d^9 + 45*a^2*b^4*d^8*e + 240*a^3*b^3*d^7*e^2 + 420*a^4*b^2*d^6*e^3 + 252*a^5*b*d^5*e^4 + 42*a^6*d^4*e^5)*x^6 + 3/5*(5*a^2*b^4*d^9 + 60*a^3*b^3*d^8*e + 180*a^4*b^2*d^7*e^2 + 168*a^5*b*d^6*e^3 + 42*a^6*d^5*e^4)*x^5 + 1/4*(20*a^3*b^3*d^9 + 135*a^4*b^2*d^8*e + 216*a^5*b*d^7*e^2 + 84*a^6*d^6*e^3)*x^4 + (5*a^4*b^2*d^9 + 18*a^5*b*d^8*e + 12*a^6*d^7*e^2)*x^3 + 3/2*(2*a^5*b*d^9 + 3*a^6*d^8*e)*x^2","B",0
1989,1,797,0,0.439812," ","integrate((b*x+a)*(e*x+d)^8*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{15} \, b^{6} e^{8} x^{15} + a^{6} d^{8} x + \frac{1}{7} \, {\left(4 \, b^{6} d e^{7} + 3 \, a b^{5} e^{8}\right)} x^{14} + \frac{1}{13} \, {\left(28 \, b^{6} d^{2} e^{6} + 48 \, a b^{5} d e^{7} + 15 \, a^{2} b^{4} e^{8}\right)} x^{13} + \frac{1}{3} \, {\left(14 \, b^{6} d^{3} e^{5} + 42 \, a b^{5} d^{2} e^{6} + 30 \, a^{2} b^{4} d e^{7} + 5 \, a^{3} b^{3} e^{8}\right)} x^{12} + \frac{1}{11} \, {\left(70 \, b^{6} d^{4} e^{4} + 336 \, a b^{5} d^{3} e^{5} + 420 \, a^{2} b^{4} d^{2} e^{6} + 160 \, a^{3} b^{3} d e^{7} + 15 \, a^{4} b^{2} e^{8}\right)} x^{11} + \frac{1}{5} \, {\left(28 \, b^{6} d^{5} e^{3} + 210 \, a b^{5} d^{4} e^{4} + 420 \, a^{2} b^{4} d^{3} e^{5} + 280 \, a^{3} b^{3} d^{2} e^{6} + 60 \, a^{4} b^{2} d e^{7} + 3 \, a^{5} b e^{8}\right)} x^{10} + \frac{1}{9} \, {\left(28 \, b^{6} d^{6} e^{2} + 336 \, a b^{5} d^{5} e^{3} + 1050 \, a^{2} b^{4} d^{4} e^{4} + 1120 \, a^{3} b^{3} d^{3} e^{5} + 420 \, a^{4} b^{2} d^{2} e^{6} + 48 \, a^{5} b d e^{7} + a^{6} e^{8}\right)} x^{9} + {\left(b^{6} d^{7} e + 21 \, a b^{5} d^{6} e^{2} + 105 \, a^{2} b^{4} d^{5} e^{3} + 175 \, a^{3} b^{3} d^{4} e^{4} + 105 \, a^{4} b^{2} d^{3} e^{5} + 21 \, a^{5} b d^{2} e^{6} + a^{6} d e^{7}\right)} x^{8} + \frac{1}{7} \, {\left(b^{6} d^{8} + 48 \, a b^{5} d^{7} e + 420 \, a^{2} b^{4} d^{6} e^{2} + 1120 \, a^{3} b^{3} d^{5} e^{3} + 1050 \, a^{4} b^{2} d^{4} e^{4} + 336 \, a^{5} b d^{3} e^{5} + 28 \, a^{6} d^{2} e^{6}\right)} x^{7} + \frac{1}{3} \, {\left(3 \, a b^{5} d^{8} + 60 \, a^{2} b^{4} d^{7} e + 280 \, a^{3} b^{3} d^{6} e^{2} + 420 \, a^{4} b^{2} d^{5} e^{3} + 210 \, a^{5} b d^{4} e^{4} + 28 \, a^{6} d^{3} e^{5}\right)} x^{6} + \frac{1}{5} \, {\left(15 \, a^{2} b^{4} d^{8} + 160 \, a^{3} b^{3} d^{7} e + 420 \, a^{4} b^{2} d^{6} e^{2} + 336 \, a^{5} b d^{5} e^{3} + 70 \, a^{6} d^{4} e^{4}\right)} x^{5} + {\left(5 \, a^{3} b^{3} d^{8} + 30 \, a^{4} b^{2} d^{7} e + 42 \, a^{5} b d^{6} e^{2} + 14 \, a^{6} d^{5} e^{3}\right)} x^{4} + \frac{1}{3} \, {\left(15 \, a^{4} b^{2} d^{8} + 48 \, a^{5} b d^{7} e + 28 \, a^{6} d^{6} e^{2}\right)} x^{3} + {\left(3 \, a^{5} b d^{8} + 4 \, a^{6} d^{7} e\right)} x^{2}"," ",0,"1/15*b^6*e^8*x^15 + a^6*d^8*x + 1/7*(4*b^6*d*e^7 + 3*a*b^5*e^8)*x^14 + 1/13*(28*b^6*d^2*e^6 + 48*a*b^5*d*e^7 + 15*a^2*b^4*e^8)*x^13 + 1/3*(14*b^6*d^3*e^5 + 42*a*b^5*d^2*e^6 + 30*a^2*b^4*d*e^7 + 5*a^3*b^3*e^8)*x^12 + 1/11*(70*b^6*d^4*e^4 + 336*a*b^5*d^3*e^5 + 420*a^2*b^4*d^2*e^6 + 160*a^3*b^3*d*e^7 + 15*a^4*b^2*e^8)*x^11 + 1/5*(28*b^6*d^5*e^3 + 210*a*b^5*d^4*e^4 + 420*a^2*b^4*d^3*e^5 + 280*a^3*b^3*d^2*e^6 + 60*a^4*b^2*d*e^7 + 3*a^5*b*e^8)*x^10 + 1/9*(28*b^6*d^6*e^2 + 336*a*b^5*d^5*e^3 + 1050*a^2*b^4*d^4*e^4 + 1120*a^3*b^3*d^3*e^5 + 420*a^4*b^2*d^2*e^6 + 48*a^5*b*d*e^7 + a^6*e^8)*x^9 + (b^6*d^7*e + 21*a*b^5*d^6*e^2 + 105*a^2*b^4*d^5*e^3 + 175*a^3*b^3*d^4*e^4 + 105*a^4*b^2*d^3*e^5 + 21*a^5*b*d^2*e^6 + a^6*d*e^7)*x^8 + 1/7*(b^6*d^8 + 48*a*b^5*d^7*e + 420*a^2*b^4*d^6*e^2 + 1120*a^3*b^3*d^5*e^3 + 1050*a^4*b^2*d^4*e^4 + 336*a^5*b*d^3*e^5 + 28*a^6*d^2*e^6)*x^7 + 1/3*(3*a*b^5*d^8 + 60*a^2*b^4*d^7*e + 280*a^3*b^3*d^6*e^2 + 420*a^4*b^2*d^5*e^3 + 210*a^5*b*d^4*e^4 + 28*a^6*d^3*e^5)*x^6 + 1/5*(15*a^2*b^4*d^8 + 160*a^3*b^3*d^7*e + 420*a^4*b^2*d^6*e^2 + 336*a^5*b*d^5*e^3 + 70*a^6*d^4*e^4)*x^5 + (5*a^3*b^3*d^8 + 30*a^4*b^2*d^7*e + 42*a^5*b*d^6*e^2 + 14*a^6*d^5*e^3)*x^4 + 1/3*(15*a^4*b^2*d^8 + 48*a^5*b*d^7*e + 28*a^6*d^6*e^2)*x^3 + (3*a^5*b*d^8 + 4*a^6*d^7*e)*x^2","B",0
1990,1,706,0,0.436670," ","integrate((b*x+a)*(e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{14} \, b^{6} e^{7} x^{14} + a^{6} d^{7} x + \frac{1}{13} \, {\left(7 \, b^{6} d e^{6} + 6 \, a b^{5} e^{7}\right)} x^{13} + \frac{1}{4} \, {\left(7 \, b^{6} d^{2} e^{5} + 14 \, a b^{5} d e^{6} + 5 \, a^{2} b^{4} e^{7}\right)} x^{12} + \frac{1}{11} \, {\left(35 \, b^{6} d^{3} e^{4} + 126 \, a b^{5} d^{2} e^{5} + 105 \, a^{2} b^{4} d e^{6} + 20 \, a^{3} b^{3} e^{7}\right)} x^{11} + \frac{1}{2} \, {\left(7 \, b^{6} d^{4} e^{3} + 42 \, a b^{5} d^{3} e^{4} + 63 \, a^{2} b^{4} d^{2} e^{5} + 28 \, a^{3} b^{3} d e^{6} + 3 \, a^{4} b^{2} e^{7}\right)} x^{10} + \frac{1}{3} \, {\left(7 \, b^{6} d^{5} e^{2} + 70 \, a b^{5} d^{4} e^{3} + 175 \, a^{2} b^{4} d^{3} e^{4} + 140 \, a^{3} b^{3} d^{2} e^{5} + 35 \, a^{4} b^{2} d e^{6} + 2 \, a^{5} b e^{7}\right)} x^{9} + \frac{1}{8} \, {\left(7 \, b^{6} d^{6} e + 126 \, a b^{5} d^{5} e^{2} + 525 \, a^{2} b^{4} d^{4} e^{3} + 700 \, a^{3} b^{3} d^{3} e^{4} + 315 \, a^{4} b^{2} d^{2} e^{5} + 42 \, a^{5} b d e^{6} + a^{6} e^{7}\right)} x^{8} + \frac{1}{7} \, {\left(b^{6} d^{7} + 42 \, a b^{5} d^{6} e + 315 \, a^{2} b^{4} d^{5} e^{2} + 700 \, a^{3} b^{3} d^{4} e^{3} + 525 \, a^{4} b^{2} d^{3} e^{4} + 126 \, a^{5} b d^{2} e^{5} + 7 \, a^{6} d e^{6}\right)} x^{7} + \frac{1}{2} \, {\left(2 \, a b^{5} d^{7} + 35 \, a^{2} b^{4} d^{6} e + 140 \, a^{3} b^{3} d^{5} e^{2} + 175 \, a^{4} b^{2} d^{4} e^{3} + 70 \, a^{5} b d^{3} e^{4} + 7 \, a^{6} d^{2} e^{5}\right)} x^{6} + {\left(3 \, a^{2} b^{4} d^{7} + 28 \, a^{3} b^{3} d^{6} e + 63 \, a^{4} b^{2} d^{5} e^{2} + 42 \, a^{5} b d^{4} e^{3} + 7 \, a^{6} d^{3} e^{4}\right)} x^{5} + \frac{1}{4} \, {\left(20 \, a^{3} b^{3} d^{7} + 105 \, a^{4} b^{2} d^{6} e + 126 \, a^{5} b d^{5} e^{2} + 35 \, a^{6} d^{4} e^{3}\right)} x^{4} + {\left(5 \, a^{4} b^{2} d^{7} + 14 \, a^{5} b d^{6} e + 7 \, a^{6} d^{5} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(6 \, a^{5} b d^{7} + 7 \, a^{6} d^{6} e\right)} x^{2}"," ",0,"1/14*b^6*e^7*x^14 + a^6*d^7*x + 1/13*(7*b^6*d*e^6 + 6*a*b^5*e^7)*x^13 + 1/4*(7*b^6*d^2*e^5 + 14*a*b^5*d*e^6 + 5*a^2*b^4*e^7)*x^12 + 1/11*(35*b^6*d^3*e^4 + 126*a*b^5*d^2*e^5 + 105*a^2*b^4*d*e^6 + 20*a^3*b^3*e^7)*x^11 + 1/2*(7*b^6*d^4*e^3 + 42*a*b^5*d^3*e^4 + 63*a^2*b^4*d^2*e^5 + 28*a^3*b^3*d*e^6 + 3*a^4*b^2*e^7)*x^10 + 1/3*(7*b^6*d^5*e^2 + 70*a*b^5*d^4*e^3 + 175*a^2*b^4*d^3*e^4 + 140*a^3*b^3*d^2*e^5 + 35*a^4*b^2*d*e^6 + 2*a^5*b*e^7)*x^9 + 1/8*(7*b^6*d^6*e + 126*a*b^5*d^5*e^2 + 525*a^2*b^4*d^4*e^3 + 700*a^3*b^3*d^3*e^4 + 315*a^4*b^2*d^2*e^5 + 42*a^5*b*d*e^6 + a^6*e^7)*x^8 + 1/7*(b^6*d^7 + 42*a*b^5*d^6*e + 315*a^2*b^4*d^5*e^2 + 700*a^3*b^3*d^4*e^3 + 525*a^4*b^2*d^3*e^4 + 126*a^5*b*d^2*e^5 + 7*a^6*d*e^6)*x^7 + 1/2*(2*a*b^5*d^7 + 35*a^2*b^4*d^6*e + 140*a^3*b^3*d^5*e^2 + 175*a^4*b^2*d^4*e^3 + 70*a^5*b*d^3*e^4 + 7*a^6*d^2*e^5)*x^6 + (3*a^2*b^4*d^7 + 28*a^3*b^3*d^6*e + 63*a^4*b^2*d^5*e^2 + 42*a^5*b*d^4*e^3 + 7*a^6*d^3*e^4)*x^5 + 1/4*(20*a^3*b^3*d^7 + 105*a^4*b^2*d^6*e + 126*a^5*b*d^5*e^2 + 35*a^6*d^4*e^3)*x^4 + (5*a^4*b^2*d^7 + 14*a^5*b*d^6*e + 7*a^6*d^5*e^2)*x^3 + 1/2*(6*a^5*b*d^7 + 7*a^6*d^6*e)*x^2","B",0
1991,1,599,0,0.429332," ","integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{13} \, b^{6} e^{6} x^{13} + a^{6} d^{6} x + \frac{1}{2} \, {\left(b^{6} d e^{5} + a b^{5} e^{6}\right)} x^{12} + \frac{3}{11} \, {\left(5 \, b^{6} d^{2} e^{4} + 12 \, a b^{5} d e^{5} + 5 \, a^{2} b^{4} e^{6}\right)} x^{11} + {\left(2 \, b^{6} d^{3} e^{3} + 9 \, a b^{5} d^{2} e^{4} + 9 \, a^{2} b^{4} d e^{5} + 2 \, a^{3} b^{3} e^{6}\right)} x^{10} + \frac{5}{3} \, {\left(b^{6} d^{4} e^{2} + 8 \, a b^{5} d^{3} e^{3} + 15 \, a^{2} b^{4} d^{2} e^{4} + 8 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{9} + \frac{3}{4} \, {\left(b^{6} d^{5} e + 15 \, a b^{5} d^{4} e^{2} + 50 \, a^{2} b^{4} d^{3} e^{3} + 50 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{8} + \frac{1}{7} \, {\left(b^{6} d^{6} + 36 \, a b^{5} d^{5} e + 225 \, a^{2} b^{4} d^{4} e^{2} + 400 \, a^{3} b^{3} d^{3} e^{3} + 225 \, a^{4} b^{2} d^{2} e^{4} + 36 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} x^{7} + {\left(a b^{5} d^{6} + 15 \, a^{2} b^{4} d^{5} e + 50 \, a^{3} b^{3} d^{4} e^{2} + 50 \, a^{4} b^{2} d^{3} e^{3} + 15 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x^{6} + 3 \, {\left(a^{2} b^{4} d^{6} + 8 \, a^{3} b^{3} d^{5} e + 15 \, a^{4} b^{2} d^{4} e^{2} + 8 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4}\right)} x^{5} + \frac{5}{2} \, {\left(2 \, a^{3} b^{3} d^{6} + 9 \, a^{4} b^{2} d^{5} e + 9 \, a^{5} b d^{4} e^{2} + 2 \, a^{6} d^{3} e^{3}\right)} x^{4} + {\left(5 \, a^{4} b^{2} d^{6} + 12 \, a^{5} b d^{5} e + 5 \, a^{6} d^{4} e^{2}\right)} x^{3} + 3 \, {\left(a^{5} b d^{6} + a^{6} d^{5} e\right)} x^{2}"," ",0,"1/13*b^6*e^6*x^13 + a^6*d^6*x + 1/2*(b^6*d*e^5 + a*b^5*e^6)*x^12 + 3/11*(5*b^6*d^2*e^4 + 12*a*b^5*d*e^5 + 5*a^2*b^4*e^6)*x^11 + (2*b^6*d^3*e^3 + 9*a*b^5*d^2*e^4 + 9*a^2*b^4*d*e^5 + 2*a^3*b^3*e^6)*x^10 + 5/3*(b^6*d^4*e^2 + 8*a*b^5*d^3*e^3 + 15*a^2*b^4*d^2*e^4 + 8*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^9 + 3/4*(b^6*d^5*e + 15*a*b^5*d^4*e^2 + 50*a^2*b^4*d^3*e^3 + 50*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5 + a^5*b*e^6)*x^8 + 1/7*(b^6*d^6 + 36*a*b^5*d^5*e + 225*a^2*b^4*d^4*e^2 + 400*a^3*b^3*d^3*e^3 + 225*a^4*b^2*d^2*e^4 + 36*a^5*b*d*e^5 + a^6*e^6)*x^7 + (a*b^5*d^6 + 15*a^2*b^4*d^5*e + 50*a^3*b^3*d^4*e^2 + 50*a^4*b^2*d^3*e^3 + 15*a^5*b*d^2*e^4 + a^6*d*e^5)*x^6 + 3*(a^2*b^4*d^6 + 8*a^3*b^3*d^5*e + 15*a^4*b^2*d^4*e^2 + 8*a^5*b*d^3*e^3 + a^6*d^2*e^4)*x^5 + 5/2*(2*a^3*b^3*d^6 + 9*a^4*b^2*d^5*e + 9*a^5*b*d^4*e^2 + 2*a^6*d^3*e^3)*x^4 + (5*a^4*b^2*d^6 + 12*a^5*b*d^5*e + 5*a^6*d^4*e^2)*x^3 + 3*(a^5*b*d^6 + a^6*d^5*e)*x^2","B",0
1992,1,517,0,0.433685," ","integrate((b*x+a)*(e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{12} \, b^{6} e^{5} x^{12} + a^{6} d^{5} x + \frac{1}{11} \, {\left(5 \, b^{6} d e^{4} + 6 \, a b^{5} e^{5}\right)} x^{11} + \frac{1}{2} \, {\left(2 \, b^{6} d^{2} e^{3} + 6 \, a b^{5} d e^{4} + 3 \, a^{2} b^{4} e^{5}\right)} x^{10} + \frac{5}{9} \, {\left(2 \, b^{6} d^{3} e^{2} + 12 \, a b^{5} d^{2} e^{3} + 15 \, a^{2} b^{4} d e^{4} + 4 \, a^{3} b^{3} e^{5}\right)} x^{9} + \frac{5}{8} \, {\left(b^{6} d^{4} e + 12 \, a b^{5} d^{3} e^{2} + 30 \, a^{2} b^{4} d^{2} e^{3} + 20 \, a^{3} b^{3} d e^{4} + 3 \, a^{4} b^{2} e^{5}\right)} x^{8} + \frac{1}{7} \, {\left(b^{6} d^{5} + 30 \, a b^{5} d^{4} e + 150 \, a^{2} b^{4} d^{3} e^{2} + 200 \, a^{3} b^{3} d^{2} e^{3} + 75 \, a^{4} b^{2} d e^{4} + 6 \, a^{5} b e^{5}\right)} x^{7} + \frac{1}{6} \, {\left(6 \, a b^{5} d^{5} + 75 \, a^{2} b^{4} d^{4} e + 200 \, a^{3} b^{3} d^{3} e^{2} + 150 \, a^{4} b^{2} d^{2} e^{3} + 30 \, a^{5} b d e^{4} + a^{6} e^{5}\right)} x^{6} + {\left(3 \, a^{2} b^{4} d^{5} + 20 \, a^{3} b^{3} d^{4} e + 30 \, a^{4} b^{2} d^{3} e^{2} + 12 \, a^{5} b d^{2} e^{3} + a^{6} d e^{4}\right)} x^{5} + \frac{5}{4} \, {\left(4 \, a^{3} b^{3} d^{5} + 15 \, a^{4} b^{2} d^{4} e + 12 \, a^{5} b d^{3} e^{2} + 2 \, a^{6} d^{2} e^{3}\right)} x^{4} + \frac{5}{3} \, {\left(3 \, a^{4} b^{2} d^{5} + 6 \, a^{5} b d^{4} e + 2 \, a^{6} d^{3} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(6 \, a^{5} b d^{5} + 5 \, a^{6} d^{4} e\right)} x^{2}"," ",0,"1/12*b^6*e^5*x^12 + a^6*d^5*x + 1/11*(5*b^6*d*e^4 + 6*a*b^5*e^5)*x^11 + 1/2*(2*b^6*d^2*e^3 + 6*a*b^5*d*e^4 + 3*a^2*b^4*e^5)*x^10 + 5/9*(2*b^6*d^3*e^2 + 12*a*b^5*d^2*e^3 + 15*a^2*b^4*d*e^4 + 4*a^3*b^3*e^5)*x^9 + 5/8*(b^6*d^4*e + 12*a*b^5*d^3*e^2 + 30*a^2*b^4*d^2*e^3 + 20*a^3*b^3*d*e^4 + 3*a^4*b^2*e^5)*x^8 + 1/7*(b^6*d^5 + 30*a*b^5*d^4*e + 150*a^2*b^4*d^3*e^2 + 200*a^3*b^3*d^2*e^3 + 75*a^4*b^2*d*e^4 + 6*a^5*b*e^5)*x^7 + 1/6*(6*a*b^5*d^5 + 75*a^2*b^4*d^4*e + 200*a^3*b^3*d^3*e^2 + 150*a^4*b^2*d^2*e^3 + 30*a^5*b*d*e^4 + a^6*e^5)*x^6 + (3*a^2*b^4*d^5 + 20*a^3*b^3*d^4*e + 30*a^4*b^2*d^3*e^2 + 12*a^5*b*d^2*e^3 + a^6*d*e^4)*x^5 + 5/4*(4*a^3*b^3*d^5 + 15*a^4*b^2*d^4*e + 12*a^5*b*d^3*e^2 + 2*a^6*d^2*e^3)*x^4 + 5/3*(3*a^4*b^2*d^5 + 6*a^5*b*d^4*e + 2*a^6*d^3*e^2)*x^3 + 1/2*(6*a^5*b*d^5 + 5*a^6*d^4*e)*x^2","B",0
1993,1,418,0,0.416198," ","integrate((b*x+a)*(e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{11} \, b^{6} e^{4} x^{11} + a^{6} d^{4} x + \frac{1}{5} \, {\left(2 \, b^{6} d e^{3} + 3 \, a b^{5} e^{4}\right)} x^{10} + \frac{1}{3} \, {\left(2 \, b^{6} d^{2} e^{2} + 8 \, a b^{5} d e^{3} + 5 \, a^{2} b^{4} e^{4}\right)} x^{9} + \frac{1}{2} \, {\left(b^{6} d^{3} e + 9 \, a b^{5} d^{2} e^{2} + 15 \, a^{2} b^{4} d e^{3} + 5 \, a^{3} b^{3} e^{4}\right)} x^{8} + \frac{1}{7} \, {\left(b^{6} d^{4} + 24 \, a b^{5} d^{3} e + 90 \, a^{2} b^{4} d^{2} e^{2} + 80 \, a^{3} b^{3} d e^{3} + 15 \, a^{4} b^{2} e^{4}\right)} x^{7} + {\left(a b^{5} d^{4} + 10 \, a^{2} b^{4} d^{3} e + 20 \, a^{3} b^{3} d^{2} e^{2} + 10 \, a^{4} b^{2} d e^{3} + a^{5} b e^{4}\right)} x^{6} + \frac{1}{5} \, {\left(15 \, a^{2} b^{4} d^{4} + 80 \, a^{3} b^{3} d^{3} e + 90 \, a^{4} b^{2} d^{2} e^{2} + 24 \, a^{5} b d e^{3} + a^{6} e^{4}\right)} x^{5} + {\left(5 \, a^{3} b^{3} d^{4} + 15 \, a^{4} b^{2} d^{3} e + 9 \, a^{5} b d^{2} e^{2} + a^{6} d e^{3}\right)} x^{4} + {\left(5 \, a^{4} b^{2} d^{4} + 8 \, a^{5} b d^{3} e + 2 \, a^{6} d^{2} e^{2}\right)} x^{3} + {\left(3 \, a^{5} b d^{4} + 2 \, a^{6} d^{3} e\right)} x^{2}"," ",0,"1/11*b^6*e^4*x^11 + a^6*d^4*x + 1/5*(2*b^6*d*e^3 + 3*a*b^5*e^4)*x^10 + 1/3*(2*b^6*d^2*e^2 + 8*a*b^5*d*e^3 + 5*a^2*b^4*e^4)*x^9 + 1/2*(b^6*d^3*e + 9*a*b^5*d^2*e^2 + 15*a^2*b^4*d*e^3 + 5*a^3*b^3*e^4)*x^8 + 1/7*(b^6*d^4 + 24*a*b^5*d^3*e + 90*a^2*b^4*d^2*e^2 + 80*a^3*b^3*d*e^3 + 15*a^4*b^2*e^4)*x^7 + (a*b^5*d^4 + 10*a^2*b^4*d^3*e + 20*a^3*b^3*d^2*e^2 + 10*a^4*b^2*d*e^3 + a^5*b*e^4)*x^6 + 1/5*(15*a^2*b^4*d^4 + 80*a^3*b^3*d^3*e + 90*a^4*b^2*d^2*e^2 + 24*a^5*b*d*e^3 + a^6*e^4)*x^5 + (5*a^3*b^3*d^4 + 15*a^4*b^2*d^3*e + 9*a^5*b*d^2*e^2 + a^6*d*e^3)*x^4 + (5*a^4*b^2*d^4 + 8*a^5*b*d^3*e + 2*a^6*d^2*e^2)*x^3 + (3*a^5*b*d^4 + 2*a^6*d^3*e)*x^2","B",0
1994,1,327,0,0.400674," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{10} \, b^{6} e^{3} x^{10} + a^{6} d^{3} x + \frac{1}{3} \, {\left(b^{6} d e^{2} + 2 \, a b^{5} e^{3}\right)} x^{9} + \frac{3}{8} \, {\left(b^{6} d^{2} e + 6 \, a b^{5} d e^{2} + 5 \, a^{2} b^{4} e^{3}\right)} x^{8} + \frac{1}{7} \, {\left(b^{6} d^{3} + 18 \, a b^{5} d^{2} e + 45 \, a^{2} b^{4} d e^{2} + 20 \, a^{3} b^{3} e^{3}\right)} x^{7} + \frac{1}{2} \, {\left(2 \, a b^{5} d^{3} + 15 \, a^{2} b^{4} d^{2} e + 20 \, a^{3} b^{3} d e^{2} + 5 \, a^{4} b^{2} e^{3}\right)} x^{6} + \frac{3}{5} \, {\left(5 \, a^{2} b^{4} d^{3} + 20 \, a^{3} b^{3} d^{2} e + 15 \, a^{4} b^{2} d e^{2} + 2 \, a^{5} b e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(20 \, a^{3} b^{3} d^{3} + 45 \, a^{4} b^{2} d^{2} e + 18 \, a^{5} b d e^{2} + a^{6} e^{3}\right)} x^{4} + {\left(5 \, a^{4} b^{2} d^{3} + 6 \, a^{5} b d^{2} e + a^{6} d e^{2}\right)} x^{3} + \frac{3}{2} \, {\left(2 \, a^{5} b d^{3} + a^{6} d^{2} e\right)} x^{2}"," ",0,"1/10*b^6*e^3*x^10 + a^6*d^3*x + 1/3*(b^6*d*e^2 + 2*a*b^5*e^3)*x^9 + 3/8*(b^6*d^2*e + 6*a*b^5*d*e^2 + 5*a^2*b^4*e^3)*x^8 + 1/7*(b^6*d^3 + 18*a*b^5*d^2*e + 45*a^2*b^4*d*e^2 + 20*a^3*b^3*e^3)*x^7 + 1/2*(2*a*b^5*d^3 + 15*a^2*b^4*d^2*e + 20*a^3*b^3*d*e^2 + 5*a^4*b^2*e^3)*x^6 + 3/5*(5*a^2*b^4*d^3 + 20*a^3*b^3*d^2*e + 15*a^4*b^2*d*e^2 + 2*a^5*b*e^3)*x^5 + 1/4*(20*a^3*b^3*d^3 + 45*a^4*b^2*d^2*e + 18*a^5*b*d*e^2 + a^6*e^3)*x^4 + (5*a^4*b^2*d^3 + 6*a^5*b*d^2*e + a^6*d*e^2)*x^3 + 3/2*(2*a^5*b*d^3 + a^6*d^2*e)*x^2","B",0
1995,1,234,0,0.414740," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{9} \, b^{6} e^{2} x^{9} + a^{6} d^{2} x + \frac{1}{4} \, {\left(b^{6} d e + 3 \, a b^{5} e^{2}\right)} x^{8} + \frac{1}{7} \, {\left(b^{6} d^{2} + 12 \, a b^{5} d e + 15 \, a^{2} b^{4} e^{2}\right)} x^{7} + \frac{1}{3} \, {\left(3 \, a b^{5} d^{2} + 15 \, a^{2} b^{4} d e + 10 \, a^{3} b^{3} e^{2}\right)} x^{6} + {\left(3 \, a^{2} b^{4} d^{2} + 8 \, a^{3} b^{3} d e + 3 \, a^{4} b^{2} e^{2}\right)} x^{5} + \frac{1}{2} \, {\left(10 \, a^{3} b^{3} d^{2} + 15 \, a^{4} b^{2} d e + 3 \, a^{5} b e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(15 \, a^{4} b^{2} d^{2} + 12 \, a^{5} b d e + a^{6} e^{2}\right)} x^{3} + {\left(3 \, a^{5} b d^{2} + a^{6} d e\right)} x^{2}"," ",0,"1/9*b^6*e^2*x^9 + a^6*d^2*x + 1/4*(b^6*d*e + 3*a*b^5*e^2)*x^8 + 1/7*(b^6*d^2 + 12*a*b^5*d*e + 15*a^2*b^4*e^2)*x^7 + 1/3*(3*a*b^5*d^2 + 15*a^2*b^4*d*e + 10*a^3*b^3*e^2)*x^6 + (3*a^2*b^4*d^2 + 8*a^3*b^3*d*e + 3*a^4*b^2*e^2)*x^5 + 1/2*(10*a^3*b^3*d^2 + 15*a^4*b^2*d*e + 3*a^5*b*e^2)*x^4 + 1/3*(15*a^4*b^2*d^2 + 12*a^5*b*d*e + a^6*e^2)*x^3 + (3*a^5*b*d^2 + a^6*d*e)*x^2","B",0
1996,1,142,0,0.400244," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{8} \, b^{6} e x^{8} + a^{6} d x + \frac{1}{7} \, {\left(b^{6} d + 6 \, a b^{5} e\right)} x^{7} + \frac{1}{2} \, {\left(2 \, a b^{5} d + 5 \, a^{2} b^{4} e\right)} x^{6} + {\left(3 \, a^{2} b^{4} d + 4 \, a^{3} b^{3} e\right)} x^{5} + \frac{5}{4} \, {\left(4 \, a^{3} b^{3} d + 3 \, a^{4} b^{2} e\right)} x^{4} + {\left(5 \, a^{4} b^{2} d + 2 \, a^{5} b e\right)} x^{3} + \frac{1}{2} \, {\left(6 \, a^{5} b d + a^{6} e\right)} x^{2}"," ",0,"1/8*b^6*e*x^8 + a^6*d*x + 1/7*(b^6*d + 6*a*b^5*e)*x^7 + 1/2*(2*a*b^5*d + 5*a^2*b^4*e)*x^6 + (3*a^2*b^4*d + 4*a^3*b^3*e)*x^5 + 5/4*(4*a^3*b^3*d + 3*a^4*b^2*e)*x^4 + (5*a^4*b^2*d + 2*a^5*b*e)*x^3 + 1/2*(6*a^5*b*d + a^6*e)*x^2","B",0
1997,1,64,0,0.397033," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{7} \, b^{6} x^{7} + a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{5} + 5 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{3} + 3 \, a^{5} b x^{2} + a^{6} x"," ",0,"1/7*b^6*x^7 + a*b^5*x^6 + 3*a^2*b^4*x^5 + 5*a^3*b^3*x^4 + 5*a^4*b^2*x^3 + 3*a^5*b*x^2 + a^6*x","B",0
1998,1,351,0,0.406528," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\frac{10 \, b^{6} e^{6} x^{6} - 12 \, {\left(b^{6} d e^{5} - 6 \, a b^{5} e^{6}\right)} x^{5} + 15 \, {\left(b^{6} d^{2} e^{4} - 6 \, a b^{5} d e^{5} + 15 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(b^{6} d^{3} e^{3} - 6 \, a b^{5} d^{2} e^{4} + 15 \, a^{2} b^{4} d e^{5} - 20 \, a^{3} b^{3} e^{6}\right)} x^{3} + 30 \, {\left(b^{6} d^{4} e^{2} - 6 \, a b^{5} d^{3} e^{3} + 15 \, a^{2} b^{4} d^{2} e^{4} - 20 \, a^{3} b^{3} d e^{5} + 15 \, a^{4} b^{2} e^{6}\right)} x^{2} - 60 \, {\left(b^{6} d^{5} e - 6 \, a b^{5} d^{4} e^{2} + 15 \, a^{2} b^{4} d^{3} e^{3} - 20 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5} - 6 \, a^{5} b e^{6}\right)} x + 60 \, {\left(b^{6} d^{6} - 6 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} \log\left(e x + d\right)}{60 \, e^{7}}"," ",0,"1/60*(10*b^6*e^6*x^6 - 12*(b^6*d*e^5 - 6*a*b^5*e^6)*x^5 + 15*(b^6*d^2*e^4 - 6*a*b^5*d*e^5 + 15*a^2*b^4*e^6)*x^4 - 20*(b^6*d^3*e^3 - 6*a*b^5*d^2*e^4 + 15*a^2*b^4*d*e^5 - 20*a^3*b^3*e^6)*x^3 + 30*(b^6*d^4*e^2 - 6*a*b^5*d^3*e^3 + 15*a^2*b^4*d^2*e^4 - 20*a^3*b^3*d*e^5 + 15*a^4*b^2*e^6)*x^2 - 60*(b^6*d^5*e - 6*a*b^5*d^4*e^2 + 15*a^2*b^4*d^3*e^3 - 20*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5 - 6*a^5*b*e^6)*x + 60*(b^6*d^6 - 6*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 + a^6*e^6)*log(e*x + d))/e^7","A",0
1999,1,496,0,0.415773," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{2 \, b^{6} e^{6} x^{6} - 10 \, b^{6} d^{6} + 60 \, a b^{5} d^{5} e - 150 \, a^{2} b^{4} d^{4} e^{2} + 200 \, a^{3} b^{3} d^{3} e^{3} - 150 \, a^{4} b^{2} d^{2} e^{4} + 60 \, a^{5} b d e^{5} - 10 \, a^{6} e^{6} - 3 \, {\left(b^{6} d e^{5} - 5 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(b^{6} d^{2} e^{4} - 5 \, a b^{5} d e^{5} + 10 \, a^{2} b^{4} e^{6}\right)} x^{4} - 10 \, {\left(b^{6} d^{3} e^{3} - 5 \, a b^{5} d^{2} e^{4} + 10 \, a^{2} b^{4} d e^{5} - 10 \, a^{3} b^{3} e^{6}\right)} x^{3} + 30 \, {\left(b^{6} d^{4} e^{2} - 5 \, a b^{5} d^{3} e^{3} + 10 \, a^{2} b^{4} d^{2} e^{4} - 10 \, a^{3} b^{3} d e^{5} + 5 \, a^{4} b^{2} e^{6}\right)} x^{2} + 10 \, {\left(5 \, b^{6} d^{5} e - 24 \, a b^{5} d^{4} e^{2} + 45 \, a^{2} b^{4} d^{3} e^{3} - 40 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5}\right)} x - 60 \, {\left(b^{6} d^{6} - 5 \, a b^{5} d^{5} e + 10 \, a^{2} b^{4} d^{4} e^{2} - 10 \, a^{3} b^{3} d^{3} e^{3} + 5 \, a^{4} b^{2} d^{2} e^{4} - a^{5} b d e^{5} + {\left(b^{6} d^{5} e - 5 \, a b^{5} d^{4} e^{2} + 10 \, a^{2} b^{4} d^{3} e^{3} - 10 \, a^{3} b^{3} d^{2} e^{4} + 5 \, a^{4} b^{2} d e^{5} - a^{5} b e^{6}\right)} x\right)} \log\left(e x + d\right)}{10 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"1/10*(2*b^6*e^6*x^6 - 10*b^6*d^6 + 60*a*b^5*d^5*e - 150*a^2*b^4*d^4*e^2 + 200*a^3*b^3*d^3*e^3 - 150*a^4*b^2*d^2*e^4 + 60*a^5*b*d*e^5 - 10*a^6*e^6 - 3*(b^6*d*e^5 - 5*a*b^5*e^6)*x^5 + 5*(b^6*d^2*e^4 - 5*a*b^5*d*e^5 + 10*a^2*b^4*e^6)*x^4 - 10*(b^6*d^3*e^3 - 5*a*b^5*d^2*e^4 + 10*a^2*b^4*d*e^5 - 10*a^3*b^3*e^6)*x^3 + 30*(b^6*d^4*e^2 - 5*a*b^5*d^3*e^3 + 10*a^2*b^4*d^2*e^4 - 10*a^3*b^3*d*e^5 + 5*a^4*b^2*e^6)*x^2 + 10*(5*b^6*d^5*e - 24*a*b^5*d^4*e^2 + 45*a^2*b^4*d^3*e^3 - 40*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5)*x - 60*(b^6*d^6 - 5*a*b^5*d^5*e + 10*a^2*b^4*d^4*e^2 - 10*a^3*b^3*d^3*e^3 + 5*a^4*b^2*d^2*e^4 - a^5*b*d*e^5 + (b^6*d^5*e - 5*a*b^5*d^4*e^2 + 10*a^2*b^4*d^3*e^3 - 10*a^3*b^3*d^2*e^4 + 5*a^4*b^2*d*e^5 - a^5*b*e^6)*x)*log(e*x + d))/(e^8*x + d*e^7)","A",0
2000,1,548,0,0.432570," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{b^{6} e^{6} x^{6} + 22 \, b^{6} d^{6} - 108 \, a b^{5} d^{5} e + 210 \, a^{2} b^{4} d^{4} e^{2} - 200 \, a^{3} b^{3} d^{3} e^{3} + 90 \, a^{4} b^{2} d^{2} e^{4} - 12 \, a^{5} b d e^{5} - 2 \, a^{6} e^{6} - 2 \, {\left(b^{6} d e^{5} - 4 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(b^{6} d^{2} e^{4} - 4 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(b^{6} d^{3} e^{3} - 4 \, a b^{5} d^{2} e^{4} + 6 \, a^{2} b^{4} d e^{5} - 4 \, a^{3} b^{3} e^{6}\right)} x^{3} - 2 \, {\left(34 \, b^{6} d^{4} e^{2} - 126 \, a b^{5} d^{3} e^{3} + 165 \, a^{2} b^{4} d^{2} e^{4} - 80 \, a^{3} b^{3} d e^{5}\right)} x^{2} - 4 \, {\left(4 \, b^{6} d^{5} e - 6 \, a b^{5} d^{4} e^{2} - 15 \, a^{2} b^{4} d^{3} e^{3} + 40 \, a^{3} b^{3} d^{2} e^{4} - 30 \, a^{4} b^{2} d e^{5} + 6 \, a^{5} b e^{6}\right)} x + 60 \, {\left(b^{6} d^{6} - 4 \, a b^{5} d^{5} e + 6 \, a^{2} b^{4} d^{4} e^{2} - 4 \, a^{3} b^{3} d^{3} e^{3} + a^{4} b^{2} d^{2} e^{4} + {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 2 \, {\left(b^{6} d^{5} e - 4 \, a b^{5} d^{4} e^{2} + 6 \, a^{2} b^{4} d^{3} e^{3} - 4 \, a^{3} b^{3} d^{2} e^{4} + a^{4} b^{2} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"1/4*(b^6*e^6*x^6 + 22*b^6*d^6 - 108*a*b^5*d^5*e + 210*a^2*b^4*d^4*e^2 - 200*a^3*b^3*d^3*e^3 + 90*a^4*b^2*d^2*e^4 - 12*a^5*b*d*e^5 - 2*a^6*e^6 - 2*(b^6*d*e^5 - 4*a*b^5*e^6)*x^5 + 5*(b^6*d^2*e^4 - 4*a*b^5*d*e^5 + 6*a^2*b^4*e^6)*x^4 - 20*(b^6*d^3*e^3 - 4*a*b^5*d^2*e^4 + 6*a^2*b^4*d*e^5 - 4*a^3*b^3*e^6)*x^3 - 2*(34*b^6*d^4*e^2 - 126*a*b^5*d^3*e^3 + 165*a^2*b^4*d^2*e^4 - 80*a^3*b^3*d*e^5)*x^2 - 4*(4*b^6*d^5*e - 6*a*b^5*d^4*e^2 - 15*a^2*b^4*d^3*e^3 + 40*a^3*b^3*d^2*e^4 - 30*a^4*b^2*d*e^5 + 6*a^5*b*e^6)*x + 60*(b^6*d^6 - 4*a*b^5*d^5*e + 6*a^2*b^4*d^4*e^2 - 4*a^3*b^3*d^3*e^3 + a^4*b^2*d^2*e^4 + (b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 2*(b^6*d^5*e - 4*a*b^5*d^4*e^2 + 6*a^2*b^4*d^3*e^3 - 4*a^3*b^3*d^2*e^4 + a^4*b^2*d*e^5)*x)*log(e*x + d))/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","B",0
2001,1,576,0,0.412364," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{b^{6} e^{6} x^{6} - 37 \, b^{6} d^{6} + 141 \, a b^{5} d^{5} e - 195 \, a^{2} b^{4} d^{4} e^{2} + 110 \, a^{3} b^{3} d^{3} e^{3} - 15 \, a^{4} b^{2} d^{2} e^{4} - 3 \, a^{5} b d e^{5} - a^{6} e^{6} - 3 \, {\left(b^{6} d e^{5} - 3 \, a b^{5} e^{6}\right)} x^{5} + 15 \, {\left(b^{6} d^{2} e^{4} - 3 \, a b^{5} d e^{5} + 3 \, a^{2} b^{4} e^{6}\right)} x^{4} + {\left(73 \, b^{6} d^{3} e^{3} - 189 \, a b^{5} d^{2} e^{4} + 135 \, a^{2} b^{4} d e^{5}\right)} x^{3} + 3 \, {\left(13 \, b^{6} d^{4} e^{2} - 9 \, a b^{5} d^{3} e^{3} - 45 \, a^{2} b^{4} d^{2} e^{4} + 60 \, a^{3} b^{3} d e^{5} - 15 \, a^{4} b^{2} e^{6}\right)} x^{2} - 3 \, {\left(17 \, b^{6} d^{5} e - 81 \, a b^{5} d^{4} e^{2} + 135 \, a^{2} b^{4} d^{3} e^{3} - 90 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5} + 3 \, a^{5} b e^{6}\right)} x - 60 \, {\left(b^{6} d^{6} - 3 \, a b^{5} d^{5} e + 3 \, a^{2} b^{4} d^{4} e^{2} - a^{3} b^{3} d^{3} e^{3} + {\left(b^{6} d^{3} e^{3} - 3 \, a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} - a^{3} b^{3} e^{6}\right)} x^{3} + 3 \, {\left(b^{6} d^{4} e^{2} - 3 \, a b^{5} d^{3} e^{3} + 3 \, a^{2} b^{4} d^{2} e^{4} - a^{3} b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 3 \, a^{2} b^{4} d^{3} e^{3} - a^{3} b^{3} d^{2} e^{4}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"1/3*(b^6*e^6*x^6 - 37*b^6*d^6 + 141*a*b^5*d^5*e - 195*a^2*b^4*d^4*e^2 + 110*a^3*b^3*d^3*e^3 - 15*a^4*b^2*d^2*e^4 - 3*a^5*b*d*e^5 - a^6*e^6 - 3*(b^6*d*e^5 - 3*a*b^5*e^6)*x^5 + 15*(b^6*d^2*e^4 - 3*a*b^5*d*e^5 + 3*a^2*b^4*e^6)*x^4 + (73*b^6*d^3*e^3 - 189*a*b^5*d^2*e^4 + 135*a^2*b^4*d*e^5)*x^3 + 3*(13*b^6*d^4*e^2 - 9*a*b^5*d^3*e^3 - 45*a^2*b^4*d^2*e^4 + 60*a^3*b^3*d*e^5 - 15*a^4*b^2*e^6)*x^2 - 3*(17*b^6*d^5*e - 81*a*b^5*d^4*e^2 + 135*a^2*b^4*d^3*e^3 - 90*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5 + 3*a^5*b*e^6)*x - 60*(b^6*d^6 - 3*a*b^5*d^5*e + 3*a^2*b^4*d^4*e^2 - a^3*b^3*d^3*e^3 + (b^6*d^3*e^3 - 3*a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 - a^3*b^3*e^6)*x^3 + 3*(b^6*d^4*e^2 - 3*a*b^5*d^3*e^3 + 3*a^2*b^4*d^2*e^4 - a^3*b^3*d*e^5)*x^2 + 3*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 3*a^2*b^4*d^3*e^3 - a^3*b^3*d^2*e^4)*x)*log(e*x + d))/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","B",0
2002,1,571,0,0.427401," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{2 \, b^{6} e^{6} x^{6} + 57 \, b^{6} d^{6} - 154 \, a b^{5} d^{5} e + 125 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} - 5 \, a^{4} b^{2} d^{2} e^{4} - 2 \, a^{5} b d e^{5} - a^{6} e^{6} - 12 \, {\left(b^{6} d e^{5} - 2 \, a b^{5} e^{6}\right)} x^{5} - 4 \, {\left(17 \, b^{6} d^{2} e^{4} - 24 \, a b^{5} d e^{5}\right)} x^{4} - 16 \, {\left(2 \, b^{6} d^{3} e^{3} + 6 \, a b^{5} d^{2} e^{4} - 15 \, a^{2} b^{4} d e^{5} + 5 \, a^{3} b^{3} e^{6}\right)} x^{3} + 6 \, {\left(22 \, b^{6} d^{4} e^{2} - 84 \, a b^{5} d^{3} e^{3} + 90 \, a^{2} b^{4} d^{2} e^{4} - 20 \, a^{3} b^{3} d e^{5} - 5 \, a^{4} b^{2} e^{6}\right)} x^{2} + 4 \, {\left(42 \, b^{6} d^{5} e - 124 \, a b^{5} d^{4} e^{2} + 110 \, a^{2} b^{4} d^{3} e^{3} - 20 \, a^{3} b^{3} d^{2} e^{4} - 5 \, a^{4} b^{2} d e^{5} - 2 \, a^{5} b e^{6}\right)} x + 60 \, {\left(b^{6} d^{6} - 2 \, a b^{5} d^{5} e + a^{2} b^{4} d^{4} e^{2} + {\left(b^{6} d^{2} e^{4} - 2 \, a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + 4 \, {\left(b^{6} d^{3} e^{3} - 2 \, a b^{5} d^{2} e^{4} + a^{2} b^{4} d e^{5}\right)} x^{3} + 6 \, {\left(b^{6} d^{4} e^{2} - 2 \, a b^{5} d^{3} e^{3} + a^{2} b^{4} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(b^{6} d^{5} e - 2 \, a b^{5} d^{4} e^{2} + a^{2} b^{4} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{11} x^{4} + 4 \, d e^{10} x^{3} + 6 \, d^{2} e^{9} x^{2} + 4 \, d^{3} e^{8} x + d^{4} e^{7}\right)}}"," ",0,"1/4*(2*b^6*e^6*x^6 + 57*b^6*d^6 - 154*a*b^5*d^5*e + 125*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 - 5*a^4*b^2*d^2*e^4 - 2*a^5*b*d*e^5 - a^6*e^6 - 12*(b^6*d*e^5 - 2*a*b^5*e^6)*x^5 - 4*(17*b^6*d^2*e^4 - 24*a*b^5*d*e^5)*x^4 - 16*(2*b^6*d^3*e^3 + 6*a*b^5*d^2*e^4 - 15*a^2*b^4*d*e^5 + 5*a^3*b^3*e^6)*x^3 + 6*(22*b^6*d^4*e^2 - 84*a*b^5*d^3*e^3 + 90*a^2*b^4*d^2*e^4 - 20*a^3*b^3*d*e^5 - 5*a^4*b^2*e^6)*x^2 + 4*(42*b^6*d^5*e - 124*a*b^5*d^4*e^2 + 110*a^2*b^4*d^3*e^3 - 20*a^3*b^3*d^2*e^4 - 5*a^4*b^2*d*e^5 - 2*a^5*b*e^6)*x + 60*(b^6*d^6 - 2*a*b^5*d^5*e + a^2*b^4*d^4*e^2 + (b^6*d^2*e^4 - 2*a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + 4*(b^6*d^3*e^3 - 2*a*b^5*d^2*e^4 + a^2*b^4*d*e^5)*x^3 + 6*(b^6*d^4*e^2 - 2*a*b^5*d^3*e^3 + a^2*b^4*d^2*e^4)*x^2 + 4*(b^6*d^5*e - 2*a*b^5*d^4*e^2 + a^2*b^4*d^3*e^3)*x)*log(e*x + d))/(e^11*x^4 + 4*d*e^10*x^3 + 6*d^2*e^9*x^2 + 4*d^3*e^8*x + d^4*e^7)","B",0
2003,1,542,0,0.421299," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^6,x, algorithm=""fricas"")","\frac{10 \, b^{6} e^{6} x^{6} + 50 \, b^{6} d e^{5} x^{5} - 87 \, b^{6} d^{6} + 137 \, a b^{5} d^{5} e - 30 \, a^{2} b^{4} d^{4} e^{2} - 10 \, a^{3} b^{3} d^{3} e^{3} - 5 \, a^{4} b^{2} d^{2} e^{4} - 3 \, a^{5} b d e^{5} - 2 \, a^{6} e^{6} - 50 \, {\left(b^{6} d^{2} e^{4} - 6 \, a b^{5} d e^{5} + 3 \, a^{2} b^{4} e^{6}\right)} x^{4} - 100 \, {\left(4 \, b^{6} d^{3} e^{3} - 9 \, a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} - 50 \, {\left(12 \, b^{6} d^{4} e^{2} - 22 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} + 2 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} - 5 \, {\left(75 \, b^{6} d^{5} e - 125 \, a b^{5} d^{4} e^{2} + 30 \, a^{2} b^{4} d^{3} e^{3} + 10 \, a^{3} b^{3} d^{2} e^{4} + 5 \, a^{4} b^{2} d e^{5} + 3 \, a^{5} b e^{6}\right)} x - 60 \, {\left(b^{6} d^{6} - a b^{5} d^{5} e + {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(b^{6} d^{2} e^{4} - a b^{5} d e^{5}\right)} x^{4} + 10 \, {\left(b^{6} d^{3} e^{3} - a b^{5} d^{2} e^{4}\right)} x^{3} + 10 \, {\left(b^{6} d^{4} e^{2} - a b^{5} d^{3} e^{3}\right)} x^{2} + 5 \, {\left(b^{6} d^{5} e - a b^{5} d^{4} e^{2}\right)} x\right)} \log\left(e x + d\right)}{10 \, {\left(e^{12} x^{5} + 5 \, d e^{11} x^{4} + 10 \, d^{2} e^{10} x^{3} + 10 \, d^{3} e^{9} x^{2} + 5 \, d^{4} e^{8} x + d^{5} e^{7}\right)}}"," ",0,"1/10*(10*b^6*e^6*x^6 + 50*b^6*d*e^5*x^5 - 87*b^6*d^6 + 137*a*b^5*d^5*e - 30*a^2*b^4*d^4*e^2 - 10*a^3*b^3*d^3*e^3 - 5*a^4*b^2*d^2*e^4 - 3*a^5*b*d*e^5 - 2*a^6*e^6 - 50*(b^6*d^2*e^4 - 6*a*b^5*d*e^5 + 3*a^2*b^4*e^6)*x^4 - 100*(4*b^6*d^3*e^3 - 9*a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 - 50*(12*b^6*d^4*e^2 - 22*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 + 2*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 - 5*(75*b^6*d^5*e - 125*a*b^5*d^4*e^2 + 30*a^2*b^4*d^3*e^3 + 10*a^3*b^3*d^2*e^4 + 5*a^4*b^2*d*e^5 + 3*a^5*b*e^6)*x - 60*(b^6*d^6 - a*b^5*d^5*e + (b^6*d*e^5 - a*b^5*e^6)*x^5 + 5*(b^6*d^2*e^4 - a*b^5*d*e^5)*x^4 + 10*(b^6*d^3*e^3 - a*b^5*d^2*e^4)*x^3 + 10*(b^6*d^4*e^2 - a*b^5*d^3*e^3)*x^2 + 5*(b^6*d^5*e - a*b^5*d^4*e^2)*x)*log(e*x + d))/(e^12*x^5 + 5*d*e^11*x^4 + 10*d^2*e^10*x^3 + 10*d^3*e^9*x^2 + 5*d^4*e^8*x + d^5*e^7)","B",0
2004,1,492,0,0.417598," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^7,x, algorithm=""fricas"")","\frac{147 \, b^{6} d^{6} - 60 \, a b^{5} d^{5} e - 30 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} - 15 \, a^{4} b^{2} d^{2} e^{4} - 12 \, a^{5} b d e^{5} - 10 \, a^{6} e^{6} + 360 \, {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 450 \, {\left(3 \, b^{6} d^{2} e^{4} - 2 \, a b^{5} d e^{5} - a^{2} b^{4} e^{6}\right)} x^{4} + 200 \, {\left(11 \, b^{6} d^{3} e^{3} - 6 \, a b^{5} d^{2} e^{4} - 3 \, a^{2} b^{4} d e^{5} - 2 \, a^{3} b^{3} e^{6}\right)} x^{3} + 75 \, {\left(25 \, b^{6} d^{4} e^{2} - 12 \, a b^{5} d^{3} e^{3} - 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} - 3 \, a^{4} b^{2} e^{6}\right)} x^{2} + 6 \, {\left(137 \, b^{6} d^{5} e - 60 \, a b^{5} d^{4} e^{2} - 30 \, a^{2} b^{4} d^{3} e^{3} - 20 \, a^{3} b^{3} d^{2} e^{4} - 15 \, a^{4} b^{2} d e^{5} - 12 \, a^{5} b e^{6}\right)} x + 60 \, {\left(b^{6} e^{6} x^{6} + 6 \, b^{6} d e^{5} x^{5} + 15 \, b^{6} d^{2} e^{4} x^{4} + 20 \, b^{6} d^{3} e^{3} x^{3} + 15 \, b^{6} d^{4} e^{2} x^{2} + 6 \, b^{6} d^{5} e x + b^{6} d^{6}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{13} x^{6} + 6 \, d e^{12} x^{5} + 15 \, d^{2} e^{11} x^{4} + 20 \, d^{3} e^{10} x^{3} + 15 \, d^{4} e^{9} x^{2} + 6 \, d^{5} e^{8} x + d^{6} e^{7}\right)}}"," ",0,"1/60*(147*b^6*d^6 - 60*a*b^5*d^5*e - 30*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 - 15*a^4*b^2*d^2*e^4 - 12*a^5*b*d*e^5 - 10*a^6*e^6 + 360*(b^6*d*e^5 - a*b^5*e^6)*x^5 + 450*(3*b^6*d^2*e^4 - 2*a*b^5*d*e^5 - a^2*b^4*e^6)*x^4 + 200*(11*b^6*d^3*e^3 - 6*a*b^5*d^2*e^4 - 3*a^2*b^4*d*e^5 - 2*a^3*b^3*e^6)*x^3 + 75*(25*b^6*d^4*e^2 - 12*a*b^5*d^3*e^3 - 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 - 3*a^4*b^2*e^6)*x^2 + 6*(137*b^6*d^5*e - 60*a*b^5*d^4*e^2 - 30*a^2*b^4*d^3*e^3 - 20*a^3*b^3*d^2*e^4 - 15*a^4*b^2*d*e^5 - 12*a^5*b*e^6)*x + 60*(b^6*e^6*x^6 + 6*b^6*d*e^5*x^5 + 15*b^6*d^2*e^4*x^4 + 20*b^6*d^3*e^3*x^3 + 15*b^6*d^4*e^2*x^2 + 6*b^6*d^5*e*x + b^6*d^6)*log(e*x + d))/(e^13*x^6 + 6*d*e^12*x^5 + 15*d^2*e^11*x^4 + 20*d^3*e^10*x^3 + 15*d^4*e^9*x^2 + 6*d^5*e^8*x + d^6*e^7)","A",0
2005,1,398,0,0.419315," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{7 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + a b^{5} d^{5} e + a^{2} b^{4} d^{4} e^{2} + a^{3} b^{3} d^{3} e^{3} + a^{4} b^{2} d^{2} e^{4} + a^{5} b d e^{5} + a^{6} e^{6} + 21 \, {\left(b^{6} d e^{5} + a b^{5} e^{6}\right)} x^{5} + 35 \, {\left(b^{6} d^{2} e^{4} + a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + 35 \, {\left(b^{6} d^{3} e^{3} + a b^{5} d^{2} e^{4} + a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + 21 \, {\left(b^{6} d^{4} e^{2} + a b^{5} d^{3} e^{3} + a^{2} b^{4} d^{2} e^{4} + a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 7 \, {\left(b^{6} d^{5} e + a b^{5} d^{4} e^{2} + a^{2} b^{4} d^{3} e^{3} + a^{3} b^{3} d^{2} e^{4} + a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x}{7 \, {\left(e^{14} x^{7} + 7 \, d e^{13} x^{6} + 21 \, d^{2} e^{12} x^{5} + 35 \, d^{3} e^{11} x^{4} + 35 \, d^{4} e^{10} x^{3} + 21 \, d^{5} e^{9} x^{2} + 7 \, d^{6} e^{8} x + d^{7} e^{7}\right)}}"," ",0,"-1/7*(7*b^6*e^6*x^6 + b^6*d^6 + a*b^5*d^5*e + a^2*b^4*d^4*e^2 + a^3*b^3*d^3*e^3 + a^4*b^2*d^2*e^4 + a^5*b*d*e^5 + a^6*e^6 + 21*(b^6*d*e^5 + a*b^5*e^6)*x^5 + 35*(b^6*d^2*e^4 + a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + 35*(b^6*d^3*e^3 + a*b^5*d^2*e^4 + a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 + 21*(b^6*d^4*e^2 + a*b^5*d^3*e^3 + a^2*b^4*d^2*e^4 + a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 7*(b^6*d^5*e + a*b^5*d^4*e^2 + a^2*b^4*d^3*e^3 + a^3*b^3*d^2*e^4 + a^4*b^2*d*e^5 + a^5*b*e^6)*x)/(e^14*x^7 + 7*d*e^13*x^6 + 21*d^2*e^12*x^5 + 35*d^3*e^11*x^4 + 35*d^4*e^10*x^3 + 21*d^5*e^9*x^2 + 7*d^6*e^8*x + d^7*e^7)","B",0
2006,1,430,0,0.414363," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{28 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 2 \, a b^{5} d^{5} e + 3 \, a^{2} b^{4} d^{4} e^{2} + 4 \, a^{3} b^{3} d^{3} e^{3} + 5 \, a^{4} b^{2} d^{2} e^{4} + 6 \, a^{5} b d e^{5} + 7 \, a^{6} e^{6} + 56 \, {\left(b^{6} d e^{5} + 2 \, a b^{5} e^{6}\right)} x^{5} + 70 \, {\left(b^{6} d^{2} e^{4} + 2 \, a b^{5} d e^{5} + 3 \, a^{2} b^{4} e^{6}\right)} x^{4} + 56 \, {\left(b^{6} d^{3} e^{3} + 2 \, a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} + 4 \, a^{3} b^{3} e^{6}\right)} x^{3} + 28 \, {\left(b^{6} d^{4} e^{2} + 2 \, a b^{5} d^{3} e^{3} + 3 \, a^{2} b^{4} d^{2} e^{4} + 4 \, a^{3} b^{3} d e^{5} + 5 \, a^{4} b^{2} e^{6}\right)} x^{2} + 8 \, {\left(b^{6} d^{5} e + 2 \, a b^{5} d^{4} e^{2} + 3 \, a^{2} b^{4} d^{3} e^{3} + 4 \, a^{3} b^{3} d^{2} e^{4} + 5 \, a^{4} b^{2} d e^{5} + 6 \, a^{5} b e^{6}\right)} x}{56 \, {\left(e^{15} x^{8} + 8 \, d e^{14} x^{7} + 28 \, d^{2} e^{13} x^{6} + 56 \, d^{3} e^{12} x^{5} + 70 \, d^{4} e^{11} x^{4} + 56 \, d^{5} e^{10} x^{3} + 28 \, d^{6} e^{9} x^{2} + 8 \, d^{7} e^{8} x + d^{8} e^{7}\right)}}"," ",0,"-1/56*(28*b^6*e^6*x^6 + b^6*d^6 + 2*a*b^5*d^5*e + 3*a^2*b^4*d^4*e^2 + 4*a^3*b^3*d^3*e^3 + 5*a^4*b^2*d^2*e^4 + 6*a^5*b*d*e^5 + 7*a^6*e^6 + 56*(b^6*d*e^5 + 2*a*b^5*e^6)*x^5 + 70*(b^6*d^2*e^4 + 2*a*b^5*d*e^5 + 3*a^2*b^4*e^6)*x^4 + 56*(b^6*d^3*e^3 + 2*a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 + 4*a^3*b^3*e^6)*x^3 + 28*(b^6*d^4*e^2 + 2*a*b^5*d^3*e^3 + 3*a^2*b^4*d^2*e^4 + 4*a^3*b^3*d*e^5 + 5*a^4*b^2*e^6)*x^2 + 8*(b^6*d^5*e + 2*a*b^5*d^4*e^2 + 3*a^2*b^4*d^3*e^3 + 4*a^3*b^3*d^2*e^4 + 5*a^4*b^2*d*e^5 + 6*a^5*b*e^6)*x)/(e^15*x^8 + 8*d*e^14*x^7 + 28*d^2*e^13*x^6 + 56*d^3*e^12*x^5 + 70*d^4*e^11*x^4 + 56*d^5*e^10*x^3 + 28*d^6*e^9*x^2 + 8*d^7*e^8*x + d^8*e^7)","B",0
2007,1,441,0,0.414428," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{84 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 3 \, a b^{5} d^{5} e + 6 \, a^{2} b^{4} d^{4} e^{2} + 10 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} + 21 \, a^{5} b d e^{5} + 28 \, a^{6} e^{6} + 126 \, {\left(b^{6} d e^{5} + 3 \, a b^{5} e^{6}\right)} x^{5} + 126 \, {\left(b^{6} d^{2} e^{4} + 3 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right)} x^{4} + 84 \, {\left(b^{6} d^{3} e^{3} + 3 \, a b^{5} d^{2} e^{4} + 6 \, a^{2} b^{4} d e^{5} + 10 \, a^{3} b^{3} e^{6}\right)} x^{3} + 36 \, {\left(b^{6} d^{4} e^{2} + 3 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} + 10 \, a^{3} b^{3} d e^{5} + 15 \, a^{4} b^{2} e^{6}\right)} x^{2} + 9 \, {\left(b^{6} d^{5} e + 3 \, a b^{5} d^{4} e^{2} + 6 \, a^{2} b^{4} d^{3} e^{3} + 10 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5} + 21 \, a^{5} b e^{6}\right)} x}{252 \, {\left(e^{16} x^{9} + 9 \, d e^{15} x^{8} + 36 \, d^{2} e^{14} x^{7} + 84 \, d^{3} e^{13} x^{6} + 126 \, d^{4} e^{12} x^{5} + 126 \, d^{5} e^{11} x^{4} + 84 \, d^{6} e^{10} x^{3} + 36 \, d^{7} e^{9} x^{2} + 9 \, d^{8} e^{8} x + d^{9} e^{7}\right)}}"," ",0,"-1/252*(84*b^6*e^6*x^6 + b^6*d^6 + 3*a*b^5*d^5*e + 6*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 + 21*a^5*b*d*e^5 + 28*a^6*e^6 + 126*(b^6*d*e^5 + 3*a*b^5*e^6)*x^5 + 126*(b^6*d^2*e^4 + 3*a*b^5*d*e^5 + 6*a^2*b^4*e^6)*x^4 + 84*(b^6*d^3*e^3 + 3*a*b^5*d^2*e^4 + 6*a^2*b^4*d*e^5 + 10*a^3*b^3*e^6)*x^3 + 36*(b^6*d^4*e^2 + 3*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 + 10*a^3*b^3*d*e^5 + 15*a^4*b^2*e^6)*x^2 + 9*(b^6*d^5*e + 3*a*b^5*d^4*e^2 + 6*a^2*b^4*d^3*e^3 + 10*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5 + 21*a^5*b*e^6)*x)/(e^16*x^9 + 9*d*e^15*x^8 + 36*d^2*e^14*x^7 + 84*d^3*e^13*x^6 + 126*d^4*e^12*x^5 + 126*d^5*e^11*x^4 + 84*d^6*e^10*x^3 + 36*d^7*e^9*x^2 + 9*d^8*e^8*x + d^9*e^7)","B",0
2008,1,452,0,0.452836," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{210 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 4 \, a b^{5} d^{5} e + 10 \, a^{2} b^{4} d^{4} e^{2} + 20 \, a^{3} b^{3} d^{3} e^{3} + 35 \, a^{4} b^{2} d^{2} e^{4} + 56 \, a^{5} b d e^{5} + 84 \, a^{6} e^{6} + 252 \, {\left(b^{6} d e^{5} + 4 \, a b^{5} e^{6}\right)} x^{5} + 210 \, {\left(b^{6} d^{2} e^{4} + 4 \, a b^{5} d e^{5} + 10 \, a^{2} b^{4} e^{6}\right)} x^{4} + 120 \, {\left(b^{6} d^{3} e^{3} + 4 \, a b^{5} d^{2} e^{4} + 10 \, a^{2} b^{4} d e^{5} + 20 \, a^{3} b^{3} e^{6}\right)} x^{3} + 45 \, {\left(b^{6} d^{4} e^{2} + 4 \, a b^{5} d^{3} e^{3} + 10 \, a^{2} b^{4} d^{2} e^{4} + 20 \, a^{3} b^{3} d e^{5} + 35 \, a^{4} b^{2} e^{6}\right)} x^{2} + 10 \, {\left(b^{6} d^{5} e + 4 \, a b^{5} d^{4} e^{2} + 10 \, a^{2} b^{4} d^{3} e^{3} + 20 \, a^{3} b^{3} d^{2} e^{4} + 35 \, a^{4} b^{2} d e^{5} + 56 \, a^{5} b e^{6}\right)} x}{840 \, {\left(e^{17} x^{10} + 10 \, d e^{16} x^{9} + 45 \, d^{2} e^{15} x^{8} + 120 \, d^{3} e^{14} x^{7} + 210 \, d^{4} e^{13} x^{6} + 252 \, d^{5} e^{12} x^{5} + 210 \, d^{6} e^{11} x^{4} + 120 \, d^{7} e^{10} x^{3} + 45 \, d^{8} e^{9} x^{2} + 10 \, d^{9} e^{8} x + d^{10} e^{7}\right)}}"," ",0,"-1/840*(210*b^6*e^6*x^6 + b^6*d^6 + 4*a*b^5*d^5*e + 10*a^2*b^4*d^4*e^2 + 20*a^3*b^3*d^3*e^3 + 35*a^4*b^2*d^2*e^4 + 56*a^5*b*d*e^5 + 84*a^6*e^6 + 252*(b^6*d*e^5 + 4*a*b^5*e^6)*x^5 + 210*(b^6*d^2*e^4 + 4*a*b^5*d*e^5 + 10*a^2*b^4*e^6)*x^4 + 120*(b^6*d^3*e^3 + 4*a*b^5*d^2*e^4 + 10*a^2*b^4*d*e^5 + 20*a^3*b^3*e^6)*x^3 + 45*(b^6*d^4*e^2 + 4*a*b^5*d^3*e^3 + 10*a^2*b^4*d^2*e^4 + 20*a^3*b^3*d*e^5 + 35*a^4*b^2*e^6)*x^2 + 10*(b^6*d^5*e + 4*a*b^5*d^4*e^2 + 10*a^2*b^4*d^3*e^3 + 20*a^3*b^3*d^2*e^4 + 35*a^4*b^2*d*e^5 + 56*a^5*b*e^6)*x)/(e^17*x^10 + 10*d*e^16*x^9 + 45*d^2*e^15*x^8 + 120*d^3*e^14*x^7 + 210*d^4*e^13*x^6 + 252*d^5*e^12*x^5 + 210*d^6*e^11*x^4 + 120*d^7*e^10*x^3 + 45*d^8*e^9*x^2 + 10*d^9*e^8*x + d^10*e^7)","B",0
2009,1,463,0,0.433696," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{462 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 5 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} + 35 \, a^{3} b^{3} d^{3} e^{3} + 70 \, a^{4} b^{2} d^{2} e^{4} + 126 \, a^{5} b d e^{5} + 210 \, a^{6} e^{6} + 462 \, {\left(b^{6} d e^{5} + 5 \, a b^{5} e^{6}\right)} x^{5} + 330 \, {\left(b^{6} d^{2} e^{4} + 5 \, a b^{5} d e^{5} + 15 \, a^{2} b^{4} e^{6}\right)} x^{4} + 165 \, {\left(b^{6} d^{3} e^{3} + 5 \, a b^{5} d^{2} e^{4} + 15 \, a^{2} b^{4} d e^{5} + 35 \, a^{3} b^{3} e^{6}\right)} x^{3} + 55 \, {\left(b^{6} d^{4} e^{2} + 5 \, a b^{5} d^{3} e^{3} + 15 \, a^{2} b^{4} d^{2} e^{4} + 35 \, a^{3} b^{3} d e^{5} + 70 \, a^{4} b^{2} e^{6}\right)} x^{2} + 11 \, {\left(b^{6} d^{5} e + 5 \, a b^{5} d^{4} e^{2} + 15 \, a^{2} b^{4} d^{3} e^{3} + 35 \, a^{3} b^{3} d^{2} e^{4} + 70 \, a^{4} b^{2} d e^{5} + 126 \, a^{5} b e^{6}\right)} x}{2310 \, {\left(e^{18} x^{11} + 11 \, d e^{17} x^{10} + 55 \, d^{2} e^{16} x^{9} + 165 \, d^{3} e^{15} x^{8} + 330 \, d^{4} e^{14} x^{7} + 462 \, d^{5} e^{13} x^{6} + 462 \, d^{6} e^{12} x^{5} + 330 \, d^{7} e^{11} x^{4} + 165 \, d^{8} e^{10} x^{3} + 55 \, d^{9} e^{9} x^{2} + 11 \, d^{10} e^{8} x + d^{11} e^{7}\right)}}"," ",0,"-1/2310*(462*b^6*e^6*x^6 + b^6*d^6 + 5*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 + 35*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^5 + 210*a^6*e^6 + 462*(b^6*d*e^5 + 5*a*b^5*e^6)*x^5 + 330*(b^6*d^2*e^4 + 5*a*b^5*d*e^5 + 15*a^2*b^4*e^6)*x^4 + 165*(b^6*d^3*e^3 + 5*a*b^5*d^2*e^4 + 15*a^2*b^4*d*e^5 + 35*a^3*b^3*e^6)*x^3 + 55*(b^6*d^4*e^2 + 5*a*b^5*d^3*e^3 + 15*a^2*b^4*d^2*e^4 + 35*a^3*b^3*d*e^5 + 70*a^4*b^2*e^6)*x^2 + 11*(b^6*d^5*e + 5*a*b^5*d^4*e^2 + 15*a^2*b^4*d^3*e^3 + 35*a^3*b^3*d^2*e^4 + 70*a^4*b^2*d*e^5 + 126*a^5*b*e^6)*x)/(e^18*x^11 + 11*d*e^17*x^10 + 55*d^2*e^16*x^9 + 165*d^3*e^15*x^8 + 330*d^4*e^14*x^7 + 462*d^5*e^13*x^6 + 462*d^6*e^12*x^5 + 330*d^7*e^11*x^4 + 165*d^8*e^10*x^3 + 55*d^9*e^9*x^2 + 11*d^10*e^8*x + d^11*e^7)","A",0
2010,1,474,0,0.435259," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^13,x, algorithm=""fricas"")","-\frac{924 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 6 \, a b^{5} d^{5} e + 21 \, a^{2} b^{4} d^{4} e^{2} + 56 \, a^{3} b^{3} d^{3} e^{3} + 126 \, a^{4} b^{2} d^{2} e^{4} + 252 \, a^{5} b d e^{5} + 462 \, a^{6} e^{6} + 792 \, {\left(b^{6} d e^{5} + 6 \, a b^{5} e^{6}\right)} x^{5} + 495 \, {\left(b^{6} d^{2} e^{4} + 6 \, a b^{5} d e^{5} + 21 \, a^{2} b^{4} e^{6}\right)} x^{4} + 220 \, {\left(b^{6} d^{3} e^{3} + 6 \, a b^{5} d^{2} e^{4} + 21 \, a^{2} b^{4} d e^{5} + 56 \, a^{3} b^{3} e^{6}\right)} x^{3} + 66 \, {\left(b^{6} d^{4} e^{2} + 6 \, a b^{5} d^{3} e^{3} + 21 \, a^{2} b^{4} d^{2} e^{4} + 56 \, a^{3} b^{3} d e^{5} + 126 \, a^{4} b^{2} e^{6}\right)} x^{2} + 12 \, {\left(b^{6} d^{5} e + 6 \, a b^{5} d^{4} e^{2} + 21 \, a^{2} b^{4} d^{3} e^{3} + 56 \, a^{3} b^{3} d^{2} e^{4} + 126 \, a^{4} b^{2} d e^{5} + 252 \, a^{5} b e^{6}\right)} x}{5544 \, {\left(e^{19} x^{12} + 12 \, d e^{18} x^{11} + 66 \, d^{2} e^{17} x^{10} + 220 \, d^{3} e^{16} x^{9} + 495 \, d^{4} e^{15} x^{8} + 792 \, d^{5} e^{14} x^{7} + 924 \, d^{6} e^{13} x^{6} + 792 \, d^{7} e^{12} x^{5} + 495 \, d^{8} e^{11} x^{4} + 220 \, d^{9} e^{10} x^{3} + 66 \, d^{10} e^{9} x^{2} + 12 \, d^{11} e^{8} x + d^{12} e^{7}\right)}}"," ",0,"-1/5544*(924*b^6*e^6*x^6 + b^6*d^6 + 6*a*b^5*d^5*e + 21*a^2*b^4*d^4*e^2 + 56*a^3*b^3*d^3*e^3 + 126*a^4*b^2*d^2*e^4 + 252*a^5*b*d*e^5 + 462*a^6*e^6 + 792*(b^6*d*e^5 + 6*a*b^5*e^6)*x^5 + 495*(b^6*d^2*e^4 + 6*a*b^5*d*e^5 + 21*a^2*b^4*e^6)*x^4 + 220*(b^6*d^3*e^3 + 6*a*b^5*d^2*e^4 + 21*a^2*b^4*d*e^5 + 56*a^3*b^3*e^6)*x^3 + 66*(b^6*d^4*e^2 + 6*a*b^5*d^3*e^3 + 21*a^2*b^4*d^2*e^4 + 56*a^3*b^3*d*e^5 + 126*a^4*b^2*e^6)*x^2 + 12*(b^6*d^5*e + 6*a*b^5*d^4*e^2 + 21*a^2*b^4*d^3*e^3 + 56*a^3*b^3*d^2*e^4 + 126*a^4*b^2*d*e^5 + 252*a^5*b*e^6)*x)/(e^19*x^12 + 12*d*e^18*x^11 + 66*d^2*e^17*x^10 + 220*d^3*e^16*x^9 + 495*d^4*e^15*x^8 + 792*d^5*e^14*x^7 + 924*d^6*e^13*x^6 + 792*d^7*e^12*x^5 + 495*d^8*e^11*x^4 + 220*d^9*e^10*x^3 + 66*d^10*e^9*x^2 + 12*d^11*e^8*x + d^12*e^7)","A",0
2011,1,485,0,0.410203," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^14,x, algorithm=""fricas"")","-\frac{1716 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 7 \, a b^{5} d^{5} e + 28 \, a^{2} b^{4} d^{4} e^{2} + 84 \, a^{3} b^{3} d^{3} e^{3} + 210 \, a^{4} b^{2} d^{2} e^{4} + 462 \, a^{5} b d e^{5} + 924 \, a^{6} e^{6} + 1287 \, {\left(b^{6} d e^{5} + 7 \, a b^{5} e^{6}\right)} x^{5} + 715 \, {\left(b^{6} d^{2} e^{4} + 7 \, a b^{5} d e^{5} + 28 \, a^{2} b^{4} e^{6}\right)} x^{4} + 286 \, {\left(b^{6} d^{3} e^{3} + 7 \, a b^{5} d^{2} e^{4} + 28 \, a^{2} b^{4} d e^{5} + 84 \, a^{3} b^{3} e^{6}\right)} x^{3} + 78 \, {\left(b^{6} d^{4} e^{2} + 7 \, a b^{5} d^{3} e^{3} + 28 \, a^{2} b^{4} d^{2} e^{4} + 84 \, a^{3} b^{3} d e^{5} + 210 \, a^{4} b^{2} e^{6}\right)} x^{2} + 13 \, {\left(b^{6} d^{5} e + 7 \, a b^{5} d^{4} e^{2} + 28 \, a^{2} b^{4} d^{3} e^{3} + 84 \, a^{3} b^{3} d^{2} e^{4} + 210 \, a^{4} b^{2} d e^{5} + 462 \, a^{5} b e^{6}\right)} x}{12012 \, {\left(e^{20} x^{13} + 13 \, d e^{19} x^{12} + 78 \, d^{2} e^{18} x^{11} + 286 \, d^{3} e^{17} x^{10} + 715 \, d^{4} e^{16} x^{9} + 1287 \, d^{5} e^{15} x^{8} + 1716 \, d^{6} e^{14} x^{7} + 1716 \, d^{7} e^{13} x^{6} + 1287 \, d^{8} e^{12} x^{5} + 715 \, d^{9} e^{11} x^{4} + 286 \, d^{10} e^{10} x^{3} + 78 \, d^{11} e^{9} x^{2} + 13 \, d^{12} e^{8} x + d^{13} e^{7}\right)}}"," ",0,"-1/12012*(1716*b^6*e^6*x^6 + b^6*d^6 + 7*a*b^5*d^5*e + 28*a^2*b^4*d^4*e^2 + 84*a^3*b^3*d^3*e^3 + 210*a^4*b^2*d^2*e^4 + 462*a^5*b*d*e^5 + 924*a^6*e^6 + 1287*(b^6*d*e^5 + 7*a*b^5*e^6)*x^5 + 715*(b^6*d^2*e^4 + 7*a*b^5*d*e^5 + 28*a^2*b^4*e^6)*x^4 + 286*(b^6*d^3*e^3 + 7*a*b^5*d^2*e^4 + 28*a^2*b^4*d*e^5 + 84*a^3*b^3*e^6)*x^3 + 78*(b^6*d^4*e^2 + 7*a*b^5*d^3*e^3 + 28*a^2*b^4*d^2*e^4 + 84*a^3*b^3*d*e^5 + 210*a^4*b^2*e^6)*x^2 + 13*(b^6*d^5*e + 7*a*b^5*d^4*e^2 + 28*a^2*b^4*d^3*e^3 + 84*a^3*b^3*d^2*e^4 + 210*a^4*b^2*d*e^5 + 462*a^5*b*e^6)*x)/(e^20*x^13 + 13*d*e^19*x^12 + 78*d^2*e^18*x^11 + 286*d^3*e^17*x^10 + 715*d^4*e^16*x^9 + 1287*d^5*e^15*x^8 + 1716*d^6*e^14*x^7 + 1716*d^7*e^13*x^6 + 1287*d^8*e^12*x^5 + 715*d^9*e^11*x^4 + 286*d^10*e^10*x^3 + 78*d^11*e^9*x^2 + 13*d^12*e^8*x + d^13*e^7)","A",0
2012,1,496,0,0.433008," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^15,x, algorithm=""fricas"")","-\frac{3003 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 8 \, a b^{5} d^{5} e + 36 \, a^{2} b^{4} d^{4} e^{2} + 120 \, a^{3} b^{3} d^{3} e^{3} + 330 \, a^{4} b^{2} d^{2} e^{4} + 792 \, a^{5} b d e^{5} + 1716 \, a^{6} e^{6} + 2002 \, {\left(b^{6} d e^{5} + 8 \, a b^{5} e^{6}\right)} x^{5} + 1001 \, {\left(b^{6} d^{2} e^{4} + 8 \, a b^{5} d e^{5} + 36 \, a^{2} b^{4} e^{6}\right)} x^{4} + 364 \, {\left(b^{6} d^{3} e^{3} + 8 \, a b^{5} d^{2} e^{4} + 36 \, a^{2} b^{4} d e^{5} + 120 \, a^{3} b^{3} e^{6}\right)} x^{3} + 91 \, {\left(b^{6} d^{4} e^{2} + 8 \, a b^{5} d^{3} e^{3} + 36 \, a^{2} b^{4} d^{2} e^{4} + 120 \, a^{3} b^{3} d e^{5} + 330 \, a^{4} b^{2} e^{6}\right)} x^{2} + 14 \, {\left(b^{6} d^{5} e + 8 \, a b^{5} d^{4} e^{2} + 36 \, a^{2} b^{4} d^{3} e^{3} + 120 \, a^{3} b^{3} d^{2} e^{4} + 330 \, a^{4} b^{2} d e^{5} + 792 \, a^{5} b e^{6}\right)} x}{24024 \, {\left(e^{21} x^{14} + 14 \, d e^{20} x^{13} + 91 \, d^{2} e^{19} x^{12} + 364 \, d^{3} e^{18} x^{11} + 1001 \, d^{4} e^{17} x^{10} + 2002 \, d^{5} e^{16} x^{9} + 3003 \, d^{6} e^{15} x^{8} + 3432 \, d^{7} e^{14} x^{7} + 3003 \, d^{8} e^{13} x^{6} + 2002 \, d^{9} e^{12} x^{5} + 1001 \, d^{10} e^{11} x^{4} + 364 \, d^{11} e^{10} x^{3} + 91 \, d^{12} e^{9} x^{2} + 14 \, d^{13} e^{8} x + d^{14} e^{7}\right)}}"," ",0,"-1/24024*(3003*b^6*e^6*x^6 + b^6*d^6 + 8*a*b^5*d^5*e + 36*a^2*b^4*d^4*e^2 + 120*a^3*b^3*d^3*e^3 + 330*a^4*b^2*d^2*e^4 + 792*a^5*b*d*e^5 + 1716*a^6*e^6 + 2002*(b^6*d*e^5 + 8*a*b^5*e^6)*x^5 + 1001*(b^6*d^2*e^4 + 8*a*b^5*d*e^5 + 36*a^2*b^4*e^6)*x^4 + 364*(b^6*d^3*e^3 + 8*a*b^5*d^2*e^4 + 36*a^2*b^4*d*e^5 + 120*a^3*b^3*e^6)*x^3 + 91*(b^6*d^4*e^2 + 8*a*b^5*d^3*e^3 + 36*a^2*b^4*d^2*e^4 + 120*a^3*b^3*d*e^5 + 330*a^4*b^2*e^6)*x^2 + 14*(b^6*d^5*e + 8*a*b^5*d^4*e^2 + 36*a^2*b^4*d^3*e^3 + 120*a^3*b^3*d^2*e^4 + 330*a^4*b^2*d*e^5 + 792*a^5*b*e^6)*x)/(e^21*x^14 + 14*d*e^20*x^13 + 91*d^2*e^19*x^12 + 364*d^3*e^18*x^11 + 1001*d^4*e^17*x^10 + 2002*d^5*e^16*x^9 + 3003*d^6*e^15*x^8 + 3432*d^7*e^14*x^7 + 3003*d^8*e^13*x^6 + 2002*d^9*e^12*x^5 + 1001*d^10*e^11*x^4 + 364*d^11*e^10*x^3 + 91*d^12*e^9*x^2 + 14*d^13*e^8*x + d^14*e^7)","A",0
2013,1,507,0,0.437288," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^16,x, algorithm=""fricas"")","-\frac{5005 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 9 \, a b^{5} d^{5} e + 45 \, a^{2} b^{4} d^{4} e^{2} + 165 \, a^{3} b^{3} d^{3} e^{3} + 495 \, a^{4} b^{2} d^{2} e^{4} + 1287 \, a^{5} b d e^{5} + 3003 \, a^{6} e^{6} + 3003 \, {\left(b^{6} d e^{5} + 9 \, a b^{5} e^{6}\right)} x^{5} + 1365 \, {\left(b^{6} d^{2} e^{4} + 9 \, a b^{5} d e^{5} + 45 \, a^{2} b^{4} e^{6}\right)} x^{4} + 455 \, {\left(b^{6} d^{3} e^{3} + 9 \, a b^{5} d^{2} e^{4} + 45 \, a^{2} b^{4} d e^{5} + 165 \, a^{3} b^{3} e^{6}\right)} x^{3} + 105 \, {\left(b^{6} d^{4} e^{2} + 9 \, a b^{5} d^{3} e^{3} + 45 \, a^{2} b^{4} d^{2} e^{4} + 165 \, a^{3} b^{3} d e^{5} + 495 \, a^{4} b^{2} e^{6}\right)} x^{2} + 15 \, {\left(b^{6} d^{5} e + 9 \, a b^{5} d^{4} e^{2} + 45 \, a^{2} b^{4} d^{3} e^{3} + 165 \, a^{3} b^{3} d^{2} e^{4} + 495 \, a^{4} b^{2} d e^{5} + 1287 \, a^{5} b e^{6}\right)} x}{45045 \, {\left(e^{22} x^{15} + 15 \, d e^{21} x^{14} + 105 \, d^{2} e^{20} x^{13} + 455 \, d^{3} e^{19} x^{12} + 1365 \, d^{4} e^{18} x^{11} + 3003 \, d^{5} e^{17} x^{10} + 5005 \, d^{6} e^{16} x^{9} + 6435 \, d^{7} e^{15} x^{8} + 6435 \, d^{8} e^{14} x^{7} + 5005 \, d^{9} e^{13} x^{6} + 3003 \, d^{10} e^{12} x^{5} + 1365 \, d^{11} e^{11} x^{4} + 455 \, d^{12} e^{10} x^{3} + 105 \, d^{13} e^{9} x^{2} + 15 \, d^{14} e^{8} x + d^{15} e^{7}\right)}}"," ",0,"-1/45045*(5005*b^6*e^6*x^6 + b^6*d^6 + 9*a*b^5*d^5*e + 45*a^2*b^4*d^4*e^2 + 165*a^3*b^3*d^3*e^3 + 495*a^4*b^2*d^2*e^4 + 1287*a^5*b*d*e^5 + 3003*a^6*e^6 + 3003*(b^6*d*e^5 + 9*a*b^5*e^6)*x^5 + 1365*(b^6*d^2*e^4 + 9*a*b^5*d*e^5 + 45*a^2*b^4*e^6)*x^4 + 455*(b^6*d^3*e^3 + 9*a*b^5*d^2*e^4 + 45*a^2*b^4*d*e^5 + 165*a^3*b^3*e^6)*x^3 + 105*(b^6*d^4*e^2 + 9*a*b^5*d^3*e^3 + 45*a^2*b^4*d^2*e^4 + 165*a^3*b^3*d*e^5 + 495*a^4*b^2*e^6)*x^2 + 15*(b^6*d^5*e + 9*a*b^5*d^4*e^2 + 45*a^2*b^4*d^3*e^3 + 165*a^3*b^3*d^2*e^4 + 495*a^4*b^2*d*e^5 + 1287*a^5*b*e^6)*x)/(e^22*x^15 + 15*d*e^21*x^14 + 105*d^2*e^20*x^13 + 455*d^3*e^19*x^12 + 1365*d^4*e^18*x^11 + 3003*d^5*e^17*x^10 + 5005*d^6*e^16*x^9 + 6435*d^7*e^15*x^8 + 6435*d^8*e^14*x^7 + 5005*d^9*e^13*x^6 + 3003*d^10*e^12*x^5 + 1365*d^11*e^11*x^4 + 455*d^12*e^10*x^3 + 105*d^13*e^9*x^2 + 15*d^14*e^8*x + d^15*e^7)","A",0
2014,1,518,0,0.423190," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^17,x, algorithm=""fricas"")","-\frac{8008 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 10 \, a b^{5} d^{5} e + 55 \, a^{2} b^{4} d^{4} e^{2} + 220 \, a^{3} b^{3} d^{3} e^{3} + 715 \, a^{4} b^{2} d^{2} e^{4} + 2002 \, a^{5} b d e^{5} + 5005 \, a^{6} e^{6} + 4368 \, {\left(b^{6} d e^{5} + 10 \, a b^{5} e^{6}\right)} x^{5} + 1820 \, {\left(b^{6} d^{2} e^{4} + 10 \, a b^{5} d e^{5} + 55 \, a^{2} b^{4} e^{6}\right)} x^{4} + 560 \, {\left(b^{6} d^{3} e^{3} + 10 \, a b^{5} d^{2} e^{4} + 55 \, a^{2} b^{4} d e^{5} + 220 \, a^{3} b^{3} e^{6}\right)} x^{3} + 120 \, {\left(b^{6} d^{4} e^{2} + 10 \, a b^{5} d^{3} e^{3} + 55 \, a^{2} b^{4} d^{2} e^{4} + 220 \, a^{3} b^{3} d e^{5} + 715 \, a^{4} b^{2} e^{6}\right)} x^{2} + 16 \, {\left(b^{6} d^{5} e + 10 \, a b^{5} d^{4} e^{2} + 55 \, a^{2} b^{4} d^{3} e^{3} + 220 \, a^{3} b^{3} d^{2} e^{4} + 715 \, a^{4} b^{2} d e^{5} + 2002 \, a^{5} b e^{6}\right)} x}{80080 \, {\left(e^{23} x^{16} + 16 \, d e^{22} x^{15} + 120 \, d^{2} e^{21} x^{14} + 560 \, d^{3} e^{20} x^{13} + 1820 \, d^{4} e^{19} x^{12} + 4368 \, d^{5} e^{18} x^{11} + 8008 \, d^{6} e^{17} x^{10} + 11440 \, d^{7} e^{16} x^{9} + 12870 \, d^{8} e^{15} x^{8} + 11440 \, d^{9} e^{14} x^{7} + 8008 \, d^{10} e^{13} x^{6} + 4368 \, d^{11} e^{12} x^{5} + 1820 \, d^{12} e^{11} x^{4} + 560 \, d^{13} e^{10} x^{3} + 120 \, d^{14} e^{9} x^{2} + 16 \, d^{15} e^{8} x + d^{16} e^{7}\right)}}"," ",0,"-1/80080*(8008*b^6*e^6*x^6 + b^6*d^6 + 10*a*b^5*d^5*e + 55*a^2*b^4*d^4*e^2 + 220*a^3*b^3*d^3*e^3 + 715*a^4*b^2*d^2*e^4 + 2002*a^5*b*d*e^5 + 5005*a^6*e^6 + 4368*(b^6*d*e^5 + 10*a*b^5*e^6)*x^5 + 1820*(b^6*d^2*e^4 + 10*a*b^5*d*e^5 + 55*a^2*b^4*e^6)*x^4 + 560*(b^6*d^3*e^3 + 10*a*b^5*d^2*e^4 + 55*a^2*b^4*d*e^5 + 220*a^3*b^3*e^6)*x^3 + 120*(b^6*d^4*e^2 + 10*a*b^5*d^3*e^3 + 55*a^2*b^4*d^2*e^4 + 220*a^3*b^3*d*e^5 + 715*a^4*b^2*e^6)*x^2 + 16*(b^6*d^5*e + 10*a*b^5*d^4*e^2 + 55*a^2*b^4*d^3*e^3 + 220*a^3*b^3*d^2*e^4 + 715*a^4*b^2*d*e^5 + 2002*a^5*b*e^6)*x)/(e^23*x^16 + 16*d*e^22*x^15 + 120*d^2*e^21*x^14 + 560*d^3*e^20*x^13 + 1820*d^4*e^19*x^12 + 4368*d^5*e^18*x^11 + 8008*d^6*e^17*x^10 + 11440*d^7*e^16*x^9 + 12870*d^8*e^15*x^8 + 11440*d^9*e^14*x^7 + 8008*d^10*e^13*x^6 + 4368*d^11*e^12*x^5 + 1820*d^12*e^11*x^4 + 560*d^13*e^10*x^3 + 120*d^14*e^9*x^2 + 16*d^15*e^8*x + d^16*e^7)","A",0
2015,1,42,0,0.415714," ","integrate((b*x+a)*(e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, e^{4} x^{5} + d e^{3} x^{4} + 2 \, d^{2} e^{2} x^{3} + 2 \, d^{3} e x^{2} + d^{4} x"," ",0,"1/5*e^4*x^5 + d*e^3*x^4 + 2*d^2*e^2*x^3 + 2*d^3*e*x^2 + d^4*x","A",0
2016,1,31,0,0.418035," ","integrate((b*x+a)*(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, e^{3} x^{4} + d e^{2} x^{3} + \frac{3}{2} \, d^{2} e x^{2} + d^{3} x"," ",0,"1/4*e^3*x^4 + d*e^2*x^3 + 3/2*d^2*e*x^2 + d^3*x","A",0
2017,1,20,0,0.406353," ","integrate((b*x+a)*(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, e^{2} x^{3} + d e x^{2} + d^{2} x"," ",0,"1/3*e^2*x^3 + d*e*x^2 + d^2*x","A",0
2018,1,10,0,0.420248," ","integrate((b*x+a)*(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, e x^{2} + d x"," ",0,"1/2*e*x^2 + d*x","A",0
2019,1,1,0,0.409707," ","integrate((b*x+a)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","x"," ",0,"x","A",0
2020,1,10,0,0.442120," ","integrate((b*x+a)/(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(e x + d\right)}{e}"," ",0,"log(e*x + d)/e","A",0
2021,1,13,0,0.424771," ","integrate((b*x+a)/(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{e^{2} x + d e}"," ",0,"-1/(e^2*x + d*e)","A",0
2022,1,24,0,0.419242," ","integrate((b*x+a)/(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-1/2/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
2023,1,35,0,0.469110," ","integrate((b*x+a)/(e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"-1/3/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","A",0
2024,1,46,0,0.422713," ","integrate((b*x+a)/(e*x+d)^5/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(e^{5} x^{4} + 4 \, d e^{4} x^{3} + 6 \, d^{2} e^{3} x^{2} + 4 \, d^{3} e^{2} x + d^{4} e\right)}}"," ",0,"-1/4/(e^5*x^4 + 4*d*e^4*x^3 + 6*d^2*e^3*x^2 + 4*d^3*e^2*x + d^4*e)","A",0
2025,1,268,0,0.419070," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{b^{4} e^{4} x^{4} - 3 \, b^{4} d^{4} + 12 \, a b^{3} d^{3} e - 18 \, a^{2} b^{2} d^{2} e^{2} + 12 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} + 2 \, {\left(3 \, b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(3 \, b^{4} d^{2} e^{2} - 3 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(6 \, a b^{3} d^{2} e^{2} - 8 \, a^{2} b^{2} d e^{3} + 3 \, a^{3} b e^{4}\right)} x + 12 \, {\left(a b^{3} d^{3} e - 3 \, a^{2} b^{2} d^{2} e^{2} + 3 \, a^{3} b d e^{3} - a^{4} e^{4} + {\left(b^{4} d^{3} e - 3 \, a b^{3} d^{2} e^{2} + 3 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x\right)} \log\left(b x + a\right)}{3 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"1/3*(b^4*e^4*x^4 - 3*b^4*d^4 + 12*a*b^3*d^3*e - 18*a^2*b^2*d^2*e^2 + 12*a^3*b*d*e^3 - 3*a^4*e^4 + 2*(3*b^4*d*e^3 - a*b^3*e^4)*x^3 + 6*(3*b^4*d^2*e^2 - 3*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 3*(6*a*b^3*d^2*e^2 - 8*a^2*b^2*d*e^3 + 3*a^3*b*e^4)*x + 12*(a*b^3*d^3*e - 3*a^2*b^2*d^2*e^2 + 3*a^3*b*d*e^3 - a^4*e^4 + (b^4*d^3*e - 3*a*b^3*d^2*e^2 + 3*a^2*b^2*d*e^3 - a^3*b*e^4)*x)*log(b*x + a))/(b^6*x + a*b^5)","A",0
2026,1,173,0,0.449012," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{b^{3} e^{3} x^{3} - 2 \, b^{3} d^{3} + 6 \, a b^{2} d^{2} e - 6 \, a^{2} b d e^{2} + 2 \, a^{3} e^{3} + 3 \, {\left(2 \, b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} d e^{2} - 2 \, a^{2} b e^{3}\right)} x + 6 \, {\left(a b^{2} d^{2} e - 2 \, a^{2} b d e^{2} + a^{3} e^{3} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(b^3*e^3*x^3 - 2*b^3*d^3 + 6*a*b^2*d^2*e - 6*a^2*b*d*e^2 + 2*a^3*e^3 + 3*(2*b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(3*a*b^2*d*e^2 - 2*a^2*b*e^3)*x + 6*(a*b^2*d^2*e - 2*a^2*b*d*e^2 + a^3*e^3 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)*log(b*x + a))/(b^5*x + a*b^4)","A",0
2027,1,92,0,0.482584," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{b^{2} e^{2} x^{2} + a b e^{2} x - b^{2} d^{2} + 2 \, a b d e - a^{2} e^{2} + 2 \, {\left(a b d e - a^{2} e^{2} + {\left(b^{2} d e - a b e^{2}\right)} x\right)} \log\left(b x + a\right)}{b^{4} x + a b^{3}}"," ",0,"(b^2*e^2*x^2 + a*b*e^2*x - b^2*d^2 + 2*a*b*d*e - a^2*e^2 + 2*(a*b*d*e - a^2*e^2 + (b^2*d*e - a*b*e^2)*x)*log(b*x + a))/(b^4*x + a*b^3)","A",0
2028,1,39,0,0.446647," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{b d - a e - {\left(b e x + a e\right)} \log\left(b x + a\right)}{b^{3} x + a b^{2}}"," ",0,"-(b*d - a*e - (b*e*x + a*e)*log(b*x + a))/(b^3*x + a*b^2)","A",0
2029,1,13,0,0.421093," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{b^{2} x + a b}"," ",0,"-1/(b^2*x + a*b)","A",0
2030,1,93,0,0.438491," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{b d - a e + {\left(b e x + a e\right)} \log\left(b x + a\right) - {\left(b e x + a e\right)} \log\left(e x + d\right)}{a b^{2} d^{2} - 2 \, a^{2} b d e + a^{3} e^{2} + {\left(b^{3} d^{2} - 2 \, a b^{2} d e + a^{2} b e^{2}\right)} x}"," ",0,"-(b*d - a*e + (b*e*x + a*e)*log(b*x + a) - (b*e*x + a*e)*log(e*x + d))/(a*b^2*d^2 - 2*a^2*b*d*e + a^3*e^2 + (b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2)*x)","A",0
2031,1,241,0,0.439517," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{b^{2} d^{2} - a^{2} e^{2} + 2 \, {\left(b^{2} d e - a b e^{2}\right)} x + 2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)} \log\left(e x + d\right)}{a b^{3} d^{4} - 3 \, a^{2} b^{2} d^{3} e + 3 \, a^{3} b d^{2} e^{2} - a^{4} d e^{3} + {\left(b^{4} d^{3} e - 3 \, a b^{3} d^{2} e^{2} + 3 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x^{2} + {\left(b^{4} d^{4} - 2 \, a b^{3} d^{3} e + 2 \, a^{3} b d e^{3} - a^{4} e^{4}\right)} x}"," ",0,"-(b^2*d^2 - a^2*e^2 + 2*(b^2*d*e - a*b*e^2)*x + 2*(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)*log(b*x + a) - 2*(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)*log(e*x + d))/(a*b^3*d^4 - 3*a^2*b^2*d^3*e + 3*a^3*b*d^2*e^2 - a^4*d*e^3 + (b^4*d^3*e - 3*a*b^3*d^2*e^2 + 3*a^2*b^2*d*e^3 - a^3*b*e^4)*x^2 + (b^4*d^4 - 2*a*b^3*d^3*e + 2*a^3*b*d*e^3 - a^4*e^4)*x)","A",0
2032,1,495,0,0.447044," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{3} + 3 \, a b^{2} d^{2} e - 6 \, a^{2} b d e^{2} + a^{3} e^{3} + 6 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 3 \, {\left(3 \, b^{3} d^{2} e - 2 \, a b^{2} d e^{2} - a^{2} b e^{3}\right)} x + 6 \, {\left(b^{3} e^{3} x^{3} + a b^{2} d^{2} e + {\left(2 \, b^{3} d e^{2} + a b^{2} e^{3}\right)} x^{2} + {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} e^{3} x^{3} + a b^{2} d^{2} e + {\left(2 \, b^{3} d e^{2} + a b^{2} e^{3}\right)} x^{2} + {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a b^{4} d^{6} - 4 \, a^{2} b^{3} d^{5} e + 6 \, a^{3} b^{2} d^{4} e^{2} - 4 \, a^{4} b d^{3} e^{3} + a^{5} d^{2} e^{4} + {\left(b^{5} d^{4} e^{2} - 4 \, a b^{4} d^{3} e^{3} + 6 \, a^{2} b^{3} d^{2} e^{4} - 4 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{3} + {\left(2 \, b^{5} d^{5} e - 7 \, a b^{4} d^{4} e^{2} + 8 \, a^{2} b^{3} d^{3} e^{3} - 2 \, a^{3} b^{2} d^{2} e^{4} - 2 \, a^{4} b d e^{5} + a^{5} e^{6}\right)} x^{2} + {\left(b^{5} d^{6} - 2 \, a b^{4} d^{5} e - 2 \, a^{2} b^{3} d^{4} e^{2} + 8 \, a^{3} b^{2} d^{3} e^{3} - 7 \, a^{4} b d^{2} e^{4} + 2 \, a^{5} d e^{5}\right)} x\right)}}"," ",0,"-1/2*(2*b^3*d^3 + 3*a*b^2*d^2*e - 6*a^2*b*d*e^2 + a^3*e^3 + 6*(b^3*d*e^2 - a*b^2*e^3)*x^2 + 3*(3*b^3*d^2*e - 2*a*b^2*d*e^2 - a^2*b*e^3)*x + 6*(b^3*e^3*x^3 + a*b^2*d^2*e + (2*b^3*d*e^2 + a*b^2*e^3)*x^2 + (b^3*d^2*e + 2*a*b^2*d*e^2)*x)*log(b*x + a) - 6*(b^3*e^3*x^3 + a*b^2*d^2*e + (2*b^3*d*e^2 + a*b^2*e^3)*x^2 + (b^3*d^2*e + 2*a*b^2*d*e^2)*x)*log(e*x + d))/(a*b^4*d^6 - 4*a^2*b^3*d^5*e + 6*a^3*b^2*d^4*e^2 - 4*a^4*b*d^3*e^3 + a^5*d^2*e^4 + (b^5*d^4*e^2 - 4*a*b^4*d^3*e^3 + 6*a^2*b^3*d^2*e^4 - 4*a^3*b^2*d*e^5 + a^4*b*e^6)*x^3 + (2*b^5*d^5*e - 7*a*b^4*d^4*e^2 + 8*a^2*b^3*d^3*e^3 - 2*a^3*b^2*d^2*e^4 - 2*a^4*b*d*e^5 + a^5*e^6)*x^2 + (b^5*d^6 - 2*a*b^4*d^5*e - 2*a^2*b^3*d^4*e^2 + 8*a^3*b^2*d^3*e^3 - 7*a^4*b*d^2*e^4 + 2*a^5*d*e^5)*x)","B",0
2033,1,426,0,0.419339," ","integrate((b*x+a)*(e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{3 \, b^{5} e^{5} x^{5} - 2 \, b^{5} d^{5} - 5 \, a b^{4} d^{4} e - 20 \, a^{2} b^{3} d^{3} e^{2} + 110 \, a^{3} b^{2} d^{2} e^{3} - 130 \, a^{4} b d e^{4} + 47 \, a^{5} e^{5} + 15 \, {\left(2 \, b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 9 \, {\left(10 \, a b^{4} d e^{4} - 7 \, a^{2} b^{3} e^{5}\right)} x^{3} - 3 \, {\left(20 \, b^{5} d^{3} e^{2} - 60 \, a b^{4} d^{2} e^{3} + 30 \, a^{2} b^{3} d e^{4} + 3 \, a^{3} b^{2} e^{5}\right)} x^{2} - 3 \, {\left(5 \, b^{5} d^{4} e + 20 \, a b^{4} d^{3} e^{2} - 90 \, a^{2} b^{3} d^{2} e^{3} + 90 \, a^{3} b^{2} d e^{4} - 27 \, a^{4} b e^{5}\right)} x + 60 \, {\left(a^{3} b^{2} d^{2} e^{3} - 2 \, a^{4} b d e^{4} + a^{5} e^{5} + {\left(b^{5} d^{2} e^{3} - 2 \, a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + 3 \, {\left(a b^{4} d^{2} e^{3} - 2 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} d^{2} e^{3} - 2 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{9} x^{3} + 3 \, a b^{8} x^{2} + 3 \, a^{2} b^{7} x + a^{3} b^{6}\right)}}"," ",0,"1/6*(3*b^5*e^5*x^5 - 2*b^5*d^5 - 5*a*b^4*d^4*e - 20*a^2*b^3*d^3*e^2 + 110*a^3*b^2*d^2*e^3 - 130*a^4*b*d*e^4 + 47*a^5*e^5 + 15*(2*b^5*d*e^4 - a*b^4*e^5)*x^4 + 9*(10*a*b^4*d*e^4 - 7*a^2*b^3*e^5)*x^3 - 3*(20*b^5*d^3*e^2 - 60*a*b^4*d^2*e^3 + 30*a^2*b^3*d*e^4 + 3*a^3*b^2*e^5)*x^2 - 3*(5*b^5*d^4*e + 20*a*b^4*d^3*e^2 - 90*a^2*b^3*d^2*e^3 + 90*a^3*b^2*d*e^4 - 27*a^4*b*e^5)*x + 60*(a^3*b^2*d^2*e^3 - 2*a^4*b*d*e^4 + a^5*e^5 + (b^5*d^2*e^3 - 2*a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + 3*(a*b^4*d^2*e^3 - 2*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 + 3*(a^2*b^3*d^2*e^3 - 2*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*log(b*x + a))/(b^9*x^3 + 3*a*b^8*x^2 + 3*a^2*b^7*x + a^3*b^6)","B",0
2034,1,292,0,0.493483," ","integrate((b*x+a)*(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{3 \, b^{4} e^{4} x^{4} + 9 \, a b^{3} e^{4} x^{3} - b^{4} d^{4} - 2 \, a b^{3} d^{3} e - 6 \, a^{2} b^{2} d^{2} e^{2} + 22 \, a^{3} b d e^{3} - 13 \, a^{4} e^{4} - 9 \, {\left(2 \, b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} - 3 \, {\left(2 \, b^{4} d^{3} e + 6 \, a b^{3} d^{2} e^{2} - 18 \, a^{2} b^{2} d e^{3} + 9 \, a^{3} b e^{4}\right)} x + 12 \, {\left(a^{3} b d e^{3} - a^{4} e^{4} + {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{3} d e^{3} - a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x\right)} \log\left(b x + a\right)}{3 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}"," ",0,"1/3*(3*b^4*e^4*x^4 + 9*a*b^3*e^4*x^3 - b^4*d^4 - 2*a*b^3*d^3*e - 6*a^2*b^2*d^2*e^2 + 22*a^3*b*d*e^3 - 13*a^4*e^4 - 9*(2*b^4*d^2*e^2 - 4*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 - 3*(2*b^4*d^3*e + 6*a*b^3*d^2*e^2 - 18*a^2*b^2*d*e^3 + 9*a^3*b*e^4)*x + 12*(a^3*b*d*e^3 - a^4*e^4 + (b^4*d*e^3 - a*b^3*e^4)*x^3 + 3*(a*b^3*d*e^3 - a^2*b^2*e^4)*x^2 + 3*(a^2*b^2*d*e^3 - a^3*b*e^4)*x)*log(b*x + a))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5)","A",0
2035,1,176,0,0.493528," ","integrate((b*x+a)*(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{3} + 3 \, a b^{2} d^{2} e + 6 \, a^{2} b d e^{2} - 11 \, a^{3} e^{3} + 18 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 9 \, {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2} - 3 \, a^{2} b e^{3}\right)} x - 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \log\left(b x + a\right)}{6 \, {\left(b^{7} x^{3} + 3 \, a b^{6} x^{2} + 3 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}"," ",0,"-1/6*(2*b^3*d^3 + 3*a*b^2*d^2*e + 6*a^2*b*d*e^2 - 11*a^3*e^3 + 18*(b^3*d*e^2 - a*b^2*e^3)*x^2 + 9*(b^3*d^2*e + 2*a*b^2*d*e^2 - 3*a^2*b*e^3)*x - 6*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*log(b*x + a))/(b^7*x^3 + 3*a*b^6*x^2 + 3*a^2*b^5*x + a^3*b^4)","A",0
2036,1,84,0,0.438107," ","integrate((b*x+a)*(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + a b d e + a^{2} e^{2} + 3 \, {\left(b^{2} d e + a b e^{2}\right)} x}{3 \, {\left(b^{6} x^{3} + 3 \, a b^{5} x^{2} + 3 \, a^{2} b^{4} x + a^{3} b^{3}\right)}}"," ",0,"-1/3*(3*b^2*e^2*x^2 + b^2*d^2 + a*b*d*e + a^2*e^2 + 3*(b^2*d*e + a*b*e^2)*x)/(b^6*x^3 + 3*a*b^5*x^2 + 3*a^2*b^4*x + a^3*b^3)","B",0
2037,1,50,0,0.437531," ","integrate((b*x+a)*(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, b e x + 2 \, b d + a e}{6 \, {\left(b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x + a^{3} b^{2}\right)}}"," ",0,"-1/6*(3*b*e*x + 2*b*d + a*e)/(b^5*x^3 + 3*a*b^4*x^2 + 3*a^2*b^3*x + a^3*b^2)","A",0
2038,1,35,0,0.426254," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"-1/3/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)","A",0
2039,1,425,0,0.454963," ","integrate((b*x+a)/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{3} - 9 \, a b^{2} d^{2} e + 18 \, a^{2} b d e^{2} - 11 \, a^{3} e^{3} + 6 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} - 3 \, {\left(b^{3} d^{2} e - 6 \, a b^{2} d e^{2} + 5 \, a^{2} b e^{3}\right)} x + 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(a^{3} b^{4} d^{4} - 4 \, a^{4} b^{3} d^{3} e + 6 \, a^{5} b^{2} d^{2} e^{2} - 4 \, a^{6} b d e^{3} + a^{7} e^{4} + {\left(b^{7} d^{4} - 4 \, a b^{6} d^{3} e + 6 \, a^{2} b^{5} d^{2} e^{2} - 4 \, a^{3} b^{4} d e^{3} + a^{4} b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{6} d^{4} - 4 \, a^{2} b^{5} d^{3} e + 6 \, a^{3} b^{4} d^{2} e^{2} - 4 \, a^{4} b^{3} d e^{3} + a^{5} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} d^{4} - 4 \, a^{3} b^{4} d^{3} e + 6 \, a^{4} b^{3} d^{2} e^{2} - 4 \, a^{5} b^{2} d e^{3} + a^{6} b e^{4}\right)} x\right)}}"," ",0,"-1/6*(2*b^3*d^3 - 9*a*b^2*d^2*e + 18*a^2*b*d*e^2 - 11*a^3*e^3 + 6*(b^3*d*e^2 - a*b^2*e^3)*x^2 - 3*(b^3*d^2*e - 6*a*b^2*d*e^2 + 5*a^2*b*e^3)*x + 6*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*log(b*x + a) - 6*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*log(e*x + d))/(a^3*b^4*d^4 - 4*a^4*b^3*d^3*e + 6*a^5*b^2*d^2*e^2 - 4*a^6*b*d*e^3 + a^7*e^4 + (b^7*d^4 - 4*a*b^6*d^3*e + 6*a^2*b^5*d^2*e^2 - 4*a^3*b^4*d*e^3 + a^4*b^3*e^4)*x^3 + 3*(a*b^6*d^4 - 4*a^2*b^5*d^3*e + 6*a^3*b^4*d^2*e^2 - 4*a^4*b^3*d*e^3 + a^5*b^2*e^4)*x^2 + 3*(a^2*b^5*d^4 - 4*a^3*b^4*d^3*e + 6*a^4*b^3*d^2*e^2 - 4*a^5*b^2*d*e^3 + a^6*b*e^4)*x)","B",0
2040,1,751,0,0.439725," ","integrate((b*x+a)/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{b^{4} d^{4} - 6 \, a b^{3} d^{3} e + 18 \, a^{2} b^{2} d^{2} e^{2} - 10 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} + 12 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(b^{4} d^{2} e^{2} + 4 \, a b^{3} d e^{3} - 5 \, a^{2} b^{2} e^{4}\right)} x^{2} - 2 \, {\left(b^{4} d^{3} e - 9 \, a b^{3} d^{2} e^{2} - 3 \, a^{2} b^{2} d e^{3} + 11 \, a^{3} b e^{4}\right)} x + 12 \, {\left(b^{4} e^{4} x^{4} + a^{3} b d e^{3} + {\left(b^{4} d e^{3} + 3 \, a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(b^{4} e^{4} x^{4} + a^{3} b d e^{3} + {\left(b^{4} d e^{3} + 3 \, a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(a^{3} b^{5} d^{6} - 5 \, a^{4} b^{4} d^{5} e + 10 \, a^{5} b^{3} d^{4} e^{2} - 10 \, a^{6} b^{2} d^{3} e^{3} + 5 \, a^{7} b d^{2} e^{4} - a^{8} d e^{5} + {\left(b^{8} d^{5} e - 5 \, a b^{7} d^{4} e^{2} + 10 \, a^{2} b^{6} d^{3} e^{3} - 10 \, a^{3} b^{5} d^{2} e^{4} + 5 \, a^{4} b^{4} d e^{5} - a^{5} b^{3} e^{6}\right)} x^{4} + {\left(b^{8} d^{6} - 2 \, a b^{7} d^{5} e - 5 \, a^{2} b^{6} d^{4} e^{2} + 20 \, a^{3} b^{5} d^{3} e^{3} - 25 \, a^{4} b^{4} d^{2} e^{4} + 14 \, a^{5} b^{3} d e^{5} - 3 \, a^{6} b^{2} e^{6}\right)} x^{3} + 3 \, {\left(a b^{7} d^{6} - 4 \, a^{2} b^{6} d^{5} e + 5 \, a^{3} b^{5} d^{4} e^{2} - 5 \, a^{5} b^{3} d^{2} e^{4} + 4 \, a^{6} b^{2} d e^{5} - a^{7} b e^{6}\right)} x^{2} + {\left(3 \, a^{2} b^{6} d^{6} - 14 \, a^{3} b^{5} d^{5} e + 25 \, a^{4} b^{4} d^{4} e^{2} - 20 \, a^{5} b^{3} d^{3} e^{3} + 5 \, a^{6} b^{2} d^{2} e^{4} + 2 \, a^{7} b d e^{5} - a^{8} e^{6}\right)} x\right)}}"," ",0,"-1/3*(b^4*d^4 - 6*a*b^3*d^3*e + 18*a^2*b^2*d^2*e^2 - 10*a^3*b*d*e^3 - 3*a^4*e^4 + 12*(b^4*d*e^3 - a*b^3*e^4)*x^3 + 6*(b^4*d^2*e^2 + 4*a*b^3*d*e^3 - 5*a^2*b^2*e^4)*x^2 - 2*(b^4*d^3*e - 9*a*b^3*d^2*e^2 - 3*a^2*b^2*d*e^3 + 11*a^3*b*e^4)*x + 12*(b^4*e^4*x^4 + a^3*b*d*e^3 + (b^4*d*e^3 + 3*a*b^3*e^4)*x^3 + 3*(a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + (3*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*log(b*x + a) - 12*(b^4*e^4*x^4 + a^3*b*d*e^3 + (b^4*d*e^3 + 3*a*b^3*e^4)*x^3 + 3*(a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + (3*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*log(e*x + d))/(a^3*b^5*d^6 - 5*a^4*b^4*d^5*e + 10*a^5*b^3*d^4*e^2 - 10*a^6*b^2*d^3*e^3 + 5*a^7*b*d^2*e^4 - a^8*d*e^5 + (b^8*d^5*e - 5*a*b^7*d^4*e^2 + 10*a^2*b^6*d^3*e^3 - 10*a^3*b^5*d^2*e^4 + 5*a^4*b^4*d*e^5 - a^5*b^3*e^6)*x^4 + (b^8*d^6 - 2*a*b^7*d^5*e - 5*a^2*b^6*d^4*e^2 + 20*a^3*b^5*d^3*e^3 - 25*a^4*b^4*d^2*e^4 + 14*a^5*b^3*d*e^5 - 3*a^6*b^2*e^6)*x^3 + 3*(a*b^7*d^6 - 4*a^2*b^6*d^5*e + 5*a^3*b^5*d^4*e^2 - 5*a^5*b^3*d^2*e^4 + 4*a^6*b^2*d*e^5 - a^7*b*e^6)*x^2 + (3*a^2*b^6*d^6 - 14*a^3*b^5*d^5*e + 25*a^4*b^4*d^4*e^2 - 20*a^5*b^3*d^3*e^3 + 5*a^6*b^2*d^2*e^4 + 2*a^7*b*d*e^5 - a^8*e^6)*x)","B",0
2041,1,1151,0,0.483984," ","integrate((b*x+a)/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, b^{5} d^{5} - 15 \, a b^{4} d^{4} e + 60 \, a^{2} b^{3} d^{3} e^{2} - 20 \, a^{3} b^{2} d^{2} e^{3} - 30 \, a^{4} b d e^{4} + 3 \, a^{5} e^{5} + 60 \, {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 30 \, {\left(3 \, b^{5} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 5 \, a^{2} b^{3} e^{5}\right)} x^{3} + 10 \, {\left(2 \, b^{5} d^{3} e^{2} + 21 \, a b^{4} d^{2} e^{3} - 12 \, a^{2} b^{3} d e^{4} - 11 \, a^{3} b^{2} e^{5}\right)} x^{2} - 5 \, {\left(b^{5} d^{4} e - 12 \, a b^{4} d^{3} e^{2} - 24 \, a^{2} b^{3} d^{2} e^{3} + 32 \, a^{3} b^{2} d e^{4} + 3 \, a^{4} b e^{5}\right)} x + 60 \, {\left(b^{5} e^{5} x^{5} + a^{3} b^{2} d^{2} e^{3} + {\left(2 \, b^{5} d e^{4} + 3 \, a b^{4} e^{5}\right)} x^{4} + {\left(b^{5} d^{2} e^{3} + 6 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + {\left(3 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} d^{2} e^{3} + 2 \, a^{3} b^{2} d e^{4}\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left(b^{5} e^{5} x^{5} + a^{3} b^{2} d^{2} e^{3} + {\left(2 \, b^{5} d e^{4} + 3 \, a b^{4} e^{5}\right)} x^{4} + {\left(b^{5} d^{2} e^{3} + 6 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + {\left(3 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} d^{2} e^{3} + 2 \, a^{3} b^{2} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(a^{3} b^{6} d^{8} - 6 \, a^{4} b^{5} d^{7} e + 15 \, a^{5} b^{4} d^{6} e^{2} - 20 \, a^{6} b^{3} d^{5} e^{3} + 15 \, a^{7} b^{2} d^{4} e^{4} - 6 \, a^{8} b d^{3} e^{5} + a^{9} d^{2} e^{6} + {\left(b^{9} d^{6} e^{2} - 6 \, a b^{8} d^{5} e^{3} + 15 \, a^{2} b^{7} d^{4} e^{4} - 20 \, a^{3} b^{6} d^{3} e^{5} + 15 \, a^{4} b^{5} d^{2} e^{6} - 6 \, a^{5} b^{4} d e^{7} + a^{6} b^{3} e^{8}\right)} x^{5} + {\left(2 \, b^{9} d^{7} e - 9 \, a b^{8} d^{6} e^{2} + 12 \, a^{2} b^{7} d^{5} e^{3} + 5 \, a^{3} b^{6} d^{4} e^{4} - 30 \, a^{4} b^{5} d^{3} e^{5} + 33 \, a^{5} b^{4} d^{2} e^{6} - 16 \, a^{6} b^{3} d e^{7} + 3 \, a^{7} b^{2} e^{8}\right)} x^{4} + {\left(b^{9} d^{8} - 18 \, a^{2} b^{7} d^{6} e^{2} + 52 \, a^{3} b^{6} d^{5} e^{3} - 60 \, a^{4} b^{5} d^{4} e^{4} + 24 \, a^{5} b^{4} d^{3} e^{5} + 10 \, a^{6} b^{3} d^{2} e^{6} - 12 \, a^{7} b^{2} d e^{7} + 3 \, a^{8} b e^{8}\right)} x^{3} + {\left(3 \, a b^{8} d^{8} - 12 \, a^{2} b^{7} d^{7} e + 10 \, a^{3} b^{6} d^{6} e^{2} + 24 \, a^{4} b^{5} d^{5} e^{3} - 60 \, a^{5} b^{4} d^{4} e^{4} + 52 \, a^{6} b^{3} d^{3} e^{5} - 18 \, a^{7} b^{2} d^{2} e^{6} + a^{9} e^{8}\right)} x^{2} + {\left(3 \, a^{2} b^{7} d^{8} - 16 \, a^{3} b^{6} d^{7} e + 33 \, a^{4} b^{5} d^{6} e^{2} - 30 \, a^{5} b^{4} d^{5} e^{3} + 5 \, a^{6} b^{3} d^{4} e^{4} + 12 \, a^{7} b^{2} d^{3} e^{5} - 9 \, a^{8} b d^{2} e^{6} + 2 \, a^{9} d e^{7}\right)} x\right)}}"," ",0,"-1/6*(2*b^5*d^5 - 15*a*b^4*d^4*e + 60*a^2*b^3*d^3*e^2 - 20*a^3*b^2*d^2*e^3 - 30*a^4*b*d*e^4 + 3*a^5*e^5 + 60*(b^5*d*e^4 - a*b^4*e^5)*x^4 + 30*(3*b^5*d^2*e^3 + 2*a*b^4*d*e^4 - 5*a^2*b^3*e^5)*x^3 + 10*(2*b^5*d^3*e^2 + 21*a*b^4*d^2*e^3 - 12*a^2*b^3*d*e^4 - 11*a^3*b^2*e^5)*x^2 - 5*(b^5*d^4*e - 12*a*b^4*d^3*e^2 - 24*a^2*b^3*d^2*e^3 + 32*a^3*b^2*d*e^4 + 3*a^4*b*e^5)*x + 60*(b^5*e^5*x^5 + a^3*b^2*d^2*e^3 + (2*b^5*d*e^4 + 3*a*b^4*e^5)*x^4 + (b^5*d^2*e^3 + 6*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + (3*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 + (3*a^2*b^3*d^2*e^3 + 2*a^3*b^2*d*e^4)*x)*log(b*x + a) - 60*(b^5*e^5*x^5 + a^3*b^2*d^2*e^3 + (2*b^5*d*e^4 + 3*a*b^4*e^5)*x^4 + (b^5*d^2*e^3 + 6*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + (3*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 + (3*a^2*b^3*d^2*e^3 + 2*a^3*b^2*d*e^4)*x)*log(e*x + d))/(a^3*b^6*d^8 - 6*a^4*b^5*d^7*e + 15*a^5*b^4*d^6*e^2 - 20*a^6*b^3*d^5*e^3 + 15*a^7*b^2*d^4*e^4 - 6*a^8*b*d^3*e^5 + a^9*d^2*e^6 + (b^9*d^6*e^2 - 6*a*b^8*d^5*e^3 + 15*a^2*b^7*d^4*e^4 - 20*a^3*b^6*d^3*e^5 + 15*a^4*b^5*d^2*e^6 - 6*a^5*b^4*d*e^7 + a^6*b^3*e^8)*x^5 + (2*b^9*d^7*e - 9*a*b^8*d^6*e^2 + 12*a^2*b^7*d^5*e^3 + 5*a^3*b^6*d^4*e^4 - 30*a^4*b^5*d^3*e^5 + 33*a^5*b^4*d^2*e^6 - 16*a^6*b^3*d*e^7 + 3*a^7*b^2*e^8)*x^4 + (b^9*d^8 - 18*a^2*b^7*d^6*e^2 + 52*a^3*b^6*d^5*e^3 - 60*a^4*b^5*d^4*e^4 + 24*a^5*b^4*d^3*e^5 + 10*a^6*b^3*d^2*e^6 - 12*a^7*b^2*d*e^7 + 3*a^8*b*e^8)*x^3 + (3*a*b^8*d^8 - 12*a^2*b^7*d^7*e + 10*a^3*b^6*d^6*e^2 + 24*a^4*b^5*d^5*e^3 - 60*a^5*b^4*d^4*e^4 + 52*a^6*b^3*d^3*e^5 - 18*a^7*b^2*d^2*e^6 + a^9*e^8)*x^2 + (3*a^2*b^7*d^8 - 16*a^3*b^6*d^7*e + 33*a^4*b^5*d^6*e^2 - 30*a^5*b^4*d^5*e^3 + 5*a^6*b^3*d^4*e^4 + 12*a^7*b^2*d^3*e^5 - 9*a^8*b*d^2*e^6 + 2*a^9*d*e^7)*x)","B",0
2042,1,320,0,0.422002," ","integrate((b*x+a)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, {\left(429 \, b^{3} e^{7} x^{7} - 16 \, b^{3} d^{7} + 120 \, a b^{2} d^{6} e - 390 \, a^{2} b d^{5} e^{2} + 715 \, a^{3} d^{4} e^{3} + 33 \, {\left(46 \, b^{3} d e^{6} + 45 \, a b^{2} e^{7}\right)} x^{6} + 9 \, {\left(206 \, b^{3} d^{2} e^{5} + 600 \, a b^{2} d e^{6} + 195 \, a^{2} b e^{7}\right)} x^{5} + 5 \, {\left(160 \, b^{3} d^{3} e^{4} + 1374 \, a b^{2} d^{2} e^{5} + 1326 \, a^{2} b d e^{6} + 143 \, a^{3} e^{7}\right)} x^{4} + 5 \, {\left(b^{3} d^{4} e^{3} + 636 \, a b^{2} d^{3} e^{4} + 1794 \, a^{2} b d^{2} e^{5} + 572 \, a^{3} d e^{6}\right)} x^{3} - 3 \, {\left(2 \, b^{3} d^{5} e^{2} - 15 \, a b^{2} d^{4} e^{3} - 1560 \, a^{2} b d^{3} e^{4} - 1430 \, a^{3} d^{2} e^{5}\right)} x^{2} + {\left(8 \, b^{3} d^{6} e - 60 \, a b^{2} d^{5} e^{2} + 195 \, a^{2} b d^{4} e^{3} + 2860 \, a^{3} d^{3} e^{4}\right)} x\right)} \sqrt{e x + d}}{6435 \, e^{4}}"," ",0,"2/6435*(429*b^3*e^7*x^7 - 16*b^3*d^7 + 120*a*b^2*d^6*e - 390*a^2*b*d^5*e^2 + 715*a^3*d^4*e^3 + 33*(46*b^3*d*e^6 + 45*a*b^2*e^7)*x^6 + 9*(206*b^3*d^2*e^5 + 600*a*b^2*d*e^6 + 195*a^2*b*e^7)*x^5 + 5*(160*b^3*d^3*e^4 + 1374*a*b^2*d^2*e^5 + 1326*a^2*b*d*e^6 + 143*a^3*e^7)*x^4 + 5*(b^3*d^4*e^3 + 636*a*b^2*d^3*e^4 + 1794*a^2*b*d^2*e^5 + 572*a^3*d*e^6)*x^3 - 3*(2*b^3*d^5*e^2 - 15*a*b^2*d^4*e^3 - 1560*a^2*b*d^3*e^4 - 1430*a^3*d^2*e^5)*x^2 + (8*b^3*d^6*e - 60*a*b^2*d^5*e^2 + 195*a^2*b*d^4*e^3 + 2860*a^3*d^3*e^4)*x)*sqrt(e*x + d)/e^4","B",0
2043,1,268,0,0.431696," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, b^{3} e^{6} x^{6} - 16 \, b^{3} d^{6} + 104 \, a b^{2} d^{5} e - 286 \, a^{2} b d^{4} e^{2} + 429 \, a^{3} d^{3} e^{3} + 63 \, {\left(9 \, b^{3} d e^{5} + 13 \, a b^{2} e^{6}\right)} x^{5} + 7 \, {\left(53 \, b^{3} d^{2} e^{4} + 299 \, a b^{2} d e^{5} + 143 \, a^{2} b e^{6}\right)} x^{4} + {\left(5 \, b^{3} d^{3} e^{3} + 1469 \, a b^{2} d^{2} e^{4} + 2717 \, a^{2} b d e^{5} + 429 \, a^{3} e^{6}\right)} x^{3} - 3 \, {\left(2 \, b^{3} d^{4} e^{2} - 13 \, a b^{2} d^{3} e^{3} - 715 \, a^{2} b d^{2} e^{4} - 429 \, a^{3} d e^{5}\right)} x^{2} + {\left(8 \, b^{3} d^{5} e - 52 \, a b^{2} d^{4} e^{2} + 143 \, a^{2} b d^{3} e^{3} + 1287 \, a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{3003 \, e^{4}}"," ",0,"2/3003*(231*b^3*e^6*x^6 - 16*b^3*d^6 + 104*a*b^2*d^5*e - 286*a^2*b*d^4*e^2 + 429*a^3*d^3*e^3 + 63*(9*b^3*d*e^5 + 13*a*b^2*e^6)*x^5 + 7*(53*b^3*d^2*e^4 + 299*a*b^2*d*e^5 + 143*a^2*b*e^6)*x^4 + (5*b^3*d^3*e^3 + 1469*a*b^2*d^2*e^4 + 2717*a^2*b*d*e^5 + 429*a^3*e^6)*x^3 - 3*(2*b^3*d^4*e^2 - 13*a*b^2*d^3*e^3 - 715*a^2*b*d^2*e^4 - 429*a^3*d*e^5)*x^2 + (8*b^3*d^5*e - 52*a*b^2*d^4*e^2 + 143*a^2*b*d^3*e^3 + 1287*a^3*d^2*e^4)*x)*sqrt(e*x + d)/e^4","B",0
2044,1,216,0,0.440903," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, b^{3} e^{5} x^{5} - 16 \, b^{3} d^{5} + 88 \, a b^{2} d^{4} e - 198 \, a^{2} b d^{3} e^{2} + 231 \, a^{3} d^{2} e^{3} + 35 \, {\left(4 \, b^{3} d e^{4} + 11 \, a b^{2} e^{5}\right)} x^{4} + 5 \, {\left(b^{3} d^{2} e^{3} + 110 \, a b^{2} d e^{4} + 99 \, a^{2} b e^{5}\right)} x^{3} - 3 \, {\left(2 \, b^{3} d^{3} e^{2} - 11 \, a b^{2} d^{2} e^{3} - 264 \, a^{2} b d e^{4} - 77 \, a^{3} e^{5}\right)} x^{2} + {\left(8 \, b^{3} d^{4} e - 44 \, a b^{2} d^{3} e^{2} + 99 \, a^{2} b d^{2} e^{3} + 462 \, a^{3} d e^{4}\right)} x\right)} \sqrt{e x + d}}{1155 \, e^{4}}"," ",0,"2/1155*(105*b^3*e^5*x^5 - 16*b^3*d^5 + 88*a*b^2*d^4*e - 198*a^2*b*d^3*e^2 + 231*a^3*d^2*e^3 + 35*(4*b^3*d*e^4 + 11*a*b^2*e^5)*x^4 + 5*(b^3*d^2*e^3 + 110*a*b^2*d*e^4 + 99*a^2*b*e^5)*x^3 - 3*(2*b^3*d^3*e^2 - 11*a*b^2*d^2*e^3 - 264*a^2*b*d*e^4 - 77*a^3*e^5)*x^2 + (8*b^3*d^4*e - 44*a*b^2*d^3*e^2 + 99*a^2*b*d^2*e^3 + 462*a^3*d*e^4)*x)*sqrt(e*x + d)/e^4","B",0
2045,1,164,0,0.412600," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{3} e^{4} x^{4} - 16 \, b^{3} d^{4} + 72 \, a b^{2} d^{3} e - 126 \, a^{2} b d^{2} e^{2} + 105 \, a^{3} d e^{3} + 5 \, {\left(b^{3} d e^{3} + 27 \, a b^{2} e^{4}\right)} x^{3} - 3 \, {\left(2 \, b^{3} d^{2} e^{2} - 9 \, a b^{2} d e^{3} - 63 \, a^{2} b e^{4}\right)} x^{2} + {\left(8 \, b^{3} d^{3} e - 36 \, a b^{2} d^{2} e^{2} + 63 \, a^{2} b d e^{3} + 105 \, a^{3} e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{4}}"," ",0,"2/315*(35*b^3*e^4*x^4 - 16*b^3*d^4 + 72*a*b^2*d^3*e - 126*a^2*b*d^2*e^2 + 105*a^3*d*e^3 + 5*(b^3*d*e^3 + 27*a*b^2*e^4)*x^3 - 3*(2*b^3*d^2*e^2 - 9*a*b^2*d*e^3 - 63*a^2*b*e^4)*x^2 + (8*b^3*d^3*e - 36*a*b^2*d^2*e^2 + 63*a^2*b*d*e^3 + 105*a^3*e^4)*x)*sqrt(e*x + d)/e^4","A",0
2046,1,115,0,0.424215," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} e^{3} x^{3} - 16 \, b^{3} d^{3} + 56 \, a b^{2} d^{2} e - 70 \, a^{2} b d e^{2} + 35 \, a^{3} e^{3} - 3 \, {\left(2 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + {\left(8 \, b^{3} d^{2} e - 28 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{35 \, e^{4}}"," ",0,"2/35*(5*b^3*e^3*x^3 - 16*b^3*d^3 + 56*a*b^2*d^2*e - 70*a^2*b*d*e^2 + 35*a^3*e^3 - 3*(2*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + (8*b^3*d^2*e - 28*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d)/e^4","A",0
2047,1,124,0,0.439179," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} e^{3} x^{3} + 16 \, b^{3} d^{3} - 40 \, a b^{2} d^{2} e + 30 \, a^{2} b d e^{2} - 5 \, a^{3} e^{3} - {\left(2 \, b^{3} d e^{2} - 5 \, a b^{2} e^{3}\right)} x^{2} + {\left(8 \, b^{3} d^{2} e - 20 \, a b^{2} d e^{2} + 15 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{5 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"2/5*(b^3*e^3*x^3 + 16*b^3*d^3 - 40*a*b^2*d^2*e + 30*a^2*b*d*e^2 - 5*a^3*e^3 - (2*b^3*d*e^2 - 5*a*b^2*e^3)*x^2 + (8*b^3*d^2*e - 20*a*b^2*d*e^2 + 15*a^2*b*e^3)*x)*sqrt(e*x + d)/(e^5*x + d*e^4)","A",0
2048,1,136,0,0.418665," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} e^{3} x^{3} - 16 \, b^{3} d^{3} + 24 \, a b^{2} d^{2} e - 6 \, a^{2} b d e^{2} - a^{3} e^{3} - 3 \, {\left(2 \, b^{3} d e^{2} - 3 \, a b^{2} e^{3}\right)} x^{2} - 3 \, {\left(8 \, b^{3} d^{2} e - 12 \, a b^{2} d e^{2} + 3 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"2/3*(b^3*e^3*x^3 - 16*b^3*d^3 + 24*a*b^2*d^2*e - 6*a^2*b*d*e^2 - a^3*e^3 - 3*(2*b^3*d*e^2 - 3*a*b^2*e^3)*x^2 - 3*(8*b^3*d^2*e - 12*a*b^2*d*e^2 + 3*a^2*b*e^3)*x)*sqrt(e*x + d)/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
2049,1,148,0,0.420849," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} e^{3} x^{3} + 16 \, b^{3} d^{3} - 8 \, a b^{2} d^{2} e - 2 \, a^{2} b d e^{2} - a^{3} e^{3} + 15 \, {\left(2 \, b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 5 \, {\left(8 \, b^{3} d^{2} e - 4 \, a b^{2} d e^{2} - a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{5 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"2/5*(5*b^3*e^3*x^3 + 16*b^3*d^3 - 8*a*b^2*d^2*e - 2*a^2*b*d*e^2 - a^3*e^3 + 15*(2*b^3*d*e^2 - a*b^2*e^3)*x^2 + 5*(8*b^3*d^2*e - 4*a*b^2*d*e^2 - a^2*b*e^3)*x)*sqrt(e*x + d)/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
2050,1,579,0,0.441257," ","integrate((b*x+a)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(21879 \, b^{5} e^{9} x^{9} - 256 \, b^{5} d^{9} + 2432 \, a b^{4} d^{8} e - 10336 \, a^{2} b^{3} d^{7} e^{2} + 25840 \, a^{3} b^{2} d^{6} e^{3} - 41990 \, a^{4} b d^{5} e^{4} + 46189 \, a^{5} d^{4} e^{5} + 1287 \, {\left(58 \, b^{5} d e^{8} + 95 \, a b^{4} e^{9}\right)} x^{8} + 858 \, {\left(101 \, b^{5} d^{2} e^{7} + 494 \, a b^{4} d e^{8} + 323 \, a^{2} b^{3} e^{9}\right)} x^{7} + 66 \, {\left(524 \, b^{5} d^{3} e^{6} + 7619 \, a b^{4} d^{2} e^{7} + 14858 \, a^{2} b^{3} d e^{8} + 4845 \, a^{3} b^{2} e^{9}\right)} x^{6} + 9 \, {\left(7 \, b^{5} d^{4} e^{5} + 23028 \, a b^{4} d^{3} e^{6} + 133076 \, a^{2} b^{3} d^{2} e^{7} + 129200 \, a^{3} b^{2} d e^{8} + 20995 \, a^{4} b e^{9}\right)} x^{5} - {\left(70 \, b^{5} d^{5} e^{4} - 665 \, a b^{4} d^{4} e^{5} - 516800 \, a^{2} b^{3} d^{3} e^{6} - 1479340 \, a^{3} b^{2} d^{2} e^{7} - 713830 \, a^{4} b d e^{8} - 46189 \, a^{5} e^{9}\right)} x^{4} + 2 \, {\left(40 \, b^{5} d^{6} e^{3} - 380 \, a b^{4} d^{5} e^{4} + 1615 \, a^{2} b^{3} d^{4} e^{5} + 342380 \, a^{3} b^{2} d^{3} e^{6} + 482885 \, a^{4} b d^{2} e^{7} + 92378 \, a^{5} d e^{8}\right)} x^{3} - 6 \, {\left(16 \, b^{5} d^{7} e^{2} - 152 \, a b^{4} d^{6} e^{3} + 646 \, a^{2} b^{3} d^{5} e^{4} - 1615 \, a^{3} b^{2} d^{4} e^{5} - 83980 \, a^{4} b d^{3} e^{6} - 46189 \, a^{5} d^{2} e^{7}\right)} x^{2} + {\left(128 \, b^{5} d^{8} e - 1216 \, a b^{4} d^{7} e^{2} + 5168 \, a^{2} b^{3} d^{6} e^{3} - 12920 \, a^{3} b^{2} d^{5} e^{4} + 20995 \, a^{4} b d^{4} e^{5} + 184756 \, a^{5} d^{3} e^{6}\right)} x\right)} \sqrt{e x + d}}{415701 \, e^{6}}"," ",0,"2/415701*(21879*b^5*e^9*x^9 - 256*b^5*d^9 + 2432*a*b^4*d^8*e - 10336*a^2*b^3*d^7*e^2 + 25840*a^3*b^2*d^6*e^3 - 41990*a^4*b*d^5*e^4 + 46189*a^5*d^4*e^5 + 1287*(58*b^5*d*e^8 + 95*a*b^4*e^9)*x^8 + 858*(101*b^5*d^2*e^7 + 494*a*b^4*d*e^8 + 323*a^2*b^3*e^9)*x^7 + 66*(524*b^5*d^3*e^6 + 7619*a*b^4*d^2*e^7 + 14858*a^2*b^3*d*e^8 + 4845*a^3*b^2*e^9)*x^6 + 9*(7*b^5*d^4*e^5 + 23028*a*b^4*d^3*e^6 + 133076*a^2*b^3*d^2*e^7 + 129200*a^3*b^2*d*e^8 + 20995*a^4*b*e^9)*x^5 - (70*b^5*d^5*e^4 - 665*a*b^4*d^4*e^5 - 516800*a^2*b^3*d^3*e^6 - 1479340*a^3*b^2*d^2*e^7 - 713830*a^4*b*d*e^8 - 46189*a^5*e^9)*x^4 + 2*(40*b^5*d^6*e^3 - 380*a*b^4*d^5*e^4 + 1615*a^2*b^3*d^4*e^5 + 342380*a^3*b^2*d^3*e^6 + 482885*a^4*b*d^2*e^7 + 92378*a^5*d*e^8)*x^3 - 6*(16*b^5*d^7*e^2 - 152*a*b^4*d^6*e^3 + 646*a^2*b^3*d^5*e^4 - 1615*a^3*b^2*d^4*e^5 - 83980*a^4*b*d^3*e^6 - 46189*a^5*d^2*e^7)*x^2 + (128*b^5*d^8*e - 1216*a*b^4*d^7*e^2 + 5168*a^2*b^3*d^6*e^3 - 12920*a^3*b^2*d^5*e^4 + 20995*a^4*b*d^4*e^5 + 184756*a^5*d^3*e^6)*x)*sqrt(e*x + d)/e^6","B",0
2051,1,497,0,0.440602," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(9009 \, b^{5} e^{8} x^{8} - 256 \, b^{5} d^{8} + 2176 \, a b^{4} d^{7} e - 8160 \, a^{2} b^{3} d^{6} e^{2} + 17680 \, a^{3} b^{2} d^{5} e^{3} - 24310 \, a^{4} b d^{4} e^{4} + 21879 \, a^{5} d^{3} e^{5} + 3003 \, {\left(7 \, b^{5} d e^{7} + 17 \, a b^{4} e^{8}\right)} x^{7} + 231 \, {\left(55 \, b^{5} d^{2} e^{6} + 527 \, a b^{4} d e^{7} + 510 \, a^{2} b^{3} e^{8}\right)} x^{6} + 63 \, {\left(b^{5} d^{3} e^{5} + 1207 \, a b^{4} d^{2} e^{6} + 4590 \, a^{2} b^{3} d e^{7} + 2210 \, a^{3} b^{2} e^{8}\right)} x^{5} - 35 \, {\left(2 \, b^{5} d^{4} e^{4} - 17 \, a b^{4} d^{3} e^{5} - 5406 \, a^{2} b^{3} d^{2} e^{6} - 10166 \, a^{3} b^{2} d e^{7} - 2431 \, a^{4} b e^{8}\right)} x^{4} + {\left(80 \, b^{5} d^{5} e^{3} - 680 \, a b^{4} d^{4} e^{4} + 2550 \, a^{2} b^{3} d^{3} e^{5} + 249730 \, a^{3} b^{2} d^{2} e^{6} + 230945 \, a^{4} b d e^{7} + 21879 \, a^{5} e^{8}\right)} x^{3} - 3 \, {\left(32 \, b^{5} d^{6} e^{2} - 272 \, a b^{4} d^{5} e^{3} + 1020 \, a^{2} b^{3} d^{4} e^{4} - 2210 \, a^{3} b^{2} d^{3} e^{5} - 60775 \, a^{4} b d^{2} e^{6} - 21879 \, a^{5} d e^{7}\right)} x^{2} + {\left(128 \, b^{5} d^{7} e - 1088 \, a b^{4} d^{6} e^{2} + 4080 \, a^{2} b^{3} d^{5} e^{3} - 8840 \, a^{3} b^{2} d^{4} e^{4} + 12155 \, a^{4} b d^{3} e^{5} + 65637 \, a^{5} d^{2} e^{6}\right)} x\right)} \sqrt{e x + d}}{153153 \, e^{6}}"," ",0,"2/153153*(9009*b^5*e^8*x^8 - 256*b^5*d^8 + 2176*a*b^4*d^7*e - 8160*a^2*b^3*d^6*e^2 + 17680*a^3*b^2*d^5*e^3 - 24310*a^4*b*d^4*e^4 + 21879*a^5*d^3*e^5 + 3003*(7*b^5*d*e^7 + 17*a*b^4*e^8)*x^7 + 231*(55*b^5*d^2*e^6 + 527*a*b^4*d*e^7 + 510*a^2*b^3*e^8)*x^6 + 63*(b^5*d^3*e^5 + 1207*a*b^4*d^2*e^6 + 4590*a^2*b^3*d*e^7 + 2210*a^3*b^2*e^8)*x^5 - 35*(2*b^5*d^4*e^4 - 17*a*b^4*d^3*e^5 - 5406*a^2*b^3*d^2*e^6 - 10166*a^3*b^2*d*e^7 - 2431*a^4*b*e^8)*x^4 + (80*b^5*d^5*e^3 - 680*a*b^4*d^4*e^4 + 2550*a^2*b^3*d^3*e^5 + 249730*a^3*b^2*d^2*e^6 + 230945*a^4*b*d*e^7 + 21879*a^5*e^8)*x^3 - 3*(32*b^5*d^6*e^2 - 272*a*b^4*d^5*e^3 + 1020*a^2*b^3*d^4*e^4 - 2210*a^3*b^2*d^3*e^5 - 60775*a^4*b*d^2*e^6 - 21879*a^5*d*e^7)*x^2 + (128*b^5*d^7*e - 1088*a*b^4*d^6*e^2 + 4080*a^2*b^3*d^5*e^3 - 8840*a^3*b^2*d^4*e^4 + 12155*a^4*b*d^3*e^5 + 65637*a^5*d^2*e^6)*x)*sqrt(e*x + d)/e^6","B",0
2052,1,418,0,0.407684," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, b^{5} e^{7} x^{7} - 256 \, b^{5} d^{7} + 1920 \, a b^{4} d^{6} e - 6240 \, a^{2} b^{3} d^{5} e^{2} + 11440 \, a^{3} b^{2} d^{4} e^{3} - 12870 \, a^{4} b d^{3} e^{4} + 9009 \, a^{5} d^{2} e^{5} + 231 \, {\left(16 \, b^{5} d e^{6} + 75 \, a b^{4} e^{7}\right)} x^{6} + 63 \, {\left(b^{5} d^{2} e^{5} + 350 \, a b^{4} d e^{6} + 650 \, a^{2} b^{3} e^{7}\right)} x^{5} - 35 \, {\left(2 \, b^{5} d^{3} e^{4} - 15 \, a b^{4} d^{2} e^{5} - 1560 \, a^{2} b^{3} d e^{6} - 1430 \, a^{3} b^{2} e^{7}\right)} x^{4} + 5 \, {\left(16 \, b^{5} d^{4} e^{3} - 120 \, a b^{4} d^{3} e^{4} + 390 \, a^{2} b^{3} d^{2} e^{5} + 14300 \, a^{3} b^{2} d e^{6} + 6435 \, a^{4} b e^{7}\right)} x^{3} - 3 \, {\left(32 \, b^{5} d^{5} e^{2} - 240 \, a b^{4} d^{4} e^{3} + 780 \, a^{2} b^{3} d^{3} e^{4} - 1430 \, a^{3} b^{2} d^{2} e^{5} - 17160 \, a^{4} b d e^{6} - 3003 \, a^{5} e^{7}\right)} x^{2} + {\left(128 \, b^{5} d^{6} e - 960 \, a b^{4} d^{5} e^{2} + 3120 \, a^{2} b^{3} d^{4} e^{3} - 5720 \, a^{3} b^{2} d^{3} e^{4} + 6435 \, a^{4} b d^{2} e^{5} + 18018 \, a^{5} d e^{6}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{6}}"," ",0,"2/45045*(3003*b^5*e^7*x^7 - 256*b^5*d^7 + 1920*a*b^4*d^6*e - 6240*a^2*b^3*d^5*e^2 + 11440*a^3*b^2*d^4*e^3 - 12870*a^4*b*d^3*e^4 + 9009*a^5*d^2*e^5 + 231*(16*b^5*d*e^6 + 75*a*b^4*e^7)*x^6 + 63*(b^5*d^2*e^5 + 350*a*b^4*d*e^6 + 650*a^2*b^3*e^7)*x^5 - 35*(2*b^5*d^3*e^4 - 15*a*b^4*d^2*e^5 - 1560*a^2*b^3*d*e^6 - 1430*a^3*b^2*e^7)*x^4 + 5*(16*b^5*d^4*e^3 - 120*a*b^4*d^3*e^4 + 390*a^2*b^3*d^2*e^5 + 14300*a^3*b^2*d*e^6 + 6435*a^4*b*e^7)*x^3 - 3*(32*b^5*d^5*e^2 - 240*a*b^4*d^4*e^3 + 780*a^2*b^3*d^3*e^4 - 1430*a^3*b^2*d^2*e^5 - 17160*a^4*b*d*e^6 - 3003*a^5*e^7)*x^2 + (128*b^5*d^6*e - 960*a*b^4*d^5*e^2 + 3120*a^2*b^3*d^4*e^3 - 5720*a^3*b^2*d^3*e^4 + 6435*a^4*b*d^2*e^5 + 18018*a^5*d*e^6)*x)*sqrt(e*x + d)/e^6","B",0
2053,1,338,0,0.431810," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, b^{5} e^{6} x^{6} - 256 \, b^{5} d^{6} + 1664 \, a b^{4} d^{5} e - 4576 \, a^{2} b^{3} d^{4} e^{2} + 6864 \, a^{3} b^{2} d^{3} e^{3} - 6006 \, a^{4} b d^{2} e^{4} + 3003 \, a^{5} d e^{5} + 63 \, {\left(b^{5} d e^{5} + 65 \, a b^{4} e^{6}\right)} x^{5} - 35 \, {\left(2 \, b^{5} d^{2} e^{4} - 13 \, a b^{4} d e^{5} - 286 \, a^{2} b^{3} e^{6}\right)} x^{4} + 10 \, {\left(8 \, b^{5} d^{3} e^{3} - 52 \, a b^{4} d^{2} e^{4} + 143 \, a^{2} b^{3} d e^{5} + 1287 \, a^{3} b^{2} e^{6}\right)} x^{3} - 3 \, {\left(32 \, b^{5} d^{4} e^{2} - 208 \, a b^{4} d^{3} e^{3} + 572 \, a^{2} b^{3} d^{2} e^{4} - 858 \, a^{3} b^{2} d e^{5} - 3003 \, a^{4} b e^{6}\right)} x^{2} + {\left(128 \, b^{5} d^{5} e - 832 \, a b^{4} d^{4} e^{2} + 2288 \, a^{2} b^{3} d^{3} e^{3} - 3432 \, a^{3} b^{2} d^{2} e^{4} + 3003 \, a^{4} b d e^{5} + 3003 \, a^{5} e^{6}\right)} x\right)} \sqrt{e x + d}}{9009 \, e^{6}}"," ",0,"2/9009*(693*b^5*e^6*x^6 - 256*b^5*d^6 + 1664*a*b^4*d^5*e - 4576*a^2*b^3*d^4*e^2 + 6864*a^3*b^2*d^3*e^3 - 6006*a^4*b*d^2*e^4 + 3003*a^5*d*e^5 + 63*(b^5*d*e^5 + 65*a*b^4*e^6)*x^5 - 35*(2*b^5*d^2*e^4 - 13*a*b^4*d*e^5 - 286*a^2*b^3*e^6)*x^4 + 10*(8*b^5*d^3*e^3 - 52*a*b^4*d^2*e^4 + 143*a^2*b^3*d*e^5 + 1287*a^3*b^2*e^6)*x^3 - 3*(32*b^5*d^4*e^2 - 208*a*b^4*d^3*e^3 + 572*a^2*b^3*d^2*e^4 - 858*a^3*b^2*d*e^5 - 3003*a^4*b*e^6)*x^2 + (128*b^5*d^5*e - 832*a*b^4*d^4*e^2 + 2288*a^2*b^3*d^3*e^3 - 3432*a^3*b^2*d^2*e^4 + 3003*a^4*b*d*e^5 + 3003*a^5*e^6)*x)*sqrt(e*x + d)/e^6","B",0
2054,1,261,0,0.433875," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, b^{5} e^{5} x^{5} - 256 \, b^{5} d^{5} + 1408 \, a b^{4} d^{4} e - 3168 \, a^{2} b^{3} d^{3} e^{2} + 3696 \, a^{3} b^{2} d^{2} e^{3} - 2310 \, a^{4} b d e^{4} + 693 \, a^{5} e^{5} - 35 \, {\left(2 \, b^{5} d e^{4} - 11 \, a b^{4} e^{5}\right)} x^{4} + 10 \, {\left(8 \, b^{5} d^{2} e^{3} - 44 \, a b^{4} d e^{4} + 99 \, a^{2} b^{3} e^{5}\right)} x^{3} - 6 \, {\left(16 \, b^{5} d^{3} e^{2} - 88 \, a b^{4} d^{2} e^{3} + 198 \, a^{2} b^{3} d e^{4} - 231 \, a^{3} b^{2} e^{5}\right)} x^{2} + {\left(128 \, b^{5} d^{4} e - 704 \, a b^{4} d^{3} e^{2} + 1584 \, a^{2} b^{3} d^{2} e^{3} - 1848 \, a^{3} b^{2} d e^{4} + 1155 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{6}}"," ",0,"2/693*(63*b^5*e^5*x^5 - 256*b^5*d^5 + 1408*a*b^4*d^4*e - 3168*a^2*b^3*d^3*e^2 + 3696*a^3*b^2*d^2*e^3 - 2310*a^4*b*d*e^4 + 693*a^5*e^5 - 35*(2*b^5*d*e^4 - 11*a*b^4*e^5)*x^4 + 10*(8*b^5*d^2*e^3 - 44*a*b^4*d*e^4 + 99*a^2*b^3*e^5)*x^3 - 6*(16*b^5*d^3*e^2 - 88*a*b^4*d^2*e^3 + 198*a^2*b^3*d*e^4 - 231*a^3*b^2*e^5)*x^2 + (128*b^5*d^4*e - 704*a*b^4*d^3*e^2 + 1584*a^2*b^3*d^2*e^3 - 1848*a^3*b^2*d*e^4 + 1155*a^4*b*e^5)*x)*sqrt(e*x + d)/e^6","A",0
2055,1,271,0,0.425444," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b^{5} e^{5} x^{5} + 256 \, b^{5} d^{5} - 1152 \, a b^{4} d^{4} e + 2016 \, a^{2} b^{3} d^{3} e^{2} - 1680 \, a^{3} b^{2} d^{2} e^{3} + 630 \, a^{4} b d e^{4} - 63 \, a^{5} e^{5} - 5 \, {\left(2 \, b^{5} d e^{4} - 9 \, a b^{4} e^{5}\right)} x^{4} + 2 \, {\left(8 \, b^{5} d^{2} e^{3} - 36 \, a b^{4} d e^{4} + 63 \, a^{2} b^{3} e^{5}\right)} x^{3} - 2 \, {\left(16 \, b^{5} d^{3} e^{2} - 72 \, a b^{4} d^{2} e^{3} + 126 \, a^{2} b^{3} d e^{4} - 105 \, a^{3} b^{2} e^{5}\right)} x^{2} + {\left(128 \, b^{5} d^{4} e - 576 \, a b^{4} d^{3} e^{2} + 1008 \, a^{2} b^{3} d^{2} e^{3} - 840 \, a^{3} b^{2} d e^{4} + 315 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{63 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"2/63*(7*b^5*e^5*x^5 + 256*b^5*d^5 - 1152*a*b^4*d^4*e + 2016*a^2*b^3*d^3*e^2 - 1680*a^3*b^2*d^2*e^3 + 630*a^4*b*d*e^4 - 63*a^5*e^5 - 5*(2*b^5*d*e^4 - 9*a*b^4*e^5)*x^4 + 2*(8*b^5*d^2*e^3 - 36*a*b^4*d*e^4 + 63*a^2*b^3*e^5)*x^3 - 2*(16*b^5*d^3*e^2 - 72*a*b^4*d^2*e^3 + 126*a^2*b^3*d*e^4 - 105*a^3*b^2*e^5)*x^2 + (128*b^5*d^4*e - 576*a*b^4*d^3*e^2 + 1008*a^2*b^3*d^2*e^3 - 840*a^3*b^2*d*e^4 + 315*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^7*x + d*e^6)","B",0
2056,1,283,0,0.430212," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{5} e^{5} x^{5} - 256 \, b^{5} d^{5} + 896 \, a b^{4} d^{4} e - 1120 \, a^{2} b^{3} d^{3} e^{2} + 560 \, a^{3} b^{2} d^{2} e^{3} - 70 \, a^{4} b d e^{4} - 7 \, a^{5} e^{5} - 3 \, {\left(2 \, b^{5} d e^{4} - 7 \, a b^{4} e^{5}\right)} x^{4} + 2 \, {\left(8 \, b^{5} d^{2} e^{3} - 28 \, a b^{4} d e^{4} + 35 \, a^{2} b^{3} e^{5}\right)} x^{3} - 6 \, {\left(16 \, b^{5} d^{3} e^{2} - 56 \, a b^{4} d^{2} e^{3} + 70 \, a^{2} b^{3} d e^{4} - 35 \, a^{3} b^{2} e^{5}\right)} x^{2} - 3 \, {\left(128 \, b^{5} d^{4} e - 448 \, a b^{4} d^{3} e^{2} + 560 \, a^{2} b^{3} d^{2} e^{3} - 280 \, a^{3} b^{2} d e^{4} + 35 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{21 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"2/21*(3*b^5*e^5*x^5 - 256*b^5*d^5 + 896*a*b^4*d^4*e - 1120*a^2*b^3*d^3*e^2 + 560*a^3*b^2*d^2*e^3 - 70*a^4*b*d*e^4 - 7*a^5*e^5 - 3*(2*b^5*d*e^4 - 7*a*b^4*e^5)*x^4 + 2*(8*b^5*d^2*e^3 - 28*a*b^4*d*e^4 + 35*a^2*b^3*e^5)*x^3 - 6*(16*b^5*d^3*e^2 - 56*a*b^4*d^2*e^3 + 70*a^2*b^3*d*e^4 - 35*a^3*b^2*e^5)*x^2 - 3*(128*b^5*d^4*e - 448*a*b^4*d^3*e^2 + 560*a^2*b^3*d^2*e^3 - 280*a^3*b^2*d*e^4 + 35*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","B",0
2057,1,294,0,0.432886," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{5} e^{5} x^{5} + 256 \, b^{5} d^{5} - 640 \, a b^{4} d^{4} e + 480 \, a^{2} b^{3} d^{3} e^{2} - 80 \, a^{3} b^{2} d^{2} e^{3} - 10 \, a^{4} b d e^{4} - 3 \, a^{5} e^{5} - 5 \, {\left(2 \, b^{5} d e^{4} - 5 \, a b^{4} e^{5}\right)} x^{4} + 10 \, {\left(8 \, b^{5} d^{2} e^{3} - 20 \, a b^{4} d e^{4} + 15 \, a^{2} b^{3} e^{5}\right)} x^{3} + 30 \, {\left(16 \, b^{5} d^{3} e^{2} - 40 \, a b^{4} d^{2} e^{3} + 30 \, a^{2} b^{3} d e^{4} - 5 \, a^{3} b^{2} e^{5}\right)} x^{2} + 5 \, {\left(128 \, b^{5} d^{4} e - 320 \, a b^{4} d^{3} e^{2} + 240 \, a^{2} b^{3} d^{2} e^{3} - 40 \, a^{3} b^{2} d e^{4} - 5 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"2/15*(3*b^5*e^5*x^5 + 256*b^5*d^5 - 640*a*b^4*d^4*e + 480*a^2*b^3*d^3*e^2 - 80*a^3*b^2*d^2*e^3 - 10*a^4*b*d*e^4 - 3*a^5*e^5 - 5*(2*b^5*d*e^4 - 5*a*b^4*e^5)*x^4 + 10*(8*b^5*d^2*e^3 - 20*a*b^4*d*e^4 + 15*a^2*b^3*e^5)*x^3 + 30*(16*b^5*d^3*e^2 - 40*a*b^4*d^2*e^3 + 30*a^2*b^3*d*e^4 - 5*a^3*b^2*e^5)*x^2 + 5*(128*b^5*d^4*e - 320*a*b^4*d^3*e^2 + 240*a^2*b^3*d^2*e^3 - 40*a^3*b^2*d*e^4 - 5*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","B",0
2058,1,891,0,0.445021," ","integrate((b*x+a)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(415701 \, b^{7} e^{11} x^{11} - 2048 \, b^{7} d^{11} + 23552 \, a b^{6} d^{10} e - 123648 \, a^{2} b^{5} d^{9} e^{2} + 391552 \, a^{3} b^{4} d^{8} e^{3} - 832048 \, a^{4} b^{3} d^{7} e^{4} + 1248072 \, a^{5} b^{2} d^{6} e^{5} - 1352078 \, a^{6} b d^{5} e^{6} + 1062347 \, a^{7} d^{4} e^{7} + 138567 \, {\left(10 \, b^{7} d e^{10} + 23 \, a b^{6} e^{11}\right)} x^{10} + 7293 \, {\left(214 \, b^{7} d^{2} e^{9} + 1472 \, a b^{6} d e^{10} + 1449 \, a^{2} b^{5} e^{11}\right)} x^{9} + 1287 \, {\left(464 \, b^{7} d^{3} e^{8} + 9522 \, a b^{6} d^{2} e^{9} + 28014 \, a^{2} b^{5} d e^{10} + 15295 \, a^{3} b^{4} e^{11}\right)} x^{8} + 429 \, {\left(b^{7} d^{4} e^{7} + 11132 \, a b^{6} d^{3} e^{8} + 97566 \, a^{2} b^{5} d^{2} e^{9} + 159068 \, a^{3} b^{4} d e^{10} + 52003 \, a^{4} b^{3} e^{11}\right)} x^{7} - 231 \, {\left(2 \, b^{7} d^{5} e^{6} - 23 \, a b^{6} d^{4} e^{7} - 72312 \, a^{2} b^{5} d^{3} e^{8} - 350474 \, a^{3} b^{4} d^{2} e^{9} - 341734 \, a^{4} b^{3} d e^{10} - 66861 \, a^{5} b^{2} e^{11}\right)} x^{6} + 63 \, {\left(8 \, b^{7} d^{6} e^{5} - 92 \, a b^{6} d^{5} e^{6} + 483 \, a^{2} b^{5} d^{4} e^{7} + 529644 \, a^{3} b^{4} d^{3} e^{8} + 1530374 \, a^{4} b^{3} d^{2} e^{9} + 891480 \, a^{5} b^{2} d e^{10} + 96577 \, a^{6} b e^{11}\right)} x^{5} - {\left(560 \, b^{7} d^{7} e^{4} - 6440 \, a b^{6} d^{6} e^{5} + 33810 \, a^{2} b^{5} d^{5} e^{6} - 107065 \, a^{3} b^{4} d^{4} e^{7} - 41602400 \, a^{4} b^{3} d^{3} e^{8} - 71452122 \, a^{5} b^{2} d^{2} e^{9} - 22985326 \, a^{6} b d e^{10} - 1062347 \, a^{7} e^{11}\right)} x^{4} + {\left(640 \, b^{7} d^{8} e^{3} - 7360 \, a b^{6} d^{7} e^{4} + 38640 \, a^{2} b^{5} d^{6} e^{5} - 122360 \, a^{3} b^{4} d^{5} e^{6} + 260015 \, a^{4} b^{3} d^{4} e^{7} + 33073908 \, a^{5} b^{2} d^{3} e^{8} + 31097794 \, a^{6} b d^{2} e^{9} + 4249388 \, a^{7} d e^{10}\right)} x^{3} - 3 \, {\left(256 \, b^{7} d^{9} e^{2} - 2944 \, a b^{6} d^{8} e^{3} + 15456 \, a^{2} b^{5} d^{7} e^{4} - 48944 \, a^{3} b^{4} d^{6} e^{5} + 104006 \, a^{4} b^{3} d^{5} e^{6} - 156009 \, a^{5} b^{2} d^{4} e^{7} - 5408312 \, a^{6} b d^{3} e^{8} - 2124694 \, a^{7} d^{2} e^{9}\right)} x^{2} + {\left(1024 \, b^{7} d^{10} e - 11776 \, a b^{6} d^{9} e^{2} + 61824 \, a^{2} b^{5} d^{8} e^{3} - 195776 \, a^{3} b^{4} d^{7} e^{4} + 416024 \, a^{4} b^{3} d^{6} e^{5} - 624036 \, a^{5} b^{2} d^{5} e^{6} + 676039 \, a^{6} b d^{4} e^{7} + 4249388 \, a^{7} d^{3} e^{8}\right)} x\right)} \sqrt{e x + d}}{9561123 \, e^{8}}"," ",0,"2/9561123*(415701*b^7*e^11*x^11 - 2048*b^7*d^11 + 23552*a*b^6*d^10*e - 123648*a^2*b^5*d^9*e^2 + 391552*a^3*b^4*d^8*e^3 - 832048*a^4*b^3*d^7*e^4 + 1248072*a^5*b^2*d^6*e^5 - 1352078*a^6*b*d^5*e^6 + 1062347*a^7*d^4*e^7 + 138567*(10*b^7*d*e^10 + 23*a*b^6*e^11)*x^10 + 7293*(214*b^7*d^2*e^9 + 1472*a*b^6*d*e^10 + 1449*a^2*b^5*e^11)*x^9 + 1287*(464*b^7*d^3*e^8 + 9522*a*b^6*d^2*e^9 + 28014*a^2*b^5*d*e^10 + 15295*a^3*b^4*e^11)*x^8 + 429*(b^7*d^4*e^7 + 11132*a*b^6*d^3*e^8 + 97566*a^2*b^5*d^2*e^9 + 159068*a^3*b^4*d*e^10 + 52003*a^4*b^3*e^11)*x^7 - 231*(2*b^7*d^5*e^6 - 23*a*b^6*d^4*e^7 - 72312*a^2*b^5*d^3*e^8 - 350474*a^3*b^4*d^2*e^9 - 341734*a^4*b^3*d*e^10 - 66861*a^5*b^2*e^11)*x^6 + 63*(8*b^7*d^6*e^5 - 92*a*b^6*d^5*e^6 + 483*a^2*b^5*d^4*e^7 + 529644*a^3*b^4*d^3*e^8 + 1530374*a^4*b^3*d^2*e^9 + 891480*a^5*b^2*d*e^10 + 96577*a^6*b*e^11)*x^5 - (560*b^7*d^7*e^4 - 6440*a*b^6*d^6*e^5 + 33810*a^2*b^5*d^5*e^6 - 107065*a^3*b^4*d^4*e^7 - 41602400*a^4*b^3*d^3*e^8 - 71452122*a^5*b^2*d^2*e^9 - 22985326*a^6*b*d*e^10 - 1062347*a^7*e^11)*x^4 + (640*b^7*d^8*e^3 - 7360*a*b^6*d^7*e^4 + 38640*a^2*b^5*d^6*e^5 - 122360*a^3*b^4*d^5*e^6 + 260015*a^4*b^3*d^4*e^7 + 33073908*a^5*b^2*d^3*e^8 + 31097794*a^6*b*d^2*e^9 + 4249388*a^7*d*e^10)*x^3 - 3*(256*b^7*d^9*e^2 - 2944*a*b^6*d^8*e^3 + 15456*a^2*b^5*d^7*e^4 - 48944*a^3*b^4*d^6*e^5 + 104006*a^4*b^3*d^5*e^6 - 156009*a^5*b^2*d^4*e^7 - 5408312*a^6*b*d^3*e^8 - 2124694*a^7*d^2*e^9)*x^2 + (1024*b^7*d^10*e - 11776*a*b^6*d^9*e^2 + 61824*a^2*b^5*d^8*e^3 - 195776*a^3*b^4*d^7*e^4 + 416024*a^4*b^3*d^6*e^5 - 624036*a^5*b^2*d^5*e^6 + 676039*a^6*b*d^4*e^7 + 4249388*a^7*d^3*e^8)*x)*sqrt(e*x + d)/e^8","B",0
2059,1,783,0,0.431293," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(138567 \, b^{7} e^{10} x^{10} - 2048 \, b^{7} d^{10} + 21504 \, a b^{6} d^{9} e - 102144 \, a^{2} b^{5} d^{8} e^{2} + 289408 \, a^{3} b^{4} d^{7} e^{3} - 542640 \, a^{4} b^{3} d^{6} e^{4} + 705432 \, a^{5} b^{2} d^{5} e^{5} - 646646 \, a^{6} b d^{4} e^{6} + 415701 \, a^{7} d^{3} e^{7} + 7293 \, {\left(43 \, b^{7} d e^{9} + 147 \, a b^{6} e^{10}\right)} x^{9} + 3861 \, {\left(47 \, b^{7} d^{2} e^{8} + 637 \, a b^{6} d e^{9} + 931 \, a^{2} b^{5} e^{10}\right)} x^{8} + 429 \, {\left(b^{7} d^{3} e^{7} + 3381 \, a b^{6} d^{2} e^{8} + 19551 \, a^{2} b^{5} d e^{9} + 15827 \, a^{3} b^{4} e^{10}\right)} x^{7} - 231 \, {\left(2 \, b^{7} d^{4} e^{6} - 21 \, a b^{6} d^{3} e^{7} - 21945 \, a^{2} b^{5} d^{2} e^{8} - 70091 \, a^{3} b^{4} d e^{9} - 33915 \, a^{4} b^{3} e^{10}\right)} x^{6} + 63 \, {\left(8 \, b^{7} d^{5} e^{5} - 84 \, a b^{6} d^{4} e^{6} + 399 \, a^{2} b^{5} d^{3} e^{7} + 160531 \, a^{3} b^{4} d^{2} e^{8} + 305235 \, a^{4} b^{3} d e^{9} + 88179 \, a^{5} b^{2} e^{10}\right)} x^{5} - 7 \, {\left(80 \, b^{7} d^{6} e^{4} - 840 \, a b^{6} d^{5} e^{5} + 3990 \, a^{2} b^{5} d^{4} e^{6} - 11305 \, a^{3} b^{4} d^{3} e^{7} - 1797495 \, a^{4} b^{3} d^{2} e^{8} - 2028117 \, a^{5} b^{2} d e^{9} - 323323 \, a^{6} b e^{10}\right)} x^{4} + {\left(640 \, b^{7} d^{7} e^{3} - 6720 \, a b^{6} d^{6} e^{4} + 31920 \, a^{2} b^{5} d^{5} e^{5} - 90440 \, a^{3} b^{4} d^{4} e^{6} + 169575 \, a^{4} b^{3} d^{3} e^{7} + 9964227 \, a^{5} b^{2} d^{2} e^{8} + 6143137 \, a^{6} b d e^{9} + 415701 \, a^{7} e^{10}\right)} x^{3} - 3 \, {\left(256 \, b^{7} d^{8} e^{2} - 2688 \, a b^{6} d^{7} e^{3} + 12768 \, a^{2} b^{5} d^{6} e^{4} - 36176 \, a^{3} b^{4} d^{5} e^{5} + 67830 \, a^{4} b^{3} d^{4} e^{6} - 88179 \, a^{5} b^{2} d^{3} e^{7} - 1616615 \, a^{6} b d^{2} e^{8} - 415701 \, a^{7} d e^{9}\right)} x^{2} + {\left(1024 \, b^{7} d^{9} e - 10752 \, a b^{6} d^{8} e^{2} + 51072 \, a^{2} b^{5} d^{7} e^{3} - 144704 \, a^{3} b^{4} d^{6} e^{4} + 271320 \, a^{4} b^{3} d^{5} e^{5} - 352716 \, a^{5} b^{2} d^{4} e^{6} + 323323 \, a^{6} b d^{3} e^{7} + 1247103 \, a^{7} d^{2} e^{8}\right)} x\right)} \sqrt{e x + d}}{2909907 \, e^{8}}"," ",0,"2/2909907*(138567*b^7*e^10*x^10 - 2048*b^7*d^10 + 21504*a*b^6*d^9*e - 102144*a^2*b^5*d^8*e^2 + 289408*a^3*b^4*d^7*e^3 - 542640*a^4*b^3*d^6*e^4 + 705432*a^5*b^2*d^5*e^5 - 646646*a^6*b*d^4*e^6 + 415701*a^7*d^3*e^7 + 7293*(43*b^7*d*e^9 + 147*a*b^6*e^10)*x^9 + 3861*(47*b^7*d^2*e^8 + 637*a*b^6*d*e^9 + 931*a^2*b^5*e^10)*x^8 + 429*(b^7*d^3*e^7 + 3381*a*b^6*d^2*e^8 + 19551*a^2*b^5*d*e^9 + 15827*a^3*b^4*e^10)*x^7 - 231*(2*b^7*d^4*e^6 - 21*a*b^6*d^3*e^7 - 21945*a^2*b^5*d^2*e^8 - 70091*a^3*b^4*d*e^9 - 33915*a^4*b^3*e^10)*x^6 + 63*(8*b^7*d^5*e^5 - 84*a*b^6*d^4*e^6 + 399*a^2*b^5*d^3*e^7 + 160531*a^3*b^4*d^2*e^8 + 305235*a^4*b^3*d*e^9 + 88179*a^5*b^2*e^10)*x^5 - 7*(80*b^7*d^6*e^4 - 840*a*b^6*d^5*e^5 + 3990*a^2*b^5*d^4*e^6 - 11305*a^3*b^4*d^3*e^7 - 1797495*a^4*b^3*d^2*e^8 - 2028117*a^5*b^2*d*e^9 - 323323*a^6*b*e^10)*x^4 + (640*b^7*d^7*e^3 - 6720*a*b^6*d^6*e^4 + 31920*a^2*b^5*d^5*e^5 - 90440*a^3*b^4*d^4*e^6 + 169575*a^4*b^3*d^3*e^7 + 9964227*a^5*b^2*d^2*e^8 + 6143137*a^6*b*d*e^9 + 415701*a^7*e^10)*x^3 - 3*(256*b^7*d^8*e^2 - 2688*a*b^6*d^7*e^3 + 12768*a^2*b^5*d^6*e^4 - 36176*a^3*b^4*d^5*e^5 + 67830*a^4*b^3*d^4*e^6 - 88179*a^5*b^2*d^3*e^7 - 1616615*a^6*b*d^2*e^8 - 415701*a^7*d*e^9)*x^2 + (1024*b^7*d^9*e - 10752*a*b^6*d^8*e^2 + 51072*a^2*b^5*d^7*e^3 - 144704*a^3*b^4*d^6*e^4 + 271320*a^4*b^3*d^5*e^5 - 352716*a^5*b^2*d^4*e^6 + 323323*a^6*b*d^3*e^7 + 1247103*a^7*d^2*e^8)*x)*sqrt(e*x + d)/e^8","B",0
2060,1,676,0,0.415257," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(36465 \, b^{7} e^{9} x^{9} - 2048 \, b^{7} d^{9} + 19456 \, a b^{6} d^{8} e - 82688 \, a^{2} b^{5} d^{7} e^{2} + 206720 \, a^{3} b^{4} d^{6} e^{3} - 335920 \, a^{4} b^{3} d^{5} e^{4} + 369512 \, a^{5} b^{2} d^{4} e^{5} - 277134 \, a^{6} b d^{3} e^{6} + 138567 \, a^{7} d^{2} e^{7} + 2145 \, {\left(20 \, b^{7} d e^{8} + 133 \, a b^{6} e^{9}\right)} x^{8} + 429 \, {\left(b^{7} d^{2} e^{7} + 798 \, a b^{6} d e^{8} + 2261 \, a^{2} b^{5} e^{9}\right)} x^{7} - 231 \, {\left(2 \, b^{7} d^{3} e^{6} - 19 \, a b^{6} d^{2} e^{7} - 5168 \, a^{2} b^{5} d e^{8} - 8075 \, a^{3} b^{4} e^{9}\right)} x^{6} + 21 \, {\left(24 \, b^{7} d^{4} e^{5} - 228 \, a b^{6} d^{3} e^{6} + 969 \, a^{2} b^{5} d^{2} e^{7} + 113050 \, a^{3} b^{4} d e^{8} + 104975 \, a^{4} b^{3} e^{9}\right)} x^{5} - 35 \, {\left(16 \, b^{7} d^{5} e^{4} - 152 \, a b^{6} d^{4} e^{5} + 646 \, a^{2} b^{5} d^{3} e^{6} - 1615 \, a^{3} b^{4} d^{2} e^{7} - 83980 \, a^{4} b^{3} d e^{8} - 46189 \, a^{5} b^{2} e^{9}\right)} x^{4} + 5 \, {\left(128 \, b^{7} d^{6} e^{3} - 1216 \, a b^{6} d^{5} e^{4} + 5168 \, a^{2} b^{5} d^{4} e^{5} - 12920 \, a^{3} b^{4} d^{3} e^{6} + 20995 \, a^{4} b^{3} d^{2} e^{7} + 461890 \, a^{5} b^{2} d e^{8} + 138567 \, a^{6} b e^{9}\right)} x^{3} - 3 \, {\left(256 \, b^{7} d^{7} e^{2} - 2432 \, a b^{6} d^{6} e^{3} + 10336 \, a^{2} b^{5} d^{5} e^{4} - 25840 \, a^{3} b^{4} d^{4} e^{5} + 41990 \, a^{4} b^{3} d^{3} e^{6} - 46189 \, a^{5} b^{2} d^{2} e^{7} - 369512 \, a^{6} b d e^{8} - 46189 \, a^{7} e^{9}\right)} x^{2} + {\left(1024 \, b^{7} d^{8} e - 9728 \, a b^{6} d^{7} e^{2} + 41344 \, a^{2} b^{5} d^{6} e^{3} - 103360 \, a^{3} b^{4} d^{5} e^{4} + 167960 \, a^{4} b^{3} d^{4} e^{5} - 184756 \, a^{5} b^{2} d^{3} e^{6} + 138567 \, a^{6} b d^{2} e^{7} + 277134 \, a^{7} d e^{8}\right)} x\right)} \sqrt{e x + d}}{692835 \, e^{8}}"," ",0,"2/692835*(36465*b^7*e^9*x^9 - 2048*b^7*d^9 + 19456*a*b^6*d^8*e - 82688*a^2*b^5*d^7*e^2 + 206720*a^3*b^4*d^6*e^3 - 335920*a^4*b^3*d^5*e^4 + 369512*a^5*b^2*d^4*e^5 - 277134*a^6*b*d^3*e^6 + 138567*a^7*d^2*e^7 + 2145*(20*b^7*d*e^8 + 133*a*b^6*e^9)*x^8 + 429*(b^7*d^2*e^7 + 798*a*b^6*d*e^8 + 2261*a^2*b^5*e^9)*x^7 - 231*(2*b^7*d^3*e^6 - 19*a*b^6*d^2*e^7 - 5168*a^2*b^5*d*e^8 - 8075*a^3*b^4*e^9)*x^6 + 21*(24*b^7*d^4*e^5 - 228*a*b^6*d^3*e^6 + 969*a^2*b^5*d^2*e^7 + 113050*a^3*b^4*d*e^8 + 104975*a^4*b^3*e^9)*x^5 - 35*(16*b^7*d^5*e^4 - 152*a*b^6*d^4*e^5 + 646*a^2*b^5*d^3*e^6 - 1615*a^3*b^4*d^2*e^7 - 83980*a^4*b^3*d*e^8 - 46189*a^5*b^2*e^9)*x^4 + 5*(128*b^7*d^6*e^3 - 1216*a*b^6*d^5*e^4 + 5168*a^2*b^5*d^4*e^5 - 12920*a^3*b^4*d^3*e^6 + 20995*a^4*b^3*d^2*e^7 + 461890*a^5*b^2*d*e^8 + 138567*a^6*b*e^9)*x^3 - 3*(256*b^7*d^7*e^2 - 2432*a*b^6*d^6*e^3 + 10336*a^2*b^5*d^5*e^4 - 25840*a^3*b^4*d^4*e^5 + 41990*a^4*b^3*d^3*e^6 - 46189*a^5*b^2*d^2*e^7 - 369512*a^6*b*d*e^8 - 46189*a^7*e^9)*x^2 + (1024*b^7*d^8*e - 9728*a*b^6*d^7*e^2 + 41344*a^2*b^5*d^6*e^3 - 103360*a^3*b^4*d^5*e^4 + 167960*a^4*b^3*d^4*e^5 - 184756*a^5*b^2*d^3*e^6 + 138567*a^6*b*d^2*e^7 + 277134*a^7*d*e^8)*x)*sqrt(e*x + d)/e^8","B",0
2061,1,568,0,0.429263," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6435 \, b^{7} e^{8} x^{8} - 2048 \, b^{7} d^{8} + 17408 \, a b^{6} d^{7} e - 65280 \, a^{2} b^{5} d^{6} e^{2} + 141440 \, a^{3} b^{4} d^{5} e^{3} - 194480 \, a^{4} b^{3} d^{4} e^{4} + 175032 \, a^{5} b^{2} d^{3} e^{5} - 102102 \, a^{6} b d^{2} e^{6} + 36465 \, a^{7} d e^{7} + 429 \, {\left(b^{7} d e^{7} + 119 \, a b^{6} e^{8}\right)} x^{7} - 231 \, {\left(2 \, b^{7} d^{2} e^{6} - 17 \, a b^{6} d e^{7} - 765 \, a^{2} b^{5} e^{8}\right)} x^{6} + 63 \, {\left(8 \, b^{7} d^{3} e^{5} - 68 \, a b^{6} d^{2} e^{6} + 255 \, a^{2} b^{5} d e^{7} + 5525 \, a^{3} b^{4} e^{8}\right)} x^{5} - 35 \, {\left(16 \, b^{7} d^{4} e^{4} - 136 \, a b^{6} d^{3} e^{5} + 510 \, a^{2} b^{5} d^{2} e^{6} - 1105 \, a^{3} b^{4} d e^{7} - 12155 \, a^{4} b^{3} e^{8}\right)} x^{4} + 5 \, {\left(128 \, b^{7} d^{5} e^{3} - 1088 \, a b^{6} d^{4} e^{4} + 4080 \, a^{2} b^{5} d^{3} e^{5} - 8840 \, a^{3} b^{4} d^{2} e^{6} + 12155 \, a^{4} b^{3} d e^{7} + 65637 \, a^{5} b^{2} e^{8}\right)} x^{3} - 3 \, {\left(256 \, b^{7} d^{6} e^{2} - 2176 \, a b^{6} d^{5} e^{3} + 8160 \, a^{2} b^{5} d^{4} e^{4} - 17680 \, a^{3} b^{4} d^{3} e^{5} + 24310 \, a^{4} b^{3} d^{2} e^{6} - 21879 \, a^{5} b^{2} d e^{7} - 51051 \, a^{6} b e^{8}\right)} x^{2} + {\left(1024 \, b^{7} d^{7} e - 8704 \, a b^{6} d^{6} e^{2} + 32640 \, a^{2} b^{5} d^{5} e^{3} - 70720 \, a^{3} b^{4} d^{4} e^{4} + 97240 \, a^{4} b^{3} d^{3} e^{5} - 87516 \, a^{5} b^{2} d^{2} e^{6} + 51051 \, a^{6} b d e^{7} + 36465 \, a^{7} e^{8}\right)} x\right)} \sqrt{e x + d}}{109395 \, e^{8}}"," ",0,"2/109395*(6435*b^7*e^8*x^8 - 2048*b^7*d^8 + 17408*a*b^6*d^7*e - 65280*a^2*b^5*d^6*e^2 + 141440*a^3*b^4*d^5*e^3 - 194480*a^4*b^3*d^4*e^4 + 175032*a^5*b^2*d^3*e^5 - 102102*a^6*b*d^2*e^6 + 36465*a^7*d*e^7 + 429*(b^7*d*e^7 + 119*a*b^6*e^8)*x^7 - 231*(2*b^7*d^2*e^6 - 17*a*b^6*d*e^7 - 765*a^2*b^5*e^8)*x^6 + 63*(8*b^7*d^3*e^5 - 68*a*b^6*d^2*e^6 + 255*a^2*b^5*d*e^7 + 5525*a^3*b^4*e^8)*x^5 - 35*(16*b^7*d^4*e^4 - 136*a*b^6*d^3*e^5 + 510*a^2*b^5*d^2*e^6 - 1105*a^3*b^4*d*e^7 - 12155*a^4*b^3*e^8)*x^4 + 5*(128*b^7*d^5*e^3 - 1088*a*b^6*d^4*e^4 + 4080*a^2*b^5*d^3*e^5 - 8840*a^3*b^4*d^2*e^6 + 12155*a^4*b^3*d*e^7 + 65637*a^5*b^2*e^8)*x^3 - 3*(256*b^7*d^6*e^2 - 2176*a*b^6*d^5*e^3 + 8160*a^2*b^5*d^4*e^4 - 17680*a^3*b^4*d^3*e^5 + 24310*a^4*b^3*d^2*e^6 - 21879*a^5*b^2*d*e^7 - 51051*a^6*b*e^8)*x^2 + (1024*b^7*d^7*e - 8704*a*b^6*d^6*e^2 + 32640*a^2*b^5*d^5*e^3 - 70720*a^3*b^4*d^4*e^4 + 97240*a^4*b^3*d^3*e^5 - 87516*a^5*b^2*d^2*e^6 + 51051*a^6*b*d*e^7 + 36465*a^7*e^8)*x)*sqrt(e*x + d)/e^8","B",0
2062,1,463,0,0.424104," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(429 \, b^{7} e^{7} x^{7} - 2048 \, b^{7} d^{7} + 15360 \, a b^{6} d^{6} e - 49920 \, a^{2} b^{5} d^{5} e^{2} + 91520 \, a^{3} b^{4} d^{4} e^{3} - 102960 \, a^{4} b^{3} d^{3} e^{4} + 72072 \, a^{5} b^{2} d^{2} e^{5} - 30030 \, a^{6} b d e^{6} + 6435 \, a^{7} e^{7} - 231 \, {\left(2 \, b^{7} d e^{6} - 15 \, a b^{6} e^{7}\right)} x^{6} + 63 \, {\left(8 \, b^{7} d^{2} e^{5} - 60 \, a b^{6} d e^{6} + 195 \, a^{2} b^{5} e^{7}\right)} x^{5} - 35 \, {\left(16 \, b^{7} d^{3} e^{4} - 120 \, a b^{6} d^{2} e^{5} + 390 \, a^{2} b^{5} d e^{6} - 715 \, a^{3} b^{4} e^{7}\right)} x^{4} + 5 \, {\left(128 \, b^{7} d^{4} e^{3} - 960 \, a b^{6} d^{3} e^{4} + 3120 \, a^{2} b^{5} d^{2} e^{5} - 5720 \, a^{3} b^{4} d e^{6} + 6435 \, a^{4} b^{3} e^{7}\right)} x^{3} - 3 \, {\left(256 \, b^{7} d^{5} e^{2} - 1920 \, a b^{6} d^{4} e^{3} + 6240 \, a^{2} b^{5} d^{3} e^{4} - 11440 \, a^{3} b^{4} d^{2} e^{5} + 12870 \, a^{4} b^{3} d e^{6} - 9009 \, a^{5} b^{2} e^{7}\right)} x^{2} + {\left(1024 \, b^{7} d^{6} e - 7680 \, a b^{6} d^{5} e^{2} + 24960 \, a^{2} b^{5} d^{4} e^{3} - 45760 \, a^{3} b^{4} d^{3} e^{4} + 51480 \, a^{4} b^{3} d^{2} e^{5} - 36036 \, a^{5} b^{2} d e^{6} + 15015 \, a^{6} b e^{7}\right)} x\right)} \sqrt{e x + d}}{6435 \, e^{8}}"," ",0,"2/6435*(429*b^7*e^7*x^7 - 2048*b^7*d^7 + 15360*a*b^6*d^6*e - 49920*a^2*b^5*d^5*e^2 + 91520*a^3*b^4*d^4*e^3 - 102960*a^4*b^3*d^3*e^4 + 72072*a^5*b^2*d^2*e^5 - 30030*a^6*b*d*e^6 + 6435*a^7*e^7 - 231*(2*b^7*d*e^6 - 15*a*b^6*e^7)*x^6 + 63*(8*b^7*d^2*e^5 - 60*a*b^6*d*e^6 + 195*a^2*b^5*e^7)*x^5 - 35*(16*b^7*d^3*e^4 - 120*a*b^6*d^2*e^5 + 390*a^2*b^5*d*e^6 - 715*a^3*b^4*e^7)*x^4 + 5*(128*b^7*d^4*e^3 - 960*a*b^6*d^3*e^4 + 3120*a^2*b^5*d^2*e^5 - 5720*a^3*b^4*d*e^6 + 6435*a^4*b^3*e^7)*x^3 - 3*(256*b^7*d^5*e^2 - 1920*a*b^6*d^4*e^3 + 6240*a^2*b^5*d^3*e^4 - 11440*a^3*b^4*d^2*e^5 + 12870*a^4*b^3*d*e^6 - 9009*a^5*b^2*e^7)*x^2 + (1024*b^7*d^6*e - 7680*a*b^6*d^5*e^2 + 24960*a^2*b^5*d^4*e^3 - 45760*a^3*b^4*d^3*e^4 + 51480*a^4*b^3*d^2*e^5 - 36036*a^5*b^2*d*e^6 + 15015*a^6*b*e^7)*x)*sqrt(e*x + d)/e^8","B",0
2063,1,472,0,0.429043," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(33 \, b^{7} e^{7} x^{7} + 2048 \, b^{7} d^{7} - 13312 \, a b^{6} d^{6} e + 36608 \, a^{2} b^{5} d^{5} e^{2} - 54912 \, a^{3} b^{4} d^{4} e^{3} + 48048 \, a^{4} b^{3} d^{3} e^{4} - 24024 \, a^{5} b^{2} d^{2} e^{5} + 6006 \, a^{6} b d e^{6} - 429 \, a^{7} e^{7} - 21 \, {\left(2 \, b^{7} d e^{6} - 13 \, a b^{6} e^{7}\right)} x^{6} + 7 \, {\left(8 \, b^{7} d^{2} e^{5} - 52 \, a b^{6} d e^{6} + 143 \, a^{2} b^{5} e^{7}\right)} x^{5} - 5 \, {\left(16 \, b^{7} d^{3} e^{4} - 104 \, a b^{6} d^{2} e^{5} + 286 \, a^{2} b^{5} d e^{6} - 429 \, a^{3} b^{4} e^{7}\right)} x^{4} + {\left(128 \, b^{7} d^{4} e^{3} - 832 \, a b^{6} d^{3} e^{4} + 2288 \, a^{2} b^{5} d^{2} e^{5} - 3432 \, a^{3} b^{4} d e^{6} + 3003 \, a^{4} b^{3} e^{7}\right)} x^{3} - {\left(256 \, b^{7} d^{5} e^{2} - 1664 \, a b^{6} d^{4} e^{3} + 4576 \, a^{2} b^{5} d^{3} e^{4} - 6864 \, a^{3} b^{4} d^{2} e^{5} + 6006 \, a^{4} b^{3} d e^{6} - 3003 \, a^{5} b^{2} e^{7}\right)} x^{2} + {\left(1024 \, b^{7} d^{6} e - 6656 \, a b^{6} d^{5} e^{2} + 18304 \, a^{2} b^{5} d^{4} e^{3} - 27456 \, a^{3} b^{4} d^{3} e^{4} + 24024 \, a^{4} b^{3} d^{2} e^{5} - 12012 \, a^{5} b^{2} d e^{6} + 3003 \, a^{6} b e^{7}\right)} x\right)} \sqrt{e x + d}}{429 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"2/429*(33*b^7*e^7*x^7 + 2048*b^7*d^7 - 13312*a*b^6*d^6*e + 36608*a^2*b^5*d^5*e^2 - 54912*a^3*b^4*d^4*e^3 + 48048*a^4*b^3*d^3*e^4 - 24024*a^5*b^2*d^2*e^5 + 6006*a^6*b*d*e^6 - 429*a^7*e^7 - 21*(2*b^7*d*e^6 - 13*a*b^6*e^7)*x^6 + 7*(8*b^7*d^2*e^5 - 52*a*b^6*d*e^6 + 143*a^2*b^5*e^7)*x^5 - 5*(16*b^7*d^3*e^4 - 104*a*b^6*d^2*e^5 + 286*a^2*b^5*d*e^6 - 429*a^3*b^4*e^7)*x^4 + (128*b^7*d^4*e^3 - 832*a*b^6*d^3*e^4 + 2288*a^2*b^5*d^2*e^5 - 3432*a^3*b^4*d*e^6 + 3003*a^4*b^3*e^7)*x^3 - (256*b^7*d^5*e^2 - 1664*a*b^6*d^4*e^3 + 4576*a^2*b^5*d^3*e^4 - 6864*a^3*b^4*d^2*e^5 + 6006*a^4*b^3*d*e^6 - 3003*a^5*b^2*e^7)*x^2 + (1024*b^7*d^6*e - 6656*a*b^6*d^5*e^2 + 18304*a^2*b^5*d^4*e^3 - 27456*a^3*b^4*d^3*e^4 + 24024*a^4*b^3*d^2*e^5 - 12012*a^5*b^2*d*e^6 + 3003*a^6*b*e^7)*x)*sqrt(e*x + d)/(e^9*x + d*e^8)","B",0
2064,1,484,0,0.429902," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(9 \, b^{7} e^{7} x^{7} - 2048 \, b^{7} d^{7} + 11264 \, a b^{6} d^{6} e - 25344 \, a^{2} b^{5} d^{5} e^{2} + 29568 \, a^{3} b^{4} d^{4} e^{3} - 18480 \, a^{4} b^{3} d^{3} e^{4} + 5544 \, a^{5} b^{2} d^{2} e^{5} - 462 \, a^{6} b d e^{6} - 33 \, a^{7} e^{7} - 7 \, {\left(2 \, b^{7} d e^{6} - 11 \, a b^{6} e^{7}\right)} x^{6} + 3 \, {\left(8 \, b^{7} d^{2} e^{5} - 44 \, a b^{6} d e^{6} + 99 \, a^{2} b^{5} e^{7}\right)} x^{5} - 3 \, {\left(16 \, b^{7} d^{3} e^{4} - 88 \, a b^{6} d^{2} e^{5} + 198 \, a^{2} b^{5} d e^{6} - 231 \, a^{3} b^{4} e^{7}\right)} x^{4} + {\left(128 \, b^{7} d^{4} e^{3} - 704 \, a b^{6} d^{3} e^{4} + 1584 \, a^{2} b^{5} d^{2} e^{5} - 1848 \, a^{3} b^{4} d e^{6} + 1155 \, a^{4} b^{3} e^{7}\right)} x^{3} - 3 \, {\left(256 \, b^{7} d^{5} e^{2} - 1408 \, a b^{6} d^{4} e^{3} + 3168 \, a^{2} b^{5} d^{3} e^{4} - 3696 \, a^{3} b^{4} d^{2} e^{5} + 2310 \, a^{4} b^{3} d e^{6} - 693 \, a^{5} b^{2} e^{7}\right)} x^{2} - 3 \, {\left(1024 \, b^{7} d^{6} e - 5632 \, a b^{6} d^{5} e^{2} + 12672 \, a^{2} b^{5} d^{4} e^{3} - 14784 \, a^{3} b^{4} d^{3} e^{4} + 9240 \, a^{4} b^{3} d^{2} e^{5} - 2772 \, a^{5} b^{2} d e^{6} + 231 \, a^{6} b e^{7}\right)} x\right)} \sqrt{e x + d}}{99 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"2/99*(9*b^7*e^7*x^7 - 2048*b^7*d^7 + 11264*a*b^6*d^6*e - 25344*a^2*b^5*d^5*e^2 + 29568*a^3*b^4*d^4*e^3 - 18480*a^4*b^3*d^3*e^4 + 5544*a^5*b^2*d^2*e^5 - 462*a^6*b*d*e^6 - 33*a^7*e^7 - 7*(2*b^7*d*e^6 - 11*a*b^6*e^7)*x^6 + 3*(8*b^7*d^2*e^5 - 44*a*b^6*d*e^6 + 99*a^2*b^5*e^7)*x^5 - 3*(16*b^7*d^3*e^4 - 88*a*b^6*d^2*e^5 + 198*a^2*b^5*d*e^6 - 231*a^3*b^4*e^7)*x^4 + (128*b^7*d^4*e^3 - 704*a*b^6*d^3*e^4 + 1584*a^2*b^5*d^2*e^5 - 1848*a^3*b^4*d*e^6 + 1155*a^4*b^3*e^7)*x^3 - 3*(256*b^7*d^5*e^2 - 1408*a*b^6*d^4*e^3 + 3168*a^2*b^5*d^3*e^4 - 3696*a^3*b^4*d^2*e^5 + 2310*a^4*b^3*d*e^6 - 693*a^5*b^2*e^7)*x^2 - 3*(1024*b^7*d^6*e - 5632*a*b^6*d^5*e^2 + 12672*a^2*b^5*d^4*e^3 - 14784*a^3*b^4*d^3*e^4 + 9240*a^4*b^3*d^2*e^5 - 2772*a^5*b^2*d*e^6 + 231*a^6*b*e^7)*x)*sqrt(e*x + d)/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","B",0
2065,1,496,0,0.431463," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{7} e^{7} x^{7} + 2048 \, b^{7} d^{7} - 9216 \, a b^{6} d^{6} e + 16128 \, a^{2} b^{5} d^{5} e^{2} - 13440 \, a^{3} b^{4} d^{4} e^{3} + 5040 \, a^{4} b^{3} d^{3} e^{4} - 504 \, a^{5} b^{2} d^{2} e^{5} - 42 \, a^{6} b d e^{6} - 9 \, a^{7} e^{7} - 5 \, {\left(2 \, b^{7} d e^{6} - 9 \, a b^{6} e^{7}\right)} x^{6} + 3 \, {\left(8 \, b^{7} d^{2} e^{5} - 36 \, a b^{6} d e^{6} + 63 \, a^{2} b^{5} e^{7}\right)} x^{5} - 5 \, {\left(16 \, b^{7} d^{3} e^{4} - 72 \, a b^{6} d^{2} e^{5} + 126 \, a^{2} b^{5} d e^{6} - 105 \, a^{3} b^{4} e^{7}\right)} x^{4} + 5 \, {\left(128 \, b^{7} d^{4} e^{3} - 576 \, a b^{6} d^{3} e^{4} + 1008 \, a^{2} b^{5} d^{2} e^{5} - 840 \, a^{3} b^{4} d e^{6} + 315 \, a^{4} b^{3} e^{7}\right)} x^{3} + 15 \, {\left(256 \, b^{7} d^{5} e^{2} - 1152 \, a b^{6} d^{4} e^{3} + 2016 \, a^{2} b^{5} d^{3} e^{4} - 1680 \, a^{3} b^{4} d^{2} e^{5} + 630 \, a^{4} b^{3} d e^{6} - 63 \, a^{5} b^{2} e^{7}\right)} x^{2} + 5 \, {\left(1024 \, b^{7} d^{6} e - 4608 \, a b^{6} d^{5} e^{2} + 8064 \, a^{2} b^{5} d^{4} e^{3} - 6720 \, a^{3} b^{4} d^{3} e^{4} + 2520 \, a^{4} b^{3} d^{2} e^{5} - 252 \, a^{5} b^{2} d e^{6} - 21 \, a^{6} b e^{7}\right)} x\right)} \sqrt{e x + d}}{45 \, {\left(e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right)}}"," ",0,"2/45*(5*b^7*e^7*x^7 + 2048*b^7*d^7 - 9216*a*b^6*d^6*e + 16128*a^2*b^5*d^5*e^2 - 13440*a^3*b^4*d^4*e^3 + 5040*a^4*b^3*d^3*e^4 - 504*a^5*b^2*d^2*e^5 - 42*a^6*b*d*e^6 - 9*a^7*e^7 - 5*(2*b^7*d*e^6 - 9*a*b^6*e^7)*x^6 + 3*(8*b^7*d^2*e^5 - 36*a*b^6*d*e^6 + 63*a^2*b^5*e^7)*x^5 - 5*(16*b^7*d^3*e^4 - 72*a*b^6*d^2*e^5 + 126*a^2*b^5*d*e^6 - 105*a^3*b^4*e^7)*x^4 + 5*(128*b^7*d^4*e^3 - 576*a*b^6*d^3*e^4 + 1008*a^2*b^5*d^2*e^5 - 840*a^3*b^4*d*e^6 + 315*a^4*b^3*e^7)*x^3 + 15*(256*b^7*d^5*e^2 - 1152*a*b^6*d^4*e^3 + 2016*a^2*b^5*d^3*e^4 - 1680*a^3*b^4*d^2*e^5 + 630*a^4*b^3*d*e^6 - 63*a^5*b^2*e^7)*x^2 + 5*(1024*b^7*d^6*e - 4608*a*b^6*d^5*e^2 + 8064*a^2*b^5*d^4*e^3 - 6720*a^3*b^4*d^3*e^4 + 2520*a^4*b^3*d^2*e^5 - 252*a^5*b^2*d*e^6 - 21*a^6*b*e^7)*x)*sqrt(e*x + d)/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8)","B",0
2066,1,424,0,0.443155," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(15 \, b^{3} e^{3} x^{3} + 176 \, b^{3} d^{3} - 406 \, a b^{2} d^{2} e + 350 \, a^{2} b d e^{2} - 105 \, a^{3} e^{3} + 3 \, {\left(22 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + {\left(122 \, b^{3} d^{2} e - 112 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, b^{4}}, -\frac{2 \, {\left(105 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(15 \, b^{3} e^{3} x^{3} + 176 \, b^{3} d^{3} - 406 \, a b^{2} d^{2} e + 350 \, a^{2} b d e^{2} - 105 \, a^{3} e^{3} + 3 \, {\left(22 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + {\left(122 \, b^{3} d^{2} e - 112 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{105 \, b^{4}}\right]"," ",0,"[-1/105*(105*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(15*b^3*e^3*x^3 + 176*b^3*d^3 - 406*a*b^2*d^2*e + 350*a^2*b*d*e^2 - 105*a^3*e^3 + 3*(22*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + (122*b^3*d^2*e - 112*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d))/b^4, -2/105*(105*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (15*b^3*e^3*x^3 + 176*b^3*d^3 - 406*a*b^2*d^2*e + 350*a^2*b*d*e^2 - 105*a^3*e^3 + 3*(22*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + (122*b^3*d^2*e - 112*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d))/b^4]","A",0
2067,1,290,0,0.486223," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(3 \, b^{2} e^{2} x^{2} + 23 \, b^{2} d^{2} - 35 \, a b d e + 15 \, a^{2} e^{2} + {\left(11 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, b^{3}}, -\frac{2 \, {\left(15 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(3 \, b^{2} e^{2} x^{2} + 23 \, b^{2} d^{2} - 35 \, a b d e + 15 \, a^{2} e^{2} + {\left(11 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, b^{3}}\right]"," ",0,"[1/15*(15*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(3*b^2*e^2*x^2 + 23*b^2*d^2 - 35*a*b*d*e + 15*a^2*e^2 + (11*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d))/b^3, -2/15*(15*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (3*b^2*e^2*x^2 + 23*b^2*d^2 - 35*a*b*d*e + 15*a^2*e^2 + (11*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d))/b^3]","A",0
2068,1,188,0,0.469979," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b d - a e\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(b e x + 4 \, b d - 3 \, a e\right)} \sqrt{e x + d}}{3 \, b^{2}}, -\frac{2 \, {\left(3 \, {\left(b d - a e\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(b e x + 4 \, b d - 3 \, a e\right)} \sqrt{e x + d}\right)}}{3 \, b^{2}}\right]"," ",0,"[-1/3*(3*(b*d - a*e)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(b*e*x + 4*b*d - 3*a*e)*sqrt(e*x + d))/b^2, -2/3*(3*(b*d - a*e)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (b*e*x + 4*b*d - 3*a*e)*sqrt(e*x + d))/b^2]","A",0
2069,1,143,0,0.445235," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, \sqrt{e x + d}}{b}, -\frac{2 \, {\left(\sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - \sqrt{e x + d}\right)}}{b}\right]"," ",0,"[(sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*sqrt(e*x + d))/b, -2*(sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - sqrt(e*x + d))/b]","A",0
2070,1,119,0,0.466710," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right)}{\sqrt{b^{2} d - a b e}}, \frac{2 \, \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right)}{b^{2} d - a b e}\right]"," ",0,"[log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a))/sqrt(b^2*d - a*b*e), 2*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d))/(b^2*d - a*b*e)]","A",0
2071,1,214,0,0.464993," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{{\left(e x + d\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, \sqrt{e x + d}}{b d^{2} - a d e + {\left(b d e - a e^{2}\right)} x}, -\frac{2 \, {\left({\left(e x + d\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - \sqrt{e x + d}\right)}}{b d^{2} - a d e + {\left(b d e - a e^{2}\right)} x}\right]"," ",0,"[-((e*x + d)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*sqrt(e*x + d))/(b*d^2 - a*d*e + (b*d*e - a*e^2)*x), -2*((e*x + d)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - sqrt(e*x + d))/(b*d^2 - a*d*e + (b*d*e - a*e^2)*x)]","A",0
2072,1,398,0,0.430388," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b e^{2} x^{2} + 2 \, b d e x + b d^{2}\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(3 \, b e x + 4 \, b d - a e\right)} \sqrt{e x + d}}{3 \, {\left(b^{2} d^{4} - 2 \, a b d^{3} e + a^{2} d^{2} e^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3}\right)} x\right)}}, -\frac{2 \, {\left(3 \, {\left(b e^{2} x^{2} + 2 \, b d e x + b d^{2}\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3 \, b e x + 4 \, b d - a e\right)} \sqrt{e x + d}\right)}}{3 \, {\left(b^{2} d^{4} - 2 \, a b d^{3} e + a^{2} d^{2} e^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3}\right)} x\right)}}\right]"," ",0,"[1/3*(3*(b*e^2*x^2 + 2*b*d*e*x + b*d^2)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(3*b*e*x + 4*b*d - a*e)*sqrt(e*x + d))/(b^2*d^4 - 2*a*b*d^3*e + a^2*d^2*e^2 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x^2 + 2*(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3)*x), -2/3*(3*(b*e^2*x^2 + 2*b*d*e*x + b*d^2)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3*b*e*x + 4*b*d - a*e)*sqrt(e*x + d))/(b^2*d^4 - 2*a*b*d^3*e + a^2*d^2*e^2 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x^2 + 2*(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3)*x)]","B",0
2073,1,706,0,0.443953," ","integrate((b*x+a)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{2} e^{3} x^{3} + 3 \, b^{2} d e^{2} x^{2} + 3 \, b^{2} d^{2} e x + b^{2} d^{3}\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(15 \, b^{2} e^{2} x^{2} + 23 \, b^{2} d^{2} - 11 \, a b d e + 3 \, a^{2} e^{2} + 5 \, {\left(7 \, b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b^{3} d^{6} - 3 \, a b^{2} d^{5} e + 3 \, a^{2} b d^{4} e^{2} - a^{3} d^{3} e^{3} + {\left(b^{3} d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} b d e^{5} - a^{3} e^{6}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{2} - 3 \, a b^{2} d^{3} e^{3} + 3 \, a^{2} b d^{2} e^{4} - a^{3} d e^{5}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e - 3 \, a b^{2} d^{4} e^{2} + 3 \, a^{2} b d^{3} e^{3} - a^{3} d^{2} e^{4}\right)} x\right)}}, -\frac{2 \, {\left(15 \, {\left(b^{2} e^{3} x^{3} + 3 \, b^{2} d e^{2} x^{2} + 3 \, b^{2} d^{2} e x + b^{2} d^{3}\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(15 \, b^{2} e^{2} x^{2} + 23 \, b^{2} d^{2} - 11 \, a b d e + 3 \, a^{2} e^{2} + 5 \, {\left(7 \, b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, {\left(b^{3} d^{6} - 3 \, a b^{2} d^{5} e + 3 \, a^{2} b d^{4} e^{2} - a^{3} d^{3} e^{3} + {\left(b^{3} d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} b d e^{5} - a^{3} e^{6}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{2} - 3 \, a b^{2} d^{3} e^{3} + 3 \, a^{2} b d^{2} e^{4} - a^{3} d e^{5}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e - 3 \, a b^{2} d^{4} e^{2} + 3 \, a^{2} b d^{3} e^{3} - a^{3} d^{2} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/15*(15*(b^2*e^3*x^3 + 3*b^2*d*e^2*x^2 + 3*b^2*d^2*e*x + b^2*d^3)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(15*b^2*e^2*x^2 + 23*b^2*d^2 - 11*a*b*d*e + 3*a^2*e^2 + 5*(7*b^2*d*e - a*b*e^2)*x)*sqrt(e*x + d))/(b^3*d^6 - 3*a*b^2*d^5*e + 3*a^2*b*d^4*e^2 - a^3*d^3*e^3 + (b^3*d^3*e^3 - 3*a*b^2*d^2*e^4 + 3*a^2*b*d*e^5 - a^3*e^6)*x^3 + 3*(b^3*d^4*e^2 - 3*a*b^2*d^3*e^3 + 3*a^2*b*d^2*e^4 - a^3*d*e^5)*x^2 + 3*(b^3*d^5*e - 3*a*b^2*d^4*e^2 + 3*a^2*b*d^3*e^3 - a^3*d^2*e^4)*x), -2/15*(15*(b^2*e^3*x^3 + 3*b^2*d*e^2*x^2 + 3*b^2*d^2*e*x + b^2*d^3)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (15*b^2*e^2*x^2 + 23*b^2*d^2 - 11*a*b*d*e + 3*a^2*e^2 + 5*(7*b^2*d*e - a*b*e^2)*x)*sqrt(e*x + d))/(b^3*d^6 - 3*a*b^2*d^5*e + 3*a^2*b*d^4*e^2 - a^3*d^3*e^3 + (b^3*d^3*e^3 - 3*a*b^2*d^2*e^4 + 3*a^2*b*d*e^5 - a^3*e^6)*x^3 + 3*(b^3*d^4*e^2 - 3*a*b^2*d^3*e^3 + 3*a^2*b*d^2*e^4 - a^3*d*e^5)*x^2 + 3*(b^3*d^5*e - 3*a*b^2*d^4*e^2 + 3*a^2*b*d^3*e^3 - a^3*d^2*e^4)*x)]","B",0
2074,1,730,0,0.443691," ","integrate((b*x+a)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{2} b^{2} d^{2} e^{2} - 2 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} - 2 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(8 \, b^{4} e^{4} x^{4} - 10 \, b^{4} d^{4} - 45 \, a b^{3} d^{3} e + 483 \, a^{2} b^{2} d^{2} e^{2} - 735 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} + 8 \, {\left(7 \, b^{4} d e^{3} - 3 \, a b^{3} e^{4}\right)} x^{3} + 24 \, {\left(12 \, b^{4} d^{2} e^{2} - 17 \, a b^{3} d e^{3} + 7 \, a^{2} b^{2} e^{4}\right)} x^{2} - {\left(85 \, b^{4} d^{3} e - 831 \, a b^{3} d^{2} e^{2} + 1239 \, a^{2} b^{2} d e^{3} - 525 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{40 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{315 \, {\left(a^{2} b^{2} d^{2} e^{2} - 2 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} - 2 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(8 \, b^{4} e^{4} x^{4} - 10 \, b^{4} d^{4} - 45 \, a b^{3} d^{3} e + 483 \, a^{2} b^{2} d^{2} e^{2} - 735 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} + 8 \, {\left(7 \, b^{4} d e^{3} - 3 \, a b^{3} e^{4}\right)} x^{3} + 24 \, {\left(12 \, b^{4} d^{2} e^{2} - 17 \, a b^{3} d e^{3} + 7 \, a^{2} b^{2} e^{4}\right)} x^{2} - {\left(85 \, b^{4} d^{3} e - 831 \, a b^{3} d^{2} e^{2} + 1239 \, a^{2} b^{2} d e^{3} - 525 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{20 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[1/40*(315*(a^2*b^2*d^2*e^2 - 2*a^3*b*d*e^3 + a^4*e^4 + (b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 - 2*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(8*b^4*e^4*x^4 - 10*b^4*d^4 - 45*a*b^3*d^3*e + 483*a^2*b^2*d^2*e^2 - 735*a^3*b*d*e^3 + 315*a^4*e^4 + 8*(7*b^4*d*e^3 - 3*a*b^3*e^4)*x^3 + 24*(12*b^4*d^2*e^2 - 17*a*b^3*d*e^3 + 7*a^2*b^2*e^4)*x^2 - (85*b^4*d^3*e - 831*a*b^3*d^2*e^2 + 1239*a^2*b^2*d*e^3 - 525*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/20*(315*(a^2*b^2*d^2*e^2 - 2*a^3*b*d*e^3 + a^4*e^4 + (b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 - 2*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (8*b^4*e^4*x^4 - 10*b^4*d^4 - 45*a*b^3*d^3*e + 483*a^2*b^2*d^2*e^2 - 735*a^3*b*d*e^3 + 315*a^4*e^4 + 8*(7*b^4*d*e^3 - 3*a*b^3*e^4)*x^3 + 24*(12*b^4*d^2*e^2 - 17*a*b^3*d*e^3 + 7*a^2*b^2*e^4)*x^2 - (85*b^4*d^3*e - 831*a*b^3*d^2*e^2 + 1239*a^2*b^2*d*e^3 - 525*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","B",0
2075,1,520,0,0.446398," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(a^{2} b d e^{2} - a^{3} e^{3} + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(a b^{2} d e^{2} - a^{2} b e^{3}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(8 \, b^{3} e^{3} x^{3} - 6 \, b^{3} d^{3} - 21 \, a b^{2} d^{2} e + 140 \, a^{2} b d e^{2} - 105 \, a^{3} e^{3} + 8 \, {\left(10 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} - {\left(39 \, b^{3} d^{2} e - 238 \, a b^{2} d e^{2} + 175 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, -\frac{105 \, {\left(a^{2} b d e^{2} - a^{3} e^{3} + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(a b^{2} d e^{2} - a^{2} b e^{3}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(8 \, b^{3} e^{3} x^{3} - 6 \, b^{3} d^{3} - 21 \, a b^{2} d^{2} e + 140 \, a^{2} b d e^{2} - 105 \, a^{3} e^{3} + 8 \, {\left(10 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} - {\left(39 \, b^{3} d^{2} e - 238 \, a b^{2} d e^{2} + 175 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[-1/24*(105*(a^2*b*d*e^2 - a^3*e^3 + (b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(a*b^2*d*e^2 - a^2*b*e^3)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(8*b^3*e^3*x^3 - 6*b^3*d^3 - 21*a*b^2*d^2*e + 140*a^2*b*d*e^2 - 105*a^3*e^3 + 8*(10*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 - (39*b^3*d^2*e - 238*a*b^2*d*e^2 + 175*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), -1/12*(105*(a^2*b*d*e^2 - a^3*e^3 + (b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(a*b^2*d*e^2 - a^2*b*e^3)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (8*b^3*e^3*x^3 - 6*b^3*d^3 - 21*a*b^2*d^2*e + 140*a^2*b*d*e^2 - 105*a^3*e^3 + 8*(10*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 - (39*b^3*d^2*e - 238*a*b^2*d*e^2 + 175*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","B",0
2076,1,344,0,0.427504," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(8 \, b^{2} e^{2} x^{2} - 2 \, b^{2} d^{2} - 5 \, a b d e + 15 \, a^{2} e^{2} - {\left(9 \, b^{2} d e - 25 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}, -\frac{15 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(8 \, b^{2} e^{2} x^{2} - 2 \, b^{2} d^{2} - 5 \, a b d e + 15 \, a^{2} e^{2} - {\left(9 \, b^{2} d e - 25 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}\right]"," ",0,"[1/8*(15*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(8*b^2*e^2*x^2 - 2*b^2*d^2 - 5*a*b*d*e + 15*a^2*e^2 - (9*b^2*d*e - 25*a*b*e^2)*x)*sqrt(e*x + d))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3), -1/4*(15*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (8*b^2*e^2*x^2 - 2*b^2*d^2 - 5*a*b*d*e + 15*a^2*e^2 - (9*b^2*d*e - 25*a*b*e^2)*x)*sqrt(e*x + d))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)]","A",0
2077,1,383,0,0.431688," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, b^{3} d^{2} + a b^{2} d e - 3 \, a^{2} b e^{2} + 5 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{4} d - a^{3} b^{3} e + {\left(b^{6} d - a b^{5} e\right)} x^{2} + 2 \, {\left(a b^{5} d - a^{2} b^{4} e\right)} x\right)}}, \frac{3 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(2 \, b^{3} d^{2} + a b^{2} d e - 3 \, a^{2} b e^{2} + 5 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{4} d - a^{3} b^{3} e + {\left(b^{6} d - a b^{5} e\right)} x^{2} + 2 \, {\left(a b^{5} d - a^{2} b^{4} e\right)} x\right)}}\right]"," ",0,"[1/8*(3*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*b^3*d^2 + a*b^2*d*e - 3*a^2*b*e^2 + 5*(b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d - a^3*b^3*e + (b^6*d - a*b^5*e)*x^2 + 2*(a*b^5*d - a^2*b^4*e)*x), 1/4*(3*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (2*b^3*d^2 + a*b^2*d*e - 3*a^2*b*e^2 + 5*(b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d - a^3*b^3*e + (b^6*d - a*b^5*e)*x^2 + 2*(a*b^5*d - a^2*b^4*e)*x)]","B",0
2078,1,456,0,0.444631," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(2 \, b^{3} d^{2} - 3 \, a b^{2} d e + a^{2} b e^{2} + {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{4} d^{2} - 2 \, a^{3} b^{3} d e + a^{4} b^{2} e^{2} + {\left(b^{6} d^{2} - 2 \, a b^{5} d e + a^{2} b^{4} e^{2}\right)} x^{2} + 2 \, {\left(a b^{5} d^{2} - 2 \, a^{2} b^{4} d e + a^{3} b^{3} e^{2}\right)} x\right)}}, -\frac{{\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(2 \, b^{3} d^{2} - 3 \, a b^{2} d e + a^{2} b e^{2} + {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{4} d^{2} - 2 \, a^{3} b^{3} d e + a^{4} b^{2} e^{2} + {\left(b^{6} d^{2} - 2 \, a b^{5} d e + a^{2} b^{4} e^{2}\right)} x^{2} + 2 \, {\left(a b^{5} d^{2} - 2 \, a^{2} b^{4} d e + a^{3} b^{3} e^{2}\right)} x\right)}}\right]"," ",0,"[-1/8*((b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(2*b^3*d^2 - 3*a*b^2*d*e + a^2*b*e^2 + (b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d^2 - 2*a^3*b^3*d*e + a^4*b^2*e^2 + (b^6*d^2 - 2*a*b^5*d*e + a^2*b^4*e^2)*x^2 + 2*(a*b^5*d^2 - 2*a^2*b^4*d*e + a^3*b^3*e^2)*x), -1/4*((b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (2*b^3*d^2 - 3*a*b^2*d*e + a^2*b*e^2 + (b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d^2 - 2*a^3*b^3*d*e + a^4*b^2*e^2 + (b^6*d^2 - 2*a*b^5*d*e + a^2*b^4*e^2)*x^2 + 2*(a*b^5*d^2 - 2*a^2*b^4*d*e + a^3*b^3*e^2)*x)]","B",0
2079,1,549,0,0.434521," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, b^{3} d^{2} - 7 \, a b^{2} d e + 5 \, a^{2} b e^{2} - 3 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{4} d^{3} - 3 \, a^{3} b^{3} d^{2} e + 3 \, a^{4} b^{2} d e^{2} - a^{5} b e^{3} + {\left(b^{6} d^{3} - 3 \, a b^{5} d^{2} e + 3 \, a^{2} b^{4} d e^{2} - a^{3} b^{3} e^{3}\right)} x^{2} + 2 \, {\left(a b^{5} d^{3} - 3 \, a^{2} b^{4} d^{2} e + 3 \, a^{3} b^{3} d e^{2} - a^{4} b^{2} e^{3}\right)} x\right)}}, \frac{3 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(2 \, b^{3} d^{2} - 7 \, a b^{2} d e + 5 \, a^{2} b e^{2} - 3 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{4} d^{3} - 3 \, a^{3} b^{3} d^{2} e + 3 \, a^{4} b^{2} d e^{2} - a^{5} b e^{3} + {\left(b^{6} d^{3} - 3 \, a b^{5} d^{2} e + 3 \, a^{2} b^{4} d e^{2} - a^{3} b^{3} e^{3}\right)} x^{2} + 2 \, {\left(a b^{5} d^{3} - 3 \, a^{2} b^{4} d^{2} e + 3 \, a^{3} b^{3} d e^{2} - a^{4} b^{2} e^{3}\right)} x\right)}}\right]"," ",0,"[1/8*(3*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*b^3*d^2 - 7*a*b^2*d*e + 5*a^2*b*e^2 - 3*(b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d^3 - 3*a^3*b^3*d^2*e + 3*a^4*b^2*d*e^2 - a^5*b*e^3 + (b^6*d^3 - 3*a*b^5*d^2*e + 3*a^2*b^4*d*e^2 - a^3*b^3*e^3)*x^2 + 2*(a*b^5*d^3 - 3*a^2*b^4*d^2*e + 3*a^3*b^3*d*e^2 - a^4*b^2*e^3)*x), 1/4*(3*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (2*b^3*d^2 - 7*a*b^2*d*e + 5*a^2*b*e^2 - 3*(b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d^3 - 3*a^3*b^3*d^2*e + 3*a^4*b^2*d*e^2 - a^5*b*e^3 + (b^6*d^3 - 3*a*b^5*d^2*e + 3*a^2*b^4*d*e^2 - a^3*b^3*e^3)*x^2 + 2*(a*b^5*d^3 - 3*a^2*b^4*d^2*e + 3*a^3*b^3*d*e^2 - a^4*b^2*e^3)*x)]","B",0
2080,1,782,0,0.450812," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{2} e^{3} x^{3} + a^{2} d e^{2} + {\left(b^{2} d e^{2} + 2 \, a b e^{3}\right)} x^{2} + {\left(2 \, a b d e^{2} + a^{2} e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(15 \, b^{2} e^{2} x^{2} - 2 \, b^{2} d^{2} + 9 \, a b d e + 8 \, a^{2} e^{2} + 5 \, {\left(b^{2} d e + 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{3} d^{4} - 3 \, a^{3} b^{2} d^{3} e + 3 \, a^{4} b d^{2} e^{2} - a^{5} d e^{3} + {\left(b^{5} d^{3} e - 3 \, a b^{4} d^{2} e^{2} + 3 \, a^{2} b^{3} d e^{3} - a^{3} b^{2} e^{4}\right)} x^{3} + {\left(b^{5} d^{4} - a b^{4} d^{3} e - 3 \, a^{2} b^{3} d^{2} e^{2} + 5 \, a^{3} b^{2} d e^{3} - 2 \, a^{4} b e^{4}\right)} x^{2} + {\left(2 \, a b^{4} d^{4} - 5 \, a^{2} b^{3} d^{3} e + 3 \, a^{3} b^{2} d^{2} e^{2} + a^{4} b d e^{3} - a^{5} e^{4}\right)} x\right)}}, -\frac{15 \, {\left(b^{2} e^{3} x^{3} + a^{2} d e^{2} + {\left(b^{2} d e^{2} + 2 \, a b e^{3}\right)} x^{2} + {\left(2 \, a b d e^{2} + a^{2} e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(15 \, b^{2} e^{2} x^{2} - 2 \, b^{2} d^{2} + 9 \, a b d e + 8 \, a^{2} e^{2} + 5 \, {\left(b^{2} d e + 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{3} d^{4} - 3 \, a^{3} b^{2} d^{3} e + 3 \, a^{4} b d^{2} e^{2} - a^{5} d e^{3} + {\left(b^{5} d^{3} e - 3 \, a b^{4} d^{2} e^{2} + 3 \, a^{2} b^{3} d e^{3} - a^{3} b^{2} e^{4}\right)} x^{3} + {\left(b^{5} d^{4} - a b^{4} d^{3} e - 3 \, a^{2} b^{3} d^{2} e^{2} + 5 \, a^{3} b^{2} d e^{3} - 2 \, a^{4} b e^{4}\right)} x^{2} + {\left(2 \, a b^{4} d^{4} - 5 \, a^{2} b^{3} d^{3} e + 3 \, a^{3} b^{2} d^{2} e^{2} + a^{4} b d e^{3} - a^{5} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/8*(15*(b^2*e^3*x^3 + a^2*d*e^2 + (b^2*d*e^2 + 2*a*b*e^3)*x^2 + (2*a*b*d*e^2 + a^2*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(15*b^2*e^2*x^2 - 2*b^2*d^2 + 9*a*b*d*e + 8*a^2*e^2 + 5*(b^2*d*e + 5*a*b*e^2)*x)*sqrt(e*x + d))/(a^2*b^3*d^4 - 3*a^3*b^2*d^3*e + 3*a^4*b*d^2*e^2 - a^5*d*e^3 + (b^5*d^3*e - 3*a*b^4*d^2*e^2 + 3*a^2*b^3*d*e^3 - a^3*b^2*e^4)*x^3 + (b^5*d^4 - a*b^4*d^3*e - 3*a^2*b^3*d^2*e^2 + 5*a^3*b^2*d*e^3 - 2*a^4*b*e^4)*x^2 + (2*a*b^4*d^4 - 5*a^2*b^3*d^3*e + 3*a^3*b^2*d^2*e^2 + a^4*b*d*e^3 - a^5*e^4)*x), -1/4*(15*(b^2*e^3*x^3 + a^2*d*e^2 + (b^2*d*e^2 + 2*a*b*e^3)*x^2 + (2*a*b*d*e^2 + a^2*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (15*b^2*e^2*x^2 - 2*b^2*d^2 + 9*a*b*d*e + 8*a^2*e^2 + 5*(b^2*d*e + 5*a*b*e^2)*x)*sqrt(e*x + d))/(a^2*b^3*d^4 - 3*a^3*b^2*d^3*e + 3*a^4*b*d^2*e^2 - a^5*d*e^3 + (b^5*d^3*e - 3*a*b^4*d^2*e^2 + 3*a^2*b^3*d*e^3 - a^3*b^2*e^4)*x^3 + (b^5*d^4 - a*b^4*d^3*e - 3*a^2*b^3*d^2*e^2 + 5*a^3*b^2*d*e^3 - 2*a^4*b*e^4)*x^2 + (2*a*b^4*d^4 - 5*a^2*b^3*d^3*e + 3*a^3*b^2*d^2*e^2 + a^4*b*d*e^3 - a^5*e^4)*x)]","B",0
2081,1,1226,0,0.468304," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} e^{4} x^{4} + a^{2} b d^{2} e^{2} + 2 \, {\left(b^{3} d e^{3} + a b^{2} e^{4}\right)} x^{3} + {\left(b^{3} d^{2} e^{2} + 4 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)} x^{2} + 2 \, {\left(a b^{2} d^{2} e^{2} + a^{2} b d e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(105 \, b^{3} e^{3} x^{3} - 6 \, b^{3} d^{3} + 39 \, a b^{2} d^{2} e + 80 \, a^{2} b d e^{2} - 8 \, a^{3} e^{3} + 35 \, {\left(4 \, b^{3} d e^{2} + 5 \, a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(3 \, b^{3} d^{2} e + 34 \, a b^{2} d e^{2} + 8 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{2} b^{4} d^{6} - 4 \, a^{3} b^{3} d^{5} e + 6 \, a^{4} b^{2} d^{4} e^{2} - 4 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4} + {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 2 \, a^{2} b^{4} d^{3} e^{3} + 2 \, a^{3} b^{3} d^{2} e^{4} - 3 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{3} + {\left(b^{6} d^{6} - 9 \, a^{2} b^{4} d^{4} e^{2} + 16 \, a^{3} b^{3} d^{3} e^{3} - 9 \, a^{4} b^{2} d^{2} e^{4} + a^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} d^{6} - 3 \, a^{2} b^{4} d^{5} e + 2 \, a^{3} b^{3} d^{4} e^{2} + 2 \, a^{4} b^{2} d^{3} e^{3} - 3 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x\right)}}, -\frac{105 \, {\left(b^{3} e^{4} x^{4} + a^{2} b d^{2} e^{2} + 2 \, {\left(b^{3} d e^{3} + a b^{2} e^{4}\right)} x^{3} + {\left(b^{3} d^{2} e^{2} + 4 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)} x^{2} + 2 \, {\left(a b^{2} d^{2} e^{2} + a^{2} b d e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(105 \, b^{3} e^{3} x^{3} - 6 \, b^{3} d^{3} + 39 \, a b^{2} d^{2} e + 80 \, a^{2} b d e^{2} - 8 \, a^{3} e^{3} + 35 \, {\left(4 \, b^{3} d e^{2} + 5 \, a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(3 \, b^{3} d^{2} e + 34 \, a b^{2} d e^{2} + 8 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(a^{2} b^{4} d^{6} - 4 \, a^{3} b^{3} d^{5} e + 6 \, a^{4} b^{2} d^{4} e^{2} - 4 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4} + {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 2 \, a^{2} b^{4} d^{3} e^{3} + 2 \, a^{3} b^{3} d^{2} e^{4} - 3 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{3} + {\left(b^{6} d^{6} - 9 \, a^{2} b^{4} d^{4} e^{2} + 16 \, a^{3} b^{3} d^{3} e^{3} - 9 \, a^{4} b^{2} d^{2} e^{4} + a^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} d^{6} - 3 \, a^{2} b^{4} d^{5} e + 2 \, a^{3} b^{3} d^{4} e^{2} + 2 \, a^{4} b^{2} d^{3} e^{3} - 3 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x\right)}}\right]"," ",0,"[1/24*(105*(b^3*e^4*x^4 + a^2*b*d^2*e^2 + 2*(b^3*d*e^3 + a*b^2*e^4)*x^3 + (b^3*d^2*e^2 + 4*a*b^2*d*e^3 + a^2*b*e^4)*x^2 + 2*(a*b^2*d^2*e^2 + a^2*b*d*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(105*b^3*e^3*x^3 - 6*b^3*d^3 + 39*a*b^2*d^2*e + 80*a^2*b*d*e^2 - 8*a^3*e^3 + 35*(4*b^3*d*e^2 + 5*a*b^2*e^3)*x^2 + 7*(3*b^3*d^2*e + 34*a*b^2*d*e^2 + 8*a^2*b*e^3)*x)*sqrt(e*x + d))/(a^2*b^4*d^6 - 4*a^3*b^3*d^5*e + 6*a^4*b^2*d^4*e^2 - 4*a^5*b*d^3*e^3 + a^6*d^2*e^4 + (b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^4 + 2*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 2*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4 - 3*a^4*b^2*d*e^5 + a^5*b*e^6)*x^3 + (b^6*d^6 - 9*a^2*b^4*d^4*e^2 + 16*a^3*b^3*d^3*e^3 - 9*a^4*b^2*d^2*e^4 + a^6*e^6)*x^2 + 2*(a*b^5*d^6 - 3*a^2*b^4*d^5*e + 2*a^3*b^3*d^4*e^2 + 2*a^4*b^2*d^3*e^3 - 3*a^5*b*d^2*e^4 + a^6*d*e^5)*x), -1/12*(105*(b^3*e^4*x^4 + a^2*b*d^2*e^2 + 2*(b^3*d*e^3 + a*b^2*e^4)*x^3 + (b^3*d^2*e^2 + 4*a*b^2*d*e^3 + a^2*b*e^4)*x^2 + 2*(a*b^2*d^2*e^2 + a^2*b*d*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (105*b^3*e^3*x^3 - 6*b^3*d^3 + 39*a*b^2*d^2*e + 80*a^2*b*d*e^2 - 8*a^3*e^3 + 35*(4*b^3*d*e^2 + 5*a*b^2*e^3)*x^2 + 7*(3*b^3*d^2*e + 34*a*b^2*d*e^2 + 8*a^2*b*e^3)*x)*sqrt(e*x + d))/(a^2*b^4*d^6 - 4*a^3*b^3*d^5*e + 6*a^4*b^2*d^4*e^2 - 4*a^5*b*d^3*e^3 + a^6*d^2*e^4 + (b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^4 + 2*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 2*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4 - 3*a^4*b^2*d*e^5 + a^5*b*e^6)*x^3 + (b^6*d^6 - 9*a^2*b^4*d^4*e^2 + 16*a^3*b^3*d^3*e^3 - 9*a^4*b^2*d^2*e^4 + a^6*e^6)*x^2 + 2*(a*b^5*d^6 - 3*a^2*b^4*d^5*e + 2*a^3*b^3*d^4*e^2 + 2*a^4*b^2*d^3*e^3 - 3*a^5*b*d^2*e^4 + a^6*d*e^5)*x)]","B",0
2082,1,1858,0,0.468499," ","integrate((b*x+a)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{2} b^{2} d^{3} e^{2} + {\left(3 \, b^{4} d e^{4} + 2 \, a b^{3} e^{5}\right)} x^{4} + {\left(3 \, b^{4} d^{2} e^{3} + 6 \, a b^{3} d e^{4} + a^{2} b^{2} e^{5}\right)} x^{3} + {\left(b^{4} d^{3} e^{2} + 6 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4}\right)} x^{2} + {\left(2 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(315 \, b^{4} e^{4} x^{4} - 10 \, b^{4} d^{4} + 85 \, a b^{3} d^{3} e + 288 \, a^{2} b^{2} d^{2} e^{2} - 56 \, a^{3} b d e^{3} + 8 \, a^{4} e^{4} + 105 \, {\left(7 \, b^{4} d e^{3} + 5 \, a b^{3} e^{4}\right)} x^{3} + 21 \, {\left(23 \, b^{4} d^{2} e^{2} + 59 \, a b^{3} d e^{3} + 8 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(15 \, b^{4} d^{3} e + 277 \, a b^{3} d^{2} e^{2} + 136 \, a^{2} b^{2} d e^{3} - 8 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{40 \, {\left(a^{2} b^{5} d^{8} - 5 \, a^{3} b^{4} d^{7} e + 10 \, a^{4} b^{3} d^{6} e^{2} - 10 \, a^{5} b^{2} d^{5} e^{3} + 5 \, a^{6} b d^{4} e^{4} - a^{7} d^{3} e^{5} + {\left(b^{7} d^{5} e^{3} - 5 \, a b^{6} d^{4} e^{4} + 10 \, a^{2} b^{5} d^{3} e^{5} - 10 \, a^{3} b^{4} d^{2} e^{6} + 5 \, a^{4} b^{3} d e^{7} - a^{5} b^{2} e^{8}\right)} x^{5} + {\left(3 \, b^{7} d^{6} e^{2} - 13 \, a b^{6} d^{5} e^{3} + 20 \, a^{2} b^{5} d^{4} e^{4} - 10 \, a^{3} b^{4} d^{3} e^{5} - 5 \, a^{4} b^{3} d^{2} e^{6} + 7 \, a^{5} b^{2} d e^{7} - 2 \, a^{6} b e^{8}\right)} x^{4} + {\left(3 \, b^{7} d^{7} e - 9 \, a b^{6} d^{6} e^{2} + a^{2} b^{5} d^{5} e^{3} + 25 \, a^{3} b^{4} d^{4} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{5} + 17 \, a^{5} b^{2} d^{2} e^{6} - a^{6} b d e^{7} - a^{7} e^{8}\right)} x^{3} + {\left(b^{7} d^{8} + a b^{6} d^{7} e - 17 \, a^{2} b^{5} d^{6} e^{2} + 35 \, a^{3} b^{4} d^{5} e^{3} - 25 \, a^{4} b^{3} d^{4} e^{4} - a^{5} b^{2} d^{3} e^{5} + 9 \, a^{6} b d^{2} e^{6} - 3 \, a^{7} d e^{7}\right)} x^{2} + {\left(2 \, a b^{6} d^{8} - 7 \, a^{2} b^{5} d^{7} e + 5 \, a^{3} b^{4} d^{6} e^{2} + 10 \, a^{4} b^{3} d^{5} e^{3} - 20 \, a^{5} b^{2} d^{4} e^{4} + 13 \, a^{6} b d^{3} e^{5} - 3 \, a^{7} d^{2} e^{6}\right)} x\right)}}, -\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{2} b^{2} d^{3} e^{2} + {\left(3 \, b^{4} d e^{4} + 2 \, a b^{3} e^{5}\right)} x^{4} + {\left(3 \, b^{4} d^{2} e^{3} + 6 \, a b^{3} d e^{4} + a^{2} b^{2} e^{5}\right)} x^{3} + {\left(b^{4} d^{3} e^{2} + 6 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4}\right)} x^{2} + {\left(2 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(315 \, b^{4} e^{4} x^{4} - 10 \, b^{4} d^{4} + 85 \, a b^{3} d^{3} e + 288 \, a^{2} b^{2} d^{2} e^{2} - 56 \, a^{3} b d e^{3} + 8 \, a^{4} e^{4} + 105 \, {\left(7 \, b^{4} d e^{3} + 5 \, a b^{3} e^{4}\right)} x^{3} + 21 \, {\left(23 \, b^{4} d^{2} e^{2} + 59 \, a b^{3} d e^{3} + 8 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(15 \, b^{4} d^{3} e + 277 \, a b^{3} d^{2} e^{2} + 136 \, a^{2} b^{2} d e^{3} - 8 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{20 \, {\left(a^{2} b^{5} d^{8} - 5 \, a^{3} b^{4} d^{7} e + 10 \, a^{4} b^{3} d^{6} e^{2} - 10 \, a^{5} b^{2} d^{5} e^{3} + 5 \, a^{6} b d^{4} e^{4} - a^{7} d^{3} e^{5} + {\left(b^{7} d^{5} e^{3} - 5 \, a b^{6} d^{4} e^{4} + 10 \, a^{2} b^{5} d^{3} e^{5} - 10 \, a^{3} b^{4} d^{2} e^{6} + 5 \, a^{4} b^{3} d e^{7} - a^{5} b^{2} e^{8}\right)} x^{5} + {\left(3 \, b^{7} d^{6} e^{2} - 13 \, a b^{6} d^{5} e^{3} + 20 \, a^{2} b^{5} d^{4} e^{4} - 10 \, a^{3} b^{4} d^{3} e^{5} - 5 \, a^{4} b^{3} d^{2} e^{6} + 7 \, a^{5} b^{2} d e^{7} - 2 \, a^{6} b e^{8}\right)} x^{4} + {\left(3 \, b^{7} d^{7} e - 9 \, a b^{6} d^{6} e^{2} + a^{2} b^{5} d^{5} e^{3} + 25 \, a^{3} b^{4} d^{4} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{5} + 17 \, a^{5} b^{2} d^{2} e^{6} - a^{6} b d e^{7} - a^{7} e^{8}\right)} x^{3} + {\left(b^{7} d^{8} + a b^{6} d^{7} e - 17 \, a^{2} b^{5} d^{6} e^{2} + 35 \, a^{3} b^{4} d^{5} e^{3} - 25 \, a^{4} b^{3} d^{4} e^{4} - a^{5} b^{2} d^{3} e^{5} + 9 \, a^{6} b d^{2} e^{6} - 3 \, a^{7} d e^{7}\right)} x^{2} + {\left(2 \, a b^{6} d^{8} - 7 \, a^{2} b^{5} d^{7} e + 5 \, a^{3} b^{4} d^{6} e^{2} + 10 \, a^{4} b^{3} d^{5} e^{3} - 20 \, a^{5} b^{2} d^{4} e^{4} + 13 \, a^{6} b d^{3} e^{5} - 3 \, a^{7} d^{2} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/40*(315*(b^4*e^5*x^5 + a^2*b^2*d^3*e^2 + (3*b^4*d*e^4 + 2*a*b^3*e^5)*x^4 + (3*b^4*d^2*e^3 + 6*a*b^3*d*e^4 + a^2*b^2*e^5)*x^3 + (b^4*d^3*e^2 + 6*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4)*x^2 + (2*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(315*b^4*e^4*x^4 - 10*b^4*d^4 + 85*a*b^3*d^3*e + 288*a^2*b^2*d^2*e^2 - 56*a^3*b*d*e^3 + 8*a^4*e^4 + 105*(7*b^4*d*e^3 + 5*a*b^3*e^4)*x^3 + 21*(23*b^4*d^2*e^2 + 59*a*b^3*d*e^3 + 8*a^2*b^2*e^4)*x^2 + 3*(15*b^4*d^3*e + 277*a*b^3*d^2*e^2 + 136*a^2*b^2*d*e^3 - 8*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^2*b^5*d^8 - 5*a^3*b^4*d^7*e + 10*a^4*b^3*d^6*e^2 - 10*a^5*b^2*d^5*e^3 + 5*a^6*b*d^4*e^4 - a^7*d^3*e^5 + (b^7*d^5*e^3 - 5*a*b^6*d^4*e^4 + 10*a^2*b^5*d^3*e^5 - 10*a^3*b^4*d^2*e^6 + 5*a^4*b^3*d*e^7 - a^5*b^2*e^8)*x^5 + (3*b^7*d^6*e^2 - 13*a*b^6*d^5*e^3 + 20*a^2*b^5*d^4*e^4 - 10*a^3*b^4*d^3*e^5 - 5*a^4*b^3*d^2*e^6 + 7*a^5*b^2*d*e^7 - 2*a^6*b*e^8)*x^4 + (3*b^7*d^7*e - 9*a*b^6*d^6*e^2 + a^2*b^5*d^5*e^3 + 25*a^3*b^4*d^4*e^4 - 35*a^4*b^3*d^3*e^5 + 17*a^5*b^2*d^2*e^6 - a^6*b*d*e^7 - a^7*e^8)*x^3 + (b^7*d^8 + a*b^6*d^7*e - 17*a^2*b^5*d^6*e^2 + 35*a^3*b^4*d^5*e^3 - 25*a^4*b^3*d^4*e^4 - a^5*b^2*d^3*e^5 + 9*a^6*b*d^2*e^6 - 3*a^7*d*e^7)*x^2 + (2*a*b^6*d^8 - 7*a^2*b^5*d^7*e + 5*a^3*b^4*d^6*e^2 + 10*a^4*b^3*d^5*e^3 - 20*a^5*b^2*d^4*e^4 + 13*a^6*b*d^3*e^5 - 3*a^7*d^2*e^6)*x), -1/20*(315*(b^4*e^5*x^5 + a^2*b^2*d^3*e^2 + (3*b^4*d*e^4 + 2*a*b^3*e^5)*x^4 + (3*b^4*d^2*e^3 + 6*a*b^3*d*e^4 + a^2*b^2*e^5)*x^3 + (b^4*d^3*e^2 + 6*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4)*x^2 + (2*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (315*b^4*e^4*x^4 - 10*b^4*d^4 + 85*a*b^3*d^3*e + 288*a^2*b^2*d^2*e^2 - 56*a^3*b*d*e^3 + 8*a^4*e^4 + 105*(7*b^4*d*e^3 + 5*a*b^3*e^4)*x^3 + 21*(23*b^4*d^2*e^2 + 59*a*b^3*d*e^3 + 8*a^2*b^2*e^4)*x^2 + 3*(15*b^4*d^3*e + 277*a*b^3*d^2*e^2 + 136*a^2*b^2*d*e^3 - 8*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^2*b^5*d^8 - 5*a^3*b^4*d^7*e + 10*a^4*b^3*d^6*e^2 - 10*a^5*b^2*d^5*e^3 + 5*a^6*b*d^4*e^4 - a^7*d^3*e^5 + (b^7*d^5*e^3 - 5*a*b^6*d^4*e^4 + 10*a^2*b^5*d^3*e^5 - 10*a^3*b^4*d^2*e^6 + 5*a^4*b^3*d*e^7 - a^5*b^2*e^8)*x^5 + (3*b^7*d^6*e^2 - 13*a*b^6*d^5*e^3 + 20*a^2*b^5*d^4*e^4 - 10*a^3*b^4*d^3*e^5 - 5*a^4*b^3*d^2*e^6 + 7*a^5*b^2*d*e^7 - 2*a^6*b*e^8)*x^4 + (3*b^7*d^7*e - 9*a*b^6*d^6*e^2 + a^2*b^5*d^5*e^3 + 25*a^3*b^4*d^4*e^4 - 35*a^4*b^3*d^3*e^5 + 17*a^5*b^2*d^2*e^6 - a^6*b*d*e^7 - a^7*e^8)*x^3 + (b^7*d^8 + a*b^6*d^7*e - 17*a^2*b^5*d^6*e^2 + 35*a^3*b^4*d^5*e^3 - 25*a^4*b^3*d^4*e^4 - a^5*b^2*d^3*e^5 + 9*a^6*b*d^2*e^6 - 3*a^7*d*e^7)*x^2 + (2*a*b^6*d^8 - 7*a^2*b^5*d^7*e + 5*a^3*b^4*d^6*e^2 + 10*a^4*b^3*d^5*e^3 - 20*a^5*b^2*d^4*e^4 + 13*a^6*b*d^3*e^5 - 3*a^7*d^2*e^6)*x)]","B",0
2083,1,968,0,0.457482," ","integrate((b*x+a)*(e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left(a^{4} b d e^{4} - a^{5} e^{5} + {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 4 \, {\left(a b^{4} d e^{4} - a^{2} b^{3} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{3} d e^{4} - a^{3} b^{2} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{2} d e^{4} - a^{4} b e^{5}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(128 \, b^{5} e^{5} x^{5} - 48 \, b^{5} d^{5} - 88 \, a b^{4} d^{4} e - 198 \, a^{2} b^{3} d^{3} e^{2} - 693 \, a^{3} b^{2} d^{2} e^{3} + 4620 \, a^{4} b d e^{4} - 3465 \, a^{5} e^{5} + 128 \, {\left(16 \, b^{5} d e^{4} - 11 \, a b^{4} e^{5}\right)} x^{4} - {\left(2295 \, b^{5} d^{2} e^{3} - 12782 \, a b^{4} d e^{4} + 9207 \, a^{2} b^{3} e^{5}\right)} x^{3} - {\left(1030 \, b^{5} d^{3} e^{2} + 3795 \, a b^{4} d^{2} e^{3} - 22968 \, a^{2} b^{3} d e^{4} + 16863 \, a^{3} b^{2} e^{5}\right)} x^{2} - {\left(328 \, b^{5} d^{4} e + 748 \, a b^{4} d^{3} e^{2} + 2673 \, a^{2} b^{3} d^{2} e^{3} - 17094 \, a^{3} b^{2} d e^{4} + 12705 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}, -\frac{3465 \, {\left(a^{4} b d e^{4} - a^{5} e^{5} + {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 4 \, {\left(a b^{4} d e^{4} - a^{2} b^{3} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{3} d e^{4} - a^{3} b^{2} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{2} d e^{4} - a^{4} b e^{5}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(128 \, b^{5} e^{5} x^{5} - 48 \, b^{5} d^{5} - 88 \, a b^{4} d^{4} e - 198 \, a^{2} b^{3} d^{3} e^{2} - 693 \, a^{3} b^{2} d^{2} e^{3} + 4620 \, a^{4} b d e^{4} - 3465 \, a^{5} e^{5} + 128 \, {\left(16 \, b^{5} d e^{4} - 11 \, a b^{4} e^{5}\right)} x^{4} - {\left(2295 \, b^{5} d^{2} e^{3} - 12782 \, a b^{4} d e^{4} + 9207 \, a^{2} b^{3} e^{5}\right)} x^{3} - {\left(1030 \, b^{5} d^{3} e^{2} + 3795 \, a b^{4} d^{2} e^{3} - 22968 \, a^{2} b^{3} d e^{4} + 16863 \, a^{3} b^{2} e^{5}\right)} x^{2} - {\left(328 \, b^{5} d^{4} e + 748 \, a b^{4} d^{3} e^{2} + 2673 \, a^{2} b^{3} d^{2} e^{3} - 17094 \, a^{3} b^{2} d e^{4} + 12705 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}\right]"," ",0,"[-1/384*(3465*(a^4*b*d*e^4 - a^5*e^5 + (b^5*d*e^4 - a*b^4*e^5)*x^4 + 4*(a*b^4*d*e^4 - a^2*b^3*e^5)*x^3 + 6*(a^2*b^3*d*e^4 - a^3*b^2*e^5)*x^2 + 4*(a^3*b^2*d*e^4 - a^4*b*e^5)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(128*b^5*e^5*x^5 - 48*b^5*d^5 - 88*a*b^4*d^4*e - 198*a^2*b^3*d^3*e^2 - 693*a^3*b^2*d^2*e^3 + 4620*a^4*b*d*e^4 - 3465*a^5*e^5 + 128*(16*b^5*d*e^4 - 11*a*b^4*e^5)*x^4 - (2295*b^5*d^2*e^3 - 12782*a*b^4*d*e^4 + 9207*a^2*b^3*e^5)*x^3 - (1030*b^5*d^3*e^2 + 3795*a*b^4*d^2*e^3 - 22968*a^2*b^3*d*e^4 + 16863*a^3*b^2*e^5)*x^2 - (328*b^5*d^4*e + 748*a*b^4*d^3*e^2 + 2673*a^2*b^3*d^2*e^3 - 17094*a^3*b^2*d*e^4 + 12705*a^4*b*e^5)*x)*sqrt(e*x + d))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6), -1/192*(3465*(a^4*b*d*e^4 - a^5*e^5 + (b^5*d*e^4 - a*b^4*e^5)*x^4 + 4*(a*b^4*d*e^4 - a^2*b^3*e^5)*x^3 + 6*(a^2*b^3*d*e^4 - a^3*b^2*e^5)*x^2 + 4*(a^3*b^2*d*e^4 - a^4*b*e^5)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (128*b^5*e^5*x^5 - 48*b^5*d^5 - 88*a*b^4*d^4*e - 198*a^2*b^3*d^3*e^2 - 693*a^3*b^2*d^2*e^3 + 4620*a^4*b*d*e^4 - 3465*a^5*e^5 + 128*(16*b^5*d*e^4 - 11*a*b^4*e^5)*x^4 - (2295*b^5*d^2*e^3 - 12782*a*b^4*d*e^4 + 9207*a^2*b^3*e^5)*x^3 - (1030*b^5*d^3*e^2 + 3795*a*b^4*d^2*e^3 - 22968*a^2*b^3*d*e^4 + 16863*a^3*b^2*e^5)*x^2 - (328*b^5*d^4*e + 748*a*b^4*d^3*e^2 + 2673*a^2*b^3*d^2*e^3 - 17094*a^3*b^2*d*e^4 + 12705*a^4*b*e^5)*x)*sqrt(e*x + d))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6)]","B",0
2084,1,680,0,0.439187," ","integrate((b*x+a)*(e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(128 \, b^{4} e^{4} x^{4} - 16 \, b^{4} d^{4} - 24 \, a b^{3} d^{3} e - 42 \, a^{2} b^{2} d^{2} e^{2} - 105 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} - {\left(325 \, b^{4} d e^{3} - 837 \, a b^{3} e^{4}\right)} x^{3} - 3 \, {\left(70 \, b^{4} d^{2} e^{2} + 185 \, a b^{3} d e^{3} - 511 \, a^{2} b^{2} e^{4}\right)} x^{2} - {\left(88 \, b^{4} d^{3} e + 156 \, a b^{3} d^{2} e^{2} + 399 \, a^{2} b^{2} d e^{3} - 1155 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{128 \, {\left(b^{9} x^{4} + 4 \, a b^{8} x^{3} + 6 \, a^{2} b^{7} x^{2} + 4 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}, -\frac{315 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(128 \, b^{4} e^{4} x^{4} - 16 \, b^{4} d^{4} - 24 \, a b^{3} d^{3} e - 42 \, a^{2} b^{2} d^{2} e^{2} - 105 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} - {\left(325 \, b^{4} d e^{3} - 837 \, a b^{3} e^{4}\right)} x^{3} - 3 \, {\left(70 \, b^{4} d^{2} e^{2} + 185 \, a b^{3} d e^{3} - 511 \, a^{2} b^{2} e^{4}\right)} x^{2} - {\left(88 \, b^{4} d^{3} e + 156 \, a b^{3} d^{2} e^{2} + 399 \, a^{2} b^{2} d e^{3} - 1155 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(b^{9} x^{4} + 4 \, a b^{8} x^{3} + 6 \, a^{2} b^{7} x^{2} + 4 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}\right]"," ",0,"[1/128*(315*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(128*b^4*e^4*x^4 - 16*b^4*d^4 - 24*a*b^3*d^3*e - 42*a^2*b^2*d^2*e^2 - 105*a^3*b*d*e^3 + 315*a^4*e^4 - (325*b^4*d*e^3 - 837*a*b^3*e^4)*x^3 - 3*(70*b^4*d^2*e^2 + 185*a*b^3*d*e^3 - 511*a^2*b^2*e^4)*x^2 - (88*b^4*d^3*e + 156*a*b^3*d^2*e^2 + 399*a^2*b^2*d*e^3 - 1155*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^9*x^4 + 4*a*b^8*x^3 + 6*a^2*b^7*x^2 + 4*a^3*b^6*x + a^4*b^5), -1/64*(315*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (128*b^4*e^4*x^4 - 16*b^4*d^4 - 24*a*b^3*d^3*e - 42*a^2*b^2*d^2*e^2 - 105*a^3*b*d*e^3 + 315*a^4*e^4 - (325*b^4*d*e^3 - 837*a*b^3*e^4)*x^3 - 3*(70*b^4*d^2*e^2 + 185*a*b^3*d*e^3 - 511*a^2*b^2*e^4)*x^2 - (88*b^4*d^3*e + 156*a*b^3*d^2*e^2 + 399*a^2*b^2*d*e^3 - 1155*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^9*x^4 + 4*a*b^8*x^3 + 6*a^2*b^7*x^2 + 4*a^3*b^6*x + a^4*b^5)]","B",0
2085,1,765,0,0.449350," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(48 \, b^{5} d^{4} + 8 \, a b^{4} d^{3} e + 14 \, a^{2} b^{3} d^{2} e^{2} + 35 \, a^{3} b^{2} d e^{3} - 105 \, a^{4} b e^{4} + 279 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(326 \, b^{5} d^{2} e^{2} + 185 \, a b^{4} d e^{3} - 511 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(200 \, b^{5} d^{3} e + 52 \, a b^{4} d^{2} e^{2} + 133 \, a^{2} b^{3} d e^{3} - 385 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d - a^{5} b^{5} e + {\left(b^{10} d - a b^{9} e\right)} x^{4} + 4 \, {\left(a b^{9} d - a^{2} b^{8} e\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d - a^{3} b^{7} e\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d - a^{4} b^{6} e\right)} x\right)}}, \frac{105 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(48 \, b^{5} d^{4} + 8 \, a b^{4} d^{3} e + 14 \, a^{2} b^{3} d^{2} e^{2} + 35 \, a^{3} b^{2} d e^{3} - 105 \, a^{4} b e^{4} + 279 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(326 \, b^{5} d^{2} e^{2} + 185 \, a b^{4} d e^{3} - 511 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(200 \, b^{5} d^{3} e + 52 \, a b^{4} d^{2} e^{2} + 133 \, a^{2} b^{3} d e^{3} - 385 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d - a^{5} b^{5} e + {\left(b^{10} d - a b^{9} e\right)} x^{4} + 4 \, {\left(a b^{9} d - a^{2} b^{8} e\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d - a^{3} b^{7} e\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d - a^{4} b^{6} e\right)} x\right)}}\right]"," ",0,"[1/384*(105*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(48*b^5*d^4 + 8*a*b^4*d^3*e + 14*a^2*b^3*d^2*e^2 + 35*a^3*b^2*d*e^3 - 105*a^4*b*e^4 + 279*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (326*b^5*d^2*e^2 + 185*a*b^4*d*e^3 - 511*a^2*b^3*e^4)*x^2 + (200*b^5*d^3*e + 52*a*b^4*d^2*e^2 + 133*a^2*b^3*d*e^3 - 385*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d - a^5*b^5*e + (b^10*d - a*b^9*e)*x^4 + 4*(a*b^9*d - a^2*b^8*e)*x^3 + 6*(a^2*b^8*d - a^3*b^7*e)*x^2 + 4*(a^3*b^7*d - a^4*b^6*e)*x), 1/192*(105*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (48*b^5*d^4 + 8*a*b^4*d^3*e + 14*a^2*b^3*d^2*e^2 + 35*a^3*b^2*d*e^3 - 105*a^4*b*e^4 + 279*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (326*b^5*d^2*e^2 + 185*a*b^4*d*e^3 - 511*a^2*b^3*e^4)*x^2 + (200*b^5*d^3*e + 52*a*b^4*d^2*e^2 + 133*a^2*b^3*d*e^3 - 385*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d - a^5*b^5*e + (b^10*d - a*b^9*e)*x^4 + 4*(a*b^9*d - a^2*b^8*e)*x^3 + 6*(a^2*b^8*d - a^3*b^7*e)*x^2 + 4*(a^3*b^7*d - a^4*b^6*e)*x)]","B",0
2086,1,894,0,0.455806," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(48 \, b^{5} d^{4} - 56 \, a b^{4} d^{3} e - 2 \, a^{2} b^{3} d^{2} e^{2} - 5 \, a^{3} b^{2} d e^{3} + 15 \, a^{4} b e^{4} + 15 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(118 \, b^{5} d^{2} e^{2} - 191 \, a b^{4} d e^{3} + 73 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(136 \, b^{5} d^{3} e - 172 \, a b^{4} d^{2} e^{2} - 19 \, a^{2} b^{3} d e^{3} + 55 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d^{2} - 2 \, a^{5} b^{5} d e + a^{6} b^{4} e^{2} + {\left(b^{10} d^{2} - 2 \, a b^{9} d e + a^{2} b^{8} e^{2}\right)} x^{4} + 4 \, {\left(a b^{9} d^{2} - 2 \, a^{2} b^{8} d e + a^{3} b^{7} e^{2}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{2} - 2 \, a^{3} b^{7} d e + a^{4} b^{6} e^{2}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{2} - 2 \, a^{4} b^{6} d e + a^{5} b^{5} e^{2}\right)} x\right)}}, -\frac{15 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(48 \, b^{5} d^{4} - 56 \, a b^{4} d^{3} e - 2 \, a^{2} b^{3} d^{2} e^{2} - 5 \, a^{3} b^{2} d e^{3} + 15 \, a^{4} b e^{4} + 15 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(118 \, b^{5} d^{2} e^{2} - 191 \, a b^{4} d e^{3} + 73 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(136 \, b^{5} d^{3} e - 172 \, a b^{4} d^{2} e^{2} - 19 \, a^{2} b^{3} d e^{3} + 55 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d^{2} - 2 \, a^{5} b^{5} d e + a^{6} b^{4} e^{2} + {\left(b^{10} d^{2} - 2 \, a b^{9} d e + a^{2} b^{8} e^{2}\right)} x^{4} + 4 \, {\left(a b^{9} d^{2} - 2 \, a^{2} b^{8} d e + a^{3} b^{7} e^{2}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{2} - 2 \, a^{3} b^{7} d e + a^{4} b^{6} e^{2}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{2} - 2 \, a^{4} b^{6} d e + a^{5} b^{5} e^{2}\right)} x\right)}}\right]"," ",0,"[-1/384*(15*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(48*b^5*d^4 - 56*a*b^4*d^3*e - 2*a^2*b^3*d^2*e^2 - 5*a^3*b^2*d*e^3 + 15*a^4*b*e^4 + 15*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (118*b^5*d^2*e^2 - 191*a*b^4*d*e^3 + 73*a^2*b^3*e^4)*x^2 + (136*b^5*d^3*e - 172*a*b^4*d^2*e^2 - 19*a^2*b^3*d*e^3 + 55*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^2 - 2*a^5*b^5*d*e + a^6*b^4*e^2 + (b^10*d^2 - 2*a*b^9*d*e + a^2*b^8*e^2)*x^4 + 4*(a*b^9*d^2 - 2*a^2*b^8*d*e + a^3*b^7*e^2)*x^3 + 6*(a^2*b^8*d^2 - 2*a^3*b^7*d*e + a^4*b^6*e^2)*x^2 + 4*(a^3*b^7*d^2 - 2*a^4*b^6*d*e + a^5*b^5*e^2)*x), -1/192*(15*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (48*b^5*d^4 - 56*a*b^4*d^3*e - 2*a^2*b^3*d^2*e^2 - 5*a^3*b^2*d*e^3 + 15*a^4*b*e^4 + 15*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (118*b^5*d^2*e^2 - 191*a*b^4*d*e^3 + 73*a^2*b^3*e^4)*x^2 + (136*b^5*d^3*e - 172*a*b^4*d^2*e^2 - 19*a^2*b^3*d*e^3 + 55*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^2 - 2*a^5*b^5*d*e + a^6*b^4*e^2 + (b^10*d^2 - 2*a*b^9*d*e + a^2*b^8*e^2)*x^4 + 4*(a*b^9*d^2 - 2*a^2*b^8*d*e + a^3*b^7*e^2)*x^3 + 6*(a^2*b^8*d^2 - 2*a^3*b^7*d*e + a^4*b^6*e^2)*x^2 + 4*(a^3*b^7*d^2 - 2*a^4*b^6*d*e + a^5*b^5*e^2)*x)]","B",0
2087,1,1043,0,0.448126," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(16 \, b^{5} d^{4} - 40 \, a b^{4} d^{3} e + 26 \, a^{2} b^{3} d^{2} e^{2} + a^{3} b^{2} d e^{3} - 3 \, a^{4} b e^{4} - 3 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(24 \, b^{5} d^{3} e - 68 \, a b^{4} d^{2} e^{2} + 55 \, a^{2} b^{3} d e^{3} - 11 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{128 \, {\left(a^{4} b^{6} d^{3} - 3 \, a^{5} b^{5} d^{2} e + 3 \, a^{6} b^{4} d e^{2} - a^{7} b^{3} e^{3} + {\left(b^{10} d^{3} - 3 \, a b^{9} d^{2} e + 3 \, a^{2} b^{8} d e^{2} - a^{3} b^{7} e^{3}\right)} x^{4} + 4 \, {\left(a b^{9} d^{3} - 3 \, a^{2} b^{8} d^{2} e + 3 \, a^{3} b^{7} d e^{2} - a^{4} b^{6} e^{3}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{3} - 3 \, a^{3} b^{7} d^{2} e + 3 \, a^{4} b^{6} d e^{2} - a^{5} b^{5} e^{3}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{3} - 3 \, a^{4} b^{6} d^{2} e + 3 \, a^{5} b^{5} d e^{2} - a^{6} b^{4} e^{3}\right)} x\right)}}, \frac{3 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(16 \, b^{5} d^{4} - 40 \, a b^{4} d^{3} e + 26 \, a^{2} b^{3} d^{2} e^{2} + a^{3} b^{2} d e^{3} - 3 \, a^{4} b e^{4} - 3 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(24 \, b^{5} d^{3} e - 68 \, a b^{4} d^{2} e^{2} + 55 \, a^{2} b^{3} d e^{3} - 11 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{4} b^{6} d^{3} - 3 \, a^{5} b^{5} d^{2} e + 3 \, a^{6} b^{4} d e^{2} - a^{7} b^{3} e^{3} + {\left(b^{10} d^{3} - 3 \, a b^{9} d^{2} e + 3 \, a^{2} b^{8} d e^{2} - a^{3} b^{7} e^{3}\right)} x^{4} + 4 \, {\left(a b^{9} d^{3} - 3 \, a^{2} b^{8} d^{2} e + 3 \, a^{3} b^{7} d e^{2} - a^{4} b^{6} e^{3}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{3} - 3 \, a^{3} b^{7} d^{2} e + 3 \, a^{4} b^{6} d e^{2} - a^{5} b^{5} e^{3}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{3} - 3 \, a^{4} b^{6} d^{2} e + 3 \, a^{5} b^{5} d e^{2} - a^{6} b^{4} e^{3}\right)} x\right)}}\right]"," ",0,"[1/128*(3*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(16*b^5*d^4 - 40*a*b^4*d^3*e + 26*a^2*b^3*d^2*e^2 + a^3*b^2*d*e^3 - 3*a^4*b*e^4 - 3*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 + (24*b^5*d^3*e - 68*a*b^4*d^2*e^2 + 55*a^2*b^3*d*e^3 - 11*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^3 - 3*a^5*b^5*d^2*e + 3*a^6*b^4*d*e^2 - a^7*b^3*e^3 + (b^10*d^3 - 3*a*b^9*d^2*e + 3*a^2*b^8*d*e^2 - a^3*b^7*e^3)*x^4 + 4*(a*b^9*d^3 - 3*a^2*b^8*d^2*e + 3*a^3*b^7*d*e^2 - a^4*b^6*e^3)*x^3 + 6*(a^2*b^8*d^3 - 3*a^3*b^7*d^2*e + 3*a^4*b^6*d*e^2 - a^5*b^5*e^3)*x^2 + 4*(a^3*b^7*d^3 - 3*a^4*b^6*d^2*e + 3*a^5*b^5*d*e^2 - a^6*b^4*e^3)*x), 1/64*(3*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (16*b^5*d^4 - 40*a*b^4*d^3*e + 26*a^2*b^3*d^2*e^2 + a^3*b^2*d*e^3 - 3*a^4*b*e^4 - 3*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 + (24*b^5*d^3*e - 68*a*b^4*d^2*e^2 + 55*a^2*b^3*d*e^3 - 11*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^3 - 3*a^5*b^5*d^2*e + 3*a^6*b^4*d*e^2 - a^7*b^3*e^3 + (b^10*d^3 - 3*a*b^9*d^2*e + 3*a^2*b^8*d*e^2 - a^3*b^7*e^3)*x^4 + 4*(a*b^9*d^3 - 3*a^2*b^8*d^2*e + 3*a^3*b^7*d*e^2 - a^4*b^6*e^3)*x^3 + 6*(a^2*b^8*d^3 - 3*a^3*b^7*d^2*e + 3*a^4*b^6*d*e^2 - a^5*b^5*e^3)*x^2 + 4*(a^3*b^7*d^3 - 3*a^4*b^6*d^2*e + 3*a^5*b^5*d*e^2 - a^6*b^4*e^3)*x)]","B",0
2088,1,1176,0,0.456290," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(48 \, b^{5} d^{4} - 184 \, a b^{4} d^{3} e + 254 \, a^{2} b^{3} d^{2} e^{2} - 133 \, a^{3} b^{2} d e^{3} + 15 \, a^{4} b e^{4} + 15 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} - 5 \, {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(8 \, b^{5} d^{3} e - 44 \, a b^{4} d^{2} e^{2} + 109 \, a^{2} b^{3} d e^{3} - 73 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d^{4} - 4 \, a^{5} b^{5} d^{3} e + 6 \, a^{6} b^{4} d^{2} e^{2} - 4 \, a^{7} b^{3} d e^{3} + a^{8} b^{2} e^{4} + {\left(b^{10} d^{4} - 4 \, a b^{9} d^{3} e + 6 \, a^{2} b^{8} d^{2} e^{2} - 4 \, a^{3} b^{7} d e^{3} + a^{4} b^{6} e^{4}\right)} x^{4} + 4 \, {\left(a b^{9} d^{4} - 4 \, a^{2} b^{8} d^{3} e + 6 \, a^{3} b^{7} d^{2} e^{2} - 4 \, a^{4} b^{6} d e^{3} + a^{5} b^{5} e^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{4} - 4 \, a^{3} b^{7} d^{3} e + 6 \, a^{4} b^{6} d^{2} e^{2} - 4 \, a^{5} b^{5} d e^{3} + a^{6} b^{4} e^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{4} - 4 \, a^{4} b^{6} d^{3} e + 6 \, a^{5} b^{5} d^{2} e^{2} - 4 \, a^{6} b^{4} d e^{3} + a^{7} b^{3} e^{4}\right)} x\right)}}, -\frac{15 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(48 \, b^{5} d^{4} - 184 \, a b^{4} d^{3} e + 254 \, a^{2} b^{3} d^{2} e^{2} - 133 \, a^{3} b^{2} d e^{3} + 15 \, a^{4} b e^{4} + 15 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} - 5 \, {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(8 \, b^{5} d^{3} e - 44 \, a b^{4} d^{2} e^{2} + 109 \, a^{2} b^{3} d e^{3} - 73 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d^{4} - 4 \, a^{5} b^{5} d^{3} e + 6 \, a^{6} b^{4} d^{2} e^{2} - 4 \, a^{7} b^{3} d e^{3} + a^{8} b^{2} e^{4} + {\left(b^{10} d^{4} - 4 \, a b^{9} d^{3} e + 6 \, a^{2} b^{8} d^{2} e^{2} - 4 \, a^{3} b^{7} d e^{3} + a^{4} b^{6} e^{4}\right)} x^{4} + 4 \, {\left(a b^{9} d^{4} - 4 \, a^{2} b^{8} d^{3} e + 6 \, a^{3} b^{7} d^{2} e^{2} - 4 \, a^{4} b^{6} d e^{3} + a^{5} b^{5} e^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{4} - 4 \, a^{3} b^{7} d^{3} e + 6 \, a^{4} b^{6} d^{2} e^{2} - 4 \, a^{5} b^{5} d e^{3} + a^{6} b^{4} e^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{4} - 4 \, a^{4} b^{6} d^{3} e + 6 \, a^{5} b^{5} d^{2} e^{2} - 4 \, a^{6} b^{4} d e^{3} + a^{7} b^{3} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/384*(15*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(48*b^5*d^4 - 184*a*b^4*d^3*e + 254*a^2*b^3*d^2*e^2 - 133*a^3*b^2*d*e^3 + 15*a^4*b*e^4 + 15*(b^5*d*e^3 - a*b^4*e^4)*x^3 - 5*(2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 + (8*b^5*d^3*e - 44*a*b^4*d^2*e^2 + 109*a^2*b^3*d*e^3 - 73*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^4 - 4*a^5*b^5*d^3*e + 6*a^6*b^4*d^2*e^2 - 4*a^7*b^3*d*e^3 + a^8*b^2*e^4 + (b^10*d^4 - 4*a*b^9*d^3*e + 6*a^2*b^8*d^2*e^2 - 4*a^3*b^7*d*e^3 + a^4*b^6*e^4)*x^4 + 4*(a*b^9*d^4 - 4*a^2*b^8*d^3*e + 6*a^3*b^7*d^2*e^2 - 4*a^4*b^6*d*e^3 + a^5*b^5*e^4)*x^3 + 6*(a^2*b^8*d^4 - 4*a^3*b^7*d^3*e + 6*a^4*b^6*d^2*e^2 - 4*a^5*b^5*d*e^3 + a^6*b^4*e^4)*x^2 + 4*(a^3*b^7*d^4 - 4*a^4*b^6*d^3*e + 6*a^5*b^5*d^2*e^2 - 4*a^6*b^4*d*e^3 + a^7*b^3*e^4)*x), -1/192*(15*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (48*b^5*d^4 - 184*a*b^4*d^3*e + 254*a^2*b^3*d^2*e^2 - 133*a^3*b^2*d*e^3 + 15*a^4*b*e^4 + 15*(b^5*d*e^3 - a*b^4*e^4)*x^3 - 5*(2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 + (8*b^5*d^3*e - 44*a*b^4*d^2*e^2 + 109*a^2*b^3*d*e^3 - 73*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^4 - 4*a^5*b^5*d^3*e + 6*a^6*b^4*d^2*e^2 - 4*a^7*b^3*d*e^3 + a^8*b^2*e^4 + (b^10*d^4 - 4*a*b^9*d^3*e + 6*a^2*b^8*d^2*e^2 - 4*a^3*b^7*d*e^3 + a^4*b^6*e^4)*x^4 + 4*(a*b^9*d^4 - 4*a^2*b^8*d^3*e + 6*a^3*b^7*d^2*e^2 - 4*a^4*b^6*d*e^3 + a^5*b^5*e^4)*x^3 + 6*(a^2*b^8*d^4 - 4*a^3*b^7*d^3*e + 6*a^4*b^6*d^2*e^2 - 4*a^5*b^5*d*e^3 + a^6*b^4*e^4)*x^2 + 4*(a^3*b^7*d^4 - 4*a^4*b^6*d^3*e + 6*a^5*b^5*d^2*e^2 - 4*a^6*b^4*d*e^3 + a^7*b^3*e^4)*x)]","B",0
2089,1,1325,0,0.464263," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(48 \, b^{5} d^{4} - 248 \, a b^{4} d^{3} e + 526 \, a^{2} b^{3} d^{2} e^{2} - 605 \, a^{3} b^{2} d e^{3} + 279 \, a^{4} b e^{4} - 105 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + 35 \, {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} - 7 \, {\left(8 \, b^{5} d^{3} e - 44 \, a b^{4} d^{2} e^{2} + 109 \, a^{2} b^{3} d e^{3} - 73 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d^{5} - 5 \, a^{5} b^{5} d^{4} e + 10 \, a^{6} b^{4} d^{3} e^{2} - 10 \, a^{7} b^{3} d^{2} e^{3} + 5 \, a^{8} b^{2} d e^{4} - a^{9} b e^{5} + {\left(b^{10} d^{5} - 5 \, a b^{9} d^{4} e + 10 \, a^{2} b^{8} d^{3} e^{2} - 10 \, a^{3} b^{7} d^{2} e^{3} + 5 \, a^{4} b^{6} d e^{4} - a^{5} b^{5} e^{5}\right)} x^{4} + 4 \, {\left(a b^{9} d^{5} - 5 \, a^{2} b^{8} d^{4} e + 10 \, a^{3} b^{7} d^{3} e^{2} - 10 \, a^{4} b^{6} d^{2} e^{3} + 5 \, a^{5} b^{5} d e^{4} - a^{6} b^{4} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{5} - 5 \, a^{3} b^{7} d^{4} e + 10 \, a^{4} b^{6} d^{3} e^{2} - 10 \, a^{5} b^{5} d^{2} e^{3} + 5 \, a^{6} b^{4} d e^{4} - a^{7} b^{3} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{5} - 5 \, a^{4} b^{6} d^{4} e + 10 \, a^{5} b^{5} d^{3} e^{2} - 10 \, a^{6} b^{4} d^{2} e^{3} + 5 \, a^{7} b^{3} d e^{4} - a^{8} b^{2} e^{5}\right)} x\right)}}, \frac{105 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(48 \, b^{5} d^{4} - 248 \, a b^{4} d^{3} e + 526 \, a^{2} b^{3} d^{2} e^{2} - 605 \, a^{3} b^{2} d e^{3} + 279 \, a^{4} b e^{4} - 105 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + 35 \, {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} - 7 \, {\left(8 \, b^{5} d^{3} e - 44 \, a b^{4} d^{2} e^{2} + 109 \, a^{2} b^{3} d e^{3} - 73 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d^{5} - 5 \, a^{5} b^{5} d^{4} e + 10 \, a^{6} b^{4} d^{3} e^{2} - 10 \, a^{7} b^{3} d^{2} e^{3} + 5 \, a^{8} b^{2} d e^{4} - a^{9} b e^{5} + {\left(b^{10} d^{5} - 5 \, a b^{9} d^{4} e + 10 \, a^{2} b^{8} d^{3} e^{2} - 10 \, a^{3} b^{7} d^{2} e^{3} + 5 \, a^{4} b^{6} d e^{4} - a^{5} b^{5} e^{5}\right)} x^{4} + 4 \, {\left(a b^{9} d^{5} - 5 \, a^{2} b^{8} d^{4} e + 10 \, a^{3} b^{7} d^{3} e^{2} - 10 \, a^{4} b^{6} d^{2} e^{3} + 5 \, a^{5} b^{5} d e^{4} - a^{6} b^{4} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{5} - 5 \, a^{3} b^{7} d^{4} e + 10 \, a^{4} b^{6} d^{3} e^{2} - 10 \, a^{5} b^{5} d^{2} e^{3} + 5 \, a^{6} b^{4} d e^{4} - a^{7} b^{3} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{5} - 5 \, a^{4} b^{6} d^{4} e + 10 \, a^{5} b^{5} d^{3} e^{2} - 10 \, a^{6} b^{4} d^{2} e^{3} + 5 \, a^{7} b^{3} d e^{4} - a^{8} b^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[1/384*(105*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(48*b^5*d^4 - 248*a*b^4*d^3*e + 526*a^2*b^3*d^2*e^2 - 605*a^3*b^2*d*e^3 + 279*a^4*b*e^4 - 105*(b^5*d*e^3 - a*b^4*e^4)*x^3 + 35*(2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 - 7*(8*b^5*d^3*e - 44*a*b^4*d^2*e^2 + 109*a^2*b^3*d*e^3 - 73*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^5 - 5*a^5*b^5*d^4*e + 10*a^6*b^4*d^3*e^2 - 10*a^7*b^3*d^2*e^3 + 5*a^8*b^2*d*e^4 - a^9*b*e^5 + (b^10*d^5 - 5*a*b^9*d^4*e + 10*a^2*b^8*d^3*e^2 - 10*a^3*b^7*d^2*e^3 + 5*a^4*b^6*d*e^4 - a^5*b^5*e^5)*x^4 + 4*(a*b^9*d^5 - 5*a^2*b^8*d^4*e + 10*a^3*b^7*d^3*e^2 - 10*a^4*b^6*d^2*e^3 + 5*a^5*b^5*d*e^4 - a^6*b^4*e^5)*x^3 + 6*(a^2*b^8*d^5 - 5*a^3*b^7*d^4*e + 10*a^4*b^6*d^3*e^2 - 10*a^5*b^5*d^2*e^3 + 5*a^6*b^4*d*e^4 - a^7*b^3*e^5)*x^2 + 4*(a^3*b^7*d^5 - 5*a^4*b^6*d^4*e + 10*a^5*b^5*d^3*e^2 - 10*a^6*b^4*d^2*e^3 + 5*a^7*b^3*d*e^4 - a^8*b^2*e^5)*x), 1/192*(105*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (48*b^5*d^4 - 248*a*b^4*d^3*e + 526*a^2*b^3*d^2*e^2 - 605*a^3*b^2*d*e^3 + 279*a^4*b*e^4 - 105*(b^5*d*e^3 - a*b^4*e^4)*x^3 + 35*(2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 - 7*(8*b^5*d^3*e - 44*a*b^4*d^2*e^2 + 109*a^2*b^3*d*e^3 - 73*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^5 - 5*a^5*b^5*d^4*e + 10*a^6*b^4*d^3*e^2 - 10*a^7*b^3*d^2*e^3 + 5*a^8*b^2*d*e^4 - a^9*b*e^5 + (b^10*d^5 - 5*a*b^9*d^4*e + 10*a^2*b^8*d^3*e^2 - 10*a^3*b^7*d^2*e^3 + 5*a^4*b^6*d*e^4 - a^5*b^5*e^5)*x^4 + 4*(a*b^9*d^5 - 5*a^2*b^8*d^4*e + 10*a^3*b^7*d^3*e^2 - 10*a^4*b^6*d^2*e^3 + 5*a^5*b^5*d*e^4 - a^6*b^4*e^5)*x^3 + 6*(a^2*b^8*d^5 - 5*a^3*b^7*d^4*e + 10*a^4*b^6*d^3*e^2 - 10*a^5*b^5*d^2*e^3 + 5*a^6*b^4*d*e^4 - a^7*b^3*e^5)*x^2 + 4*(a^3*b^7*d^5 - 5*a^4*b^6*d^4*e + 10*a^5*b^5*d^3*e^2 - 10*a^6*b^4*d^2*e^3 + 5*a^7*b^3*d*e^4 - a^8*b^2*e^5)*x)]","B",0
2090,1,1734,0,0.480000," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{4} d e^{4} + {\left(b^{4} d e^{4} + 4 \, a b^{3} e^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} d e^{4} + 2 \, a^{3} b e^{5}\right)} x^{2} + {\left(4 \, a^{3} b d e^{4} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(315 \, b^{4} e^{4} x^{4} - 16 \, b^{4} d^{4} + 88 \, a b^{3} d^{3} e - 210 \, a^{2} b^{2} d^{2} e^{2} + 325 \, a^{3} b d e^{3} + 128 \, a^{4} e^{4} + 105 \, {\left(b^{4} d e^{3} + 11 \, a b^{3} e^{4}\right)} x^{3} - 21 \, {\left(2 \, b^{4} d^{2} e^{2} - 19 \, a b^{3} d e^{3} - 73 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(8 \, b^{4} d^{3} e - 52 \, a b^{3} d^{2} e^{2} + 185 \, a^{2} b^{2} d e^{3} + 279 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{128 \, {\left(a^{4} b^{5} d^{6} - 5 \, a^{5} b^{4} d^{5} e + 10 \, a^{6} b^{3} d^{4} e^{2} - 10 \, a^{7} b^{2} d^{3} e^{3} + 5 \, a^{8} b d^{2} e^{4} - a^{9} d e^{5} + {\left(b^{9} d^{5} e - 5 \, a b^{8} d^{4} e^{2} + 10 \, a^{2} b^{7} d^{3} e^{3} - 10 \, a^{3} b^{6} d^{2} e^{4} + 5 \, a^{4} b^{5} d e^{5} - a^{5} b^{4} e^{6}\right)} x^{5} + {\left(b^{9} d^{6} - a b^{8} d^{5} e - 10 \, a^{2} b^{7} d^{4} e^{2} + 30 \, a^{3} b^{6} d^{3} e^{3} - 35 \, a^{4} b^{5} d^{2} e^{4} + 19 \, a^{5} b^{4} d e^{5} - 4 \, a^{6} b^{3} e^{6}\right)} x^{4} + 2 \, {\left(2 \, a b^{8} d^{6} - 7 \, a^{2} b^{7} d^{5} e + 5 \, a^{3} b^{6} d^{4} e^{2} + 10 \, a^{4} b^{5} d^{3} e^{3} - 20 \, a^{5} b^{4} d^{2} e^{4} + 13 \, a^{6} b^{3} d e^{5} - 3 \, a^{7} b^{2} e^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{7} d^{6} - 13 \, a^{3} b^{6} d^{5} e + 20 \, a^{4} b^{5} d^{4} e^{2} - 10 \, a^{5} b^{4} d^{3} e^{3} - 5 \, a^{6} b^{3} d^{2} e^{4} + 7 \, a^{7} b^{2} d e^{5} - 2 \, a^{8} b e^{6}\right)} x^{2} + {\left(4 \, a^{3} b^{6} d^{6} - 19 \, a^{4} b^{5} d^{5} e + 35 \, a^{5} b^{4} d^{4} e^{2} - 30 \, a^{6} b^{3} d^{3} e^{3} + 10 \, a^{7} b^{2} d^{2} e^{4} + a^{8} b d e^{5} - a^{9} e^{6}\right)} x\right)}}, -\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{4} d e^{4} + {\left(b^{4} d e^{4} + 4 \, a b^{3} e^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} d e^{4} + 2 \, a^{3} b e^{5}\right)} x^{2} + {\left(4 \, a^{3} b d e^{4} + a^{4} e^{5}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(315 \, b^{4} e^{4} x^{4} - 16 \, b^{4} d^{4} + 88 \, a b^{3} d^{3} e - 210 \, a^{2} b^{2} d^{2} e^{2} + 325 \, a^{3} b d e^{3} + 128 \, a^{4} e^{4} + 105 \, {\left(b^{4} d e^{3} + 11 \, a b^{3} e^{4}\right)} x^{3} - 21 \, {\left(2 \, b^{4} d^{2} e^{2} - 19 \, a b^{3} d e^{3} - 73 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(8 \, b^{4} d^{3} e - 52 \, a b^{3} d^{2} e^{2} + 185 \, a^{2} b^{2} d e^{3} + 279 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{4} b^{5} d^{6} - 5 \, a^{5} b^{4} d^{5} e + 10 \, a^{6} b^{3} d^{4} e^{2} - 10 \, a^{7} b^{2} d^{3} e^{3} + 5 \, a^{8} b d^{2} e^{4} - a^{9} d e^{5} + {\left(b^{9} d^{5} e - 5 \, a b^{8} d^{4} e^{2} + 10 \, a^{2} b^{7} d^{3} e^{3} - 10 \, a^{3} b^{6} d^{2} e^{4} + 5 \, a^{4} b^{5} d e^{5} - a^{5} b^{4} e^{6}\right)} x^{5} + {\left(b^{9} d^{6} - a b^{8} d^{5} e - 10 \, a^{2} b^{7} d^{4} e^{2} + 30 \, a^{3} b^{6} d^{3} e^{3} - 35 \, a^{4} b^{5} d^{2} e^{4} + 19 \, a^{5} b^{4} d e^{5} - 4 \, a^{6} b^{3} e^{6}\right)} x^{4} + 2 \, {\left(2 \, a b^{8} d^{6} - 7 \, a^{2} b^{7} d^{5} e + 5 \, a^{3} b^{6} d^{4} e^{2} + 10 \, a^{4} b^{5} d^{3} e^{3} - 20 \, a^{5} b^{4} d^{2} e^{4} + 13 \, a^{6} b^{3} d e^{5} - 3 \, a^{7} b^{2} e^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{7} d^{6} - 13 \, a^{3} b^{6} d^{5} e + 20 \, a^{4} b^{5} d^{4} e^{2} - 10 \, a^{5} b^{4} d^{3} e^{3} - 5 \, a^{6} b^{3} d^{2} e^{4} + 7 \, a^{7} b^{2} d e^{5} - 2 \, a^{8} b e^{6}\right)} x^{2} + {\left(4 \, a^{3} b^{6} d^{6} - 19 \, a^{4} b^{5} d^{5} e + 35 \, a^{5} b^{4} d^{4} e^{2} - 30 \, a^{6} b^{3} d^{3} e^{3} + 10 \, a^{7} b^{2} d^{2} e^{4} + a^{8} b d e^{5} - a^{9} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/128*(315*(b^4*e^5*x^5 + a^4*d*e^4 + (b^4*d*e^4 + 4*a*b^3*e^5)*x^4 + 2*(2*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*x^3 + 2*(3*a^2*b^2*d*e^4 + 2*a^3*b*e^5)*x^2 + (4*a^3*b*d*e^4 + a^4*e^5)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(315*b^4*e^4*x^4 - 16*b^4*d^4 + 88*a*b^3*d^3*e - 210*a^2*b^2*d^2*e^2 + 325*a^3*b*d*e^3 + 128*a^4*e^4 + 105*(b^4*d*e^3 + 11*a*b^3*e^4)*x^3 - 21*(2*b^4*d^2*e^2 - 19*a*b^3*d*e^3 - 73*a^2*b^2*e^4)*x^2 + 3*(8*b^4*d^3*e - 52*a*b^3*d^2*e^2 + 185*a^2*b^2*d*e^3 + 279*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^4*b^5*d^6 - 5*a^5*b^4*d^5*e + 10*a^6*b^3*d^4*e^2 - 10*a^7*b^2*d^3*e^3 + 5*a^8*b*d^2*e^4 - a^9*d*e^5 + (b^9*d^5*e - 5*a*b^8*d^4*e^2 + 10*a^2*b^7*d^3*e^3 - 10*a^3*b^6*d^2*e^4 + 5*a^4*b^5*d*e^5 - a^5*b^4*e^6)*x^5 + (b^9*d^6 - a*b^8*d^5*e - 10*a^2*b^7*d^4*e^2 + 30*a^3*b^6*d^3*e^3 - 35*a^4*b^5*d^2*e^4 + 19*a^5*b^4*d*e^5 - 4*a^6*b^3*e^6)*x^4 + 2*(2*a*b^8*d^6 - 7*a^2*b^7*d^5*e + 5*a^3*b^6*d^4*e^2 + 10*a^4*b^5*d^3*e^3 - 20*a^5*b^4*d^2*e^4 + 13*a^6*b^3*d*e^5 - 3*a^7*b^2*e^6)*x^3 + 2*(3*a^2*b^7*d^6 - 13*a^3*b^6*d^5*e + 20*a^4*b^5*d^4*e^2 - 10*a^5*b^4*d^3*e^3 - 5*a^6*b^3*d^2*e^4 + 7*a^7*b^2*d*e^5 - 2*a^8*b*e^6)*x^2 + (4*a^3*b^6*d^6 - 19*a^4*b^5*d^5*e + 35*a^5*b^4*d^4*e^2 - 30*a^6*b^3*d^3*e^3 + 10*a^7*b^2*d^2*e^4 + a^8*b*d*e^5 - a^9*e^6)*x), -1/64*(315*(b^4*e^5*x^5 + a^4*d*e^4 + (b^4*d*e^4 + 4*a*b^3*e^5)*x^4 + 2*(2*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*x^3 + 2*(3*a^2*b^2*d*e^4 + 2*a^3*b*e^5)*x^2 + (4*a^3*b*d*e^4 + a^4*e^5)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (315*b^4*e^4*x^4 - 16*b^4*d^4 + 88*a*b^3*d^3*e - 210*a^2*b^2*d^2*e^2 + 325*a^3*b*d*e^3 + 128*a^4*e^4 + 105*(b^4*d*e^3 + 11*a*b^3*e^4)*x^3 - 21*(2*b^4*d^2*e^2 - 19*a*b^3*d*e^3 - 73*a^2*b^2*e^4)*x^2 + 3*(8*b^4*d^3*e - 52*a*b^3*d^2*e^2 + 185*a^2*b^2*d*e^3 + 279*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^4*b^5*d^6 - 5*a^5*b^4*d^5*e + 10*a^6*b^3*d^4*e^2 - 10*a^7*b^2*d^3*e^3 + 5*a^8*b*d^2*e^4 - a^9*d*e^5 + (b^9*d^5*e - 5*a*b^8*d^4*e^2 + 10*a^2*b^7*d^3*e^3 - 10*a^3*b^6*d^2*e^4 + 5*a^4*b^5*d*e^5 - a^5*b^4*e^6)*x^5 + (b^9*d^6 - a*b^8*d^5*e - 10*a^2*b^7*d^4*e^2 + 30*a^3*b^6*d^3*e^3 - 35*a^4*b^5*d^2*e^4 + 19*a^5*b^4*d*e^5 - 4*a^6*b^3*e^6)*x^4 + 2*(2*a*b^8*d^6 - 7*a^2*b^7*d^5*e + 5*a^3*b^6*d^4*e^2 + 10*a^4*b^5*d^3*e^3 - 20*a^5*b^4*d^2*e^4 + 13*a^6*b^3*d*e^5 - 3*a^7*b^2*e^6)*x^3 + 2*(3*a^2*b^7*d^6 - 13*a^3*b^6*d^5*e + 20*a^4*b^5*d^4*e^2 - 10*a^5*b^4*d^3*e^3 - 5*a^6*b^3*d^2*e^4 + 7*a^7*b^2*d*e^5 - 2*a^8*b*e^6)*x^2 + (4*a^3*b^6*d^6 - 19*a^4*b^5*d^5*e + 35*a^5*b^4*d^4*e^2 - 30*a^6*b^3*d^3*e^3 + 10*a^7*b^2*d^2*e^4 + a^8*b*d*e^5 - a^9*e^6)*x)]","B",0
2091,1,2494,0,0.493361," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{4} b d^{2} e^{4} + 2 \, {\left(b^{5} d e^{5} + 2 \, a b^{4} e^{6}\right)} x^{5} + {\left(b^{5} d^{2} e^{4} + 8 \, a b^{4} d e^{5} + 6 \, a^{2} b^{3} e^{6}\right)} x^{4} + 4 \, {\left(a b^{4} d^{2} e^{4} + 3 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + {\left(6 \, a^{2} b^{3} d^{2} e^{4} + 8 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} d^{2} e^{4} + a^{4} b d e^{5}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(3465 \, b^{5} e^{5} x^{5} - 48 \, b^{5} d^{5} + 328 \, a b^{4} d^{4} e - 1030 \, a^{2} b^{3} d^{3} e^{2} + 2295 \, a^{3} b^{2} d^{2} e^{3} + 2048 \, a^{4} b d e^{4} - 128 \, a^{5} e^{5} + 1155 \, {\left(4 \, b^{5} d e^{4} + 11 \, a b^{4} e^{5}\right)} x^{4} + 231 \, {\left(3 \, b^{5} d^{2} e^{3} + 74 \, a b^{4} d e^{4} + 73 \, a^{2} b^{3} e^{5}\right)} x^{3} - 99 \, {\left(2 \, b^{5} d^{3} e^{2} - 27 \, a b^{4} d^{2} e^{3} - 232 \, a^{2} b^{3} d e^{4} - 93 \, a^{3} b^{2} e^{5}\right)} x^{2} + 11 \, {\left(8 \, b^{5} d^{4} e - 68 \, a b^{4} d^{3} e^{2} + 345 \, a^{2} b^{3} d^{2} e^{3} + 1162 \, a^{3} b^{2} d e^{4} + 128 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d^{8} - 6 \, a^{5} b^{5} d^{7} e + 15 \, a^{6} b^{4} d^{6} e^{2} - 20 \, a^{7} b^{3} d^{5} e^{3} + 15 \, a^{8} b^{2} d^{4} e^{4} - 6 \, a^{9} b d^{3} e^{5} + a^{10} d^{2} e^{6} + {\left(b^{10} d^{6} e^{2} - 6 \, a b^{9} d^{5} e^{3} + 15 \, a^{2} b^{8} d^{4} e^{4} - 20 \, a^{3} b^{7} d^{3} e^{5} + 15 \, a^{4} b^{6} d^{2} e^{6} - 6 \, a^{5} b^{5} d e^{7} + a^{6} b^{4} e^{8}\right)} x^{6} + 2 \, {\left(b^{10} d^{7} e - 4 \, a b^{9} d^{6} e^{2} + 3 \, a^{2} b^{8} d^{5} e^{3} + 10 \, a^{3} b^{7} d^{4} e^{4} - 25 \, a^{4} b^{6} d^{3} e^{5} + 24 \, a^{5} b^{5} d^{2} e^{6} - 11 \, a^{6} b^{4} d e^{7} + 2 \, a^{7} b^{3} e^{8}\right)} x^{5} + {\left(b^{10} d^{8} + 2 \, a b^{9} d^{7} e - 27 \, a^{2} b^{8} d^{6} e^{2} + 64 \, a^{3} b^{7} d^{5} e^{3} - 55 \, a^{4} b^{6} d^{4} e^{4} - 6 \, a^{5} b^{5} d^{3} e^{5} + 43 \, a^{6} b^{4} d^{2} e^{6} - 28 \, a^{7} b^{3} d e^{7} + 6 \, a^{8} b^{2} e^{8}\right)} x^{4} + 4 \, {\left(a b^{9} d^{8} - 3 \, a^{2} b^{8} d^{7} e - 2 \, a^{3} b^{7} d^{6} e^{2} + 19 \, a^{4} b^{6} d^{5} e^{3} - 30 \, a^{5} b^{5} d^{4} e^{4} + 19 \, a^{6} b^{4} d^{3} e^{5} - 2 \, a^{7} b^{3} d^{2} e^{6} - 3 \, a^{8} b^{2} d e^{7} + a^{9} b e^{8}\right)} x^{3} + {\left(6 \, a^{2} b^{8} d^{8} - 28 \, a^{3} b^{7} d^{7} e + 43 \, a^{4} b^{6} d^{6} e^{2} - 6 \, a^{5} b^{5} d^{5} e^{3} - 55 \, a^{6} b^{4} d^{4} e^{4} + 64 \, a^{7} b^{3} d^{3} e^{5} - 27 \, a^{8} b^{2} d^{2} e^{6} + 2 \, a^{9} b d e^{7} + a^{10} e^{8}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{7} d^{8} - 11 \, a^{4} b^{6} d^{7} e + 24 \, a^{5} b^{5} d^{6} e^{2} - 25 \, a^{6} b^{4} d^{5} e^{3} + 10 \, a^{7} b^{3} d^{4} e^{4} + 3 \, a^{8} b^{2} d^{3} e^{5} - 4 \, a^{9} b d^{2} e^{6} + a^{10} d e^{7}\right)} x\right)}}, -\frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{4} b d^{2} e^{4} + 2 \, {\left(b^{5} d e^{5} + 2 \, a b^{4} e^{6}\right)} x^{5} + {\left(b^{5} d^{2} e^{4} + 8 \, a b^{4} d e^{5} + 6 \, a^{2} b^{3} e^{6}\right)} x^{4} + 4 \, {\left(a b^{4} d^{2} e^{4} + 3 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + {\left(6 \, a^{2} b^{3} d^{2} e^{4} + 8 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} d^{2} e^{4} + a^{4} b d e^{5}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3465 \, b^{5} e^{5} x^{5} - 48 \, b^{5} d^{5} + 328 \, a b^{4} d^{4} e - 1030 \, a^{2} b^{3} d^{3} e^{2} + 2295 \, a^{3} b^{2} d^{2} e^{3} + 2048 \, a^{4} b d e^{4} - 128 \, a^{5} e^{5} + 1155 \, {\left(4 \, b^{5} d e^{4} + 11 \, a b^{4} e^{5}\right)} x^{4} + 231 \, {\left(3 \, b^{5} d^{2} e^{3} + 74 \, a b^{4} d e^{4} + 73 \, a^{2} b^{3} e^{5}\right)} x^{3} - 99 \, {\left(2 \, b^{5} d^{3} e^{2} - 27 \, a b^{4} d^{2} e^{3} - 232 \, a^{2} b^{3} d e^{4} - 93 \, a^{3} b^{2} e^{5}\right)} x^{2} + 11 \, {\left(8 \, b^{5} d^{4} e - 68 \, a b^{4} d^{3} e^{2} + 345 \, a^{2} b^{3} d^{2} e^{3} + 1162 \, a^{3} b^{2} d e^{4} + 128 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d^{8} - 6 \, a^{5} b^{5} d^{7} e + 15 \, a^{6} b^{4} d^{6} e^{2} - 20 \, a^{7} b^{3} d^{5} e^{3} + 15 \, a^{8} b^{2} d^{4} e^{4} - 6 \, a^{9} b d^{3} e^{5} + a^{10} d^{2} e^{6} + {\left(b^{10} d^{6} e^{2} - 6 \, a b^{9} d^{5} e^{3} + 15 \, a^{2} b^{8} d^{4} e^{4} - 20 \, a^{3} b^{7} d^{3} e^{5} + 15 \, a^{4} b^{6} d^{2} e^{6} - 6 \, a^{5} b^{5} d e^{7} + a^{6} b^{4} e^{8}\right)} x^{6} + 2 \, {\left(b^{10} d^{7} e - 4 \, a b^{9} d^{6} e^{2} + 3 \, a^{2} b^{8} d^{5} e^{3} + 10 \, a^{3} b^{7} d^{4} e^{4} - 25 \, a^{4} b^{6} d^{3} e^{5} + 24 \, a^{5} b^{5} d^{2} e^{6} - 11 \, a^{6} b^{4} d e^{7} + 2 \, a^{7} b^{3} e^{8}\right)} x^{5} + {\left(b^{10} d^{8} + 2 \, a b^{9} d^{7} e - 27 \, a^{2} b^{8} d^{6} e^{2} + 64 \, a^{3} b^{7} d^{5} e^{3} - 55 \, a^{4} b^{6} d^{4} e^{4} - 6 \, a^{5} b^{5} d^{3} e^{5} + 43 \, a^{6} b^{4} d^{2} e^{6} - 28 \, a^{7} b^{3} d e^{7} + 6 \, a^{8} b^{2} e^{8}\right)} x^{4} + 4 \, {\left(a b^{9} d^{8} - 3 \, a^{2} b^{8} d^{7} e - 2 \, a^{3} b^{7} d^{6} e^{2} + 19 \, a^{4} b^{6} d^{5} e^{3} - 30 \, a^{5} b^{5} d^{4} e^{4} + 19 \, a^{6} b^{4} d^{3} e^{5} - 2 \, a^{7} b^{3} d^{2} e^{6} - 3 \, a^{8} b^{2} d e^{7} + a^{9} b e^{8}\right)} x^{3} + {\left(6 \, a^{2} b^{8} d^{8} - 28 \, a^{3} b^{7} d^{7} e + 43 \, a^{4} b^{6} d^{6} e^{2} - 6 \, a^{5} b^{5} d^{5} e^{3} - 55 \, a^{6} b^{4} d^{4} e^{4} + 64 \, a^{7} b^{3} d^{3} e^{5} - 27 \, a^{8} b^{2} d^{2} e^{6} + 2 \, a^{9} b d e^{7} + a^{10} e^{8}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{7} d^{8} - 11 \, a^{4} b^{6} d^{7} e + 24 \, a^{5} b^{5} d^{6} e^{2} - 25 \, a^{6} b^{4} d^{5} e^{3} + 10 \, a^{7} b^{3} d^{4} e^{4} + 3 \, a^{8} b^{2} d^{3} e^{5} - 4 \, a^{9} b d^{2} e^{6} + a^{10} d e^{7}\right)} x\right)}}\right]"," ",0,"[1/384*(3465*(b^5*e^6*x^6 + a^4*b*d^2*e^4 + 2*(b^5*d*e^5 + 2*a*b^4*e^6)*x^5 + (b^5*d^2*e^4 + 8*a*b^4*d*e^5 + 6*a^2*b^3*e^6)*x^4 + 4*(a*b^4*d^2*e^4 + 3*a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + (6*a^2*b^3*d^2*e^4 + 8*a^3*b^2*d*e^5 + a^4*b*e^6)*x^2 + 2*(2*a^3*b^2*d^2*e^4 + a^4*b*d*e^5)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(3465*b^5*e^5*x^5 - 48*b^5*d^5 + 328*a*b^4*d^4*e - 1030*a^2*b^3*d^3*e^2 + 2295*a^3*b^2*d^2*e^3 + 2048*a^4*b*d*e^4 - 128*a^5*e^5 + 1155*(4*b^5*d*e^4 + 11*a*b^4*e^5)*x^4 + 231*(3*b^5*d^2*e^3 + 74*a*b^4*d*e^4 + 73*a^2*b^3*e^5)*x^3 - 99*(2*b^5*d^3*e^2 - 27*a*b^4*d^2*e^3 - 232*a^2*b^3*d*e^4 - 93*a^3*b^2*e^5)*x^2 + 11*(8*b^5*d^4*e - 68*a*b^4*d^3*e^2 + 345*a^2*b^3*d^2*e^3 + 1162*a^3*b^2*d*e^4 + 128*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^4*b^6*d^8 - 6*a^5*b^5*d^7*e + 15*a^6*b^4*d^6*e^2 - 20*a^7*b^3*d^5*e^3 + 15*a^8*b^2*d^4*e^4 - 6*a^9*b*d^3*e^5 + a^10*d^2*e^6 + (b^10*d^6*e^2 - 6*a*b^9*d^5*e^3 + 15*a^2*b^8*d^4*e^4 - 20*a^3*b^7*d^3*e^5 + 15*a^4*b^6*d^2*e^6 - 6*a^5*b^5*d*e^7 + a^6*b^4*e^8)*x^6 + 2*(b^10*d^7*e - 4*a*b^9*d^6*e^2 + 3*a^2*b^8*d^5*e^3 + 10*a^3*b^7*d^4*e^4 - 25*a^4*b^6*d^3*e^5 + 24*a^5*b^5*d^2*e^6 - 11*a^6*b^4*d*e^7 + 2*a^7*b^3*e^8)*x^5 + (b^10*d^8 + 2*a*b^9*d^7*e - 27*a^2*b^8*d^6*e^2 + 64*a^3*b^7*d^5*e^3 - 55*a^4*b^6*d^4*e^4 - 6*a^5*b^5*d^3*e^5 + 43*a^6*b^4*d^2*e^6 - 28*a^7*b^3*d*e^7 + 6*a^8*b^2*e^8)*x^4 + 4*(a*b^9*d^8 - 3*a^2*b^8*d^7*e - 2*a^3*b^7*d^6*e^2 + 19*a^4*b^6*d^5*e^3 - 30*a^5*b^5*d^4*e^4 + 19*a^6*b^4*d^3*e^5 - 2*a^7*b^3*d^2*e^6 - 3*a^8*b^2*d*e^7 + a^9*b*e^8)*x^3 + (6*a^2*b^8*d^8 - 28*a^3*b^7*d^7*e + 43*a^4*b^6*d^6*e^2 - 6*a^5*b^5*d^5*e^3 - 55*a^6*b^4*d^4*e^4 + 64*a^7*b^3*d^3*e^5 - 27*a^8*b^2*d^2*e^6 + 2*a^9*b*d*e^7 + a^10*e^8)*x^2 + 2*(2*a^3*b^7*d^8 - 11*a^4*b^6*d^7*e + 24*a^5*b^5*d^6*e^2 - 25*a^6*b^4*d^5*e^3 + 10*a^7*b^3*d^4*e^4 + 3*a^8*b^2*d^3*e^5 - 4*a^9*b*d^2*e^6 + a^10*d*e^7)*x), -1/192*(3465*(b^5*e^6*x^6 + a^4*b*d^2*e^4 + 2*(b^5*d*e^5 + 2*a*b^4*e^6)*x^5 + (b^5*d^2*e^4 + 8*a*b^4*d*e^5 + 6*a^2*b^3*e^6)*x^4 + 4*(a*b^4*d^2*e^4 + 3*a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + (6*a^2*b^3*d^2*e^4 + 8*a^3*b^2*d*e^5 + a^4*b*e^6)*x^2 + 2*(2*a^3*b^2*d^2*e^4 + a^4*b*d*e^5)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3465*b^5*e^5*x^5 - 48*b^5*d^5 + 328*a*b^4*d^4*e - 1030*a^2*b^3*d^3*e^2 + 2295*a^3*b^2*d^2*e^3 + 2048*a^4*b*d*e^4 - 128*a^5*e^5 + 1155*(4*b^5*d*e^4 + 11*a*b^4*e^5)*x^4 + 231*(3*b^5*d^2*e^3 + 74*a*b^4*d*e^4 + 73*a^2*b^3*e^5)*x^3 - 99*(2*b^5*d^3*e^2 - 27*a*b^4*d^2*e^3 - 232*a^2*b^3*d*e^4 - 93*a^3*b^2*e^5)*x^2 + 11*(8*b^5*d^4*e - 68*a*b^4*d^3*e^2 + 345*a^2*b^3*d^2*e^3 + 1162*a^3*b^2*d*e^4 + 128*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^4*b^6*d^8 - 6*a^5*b^5*d^7*e + 15*a^6*b^4*d^6*e^2 - 20*a^7*b^3*d^5*e^3 + 15*a^8*b^2*d^4*e^4 - 6*a^9*b*d^3*e^5 + a^10*d^2*e^6 + (b^10*d^6*e^2 - 6*a*b^9*d^5*e^3 + 15*a^2*b^8*d^4*e^4 - 20*a^3*b^7*d^3*e^5 + 15*a^4*b^6*d^2*e^6 - 6*a^5*b^5*d*e^7 + a^6*b^4*e^8)*x^6 + 2*(b^10*d^7*e - 4*a*b^9*d^6*e^2 + 3*a^2*b^8*d^5*e^3 + 10*a^3*b^7*d^4*e^4 - 25*a^4*b^6*d^3*e^5 + 24*a^5*b^5*d^2*e^6 - 11*a^6*b^4*d*e^7 + 2*a^7*b^3*e^8)*x^5 + (b^10*d^8 + 2*a*b^9*d^7*e - 27*a^2*b^8*d^6*e^2 + 64*a^3*b^7*d^5*e^3 - 55*a^4*b^6*d^4*e^4 - 6*a^5*b^5*d^3*e^5 + 43*a^6*b^4*d^2*e^6 - 28*a^7*b^3*d*e^7 + 6*a^8*b^2*e^8)*x^4 + 4*(a*b^9*d^8 - 3*a^2*b^8*d^7*e - 2*a^3*b^7*d^6*e^2 + 19*a^4*b^6*d^5*e^3 - 30*a^5*b^5*d^4*e^4 + 19*a^6*b^4*d^3*e^5 - 2*a^7*b^3*d^2*e^6 - 3*a^8*b^2*d*e^7 + a^9*b*e^8)*x^3 + (6*a^2*b^8*d^8 - 28*a^3*b^7*d^7*e + 43*a^4*b^6*d^6*e^2 - 6*a^5*b^5*d^5*e^3 - 55*a^6*b^4*d^4*e^4 + 64*a^7*b^3*d^3*e^5 - 27*a^8*b^2*d^2*e^6 + 2*a^9*b*d*e^7 + a^10*e^8)*x^2 + 2*(2*a^3*b^7*d^8 - 11*a^4*b^6*d^7*e + 24*a^5*b^5*d^6*e^2 - 25*a^6*b^4*d^5*e^3 + 10*a^7*b^3*d^4*e^4 + 3*a^8*b^2*d^3*e^5 - 4*a^9*b*d^2*e^6 + a^10*d*e^7)*x)]","B",0
2092,1,212,0,0.416907," ","integrate((b*x+a)*(e*x+d)^(7/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(99 \, b^{2} e^{6} x^{6} + 8 \, b^{2} d^{6} - 52 \, a b d^{5} e + 143 \, a^{2} d^{4} e^{2} + 18 \, {\left(20 \, b^{2} d e^{5} + 13 \, a b e^{6}\right)} x^{5} + {\left(458 \, b^{2} d^{2} e^{4} + 884 \, a b d e^{5} + 143 \, a^{2} e^{6}\right)} x^{4} + 4 \, {\left(53 \, b^{2} d^{3} e^{3} + 299 \, a b d^{2} e^{4} + 143 \, a^{2} d e^{5}\right)} x^{3} + 3 \, {\left(b^{2} d^{4} e^{2} + 208 \, a b d^{3} e^{3} + 286 \, a^{2} d^{2} e^{4}\right)} x^{2} - 2 \, {\left(2 \, b^{2} d^{5} e - 13 \, a b d^{4} e^{2} - 286 \, a^{2} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{1287 \, e^{3}}"," ",0,"2/1287*(99*b^2*e^6*x^6 + 8*b^2*d^6 - 52*a*b*d^5*e + 143*a^2*d^4*e^2 + 18*(20*b^2*d*e^5 + 13*a*b*e^6)*x^5 + (458*b^2*d^2*e^4 + 884*a*b*d*e^5 + 143*a^2*e^6)*x^4 + 4*(53*b^2*d^3*e^3 + 299*a*b*d^2*e^4 + 143*a^2*d*e^5)*x^3 + 3*(b^2*d^4*e^2 + 208*a*b*d^3*e^3 + 286*a^2*d^2*e^4)*x^2 - 2*(2*b^2*d^5*e - 13*a*b*d^4*e^2 - 286*a^2*d^3*e^3)*x)*sqrt(e*x + d)/e^3","A",0
2093,1,174,0,0.419162," ","integrate((b*x+a)*(e*x+d)^(5/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, b^{2} e^{5} x^{5} + 8 \, b^{2} d^{5} - 44 \, a b d^{4} e + 99 \, a^{2} d^{3} e^{2} + 7 \, {\left(23 \, b^{2} d e^{4} + 22 \, a b e^{5}\right)} x^{4} + {\left(113 \, b^{2} d^{2} e^{3} + 418 \, a b d e^{4} + 99 \, a^{2} e^{5}\right)} x^{3} + 3 \, {\left(b^{2} d^{3} e^{2} + 110 \, a b d^{2} e^{3} + 99 \, a^{2} d e^{4}\right)} x^{2} - {\left(4 \, b^{2} d^{4} e - 22 \, a b d^{3} e^{2} - 297 \, a^{2} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{3}}"," ",0,"2/693*(63*b^2*e^5*x^5 + 8*b^2*d^5 - 44*a*b*d^4*e + 99*a^2*d^3*e^2 + 7*(23*b^2*d*e^4 + 22*a*b*e^5)*x^4 + (113*b^2*d^2*e^3 + 418*a*b*d*e^4 + 99*a^2*e^5)*x^3 + 3*(b^2*d^3*e^2 + 110*a*b*d^2*e^3 + 99*a^2*d*e^4)*x^2 - (4*b^2*d^4*e - 22*a*b*d^3*e^2 - 297*a^2*d^2*e^3)*x)*sqrt(e*x + d)/e^3","A",0
2094,1,137,0,0.401844," ","integrate((b*x+a)*(e*x+d)^(3/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{2} e^{4} x^{4} + 8 \, b^{2} d^{4} - 36 \, a b d^{3} e + 63 \, a^{2} d^{2} e^{2} + 10 \, {\left(5 \, b^{2} d e^{3} + 9 \, a b e^{4}\right)} x^{3} + 3 \, {\left(b^{2} d^{2} e^{2} + 48 \, a b d e^{3} + 21 \, a^{2} e^{4}\right)} x^{2} - 2 \, {\left(2 \, b^{2} d^{3} e - 9 \, a b d^{2} e^{2} - 63 \, a^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{3}}"," ",0,"2/315*(35*b^2*e^4*x^4 + 8*b^2*d^4 - 36*a*b*d^3*e + 63*a^2*d^2*e^2 + 10*(5*b^2*d*e^3 + 9*a*b*e^4)*x^3 + 3*(b^2*d^2*e^2 + 48*a*b*d*e^3 + 21*a^2*e^4)*x^2 - 2*(2*b^2*d^3*e - 9*a*b*d^2*e^2 - 63*a^2*d*e^3)*x)*sqrt(e*x + d)/e^3","A",0
2095,1,99,0,0.407535," ","integrate((b*x+a)*(e*x+d)^(1/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{2} e^{3} x^{3} + 8 \, b^{2} d^{3} - 28 \, a b d^{2} e + 35 \, a^{2} d e^{2} + 3 \, {\left(b^{2} d e^{2} + 14 \, a b e^{3}\right)} x^{2} - {\left(4 \, b^{2} d^{2} e - 14 \, a b d e^{2} - 35 \, a^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{3}}"," ",0,"2/105*(15*b^2*e^3*x^3 + 8*b^2*d^3 - 28*a*b*d^2*e + 35*a^2*d*e^2 + 3*(b^2*d*e^2 + 14*a*b*e^3)*x^2 - (4*b^2*d^2*e - 14*a*b*d*e^2 - 35*a^2*e^3)*x)*sqrt(e*x + d)/e^3","A",0
2096,1,64,0,0.424201," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} e^{2} x^{2} + 8 \, b^{2} d^{2} - 20 \, a b d e + 15 \, a^{2} e^{2} - 2 \, {\left(2 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, e^{3}}"," ",0,"2/15*(3*b^2*e^2*x^2 + 8*b^2*d^2 - 20*a*b*d*e + 15*a^2*e^2 - 2*(2*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d)/e^3","A",0
2097,1,73,0,0.409132," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} e^{2} x^{2} - 8 \, b^{2} d^{2} + 12 \, a b d e - 3 \, a^{2} e^{2} - 2 \, {\left(2 \, b^{2} d e - 3 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"2/3*(b^2*e^2*x^2 - 8*b^2*d^2 + 12*a*b*d*e - 3*a^2*e^2 - 2*(2*b^2*d*e - 3*a*b*e^2)*x)*sqrt(e*x + d)/(e^4*x + d*e^3)","A",0
2098,1,85,0,0.401836," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} e^{2} x^{2} + 8 \, b^{2} d^{2} - 4 \, a b d e - a^{2} e^{2} + 6 \, {\left(2 \, b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"2/3*(3*b^2*e^2*x^2 + 8*b^2*d^2 - 4*a*b*d*e - a^2*e^2 + 6*(2*b^2*d*e - a*b*e^2)*x)*sqrt(e*x + d)/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
2099,1,95,0,0.419660," ","integrate((b*x+a)*((b*x+a)^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, b^{2} e^{2} x^{2} + 8 \, b^{2} d^{2} + 4 \, a b d e + 3 \, a^{2} e^{2} + 10 \, {\left(2 \, b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-2/15*(15*b^2*e^2*x^2 + 8*b^2*d^2 + 4*a*b*d*e + 3*a^2*e^2 + 10*(2*b^2*d*e + a*b*e^2)*x)*sqrt(e*x + d)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
2100,1,377,0,0.440427," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, b^{4} e^{7} x^{7} + 128 \, b^{4} d^{7} - 960 \, a b^{3} d^{6} e + 3120 \, a^{2} b^{2} d^{5} e^{2} - 5720 \, a^{3} b d^{4} e^{3} + 6435 \, a^{4} d^{3} e^{4} + 231 \, {\left(31 \, b^{4} d e^{6} + 60 \, a b^{3} e^{7}\right)} x^{6} + 63 \, {\left(71 \, b^{4} d^{2} e^{5} + 540 \, a b^{3} d e^{6} + 390 \, a^{2} b^{2} e^{7}\right)} x^{5} + 35 \, {\left(b^{4} d^{3} e^{4} + 636 \, a b^{3} d^{2} e^{5} + 1794 \, a^{2} b^{2} d e^{6} + 572 \, a^{3} b e^{7}\right)} x^{4} - 5 \, {\left(8 \, b^{4} d^{4} e^{3} - 60 \, a b^{3} d^{3} e^{4} - 8814 \, a^{2} b^{2} d^{2} e^{5} - 10868 \, a^{3} b d e^{6} - 1287 \, a^{4} e^{7}\right)} x^{3} + 3 \, {\left(16 \, b^{4} d^{5} e^{2} - 120 \, a b^{3} d^{4} e^{3} + 390 \, a^{2} b^{2} d^{3} e^{4} + 14300 \, a^{3} b d^{2} e^{5} + 6435 \, a^{4} d e^{6}\right)} x^{2} - {\left(64 \, b^{4} d^{6} e - 480 \, a b^{3} d^{5} e^{2} + 1560 \, a^{2} b^{2} d^{4} e^{3} - 2860 \, a^{3} b d^{3} e^{4} - 19305 \, a^{4} d^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3003*b^4*e^7*x^7 + 128*b^4*d^7 - 960*a*b^3*d^6*e + 3120*a^2*b^2*d^5*e^2 - 5720*a^3*b*d^4*e^3 + 6435*a^4*d^3*e^4 + 231*(31*b^4*d*e^6 + 60*a*b^3*e^7)*x^6 + 63*(71*b^4*d^2*e^5 + 540*a*b^3*d*e^6 + 390*a^2*b^2*e^7)*x^5 + 35*(b^4*d^3*e^4 + 636*a*b^3*d^2*e^5 + 1794*a^2*b^2*d*e^6 + 572*a^3*b*e^7)*x^4 - 5*(8*b^4*d^4*e^3 - 60*a*b^3*d^3*e^4 - 8814*a^2*b^2*d^2*e^5 - 10868*a^3*b*d*e^6 - 1287*a^4*e^7)*x^3 + 3*(16*b^4*d^5*e^2 - 120*a*b^3*d^4*e^3 + 390*a^2*b^2*d^3*e^4 + 14300*a^3*b*d^2*e^5 + 6435*a^4*d*e^6)*x^2 - (64*b^4*d^6*e - 480*a*b^3*d^5*e^2 + 1560*a^2*b^2*d^4*e^3 - 2860*a^3*b*d^3*e^4 - 19305*a^4*d^2*e^5)*x)*sqrt(e*x + d)/e^5","A",0
2101,1,311,0,0.435135," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, b^{4} e^{6} x^{6} + 128 \, b^{4} d^{6} - 832 \, a b^{3} d^{5} e + 2288 \, a^{2} b^{2} d^{4} e^{2} - 3432 \, a^{3} b d^{3} e^{3} + 3003 \, a^{4} d^{2} e^{4} + 210 \, {\left(7 \, b^{4} d e^{5} + 26 \, a b^{3} e^{6}\right)} x^{5} + 35 \, {\left(b^{4} d^{2} e^{4} + 208 \, a b^{3} d e^{5} + 286 \, a^{2} b^{2} e^{6}\right)} x^{4} - 20 \, {\left(2 \, b^{4} d^{3} e^{3} - 13 \, a b^{3} d^{2} e^{4} - 715 \, a^{2} b^{2} d e^{5} - 429 \, a^{3} b e^{6}\right)} x^{3} + 3 \, {\left(16 \, b^{4} d^{4} e^{2} - 104 \, a b^{3} d^{3} e^{3} + 286 \, a^{2} b^{2} d^{2} e^{4} + 4576 \, a^{3} b d e^{5} + 1001 \, a^{4} e^{6}\right)} x^{2} - 2 \, {\left(32 \, b^{4} d^{5} e - 208 \, a b^{3} d^{4} e^{2} + 572 \, a^{2} b^{2} d^{3} e^{3} - 858 \, a^{3} b d^{2} e^{4} - 3003 \, a^{4} d e^{5}\right)} x\right)} \sqrt{e x + d}}{15015 \, e^{5}}"," ",0,"2/15015*(1155*b^4*e^6*x^6 + 128*b^4*d^6 - 832*a*b^3*d^5*e + 2288*a^2*b^2*d^4*e^2 - 3432*a^3*b*d^3*e^3 + 3003*a^4*d^2*e^4 + 210*(7*b^4*d*e^5 + 26*a*b^3*e^6)*x^5 + 35*(b^4*d^2*e^4 + 208*a*b^3*d*e^5 + 286*a^2*b^2*e^6)*x^4 - 20*(2*b^4*d^3*e^3 - 13*a*b^3*d^2*e^4 - 715*a^2*b^2*d*e^5 - 429*a^3*b*e^6)*x^3 + 3*(16*b^4*d^4*e^2 - 104*a*b^3*d^3*e^3 + 286*a^2*b^2*d^2*e^4 + 4576*a^3*b*d*e^5 + 1001*a^4*e^6)*x^2 - 2*(32*b^4*d^5*e - 208*a*b^3*d^4*e^2 + 572*a^2*b^2*d^3*e^3 - 858*a^3*b*d^2*e^4 - 3003*a^4*d*e^5)*x)*sqrt(e*x + d)/e^5","A",0
2102,1,245,0,0.431205," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, b^{4} e^{5} x^{5} + 128 \, b^{4} d^{5} - 704 \, a b^{3} d^{4} e + 1584 \, a^{2} b^{2} d^{3} e^{2} - 1848 \, a^{3} b d^{2} e^{3} + 1155 \, a^{4} d e^{4} + 35 \, {\left(b^{4} d e^{4} + 44 \, a b^{3} e^{5}\right)} x^{4} - 10 \, {\left(4 \, b^{4} d^{2} e^{3} - 22 \, a b^{3} d e^{4} - 297 \, a^{2} b^{2} e^{5}\right)} x^{3} + 6 \, {\left(8 \, b^{4} d^{3} e^{2} - 44 \, a b^{3} d^{2} e^{3} + 99 \, a^{2} b^{2} d e^{4} + 462 \, a^{3} b e^{5}\right)} x^{2} - {\left(64 \, b^{4} d^{4} e - 352 \, a b^{3} d^{3} e^{2} + 792 \, a^{2} b^{2} d^{2} e^{3} - 924 \, a^{3} b d e^{4} - 1155 \, a^{4} e^{5}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{5}}"," ",0,"2/3465*(315*b^4*e^5*x^5 + 128*b^4*d^5 - 704*a*b^3*d^4*e + 1584*a^2*b^2*d^3*e^2 - 1848*a^3*b*d^2*e^3 + 1155*a^4*d*e^4 + 35*(b^4*d*e^4 + 44*a*b^3*e^5)*x^4 - 10*(4*b^4*d^2*e^3 - 22*a*b^3*d*e^4 - 297*a^2*b^2*e^5)*x^3 + 6*(8*b^4*d^3*e^2 - 44*a*b^3*d^2*e^3 + 99*a^2*b^2*d*e^4 + 462*a^3*b*e^5)*x^2 - (64*b^4*d^4*e - 352*a*b^3*d^3*e^2 + 792*a^2*b^2*d^2*e^3 - 924*a^3*b*d*e^4 - 1155*a^4*e^5)*x)*sqrt(e*x + d)/e^5","A",0
2103,1,182,0,0.429325," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} e^{4} x^{4} + 128 \, b^{4} d^{4} - 576 \, a b^{3} d^{3} e + 1008 \, a^{2} b^{2} d^{2} e^{2} - 840 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} - 20 \, {\left(2 \, b^{4} d e^{3} - 9 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(8 \, b^{4} d^{2} e^{2} - 36 \, a b^{3} d e^{3} + 63 \, a^{2} b^{2} e^{4}\right)} x^{2} - 4 \, {\left(16 \, b^{4} d^{3} e - 72 \, a b^{3} d^{2} e^{2} + 126 \, a^{2} b^{2} d e^{3} - 105 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{5}}"," ",0,"2/315*(35*b^4*e^4*x^4 + 128*b^4*d^4 - 576*a*b^3*d^3*e + 1008*a^2*b^2*d^2*e^2 - 840*a^3*b*d*e^3 + 315*a^4*e^4 - 20*(2*b^4*d*e^3 - 9*a*b^3*e^4)*x^3 + 6*(8*b^4*d^2*e^2 - 36*a*b^3*d*e^3 + 63*a^2*b^2*e^4)*x^2 - 4*(16*b^4*d^3*e - 72*a*b^3*d^2*e^2 + 126*a^2*b^2*d*e^3 - 105*a^3*b*e^4)*x)*sqrt(e*x + d)/e^5","A",0
2104,1,192,0,0.420617," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{4} e^{4} x^{4} - 128 \, b^{4} d^{4} + 448 \, a b^{3} d^{3} e - 560 \, a^{2} b^{2} d^{2} e^{2} + 280 \, a^{3} b d e^{3} - 35 \, a^{4} e^{4} - 4 \, {\left(2 \, b^{4} d e^{3} - 7 \, a b^{3} e^{4}\right)} x^{3} + 2 \, {\left(8 \, b^{4} d^{2} e^{2} - 28 \, a b^{3} d e^{3} + 35 \, a^{2} b^{2} e^{4}\right)} x^{2} - 4 \, {\left(16 \, b^{4} d^{3} e - 56 \, a b^{3} d^{2} e^{2} + 70 \, a^{2} b^{2} d e^{3} - 35 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"2/35*(5*b^4*e^4*x^4 - 128*b^4*d^4 + 448*a*b^3*d^3*e - 560*a^2*b^2*d^2*e^2 + 280*a^3*b*d*e^3 - 35*a^4*e^4 - 4*(2*b^4*d*e^3 - 7*a*b^3*e^4)*x^3 + 2*(8*b^4*d^2*e^2 - 28*a*b^3*d*e^3 + 35*a^2*b^2*e^4)*x^2 - 4*(16*b^4*d^3*e - 56*a*b^3*d^2*e^2 + 70*a^2*b^2*d*e^3 - 35*a^3*b*e^4)*x)*sqrt(e*x + d)/(e^6*x + d*e^5)","A",0
2105,1,203,0,0.428076," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{4} e^{4} x^{4} + 128 \, b^{4} d^{4} - 320 \, a b^{3} d^{3} e + 240 \, a^{2} b^{2} d^{2} e^{2} - 40 \, a^{3} b d e^{3} - 5 \, a^{4} e^{4} - 4 \, {\left(2 \, b^{4} d e^{3} - 5 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(8 \, b^{4} d^{2} e^{2} - 20 \, a b^{3} d e^{3} + 15 \, a^{2} b^{2} e^{4}\right)} x^{2} + 12 \, {\left(16 \, b^{4} d^{3} e - 40 \, a b^{3} d^{2} e^{2} + 30 \, a^{2} b^{2} d e^{3} - 5 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"2/15*(3*b^4*e^4*x^4 + 128*b^4*d^4 - 320*a*b^3*d^3*e + 240*a^2*b^2*d^2*e^2 - 40*a^3*b*d*e^3 - 5*a^4*e^4 - 4*(2*b^4*d*e^3 - 5*a*b^3*e^4)*x^3 + 6*(8*b^4*d^2*e^2 - 20*a*b^3*d*e^3 + 15*a^2*b^2*e^4)*x^2 + 12*(16*b^4*d^3*e - 40*a*b^3*d^2*e^2 + 30*a^2*b^2*d*e^3 - 5*a^3*b*e^4)*x)*sqrt(e*x + d)/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
2106,1,213,0,0.421007," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{4} e^{4} x^{4} - 128 \, b^{4} d^{4} + 192 \, a b^{3} d^{3} e - 48 \, a^{2} b^{2} d^{2} e^{2} - 8 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} - 20 \, {\left(2 \, b^{4} d e^{3} - 3 \, a b^{3} e^{4}\right)} x^{3} - 30 \, {\left(8 \, b^{4} d^{2} e^{2} - 12 \, a b^{3} d e^{3} + 3 \, a^{2} b^{2} e^{4}\right)} x^{2} - 20 \, {\left(16 \, b^{4} d^{3} e - 24 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"2/15*(5*b^4*e^4*x^4 - 128*b^4*d^4 + 192*a*b^3*d^3*e - 48*a^2*b^2*d^2*e^2 - 8*a^3*b*d*e^3 - 3*a^4*e^4 - 20*(2*b^4*d*e^3 - 3*a*b^3*e^4)*x^3 - 30*(8*b^4*d^2*e^2 - 12*a*b^3*d*e^3 + 3*a^2*b^2*e^4)*x^2 - 20*(16*b^4*d^3*e - 24*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*sqrt(e*x + d)/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
2107,1,225,0,0.442787," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} e^{4} x^{4} + 128 \, b^{4} d^{4} - 64 \, a b^{3} d^{3} e - 16 \, a^{2} b^{2} d^{2} e^{2} - 8 \, a^{3} b d e^{3} - 5 \, a^{4} e^{4} + 140 \, {\left(2 \, b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 70 \, {\left(8 \, b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} - a^{2} b^{2} e^{4}\right)} x^{2} + 28 \, {\left(16 \, b^{4} d^{3} e - 8 \, a b^{3} d^{2} e^{2} - 2 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{9} x^{4} + 4 \, d e^{8} x^{3} + 6 \, d^{2} e^{7} x^{2} + 4 \, d^{3} e^{6} x + d^{4} e^{5}\right)}}"," ",0,"2/35*(35*b^4*e^4*x^4 + 128*b^4*d^4 - 64*a*b^3*d^3*e - 16*a^2*b^2*d^2*e^2 - 8*a^3*b*d*e^3 - 5*a^4*e^4 + 140*(2*b^4*d*e^3 - a*b^3*e^4)*x^3 + 70*(8*b^4*d^2*e^2 - 4*a*b^3*d*e^3 - a^2*b^2*e^4)*x^2 + 28*(16*b^4*d^3*e - 8*a*b^3*d^2*e^2 - 2*a^2*b^2*d*e^3 - a^3*b*e^4)*x)*sqrt(e*x + d)/(e^9*x^4 + 4*d*e^8*x^3 + 6*d^2*e^7*x^2 + 4*d^3*e^6*x + d^4*e^5)","A",0
2108,1,235,0,0.425218," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, b^{4} e^{4} x^{4} + 128 \, b^{4} d^{4} + 64 \, a b^{3} d^{3} e + 48 \, a^{2} b^{2} d^{2} e^{2} + 40 \, a^{3} b d e^{3} + 35 \, a^{4} e^{4} + 420 \, {\left(2 \, b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + 126 \, {\left(8 \, b^{4} d^{2} e^{2} + 4 \, a b^{3} d e^{3} + 3 \, a^{2} b^{2} e^{4}\right)} x^{2} + 36 \, {\left(16 \, b^{4} d^{3} e + 8 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} + 5 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{10} x^{5} + 5 \, d e^{9} x^{4} + 10 \, d^{2} e^{8} x^{3} + 10 \, d^{3} e^{7} x^{2} + 5 \, d^{4} e^{6} x + d^{5} e^{5}\right)}}"," ",0,"-2/315*(315*b^4*e^4*x^4 + 128*b^4*d^4 + 64*a*b^3*d^3*e + 48*a^2*b^2*d^2*e^2 + 40*a^3*b*d*e^3 + 35*a^4*e^4 + 420*(2*b^4*d*e^3 + a*b^3*e^4)*x^3 + 126*(8*b^4*d^2*e^2 + 4*a*b^3*d*e^3 + 3*a^2*b^2*e^4)*x^2 + 36*(16*b^4*d^3*e + 8*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 + 5*a^3*b*e^4)*x)*sqrt(e*x + d)/(e^10*x^5 + 5*d*e^9*x^4 + 10*d^2*e^8*x^3 + 10*d^3*e^7*x^2 + 5*d^4*e^6*x + d^5*e^5)","A",0
2109,1,247,0,0.416809," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(13/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(1155 \, b^{4} e^{4} x^{4} + 128 \, b^{4} d^{4} + 192 \, a b^{3} d^{3} e + 240 \, a^{2} b^{2} d^{2} e^{2} + 280 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} + 924 \, {\left(2 \, b^{4} d e^{3} + 3 \, a b^{3} e^{4}\right)} x^{3} + 198 \, {\left(8 \, b^{4} d^{2} e^{2} + 12 \, a b^{3} d e^{3} + 15 \, a^{2} b^{2} e^{4}\right)} x^{2} + 44 \, {\left(16 \, b^{4} d^{3} e + 24 \, a b^{3} d^{2} e^{2} + 30 \, a^{2} b^{2} d e^{3} + 35 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{3465 \, {\left(e^{11} x^{6} + 6 \, d e^{10} x^{5} + 15 \, d^{2} e^{9} x^{4} + 20 \, d^{3} e^{8} x^{3} + 15 \, d^{4} e^{7} x^{2} + 6 \, d^{5} e^{6} x + d^{6} e^{5}\right)}}"," ",0,"-2/3465*(1155*b^4*e^4*x^4 + 128*b^4*d^4 + 192*a*b^3*d^3*e + 240*a^2*b^2*d^2*e^2 + 280*a^3*b*d*e^3 + 315*a^4*e^4 + 924*(2*b^4*d*e^3 + 3*a*b^3*e^4)*x^3 + 198*(8*b^4*d^2*e^2 + 12*a*b^3*d*e^3 + 15*a^2*b^2*e^4)*x^2 + 44*(16*b^4*d^3*e + 24*a*b^3*d^2*e^2 + 30*a^2*b^2*d*e^3 + 35*a^3*b*e^4)*x)*sqrt(e*x + d)/(e^11*x^6 + 6*d*e^10*x^5 + 15*d^2*e^9*x^4 + 20*d^3*e^8*x^3 + 15*d^4*e^7*x^2 + 6*d^5*e^6*x + d^6*e^5)","A",0
2110,1,635,0,0.432489," ","integrate((b*x+a)*(e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(51051 \, b^{6} e^{9} x^{9} + 1024 \, b^{6} d^{9} - 9728 \, a b^{5} d^{8} e + 41344 \, a^{2} b^{4} d^{7} e^{2} - 103360 \, a^{3} b^{3} d^{6} e^{3} + 167960 \, a^{4} b^{2} d^{5} e^{4} - 184756 \, a^{5} b d^{4} e^{5} + 138567 \, a^{6} d^{3} e^{6} + 9009 \, {\left(13 \, b^{6} d e^{8} + 38 \, a b^{5} e^{9}\right)} x^{8} + 3003 \, {\left(23 \, b^{6} d^{2} e^{7} + 266 \, a b^{5} d e^{8} + 323 \, a^{2} b^{4} e^{9}\right)} x^{7} + 231 \, {\left(b^{6} d^{3} e^{6} + 2090 \, a b^{5} d^{2} e^{7} + 10013 \, a^{2} b^{4} d e^{8} + 6460 \, a^{3} b^{3} e^{9}\right)} x^{6} - 63 \, {\left(4 \, b^{6} d^{4} e^{5} - 38 \, a b^{5} d^{3} e^{6} - 22933 \, a^{2} b^{4} d^{2} e^{7} - 58140 \, a^{3} b^{3} d e^{8} - 20995 \, a^{4} b^{2} e^{9}\right)} x^{5} + 7 \, {\left(40 \, b^{6} d^{5} e^{4} - 380 \, a b^{5} d^{4} e^{5} + 1615 \, a^{2} b^{4} d^{3} e^{6} + 342380 \, a^{3} b^{3} d^{2} e^{7} + 482885 \, a^{4} b^{2} d e^{8} + 92378 \, a^{5} b e^{9}\right)} x^{4} - {\left(320 \, b^{6} d^{6} e^{3} - 3040 \, a b^{5} d^{5} e^{4} + 12920 \, a^{2} b^{4} d^{4} e^{5} - 32300 \, a^{3} b^{3} d^{3} e^{6} - 2372435 \, a^{4} b^{2} d^{2} e^{7} - 1755182 \, a^{5} b d e^{8} - 138567 \, a^{6} e^{9}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{7} e^{2} - 1216 \, a b^{5} d^{6} e^{3} + 5168 \, a^{2} b^{4} d^{5} e^{4} - 12920 \, a^{3} b^{3} d^{4} e^{5} + 20995 \, a^{4} b^{2} d^{3} e^{6} + 461890 \, a^{5} b d^{2} e^{7} + 138567 \, a^{6} d e^{8}\right)} x^{2} - {\left(512 \, b^{6} d^{8} e - 4864 \, a b^{5} d^{7} e^{2} + 20672 \, a^{2} b^{4} d^{6} e^{3} - 51680 \, a^{3} b^{3} d^{5} e^{4} + 83980 \, a^{4} b^{2} d^{4} e^{5} - 92378 \, a^{5} b d^{3} e^{6} - 415701 \, a^{6} d^{2} e^{7}\right)} x\right)} \sqrt{e x + d}}{969969 \, e^{7}}"," ",0,"2/969969*(51051*b^6*e^9*x^9 + 1024*b^6*d^9 - 9728*a*b^5*d^8*e + 41344*a^2*b^4*d^7*e^2 - 103360*a^3*b^3*d^6*e^3 + 167960*a^4*b^2*d^5*e^4 - 184756*a^5*b*d^4*e^5 + 138567*a^6*d^3*e^6 + 9009*(13*b^6*d*e^8 + 38*a*b^5*e^9)*x^8 + 3003*(23*b^6*d^2*e^7 + 266*a*b^5*d*e^8 + 323*a^2*b^4*e^9)*x^7 + 231*(b^6*d^3*e^6 + 2090*a*b^5*d^2*e^7 + 10013*a^2*b^4*d*e^8 + 6460*a^3*b^3*e^9)*x^6 - 63*(4*b^6*d^4*e^5 - 38*a*b^5*d^3*e^6 - 22933*a^2*b^4*d^2*e^7 - 58140*a^3*b^3*d*e^8 - 20995*a^4*b^2*e^9)*x^5 + 7*(40*b^6*d^5*e^4 - 380*a*b^5*d^4*e^5 + 1615*a^2*b^4*d^3*e^6 + 342380*a^3*b^3*d^2*e^7 + 482885*a^4*b^2*d*e^8 + 92378*a^5*b*e^9)*x^4 - (320*b^6*d^6*e^3 - 3040*a*b^5*d^5*e^4 + 12920*a^2*b^4*d^4*e^5 - 32300*a^3*b^3*d^3*e^6 - 2372435*a^4*b^2*d^2*e^7 - 1755182*a^5*b*d*e^8 - 138567*a^6*e^9)*x^3 + 3*(128*b^6*d^7*e^2 - 1216*a*b^5*d^6*e^3 + 5168*a^2*b^4*d^5*e^4 - 12920*a^3*b^3*d^4*e^5 + 20995*a^4*b^2*d^3*e^6 + 461890*a^5*b*d^2*e^7 + 138567*a^6*d*e^8)*x^2 - (512*b^6*d^8*e - 4864*a*b^5*d^7*e^2 + 20672*a^2*b^4*d^6*e^3 - 51680*a^3*b^3*d^5*e^4 + 83980*a^4*b^2*d^4*e^5 - 92378*a^5*b*d^3*e^6 - 415701*a^6*d^2*e^7)*x)*sqrt(e*x + d)/e^7","B",0
2111,1,541,0,0.435867," ","integrate((b*x+a)*(e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15015 \, b^{6} e^{8} x^{8} + 1024 \, b^{6} d^{8} - 8704 \, a b^{5} d^{7} e + 32640 \, a^{2} b^{4} d^{6} e^{2} - 70720 \, a^{3} b^{3} d^{5} e^{3} + 97240 \, a^{4} b^{2} d^{4} e^{4} - 87516 \, a^{5} b d^{3} e^{5} + 51051 \, a^{6} d^{2} e^{6} + 6006 \, {\left(3 \, b^{6} d e^{7} + 17 \, a b^{5} e^{8}\right)} x^{7} + 231 \, {\left(b^{6} d^{2} e^{6} + 544 \, a b^{5} d e^{7} + 1275 \, a^{2} b^{4} e^{8}\right)} x^{6} - 42 \, {\left(6 \, b^{6} d^{3} e^{5} - 51 \, a b^{5} d^{2} e^{6} - 8925 \, a^{2} b^{4} d e^{7} - 11050 \, a^{3} b^{3} e^{8}\right)} x^{5} + 35 \, {\left(8 \, b^{6} d^{4} e^{4} - 68 \, a b^{5} d^{3} e^{5} + 255 \, a^{2} b^{4} d^{2} e^{6} + 17680 \, a^{3} b^{3} d e^{7} + 12155 \, a^{4} b^{2} e^{8}\right)} x^{4} - 10 \, {\left(32 \, b^{6} d^{5} e^{3} - 272 \, a b^{5} d^{4} e^{4} + 1020 \, a^{2} b^{4} d^{3} e^{5} - 2210 \, a^{3} b^{3} d^{2} e^{6} - 60775 \, a^{4} b^{2} d e^{7} - 21879 \, a^{5} b e^{8}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{6} e^{2} - 1088 \, a b^{5} d^{5} e^{3} + 4080 \, a^{2} b^{4} d^{4} e^{4} - 8840 \, a^{3} b^{3} d^{3} e^{5} + 12155 \, a^{4} b^{2} d^{2} e^{6} + 116688 \, a^{5} b d e^{7} + 17017 \, a^{6} e^{8}\right)} x^{2} - 2 \, {\left(256 \, b^{6} d^{7} e - 2176 \, a b^{5} d^{6} e^{2} + 8160 \, a^{2} b^{4} d^{5} e^{3} - 17680 \, a^{3} b^{3} d^{4} e^{4} + 24310 \, a^{4} b^{2} d^{3} e^{5} - 21879 \, a^{5} b d^{2} e^{6} - 51051 \, a^{6} d e^{7}\right)} x\right)} \sqrt{e x + d}}{255255 \, e^{7}}"," ",0,"2/255255*(15015*b^6*e^8*x^8 + 1024*b^6*d^8 - 8704*a*b^5*d^7*e + 32640*a^2*b^4*d^6*e^2 - 70720*a^3*b^3*d^5*e^3 + 97240*a^4*b^2*d^4*e^4 - 87516*a^5*b*d^3*e^5 + 51051*a^6*d^2*e^6 + 6006*(3*b^6*d*e^7 + 17*a*b^5*e^8)*x^7 + 231*(b^6*d^2*e^6 + 544*a*b^5*d*e^7 + 1275*a^2*b^4*e^8)*x^6 - 42*(6*b^6*d^3*e^5 - 51*a*b^5*d^2*e^6 - 8925*a^2*b^4*d*e^7 - 11050*a^3*b^3*e^8)*x^5 + 35*(8*b^6*d^4*e^4 - 68*a*b^5*d^3*e^5 + 255*a^2*b^4*d^2*e^6 + 17680*a^3*b^3*d*e^7 + 12155*a^4*b^2*e^8)*x^4 - 10*(32*b^6*d^5*e^3 - 272*a*b^5*d^4*e^4 + 1020*a^2*b^4*d^3*e^5 - 2210*a^3*b^3*d^2*e^6 - 60775*a^4*b^2*d*e^7 - 21879*a^5*b*e^8)*x^3 + 3*(128*b^6*d^6*e^2 - 1088*a*b^5*d^5*e^3 + 4080*a^2*b^4*d^4*e^4 - 8840*a^3*b^3*d^3*e^5 + 12155*a^4*b^2*d^2*e^6 + 116688*a^5*b*d*e^7 + 17017*a^6*e^8)*x^2 - 2*(256*b^6*d^7*e - 2176*a*b^5*d^6*e^2 + 8160*a^2*b^4*d^5*e^3 - 17680*a^3*b^3*d^4*e^4 + 24310*a^4*b^2*d^3*e^5 - 21879*a^5*b*d^2*e^6 - 51051*a^6*d*e^7)*x)*sqrt(e*x + d)/e^7","A",0
2112,1,447,0,0.435542," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, b^{6} e^{7} x^{7} + 1024 \, b^{6} d^{7} - 7680 \, a b^{5} d^{6} e + 24960 \, a^{2} b^{4} d^{5} e^{2} - 45760 \, a^{3} b^{3} d^{4} e^{3} + 51480 \, a^{4} b^{2} d^{3} e^{4} - 36036 \, a^{5} b d^{2} e^{5} + 15015 \, a^{6} d e^{6} + 231 \, {\left(b^{6} d e^{6} + 90 \, a b^{5} e^{7}\right)} x^{6} - 63 \, {\left(4 \, b^{6} d^{2} e^{5} - 30 \, a b^{5} d e^{6} - 975 \, a^{2} b^{4} e^{7}\right)} x^{5} + 35 \, {\left(8 \, b^{6} d^{3} e^{4} - 60 \, a b^{5} d^{2} e^{5} + 195 \, a^{2} b^{4} d e^{6} + 2860 \, a^{3} b^{3} e^{7}\right)} x^{4} - 5 \, {\left(64 \, b^{6} d^{4} e^{3} - 480 \, a b^{5} d^{3} e^{4} + 1560 \, a^{2} b^{4} d^{2} e^{5} - 2860 \, a^{3} b^{3} d e^{6} - 19305 \, a^{4} b^{2} e^{7}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{5} e^{2} - 960 \, a b^{5} d^{4} e^{3} + 3120 \, a^{2} b^{4} d^{3} e^{4} - 5720 \, a^{3} b^{3} d^{2} e^{5} + 6435 \, a^{4} b^{2} d e^{6} + 18018 \, a^{5} b e^{7}\right)} x^{2} - {\left(512 \, b^{6} d^{6} e - 3840 \, a b^{5} d^{5} e^{2} + 12480 \, a^{2} b^{4} d^{4} e^{3} - 22880 \, a^{3} b^{3} d^{3} e^{4} + 25740 \, a^{4} b^{2} d^{2} e^{5} - 18018 \, a^{5} b d e^{6} - 15015 \, a^{6} e^{7}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{7}}"," ",0,"2/45045*(3003*b^6*e^7*x^7 + 1024*b^6*d^7 - 7680*a*b^5*d^6*e + 24960*a^2*b^4*d^5*e^2 - 45760*a^3*b^3*d^4*e^3 + 51480*a^4*b^2*d^3*e^4 - 36036*a^5*b*d^2*e^5 + 15015*a^6*d*e^6 + 231*(b^6*d*e^6 + 90*a*b^5*e^7)*x^6 - 63*(4*b^6*d^2*e^5 - 30*a*b^5*d*e^6 - 975*a^2*b^4*e^7)*x^5 + 35*(8*b^6*d^3*e^4 - 60*a*b^5*d^2*e^5 + 195*a^2*b^4*d*e^6 + 2860*a^3*b^3*e^7)*x^4 - 5*(64*b^6*d^4*e^3 - 480*a*b^5*d^3*e^4 + 1560*a^2*b^4*d^2*e^5 - 2860*a^3*b^3*d*e^6 - 19305*a^4*b^2*e^7)*x^3 + 3*(128*b^6*d^5*e^2 - 960*a*b^5*d^4*e^3 + 3120*a^2*b^4*d^3*e^4 - 5720*a^3*b^3*d^2*e^5 + 6435*a^4*b^2*d*e^6 + 18018*a^5*b*e^7)*x^2 - (512*b^6*d^6*e - 3840*a*b^5*d^5*e^2 + 12480*a^2*b^4*d^4*e^3 - 22880*a^3*b^3*d^3*e^4 + 25740*a^4*b^2*d^2*e^5 - 18018*a^5*b*d*e^6 - 15015*a^6*e^7)*x)*sqrt(e*x + d)/e^7","A",0
2113,1,356,0,0.423047," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, b^{6} e^{6} x^{6} + 1024 \, b^{6} d^{6} - 6656 \, a b^{5} d^{5} e + 18304 \, a^{2} b^{4} d^{4} e^{2} - 27456 \, a^{3} b^{3} d^{3} e^{3} + 24024 \, a^{4} b^{2} d^{2} e^{4} - 12012 \, a^{5} b d e^{5} + 3003 \, a^{6} e^{6} - 126 \, {\left(2 \, b^{6} d e^{5} - 13 \, a b^{5} e^{6}\right)} x^{5} + 35 \, {\left(8 \, b^{6} d^{2} e^{4} - 52 \, a b^{5} d e^{5} + 143 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(16 \, b^{6} d^{3} e^{3} - 104 \, a b^{5} d^{2} e^{4} + 286 \, a^{2} b^{4} d e^{5} - 429 \, a^{3} b^{3} e^{6}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{4} e^{2} - 832 \, a b^{5} d^{3} e^{3} + 2288 \, a^{2} b^{4} d^{2} e^{4} - 3432 \, a^{3} b^{3} d e^{5} + 3003 \, a^{4} b^{2} e^{6}\right)} x^{2} - 2 \, {\left(256 \, b^{6} d^{5} e - 1664 \, a b^{5} d^{4} e^{2} + 4576 \, a^{2} b^{4} d^{3} e^{3} - 6864 \, a^{3} b^{3} d^{2} e^{4} + 6006 \, a^{4} b^{2} d e^{5} - 3003 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{3003 \, e^{7}}"," ",0,"2/3003*(231*b^6*e^6*x^6 + 1024*b^6*d^6 - 6656*a*b^5*d^5*e + 18304*a^2*b^4*d^4*e^2 - 27456*a^3*b^3*d^3*e^3 + 24024*a^4*b^2*d^2*e^4 - 12012*a^5*b*d*e^5 + 3003*a^6*e^6 - 126*(2*b^6*d*e^5 - 13*a*b^5*e^6)*x^5 + 35*(8*b^6*d^2*e^4 - 52*a*b^5*d*e^5 + 143*a^2*b^4*e^6)*x^4 - 20*(16*b^6*d^3*e^3 - 104*a*b^5*d^2*e^4 + 286*a^2*b^4*d*e^5 - 429*a^3*b^3*e^6)*x^3 + 3*(128*b^6*d^4*e^2 - 832*a*b^5*d^3*e^3 + 2288*a^2*b^4*d^2*e^4 - 3432*a^3*b^3*d*e^5 + 3003*a^4*b^2*e^6)*x^2 - 2*(256*b^6*d^5*e - 1664*a*b^5*d^4*e^2 + 4576*a^2*b^4*d^3*e^3 - 6864*a^3*b^3*d^2*e^4 + 6006*a^4*b^2*d*e^5 - 3003*a^5*b*e^6)*x)*sqrt(e*x + d)/e^7","A",0
2114,1,365,0,0.410940," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(21 \, b^{6} e^{6} x^{6} - 1024 \, b^{6} d^{6} + 5632 \, a b^{5} d^{5} e - 12672 \, a^{2} b^{4} d^{4} e^{2} + 14784 \, a^{3} b^{3} d^{3} e^{3} - 9240 \, a^{4} b^{2} d^{2} e^{4} + 2772 \, a^{5} b d e^{5} - 231 \, a^{6} e^{6} - 14 \, {\left(2 \, b^{6} d e^{5} - 11 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(8 \, b^{6} d^{2} e^{4} - 44 \, a b^{5} d e^{5} + 99 \, a^{2} b^{4} e^{6}\right)} x^{4} - 4 \, {\left(16 \, b^{6} d^{3} e^{3} - 88 \, a b^{5} d^{2} e^{4} + 198 \, a^{2} b^{4} d e^{5} - 231 \, a^{3} b^{3} e^{6}\right)} x^{3} + {\left(128 \, b^{6} d^{4} e^{2} - 704 \, a b^{5} d^{3} e^{3} + 1584 \, a^{2} b^{4} d^{2} e^{4} - 1848 \, a^{3} b^{3} d e^{5} + 1155 \, a^{4} b^{2} e^{6}\right)} x^{2} - 2 \, {\left(256 \, b^{6} d^{5} e - 1408 \, a b^{5} d^{4} e^{2} + 3168 \, a^{2} b^{4} d^{3} e^{3} - 3696 \, a^{3} b^{3} d^{2} e^{4} + 2310 \, a^{4} b^{2} d e^{5} - 693 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{231 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"2/231*(21*b^6*e^6*x^6 - 1024*b^6*d^6 + 5632*a*b^5*d^5*e - 12672*a^2*b^4*d^4*e^2 + 14784*a^3*b^3*d^3*e^3 - 9240*a^4*b^2*d^2*e^4 + 2772*a^5*b*d*e^5 - 231*a^6*e^6 - 14*(2*b^6*d*e^5 - 11*a*b^5*e^6)*x^5 + 5*(8*b^6*d^2*e^4 - 44*a*b^5*d*e^5 + 99*a^2*b^4*e^6)*x^4 - 4*(16*b^6*d^3*e^3 - 88*a*b^5*d^2*e^4 + 198*a^2*b^4*d*e^5 - 231*a^3*b^3*e^6)*x^3 + (128*b^6*d^4*e^2 - 704*a*b^5*d^3*e^3 + 1584*a^2*b^4*d^2*e^4 - 1848*a^3*b^3*d*e^5 + 1155*a^4*b^2*e^6)*x^2 - 2*(256*b^6*d^5*e - 1408*a*b^5*d^4*e^2 + 3168*a^2*b^4*d^3*e^3 - 3696*a^3*b^3*d^2*e^4 + 2310*a^4*b^2*d*e^5 - 693*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^8*x + d*e^7)","A",0
2115,1,377,0,0.422182," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b^{6} e^{6} x^{6} + 1024 \, b^{6} d^{6} - 4608 \, a b^{5} d^{5} e + 8064 \, a^{2} b^{4} d^{4} e^{2} - 6720 \, a^{3} b^{3} d^{3} e^{3} + 2520 \, a^{4} b^{2} d^{2} e^{4} - 252 \, a^{5} b d e^{5} - 21 \, a^{6} e^{6} - 6 \, {\left(2 \, b^{6} d e^{5} - 9 \, a b^{5} e^{6}\right)} x^{5} + 3 \, {\left(8 \, b^{6} d^{2} e^{4} - 36 \, a b^{5} d e^{5} + 63 \, a^{2} b^{4} e^{6}\right)} x^{4} - 4 \, {\left(16 \, b^{6} d^{3} e^{3} - 72 \, a b^{5} d^{2} e^{4} + 126 \, a^{2} b^{4} d e^{5} - 105 \, a^{3} b^{3} e^{6}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{4} e^{2} - 576 \, a b^{5} d^{3} e^{3} + 1008 \, a^{2} b^{4} d^{2} e^{4} - 840 \, a^{3} b^{3} d e^{5} + 315 \, a^{4} b^{2} e^{6}\right)} x^{2} + 6 \, {\left(256 \, b^{6} d^{5} e - 1152 \, a b^{5} d^{4} e^{2} + 2016 \, a^{2} b^{4} d^{3} e^{3} - 1680 \, a^{3} b^{3} d^{2} e^{4} + 630 \, a^{4} b^{2} d e^{5} - 63 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{63 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"2/63*(7*b^6*e^6*x^6 + 1024*b^6*d^6 - 4608*a*b^5*d^5*e + 8064*a^2*b^4*d^4*e^2 - 6720*a^3*b^3*d^3*e^3 + 2520*a^4*b^2*d^2*e^4 - 252*a^5*b*d*e^5 - 21*a^6*e^6 - 6*(2*b^6*d*e^5 - 9*a*b^5*e^6)*x^5 + 3*(8*b^6*d^2*e^4 - 36*a*b^5*d*e^5 + 63*a^2*b^4*e^6)*x^4 - 4*(16*b^6*d^3*e^3 - 72*a*b^5*d^2*e^4 + 126*a^2*b^4*d*e^5 - 105*a^3*b^3*e^6)*x^3 + 3*(128*b^6*d^4*e^2 - 576*a*b^5*d^3*e^3 + 1008*a^2*b^4*d^2*e^4 - 840*a^3*b^3*d*e^5 + 315*a^4*b^2*e^6)*x^2 + 6*(256*b^6*d^5*e - 1152*a*b^5*d^4*e^2 + 2016*a^2*b^4*d^3*e^3 - 1680*a^3*b^3*d^2*e^4 + 630*a^4*b^2*d*e^5 - 63*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","A",0
2116,1,388,0,0.428647," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{6} e^{6} x^{6} - 1024 \, b^{6} d^{6} + 3584 \, a b^{5} d^{5} e - 4480 \, a^{2} b^{4} d^{4} e^{2} + 2240 \, a^{3} b^{3} d^{3} e^{3} - 280 \, a^{4} b^{2} d^{2} e^{4} - 28 \, a^{5} b d e^{5} - 7 \, a^{6} e^{6} - 6 \, {\left(2 \, b^{6} d e^{5} - 7 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(8 \, b^{6} d^{2} e^{4} - 28 \, a b^{5} d e^{5} + 35 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(16 \, b^{6} d^{3} e^{3} - 56 \, a b^{5} d^{2} e^{4} + 70 \, a^{2} b^{4} d e^{5} - 35 \, a^{3} b^{3} e^{6}\right)} x^{3} - 15 \, {\left(128 \, b^{6} d^{4} e^{2} - 448 \, a b^{5} d^{3} e^{3} + 560 \, a^{2} b^{4} d^{2} e^{4} - 280 \, a^{3} b^{3} d e^{5} + 35 \, a^{4} b^{2} e^{6}\right)} x^{2} - 10 \, {\left(256 \, b^{6} d^{5} e - 896 \, a b^{5} d^{4} e^{2} + 1120 \, a^{2} b^{4} d^{3} e^{3} - 560 \, a^{3} b^{3} d^{2} e^{4} + 70 \, a^{4} b^{2} d e^{5} + 7 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"2/35*(5*b^6*e^6*x^6 - 1024*b^6*d^6 + 3584*a*b^5*d^5*e - 4480*a^2*b^4*d^4*e^2 + 2240*a^3*b^3*d^3*e^3 - 280*a^4*b^2*d^2*e^4 - 28*a^5*b*d*e^5 - 7*a^6*e^6 - 6*(2*b^6*d*e^5 - 7*a*b^5*e^6)*x^5 + 5*(8*b^6*d^2*e^4 - 28*a*b^5*d*e^5 + 35*a^2*b^4*e^6)*x^4 - 20*(16*b^6*d^3*e^3 - 56*a*b^5*d^2*e^4 + 70*a^2*b^4*d*e^5 - 35*a^3*b^3*e^6)*x^3 - 15*(128*b^6*d^4*e^2 - 448*a*b^5*d^3*e^3 + 560*a^2*b^4*d^2*e^4 - 280*a^3*b^3*d*e^5 + 35*a^4*b^2*e^6)*x^2 - 10*(256*b^6*d^5*e - 896*a*b^5*d^4*e^2 + 1120*a^2*b^4*d^3*e^3 - 560*a^3*b^3*d^2*e^4 + 70*a^4*b^2*d*e^5 + 7*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","A",0
2117,1,399,0,0.418810," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b^{6} e^{6} x^{6} + 1024 \, b^{6} d^{6} - 2560 \, a b^{5} d^{5} e + 1920 \, a^{2} b^{4} d^{4} e^{2} - 320 \, a^{3} b^{3} d^{3} e^{3} - 40 \, a^{4} b^{2} d^{2} e^{4} - 12 \, a^{5} b d e^{5} - 5 \, a^{6} e^{6} - 14 \, {\left(2 \, b^{6} d e^{5} - 5 \, a b^{5} e^{6}\right)} x^{5} + 35 \, {\left(8 \, b^{6} d^{2} e^{4} - 20 \, a b^{5} d e^{5} + 15 \, a^{2} b^{4} e^{6}\right)} x^{4} + 140 \, {\left(16 \, b^{6} d^{3} e^{3} - 40 \, a b^{5} d^{2} e^{4} + 30 \, a^{2} b^{4} d e^{5} - 5 \, a^{3} b^{3} e^{6}\right)} x^{3} + 35 \, {\left(128 \, b^{6} d^{4} e^{2} - 320 \, a b^{5} d^{3} e^{3} + 240 \, a^{2} b^{4} d^{2} e^{4} - 40 \, a^{3} b^{3} d e^{5} - 5 \, a^{4} b^{2} e^{6}\right)} x^{2} + 14 \, {\left(256 \, b^{6} d^{5} e - 640 \, a b^{5} d^{4} e^{2} + 480 \, a^{2} b^{4} d^{3} e^{3} - 80 \, a^{3} b^{3} d^{2} e^{4} - 10 \, a^{4} b^{2} d e^{5} - 3 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{11} x^{4} + 4 \, d e^{10} x^{3} + 6 \, d^{2} e^{9} x^{2} + 4 \, d^{3} e^{8} x + d^{4} e^{7}\right)}}"," ",0,"2/35*(7*b^6*e^6*x^6 + 1024*b^6*d^6 - 2560*a*b^5*d^5*e + 1920*a^2*b^4*d^4*e^2 - 320*a^3*b^3*d^3*e^3 - 40*a^4*b^2*d^2*e^4 - 12*a^5*b*d*e^5 - 5*a^6*e^6 - 14*(2*b^6*d*e^5 - 5*a*b^5*e^6)*x^5 + 35*(8*b^6*d^2*e^4 - 20*a*b^5*d*e^5 + 15*a^2*b^4*e^6)*x^4 + 140*(16*b^6*d^3*e^3 - 40*a*b^5*d^2*e^4 + 30*a^2*b^4*d*e^5 - 5*a^3*b^3*e^6)*x^3 + 35*(128*b^6*d^4*e^2 - 320*a*b^5*d^3*e^3 + 240*a^2*b^4*d^2*e^4 - 40*a^3*b^3*d*e^5 - 5*a^4*b^2*e^6)*x^2 + 14*(256*b^6*d^5*e - 640*a*b^5*d^4*e^2 + 480*a^2*b^4*d^3*e^3 - 80*a^3*b^3*d^2*e^4 - 10*a^4*b^2*d*e^5 - 3*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^11*x^4 + 4*d*e^10*x^3 + 6*d^2*e^9*x^2 + 4*d^3*e^8*x + d^4*e^7)","A",0
2118,1,409,0,0.433838," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(21 \, b^{6} e^{6} x^{6} - 1024 \, b^{6} d^{6} + 1536 \, a b^{5} d^{5} e - 384 \, a^{2} b^{4} d^{4} e^{2} - 64 \, a^{3} b^{3} d^{3} e^{3} - 24 \, a^{4} b^{2} d^{2} e^{4} - 12 \, a^{5} b d e^{5} - 7 \, a^{6} e^{6} - 126 \, {\left(2 \, b^{6} d e^{5} - 3 \, a b^{5} e^{6}\right)} x^{5} - 315 \, {\left(8 \, b^{6} d^{2} e^{4} - 12 \, a b^{5} d e^{5} + 3 \, a^{2} b^{4} e^{6}\right)} x^{4} - 420 \, {\left(16 \, b^{6} d^{3} e^{3} - 24 \, a b^{5} d^{2} e^{4} + 6 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} - 63 \, {\left(128 \, b^{6} d^{4} e^{2} - 192 \, a b^{5} d^{3} e^{3} + 48 \, a^{2} b^{4} d^{2} e^{4} + 8 \, a^{3} b^{3} d e^{5} + 3 \, a^{4} b^{2} e^{6}\right)} x^{2} - 18 \, {\left(256 \, b^{6} d^{5} e - 384 \, a b^{5} d^{4} e^{2} + 96 \, a^{2} b^{4} d^{3} e^{3} + 16 \, a^{3} b^{3} d^{2} e^{4} + 6 \, a^{4} b^{2} d e^{5} + 3 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{63 \, {\left(e^{12} x^{5} + 5 \, d e^{11} x^{4} + 10 \, d^{2} e^{10} x^{3} + 10 \, d^{3} e^{9} x^{2} + 5 \, d^{4} e^{8} x + d^{5} e^{7}\right)}}"," ",0,"2/63*(21*b^6*e^6*x^6 - 1024*b^6*d^6 + 1536*a*b^5*d^5*e - 384*a^2*b^4*d^4*e^2 - 64*a^3*b^3*d^3*e^3 - 24*a^4*b^2*d^2*e^4 - 12*a^5*b*d*e^5 - 7*a^6*e^6 - 126*(2*b^6*d*e^5 - 3*a*b^5*e^6)*x^5 - 315*(8*b^6*d^2*e^4 - 12*a*b^5*d*e^5 + 3*a^2*b^4*e^6)*x^4 - 420*(16*b^6*d^3*e^3 - 24*a*b^5*d^2*e^4 + 6*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 - 63*(128*b^6*d^4*e^2 - 192*a*b^5*d^3*e^3 + 48*a^2*b^4*d^2*e^4 + 8*a^3*b^3*d*e^5 + 3*a^4*b^2*e^6)*x^2 - 18*(256*b^6*d^5*e - 384*a*b^5*d^4*e^2 + 96*a^2*b^4*d^3*e^3 + 16*a^3*b^3*d^2*e^4 + 6*a^4*b^2*d*e^5 + 3*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^12*x^5 + 5*d*e^11*x^4 + 10*d^2*e^10*x^3 + 10*d^3*e^9*x^2 + 5*d^4*e^8*x + d^5*e^7)","A",0
2119,1,421,0,0.438431," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, b^{6} e^{6} x^{6} + 1024 \, b^{6} d^{6} - 512 \, a b^{5} d^{5} e - 128 \, a^{2} b^{4} d^{4} e^{2} - 64 \, a^{3} b^{3} d^{3} e^{3} - 40 \, a^{4} b^{2} d^{2} e^{4} - 28 \, a^{5} b d e^{5} - 21 \, a^{6} e^{6} + 1386 \, {\left(2 \, b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 1155 \, {\left(8 \, b^{6} d^{2} e^{4} - 4 \, a b^{5} d e^{5} - a^{2} b^{4} e^{6}\right)} x^{4} + 924 \, {\left(16 \, b^{6} d^{3} e^{3} - 8 \, a b^{5} d^{2} e^{4} - 2 \, a^{2} b^{4} d e^{5} - a^{3} b^{3} e^{6}\right)} x^{3} + 99 \, {\left(128 \, b^{6} d^{4} e^{2} - 64 \, a b^{5} d^{3} e^{3} - 16 \, a^{2} b^{4} d^{2} e^{4} - 8 \, a^{3} b^{3} d e^{5} - 5 \, a^{4} b^{2} e^{6}\right)} x^{2} + 22 \, {\left(256 \, b^{6} d^{5} e - 128 \, a b^{5} d^{4} e^{2} - 32 \, a^{2} b^{4} d^{3} e^{3} - 16 \, a^{3} b^{3} d^{2} e^{4} - 10 \, a^{4} b^{2} d e^{5} - 7 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{231 \, {\left(e^{13} x^{6} + 6 \, d e^{12} x^{5} + 15 \, d^{2} e^{11} x^{4} + 20 \, d^{3} e^{10} x^{3} + 15 \, d^{4} e^{9} x^{2} + 6 \, d^{5} e^{8} x + d^{6} e^{7}\right)}}"," ",0,"2/231*(231*b^6*e^6*x^6 + 1024*b^6*d^6 - 512*a*b^5*d^5*e - 128*a^2*b^4*d^4*e^2 - 64*a^3*b^3*d^3*e^3 - 40*a^4*b^2*d^2*e^4 - 28*a^5*b*d*e^5 - 21*a^6*e^6 + 1386*(2*b^6*d*e^5 - a*b^5*e^6)*x^5 + 1155*(8*b^6*d^2*e^4 - 4*a*b^5*d*e^5 - a^2*b^4*e^6)*x^4 + 924*(16*b^6*d^3*e^3 - 8*a*b^5*d^2*e^4 - 2*a^2*b^4*d*e^5 - a^3*b^3*e^6)*x^3 + 99*(128*b^6*d^4*e^2 - 64*a*b^5*d^3*e^3 - 16*a^2*b^4*d^2*e^4 - 8*a^3*b^3*d*e^5 - 5*a^4*b^2*e^6)*x^2 + 22*(256*b^6*d^5*e - 128*a*b^5*d^4*e^2 - 32*a^2*b^4*d^3*e^3 - 16*a^3*b^3*d^2*e^4 - 10*a^4*b^2*d*e^5 - 7*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^13*x^6 + 6*d*e^12*x^5 + 15*d^2*e^11*x^4 + 20*d^3*e^10*x^3 + 15*d^4*e^9*x^2 + 6*d^5*e^8*x + d^6*e^7)","A",0
2120,1,431,0,0.442067," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(15/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3003 \, b^{6} e^{6} x^{6} + 1024 \, b^{6} d^{6} + 512 \, a b^{5} d^{5} e + 384 \, a^{2} b^{4} d^{4} e^{2} + 320 \, a^{3} b^{3} d^{3} e^{3} + 280 \, a^{4} b^{2} d^{2} e^{4} + 252 \, a^{5} b d e^{5} + 231 \, a^{6} e^{6} + 6006 \, {\left(2 \, b^{6} d e^{5} + a b^{5} e^{6}\right)} x^{5} + 3003 \, {\left(8 \, b^{6} d^{2} e^{4} + 4 \, a b^{5} d e^{5} + 3 \, a^{2} b^{4} e^{6}\right)} x^{4} + 1716 \, {\left(16 \, b^{6} d^{3} e^{3} + 8 \, a b^{5} d^{2} e^{4} + 6 \, a^{2} b^{4} d e^{5} + 5 \, a^{3} b^{3} e^{6}\right)} x^{3} + 143 \, {\left(128 \, b^{6} d^{4} e^{2} + 64 \, a b^{5} d^{3} e^{3} + 48 \, a^{2} b^{4} d^{2} e^{4} + 40 \, a^{3} b^{3} d e^{5} + 35 \, a^{4} b^{2} e^{6}\right)} x^{2} + 26 \, {\left(256 \, b^{6} d^{5} e + 128 \, a b^{5} d^{4} e^{2} + 96 \, a^{2} b^{4} d^{3} e^{3} + 80 \, a^{3} b^{3} d^{2} e^{4} + 70 \, a^{4} b^{2} d e^{5} + 63 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{3003 \, {\left(e^{14} x^{7} + 7 \, d e^{13} x^{6} + 21 \, d^{2} e^{12} x^{5} + 35 \, d^{3} e^{11} x^{4} + 35 \, d^{4} e^{10} x^{3} + 21 \, d^{5} e^{9} x^{2} + 7 \, d^{6} e^{8} x + d^{7} e^{7}\right)}}"," ",0,"-2/3003*(3003*b^6*e^6*x^6 + 1024*b^6*d^6 + 512*a*b^5*d^5*e + 384*a^2*b^4*d^4*e^2 + 320*a^3*b^3*d^3*e^3 + 280*a^4*b^2*d^2*e^4 + 252*a^5*b*d*e^5 + 231*a^6*e^6 + 6006*(2*b^6*d*e^5 + a*b^5*e^6)*x^5 + 3003*(8*b^6*d^2*e^4 + 4*a*b^5*d*e^5 + 3*a^2*b^4*e^6)*x^4 + 1716*(16*b^6*d^3*e^3 + 8*a*b^5*d^2*e^4 + 6*a^2*b^4*d*e^5 + 5*a^3*b^3*e^6)*x^3 + 143*(128*b^6*d^4*e^2 + 64*a*b^5*d^3*e^3 + 48*a^2*b^4*d^2*e^4 + 40*a^3*b^3*d*e^5 + 35*a^4*b^2*e^6)*x^2 + 26*(256*b^6*d^5*e + 128*a*b^5*d^4*e^2 + 96*a^2*b^4*d^3*e^3 + 80*a^3*b^3*d^2*e^4 + 70*a^4*b^2*d*e^5 + 63*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^14*x^7 + 7*d*e^13*x^6 + 21*d^2*e^12*x^5 + 35*d^3*e^11*x^4 + 35*d^4*e^10*x^3 + 21*d^5*e^9*x^2 + 7*d^6*e^8*x + d^7*e^7)","A",0
2121,1,443,0,0.432730," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(17/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15015 \, b^{6} e^{6} x^{6} + 1024 \, b^{6} d^{6} + 1536 \, a b^{5} d^{5} e + 1920 \, a^{2} b^{4} d^{4} e^{2} + 2240 \, a^{3} b^{3} d^{3} e^{3} + 2520 \, a^{4} b^{2} d^{2} e^{4} + 2772 \, a^{5} b d e^{5} + 3003 \, a^{6} e^{6} + 18018 \, {\left(2 \, b^{6} d e^{5} + 3 \, a b^{5} e^{6}\right)} x^{5} + 6435 \, {\left(8 \, b^{6} d^{2} e^{4} + 12 \, a b^{5} d e^{5} + 15 \, a^{2} b^{4} e^{6}\right)} x^{4} + 2860 \, {\left(16 \, b^{6} d^{3} e^{3} + 24 \, a b^{5} d^{2} e^{4} + 30 \, a^{2} b^{4} d e^{5} + 35 \, a^{3} b^{3} e^{6}\right)} x^{3} + 195 \, {\left(128 \, b^{6} d^{4} e^{2} + 192 \, a b^{5} d^{3} e^{3} + 240 \, a^{2} b^{4} d^{2} e^{4} + 280 \, a^{3} b^{3} d e^{5} + 315 \, a^{4} b^{2} e^{6}\right)} x^{2} + 30 \, {\left(256 \, b^{6} d^{5} e + 384 \, a b^{5} d^{4} e^{2} + 480 \, a^{2} b^{4} d^{3} e^{3} + 560 \, a^{3} b^{3} d^{2} e^{4} + 630 \, a^{4} b^{2} d e^{5} + 693 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{45045 \, {\left(e^{15} x^{8} + 8 \, d e^{14} x^{7} + 28 \, d^{2} e^{13} x^{6} + 56 \, d^{3} e^{12} x^{5} + 70 \, d^{4} e^{11} x^{4} + 56 \, d^{5} e^{10} x^{3} + 28 \, d^{6} e^{9} x^{2} + 8 \, d^{7} e^{8} x + d^{8} e^{7}\right)}}"," ",0,"-2/45045*(15015*b^6*e^6*x^6 + 1024*b^6*d^6 + 1536*a*b^5*d^5*e + 1920*a^2*b^4*d^4*e^2 + 2240*a^3*b^3*d^3*e^3 + 2520*a^4*b^2*d^2*e^4 + 2772*a^5*b*d*e^5 + 3003*a^6*e^6 + 18018*(2*b^6*d*e^5 + 3*a*b^5*e^6)*x^5 + 6435*(8*b^6*d^2*e^4 + 12*a*b^5*d*e^5 + 15*a^2*b^4*e^6)*x^4 + 2860*(16*b^6*d^3*e^3 + 24*a*b^5*d^2*e^4 + 30*a^2*b^4*d*e^5 + 35*a^3*b^3*e^6)*x^3 + 195*(128*b^6*d^4*e^2 + 192*a*b^5*d^3*e^3 + 240*a^2*b^4*d^2*e^4 + 280*a^3*b^3*d*e^5 + 315*a^4*b^2*e^6)*x^2 + 30*(256*b^6*d^5*e + 384*a*b^5*d^4*e^2 + 480*a^2*b^4*d^3*e^3 + 560*a^3*b^3*d^2*e^4 + 630*a^4*b^2*d*e^5 + 693*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^15*x^8 + 8*d*e^14*x^7 + 28*d^2*e^13*x^6 + 56*d^3*e^12*x^5 + 70*d^4*e^11*x^4 + 56*d^5*e^10*x^3 + 28*d^6*e^9*x^2 + 8*d^7*e^8*x + d^8*e^7)","A",0
2122,1,50,0,0.403212," ","integrate((b*x+a)*(e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}\right)} \sqrt{e x + d}}{9 \, e}"," ",0,"2/9*(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4)*sqrt(e*x + d)/e","A",0
2123,1,39,0,0.409024," ","integrate((b*x+a)*(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{e x + d}}{7 \, e}"," ",0,"2/7*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(e*x + d)/e","A",0
2124,1,28,0,0.426370," ","integrate((b*x+a)*(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{e x + d}}{5 \, e}"," ",0,"2/5*(e^2*x^2 + 2*d*e*x + d^2)*sqrt(e*x + d)/e","A",0
2125,1,12,0,0.406808," ","integrate((b*x+a)*(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e x + d\right)}^{\frac{3}{2}}}{3 \, e}"," ",0,"2/3*(e*x + d)^(3/2)/e","A",0
2126,1,12,0,0.414943," ","integrate((b*x+a)/(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e x + d}}{e}"," ",0,"2*sqrt(e*x + d)/e","A",0
2127,1,20,0,0.421277," ","integrate((b*x+a)/(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e x + d}}{e^{2} x + d e}"," ",0,"-2*sqrt(e*x + d)/(e^2*x + d*e)","A",0
2128,1,31,0,0.405276," ","integrate((b*x+a)/(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e x + d}}{3 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-2/3*sqrt(e*x + d)/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
2129,1,42,0,0.417005," ","integrate((b*x+a)/(e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e x + d}}{5 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"-2/5*sqrt(e*x + d)/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","A",0
2130,1,486,0,0.466501," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a b^{2} d^{2} e - 2 \, a^{2} b d e^{2} + a^{3} e^{3} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(6 \, b^{3} e^{3} x^{3} - 15 \, b^{3} d^{3} + 161 \, a b^{2} d^{2} e - 245 \, a^{2} b d e^{2} + 105 \, a^{3} e^{3} + 2 \, {\left(16 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(58 \, b^{3} d^{2} e - 84 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{105 \, {\left(a b^{2} d^{2} e - 2 \, a^{2} b d e^{2} + a^{3} e^{3} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(6 \, b^{3} e^{3} x^{3} - 15 \, b^{3} d^{3} + 161 \, a b^{2} d^{2} e - 245 \, a^{2} b d e^{2} + 105 \, a^{3} e^{3} + 2 \, {\left(16 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(58 \, b^{3} d^{2} e - 84 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[1/30*(105*(a*b^2*d^2*e - 2*a^2*b*d*e^2 + a^3*e^3 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(6*b^3*e^3*x^3 - 15*b^3*d^3 + 161*a*b^2*d^2*e - 245*a^2*b*d*e^2 + 105*a^3*e^3 + 2*(16*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + 2*(58*b^3*d^2*e - 84*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^5*x + a*b^4), -1/15*(105*(a*b^2*d^2*e - 2*a^2*b*d*e^2 + a^3*e^3 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (6*b^3*e^3*x^3 - 15*b^3*d^3 + 161*a*b^2*d^2*e - 245*a^2*b*d*e^2 + 105*a^3*e^3 + 2*(16*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + 2*(58*b^3*d^2*e - 84*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^5*x + a*b^4)]","A",0
2131,1,330,0,0.439866," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a b d e - a^{2} e^{2} + {\left(b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(2 \, b^{2} e^{2} x^{2} - 3 \, b^{2} d^{2} + 20 \, a b d e - 15 \, a^{2} e^{2} + 2 \, {\left(7 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{4} x + a b^{3}\right)}}, -\frac{15 \, {\left(a b d e - a^{2} e^{2} + {\left(b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(2 \, b^{2} e^{2} x^{2} - 3 \, b^{2} d^{2} + 20 \, a b d e - 15 \, a^{2} e^{2} + 2 \, {\left(7 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b^{4} x + a b^{3}\right)}}\right]"," ",0,"[-1/6*(15*(a*b*d*e - a^2*e^2 + (b^2*d*e - a*b*e^2)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(2*b^2*e^2*x^2 - 3*b^2*d^2 + 20*a*b*d*e - 15*a^2*e^2 + 2*(7*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d))/(b^4*x + a*b^3), -1/3*(15*(a*b*d*e - a^2*e^2 + (b^2*d*e - a*b*e^2)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (2*b^2*e^2*x^2 - 3*b^2*d^2 + 20*a*b*d*e - 15*a^2*e^2 + 2*(7*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d))/(b^4*x + a*b^3)]","A",0
2132,1,210,0,0.434415," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b e x + a e\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(2 \, b e x - b d + 3 \, a e\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} x + a b^{2}\right)}}, -\frac{3 \, {\left(b e x + a e\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(2 \, b e x - b d + 3 \, a e\right)} \sqrt{e x + d}}{b^{3} x + a b^{2}}\right]"," ",0,"[1/2*(3*(b*e*x + a*e)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(2*b*e*x - b*d + 3*a*e)*sqrt(e*x + d))/(b^3*x + a*b^2), -(3*(b*e*x + a*e)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (2*b*e*x - b*d + 3*a*e)*sqrt(e*x + d))/(b^3*x + a*b^2)]","A",0
2133,1,232,0,0.445623," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} d - a b e} {\left(b e x + a e\right)} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(b^{2} d - a b e\right)} \sqrt{e x + d}}{2 \, {\left(a b^{3} d - a^{2} b^{2} e + {\left(b^{4} d - a b^{3} e\right)} x\right)}}, \frac{\sqrt{-b^{2} d + a b e} {\left(b e x + a e\right)} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(b^{2} d - a b e\right)} \sqrt{e x + d}}{a b^{3} d - a^{2} b^{2} e + {\left(b^{4} d - a b^{3} e\right)} x}\right]"," ",0,"[1/2*(sqrt(b^2*d - a*b*e)*(b*e*x + a*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(b^2*d - a*b*e)*sqrt(e*x + d))/(a*b^3*d - a^2*b^2*e + (b^4*d - a*b^3*e)*x), (sqrt(-b^2*d + a*b*e)*(b*e*x + a*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (b^2*d - a*b*e)*sqrt(e*x + d))/(a*b^3*d - a^2*b^2*e + (b^4*d - a*b^3*e)*x)]","A",0
2134,1,280,0,0.447176," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{b^{2} d - a b e} {\left(b e x + a e\right)} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(b^{2} d - a b e\right)} \sqrt{e x + d}}{2 \, {\left(a b^{3} d^{2} - 2 \, a^{2} b^{2} d e + a^{3} b e^{2} + {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} x\right)}}, -\frac{\sqrt{-b^{2} d + a b e} {\left(b e x + a e\right)} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(b^{2} d - a b e\right)} \sqrt{e x + d}}{a b^{3} d^{2} - 2 \, a^{2} b^{2} d e + a^{3} b e^{2} + {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} x}\right]"," ",0,"[-1/2*(sqrt(b^2*d - a*b*e)*(b*e*x + a*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(b^2*d - a*b*e)*sqrt(e*x + d))/(a*b^3*d^2 - 2*a^2*b^2*d*e + a^3*b*e^2 + (b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*x), -(sqrt(-b^2*d + a*b*e)*(b*e*x + a*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (b^2*d - a*b*e)*sqrt(e*x + d))/(a*b^3*d^2 - 2*a^2*b^2*d*e + a^3*b*e^2 + (b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*x)]","A",0
2135,1,423,0,0.445599," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b e^{2} x^{2} + a d e + {\left(b d e + a e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(3 \, b e x + b d + 2 \, a e\right)} \sqrt{e x + d}}{2 \, {\left(a b^{2} d^{3} - 2 \, a^{2} b d^{2} e + a^{3} d e^{2} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x^{2} + {\left(b^{3} d^{3} - a b^{2} d^{2} e - a^{2} b d e^{2} + a^{3} e^{3}\right)} x\right)}}, \frac{3 \, {\left(b e^{2} x^{2} + a d e + {\left(b d e + a e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3 \, b e x + b d + 2 \, a e\right)} \sqrt{e x + d}}{a b^{2} d^{3} - 2 \, a^{2} b d^{2} e + a^{3} d e^{2} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x^{2} + {\left(b^{3} d^{3} - a b^{2} d^{2} e - a^{2} b d e^{2} + a^{3} e^{3}\right)} x}\right]"," ",0,"[1/2*(3*(b*e^2*x^2 + a*d*e + (b*d*e + a*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(3*b*e*x + b*d + 2*a*e)*sqrt(e*x + d))/(a*b^2*d^3 - 2*a^2*b*d^2*e + a^3*d*e^2 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x^2 + (b^3*d^3 - a*b^2*d^2*e - a^2*b*d*e^2 + a^3*e^3)*x), (3*(b*e^2*x^2 + a*d*e + (b*d*e + a*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3*b*e*x + b*d + 2*a*e)*sqrt(e*x + d))/(a*b^2*d^3 - 2*a^2*b*d^2*e + a^3*d*e^2 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x^2 + (b^3*d^3 - a*b^2*d^2*e - a^2*b*d*e^2 + a^3*e^3)*x)]","A",0
2136,1,782,0,0.458010," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{2} e^{3} x^{3} + a b d^{2} e + {\left(2 \, b^{2} d e^{2} + a b e^{3}\right)} x^{2} + {\left(b^{2} d^{2} e + 2 \, a b d e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(15 \, b^{2} e^{2} x^{2} + 3 \, b^{2} d^{2} + 14 \, a b d e - 2 \, a^{2} e^{2} + 10 \, {\left(2 \, b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(a b^{3} d^{5} - 3 \, a^{2} b^{2} d^{4} e + 3 \, a^{3} b d^{3} e^{2} - a^{4} d^{2} e^{3} + {\left(b^{4} d^{3} e^{2} - 3 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4} - a^{3} b e^{5}\right)} x^{3} + {\left(2 \, b^{4} d^{4} e - 5 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3} + a^{3} b d e^{4} - a^{4} e^{5}\right)} x^{2} + {\left(b^{4} d^{5} - a b^{3} d^{4} e - 3 \, a^{2} b^{2} d^{3} e^{2} + 5 \, a^{3} b d^{2} e^{3} - 2 \, a^{4} d e^{4}\right)} x\right)}}, \frac{15 \, {\left(b^{2} e^{3} x^{3} + a b d^{2} e + {\left(2 \, b^{2} d e^{2} + a b e^{3}\right)} x^{2} + {\left(b^{2} d^{2} e + 2 \, a b d e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(15 \, b^{2} e^{2} x^{2} + 3 \, b^{2} d^{2} + 14 \, a b d e - 2 \, a^{2} e^{2} + 10 \, {\left(2 \, b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(a b^{3} d^{5} - 3 \, a^{2} b^{2} d^{4} e + 3 \, a^{3} b d^{3} e^{2} - a^{4} d^{2} e^{3} + {\left(b^{4} d^{3} e^{2} - 3 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4} - a^{3} b e^{5}\right)} x^{3} + {\left(2 \, b^{4} d^{4} e - 5 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3} + a^{3} b d e^{4} - a^{4} e^{5}\right)} x^{2} + {\left(b^{4} d^{5} - a b^{3} d^{4} e - 3 \, a^{2} b^{2} d^{3} e^{2} + 5 \, a^{3} b d^{2} e^{3} - 2 \, a^{4} d e^{4}\right)} x\right)}}\right]"," ",0,"[-1/6*(15*(b^2*e^3*x^3 + a*b*d^2*e + (2*b^2*d*e^2 + a*b*e^3)*x^2 + (b^2*d^2*e + 2*a*b*d*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(15*b^2*e^2*x^2 + 3*b^2*d^2 + 14*a*b*d*e - 2*a^2*e^2 + 10*(2*b^2*d*e + a*b*e^2)*x)*sqrt(e*x + d))/(a*b^3*d^5 - 3*a^2*b^2*d^4*e + 3*a^3*b*d^3*e^2 - a^4*d^2*e^3 + (b^4*d^3*e^2 - 3*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4 - a^3*b*e^5)*x^3 + (2*b^4*d^4*e - 5*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3 + a^3*b*d*e^4 - a^4*e^5)*x^2 + (b^4*d^5 - a*b^3*d^4*e - 3*a^2*b^2*d^3*e^2 + 5*a^3*b*d^2*e^3 - 2*a^4*d*e^4)*x), 1/3*(15*(b^2*e^3*x^3 + a*b*d^2*e + (2*b^2*d*e^2 + a*b*e^3)*x^2 + (b^2*d^2*e + 2*a*b*d*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (15*b^2*e^2*x^2 + 3*b^2*d^2 + 14*a*b*d*e - 2*a^2*e^2 + 10*(2*b^2*d*e + a*b*e^2)*x)*sqrt(e*x + d))/(a*b^3*d^5 - 3*a^2*b^2*d^4*e + 3*a^3*b*d^3*e^2 - a^4*d^2*e^3 + (b^4*d^3*e^2 - 3*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4 - a^3*b*e^5)*x^3 + (2*b^4*d^4*e - 5*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3 + a^3*b*d*e^4 - a^4*e^5)*x^2 + (b^4*d^5 - a*b^3*d^4*e - 3*a^2*b^2*d^3*e^2 + 5*a^3*b*d^2*e^3 - 2*a^4*d*e^4)*x)]","B",0
2137,1,1218,0,0.462491," ","integrate((b*x+a)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} e^{4} x^{4} + a b^{2} d^{3} e + {\left(3 \, b^{3} d e^{3} + a b^{2} e^{4}\right)} x^{3} + 3 \, {\left(b^{3} d^{2} e^{2} + a b^{2} d e^{3}\right)} x^{2} + {\left(b^{3} d^{3} e + 3 \, a b^{2} d^{2} e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(105 \, b^{3} e^{3} x^{3} + 15 \, b^{3} d^{3} + 116 \, a b^{2} d^{2} e - 32 \, a^{2} b d e^{2} + 6 \, a^{3} e^{3} + 35 \, {\left(7 \, b^{3} d e^{2} + 2 \, a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(23 \, b^{3} d^{2} e + 24 \, a b^{2} d e^{2} - 2 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(a b^{4} d^{7} - 4 \, a^{2} b^{3} d^{6} e + 6 \, a^{3} b^{2} d^{5} e^{2} - 4 \, a^{4} b d^{4} e^{3} + a^{5} d^{3} e^{4} + {\left(b^{5} d^{4} e^{3} - 4 \, a b^{4} d^{3} e^{4} + 6 \, a^{2} b^{3} d^{2} e^{5} - 4 \, a^{3} b^{2} d e^{6} + a^{4} b e^{7}\right)} x^{4} + {\left(3 \, b^{5} d^{5} e^{2} - 11 \, a b^{4} d^{4} e^{3} + 14 \, a^{2} b^{3} d^{3} e^{4} - 6 \, a^{3} b^{2} d^{2} e^{5} - a^{4} b d e^{6} + a^{5} e^{7}\right)} x^{3} + 3 \, {\left(b^{5} d^{6} e - 3 \, a b^{4} d^{5} e^{2} + 2 \, a^{2} b^{3} d^{4} e^{3} + 2 \, a^{3} b^{2} d^{3} e^{4} - 3 \, a^{4} b d^{2} e^{5} + a^{5} d e^{6}\right)} x^{2} + {\left(b^{5} d^{7} - a b^{4} d^{6} e - 6 \, a^{2} b^{3} d^{5} e^{2} + 14 \, a^{3} b^{2} d^{4} e^{3} - 11 \, a^{4} b d^{3} e^{4} + 3 \, a^{5} d^{2} e^{5}\right)} x\right)}}, \frac{105 \, {\left(b^{3} e^{4} x^{4} + a b^{2} d^{3} e + {\left(3 \, b^{3} d e^{3} + a b^{2} e^{4}\right)} x^{3} + 3 \, {\left(b^{3} d^{2} e^{2} + a b^{2} d e^{3}\right)} x^{2} + {\left(b^{3} d^{3} e + 3 \, a b^{2} d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(105 \, b^{3} e^{3} x^{3} + 15 \, b^{3} d^{3} + 116 \, a b^{2} d^{2} e - 32 \, a^{2} b d e^{2} + 6 \, a^{3} e^{3} + 35 \, {\left(7 \, b^{3} d e^{2} + 2 \, a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(23 \, b^{3} d^{2} e + 24 \, a b^{2} d e^{2} - 2 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(a b^{4} d^{7} - 4 \, a^{2} b^{3} d^{6} e + 6 \, a^{3} b^{2} d^{5} e^{2} - 4 \, a^{4} b d^{4} e^{3} + a^{5} d^{3} e^{4} + {\left(b^{5} d^{4} e^{3} - 4 \, a b^{4} d^{3} e^{4} + 6 \, a^{2} b^{3} d^{2} e^{5} - 4 \, a^{3} b^{2} d e^{6} + a^{4} b e^{7}\right)} x^{4} + {\left(3 \, b^{5} d^{5} e^{2} - 11 \, a b^{4} d^{4} e^{3} + 14 \, a^{2} b^{3} d^{3} e^{4} - 6 \, a^{3} b^{2} d^{2} e^{5} - a^{4} b d e^{6} + a^{5} e^{7}\right)} x^{3} + 3 \, {\left(b^{5} d^{6} e - 3 \, a b^{4} d^{5} e^{2} + 2 \, a^{2} b^{3} d^{4} e^{3} + 2 \, a^{3} b^{2} d^{3} e^{4} - 3 \, a^{4} b d^{2} e^{5} + a^{5} d e^{6}\right)} x^{2} + {\left(b^{5} d^{7} - a b^{4} d^{6} e - 6 \, a^{2} b^{3} d^{5} e^{2} + 14 \, a^{3} b^{2} d^{4} e^{3} - 11 \, a^{4} b d^{3} e^{4} + 3 \, a^{5} d^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[1/30*(105*(b^3*e^4*x^4 + a*b^2*d^3*e + (3*b^3*d*e^3 + a*b^2*e^4)*x^3 + 3*(b^3*d^2*e^2 + a*b^2*d*e^3)*x^2 + (b^3*d^3*e + 3*a*b^2*d^2*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(105*b^3*e^3*x^3 + 15*b^3*d^3 + 116*a*b^2*d^2*e - 32*a^2*b*d*e^2 + 6*a^3*e^3 + 35*(7*b^3*d*e^2 + 2*a*b^2*e^3)*x^2 + 7*(23*b^3*d^2*e + 24*a*b^2*d*e^2 - 2*a^2*b*e^3)*x)*sqrt(e*x + d))/(a*b^4*d^7 - 4*a^2*b^3*d^6*e + 6*a^3*b^2*d^5*e^2 - 4*a^4*b*d^4*e^3 + a^5*d^3*e^4 + (b^5*d^4*e^3 - 4*a*b^4*d^3*e^4 + 6*a^2*b^3*d^2*e^5 - 4*a^3*b^2*d*e^6 + a^4*b*e^7)*x^4 + (3*b^5*d^5*e^2 - 11*a*b^4*d^4*e^3 + 14*a^2*b^3*d^3*e^4 - 6*a^3*b^2*d^2*e^5 - a^4*b*d*e^6 + a^5*e^7)*x^3 + 3*(b^5*d^6*e - 3*a*b^4*d^5*e^2 + 2*a^2*b^3*d^4*e^3 + 2*a^3*b^2*d^3*e^4 - 3*a^4*b*d^2*e^5 + a^5*d*e^6)*x^2 + (b^5*d^7 - a*b^4*d^6*e - 6*a^2*b^3*d^5*e^2 + 14*a^3*b^2*d^4*e^3 - 11*a^4*b*d^3*e^4 + 3*a^5*d^2*e^5)*x), 1/15*(105*(b^3*e^4*x^4 + a*b^2*d^3*e + (3*b^3*d*e^3 + a*b^2*e^4)*x^3 + 3*(b^3*d^2*e^2 + a*b^2*d*e^3)*x^2 + (b^3*d^3*e + 3*a*b^2*d^2*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (105*b^3*e^3*x^3 + 15*b^3*d^3 + 116*a*b^2*d^2*e - 32*a^2*b*d*e^2 + 6*a^3*e^3 + 35*(7*b^3*d*e^2 + 2*a*b^2*e^3)*x^2 + 7*(23*b^3*d^2*e + 24*a*b^2*d*e^2 - 2*a^2*b*e^3)*x)*sqrt(e*x + d))/(a*b^4*d^7 - 4*a^2*b^3*d^6*e + 6*a^3*b^2*d^5*e^2 - 4*a^4*b*d^4*e^3 + a^5*d^3*e^4 + (b^5*d^4*e^3 - 4*a*b^4*d^3*e^4 + 6*a^2*b^3*d^2*e^5 - 4*a^3*b^2*d*e^6 + a^4*b*e^7)*x^4 + (3*b^5*d^5*e^2 - 11*a*b^4*d^4*e^3 + 14*a^2*b^3*d^3*e^4 - 6*a^3*b^2*d^2*e^5 - a^4*b*d*e^6 + a^5*e^7)*x^3 + 3*(b^5*d^6*e - 3*a*b^4*d^5*e^2 + 2*a^2*b^3*d^4*e^3 + 2*a^3*b^2*d^3*e^4 - 3*a^4*b*d^2*e^5 + a^5*d*e^6)*x^2 + (b^5*d^7 - a*b^4*d^6*e - 6*a^2*b^3*d^5*e^2 + 14*a^3*b^2*d^4*e^3 - 11*a^4*b*d^3*e^4 + 3*a^5*d^2*e^5)*x)]","B",0
2138,1,498,0,0.455584," ","integrate((b*x+a)*(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(48 \, b^{3} e^{3} x^{3} - 8 \, b^{3} d^{3} - 14 \, a b^{2} d^{2} e - 35 \, a^{2} b d e^{2} + 105 \, a^{3} e^{3} - 3 \, {\left(29 \, b^{3} d e^{2} - 77 \, a b^{2} e^{3}\right)} x^{2} - 2 \, {\left(19 \, b^{3} d^{2} e + 49 \, a b^{2} d e^{2} - 140 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(b^{7} x^{3} + 3 \, a b^{6} x^{2} + 3 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}, -\frac{105 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(48 \, b^{3} e^{3} x^{3} - 8 \, b^{3} d^{3} - 14 \, a b^{2} d^{2} e - 35 \, a^{2} b d e^{2} + 105 \, a^{3} e^{3} - 3 \, {\left(29 \, b^{3} d e^{2} - 77 \, a b^{2} e^{3}\right)} x^{2} - 2 \, {\left(19 \, b^{3} d^{2} e + 49 \, a b^{2} d e^{2} - 140 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(b^{7} x^{3} + 3 \, a b^{6} x^{2} + 3 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}\right]"," ",0,"[1/48*(105*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(48*b^3*e^3*x^3 - 8*b^3*d^3 - 14*a*b^2*d^2*e - 35*a^2*b*d*e^2 + 105*a^3*e^3 - 3*(29*b^3*d*e^2 - 77*a*b^2*e^3)*x^2 - 2*(19*b^3*d^2*e + 49*a*b^2*d*e^2 - 140*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^7*x^3 + 3*a*b^6*x^2 + 3*a^2*b^5*x + a^3*b^4), -1/24*(105*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (48*b^3*e^3*x^3 - 8*b^3*d^3 - 14*a*b^2*d^2*e - 35*a^2*b*d*e^2 + 105*a^3*e^3 - 3*(29*b^3*d*e^2 - 77*a*b^2*e^3)*x^2 - 2*(19*b^3*d^2*e + 49*a*b^2*d*e^2 - 140*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^7*x^3 + 3*a*b^6*x^2 + 3*a^2*b^5*x + a^3*b^4)]","A",0
2139,1,563,0,0.454013," ","integrate((b*x+a)*(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(8 \, b^{4} d^{3} + 2 \, a b^{3} d^{2} e + 5 \, a^{2} b^{2} d e^{2} - 15 \, a^{3} b e^{3} + 33 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(13 \, b^{4} d^{2} e + 7 \, a b^{3} d e^{2} - 20 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d - a^{4} b^{4} e + {\left(b^{8} d - a b^{7} e\right)} x^{3} + 3 \, {\left(a b^{7} d - a^{2} b^{6} e\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d - a^{3} b^{5} e\right)} x\right)}}, \frac{15 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(8 \, b^{4} d^{3} + 2 \, a b^{3} d^{2} e + 5 \, a^{2} b^{2} d e^{2} - 15 \, a^{3} b e^{3} + 33 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(13 \, b^{4} d^{2} e + 7 \, a b^{3} d e^{2} - 20 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d - a^{4} b^{4} e + {\left(b^{8} d - a b^{7} e\right)} x^{3} + 3 \, {\left(a b^{7} d - a^{2} b^{6} e\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d - a^{3} b^{5} e\right)} x\right)}}\right]"," ",0,"[1/48*(15*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(8*b^4*d^3 + 2*a*b^3*d^2*e + 5*a^2*b^2*d*e^2 - 15*a^3*b*e^3 + 33*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(13*b^4*d^2*e + 7*a*b^3*d*e^2 - 20*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d - a^4*b^4*e + (b^8*d - a*b^7*e)*x^3 + 3*(a*b^7*d - a^2*b^6*e)*x^2 + 3*(a^2*b^6*d - a^3*b^5*e)*x), 1/24*(15*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (8*b^4*d^3 + 2*a*b^3*d^2*e + 5*a^2*b^2*d*e^2 - 15*a^3*b*e^3 + 33*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(13*b^4*d^2*e + 7*a*b^3*d*e^2 - 20*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d - a^4*b^4*e + (b^8*d - a*b^7*e)*x^3 + 3*(a*b^7*d - a^2*b^6*e)*x^2 + 3*(a^2*b^6*d - a^3*b^5*e)*x)]","A",0
2140,1,666,0,0.454325," ","integrate((b*x+a)*(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(8 \, b^{4} d^{3} - 10 \, a b^{3} d^{2} e - a^{2} b^{2} d e^{2} + 3 \, a^{3} b e^{3} + 3 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(7 \, b^{4} d^{2} e - 11 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d^{2} - 2 \, a^{4} b^{4} d e + a^{5} b^{3} e^{2} + {\left(b^{8} d^{2} - 2 \, a b^{7} d e + a^{2} b^{6} e^{2}\right)} x^{3} + 3 \, {\left(a b^{7} d^{2} - 2 \, a^{2} b^{6} d e + a^{3} b^{5} e^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{2} - 2 \, a^{3} b^{5} d e + a^{4} b^{4} e^{2}\right)} x\right)}}, -\frac{3 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(8 \, b^{4} d^{3} - 10 \, a b^{3} d^{2} e - a^{2} b^{2} d e^{2} + 3 \, a^{3} b e^{3} + 3 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(7 \, b^{4} d^{2} e - 11 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d^{2} - 2 \, a^{4} b^{4} d e + a^{5} b^{3} e^{2} + {\left(b^{8} d^{2} - 2 \, a b^{7} d e + a^{2} b^{6} e^{2}\right)} x^{3} + 3 \, {\left(a b^{7} d^{2} - 2 \, a^{2} b^{6} d e + a^{3} b^{5} e^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{2} - 2 \, a^{3} b^{5} d e + a^{4} b^{4} e^{2}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(8*b^4*d^3 - 10*a*b^3*d^2*e - a^2*b^2*d*e^2 + 3*a^3*b*e^3 + 3*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(7*b^4*d^2*e - 11*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^2 - 2*a^4*b^4*d*e + a^5*b^3*e^2 + (b^8*d^2 - 2*a*b^7*d*e + a^2*b^6*e^2)*x^3 + 3*(a*b^7*d^2 - 2*a^2*b^6*d*e + a^3*b^5*e^2)*x^2 + 3*(a^2*b^6*d^2 - 2*a^3*b^5*d*e + a^4*b^4*e^2)*x), -1/24*(3*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (8*b^4*d^3 - 10*a*b^3*d^2*e - a^2*b^2*d*e^2 + 3*a^3*b*e^3 + 3*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(7*b^4*d^2*e - 11*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^2 - 2*a^4*b^4*d*e + a^5*b^3*e^2 + (b^8*d^2 - 2*a*b^7*d*e + a^2*b^6*e^2)*x^3 + 3*(a*b^7*d^2 - 2*a^2*b^6*d*e + a^3*b^5*e^2)*x^2 + 3*(a^2*b^6*d^2 - 2*a^3*b^5*d*e + a^4*b^4*e^2)*x)]","B",0
2141,1,785,0,0.458629," ","integrate((b*x+a)*(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(8 \, b^{4} d^{3} - 22 \, a b^{3} d^{2} e + 17 \, a^{2} b^{2} d e^{2} - 3 \, a^{3} b e^{3} - 3 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(b^{4} d^{2} e - 5 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d^{3} - 3 \, a^{4} b^{4} d^{2} e + 3 \, a^{5} b^{3} d e^{2} - a^{6} b^{2} e^{3} + {\left(b^{8} d^{3} - 3 \, a b^{7} d^{2} e + 3 \, a^{2} b^{6} d e^{2} - a^{3} b^{5} e^{3}\right)} x^{3} + 3 \, {\left(a b^{7} d^{3} - 3 \, a^{2} b^{6} d^{2} e + 3 \, a^{3} b^{5} d e^{2} - a^{4} b^{4} e^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{3} - 3 \, a^{3} b^{5} d^{2} e + 3 \, a^{4} b^{4} d e^{2} - a^{5} b^{3} e^{3}\right)} x\right)}}, \frac{3 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(8 \, b^{4} d^{3} - 22 \, a b^{3} d^{2} e + 17 \, a^{2} b^{2} d e^{2} - 3 \, a^{3} b e^{3} - 3 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(b^{4} d^{2} e - 5 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d^{3} - 3 \, a^{4} b^{4} d^{2} e + 3 \, a^{5} b^{3} d e^{2} - a^{6} b^{2} e^{3} + {\left(b^{8} d^{3} - 3 \, a b^{7} d^{2} e + 3 \, a^{2} b^{6} d e^{2} - a^{3} b^{5} e^{3}\right)} x^{3} + 3 \, {\left(a b^{7} d^{3} - 3 \, a^{2} b^{6} d^{2} e + 3 \, a^{3} b^{5} d e^{2} - a^{4} b^{4} e^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{3} - 3 \, a^{3} b^{5} d^{2} e + 3 \, a^{4} b^{4} d e^{2} - a^{5} b^{3} e^{3}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(8*b^4*d^3 - 22*a*b^3*d^2*e + 17*a^2*b^2*d*e^2 - 3*a^3*b*e^3 - 3*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(b^4*d^2*e - 5*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^3 - 3*a^4*b^4*d^2*e + 3*a^5*b^3*d*e^2 - a^6*b^2*e^3 + (b^8*d^3 - 3*a*b^7*d^2*e + 3*a^2*b^6*d*e^2 - a^3*b^5*e^3)*x^3 + 3*(a*b^7*d^3 - 3*a^2*b^6*d^2*e + 3*a^3*b^5*d*e^2 - a^4*b^4*e^3)*x^2 + 3*(a^2*b^6*d^3 - 3*a^3*b^5*d^2*e + 3*a^4*b^4*d*e^2 - a^5*b^3*e^3)*x), 1/24*(3*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (8*b^4*d^3 - 22*a*b^3*d^2*e + 17*a^2*b^2*d*e^2 - 3*a^3*b*e^3 - 3*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(b^4*d^2*e - 5*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^3 - 3*a^4*b^4*d^2*e + 3*a^5*b^3*d*e^2 - a^6*b^2*e^3 + (b^8*d^3 - 3*a*b^7*d^2*e + 3*a^2*b^6*d*e^2 - a^3*b^5*e^3)*x^3 + 3*(a*b^7*d^3 - 3*a^2*b^6*d^2*e + 3*a^3*b^5*d*e^2 - a^4*b^4*e^3)*x^2 + 3*(a^2*b^6*d^3 - 3*a^3*b^5*d^2*e + 3*a^4*b^4*d*e^2 - a^5*b^3*e^3)*x)]","B",0
2142,1,884,0,0.450082," ","integrate((b*x+a)/(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(8 \, b^{4} d^{3} - 34 \, a b^{3} d^{2} e + 59 \, a^{2} b^{2} d e^{2} - 33 \, a^{3} b e^{3} + 15 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} - 10 \, {\left(b^{4} d^{2} e - 5 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d^{4} - 4 \, a^{4} b^{4} d^{3} e + 6 \, a^{5} b^{3} d^{2} e^{2} - 4 \, a^{6} b^{2} d e^{3} + a^{7} b e^{4} + {\left(b^{8} d^{4} - 4 \, a b^{7} d^{3} e + 6 \, a^{2} b^{6} d^{2} e^{2} - 4 \, a^{3} b^{5} d e^{3} + a^{4} b^{4} e^{4}\right)} x^{3} + 3 \, {\left(a b^{7} d^{4} - 4 \, a^{2} b^{6} d^{3} e + 6 \, a^{3} b^{5} d^{2} e^{2} - 4 \, a^{4} b^{4} d e^{3} + a^{5} b^{3} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{4} - 4 \, a^{3} b^{5} d^{3} e + 6 \, a^{4} b^{4} d^{2} e^{2} - 4 \, a^{5} b^{3} d e^{3} + a^{6} b^{2} e^{4}\right)} x\right)}}, -\frac{15 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(8 \, b^{4} d^{3} - 34 \, a b^{3} d^{2} e + 59 \, a^{2} b^{2} d e^{2} - 33 \, a^{3} b e^{3} + 15 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} - 10 \, {\left(b^{4} d^{2} e - 5 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d^{4} - 4 \, a^{4} b^{4} d^{3} e + 6 \, a^{5} b^{3} d^{2} e^{2} - 4 \, a^{6} b^{2} d e^{3} + a^{7} b e^{4} + {\left(b^{8} d^{4} - 4 \, a b^{7} d^{3} e + 6 \, a^{2} b^{6} d^{2} e^{2} - 4 \, a^{3} b^{5} d e^{3} + a^{4} b^{4} e^{4}\right)} x^{3} + 3 \, {\left(a b^{7} d^{4} - 4 \, a^{2} b^{6} d^{3} e + 6 \, a^{3} b^{5} d^{2} e^{2} - 4 \, a^{4} b^{4} d e^{3} + a^{5} b^{3} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{4} - 4 \, a^{3} b^{5} d^{3} e + 6 \, a^{4} b^{4} d^{2} e^{2} - 4 \, a^{5} b^{3} d e^{3} + a^{6} b^{2} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/48*(15*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(8*b^4*d^3 - 34*a*b^3*d^2*e + 59*a^2*b^2*d*e^2 - 33*a^3*b*e^3 + 15*(b^4*d*e^2 - a*b^3*e^3)*x^2 - 10*(b^4*d^2*e - 5*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^4 - 4*a^4*b^4*d^3*e + 6*a^5*b^3*d^2*e^2 - 4*a^6*b^2*d*e^3 + a^7*b*e^4 + (b^8*d^4 - 4*a*b^7*d^3*e + 6*a^2*b^6*d^2*e^2 - 4*a^3*b^5*d*e^3 + a^4*b^4*e^4)*x^3 + 3*(a*b^7*d^4 - 4*a^2*b^6*d^3*e + 6*a^3*b^5*d^2*e^2 - 4*a^4*b^4*d*e^3 + a^5*b^3*e^4)*x^2 + 3*(a^2*b^6*d^4 - 4*a^3*b^5*d^3*e + 6*a^4*b^4*d^2*e^2 - 4*a^5*b^3*d*e^3 + a^6*b^2*e^4)*x), -1/24*(15*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (8*b^4*d^3 - 34*a*b^3*d^2*e + 59*a^2*b^2*d*e^2 - 33*a^3*b*e^3 + 15*(b^4*d*e^2 - a*b^3*e^3)*x^2 - 10*(b^4*d^2*e - 5*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^4 - 4*a^4*b^4*d^3*e + 6*a^5*b^3*d^2*e^2 - 4*a^6*b^2*d*e^3 + a^7*b*e^4 + (b^8*d^4 - 4*a*b^7*d^3*e + 6*a^2*b^6*d^2*e^2 - 4*a^3*b^5*d*e^3 + a^4*b^4*e^4)*x^3 + 3*(a*b^7*d^4 - 4*a^2*b^6*d^3*e + 6*a^3*b^5*d^2*e^2 - 4*a^4*b^4*d*e^3 + a^5*b^3*e^4)*x^2 + 3*(a^2*b^6*d^4 - 4*a^3*b^5*d^3*e + 6*a^4*b^4*d^2*e^2 - 4*a^5*b^3*d*e^3 + a^6*b^2*e^4)*x)]","B",0
2143,1,1204,0,0.471282," ","integrate((b*x+a)/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} e^{4} x^{4} + a^{3} d e^{3} + {\left(b^{3} d e^{3} + 3 \, a b^{2} e^{4}\right)} x^{3} + 3 \, {\left(a b^{2} d e^{3} + a^{2} b e^{4}\right)} x^{2} + {\left(3 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(105 \, b^{3} e^{3} x^{3} + 8 \, b^{3} d^{3} - 38 \, a b^{2} d^{2} e + 87 \, a^{2} b d e^{2} + 48 \, a^{3} e^{3} + 35 \, {\left(b^{3} d e^{2} + 8 \, a b^{2} e^{3}\right)} x^{2} - 7 \, {\left(2 \, b^{3} d^{2} e - 14 \, a b^{2} d e^{2} - 33 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{4} d^{5} - 4 \, a^{4} b^{3} d^{4} e + 6 \, a^{5} b^{2} d^{3} e^{2} - 4 \, a^{6} b d^{2} e^{3} + a^{7} d e^{4} + {\left(b^{7} d^{4} e - 4 \, a b^{6} d^{3} e^{2} + 6 \, a^{2} b^{5} d^{2} e^{3} - 4 \, a^{3} b^{4} d e^{4} + a^{4} b^{3} e^{5}\right)} x^{4} + {\left(b^{7} d^{5} - a b^{6} d^{4} e - 6 \, a^{2} b^{5} d^{3} e^{2} + 14 \, a^{3} b^{4} d^{2} e^{3} - 11 \, a^{4} b^{3} d e^{4} + 3 \, a^{5} b^{2} e^{5}\right)} x^{3} + 3 \, {\left(a b^{6} d^{5} - 3 \, a^{2} b^{5} d^{4} e + 2 \, a^{3} b^{4} d^{3} e^{2} + 2 \, a^{4} b^{3} d^{2} e^{3} - 3 \, a^{5} b^{2} d e^{4} + a^{6} b e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{5} d^{5} - 11 \, a^{3} b^{4} d^{4} e + 14 \, a^{4} b^{3} d^{3} e^{2} - 6 \, a^{5} b^{2} d^{2} e^{3} - a^{6} b d e^{4} + a^{7} e^{5}\right)} x\right)}}, \frac{105 \, {\left(b^{3} e^{4} x^{4} + a^{3} d e^{3} + {\left(b^{3} d e^{3} + 3 \, a b^{2} e^{4}\right)} x^{3} + 3 \, {\left(a b^{2} d e^{3} + a^{2} b e^{4}\right)} x^{2} + {\left(3 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(105 \, b^{3} e^{3} x^{3} + 8 \, b^{3} d^{3} - 38 \, a b^{2} d^{2} e + 87 \, a^{2} b d e^{2} + 48 \, a^{3} e^{3} + 35 \, {\left(b^{3} d e^{2} + 8 \, a b^{2} e^{3}\right)} x^{2} - 7 \, {\left(2 \, b^{3} d^{2} e - 14 \, a b^{2} d e^{2} - 33 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{4} d^{5} - 4 \, a^{4} b^{3} d^{4} e + 6 \, a^{5} b^{2} d^{3} e^{2} - 4 \, a^{6} b d^{2} e^{3} + a^{7} d e^{4} + {\left(b^{7} d^{4} e - 4 \, a b^{6} d^{3} e^{2} + 6 \, a^{2} b^{5} d^{2} e^{3} - 4 \, a^{3} b^{4} d e^{4} + a^{4} b^{3} e^{5}\right)} x^{4} + {\left(b^{7} d^{5} - a b^{6} d^{4} e - 6 \, a^{2} b^{5} d^{3} e^{2} + 14 \, a^{3} b^{4} d^{2} e^{3} - 11 \, a^{4} b^{3} d e^{4} + 3 \, a^{5} b^{2} e^{5}\right)} x^{3} + 3 \, {\left(a b^{6} d^{5} - 3 \, a^{2} b^{5} d^{4} e + 2 \, a^{3} b^{4} d^{3} e^{2} + 2 \, a^{4} b^{3} d^{2} e^{3} - 3 \, a^{5} b^{2} d e^{4} + a^{6} b e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{5} d^{5} - 11 \, a^{3} b^{4} d^{4} e + 14 \, a^{4} b^{3} d^{3} e^{2} - 6 \, a^{5} b^{2} d^{2} e^{3} - a^{6} b d e^{4} + a^{7} e^{5}\right)} x\right)}}\right]"," ",0,"[1/48*(105*(b^3*e^4*x^4 + a^3*d*e^3 + (b^3*d*e^3 + 3*a*b^2*e^4)*x^3 + 3*(a*b^2*d*e^3 + a^2*b*e^4)*x^2 + (3*a^2*b*d*e^3 + a^3*e^4)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(105*b^3*e^3*x^3 + 8*b^3*d^3 - 38*a*b^2*d^2*e + 87*a^2*b*d*e^2 + 48*a^3*e^3 + 35*(b^3*d*e^2 + 8*a*b^2*e^3)*x^2 - 7*(2*b^3*d^2*e - 14*a*b^2*d*e^2 - 33*a^2*b*e^3)*x)*sqrt(e*x + d))/(a^3*b^4*d^5 - 4*a^4*b^3*d^4*e + 6*a^5*b^2*d^3*e^2 - 4*a^6*b*d^2*e^3 + a^7*d*e^4 + (b^7*d^4*e - 4*a*b^6*d^3*e^2 + 6*a^2*b^5*d^2*e^3 - 4*a^3*b^4*d*e^4 + a^4*b^3*e^5)*x^4 + (b^7*d^5 - a*b^6*d^4*e - 6*a^2*b^5*d^3*e^2 + 14*a^3*b^4*d^2*e^3 - 11*a^4*b^3*d*e^4 + 3*a^5*b^2*e^5)*x^3 + 3*(a*b^6*d^5 - 3*a^2*b^5*d^4*e + 2*a^3*b^4*d^3*e^2 + 2*a^4*b^3*d^2*e^3 - 3*a^5*b^2*d*e^4 + a^6*b*e^5)*x^2 + (3*a^2*b^5*d^5 - 11*a^3*b^4*d^4*e + 14*a^4*b^3*d^3*e^2 - 6*a^5*b^2*d^2*e^3 - a^6*b*d*e^4 + a^7*e^5)*x), 1/24*(105*(b^3*e^4*x^4 + a^3*d*e^3 + (b^3*d*e^3 + 3*a*b^2*e^4)*x^3 + 3*(a*b^2*d*e^3 + a^2*b*e^4)*x^2 + (3*a^2*b*d*e^3 + a^3*e^4)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (105*b^3*e^3*x^3 + 8*b^3*d^3 - 38*a*b^2*d^2*e + 87*a^2*b*d*e^2 + 48*a^3*e^3 + 35*(b^3*d*e^2 + 8*a*b^2*e^3)*x^2 - 7*(2*b^3*d^2*e - 14*a*b^2*d*e^2 - 33*a^2*b*e^3)*x)*sqrt(e*x + d))/(a^3*b^4*d^5 - 4*a^4*b^3*d^4*e + 6*a^5*b^2*d^3*e^2 - 4*a^6*b*d^2*e^3 + a^7*d*e^4 + (b^7*d^4*e - 4*a*b^6*d^3*e^2 + 6*a^2*b^5*d^2*e^3 - 4*a^3*b^4*d*e^4 + a^4*b^3*e^5)*x^4 + (b^7*d^5 - a*b^6*d^4*e - 6*a^2*b^5*d^3*e^2 + 14*a^3*b^4*d^2*e^3 - 11*a^4*b^3*d*e^4 + 3*a^5*b^2*e^5)*x^3 + 3*(a*b^6*d^5 - 3*a^2*b^5*d^4*e + 2*a^3*b^4*d^3*e^2 + 2*a^4*b^3*d^2*e^3 - 3*a^5*b^2*d*e^4 + a^6*b*e^5)*x^2 + (3*a^2*b^5*d^5 - 11*a^3*b^4*d^4*e + 14*a^4*b^3*d^3*e^2 - 6*a^5*b^2*d^2*e^3 - a^6*b*d*e^4 + a^7*e^5)*x)]","B",0
2144,1,1840,0,0.483889," ","integrate((b*x+a)/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{3} b d^{2} e^{3} + {\left(2 \, b^{4} d e^{4} + 3 \, a b^{3} e^{5}\right)} x^{4} + {\left(b^{4} d^{2} e^{3} + 6 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} x^{3} + {\left(3 \, a b^{3} d^{2} e^{3} + 6 \, a^{2} b^{2} d e^{4} + a^{3} b e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{2} d^{2} e^{3} + 2 \, a^{3} b d e^{4}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(315 \, b^{4} e^{4} x^{4} + 8 \, b^{4} d^{4} - 50 \, a b^{3} d^{3} e + 165 \, a^{2} b^{2} d^{2} e^{2} + 208 \, a^{3} b d e^{3} - 16 \, a^{4} e^{4} + 420 \, {\left(b^{4} d e^{3} + 2 \, a b^{3} e^{4}\right)} x^{3} + 63 \, {\left(b^{4} d^{2} e^{2} + 18 \, a b^{3} d e^{3} + 11 \, a^{2} b^{2} e^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{3} e - 10 \, a b^{3} d^{2} e^{2} - 53 \, a^{2} b^{2} d e^{3} - 8 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d^{7} - 5 \, a^{4} b^{4} d^{6} e + 10 \, a^{5} b^{3} d^{5} e^{2} - 10 \, a^{6} b^{2} d^{4} e^{3} + 5 \, a^{7} b d^{3} e^{4} - a^{8} d^{2} e^{5} + {\left(b^{8} d^{5} e^{2} - 5 \, a b^{7} d^{4} e^{3} + 10 \, a^{2} b^{6} d^{3} e^{4} - 10 \, a^{3} b^{5} d^{2} e^{5} + 5 \, a^{4} b^{4} d e^{6} - a^{5} b^{3} e^{7}\right)} x^{5} + {\left(2 \, b^{8} d^{6} e - 7 \, a b^{7} d^{5} e^{2} + 5 \, a^{2} b^{6} d^{4} e^{3} + 10 \, a^{3} b^{5} d^{3} e^{4} - 20 \, a^{4} b^{4} d^{2} e^{5} + 13 \, a^{5} b^{3} d e^{6} - 3 \, a^{6} b^{2} e^{7}\right)} x^{4} + {\left(b^{8} d^{7} + a b^{7} d^{6} e - 17 \, a^{2} b^{6} d^{5} e^{2} + 35 \, a^{3} b^{5} d^{4} e^{3} - 25 \, a^{4} b^{4} d^{3} e^{4} - a^{5} b^{3} d^{2} e^{5} + 9 \, a^{6} b^{2} d e^{6} - 3 \, a^{7} b e^{7}\right)} x^{3} + {\left(3 \, a b^{7} d^{7} - 9 \, a^{2} b^{6} d^{6} e + a^{3} b^{5} d^{5} e^{2} + 25 \, a^{4} b^{4} d^{4} e^{3} - 35 \, a^{5} b^{3} d^{3} e^{4} + 17 \, a^{6} b^{2} d^{2} e^{5} - a^{7} b d e^{6} - a^{8} e^{7}\right)} x^{2} + {\left(3 \, a^{2} b^{6} d^{7} - 13 \, a^{3} b^{5} d^{6} e + 20 \, a^{4} b^{4} d^{5} e^{2} - 10 \, a^{5} b^{3} d^{4} e^{3} - 5 \, a^{6} b^{2} d^{3} e^{4} + 7 \, a^{7} b d^{2} e^{5} - 2 \, a^{8} d e^{6}\right)} x\right)}}, \frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{3} b d^{2} e^{3} + {\left(2 \, b^{4} d e^{4} + 3 \, a b^{3} e^{5}\right)} x^{4} + {\left(b^{4} d^{2} e^{3} + 6 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} x^{3} + {\left(3 \, a b^{3} d^{2} e^{3} + 6 \, a^{2} b^{2} d e^{4} + a^{3} b e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{2} d^{2} e^{3} + 2 \, a^{3} b d e^{4}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(315 \, b^{4} e^{4} x^{4} + 8 \, b^{4} d^{4} - 50 \, a b^{3} d^{3} e + 165 \, a^{2} b^{2} d^{2} e^{2} + 208 \, a^{3} b d e^{3} - 16 \, a^{4} e^{4} + 420 \, {\left(b^{4} d e^{3} + 2 \, a b^{3} e^{4}\right)} x^{3} + 63 \, {\left(b^{4} d^{2} e^{2} + 18 \, a b^{3} d e^{3} + 11 \, a^{2} b^{2} e^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{3} e - 10 \, a b^{3} d^{2} e^{2} - 53 \, a^{2} b^{2} d e^{3} - 8 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d^{7} - 5 \, a^{4} b^{4} d^{6} e + 10 \, a^{5} b^{3} d^{5} e^{2} - 10 \, a^{6} b^{2} d^{4} e^{3} + 5 \, a^{7} b d^{3} e^{4} - a^{8} d^{2} e^{5} + {\left(b^{8} d^{5} e^{2} - 5 \, a b^{7} d^{4} e^{3} + 10 \, a^{2} b^{6} d^{3} e^{4} - 10 \, a^{3} b^{5} d^{2} e^{5} + 5 \, a^{4} b^{4} d e^{6} - a^{5} b^{3} e^{7}\right)} x^{5} + {\left(2 \, b^{8} d^{6} e - 7 \, a b^{7} d^{5} e^{2} + 5 \, a^{2} b^{6} d^{4} e^{3} + 10 \, a^{3} b^{5} d^{3} e^{4} - 20 \, a^{4} b^{4} d^{2} e^{5} + 13 \, a^{5} b^{3} d e^{6} - 3 \, a^{6} b^{2} e^{7}\right)} x^{4} + {\left(b^{8} d^{7} + a b^{7} d^{6} e - 17 \, a^{2} b^{6} d^{5} e^{2} + 35 \, a^{3} b^{5} d^{4} e^{3} - 25 \, a^{4} b^{4} d^{3} e^{4} - a^{5} b^{3} d^{2} e^{5} + 9 \, a^{6} b^{2} d e^{6} - 3 \, a^{7} b e^{7}\right)} x^{3} + {\left(3 \, a b^{7} d^{7} - 9 \, a^{2} b^{6} d^{6} e + a^{3} b^{5} d^{5} e^{2} + 25 \, a^{4} b^{4} d^{4} e^{3} - 35 \, a^{5} b^{3} d^{3} e^{4} + 17 \, a^{6} b^{2} d^{2} e^{5} - a^{7} b d e^{6} - a^{8} e^{7}\right)} x^{2} + {\left(3 \, a^{2} b^{6} d^{7} - 13 \, a^{3} b^{5} d^{6} e + 20 \, a^{4} b^{4} d^{5} e^{2} - 10 \, a^{5} b^{3} d^{4} e^{3} - 5 \, a^{6} b^{2} d^{3} e^{4} + 7 \, a^{7} b d^{2} e^{5} - 2 \, a^{8} d e^{6}\right)} x\right)}}\right]"," ",0,"[-1/48*(315*(b^4*e^5*x^5 + a^3*b*d^2*e^3 + (2*b^4*d*e^4 + 3*a*b^3*e^5)*x^4 + (b^4*d^2*e^3 + 6*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*x^3 + (3*a*b^3*d^2*e^3 + 6*a^2*b^2*d*e^4 + a^3*b*e^5)*x^2 + (3*a^2*b^2*d^2*e^3 + 2*a^3*b*d*e^4)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(315*b^4*e^4*x^4 + 8*b^4*d^4 - 50*a*b^3*d^3*e + 165*a^2*b^2*d^2*e^2 + 208*a^3*b*d*e^3 - 16*a^4*e^4 + 420*(b^4*d*e^3 + 2*a*b^3*e^4)*x^3 + 63*(b^4*d^2*e^2 + 18*a*b^3*d*e^3 + 11*a^2*b^2*e^4)*x^2 - 18*(b^4*d^3*e - 10*a*b^3*d^2*e^2 - 53*a^2*b^2*d*e^3 - 8*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^3*b^5*d^7 - 5*a^4*b^4*d^6*e + 10*a^5*b^3*d^5*e^2 - 10*a^6*b^2*d^4*e^3 + 5*a^7*b*d^3*e^4 - a^8*d^2*e^5 + (b^8*d^5*e^2 - 5*a*b^7*d^4*e^3 + 10*a^2*b^6*d^3*e^4 - 10*a^3*b^5*d^2*e^5 + 5*a^4*b^4*d*e^6 - a^5*b^3*e^7)*x^5 + (2*b^8*d^6*e - 7*a*b^7*d^5*e^2 + 5*a^2*b^6*d^4*e^3 + 10*a^3*b^5*d^3*e^4 - 20*a^4*b^4*d^2*e^5 + 13*a^5*b^3*d*e^6 - 3*a^6*b^2*e^7)*x^4 + (b^8*d^7 + a*b^7*d^6*e - 17*a^2*b^6*d^5*e^2 + 35*a^3*b^5*d^4*e^3 - 25*a^4*b^4*d^3*e^4 - a^5*b^3*d^2*e^5 + 9*a^6*b^2*d*e^6 - 3*a^7*b*e^7)*x^3 + (3*a*b^7*d^7 - 9*a^2*b^6*d^6*e + a^3*b^5*d^5*e^2 + 25*a^4*b^4*d^4*e^3 - 35*a^5*b^3*d^3*e^4 + 17*a^6*b^2*d^2*e^5 - a^7*b*d*e^6 - a^8*e^7)*x^2 + (3*a^2*b^6*d^7 - 13*a^3*b^5*d^6*e + 20*a^4*b^4*d^5*e^2 - 10*a^5*b^3*d^4*e^3 - 5*a^6*b^2*d^3*e^4 + 7*a^7*b*d^2*e^5 - 2*a^8*d*e^6)*x), 1/24*(315*(b^4*e^5*x^5 + a^3*b*d^2*e^3 + (2*b^4*d*e^4 + 3*a*b^3*e^5)*x^4 + (b^4*d^2*e^3 + 6*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*x^3 + (3*a*b^3*d^2*e^3 + 6*a^2*b^2*d*e^4 + a^3*b*e^5)*x^2 + (3*a^2*b^2*d^2*e^3 + 2*a^3*b*d*e^4)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (315*b^4*e^4*x^4 + 8*b^4*d^4 - 50*a*b^3*d^3*e + 165*a^2*b^2*d^2*e^2 + 208*a^3*b*d*e^3 - 16*a^4*e^4 + 420*(b^4*d*e^3 + 2*a*b^3*e^4)*x^3 + 63*(b^4*d^2*e^2 + 18*a*b^3*d*e^3 + 11*a^2*b^2*e^4)*x^2 - 18*(b^4*d^3*e - 10*a*b^3*d^2*e^2 - 53*a^2*b^2*d*e^3 - 8*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^3*b^5*d^7 - 5*a^4*b^4*d^6*e + 10*a^5*b^3*d^5*e^2 - 10*a^6*b^2*d^4*e^3 + 5*a^7*b*d^3*e^4 - a^8*d^2*e^5 + (b^8*d^5*e^2 - 5*a*b^7*d^4*e^3 + 10*a^2*b^6*d^3*e^4 - 10*a^3*b^5*d^2*e^5 + 5*a^4*b^4*d*e^6 - a^5*b^3*e^7)*x^5 + (2*b^8*d^6*e - 7*a*b^7*d^5*e^2 + 5*a^2*b^6*d^4*e^3 + 10*a^3*b^5*d^3*e^4 - 20*a^4*b^4*d^2*e^5 + 13*a^5*b^3*d*e^6 - 3*a^6*b^2*e^7)*x^4 + (b^8*d^7 + a*b^7*d^6*e - 17*a^2*b^6*d^5*e^2 + 35*a^3*b^5*d^4*e^3 - 25*a^4*b^4*d^3*e^4 - a^5*b^3*d^2*e^5 + 9*a^6*b^2*d*e^6 - 3*a^7*b*e^7)*x^3 + (3*a*b^7*d^7 - 9*a^2*b^6*d^6*e + a^3*b^5*d^5*e^2 + 25*a^4*b^4*d^4*e^3 - 35*a^5*b^3*d^3*e^4 + 17*a^6*b^2*d^2*e^5 - a^7*b*d*e^6 - a^8*e^7)*x^2 + (3*a^2*b^6*d^7 - 13*a^3*b^5*d^6*e + 20*a^4*b^4*d^5*e^2 - 10*a^5*b^3*d^4*e^3 - 5*a^6*b^2*d^3*e^4 + 7*a^7*b*d^2*e^5 - 2*a^8*d*e^6)*x)]","B",0
2145,1,2550,0,0.500587," ","integrate((b*x+a)/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{3} b^{2} d^{3} e^{3} + 3 \, {\left(b^{5} d e^{5} + a b^{4} e^{6}\right)} x^{5} + 3 \, {\left(b^{5} d^{2} e^{4} + 3 \, a b^{4} d e^{5} + a^{2} b^{3} e^{6}\right)} x^{4} + {\left(b^{5} d^{3} e^{3} + 9 \, a b^{4} d^{2} e^{4} + 9 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + 3 \, {\left(a b^{4} d^{3} e^{3} + 3 \, a^{2} b^{3} d^{2} e^{4} + a^{3} b^{2} d e^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} d^{3} e^{3} + a^{3} b^{2} d^{2} e^{4}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(3465 \, b^{5} e^{5} x^{5} + 40 \, b^{5} d^{5} - 310 \, a b^{4} d^{4} e + 1335 \, a^{2} b^{3} d^{3} e^{2} + 2768 \, a^{3} b^{2} d^{2} e^{3} - 416 \, a^{4} b d e^{4} + 48 \, a^{5} e^{5} + 1155 \, {\left(7 \, b^{5} d e^{4} + 8 \, a b^{4} e^{5}\right)} x^{4} + 231 \, {\left(23 \, b^{5} d^{2} e^{3} + 94 \, a b^{4} d e^{4} + 33 \, a^{2} b^{3} e^{5}\right)} x^{3} + 99 \, {\left(5 \, b^{5} d^{3} e^{2} + 146 \, a b^{4} d^{2} e^{3} + 183 \, a^{2} b^{3} d e^{4} + 16 \, a^{3} b^{2} e^{5}\right)} x^{2} - 11 \, {\left(10 \, b^{5} d^{4} e - 130 \, a b^{4} d^{3} e^{2} - 1119 \, a^{2} b^{3} d^{2} e^{3} - 352 \, a^{3} b^{2} d e^{4} + 16 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{240 \, {\left(a^{3} b^{6} d^{9} - 6 \, a^{4} b^{5} d^{8} e + 15 \, a^{5} b^{4} d^{7} e^{2} - 20 \, a^{6} b^{3} d^{6} e^{3} + 15 \, a^{7} b^{2} d^{5} e^{4} - 6 \, a^{8} b d^{4} e^{5} + a^{9} d^{3} e^{6} + {\left(b^{9} d^{6} e^{3} - 6 \, a b^{8} d^{5} e^{4} + 15 \, a^{2} b^{7} d^{4} e^{5} - 20 \, a^{3} b^{6} d^{3} e^{6} + 15 \, a^{4} b^{5} d^{2} e^{7} - 6 \, a^{5} b^{4} d e^{8} + a^{6} b^{3} e^{9}\right)} x^{6} + 3 \, {\left(b^{9} d^{7} e^{2} - 5 \, a b^{8} d^{6} e^{3} + 9 \, a^{2} b^{7} d^{5} e^{4} - 5 \, a^{3} b^{6} d^{4} e^{5} - 5 \, a^{4} b^{5} d^{3} e^{6} + 9 \, a^{5} b^{4} d^{2} e^{7} - 5 \, a^{6} b^{3} d e^{8} + a^{7} b^{2} e^{9}\right)} x^{5} + 3 \, {\left(b^{9} d^{8} e - 3 \, a b^{8} d^{7} e^{2} - 2 \, a^{2} b^{7} d^{6} e^{3} + 19 \, a^{3} b^{6} d^{5} e^{4} - 30 \, a^{4} b^{5} d^{4} e^{5} + 19 \, a^{5} b^{4} d^{3} e^{6} - 2 \, a^{6} b^{3} d^{2} e^{7} - 3 \, a^{7} b^{2} d e^{8} + a^{8} b e^{9}\right)} x^{4} + {\left(b^{9} d^{9} + 3 \, a b^{8} d^{8} e - 30 \, a^{2} b^{7} d^{7} e^{2} + 62 \, a^{3} b^{6} d^{6} e^{3} - 36 \, a^{4} b^{5} d^{5} e^{4} - 36 \, a^{5} b^{4} d^{4} e^{5} + 62 \, a^{6} b^{3} d^{3} e^{6} - 30 \, a^{7} b^{2} d^{2} e^{7} + 3 \, a^{8} b d e^{8} + a^{9} e^{9}\right)} x^{3} + 3 \, {\left(a b^{8} d^{9} - 3 \, a^{2} b^{7} d^{8} e - 2 \, a^{3} b^{6} d^{7} e^{2} + 19 \, a^{4} b^{5} d^{6} e^{3} - 30 \, a^{5} b^{4} d^{5} e^{4} + 19 \, a^{6} b^{3} d^{4} e^{5} - 2 \, a^{7} b^{2} d^{3} e^{6} - 3 \, a^{8} b d^{2} e^{7} + a^{9} d e^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{9} - 5 \, a^{3} b^{6} d^{8} e + 9 \, a^{4} b^{5} d^{7} e^{2} - 5 \, a^{5} b^{4} d^{6} e^{3} - 5 \, a^{6} b^{3} d^{5} e^{4} + 9 \, a^{7} b^{2} d^{4} e^{5} - 5 \, a^{8} b d^{3} e^{6} + a^{9} d^{2} e^{7}\right)} x\right)}}, \frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{3} b^{2} d^{3} e^{3} + 3 \, {\left(b^{5} d e^{5} + a b^{4} e^{6}\right)} x^{5} + 3 \, {\left(b^{5} d^{2} e^{4} + 3 \, a b^{4} d e^{5} + a^{2} b^{3} e^{6}\right)} x^{4} + {\left(b^{5} d^{3} e^{3} + 9 \, a b^{4} d^{2} e^{4} + 9 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + 3 \, {\left(a b^{4} d^{3} e^{3} + 3 \, a^{2} b^{3} d^{2} e^{4} + a^{3} b^{2} d e^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} d^{3} e^{3} + a^{3} b^{2} d^{2} e^{4}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3465 \, b^{5} e^{5} x^{5} + 40 \, b^{5} d^{5} - 310 \, a b^{4} d^{4} e + 1335 \, a^{2} b^{3} d^{3} e^{2} + 2768 \, a^{3} b^{2} d^{2} e^{3} - 416 \, a^{4} b d e^{4} + 48 \, a^{5} e^{5} + 1155 \, {\left(7 \, b^{5} d e^{4} + 8 \, a b^{4} e^{5}\right)} x^{4} + 231 \, {\left(23 \, b^{5} d^{2} e^{3} + 94 \, a b^{4} d e^{4} + 33 \, a^{2} b^{3} e^{5}\right)} x^{3} + 99 \, {\left(5 \, b^{5} d^{3} e^{2} + 146 \, a b^{4} d^{2} e^{3} + 183 \, a^{2} b^{3} d e^{4} + 16 \, a^{3} b^{2} e^{5}\right)} x^{2} - 11 \, {\left(10 \, b^{5} d^{4} e - 130 \, a b^{4} d^{3} e^{2} - 1119 \, a^{2} b^{3} d^{2} e^{3} - 352 \, a^{3} b^{2} d e^{4} + 16 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{120 \, {\left(a^{3} b^{6} d^{9} - 6 \, a^{4} b^{5} d^{8} e + 15 \, a^{5} b^{4} d^{7} e^{2} - 20 \, a^{6} b^{3} d^{6} e^{3} + 15 \, a^{7} b^{2} d^{5} e^{4} - 6 \, a^{8} b d^{4} e^{5} + a^{9} d^{3} e^{6} + {\left(b^{9} d^{6} e^{3} - 6 \, a b^{8} d^{5} e^{4} + 15 \, a^{2} b^{7} d^{4} e^{5} - 20 \, a^{3} b^{6} d^{3} e^{6} + 15 \, a^{4} b^{5} d^{2} e^{7} - 6 \, a^{5} b^{4} d e^{8} + a^{6} b^{3} e^{9}\right)} x^{6} + 3 \, {\left(b^{9} d^{7} e^{2} - 5 \, a b^{8} d^{6} e^{3} + 9 \, a^{2} b^{7} d^{5} e^{4} - 5 \, a^{3} b^{6} d^{4} e^{5} - 5 \, a^{4} b^{5} d^{3} e^{6} + 9 \, a^{5} b^{4} d^{2} e^{7} - 5 \, a^{6} b^{3} d e^{8} + a^{7} b^{2} e^{9}\right)} x^{5} + 3 \, {\left(b^{9} d^{8} e - 3 \, a b^{8} d^{7} e^{2} - 2 \, a^{2} b^{7} d^{6} e^{3} + 19 \, a^{3} b^{6} d^{5} e^{4} - 30 \, a^{4} b^{5} d^{4} e^{5} + 19 \, a^{5} b^{4} d^{3} e^{6} - 2 \, a^{6} b^{3} d^{2} e^{7} - 3 \, a^{7} b^{2} d e^{8} + a^{8} b e^{9}\right)} x^{4} + {\left(b^{9} d^{9} + 3 \, a b^{8} d^{8} e - 30 \, a^{2} b^{7} d^{7} e^{2} + 62 \, a^{3} b^{6} d^{6} e^{3} - 36 \, a^{4} b^{5} d^{5} e^{4} - 36 \, a^{5} b^{4} d^{4} e^{5} + 62 \, a^{6} b^{3} d^{3} e^{6} - 30 \, a^{7} b^{2} d^{2} e^{7} + 3 \, a^{8} b d e^{8} + a^{9} e^{9}\right)} x^{3} + 3 \, {\left(a b^{8} d^{9} - 3 \, a^{2} b^{7} d^{8} e - 2 \, a^{3} b^{6} d^{7} e^{2} + 19 \, a^{4} b^{5} d^{6} e^{3} - 30 \, a^{5} b^{4} d^{5} e^{4} + 19 \, a^{6} b^{3} d^{4} e^{5} - 2 \, a^{7} b^{2} d^{3} e^{6} - 3 \, a^{8} b d^{2} e^{7} + a^{9} d e^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{9} - 5 \, a^{3} b^{6} d^{8} e + 9 \, a^{4} b^{5} d^{7} e^{2} - 5 \, a^{5} b^{4} d^{6} e^{3} - 5 \, a^{6} b^{3} d^{5} e^{4} + 9 \, a^{7} b^{2} d^{4} e^{5} - 5 \, a^{8} b d^{3} e^{6} + a^{9} d^{2} e^{7}\right)} x\right)}}\right]"," ",0,"[1/240*(3465*(b^5*e^6*x^6 + a^3*b^2*d^3*e^3 + 3*(b^5*d*e^5 + a*b^4*e^6)*x^5 + 3*(b^5*d^2*e^4 + 3*a*b^4*d*e^5 + a^2*b^3*e^6)*x^4 + (b^5*d^3*e^3 + 9*a*b^4*d^2*e^4 + 9*a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + 3*(a*b^4*d^3*e^3 + 3*a^2*b^3*d^2*e^4 + a^3*b^2*d*e^5)*x^2 + 3*(a^2*b^3*d^3*e^3 + a^3*b^2*d^2*e^4)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(3465*b^5*e^5*x^5 + 40*b^5*d^5 - 310*a*b^4*d^4*e + 1335*a^2*b^3*d^3*e^2 + 2768*a^3*b^2*d^2*e^3 - 416*a^4*b*d*e^4 + 48*a^5*e^5 + 1155*(7*b^5*d*e^4 + 8*a*b^4*e^5)*x^4 + 231*(23*b^5*d^2*e^3 + 94*a*b^4*d*e^4 + 33*a^2*b^3*e^5)*x^3 + 99*(5*b^5*d^3*e^2 + 146*a*b^4*d^2*e^3 + 183*a^2*b^3*d*e^4 + 16*a^3*b^2*e^5)*x^2 - 11*(10*b^5*d^4*e - 130*a*b^4*d^3*e^2 - 1119*a^2*b^3*d^2*e^3 - 352*a^3*b^2*d*e^4 + 16*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^3*b^6*d^9 - 6*a^4*b^5*d^8*e + 15*a^5*b^4*d^7*e^2 - 20*a^6*b^3*d^6*e^3 + 15*a^7*b^2*d^5*e^4 - 6*a^8*b*d^4*e^5 + a^9*d^3*e^6 + (b^9*d^6*e^3 - 6*a*b^8*d^5*e^4 + 15*a^2*b^7*d^4*e^5 - 20*a^3*b^6*d^3*e^6 + 15*a^4*b^5*d^2*e^7 - 6*a^5*b^4*d*e^8 + a^6*b^3*e^9)*x^6 + 3*(b^9*d^7*e^2 - 5*a*b^8*d^6*e^3 + 9*a^2*b^7*d^5*e^4 - 5*a^3*b^6*d^4*e^5 - 5*a^4*b^5*d^3*e^6 + 9*a^5*b^4*d^2*e^7 - 5*a^6*b^3*d*e^8 + a^7*b^2*e^9)*x^5 + 3*(b^9*d^8*e - 3*a*b^8*d^7*e^2 - 2*a^2*b^7*d^6*e^3 + 19*a^3*b^6*d^5*e^4 - 30*a^4*b^5*d^4*e^5 + 19*a^5*b^4*d^3*e^6 - 2*a^6*b^3*d^2*e^7 - 3*a^7*b^2*d*e^8 + a^8*b*e^9)*x^4 + (b^9*d^9 + 3*a*b^8*d^8*e - 30*a^2*b^7*d^7*e^2 + 62*a^3*b^6*d^6*e^3 - 36*a^4*b^5*d^5*e^4 - 36*a^5*b^4*d^4*e^5 + 62*a^6*b^3*d^3*e^6 - 30*a^7*b^2*d^2*e^7 + 3*a^8*b*d*e^8 + a^9*e^9)*x^3 + 3*(a*b^8*d^9 - 3*a^2*b^7*d^8*e - 2*a^3*b^6*d^7*e^2 + 19*a^4*b^5*d^6*e^3 - 30*a^5*b^4*d^5*e^4 + 19*a^6*b^3*d^4*e^5 - 2*a^7*b^2*d^3*e^6 - 3*a^8*b*d^2*e^7 + a^9*d*e^8)*x^2 + 3*(a^2*b^7*d^9 - 5*a^3*b^6*d^8*e + 9*a^4*b^5*d^7*e^2 - 5*a^5*b^4*d^6*e^3 - 5*a^6*b^3*d^5*e^4 + 9*a^7*b^2*d^4*e^5 - 5*a^8*b*d^3*e^6 + a^9*d^2*e^7)*x), 1/120*(3465*(b^5*e^6*x^6 + a^3*b^2*d^3*e^3 + 3*(b^5*d*e^5 + a*b^4*e^6)*x^5 + 3*(b^5*d^2*e^4 + 3*a*b^4*d*e^5 + a^2*b^3*e^6)*x^4 + (b^5*d^3*e^3 + 9*a*b^4*d^2*e^4 + 9*a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + 3*(a*b^4*d^3*e^3 + 3*a^2*b^3*d^2*e^4 + a^3*b^2*d*e^5)*x^2 + 3*(a^2*b^3*d^3*e^3 + a^3*b^2*d^2*e^4)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3465*b^5*e^5*x^5 + 40*b^5*d^5 - 310*a*b^4*d^4*e + 1335*a^2*b^3*d^3*e^2 + 2768*a^3*b^2*d^2*e^3 - 416*a^4*b*d*e^4 + 48*a^5*e^5 + 1155*(7*b^5*d*e^4 + 8*a*b^4*e^5)*x^4 + 231*(23*b^5*d^2*e^3 + 94*a*b^4*d*e^4 + 33*a^2*b^3*e^5)*x^3 + 99*(5*b^5*d^3*e^2 + 146*a*b^4*d^2*e^3 + 183*a^2*b^3*d*e^4 + 16*a^3*b^2*e^5)*x^2 - 11*(10*b^5*d^4*e - 130*a*b^4*d^3*e^2 - 1119*a^2*b^3*d^2*e^3 - 352*a^3*b^2*d*e^4 + 16*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^3*b^6*d^9 - 6*a^4*b^5*d^8*e + 15*a^5*b^4*d^7*e^2 - 20*a^6*b^3*d^6*e^3 + 15*a^7*b^2*d^5*e^4 - 6*a^8*b*d^4*e^5 + a^9*d^3*e^6 + (b^9*d^6*e^3 - 6*a*b^8*d^5*e^4 + 15*a^2*b^7*d^4*e^5 - 20*a^3*b^6*d^3*e^6 + 15*a^4*b^5*d^2*e^7 - 6*a^5*b^4*d*e^8 + a^6*b^3*e^9)*x^6 + 3*(b^9*d^7*e^2 - 5*a*b^8*d^6*e^3 + 9*a^2*b^7*d^5*e^4 - 5*a^3*b^6*d^4*e^5 - 5*a^4*b^5*d^3*e^6 + 9*a^5*b^4*d^2*e^7 - 5*a^6*b^3*d*e^8 + a^7*b^2*e^9)*x^5 + 3*(b^9*d^8*e - 3*a*b^8*d^7*e^2 - 2*a^2*b^7*d^6*e^3 + 19*a^3*b^6*d^5*e^4 - 30*a^4*b^5*d^4*e^5 + 19*a^5*b^4*d^3*e^6 - 2*a^6*b^3*d^2*e^7 - 3*a^7*b^2*d*e^8 + a^8*b*e^9)*x^4 + (b^9*d^9 + 3*a*b^8*d^8*e - 30*a^2*b^7*d^7*e^2 + 62*a^3*b^6*d^6*e^3 - 36*a^4*b^5*d^5*e^4 - 36*a^5*b^4*d^4*e^5 + 62*a^6*b^3*d^3*e^6 - 30*a^7*b^2*d^2*e^7 + 3*a^8*b*d*e^8 + a^9*e^9)*x^3 + 3*(a*b^8*d^9 - 3*a^2*b^7*d^8*e - 2*a^3*b^6*d^7*e^2 + 19*a^4*b^5*d^6*e^3 - 30*a^5*b^4*d^5*e^4 + 19*a^6*b^3*d^4*e^5 - 2*a^7*b^2*d^3*e^6 - 3*a^8*b*d^2*e^7 + a^9*d*e^8)*x^2 + 3*(a^2*b^7*d^9 - 5*a^3*b^6*d^8*e + 9*a^4*b^5*d^7*e^2 - 5*a^5*b^4*d^6*e^3 - 5*a^6*b^3*d^5*e^4 + 9*a^7*b^2*d^4*e^5 - 5*a^8*b*d^3*e^6 + a^9*d^2*e^7)*x)]","B",0
2146,1,3201,0,0.482724," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{{\left(a^{7} d e^{7} m^{7} - 5040 \, b^{7} d^{8} + 40320 \, a b^{6} d^{7} e - 141120 \, a^{2} b^{5} d^{6} e^{2} + 282240 \, a^{3} b^{4} d^{5} e^{3} - 352800 \, a^{4} b^{3} d^{4} e^{4} + 282240 \, a^{5} b^{2} d^{3} e^{5} - 141120 \, a^{6} b d^{2} e^{6} + 40320 \, a^{7} d e^{7} + {\left(b^{7} e^{8} m^{7} + 28 \, b^{7} e^{8} m^{6} + 322 \, b^{7} e^{8} m^{5} + 1960 \, b^{7} e^{8} m^{4} + 6769 \, b^{7} e^{8} m^{3} + 13132 \, b^{7} e^{8} m^{2} + 13068 \, b^{7} e^{8} m + 5040 \, b^{7} e^{8}\right)} x^{8} + {\left(40320 \, a b^{6} e^{8} + {\left(b^{7} d e^{7} + 7 \, a b^{6} e^{8}\right)} m^{7} + 7 \, {\left(3 \, b^{7} d e^{7} + 29 \, a b^{6} e^{8}\right)} m^{6} + 7 \, {\left(25 \, b^{7} d e^{7} + 343 \, a b^{6} e^{8}\right)} m^{5} + 245 \, {\left(3 \, b^{7} d e^{7} + 61 \, a b^{6} e^{8}\right)} m^{4} + 56 \, {\left(29 \, b^{7} d e^{7} + 938 \, a b^{6} e^{8}\right)} m^{3} + 196 \, {\left(9 \, b^{7} d e^{7} + 527 \, a b^{6} e^{8}\right)} m^{2} + 144 \, {\left(5 \, b^{7} d e^{7} + 721 \, a b^{6} e^{8}\right)} m\right)} x^{7} - 7 \, {\left(a^{6} b d^{2} e^{6} - 5 \, a^{7} d e^{7}\right)} m^{6} + 7 \, {\left(20160 \, a^{2} b^{5} e^{8} + {\left(a b^{6} d e^{7} + 3 \, a^{2} b^{5} e^{8}\right)} m^{7} - {\left(b^{7} d^{2} e^{6} - 23 \, a b^{6} d e^{7} - 90 \, a^{2} b^{5} e^{8}\right)} m^{6} - {\left(15 \, b^{7} d^{2} e^{6} - 205 \, a b^{6} d e^{7} - 1098 \, a^{2} b^{5} e^{8}\right)} m^{5} - 5 \, {\left(17 \, b^{7} d^{2} e^{6} - 181 \, a b^{6} d e^{7} - 1404 \, a^{2} b^{5} e^{8}\right)} m^{4} - {\left(225 \, b^{7} d^{2} e^{6} - 2074 \, a b^{6} d e^{7} - 25227 \, a^{2} b^{5} e^{8}\right)} m^{3} - 2 \, {\left(137 \, b^{7} d^{2} e^{6} - 1156 \, a b^{6} d e^{7} - 25245 \, a^{2} b^{5} e^{8}\right)} m^{2} - 24 \, {\left(5 \, b^{7} d^{2} e^{6} - 40 \, a b^{6} d e^{7} - 2143 \, a^{2} b^{5} e^{8}\right)} m\right)} x^{6} + 7 \, {\left(6 \, a^{5} b^{2} d^{3} e^{5} - 33 \, a^{6} b d^{2} e^{6} + 73 \, a^{7} d e^{7}\right)} m^{5} + 7 \, {\left(40320 \, a^{3} b^{4} e^{8} + {\left(3 \, a^{2} b^{5} d e^{7} + 5 \, a^{3} b^{4} e^{8}\right)} m^{7} - {\left(6 \, a b^{6} d^{2} e^{6} - 75 \, a^{2} b^{5} d e^{7} - 155 \, a^{3} b^{4} e^{8}\right)} m^{6} + {\left(6 \, b^{7} d^{3} e^{5} - 108 \, a b^{6} d^{2} e^{6} + 723 \, a^{2} b^{5} d e^{7} + 1955 \, a^{3} b^{4} e^{8}\right)} m^{5} + 5 \, {\left(12 \, b^{7} d^{3} e^{5} - 138 \, a b^{6} d^{2} e^{6} + 681 \, a^{2} b^{5} d e^{7} + 2581 \, a^{3} b^{4} e^{8}\right)} m^{4} + 2 \, {\left(105 \, b^{7} d^{3} e^{5} - 990 \, a b^{6} d^{2} e^{6} + 4101 \, a^{2} b^{5} d e^{7} + 23860 \, a^{3} b^{4} e^{8}\right)} m^{3} + 4 \, {\left(75 \, b^{7} d^{3} e^{5} - 636 \, a b^{6} d^{2} e^{6} + 2370 \, a^{2} b^{5} d e^{7} + 24455 \, a^{3} b^{4} e^{8}\right)} m^{2} + 144 \, {\left(b^{7} d^{3} e^{5} - 8 \, a b^{6} d^{2} e^{6} + 28 \, a^{2} b^{5} d e^{7} + 705 \, a^{3} b^{4} e^{8}\right)} m\right)} x^{5} - 35 \, {\left(6 \, a^{4} b^{3} d^{4} e^{4} - 36 \, a^{5} b^{2} d^{3} e^{5} + 89 \, a^{6} b d^{2} e^{6} - 115 \, a^{7} d e^{7}\right)} m^{4} + 35 \, {\left(10080 \, a^{4} b^{3} e^{8} + {\left(a^{3} b^{4} d e^{7} + a^{4} b^{3} e^{8}\right)} m^{7} - {\left(3 \, a^{2} b^{5} d^{2} e^{6} - 27 \, a^{3} b^{4} d e^{7} - 32 \, a^{4} b^{3} e^{8}\right)} m^{6} + {\left(6 \, a b^{6} d^{3} e^{5} - 63 \, a^{2} b^{5} d^{2} e^{6} + 283 \, a^{3} b^{4} d e^{7} + 418 \, a^{4} b^{3} e^{8}\right)} m^{5} - {\left(6 \, b^{7} d^{4} e^{4} - 84 \, a b^{6} d^{3} e^{5} + 471 \, a^{2} b^{5} d^{2} e^{6} - 1449 \, a^{3} b^{4} d e^{7} - 2864 \, a^{4} b^{3} e^{8}\right)} m^{4} - {\left(36 \, b^{7} d^{4} e^{4} - 354 \, a b^{6} d^{3} e^{5} + 1521 \, a^{2} b^{5} d^{2} e^{6} - 3748 \, a^{3} b^{4} d e^{7} - 10993 \, a^{4} b^{3} e^{8}\right)} m^{3} - 2 \, {\left(33 \, b^{7} d^{4} e^{4} - 282 \, a b^{6} d^{3} e^{5} + 1059 \, a^{2} b^{5} d^{2} e^{6} - 2286 \, a^{3} b^{4} d e^{7} - 11656 \, a^{4} b^{3} e^{8}\right)} m^{2} - 36 \, {\left(b^{7} d^{4} e^{4} - 8 \, a b^{6} d^{3} e^{5} + 28 \, a^{2} b^{5} d^{2} e^{6} - 56 \, a^{3} b^{4} d e^{7} - 691 \, a^{4} b^{3} e^{8}\right)} m\right)} x^{4} + 7 \, {\left(120 \, a^{3} b^{4} d^{5} e^{3} - 780 \, a^{4} b^{3} d^{4} e^{4} + 2130 \, a^{5} b^{2} d^{3} e^{5} - 3135 \, a^{6} b d^{2} e^{6} + 2632 \, a^{7} d e^{7}\right)} m^{3} + 7 \, {\left(40320 \, a^{5} b^{2} e^{8} + {\left(5 \, a^{4} b^{3} d e^{7} + 3 \, a^{5} b^{2} e^{8}\right)} m^{7} - {\left(20 \, a^{3} b^{4} d^{2} e^{6} - 145 \, a^{4} b^{3} d e^{7} - 99 \, a^{5} b^{2} e^{8}\right)} m^{6} + {\left(60 \, a^{2} b^{5} d^{3} e^{5} - 480 \, a^{3} b^{4} d^{2} e^{6} + 1655 \, a^{4} b^{3} d e^{7} + 1341 \, a^{5} b^{2} e^{8}\right)} m^{5} - 5 \, {\left(24 \, a b^{6} d^{4} e^{4} - 216 \, a^{2} b^{5} d^{3} e^{5} + 844 \, a^{3} b^{4} d^{2} e^{6} - 1871 \, a^{4} b^{3} d e^{7} - 1917 \, a^{5} b^{2} e^{8}\right)} m^{4} + 4 \, {\left(30 \, b^{7} d^{5} e^{3} - 330 \, a b^{6} d^{4} e^{4} + 1545 \, a^{2} b^{5} d^{3} e^{5} - 4080 \, a^{3} b^{4} d^{2} e^{6} + 6725 \, a^{4} b^{3} d e^{7} + 9648 \, a^{5} b^{2} e^{8}\right)} m^{3} + 4 \, {\left(90 \, b^{7} d^{5} e^{3} - 780 \, a b^{6} d^{4} e^{4} + 2970 \, a^{2} b^{5} d^{3} e^{5} - 6500 \, a^{3} b^{4} d^{2} e^{6} + 8965 \, a^{4} b^{3} d e^{7} + 21519 \, a^{5} b^{2} e^{8}\right)} m^{2} + 48 \, {\left(5 \, b^{7} d^{5} e^{3} - 40 \, a b^{6} d^{4} e^{4} + 140 \, a^{2} b^{5} d^{3} e^{5} - 280 \, a^{3} b^{4} d^{2} e^{6} + 350 \, a^{4} b^{3} d e^{7} + 2003 \, a^{5} b^{2} e^{8}\right)} m\right)} x^{3} - 14 \, {\left(180 \, a^{2} b^{5} d^{6} e^{2} - 1260 \, a^{3} b^{4} d^{5} e^{3} + 3765 \, a^{4} b^{3} d^{4} e^{4} - 6210 \, a^{5} b^{2} d^{3} e^{5} + 6077 \, a^{6} b d^{2} e^{6} - 3490 \, a^{7} d e^{7}\right)} m^{2} + 7 \, {\left(20160 \, a^{6} b e^{8} + {\left(3 \, a^{5} b^{2} d e^{7} + a^{6} b e^{8}\right)} m^{7} - {\left(15 \, a^{4} b^{3} d^{2} e^{6} - 93 \, a^{5} b^{2} d e^{7} - 34 \, a^{6} b e^{8}\right)} m^{6} + {\left(60 \, a^{3} b^{4} d^{3} e^{5} - 405 \, a^{4} b^{3} d^{2} e^{6} + 1155 \, a^{5} b^{2} d e^{7} + 478 \, a^{6} b e^{8}\right)} m^{5} - 5 \, {\left(36 \, a^{2} b^{5} d^{4} e^{4} - 264 \, a^{3} b^{4} d^{3} e^{5} + 831 \, a^{4} b^{3} d^{2} e^{6} - 1455 \, a^{5} b^{2} d e^{7} - 716 \, a^{6} b e^{8}\right)} m^{4} + {\left(360 \, a b^{6} d^{5} e^{3} - 2880 \, a^{2} b^{5} d^{4} e^{4} + 10020 \, a^{3} b^{4} d^{3} e^{5} - 19755 \, a^{4} b^{3} d^{2} e^{6} + 24042 \, a^{5} b^{2} d e^{7} + 15289 \, a^{6} b e^{8}\right)} m^{3} - 2 \, {\left(180 \, b^{7} d^{6} e^{2} - 1620 \, a b^{6} d^{5} e^{3} + 6390 \, a^{2} b^{5} d^{4} e^{4} - 14460 \, a^{3} b^{4} d^{3} e^{5} + 20595 \, a^{4} b^{3} d^{2} e^{6} - 18996 \, a^{5} b^{2} d e^{7} - 18353 \, a^{6} b e^{8}\right)} m^{2} - 72 \, {\left(5 \, b^{7} d^{6} e^{2} - 40 \, a b^{6} d^{5} e^{3} + 140 \, a^{2} b^{5} d^{4} e^{4} - 280 \, a^{3} b^{4} d^{3} e^{5} + 350 \, a^{4} b^{3} d^{2} e^{6} - 280 \, a^{5} b^{2} d e^{7} - 621 \, a^{6} b e^{8}\right)} m\right)} x^{2} + 12 \, {\left(420 \, a b^{6} d^{7} e - 3150 \, a^{2} b^{5} d^{6} e^{2} + 10220 \, a^{3} b^{4} d^{5} e^{3} - 18655 \, a^{4} b^{3} d^{4} e^{4} + 20804 \, a^{5} b^{2} d^{3} e^{5} - 14322 \, a^{6} b d^{2} e^{6} + 5772 \, a^{7} d e^{7}\right)} m + {\left(40320 \, a^{7} e^{8} + {\left(7 \, a^{6} b d e^{7} + a^{7} e^{8}\right)} m^{7} - 7 \, {\left(6 \, a^{5} b^{2} d^{2} e^{6} - 33 \, a^{6} b d e^{7} - 5 \, a^{7} e^{8}\right)} m^{6} + 7 \, {\left(30 \, a^{4} b^{3} d^{3} e^{5} - 180 \, a^{5} b^{2} d^{2} e^{6} + 445 \, a^{6} b d e^{7} + 73 \, a^{7} e^{8}\right)} m^{5} - 35 \, {\left(24 \, a^{3} b^{4} d^{4} e^{4} - 156 \, a^{4} b^{3} d^{3} e^{5} + 426 \, a^{5} b^{2} d^{2} e^{6} - 627 \, a^{6} b d e^{7} - 115 \, a^{7} e^{8}\right)} m^{4} + 14 \, {\left(180 \, a^{2} b^{5} d^{5} e^{3} - 1260 \, a^{3} b^{4} d^{4} e^{4} + 3765 \, a^{4} b^{3} d^{3} e^{5} - 6210 \, a^{5} b^{2} d^{2} e^{6} + 6077 \, a^{6} b d e^{7} + 1316 \, a^{7} e^{8}\right)} m^{3} - 28 \, {\left(180 \, a b^{6} d^{6} e^{2} - 1350 \, a^{2} b^{5} d^{5} e^{3} + 4380 \, a^{3} b^{4} d^{4} e^{4} - 7995 \, a^{4} b^{3} d^{3} e^{5} + 8916 \, a^{5} b^{2} d^{2} e^{6} - 6138 \, a^{6} b d e^{7} - 1745 \, a^{7} e^{8}\right)} m^{2} + 144 \, {\left(35 \, b^{7} d^{7} e - 280 \, a b^{6} d^{6} e^{2} + 980 \, a^{2} b^{5} d^{5} e^{3} - 1960 \, a^{3} b^{4} d^{4} e^{4} + 2450 \, a^{4} b^{3} d^{3} e^{5} - 1960 \, a^{5} b^{2} d^{2} e^{6} + 980 \, a^{6} b d e^{7} + 481 \, a^{7} e^{8}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{8} m^{8} + 36 \, e^{8} m^{7} + 546 \, e^{8} m^{6} + 4536 \, e^{8} m^{5} + 22449 \, e^{8} m^{4} + 67284 \, e^{8} m^{3} + 118124 \, e^{8} m^{2} + 109584 \, e^{8} m + 40320 \, e^{8}}"," ",0,"(a^7*d*e^7*m^7 - 5040*b^7*d^8 + 40320*a*b^6*d^7*e - 141120*a^2*b^5*d^6*e^2 + 282240*a^3*b^4*d^5*e^3 - 352800*a^4*b^3*d^4*e^4 + 282240*a^5*b^2*d^3*e^5 - 141120*a^6*b*d^2*e^6 + 40320*a^7*d*e^7 + (b^7*e^8*m^7 + 28*b^7*e^8*m^6 + 322*b^7*e^8*m^5 + 1960*b^7*e^8*m^4 + 6769*b^7*e^8*m^3 + 13132*b^7*e^8*m^2 + 13068*b^7*e^8*m + 5040*b^7*e^8)*x^8 + (40320*a*b^6*e^8 + (b^7*d*e^7 + 7*a*b^6*e^8)*m^7 + 7*(3*b^7*d*e^7 + 29*a*b^6*e^8)*m^6 + 7*(25*b^7*d*e^7 + 343*a*b^6*e^8)*m^5 + 245*(3*b^7*d*e^7 + 61*a*b^6*e^8)*m^4 + 56*(29*b^7*d*e^7 + 938*a*b^6*e^8)*m^3 + 196*(9*b^7*d*e^7 + 527*a*b^6*e^8)*m^2 + 144*(5*b^7*d*e^7 + 721*a*b^6*e^8)*m)*x^7 - 7*(a^6*b*d^2*e^6 - 5*a^7*d*e^7)*m^6 + 7*(20160*a^2*b^5*e^8 + (a*b^6*d*e^7 + 3*a^2*b^5*e^8)*m^7 - (b^7*d^2*e^6 - 23*a*b^6*d*e^7 - 90*a^2*b^5*e^8)*m^6 - (15*b^7*d^2*e^6 - 205*a*b^6*d*e^7 - 1098*a^2*b^5*e^8)*m^5 - 5*(17*b^7*d^2*e^6 - 181*a*b^6*d*e^7 - 1404*a^2*b^5*e^8)*m^4 - (225*b^7*d^2*e^6 - 2074*a*b^6*d*e^7 - 25227*a^2*b^5*e^8)*m^3 - 2*(137*b^7*d^2*e^6 - 1156*a*b^6*d*e^7 - 25245*a^2*b^5*e^8)*m^2 - 24*(5*b^7*d^2*e^6 - 40*a*b^6*d*e^7 - 2143*a^2*b^5*e^8)*m)*x^6 + 7*(6*a^5*b^2*d^3*e^5 - 33*a^6*b*d^2*e^6 + 73*a^7*d*e^7)*m^5 + 7*(40320*a^3*b^4*e^8 + (3*a^2*b^5*d*e^7 + 5*a^3*b^4*e^8)*m^7 - (6*a*b^6*d^2*e^6 - 75*a^2*b^5*d*e^7 - 155*a^3*b^4*e^8)*m^6 + (6*b^7*d^3*e^5 - 108*a*b^6*d^2*e^6 + 723*a^2*b^5*d*e^7 + 1955*a^3*b^4*e^8)*m^5 + 5*(12*b^7*d^3*e^5 - 138*a*b^6*d^2*e^6 + 681*a^2*b^5*d*e^7 + 2581*a^3*b^4*e^8)*m^4 + 2*(105*b^7*d^3*e^5 - 990*a*b^6*d^2*e^6 + 4101*a^2*b^5*d*e^7 + 23860*a^3*b^4*e^8)*m^3 + 4*(75*b^7*d^3*e^5 - 636*a*b^6*d^2*e^6 + 2370*a^2*b^5*d*e^7 + 24455*a^3*b^4*e^8)*m^2 + 144*(b^7*d^3*e^5 - 8*a*b^6*d^2*e^6 + 28*a^2*b^5*d*e^7 + 705*a^3*b^4*e^8)*m)*x^5 - 35*(6*a^4*b^3*d^4*e^4 - 36*a^5*b^2*d^3*e^5 + 89*a^6*b*d^2*e^6 - 115*a^7*d*e^7)*m^4 + 35*(10080*a^4*b^3*e^8 + (a^3*b^4*d*e^7 + a^4*b^3*e^8)*m^7 - (3*a^2*b^5*d^2*e^6 - 27*a^3*b^4*d*e^7 - 32*a^4*b^3*e^8)*m^6 + (6*a*b^6*d^3*e^5 - 63*a^2*b^5*d^2*e^6 + 283*a^3*b^4*d*e^7 + 418*a^4*b^3*e^8)*m^5 - (6*b^7*d^4*e^4 - 84*a*b^6*d^3*e^5 + 471*a^2*b^5*d^2*e^6 - 1449*a^3*b^4*d*e^7 - 2864*a^4*b^3*e^8)*m^4 - (36*b^7*d^4*e^4 - 354*a*b^6*d^3*e^5 + 1521*a^2*b^5*d^2*e^6 - 3748*a^3*b^4*d*e^7 - 10993*a^4*b^3*e^8)*m^3 - 2*(33*b^7*d^4*e^4 - 282*a*b^6*d^3*e^5 + 1059*a^2*b^5*d^2*e^6 - 2286*a^3*b^4*d*e^7 - 11656*a^4*b^3*e^8)*m^2 - 36*(b^7*d^4*e^4 - 8*a*b^6*d^3*e^5 + 28*a^2*b^5*d^2*e^6 - 56*a^3*b^4*d*e^7 - 691*a^4*b^3*e^8)*m)*x^4 + 7*(120*a^3*b^4*d^5*e^3 - 780*a^4*b^3*d^4*e^4 + 2130*a^5*b^2*d^3*e^5 - 3135*a^6*b*d^2*e^6 + 2632*a^7*d*e^7)*m^3 + 7*(40320*a^5*b^2*e^8 + (5*a^4*b^3*d*e^7 + 3*a^5*b^2*e^8)*m^7 - (20*a^3*b^4*d^2*e^6 - 145*a^4*b^3*d*e^7 - 99*a^5*b^2*e^8)*m^6 + (60*a^2*b^5*d^3*e^5 - 480*a^3*b^4*d^2*e^6 + 1655*a^4*b^3*d*e^7 + 1341*a^5*b^2*e^8)*m^5 - 5*(24*a*b^6*d^4*e^4 - 216*a^2*b^5*d^3*e^5 + 844*a^3*b^4*d^2*e^6 - 1871*a^4*b^3*d*e^7 - 1917*a^5*b^2*e^8)*m^4 + 4*(30*b^7*d^5*e^3 - 330*a*b^6*d^4*e^4 + 1545*a^2*b^5*d^3*e^5 - 4080*a^3*b^4*d^2*e^6 + 6725*a^4*b^3*d*e^7 + 9648*a^5*b^2*e^8)*m^3 + 4*(90*b^7*d^5*e^3 - 780*a*b^6*d^4*e^4 + 2970*a^2*b^5*d^3*e^5 - 6500*a^3*b^4*d^2*e^6 + 8965*a^4*b^3*d*e^7 + 21519*a^5*b^2*e^8)*m^2 + 48*(5*b^7*d^5*e^3 - 40*a*b^6*d^4*e^4 + 140*a^2*b^5*d^3*e^5 - 280*a^3*b^4*d^2*e^6 + 350*a^4*b^3*d*e^7 + 2003*a^5*b^2*e^8)*m)*x^3 - 14*(180*a^2*b^5*d^6*e^2 - 1260*a^3*b^4*d^5*e^3 + 3765*a^4*b^3*d^4*e^4 - 6210*a^5*b^2*d^3*e^5 + 6077*a^6*b*d^2*e^6 - 3490*a^7*d*e^7)*m^2 + 7*(20160*a^6*b*e^8 + (3*a^5*b^2*d*e^7 + a^6*b*e^8)*m^7 - (15*a^4*b^3*d^2*e^6 - 93*a^5*b^2*d*e^7 - 34*a^6*b*e^8)*m^6 + (60*a^3*b^4*d^3*e^5 - 405*a^4*b^3*d^2*e^6 + 1155*a^5*b^2*d*e^7 + 478*a^6*b*e^8)*m^5 - 5*(36*a^2*b^5*d^4*e^4 - 264*a^3*b^4*d^3*e^5 + 831*a^4*b^3*d^2*e^6 - 1455*a^5*b^2*d*e^7 - 716*a^6*b*e^8)*m^4 + (360*a*b^6*d^5*e^3 - 2880*a^2*b^5*d^4*e^4 + 10020*a^3*b^4*d^3*e^5 - 19755*a^4*b^3*d^2*e^6 + 24042*a^5*b^2*d*e^7 + 15289*a^6*b*e^8)*m^3 - 2*(180*b^7*d^6*e^2 - 1620*a*b^6*d^5*e^3 + 6390*a^2*b^5*d^4*e^4 - 14460*a^3*b^4*d^3*e^5 + 20595*a^4*b^3*d^2*e^6 - 18996*a^5*b^2*d*e^7 - 18353*a^6*b*e^8)*m^2 - 72*(5*b^7*d^6*e^2 - 40*a*b^6*d^5*e^3 + 140*a^2*b^5*d^4*e^4 - 280*a^3*b^4*d^3*e^5 + 350*a^4*b^3*d^2*e^6 - 280*a^5*b^2*d*e^7 - 621*a^6*b*e^8)*m)*x^2 + 12*(420*a*b^6*d^7*e - 3150*a^2*b^5*d^6*e^2 + 10220*a^3*b^4*d^5*e^3 - 18655*a^4*b^3*d^4*e^4 + 20804*a^5*b^2*d^3*e^5 - 14322*a^6*b*d^2*e^6 + 5772*a^7*d*e^7)*m + (40320*a^7*e^8 + (7*a^6*b*d*e^7 + a^7*e^8)*m^7 - 7*(6*a^5*b^2*d^2*e^6 - 33*a^6*b*d*e^7 - 5*a^7*e^8)*m^6 + 7*(30*a^4*b^3*d^3*e^5 - 180*a^5*b^2*d^2*e^6 + 445*a^6*b*d*e^7 + 73*a^7*e^8)*m^5 - 35*(24*a^3*b^4*d^4*e^4 - 156*a^4*b^3*d^3*e^5 + 426*a^5*b^2*d^2*e^6 - 627*a^6*b*d*e^7 - 115*a^7*e^8)*m^4 + 14*(180*a^2*b^5*d^5*e^3 - 1260*a^3*b^4*d^4*e^4 + 3765*a^4*b^3*d^3*e^5 - 6210*a^5*b^2*d^2*e^6 + 6077*a^6*b*d*e^7 + 1316*a^7*e^8)*m^3 - 28*(180*a*b^6*d^6*e^2 - 1350*a^2*b^5*d^5*e^3 + 4380*a^3*b^4*d^4*e^4 - 7995*a^4*b^3*d^3*e^5 + 8916*a^5*b^2*d^2*e^6 - 6138*a^6*b*d*e^7 - 1745*a^7*e^8)*m^2 + 144*(35*b^7*d^7*e - 280*a*b^6*d^6*e^2 + 980*a^2*b^5*d^5*e^3 - 1960*a^3*b^4*d^4*e^4 + 2450*a^4*b^3*d^3*e^5 - 1960*a^5*b^2*d^2*e^6 + 980*a^6*b*d*e^7 + 481*a^7*e^8)*m)*x)*(e*x + d)^m/(e^8*m^8 + 36*e^8*m^7 + 546*e^8*m^6 + 4536*e^8*m^5 + 22449*e^8*m^4 + 67284*e^8*m^3 + 118124*e^8*m^2 + 109584*e^8*m + 40320*e^8)","B",0
2147,1,1460,0,0.470391," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{{\left(a^{5} d e^{5} m^{5} - 120 \, b^{5} d^{6} + 720 \, a b^{4} d^{5} e - 1800 \, a^{2} b^{3} d^{4} e^{2} + 2400 \, a^{3} b^{2} d^{3} e^{3} - 1800 \, a^{4} b d^{2} e^{4} + 720 \, a^{5} d e^{5} + {\left(b^{5} e^{6} m^{5} + 15 \, b^{5} e^{6} m^{4} + 85 \, b^{5} e^{6} m^{3} + 225 \, b^{5} e^{6} m^{2} + 274 \, b^{5} e^{6} m + 120 \, b^{5} e^{6}\right)} x^{6} + {\left(720 \, a b^{4} e^{6} + {\left(b^{5} d e^{5} + 5 \, a b^{4} e^{6}\right)} m^{5} + 10 \, {\left(b^{5} d e^{5} + 8 \, a b^{4} e^{6}\right)} m^{4} + 5 \, {\left(7 \, b^{5} d e^{5} + 95 \, a b^{4} e^{6}\right)} m^{3} + 50 \, {\left(b^{5} d e^{5} + 26 \, a b^{4} e^{6}\right)} m^{2} + 12 \, {\left(2 \, b^{5} d e^{5} + 135 \, a b^{4} e^{6}\right)} m\right)} x^{5} - 5 \, {\left(a^{4} b d^{2} e^{4} - 4 \, a^{5} d e^{5}\right)} m^{4} + 5 \, {\left(360 \, a^{2} b^{3} e^{6} + {\left(a b^{4} d e^{5} + 2 \, a^{2} b^{3} e^{6}\right)} m^{5} - {\left(b^{5} d^{2} e^{4} - 12 \, a b^{4} d e^{5} - 34 \, a^{2} b^{3} e^{6}\right)} m^{4} - {\left(6 \, b^{5} d^{2} e^{4} - 47 \, a b^{4} d e^{5} - 214 \, a^{2} b^{3} e^{6}\right)} m^{3} - {\left(11 \, b^{5} d^{2} e^{4} - 72 \, a b^{4} d e^{5} - 614 \, a^{2} b^{3} e^{6}\right)} m^{2} - 6 \, {\left(b^{5} d^{2} e^{4} - 6 \, a b^{4} d e^{5} - 132 \, a^{2} b^{3} e^{6}\right)} m\right)} x^{4} + 5 \, {\left(4 \, a^{3} b^{2} d^{3} e^{3} - 18 \, a^{4} b d^{2} e^{4} + 31 \, a^{5} d e^{5}\right)} m^{3} + 10 \, {\left(240 \, a^{3} b^{2} e^{6} + {\left(a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} m^{5} - 2 \, {\left(a b^{4} d^{2} e^{4} - 7 \, a^{2} b^{3} d e^{5} - 9 \, a^{3} b^{2} e^{6}\right)} m^{4} + {\left(2 \, b^{5} d^{3} e^{3} - 18 \, a b^{4} d^{2} e^{4} + 65 \, a^{2} b^{3} d e^{5} + 121 \, a^{3} b^{2} e^{6}\right)} m^{3} + 2 \, {\left(3 \, b^{5} d^{3} e^{3} - 20 \, a b^{4} d^{2} e^{4} + 56 \, a^{2} b^{3} d e^{5} + 186 \, a^{3} b^{2} e^{6}\right)} m^{2} + 4 \, {\left(b^{5} d^{3} e^{3} - 6 \, a b^{4} d^{2} e^{4} + 15 \, a^{2} b^{3} d e^{5} + 127 \, a^{3} b^{2} e^{6}\right)} m\right)} x^{3} - 5 \, {\left(12 \, a^{2} b^{3} d^{4} e^{2} - 60 \, a^{3} b^{2} d^{3} e^{3} + 119 \, a^{4} b d^{2} e^{4} - 116 \, a^{5} d e^{5}\right)} m^{2} + 5 \, {\left(360 \, a^{4} b e^{6} + {\left(2 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} m^{5} - {\left(6 \, a^{2} b^{3} d^{2} e^{4} - 32 \, a^{3} b^{2} d e^{5} - 19 \, a^{4} b e^{6}\right)} m^{4} + {\left(12 \, a b^{4} d^{3} e^{3} - 72 \, a^{2} b^{3} d^{2} e^{4} + 178 \, a^{3} b^{2} d e^{5} + 137 \, a^{4} b e^{6}\right)} m^{3} - {\left(12 \, b^{5} d^{4} e^{2} - 84 \, a b^{4} d^{3} e^{3} + 246 \, a^{2} b^{3} d^{2} e^{4} - 388 \, a^{3} b^{2} d e^{5} - 461 \, a^{4} b e^{6}\right)} m^{2} - 6 \, {\left(2 \, b^{5} d^{4} e^{2} - 12 \, a b^{4} d^{3} e^{3} + 30 \, a^{2} b^{3} d^{2} e^{4} - 40 \, a^{3} b^{2} d e^{5} - 117 \, a^{4} b e^{6}\right)} m\right)} x^{2} + 2 \, {\left(60 \, a b^{4} d^{5} e - 330 \, a^{2} b^{3} d^{4} e^{2} + 740 \, a^{3} b^{2} d^{3} e^{3} - 855 \, a^{4} b d^{2} e^{4} + 522 \, a^{5} d e^{5}\right)} m + {\left(720 \, a^{5} e^{6} + {\left(5 \, a^{4} b d e^{5} + a^{5} e^{6}\right)} m^{5} - 10 \, {\left(2 \, a^{3} b^{2} d^{2} e^{4} - 9 \, a^{4} b d e^{5} - 2 \, a^{5} e^{6}\right)} m^{4} + 5 \, {\left(12 \, a^{2} b^{3} d^{3} e^{3} - 60 \, a^{3} b^{2} d^{2} e^{4} + 119 \, a^{4} b d e^{5} + 31 \, a^{5} e^{6}\right)} m^{3} - 10 \, {\left(12 \, a b^{4} d^{4} e^{2} - 66 \, a^{2} b^{3} d^{3} e^{3} + 148 \, a^{3} b^{2} d^{2} e^{4} - 171 \, a^{4} b d e^{5} - 58 \, a^{5} e^{6}\right)} m^{2} + 12 \, {\left(10 \, b^{5} d^{5} e - 60 \, a b^{4} d^{4} e^{2} + 150 \, a^{2} b^{3} d^{3} e^{3} - 200 \, a^{3} b^{2} d^{2} e^{4} + 150 \, a^{4} b d e^{5} + 87 \, a^{5} e^{6}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{6} m^{6} + 21 \, e^{6} m^{5} + 175 \, e^{6} m^{4} + 735 \, e^{6} m^{3} + 1624 \, e^{6} m^{2} + 1764 \, e^{6} m + 720 \, e^{6}}"," ",0,"(a^5*d*e^5*m^5 - 120*b^5*d^6 + 720*a*b^4*d^5*e - 1800*a^2*b^3*d^4*e^2 + 2400*a^3*b^2*d^3*e^3 - 1800*a^4*b*d^2*e^4 + 720*a^5*d*e^5 + (b^5*e^6*m^5 + 15*b^5*e^6*m^4 + 85*b^5*e^6*m^3 + 225*b^5*e^6*m^2 + 274*b^5*e^6*m + 120*b^5*e^6)*x^6 + (720*a*b^4*e^6 + (b^5*d*e^5 + 5*a*b^4*e^6)*m^5 + 10*(b^5*d*e^5 + 8*a*b^4*e^6)*m^4 + 5*(7*b^5*d*e^5 + 95*a*b^4*e^6)*m^3 + 50*(b^5*d*e^5 + 26*a*b^4*e^6)*m^2 + 12*(2*b^5*d*e^5 + 135*a*b^4*e^6)*m)*x^5 - 5*(a^4*b*d^2*e^4 - 4*a^5*d*e^5)*m^4 + 5*(360*a^2*b^3*e^6 + (a*b^4*d*e^5 + 2*a^2*b^3*e^6)*m^5 - (b^5*d^2*e^4 - 12*a*b^4*d*e^5 - 34*a^2*b^3*e^6)*m^4 - (6*b^5*d^2*e^4 - 47*a*b^4*d*e^5 - 214*a^2*b^3*e^6)*m^3 - (11*b^5*d^2*e^4 - 72*a*b^4*d*e^5 - 614*a^2*b^3*e^6)*m^2 - 6*(b^5*d^2*e^4 - 6*a*b^4*d*e^5 - 132*a^2*b^3*e^6)*m)*x^4 + 5*(4*a^3*b^2*d^3*e^3 - 18*a^4*b*d^2*e^4 + 31*a^5*d*e^5)*m^3 + 10*(240*a^3*b^2*e^6 + (a^2*b^3*d*e^5 + a^3*b^2*e^6)*m^5 - 2*(a*b^4*d^2*e^4 - 7*a^2*b^3*d*e^5 - 9*a^3*b^2*e^6)*m^4 + (2*b^5*d^3*e^3 - 18*a*b^4*d^2*e^4 + 65*a^2*b^3*d*e^5 + 121*a^3*b^2*e^6)*m^3 + 2*(3*b^5*d^3*e^3 - 20*a*b^4*d^2*e^4 + 56*a^2*b^3*d*e^5 + 186*a^3*b^2*e^6)*m^2 + 4*(b^5*d^3*e^3 - 6*a*b^4*d^2*e^4 + 15*a^2*b^3*d*e^5 + 127*a^3*b^2*e^6)*m)*x^3 - 5*(12*a^2*b^3*d^4*e^2 - 60*a^3*b^2*d^3*e^3 + 119*a^4*b*d^2*e^4 - 116*a^5*d*e^5)*m^2 + 5*(360*a^4*b*e^6 + (2*a^3*b^2*d*e^5 + a^4*b*e^6)*m^5 - (6*a^2*b^3*d^2*e^4 - 32*a^3*b^2*d*e^5 - 19*a^4*b*e^6)*m^4 + (12*a*b^4*d^3*e^3 - 72*a^2*b^3*d^2*e^4 + 178*a^3*b^2*d*e^5 + 137*a^4*b*e^6)*m^3 - (12*b^5*d^4*e^2 - 84*a*b^4*d^3*e^3 + 246*a^2*b^3*d^2*e^4 - 388*a^3*b^2*d*e^5 - 461*a^4*b*e^6)*m^2 - 6*(2*b^5*d^4*e^2 - 12*a*b^4*d^3*e^3 + 30*a^2*b^3*d^2*e^4 - 40*a^3*b^2*d*e^5 - 117*a^4*b*e^6)*m)*x^2 + 2*(60*a*b^4*d^5*e - 330*a^2*b^3*d^4*e^2 + 740*a^3*b^2*d^3*e^3 - 855*a^4*b*d^2*e^4 + 522*a^5*d*e^5)*m + (720*a^5*e^6 + (5*a^4*b*d*e^5 + a^5*e^6)*m^5 - 10*(2*a^3*b^2*d^2*e^4 - 9*a^4*b*d*e^5 - 2*a^5*e^6)*m^4 + 5*(12*a^2*b^3*d^3*e^3 - 60*a^3*b^2*d^2*e^4 + 119*a^4*b*d*e^5 + 31*a^5*e^6)*m^3 - 10*(12*a*b^4*d^4*e^2 - 66*a^2*b^3*d^3*e^3 + 148*a^3*b^2*d^2*e^4 - 171*a^4*b*d*e^5 - 58*a^5*e^6)*m^2 + 12*(10*b^5*d^5*e - 60*a*b^4*d^4*e^2 + 150*a^2*b^3*d^3*e^3 - 200*a^3*b^2*d^2*e^4 + 150*a^4*b*d*e^5 + 87*a^5*e^6)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)","B",0
2148,1,496,0,0.437482," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{{\left(a^{3} d e^{3} m^{3} - 6 \, b^{3} d^{4} + 24 \, a b^{2} d^{3} e - 36 \, a^{2} b d^{2} e^{2} + 24 \, a^{3} d e^{3} + {\left(b^{3} e^{4} m^{3} + 6 \, b^{3} e^{4} m^{2} + 11 \, b^{3} e^{4} m + 6 \, b^{3} e^{4}\right)} x^{4} + {\left(24 \, a b^{2} e^{4} + {\left(b^{3} d e^{3} + 3 \, a b^{2} e^{4}\right)} m^{3} + 3 \, {\left(b^{3} d e^{3} + 7 \, a b^{2} e^{4}\right)} m^{2} + 2 \, {\left(b^{3} d e^{3} + 21 \, a b^{2} e^{4}\right)} m\right)} x^{3} - 3 \, {\left(a^{2} b d^{2} e^{2} - 3 \, a^{3} d e^{3}\right)} m^{2} + 3 \, {\left(12 \, a^{2} b e^{4} + {\left(a b^{2} d e^{3} + a^{2} b e^{4}\right)} m^{3} - {\left(b^{3} d^{2} e^{2} - 5 \, a b^{2} d e^{3} - 8 \, a^{2} b e^{4}\right)} m^{2} - {\left(b^{3} d^{2} e^{2} - 4 \, a b^{2} d e^{3} - 19 \, a^{2} b e^{4}\right)} m\right)} x^{2} + {\left(6 \, a b^{2} d^{3} e - 21 \, a^{2} b d^{2} e^{2} + 26 \, a^{3} d e^{3}\right)} m + {\left(24 \, a^{3} e^{4} + {\left(3 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} m^{3} - 3 \, {\left(2 \, a b^{2} d^{2} e^{2} - 7 \, a^{2} b d e^{3} - 3 \, a^{3} e^{4}\right)} m^{2} + 2 \, {\left(3 \, b^{3} d^{3} e - 12 \, a b^{2} d^{2} e^{2} + 18 \, a^{2} b d e^{3} + 13 \, a^{3} e^{4}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"(a^3*d*e^3*m^3 - 6*b^3*d^4 + 24*a*b^2*d^3*e - 36*a^2*b*d^2*e^2 + 24*a^3*d*e^3 + (b^3*e^4*m^3 + 6*b^3*e^4*m^2 + 11*b^3*e^4*m + 6*b^3*e^4)*x^4 + (24*a*b^2*e^4 + (b^3*d*e^3 + 3*a*b^2*e^4)*m^3 + 3*(b^3*d*e^3 + 7*a*b^2*e^4)*m^2 + 2*(b^3*d*e^3 + 21*a*b^2*e^4)*m)*x^3 - 3*(a^2*b*d^2*e^2 - 3*a^3*d*e^3)*m^2 + 3*(12*a^2*b*e^4 + (a*b^2*d*e^3 + a^2*b*e^4)*m^3 - (b^3*d^2*e^2 - 5*a*b^2*d*e^3 - 8*a^2*b*e^4)*m^2 - (b^3*d^2*e^2 - 4*a*b^2*d*e^3 - 19*a^2*b*e^4)*m)*x^2 + (6*a*b^2*d^3*e - 21*a^2*b*d^2*e^2 + 26*a^3*d*e^3)*m + (24*a^3*e^4 + (3*a^2*b*d*e^3 + a^3*e^4)*m^3 - 3*(2*a*b^2*d^2*e^2 - 7*a^2*b*d*e^3 - 3*a^3*e^4)*m^2 + 2*(3*b^3*d^3*e - 12*a*b^2*d^2*e^2 + 18*a^2*b*d*e^3 + 13*a^3*e^4)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
2149,0,0,0,0.418835," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{b x + a}, x\right)"," ",0,"integral((e*x + d)^m/(b*x + a), x)","F",0
2150,0,0,0,0.435327," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}, x\right)"," ",0,"integral((e*x + d)^m/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3), x)","F",0
2151,1,2230,0,0.471416," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(a^{6} d e^{6} m^{6} + 720 \, b^{6} d^{7} - 5040 \, a b^{5} d^{6} e + 15120 \, a^{2} b^{4} d^{5} e^{2} - 25200 \, a^{3} b^{3} d^{4} e^{3} + 25200 \, a^{4} b^{2} d^{3} e^{4} - 15120 \, a^{5} b d^{2} e^{5} + 5040 \, a^{6} d e^{6} + {\left(b^{6} e^{7} m^{6} + 21 \, b^{6} e^{7} m^{5} + 175 \, b^{6} e^{7} m^{4} + 735 \, b^{6} e^{7} m^{3} + 1624 \, b^{6} e^{7} m^{2} + 1764 \, b^{6} e^{7} m + 720 \, b^{6} e^{7}\right)} x^{7} + {\left(5040 \, a b^{5} e^{7} + {\left(b^{6} d e^{6} + 6 \, a b^{5} e^{7}\right)} m^{6} + 3 \, {\left(5 \, b^{6} d e^{6} + 44 \, a b^{5} e^{7}\right)} m^{5} + 5 \, {\left(17 \, b^{6} d e^{6} + 228 \, a b^{5} e^{7}\right)} m^{4} + 15 \, {\left(15 \, b^{6} d e^{6} + 328 \, a b^{5} e^{7}\right)} m^{3} + 2 \, {\left(137 \, b^{6} d e^{6} + 5547 \, a b^{5} e^{7}\right)} m^{2} + 12 \, {\left(10 \, b^{6} d e^{6} + 1019 \, a b^{5} e^{7}\right)} m\right)} x^{6} - 3 \, {\left(2 \, a^{5} b d^{2} e^{5} - 9 \, a^{6} d e^{6}\right)} m^{5} + 3 \, {\left(5040 \, a^{2} b^{4} e^{7} + {\left(2 \, a b^{5} d e^{6} + 5 \, a^{2} b^{4} e^{7}\right)} m^{6} - {\left(2 \, b^{6} d^{2} e^{5} - 34 \, a b^{5} d e^{6} - 115 \, a^{2} b^{4} e^{7}\right)} m^{5} - 5 \, {\left(4 \, b^{6} d^{2} e^{5} - 42 \, a b^{5} d e^{6} - 207 \, a^{2} b^{4} e^{7}\right)} m^{4} - 5 \, {\left(14 \, b^{6} d^{2} e^{5} - 118 \, a b^{5} d e^{6} - 925 \, a^{2} b^{4} e^{7}\right)} m^{3} - 4 \, {\left(25 \, b^{6} d^{2} e^{5} - 187 \, a b^{5} d e^{6} - 2680 \, a^{2} b^{4} e^{7}\right)} m^{2} - 12 \, {\left(4 \, b^{6} d^{2} e^{5} - 28 \, a b^{5} d e^{6} - 1005 \, a^{2} b^{4} e^{7}\right)} m\right)} x^{5} + 5 \, {\left(6 \, a^{4} b^{2} d^{3} e^{4} - 30 \, a^{5} b d^{2} e^{5} + 59 \, a^{6} d e^{6}\right)} m^{4} + 5 \, {\left(5040 \, a^{3} b^{3} e^{7} + {\left(3 \, a^{2} b^{4} d e^{6} + 4 \, a^{3} b^{3} e^{7}\right)} m^{6} - 3 \, {\left(2 \, a b^{5} d^{2} e^{5} - 19 \, a^{2} b^{4} d e^{6} - 32 \, a^{3} b^{3} e^{7}\right)} m^{5} + {\left(6 \, b^{6} d^{3} e^{4} - 78 \, a b^{5} d^{2} e^{5} + 393 \, a^{2} b^{4} d e^{6} + 904 \, a^{3} b^{3} e^{7}\right)} m^{4} + 3 \, {\left(12 \, b^{6} d^{3} e^{4} - 106 \, a b^{5} d^{2} e^{5} + 401 \, a^{2} b^{4} d e^{6} + 1408 \, a^{3} b^{3} e^{7}\right)} m^{3} + 2 \, {\left(33 \, b^{6} d^{3} e^{4} - 249 \, a b^{5} d^{2} e^{5} + 810 \, a^{2} b^{4} d e^{6} + 5090 \, a^{3} b^{3} e^{7}\right)} m^{2} + 36 \, {\left(b^{6} d^{3} e^{4} - 7 \, a b^{5} d^{2} e^{5} + 21 \, a^{2} b^{4} d e^{6} + 328 \, a^{3} b^{3} e^{7}\right)} m\right)} x^{4} - 15 \, {\left(8 \, a^{3} b^{3} d^{4} e^{3} - 44 \, a^{4} b^{2} d^{3} e^{4} + 98 \, a^{5} b d^{2} e^{5} - 111 \, a^{6} d e^{6}\right)} m^{3} + 5 \, {\left(5040 \, a^{4} b^{2} e^{7} + {\left(4 \, a^{3} b^{3} d e^{6} + 3 \, a^{4} b^{2} e^{7}\right)} m^{6} - 3 \, {\left(4 \, a^{2} b^{4} d^{2} e^{5} - 28 \, a^{3} b^{3} d e^{6} - 25 \, a^{4} b^{2} e^{7}\right)} m^{5} + {\left(24 \, a b^{5} d^{3} e^{4} - 192 \, a^{2} b^{4} d^{2} e^{5} + 652 \, a^{3} b^{3} d e^{6} + 741 \, a^{4} b^{2} e^{7}\right)} m^{4} - 3 \, {\left(8 \, b^{6} d^{4} e^{3} - 80 \, a b^{5} d^{3} e^{4} + 332 \, a^{2} b^{4} d^{2} e^{5} - 756 \, a^{3} b^{3} d e^{6} - 1219 \, a^{4} b^{2} e^{7}\right)} m^{3} - 8 \, {\left(9 \, b^{6} d^{4} e^{3} - 69 \, a b^{5} d^{3} e^{4} + 228 \, a^{2} b^{4} d^{2} e^{5} - 422 \, a^{3} b^{3} d e^{6} - 1167 \, a^{4} b^{2} e^{7}\right)} m^{2} - 12 \, {\left(4 \, b^{6} d^{4} e^{3} - 28 \, a b^{5} d^{3} e^{4} + 84 \, a^{2} b^{4} d^{2} e^{5} - 140 \, a^{3} b^{3} d e^{6} - 949 \, a^{4} b^{2} e^{7}\right)} m\right)} x^{3} + 2 \, {\left(180 \, a^{2} b^{4} d^{5} e^{2} - 1080 \, a^{3} b^{3} d^{4} e^{3} + 2685 \, a^{4} b^{2} d^{3} e^{4} - 3525 \, a^{5} b d^{2} e^{5} + 2552 \, a^{6} d e^{6}\right)} m^{2} + 3 \, {\left(5040 \, a^{5} b e^{7} + {\left(5 \, a^{4} b^{2} d e^{6} + 2 \, a^{5} b e^{7}\right)} m^{6} - {\left(20 \, a^{3} b^{3} d^{2} e^{5} - 115 \, a^{4} b^{2} d e^{6} - 52 \, a^{5} b e^{7}\right)} m^{5} + 5 \, {\left(12 \, a^{2} b^{4} d^{3} e^{4} - 76 \, a^{3} b^{3} d^{2} e^{5} + 201 \, a^{4} b^{2} d e^{6} + 108 \, a^{5} b e^{7}\right)} m^{4} - 5 \, {\left(24 \, a b^{5} d^{4} e^{3} - 168 \, a^{2} b^{4} d^{3} e^{4} + 500 \, a^{3} b^{3} d^{2} e^{5} - 817 \, a^{4} b^{2} d e^{6} - 568 \, a^{5} b e^{7}\right)} m^{3} + 2 \, {\left(60 \, b^{6} d^{5} e^{2} - 480 \, a b^{5} d^{4} e^{3} + 1650 \, a^{2} b^{4} d^{3} e^{4} - 3170 \, a^{3} b^{3} d^{2} e^{5} + 3695 \, a^{4} b^{2} d e^{6} + 3929 \, a^{5} b e^{7}\right)} m^{2} + 12 \, {\left(10 \, b^{6} d^{5} e^{2} - 70 \, a b^{5} d^{4} e^{3} + 210 \, a^{2} b^{4} d^{3} e^{4} - 350 \, a^{3} b^{3} d^{2} e^{5} + 350 \, a^{4} b^{2} d e^{6} + 879 \, a^{5} b e^{7}\right)} m\right)} x^{2} - 12 \, {\left(60 \, a b^{5} d^{6} e - 390 \, a^{2} b^{4} d^{5} e^{2} + 1070 \, a^{3} b^{3} d^{4} e^{3} - 1595 \, a^{4} b^{2} d^{3} e^{4} + 1377 \, a^{5} b d^{2} e^{5} - 669 \, a^{6} d e^{6}\right)} m + {\left(5040 \, a^{6} e^{7} + {\left(6 \, a^{5} b d e^{6} + a^{6} e^{7}\right)} m^{6} - 3 \, {\left(10 \, a^{4} b^{2} d^{2} e^{5} - 50 \, a^{5} b d e^{6} - 9 \, a^{6} e^{7}\right)} m^{5} + 5 \, {\left(24 \, a^{3} b^{3} d^{3} e^{4} - 132 \, a^{4} b^{2} d^{2} e^{5} + 294 \, a^{5} b d e^{6} + 59 \, a^{6} e^{7}\right)} m^{4} - 15 \, {\left(24 \, a^{2} b^{4} d^{4} e^{3} - 144 \, a^{3} b^{3} d^{3} e^{4} + 358 \, a^{4} b^{2} d^{2} e^{5} - 470 \, a^{5} b d e^{6} - 111 \, a^{6} e^{7}\right)} m^{3} + 4 \, {\left(180 \, a b^{5} d^{5} e^{2} - 1170 \, a^{2} b^{4} d^{4} e^{3} + 3210 \, a^{3} b^{3} d^{3} e^{4} - 4785 \, a^{4} b^{2} d^{2} e^{5} + 4131 \, a^{5} b d e^{6} + 1276 \, a^{6} e^{7}\right)} m^{2} - 36 \, {\left(20 \, b^{6} d^{6} e - 140 \, a b^{5} d^{5} e^{2} + 420 \, a^{2} b^{4} d^{4} e^{3} - 700 \, a^{3} b^{3} d^{3} e^{4} + 700 \, a^{4} b^{2} d^{2} e^{5} - 420 \, a^{5} b d e^{6} - 223 \, a^{6} e^{7}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{7} m^{7} + 28 \, e^{7} m^{6} + 322 \, e^{7} m^{5} + 1960 \, e^{7} m^{4} + 6769 \, e^{7} m^{3} + 13132 \, e^{7} m^{2} + 13068 \, e^{7} m + 5040 \, e^{7}}"," ",0,"(a^6*d*e^6*m^6 + 720*b^6*d^7 - 5040*a*b^5*d^6*e + 15120*a^2*b^4*d^5*e^2 - 25200*a^3*b^3*d^4*e^3 + 25200*a^4*b^2*d^3*e^4 - 15120*a^5*b*d^2*e^5 + 5040*a^6*d*e^6 + (b^6*e^7*m^6 + 21*b^6*e^7*m^5 + 175*b^6*e^7*m^4 + 735*b^6*e^7*m^3 + 1624*b^6*e^7*m^2 + 1764*b^6*e^7*m + 720*b^6*e^7)*x^7 + (5040*a*b^5*e^7 + (b^6*d*e^6 + 6*a*b^5*e^7)*m^6 + 3*(5*b^6*d*e^6 + 44*a*b^5*e^7)*m^5 + 5*(17*b^6*d*e^6 + 228*a*b^5*e^7)*m^4 + 15*(15*b^6*d*e^6 + 328*a*b^5*e^7)*m^3 + 2*(137*b^6*d*e^6 + 5547*a*b^5*e^7)*m^2 + 12*(10*b^6*d*e^6 + 1019*a*b^5*e^7)*m)*x^6 - 3*(2*a^5*b*d^2*e^5 - 9*a^6*d*e^6)*m^5 + 3*(5040*a^2*b^4*e^7 + (2*a*b^5*d*e^6 + 5*a^2*b^4*e^7)*m^6 - (2*b^6*d^2*e^5 - 34*a*b^5*d*e^6 - 115*a^2*b^4*e^7)*m^5 - 5*(4*b^6*d^2*e^5 - 42*a*b^5*d*e^6 - 207*a^2*b^4*e^7)*m^4 - 5*(14*b^6*d^2*e^5 - 118*a*b^5*d*e^6 - 925*a^2*b^4*e^7)*m^3 - 4*(25*b^6*d^2*e^5 - 187*a*b^5*d*e^6 - 2680*a^2*b^4*e^7)*m^2 - 12*(4*b^6*d^2*e^5 - 28*a*b^5*d*e^6 - 1005*a^2*b^4*e^7)*m)*x^5 + 5*(6*a^4*b^2*d^3*e^4 - 30*a^5*b*d^2*e^5 + 59*a^6*d*e^6)*m^4 + 5*(5040*a^3*b^3*e^7 + (3*a^2*b^4*d*e^6 + 4*a^3*b^3*e^7)*m^6 - 3*(2*a*b^5*d^2*e^5 - 19*a^2*b^4*d*e^6 - 32*a^3*b^3*e^7)*m^5 + (6*b^6*d^3*e^4 - 78*a*b^5*d^2*e^5 + 393*a^2*b^4*d*e^6 + 904*a^3*b^3*e^7)*m^4 + 3*(12*b^6*d^3*e^4 - 106*a*b^5*d^2*e^5 + 401*a^2*b^4*d*e^6 + 1408*a^3*b^3*e^7)*m^3 + 2*(33*b^6*d^3*e^4 - 249*a*b^5*d^2*e^5 + 810*a^2*b^4*d*e^6 + 5090*a^3*b^3*e^7)*m^2 + 36*(b^6*d^3*e^4 - 7*a*b^5*d^2*e^5 + 21*a^2*b^4*d*e^6 + 328*a^3*b^3*e^7)*m)*x^4 - 15*(8*a^3*b^3*d^4*e^3 - 44*a^4*b^2*d^3*e^4 + 98*a^5*b*d^2*e^5 - 111*a^6*d*e^6)*m^3 + 5*(5040*a^4*b^2*e^7 + (4*a^3*b^3*d*e^6 + 3*a^4*b^2*e^7)*m^6 - 3*(4*a^2*b^4*d^2*e^5 - 28*a^3*b^3*d*e^6 - 25*a^4*b^2*e^7)*m^5 + (24*a*b^5*d^3*e^4 - 192*a^2*b^4*d^2*e^5 + 652*a^3*b^3*d*e^6 + 741*a^4*b^2*e^7)*m^4 - 3*(8*b^6*d^4*e^3 - 80*a*b^5*d^3*e^4 + 332*a^2*b^4*d^2*e^5 - 756*a^3*b^3*d*e^6 - 1219*a^4*b^2*e^7)*m^3 - 8*(9*b^6*d^4*e^3 - 69*a*b^5*d^3*e^4 + 228*a^2*b^4*d^2*e^5 - 422*a^3*b^3*d*e^6 - 1167*a^4*b^2*e^7)*m^2 - 12*(4*b^6*d^4*e^3 - 28*a*b^5*d^3*e^4 + 84*a^2*b^4*d^2*e^5 - 140*a^3*b^3*d*e^6 - 949*a^4*b^2*e^7)*m)*x^3 + 2*(180*a^2*b^4*d^5*e^2 - 1080*a^3*b^3*d^4*e^3 + 2685*a^4*b^2*d^3*e^4 - 3525*a^5*b*d^2*e^5 + 2552*a^6*d*e^6)*m^2 + 3*(5040*a^5*b*e^7 + (5*a^4*b^2*d*e^6 + 2*a^5*b*e^7)*m^6 - (20*a^3*b^3*d^2*e^5 - 115*a^4*b^2*d*e^6 - 52*a^5*b*e^7)*m^5 + 5*(12*a^2*b^4*d^3*e^4 - 76*a^3*b^3*d^2*e^5 + 201*a^4*b^2*d*e^6 + 108*a^5*b*e^7)*m^4 - 5*(24*a*b^5*d^4*e^3 - 168*a^2*b^4*d^3*e^4 + 500*a^3*b^3*d^2*e^5 - 817*a^4*b^2*d*e^6 - 568*a^5*b*e^7)*m^3 + 2*(60*b^6*d^5*e^2 - 480*a*b^5*d^4*e^3 + 1650*a^2*b^4*d^3*e^4 - 3170*a^3*b^3*d^2*e^5 + 3695*a^4*b^2*d*e^6 + 3929*a^5*b*e^7)*m^2 + 12*(10*b^6*d^5*e^2 - 70*a*b^5*d^4*e^3 + 210*a^2*b^4*d^3*e^4 - 350*a^3*b^3*d^2*e^5 + 350*a^4*b^2*d*e^6 + 879*a^5*b*e^7)*m)*x^2 - 12*(60*a*b^5*d^6*e - 390*a^2*b^4*d^5*e^2 + 1070*a^3*b^3*d^4*e^3 - 1595*a^4*b^2*d^3*e^4 + 1377*a^5*b*d^2*e^5 - 669*a^6*d*e^6)*m + (5040*a^6*e^7 + (6*a^5*b*d*e^6 + a^6*e^7)*m^6 - 3*(10*a^4*b^2*d^2*e^5 - 50*a^5*b*d*e^6 - 9*a^6*e^7)*m^5 + 5*(24*a^3*b^3*d^3*e^4 - 132*a^4*b^2*d^2*e^5 + 294*a^5*b*d*e^6 + 59*a^6*e^7)*m^4 - 15*(24*a^2*b^4*d^4*e^3 - 144*a^3*b^3*d^3*e^4 + 358*a^4*b^2*d^2*e^5 - 470*a^5*b*d*e^6 - 111*a^6*e^7)*m^3 + 4*(180*a*b^5*d^5*e^2 - 1170*a^2*b^4*d^4*e^3 + 3210*a^3*b^3*d^3*e^4 - 4785*a^4*b^2*d^2*e^5 + 4131*a^5*b*d*e^6 + 1276*a^6*e^7)*m^2 - 36*(20*b^6*d^6*e - 140*a*b^5*d^5*e^2 + 420*a^2*b^4*d^4*e^3 - 700*a^3*b^3*d^3*e^4 + 700*a^4*b^2*d^2*e^5 - 420*a^5*b*d*e^6 - 223*a^6*e^7)*m)*x)*(e*x + d)^m/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m^4 + 6769*e^7*m^3 + 13132*e^7*m^2 + 13068*e^7*m + 5040*e^7)","B",0
2152,1,901,0,0.450697," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{4} d e^{4} m^{4} + 24 \, b^{4} d^{5} - 120 \, a b^{3} d^{4} e + 240 \, a^{2} b^{2} d^{3} e^{2} - 240 \, a^{3} b d^{2} e^{3} + 120 \, a^{4} d e^{4} + {\left(b^{4} e^{5} m^{4} + 10 \, b^{4} e^{5} m^{3} + 35 \, b^{4} e^{5} m^{2} + 50 \, b^{4} e^{5} m + 24 \, b^{4} e^{5}\right)} x^{5} + {\left(120 \, a b^{3} e^{5} + {\left(b^{4} d e^{4} + 4 \, a b^{3} e^{5}\right)} m^{4} + 2 \, {\left(3 \, b^{4} d e^{4} + 22 \, a b^{3} e^{5}\right)} m^{3} + {\left(11 \, b^{4} d e^{4} + 164 \, a b^{3} e^{5}\right)} m^{2} + 2 \, {\left(3 \, b^{4} d e^{4} + 122 \, a b^{3} e^{5}\right)} m\right)} x^{4} - 2 \, {\left(2 \, a^{3} b d^{2} e^{3} - 7 \, a^{4} d e^{4}\right)} m^{3} + 2 \, {\left(120 \, a^{2} b^{2} e^{5} + {\left(2 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} m^{4} - 2 \, {\left(b^{4} d^{2} e^{3} - 8 \, a b^{3} d e^{4} - 18 \, a^{2} b^{2} e^{5}\right)} m^{3} - {\left(6 \, b^{4} d^{2} e^{3} - 34 \, a b^{3} d e^{4} - 147 \, a^{2} b^{2} e^{5}\right)} m^{2} - 2 \, {\left(2 \, b^{4} d^{2} e^{3} - 10 \, a b^{3} d e^{4} - 117 \, a^{2} b^{2} e^{5}\right)} m\right)} x^{3} + {\left(12 \, a^{2} b^{2} d^{3} e^{2} - 48 \, a^{3} b d^{2} e^{3} + 71 \, a^{4} d e^{4}\right)} m^{2} + 2 \, {\left(120 \, a^{3} b e^{5} + {\left(3 \, a^{2} b^{2} d e^{4} + 2 \, a^{3} b e^{5}\right)} m^{4} - 2 \, {\left(3 \, a b^{3} d^{2} e^{3} - 15 \, a^{2} b^{2} d e^{4} - 13 \, a^{3} b e^{5}\right)} m^{3} + {\left(6 \, b^{4} d^{3} e^{2} - 36 \, a b^{3} d^{2} e^{3} + 87 \, a^{2} b^{2} d e^{4} + 118 \, a^{3} b e^{5}\right)} m^{2} + 2 \, {\left(3 \, b^{4} d^{3} e^{2} - 15 \, a b^{3} d^{2} e^{3} + 30 \, a^{2} b^{2} d e^{4} + 107 \, a^{3} b e^{5}\right)} m\right)} x^{2} - 2 \, {\left(12 \, a b^{3} d^{4} e - 54 \, a^{2} b^{2} d^{3} e^{2} + 94 \, a^{3} b d^{2} e^{3} - 77 \, a^{4} d e^{4}\right)} m + {\left(120 \, a^{4} e^{5} + {\left(4 \, a^{3} b d e^{4} + a^{4} e^{5}\right)} m^{4} - 2 \, {\left(6 \, a^{2} b^{2} d^{2} e^{3} - 24 \, a^{3} b d e^{4} - 7 \, a^{4} e^{5}\right)} m^{3} + {\left(24 \, a b^{3} d^{3} e^{2} - 108 \, a^{2} b^{2} d^{2} e^{3} + 188 \, a^{3} b d e^{4} + 71 \, a^{4} e^{5}\right)} m^{2} - 2 \, {\left(12 \, b^{4} d^{4} e - 60 \, a b^{3} d^{3} e^{2} + 120 \, a^{2} b^{2} d^{2} e^{3} - 120 \, a^{3} b d e^{4} - 77 \, a^{4} e^{5}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{5} m^{5} + 15 \, e^{5} m^{4} + 85 \, e^{5} m^{3} + 225 \, e^{5} m^{2} + 274 \, e^{5} m + 120 \, e^{5}}"," ",0,"(a^4*d*e^4*m^4 + 24*b^4*d^5 - 120*a*b^3*d^4*e + 240*a^2*b^2*d^3*e^2 - 240*a^3*b*d^2*e^3 + 120*a^4*d*e^4 + (b^4*e^5*m^4 + 10*b^4*e^5*m^3 + 35*b^4*e^5*m^2 + 50*b^4*e^5*m + 24*b^4*e^5)*x^5 + (120*a*b^3*e^5 + (b^4*d*e^4 + 4*a*b^3*e^5)*m^4 + 2*(3*b^4*d*e^4 + 22*a*b^3*e^5)*m^3 + (11*b^4*d*e^4 + 164*a*b^3*e^5)*m^2 + 2*(3*b^4*d*e^4 + 122*a*b^3*e^5)*m)*x^4 - 2*(2*a^3*b*d^2*e^3 - 7*a^4*d*e^4)*m^3 + 2*(120*a^2*b^2*e^5 + (2*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*m^4 - 2*(b^4*d^2*e^3 - 8*a*b^3*d*e^4 - 18*a^2*b^2*e^5)*m^3 - (6*b^4*d^2*e^3 - 34*a*b^3*d*e^4 - 147*a^2*b^2*e^5)*m^2 - 2*(2*b^4*d^2*e^3 - 10*a*b^3*d*e^4 - 117*a^2*b^2*e^5)*m)*x^3 + (12*a^2*b^2*d^3*e^2 - 48*a^3*b*d^2*e^3 + 71*a^4*d*e^4)*m^2 + 2*(120*a^3*b*e^5 + (3*a^2*b^2*d*e^4 + 2*a^3*b*e^5)*m^4 - 2*(3*a*b^3*d^2*e^3 - 15*a^2*b^2*d*e^4 - 13*a^3*b*e^5)*m^3 + (6*b^4*d^3*e^2 - 36*a*b^3*d^2*e^3 + 87*a^2*b^2*d*e^4 + 118*a^3*b*e^5)*m^2 + 2*(3*b^4*d^3*e^2 - 15*a*b^3*d^2*e^3 + 30*a^2*b^2*d*e^4 + 107*a^3*b*e^5)*m)*x^2 - 2*(12*a*b^3*d^4*e - 54*a^2*b^2*d^3*e^2 + 94*a^3*b*d^2*e^3 - 77*a^4*d*e^4)*m + (120*a^4*e^5 + (4*a^3*b*d*e^4 + a^4*e^5)*m^4 - 2*(6*a^2*b^2*d^2*e^3 - 24*a^3*b*d*e^4 - 7*a^4*e^5)*m^3 + (24*a*b^3*d^3*e^2 - 108*a^2*b^2*d^2*e^3 + 188*a^3*b*d*e^4 + 71*a^4*e^5)*m^2 - 2*(12*b^4*d^4*e - 60*a*b^3*d^3*e^2 + 120*a^2*b^2*d^2*e^3 - 120*a^3*b*d*e^4 - 77*a^4*e^5)*m)*x)*(e*x + d)^m/(e^5*m^5 + 15*e^5*m^4 + 85*e^5*m^3 + 225*e^5*m^2 + 274*e^5*m + 120*e^5)","B",0
2153,1,237,0,0.439816," ","integrate((b*x+a)*(e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} d e^{2} m^{2} + 2 \, b^{2} d^{3} - 6 \, a b d^{2} e + 6 \, a^{2} d e^{2} + {\left(b^{2} e^{3} m^{2} + 3 \, b^{2} e^{3} m + 2 \, b^{2} e^{3}\right)} x^{3} + {\left(6 \, a b e^{3} + {\left(b^{2} d e^{2} + 2 \, a b e^{3}\right)} m^{2} + {\left(b^{2} d e^{2} + 8 \, a b e^{3}\right)} m\right)} x^{2} - {\left(2 \, a b d^{2} e - 5 \, a^{2} d e^{2}\right)} m + {\left(6 \, a^{2} e^{3} + {\left(2 \, a b d e^{2} + a^{2} e^{3}\right)} m^{2} - {\left(2 \, b^{2} d^{2} e - 6 \, a b d e^{2} - 5 \, a^{2} e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{3} m^{3} + 6 \, e^{3} m^{2} + 11 \, e^{3} m + 6 \, e^{3}}"," ",0,"(a^2*d*e^2*m^2 + 2*b^2*d^3 - 6*a*b*d^2*e + 6*a^2*d*e^2 + (b^2*e^3*m^2 + 3*b^2*e^3*m + 2*b^2*e^3)*x^3 + (6*a*b*e^3 + (b^2*d*e^2 + 2*a*b*e^3)*m^2 + (b^2*d*e^2 + 8*a*b*e^3)*m)*x^2 - (2*a*b*d^2*e - 5*a^2*d*e^2)*m + (6*a^2*e^3 + (2*a*b*d*e^2 + a^2*e^3)*m^2 - (2*b^2*d^2*e - 6*a*b*d*e^2 - 5*a^2*e^3)*m)*x)*(e*x + d)^m/(e^3*m^3 + 6*e^3*m^2 + 11*e^3*m + 6*e^3)","A",0
2154,1,20,0,0.444615," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(e x + d\right)} {\left(e x + d\right)}^{m}}{e m + e}"," ",0,"(e*x + d)*(e*x + d)^m/(e*m + e)","A",0
2155,0,0,0,0.450781," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}} {\left(e x + d\right)}^{m}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}, x\right)"," ",0,"integral(sqrt(b^2*x^2 + 2*a*b*x + a^2)*(e*x + d)^m/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3), x)","F",0
2156,0,0,0,0.436286," ","integrate((b*x+a)*(e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}} {\left(e x + d\right)}^{m}}{b^{5} x^{5} + 5 \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x^{3} + 10 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5}}, x\right)"," ",0,"integral(sqrt(b^2*x^2 + 2*a*b*x + a^2)*(e*x + d)^m/(b^5*x^5 + 5*a*b^4*x^4 + 10*a^2*b^3*x^3 + 10*a^3*b^2*x^2 + 5*a^4*b*x + a^5), x)","F",0
2157,1,99,0,0.459752," ","integrate((b*c*x+a*c)*(e*x+d)^(-3-2*p)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(b^{2} c e x^{3} + a^{2} c d + {\left(b^{2} c d + 2 \, a b c e\right)} x^{2} + {\left(2 \, a b c d + a^{2} c e\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}}{2 \, {\left(b d - a e + {\left(b d - a e\right)} p\right)}}"," ",0,"1/2*(b^2*c*e*x^3 + a^2*c*d + (b^2*c*d + 2*a*b*c*e)*x^2 + (2*a*b*c*d + a^2*c*e)*x)*(b^2*x^2 + 2*a*b*x + a^2)^p*(e*x + d)^(-2*p - 3)/(b*d - a*e + (b*d - a*e)*p)","A",0
2158,1,715,0,0.468148," ","integrate((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} b^{3} d^{3} p^{3} + 30 \, a^{2} b^{3} d^{3} - 30 \, a^{3} b^{2} d^{2} e + 15 \, a^{4} b d e^{2} - 3 \, a^{5} e^{3} + 2 \, {\left(2 \, b^{5} e^{3} p^{3} + 9 \, b^{5} e^{3} p^{2} + 13 \, b^{5} e^{3} p + 6 \, b^{5} e^{3}\right)} x^{5} + {\left(45 \, b^{5} d e^{2} + 15 \, a b^{4} e^{3} + 4 \, {\left(3 \, b^{5} d e^{2} + 2 \, a b^{4} e^{3}\right)} p^{3} + 30 \, {\left(2 \, b^{5} d e^{2} + a b^{4} e^{3}\right)} p^{2} + {\left(93 \, b^{5} d e^{2} + 37 \, a b^{4} e^{3}\right)} p\right)} x^{4} + 2 \, {\left(30 \, b^{5} d^{2} e + 30 \, a b^{4} d e^{2} + 2 \, {\left(3 \, b^{5} d^{2} e + 6 \, a b^{4} d e^{2} + a^{2} b^{3} e^{3}\right)} p^{3} + 3 \, {\left(11 \, b^{5} d^{2} e + 18 \, a b^{4} d e^{2} + a^{2} b^{3} e^{3}\right)} p^{2} + {\left(57 \, b^{5} d^{2} e + 72 \, a b^{4} d e^{2} + a^{2} b^{3} e^{3}\right)} p\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} d^{3} - a^{3} b^{2} d^{2} e\right)} p^{2} + {\left(30 \, b^{5} d^{3} + 90 \, a b^{4} d^{2} e + 4 \, {\left(b^{5} d^{3} + 6 \, a b^{4} d^{2} e + 3 \, a^{2} b^{3} d e^{2}\right)} p^{3} + 6 \, {\left(4 \, b^{5} d^{3} + 21 \, a b^{4} d^{2} e + 6 \, a^{2} b^{3} d e^{2} - a^{3} b^{2} e^{3}\right)} p^{2} + {\left(47 \, b^{5} d^{3} + 201 \, a b^{4} d^{2} e + 15 \, a^{2} b^{3} d e^{2} - 3 \, a^{3} b^{2} e^{3}\right)} p\right)} x^{2} + {\left(47 \, a^{2} b^{3} d^{3} - 27 \, a^{3} b^{2} d^{2} e + 6 \, a^{4} b d e^{2}\right)} p + 2 \, {\left(30 \, a b^{4} d^{3} + 2 \, {\left(2 \, a b^{4} d^{3} + 3 \, a^{2} b^{3} d^{2} e\right)} p^{3} + 3 \, {\left(8 \, a b^{4} d^{3} + 9 \, a^{2} b^{3} d^{2} e - 2 \, a^{3} b^{2} d e^{2}\right)} p^{2} + {\left(47 \, a b^{4} d^{3} + 30 \, a^{2} b^{3} d^{2} e - 15 \, a^{3} b^{2} d e^{2} + 3 \, a^{4} b e^{3}\right)} p\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{2 \, {\left(4 \, b^{4} p^{4} + 28 \, b^{4} p^{3} + 71 \, b^{4} p^{2} + 77 \, b^{4} p + 30 \, b^{4}\right)}}"," ",0,"1/2*(4*a^2*b^3*d^3*p^3 + 30*a^2*b^3*d^3 - 30*a^3*b^2*d^2*e + 15*a^4*b*d*e^2 - 3*a^5*e^3 + 2*(2*b^5*e^3*p^3 + 9*b^5*e^3*p^2 + 13*b^5*e^3*p + 6*b^5*e^3)*x^5 + (45*b^5*d*e^2 + 15*a*b^4*e^3 + 4*(3*b^5*d*e^2 + 2*a*b^4*e^3)*p^3 + 30*(2*b^5*d*e^2 + a*b^4*e^3)*p^2 + (93*b^5*d*e^2 + 37*a*b^4*e^3)*p)*x^4 + 2*(30*b^5*d^2*e + 30*a*b^4*d*e^2 + 2*(3*b^5*d^2*e + 6*a*b^4*d*e^2 + a^2*b^3*e^3)*p^3 + 3*(11*b^5*d^2*e + 18*a*b^4*d*e^2 + a^2*b^3*e^3)*p^2 + (57*b^5*d^2*e + 72*a*b^4*d*e^2 + a^2*b^3*e^3)*p)*x^3 + 6*(4*a^2*b^3*d^3 - a^3*b^2*d^2*e)*p^2 + (30*b^5*d^3 + 90*a*b^4*d^2*e + 4*(b^5*d^3 + 6*a*b^4*d^2*e + 3*a^2*b^3*d*e^2)*p^3 + 6*(4*b^5*d^3 + 21*a*b^4*d^2*e + 6*a^2*b^3*d*e^2 - a^3*b^2*e^3)*p^2 + (47*b^5*d^3 + 201*a*b^4*d^2*e + 15*a^2*b^3*d*e^2 - 3*a^3*b^2*e^3)*p)*x^2 + (47*a^2*b^3*d^3 - 27*a^3*b^2*d^2*e + 6*a^4*b*d*e^2)*p + 2*(30*a*b^4*d^3 + 2*(2*a*b^4*d^3 + 3*a^2*b^3*d^2*e)*p^3 + 3*(8*a*b^4*d^3 + 9*a^2*b^3*d^2*e - 2*a^3*b^2*d*e^2)*p^2 + (47*a*b^4*d^3 + 30*a^2*b^3*d^2*e - 15*a^3*b^2*d*e^2 + 3*a^4*b*e^3)*p)*x)*(b^2*x^2 + 2*a*b*x + a^2)^p/(4*b^4*p^4 + 28*b^4*p^3 + 71*b^4*p^2 + 77*b^4*p + 30*b^4)","B",0
2159,1,353,0,0.453653," ","integrate((b*x+a)*(e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} b^{2} d^{2} p^{2} + 6 \, a^{2} b^{2} d^{2} - 4 \, a^{3} b d e + a^{4} e^{2} + {\left(2 \, b^{4} e^{2} p^{2} + 5 \, b^{4} e^{2} p + 3 \, b^{4} e^{2}\right)} x^{4} + 4 \, {\left(2 \, b^{4} d e + a b^{3} e^{2} + {\left(b^{4} d e + a b^{3} e^{2}\right)} p^{2} + {\left(3 \, b^{4} d e + 2 \, a b^{3} e^{2}\right)} p\right)} x^{3} + {\left(6 \, b^{4} d^{2} + 12 \, a b^{3} d e + 2 \, {\left(b^{4} d^{2} + 4 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} p^{2} + {\left(7 \, b^{4} d^{2} + 22 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} p\right)} x^{2} + {\left(7 \, a^{2} b^{2} d^{2} - 2 \, a^{3} b d e\right)} p + 2 \, {\left(6 \, a b^{3} d^{2} + 2 \, {\left(a b^{3} d^{2} + a^{2} b^{2} d e\right)} p^{2} + {\left(7 \, a b^{3} d^{2} + 4 \, a^{2} b^{2} d e - a^{3} b e^{2}\right)} p\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{2 \, {\left(2 \, b^{3} p^{3} + 9 \, b^{3} p^{2} + 13 \, b^{3} p + 6 \, b^{3}\right)}}"," ",0,"1/2*(2*a^2*b^2*d^2*p^2 + 6*a^2*b^2*d^2 - 4*a^3*b*d*e + a^4*e^2 + (2*b^4*e^2*p^2 + 5*b^4*e^2*p + 3*b^4*e^2)*x^4 + 4*(2*b^4*d*e + a*b^3*e^2 + (b^4*d*e + a*b^3*e^2)*p^2 + (3*b^4*d*e + 2*a*b^3*e^2)*p)*x^3 + (6*b^4*d^2 + 12*a*b^3*d*e + 2*(b^4*d^2 + 4*a*b^3*d*e + a^2*b^2*e^2)*p^2 + (7*b^4*d^2 + 22*a*b^3*d*e + a^2*b^2*e^2)*p)*x^2 + (7*a^2*b^2*d^2 - 2*a^3*b*d*e)*p + 2*(6*a*b^3*d^2 + 2*(a*b^3*d^2 + a^2*b^2*d*e)*p^2 + (7*a*b^3*d^2 + 4*a^2*b^2*d*e - a^3*b*e^2)*p)*x)*(b^2*x^2 + 2*a*b*x + a^2)^p/(2*b^3*p^3 + 9*b^3*p^2 + 13*b^3*p + 6*b^3)","B",0
2160,1,142,0,0.454771," ","integrate((b*x+a)*(e*x+d)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} b d p + 3 \, a^{2} b d - a^{3} e + 2 \, {\left(b^{3} e p + b^{3} e\right)} x^{3} + {\left(3 \, b^{3} d + 3 \, a b^{2} e + 2 \, {\left(b^{3} d + 2 \, a b^{2} e\right)} p\right)} x^{2} + 2 \, {\left(3 \, a b^{2} d + {\left(2 \, a b^{2} d + a^{2} b e\right)} p\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{2 \, {\left(2 \, b^{2} p^{2} + 5 \, b^{2} p + 3 \, b^{2}\right)}}"," ",0,"1/2*(2*a^2*b*d*p + 3*a^2*b*d - a^3*e + 2*(b^3*e*p + b^3*e)*x^3 + (3*b^3*d + 3*a*b^2*e + 2*(b^3*d + 2*a*b^2*e)*p)*x^2 + 2*(3*a*b^2*d + (2*a*b^2*d + a^2*b*e)*p)*x)*(b^2*x^2 + 2*a*b*x + a^2)^p/(2*b^2*p^2 + 5*b^2*p + 3*b^2)","A",0
2161,1,43,0,0.438884," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{2 \, {\left(b p + b\right)}}"," ",0,"1/2*(b^2*x^2 + 2*a*b*x + a^2)*(b^2*x^2 + 2*a*b*x + a^2)^p/(b*p + b)","A",0
2162,0,0,0,0.435762," ","integrate((b*x+a)*(b^2*x^2+2*a*b*x+a^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{e x + d}, x\right)"," ",0,"integral((b*x + a)*(b^2*x^2 + 2*a*b*x + a^2)^p/(e*x + d), x)","F",0
2163,1,350,0,0.441433," ","integrate((B*x+A)*(b*c*x+a*c)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{{\left(A a^{7} b m - B a^{8} + 8 \, A a^{7} b + {\left(B b^{8} m + 7 \, B b^{8}\right)} x^{8} + {\left(48 \, B a b^{7} + 8 \, A b^{8} + {\left(7 \, B a b^{7} + A b^{8}\right)} m\right)} x^{7} + 7 \, {\left(20 \, B a^{2} b^{6} + 8 \, A a b^{7} + {\left(3 \, B a^{2} b^{6} + A a b^{7}\right)} m\right)} x^{6} + 7 \, {\left(32 \, B a^{3} b^{5} + 24 \, A a^{2} b^{6} + {\left(5 \, B a^{3} b^{5} + 3 \, A a^{2} b^{6}\right)} m\right)} x^{5} + 35 \, {\left(6 \, B a^{4} b^{4} + 8 \, A a^{3} b^{5} + {\left(B a^{4} b^{4} + A a^{3} b^{5}\right)} m\right)} x^{4} + 7 \, {\left(16 \, B a^{5} b^{3} + 40 \, A a^{4} b^{4} + {\left(3 \, B a^{5} b^{3} + 5 \, A a^{4} b^{4}\right)} m\right)} x^{3} + 7 \, {\left(4 \, B a^{6} b^{2} + 24 \, A a^{5} b^{3} + {\left(B a^{6} b^{2} + 3 \, A a^{5} b^{3}\right)} m\right)} x^{2} + {\left(56 \, A a^{6} b^{2} + {\left(B a^{7} b + 7 \, A a^{6} b^{2}\right)} m\right)} x\right)} {\left(b c x + a c\right)}^{m}}{b^{2} m^{2} + 15 \, b^{2} m + 56 \, b^{2}}"," ",0,"(A*a^7*b*m - B*a^8 + 8*A*a^7*b + (B*b^8*m + 7*B*b^8)*x^8 + (48*B*a*b^7 + 8*A*b^8 + (7*B*a*b^7 + A*b^8)*m)*x^7 + 7*(20*B*a^2*b^6 + 8*A*a*b^7 + (3*B*a^2*b^6 + A*a*b^7)*m)*x^6 + 7*(32*B*a^3*b^5 + 24*A*a^2*b^6 + (5*B*a^3*b^5 + 3*A*a^2*b^6)*m)*x^5 + 35*(6*B*a^4*b^4 + 8*A*a^3*b^5 + (B*a^4*b^4 + A*a^3*b^5)*m)*x^4 + 7*(16*B*a^5*b^3 + 40*A*a^4*b^4 + (3*B*a^5*b^3 + 5*A*a^4*b^4)*m)*x^3 + 7*(4*B*a^6*b^2 + 24*A*a^5*b^3 + (B*a^6*b^2 + 3*A*a^5*b^3)*m)*x^2 + (56*A*a^6*b^2 + (B*a^7*b + 7*A*a^6*b^2)*m)*x)*(b*c*x + a*c)^m/(b^2*m^2 + 15*b^2*m + 56*b^2)","B",0
2164,1,212,0,0.448122," ","integrate((B*x+A)*(b*c*x+a*c)^m/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{{\left(A b m - B a - 4 \, A b + {\left(B b m - 5 \, B b\right)} x\right)} {\left(b c x + a c\right)}^{m}}{a^{5} b^{2} m^{2} - 9 \, a^{5} b^{2} m + 20 \, a^{5} b^{2} + {\left(b^{7} m^{2} - 9 \, b^{7} m + 20 \, b^{7}\right)} x^{5} + 5 \, {\left(a b^{6} m^{2} - 9 \, a b^{6} m + 20 \, a b^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{5} m^{2} - 9 \, a^{2} b^{5} m + 20 \, a^{2} b^{5}\right)} x^{3} + 10 \, {\left(a^{3} b^{4} m^{2} - 9 \, a^{3} b^{4} m + 20 \, a^{3} b^{4}\right)} x^{2} + 5 \, {\left(a^{4} b^{3} m^{2} - 9 \, a^{4} b^{3} m + 20 \, a^{4} b^{3}\right)} x}"," ",0,"(A*b*m - B*a - 4*A*b + (B*b*m - 5*B*b)*x)*(b*c*x + a*c)^m/(a^5*b^2*m^2 - 9*a^5*b^2*m + 20*a^5*b^2 + (b^7*m^2 - 9*b^7*m + 20*b^7)*x^5 + 5*(a*b^6*m^2 - 9*a*b^6*m + 20*a*b^6)*x^4 + 10*(a^2*b^5*m^2 - 9*a^2*b^5*m + 20*a^2*b^5)*x^3 + 10*(a^3*b^4*m^2 - 9*a^3*b^4*m + 20*a^3*b^4)*x^2 + 5*(a^4*b^3*m^2 - 9*a^4*b^3*m + 20*a^4*b^3)*x)","B",0
2165,1,219,0,0.448034," ","integrate((B*x+A)*(b*c*x+a*c)^m*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(A a^{4} b m - B a^{5} + 5 \, A a^{4} b + {\left(B b^{5} m + 4 \, B b^{5}\right)} x^{5} + {\left(15 \, B a b^{4} + 5 \, A b^{5} + {\left(4 \, B a b^{4} + A b^{5}\right)} m\right)} x^{4} + 2 \, {\left(10 \, B a^{2} b^{3} + 10 \, A a b^{4} + {\left(3 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} m\right)} x^{3} + 2 \, {\left(5 \, B a^{3} b^{2} + 15 \, A a^{2} b^{3} + {\left(2 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} m\right)} x^{2} + {\left(20 \, A a^{3} b^{2} + {\left(B a^{4} b + 4 \, A a^{3} b^{2}\right)} m\right)} x\right)} {\left(b c x + a c\right)}^{m}}{b^{2} m^{2} + 9 \, b^{2} m + 20 \, b^{2}}"," ",0,"(A*a^4*b*m - B*a^5 + 5*A*a^4*b + (B*b^5*m + 4*B*b^5)*x^5 + (15*B*a*b^4 + 5*A*b^5 + (4*B*a*b^4 + A*b^5)*m)*x^4 + 2*(10*B*a^2*b^3 + 10*A*a*b^4 + (3*B*a^2*b^3 + 2*A*a*b^4)*m)*x^3 + 2*(5*B*a^3*b^2 + 15*A*a^2*b^3 + (2*B*a^3*b^2 + 3*A*a^2*b^3)*m)*x^2 + (20*A*a^3*b^2 + (B*a^4*b + 4*A*a^3*b^2)*m)*x)*(b*c*x + a*c)^m/(b^2*m^2 + 9*b^2*m + 20*b^2)","B",0
2166,1,113,0,0.443508," ","integrate((B*x+A)*(b*c*x+a*c)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(A b m - B a - A b + {\left(B b m - 2 \, B b\right)} x\right)} {\left(b c x + a c\right)}^{m}}{a^{2} b^{2} m^{2} - 3 \, a^{2} b^{2} m + 2 \, a^{2} b^{2} + {\left(b^{4} m^{2} - 3 \, b^{4} m + 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a b^{3} m^{2} - 3 \, a b^{3} m + 2 \, a b^{3}\right)} x}"," ",0,"(A*b*m - B*a - A*b + (B*b*m - 2*B*b)*x)*(b*c*x + a*c)^m/(a^2*b^2*m^2 - 3*a^2*b^2*m + 2*a^2*b^2 + (b^4*m^2 - 3*b^4*m + 2*b^4)*x^2 + 2*(a*b^3*m^2 - 3*a*b^3*m + 2*a*b^3)*x)","A",0
2167,1,155,0,0.431020," ","integrate((b*c*x+a*c)^m*(g*x+f)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(a b f m + 2 \, a b f p + 2 \, a b f - a^{2} g + {\left(b^{2} g m + 2 \, b^{2} g p + b^{2} g\right)} x^{2} + {\left(2 \, b^{2} f + {\left(b^{2} f + a b g\right)} m + 2 \, {\left(b^{2} f + a b g\right)} p\right)} x\right)} {\left(b c x + a c\right)}^{m} e^{\left(2 \, p \log\left(b c x + a c\right) + p \log\left(\frac{1}{c^{2}}\right)\right)}}{b^{2} m^{2} + 4 \, b^{2} p^{2} + 3 \, b^{2} m + 2 \, b^{2} + 2 \, {\left(2 \, b^{2} m + 3 \, b^{2}\right)} p}"," ",0,"(a*b*f*m + 2*a*b*f*p + 2*a*b*f - a^2*g + (b^2*g*m + 2*b^2*g*p + b^2*g)*x^2 + (2*b^2*f + (b^2*f + a*b*g)*m + 2*(b^2*f + a*b*g)*p)*x)*(b*c*x + a*c)^m*e^(2*p*log(b*c*x + a*c) + p*log(c^(-2)))/(b^2*m^2 + 4*b^2*p^2 + 3*b^2*m + 2*b^2 + 2*(2*b^2*m + 3*b^2)*p)","A",0
2168,1,52,0,0.435378," ","integrate((b*c*x+a*c)^(-3-2*p)*(g*x+f)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","-\frac{{\left(2 \, b g x + b f + a g\right)} \frac{1}{c^{2}}^{p}}{2 \, {\left(b^{4} c^{3} x^{2} + 2 \, a b^{3} c^{3} x + a^{2} b^{2} c^{3}\right)}}"," ",0,"-1/2*(2*b*g*x + b*f + a*g)*(c^(-2))^p/(b^4*c^3*x^2 + 2*a*b^3*c^3*x + a^2*b^2*c^3)","A",0
2169,1,60,0,0.448376," ","integrate((b*x+a)*(b*c*x+a*c)^m*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} {\left(b c x + a c\right)}^{m} e^{\left(2 \, p \log\left(b c x + a c\right) + p \log\left(\frac{1}{c^{2}}\right)\right)}}{b m + 2 \, b p + 2 \, b}"," ",0,"(b^2*x^2 + 2*a*b*x + a^2)*(b*c*x + a*c)^m*e^(2*p*log(b*c*x + a*c) + p*log(c^(-2)))/(b*m + 2*b*p + 2*b)","A",0
2170,1,102,0,0.420535," ","integrate((b*x+a)*(b*c*x+a*c)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{{\left(b^{8} x^{8} + 8 \, a b^{7} x^{7} + 28 \, a^{2} b^{6} x^{6} + 56 \, a^{3} b^{5} x^{5} + 70 \, a^{4} b^{4} x^{4} + 56 \, a^{5} b^{3} x^{3} + 28 \, a^{6} b^{2} x^{2} + 8 \, a^{7} b x + a^{8}\right)} {\left(b c x + a c\right)}^{m}}{b m + 8 \, b}"," ",0,"(b^8*x^8 + 8*a*b^7*x^7 + 28*a^2*b^6*x^6 + 56*a^3*b^5*x^5 + 70*a^4*b^4*x^4 + 56*a^5*b^3*x^3 + 28*a^6*b^2*x^2 + 8*a^7*b*x + a^8)*(b*c*x + a*c)^m/(b*m + 8*b)","B",0
2171,1,101,0,0.427079," ","integrate((b*x+a)*(b*c*x+a*c)^m/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{{\left(b c x + a c\right)}^{m}}{a^{4} b m - 4 \, a^{4} b + {\left(b^{5} m - 4 \, b^{5}\right)} x^{4} + 4 \, {\left(a b^{4} m - 4 \, a b^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{3} m - 4 \, a^{2} b^{3}\right)} x^{2} + 4 \, {\left(a^{3} b^{2} m - 4 \, a^{3} b^{2}\right)} x}"," ",0,"(b*c*x + a*c)^m/(a^4*b*m - 4*a^4*b + (b^5*m - 4*b^5)*x^4 + 4*(a*b^4*m - 4*a*b^4)*x^3 + 6*(a^2*b^3*m - 4*a^2*b^3)*x^2 + 4*(a^3*b^2*m - 4*a^3*b^2)*x)","B",0
2172,1,1469,0,1.585249," ","integrate((e*x+d)^3*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(4 \, {\left(32 \, c^{6} d^{5} e - 80 \, b c^{5} d^{4} e^{2} + 80 \, b^{2} c^{4} d^{3} e^{3} - 40 \, b^{3} c^{3} d^{2} e^{4} + 10 \, b^{4} c^{2} d e^{5} - b^{5} c e^{6}\right)} f + {\left(64 \, c^{6} d^{6} - 256 \, b c^{5} d^{5} e + 400 \, b^{2} c^{4} d^{4} e^{2} - 320 \, b^{3} c^{3} d^{3} e^{3} + 140 \, b^{4} c^{2} d^{2} e^{4} - 32 \, b^{5} c d e^{5} + 3 \, b^{6} e^{6}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(1280 \, c^{6} e^{5} g x^{5} + 128 \, {\left(12 \, c^{6} e^{5} f + {\left(36 \, c^{6} d e^{4} + b c^{5} e^{5}\right)} g\right)} x^{4} + 16 \, {\left(12 \, {\left(30 \, c^{6} d e^{4} + b c^{5} e^{5}\right)} f + {\left(340 \, c^{6} d^{2} e^{3} + 56 \, b c^{5} d e^{4} - 9 \, b^{2} c^{4} e^{5}\right)} g\right)} x^{3} + 8 \, {\left(4 \, {\left(224 \, c^{6} d^{2} e^{3} + 46 \, b c^{5} d e^{4} - 7 \, b^{2} c^{4} e^{5}\right)} f + {\left(128 \, c^{6} d^{3} e^{2} + 380 \, b c^{5} d^{2} e^{3} - 152 \, b^{2} c^{4} d e^{4} + 21 \, b^{3} c^{3} e^{5}\right)} g\right)} x^{2} - 4 \, {\left(2176 \, c^{6} d^{4} e - 4472 \, b c^{5} d^{3} e^{2} + 2996 \, b^{2} c^{4} d^{2} e^{3} - 910 \, b^{3} c^{3} d e^{4} + 105 \, b^{4} c^{2} e^{5}\right)} f - {\left(5632 \, c^{6} d^{5} - 16752 \, b c^{5} d^{4} e + 19408 \, b^{2} c^{4} d^{3} e^{2} - 10808 \, b^{3} c^{3} d^{2} e^{3} + 2940 \, b^{4} c^{2} d e^{4} - 315 \, b^{5} c e^{5}\right)} g + 2 \, {\left(4 \, {\left(120 \, c^{6} d^{3} e^{2} + 716 \, b c^{5} d^{2} e^{3} - 266 \, b^{2} c^{4} d e^{4} + 35 \, b^{3} c^{3} e^{5}\right)} f - {\left(1680 \, c^{6} d^{4} e - 3632 \, b c^{5} d^{3} e^{2} + 2680 \, b^{2} c^{4} d^{2} e^{3} - 868 \, b^{3} c^{3} d e^{4} + 105 \, b^{4} c^{2} e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{30720 \, c^{6} e^{2}}, -\frac{105 \, {\left(4 \, {\left(32 \, c^{6} d^{5} e - 80 \, b c^{5} d^{4} e^{2} + 80 \, b^{2} c^{4} d^{3} e^{3} - 40 \, b^{3} c^{3} d^{2} e^{4} + 10 \, b^{4} c^{2} d e^{5} - b^{5} c e^{6}\right)} f + {\left(64 \, c^{6} d^{6} - 256 \, b c^{5} d^{5} e + 400 \, b^{2} c^{4} d^{4} e^{2} - 320 \, b^{3} c^{3} d^{3} e^{3} + 140 \, b^{4} c^{2} d^{2} e^{4} - 32 \, b^{5} c d e^{5} + 3 \, b^{6} e^{6}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(1280 \, c^{6} e^{5} g x^{5} + 128 \, {\left(12 \, c^{6} e^{5} f + {\left(36 \, c^{6} d e^{4} + b c^{5} e^{5}\right)} g\right)} x^{4} + 16 \, {\left(12 \, {\left(30 \, c^{6} d e^{4} + b c^{5} e^{5}\right)} f + {\left(340 \, c^{6} d^{2} e^{3} + 56 \, b c^{5} d e^{4} - 9 \, b^{2} c^{4} e^{5}\right)} g\right)} x^{3} + 8 \, {\left(4 \, {\left(224 \, c^{6} d^{2} e^{3} + 46 \, b c^{5} d e^{4} - 7 \, b^{2} c^{4} e^{5}\right)} f + {\left(128 \, c^{6} d^{3} e^{2} + 380 \, b c^{5} d^{2} e^{3} - 152 \, b^{2} c^{4} d e^{4} + 21 \, b^{3} c^{3} e^{5}\right)} g\right)} x^{2} - 4 \, {\left(2176 \, c^{6} d^{4} e - 4472 \, b c^{5} d^{3} e^{2} + 2996 \, b^{2} c^{4} d^{2} e^{3} - 910 \, b^{3} c^{3} d e^{4} + 105 \, b^{4} c^{2} e^{5}\right)} f - {\left(5632 \, c^{6} d^{5} - 16752 \, b c^{5} d^{4} e + 19408 \, b^{2} c^{4} d^{3} e^{2} - 10808 \, b^{3} c^{3} d^{2} e^{3} + 2940 \, b^{4} c^{2} d e^{4} - 315 \, b^{5} c e^{5}\right)} g + 2 \, {\left(4 \, {\left(120 \, c^{6} d^{3} e^{2} + 716 \, b c^{5} d^{2} e^{3} - 266 \, b^{2} c^{4} d e^{4} + 35 \, b^{3} c^{3} e^{5}\right)} f - {\left(1680 \, c^{6} d^{4} e - 3632 \, b c^{5} d^{3} e^{2} + 2680 \, b^{2} c^{4} d^{2} e^{3} - 868 \, b^{3} c^{3} d e^{4} + 105 \, b^{4} c^{2} e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{15360 \, c^{6} e^{2}}\right]"," ",0,"[-1/30720*(105*(4*(32*c^6*d^5*e - 80*b*c^5*d^4*e^2 + 80*b^2*c^4*d^3*e^3 - 40*b^3*c^3*d^2*e^4 + 10*b^4*c^2*d*e^5 - b^5*c*e^6)*f + (64*c^6*d^6 - 256*b*c^5*d^5*e + 400*b^2*c^4*d^4*e^2 - 320*b^3*c^3*d^3*e^3 + 140*b^4*c^2*d^2*e^4 - 32*b^5*c*d*e^5 + 3*b^6*e^6)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(1280*c^6*e^5*g*x^5 + 128*(12*c^6*e^5*f + (36*c^6*d*e^4 + b*c^5*e^5)*g)*x^4 + 16*(12*(30*c^6*d*e^4 + b*c^5*e^5)*f + (340*c^6*d^2*e^3 + 56*b*c^5*d*e^4 - 9*b^2*c^4*e^5)*g)*x^3 + 8*(4*(224*c^6*d^2*e^3 + 46*b*c^5*d*e^4 - 7*b^2*c^4*e^5)*f + (128*c^6*d^3*e^2 + 380*b*c^5*d^2*e^3 - 152*b^2*c^4*d*e^4 + 21*b^3*c^3*e^5)*g)*x^2 - 4*(2176*c^6*d^4*e - 4472*b*c^5*d^3*e^2 + 2996*b^2*c^4*d^2*e^3 - 910*b^3*c^3*d*e^4 + 105*b^4*c^2*e^5)*f - (5632*c^6*d^5 - 16752*b*c^5*d^4*e + 19408*b^2*c^4*d^3*e^2 - 10808*b^3*c^3*d^2*e^3 + 2940*b^4*c^2*d*e^4 - 315*b^5*c*e^5)*g + 2*(4*(120*c^6*d^3*e^2 + 716*b*c^5*d^2*e^3 - 266*b^2*c^4*d*e^4 + 35*b^3*c^3*e^5)*f - (1680*c^6*d^4*e - 3632*b*c^5*d^3*e^2 + 2680*b^2*c^4*d^2*e^3 - 868*b^3*c^3*d*e^4 + 105*b^4*c^2*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^6*e^2), -1/15360*(105*(4*(32*c^6*d^5*e - 80*b*c^5*d^4*e^2 + 80*b^2*c^4*d^3*e^3 - 40*b^3*c^3*d^2*e^4 + 10*b^4*c^2*d*e^5 - b^5*c*e^6)*f + (64*c^6*d^6 - 256*b*c^5*d^5*e + 400*b^2*c^4*d^4*e^2 - 320*b^3*c^3*d^3*e^3 + 140*b^4*c^2*d^2*e^4 - 32*b^5*c*d*e^5 + 3*b^6*e^6)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(1280*c^6*e^5*g*x^5 + 128*(12*c^6*e^5*f + (36*c^6*d*e^4 + b*c^5*e^5)*g)*x^4 + 16*(12*(30*c^6*d*e^4 + b*c^5*e^5)*f + (340*c^6*d^2*e^3 + 56*b*c^5*d*e^4 - 9*b^2*c^4*e^5)*g)*x^3 + 8*(4*(224*c^6*d^2*e^3 + 46*b*c^5*d*e^4 - 7*b^2*c^4*e^5)*f + (128*c^6*d^3*e^2 + 380*b*c^5*d^2*e^3 - 152*b^2*c^4*d*e^4 + 21*b^3*c^3*e^5)*g)*x^2 - 4*(2176*c^6*d^4*e - 4472*b*c^5*d^3*e^2 + 2996*b^2*c^4*d^2*e^3 - 910*b^3*c^3*d*e^4 + 105*b^4*c^2*e^5)*f - (5632*c^6*d^5 - 16752*b*c^5*d^4*e + 19408*b^2*c^4*d^3*e^2 - 10808*b^3*c^3*d^2*e^3 + 2940*b^4*c^2*d*e^4 - 315*b^5*c*e^5)*g + 2*(4*(120*c^6*d^3*e^2 + 716*b*c^5*d^2*e^3 - 266*b^2*c^4*d*e^4 + 35*b^3*c^3*e^5)*f - (1680*c^6*d^4*e - 3632*b*c^5*d^3*e^2 + 2680*b^2*c^4*d^2*e^3 - 868*b^3*c^3*d*e^4 + 105*b^4*c^2*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^6*e^2)]","A",0
2173,1,1117,0,0.898987," ","integrate((e*x+d)^2*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(10 \, {\left(16 \, c^{5} d^{4} e - 32 \, b c^{4} d^{3} e^{2} + 24 \, b^{2} c^{3} d^{2} e^{3} - 8 \, b^{3} c^{2} d e^{4} + b^{4} c e^{5}\right)} f + {\left(64 \, c^{5} d^{5} - 240 \, b c^{4} d^{4} e + 320 \, b^{2} c^{3} d^{3} e^{2} - 200 \, b^{3} c^{2} d^{2} e^{3} + 60 \, b^{4} c d e^{4} - 7 \, b^{5} e^{5}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(384 \, c^{5} e^{4} g x^{4} + 48 \, {\left(10 \, c^{5} e^{4} f + {\left(20 \, c^{5} d e^{3} + b c^{4} e^{4}\right)} g\right)} x^{3} + 8 \, {\left(10 \, {\left(16 \, c^{5} d e^{3} + b c^{4} e^{4}\right)} f + {\left(64 \, c^{5} d^{2} e^{2} + 36 \, b c^{4} d e^{3} - 7 \, b^{2} c^{3} e^{4}\right)} g\right)} x^{2} - 10 \, {\left(128 \, c^{5} d^{3} e - 228 \, b c^{4} d^{2} e^{2} + 100 \, b^{2} c^{3} d e^{3} - 15 \, b^{3} c^{2} e^{4}\right)} f - {\left(896 \, c^{5} d^{4} - 2192 \, b c^{4} d^{3} e + 1996 \, b^{2} c^{3} d^{2} e^{2} - 760 \, b^{3} c^{2} d e^{3} + 105 \, b^{4} c e^{4}\right)} g + 2 \, {\left(10 \, {\left(36 \, c^{5} d^{2} e^{2} + 28 \, b c^{4} d e^{3} - 5 \, b^{2} c^{3} e^{4}\right)} f - {\left(240 \, c^{5} d^{3} e - 436 \, b c^{4} d^{2} e^{2} + 216 \, b^{2} c^{3} d e^{3} - 35 \, b^{3} c^{2} e^{4}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{7680 \, c^{5} e^{2}}, -\frac{15 \, {\left(10 \, {\left(16 \, c^{5} d^{4} e - 32 \, b c^{4} d^{3} e^{2} + 24 \, b^{2} c^{3} d^{2} e^{3} - 8 \, b^{3} c^{2} d e^{4} + b^{4} c e^{5}\right)} f + {\left(64 \, c^{5} d^{5} - 240 \, b c^{4} d^{4} e + 320 \, b^{2} c^{3} d^{3} e^{2} - 200 \, b^{3} c^{2} d^{2} e^{3} + 60 \, b^{4} c d e^{4} - 7 \, b^{5} e^{5}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(384 \, c^{5} e^{4} g x^{4} + 48 \, {\left(10 \, c^{5} e^{4} f + {\left(20 \, c^{5} d e^{3} + b c^{4} e^{4}\right)} g\right)} x^{3} + 8 \, {\left(10 \, {\left(16 \, c^{5} d e^{3} + b c^{4} e^{4}\right)} f + {\left(64 \, c^{5} d^{2} e^{2} + 36 \, b c^{4} d e^{3} - 7 \, b^{2} c^{3} e^{4}\right)} g\right)} x^{2} - 10 \, {\left(128 \, c^{5} d^{3} e - 228 \, b c^{4} d^{2} e^{2} + 100 \, b^{2} c^{3} d e^{3} - 15 \, b^{3} c^{2} e^{4}\right)} f - {\left(896 \, c^{5} d^{4} - 2192 \, b c^{4} d^{3} e + 1996 \, b^{2} c^{3} d^{2} e^{2} - 760 \, b^{3} c^{2} d e^{3} + 105 \, b^{4} c e^{4}\right)} g + 2 \, {\left(10 \, {\left(36 \, c^{5} d^{2} e^{2} + 28 \, b c^{4} d e^{3} - 5 \, b^{2} c^{3} e^{4}\right)} f - {\left(240 \, c^{5} d^{3} e - 436 \, b c^{4} d^{2} e^{2} + 216 \, b^{2} c^{3} d e^{3} - 35 \, b^{3} c^{2} e^{4}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{3840 \, c^{5} e^{2}}\right]"," ",0,"[1/7680*(15*(10*(16*c^5*d^4*e - 32*b*c^4*d^3*e^2 + 24*b^2*c^3*d^2*e^3 - 8*b^3*c^2*d*e^4 + b^4*c*e^5)*f + (64*c^5*d^5 - 240*b*c^4*d^4*e + 320*b^2*c^3*d^3*e^2 - 200*b^3*c^2*d^2*e^3 + 60*b^4*c*d*e^4 - 7*b^5*e^5)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(384*c^5*e^4*g*x^4 + 48*(10*c^5*e^4*f + (20*c^5*d*e^3 + b*c^4*e^4)*g)*x^3 + 8*(10*(16*c^5*d*e^3 + b*c^4*e^4)*f + (64*c^5*d^2*e^2 + 36*b*c^4*d*e^3 - 7*b^2*c^3*e^4)*g)*x^2 - 10*(128*c^5*d^3*e - 228*b*c^4*d^2*e^2 + 100*b^2*c^3*d*e^3 - 15*b^3*c^2*e^4)*f - (896*c^5*d^4 - 2192*b*c^4*d^3*e + 1996*b^2*c^3*d^2*e^2 - 760*b^3*c^2*d*e^3 + 105*b^4*c*e^4)*g + 2*(10*(36*c^5*d^2*e^2 + 28*b*c^4*d*e^3 - 5*b^2*c^3*e^4)*f - (240*c^5*d^3*e - 436*b*c^4*d^2*e^2 + 216*b^2*c^3*d*e^3 - 35*b^3*c^2*e^4)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^5*e^2), -1/3840*(15*(10*(16*c^5*d^4*e - 32*b*c^4*d^3*e^2 + 24*b^2*c^3*d^2*e^3 - 8*b^3*c^2*d*e^4 + b^4*c*e^5)*f + (64*c^5*d^5 - 240*b*c^4*d^4*e + 320*b^2*c^3*d^3*e^2 - 200*b^3*c^2*d^2*e^3 + 60*b^4*c*d*e^4 - 7*b^5*e^5)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(384*c^5*e^4*g*x^4 + 48*(10*c^5*e^4*f + (20*c^5*d*e^3 + b*c^4*e^4)*g)*x^3 + 8*(10*(16*c^5*d*e^3 + b*c^4*e^4)*f + (64*c^5*d^2*e^2 + 36*b*c^4*d*e^3 - 7*b^2*c^3*e^4)*g)*x^2 - 10*(128*c^5*d^3*e - 228*b*c^4*d^2*e^2 + 100*b^2*c^3*d*e^3 - 15*b^3*c^2*e^4)*f - (896*c^5*d^4 - 2192*b*c^4*d^3*e + 1996*b^2*c^3*d^2*e^2 - 760*b^3*c^2*d*e^3 + 105*b^4*c*e^4)*g + 2*(10*(36*c^5*d^2*e^2 + 28*b*c^4*d*e^3 - 5*b^2*c^3*e^4)*f - (240*c^5*d^3*e - 436*b*c^4*d^2*e^2 + 216*b^2*c^3*d*e^3 - 35*b^3*c^2*e^4)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^5*e^2)]","A",0
2174,1,825,0,0.597641," ","integrate((e*x+d)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, {\left(8 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f + {\left(16 \, c^{4} d^{4} - 64 \, b c^{3} d^{3} e + 72 \, b^{2} c^{2} d^{2} e^{2} - 32 \, b^{3} c d e^{3} + 5 \, b^{4} e^{4}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(48 \, c^{4} e^{3} g x^{3} + 8 \, {\left(8 \, c^{4} e^{3} f + {\left(8 \, c^{4} d e^{2} + b c^{3} e^{3}\right)} g\right)} x^{2} - 8 \, {\left(8 \, c^{4} d^{2} e - 14 \, b c^{3} d e^{2} + 3 \, b^{2} c^{2} e^{3}\right)} f - {\left(64 \, c^{4} d^{3} - 116 \, b c^{3} d^{2} e + 76 \, b^{2} c^{2} d e^{2} - 15 \, b^{3} c e^{3}\right)} g + 2 \, {\left(8 \, {\left(6 \, c^{4} d e^{2} + b c^{3} e^{3}\right)} f - {\left(12 \, c^{4} d^{2} e - 20 \, b c^{3} d e^{2} + 5 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{768 \, c^{4} e^{2}}, -\frac{3 \, {\left(8 \, {\left(8 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f + {\left(16 \, c^{4} d^{4} - 64 \, b c^{3} d^{3} e + 72 \, b^{2} c^{2} d^{2} e^{2} - 32 \, b^{3} c d e^{3} + 5 \, b^{4} e^{4}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(48 \, c^{4} e^{3} g x^{3} + 8 \, {\left(8 \, c^{4} e^{3} f + {\left(8 \, c^{4} d e^{2} + b c^{3} e^{3}\right)} g\right)} x^{2} - 8 \, {\left(8 \, c^{4} d^{2} e - 14 \, b c^{3} d e^{2} + 3 \, b^{2} c^{2} e^{3}\right)} f - {\left(64 \, c^{4} d^{3} - 116 \, b c^{3} d^{2} e + 76 \, b^{2} c^{2} d e^{2} - 15 \, b^{3} c e^{3}\right)} g + 2 \, {\left(8 \, {\left(6 \, c^{4} d e^{2} + b c^{3} e^{3}\right)} f - {\left(12 \, c^{4} d^{2} e - 20 \, b c^{3} d e^{2} + 5 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{384 \, c^{4} e^{2}}\right]"," ",0,"[-1/768*(3*(8*(8*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*f + (16*c^4*d^4 - 64*b*c^3*d^3*e + 72*b^2*c^2*d^2*e^2 - 32*b^3*c*d*e^3 + 5*b^4*e^4)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(48*c^4*e^3*g*x^3 + 8*(8*c^4*e^3*f + (8*c^4*d*e^2 + b*c^3*e^3)*g)*x^2 - 8*(8*c^4*d^2*e - 14*b*c^3*d*e^2 + 3*b^2*c^2*e^3)*f - (64*c^4*d^3 - 116*b*c^3*d^2*e + 76*b^2*c^2*d*e^2 - 15*b^3*c*e^3)*g + 2*(8*(6*c^4*d*e^2 + b*c^3*e^3)*f - (12*c^4*d^2*e - 20*b*c^3*d*e^2 + 5*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^4*e^2), -1/384*(3*(8*(8*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*f + (16*c^4*d^4 - 64*b*c^3*d^3*e + 72*b^2*c^2*d^2*e^2 - 32*b^3*c*d*e^3 + 5*b^4*e^4)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(48*c^4*e^3*g*x^3 + 8*(8*c^4*e^3*f + (8*c^4*d*e^2 + b*c^3*e^3)*g)*x^2 - 8*(8*c^4*d^2*e - 14*b*c^3*d*e^2 + 3*b^2*c^2*e^3)*f - (64*c^4*d^3 - 116*b*c^3*d^2*e + 76*b^2*c^2*d*e^2 - 15*b^3*c*e^3)*g + 2*(8*(6*c^4*d*e^2 + b*c^3*e^3)*f - (12*c^4*d^2*e - 20*b*c^3*d*e^2 + 5*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^4*e^2)]","A",0
2175,1,395,0,0.470960," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} f - {\left(4 \, c^{2} d^{2} - b^{2} e^{2}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(2 \, c^{2} e g x + 4 \, c^{2} e f - {\left(4 \, c^{2} d - b c e\right)} g\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{16 \, c^{2} e^{2}}, -\frac{{\left(4 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} f - {\left(4 \, c^{2} d^{2} - b^{2} e^{2}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(2 \, c^{2} e g x + 4 \, c^{2} e f - {\left(4 \, c^{2} d - b c e\right)} g\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{8 \, c^{2} e^{2}}\right]"," ",0,"[-1/16*((4*(2*c^2*d*e - b*c*e^2)*f - (4*c^2*d^2 - b^2*e^2)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(2*c^2*e*g*x + 4*c^2*e*f - (4*c^2*d - b*c*e)*g)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^2*e^2), -1/8*((4*(2*c^2*d*e - b*c*e^2)*f - (4*c^2*d^2 - b^2*e^2)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(2*c^2*e*g*x + 4*c^2*e*f - (4*c^2*d - b*c*e)*g)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^2*e^2)]","A",0
2176,1,399,0,0.967671," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, c d e f - {\left(4 \, c d^{2} - b d e\right)} g + {\left(2 \, c e^{2} f - {\left(4 \, c d e - b e^{2}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c e g x - 2 \, c e f + 3 \, c d g\right)}}{4 \, {\left(c e^{3} x + c d e^{2}\right)}}, \frac{{\left(2 \, c d e f - {\left(4 \, c d^{2} - b d e\right)} g + {\left(2 \, c e^{2} f - {\left(4 \, c d e - b e^{2}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c e g x - 2 \, c e f + 3 \, c d g\right)}}{2 \, {\left(c e^{3} x + c d e^{2}\right)}}\right]"," ",0,"[-1/4*((2*c*d*e*f - (4*c*d^2 - b*d*e)*g + (2*c*e^2*f - (4*c*d*e - b*e^2)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c*e*g*x - 2*c*e*f + 3*c*d*g))/(c*e^3*x + c*d*e^2), 1/2*((2*c*d*e*f - (4*c*d^2 - b*d*e)*g + (2*c*e^2*f - (4*c*d*e - b*e^2)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c*e*g*x - 2*c*e*f + 3*c*d*g))/(c*e^3*x + c*d*e^2)]","A",0
2177,1,579,0,1.501913," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(2 \, c d e^{2} - b e^{3}\right)} g x^{2} + 2 \, {\left(2 \, c d^{2} e - b d e^{2}\right)} g x + {\left(2 \, c d^{3} - b d^{2} e\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(c d e - b e^{2}\right)} f + {\left(5 \, c d^{2} - 2 \, b d e\right)} g - {\left(c e^{2} f - {\left(7 \, c d e - 3 \, b e^{2}\right)} g\right)} x\right)}}{6 \, {\left(2 \, c d^{3} e^{2} - b d^{2} e^{3} + {\left(2 \, c d e^{4} - b e^{5}\right)} x^{2} + 2 \, {\left(2 \, c d^{2} e^{3} - b d e^{4}\right)} x\right)}}, \frac{3 \, {\left({\left(2 \, c d e^{2} - b e^{3}\right)} g x^{2} + 2 \, {\left(2 \, c d^{2} e - b d e^{2}\right)} g x + {\left(2 \, c d^{3} - b d^{2} e\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(c d e - b e^{2}\right)} f + {\left(5 \, c d^{2} - 2 \, b d e\right)} g - {\left(c e^{2} f - {\left(7 \, c d e - 3 \, b e^{2}\right)} g\right)} x\right)}}{3 \, {\left(2 \, c d^{3} e^{2} - b d^{2} e^{3} + {\left(2 \, c d e^{4} - b e^{5}\right)} x^{2} + 2 \, {\left(2 \, c d^{2} e^{3} - b d e^{4}\right)} x\right)}}\right]"," ",0,"[1/6*(3*((2*c*d*e^2 - b*e^3)*g*x^2 + 2*(2*c*d^2*e - b*d*e^2)*g*x + (2*c*d^3 - b*d^2*e)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((c*d*e - b*e^2)*f + (5*c*d^2 - 2*b*d*e)*g - (c*e^2*f - (7*c*d*e - 3*b*e^2)*g)*x))/(2*c*d^3*e^2 - b*d^2*e^3 + (2*c*d*e^4 - b*e^5)*x^2 + 2*(2*c*d^2*e^3 - b*d*e^4)*x), 1/3*(3*((2*c*d*e^2 - b*e^3)*g*x^2 + 2*(2*c*d^2*e - b*d*e^2)*g*x + (2*c*d^3 - b*d^2*e)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((c*d*e - b*e^2)*f + (5*c*d^2 - 2*b*d*e)*g - (c*e^2*f - (7*c*d*e - 3*b*e^2)*g)*x))/(2*c*d^3*e^2 - b*d^2*e^3 + (2*c*d*e^4 - b*e^5)*x^2 + 2*(2*c*d^2*e^3 - b*d*e^4)*x)]","A",0
2178,1,307,0,7.007537," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(2 \, c^{2} e^{3} f + {\left(8 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} g\right)} x^{2} - {\left(8 \, c^{2} d^{2} e - 11 \, b c d e^{2} + 3 \, b^{2} e^{3}\right)} f - 2 \, {\left(c^{2} d^{3} - 2 \, b c d^{2} e + b^{2} d e^{2}\right)} g + {\left({\left(6 \, c^{2} d e^{2} - b c e^{3}\right)} f - {\left(6 \, c^{2} d^{2} e - 11 \, b c d e^{2} + 5 \, b^{2} e^{3}\right)} g\right)} x\right)}}{15 \, {\left(4 \, c^{2} d^{5} e^{2} - 4 \, b c d^{4} e^{3} + b^{2} d^{3} e^{4} + {\left(4 \, c^{2} d^{2} e^{5} - 4 \, b c d e^{6} + b^{2} e^{7}\right)} x^{3} + 3 \, {\left(4 \, c^{2} d^{3} e^{4} - 4 \, b c d^{2} e^{5} + b^{2} d e^{6}\right)} x^{2} + 3 \, {\left(4 \, c^{2} d^{4} e^{3} - 4 \, b c d^{3} e^{4} + b^{2} d^{2} e^{5}\right)} x\right)}}"," ",0,"2/15*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((2*c^2*e^3*f + (8*c^2*d*e^2 - 5*b*c*e^3)*g)*x^2 - (8*c^2*d^2*e - 11*b*c*d*e^2 + 3*b^2*e^3)*f - 2*(c^2*d^3 - 2*b*c*d^2*e + b^2*d*e^2)*g + ((6*c^2*d*e^2 - b*c*e^3)*f - (6*c^2*d^2*e - 11*b*c*d*e^2 + 5*b^2*e^3)*g)*x)/(4*c^2*d^5*e^2 - 4*b*c*d^4*e^3 + b^2*d^3*e^4 + (4*c^2*d^2*e^5 - 4*b*c*d*e^6 + b^2*e^7)*x^3 + 3*(4*c^2*d^3*e^4 - 4*b*c*d^2*e^5 + b^2*d*e^6)*x^2 + 3*(4*c^2*d^4*e^3 - 4*b*c*d^3*e^4 + b^2*d^2*e^5)*x)","B",0
2179,1,540,0,47.057842," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, {\left(4 \, c^{3} e^{4} f + {\left(10 \, c^{3} d e^{3} - 7 \, b c^{2} e^{4}\right)} g\right)} x^{3} + {\left(4 \, {\left(8 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f + {\left(80 \, c^{3} d^{2} e^{2} - 66 \, b c^{2} d e^{3} + 7 \, b^{2} c e^{4}\right)} g\right)} x^{2} - {\left(92 \, c^{3} d^{3} e - 164 \, b c^{2} d^{2} e^{2} + 87 \, b^{2} c d e^{3} - 15 \, b^{3} e^{4}\right)} f - 2 \, {\left(10 \, c^{3} d^{4} - 23 \, b c^{2} d^{3} e + 16 \, b^{2} c d^{2} e^{2} - 3 \, b^{3} d e^{3}\right)} g + {\left({\left(52 \, c^{3} d^{2} e^{2} - 20 \, b c^{2} d e^{3} + 3 \, b^{2} c e^{4}\right)} f - {\left(80 \, c^{3} d^{3} e - 174 \, b c^{2} d^{2} e^{2} + 115 \, b^{2} c d e^{3} - 21 \, b^{3} e^{4}\right)} g\right)} x\right)}}{105 \, {\left(8 \, c^{3} d^{7} e^{2} - 12 \, b c^{2} d^{6} e^{3} + 6 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5} + {\left(8 \, c^{3} d^{3} e^{6} - 12 \, b c^{2} d^{2} e^{7} + 6 \, b^{2} c d e^{8} - b^{3} e^{9}\right)} x^{4} + 4 \, {\left(8 \, c^{3} d^{4} e^{5} - 12 \, b c^{2} d^{3} e^{6} + 6 \, b^{2} c d^{2} e^{7} - b^{3} d e^{8}\right)} x^{3} + 6 \, {\left(8 \, c^{3} d^{5} e^{4} - 12 \, b c^{2} d^{4} e^{5} + 6 \, b^{2} c d^{3} e^{6} - b^{3} d^{2} e^{7}\right)} x^{2} + 4 \, {\left(8 \, c^{3} d^{6} e^{3} - 12 \, b c^{2} d^{5} e^{4} + 6 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x\right)}}"," ",0,"2/105*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*(4*c^3*e^4*f + (10*c^3*d*e^3 - 7*b*c^2*e^4)*g)*x^3 + (4*(8*c^3*d*e^3 - b*c^2*e^4)*f + (80*c^3*d^2*e^2 - 66*b*c^2*d*e^3 + 7*b^2*c*e^4)*g)*x^2 - (92*c^3*d^3*e - 164*b*c^2*d^2*e^2 + 87*b^2*c*d*e^3 - 15*b^3*e^4)*f - 2*(10*c^3*d^4 - 23*b*c^2*d^3*e + 16*b^2*c*d^2*e^2 - 3*b^3*d*e^3)*g + ((52*c^3*d^2*e^2 - 20*b*c^2*d*e^3 + 3*b^2*c*e^4)*f - (80*c^3*d^3*e - 174*b*c^2*d^2*e^2 + 115*b^2*c*d*e^3 - 21*b^3*e^4)*g)*x)/(8*c^3*d^7*e^2 - 12*b*c^2*d^6*e^3 + 6*b^2*c*d^5*e^4 - b^3*d^4*e^5 + (8*c^3*d^3*e^6 - 12*b*c^2*d^2*e^7 + 6*b^2*c*d*e^8 - b^3*e^9)*x^4 + 4*(8*c^3*d^4*e^5 - 12*b*c^2*d^3*e^6 + 6*b^2*c*d^2*e^7 - b^3*d*e^8)*x^3 + 6*(8*c^3*d^5*e^4 - 12*b*c^2*d^4*e^5 + 6*b^2*c*d^3*e^6 - b^3*d^2*e^7)*x^2 + 4*(8*c^3*d^6*e^3 - 12*b*c^2*d^5*e^4 + 6*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x)","B",0
2180,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2181,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^7,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2182,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^8,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2183,1,2337,0,6.772043," ","integrate((e*x+d)^3*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(16 \, {\left(128 \, c^{8} d^{7} e - 448 \, b c^{7} d^{6} e^{2} + 672 \, b^{2} c^{6} d^{5} e^{3} - 560 \, b^{3} c^{5} d^{4} e^{4} + 280 \, b^{4} c^{4} d^{3} e^{5} - 84 \, b^{5} c^{3} d^{2} e^{6} + 14 \, b^{6} c^{2} d e^{7} - b^{7} c e^{8}\right)} f + {\left(768 \, c^{8} d^{8} - 4096 \, b c^{7} d^{7} e + 8960 \, b^{2} c^{6} d^{6} e^{2} - 10752 \, b^{3} c^{5} d^{5} e^{3} + 7840 \, b^{4} c^{4} d^{4} e^{4} - 3584 \, b^{5} c^{3} d^{3} e^{5} + 1008 \, b^{6} c^{2} d^{2} e^{6} - 160 \, b^{7} c d e^{7} + 11 \, b^{8} e^{8}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(71680 \, c^{8} e^{7} g x^{7} + 5120 \, {\left(16 \, c^{8} e^{7} f + {\left(48 \, c^{8} d e^{6} + 17 \, b c^{7} e^{7}\right)} g\right)} x^{6} + 1280 \, {\left(16 \, {\left(14 \, c^{8} d e^{6} + 5 \, b c^{7} e^{7}\right)} f + {\left(140 \, c^{8} d^{2} e^{5} + 324 \, b c^{7} d e^{6} + b^{2} c^{6} e^{7}\right)} g\right)} x^{5} + 128 \, {\left(16 \, {\left(104 \, c^{8} d^{2} e^{5} + 246 \, b c^{7} d e^{6} + b^{2} c^{6} e^{7}\right)} f - {\left(2176 \, c^{8} d^{3} e^{4} - 5932 \, b c^{7} d^{2} e^{5} - 100 \, b^{2} c^{6} d e^{6} + 11 \, b^{3} c^{5} e^{7}\right)} g\right)} x^{4} - 16 \, {\left(16 \, {\left(1400 \, c^{8} d^{3} e^{4} - 3764 \, b c^{7} d^{2} e^{5} - 86 \, b^{2} c^{6} d e^{6} + 9 \, b^{3} c^{5} e^{7}\right)} f + {\left(30800 \, c^{8} d^{4} e^{3} - 37984 \, b c^{7} d^{3} e^{4} - 3912 \, b^{2} c^{6} d^{2} e^{5} + 1000 \, b^{3} c^{5} d e^{6} - 99 \, b^{4} c^{4} e^{7}\right)} g\right)} x^{3} - 8 \, {\left(16 \, {\left(5248 \, c^{8} d^{4} e^{3} - 6296 \, b c^{7} d^{3} e^{4} - 924 \, b^{2} c^{6} d^{2} e^{5} + 222 \, b^{3} c^{5} d e^{6} - 21 \, b^{4} c^{4} e^{7}\right)} f + {\left(22528 \, c^{8} d^{5} e^{2} - 5904 \, b c^{7} d^{4} e^{3} - 25888 \, b^{2} c^{6} d^{3} e^{4} + 11496 \, b^{3} c^{5} d^{2} e^{5} - 2568 \, b^{4} c^{4} d e^{6} + 231 \, b^{5} c^{3} e^{7}\right)} g\right)} x^{2} + 16 \, {\left(23552 \, c^{8} d^{6} e - 78496 \, b c^{7} d^{5} e^{2} + 97424 \, b^{2} c^{6} d^{4} e^{3} - 60288 \, b^{3} c^{5} d^{3} e^{4} + 21168 \, b^{4} c^{4} d^{2} e^{5} - 3990 \, b^{5} c^{3} d e^{6} + 315 \, b^{6} c^{2} e^{7}\right)} f + {\left(212992 \, c^{8} d^{7} - 873408 \, b c^{7} d^{6} e + 1519680 \, b^{2} c^{6} d^{5} e^{2} - 1433392 \, b^{3} c^{5} d^{4} e^{3} + 790176 \, b^{4} c^{4} d^{3} e^{4} - 256788 \, b^{5} c^{3} d^{2} e^{5} + 45780 \, b^{6} c^{2} d e^{6} - 3465 \, b^{7} c e^{7}\right)} g - 2 \, {\left(16 \, {\left(7840 \, c^{8} d^{5} e^{2} + 1392 \, b c^{7} d^{4} e^{3} - 13984 \, b^{2} c^{6} d^{3} e^{4} + 5760 \, b^{3} c^{5} d^{2} e^{5} - 1218 \, b^{4} c^{4} d e^{6} + 105 \, b^{5} c^{3} e^{7}\right)} f - {\left(60480 \, c^{8} d^{6} e - 208832 \, b c^{7} d^{5} e^{2} + 278416 \, b^{2} c^{6} d^{4} e^{3} - 188384 \, b^{3} c^{5} d^{3} e^{4} + 70668 \, b^{4} c^{4} d^{2} e^{5} - 14028 \, b^{5} c^{3} d e^{6} + 1155 \, b^{6} c^{2} e^{7}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{2293760 \, c^{7} e^{2}}, -\frac{315 \, {\left(16 \, {\left(128 \, c^{8} d^{7} e - 448 \, b c^{7} d^{6} e^{2} + 672 \, b^{2} c^{6} d^{5} e^{3} - 560 \, b^{3} c^{5} d^{4} e^{4} + 280 \, b^{4} c^{4} d^{3} e^{5} - 84 \, b^{5} c^{3} d^{2} e^{6} + 14 \, b^{6} c^{2} d e^{7} - b^{7} c e^{8}\right)} f + {\left(768 \, c^{8} d^{8} - 4096 \, b c^{7} d^{7} e + 8960 \, b^{2} c^{6} d^{6} e^{2} - 10752 \, b^{3} c^{5} d^{5} e^{3} + 7840 \, b^{4} c^{4} d^{4} e^{4} - 3584 \, b^{5} c^{3} d^{3} e^{5} + 1008 \, b^{6} c^{2} d^{2} e^{6} - 160 \, b^{7} c d e^{7} + 11 \, b^{8} e^{8}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(71680 \, c^{8} e^{7} g x^{7} + 5120 \, {\left(16 \, c^{8} e^{7} f + {\left(48 \, c^{8} d e^{6} + 17 \, b c^{7} e^{7}\right)} g\right)} x^{6} + 1280 \, {\left(16 \, {\left(14 \, c^{8} d e^{6} + 5 \, b c^{7} e^{7}\right)} f + {\left(140 \, c^{8} d^{2} e^{5} + 324 \, b c^{7} d e^{6} + b^{2} c^{6} e^{7}\right)} g\right)} x^{5} + 128 \, {\left(16 \, {\left(104 \, c^{8} d^{2} e^{5} + 246 \, b c^{7} d e^{6} + b^{2} c^{6} e^{7}\right)} f - {\left(2176 \, c^{8} d^{3} e^{4} - 5932 \, b c^{7} d^{2} e^{5} - 100 \, b^{2} c^{6} d e^{6} + 11 \, b^{3} c^{5} e^{7}\right)} g\right)} x^{4} - 16 \, {\left(16 \, {\left(1400 \, c^{8} d^{3} e^{4} - 3764 \, b c^{7} d^{2} e^{5} - 86 \, b^{2} c^{6} d e^{6} + 9 \, b^{3} c^{5} e^{7}\right)} f + {\left(30800 \, c^{8} d^{4} e^{3} - 37984 \, b c^{7} d^{3} e^{4} - 3912 \, b^{2} c^{6} d^{2} e^{5} + 1000 \, b^{3} c^{5} d e^{6} - 99 \, b^{4} c^{4} e^{7}\right)} g\right)} x^{3} - 8 \, {\left(16 \, {\left(5248 \, c^{8} d^{4} e^{3} - 6296 \, b c^{7} d^{3} e^{4} - 924 \, b^{2} c^{6} d^{2} e^{5} + 222 \, b^{3} c^{5} d e^{6} - 21 \, b^{4} c^{4} e^{7}\right)} f + {\left(22528 \, c^{8} d^{5} e^{2} - 5904 \, b c^{7} d^{4} e^{3} - 25888 \, b^{2} c^{6} d^{3} e^{4} + 11496 \, b^{3} c^{5} d^{2} e^{5} - 2568 \, b^{4} c^{4} d e^{6} + 231 \, b^{5} c^{3} e^{7}\right)} g\right)} x^{2} + 16 \, {\left(23552 \, c^{8} d^{6} e - 78496 \, b c^{7} d^{5} e^{2} + 97424 \, b^{2} c^{6} d^{4} e^{3} - 60288 \, b^{3} c^{5} d^{3} e^{4} + 21168 \, b^{4} c^{4} d^{2} e^{5} - 3990 \, b^{5} c^{3} d e^{6} + 315 \, b^{6} c^{2} e^{7}\right)} f + {\left(212992 \, c^{8} d^{7} - 873408 \, b c^{7} d^{6} e + 1519680 \, b^{2} c^{6} d^{5} e^{2} - 1433392 \, b^{3} c^{5} d^{4} e^{3} + 790176 \, b^{4} c^{4} d^{3} e^{4} - 256788 \, b^{5} c^{3} d^{2} e^{5} + 45780 \, b^{6} c^{2} d e^{6} - 3465 \, b^{7} c e^{7}\right)} g - 2 \, {\left(16 \, {\left(7840 \, c^{8} d^{5} e^{2} + 1392 \, b c^{7} d^{4} e^{3} - 13984 \, b^{2} c^{6} d^{3} e^{4} + 5760 \, b^{3} c^{5} d^{2} e^{5} - 1218 \, b^{4} c^{4} d e^{6} + 105 \, b^{5} c^{3} e^{7}\right)} f - {\left(60480 \, c^{8} d^{6} e - 208832 \, b c^{7} d^{5} e^{2} + 278416 \, b^{2} c^{6} d^{4} e^{3} - 188384 \, b^{3} c^{5} d^{3} e^{4} + 70668 \, b^{4} c^{4} d^{2} e^{5} - 14028 \, b^{5} c^{3} d e^{6} + 1155 \, b^{6} c^{2} e^{7}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{1146880 \, c^{7} e^{2}}\right]"," ",0,"[-1/2293760*(315*(16*(128*c^8*d^7*e - 448*b*c^7*d^6*e^2 + 672*b^2*c^6*d^5*e^3 - 560*b^3*c^5*d^4*e^4 + 280*b^4*c^4*d^3*e^5 - 84*b^5*c^3*d^2*e^6 + 14*b^6*c^2*d*e^7 - b^7*c*e^8)*f + (768*c^8*d^8 - 4096*b*c^7*d^7*e + 8960*b^2*c^6*d^6*e^2 - 10752*b^3*c^5*d^5*e^3 + 7840*b^4*c^4*d^4*e^4 - 3584*b^5*c^3*d^3*e^5 + 1008*b^6*c^2*d^2*e^6 - 160*b^7*c*d*e^7 + 11*b^8*e^8)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(71680*c^8*e^7*g*x^7 + 5120*(16*c^8*e^7*f + (48*c^8*d*e^6 + 17*b*c^7*e^7)*g)*x^6 + 1280*(16*(14*c^8*d*e^6 + 5*b*c^7*e^7)*f + (140*c^8*d^2*e^5 + 324*b*c^7*d*e^6 + b^2*c^6*e^7)*g)*x^5 + 128*(16*(104*c^8*d^2*e^5 + 246*b*c^7*d*e^6 + b^2*c^6*e^7)*f - (2176*c^8*d^3*e^4 - 5932*b*c^7*d^2*e^5 - 100*b^2*c^6*d*e^6 + 11*b^3*c^5*e^7)*g)*x^4 - 16*(16*(1400*c^8*d^3*e^4 - 3764*b*c^7*d^2*e^5 - 86*b^2*c^6*d*e^6 + 9*b^3*c^5*e^7)*f + (30800*c^8*d^4*e^3 - 37984*b*c^7*d^3*e^4 - 3912*b^2*c^6*d^2*e^5 + 1000*b^3*c^5*d*e^6 - 99*b^4*c^4*e^7)*g)*x^3 - 8*(16*(5248*c^8*d^4*e^3 - 6296*b*c^7*d^3*e^4 - 924*b^2*c^6*d^2*e^5 + 222*b^3*c^5*d*e^6 - 21*b^4*c^4*e^7)*f + (22528*c^8*d^5*e^2 - 5904*b*c^7*d^4*e^3 - 25888*b^2*c^6*d^3*e^4 + 11496*b^3*c^5*d^2*e^5 - 2568*b^4*c^4*d*e^6 + 231*b^5*c^3*e^7)*g)*x^2 + 16*(23552*c^8*d^6*e - 78496*b*c^7*d^5*e^2 + 97424*b^2*c^6*d^4*e^3 - 60288*b^3*c^5*d^3*e^4 + 21168*b^4*c^4*d^2*e^5 - 3990*b^5*c^3*d*e^6 + 315*b^6*c^2*e^7)*f + (212992*c^8*d^7 - 873408*b*c^7*d^6*e + 1519680*b^2*c^6*d^5*e^2 - 1433392*b^3*c^5*d^4*e^3 + 790176*b^4*c^4*d^3*e^4 - 256788*b^5*c^3*d^2*e^5 + 45780*b^6*c^2*d*e^6 - 3465*b^7*c*e^7)*g - 2*(16*(7840*c^8*d^5*e^2 + 1392*b*c^7*d^4*e^3 - 13984*b^2*c^6*d^3*e^4 + 5760*b^3*c^5*d^2*e^5 - 1218*b^4*c^4*d*e^6 + 105*b^5*c^3*e^7)*f - (60480*c^8*d^6*e - 208832*b*c^7*d^5*e^2 + 278416*b^2*c^6*d^4*e^3 - 188384*b^3*c^5*d^3*e^4 + 70668*b^4*c^4*d^2*e^5 - 14028*b^5*c^3*d*e^6 + 1155*b^6*c^2*e^7)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^7*e^2), -1/1146880*(315*(16*(128*c^8*d^7*e - 448*b*c^7*d^6*e^2 + 672*b^2*c^6*d^5*e^3 - 560*b^3*c^5*d^4*e^4 + 280*b^4*c^4*d^3*e^5 - 84*b^5*c^3*d^2*e^6 + 14*b^6*c^2*d*e^7 - b^7*c*e^8)*f + (768*c^8*d^8 - 4096*b*c^7*d^7*e + 8960*b^2*c^6*d^6*e^2 - 10752*b^3*c^5*d^5*e^3 + 7840*b^4*c^4*d^4*e^4 - 3584*b^5*c^3*d^3*e^5 + 1008*b^6*c^2*d^2*e^6 - 160*b^7*c*d*e^7 + 11*b^8*e^8)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(71680*c^8*e^7*g*x^7 + 5120*(16*c^8*e^7*f + (48*c^8*d*e^6 + 17*b*c^7*e^7)*g)*x^6 + 1280*(16*(14*c^8*d*e^6 + 5*b*c^7*e^7)*f + (140*c^8*d^2*e^5 + 324*b*c^7*d*e^6 + b^2*c^6*e^7)*g)*x^5 + 128*(16*(104*c^8*d^2*e^5 + 246*b*c^7*d*e^6 + b^2*c^6*e^7)*f - (2176*c^8*d^3*e^4 - 5932*b*c^7*d^2*e^5 - 100*b^2*c^6*d*e^6 + 11*b^3*c^5*e^7)*g)*x^4 - 16*(16*(1400*c^8*d^3*e^4 - 3764*b*c^7*d^2*e^5 - 86*b^2*c^6*d*e^6 + 9*b^3*c^5*e^7)*f + (30800*c^8*d^4*e^3 - 37984*b*c^7*d^3*e^4 - 3912*b^2*c^6*d^2*e^5 + 1000*b^3*c^5*d*e^6 - 99*b^4*c^4*e^7)*g)*x^3 - 8*(16*(5248*c^8*d^4*e^3 - 6296*b*c^7*d^3*e^4 - 924*b^2*c^6*d^2*e^5 + 222*b^3*c^5*d*e^6 - 21*b^4*c^4*e^7)*f + (22528*c^8*d^5*e^2 - 5904*b*c^7*d^4*e^3 - 25888*b^2*c^6*d^3*e^4 + 11496*b^3*c^5*d^2*e^5 - 2568*b^4*c^4*d*e^6 + 231*b^5*c^3*e^7)*g)*x^2 + 16*(23552*c^8*d^6*e - 78496*b*c^7*d^5*e^2 + 97424*b^2*c^6*d^4*e^3 - 60288*b^3*c^5*d^3*e^4 + 21168*b^4*c^4*d^2*e^5 - 3990*b^5*c^3*d*e^6 + 315*b^6*c^2*e^7)*f + (212992*c^8*d^7 - 873408*b*c^7*d^6*e + 1519680*b^2*c^6*d^5*e^2 - 1433392*b^3*c^5*d^4*e^3 + 790176*b^4*c^4*d^3*e^4 - 256788*b^5*c^3*d^2*e^5 + 45780*b^6*c^2*d*e^6 - 3465*b^7*c*e^7)*g - 2*(16*(7840*c^8*d^5*e^2 + 1392*b*c^7*d^4*e^3 - 13984*b^2*c^6*d^3*e^4 + 5760*b^3*c^5*d^2*e^5 - 1218*b^4*c^4*d*e^6 + 105*b^5*c^3*e^7)*f - (60480*c^8*d^6*e - 208832*b*c^7*d^5*e^2 + 278416*b^2*c^6*d^4*e^3 - 188384*b^3*c^5*d^3*e^4 + 70668*b^4*c^4*d^2*e^5 - 14028*b^5*c^3*d*e^6 + 1155*b^6*c^2*e^7)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^7*e^2)]","B",0
2184,1,1877,0,3.349937," ","integrate((e*x+d)^2*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(14 \, {\left(64 \, c^{7} d^{6} e - 192 \, b c^{6} d^{5} e^{2} + 240 \, b^{2} c^{5} d^{4} e^{3} - 160 \, b^{3} c^{4} d^{3} e^{4} + 60 \, b^{4} c^{3} d^{2} e^{5} - 12 \, b^{5} c^{2} d e^{6} + b^{6} c e^{7}\right)} f + {\left(256 \, c^{7} d^{7} - 1344 \, b c^{6} d^{6} e + 2688 \, b^{2} c^{5} d^{5} e^{2} - 2800 \, b^{3} c^{4} d^{4} e^{3} + 1680 \, b^{4} c^{3} d^{3} e^{4} - 588 \, b^{5} c^{2} d^{2} e^{5} + 112 \, b^{6} c d e^{6} - 9 \, b^{7} e^{7}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(15360 \, c^{7} e^{6} g x^{6} + 1280 \, {\left(14 \, c^{7} e^{6} f + {\left(28 \, c^{7} d e^{5} + 15 \, b c^{6} e^{6}\right)} g\right)} x^{5} + 128 \, {\left(14 \, {\left(24 \, c^{7} d e^{5} + 13 \, b c^{6} e^{6}\right)} f - {\left(24 \, c^{7} d^{2} e^{4} - 556 \, b c^{6} d e^{5} - 3 \, b^{2} c^{5} e^{6}\right)} g\right)} x^{4} - 16 \, {\left(14 \, {\left(20 \, c^{7} d^{2} e^{4} - 404 \, b c^{6} d e^{5} - 3 \, b^{2} c^{5} e^{6}\right)} f + {\left(3920 \, c^{7} d^{3} e^{3} - 5636 \, b c^{6} d^{2} e^{4} - 216 \, b^{2} c^{5} d e^{5} + 27 \, b^{3} c^{4} e^{6}\right)} g\right)} x^{3} - 8 \, {\left(14 \, {\left(768 \, c^{7} d^{3} e^{3} - 1092 \, b c^{6} d^{2} e^{4} - 60 \, b^{2} c^{5} d e^{5} + 7 \, b^{3} c^{4} e^{6}\right)} f + {\left(4992 \, c^{7} d^{4} e^{2} - 3600 \, b c^{6} d^{3} e^{3} - 1932 \, b^{2} c^{5} d^{2} e^{4} + 568 \, b^{3} c^{4} d e^{5} - 63 \, b^{4} c^{3} e^{6}\right)} g\right)} x^{2} + 14 \, {\left(3072 \, c^{7} d^{5} e - 9840 \, b c^{6} d^{4} e^{2} + 10464 \, b^{2} c^{5} d^{3} e^{3} - 4816 \, b^{3} c^{4} d^{2} e^{4} + 1120 \, b^{4} c^{3} d e^{5} - 105 \, b^{5} c^{2} e^{6}\right)} f + {\left(27648 \, c^{7} d^{6} - 97728 \, b c^{6} d^{5} e + 145776 \, b^{2} c^{5} d^{4} e^{2} - 113440 \, b^{3} c^{4} d^{3} e^{3} + 47824 \, b^{4} c^{3} d^{2} e^{4} - 10500 \, b^{5} c^{2} d e^{5} + 945 \, b^{6} c e^{6}\right)} g - 2 \, {\left(14 \, {\left(2160 \, c^{7} d^{4} e^{2} - 1248 \, b c^{6} d^{3} e^{3} - 1248 \, b^{2} c^{5} d^{2} e^{4} + 336 \, b^{3} c^{4} d e^{5} - 35 \, b^{4} c^{3} e^{6}\right)} f - {\left(6720 \, c^{7} d^{5} e - 21648 \, b c^{6} d^{4} e^{2} + 24480 \, b^{2} c^{5} d^{3} e^{3} - 12576 \, b^{3} c^{4} d^{2} e^{4} + 3164 \, b^{4} c^{3} d e^{5} - 315 \, b^{5} c^{2} e^{6}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{430080 \, c^{6} e^{2}}, -\frac{105 \, {\left(14 \, {\left(64 \, c^{7} d^{6} e - 192 \, b c^{6} d^{5} e^{2} + 240 \, b^{2} c^{5} d^{4} e^{3} - 160 \, b^{3} c^{4} d^{3} e^{4} + 60 \, b^{4} c^{3} d^{2} e^{5} - 12 \, b^{5} c^{2} d e^{6} + b^{6} c e^{7}\right)} f + {\left(256 \, c^{7} d^{7} - 1344 \, b c^{6} d^{6} e + 2688 \, b^{2} c^{5} d^{5} e^{2} - 2800 \, b^{3} c^{4} d^{4} e^{3} + 1680 \, b^{4} c^{3} d^{3} e^{4} - 588 \, b^{5} c^{2} d^{2} e^{5} + 112 \, b^{6} c d e^{6} - 9 \, b^{7} e^{7}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(15360 \, c^{7} e^{6} g x^{6} + 1280 \, {\left(14 \, c^{7} e^{6} f + {\left(28 \, c^{7} d e^{5} + 15 \, b c^{6} e^{6}\right)} g\right)} x^{5} + 128 \, {\left(14 \, {\left(24 \, c^{7} d e^{5} + 13 \, b c^{6} e^{6}\right)} f - {\left(24 \, c^{7} d^{2} e^{4} - 556 \, b c^{6} d e^{5} - 3 \, b^{2} c^{5} e^{6}\right)} g\right)} x^{4} - 16 \, {\left(14 \, {\left(20 \, c^{7} d^{2} e^{4} - 404 \, b c^{6} d e^{5} - 3 \, b^{2} c^{5} e^{6}\right)} f + {\left(3920 \, c^{7} d^{3} e^{3} - 5636 \, b c^{6} d^{2} e^{4} - 216 \, b^{2} c^{5} d e^{5} + 27 \, b^{3} c^{4} e^{6}\right)} g\right)} x^{3} - 8 \, {\left(14 \, {\left(768 \, c^{7} d^{3} e^{3} - 1092 \, b c^{6} d^{2} e^{4} - 60 \, b^{2} c^{5} d e^{5} + 7 \, b^{3} c^{4} e^{6}\right)} f + {\left(4992 \, c^{7} d^{4} e^{2} - 3600 \, b c^{6} d^{3} e^{3} - 1932 \, b^{2} c^{5} d^{2} e^{4} + 568 \, b^{3} c^{4} d e^{5} - 63 \, b^{4} c^{3} e^{6}\right)} g\right)} x^{2} + 14 \, {\left(3072 \, c^{7} d^{5} e - 9840 \, b c^{6} d^{4} e^{2} + 10464 \, b^{2} c^{5} d^{3} e^{3} - 4816 \, b^{3} c^{4} d^{2} e^{4} + 1120 \, b^{4} c^{3} d e^{5} - 105 \, b^{5} c^{2} e^{6}\right)} f + {\left(27648 \, c^{7} d^{6} - 97728 \, b c^{6} d^{5} e + 145776 \, b^{2} c^{5} d^{4} e^{2} - 113440 \, b^{3} c^{4} d^{3} e^{3} + 47824 \, b^{4} c^{3} d^{2} e^{4} - 10500 \, b^{5} c^{2} d e^{5} + 945 \, b^{6} c e^{6}\right)} g - 2 \, {\left(14 \, {\left(2160 \, c^{7} d^{4} e^{2} - 1248 \, b c^{6} d^{3} e^{3} - 1248 \, b^{2} c^{5} d^{2} e^{4} + 336 \, b^{3} c^{4} d e^{5} - 35 \, b^{4} c^{3} e^{6}\right)} f - {\left(6720 \, c^{7} d^{5} e - 21648 \, b c^{6} d^{4} e^{2} + 24480 \, b^{2} c^{5} d^{3} e^{3} - 12576 \, b^{3} c^{4} d^{2} e^{4} + 3164 \, b^{4} c^{3} d e^{5} - 315 \, b^{5} c^{2} e^{6}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{215040 \, c^{6} e^{2}}\right]"," ",0,"[1/430080*(105*(14*(64*c^7*d^6*e - 192*b*c^6*d^5*e^2 + 240*b^2*c^5*d^4*e^3 - 160*b^3*c^4*d^3*e^4 + 60*b^4*c^3*d^2*e^5 - 12*b^5*c^2*d*e^6 + b^6*c*e^7)*f + (256*c^7*d^7 - 1344*b*c^6*d^6*e + 2688*b^2*c^5*d^5*e^2 - 2800*b^3*c^4*d^4*e^3 + 1680*b^4*c^3*d^3*e^4 - 588*b^5*c^2*d^2*e^5 + 112*b^6*c*d*e^6 - 9*b^7*e^7)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(15360*c^7*e^6*g*x^6 + 1280*(14*c^7*e^6*f + (28*c^7*d*e^5 + 15*b*c^6*e^6)*g)*x^5 + 128*(14*(24*c^7*d*e^5 + 13*b*c^6*e^6)*f - (24*c^7*d^2*e^4 - 556*b*c^6*d*e^5 - 3*b^2*c^5*e^6)*g)*x^4 - 16*(14*(20*c^7*d^2*e^4 - 404*b*c^6*d*e^5 - 3*b^2*c^5*e^6)*f + (3920*c^7*d^3*e^3 - 5636*b*c^6*d^2*e^4 - 216*b^2*c^5*d*e^5 + 27*b^3*c^4*e^6)*g)*x^3 - 8*(14*(768*c^7*d^3*e^3 - 1092*b*c^6*d^2*e^4 - 60*b^2*c^5*d*e^5 + 7*b^3*c^4*e^6)*f + (4992*c^7*d^4*e^2 - 3600*b*c^6*d^3*e^3 - 1932*b^2*c^5*d^2*e^4 + 568*b^3*c^4*d*e^5 - 63*b^4*c^3*e^6)*g)*x^2 + 14*(3072*c^7*d^5*e - 9840*b*c^6*d^4*e^2 + 10464*b^2*c^5*d^3*e^3 - 4816*b^3*c^4*d^2*e^4 + 1120*b^4*c^3*d*e^5 - 105*b^5*c^2*e^6)*f + (27648*c^7*d^6 - 97728*b*c^6*d^5*e + 145776*b^2*c^5*d^4*e^2 - 113440*b^3*c^4*d^3*e^3 + 47824*b^4*c^3*d^2*e^4 - 10500*b^5*c^2*d*e^5 + 945*b^6*c*e^6)*g - 2*(14*(2160*c^7*d^4*e^2 - 1248*b*c^6*d^3*e^3 - 1248*b^2*c^5*d^2*e^4 + 336*b^3*c^4*d*e^5 - 35*b^4*c^3*e^6)*f - (6720*c^7*d^5*e - 21648*b*c^6*d^4*e^2 + 24480*b^2*c^5*d^3*e^3 - 12576*b^3*c^4*d^2*e^4 + 3164*b^4*c^3*d*e^5 - 315*b^5*c^2*e^6)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^6*e^2), -1/215040*(105*(14*(64*c^7*d^6*e - 192*b*c^6*d^5*e^2 + 240*b^2*c^5*d^4*e^3 - 160*b^3*c^4*d^3*e^4 + 60*b^4*c^3*d^2*e^5 - 12*b^5*c^2*d*e^6 + b^6*c*e^7)*f + (256*c^7*d^7 - 1344*b*c^6*d^6*e + 2688*b^2*c^5*d^5*e^2 - 2800*b^3*c^4*d^4*e^3 + 1680*b^4*c^3*d^3*e^4 - 588*b^5*c^2*d^2*e^5 + 112*b^6*c*d*e^6 - 9*b^7*e^7)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(15360*c^7*e^6*g*x^6 + 1280*(14*c^7*e^6*f + (28*c^7*d*e^5 + 15*b*c^6*e^6)*g)*x^5 + 128*(14*(24*c^7*d*e^5 + 13*b*c^6*e^6)*f - (24*c^7*d^2*e^4 - 556*b*c^6*d*e^5 - 3*b^2*c^5*e^6)*g)*x^4 - 16*(14*(20*c^7*d^2*e^4 - 404*b*c^6*d*e^5 - 3*b^2*c^5*e^6)*f + (3920*c^7*d^3*e^3 - 5636*b*c^6*d^2*e^4 - 216*b^2*c^5*d*e^5 + 27*b^3*c^4*e^6)*g)*x^3 - 8*(14*(768*c^7*d^3*e^3 - 1092*b*c^6*d^2*e^4 - 60*b^2*c^5*d*e^5 + 7*b^3*c^4*e^6)*f + (4992*c^7*d^4*e^2 - 3600*b*c^6*d^3*e^3 - 1932*b^2*c^5*d^2*e^4 + 568*b^3*c^4*d*e^5 - 63*b^4*c^3*e^6)*g)*x^2 + 14*(3072*c^7*d^5*e - 9840*b*c^6*d^4*e^2 + 10464*b^2*c^5*d^3*e^3 - 4816*b^3*c^4*d^2*e^4 + 1120*b^4*c^3*d*e^5 - 105*b^5*c^2*e^6)*f + (27648*c^7*d^6 - 97728*b*c^6*d^5*e + 145776*b^2*c^5*d^4*e^2 - 113440*b^3*c^4*d^3*e^3 + 47824*b^4*c^3*d^2*e^4 - 10500*b^5*c^2*d*e^5 + 945*b^6*c*e^6)*g - 2*(14*(2160*c^7*d^4*e^2 - 1248*b*c^6*d^3*e^3 - 1248*b^2*c^5*d^2*e^4 + 336*b^3*c^4*d*e^5 - 35*b^4*c^3*e^6)*f - (6720*c^7*d^5*e - 21648*b*c^6*d^4*e^2 + 24480*b^2*c^5*d^3*e^3 - 12576*b^3*c^4*d^2*e^4 + 3164*b^4*c^3*d*e^5 - 315*b^5*c^2*e^6)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^6*e^2)]","B",0
2185,1,1473,0,1.584044," ","integrate((e*x+d)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(12 \, {\left(32 \, c^{6} d^{5} e - 80 \, b c^{5} d^{4} e^{2} + 80 \, b^{2} c^{4} d^{3} e^{3} - 40 \, b^{3} c^{3} d^{2} e^{4} + 10 \, b^{4} c^{2} d e^{5} - b^{5} c e^{6}\right)} f + {\left(64 \, c^{6} d^{6} - 384 \, b c^{5} d^{5} e + 720 \, b^{2} c^{4} d^{4} e^{2} - 640 \, b^{3} c^{3} d^{3} e^{3} + 300 \, b^{4} c^{2} d^{2} e^{4} - 72 \, b^{5} c d e^{5} + 7 \, b^{6} e^{6}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(1280 \, c^{6} e^{5} g x^{5} + 128 \, {\left(12 \, c^{6} e^{5} f + {\left(12 \, c^{6} d e^{4} + 13 \, b c^{5} e^{5}\right)} g\right)} x^{4} + 16 \, {\left(12 \, {\left(10 \, c^{6} d e^{4} + 11 \, b c^{5} e^{5}\right)} f - {\left(140 \, c^{6} d^{2} e^{3} - 272 \, b c^{5} d e^{4} - 3 \, b^{2} c^{4} e^{5}\right)} g\right)} x^{3} - 8 \, {\left(12 \, {\left(32 \, c^{6} d^{2} e^{3} - 62 \, b c^{5} d e^{4} - b^{2} c^{4} e^{5}\right)} f + {\left(384 \, c^{6} d^{3} e^{2} - 348 \, b c^{5} d^{2} e^{3} - 48 \, b^{2} c^{4} d e^{4} + 7 \, b^{3} c^{3} e^{5}\right)} g\right)} x^{2} + 12 \, {\left(128 \, c^{6} d^{4} e - 456 \, b c^{5} d^{3} e^{2} + 428 \, b^{2} c^{4} d^{2} e^{3} - 130 \, b^{3} c^{3} d e^{4} + 15 \, b^{4} c^{2} e^{5}\right)} f + {\left(1536 \, c^{6} d^{5} - 4368 \, b c^{5} d^{4} e + 5328 \, b^{2} c^{4} d^{3} e^{2} - 3256 \, b^{3} c^{3} d^{2} e^{3} + 940 \, b^{4} c^{2} d e^{4} - 105 \, b^{5} c e^{5}\right)} g - 2 \, {\left(12 \, {\left(200 \, c^{6} d^{3} e^{2} - 172 \, b c^{5} d^{2} e^{3} - 38 \, b^{2} c^{4} d e^{4} + 5 \, b^{3} c^{3} e^{5}\right)} f - {\left(240 \, c^{6} d^{4} e - 816 \, b c^{5} d^{3} e^{2} + 792 \, b^{2} c^{4} d^{2} e^{3} - 276 \, b^{3} c^{3} d e^{4} + 35 \, b^{4} c^{2} e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{30720 \, c^{5} e^{2}}, -\frac{15 \, {\left(12 \, {\left(32 \, c^{6} d^{5} e - 80 \, b c^{5} d^{4} e^{2} + 80 \, b^{2} c^{4} d^{3} e^{3} - 40 \, b^{3} c^{3} d^{2} e^{4} + 10 \, b^{4} c^{2} d e^{5} - b^{5} c e^{6}\right)} f + {\left(64 \, c^{6} d^{6} - 384 \, b c^{5} d^{5} e + 720 \, b^{2} c^{4} d^{4} e^{2} - 640 \, b^{3} c^{3} d^{3} e^{3} + 300 \, b^{4} c^{2} d^{2} e^{4} - 72 \, b^{5} c d e^{5} + 7 \, b^{6} e^{6}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(1280 \, c^{6} e^{5} g x^{5} + 128 \, {\left(12 \, c^{6} e^{5} f + {\left(12 \, c^{6} d e^{4} + 13 \, b c^{5} e^{5}\right)} g\right)} x^{4} + 16 \, {\left(12 \, {\left(10 \, c^{6} d e^{4} + 11 \, b c^{5} e^{5}\right)} f - {\left(140 \, c^{6} d^{2} e^{3} - 272 \, b c^{5} d e^{4} - 3 \, b^{2} c^{4} e^{5}\right)} g\right)} x^{3} - 8 \, {\left(12 \, {\left(32 \, c^{6} d^{2} e^{3} - 62 \, b c^{5} d e^{4} - b^{2} c^{4} e^{5}\right)} f + {\left(384 \, c^{6} d^{3} e^{2} - 348 \, b c^{5} d^{2} e^{3} - 48 \, b^{2} c^{4} d e^{4} + 7 \, b^{3} c^{3} e^{5}\right)} g\right)} x^{2} + 12 \, {\left(128 \, c^{6} d^{4} e - 456 \, b c^{5} d^{3} e^{2} + 428 \, b^{2} c^{4} d^{2} e^{3} - 130 \, b^{3} c^{3} d e^{4} + 15 \, b^{4} c^{2} e^{5}\right)} f + {\left(1536 \, c^{6} d^{5} - 4368 \, b c^{5} d^{4} e + 5328 \, b^{2} c^{4} d^{3} e^{2} - 3256 \, b^{3} c^{3} d^{2} e^{3} + 940 \, b^{4} c^{2} d e^{4} - 105 \, b^{5} c e^{5}\right)} g - 2 \, {\left(12 \, {\left(200 \, c^{6} d^{3} e^{2} - 172 \, b c^{5} d^{2} e^{3} - 38 \, b^{2} c^{4} d e^{4} + 5 \, b^{3} c^{3} e^{5}\right)} f - {\left(240 \, c^{6} d^{4} e - 816 \, b c^{5} d^{3} e^{2} + 792 \, b^{2} c^{4} d^{2} e^{3} - 276 \, b^{3} c^{3} d e^{4} + 35 \, b^{4} c^{2} e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{15360 \, c^{5} e^{2}}\right]"," ",0,"[-1/30720*(15*(12*(32*c^6*d^5*e - 80*b*c^5*d^4*e^2 + 80*b^2*c^4*d^3*e^3 - 40*b^3*c^3*d^2*e^4 + 10*b^4*c^2*d*e^5 - b^5*c*e^6)*f + (64*c^6*d^6 - 384*b*c^5*d^5*e + 720*b^2*c^4*d^4*e^2 - 640*b^3*c^3*d^3*e^3 + 300*b^4*c^2*d^2*e^4 - 72*b^5*c*d*e^5 + 7*b^6*e^6)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(1280*c^6*e^5*g*x^5 + 128*(12*c^6*e^5*f + (12*c^6*d*e^4 + 13*b*c^5*e^5)*g)*x^4 + 16*(12*(10*c^6*d*e^4 + 11*b*c^5*e^5)*f - (140*c^6*d^2*e^3 - 272*b*c^5*d*e^4 - 3*b^2*c^4*e^5)*g)*x^3 - 8*(12*(32*c^6*d^2*e^3 - 62*b*c^5*d*e^4 - b^2*c^4*e^5)*f + (384*c^6*d^3*e^2 - 348*b*c^5*d^2*e^3 - 48*b^2*c^4*d*e^4 + 7*b^3*c^3*e^5)*g)*x^2 + 12*(128*c^6*d^4*e - 456*b*c^5*d^3*e^2 + 428*b^2*c^4*d^2*e^3 - 130*b^3*c^3*d*e^4 + 15*b^4*c^2*e^5)*f + (1536*c^6*d^5 - 4368*b*c^5*d^4*e + 5328*b^2*c^4*d^3*e^2 - 3256*b^3*c^3*d^2*e^3 + 940*b^4*c^2*d*e^4 - 105*b^5*c*e^5)*g - 2*(12*(200*c^6*d^3*e^2 - 172*b*c^5*d^2*e^3 - 38*b^2*c^4*d*e^4 + 5*b^3*c^3*e^5)*f - (240*c^6*d^4*e - 816*b*c^5*d^3*e^2 + 792*b^2*c^4*d^2*e^3 - 276*b^3*c^3*d*e^4 + 35*b^4*c^2*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^5*e^2), -1/15360*(15*(12*(32*c^6*d^5*e - 80*b*c^5*d^4*e^2 + 80*b^2*c^4*d^3*e^3 - 40*b^3*c^3*d^2*e^4 + 10*b^4*c^2*d*e^5 - b^5*c*e^6)*f + (64*c^6*d^6 - 384*b*c^5*d^5*e + 720*b^2*c^4*d^4*e^2 - 640*b^3*c^3*d^3*e^3 + 300*b^4*c^2*d^2*e^4 - 72*b^5*c*d*e^5 + 7*b^6*e^6)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(1280*c^6*e^5*g*x^5 + 128*(12*c^6*e^5*f + (12*c^6*d*e^4 + 13*b*c^5*e^5)*g)*x^4 + 16*(12*(10*c^6*d*e^4 + 11*b*c^5*e^5)*f - (140*c^6*d^2*e^3 - 272*b*c^5*d*e^4 - 3*b^2*c^4*e^5)*g)*x^3 - 8*(12*(32*c^6*d^2*e^3 - 62*b*c^5*d*e^4 - b^2*c^4*e^5)*f + (384*c^6*d^3*e^2 - 348*b*c^5*d^2*e^3 - 48*b^2*c^4*d*e^4 + 7*b^3*c^3*e^5)*g)*x^2 + 12*(128*c^6*d^4*e - 456*b*c^5*d^3*e^2 + 428*b^2*c^4*d^2*e^3 - 130*b^3*c^3*d*e^4 + 15*b^4*c^2*e^5)*f + (1536*c^6*d^5 - 4368*b*c^5*d^4*e + 5328*b^2*c^4*d^3*e^2 - 3256*b^3*c^3*d^2*e^3 + 940*b^4*c^2*d*e^4 - 105*b^5*c*e^5)*g - 2*(12*(200*c^6*d^3*e^2 - 172*b*c^5*d^2*e^3 - 38*b^2*c^4*d*e^4 + 5*b^3*c^3*e^5)*f - (240*c^6*d^4*e - 816*b*c^5*d^3*e^2 + 792*b^2*c^4*d^2*e^3 - 276*b^3*c^3*d*e^4 + 35*b^4*c^2*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^5*e^2)]","B",0
2186,1,809,0,0.586411," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, {\left(8 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f - {\left(16 \, c^{4} d^{4} - 24 \, b^{2} c^{2} d^{2} e^{2} + 16 \, b^{3} c d e^{3} - 3 \, b^{4} e^{4}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(48 \, c^{4} e^{3} g x^{3} + 8 \, {\left(8 \, c^{4} e^{3} f - {\left(8 \, c^{4} d e^{2} - 9 \, b c^{3} e^{3}\right)} g\right)} x^{2} - 8 \, {\left(8 \, c^{4} d^{2} e - 2 \, b c^{3} d e^{2} - 3 \, b^{2} c^{2} e^{3}\right)} f + {\left(64 \, c^{4} d^{3} - 76 \, b c^{3} d^{2} e + 36 \, b^{2} c^{2} d e^{2} - 9 \, b^{3} c e^{3}\right)} g - 2 \, {\left(8 \, {\left(6 \, c^{4} d e^{2} - 7 \, b c^{3} e^{3}\right)} f + {\left(12 \, c^{4} d^{2} e - 4 \, b c^{3} d e^{2} - 3 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{768 \, c^{3} e^{2}}, -\frac{3 \, {\left(8 \, {\left(8 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f - {\left(16 \, c^{4} d^{4} - 24 \, b^{2} c^{2} d^{2} e^{2} + 16 \, b^{3} c d e^{3} - 3 \, b^{4} e^{4}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(48 \, c^{4} e^{3} g x^{3} + 8 \, {\left(8 \, c^{4} e^{3} f - {\left(8 \, c^{4} d e^{2} - 9 \, b c^{3} e^{3}\right)} g\right)} x^{2} - 8 \, {\left(8 \, c^{4} d^{2} e - 2 \, b c^{3} d e^{2} - 3 \, b^{2} c^{2} e^{3}\right)} f + {\left(64 \, c^{4} d^{3} - 76 \, b c^{3} d^{2} e + 36 \, b^{2} c^{2} d e^{2} - 9 \, b^{3} c e^{3}\right)} g - 2 \, {\left(8 \, {\left(6 \, c^{4} d e^{2} - 7 \, b c^{3} e^{3}\right)} f + {\left(12 \, c^{4} d^{2} e - 4 \, b c^{3} d e^{2} - 3 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{384 \, c^{3} e^{2}}\right]"," ",0,"[-1/768*(3*(8*(8*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*f - (16*c^4*d^4 - 24*b^2*c^2*d^2*e^2 + 16*b^3*c*d*e^3 - 3*b^4*e^4)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(48*c^4*e^3*g*x^3 + 8*(8*c^4*e^3*f - (8*c^4*d*e^2 - 9*b*c^3*e^3)*g)*x^2 - 8*(8*c^4*d^2*e - 2*b*c^3*d*e^2 - 3*b^2*c^2*e^3)*f + (64*c^4*d^3 - 76*b*c^3*d^2*e + 36*b^2*c^2*d*e^2 - 9*b^3*c*e^3)*g - 2*(8*(6*c^4*d*e^2 - 7*b*c^3*e^3)*f + (12*c^4*d^2*e - 4*b*c^3*d*e^2 - 3*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^3*e^2), -1/384*(3*(8*(8*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*f - (16*c^4*d^4 - 24*b^2*c^2*d^2*e^2 + 16*b^3*c*d*e^3 - 3*b^4*e^4)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(48*c^4*e^3*g*x^3 + 8*(8*c^4*e^3*f - (8*c^4*d*e^2 - 9*b*c^3*e^3)*g)*x^2 - 8*(8*c^4*d^2*e - 2*b*c^3*d*e^2 - 3*b^2*c^2*e^3)*f + (64*c^4*d^3 - 76*b*c^3*d^2*e + 36*b^2*c^2*d*e^2 - 9*b^3*c*e^3)*g - 2*(8*(6*c^4*d*e^2 - 7*b*c^3*e^3)*f + (12*c^4*d^2*e - 4*b*c^3*d*e^2 - 3*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^3*e^2)]","A",0
2187,1,567,0,0.584779," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(6 \, {\left(4 \, c^{3} d^{2} e - 4 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} f - {\left(16 \, c^{3} d^{3} - 12 \, b c^{2} d^{2} e + b^{3} e^{3}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(8 \, c^{3} e^{2} g x^{2} - 6 \, {\left(8 \, c^{3} d e - 5 \, b c^{2} e^{2}\right)} f + {\left(40 \, c^{3} d^{2} - 28 \, b c^{2} d e + 3 \, b^{2} c e^{2}\right)} g + 2 \, {\left(6 \, c^{3} e^{2} f - {\left(12 \, c^{3} d e - 7 \, b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{96 \, c^{2} e^{2}}, -\frac{3 \, {\left(6 \, {\left(4 \, c^{3} d^{2} e - 4 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} f - {\left(16 \, c^{3} d^{3} - 12 \, b c^{2} d^{2} e + b^{3} e^{3}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(8 \, c^{3} e^{2} g x^{2} - 6 \, {\left(8 \, c^{3} d e - 5 \, b c^{2} e^{2}\right)} f + {\left(40 \, c^{3} d^{2} - 28 \, b c^{2} d e + 3 \, b^{2} c e^{2}\right)} g + 2 \, {\left(6 \, c^{3} e^{2} f - {\left(12 \, c^{3} d e - 7 \, b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{48 \, c^{2} e^{2}}\right]"," ",0,"[1/96*(3*(6*(4*c^3*d^2*e - 4*b*c^2*d*e^2 + b^2*c*e^3)*f - (16*c^3*d^3 - 12*b*c^2*d^2*e + b^3*e^3)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(8*c^3*e^2*g*x^2 - 6*(8*c^3*d*e - 5*b*c^2*e^2)*f + (40*c^3*d^2 - 28*b*c^2*d*e + 3*b^2*c*e^2)*g + 2*(6*c^3*e^2*f - (12*c^3*d*e - 7*b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^2*e^2), -1/48*(3*(6*(4*c^3*d^2*e - 4*b*c^2*d*e^2 + b^2*c*e^3)*f - (16*c^3*d^3 - 12*b*c^2*d^2*e + b^3*e^3)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(8*c^3*e^2*g*x^2 - 6*(8*c^3*d*e - 5*b*c^2*e^2)*f + (40*c^3*d^2 - 28*b*c^2*d*e + 3*b^2*c*e^2)*g + 2*(6*c^3*e^2*f - (12*c^3*d*e - 7*b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^2*e^2)]","A",0
2188,1,635,0,1.281818," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, {\left(2 \, c^{2} d^{2} e - b c d e^{2}\right)} f - {\left(12 \, c^{2} d^{3} - 8 \, b c d^{2} e + b^{2} d e^{2}\right)} g + {\left(4 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f - {\left(12 \, c^{2} d^{2} e - 8 \, b c d e^{2} + b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(2 \, c^{2} e^{2} g x^{2} + 4 \, {\left(5 \, c^{2} d e - 2 \, b c e^{2}\right)} f - {\left(28 \, c^{2} d^{2} - 13 \, b c d e\right)} g + {\left(4 \, c^{2} e^{2} f - 5 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{16 \, {\left(c e^{3} x + c d e^{2}\right)}}, \frac{3 \, {\left(4 \, {\left(2 \, c^{2} d^{2} e - b c d e^{2}\right)} f - {\left(12 \, c^{2} d^{3} - 8 \, b c d^{2} e + b^{2} d e^{2}\right)} g + {\left(4 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f - {\left(12 \, c^{2} d^{2} e - 8 \, b c d e^{2} + b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(2 \, c^{2} e^{2} g x^{2} + 4 \, {\left(5 \, c^{2} d e - 2 \, b c e^{2}\right)} f - {\left(28 \, c^{2} d^{2} - 13 \, b c d e\right)} g + {\left(4 \, c^{2} e^{2} f - 5 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{8 \, {\left(c e^{3} x + c d e^{2}\right)}}\right]"," ",0,"[1/16*(3*(4*(2*c^2*d^2*e - b*c*d*e^2)*f - (12*c^2*d^3 - 8*b*c*d^2*e + b^2*d*e^2)*g + (4*(2*c^2*d*e^2 - b*c*e^3)*f - (12*c^2*d^2*e - 8*b*c*d*e^2 + b^2*e^3)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(2*c^2*e^2*g*x^2 + 4*(5*c^2*d*e - 2*b*c*e^2)*f - (28*c^2*d^2 - 13*b*c*d*e)*g + (4*c^2*e^2*f - 5*(2*c^2*d*e - b*c*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c*e^3*x + c*d*e^2), 1/8*(3*(4*(2*c^2*d^2*e - b*c*d*e^2)*f - (12*c^2*d^3 - 8*b*c*d^2*e + b^2*d*e^2)*g + (4*(2*c^2*d*e^2 - b*c*e^3)*f - (12*c^2*d^2*e - 8*b*c*d*e^2 + b^2*e^3)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(2*c^2*e^2*g*x^2 + 4*(5*c^2*d*e - 2*b*c*e^2)*f - (28*c^2*d^2 - 13*b*c*d*e)*g + (4*c^2*e^2*f - 5*(2*c^2*d*e - b*c*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c*e^3*x + c*d*e^2)]","A",0
2189,1,593,0,2.152804," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, c d^{2} e f + {\left(2 \, c e^{3} f - {\left(8 \, c d e^{2} - 3 \, b e^{3}\right)} g\right)} x^{2} - {\left(8 \, c d^{3} - 3 \, b d^{2} e\right)} g + 2 \, {\left(2 \, c d e^{2} f - {\left(8 \, c d^{2} e - 3 \, b d e^{2}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(3 \, c e^{2} g x^{2} - 2 \, {\left(2 \, c d e + b e^{2}\right)} f + {\left(19 \, c d^{2} - 4 \, b d e\right)} g - 2 \, {\left(4 \, c e^{2} f - {\left(13 \, c d e - 3 \, b e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{12 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}, -\frac{3 \, {\left(2 \, c d^{2} e f + {\left(2 \, c e^{3} f - {\left(8 \, c d e^{2} - 3 \, b e^{3}\right)} g\right)} x^{2} - {\left(8 \, c d^{3} - 3 \, b d^{2} e\right)} g + 2 \, {\left(2 \, c d e^{2} f - {\left(8 \, c d^{2} e - 3 \, b d e^{2}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(3 \, c e^{2} g x^{2} - 2 \, {\left(2 \, c d e + b e^{2}\right)} f + {\left(19 \, c d^{2} - 4 \, b d e\right)} g - 2 \, {\left(4 \, c e^{2} f - {\left(13 \, c d e - 3 \, b e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{6 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}\right]"," ",0,"[1/12*(3*(2*c*d^2*e*f + (2*c*e^3*f - (8*c*d*e^2 - 3*b*e^3)*g)*x^2 - (8*c*d^3 - 3*b*d^2*e)*g + 2*(2*c*d*e^2*f - (8*c*d^2*e - 3*b*d*e^2)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(3*c*e^2*g*x^2 - 2*(2*c*d*e + b*e^2)*f + (19*c*d^2 - 4*b*d*e)*g - 2*(4*c*e^2*f - (13*c*d*e - 3*b*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2), -1/6*(3*(2*c*d^2*e*f + (2*c*e^3*f - (8*c*d*e^2 - 3*b*e^3)*g)*x^2 - (8*c*d^3 - 3*b*d^2*e)*g + 2*(2*c*d*e^2*f - (8*c*d^2*e - 3*b*d*e^2)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(3*c*e^2*g*x^2 - 2*(2*c*d*e + b*e^2)*f + (19*c*d^2 - 4*b*d*e)*g - 2*(4*c*e^2*f - (13*c*d*e - 3*b*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)]","A",0
2190,1,879,0,9.807383," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} g x^{3} + 3 \, {\left(2 \, c^{2} d^{2} e^{2} - b c d e^{3}\right)} g x^{2} + 3 \, {\left(2 \, c^{2} d^{3} e - b c d^{2} e^{2}\right)} g x + {\left(2 \, c^{2} d^{4} - b c d^{3} e\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(3 \, c^{2} e^{3} f - {\left(43 \, c^{2} d e^{2} - 20 \, b c e^{3}\right)} g\right)} x^{2} + 3 \, {\left(c^{2} d^{2} e - 2 \, b c d e^{2} + b^{2} e^{3}\right)} f - {\left(23 \, c^{2} d^{3} - 6 \, b c d^{2} e - 2 \, b^{2} d e^{2}\right)} g - {\left(6 \, {\left(c^{2} d e^{2} - b c e^{3}\right)} f + {\left(54 \, c^{2} d^{2} e - 14 \, b c d e^{2} - 5 \, b^{2} e^{3}\right)} g\right)} x\right)}}{30 \, {\left(2 \, c d^{4} e^{2} - b d^{3} e^{3} + {\left(2 \, c d e^{5} - b e^{6}\right)} x^{3} + 3 \, {\left(2 \, c d^{2} e^{4} - b d e^{5}\right)} x^{2} + 3 \, {\left(2 \, c d^{3} e^{3} - b d^{2} e^{4}\right)} x\right)}}, -\frac{15 \, {\left({\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} g x^{3} + 3 \, {\left(2 \, c^{2} d^{2} e^{2} - b c d e^{3}\right)} g x^{2} + 3 \, {\left(2 \, c^{2} d^{3} e - b c d^{2} e^{2}\right)} g x + {\left(2 \, c^{2} d^{4} - b c d^{3} e\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(3 \, c^{2} e^{3} f - {\left(43 \, c^{2} d e^{2} - 20 \, b c e^{3}\right)} g\right)} x^{2} + 3 \, {\left(c^{2} d^{2} e - 2 \, b c d e^{2} + b^{2} e^{3}\right)} f - {\left(23 \, c^{2} d^{3} - 6 \, b c d^{2} e - 2 \, b^{2} d e^{2}\right)} g - {\left(6 \, {\left(c^{2} d e^{2} - b c e^{3}\right)} f + {\left(54 \, c^{2} d^{2} e - 14 \, b c d e^{2} - 5 \, b^{2} e^{3}\right)} g\right)} x\right)}}{15 \, {\left(2 \, c d^{4} e^{2} - b d^{3} e^{3} + {\left(2 \, c d e^{5} - b e^{6}\right)} x^{3} + 3 \, {\left(2 \, c d^{2} e^{4} - b d e^{5}\right)} x^{2} + 3 \, {\left(2 \, c d^{3} e^{3} - b d^{2} e^{4}\right)} x\right)}}\right]"," ",0,"[1/30*(15*((2*c^2*d*e^3 - b*c*e^4)*g*x^3 + 3*(2*c^2*d^2*e^2 - b*c*d*e^3)*g*x^2 + 3*(2*c^2*d^3*e - b*c*d^2*e^2)*g*x + (2*c^2*d^4 - b*c*d^3*e)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((3*c^2*e^3*f - (43*c^2*d*e^2 - 20*b*c*e^3)*g)*x^2 + 3*(c^2*d^2*e - 2*b*c*d*e^2 + b^2*e^3)*f - (23*c^2*d^3 - 6*b*c*d^2*e - 2*b^2*d*e^2)*g - (6*(c^2*d*e^2 - b*c*e^3)*f + (54*c^2*d^2*e - 14*b*c*d*e^2 - 5*b^2*e^3)*g)*x))/(2*c*d^4*e^2 - b*d^3*e^3 + (2*c*d*e^5 - b*e^6)*x^3 + 3*(2*c*d^2*e^4 - b*d*e^5)*x^2 + 3*(2*c*d^3*e^3 - b*d^2*e^4)*x), -1/15*(15*((2*c^2*d*e^3 - b*c*e^4)*g*x^3 + 3*(2*c^2*d^2*e^2 - b*c*d*e^3)*g*x^2 + 3*(2*c^2*d^3*e - b*c*d^2*e^2)*g*x + (2*c^2*d^4 - b*c*d^3*e)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((3*c^2*e^3*f - (43*c^2*d*e^2 - 20*b*c*e^3)*g)*x^2 + 3*(c^2*d^2*e - 2*b*c*d*e^2 + b^2*e^3)*f - (23*c^2*d^3 - 6*b*c*d^2*e - 2*b^2*d*e^2)*g - (6*(c^2*d*e^2 - b*c*e^3)*f + (54*c^2*d^2*e - 14*b*c*d*e^2 - 5*b^2*e^3)*g)*x))/(2*c*d^4*e^2 - b*d^3*e^3 + (2*c*d*e^5 - b*e^6)*x^3 + 3*(2*c*d^2*e^4 - b*d*e^5)*x^2 + 3*(2*c*d^3*e^3 - b*d^2*e^4)*x)]","B",0
2191,1,464,0,47.455288," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(2 \, c^{3} e^{4} f + {\left(12 \, c^{3} d e^{3} - 7 \, b c^{2} e^{4}\right)} g\right)} x^{3} + {\left({\left(8 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f - 2 \, {\left(11 \, c^{3} d^{2} e^{2} - 18 \, b c^{2} d e^{3} + 7 \, b^{2} c e^{4}\right)} g\right)} x^{2} + {\left(12 \, c^{3} d^{3} e - 29 \, b c^{2} d^{2} e^{2} + 22 \, b^{2} c d e^{3} - 5 \, b^{3} e^{4}\right)} f + 2 \, {\left(c^{3} d^{4} - 3 \, b c^{2} d^{3} e + 3 \, b^{2} c d^{2} e^{2} - b^{3} d e^{3}\right)} g - {\left(2 \, {\left(11 \, c^{3} d^{2} e^{2} - 15 \, b c^{2} d e^{3} + 4 \, b^{2} c e^{4}\right)} f - {\left(8 \, c^{3} d^{3} e - 23 \, b c^{2} d^{2} e^{2} + 22 \, b^{2} c d e^{3} - 7 \, b^{3} e^{4}\right)} g\right)} x\right)}}{35 \, {\left(4 \, c^{2} d^{6} e^{2} - 4 \, b c d^{5} e^{3} + b^{2} d^{4} e^{4} + {\left(4 \, c^{2} d^{2} e^{6} - 4 \, b c d e^{7} + b^{2} e^{8}\right)} x^{4} + 4 \, {\left(4 \, c^{2} d^{3} e^{5} - 4 \, b c d^{2} e^{6} + b^{2} d e^{7}\right)} x^{3} + 6 \, {\left(4 \, c^{2} d^{4} e^{4} - 4 \, b c d^{3} e^{5} + b^{2} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(4 \, c^{2} d^{5} e^{3} - 4 \, b c d^{4} e^{4} + b^{2} d^{3} e^{5}\right)} x\right)}}"," ",0,"-2/35*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((2*c^3*e^4*f + (12*c^3*d*e^3 - 7*b*c^2*e^4)*g)*x^3 + ((8*c^3*d*e^3 - b*c^2*e^4)*f - 2*(11*c^3*d^2*e^2 - 18*b*c^2*d*e^3 + 7*b^2*c*e^4)*g)*x^2 + (12*c^3*d^3*e - 29*b*c^2*d^2*e^2 + 22*b^2*c*d*e^3 - 5*b^3*e^4)*f + 2*(c^3*d^4 - 3*b*c^2*d^3*e + 3*b^2*c*d^2*e^2 - b^3*d*e^3)*g - (2*(11*c^3*d^2*e^2 - 15*b*c^2*d*e^3 + 4*b^2*c*e^4)*f - (8*c^3*d^3*e - 23*b*c^2*d^2*e^2 + 22*b^2*c*d*e^3 - 7*b^3*e^4)*g)*x)/(4*c^2*d^6*e^2 - 4*b*c*d^5*e^3 + b^2*d^4*e^4 + (4*c^2*d^2*e^6 - 4*b*c*d*e^7 + b^2*e^8)*x^4 + 4*(4*c^2*d^3*e^5 - 4*b*c*d^2*e^6 + b^2*d*e^7)*x^3 + 6*(4*c^2*d^4*e^4 - 4*b*c*d^3*e^5 + b^2*d^2*e^6)*x^2 + 4*(4*c^2*d^5*e^3 - 4*b*c*d^4*e^4 + b^2*d^3*e^5)*x)","B",0
2192,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^7,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2193,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^8,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2194,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^9,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2195,1,3437,0,25.578354," ","integrate((e*x+d)^3*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left(20 \, {\left(512 \, c^{10} d^{9} e - 2304 \, b c^{9} d^{8} e^{2} + 4608 \, b^{2} c^{8} d^{7} e^{3} - 5376 \, b^{3} c^{7} d^{6} e^{4} + 4032 \, b^{4} c^{6} d^{5} e^{5} - 2016 \, b^{5} c^{5} d^{4} e^{6} + 672 \, b^{6} c^{4} d^{3} e^{7} - 144 \, b^{7} c^{3} d^{2} e^{8} + 18 \, b^{8} c^{2} d e^{9} - b^{9} c e^{10}\right)} f + {\left(3072 \, c^{10} d^{10} - 20480 \, b c^{9} d^{9} e + 57600 \, b^{2} c^{8} d^{8} e^{2} - 92160 \, b^{3} c^{7} d^{7} e^{3} + 94080 \, b^{4} c^{6} d^{6} e^{4} - 64512 \, b^{5} c^{5} d^{5} e^{5} + 30240 \, b^{6} c^{4} d^{4} e^{6} - 9600 \, b^{7} c^{3} d^{3} e^{7} + 1980 \, b^{8} c^{2} d^{2} e^{8} - 240 \, b^{9} c d e^{9} + 13 \, b^{10} e^{10}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(4128768 \, c^{10} e^{9} g x^{9} + 229376 \, {\left(20 \, c^{10} e^{9} f + {\left(60 \, c^{10} d e^{8} + 41 \, b c^{9} e^{9}\right)} g\right)} x^{8} + 14336 \, {\left(20 \, {\left(54 \, c^{10} d e^{8} + 37 \, b c^{9} e^{9}\right)} f + {\left(324 \, c^{10} d^{2} e^{7} + 2976 \, b c^{9} d e^{8} + 383 \, b^{2} c^{8} e^{9}\right)} g\right)} x^{7} + 1024 \, {\left(20 \, {\left(256 \, c^{10} d^{2} e^{7} + 2390 \, b c^{9} d e^{8} + 309 \, b^{2} c^{8} e^{9}\right)} f - {\left(30720 \, c^{10} d^{3} e^{6} - 59396 \, b c^{9} d^{2} e^{7} - 31264 \, b^{2} c^{8} d e^{8} - 15 \, b^{3} c^{7} e^{9}\right)} g\right)} x^{6} - 256 \, {\left(20 \, {\left(7224 \, c^{10} d^{3} e^{6} - 13908 \, b c^{9} d^{2} e^{7} - 7386 \, b^{2} c^{8} d e^{8} - 5 \, b^{3} c^{7} e^{9}\right)} f + {\left(140112 \, c^{10} d^{4} e^{5} + 16176 \, b c^{9} d^{3} e^{6} - 298968 \, b^{2} c^{8} d^{2} e^{7} - 780 \, b^{3} c^{7} d e^{8} + 65 \, b^{4} c^{6} e^{9}\right)} g\right)} x^{5} - 128 \, {\left(20 \, {\left(16896 \, c^{10} d^{4} e^{5} + 2328 \, b c^{9} d^{3} e^{6} - 36516 \, b^{2} c^{8} d^{2} e^{7} - 138 \, b^{3} c^{7} d e^{8} + 11 \, b^{4} c^{6} e^{9}\right)} f - {\left(92160 \, c^{10} d^{5} e^{4} - 762000 \, b c^{9} d^{4} e^{5} + 733200 \, b^{2} c^{8} d^{3} e^{6} + 9960 \, b^{3} c^{7} d^{2} e^{7} - 1860 \, b^{4} c^{6} d e^{8} + 143 \, b^{5} c^{5} e^{9}\right)} g\right)} x^{4} + 16 \, {\left(20 \, {\left(49056 \, c^{10} d^{5} e^{4} - 392976 \, b c^{9} d^{4} e^{5} + 374352 \, b^{2} c^{8} d^{3} e^{6} + 7576 \, b^{3} c^{7} d^{2} e^{7} - 1342 \, b^{4} c^{6} d e^{8} + 99 \, b^{5} c^{5} e^{9}\right)} f + {\left(2358720 \, c^{10} d^{6} e^{3} - 6092160 \, b c^{9} d^{5} e^{4} + 3484080 \, b^{2} c^{8} d^{4} e^{5} + 339840 \, b^{3} c^{7} d^{3} e^{6} - 106540 \, b^{4} c^{6} d^{2} e^{7} + 18040 \, b^{5} c^{5} d e^{8} - 1287 \, b^{6} c^{4} e^{9}\right)} g\right)} x^{3} + 8 \, {\left(20 \, {\left(327680 \, c^{10} d^{6} e^{3} - 835872 \, b c^{9} d^{5} e^{4} + 455376 \, b^{2} c^{8} d^{4} e^{5} + 70768 \, b^{3} c^{7} d^{3} e^{6} - 20856 \, b^{4} c^{6} d^{2} e^{7} + 3366 \, b^{5} c^{5} d e^{8} - 231 \, b^{6} c^{4} e^{9}\right)} f + {\left(1966080 \, c^{10} d^{7} e^{2} - 3081920 \, b c^{9} d^{6} e^{3} - 336000 \, b^{2} c^{8} d^{5} e^{4} + 2246160 \, b^{3} c^{7} d^{4} e^{5} - 1045120 \, b^{4} c^{6} d^{3} e^{6} + 291324 \, b^{5} c^{5} d^{2} e^{7} - 45144 \, b^{6} c^{4} d e^{8} + 3003 \, b^{7} c^{3} e^{9}\right)} g\right)} x^{2} - 20 \, {\left(950272 \, c^{10} d^{8} e - 4389760 \, b c^{9} d^{7} e^{2} + 8056896 \, b^{2} c^{8} d^{6} e^{3} - 7874464 \, b^{3} c^{7} d^{5} e^{4} + 4655728 \, b^{4} c^{6} d^{4} e^{5} - 1770120 \, b^{5} c^{5} d^{3} e^{6} + 422268 \, b^{6} c^{4} d^{2} e^{7} - 57750 \, b^{7} c^{3} d e^{8} + 3465 \, b^{8} c^{2} e^{9}\right)} f - {\left(9830400 \, c^{10} d^{9} - 51078400 \, b c^{9} d^{8} e + 117794560 \, b^{2} c^{8} d^{7} e^{2} - 156115200 \, b^{3} c^{7} d^{6} e^{3} + 130302400 \, b^{4} c^{6} d^{5} e^{4} - 71145184 \, b^{5} c^{5} d^{4} e^{5} + 25545168 \, b^{6} c^{4} d^{3} e^{6} - 5835984 \, b^{7} c^{3} d^{2} e^{7} + 771540 \, b^{8} c^{2} d e^{8} - 45045 \, b^{9} c e^{9}\right)} g + 2 \, {\left(20 \, {\left(588672 \, c^{10} d^{7} e^{2} - 749632 \, b c^{9} d^{6} e^{3} - 547296 \, b^{2} c^{8} d^{5} e^{4} + 1063248 \, b^{3} c^{7} d^{4} e^{5} - 460856 \, b^{4} c^{6} d^{3} e^{6} + 121572 \, b^{5} c^{5} d^{2} e^{7} - 18018 \, b^{6} c^{4} d e^{8} + 1155 \, b^{7} c^{3} e^{9}\right)} f - {\left(2661120 \, c^{10} d^{8} e - 12622080 \, b c^{9} d^{7} e^{2} + 24504320 \, b^{2} c^{8} d^{6} e^{3} - 25880640 \, b^{3} c^{7} d^{5} e^{4} + 16587360 \, b^{4} c^{6} d^{4} e^{5} - 6720560 \, b^{5} c^{5} d^{3} e^{6} + 1688544 \, b^{6} c^{4} d^{2} e^{7} - 241164 \, b^{7} c^{3} d e^{8} + 15015 \, b^{8} c^{2} e^{9}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{165150720 \, c^{8} e^{2}}, -\frac{3465 \, {\left(20 \, {\left(512 \, c^{10} d^{9} e - 2304 \, b c^{9} d^{8} e^{2} + 4608 \, b^{2} c^{8} d^{7} e^{3} - 5376 \, b^{3} c^{7} d^{6} e^{4} + 4032 \, b^{4} c^{6} d^{5} e^{5} - 2016 \, b^{5} c^{5} d^{4} e^{6} + 672 \, b^{6} c^{4} d^{3} e^{7} - 144 \, b^{7} c^{3} d^{2} e^{8} + 18 \, b^{8} c^{2} d e^{9} - b^{9} c e^{10}\right)} f + {\left(3072 \, c^{10} d^{10} - 20480 \, b c^{9} d^{9} e + 57600 \, b^{2} c^{8} d^{8} e^{2} - 92160 \, b^{3} c^{7} d^{7} e^{3} + 94080 \, b^{4} c^{6} d^{6} e^{4} - 64512 \, b^{5} c^{5} d^{5} e^{5} + 30240 \, b^{6} c^{4} d^{4} e^{6} - 9600 \, b^{7} c^{3} d^{3} e^{7} + 1980 \, b^{8} c^{2} d^{2} e^{8} - 240 \, b^{9} c d e^{9} + 13 \, b^{10} e^{10}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(4128768 \, c^{10} e^{9} g x^{9} + 229376 \, {\left(20 \, c^{10} e^{9} f + {\left(60 \, c^{10} d e^{8} + 41 \, b c^{9} e^{9}\right)} g\right)} x^{8} + 14336 \, {\left(20 \, {\left(54 \, c^{10} d e^{8} + 37 \, b c^{9} e^{9}\right)} f + {\left(324 \, c^{10} d^{2} e^{7} + 2976 \, b c^{9} d e^{8} + 383 \, b^{2} c^{8} e^{9}\right)} g\right)} x^{7} + 1024 \, {\left(20 \, {\left(256 \, c^{10} d^{2} e^{7} + 2390 \, b c^{9} d e^{8} + 309 \, b^{2} c^{8} e^{9}\right)} f - {\left(30720 \, c^{10} d^{3} e^{6} - 59396 \, b c^{9} d^{2} e^{7} - 31264 \, b^{2} c^{8} d e^{8} - 15 \, b^{3} c^{7} e^{9}\right)} g\right)} x^{6} - 256 \, {\left(20 \, {\left(7224 \, c^{10} d^{3} e^{6} - 13908 \, b c^{9} d^{2} e^{7} - 7386 \, b^{2} c^{8} d e^{8} - 5 \, b^{3} c^{7} e^{9}\right)} f + {\left(140112 \, c^{10} d^{4} e^{5} + 16176 \, b c^{9} d^{3} e^{6} - 298968 \, b^{2} c^{8} d^{2} e^{7} - 780 \, b^{3} c^{7} d e^{8} + 65 \, b^{4} c^{6} e^{9}\right)} g\right)} x^{5} - 128 \, {\left(20 \, {\left(16896 \, c^{10} d^{4} e^{5} + 2328 \, b c^{9} d^{3} e^{6} - 36516 \, b^{2} c^{8} d^{2} e^{7} - 138 \, b^{3} c^{7} d e^{8} + 11 \, b^{4} c^{6} e^{9}\right)} f - {\left(92160 \, c^{10} d^{5} e^{4} - 762000 \, b c^{9} d^{4} e^{5} + 733200 \, b^{2} c^{8} d^{3} e^{6} + 9960 \, b^{3} c^{7} d^{2} e^{7} - 1860 \, b^{4} c^{6} d e^{8} + 143 \, b^{5} c^{5} e^{9}\right)} g\right)} x^{4} + 16 \, {\left(20 \, {\left(49056 \, c^{10} d^{5} e^{4} - 392976 \, b c^{9} d^{4} e^{5} + 374352 \, b^{2} c^{8} d^{3} e^{6} + 7576 \, b^{3} c^{7} d^{2} e^{7} - 1342 \, b^{4} c^{6} d e^{8} + 99 \, b^{5} c^{5} e^{9}\right)} f + {\left(2358720 \, c^{10} d^{6} e^{3} - 6092160 \, b c^{9} d^{5} e^{4} + 3484080 \, b^{2} c^{8} d^{4} e^{5} + 339840 \, b^{3} c^{7} d^{3} e^{6} - 106540 \, b^{4} c^{6} d^{2} e^{7} + 18040 \, b^{5} c^{5} d e^{8} - 1287 \, b^{6} c^{4} e^{9}\right)} g\right)} x^{3} + 8 \, {\left(20 \, {\left(327680 \, c^{10} d^{6} e^{3} - 835872 \, b c^{9} d^{5} e^{4} + 455376 \, b^{2} c^{8} d^{4} e^{5} + 70768 \, b^{3} c^{7} d^{3} e^{6} - 20856 \, b^{4} c^{6} d^{2} e^{7} + 3366 \, b^{5} c^{5} d e^{8} - 231 \, b^{6} c^{4} e^{9}\right)} f + {\left(1966080 \, c^{10} d^{7} e^{2} - 3081920 \, b c^{9} d^{6} e^{3} - 336000 \, b^{2} c^{8} d^{5} e^{4} + 2246160 \, b^{3} c^{7} d^{4} e^{5} - 1045120 \, b^{4} c^{6} d^{3} e^{6} + 291324 \, b^{5} c^{5} d^{2} e^{7} - 45144 \, b^{6} c^{4} d e^{8} + 3003 \, b^{7} c^{3} e^{9}\right)} g\right)} x^{2} - 20 \, {\left(950272 \, c^{10} d^{8} e - 4389760 \, b c^{9} d^{7} e^{2} + 8056896 \, b^{2} c^{8} d^{6} e^{3} - 7874464 \, b^{3} c^{7} d^{5} e^{4} + 4655728 \, b^{4} c^{6} d^{4} e^{5} - 1770120 \, b^{5} c^{5} d^{3} e^{6} + 422268 \, b^{6} c^{4} d^{2} e^{7} - 57750 \, b^{7} c^{3} d e^{8} + 3465 \, b^{8} c^{2} e^{9}\right)} f - {\left(9830400 \, c^{10} d^{9} - 51078400 \, b c^{9} d^{8} e + 117794560 \, b^{2} c^{8} d^{7} e^{2} - 156115200 \, b^{3} c^{7} d^{6} e^{3} + 130302400 \, b^{4} c^{6} d^{5} e^{4} - 71145184 \, b^{5} c^{5} d^{4} e^{5} + 25545168 \, b^{6} c^{4} d^{3} e^{6} - 5835984 \, b^{7} c^{3} d^{2} e^{7} + 771540 \, b^{8} c^{2} d e^{8} - 45045 \, b^{9} c e^{9}\right)} g + 2 \, {\left(20 \, {\left(588672 \, c^{10} d^{7} e^{2} - 749632 \, b c^{9} d^{6} e^{3} - 547296 \, b^{2} c^{8} d^{5} e^{4} + 1063248 \, b^{3} c^{7} d^{4} e^{5} - 460856 \, b^{4} c^{6} d^{3} e^{6} + 121572 \, b^{5} c^{5} d^{2} e^{7} - 18018 \, b^{6} c^{4} d e^{8} + 1155 \, b^{7} c^{3} e^{9}\right)} f - {\left(2661120 \, c^{10} d^{8} e - 12622080 \, b c^{9} d^{7} e^{2} + 24504320 \, b^{2} c^{8} d^{6} e^{3} - 25880640 \, b^{3} c^{7} d^{5} e^{4} + 16587360 \, b^{4} c^{6} d^{4} e^{5} - 6720560 \, b^{5} c^{5} d^{3} e^{6} + 1688544 \, b^{6} c^{4} d^{2} e^{7} - 241164 \, b^{7} c^{3} d e^{8} + 15015 \, b^{8} c^{2} e^{9}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{82575360 \, c^{8} e^{2}}\right]"," ",0,"[-1/165150720*(3465*(20*(512*c^10*d^9*e - 2304*b*c^9*d^8*e^2 + 4608*b^2*c^8*d^7*e^3 - 5376*b^3*c^7*d^6*e^4 + 4032*b^4*c^6*d^5*e^5 - 2016*b^5*c^5*d^4*e^6 + 672*b^6*c^4*d^3*e^7 - 144*b^7*c^3*d^2*e^8 + 18*b^8*c^2*d*e^9 - b^9*c*e^10)*f + (3072*c^10*d^10 - 20480*b*c^9*d^9*e + 57600*b^2*c^8*d^8*e^2 - 92160*b^3*c^7*d^7*e^3 + 94080*b^4*c^6*d^6*e^4 - 64512*b^5*c^5*d^5*e^5 + 30240*b^6*c^4*d^4*e^6 - 9600*b^7*c^3*d^3*e^7 + 1980*b^8*c^2*d^2*e^8 - 240*b^9*c*d*e^9 + 13*b^10*e^10)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(4128768*c^10*e^9*g*x^9 + 229376*(20*c^10*e^9*f + (60*c^10*d*e^8 + 41*b*c^9*e^9)*g)*x^8 + 14336*(20*(54*c^10*d*e^8 + 37*b*c^9*e^9)*f + (324*c^10*d^2*e^7 + 2976*b*c^9*d*e^8 + 383*b^2*c^8*e^9)*g)*x^7 + 1024*(20*(256*c^10*d^2*e^7 + 2390*b*c^9*d*e^8 + 309*b^2*c^8*e^9)*f - (30720*c^10*d^3*e^6 - 59396*b*c^9*d^2*e^7 - 31264*b^2*c^8*d*e^8 - 15*b^3*c^7*e^9)*g)*x^6 - 256*(20*(7224*c^10*d^3*e^6 - 13908*b*c^9*d^2*e^7 - 7386*b^2*c^8*d*e^8 - 5*b^3*c^7*e^9)*f + (140112*c^10*d^4*e^5 + 16176*b*c^9*d^3*e^6 - 298968*b^2*c^8*d^2*e^7 - 780*b^3*c^7*d*e^8 + 65*b^4*c^6*e^9)*g)*x^5 - 128*(20*(16896*c^10*d^4*e^5 + 2328*b*c^9*d^3*e^6 - 36516*b^2*c^8*d^2*e^7 - 138*b^3*c^7*d*e^8 + 11*b^4*c^6*e^9)*f - (92160*c^10*d^5*e^4 - 762000*b*c^9*d^4*e^5 + 733200*b^2*c^8*d^3*e^6 + 9960*b^3*c^7*d^2*e^7 - 1860*b^4*c^6*d*e^8 + 143*b^5*c^5*e^9)*g)*x^4 + 16*(20*(49056*c^10*d^5*e^4 - 392976*b*c^9*d^4*e^5 + 374352*b^2*c^8*d^3*e^6 + 7576*b^3*c^7*d^2*e^7 - 1342*b^4*c^6*d*e^8 + 99*b^5*c^5*e^9)*f + (2358720*c^10*d^6*e^3 - 6092160*b*c^9*d^5*e^4 + 3484080*b^2*c^8*d^4*e^5 + 339840*b^3*c^7*d^3*e^6 - 106540*b^4*c^6*d^2*e^7 + 18040*b^5*c^5*d*e^8 - 1287*b^6*c^4*e^9)*g)*x^3 + 8*(20*(327680*c^10*d^6*e^3 - 835872*b*c^9*d^5*e^4 + 455376*b^2*c^8*d^4*e^5 + 70768*b^3*c^7*d^3*e^6 - 20856*b^4*c^6*d^2*e^7 + 3366*b^5*c^5*d*e^8 - 231*b^6*c^4*e^9)*f + (1966080*c^10*d^7*e^2 - 3081920*b*c^9*d^6*e^3 - 336000*b^2*c^8*d^5*e^4 + 2246160*b^3*c^7*d^4*e^5 - 1045120*b^4*c^6*d^3*e^6 + 291324*b^5*c^5*d^2*e^7 - 45144*b^6*c^4*d*e^8 + 3003*b^7*c^3*e^9)*g)*x^2 - 20*(950272*c^10*d^8*e - 4389760*b*c^9*d^7*e^2 + 8056896*b^2*c^8*d^6*e^3 - 7874464*b^3*c^7*d^5*e^4 + 4655728*b^4*c^6*d^4*e^5 - 1770120*b^5*c^5*d^3*e^6 + 422268*b^6*c^4*d^2*e^7 - 57750*b^7*c^3*d*e^8 + 3465*b^8*c^2*e^9)*f - (9830400*c^10*d^9 - 51078400*b*c^9*d^8*e + 117794560*b^2*c^8*d^7*e^2 - 156115200*b^3*c^7*d^6*e^3 + 130302400*b^4*c^6*d^5*e^4 - 71145184*b^5*c^5*d^4*e^5 + 25545168*b^6*c^4*d^3*e^6 - 5835984*b^7*c^3*d^2*e^7 + 771540*b^8*c^2*d*e^8 - 45045*b^9*c*e^9)*g + 2*(20*(588672*c^10*d^7*e^2 - 749632*b*c^9*d^6*e^3 - 547296*b^2*c^8*d^5*e^4 + 1063248*b^3*c^7*d^4*e^5 - 460856*b^4*c^6*d^3*e^6 + 121572*b^5*c^5*d^2*e^7 - 18018*b^6*c^4*d*e^8 + 1155*b^7*c^3*e^9)*f - (2661120*c^10*d^8*e - 12622080*b*c^9*d^7*e^2 + 24504320*b^2*c^8*d^6*e^3 - 25880640*b^3*c^7*d^5*e^4 + 16587360*b^4*c^6*d^4*e^5 - 6720560*b^5*c^5*d^3*e^6 + 1688544*b^6*c^4*d^2*e^7 - 241164*b^7*c^3*d*e^8 + 15015*b^8*c^2*e^9)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^8*e^2), -1/82575360*(3465*(20*(512*c^10*d^9*e - 2304*b*c^9*d^8*e^2 + 4608*b^2*c^8*d^7*e^3 - 5376*b^3*c^7*d^6*e^4 + 4032*b^4*c^6*d^5*e^5 - 2016*b^5*c^5*d^4*e^6 + 672*b^6*c^4*d^3*e^7 - 144*b^7*c^3*d^2*e^8 + 18*b^8*c^2*d*e^9 - b^9*c*e^10)*f + (3072*c^10*d^10 - 20480*b*c^9*d^9*e + 57600*b^2*c^8*d^8*e^2 - 92160*b^3*c^7*d^7*e^3 + 94080*b^4*c^6*d^6*e^4 - 64512*b^5*c^5*d^5*e^5 + 30240*b^6*c^4*d^4*e^6 - 9600*b^7*c^3*d^3*e^7 + 1980*b^8*c^2*d^2*e^8 - 240*b^9*c*d*e^9 + 13*b^10*e^10)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(4128768*c^10*e^9*g*x^9 + 229376*(20*c^10*e^9*f + (60*c^10*d*e^8 + 41*b*c^9*e^9)*g)*x^8 + 14336*(20*(54*c^10*d*e^8 + 37*b*c^9*e^9)*f + (324*c^10*d^2*e^7 + 2976*b*c^9*d*e^8 + 383*b^2*c^8*e^9)*g)*x^7 + 1024*(20*(256*c^10*d^2*e^7 + 2390*b*c^9*d*e^8 + 309*b^2*c^8*e^9)*f - (30720*c^10*d^3*e^6 - 59396*b*c^9*d^2*e^7 - 31264*b^2*c^8*d*e^8 - 15*b^3*c^7*e^9)*g)*x^6 - 256*(20*(7224*c^10*d^3*e^6 - 13908*b*c^9*d^2*e^7 - 7386*b^2*c^8*d*e^8 - 5*b^3*c^7*e^9)*f + (140112*c^10*d^4*e^5 + 16176*b*c^9*d^3*e^6 - 298968*b^2*c^8*d^2*e^7 - 780*b^3*c^7*d*e^8 + 65*b^4*c^6*e^9)*g)*x^5 - 128*(20*(16896*c^10*d^4*e^5 + 2328*b*c^9*d^3*e^6 - 36516*b^2*c^8*d^2*e^7 - 138*b^3*c^7*d*e^8 + 11*b^4*c^6*e^9)*f - (92160*c^10*d^5*e^4 - 762000*b*c^9*d^4*e^5 + 733200*b^2*c^8*d^3*e^6 + 9960*b^3*c^7*d^2*e^7 - 1860*b^4*c^6*d*e^8 + 143*b^5*c^5*e^9)*g)*x^4 + 16*(20*(49056*c^10*d^5*e^4 - 392976*b*c^9*d^4*e^5 + 374352*b^2*c^8*d^3*e^6 + 7576*b^3*c^7*d^2*e^7 - 1342*b^4*c^6*d*e^8 + 99*b^5*c^5*e^9)*f + (2358720*c^10*d^6*e^3 - 6092160*b*c^9*d^5*e^4 + 3484080*b^2*c^8*d^4*e^5 + 339840*b^3*c^7*d^3*e^6 - 106540*b^4*c^6*d^2*e^7 + 18040*b^5*c^5*d*e^8 - 1287*b^6*c^4*e^9)*g)*x^3 + 8*(20*(327680*c^10*d^6*e^3 - 835872*b*c^9*d^5*e^4 + 455376*b^2*c^8*d^4*e^5 + 70768*b^3*c^7*d^3*e^6 - 20856*b^4*c^6*d^2*e^7 + 3366*b^5*c^5*d*e^8 - 231*b^6*c^4*e^9)*f + (1966080*c^10*d^7*e^2 - 3081920*b*c^9*d^6*e^3 - 336000*b^2*c^8*d^5*e^4 + 2246160*b^3*c^7*d^4*e^5 - 1045120*b^4*c^6*d^3*e^6 + 291324*b^5*c^5*d^2*e^7 - 45144*b^6*c^4*d*e^8 + 3003*b^7*c^3*e^9)*g)*x^2 - 20*(950272*c^10*d^8*e - 4389760*b*c^9*d^7*e^2 + 8056896*b^2*c^8*d^6*e^3 - 7874464*b^3*c^7*d^5*e^4 + 4655728*b^4*c^6*d^4*e^5 - 1770120*b^5*c^5*d^3*e^6 + 422268*b^6*c^4*d^2*e^7 - 57750*b^7*c^3*d*e^8 + 3465*b^8*c^2*e^9)*f - (9830400*c^10*d^9 - 51078400*b*c^9*d^8*e + 117794560*b^2*c^8*d^7*e^2 - 156115200*b^3*c^7*d^6*e^3 + 130302400*b^4*c^6*d^5*e^4 - 71145184*b^5*c^5*d^4*e^5 + 25545168*b^6*c^4*d^3*e^6 - 5835984*b^7*c^3*d^2*e^7 + 771540*b^8*c^2*d*e^8 - 45045*b^9*c*e^9)*g + 2*(20*(588672*c^10*d^7*e^2 - 749632*b*c^9*d^6*e^3 - 547296*b^2*c^8*d^5*e^4 + 1063248*b^3*c^7*d^4*e^5 - 460856*b^4*c^6*d^3*e^6 + 121572*b^5*c^5*d^2*e^7 - 18018*b^6*c^4*d*e^8 + 1155*b^7*c^3*e^9)*f - (2661120*c^10*d^8*e - 12622080*b*c^9*d^7*e^2 + 24504320*b^2*c^8*d^6*e^3 - 25880640*b^3*c^7*d^5*e^4 + 16587360*b^4*c^6*d^4*e^5 - 6720560*b^5*c^5*d^3*e^6 + 1688544*b^6*c^4*d^2*e^7 - 241164*b^7*c^3*d*e^8 + 15015*b^8*c^2*e^9)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^8*e^2)]","B",0
2196,1,2861,0,12.060778," ","integrate((e*x+d)^2*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(18 \, {\left(256 \, c^{9} d^{8} e - 1024 \, b c^{8} d^{7} e^{2} + 1792 \, b^{2} c^{7} d^{6} e^{3} - 1792 \, b^{3} c^{6} d^{5} e^{4} + 1120 \, b^{4} c^{5} d^{4} e^{5} - 448 \, b^{5} c^{4} d^{3} e^{6} + 112 \, b^{6} c^{3} d^{2} e^{7} - 16 \, b^{7} c^{2} d e^{8} + b^{8} c e^{9}\right)} f + {\left(1024 \, c^{9} d^{9} - 6912 \, b c^{8} d^{8} e + 18432 \, b^{2} c^{7} d^{7} e^{2} - 26880 \, b^{3} c^{6} d^{6} e^{3} + 24192 \, b^{4} c^{5} d^{5} e^{4} - 14112 \, b^{5} c^{4} d^{4} e^{5} + 5376 \, b^{6} c^{3} d^{3} e^{6} - 1296 \, b^{7} c^{2} d^{2} e^{7} + 180 \, b^{8} c d e^{8} - 11 \, b^{9} e^{9}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(229376 \, c^{9} e^{8} g x^{8} + 14336 \, {\left(18 \, c^{9} e^{8} f + {\left(36 \, c^{9} d e^{7} + 37 \, b c^{8} e^{8}\right)} g\right)} x^{7} + 1024 \, {\left(18 \, {\left(32 \, c^{9} d e^{7} + 33 \, b c^{8} e^{8}\right)} f - {\left(320 \, c^{9} d^{2} e^{6} - 1796 \, b c^{8} d e^{7} - 309 \, b^{2} c^{7} e^{8}\right)} g\right)} x^{6} - 256 \, {\left(54 \, {\left(28 \, c^{9} d^{2} e^{6} - 156 \, b c^{8} d e^{7} - 27 \, b^{2} c^{7} e^{8}\right)} f + {\left(5712 \, c^{9} d^{3} e^{5} - 5484 \, b c^{8} d^{2} e^{6} - 5928 \, b^{2} c^{7} d e^{7} - 5 \, b^{3} c^{6} e^{8}\right)} g\right)} x^{5} - 128 \, {\left(18 \, {\left(768 \, c^{9} d^{3} e^{5} - 732 \, b c^{8} d^{2} e^{6} - 804 \, b^{2} c^{7} d e^{7} - b^{3} c^{6} e^{8}\right)} f + {\left(3072 \, c^{9} d^{4} e^{4} + 15504 \, b c^{8} d^{3} e^{5} - 22044 \, b^{2} c^{7} d^{2} e^{6} - 120 \, b^{3} c^{6} d e^{7} + 11 \, b^{4} c^{5} e^{8}\right)} g\right)} x^{4} - 16 \, {\left(18 \, {\left(1680 \, c^{9} d^{4} e^{4} + 8928 \, b c^{8} d^{3} e^{5} - 12552 \, b^{2} c^{7} d^{2} e^{6} - 104 \, b^{3} c^{6} d e^{7} + 9 \, b^{4} c^{5} e^{8}\right)} f - {\left(79296 \, c^{9} d^{5} e^{3} - 232272 \, b c^{8} d^{4} e^{4} + 148416 \, b^{2} c^{7} d^{3} e^{5} + 5704 \, b^{3} c^{6} d^{2} e^{6} - 1180 \, b^{4} c^{5} d e^{7} + 99 \, b^{5} c^{4} e^{8}\right)} g\right)} x^{3} + 8 \, {\left(54 \, {\left(4096 \, c^{9} d^{5} e^{3} - 11920 \, b c^{8} d^{4} e^{4} + 7456 \, b^{2} c^{7} d^{3} e^{5} + 456 \, b^{3} c^{6} d^{2} e^{6} - 88 \, b^{4} c^{5} d e^{7} + 7 \, b^{5} c^{4} e^{8}\right)} f + {\left(106496 \, c^{9} d^{6} e^{2} - 192192 \, b c^{8} d^{5} e^{3} + 52752 \, b^{2} c^{7} d^{4} e^{4} + 46144 \, b^{3} c^{6} d^{3} e^{5} - 16104 \, b^{4} c^{5} d^{2} e^{6} + 2988 \, b^{5} c^{4} d e^{7} - 231 \, b^{6} c^{3} e^{8}\right)} g\right)} x^{2} - 18 \, {\left(32768 \, c^{9} d^{7} e - 151872 \, b c^{8} d^{6} e^{2} + 259008 \, b^{2} c^{7} d^{5} e^{3} - 218000 \, b^{3} c^{6} d^{4} e^{4} + 102624 \, b^{4} c^{5} d^{3} e^{5} - 29148 \, b^{5} c^{4} d^{2} e^{6} + 4620 \, b^{6} c^{3} d e^{7} - 315 \, b^{7} c^{2} e^{8}\right)} f - {\left(360448 \, c^{9} d^{8} - 1656064 \, b c^{8} d^{7} e + 3394752 \, b^{2} c^{7} d^{6} e^{2} - 3950464 \, b^{3} c^{6} d^{5} e^{3} + 2808496 \, b^{4} c^{5} d^{4} e^{4} - 1245456 \, b^{5} c^{4} d^{3} e^{5} + 339108 \, b^{6} c^{3} d^{2} e^{6} - 52080 \, b^{7} c^{2} d e^{7} + 3465 \, b^{8} c e^{8}\right)} g + 2 \, {\left(18 \, {\left(37184 \, c^{9} d^{6} e^{2} - 62400 \, b c^{8} d^{5} e^{3} + 6480 \, b^{2} c^{7} d^{4} e^{4} + 25504 \, b^{3} c^{6} d^{3} e^{5} - 8196 \, b^{4} c^{5} d^{2} e^{6} + 1428 \, b^{5} c^{4} d e^{7} - 105 \, b^{6} c^{3} e^{8}\right)} f - {\left(80640 \, c^{9} d^{7} e - 373568 \, b c^{8} d^{6} e^{2} + 663936 \, b^{2} c^{7} d^{5} e^{3} - 604176 \, b^{3} c^{6} d^{4} e^{4} + 313328 \, b^{4} c^{5} d^{3} e^{5} - 95868 \, b^{5} c^{4} d^{2} e^{6} + 16128 \, b^{6} c^{3} d e^{7} - 1155 \, b^{7} c^{2} e^{8}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{8257536 \, c^{7} e^{2}}, -\frac{315 \, {\left(18 \, {\left(256 \, c^{9} d^{8} e - 1024 \, b c^{8} d^{7} e^{2} + 1792 \, b^{2} c^{7} d^{6} e^{3} - 1792 \, b^{3} c^{6} d^{5} e^{4} + 1120 \, b^{4} c^{5} d^{4} e^{5} - 448 \, b^{5} c^{4} d^{3} e^{6} + 112 \, b^{6} c^{3} d^{2} e^{7} - 16 \, b^{7} c^{2} d e^{8} + b^{8} c e^{9}\right)} f + {\left(1024 \, c^{9} d^{9} - 6912 \, b c^{8} d^{8} e + 18432 \, b^{2} c^{7} d^{7} e^{2} - 26880 \, b^{3} c^{6} d^{6} e^{3} + 24192 \, b^{4} c^{5} d^{5} e^{4} - 14112 \, b^{5} c^{4} d^{4} e^{5} + 5376 \, b^{6} c^{3} d^{3} e^{6} - 1296 \, b^{7} c^{2} d^{2} e^{7} + 180 \, b^{8} c d e^{8} - 11 \, b^{9} e^{9}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(229376 \, c^{9} e^{8} g x^{8} + 14336 \, {\left(18 \, c^{9} e^{8} f + {\left(36 \, c^{9} d e^{7} + 37 \, b c^{8} e^{8}\right)} g\right)} x^{7} + 1024 \, {\left(18 \, {\left(32 \, c^{9} d e^{7} + 33 \, b c^{8} e^{8}\right)} f - {\left(320 \, c^{9} d^{2} e^{6} - 1796 \, b c^{8} d e^{7} - 309 \, b^{2} c^{7} e^{8}\right)} g\right)} x^{6} - 256 \, {\left(54 \, {\left(28 \, c^{9} d^{2} e^{6} - 156 \, b c^{8} d e^{7} - 27 \, b^{2} c^{7} e^{8}\right)} f + {\left(5712 \, c^{9} d^{3} e^{5} - 5484 \, b c^{8} d^{2} e^{6} - 5928 \, b^{2} c^{7} d e^{7} - 5 \, b^{3} c^{6} e^{8}\right)} g\right)} x^{5} - 128 \, {\left(18 \, {\left(768 \, c^{9} d^{3} e^{5} - 732 \, b c^{8} d^{2} e^{6} - 804 \, b^{2} c^{7} d e^{7} - b^{3} c^{6} e^{8}\right)} f + {\left(3072 \, c^{9} d^{4} e^{4} + 15504 \, b c^{8} d^{3} e^{5} - 22044 \, b^{2} c^{7} d^{2} e^{6} - 120 \, b^{3} c^{6} d e^{7} + 11 \, b^{4} c^{5} e^{8}\right)} g\right)} x^{4} - 16 \, {\left(18 \, {\left(1680 \, c^{9} d^{4} e^{4} + 8928 \, b c^{8} d^{3} e^{5} - 12552 \, b^{2} c^{7} d^{2} e^{6} - 104 \, b^{3} c^{6} d e^{7} + 9 \, b^{4} c^{5} e^{8}\right)} f - {\left(79296 \, c^{9} d^{5} e^{3} - 232272 \, b c^{8} d^{4} e^{4} + 148416 \, b^{2} c^{7} d^{3} e^{5} + 5704 \, b^{3} c^{6} d^{2} e^{6} - 1180 \, b^{4} c^{5} d e^{7} + 99 \, b^{5} c^{4} e^{8}\right)} g\right)} x^{3} + 8 \, {\left(54 \, {\left(4096 \, c^{9} d^{5} e^{3} - 11920 \, b c^{8} d^{4} e^{4} + 7456 \, b^{2} c^{7} d^{3} e^{5} + 456 \, b^{3} c^{6} d^{2} e^{6} - 88 \, b^{4} c^{5} d e^{7} + 7 \, b^{5} c^{4} e^{8}\right)} f + {\left(106496 \, c^{9} d^{6} e^{2} - 192192 \, b c^{8} d^{5} e^{3} + 52752 \, b^{2} c^{7} d^{4} e^{4} + 46144 \, b^{3} c^{6} d^{3} e^{5} - 16104 \, b^{4} c^{5} d^{2} e^{6} + 2988 \, b^{5} c^{4} d e^{7} - 231 \, b^{6} c^{3} e^{8}\right)} g\right)} x^{2} - 18 \, {\left(32768 \, c^{9} d^{7} e - 151872 \, b c^{8} d^{6} e^{2} + 259008 \, b^{2} c^{7} d^{5} e^{3} - 218000 \, b^{3} c^{6} d^{4} e^{4} + 102624 \, b^{4} c^{5} d^{3} e^{5} - 29148 \, b^{5} c^{4} d^{2} e^{6} + 4620 \, b^{6} c^{3} d e^{7} - 315 \, b^{7} c^{2} e^{8}\right)} f - {\left(360448 \, c^{9} d^{8} - 1656064 \, b c^{8} d^{7} e + 3394752 \, b^{2} c^{7} d^{6} e^{2} - 3950464 \, b^{3} c^{6} d^{5} e^{3} + 2808496 \, b^{4} c^{5} d^{4} e^{4} - 1245456 \, b^{5} c^{4} d^{3} e^{5} + 339108 \, b^{6} c^{3} d^{2} e^{6} - 52080 \, b^{7} c^{2} d e^{7} + 3465 \, b^{8} c e^{8}\right)} g + 2 \, {\left(18 \, {\left(37184 \, c^{9} d^{6} e^{2} - 62400 \, b c^{8} d^{5} e^{3} + 6480 \, b^{2} c^{7} d^{4} e^{4} + 25504 \, b^{3} c^{6} d^{3} e^{5} - 8196 \, b^{4} c^{5} d^{2} e^{6} + 1428 \, b^{5} c^{4} d e^{7} - 105 \, b^{6} c^{3} e^{8}\right)} f - {\left(80640 \, c^{9} d^{7} e - 373568 \, b c^{8} d^{6} e^{2} + 663936 \, b^{2} c^{7} d^{5} e^{3} - 604176 \, b^{3} c^{6} d^{4} e^{4} + 313328 \, b^{4} c^{5} d^{3} e^{5} - 95868 \, b^{5} c^{4} d^{2} e^{6} + 16128 \, b^{6} c^{3} d e^{7} - 1155 \, b^{7} c^{2} e^{8}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{4128768 \, c^{7} e^{2}}\right]"," ",0,"[1/8257536*(315*(18*(256*c^9*d^8*e - 1024*b*c^8*d^7*e^2 + 1792*b^2*c^7*d^6*e^3 - 1792*b^3*c^6*d^5*e^4 + 1120*b^4*c^5*d^4*e^5 - 448*b^5*c^4*d^3*e^6 + 112*b^6*c^3*d^2*e^7 - 16*b^7*c^2*d*e^8 + b^8*c*e^9)*f + (1024*c^9*d^9 - 6912*b*c^8*d^8*e + 18432*b^2*c^7*d^7*e^2 - 26880*b^3*c^6*d^6*e^3 + 24192*b^4*c^5*d^5*e^4 - 14112*b^5*c^4*d^4*e^5 + 5376*b^6*c^3*d^3*e^6 - 1296*b^7*c^2*d^2*e^7 + 180*b^8*c*d*e^8 - 11*b^9*e^9)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(229376*c^9*e^8*g*x^8 + 14336*(18*c^9*e^8*f + (36*c^9*d*e^7 + 37*b*c^8*e^8)*g)*x^7 + 1024*(18*(32*c^9*d*e^7 + 33*b*c^8*e^8)*f - (320*c^9*d^2*e^6 - 1796*b*c^8*d*e^7 - 309*b^2*c^7*e^8)*g)*x^6 - 256*(54*(28*c^9*d^2*e^6 - 156*b*c^8*d*e^7 - 27*b^2*c^7*e^8)*f + (5712*c^9*d^3*e^5 - 5484*b*c^8*d^2*e^6 - 5928*b^2*c^7*d*e^7 - 5*b^3*c^6*e^8)*g)*x^5 - 128*(18*(768*c^9*d^3*e^5 - 732*b*c^8*d^2*e^6 - 804*b^2*c^7*d*e^7 - b^3*c^6*e^8)*f + (3072*c^9*d^4*e^4 + 15504*b*c^8*d^3*e^5 - 22044*b^2*c^7*d^2*e^6 - 120*b^3*c^6*d*e^7 + 11*b^4*c^5*e^8)*g)*x^4 - 16*(18*(1680*c^9*d^4*e^4 + 8928*b*c^8*d^3*e^5 - 12552*b^2*c^7*d^2*e^6 - 104*b^3*c^6*d*e^7 + 9*b^4*c^5*e^8)*f - (79296*c^9*d^5*e^3 - 232272*b*c^8*d^4*e^4 + 148416*b^2*c^7*d^3*e^5 + 5704*b^3*c^6*d^2*e^6 - 1180*b^4*c^5*d*e^7 + 99*b^5*c^4*e^8)*g)*x^3 + 8*(54*(4096*c^9*d^5*e^3 - 11920*b*c^8*d^4*e^4 + 7456*b^2*c^7*d^3*e^5 + 456*b^3*c^6*d^2*e^6 - 88*b^4*c^5*d*e^7 + 7*b^5*c^4*e^8)*f + (106496*c^9*d^6*e^2 - 192192*b*c^8*d^5*e^3 + 52752*b^2*c^7*d^4*e^4 + 46144*b^3*c^6*d^3*e^5 - 16104*b^4*c^5*d^2*e^6 + 2988*b^5*c^4*d*e^7 - 231*b^6*c^3*e^8)*g)*x^2 - 18*(32768*c^9*d^7*e - 151872*b*c^8*d^6*e^2 + 259008*b^2*c^7*d^5*e^3 - 218000*b^3*c^6*d^4*e^4 + 102624*b^4*c^5*d^3*e^5 - 29148*b^5*c^4*d^2*e^6 + 4620*b^6*c^3*d*e^7 - 315*b^7*c^2*e^8)*f - (360448*c^9*d^8 - 1656064*b*c^8*d^7*e + 3394752*b^2*c^7*d^6*e^2 - 3950464*b^3*c^6*d^5*e^3 + 2808496*b^4*c^5*d^4*e^4 - 1245456*b^5*c^4*d^3*e^5 + 339108*b^6*c^3*d^2*e^6 - 52080*b^7*c^2*d*e^7 + 3465*b^8*c*e^8)*g + 2*(18*(37184*c^9*d^6*e^2 - 62400*b*c^8*d^5*e^3 + 6480*b^2*c^7*d^4*e^4 + 25504*b^3*c^6*d^3*e^5 - 8196*b^4*c^5*d^2*e^6 + 1428*b^5*c^4*d*e^7 - 105*b^6*c^3*e^8)*f - (80640*c^9*d^7*e - 373568*b*c^8*d^6*e^2 + 663936*b^2*c^7*d^5*e^3 - 604176*b^3*c^6*d^4*e^4 + 313328*b^4*c^5*d^3*e^5 - 95868*b^5*c^4*d^2*e^6 + 16128*b^6*c^3*d*e^7 - 1155*b^7*c^2*e^8)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^7*e^2), -1/4128768*(315*(18*(256*c^9*d^8*e - 1024*b*c^8*d^7*e^2 + 1792*b^2*c^7*d^6*e^3 - 1792*b^3*c^6*d^5*e^4 + 1120*b^4*c^5*d^4*e^5 - 448*b^5*c^4*d^3*e^6 + 112*b^6*c^3*d^2*e^7 - 16*b^7*c^2*d*e^8 + b^8*c*e^9)*f + (1024*c^9*d^9 - 6912*b*c^8*d^8*e + 18432*b^2*c^7*d^7*e^2 - 26880*b^3*c^6*d^6*e^3 + 24192*b^4*c^5*d^5*e^4 - 14112*b^5*c^4*d^4*e^5 + 5376*b^6*c^3*d^3*e^6 - 1296*b^7*c^2*d^2*e^7 + 180*b^8*c*d*e^8 - 11*b^9*e^9)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(229376*c^9*e^8*g*x^8 + 14336*(18*c^9*e^8*f + (36*c^9*d*e^7 + 37*b*c^8*e^8)*g)*x^7 + 1024*(18*(32*c^9*d*e^7 + 33*b*c^8*e^8)*f - (320*c^9*d^2*e^6 - 1796*b*c^8*d*e^7 - 309*b^2*c^7*e^8)*g)*x^6 - 256*(54*(28*c^9*d^2*e^6 - 156*b*c^8*d*e^7 - 27*b^2*c^7*e^8)*f + (5712*c^9*d^3*e^5 - 5484*b*c^8*d^2*e^6 - 5928*b^2*c^7*d*e^7 - 5*b^3*c^6*e^8)*g)*x^5 - 128*(18*(768*c^9*d^3*e^5 - 732*b*c^8*d^2*e^6 - 804*b^2*c^7*d*e^7 - b^3*c^6*e^8)*f + (3072*c^9*d^4*e^4 + 15504*b*c^8*d^3*e^5 - 22044*b^2*c^7*d^2*e^6 - 120*b^3*c^6*d*e^7 + 11*b^4*c^5*e^8)*g)*x^4 - 16*(18*(1680*c^9*d^4*e^4 + 8928*b*c^8*d^3*e^5 - 12552*b^2*c^7*d^2*e^6 - 104*b^3*c^6*d*e^7 + 9*b^4*c^5*e^8)*f - (79296*c^9*d^5*e^3 - 232272*b*c^8*d^4*e^4 + 148416*b^2*c^7*d^3*e^5 + 5704*b^3*c^6*d^2*e^6 - 1180*b^4*c^5*d*e^7 + 99*b^5*c^4*e^8)*g)*x^3 + 8*(54*(4096*c^9*d^5*e^3 - 11920*b*c^8*d^4*e^4 + 7456*b^2*c^7*d^3*e^5 + 456*b^3*c^6*d^2*e^6 - 88*b^4*c^5*d*e^7 + 7*b^5*c^4*e^8)*f + (106496*c^9*d^6*e^2 - 192192*b*c^8*d^5*e^3 + 52752*b^2*c^7*d^4*e^4 + 46144*b^3*c^6*d^3*e^5 - 16104*b^4*c^5*d^2*e^6 + 2988*b^5*c^4*d*e^7 - 231*b^6*c^3*e^8)*g)*x^2 - 18*(32768*c^9*d^7*e - 151872*b*c^8*d^6*e^2 + 259008*b^2*c^7*d^5*e^3 - 218000*b^3*c^6*d^4*e^4 + 102624*b^4*c^5*d^3*e^5 - 29148*b^5*c^4*d^2*e^6 + 4620*b^6*c^3*d*e^7 - 315*b^7*c^2*e^8)*f - (360448*c^9*d^8 - 1656064*b*c^8*d^7*e + 3394752*b^2*c^7*d^6*e^2 - 3950464*b^3*c^6*d^5*e^3 + 2808496*b^4*c^5*d^4*e^4 - 1245456*b^5*c^4*d^3*e^5 + 339108*b^6*c^3*d^2*e^6 - 52080*b^7*c^2*d*e^7 + 3465*b^8*c*e^8)*g + 2*(18*(37184*c^9*d^6*e^2 - 62400*b*c^8*d^5*e^3 + 6480*b^2*c^7*d^4*e^4 + 25504*b^3*c^6*d^3*e^5 - 8196*b^4*c^5*d^2*e^6 + 1428*b^5*c^4*d*e^7 - 105*b^6*c^3*e^8)*f - (80640*c^9*d^7*e - 373568*b*c^8*d^6*e^2 + 663936*b^2*c^7*d^5*e^3 - 604176*b^3*c^6*d^4*e^4 + 313328*b^4*c^5*d^3*e^5 - 95868*b^5*c^4*d^2*e^6 + 16128*b^6*c^3*d*e^7 - 1155*b^7*c^2*e^8)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^7*e^2)]","B",0
2197,1,2345,0,6.589950," ","integrate((e*x+d)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(16 \, {\left(128 \, c^{8} d^{7} e - 448 \, b c^{7} d^{6} e^{2} + 672 \, b^{2} c^{6} d^{5} e^{3} - 560 \, b^{3} c^{5} d^{4} e^{4} + 280 \, b^{4} c^{4} d^{3} e^{5} - 84 \, b^{5} c^{3} d^{2} e^{6} + 14 \, b^{6} c^{2} d e^{7} - b^{7} c e^{8}\right)} f + {\left(256 \, c^{8} d^{8} - 2048 \, b c^{7} d^{7} e + 5376 \, b^{2} c^{6} d^{6} e^{2} - 7168 \, b^{3} c^{5} d^{5} e^{3} + 5600 \, b^{4} c^{4} d^{4} e^{4} - 2688 \, b^{5} c^{3} d^{3} e^{5} + 784 \, b^{6} c^{2} d^{2} e^{6} - 128 \, b^{7} c d e^{7} + 9 \, b^{8} e^{8}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(43008 \, c^{8} e^{7} g x^{7} + 3072 \, {\left(16 \, c^{8} e^{7} f + {\left(16 \, c^{8} d e^{6} + 33 \, b c^{7} e^{7}\right)} g\right)} x^{6} + 256 \, {\left(16 \, {\left(14 \, c^{8} d e^{6} + 29 \, b c^{7} e^{7}\right)} f - {\left(476 \, c^{8} d^{2} e^{5} - 940 \, b c^{7} d e^{6} - 243 \, b^{2} c^{6} e^{7}\right)} g\right)} x^{5} - 128 \, {\left(16 \, {\left(72 \, c^{8} d^{2} e^{5} - 142 \, b c^{7} d e^{6} - 37 \, b^{2} c^{6} e^{7}\right)} f + {\left(1152 \, c^{8} d^{3} e^{4} + 76 \, b c^{7} d^{2} e^{5} - 1820 \, b^{2} c^{6} d e^{6} - 3 \, b^{3} c^{5} e^{7}\right)} g\right)} x^{4} - 16 \, {\left(16 \, {\left(728 \, c^{8} d^{3} e^{4} + 60 \, b c^{7} d^{2} e^{5} - 1166 \, b^{2} c^{6} d e^{6} - 3 \, b^{3} c^{5} e^{7}\right)} f - {\left(6608 \, c^{8} d^{4} e^{3} - 25824 \, b c^{7} d^{3} e^{4} + 19000 \, b^{2} c^{6} d^{2} e^{5} + 264 \, b^{3} c^{5} d e^{6} - 27 \, b^{4} c^{4} e^{7}\right)} g\right)} x^{3} + 8 \, {\left(16 \, {\left(1152 \, c^{8} d^{4} e^{3} - 4488 \, b c^{7} d^{3} e^{4} + 3276 \, b^{2} c^{6} d^{2} e^{5} + 74 \, b^{3} c^{5} d e^{6} - 7 \, b^{4} c^{4} e^{7}\right)} f + {\left(18432 \, c^{8} d^{5} e^{2} - 35472 \, b c^{7} d^{4} e^{3} + 14688 \, b^{2} c^{6} d^{3} e^{4} + 2920 \, b^{3} c^{5} d^{2} e^{5} - 680 \, b^{4} c^{4} d e^{6} + 63 \, b^{5} c^{3} e^{7}\right)} g\right)} x^{2} - 16 \, {\left(3072 \, c^{8} d^{6} e - 16608 \, b c^{7} d^{5} e^{2} + 27696 \, b^{2} c^{6} d^{4} e^{3} - 20096 \, b^{3} c^{5} d^{3} e^{4} + 7056 \, b^{4} c^{4} d^{2} e^{5} - 1330 \, b^{5} c^{3} d e^{6} + 105 \, b^{6} c^{2} e^{7}\right)} f - {\left(49152 \, c^{8} d^{7} - 189888 \, b c^{7} d^{6} e + 333888 \, b^{2} c^{6} d^{5} e^{2} - 332464 \, b^{3} c^{5} d^{4} e^{3} + 194976 \, b^{4} c^{4} d^{3} e^{4} - 66164 \, b^{5} c^{3} d^{2} e^{5} + 12180 \, b^{6} c^{2} d e^{6} - 945 \, b^{7} c e^{7}\right)} g + 2 \, {\left(16 \, {\left(7392 \, c^{8} d^{5} e^{2} - 13872 \, b c^{7} d^{4} e^{3} + 4896 \, b^{2} c^{6} d^{3} e^{4} + 1920 \, b^{3} c^{5} d^{2} e^{5} - 406 \, b^{4} c^{4} d e^{6} + 35 \, b^{5} c^{3} e^{7}\right)} f - {\left(6720 \, c^{8} d^{6} e - 34752 \, b c^{7} d^{5} e^{2} + 58896 \, b^{2} c^{6} d^{4} e^{3} - 45792 \, b^{3} c^{5} d^{3} e^{4} + 18092 \, b^{4} c^{4} d^{2} e^{5} - 3724 \, b^{5} c^{3} d e^{6} + 315 \, b^{6} c^{2} e^{7}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{1376256 \, c^{6} e^{2}}, -\frac{105 \, {\left(16 \, {\left(128 \, c^{8} d^{7} e - 448 \, b c^{7} d^{6} e^{2} + 672 \, b^{2} c^{6} d^{5} e^{3} - 560 \, b^{3} c^{5} d^{4} e^{4} + 280 \, b^{4} c^{4} d^{3} e^{5} - 84 \, b^{5} c^{3} d^{2} e^{6} + 14 \, b^{6} c^{2} d e^{7} - b^{7} c e^{8}\right)} f + {\left(256 \, c^{8} d^{8} - 2048 \, b c^{7} d^{7} e + 5376 \, b^{2} c^{6} d^{6} e^{2} - 7168 \, b^{3} c^{5} d^{5} e^{3} + 5600 \, b^{4} c^{4} d^{4} e^{4} - 2688 \, b^{5} c^{3} d^{3} e^{5} + 784 \, b^{6} c^{2} d^{2} e^{6} - 128 \, b^{7} c d e^{7} + 9 \, b^{8} e^{8}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(43008 \, c^{8} e^{7} g x^{7} + 3072 \, {\left(16 \, c^{8} e^{7} f + {\left(16 \, c^{8} d e^{6} + 33 \, b c^{7} e^{7}\right)} g\right)} x^{6} + 256 \, {\left(16 \, {\left(14 \, c^{8} d e^{6} + 29 \, b c^{7} e^{7}\right)} f - {\left(476 \, c^{8} d^{2} e^{5} - 940 \, b c^{7} d e^{6} - 243 \, b^{2} c^{6} e^{7}\right)} g\right)} x^{5} - 128 \, {\left(16 \, {\left(72 \, c^{8} d^{2} e^{5} - 142 \, b c^{7} d e^{6} - 37 \, b^{2} c^{6} e^{7}\right)} f + {\left(1152 \, c^{8} d^{3} e^{4} + 76 \, b c^{7} d^{2} e^{5} - 1820 \, b^{2} c^{6} d e^{6} - 3 \, b^{3} c^{5} e^{7}\right)} g\right)} x^{4} - 16 \, {\left(16 \, {\left(728 \, c^{8} d^{3} e^{4} + 60 \, b c^{7} d^{2} e^{5} - 1166 \, b^{2} c^{6} d e^{6} - 3 \, b^{3} c^{5} e^{7}\right)} f - {\left(6608 \, c^{8} d^{4} e^{3} - 25824 \, b c^{7} d^{3} e^{4} + 19000 \, b^{2} c^{6} d^{2} e^{5} + 264 \, b^{3} c^{5} d e^{6} - 27 \, b^{4} c^{4} e^{7}\right)} g\right)} x^{3} + 8 \, {\left(16 \, {\left(1152 \, c^{8} d^{4} e^{3} - 4488 \, b c^{7} d^{3} e^{4} + 3276 \, b^{2} c^{6} d^{2} e^{5} + 74 \, b^{3} c^{5} d e^{6} - 7 \, b^{4} c^{4} e^{7}\right)} f + {\left(18432 \, c^{8} d^{5} e^{2} - 35472 \, b c^{7} d^{4} e^{3} + 14688 \, b^{2} c^{6} d^{3} e^{4} + 2920 \, b^{3} c^{5} d^{2} e^{5} - 680 \, b^{4} c^{4} d e^{6} + 63 \, b^{5} c^{3} e^{7}\right)} g\right)} x^{2} - 16 \, {\left(3072 \, c^{8} d^{6} e - 16608 \, b c^{7} d^{5} e^{2} + 27696 \, b^{2} c^{6} d^{4} e^{3} - 20096 \, b^{3} c^{5} d^{3} e^{4} + 7056 \, b^{4} c^{4} d^{2} e^{5} - 1330 \, b^{5} c^{3} d e^{6} + 105 \, b^{6} c^{2} e^{7}\right)} f - {\left(49152 \, c^{8} d^{7} - 189888 \, b c^{7} d^{6} e + 333888 \, b^{2} c^{6} d^{5} e^{2} - 332464 \, b^{3} c^{5} d^{4} e^{3} + 194976 \, b^{4} c^{4} d^{3} e^{4} - 66164 \, b^{5} c^{3} d^{2} e^{5} + 12180 \, b^{6} c^{2} d e^{6} - 945 \, b^{7} c e^{7}\right)} g + 2 \, {\left(16 \, {\left(7392 \, c^{8} d^{5} e^{2} - 13872 \, b c^{7} d^{4} e^{3} + 4896 \, b^{2} c^{6} d^{3} e^{4} + 1920 \, b^{3} c^{5} d^{2} e^{5} - 406 \, b^{4} c^{4} d e^{6} + 35 \, b^{5} c^{3} e^{7}\right)} f - {\left(6720 \, c^{8} d^{6} e - 34752 \, b c^{7} d^{5} e^{2} + 58896 \, b^{2} c^{6} d^{4} e^{3} - 45792 \, b^{3} c^{5} d^{3} e^{4} + 18092 \, b^{4} c^{4} d^{2} e^{5} - 3724 \, b^{5} c^{3} d e^{6} + 315 \, b^{6} c^{2} e^{7}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{688128 \, c^{6} e^{2}}\right]"," ",0,"[-1/1376256*(105*(16*(128*c^8*d^7*e - 448*b*c^7*d^6*e^2 + 672*b^2*c^6*d^5*e^3 - 560*b^3*c^5*d^4*e^4 + 280*b^4*c^4*d^3*e^5 - 84*b^5*c^3*d^2*e^6 + 14*b^6*c^2*d*e^7 - b^7*c*e^8)*f + (256*c^8*d^8 - 2048*b*c^7*d^7*e + 5376*b^2*c^6*d^6*e^2 - 7168*b^3*c^5*d^5*e^3 + 5600*b^4*c^4*d^4*e^4 - 2688*b^5*c^3*d^3*e^5 + 784*b^6*c^2*d^2*e^6 - 128*b^7*c*d*e^7 + 9*b^8*e^8)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(43008*c^8*e^7*g*x^7 + 3072*(16*c^8*e^7*f + (16*c^8*d*e^6 + 33*b*c^7*e^7)*g)*x^6 + 256*(16*(14*c^8*d*e^6 + 29*b*c^7*e^7)*f - (476*c^8*d^2*e^5 - 940*b*c^7*d*e^6 - 243*b^2*c^6*e^7)*g)*x^5 - 128*(16*(72*c^8*d^2*e^5 - 142*b*c^7*d*e^6 - 37*b^2*c^6*e^7)*f + (1152*c^8*d^3*e^4 + 76*b*c^7*d^2*e^5 - 1820*b^2*c^6*d*e^6 - 3*b^3*c^5*e^7)*g)*x^4 - 16*(16*(728*c^8*d^3*e^4 + 60*b*c^7*d^2*e^5 - 1166*b^2*c^6*d*e^6 - 3*b^3*c^5*e^7)*f - (6608*c^8*d^4*e^3 - 25824*b*c^7*d^3*e^4 + 19000*b^2*c^6*d^2*e^5 + 264*b^3*c^5*d*e^6 - 27*b^4*c^4*e^7)*g)*x^3 + 8*(16*(1152*c^8*d^4*e^3 - 4488*b*c^7*d^3*e^4 + 3276*b^2*c^6*d^2*e^5 + 74*b^3*c^5*d*e^6 - 7*b^4*c^4*e^7)*f + (18432*c^8*d^5*e^2 - 35472*b*c^7*d^4*e^3 + 14688*b^2*c^6*d^3*e^4 + 2920*b^3*c^5*d^2*e^5 - 680*b^4*c^4*d*e^6 + 63*b^5*c^3*e^7)*g)*x^2 - 16*(3072*c^8*d^6*e - 16608*b*c^7*d^5*e^2 + 27696*b^2*c^6*d^4*e^3 - 20096*b^3*c^5*d^3*e^4 + 7056*b^4*c^4*d^2*e^5 - 1330*b^5*c^3*d*e^6 + 105*b^6*c^2*e^7)*f - (49152*c^8*d^7 - 189888*b*c^7*d^6*e + 333888*b^2*c^6*d^5*e^2 - 332464*b^3*c^5*d^4*e^3 + 194976*b^4*c^4*d^3*e^4 - 66164*b^5*c^3*d^2*e^5 + 12180*b^6*c^2*d*e^6 - 945*b^7*c*e^7)*g + 2*(16*(7392*c^8*d^5*e^2 - 13872*b*c^7*d^4*e^3 + 4896*b^2*c^6*d^3*e^4 + 1920*b^3*c^5*d^2*e^5 - 406*b^4*c^4*d*e^6 + 35*b^5*c^3*e^7)*f - (6720*c^8*d^6*e - 34752*b*c^7*d^5*e^2 + 58896*b^2*c^6*d^4*e^3 - 45792*b^3*c^5*d^3*e^4 + 18092*b^4*c^4*d^2*e^5 - 3724*b^5*c^3*d*e^6 + 315*b^6*c^2*e^7)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^6*e^2), -1/688128*(105*(16*(128*c^8*d^7*e - 448*b*c^7*d^6*e^2 + 672*b^2*c^6*d^5*e^3 - 560*b^3*c^5*d^4*e^4 + 280*b^4*c^4*d^3*e^5 - 84*b^5*c^3*d^2*e^6 + 14*b^6*c^2*d*e^7 - b^7*c*e^8)*f + (256*c^8*d^8 - 2048*b*c^7*d^7*e + 5376*b^2*c^6*d^6*e^2 - 7168*b^3*c^5*d^5*e^3 + 5600*b^4*c^4*d^4*e^4 - 2688*b^5*c^3*d^3*e^5 + 784*b^6*c^2*d^2*e^6 - 128*b^7*c*d*e^7 + 9*b^8*e^8)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(43008*c^8*e^7*g*x^7 + 3072*(16*c^8*e^7*f + (16*c^8*d*e^6 + 33*b*c^7*e^7)*g)*x^6 + 256*(16*(14*c^8*d*e^6 + 29*b*c^7*e^7)*f - (476*c^8*d^2*e^5 - 940*b*c^7*d*e^6 - 243*b^2*c^6*e^7)*g)*x^5 - 128*(16*(72*c^8*d^2*e^5 - 142*b*c^7*d*e^6 - 37*b^2*c^6*e^7)*f + (1152*c^8*d^3*e^4 + 76*b*c^7*d^2*e^5 - 1820*b^2*c^6*d*e^6 - 3*b^3*c^5*e^7)*g)*x^4 - 16*(16*(728*c^8*d^3*e^4 + 60*b*c^7*d^2*e^5 - 1166*b^2*c^6*d*e^6 - 3*b^3*c^5*e^7)*f - (6608*c^8*d^4*e^3 - 25824*b*c^7*d^3*e^4 + 19000*b^2*c^6*d^2*e^5 + 264*b^3*c^5*d*e^6 - 27*b^4*c^4*e^7)*g)*x^3 + 8*(16*(1152*c^8*d^4*e^3 - 4488*b*c^7*d^3*e^4 + 3276*b^2*c^6*d^2*e^5 + 74*b^3*c^5*d*e^6 - 7*b^4*c^4*e^7)*f + (18432*c^8*d^5*e^2 - 35472*b*c^7*d^4*e^3 + 14688*b^2*c^6*d^3*e^4 + 2920*b^3*c^5*d^2*e^5 - 680*b^4*c^4*d*e^6 + 63*b^5*c^3*e^7)*g)*x^2 - 16*(3072*c^8*d^6*e - 16608*b*c^7*d^5*e^2 + 27696*b^2*c^6*d^4*e^3 - 20096*b^3*c^5*d^3*e^4 + 7056*b^4*c^4*d^2*e^5 - 1330*b^5*c^3*d*e^6 + 105*b^6*c^2*e^7)*f - (49152*c^8*d^7 - 189888*b*c^7*d^6*e + 333888*b^2*c^6*d^5*e^2 - 332464*b^3*c^5*d^4*e^3 + 194976*b^4*c^4*d^3*e^4 - 66164*b^5*c^3*d^2*e^5 + 12180*b^6*c^2*d*e^6 - 945*b^7*c*e^7)*g + 2*(16*(7392*c^8*d^5*e^2 - 13872*b*c^7*d^4*e^3 + 4896*b^2*c^6*d^3*e^4 + 1920*b^3*c^5*d^2*e^5 - 406*b^4*c^4*d*e^6 + 35*b^5*c^3*e^7)*f - (6720*c^8*d^6*e - 34752*b*c^7*d^5*e^2 + 58896*b^2*c^6*d^4*e^3 - 45792*b^3*c^5*d^3*e^4 + 18092*b^4*c^4*d^2*e^5 - 3724*b^5*c^3*d*e^6 + 315*b^6*c^2*e^7)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^6*e^2)]","B",0
2198,1,1457,0,1.592876," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(12 \, {\left(32 \, c^{6} d^{5} e - 80 \, b c^{5} d^{4} e^{2} + 80 \, b^{2} c^{4} d^{3} e^{3} - 40 \, b^{3} c^{3} d^{2} e^{4} + 10 \, b^{4} c^{2} d e^{5} - b^{5} c e^{6}\right)} f - {\left(64 \, c^{6} d^{6} - 240 \, b^{2} c^{4} d^{4} e^{2} + 320 \, b^{3} c^{3} d^{3} e^{3} - 180 \, b^{4} c^{2} d^{2} e^{4} + 48 \, b^{5} c d e^{5} - 5 \, b^{6} e^{6}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(1280 \, c^{6} e^{5} g x^{5} + 128 \, {\left(12 \, c^{6} e^{5} f - {\left(12 \, c^{6} d e^{4} - 25 \, b c^{5} e^{5}\right)} g\right)} x^{4} - 16 \, {\left(12 \, {\left(10 \, c^{6} d e^{4} - 21 \, b c^{5} e^{5}\right)} f + {\left(140 \, c^{6} d^{2} e^{3} - 8 \, b c^{5} d e^{4} - 135 \, b^{2} c^{4} e^{5}\right)} g\right)} x^{3} - 8 \, {\left(12 \, {\left(32 \, c^{6} d^{2} e^{3} - 2 \, b c^{5} d e^{4} - 31 \, b^{2} c^{4} e^{5}\right)} f - {\left(384 \, c^{6} d^{3} e^{2} - 804 \, b c^{5} d^{2} e^{3} + 408 \, b^{2} c^{4} d e^{4} + 5 \, b^{3} c^{3} e^{5}\right)} g\right)} x^{2} + 12 \, {\left(128 \, c^{6} d^{4} e - 56 \, b c^{5} d^{3} e^{2} - 172 \, b^{2} c^{4} d^{2} e^{3} + 130 \, b^{3} c^{3} d e^{4} - 15 \, b^{4} c^{2} e^{5}\right)} f - {\left(1536 \, c^{6} d^{5} - 3312 \, b c^{5} d^{4} e + 3216 \, b^{2} c^{4} d^{3} e^{2} - 1880 \, b^{3} c^{3} d^{2} e^{3} + 620 \, b^{4} c^{2} d e^{4} - 75 \, b^{5} c e^{5}\right)} g + 2 \, {\left(12 \, {\left(200 \, c^{6} d^{3} e^{2} - 428 \, b c^{5} d^{2} e^{3} + 218 \, b^{2} c^{4} d e^{4} + 5 \, b^{3} c^{3} e^{5}\right)} f + {\left(240 \, c^{6} d^{4} e - 144 \, b c^{5} d^{3} e^{2} - 216 \, b^{2} c^{4} d^{2} e^{3} + 180 \, b^{3} c^{3} d e^{4} - 25 \, b^{4} c^{2} e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{30720 \, c^{4} e^{2}}, -\frac{15 \, {\left(12 \, {\left(32 \, c^{6} d^{5} e - 80 \, b c^{5} d^{4} e^{2} + 80 \, b^{2} c^{4} d^{3} e^{3} - 40 \, b^{3} c^{3} d^{2} e^{4} + 10 \, b^{4} c^{2} d e^{5} - b^{5} c e^{6}\right)} f - {\left(64 \, c^{6} d^{6} - 240 \, b^{2} c^{4} d^{4} e^{2} + 320 \, b^{3} c^{3} d^{3} e^{3} - 180 \, b^{4} c^{2} d^{2} e^{4} + 48 \, b^{5} c d e^{5} - 5 \, b^{6} e^{6}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(1280 \, c^{6} e^{5} g x^{5} + 128 \, {\left(12 \, c^{6} e^{5} f - {\left(12 \, c^{6} d e^{4} - 25 \, b c^{5} e^{5}\right)} g\right)} x^{4} - 16 \, {\left(12 \, {\left(10 \, c^{6} d e^{4} - 21 \, b c^{5} e^{5}\right)} f + {\left(140 \, c^{6} d^{2} e^{3} - 8 \, b c^{5} d e^{4} - 135 \, b^{2} c^{4} e^{5}\right)} g\right)} x^{3} - 8 \, {\left(12 \, {\left(32 \, c^{6} d^{2} e^{3} - 2 \, b c^{5} d e^{4} - 31 \, b^{2} c^{4} e^{5}\right)} f - {\left(384 \, c^{6} d^{3} e^{2} - 804 \, b c^{5} d^{2} e^{3} + 408 \, b^{2} c^{4} d e^{4} + 5 \, b^{3} c^{3} e^{5}\right)} g\right)} x^{2} + 12 \, {\left(128 \, c^{6} d^{4} e - 56 \, b c^{5} d^{3} e^{2} - 172 \, b^{2} c^{4} d^{2} e^{3} + 130 \, b^{3} c^{3} d e^{4} - 15 \, b^{4} c^{2} e^{5}\right)} f - {\left(1536 \, c^{6} d^{5} - 3312 \, b c^{5} d^{4} e + 3216 \, b^{2} c^{4} d^{3} e^{2} - 1880 \, b^{3} c^{3} d^{2} e^{3} + 620 \, b^{4} c^{2} d e^{4} - 75 \, b^{5} c e^{5}\right)} g + 2 \, {\left(12 \, {\left(200 \, c^{6} d^{3} e^{2} - 428 \, b c^{5} d^{2} e^{3} + 218 \, b^{2} c^{4} d e^{4} + 5 \, b^{3} c^{3} e^{5}\right)} f + {\left(240 \, c^{6} d^{4} e - 144 \, b c^{5} d^{3} e^{2} - 216 \, b^{2} c^{4} d^{2} e^{3} + 180 \, b^{3} c^{3} d e^{4} - 25 \, b^{4} c^{2} e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{15360 \, c^{4} e^{2}}\right]"," ",0,"[-1/30720*(15*(12*(32*c^6*d^5*e - 80*b*c^5*d^4*e^2 + 80*b^2*c^4*d^3*e^3 - 40*b^3*c^3*d^2*e^4 + 10*b^4*c^2*d*e^5 - b^5*c*e^6)*f - (64*c^6*d^6 - 240*b^2*c^4*d^4*e^2 + 320*b^3*c^3*d^3*e^3 - 180*b^4*c^2*d^2*e^4 + 48*b^5*c*d*e^5 - 5*b^6*e^6)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(1280*c^6*e^5*g*x^5 + 128*(12*c^6*e^5*f - (12*c^6*d*e^4 - 25*b*c^5*e^5)*g)*x^4 - 16*(12*(10*c^6*d*e^4 - 21*b*c^5*e^5)*f + (140*c^6*d^2*e^3 - 8*b*c^5*d*e^4 - 135*b^2*c^4*e^5)*g)*x^3 - 8*(12*(32*c^6*d^2*e^3 - 2*b*c^5*d*e^4 - 31*b^2*c^4*e^5)*f - (384*c^6*d^3*e^2 - 804*b*c^5*d^2*e^3 + 408*b^2*c^4*d*e^4 + 5*b^3*c^3*e^5)*g)*x^2 + 12*(128*c^6*d^4*e - 56*b*c^5*d^3*e^2 - 172*b^2*c^4*d^2*e^3 + 130*b^3*c^3*d*e^4 - 15*b^4*c^2*e^5)*f - (1536*c^6*d^5 - 3312*b*c^5*d^4*e + 3216*b^2*c^4*d^3*e^2 - 1880*b^3*c^3*d^2*e^3 + 620*b^4*c^2*d*e^4 - 75*b^5*c*e^5)*g + 2*(12*(200*c^6*d^3*e^2 - 428*b*c^5*d^2*e^3 + 218*b^2*c^4*d*e^4 + 5*b^3*c^3*e^5)*f + (240*c^6*d^4*e - 144*b*c^5*d^3*e^2 - 216*b^2*c^4*d^2*e^3 + 180*b^3*c^3*d*e^4 - 25*b^4*c^2*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^4*e^2), -1/15360*(15*(12*(32*c^6*d^5*e - 80*b*c^5*d^4*e^2 + 80*b^2*c^4*d^3*e^3 - 40*b^3*c^3*d^2*e^4 + 10*b^4*c^2*d*e^5 - b^5*c*e^6)*f - (64*c^6*d^6 - 240*b^2*c^4*d^4*e^2 + 320*b^3*c^3*d^3*e^3 - 180*b^4*c^2*d^2*e^4 + 48*b^5*c*d*e^5 - 5*b^6*e^6)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(1280*c^6*e^5*g*x^5 + 128*(12*c^6*e^5*f - (12*c^6*d*e^4 - 25*b*c^5*e^5)*g)*x^4 - 16*(12*(10*c^6*d*e^4 - 21*b*c^5*e^5)*f + (140*c^6*d^2*e^3 - 8*b*c^5*d*e^4 - 135*b^2*c^4*e^5)*g)*x^3 - 8*(12*(32*c^6*d^2*e^3 - 2*b*c^5*d*e^4 - 31*b^2*c^4*e^5)*f - (384*c^6*d^3*e^2 - 804*b*c^5*d^2*e^3 + 408*b^2*c^4*d*e^4 + 5*b^3*c^3*e^5)*g)*x^2 + 12*(128*c^6*d^4*e - 56*b*c^5*d^3*e^2 - 172*b^2*c^4*d^2*e^3 + 130*b^3*c^3*d*e^4 - 15*b^4*c^2*e^5)*f - (1536*c^6*d^5 - 3312*b*c^5*d^4*e + 3216*b^2*c^4*d^3*e^2 - 1880*b^3*c^3*d^2*e^3 + 620*b^4*c^2*d*e^4 - 75*b^5*c*e^5)*g + 2*(12*(200*c^6*d^3*e^2 - 428*b*c^5*d^2*e^3 + 218*b^2*c^4*d*e^4 + 5*b^3*c^3*e^5)*f + (240*c^6*d^4*e - 144*b*c^5*d^3*e^2 - 216*b^2*c^4*d^2*e^3 + 180*b^3*c^3*d*e^4 - 25*b^4*c^2*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^4*e^2)]","B",0
2199,1,1097,0,0.924548," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(10 \, {\left(16 \, c^{5} d^{4} e - 32 \, b c^{4} d^{3} e^{2} + 24 \, b^{2} c^{3} d^{2} e^{3} - 8 \, b^{3} c^{2} d e^{4} + b^{4} c e^{5}\right)} f - {\left(64 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 40 \, b^{3} c^{2} d^{2} e^{3} - 20 \, b^{4} c d e^{4} + 3 \, b^{5} e^{5}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(384 \, c^{5} e^{4} g x^{4} + 48 \, {\left(10 \, c^{5} e^{4} f - {\left(20 \, c^{5} d e^{3} - 21 \, b c^{4} e^{4}\right)} g\right)} x^{3} - 8 \, {\left(10 \, {\left(16 \, c^{5} d e^{3} - 17 \, b c^{4} e^{4}\right)} f - {\left(64 \, c^{5} d^{2} e^{2} - 164 \, b c^{4} d e^{3} + 93 \, b^{2} c^{3} e^{4}\right)} g\right)} x^{2} + 10 \, {\left(128 \, c^{5} d^{3} e - 156 \, b c^{4} d^{2} e^{2} + 28 \, b^{2} c^{3} d e^{3} + 15 \, b^{3} c^{2} e^{4}\right)} f - {\left(896 \, c^{5} d^{4} - 1392 \, b c^{4} d^{3} e + 796 \, b^{2} c^{3} d^{2} e^{2} - 240 \, b^{3} c^{2} d e^{3} + 45 \, b^{4} c e^{4}\right)} g + 2 \, {\left(10 \, {\left(36 \, c^{5} d^{2} e^{2} - 100 \, b c^{4} d e^{3} + 59 \, b^{2} c^{3} e^{4}\right)} f + {\left(240 \, c^{5} d^{3} e - 284 \, b c^{4} d^{2} e^{2} + 64 \, b^{2} c^{3} d e^{3} + 15 \, b^{3} c^{2} e^{4}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{7680 \, c^{3} e^{2}}, -\frac{15 \, {\left(10 \, {\left(16 \, c^{5} d^{4} e - 32 \, b c^{4} d^{3} e^{2} + 24 \, b^{2} c^{3} d^{2} e^{3} - 8 \, b^{3} c^{2} d e^{4} + b^{4} c e^{5}\right)} f - {\left(64 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 40 \, b^{3} c^{2} d^{2} e^{3} - 20 \, b^{4} c d e^{4} + 3 \, b^{5} e^{5}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(384 \, c^{5} e^{4} g x^{4} + 48 \, {\left(10 \, c^{5} e^{4} f - {\left(20 \, c^{5} d e^{3} - 21 \, b c^{4} e^{4}\right)} g\right)} x^{3} - 8 \, {\left(10 \, {\left(16 \, c^{5} d e^{3} - 17 \, b c^{4} e^{4}\right)} f - {\left(64 \, c^{5} d^{2} e^{2} - 164 \, b c^{4} d e^{3} + 93 \, b^{2} c^{3} e^{4}\right)} g\right)} x^{2} + 10 \, {\left(128 \, c^{5} d^{3} e - 156 \, b c^{4} d^{2} e^{2} + 28 \, b^{2} c^{3} d e^{3} + 15 \, b^{3} c^{2} e^{4}\right)} f - {\left(896 \, c^{5} d^{4} - 1392 \, b c^{4} d^{3} e + 796 \, b^{2} c^{3} d^{2} e^{2} - 240 \, b^{3} c^{2} d e^{3} + 45 \, b^{4} c e^{4}\right)} g + 2 \, {\left(10 \, {\left(36 \, c^{5} d^{2} e^{2} - 100 \, b c^{4} d e^{3} + 59 \, b^{2} c^{3} e^{4}\right)} f + {\left(240 \, c^{5} d^{3} e - 284 \, b c^{4} d^{2} e^{2} + 64 \, b^{2} c^{3} d e^{3} + 15 \, b^{3} c^{2} e^{4}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{3840 \, c^{3} e^{2}}\right]"," ",0,"[1/7680*(15*(10*(16*c^5*d^4*e - 32*b*c^4*d^3*e^2 + 24*b^2*c^3*d^2*e^3 - 8*b^3*c^2*d*e^4 + b^4*c*e^5)*f - (64*c^5*d^5 - 80*b*c^4*d^4*e + 40*b^3*c^2*d^2*e^3 - 20*b^4*c*d*e^4 + 3*b^5*e^5)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(384*c^5*e^4*g*x^4 + 48*(10*c^5*e^4*f - (20*c^5*d*e^3 - 21*b*c^4*e^4)*g)*x^3 - 8*(10*(16*c^5*d*e^3 - 17*b*c^4*e^4)*f - (64*c^5*d^2*e^2 - 164*b*c^4*d*e^3 + 93*b^2*c^3*e^4)*g)*x^2 + 10*(128*c^5*d^3*e - 156*b*c^4*d^2*e^2 + 28*b^2*c^3*d*e^3 + 15*b^3*c^2*e^4)*f - (896*c^5*d^4 - 1392*b*c^4*d^3*e + 796*b^2*c^3*d^2*e^2 - 240*b^3*c^2*d*e^3 + 45*b^4*c*e^4)*g + 2*(10*(36*c^5*d^2*e^2 - 100*b*c^4*d*e^3 + 59*b^2*c^3*e^4)*f + (240*c^5*d^3*e - 284*b*c^4*d^2*e^2 + 64*b^2*c^3*d*e^3 + 15*b^3*c^2*e^4)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^3*e^2), -1/3840*(15*(10*(16*c^5*d^4*e - 32*b*c^4*d^3*e^2 + 24*b^2*c^3*d^2*e^3 - 8*b^3*c^2*d*e^4 + b^4*c*e^5)*f - (64*c^5*d^5 - 80*b*c^4*d^4*e + 40*b^3*c^2*d^2*e^3 - 20*b^4*c*d*e^4 + 3*b^5*e^5)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(384*c^5*e^4*g*x^4 + 48*(10*c^5*e^4*f - (20*c^5*d*e^3 - 21*b*c^4*e^4)*g)*x^3 - 8*(10*(16*c^5*d*e^3 - 17*b*c^4*e^4)*f - (64*c^5*d^2*e^2 - 164*b*c^4*d*e^3 + 93*b^2*c^3*e^4)*g)*x^2 + 10*(128*c^5*d^3*e - 156*b*c^4*d^2*e^2 + 28*b^2*c^3*d*e^3 + 15*b^3*c^2*e^4)*f - (896*c^5*d^4 - 1392*b*c^4*d^3*e + 796*b^2*c^3*d^2*e^2 - 240*b^3*c^2*d*e^3 + 45*b^4*c*e^4)*g + 2*(10*(36*c^5*d^2*e^2 - 100*b*c^4*d*e^3 + 59*b^2*c^3*e^4)*f + (240*c^5*d^3*e - 284*b*c^4*d^2*e^2 + 64*b^2*c^3*d*e^3 + 15*b^3*c^2*e^4)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^3*e^2)]","A",0
2200,1,813,0,0.972534," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(8 \, {\left(8 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f - {\left(48 \, c^{4} d^{4} - 64 \, b c^{3} d^{3} e + 24 \, b^{2} c^{2} d^{2} e^{2} - b^{4} e^{4}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(48 \, c^{4} e^{3} g x^{3} + 8 \, {\left(8 \, c^{4} e^{3} f - {\left(24 \, c^{4} d e^{2} - 17 \, b c^{3} e^{3}\right)} g\right)} x^{2} + 8 \, {\left(88 \, c^{4} d^{2} e - 106 \, b c^{3} d e^{2} + 33 \, b^{2} c^{2} e^{3}\right)} f - {\left(576 \, c^{4} d^{3} - 692 \, b c^{3} d^{2} e + 236 \, b^{2} c^{2} d e^{2} - 15 \, b^{3} c e^{3}\right)} g - 2 \, {\left(8 \, {\left(18 \, c^{4} d e^{2} - 13 \, b c^{3} e^{3}\right)} f - {\left(180 \, c^{4} d^{2} e - 204 \, b c^{3} d e^{2} + 59 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{768 \, c^{2} e^{2}}, -\frac{15 \, {\left(8 \, {\left(8 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f - {\left(48 \, c^{4} d^{4} - 64 \, b c^{3} d^{3} e + 24 \, b^{2} c^{2} d^{2} e^{2} - b^{4} e^{4}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(48 \, c^{4} e^{3} g x^{3} + 8 \, {\left(8 \, c^{4} e^{3} f - {\left(24 \, c^{4} d e^{2} - 17 \, b c^{3} e^{3}\right)} g\right)} x^{2} + 8 \, {\left(88 \, c^{4} d^{2} e - 106 \, b c^{3} d e^{2} + 33 \, b^{2} c^{2} e^{3}\right)} f - {\left(576 \, c^{4} d^{3} - 692 \, b c^{3} d^{2} e + 236 \, b^{2} c^{2} d e^{2} - 15 \, b^{3} c e^{3}\right)} g - 2 \, {\left(8 \, {\left(18 \, c^{4} d e^{2} - 13 \, b c^{3} e^{3}\right)} f - {\left(180 \, c^{4} d^{2} e - 204 \, b c^{3} d e^{2} + 59 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{384 \, c^{2} e^{2}}\right]"," ",0,"[-1/768*(15*(8*(8*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*f - (48*c^4*d^4 - 64*b*c^3*d^3*e + 24*b^2*c^2*d^2*e^2 - b^4*e^4)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(48*c^4*e^3*g*x^3 + 8*(8*c^4*e^3*f - (24*c^4*d*e^2 - 17*b*c^3*e^3)*g)*x^2 + 8*(88*c^4*d^2*e - 106*b*c^3*d*e^2 + 33*b^2*c^2*e^3)*f - (576*c^4*d^3 - 692*b*c^3*d^2*e + 236*b^2*c^2*d*e^2 - 15*b^3*c*e^3)*g - 2*(8*(18*c^4*d*e^2 - 13*b*c^3*e^3)*f - (180*c^4*d^2*e - 204*b*c^3*d*e^2 + 59*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^2*e^2), -1/384*(15*(8*(8*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*f - (48*c^4*d^4 - 64*b*c^3*d^3*e + 24*b^2*c^2*d^2*e^2 - b^4*e^4)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(48*c^4*e^3*g*x^3 + 8*(8*c^4*e^3*f - (24*c^4*d*e^2 - 17*b*c^3*e^3)*g)*x^2 + 8*(88*c^4*d^2*e - 106*b*c^3*d*e^2 + 33*b^2*c^2*e^3)*f - (576*c^4*d^3 - 692*b*c^3*d^2*e + 236*b^2*c^2*d*e^2 - 15*b^3*c*e^3)*g - 2*(8*(18*c^4*d*e^2 - 13*b*c^3*e^3)*f - (180*c^4*d^2*e - 204*b*c^3*d*e^2 + 59*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^2*e^2)]","A",0
2201,1,931,0,2.171858," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(6 \, {\left(4 \, c^{3} d^{3} e - 4 \, b c^{2} d^{2} e^{2} + b^{2} c d e^{3}\right)} f - {\left(32 \, c^{3} d^{4} - 36 \, b c^{2} d^{3} e + 12 \, b^{2} c d^{2} e^{2} - b^{3} d e^{3}\right)} g + {\left(6 \, {\left(4 \, c^{3} d^{2} e^{2} - 4 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} f - {\left(32 \, c^{3} d^{3} e - 36 \, b c^{2} d^{2} e^{2} + 12 \, b^{2} c d e^{3} - b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(8 \, c^{3} e^{3} g x^{3} + 2 \, {\left(6 \, c^{3} e^{3} f - {\left(20 \, c^{3} d e^{2} - 13 \, b c^{2} e^{3}\right)} g\right)} x^{2} - 6 \, {\left(48 \, c^{3} d^{2} e - 41 \, b c^{2} d e^{2} + 8 \, b^{2} c e^{3}\right)} f + {\left(376 \, c^{3} d^{3} - 352 \, b c^{2} d^{2} e + 81 \, b^{2} c d e^{2}\right)} g - {\left(6 \, {\left(14 \, c^{3} d e^{2} - 9 \, b c^{2} e^{3}\right)} f - {\left(136 \, c^{3} d^{2} e - 134 \, b c^{2} d e^{2} + 33 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{96 \, {\left(c e^{3} x + c d e^{2}\right)}}, \frac{15 \, {\left(6 \, {\left(4 \, c^{3} d^{3} e - 4 \, b c^{2} d^{2} e^{2} + b^{2} c d e^{3}\right)} f - {\left(32 \, c^{3} d^{4} - 36 \, b c^{2} d^{3} e + 12 \, b^{2} c d^{2} e^{2} - b^{3} d e^{3}\right)} g + {\left(6 \, {\left(4 \, c^{3} d^{2} e^{2} - 4 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} f - {\left(32 \, c^{3} d^{3} e - 36 \, b c^{2} d^{2} e^{2} + 12 \, b^{2} c d e^{3} - b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(8 \, c^{3} e^{3} g x^{3} + 2 \, {\left(6 \, c^{3} e^{3} f - {\left(20 \, c^{3} d e^{2} - 13 \, b c^{2} e^{3}\right)} g\right)} x^{2} - 6 \, {\left(48 \, c^{3} d^{2} e - 41 \, b c^{2} d e^{2} + 8 \, b^{2} c e^{3}\right)} f + {\left(376 \, c^{3} d^{3} - 352 \, b c^{2} d^{2} e + 81 \, b^{2} c d e^{2}\right)} g - {\left(6 \, {\left(14 \, c^{3} d e^{2} - 9 \, b c^{2} e^{3}\right)} f - {\left(136 \, c^{3} d^{2} e - 134 \, b c^{2} d e^{2} + 33 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{48 \, {\left(c e^{3} x + c d e^{2}\right)}}\right]"," ",0,"[-1/96*(15*(6*(4*c^3*d^3*e - 4*b*c^2*d^2*e^2 + b^2*c*d*e^3)*f - (32*c^3*d^4 - 36*b*c^2*d^3*e + 12*b^2*c*d^2*e^2 - b^3*d*e^3)*g + (6*(4*c^3*d^2*e^2 - 4*b*c^2*d*e^3 + b^2*c*e^4)*f - (32*c^3*d^3*e - 36*b*c^2*d^2*e^2 + 12*b^2*c*d*e^3 - b^3*e^4)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(8*c^3*e^3*g*x^3 + 2*(6*c^3*e^3*f - (20*c^3*d*e^2 - 13*b*c^2*e^3)*g)*x^2 - 6*(48*c^3*d^2*e - 41*b*c^2*d*e^2 + 8*b^2*c*e^3)*f + (376*c^3*d^3 - 352*b*c^2*d^2*e + 81*b^2*c*d*e^2)*g - (6*(14*c^3*d*e^2 - 9*b*c^2*e^3)*f - (136*c^3*d^2*e - 134*b*c^2*d*e^2 + 33*b^2*c*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c*e^3*x + c*d*e^2), 1/48*(15*(6*(4*c^3*d^3*e - 4*b*c^2*d^2*e^2 + b^2*c*d*e^3)*f - (32*c^3*d^4 - 36*b*c^2*d^3*e + 12*b^2*c*d^2*e^2 - b^3*d*e^3)*g + (6*(4*c^3*d^2*e^2 - 4*b*c^2*d*e^3 + b^2*c*e^4)*f - (32*c^3*d^3*e - 36*b*c^2*d^2*e^2 + 12*b^2*c*d*e^3 - b^3*e^4)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(8*c^3*e^3*g*x^3 + 2*(6*c^3*e^3*f - (20*c^3*d*e^2 - 13*b*c^2*e^3)*g)*x^2 - 6*(48*c^3*d^2*e - 41*b*c^2*d*e^2 + 8*b^2*c*e^3)*f + (376*c^3*d^3 - 352*b*c^2*d^2*e + 81*b^2*c*d*e^2)*g - (6*(14*c^3*d*e^2 - 9*b*c^2*e^3)*f - (136*c^3*d^2*e - 134*b*c^2*d*e^2 + 33*b^2*c*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c*e^3*x + c*d*e^2)]","A",0
2202,1,951,0,3.722312," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(4 \, {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} f - {\left(20 \, c^{2} d^{2} e^{2} - 16 \, b c d e^{3} + 3 \, b^{2} e^{4}\right)} g\right)} x^{2} + 4 \, {\left(2 \, c^{2} d^{3} e - b c d^{2} e^{2}\right)} f - {\left(20 \, c^{2} d^{4} - 16 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2}\right)} g + 2 \, {\left(4 \, {\left(2 \, c^{2} d^{2} e^{2} - b c d e^{3}\right)} f - {\left(20 \, c^{2} d^{3} e - 16 \, b c d^{2} e^{2} + 3 \, b^{2} d e^{3}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(6 \, c^{2} e^{3} g x^{3} + 3 \, {\left(4 \, c^{2} e^{3} f - {\left(16 \, c^{2} d e^{2} - 9 \, b c e^{3}\right)} g\right)} x^{2} + 4 \, {\left(23 \, c^{2} d^{2} e - 6 \, b c d e^{2} - 2 \, b^{2} e^{3}\right)} f - {\left(236 \, c^{2} d^{3} - 147 \, b c d^{2} e + 16 \, b^{2} d e^{2}\right)} g + 2 \, {\left(4 \, {\left(17 \, c^{2} d e^{2} - 7 \, b c e^{3}\right)} f - {\left(161 \, c^{2} d^{2} e - 103 \, b c d e^{2} + 12 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{48 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}, -\frac{15 \, {\left({\left(4 \, {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} f - {\left(20 \, c^{2} d^{2} e^{2} - 16 \, b c d e^{3} + 3 \, b^{2} e^{4}\right)} g\right)} x^{2} + 4 \, {\left(2 \, c^{2} d^{3} e - b c d^{2} e^{2}\right)} f - {\left(20 \, c^{2} d^{4} - 16 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2}\right)} g + 2 \, {\left(4 \, {\left(2 \, c^{2} d^{2} e^{2} - b c d e^{3}\right)} f - {\left(20 \, c^{2} d^{3} e - 16 \, b c d^{2} e^{2} + 3 \, b^{2} d e^{3}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(6 \, c^{2} e^{3} g x^{3} + 3 \, {\left(4 \, c^{2} e^{3} f - {\left(16 \, c^{2} d e^{2} - 9 \, b c e^{3}\right)} g\right)} x^{2} + 4 \, {\left(23 \, c^{2} d^{2} e - 6 \, b c d e^{2} - 2 \, b^{2} e^{3}\right)} f - {\left(236 \, c^{2} d^{3} - 147 \, b c d^{2} e + 16 \, b^{2} d e^{2}\right)} g + 2 \, {\left(4 \, {\left(17 \, c^{2} d e^{2} - 7 \, b c e^{3}\right)} f - {\left(161 \, c^{2} d^{2} e - 103 \, b c d e^{2} + 12 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{24 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}\right]"," ",0,"[-1/48*(15*((4*(2*c^2*d*e^3 - b*c*e^4)*f - (20*c^2*d^2*e^2 - 16*b*c*d*e^3 + 3*b^2*e^4)*g)*x^2 + 4*(2*c^2*d^3*e - b*c*d^2*e^2)*f - (20*c^2*d^4 - 16*b*c*d^3*e + 3*b^2*d^2*e^2)*g + 2*(4*(2*c^2*d^2*e^2 - b*c*d*e^3)*f - (20*c^2*d^3*e - 16*b*c*d^2*e^2 + 3*b^2*d*e^3)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(6*c^2*e^3*g*x^3 + 3*(4*c^2*e^3*f - (16*c^2*d*e^2 - 9*b*c*e^3)*g)*x^2 + 4*(23*c^2*d^2*e - 6*b*c*d*e^2 - 2*b^2*e^3)*f - (236*c^2*d^3 - 147*b*c*d^2*e + 16*b^2*d*e^2)*g + 2*(4*(17*c^2*d*e^2 - 7*b*c*e^3)*f - (161*c^2*d^2*e - 103*b*c*d*e^2 + 12*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2), -1/24*(15*((4*(2*c^2*d*e^3 - b*c*e^4)*f - (20*c^2*d^2*e^2 - 16*b*c*d*e^3 + 3*b^2*e^4)*g)*x^2 + 4*(2*c^2*d^3*e - b*c*d^2*e^2)*f - (20*c^2*d^4 - 16*b*c*d^3*e + 3*b^2*d^2*e^2)*g + 2*(4*(2*c^2*d^2*e^2 - b*c*d*e^3)*f - (20*c^2*d^3*e - 16*b*c*d^2*e^2 + 3*b^2*d*e^3)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(6*c^2*e^3*g*x^3 + 3*(4*c^2*e^3*f - (16*c^2*d*e^2 - 9*b*c*e^3)*g)*x^2 + 4*(23*c^2*d^2*e - 6*b*c*d*e^2 - 2*b^2*e^3)*f - (236*c^2*d^3 - 147*b*c*d^2*e + 16*b^2*d*e^2)*g + 2*(4*(17*c^2*d*e^2 - 7*b*c*e^3)*f - (161*c^2*d^2*e - 103*b*c*d*e^2 + 12*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)]","A",0
2203,1,917,0,13.896021," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(2 \, c^{2} d^{3} e f + {\left(2 \, c^{2} e^{4} f - {\left(12 \, c^{2} d e^{3} - 5 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(2 \, c^{2} d e^{3} f - {\left(12 \, c^{2} d^{2} e^{2} - 5 \, b c d e^{3}\right)} g\right)} x^{2} - {\left(12 \, c^{2} d^{4} - 5 \, b c d^{3} e\right)} g + 3 \, {\left(2 \, c^{2} d^{2} e^{2} f - {\left(12 \, c^{2} d^{3} e - 5 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(15 \, c^{2} e^{3} g x^{3} - {\left(46 \, c^{2} e^{3} f - 7 \, {\left(33 \, c^{2} d e^{2} - 10 \, b c e^{3}\right)} g\right)} x^{2} - 2 \, {\left(13 \, c^{2} d^{2} e - b c d e^{2} + 3 \, b^{2} e^{3}\right)} f + {\left(141 \, c^{2} d^{3} - 32 \, b c d^{2} e - 4 \, b^{2} d e^{2}\right)} g - {\left(2 \, {\left(24 \, c^{2} d e^{2} + 11 \, b c e^{3}\right)} f - {\left(333 \, c^{2} d^{2} e - 78 \, b c d e^{2} - 10 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{60 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}}, \frac{15 \, {\left(2 \, c^{2} d^{3} e f + {\left(2 \, c^{2} e^{4} f - {\left(12 \, c^{2} d e^{3} - 5 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(2 \, c^{2} d e^{3} f - {\left(12 \, c^{2} d^{2} e^{2} - 5 \, b c d e^{3}\right)} g\right)} x^{2} - {\left(12 \, c^{2} d^{4} - 5 \, b c d^{3} e\right)} g + 3 \, {\left(2 \, c^{2} d^{2} e^{2} f - {\left(12 \, c^{2} d^{3} e - 5 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(15 \, c^{2} e^{3} g x^{3} - {\left(46 \, c^{2} e^{3} f - 7 \, {\left(33 \, c^{2} d e^{2} - 10 \, b c e^{3}\right)} g\right)} x^{2} - 2 \, {\left(13 \, c^{2} d^{2} e - b c d e^{2} + 3 \, b^{2} e^{3}\right)} f + {\left(141 \, c^{2} d^{3} - 32 \, b c d^{2} e - 4 \, b^{2} d e^{2}\right)} g - {\left(2 \, {\left(24 \, c^{2} d e^{2} + 11 \, b c e^{3}\right)} f - {\left(333 \, c^{2} d^{2} e - 78 \, b c d e^{2} - 10 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{30 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}}\right]"," ",0,"[1/60*(15*(2*c^2*d^3*e*f + (2*c^2*e^4*f - (12*c^2*d*e^3 - 5*b*c*e^4)*g)*x^3 + 3*(2*c^2*d*e^3*f - (12*c^2*d^2*e^2 - 5*b*c*d*e^3)*g)*x^2 - (12*c^2*d^4 - 5*b*c*d^3*e)*g + 3*(2*c^2*d^2*e^2*f - (12*c^2*d^3*e - 5*b*c*d^2*e^2)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(15*c^2*e^3*g*x^3 - (46*c^2*e^3*f - 7*(33*c^2*d*e^2 - 10*b*c*e^3)*g)*x^2 - 2*(13*c^2*d^2*e - b*c*d*e^2 + 3*b^2*e^3)*f + (141*c^2*d^3 - 32*b*c*d^2*e - 4*b^2*d*e^2)*g - (2*(24*c^2*d*e^2 + 11*b*c*e^3)*f - (333*c^2*d^2*e - 78*b*c*d*e^2 - 10*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2), 1/30*(15*(2*c^2*d^3*e*f + (2*c^2*e^4*f - (12*c^2*d*e^3 - 5*b*c*e^4)*g)*x^3 + 3*(2*c^2*d*e^3*f - (12*c^2*d^2*e^2 - 5*b*c*d*e^3)*g)*x^2 - (12*c^2*d^4 - 5*b*c*d^3*e)*g + 3*(2*c^2*d^2*e^2*f - (12*c^2*d^3*e - 5*b*c*d^2*e^2)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(15*c^2*e^3*g*x^3 - (46*c^2*e^3*f - 7*(33*c^2*d*e^2 - 10*b*c*e^3)*g)*x^2 - 2*(13*c^2*d^2*e - b*c*d*e^2 + 3*b^2*e^3)*f + (141*c^2*d^3 - 32*b*c*d^2*e - 4*b^2*d*e^2)*g - (2*(24*c^2*d*e^2 + 11*b*c*e^3)*f - (333*c^2*d^2*e - 78*b*c*d*e^2 - 10*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2)]","A",0
2204,1,1239,0,64.623357," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^7,x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(2 \, c^{3} d e^{4} - b c^{2} e^{5}\right)} g x^{4} + 4 \, {\left(2 \, c^{3} d^{2} e^{3} - b c^{2} d e^{4}\right)} g x^{3} + 6 \, {\left(2 \, c^{3} d^{3} e^{2} - b c^{2} d^{2} e^{3}\right)} g x^{2} + 4 \, {\left(2 \, c^{3} d^{4} e - b c^{2} d^{3} e^{2}\right)} g x + {\left(2 \, c^{3} d^{5} - b c^{2} d^{4} e\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(15 \, c^{3} e^{4} f - {\left(337 \, c^{3} d e^{3} - 161 \, b c^{2} e^{4}\right)} g\right)} x^{3} - {\left(45 \, {\left(c^{3} d e^{3} - b c^{2} e^{4}\right)} f + {\left(613 \, c^{3} d^{2} e^{2} - 130 \, b c^{2} d e^{3} - 77 \, b^{2} c e^{4}\right)} g\right)} x^{2} - 15 \, {\left(c^{3} d^{3} e - 3 \, b c^{2} d^{2} e^{2} + 3 \, b^{2} c d e^{3} - b^{3} e^{4}\right)} f - {\left(167 \, c^{3} d^{4} - 60 \, b c^{2} d^{3} e + 4 \, b^{2} c d^{2} e^{2} - 6 \, b^{3} d e^{3}\right)} g + {\left(45 \, {\left(c^{3} d^{2} e^{2} - 2 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} f - {\left(563 \, c^{3} d^{3} e - 209 \, b c^{2} d^{2} e^{2} + 17 \, b^{2} c d e^{3} - 21 \, b^{3} e^{4}\right)} g\right)} x\right)}}{210 \, {\left(2 \, c d^{5} e^{2} - b d^{4} e^{3} + {\left(2 \, c d e^{6} - b e^{7}\right)} x^{4} + 4 \, {\left(2 \, c d^{2} e^{5} - b d e^{6}\right)} x^{3} + 6 \, {\left(2 \, c d^{3} e^{4} - b d^{2} e^{5}\right)} x^{2} + 4 \, {\left(2 \, c d^{4} e^{3} - b d^{3} e^{4}\right)} x\right)}}, \frac{105 \, {\left({\left(2 \, c^{3} d e^{4} - b c^{2} e^{5}\right)} g x^{4} + 4 \, {\left(2 \, c^{3} d^{2} e^{3} - b c^{2} d e^{4}\right)} g x^{3} + 6 \, {\left(2 \, c^{3} d^{3} e^{2} - b c^{2} d^{2} e^{3}\right)} g x^{2} + 4 \, {\left(2 \, c^{3} d^{4} e - b c^{2} d^{3} e^{2}\right)} g x + {\left(2 \, c^{3} d^{5} - b c^{2} d^{4} e\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(15 \, c^{3} e^{4} f - {\left(337 \, c^{3} d e^{3} - 161 \, b c^{2} e^{4}\right)} g\right)} x^{3} - {\left(45 \, {\left(c^{3} d e^{3} - b c^{2} e^{4}\right)} f + {\left(613 \, c^{3} d^{2} e^{2} - 130 \, b c^{2} d e^{3} - 77 \, b^{2} c e^{4}\right)} g\right)} x^{2} - 15 \, {\left(c^{3} d^{3} e - 3 \, b c^{2} d^{2} e^{2} + 3 \, b^{2} c d e^{3} - b^{3} e^{4}\right)} f - {\left(167 \, c^{3} d^{4} - 60 \, b c^{2} d^{3} e + 4 \, b^{2} c d^{2} e^{2} - 6 \, b^{3} d e^{3}\right)} g + {\left(45 \, {\left(c^{3} d^{2} e^{2} - 2 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} f - {\left(563 \, c^{3} d^{3} e - 209 \, b c^{2} d^{2} e^{2} + 17 \, b^{2} c d e^{3} - 21 \, b^{3} e^{4}\right)} g\right)} x\right)}}{105 \, {\left(2 \, c d^{5} e^{2} - b d^{4} e^{3} + {\left(2 \, c d e^{6} - b e^{7}\right)} x^{4} + 4 \, {\left(2 \, c d^{2} e^{5} - b d e^{6}\right)} x^{3} + 6 \, {\left(2 \, c d^{3} e^{4} - b d^{2} e^{5}\right)} x^{2} + 4 \, {\left(2 \, c d^{4} e^{3} - b d^{3} e^{4}\right)} x\right)}}\right]"," ",0,"[1/210*(105*((2*c^3*d*e^4 - b*c^2*e^5)*g*x^4 + 4*(2*c^3*d^2*e^3 - b*c^2*d*e^4)*g*x^3 + 6*(2*c^3*d^3*e^2 - b*c^2*d^2*e^3)*g*x^2 + 4*(2*c^3*d^4*e - b*c^2*d^3*e^2)*g*x + (2*c^3*d^5 - b*c^2*d^4*e)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((15*c^3*e^4*f - (337*c^3*d*e^3 - 161*b*c^2*e^4)*g)*x^3 - (45*(c^3*d*e^3 - b*c^2*e^4)*f + (613*c^3*d^2*e^2 - 130*b*c^2*d*e^3 - 77*b^2*c*e^4)*g)*x^2 - 15*(c^3*d^3*e - 3*b*c^2*d^2*e^2 + 3*b^2*c*d*e^3 - b^3*e^4)*f - (167*c^3*d^4 - 60*b*c^2*d^3*e + 4*b^2*c*d^2*e^2 - 6*b^3*d*e^3)*g + (45*(c^3*d^2*e^2 - 2*b*c^2*d*e^3 + b^2*c*e^4)*f - (563*c^3*d^3*e - 209*b*c^2*d^2*e^2 + 17*b^2*c*d*e^3 - 21*b^3*e^4)*g)*x))/(2*c*d^5*e^2 - b*d^4*e^3 + (2*c*d*e^6 - b*e^7)*x^4 + 4*(2*c*d^2*e^5 - b*d*e^6)*x^3 + 6*(2*c*d^3*e^4 - b*d^2*e^5)*x^2 + 4*(2*c*d^4*e^3 - b*d^3*e^4)*x), 1/105*(105*((2*c^3*d*e^4 - b*c^2*e^5)*g*x^4 + 4*(2*c^3*d^2*e^3 - b*c^2*d*e^4)*g*x^3 + 6*(2*c^3*d^3*e^2 - b*c^2*d^2*e^3)*g*x^2 + 4*(2*c^3*d^4*e - b*c^2*d^3*e^2)*g*x + (2*c^3*d^5 - b*c^2*d^4*e)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((15*c^3*e^4*f - (337*c^3*d*e^3 - 161*b*c^2*e^4)*g)*x^3 - (45*(c^3*d*e^3 - b*c^2*e^4)*f + (613*c^3*d^2*e^2 - 130*b*c^2*d*e^3 - 77*b^2*c*e^4)*g)*x^2 - 15*(c^3*d^3*e - 3*b*c^2*d^2*e^2 + 3*b^2*c*d*e^3 - b^3*e^4)*f - (167*c^3*d^4 - 60*b*c^2*d^3*e + 4*b^2*c*d^2*e^2 - 6*b^3*d*e^3)*g + (45*(c^3*d^2*e^2 - 2*b*c^2*d*e^3 + b^2*c*e^4)*f - (563*c^3*d^3*e - 209*b*c^2*d^2*e^2 + 17*b^2*c*d*e^3 - 21*b^3*e^4)*g)*x))/(2*c*d^5*e^2 - b*d^4*e^3 + (2*c*d*e^6 - b*e^7)*x^4 + 4*(2*c*d^2*e^5 - b*d*e^6)*x^3 + 6*(2*c*d^3*e^4 - b*d^2*e^5)*x^2 + 4*(2*c*d^4*e^3 - b*d^3*e^4)*x)]","B",0
2205,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^8,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2206,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^9,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2207,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^10,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2208,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^11,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2209,1,825,0,1.148899," ","integrate((e*x+d)^3*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(8 \, {\left(8 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f + {\left(48 \, c^{4} d^{4} - 128 \, b c^{3} d^{3} e + 120 \, b^{2} c^{2} d^{2} e^{2} - 48 \, b^{3} c d e^{3} + 7 \, b^{4} e^{4}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(48 \, c^{4} e^{3} g x^{3} + 8 \, {\left(8 \, c^{4} e^{3} f + {\left(24 \, c^{4} d e^{2} - 7 \, b c^{3} e^{3}\right)} g\right)} x^{2} + 8 \, {\left(88 \, c^{4} d^{2} e - 70 \, b c^{3} d e^{2} + 15 \, b^{2} c^{2} e^{3}\right)} f + {\left(576 \, c^{4} d^{3} - 1036 \, b c^{3} d^{2} e + 580 \, b^{2} c^{2} d e^{2} - 105 \, b^{3} c e^{3}\right)} g + 2 \, {\left(8 \, {\left(18 \, c^{4} d e^{2} - 5 \, b c^{3} e^{3}\right)} f + {\left(180 \, c^{4} d^{2} e - 156 \, b c^{3} d e^{2} + 35 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{768 \, c^{5} e^{2}}, -\frac{15 \, {\left(8 \, {\left(8 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f + {\left(48 \, c^{4} d^{4} - 128 \, b c^{3} d^{3} e + 120 \, b^{2} c^{2} d^{2} e^{2} - 48 \, b^{3} c d e^{3} + 7 \, b^{4} e^{4}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(48 \, c^{4} e^{3} g x^{3} + 8 \, {\left(8 \, c^{4} e^{3} f + {\left(24 \, c^{4} d e^{2} - 7 \, b c^{3} e^{3}\right)} g\right)} x^{2} + 8 \, {\left(88 \, c^{4} d^{2} e - 70 \, b c^{3} d e^{2} + 15 \, b^{2} c^{2} e^{3}\right)} f + {\left(576 \, c^{4} d^{3} - 1036 \, b c^{3} d^{2} e + 580 \, b^{2} c^{2} d e^{2} - 105 \, b^{3} c e^{3}\right)} g + 2 \, {\left(8 \, {\left(18 \, c^{4} d e^{2} - 5 \, b c^{3} e^{3}\right)} f + {\left(180 \, c^{4} d^{2} e - 156 \, b c^{3} d e^{2} + 35 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{384 \, c^{5} e^{2}}\right]"," ",0,"[-1/768*(15*(8*(8*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*f + (48*c^4*d^4 - 128*b*c^3*d^3*e + 120*b^2*c^2*d^2*e^2 - 48*b^3*c*d*e^3 + 7*b^4*e^4)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(48*c^4*e^3*g*x^3 + 8*(8*c^4*e^3*f + (24*c^4*d*e^2 - 7*b*c^3*e^3)*g)*x^2 + 8*(88*c^4*d^2*e - 70*b*c^3*d*e^2 + 15*b^2*c^2*e^3)*f + (576*c^4*d^3 - 1036*b*c^3*d^2*e + 580*b^2*c^2*d*e^2 - 105*b^3*c*e^3)*g + 2*(8*(18*c^4*d*e^2 - 5*b*c^3*e^3)*f + (180*c^4*d^2*e - 156*b*c^3*d*e^2 + 35*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^5*e^2), -1/384*(15*(8*(8*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*f + (48*c^4*d^4 - 128*b*c^3*d^3*e + 120*b^2*c^2*d^2*e^2 - 48*b^3*c*d*e^3 + 7*b^4*e^4)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(48*c^4*e^3*g*x^3 + 8*(8*c^4*e^3*f + (24*c^4*d*e^2 - 7*b*c^3*e^3)*g)*x^2 + 8*(88*c^4*d^2*e - 70*b*c^3*d*e^2 + 15*b^2*c^2*e^3)*f + (576*c^4*d^3 - 1036*b*c^3*d^2*e + 580*b^2*c^2*d*e^2 - 105*b^3*c*e^3)*g + 2*(8*(18*c^4*d*e^2 - 5*b*c^3*e^3)*f + (180*c^4*d^2*e - 156*b*c^3*d*e^2 + 35*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^5*e^2)]","A",0
2210,1,585,0,0.867776," ","integrate((e*x+d)^2*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(6 \, {\left(4 \, c^{3} d^{2} e - 4 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} f + {\left(16 \, c^{3} d^{3} - 36 \, b c^{2} d^{2} e + 24 \, b^{2} c d e^{2} - 5 \, b^{3} e^{3}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(8 \, c^{3} e^{2} g x^{2} + 6 \, {\left(8 \, c^{3} d e - 3 \, b c^{2} e^{2}\right)} f + {\left(40 \, c^{3} d^{2} - 52 \, b c^{2} d e + 15 \, b^{2} c e^{2}\right)} g + 2 \, {\left(6 \, c^{3} e^{2} f + {\left(12 \, c^{3} d e - 5 \, b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{96 \, c^{4} e^{2}}, -\frac{3 \, {\left(6 \, {\left(4 \, c^{3} d^{2} e - 4 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} f + {\left(16 \, c^{3} d^{3} - 36 \, b c^{2} d^{2} e + 24 \, b^{2} c d e^{2} - 5 \, b^{3} e^{3}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(8 \, c^{3} e^{2} g x^{2} + 6 \, {\left(8 \, c^{3} d e - 3 \, b c^{2} e^{2}\right)} f + {\left(40 \, c^{3} d^{2} - 52 \, b c^{2} d e + 15 \, b^{2} c e^{2}\right)} g + 2 \, {\left(6 \, c^{3} e^{2} f + {\left(12 \, c^{3} d e - 5 \, b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{48 \, c^{4} e^{2}}\right]"," ",0,"[1/96*(3*(6*(4*c^3*d^2*e - 4*b*c^2*d*e^2 + b^2*c*e^3)*f + (16*c^3*d^3 - 36*b*c^2*d^2*e + 24*b^2*c*d*e^2 - 5*b^3*e^3)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(8*c^3*e^2*g*x^2 + 6*(8*c^3*d*e - 3*b*c^2*e^2)*f + (40*c^3*d^2 - 52*b*c^2*d*e + 15*b^2*c*e^2)*g + 2*(6*c^3*e^2*f + (12*c^3*d*e - 5*b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^4*e^2), -1/48*(3*(6*(4*c^3*d^2*e - 4*b*c^2*d*e^2 + b^2*c*e^3)*f + (16*c^3*d^3 - 36*b*c^2*d^2*e + 24*b^2*c*d*e^2 - 5*b^3*e^3)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(8*c^3*e^2*g*x^2 + 6*(8*c^3*d*e - 3*b*c^2*e^2)*f + (40*c^3*d^2 - 52*b*c^2*d*e + 15*b^2*c*e^2)*g + 2*(6*c^3*e^2*f + (12*c^3*d*e - 5*b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^4*e^2)]","A",0
2211,1,403,0,0.634471," ","integrate((e*x+d)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} f + {\left(4 \, c^{2} d^{2} - 8 \, b c d e + 3 \, b^{2} e^{2}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(2 \, c^{2} e g x + 4 \, c^{2} e f + {\left(4 \, c^{2} d - 3 \, b c e\right)} g\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{16 \, c^{3} e^{2}}, -\frac{{\left(4 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} f + {\left(4 \, c^{2} d^{2} - 8 \, b c d e + 3 \, b^{2} e^{2}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(2 \, c^{2} e g x + 4 \, c^{2} e f + {\left(4 \, c^{2} d - 3 \, b c e\right)} g\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{8 \, c^{3} e^{2}}\right]"," ",0,"[-1/16*((4*(2*c^2*d*e - b*c*e^2)*f + (4*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(2*c^2*e*g*x + 4*c^2*e*f + (4*c^2*d - 3*b*c*e)*g)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^3*e^2), -1/8*((4*(2*c^2*d*e - b*c*e^2)*f + (4*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(2*c^2*e*g*x + 4*c^2*e*f + (4*c^2*d - 3*b*c*e)*g)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^3*e^2)]","A",0
2212,1,405,0,1.220812," ","integrate((g*x+f)/(e*x+d)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, c d e - b e^{2}\right)} g x + {\left(2 \, c d^{2} - b d e\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c e f - c d g\right)}}{2 \, {\left(2 \, c^{2} d^{2} e^{2} - b c d e^{3} + {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} x\right)}}, -\frac{{\left({\left(2 \, c d e - b e^{2}\right)} g x + {\left(2 \, c d^{2} - b d e\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c e f - c d g\right)}}{2 \, c^{2} d^{2} e^{2} - b c d e^{3} + {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} x}\right]"," ",0,"[-1/2*(((2*c*d*e - b*e^2)*g*x + (2*c*d^2 - b*d*e)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c*e*f - c*d*g))/(2*c^2*d^2*e^2 - b*c*d*e^3 + (2*c^2*d*e^3 - b*c*e^4)*x), -(((2*c*d*e - b*e^2)*g*x + (2*c*d^2 - b*d*e)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c*e*f - c*d*g))/(2*c^2*d^2*e^2 - b*c*d*e^3 + (2*c^2*d*e^3 - b*c*e^4)*x)]","A",0
2213,1,182,0,2.440344," ","integrate((g*x+f)/(e*x+d)^2/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(4 \, c d e - b e^{2}\right)} f + 2 \, {\left(c d^{2} - b d e\right)} g + {\left(2 \, c e^{2} f + {\left(4 \, c d e - 3 \, b e^{2}\right)} g\right)} x\right)}}{3 \, {\left(4 \, c^{2} d^{4} e^{2} - 4 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4} + {\left(4 \, c^{2} d^{2} e^{4} - 4 \, b c d e^{5} + b^{2} e^{6}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{3} e^{3} - 4 \, b c d^{2} e^{4} + b^{2} d e^{5}\right)} x\right)}}"," ",0,"-2/3*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((4*c*d*e - b*e^2)*f + 2*(c*d^2 - b*d*e)*g + (2*c*e^2*f + (4*c*d*e - 3*b*e^2)*g)*x)/(4*c^2*d^4*e^2 - 4*b*c*d^3*e^3 + b^2*d^2*e^4 + (4*c^2*d^2*e^4 - 4*b*c*d*e^5 + b^2*e^6)*x^2 + 2*(4*c^2*d^3*e^3 - 4*b*c*d^2*e^4 + b^2*d*e^5)*x)","A",0
2214,1,368,0,8.446529," ","integrate((g*x+f)/(e*x+d)^3/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, {\left(4 \, c^{2} e^{3} f + {\left(6 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} g\right)} x^{2} + {\left(28 \, c^{2} d^{2} e - 16 \, b c d e^{2} + 3 \, b^{2} e^{3}\right)} f + 2 \, {\left(6 \, c^{2} d^{3} - 7 \, b c d^{2} e + b^{2} d e^{2}\right)} g + {\left(4 \, {\left(6 \, c^{2} d e^{2} - b c e^{3}\right)} f + {\left(36 \, c^{2} d^{2} e - 36 \, b c d e^{2} + 5 \, b^{2} e^{3}\right)} g\right)} x\right)}}{15 \, {\left(8 \, c^{3} d^{6} e^{2} - 12 \, b c^{2} d^{5} e^{3} + 6 \, b^{2} c d^{4} e^{4} - b^{3} d^{3} e^{5} + {\left(8 \, c^{3} d^{3} e^{5} - 12 \, b c^{2} d^{2} e^{6} + 6 \, b^{2} c d e^{7} - b^{3} e^{8}\right)} x^{3} + 3 \, {\left(8 \, c^{3} d^{4} e^{4} - 12 \, b c^{2} d^{3} e^{5} + 6 \, b^{2} c d^{2} e^{6} - b^{3} d e^{7}\right)} x^{2} + 3 \, {\left(8 \, c^{3} d^{5} e^{3} - 12 \, b c^{2} d^{4} e^{4} + 6 \, b^{2} c d^{3} e^{5} - b^{3} d^{2} e^{6}\right)} x\right)}}"," ",0,"-2/15*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*(4*c^2*e^3*f + (6*c^2*d*e^2 - 5*b*c*e^3)*g)*x^2 + (28*c^2*d^2*e - 16*b*c*d*e^2 + 3*b^2*e^3)*f + 2*(6*c^2*d^3 - 7*b*c*d^2*e + b^2*d*e^2)*g + (4*(6*c^2*d*e^2 - b*c*e^3)*f + (36*c^2*d^2*e - 36*b*c*d*e^2 + 5*b^2*e^3)*g)*x)/(8*c^3*d^6*e^2 - 12*b*c^2*d^5*e^3 + 6*b^2*c*d^4*e^4 - b^3*d^3*e^5 + (8*c^3*d^3*e^5 - 12*b*c^2*d^2*e^6 + 6*b^2*c*d*e^7 - b^3*e^8)*x^3 + 3*(8*c^3*d^4*e^4 - 12*b*c^2*d^3*e^5 + 6*b^2*c*d^2*e^6 - b^3*d*e^7)*x^2 + 3*(8*c^3*d^5*e^3 - 12*b*c^2*d^4*e^4 + 6*b^2*c*d^3*e^5 - b^3*d^2*e^6)*x)","A",0
2215,1,606,0,59.826917," ","integrate((g*x+f)/(e*x+d)^4/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(8 \, {\left(6 \, c^{3} e^{4} f + {\left(8 \, c^{3} d e^{3} - 7 \, b c^{2} e^{4}\right)} g\right)} x^{3} + 4 \, {\left(6 \, {\left(8 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f + {\left(64 \, c^{3} d^{2} e^{2} - 64 \, b c^{2} d e^{3} + 7 \, b^{2} c e^{4}\right)} g\right)} x^{2} + 3 \, {\left(96 \, c^{3} d^{3} e - 92 \, b c^{2} d^{2} e^{2} + 36 \, b^{2} c d e^{3} - 5 \, b^{3} e^{4}\right)} f + 2 \, {\left(52 \, c^{3} d^{4} - 72 \, b c^{2} d^{3} e + 23 \, b^{2} c d^{2} e^{2} - 3 \, b^{3} d e^{3}\right)} g + {\left(6 \, {\left(52 \, c^{3} d^{2} e^{2} - 20 \, b c^{2} d e^{3} + 3 \, b^{2} c e^{4}\right)} f + {\left(416 \, c^{3} d^{3} e - 524 \, b c^{2} d^{2} e^{2} + 164 \, b^{2} c d e^{3} - 21 \, b^{3} e^{4}\right)} g\right)} x\right)}}{105 \, {\left(16 \, c^{4} d^{8} e^{2} - 32 \, b c^{3} d^{7} e^{3} + 24 \, b^{2} c^{2} d^{6} e^{4} - 8 \, b^{3} c d^{5} e^{5} + b^{4} d^{4} e^{6} + {\left(16 \, c^{4} d^{4} e^{6} - 32 \, b c^{3} d^{3} e^{7} + 24 \, b^{2} c^{2} d^{2} e^{8} - 8 \, b^{3} c d e^{9} + b^{4} e^{10}\right)} x^{4} + 4 \, {\left(16 \, c^{4} d^{5} e^{5} - 32 \, b c^{3} d^{4} e^{6} + 24 \, b^{2} c^{2} d^{3} e^{7} - 8 \, b^{3} c d^{2} e^{8} + b^{4} d e^{9}\right)} x^{3} + 6 \, {\left(16 \, c^{4} d^{6} e^{4} - 32 \, b c^{3} d^{5} e^{5} + 24 \, b^{2} c^{2} d^{4} e^{6} - 8 \, b^{3} c d^{3} e^{7} + b^{4} d^{2} e^{8}\right)} x^{2} + 4 \, {\left(16 \, c^{4} d^{7} e^{3} - 32 \, b c^{3} d^{6} e^{4} + 24 \, b^{2} c^{2} d^{5} e^{5} - 8 \, b^{3} c d^{4} e^{6} + b^{4} d^{3} e^{7}\right)} x\right)}}"," ",0,"-2/105*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(8*(6*c^3*e^4*f + (8*c^3*d*e^3 - 7*b*c^2*e^4)*g)*x^3 + 4*(6*(8*c^3*d*e^3 - b*c^2*e^4)*f + (64*c^3*d^2*e^2 - 64*b*c^2*d*e^3 + 7*b^2*c*e^4)*g)*x^2 + 3*(96*c^3*d^3*e - 92*b*c^2*d^2*e^2 + 36*b^2*c*d*e^3 - 5*b^3*e^4)*f + 2*(52*c^3*d^4 - 72*b*c^2*d^3*e + 23*b^2*c*d^2*e^2 - 3*b^3*d*e^3)*g + (6*(52*c^3*d^2*e^2 - 20*b*c^2*d*e^3 + 3*b^2*c*e^4)*f + (416*c^3*d^3*e - 524*b*c^2*d^2*e^2 + 164*b^2*c*d*e^3 - 21*b^3*e^4)*g)*x)/(16*c^4*d^8*e^2 - 32*b*c^3*d^7*e^3 + 24*b^2*c^2*d^6*e^4 - 8*b^3*c*d^5*e^5 + b^4*d^4*e^6 + (16*c^4*d^4*e^6 - 32*b*c^3*d^3*e^7 + 24*b^2*c^2*d^2*e^8 - 8*b^3*c*d*e^9 + b^4*e^10)*x^4 + 4*(16*c^4*d^5*e^5 - 32*b*c^3*d^4*e^6 + 24*b^2*c^2*d^3*e^7 - 8*b^3*c*d^2*e^8 + b^4*d*e^9)*x^3 + 6*(16*c^4*d^6*e^4 - 32*b*c^3*d^5*e^5 + 24*b^2*c^2*d^4*e^6 - 8*b^3*c*d^3*e^7 + b^4*d^2*e^8)*x^2 + 4*(16*c^4*d^7*e^3 - 32*b*c^3*d^6*e^4 + 24*b^2*c^2*d^5*e^5 - 8*b^3*c*d^4*e^6 + b^4*d^3*e^7)*x)","B",0
2216,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)^5/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2217,1,745,0,1.332872," ","integrate((e*x+d)^3*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, {\left(2 \, c^{3} d^{2} e - 3 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} f + {\left(12 \, c^{3} d^{3} - 28 \, b c^{2} d^{2} e + 21 \, b^{2} c d e^{2} - 5 \, b^{3} e^{3}\right)} g - {\left(4 \, {\left(2 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} f + {\left(12 \, c^{3} d^{2} e - 16 \, b c^{2} d e^{2} + 5 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(2 \, c^{3} e^{2} g x^{2} - 4 \, {\left(5 \, c^{3} d e - 3 \, b c^{2} e^{2}\right)} f - {\left(28 \, c^{3} d^{2} - 43 \, b c^{2} d e + 15 \, b^{2} c e^{2}\right)} g + {\left(4 \, c^{3} e^{2} f + 5 \, {\left(2 \, c^{3} d e - b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{16 \, {\left(c^{5} e^{3} x - c^{5} d e^{2} + b c^{4} e^{3}\right)}}, -\frac{3 \, {\left(4 \, {\left(2 \, c^{3} d^{2} e - 3 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} f + {\left(12 \, c^{3} d^{3} - 28 \, b c^{2} d^{2} e + 21 \, b^{2} c d e^{2} - 5 \, b^{3} e^{3}\right)} g - {\left(4 \, {\left(2 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} f + {\left(12 \, c^{3} d^{2} e - 16 \, b c^{2} d e^{2} + 5 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(2 \, c^{3} e^{2} g x^{2} - 4 \, {\left(5 \, c^{3} d e - 3 \, b c^{2} e^{2}\right)} f - {\left(28 \, c^{3} d^{2} - 43 \, b c^{2} d e + 15 \, b^{2} c e^{2}\right)} g + {\left(4 \, c^{3} e^{2} f + 5 \, {\left(2 \, c^{3} d e - b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{8 \, {\left(c^{5} e^{3} x - c^{5} d e^{2} + b c^{4} e^{3}\right)}}\right]"," ",0,"[1/16*(3*(4*(2*c^3*d^2*e - 3*b*c^2*d*e^2 + b^2*c*e^3)*f + (12*c^3*d^3 - 28*b*c^2*d^2*e + 21*b^2*c*d*e^2 - 5*b^3*e^3)*g - (4*(2*c^3*d*e^2 - b*c^2*e^3)*f + (12*c^3*d^2*e - 16*b*c^2*d*e^2 + 5*b^2*c*e^3)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(2*c^3*e^2*g*x^2 - 4*(5*c^3*d*e - 3*b*c^2*e^2)*f - (28*c^3*d^2 - 43*b*c^2*d*e + 15*b^2*c*e^2)*g + (4*c^3*e^2*f + 5*(2*c^3*d*e - b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^5*e^3*x - c^5*d*e^2 + b*c^4*e^3), -1/8*(3*(4*(2*c^3*d^2*e - 3*b*c^2*d*e^2 + b^2*c*e^3)*f + (12*c^3*d^3 - 28*b*c^2*d^2*e + 21*b^2*c*d*e^2 - 5*b^3*e^3)*g - (4*(2*c^3*d*e^2 - b*c^2*e^3)*f + (12*c^3*d^2*e - 16*b*c^2*d*e^2 + 5*b^2*c*e^3)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(2*c^3*e^2*g*x^2 - 4*(5*c^3*d*e - 3*b*c^2*e^2)*f - (28*c^3*d^2 - 43*b*c^2*d*e + 15*b^2*c*e^2)*g + (4*c^3*e^2*f + 5*(2*c^3*d*e - b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^5*e^3*x - c^5*d*e^2 + b*c^4*e^3)]","A",0
2218,1,503,0,0.953857," ","integrate((e*x+d)^2*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, {\left(c^{2} d e - b c e^{2}\right)} f + {\left(4 \, c^{2} d^{2} - 7 \, b c d e + 3 \, b^{2} e^{2}\right)} g - {\left(2 \, c^{2} e^{2} f + {\left(4 \, c^{2} d e - 3 \, b c e^{2}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(c^{2} e g x - 2 \, c^{2} e f - 3 \, {\left(c^{2} d - b c e\right)} g\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{4 \, {\left(c^{4} e^{3} x - c^{4} d e^{2} + b c^{3} e^{3}\right)}}, -\frac{{\left(2 \, {\left(c^{2} d e - b c e^{2}\right)} f + {\left(4 \, c^{2} d^{2} - 7 \, b c d e + 3 \, b^{2} e^{2}\right)} g - {\left(2 \, c^{2} e^{2} f + {\left(4 \, c^{2} d e - 3 \, b c e^{2}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(c^{2} e g x - 2 \, c^{2} e f - 3 \, {\left(c^{2} d - b c e\right)} g\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{2 \, {\left(c^{4} e^{3} x - c^{4} d e^{2} + b c^{3} e^{3}\right)}}\right]"," ",0,"[-1/4*((2*(c^2*d*e - b*c*e^2)*f + (4*c^2*d^2 - 7*b*c*d*e + 3*b^2*e^2)*g - (2*c^2*e^2*f + (4*c^2*d*e - 3*b*c*e^2)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(c^2*e*g*x - 2*c^2*e*f - 3*(c^2*d - b*c*e)*g)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^4*e^3*x - c^4*d*e^2 + b*c^3*e^3), -1/2*((2*(c^2*d*e - b*c*e^2)*f + (4*c^2*d^2 - 7*b*c*d*e + 3*b^2*e^2)*g - (2*c^2*e^2*f + (4*c^2*d*e - 3*b*c*e^2)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(c^2*e*g*x - 2*c^2*e*f - 3*(c^2*d - b*c*e)*g)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^4*e^3*x - c^4*d*e^2 + b*c^3*e^3)]","A",0
2219,1,483,0,0.886776," ","integrate((e*x+d)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, c^{2} d e - b c e^{2}\right)} g x - {\left(2 \, c^{2} d^{2} - 3 \, b c d e + b^{2} e^{2}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c^{2} e f + {\left(c^{2} d - b c e\right)} g\right)}}{2 \, {\left(2 \, c^{4} d^{2} e^{2} - 3 \, b c^{3} d e^{3} + b^{2} c^{2} e^{4} - {\left(2 \, c^{4} d e^{3} - b c^{3} e^{4}\right)} x\right)}}, -\frac{{\left({\left(2 \, c^{2} d e - b c e^{2}\right)} g x - {\left(2 \, c^{2} d^{2} - 3 \, b c d e + b^{2} e^{2}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c^{2} e f + {\left(c^{2} d - b c e\right)} g\right)}}{2 \, c^{4} d^{2} e^{2} - 3 \, b c^{3} d e^{3} + b^{2} c^{2} e^{4} - {\left(2 \, c^{4} d e^{3} - b c^{3} e^{4}\right)} x}\right]"," ",0,"[1/2*(((2*c^2*d*e - b*c*e^2)*g*x - (2*c^2*d^2 - 3*b*c*d*e + b^2*e^2)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c^2*e*f + (c^2*d - b*c*e)*g))/(2*c^4*d^2*e^2 - 3*b*c^3*d*e^3 + b^2*c^2*e^4 - (2*c^4*d*e^3 - b*c^3*e^4)*x), -(((2*c^2*d*e - b*c*e^2)*g*x - (2*c^2*d^2 - 3*b*c*d*e + b^2*e^2)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c^2*e*f + (c^2*d - b*c*e)*g))/(2*c^4*d^2*e^2 - 3*b*c^3*d*e^3 + b^2*c^2*e^4 - (2*c^4*d*e^3 - b*c^3*e^4)*x)]","A",0
2220,1,407,0,7.158032," ","integrate((g*x+f)/(e*x+d)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, {\left(4 \, c^{2} e^{3} f + {\left(2 \, c^{2} d e^{2} - 3 \, b c e^{3}\right)} g\right)} x^{2} - {\left(4 \, c^{2} d^{2} e - 8 \, b c d e^{2} + b^{2} e^{3}\right)} f + 2 \, {\left(2 \, c^{2} d^{3} - b c d^{2} e - b^{2} d e^{2}\right)} g + {\left(4 \, {\left(2 \, c^{2} d e^{2} + b c e^{3}\right)} f + {\left(4 \, c^{2} d^{2} e - 4 \, b c d e^{2} - 3 \, b^{2} e^{3}\right)} g\right)} x\right)}}{3 \, {\left(8 \, c^{4} d^{6} e^{2} - 20 \, b c^{3} d^{5} e^{3} + 18 \, b^{2} c^{2} d^{4} e^{4} - 7 \, b^{3} c d^{3} e^{5} + b^{4} d^{2} e^{6} - {\left(8 \, c^{4} d^{3} e^{5} - 12 \, b c^{3} d^{2} e^{6} + 6 \, b^{2} c^{2} d e^{7} - b^{3} c e^{8}\right)} x^{3} - {\left(8 \, c^{4} d^{4} e^{4} - 4 \, b c^{3} d^{3} e^{5} - 6 \, b^{2} c^{2} d^{2} e^{6} + 5 \, b^{3} c d e^{7} - b^{4} e^{8}\right)} x^{2} + {\left(8 \, c^{4} d^{5} e^{3} - 28 \, b c^{3} d^{4} e^{4} + 30 \, b^{2} c^{2} d^{3} e^{5} - 13 \, b^{3} c d^{2} e^{6} + 2 \, b^{4} d e^{7}\right)} x\right)}}"," ",0,"2/3*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*(4*c^2*e^3*f + (2*c^2*d*e^2 - 3*b*c*e^3)*g)*x^2 - (4*c^2*d^2*e - 8*b*c*d*e^2 + b^2*e^3)*f + 2*(2*c^2*d^3 - b*c*d^2*e - b^2*d*e^2)*g + (4*(2*c^2*d*e^2 + b*c*e^3)*f + (4*c^2*d^2*e - 4*b*c*d*e^2 - 3*b^2*e^3)*g)*x)/(8*c^4*d^6*e^2 - 20*b*c^3*d^5*e^3 + 18*b^2*c^2*d^4*e^4 - 7*b^3*c*d^3*e^5 + b^4*d^2*e^6 - (8*c^4*d^3*e^5 - 12*b*c^3*d^2*e^6 + 6*b^2*c^2*d*e^7 - b^3*c*e^8)*x^3 - (8*c^4*d^4*e^4 - 4*b*c^3*d^3*e^5 - 6*b^2*c^2*d^2*e^6 + 5*b^3*c*d*e^7 - b^4*e^8)*x^2 + (8*c^4*d^5*e^3 - 28*b*c^3*d^4*e^4 + 30*b^2*c^2*d^3*e^5 - 13*b^3*c*d^2*e^6 + 2*b^4*d*e^7)*x)","B",0
2221,1,649,0,28.895452," ","integrate((g*x+f)/(e*x+d)^2/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(8 \, {\left(6 \, c^{3} e^{4} f + {\left(4 \, c^{3} d e^{3} - 5 \, b c^{2} e^{4}\right)} g\right)} x^{3} + 4 \, {\left(6 \, {\left(4 \, c^{3} d e^{3} + b c^{2} e^{4}\right)} f + {\left(16 \, c^{3} d^{2} e^{2} - 16 \, b c^{2} d e^{3} - 5 \, b^{2} c e^{4}\right)} g\right)} x^{2} - 3 \, {\left(16 \, c^{3} d^{3} e - 28 \, b c^{2} d^{2} e^{2} + 8 \, b^{2} c d e^{3} - b^{3} e^{4}\right)} f + 2 \, {\left(4 \, c^{3} d^{4} + 8 \, b c^{2} d^{3} e - 13 \, b^{2} c d^{2} e^{2} + b^{3} d e^{3}\right)} g + {\left(6 \, {\left(4 \, c^{3} d^{2} e^{2} + 12 \, b c^{2} d e^{3} - b^{2} c e^{4}\right)} f + {\left(16 \, c^{3} d^{3} e + 28 \, b c^{2} d^{2} e^{2} - 64 \, b^{2} c d e^{3} + 5 \, b^{3} e^{4}\right)} g\right)} x\right)}}{15 \, {\left(16 \, c^{5} d^{8} e^{2} - 48 \, b c^{4} d^{7} e^{3} + 56 \, b^{2} c^{3} d^{6} e^{4} - 32 \, b^{3} c^{2} d^{5} e^{5} + 9 \, b^{4} c d^{4} e^{6} - b^{5} d^{3} e^{7} - {\left(16 \, c^{5} d^{4} e^{6} - 32 \, b c^{4} d^{3} e^{7} + 24 \, b^{2} c^{3} d^{2} e^{8} - 8 \, b^{3} c^{2} d e^{9} + b^{4} c e^{10}\right)} x^{4} - {\left(32 \, c^{5} d^{5} e^{5} - 48 \, b c^{4} d^{4} e^{6} + 16 \, b^{2} c^{3} d^{3} e^{7} + 8 \, b^{3} c^{2} d^{2} e^{8} - 6 \, b^{4} c d e^{9} + b^{5} e^{10}\right)} x^{3} - 3 \, {\left(16 \, b c^{4} d^{5} e^{5} - 32 \, b^{2} c^{3} d^{4} e^{6} + 24 \, b^{3} c^{2} d^{3} e^{7} - 8 \, b^{4} c d^{2} e^{8} + b^{5} d e^{9}\right)} x^{2} + {\left(32 \, c^{5} d^{7} e^{3} - 112 \, b c^{4} d^{6} e^{4} + 144 \, b^{2} c^{3} d^{5} e^{5} - 88 \, b^{3} c^{2} d^{4} e^{6} + 26 \, b^{4} c d^{3} e^{7} - 3 \, b^{5} d^{2} e^{8}\right)} x\right)}}"," ",0,"2/15*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(8*(6*c^3*e^4*f + (4*c^3*d*e^3 - 5*b*c^2*e^4)*g)*x^3 + 4*(6*(4*c^3*d*e^3 + b*c^2*e^4)*f + (16*c^3*d^2*e^2 - 16*b*c^2*d*e^3 - 5*b^2*c*e^4)*g)*x^2 - 3*(16*c^3*d^3*e - 28*b*c^2*d^2*e^2 + 8*b^2*c*d*e^3 - b^3*e^4)*f + 2*(4*c^3*d^4 + 8*b*c^2*d^3*e - 13*b^2*c*d^2*e^2 + b^3*d*e^3)*g + (6*(4*c^3*d^2*e^2 + 12*b*c^2*d*e^3 - b^2*c*e^4)*f + (16*c^3*d^3*e + 28*b*c^2*d^2*e^2 - 64*b^2*c*d*e^3 + 5*b^3*e^4)*g)*x)/(16*c^5*d^8*e^2 - 48*b*c^4*d^7*e^3 + 56*b^2*c^3*d^6*e^4 - 32*b^3*c^2*d^5*e^5 + 9*b^4*c*d^4*e^6 - b^5*d^3*e^7 - (16*c^5*d^4*e^6 - 32*b*c^4*d^3*e^7 + 24*b^2*c^3*d^2*e^8 - 8*b^3*c^2*d*e^9 + b^4*c*e^10)*x^4 - (32*c^5*d^5*e^5 - 48*b*c^4*d^4*e^6 + 16*b^2*c^3*d^3*e^7 + 8*b^3*c^2*d^2*e^8 - 6*b^4*c*d*e^9 + b^5*e^10)*x^3 - 3*(16*b*c^4*d^5*e^5 - 32*b^2*c^3*d^4*e^6 + 24*b^3*c^2*d^3*e^7 - 8*b^4*c*d^2*e^8 + b^5*d*e^9)*x^2 + (32*c^5*d^7*e^3 - 112*b*c^4*d^6*e^4 + 144*b^2*c^3*d^5*e^5 - 88*b^3*c^2*d^4*e^6 + 26*b^4*c*d^3*e^7 - 3*b^5*d^2*e^8)*x)","B",0
2222,1,974,0,137.522608," ","integrate((g*x+f)/(e*x+d)^3/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(16 \, {\left(8 \, c^{4} e^{5} f + {\left(6 \, c^{4} d e^{4} - 7 \, b c^{3} e^{5}\right)} g\right)} x^{4} + 8 \, {\left(8 \, {\left(6 \, c^{4} d e^{4} + b c^{3} e^{5}\right)} f + {\left(36 \, c^{4} d^{2} e^{3} - 36 \, b c^{3} d e^{4} - 7 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} + 2 \, {\left(8 \, {\left(20 \, c^{4} d^{2} e^{3} + 16 \, b c^{3} d e^{4} - b^{2} c^{2} e^{5}\right)} f + {\left(120 \, c^{4} d^{3} e^{2} - 44 \, b c^{3} d^{2} e^{3} - 118 \, b^{2} c^{2} d e^{4} + 7 \, b^{3} c e^{5}\right)} g\right)} x^{2} - {\left(208 \, c^{4} d^{4} e - 384 \, b c^{3} d^{3} e^{2} + 184 \, b^{2} c^{2} d^{2} e^{3} - 48 \, b^{3} c d e^{4} + 5 \, b^{4} e^{5}\right)} f - 2 \, {\left(8 \, c^{4} d^{5} - 60 \, b c^{3} d^{4} e + 62 \, b^{2} c^{2} d^{3} e^{2} - 11 \, b^{3} c d^{2} e^{3} + b^{4} d e^{4}\right)} g - {\left(8 \, {\left(8 \, c^{4} d^{3} e^{2} - 52 \, b c^{3} d^{2} e^{3} + 10 \, b^{2} c^{2} d e^{4} - b^{3} c e^{5}\right)} f + {\left(48 \, c^{4} d^{4} e - 368 \, b c^{3} d^{3} e^{2} + 424 \, b^{2} c^{2} d^{2} e^{3} - 76 \, b^{3} c d e^{4} + 7 \, b^{4} e^{5}\right)} g\right)} x\right)}}{35 \, {\left(32 \, c^{6} d^{10} e^{2} - 112 \, b c^{5} d^{9} e^{3} + 160 \, b^{2} c^{4} d^{8} e^{4} - 120 \, b^{3} c^{3} d^{7} e^{5} + 50 \, b^{4} c^{2} d^{6} e^{6} - 11 \, b^{5} c d^{5} e^{7} + b^{6} d^{4} e^{8} - {\left(32 \, c^{6} d^{5} e^{7} - 80 \, b c^{5} d^{4} e^{8} + 80 \, b^{2} c^{4} d^{3} e^{9} - 40 \, b^{3} c^{3} d^{2} e^{10} + 10 \, b^{4} c^{2} d e^{11} - b^{5} c e^{12}\right)} x^{5} - {\left(96 \, c^{6} d^{6} e^{6} - 208 \, b c^{5} d^{5} e^{7} + 160 \, b^{2} c^{4} d^{4} e^{8} - 40 \, b^{3} c^{3} d^{3} e^{9} - 10 \, b^{4} c^{2} d^{2} e^{10} + 7 \, b^{5} c d e^{11} - b^{6} e^{12}\right)} x^{4} - 2 \, {\left(32 \, c^{6} d^{7} e^{5} - 16 \, b c^{5} d^{6} e^{6} - 80 \, b^{2} c^{4} d^{5} e^{7} + 120 \, b^{3} c^{3} d^{4} e^{8} - 70 \, b^{4} c^{2} d^{3} e^{9} + 19 \, b^{5} c d^{2} e^{10} - 2 \, b^{6} d e^{11}\right)} x^{3} + 2 \, {\left(32 \, c^{6} d^{8} e^{4} - 176 \, b c^{5} d^{7} e^{5} + 320 \, b^{2} c^{4} d^{6} e^{6} - 280 \, b^{3} c^{3} d^{5} e^{7} + 130 \, b^{4} c^{2} d^{4} e^{8} - 31 \, b^{5} c d^{3} e^{9} + 3 \, b^{6} d^{2} e^{10}\right)} x^{2} + {\left(96 \, c^{6} d^{9} e^{3} - 368 \, b c^{5} d^{8} e^{4} + 560 \, b^{2} c^{4} d^{7} e^{5} - 440 \, b^{3} c^{3} d^{6} e^{6} + 190 \, b^{4} c^{2} d^{5} e^{7} - 43 \, b^{5} c d^{4} e^{8} + 4 \, b^{6} d^{3} e^{9}\right)} x\right)}}"," ",0,"2/35*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(16*(8*c^4*e^5*f + (6*c^4*d*e^4 - 7*b*c^3*e^5)*g)*x^4 + 8*(8*(6*c^4*d*e^4 + b*c^3*e^5)*f + (36*c^4*d^2*e^3 - 36*b*c^3*d*e^4 - 7*b^2*c^2*e^5)*g)*x^3 + 2*(8*(20*c^4*d^2*e^3 + 16*b*c^3*d*e^4 - b^2*c^2*e^5)*f + (120*c^4*d^3*e^2 - 44*b*c^3*d^2*e^3 - 118*b^2*c^2*d*e^4 + 7*b^3*c*e^5)*g)*x^2 - (208*c^4*d^4*e - 384*b*c^3*d^3*e^2 + 184*b^2*c^2*d^2*e^3 - 48*b^3*c*d*e^4 + 5*b^4*e^5)*f - 2*(8*c^4*d^5 - 60*b*c^3*d^4*e + 62*b^2*c^2*d^3*e^2 - 11*b^3*c*d^2*e^3 + b^4*d*e^4)*g - (8*(8*c^4*d^3*e^2 - 52*b*c^3*d^2*e^3 + 10*b^2*c^2*d*e^4 - b^3*c*e^5)*f + (48*c^4*d^4*e - 368*b*c^3*d^3*e^2 + 424*b^2*c^2*d^2*e^3 - 76*b^3*c*d*e^4 + 7*b^4*e^5)*g)*x)/(32*c^6*d^10*e^2 - 112*b*c^5*d^9*e^3 + 160*b^2*c^4*d^8*e^4 - 120*b^3*c^3*d^7*e^5 + 50*b^4*c^2*d^6*e^6 - 11*b^5*c*d^5*e^7 + b^6*d^4*e^8 - (32*c^6*d^5*e^7 - 80*b*c^5*d^4*e^8 + 80*b^2*c^4*d^3*e^9 - 40*b^3*c^3*d^2*e^10 + 10*b^4*c^2*d*e^11 - b^5*c*e^12)*x^5 - (96*c^6*d^6*e^6 - 208*b*c^5*d^5*e^7 + 160*b^2*c^4*d^4*e^8 - 40*b^3*c^3*d^3*e^9 - 10*b^4*c^2*d^2*e^10 + 7*b^5*c*d*e^11 - b^6*e^12)*x^4 - 2*(32*c^6*d^7*e^5 - 16*b*c^5*d^6*e^6 - 80*b^2*c^4*d^5*e^7 + 120*b^3*c^3*d^4*e^8 - 70*b^4*c^2*d^3*e^9 + 19*b^5*c*d^2*e^10 - 2*b^6*d*e^11)*x^3 + 2*(32*c^6*d^8*e^4 - 176*b*c^5*d^7*e^5 + 320*b^2*c^4*d^6*e^6 - 280*b^3*c^3*d^5*e^7 + 130*b^4*c^2*d^4*e^8 - 31*b^5*c*d^3*e^9 + 3*b^6*d^2*e^10)*x^2 + (96*c^6*d^9*e^3 - 368*b*c^5*d^8*e^4 + 560*b^2*c^4*d^7*e^5 - 440*b^3*c^3*d^6*e^6 + 190*b^4*c^2*d^5*e^7 - 43*b^5*c*d^4*e^8 + 4*b^6*d^3*e^9)*x)","B",0
2223,1,1233,0,5.802975," ","integrate((e*x+d)^5*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(4 \, {\left(2 \, c^{4} d e^{3} - b c^{3} e^{4}\right)} f + {\left(20 \, c^{4} d^{2} e^{2} - 24 \, b c^{3} d e^{3} + 7 \, b^{2} c^{2} e^{4}\right)} g\right)} x^{2} + 4 \, {\left(2 \, c^{4} d^{3} e - 5 \, b c^{3} d^{2} e^{2} + 4 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f + {\left(20 \, c^{4} d^{4} - 64 \, b c^{3} d^{3} e + 75 \, b^{2} c^{2} d^{2} e^{2} - 38 \, b^{3} c d e^{3} + 7 \, b^{4} e^{4}\right)} g - 2 \, {\left(4 \, {\left(2 \, c^{4} d^{2} e^{2} - 3 \, b c^{3} d e^{3} + b^{2} c^{2} e^{4}\right)} f + {\left(20 \, c^{4} d^{3} e - 44 \, b c^{3} d^{2} e^{2} + 31 \, b^{2} c^{2} d e^{3} - 7 \, b^{3} c e^{4}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) + 4 \, {\left(6 \, c^{4} e^{3} g x^{3} + 3 \, {\left(4 \, c^{4} e^{3} f + {\left(16 \, c^{4} d e^{2} - 7 \, b c^{3} e^{3}\right)} g\right)} x^{2} + 4 \, {\left(23 \, c^{4} d^{2} e - 40 \, b c^{3} d e^{2} + 15 \, b^{2} c^{2} e^{3}\right)} f + {\left(236 \, c^{4} d^{3} - 561 \, b c^{3} d^{2} e + 430 \, b^{2} c^{2} d e^{2} - 105 \, b^{3} c e^{3}\right)} g - 2 \, {\left(4 \, {\left(17 \, c^{4} d e^{2} - 10 \, b c^{3} e^{3}\right)} f + {\left(161 \, c^{4} d^{2} e - 219 \, b c^{3} d e^{2} + 70 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{48 \, {\left(c^{7} e^{4} x^{2} + c^{7} d^{2} e^{2} - 2 \, b c^{6} d e^{3} + b^{2} c^{5} e^{4} - 2 \, {\left(c^{7} d e^{3} - b c^{6} e^{4}\right)} x\right)}}, -\frac{15 \, {\left({\left(4 \, {\left(2 \, c^{4} d e^{3} - b c^{3} e^{4}\right)} f + {\left(20 \, c^{4} d^{2} e^{2} - 24 \, b c^{3} d e^{3} + 7 \, b^{2} c^{2} e^{4}\right)} g\right)} x^{2} + 4 \, {\left(2 \, c^{4} d^{3} e - 5 \, b c^{3} d^{2} e^{2} + 4 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f + {\left(20 \, c^{4} d^{4} - 64 \, b c^{3} d^{3} e + 75 \, b^{2} c^{2} d^{2} e^{2} - 38 \, b^{3} c d e^{3} + 7 \, b^{4} e^{4}\right)} g - 2 \, {\left(4 \, {\left(2 \, c^{4} d^{2} e^{2} - 3 \, b c^{3} d e^{3} + b^{2} c^{2} e^{4}\right)} f + {\left(20 \, c^{4} d^{3} e - 44 \, b c^{3} d^{2} e^{2} + 31 \, b^{2} c^{2} d e^{3} - 7 \, b^{3} c e^{4}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(6 \, c^{4} e^{3} g x^{3} + 3 \, {\left(4 \, c^{4} e^{3} f + {\left(16 \, c^{4} d e^{2} - 7 \, b c^{3} e^{3}\right)} g\right)} x^{2} + 4 \, {\left(23 \, c^{4} d^{2} e - 40 \, b c^{3} d e^{2} + 15 \, b^{2} c^{2} e^{3}\right)} f + {\left(236 \, c^{4} d^{3} - 561 \, b c^{3} d^{2} e + 430 \, b^{2} c^{2} d e^{2} - 105 \, b^{3} c e^{3}\right)} g - 2 \, {\left(4 \, {\left(17 \, c^{4} d e^{2} - 10 \, b c^{3} e^{3}\right)} f + {\left(161 \, c^{4} d^{2} e - 219 \, b c^{3} d e^{2} + 70 \, b^{2} c^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{24 \, {\left(c^{7} e^{4} x^{2} + c^{7} d^{2} e^{2} - 2 \, b c^{6} d e^{3} + b^{2} c^{5} e^{4} - 2 \, {\left(c^{7} d e^{3} - b c^{6} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/48*(15*((4*(2*c^4*d*e^3 - b*c^3*e^4)*f + (20*c^4*d^2*e^2 - 24*b*c^3*d*e^3 + 7*b^2*c^2*e^4)*g)*x^2 + 4*(2*c^4*d^3*e - 5*b*c^3*d^2*e^2 + 4*b^2*c^2*d*e^3 - b^3*c*e^4)*f + (20*c^4*d^4 - 64*b*c^3*d^3*e + 75*b^2*c^2*d^2*e^2 - 38*b^3*c*d*e^3 + 7*b^4*e^4)*g - 2*(4*(2*c^4*d^2*e^2 - 3*b*c^3*d*e^3 + b^2*c^2*e^4)*f + (20*c^4*d^3*e - 44*b*c^3*d^2*e^2 + 31*b^2*c^2*d*e^3 - 7*b^3*c*e^4)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) + 4*(6*c^4*e^3*g*x^3 + 3*(4*c^4*e^3*f + (16*c^4*d*e^2 - 7*b*c^3*e^3)*g)*x^2 + 4*(23*c^4*d^2*e - 40*b*c^3*d*e^2 + 15*b^2*c^2*e^3)*f + (236*c^4*d^3 - 561*b*c^3*d^2*e + 430*b^2*c^2*d*e^2 - 105*b^3*c*e^3)*g - 2*(4*(17*c^4*d*e^2 - 10*b*c^3*e^3)*f + (161*c^4*d^2*e - 219*b*c^3*d*e^2 + 70*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^7*e^4*x^2 + c^7*d^2*e^2 - 2*b*c^6*d*e^3 + b^2*c^5*e^4 - 2*(c^7*d*e^3 - b*c^6*e^4)*x), -1/24*(15*((4*(2*c^4*d*e^3 - b*c^3*e^4)*f + (20*c^4*d^2*e^2 - 24*b*c^3*d*e^3 + 7*b^2*c^2*e^4)*g)*x^2 + 4*(2*c^4*d^3*e - 5*b*c^3*d^2*e^2 + 4*b^2*c^2*d*e^3 - b^3*c*e^4)*f + (20*c^4*d^4 - 64*b*c^3*d^3*e + 75*b^2*c^2*d^2*e^2 - 38*b^3*c*d*e^3 + 7*b^4*e^4)*g - 2*(4*(2*c^4*d^2*e^2 - 3*b*c^3*d*e^3 + b^2*c^2*e^4)*f + (20*c^4*d^3*e - 44*b*c^3*d^2*e^2 + 31*b^2*c^2*d*e^3 - 7*b^3*c*e^4)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(6*c^4*e^3*g*x^3 + 3*(4*c^4*e^3*f + (16*c^4*d*e^2 - 7*b*c^3*e^3)*g)*x^2 + 4*(23*c^4*d^2*e - 40*b*c^3*d*e^2 + 15*b^2*c^2*e^3)*f + (236*c^4*d^3 - 561*b*c^3*d^2*e + 430*b^2*c^2*d*e^2 - 105*b^3*c*e^3)*g - 2*(4*(17*c^4*d*e^2 - 10*b*c^3*e^3)*f + (161*c^4*d^2*e - 219*b*c^3*d*e^2 + 70*b^2*c^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^7*e^4*x^2 + c^7*d^2*e^2 - 2*b*c^6*d*e^3 + b^2*c^5*e^4 - 2*(c^7*d*e^3 - b*c^6*e^4)*x)]","A",0
2224,1,881,0,3.549357," ","integrate((e*x+d)^4*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(2 \, c^{3} e^{3} f + {\left(8 \, c^{3} d e^{2} - 5 \, b c^{2} e^{3}\right)} g\right)} x^{2} + 2 \, {\left(c^{3} d^{2} e - 2 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} f + {\left(8 \, c^{3} d^{3} - 21 \, b c^{2} d^{2} e + 18 \, b^{2} c d e^{2} - 5 \, b^{3} e^{3}\right)} g - 2 \, {\left(2 \, {\left(c^{3} d e^{2} - b c^{2} e^{3}\right)} f + {\left(8 \, c^{3} d^{2} e - 13 \, b c^{2} d e^{2} + 5 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} + 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(3 \, c^{3} e^{2} g x^{2} + 2 \, {\left(2 \, c^{3} d e - 3 \, b c^{2} e^{2}\right)} f + {\left(19 \, c^{3} d^{2} - 34 \, b c^{2} d e + 15 \, b^{2} c e^{2}\right)} g - 2 \, {\left(4 \, c^{3} e^{2} f + {\left(13 \, c^{3} d e - 10 \, b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{12 \, {\left(c^{6} e^{4} x^{2} + c^{6} d^{2} e^{2} - 2 \, b c^{5} d e^{3} + b^{2} c^{4} e^{4} - 2 \, {\left(c^{6} d e^{3} - b c^{5} e^{4}\right)} x\right)}}, -\frac{3 \, {\left({\left(2 \, c^{3} e^{3} f + {\left(8 \, c^{3} d e^{2} - 5 \, b c^{2} e^{3}\right)} g\right)} x^{2} + 2 \, {\left(c^{3} d^{2} e - 2 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} f + {\left(8 \, c^{3} d^{3} - 21 \, b c^{2} d^{2} e + 18 \, b^{2} c d e^{2} - 5 \, b^{3} e^{3}\right)} g - 2 \, {\left(2 \, {\left(c^{3} d e^{2} - b c^{2} e^{3}\right)} f + {\left(8 \, c^{3} d^{2} e - 13 \, b c^{2} d e^{2} + 5 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) + 2 \, {\left(3 \, c^{3} e^{2} g x^{2} + 2 \, {\left(2 \, c^{3} d e - 3 \, b c^{2} e^{2}\right)} f + {\left(19 \, c^{3} d^{2} - 34 \, b c^{2} d e + 15 \, b^{2} c e^{2}\right)} g - 2 \, {\left(4 \, c^{3} e^{2} f + {\left(13 \, c^{3} d e - 10 \, b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{6 \, {\left(c^{6} e^{4} x^{2} + c^{6} d^{2} e^{2} - 2 \, b c^{5} d e^{3} + b^{2} c^{4} e^{4} - 2 \, {\left(c^{6} d e^{3} - b c^{5} e^{4}\right)} x\right)}}\right]"," ",0,"[1/12*(3*((2*c^3*e^3*f + (8*c^3*d*e^2 - 5*b*c^2*e^3)*g)*x^2 + 2*(c^3*d^2*e - 2*b*c^2*d*e^2 + b^2*c*e^3)*f + (8*c^3*d^3 - 21*b*c^2*d^2*e + 18*b^2*c*d*e^2 - 5*b^3*e^3)*g - 2*(2*(c^3*d*e^2 - b*c^2*e^3)*f + (8*c^3*d^2*e - 13*b*c^2*d*e^2 + 5*b^2*c*e^3)*g)*x)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 + 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(3*c^3*e^2*g*x^2 + 2*(2*c^3*d*e - 3*b*c^2*e^2)*f + (19*c^3*d^2 - 34*b*c^2*d*e + 15*b^2*c*e^2)*g - 2*(4*c^3*e^2*f + (13*c^3*d*e - 10*b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^6*e^4*x^2 + c^6*d^2*e^2 - 2*b*c^5*d*e^3 + b^2*c^4*e^4 - 2*(c^6*d*e^3 - b*c^5*e^4)*x), -1/6*(3*((2*c^3*e^3*f + (8*c^3*d*e^2 - 5*b*c^2*e^3)*g)*x^2 + 2*(c^3*d^2*e - 2*b*c^2*d*e^2 + b^2*c*e^3)*f + (8*c^3*d^3 - 21*b*c^2*d^2*e + 18*b^2*c*d*e^2 - 5*b^3*e^3)*g - 2*(2*(c^3*d*e^2 - b*c^2*e^3)*f + (8*c^3*d^2*e - 13*b*c^2*d*e^2 + 5*b^2*c*e^3)*g)*x)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) + 2*(3*c^3*e^2*g*x^2 + 2*(2*c^3*d*e - 3*b*c^2*e^2)*f + (19*c^3*d^2 - 34*b*c^2*d*e + 15*b^2*c*e^2)*g - 2*(4*c^3*e^2*f + (13*c^3*d*e - 10*b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(c^6*e^4*x^2 + c^6*d^2*e^2 - 2*b*c^5*d*e^3 + b^2*c^4*e^4 - 2*(c^6*d*e^3 - b*c^5*e^4)*x)]","A",0
2225,1,785,0,2.385848," ","integrate((e*x+d)^3*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} g x^{2} - 2 \, {\left(2 \, c^{3} d^{2} e - 3 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} g x + {\left(2 \, c^{3} d^{3} - 5 \, b c^{2} d^{2} e + 4 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} g\right)} \sqrt{-c} \log\left(8 \, c^{2} e^{2} x^{2} + 8 \, b c e^{2} x - 4 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2} - 4 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{-c}\right) - 4 \, {\left(c^{3} d e f - {\left(5 \, c^{3} d^{2} - 8 \, b c^{2} d e + 3 \, b^{2} c e^{2}\right)} g + {\left(c^{3} e^{2} f + {\left(7 \, c^{3} d e - 4 \, b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{6 \, {\left(2 \, c^{6} d^{3} e^{2} - 5 \, b c^{5} d^{2} e^{3} + 4 \, b^{2} c^{4} d e^{4} - b^{3} c^{3} e^{5} + {\left(2 \, c^{6} d e^{4} - b c^{5} e^{5}\right)} x^{2} - 2 \, {\left(2 \, c^{6} d^{2} e^{3} - 3 \, b c^{5} d e^{4} + b^{2} c^{4} e^{5}\right)} x\right)}}, -\frac{3 \, {\left({\left(2 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} g x^{2} - 2 \, {\left(2 \, c^{3} d^{2} e - 3 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} g x + {\left(2 \, c^{3} d^{3} - 5 \, b c^{2} d^{2} e + 4 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} g\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c e x + b e\right)} \sqrt{c}}{2 \, {\left(c^{2} e^{2} x^{2} + b c e^{2} x - c^{2} d^{2} + b c d e\right)}}\right) - 2 \, {\left(c^{3} d e f - {\left(5 \, c^{3} d^{2} - 8 \, b c^{2} d e + 3 \, b^{2} c e^{2}\right)} g + {\left(c^{3} e^{2} f + {\left(7 \, c^{3} d e - 4 \, b c^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e}}{3 \, {\left(2 \, c^{6} d^{3} e^{2} - 5 \, b c^{5} d^{2} e^{3} + 4 \, b^{2} c^{4} d e^{4} - b^{3} c^{3} e^{5} + {\left(2 \, c^{6} d e^{4} - b c^{5} e^{5}\right)} x^{2} - 2 \, {\left(2 \, c^{6} d^{2} e^{3} - 3 \, b c^{5} d e^{4} + b^{2} c^{4} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/6*(3*((2*c^3*d*e^2 - b*c^2*e^3)*g*x^2 - 2*(2*c^3*d^2*e - 3*b*c^2*d*e^2 + b^2*c*e^3)*g*x + (2*c^3*d^3 - 5*b*c^2*d^2*e + 4*b^2*c*d*e^2 - b^3*e^3)*g)*sqrt(-c)*log(8*c^2*e^2*x^2 + 8*b*c*e^2*x - 4*c^2*d^2 + 4*b*c*d*e + b^2*e^2 - 4*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(-c)) - 4*(c^3*d*e*f - (5*c^3*d^2 - 8*b*c^2*d*e + 3*b^2*c*e^2)*g + (c^3*e^2*f + (7*c^3*d*e - 4*b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(2*c^6*d^3*e^2 - 5*b*c^5*d^2*e^3 + 4*b^2*c^4*d*e^4 - b^3*c^3*e^5 + (2*c^6*d*e^4 - b*c^5*e^5)*x^2 - 2*(2*c^6*d^2*e^3 - 3*b*c^5*d*e^4 + b^2*c^4*e^5)*x), -1/3*(3*((2*c^3*d*e^2 - b*c^2*e^3)*g*x^2 - 2*(2*c^3*d^2*e - 3*b*c^2*d*e^2 + b^2*c*e^3)*g*x + (2*c^3*d^3 - 5*b*c^2*d^2*e + 4*b^2*c*d*e^2 - b^3*e^3)*g)*sqrt(c)*arctan(1/2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*e*x + b*e)*sqrt(c)/(c^2*e^2*x^2 + b*c*e^2*x - c^2*d^2 + b*c*d*e)) - 2*(c^3*d*e*f - (5*c^3*d^2 - 8*b*c^2*d*e + 3*b^2*c*e^2)*g + (c^3*e^2*f + (7*c^3*d*e - 4*b*c^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e))/(2*c^6*d^3*e^2 - 5*b*c^5*d^2*e^3 + 4*b^2*c^4*d*e^4 - b^3*c^3*e^5 + (2*c^6*d*e^4 - b*c^5*e^5)*x^2 - 2*(2*c^6*d^2*e^3 - 3*b*c^5*d*e^4 + b^2*c^4*e^5)*x)]","B",0
2226,1,227,0,2.461382," ","integrate((e*x+d)^2*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(4 \, c d e - 3 \, b e^{2}\right)} f - 2 \, {\left(c d^{2} - b d e\right)} g - {\left(2 \, c e^{2} f - {\left(4 \, c d e - b e^{2}\right)} g\right)} x\right)}}{3 \, {\left(4 \, c^{4} d^{4} e^{2} - 12 \, b c^{3} d^{3} e^{3} + 13 \, b^{2} c^{2} d^{2} e^{4} - 6 \, b^{3} c d e^{5} + b^{4} e^{6} + {\left(4 \, c^{4} d^{2} e^{4} - 4 \, b c^{3} d e^{5} + b^{2} c^{2} e^{6}\right)} x^{2} - 2 \, {\left(4 \, c^{4} d^{3} e^{3} - 8 \, b c^{3} d^{2} e^{4} + 5 \, b^{2} c^{2} d e^{5} - b^{3} c e^{6}\right)} x\right)}}"," ",0,"2/3*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((4*c*d*e - 3*b*e^2)*f - 2*(c*d^2 - b*d*e)*g - (2*c*e^2*f - (4*c*d*e - b*e^2)*g)*x)/(4*c^4*d^4*e^2 - 12*b*c^3*d^3*e^3 + 13*b^2*c^2*d^2*e^4 - 6*b^3*c*d*e^5 + b^4*e^6 + (4*c^4*d^2*e^4 - 4*b*c^3*d*e^5 + b^2*c^2*e^6)*x^2 - 2*(4*c^4*d^3*e^3 - 8*b*c^3*d^2*e^4 + 5*b^2*c^2*d*e^5 - b^3*c*e^6)*x)","A",0
2227,1,431,0,9.471568," ","integrate((e*x+d)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, {\left(4 \, c^{2} e^{3} f - {\left(2 \, c^{2} d e^{2} + b c e^{3}\right)} g\right)} x^{2} - {\left(4 \, c^{2} d^{2} e - 3 \, b^{2} e^{3}\right)} f - 2 \, {\left(2 \, c^{2} d^{3} - 5 \, b c d^{2} e + 3 \, b^{2} d e^{2}\right)} g - {\left(4 \, {\left(2 \, c^{2} d e^{2} - 3 \, b c e^{3}\right)} f - {\left(4 \, c^{2} d^{2} e - 4 \, b c d e^{2} - 3 \, b^{2} e^{3}\right)} g\right)} x\right)}}{3 \, {\left(8 \, c^{5} d^{6} e^{2} - 28 \, b c^{4} d^{5} e^{3} + 38 \, b^{2} c^{3} d^{4} e^{4} - 25 \, b^{3} c^{2} d^{3} e^{5} + 8 \, b^{4} c d^{2} e^{6} - b^{5} d e^{7} + {\left(8 \, c^{5} d^{3} e^{5} - 12 \, b c^{4} d^{2} e^{6} + 6 \, b^{2} c^{3} d e^{7} - b^{3} c^{2} e^{8}\right)} x^{3} - {\left(8 \, c^{5} d^{4} e^{4} - 28 \, b c^{4} d^{3} e^{5} + 30 \, b^{2} c^{3} d^{2} e^{6} - 13 \, b^{3} c^{2} d e^{7} + 2 \, b^{4} c e^{8}\right)} x^{2} - {\left(8 \, c^{5} d^{5} e^{3} - 12 \, b c^{4} d^{4} e^{4} - 2 \, b^{2} c^{3} d^{3} e^{5} + 11 \, b^{3} c^{2} d^{2} e^{6} - 6 \, b^{4} c d e^{7} + b^{5} e^{8}\right)} x\right)}}"," ",0,"-2/3*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*(4*c^2*e^3*f - (2*c^2*d*e^2 + b*c*e^3)*g)*x^2 - (4*c^2*d^2*e - 3*b^2*e^3)*f - 2*(2*c^2*d^3 - 5*b*c*d^2*e + 3*b^2*d*e^2)*g - (4*(2*c^2*d*e^2 - 3*b*c*e^3)*f - (4*c^2*d^2*e - 4*b*c*d*e^2 - 3*b^2*e^3)*g)*x)/(8*c^5*d^6*e^2 - 28*b*c^4*d^5*e^3 + 38*b^2*c^3*d^4*e^4 - 25*b^3*c^2*d^3*e^5 + 8*b^4*c*d^2*e^6 - b^5*d*e^7 + (8*c^5*d^3*e^5 - 12*b*c^4*d^2*e^6 + 6*b^2*c^3*d*e^7 - b^3*c^2*e^8)*x^3 - (8*c^5*d^4*e^4 - 28*b*c^4*d^3*e^5 + 30*b^2*c^3*d^2*e^6 - 13*b^3*c^2*d*e^7 + 2*b^4*c*e^8)*x^2 - (8*c^5*d^5*e^3 - 12*b*c^4*d^4*e^4 - 2*b^2*c^3*d^3*e^5 + 11*b^3*c^2*d^2*e^6 - 6*b^4*c*d*e^7 + b^5*e^8)*x)","B",0
2228,1,1028,0,93.100858," ","integrate((g*x+f)/(e*x+d)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(16 \, {\left(8 \, c^{4} e^{5} f + {\left(2 \, c^{4} d e^{4} - 5 \, b c^{3} e^{5}\right)} g\right)} x^{4} + 8 \, {\left(8 \, {\left(2 \, c^{4} d e^{4} + 3 \, b c^{3} e^{5}\right)} f + {\left(4 \, c^{4} d^{2} e^{3} - 4 \, b c^{3} d e^{4} - 15 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} - 6 \, {\left(8 \, {\left(4 \, c^{4} d^{2} e^{3} - 8 \, b c^{3} d e^{4} - b^{2} c^{2} e^{5}\right)} f + {\left(8 \, c^{4} d^{3} e^{2} - 36 \, b c^{3} d^{2} e^{3} + 38 \, b^{2} c^{2} d e^{4} + 5 \, b^{3} c e^{5}\right)} g\right)} x^{2} + {\left(48 \, c^{4} d^{4} e - 192 \, b c^{3} d^{3} e^{2} + 168 \, b^{2} c^{2} d^{2} e^{3} - 32 \, b^{3} c d e^{4} + 3 \, b^{4} e^{5}\right)} f - 2 \, {\left(24 \, c^{4} d^{5} - 36 \, b c^{3} d^{4} e - 6 \, b^{2} c^{2} d^{3} e^{2} + 19 \, b^{3} c d^{2} e^{3} - b^{4} d e^{4}\right)} g - {\left(8 \, {\left(24 \, c^{4} d^{3} e^{2} - 12 \, b c^{3} d^{2} e^{3} - 18 \, b^{2} c^{2} d e^{4} + b^{3} c e^{5}\right)} f + {\left(48 \, c^{4} d^{4} e - 144 \, b c^{3} d^{3} e^{2} + 24 \, b^{2} c^{2} d^{2} e^{3} + 92 \, b^{3} c d e^{4} - 5 \, b^{4} e^{5}\right)} g\right)} x\right)}}{15 \, {\left(32 \, c^{7} d^{10} e^{2} - 144 \, b c^{6} d^{9} e^{3} + 272 \, b^{2} c^{5} d^{8} e^{4} - 280 \, b^{3} c^{4} d^{7} e^{5} + 170 \, b^{4} c^{3} d^{6} e^{6} - 61 \, b^{5} c^{2} d^{5} e^{7} + 12 \, b^{6} c d^{4} e^{8} - b^{7} d^{3} e^{9} + {\left(32 \, c^{7} d^{5} e^{7} - 80 \, b c^{6} d^{4} e^{8} + 80 \, b^{2} c^{5} d^{3} e^{9} - 40 \, b^{3} c^{4} d^{2} e^{10} + 10 \, b^{4} c^{3} d e^{11} - b^{5} c^{2} e^{12}\right)} x^{5} + {\left(32 \, c^{7} d^{6} e^{6} - 16 \, b c^{6} d^{5} e^{7} - 80 \, b^{2} c^{5} d^{4} e^{8} + 120 \, b^{3} c^{4} d^{3} e^{9} - 70 \, b^{4} c^{3} d^{2} e^{10} + 19 \, b^{5} c^{2} d e^{11} - 2 \, b^{6} c e^{12}\right)} x^{4} - {\left(64 \, c^{7} d^{7} e^{5} - 288 \, b c^{6} d^{6} e^{6} + 448 \, b^{2} c^{5} d^{5} e^{7} - 320 \, b^{3} c^{4} d^{4} e^{8} + 100 \, b^{4} c^{3} d^{3} e^{9} - 2 \, b^{5} c^{2} d^{2} e^{10} - 6 \, b^{6} c d e^{11} + b^{7} e^{12}\right)} x^{3} - {\left(64 \, c^{7} d^{8} e^{4} - 160 \, b c^{6} d^{7} e^{5} + 64 \, b^{2} c^{5} d^{6} e^{6} + 160 \, b^{3} c^{4} d^{5} e^{7} - 220 \, b^{4} c^{3} d^{4} e^{8} + 118 \, b^{5} c^{2} d^{3} e^{9} - 30 \, b^{6} c d^{2} e^{10} + 3 \, b^{7} d e^{11}\right)} x^{2} + {\left(32 \, c^{7} d^{9} e^{3} - 208 \, b c^{6} d^{8} e^{4} + 496 \, b^{2} c^{5} d^{7} e^{5} - 600 \, b^{3} c^{4} d^{6} e^{6} + 410 \, b^{4} c^{3} d^{5} e^{7} - 161 \, b^{5} c^{2} d^{4} e^{8} + 34 \, b^{6} c d^{3} e^{9} - 3 \, b^{7} d^{2} e^{10}\right)} x\right)}}"," ",0,"-2/15*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(16*(8*c^4*e^5*f + (2*c^4*d*e^4 - 5*b*c^3*e^5)*g)*x^4 + 8*(8*(2*c^4*d*e^4 + 3*b*c^3*e^5)*f + (4*c^4*d^2*e^3 - 4*b*c^3*d*e^4 - 15*b^2*c^2*e^5)*g)*x^3 - 6*(8*(4*c^4*d^2*e^3 - 8*b*c^3*d*e^4 - b^2*c^2*e^5)*f + (8*c^4*d^3*e^2 - 36*b*c^3*d^2*e^3 + 38*b^2*c^2*d*e^4 + 5*b^3*c*e^5)*g)*x^2 + (48*c^4*d^4*e - 192*b*c^3*d^3*e^2 + 168*b^2*c^2*d^2*e^3 - 32*b^3*c*d*e^4 + 3*b^4*e^5)*f - 2*(24*c^4*d^5 - 36*b*c^3*d^4*e - 6*b^2*c^2*d^3*e^2 + 19*b^3*c*d^2*e^3 - b^4*d*e^4)*g - (8*(24*c^4*d^3*e^2 - 12*b*c^3*d^2*e^3 - 18*b^2*c^2*d*e^4 + b^3*c*e^5)*f + (48*c^4*d^4*e - 144*b*c^3*d^3*e^2 + 24*b^2*c^2*d^2*e^3 + 92*b^3*c*d*e^4 - 5*b^4*e^5)*g)*x)/(32*c^7*d^10*e^2 - 144*b*c^6*d^9*e^3 + 272*b^2*c^5*d^8*e^4 - 280*b^3*c^4*d^7*e^5 + 170*b^4*c^3*d^6*e^6 - 61*b^5*c^2*d^5*e^7 + 12*b^6*c*d^4*e^8 - b^7*d^3*e^9 + (32*c^7*d^5*e^7 - 80*b*c^6*d^4*e^8 + 80*b^2*c^5*d^3*e^9 - 40*b^3*c^4*d^2*e^10 + 10*b^4*c^3*d*e^11 - b^5*c^2*e^12)*x^5 + (32*c^7*d^6*e^6 - 16*b*c^6*d^5*e^7 - 80*b^2*c^5*d^4*e^8 + 120*b^3*c^4*d^3*e^9 - 70*b^4*c^3*d^2*e^10 + 19*b^5*c^2*d*e^11 - 2*b^6*c*e^12)*x^4 - (64*c^7*d^7*e^5 - 288*b*c^6*d^6*e^6 + 448*b^2*c^5*d^5*e^7 - 320*b^3*c^4*d^4*e^8 + 100*b^4*c^3*d^3*e^9 - 2*b^5*c^2*d^2*e^10 - 6*b^6*c*d*e^11 + b^7*e^12)*x^3 - (64*c^7*d^8*e^4 - 160*b*c^6*d^7*e^5 + 64*b^2*c^5*d^6*e^6 + 160*b^3*c^4*d^5*e^7 - 220*b^4*c^3*d^4*e^8 + 118*b^5*c^2*d^3*e^9 - 30*b^6*c*d^2*e^10 + 3*b^7*d*e^11)*x^2 + (32*c^7*d^9*e^3 - 208*b*c^6*d^8*e^4 + 496*b^2*c^5*d^7*e^5 - 600*b^3*c^4*d^6*e^6 + 410*b^4*c^3*d^5*e^7 - 161*b^5*c^2*d^4*e^8 + 34*b^6*c*d^3*e^9 - 3*b^7*d^2*e^10)*x)","B",0
2229,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)^2/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2230,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)^3/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2231,1,499,0,0.491472," ","integrate((e*x+d)^(5/2)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, c^{5} e^{5} g x^{5} + 35 \, {\left(11 \, c^{5} e^{5} f + {\left(32 \, c^{5} d e^{4} + b c^{4} e^{5}\right)} g\right)} x^{4} + 5 \, {\left(11 \, {\left(26 \, c^{5} d e^{4} + b c^{4} e^{5}\right)} f + {\left(256 \, c^{5} d^{2} e^{3} + 49 \, b c^{4} d e^{4} - 8 \, b^{2} c^{3} e^{5}\right)} g\right)} x^{3} + 3 \, {\left(11 \, {\left(52 \, c^{5} d^{2} e^{3} + 13 \, b c^{4} d e^{4} - 2 \, b^{2} c^{3} e^{5}\right)} f + {\left(50 \, c^{5} d^{3} e^{2} + 279 \, b c^{4} d^{2} e^{3} - 114 \, b^{2} c^{3} d e^{4} + 16 \, b^{3} c^{2} e^{5}\right)} g\right)} x^{2} - 11 \, {\left(319 \, c^{5} d^{4} e - 637 \, b c^{4} d^{3} e^{2} + 438 \, b^{2} c^{3} d^{2} e^{3} - 136 \, b^{3} c^{2} d e^{4} + 16 \, b^{4} c e^{5}\right)} f - 2 \, {\left(955 \, c^{5} d^{5} - 3026 \, b c^{4} d^{4} e + 3643 \, b^{2} c^{3} d^{3} e^{2} - 2092 \, b^{3} c^{2} d^{2} e^{3} + 584 \, b^{4} c d e^{4} - 64 \, b^{5} e^{5}\right)} g - {\left(11 \, {\left(2 \, c^{5} d^{3} e^{2} - 159 \, b c^{4} d^{2} e^{3} + 60 \, b^{2} c^{3} d e^{4} - 8 \, b^{3} c^{2} e^{5}\right)} f + {\left(955 \, c^{5} d^{4} e - 2071 \, b c^{4} d^{3} e^{2} + 1572 \, b^{2} c^{3} d^{2} e^{3} - 520 \, b^{3} c^{2} d e^{4} + 64 \, b^{4} c e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{3465 \, {\left(c^{5} e^{3} x + c^{5} d e^{2}\right)}}"," ",0,"2/3465*(315*c^5*e^5*g*x^5 + 35*(11*c^5*e^5*f + (32*c^5*d*e^4 + b*c^4*e^5)*g)*x^4 + 5*(11*(26*c^5*d*e^4 + b*c^4*e^5)*f + (256*c^5*d^2*e^3 + 49*b*c^4*d*e^4 - 8*b^2*c^3*e^5)*g)*x^3 + 3*(11*(52*c^5*d^2*e^3 + 13*b*c^4*d*e^4 - 2*b^2*c^3*e^5)*f + (50*c^5*d^3*e^2 + 279*b*c^4*d^2*e^3 - 114*b^2*c^3*d*e^4 + 16*b^3*c^2*e^5)*g)*x^2 - 11*(319*c^5*d^4*e - 637*b*c^4*d^3*e^2 + 438*b^2*c^3*d^2*e^3 - 136*b^3*c^2*d*e^4 + 16*b^4*c*e^5)*f - 2*(955*c^5*d^5 - 3026*b*c^4*d^4*e + 3643*b^2*c^3*d^3*e^2 - 2092*b^3*c^2*d^2*e^3 + 584*b^4*c*d*e^4 - 64*b^5*e^5)*g - (11*(2*c^5*d^3*e^2 - 159*b*c^4*d^2*e^3 + 60*b^2*c^3*d*e^4 - 8*b^3*c^2*e^5)*f + (955*c^5*d^4*e - 2071*b*c^4*d^3*e^2 + 1572*b^2*c^3*d^2*e^3 - 520*b^3*c^2*d*e^4 + 64*b^4*c*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^5*e^3*x + c^5*d*e^2)","A",0
2232,1,352,0,0.709106," ","integrate((e*x+d)^(3/2)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{4} e^{4} g x^{4} + 5 \, {\left(9 \, c^{4} e^{4} f + {\left(17 \, c^{4} d e^{3} + b c^{3} e^{4}\right)} g\right)} x^{3} + 3 \, {\left(3 \, {\left(13 \, c^{4} d e^{3} + b c^{3} e^{4}\right)} f + {\left(13 \, c^{4} d^{2} e^{2} + 10 \, b c^{3} d e^{3} - 2 \, b^{2} c^{2} e^{4}\right)} g\right)} x^{2} - 3 \, {\left(71 \, c^{4} d^{3} e - 115 \, b c^{3} d^{2} e^{2} + 52 \, b^{2} c^{2} d e^{3} - 8 \, b^{3} c e^{4}\right)} f - 2 \, {\left(53 \, c^{4} d^{4} - 146 \, b c^{3} d^{3} e + 141 \, b^{2} c^{2} d^{2} e^{2} - 56 \, b^{3} c d e^{3} + 8 \, b^{4} e^{4}\right)} g + {\left(3 \, {\left(17 \, c^{4} d^{2} e^{2} + 22 \, b c^{3} d e^{3} - 4 \, b^{2} c^{2} e^{4}\right)} f - {\left(53 \, c^{4} d^{3} e - 93 \, b c^{3} d^{2} e^{2} + 48 \, b^{2} c^{2} d e^{3} - 8 \, b^{3} c e^{4}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{315 \, {\left(c^{4} e^{3} x + c^{4} d e^{2}\right)}}"," ",0,"2/315*(35*c^4*e^4*g*x^4 + 5*(9*c^4*e^4*f + (17*c^4*d*e^3 + b*c^3*e^4)*g)*x^3 + 3*(3*(13*c^4*d*e^3 + b*c^3*e^4)*f + (13*c^4*d^2*e^2 + 10*b*c^3*d*e^3 - 2*b^2*c^2*e^4)*g)*x^2 - 3*(71*c^4*d^3*e - 115*b*c^3*d^2*e^2 + 52*b^2*c^2*d*e^3 - 8*b^3*c*e^4)*f - 2*(53*c^4*d^4 - 146*b*c^3*d^3*e + 141*b^2*c^2*d^2*e^2 - 56*b^3*c*d*e^3 + 8*b^4*e^4)*g + (3*(17*c^4*d^2*e^2 + 22*b*c^3*d*e^3 - 4*b^2*c^2*e^4)*f - (53*c^4*d^3*e - 93*b*c^3*d^2*e^2 + 48*b^2*c^2*d*e^3 - 8*b^3*c*e^4)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^4*e^3*x + c^4*d*e^2)","A",0
2233,1,233,0,0.672515," ","integrate((e*x+d)^(1/2)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{3} e^{3} g x^{3} + 3 \, {\left(7 \, c^{3} e^{3} f + {\left(6 \, c^{3} d e^{2} + b c^{2} e^{3}\right)} g\right)} x^{2} - 7 \, {\left(7 \, c^{3} d^{2} e - 9 \, b c^{2} d e^{2} + 2 \, b^{2} c e^{3}\right)} f - 2 \, {\left(11 \, c^{3} d^{3} - 26 \, b c^{2} d^{2} e + 19 \, b^{2} c d e^{2} - 4 \, b^{3} e^{3}\right)} g + {\left(7 \, {\left(4 \, c^{3} d e^{2} + b c^{2} e^{3}\right)} f - {\left(11 \, c^{3} d^{2} e - 15 \, b c^{2} d e^{2} + 4 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{105 \, {\left(c^{3} e^{3} x + c^{3} d e^{2}\right)}}"," ",0,"2/105*(15*c^3*e^3*g*x^3 + 3*(7*c^3*e^3*f + (6*c^3*d*e^2 + b*c^2*e^3)*g)*x^2 - 7*(7*c^3*d^2*e - 9*b*c^2*d*e^2 + 2*b^2*c*e^3)*f - 2*(11*c^3*d^3 - 26*b*c^2*d^2*e + 19*b^2*c*d*e^2 - 4*b^3*e^3)*g + (7*(4*c^3*d*e^2 + b*c^2*e^3)*f - (11*c^3*d^2*e - 15*b*c^2*d*e^2 + 4*b^2*c*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^3*e^3*x + c^3*d*e^2)","A",0
2234,1,140,0,0.573611," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} e^{2} g x^{2} - 5 \, {\left(c^{2} d e - b c e^{2}\right)} f - 2 \, {\left(c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}\right)} g + {\left(5 \, c^{2} e^{2} f - {\left(c^{2} d e - b c e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{15 \, {\left(c^{2} e^{3} x + c^{2} d e^{2}\right)}}"," ",0,"2/15*(3*c^2*e^2*g*x^2 - 5*(c^2*d*e - b*c*e^2)*f - 2*(c^2*d^2 - 2*b*c*d*e + b^2*e^2)*g + (5*c^2*e^2*f - (c^2*d*e - b*c*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^2*e^3*x + c^2*d*e^2)","A",0
2235,1,419,0,0.808704," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c d e f - c d^{2} g + {\left(c e^{2} f - c d e g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c e g x + 3 \, c e f - {\left(4 \, c d - b e\right)} g\right)} \sqrt{e x + d}}{3 \, {\left(c e^{3} x + c d e^{2}\right)}}, -\frac{2 \, {\left(3 \, {\left(c d e f - c d^{2} g + {\left(c e^{2} f - c d e g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) - \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c e g x + 3 \, c e f - {\left(4 \, c d - b e\right)} g\right)} \sqrt{e x + d}\right)}}{3 \, {\left(c e^{3} x + c d e^{2}\right)}}\right]"," ",0,"[-1/3*(3*(c*d*e*f - c*d^2*g + (c*e^2*f - c*d*e*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c*e*g*x + 3*c*e*f - (4*c*d - b*e)*g)*sqrt(e*x + d))/(c*e^3*x + c*d*e^2), -2/3*(3*(c*d*e*f - c*d^2*g + (c*e^2*f - c*d*e*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) - sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c*e*g*x + 3*c*e*f - (4*c*d - b*e)*g)*sqrt(e*x + d))/(c*e^3*x + c*d*e^2)]","A",0
2236,1,659,0,0.546649," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d^{2} e f + {\left(c e^{3} f - {\left(5 \, c d e^{2} - 2 \, b e^{3}\right)} g\right)} x^{2} - {\left(5 \, c d^{3} - 2 \, b d^{2} e\right)} g + 2 \, {\left(c d e^{2} f - {\left(5 \, c d^{2} e - 2 \, b d e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, {\left(2 \, c d e - b e^{2}\right)} g x - {\left(2 \, c d e - b e^{2}\right)} f + 3 \, {\left(2 \, c d^{2} - b d e\right)} g\right)} \sqrt{e x + d}}{2 \, {\left(2 \, c d^{3} e^{2} - b d^{2} e^{3} + {\left(2 \, c d e^{4} - b e^{5}\right)} x^{2} + 2 \, {\left(2 \, c d^{2} e^{3} - b d e^{4}\right)} x\right)}}, \frac{{\left(c d^{2} e f + {\left(c e^{3} f - {\left(5 \, c d e^{2} - 2 \, b e^{3}\right)} g\right)} x^{2} - {\left(5 \, c d^{3} - 2 \, b d^{2} e\right)} g + 2 \, {\left(c d e^{2} f - {\left(5 \, c d^{2} e - 2 \, b d e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, {\left(2 \, c d e - b e^{2}\right)} g x - {\left(2 \, c d e - b e^{2}\right)} f + 3 \, {\left(2 \, c d^{2} - b d e\right)} g\right)} \sqrt{e x + d}}{2 \, c d^{3} e^{2} - b d^{2} e^{3} + {\left(2 \, c d e^{4} - b e^{5}\right)} x^{2} + 2 \, {\left(2 \, c d^{2} e^{3} - b d e^{4}\right)} x}\right]"," ",0,"[1/2*((c*d^2*e*f + (c*e^3*f - (5*c*d*e^2 - 2*b*e^3)*g)*x^2 - (5*c*d^3 - 2*b*d^2*e)*g + 2*(c*d*e^2*f - (5*c*d^2*e - 2*b*d*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*(2*c*d*e - b*e^2)*g*x - (2*c*d*e - b*e^2)*f + 3*(2*c*d^2 - b*d*e)*g)*sqrt(e*x + d))/(2*c*d^3*e^2 - b*d^2*e^3 + (2*c*d*e^4 - b*e^5)*x^2 + 2*(2*c*d^2*e^3 - b*d*e^4)*x), ((c*d^2*e*f + (c*e^3*f - (5*c*d*e^2 - 2*b*e^3)*g)*x^2 - (5*c*d^3 - 2*b*d^2*e)*g + 2*(c*d*e^2*f - (5*c*d^2*e - 2*b*d*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*(2*c*d*e - b*e^2)*g*x - (2*c*d*e - b*e^2)*f + 3*(2*c*d^2 - b*d*e)*g)*sqrt(e*x + d))/(2*c*d^3*e^2 - b*d^2*e^3 + (2*c*d*e^4 - b*e^5)*x^2 + 2*(2*c*d^2*e^3 - b*d*e^4)*x)]","A",0
2237,1,1043,0,0.567131," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[\frac{{\left(c^{2} d^{3} e f + {\left(c^{2} e^{4} f + {\left(7 \, c^{2} d e^{3} - 4 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(c^{2} d e^{3} f + {\left(7 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3}\right)} g\right)} x^{2} + {\left(7 \, c^{2} d^{4} - 4 \, b c d^{3} e\right)} g + 3 \, {\left(c^{2} d^{2} e^{2} f + {\left(7 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(6 \, c^{2} d^{2} e - 7 \, b c d e^{2} + 2 \, b^{2} e^{3}\right)} f + {\left(10 \, c^{2} d^{3} - 9 \, b c d^{2} e + 2 \, b^{2} d e^{2}\right)} g - {\left({\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f - {\left(18 \, c^{2} d^{2} e - 17 \, b c d e^{2} + 4 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(4 \, c^{2} d^{5} e^{2} - 4 \, b c d^{4} e^{3} + b^{2} d^{3} e^{4} + {\left(4 \, c^{2} d^{2} e^{5} - 4 \, b c d e^{6} + b^{2} e^{7}\right)} x^{3} + 3 \, {\left(4 \, c^{2} d^{3} e^{4} - 4 \, b c d^{2} e^{5} + b^{2} d e^{6}\right)} x^{2} + 3 \, {\left(4 \, c^{2} d^{4} e^{3} - 4 \, b c d^{3} e^{4} + b^{2} d^{2} e^{5}\right)} x\right)}}, \frac{{\left(c^{2} d^{3} e f + {\left(c^{2} e^{4} f + {\left(7 \, c^{2} d e^{3} - 4 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(c^{2} d e^{3} f + {\left(7 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3}\right)} g\right)} x^{2} + {\left(7 \, c^{2} d^{4} - 4 \, b c d^{3} e\right)} g + 3 \, {\left(c^{2} d^{2} e^{2} f + {\left(7 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) - \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(6 \, c^{2} d^{2} e - 7 \, b c d e^{2} + 2 \, b^{2} e^{3}\right)} f + {\left(10 \, c^{2} d^{3} - 9 \, b c d^{2} e + 2 \, b^{2} d e^{2}\right)} g - {\left({\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f - {\left(18 \, c^{2} d^{2} e - 17 \, b c d e^{2} + 4 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(4 \, c^{2} d^{5} e^{2} - 4 \, b c d^{4} e^{3} + b^{2} d^{3} e^{4} + {\left(4 \, c^{2} d^{2} e^{5} - 4 \, b c d e^{6} + b^{2} e^{7}\right)} x^{3} + 3 \, {\left(4 \, c^{2} d^{3} e^{4} - 4 \, b c d^{2} e^{5} + b^{2} d e^{6}\right)} x^{2} + 3 \, {\left(4 \, c^{2} d^{4} e^{3} - 4 \, b c d^{3} e^{4} + b^{2} d^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[1/8*((c^2*d^3*e*f + (c^2*e^4*f + (7*c^2*d*e^3 - 4*b*c*e^4)*g)*x^3 + 3*(c^2*d*e^3*f + (7*c^2*d^2*e^2 - 4*b*c*d*e^3)*g)*x^2 + (7*c^2*d^4 - 4*b*c*d^3*e)*g + 3*(c^2*d^2*e^2*f + (7*c^2*d^3*e - 4*b*c*d^2*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((6*c^2*d^2*e - 7*b*c*d*e^2 + 2*b^2*e^3)*f + (10*c^2*d^3 - 9*b*c*d^2*e + 2*b^2*d*e^2)*g - ((2*c^2*d*e^2 - b*c*e^3)*f - (18*c^2*d^2*e - 17*b*c*d*e^2 + 4*b^2*e^3)*g)*x)*sqrt(e*x + d))/(4*c^2*d^5*e^2 - 4*b*c*d^4*e^3 + b^2*d^3*e^4 + (4*c^2*d^2*e^5 - 4*b*c*d*e^6 + b^2*e^7)*x^3 + 3*(4*c^2*d^3*e^4 - 4*b*c*d^2*e^5 + b^2*d*e^6)*x^2 + 3*(4*c^2*d^4*e^3 - 4*b*c*d^3*e^4 + b^2*d^2*e^5)*x), 1/4*((c^2*d^3*e*f + (c^2*e^4*f + (7*c^2*d*e^3 - 4*b*c*e^4)*g)*x^3 + 3*(c^2*d*e^3*f + (7*c^2*d^2*e^2 - 4*b*c*d*e^3)*g)*x^2 + (7*c^2*d^4 - 4*b*c*d^3*e)*g + 3*(c^2*d^2*e^2*f + (7*c^2*d^3*e - 4*b*c*d^2*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) - sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((6*c^2*d^2*e - 7*b*c*d*e^2 + 2*b^2*e^3)*f + (10*c^2*d^3 - 9*b*c*d^2*e + 2*b^2*d*e^2)*g - ((2*c^2*d*e^2 - b*c*e^3)*f - (18*c^2*d^2*e - 17*b*c*d*e^2 + 4*b^2*e^3)*g)*x)*sqrt(e*x + d))/(4*c^2*d^5*e^2 - 4*b*c*d^4*e^3 + b^2*d^3*e^4 + (4*c^2*d^2*e^5 - 4*b*c*d*e^6 + b^2*e^7)*x^3 + 3*(4*c^2*d^3*e^4 - 4*b*c*d^2*e^5 + b^2*d*e^6)*x^2 + 3*(4*c^2*d^4*e^3 - 4*b*c*d^3*e^4 + b^2*d^2*e^5)*x)]","B",0
2238,1,1604,0,0.454161," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{3} d^{4} e f + {\left(c^{3} e^{5} f + {\left(3 \, c^{3} d e^{4} - 2 \, b c^{2} e^{5}\right)} g\right)} x^{4} + 4 \, {\left(c^{3} d e^{4} f + {\left(3 \, c^{3} d^{2} e^{3} - 2 \, b c^{2} d e^{4}\right)} g\right)} x^{3} + 6 \, {\left(c^{3} d^{2} e^{3} f + {\left(3 \, c^{3} d^{3} e^{2} - 2 \, b c^{2} d^{2} e^{3}\right)} g\right)} x^{2} + {\left(3 \, c^{3} d^{5} - 2 \, b c^{2} d^{4} e\right)} g + 4 \, {\left(c^{3} d^{3} e^{2} f + {\left(3 \, c^{3} d^{4} e - 2 \, b c^{2} d^{3} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left({\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f + {\left(6 \, c^{3} d^{2} e^{2} - 7 \, b c^{2} d e^{3} + 2 \, b^{2} c e^{4}\right)} g\right)} x^{2} - {\left(50 \, c^{3} d^{3} e - 85 \, b c^{2} d^{2} e^{2} + 46 \, b^{2} c d e^{3} - 8 \, b^{3} e^{4}\right)} f - {\left(22 \, c^{3} d^{4} - 35 \, b c^{2} d^{3} e + 20 \, b^{2} c d^{2} e^{2} - 4 \, b^{3} d e^{3}\right)} g + 2 \, {\left({\left(10 \, c^{3} d^{2} e^{2} - 7 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} f - {\left(34 \, c^{3} d^{3} e - 55 \, b c^{2} d^{2} e^{2} + 31 \, b^{2} c d e^{3} - 6 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(8 \, c^{3} d^{7} e^{2} - 12 \, b c^{2} d^{6} e^{3} + 6 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5} + {\left(8 \, c^{3} d^{3} e^{6} - 12 \, b c^{2} d^{2} e^{7} + 6 \, b^{2} c d e^{8} - b^{3} e^{9}\right)} x^{4} + 4 \, {\left(8 \, c^{3} d^{4} e^{5} - 12 \, b c^{2} d^{3} e^{6} + 6 \, b^{2} c d^{2} e^{7} - b^{3} d e^{8}\right)} x^{3} + 6 \, {\left(8 \, c^{3} d^{5} e^{4} - 12 \, b c^{2} d^{4} e^{5} + 6 \, b^{2} c d^{3} e^{6} - b^{3} d^{2} e^{7}\right)} x^{2} + 4 \, {\left(8 \, c^{3} d^{6} e^{3} - 12 \, b c^{2} d^{5} e^{4} + 6 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x\right)}}, \frac{3 \, {\left(c^{3} d^{4} e f + {\left(c^{3} e^{5} f + {\left(3 \, c^{3} d e^{4} - 2 \, b c^{2} e^{5}\right)} g\right)} x^{4} + 4 \, {\left(c^{3} d e^{4} f + {\left(3 \, c^{3} d^{2} e^{3} - 2 \, b c^{2} d e^{4}\right)} g\right)} x^{3} + 6 \, {\left(c^{3} d^{2} e^{3} f + {\left(3 \, c^{3} d^{3} e^{2} - 2 \, b c^{2} d^{2} e^{3}\right)} g\right)} x^{2} + {\left(3 \, c^{3} d^{5} - 2 \, b c^{2} d^{4} e\right)} g + 4 \, {\left(c^{3} d^{3} e^{2} f + {\left(3 \, c^{3} d^{4} e - 2 \, b c^{2} d^{3} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left({\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f + {\left(6 \, c^{3} d^{2} e^{2} - 7 \, b c^{2} d e^{3} + 2 \, b^{2} c e^{4}\right)} g\right)} x^{2} - {\left(50 \, c^{3} d^{3} e - 85 \, b c^{2} d^{2} e^{2} + 46 \, b^{2} c d e^{3} - 8 \, b^{3} e^{4}\right)} f - {\left(22 \, c^{3} d^{4} - 35 \, b c^{2} d^{3} e + 20 \, b^{2} c d^{2} e^{2} - 4 \, b^{3} d e^{3}\right)} g + 2 \, {\left({\left(10 \, c^{3} d^{2} e^{2} - 7 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} f - {\left(34 \, c^{3} d^{3} e - 55 \, b c^{2} d^{2} e^{2} + 31 \, b^{2} c d e^{3} - 6 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(8 \, c^{3} d^{7} e^{2} - 12 \, b c^{2} d^{6} e^{3} + 6 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5} + {\left(8 \, c^{3} d^{3} e^{6} - 12 \, b c^{2} d^{2} e^{7} + 6 \, b^{2} c d e^{8} - b^{3} e^{9}\right)} x^{4} + 4 \, {\left(8 \, c^{3} d^{4} e^{5} - 12 \, b c^{2} d^{3} e^{6} + 6 \, b^{2} c d^{2} e^{7} - b^{3} d e^{8}\right)} x^{3} + 6 \, {\left(8 \, c^{3} d^{5} e^{4} - 12 \, b c^{2} d^{4} e^{5} + 6 \, b^{2} c d^{3} e^{6} - b^{3} d^{2} e^{7}\right)} x^{2} + 4 \, {\left(8 \, c^{3} d^{6} e^{3} - 12 \, b c^{2} d^{5} e^{4} + 6 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(c^3*d^4*e*f + (c^3*e^5*f + (3*c^3*d*e^4 - 2*b*c^2*e^5)*g)*x^4 + 4*(c^3*d*e^4*f + (3*c^3*d^2*e^3 - 2*b*c^2*d*e^4)*g)*x^3 + 6*(c^3*d^2*e^3*f + (3*c^3*d^3*e^2 - 2*b*c^2*d^2*e^3)*g)*x^2 + (3*c^3*d^5 - 2*b*c^2*d^4*e)*g + 4*(c^3*d^3*e^2*f + (3*c^3*d^4*e - 2*b*c^2*d^3*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*((2*c^3*d*e^3 - b*c^2*e^4)*f + (6*c^3*d^2*e^2 - 7*b*c^2*d*e^3 + 2*b^2*c*e^4)*g)*x^2 - (50*c^3*d^3*e - 85*b*c^2*d^2*e^2 + 46*b^2*c*d*e^3 - 8*b^3*e^4)*f - (22*c^3*d^4 - 35*b*c^2*d^3*e + 20*b^2*c*d^2*e^2 - 4*b^3*d*e^3)*g + 2*((10*c^3*d^2*e^2 - 7*b*c^2*d*e^3 + b^2*c*e^4)*f - (34*c^3*d^3*e - 55*b*c^2*d^2*e^2 + 31*b^2*c*d*e^3 - 6*b^3*e^4)*g)*x)*sqrt(e*x + d))/(8*c^3*d^7*e^2 - 12*b*c^2*d^6*e^3 + 6*b^2*c*d^5*e^4 - b^3*d^4*e^5 + (8*c^3*d^3*e^6 - 12*b*c^2*d^2*e^7 + 6*b^2*c*d*e^8 - b^3*e^9)*x^4 + 4*(8*c^3*d^4*e^5 - 12*b*c^2*d^3*e^6 + 6*b^2*c*d^2*e^7 - b^3*d*e^8)*x^3 + 6*(8*c^3*d^5*e^4 - 12*b*c^2*d^4*e^5 + 6*b^2*c*d^3*e^6 - b^3*d^2*e^7)*x^2 + 4*(8*c^3*d^6*e^3 - 12*b*c^2*d^5*e^4 + 6*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x), 1/24*(3*(c^3*d^4*e*f + (c^3*e^5*f + (3*c^3*d*e^4 - 2*b*c^2*e^5)*g)*x^4 + 4*(c^3*d*e^4*f + (3*c^3*d^2*e^3 - 2*b*c^2*d*e^4)*g)*x^3 + 6*(c^3*d^2*e^3*f + (3*c^3*d^3*e^2 - 2*b*c^2*d^2*e^3)*g)*x^2 + (3*c^3*d^5 - 2*b*c^2*d^4*e)*g + 4*(c^3*d^3*e^2*f + (3*c^3*d^4*e - 2*b*c^2*d^3*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*((2*c^3*d*e^3 - b*c^2*e^4)*f + (6*c^3*d^2*e^2 - 7*b*c^2*d*e^3 + 2*b^2*c*e^4)*g)*x^2 - (50*c^3*d^3*e - 85*b*c^2*d^2*e^2 + 46*b^2*c*d*e^3 - 8*b^3*e^4)*f - (22*c^3*d^4 - 35*b*c^2*d^3*e + 20*b^2*c*d^2*e^2 - 4*b^3*d*e^3)*g + 2*((10*c^3*d^2*e^2 - 7*b*c^2*d*e^3 + b^2*c*e^4)*f - (34*c^3*d^3*e - 55*b*c^2*d^2*e^2 + 31*b^2*c*d*e^3 - 6*b^3*e^4)*g)*x)*sqrt(e*x + d))/(8*c^3*d^7*e^2 - 12*b*c^2*d^6*e^3 + 6*b^2*c*d^5*e^4 - b^3*d^4*e^5 + (8*c^3*d^3*e^6 - 12*b*c^2*d^2*e^7 + 6*b^2*c*d*e^8 - b^3*e^9)*x^4 + 4*(8*c^3*d^4*e^5 - 12*b*c^2*d^3*e^6 + 6*b^2*c*d^2*e^7 - b^3*d*e^8)*x^3 + 6*(8*c^3*d^5*e^4 - 12*b*c^2*d^4*e^5 + 6*b^2*c*d^3*e^6 - b^3*d^2*e^7)*x^2 + 4*(8*c^3*d^6*e^3 - 12*b*c^2*d^5*e^4 + 6*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x)]","B",0
2239,1,2256,0,0.506644," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, c^{4} d^{5} e f + {\left(5 \, c^{4} e^{6} f + {\left(11 \, c^{4} d e^{5} - 8 \, b c^{3} e^{6}\right)} g\right)} x^{5} + 5 \, {\left(5 \, c^{4} d e^{5} f + {\left(11 \, c^{4} d^{2} e^{4} - 8 \, b c^{3} d e^{5}\right)} g\right)} x^{4} + 10 \, {\left(5 \, c^{4} d^{2} e^{4} f + {\left(11 \, c^{4} d^{3} e^{3} - 8 \, b c^{3} d^{2} e^{4}\right)} g\right)} x^{3} + 10 \, {\left(5 \, c^{4} d^{3} e^{3} f + {\left(11 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3}\right)} g\right)} x^{2} + {\left(11 \, c^{4} d^{6} - 8 \, b c^{3} d^{5} e\right)} g + 5 \, {\left(5 \, c^{4} d^{4} e^{2} f + {\left(11 \, c^{4} d^{5} e - 8 \, b c^{3} d^{4} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(5 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f + {\left(22 \, c^{4} d^{2} e^{3} - 27 \, b c^{3} d e^{4} + 8 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} + {\left(5 \, {\left(26 \, c^{4} d^{2} e^{3} - 17 \, b c^{3} d e^{4} + 2 \, b^{2} c^{2} e^{5}\right)} f + {\left(286 \, c^{4} d^{3} e^{2} - 395 \, b c^{3} d^{2} e^{3} + 158 \, b^{2} c^{2} d e^{4} - 16 \, b^{3} c e^{5}\right)} g\right)} x^{2} - {\left(634 \, c^{4} d^{4} e - 1385 \, b c^{3} d^{3} e^{2} + 1094 \, b^{2} c^{2} d^{2} e^{3} - 376 \, b^{3} c d e^{4} + 48 \, b^{4} e^{5}\right)} f - {\left(166 \, c^{4} d^{5} - 375 \, b c^{3} d^{4} e + 322 \, b^{2} c^{2} d^{3} e^{2} - 120 \, b^{3} c d^{2} e^{3} + 16 \, b^{4} d e^{4}\right)} g + {\left({\left(234 \, c^{4} d^{3} e^{2} - 221 \, b c^{3} d^{2} e^{3} + 68 \, b^{2} c^{2} d e^{4} - 8 \, b^{3} c e^{5}\right)} f - {\left(714 \, c^{4} d^{4} e - 1597 \, b c^{3} d^{3} e^{2} + 1340 \, b^{2} c^{2} d^{2} e^{3} - 488 \, b^{3} c d e^{4} + 64 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(16 \, c^{4} d^{9} e^{2} - 32 \, b c^{3} d^{8} e^{3} + 24 \, b^{2} c^{2} d^{7} e^{4} - 8 \, b^{3} c d^{6} e^{5} + b^{4} d^{5} e^{6} + {\left(16 \, c^{4} d^{4} e^{7} - 32 \, b c^{3} d^{3} e^{8} + 24 \, b^{2} c^{2} d^{2} e^{9} - 8 \, b^{3} c d e^{10} + b^{4} e^{11}\right)} x^{5} + 5 \, {\left(16 \, c^{4} d^{5} e^{6} - 32 \, b c^{3} d^{4} e^{7} + 24 \, b^{2} c^{2} d^{3} e^{8} - 8 \, b^{3} c d^{2} e^{9} + b^{4} d e^{10}\right)} x^{4} + 10 \, {\left(16 \, c^{4} d^{6} e^{5} - 32 \, b c^{3} d^{5} e^{6} + 24 \, b^{2} c^{2} d^{4} e^{7} - 8 \, b^{3} c d^{3} e^{8} + b^{4} d^{2} e^{9}\right)} x^{3} + 10 \, {\left(16 \, c^{4} d^{7} e^{4} - 32 \, b c^{3} d^{6} e^{5} + 24 \, b^{2} c^{2} d^{5} e^{6} - 8 \, b^{3} c d^{4} e^{7} + b^{4} d^{3} e^{8}\right)} x^{2} + 5 \, {\left(16 \, c^{4} d^{8} e^{3} - 32 \, b c^{3} d^{7} e^{4} + 24 \, b^{2} c^{2} d^{6} e^{5} - 8 \, b^{3} c d^{5} e^{6} + b^{4} d^{4} e^{7}\right)} x\right)}}, \frac{3 \, {\left(5 \, c^{4} d^{5} e f + {\left(5 \, c^{4} e^{6} f + {\left(11 \, c^{4} d e^{5} - 8 \, b c^{3} e^{6}\right)} g\right)} x^{5} + 5 \, {\left(5 \, c^{4} d e^{5} f + {\left(11 \, c^{4} d^{2} e^{4} - 8 \, b c^{3} d e^{5}\right)} g\right)} x^{4} + 10 \, {\left(5 \, c^{4} d^{2} e^{4} f + {\left(11 \, c^{4} d^{3} e^{3} - 8 \, b c^{3} d^{2} e^{4}\right)} g\right)} x^{3} + 10 \, {\left(5 \, c^{4} d^{3} e^{3} f + {\left(11 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3}\right)} g\right)} x^{2} + {\left(11 \, c^{4} d^{6} - 8 \, b c^{3} d^{5} e\right)} g + 5 \, {\left(5 \, c^{4} d^{4} e^{2} f + {\left(11 \, c^{4} d^{5} e - 8 \, b c^{3} d^{4} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(5 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f + {\left(22 \, c^{4} d^{2} e^{3} - 27 \, b c^{3} d e^{4} + 8 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} + {\left(5 \, {\left(26 \, c^{4} d^{2} e^{3} - 17 \, b c^{3} d e^{4} + 2 \, b^{2} c^{2} e^{5}\right)} f + {\left(286 \, c^{4} d^{3} e^{2} - 395 \, b c^{3} d^{2} e^{3} + 158 \, b^{2} c^{2} d e^{4} - 16 \, b^{3} c e^{5}\right)} g\right)} x^{2} - {\left(634 \, c^{4} d^{4} e - 1385 \, b c^{3} d^{3} e^{2} + 1094 \, b^{2} c^{2} d^{2} e^{3} - 376 \, b^{3} c d e^{4} + 48 \, b^{4} e^{5}\right)} f - {\left(166 \, c^{4} d^{5} - 375 \, b c^{3} d^{4} e + 322 \, b^{2} c^{2} d^{3} e^{2} - 120 \, b^{3} c d^{2} e^{3} + 16 \, b^{4} d e^{4}\right)} g + {\left({\left(234 \, c^{4} d^{3} e^{2} - 221 \, b c^{3} d^{2} e^{3} + 68 \, b^{2} c^{2} d e^{4} - 8 \, b^{3} c e^{5}\right)} f - {\left(714 \, c^{4} d^{4} e - 1597 \, b c^{3} d^{3} e^{2} + 1340 \, b^{2} c^{2} d^{2} e^{3} - 488 \, b^{3} c d e^{4} + 64 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(16 \, c^{4} d^{9} e^{2} - 32 \, b c^{3} d^{8} e^{3} + 24 \, b^{2} c^{2} d^{7} e^{4} - 8 \, b^{3} c d^{6} e^{5} + b^{4} d^{5} e^{6} + {\left(16 \, c^{4} d^{4} e^{7} - 32 \, b c^{3} d^{3} e^{8} + 24 \, b^{2} c^{2} d^{2} e^{9} - 8 \, b^{3} c d e^{10} + b^{4} e^{11}\right)} x^{5} + 5 \, {\left(16 \, c^{4} d^{5} e^{6} - 32 \, b c^{3} d^{4} e^{7} + 24 \, b^{2} c^{2} d^{3} e^{8} - 8 \, b^{3} c d^{2} e^{9} + b^{4} d e^{10}\right)} x^{4} + 10 \, {\left(16 \, c^{4} d^{6} e^{5} - 32 \, b c^{3} d^{5} e^{6} + 24 \, b^{2} c^{2} d^{4} e^{7} - 8 \, b^{3} c d^{3} e^{8} + b^{4} d^{2} e^{9}\right)} x^{3} + 10 \, {\left(16 \, c^{4} d^{7} e^{4} - 32 \, b c^{3} d^{6} e^{5} + 24 \, b^{2} c^{2} d^{5} e^{6} - 8 \, b^{3} c d^{4} e^{7} + b^{4} d^{3} e^{8}\right)} x^{2} + 5 \, {\left(16 \, c^{4} d^{8} e^{3} - 32 \, b c^{3} d^{7} e^{4} + 24 \, b^{2} c^{2} d^{6} e^{5} - 8 \, b^{3} c d^{5} e^{6} + b^{4} d^{4} e^{7}\right)} x\right)}}\right]"," ",0,"[1/384*(3*(5*c^4*d^5*e*f + (5*c^4*e^6*f + (11*c^4*d*e^5 - 8*b*c^3*e^6)*g)*x^5 + 5*(5*c^4*d*e^5*f + (11*c^4*d^2*e^4 - 8*b*c^3*d*e^5)*g)*x^4 + 10*(5*c^4*d^2*e^4*f + (11*c^4*d^3*e^3 - 8*b*c^3*d^2*e^4)*g)*x^3 + 10*(5*c^4*d^3*e^3*f + (11*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3)*g)*x^2 + (11*c^4*d^6 - 8*b*c^3*d^5*e)*g + 5*(5*c^4*d^4*e^2*f + (11*c^4*d^5*e - 8*b*c^3*d^4*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(5*(2*c^4*d*e^4 - b*c^3*e^5)*f + (22*c^4*d^2*e^3 - 27*b*c^3*d*e^4 + 8*b^2*c^2*e^5)*g)*x^3 + (5*(26*c^4*d^2*e^3 - 17*b*c^3*d*e^4 + 2*b^2*c^2*e^5)*f + (286*c^4*d^3*e^2 - 395*b*c^3*d^2*e^3 + 158*b^2*c^2*d*e^4 - 16*b^3*c*e^5)*g)*x^2 - (634*c^4*d^4*e - 1385*b*c^3*d^3*e^2 + 1094*b^2*c^2*d^2*e^3 - 376*b^3*c*d*e^4 + 48*b^4*e^5)*f - (166*c^4*d^5 - 375*b*c^3*d^4*e + 322*b^2*c^2*d^3*e^2 - 120*b^3*c*d^2*e^3 + 16*b^4*d*e^4)*g + ((234*c^4*d^3*e^2 - 221*b*c^3*d^2*e^3 + 68*b^2*c^2*d*e^4 - 8*b^3*c*e^5)*f - (714*c^4*d^4*e - 1597*b*c^3*d^3*e^2 + 1340*b^2*c^2*d^2*e^3 - 488*b^3*c*d*e^4 + 64*b^4*e^5)*g)*x)*sqrt(e*x + d))/(16*c^4*d^9*e^2 - 32*b*c^3*d^8*e^3 + 24*b^2*c^2*d^7*e^4 - 8*b^3*c*d^6*e^5 + b^4*d^5*e^6 + (16*c^4*d^4*e^7 - 32*b*c^3*d^3*e^8 + 24*b^2*c^2*d^2*e^9 - 8*b^3*c*d*e^10 + b^4*e^11)*x^5 + 5*(16*c^4*d^5*e^6 - 32*b*c^3*d^4*e^7 + 24*b^2*c^2*d^3*e^8 - 8*b^3*c*d^2*e^9 + b^4*d*e^10)*x^4 + 10*(16*c^4*d^6*e^5 - 32*b*c^3*d^5*e^6 + 24*b^2*c^2*d^4*e^7 - 8*b^3*c*d^3*e^8 + b^4*d^2*e^9)*x^3 + 10*(16*c^4*d^7*e^4 - 32*b*c^3*d^6*e^5 + 24*b^2*c^2*d^5*e^6 - 8*b^3*c*d^4*e^7 + b^4*d^3*e^8)*x^2 + 5*(16*c^4*d^8*e^3 - 32*b*c^3*d^7*e^4 + 24*b^2*c^2*d^6*e^5 - 8*b^3*c*d^5*e^6 + b^4*d^4*e^7)*x), 1/192*(3*(5*c^4*d^5*e*f + (5*c^4*e^6*f + (11*c^4*d*e^5 - 8*b*c^3*e^6)*g)*x^5 + 5*(5*c^4*d*e^5*f + (11*c^4*d^2*e^4 - 8*b*c^3*d*e^5)*g)*x^4 + 10*(5*c^4*d^2*e^4*f + (11*c^4*d^3*e^3 - 8*b*c^3*d^2*e^4)*g)*x^3 + 10*(5*c^4*d^3*e^3*f + (11*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3)*g)*x^2 + (11*c^4*d^6 - 8*b*c^3*d^5*e)*g + 5*(5*c^4*d^4*e^2*f + (11*c^4*d^5*e - 8*b*c^3*d^4*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(5*(2*c^4*d*e^4 - b*c^3*e^5)*f + (22*c^4*d^2*e^3 - 27*b*c^3*d*e^4 + 8*b^2*c^2*e^5)*g)*x^3 + (5*(26*c^4*d^2*e^3 - 17*b*c^3*d*e^4 + 2*b^2*c^2*e^5)*f + (286*c^4*d^3*e^2 - 395*b*c^3*d^2*e^3 + 158*b^2*c^2*d*e^4 - 16*b^3*c*e^5)*g)*x^2 - (634*c^4*d^4*e - 1385*b*c^3*d^3*e^2 + 1094*b^2*c^2*d^2*e^3 - 376*b^3*c*d*e^4 + 48*b^4*e^5)*f - (166*c^4*d^5 - 375*b*c^3*d^4*e + 322*b^2*c^2*d^3*e^2 - 120*b^3*c*d^2*e^3 + 16*b^4*d*e^4)*g + ((234*c^4*d^3*e^2 - 221*b*c^3*d^2*e^3 + 68*b^2*c^2*d*e^4 - 8*b^3*c*e^5)*f - (714*c^4*d^4*e - 1597*b*c^3*d^3*e^2 + 1340*b^2*c^2*d^2*e^3 - 488*b^3*c*d*e^4 + 64*b^4*e^5)*g)*x)*sqrt(e*x + d))/(16*c^4*d^9*e^2 - 32*b*c^3*d^8*e^3 + 24*b^2*c^2*d^7*e^4 - 8*b^3*c*d^6*e^5 + b^4*d^5*e^6 + (16*c^4*d^4*e^7 - 32*b*c^3*d^3*e^8 + 24*b^2*c^2*d^2*e^9 - 8*b^3*c*d*e^10 + b^4*e^11)*x^5 + 5*(16*c^4*d^5*e^6 - 32*b*c^3*d^4*e^7 + 24*b^2*c^2*d^3*e^8 - 8*b^3*c*d^2*e^9 + b^4*d*e^10)*x^4 + 10*(16*c^4*d^6*e^5 - 32*b*c^3*d^5*e^6 + 24*b^2*c^2*d^4*e^7 - 8*b^3*c*d^3*e^8 + b^4*d^2*e^9)*x^3 + 10*(16*c^4*d^7*e^4 - 32*b*c^3*d^6*e^5 + 24*b^2*c^2*d^5*e^6 - 8*b^3*c*d^4*e^7 + b^4*d^3*e^8)*x^2 + 5*(16*c^4*d^8*e^3 - 32*b*c^3*d^7*e^4 + 24*b^2*c^2*d^6*e^5 - 8*b^3*c*d^5*e^6 + b^4*d^4*e^7)*x)]","B",0
2240,1,880,0,0.449148," ","integrate((e*x+d)^(5/2)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3003 \, c^{7} e^{7} g x^{7} + 231 \, {\left(15 \, c^{7} e^{7} f + 4 \, {\left(11 \, c^{7} d e^{6} + 4 \, b c^{6} e^{7}\right)} g\right)} x^{6} + 63 \, {\left(10 \, {\left(19 \, c^{7} d e^{6} + 7 \, b c^{6} e^{7}\right)} f + {\left(111 \, c^{7} d^{2} e^{5} + 278 \, b c^{6} d e^{6} + b^{2} c^{5} e^{7}\right)} g\right)} x^{5} + 35 \, {\left(3 \, {\left(79 \, c^{7} d^{2} e^{5} + 206 \, b c^{6} d e^{6} + b^{2} c^{5} e^{7}\right)} f - 2 \, {\left(175 \, c^{7} d^{3} e^{4} - 453 \, b c^{6} d^{2} e^{5} - 9 \, b^{2} c^{5} d e^{6} + b^{3} c^{4} e^{7}\right)} g\right)} x^{4} - 5 \, {\left(12 \, {\left(271 \, c^{7} d^{3} e^{4} - 683 \, b c^{6} d^{2} e^{5} - 19 \, b^{2} c^{5} d e^{6} + 2 \, b^{3} c^{4} e^{7}\right)} f + {\left(4087 \, c^{7} d^{4} e^{3} - 4900 \, b c^{6} d^{3} e^{4} - 618 \, b^{2} c^{5} d^{2} e^{5} + 160 \, b^{3} c^{4} d e^{6} - 16 \, b^{4} c^{3} e^{7}\right)} g\right)} x^{3} - 3 \, {\left(3 \, {\left(3169 \, c^{7} d^{4} e^{3} - 3628 \, b c^{6} d^{3} e^{4} - 694 \, b^{2} c^{5} d^{2} e^{5} + 168 \, b^{3} c^{4} d e^{6} - 16 \, b^{4} c^{3} e^{7}\right)} f + 4 \, {\left(542 \, c^{7} d^{5} e^{2} + 11 \, b c^{6} d^{4} e^{3} - 862 \, b^{2} c^{5} d^{3} e^{4} + 389 \, b^{3} c^{4} d^{2} e^{5} - 88 \, b^{4} c^{3} d e^{6} + 8 \, b^{5} c^{2} e^{7}\right)} g\right)} x^{2} + 3 \, {\left(9683 \, c^{7} d^{6} e - 30382 \, b c^{6} d^{5} e^{2} + 37267 \, b^{2} c^{5} d^{4} e^{3} - 23464 \, b^{3} c^{4} d^{3} e^{4} + 8368 \, b^{4} c^{3} d^{2} e^{5} - 1600 \, b^{5} c^{2} d e^{6} + 128 \, b^{6} c e^{7}\right)} f + 2 \, {\left(6343 \, c^{7} d^{7} - 27877 \, b c^{6} d^{6} e + 50517 \, b^{2} c^{5} d^{5} e^{2} - 48999 \, b^{3} c^{4} d^{4} e^{3} + 27648 \, b^{4} c^{3} d^{3} e^{4} - 9168 \, b^{5} c^{2} d^{2} e^{5} + 1664 \, b^{6} c d e^{6} - 128 \, b^{7} e^{7}\right)} g - {\left(6 \, {\left(1333 \, c^{7} d^{5} e^{2} + 1421 \, b c^{6} d^{4} e^{3} - 4142 \, b^{2} c^{5} d^{3} e^{4} + 1724 \, b^{3} c^{4} d^{2} e^{5} - 368 \, b^{4} c^{3} d e^{6} + 32 \, b^{5} c^{2} e^{7}\right)} f - {\left(6343 \, c^{7} d^{6} e - 21534 \, b c^{6} d^{5} e^{2} + 28983 \, b^{2} c^{5} d^{4} e^{3} - 20016 \, b^{3} c^{4} d^{3} e^{4} + 7632 \, b^{4} c^{3} d^{2} e^{5} - 1536 \, b^{5} c^{2} d e^{6} + 128 \, b^{6} c e^{7}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{45045 \, {\left(c^{6} e^{3} x + c^{6} d e^{2}\right)}}"," ",0,"-2/45045*(3003*c^7*e^7*g*x^7 + 231*(15*c^7*e^7*f + 4*(11*c^7*d*e^6 + 4*b*c^6*e^7)*g)*x^6 + 63*(10*(19*c^7*d*e^6 + 7*b*c^6*e^7)*f + (111*c^7*d^2*e^5 + 278*b*c^6*d*e^6 + b^2*c^5*e^7)*g)*x^5 + 35*(3*(79*c^7*d^2*e^5 + 206*b*c^6*d*e^6 + b^2*c^5*e^7)*f - 2*(175*c^7*d^3*e^4 - 453*b*c^6*d^2*e^5 - 9*b^2*c^5*d*e^6 + b^3*c^4*e^7)*g)*x^4 - 5*(12*(271*c^7*d^3*e^4 - 683*b*c^6*d^2*e^5 - 19*b^2*c^5*d*e^6 + 2*b^3*c^4*e^7)*f + (4087*c^7*d^4*e^3 - 4900*b*c^6*d^3*e^4 - 618*b^2*c^5*d^2*e^5 + 160*b^3*c^4*d*e^6 - 16*b^4*c^3*e^7)*g)*x^3 - 3*(3*(3169*c^7*d^4*e^3 - 3628*b*c^6*d^3*e^4 - 694*b^2*c^5*d^2*e^5 + 168*b^3*c^4*d*e^6 - 16*b^4*c^3*e^7)*f + 4*(542*c^7*d^5*e^2 + 11*b*c^6*d^4*e^3 - 862*b^2*c^5*d^3*e^4 + 389*b^3*c^4*d^2*e^5 - 88*b^4*c^3*d*e^6 + 8*b^5*c^2*e^7)*g)*x^2 + 3*(9683*c^7*d^6*e - 30382*b*c^6*d^5*e^2 + 37267*b^2*c^5*d^4*e^3 - 23464*b^3*c^4*d^3*e^4 + 8368*b^4*c^3*d^2*e^5 - 1600*b^5*c^2*d*e^6 + 128*b^6*c*e^7)*f + 2*(6343*c^7*d^7 - 27877*b*c^6*d^6*e + 50517*b^2*c^5*d^5*e^2 - 48999*b^3*c^4*d^4*e^3 + 27648*b^4*c^3*d^3*e^4 - 9168*b^5*c^2*d^2*e^5 + 1664*b^6*c*d*e^6 - 128*b^7*e^7)*g - (6*(1333*c^7*d^5*e^2 + 1421*b*c^6*d^4*e^3 - 4142*b^2*c^5*d^3*e^4 + 1724*b^3*c^4*d^2*e^5 - 368*b^4*c^3*d*e^6 + 32*b^5*c^2*e^7)*f - (6343*c^7*d^6*e - 21534*b*c^6*d^5*e^2 + 28983*b^2*c^5*d^4*e^3 - 20016*b^3*c^4*d^3*e^4 + 7632*b^4*c^3*d^2*e^5 - 1536*b^5*c^2*d*e^6 + 128*b^6*c*e^7)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^6*e^3*x + c^6*d*e^2)","B",0
2241,1,678,0,0.419721," ","integrate((e*x+d)^(3/2)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(1155 \, c^{6} e^{6} g x^{6} + 105 \, {\left(13 \, c^{6} e^{6} f + {\left(25 \, c^{6} d e^{5} + 14 \, b c^{5} e^{6}\right)} g\right)} x^{5} + 35 \, {\left(13 \, {\left(7 \, c^{6} d e^{5} + 4 \, b c^{5} e^{6}\right)} f - {\left(12 \, c^{6} d^{2} e^{4} - 154 \, b c^{5} d e^{5} - b^{2} c^{4} e^{6}\right)} g\right)} x^{4} - 5 \, {\left(13 \, {\left(10 \, c^{6} d^{2} e^{4} - 108 \, b c^{5} d e^{5} - b^{2} c^{4} e^{6}\right)} f + {\left(954 \, c^{6} d^{3} e^{3} - 1328 \, b c^{5} d^{2} e^{4} - 63 \, b^{2} c^{4} d e^{5} + 8 \, b^{3} c^{3} e^{6}\right)} g\right)} x^{3} - 3 \, {\left(13 \, {\left(174 \, c^{6} d^{3} e^{3} - 236 \, b c^{5} d^{2} e^{4} - 17 \, b^{2} c^{4} d e^{5} + 2 \, b^{3} c^{3} e^{6}\right)} f + {\left(907 \, c^{6} d^{4} e^{2} - 560 \, b c^{5} d^{3} e^{3} - 473 \, b^{2} c^{4} d^{2} e^{4} + 142 \, b^{3} c^{3} d e^{5} - 16 \, b^{4} c^{2} e^{6}\right)} g\right)} x^{2} + 13 \, {\left(533 \, c^{6} d^{5} e - 1488 \, b c^{5} d^{4} e^{2} + 1513 \, b^{2} c^{4} d^{3} e^{3} - 710 \, b^{3} c^{3} d^{2} e^{4} + 168 \, b^{4} c^{2} d e^{5} - 16 \, b^{5} c e^{6}\right)} f + 2 \, {\left(1377 \, c^{6} d^{6} - 5519 \, b c^{5} d^{5} e + 8799 \, b^{2} c^{4} d^{4} e^{2} - 7117 \, b^{3} c^{3} d^{3} e^{3} + 3092 \, b^{4} c^{2} d^{2} e^{4} - 696 \, b^{5} c d e^{5} + 64 \, b^{6} e^{6}\right)} g - {\left(13 \, {\left(311 \, c^{6} d^{4} e^{2} - 100 \, b c^{5} d^{3} e^{3} - 279 \, b^{2} c^{4} d^{2} e^{4} + 76 \, b^{3} c^{3} d e^{5} - 8 \, b^{4} c^{2} e^{6}\right)} f - {\left(1377 \, c^{6} d^{5} e - 4142 \, b c^{5} d^{4} e^{2} + 4657 \, b^{2} c^{4} d^{3} e^{3} - 2460 \, b^{3} c^{3} d^{2} e^{4} + 632 \, b^{4} c^{2} d e^{5} - 64 \, b^{5} c e^{6}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{15015 \, {\left(c^{5} e^{3} x + c^{5} d e^{2}\right)}}"," ",0,"-2/15015*(1155*c^6*e^6*g*x^6 + 105*(13*c^6*e^6*f + (25*c^6*d*e^5 + 14*b*c^5*e^6)*g)*x^5 + 35*(13*(7*c^6*d*e^5 + 4*b*c^5*e^6)*f - (12*c^6*d^2*e^4 - 154*b*c^5*d*e^5 - b^2*c^4*e^6)*g)*x^4 - 5*(13*(10*c^6*d^2*e^4 - 108*b*c^5*d*e^5 - b^2*c^4*e^6)*f + (954*c^6*d^3*e^3 - 1328*b*c^5*d^2*e^4 - 63*b^2*c^4*d*e^5 + 8*b^3*c^3*e^6)*g)*x^3 - 3*(13*(174*c^6*d^3*e^3 - 236*b*c^5*d^2*e^4 - 17*b^2*c^4*d*e^5 + 2*b^3*c^3*e^6)*f + (907*c^6*d^4*e^2 - 560*b*c^5*d^3*e^3 - 473*b^2*c^4*d^2*e^4 + 142*b^3*c^3*d*e^5 - 16*b^4*c^2*e^6)*g)*x^2 + 13*(533*c^6*d^5*e - 1488*b*c^5*d^4*e^2 + 1513*b^2*c^4*d^3*e^3 - 710*b^3*c^3*d^2*e^4 + 168*b^4*c^2*d*e^5 - 16*b^5*c*e^6)*f + 2*(1377*c^6*d^6 - 5519*b*c^5*d^5*e + 8799*b^2*c^4*d^4*e^2 - 7117*b^3*c^3*d^3*e^3 + 3092*b^4*c^2*d^2*e^4 - 696*b^5*c*d*e^5 + 64*b^6*e^6)*g - (13*(311*c^6*d^4*e^2 - 100*b*c^5*d^3*e^3 - 279*b^2*c^4*d^2*e^4 + 76*b^3*c^3*d*e^5 - 8*b^4*c^2*e^6)*f - (1377*c^6*d^5*e - 4142*b*c^5*d^4*e^2 + 4657*b^2*c^4*d^3*e^3 - 2460*b^3*c^3*d^2*e^4 + 632*b^4*c^2*d*e^5 - 64*b^5*c*e^6)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^5*e^3*x + c^5*d*e^2)","B",0
2242,1,505,0,0.420636," ","integrate((e*x+d)^(1/2)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, c^{5} e^{5} g x^{5} + 35 \, {\left(11 \, c^{5} e^{5} f + 2 \, {\left(5 \, c^{5} d e^{4} + 6 \, b c^{4} e^{5}\right)} g\right)} x^{4} + 5 \, {\left(22 \, {\left(4 \, c^{5} d e^{4} + 5 \, b c^{4} e^{5}\right)} f - {\left(118 \, c^{5} d^{2} e^{3} - 214 \, b c^{4} d e^{4} - 3 \, b^{2} c^{3} e^{5}\right)} g\right)} x^{3} - 3 \, {\left(11 \, {\left(26 \, c^{5} d^{2} e^{3} - 46 \, b c^{4} d e^{4} - b^{2} c^{3} e^{5}\right)} f + 2 \, {\left(118 \, c^{5} d^{3} e^{2} - 101 \, b c^{4} d^{2} e^{3} - 20 \, b^{2} c^{3} d e^{4} + 3 \, b^{3} c^{2} e^{5}\right)} g\right)} x^{2} + 11 \, {\left(107 \, c^{5} d^{4} e - 266 \, b c^{4} d^{3} e^{2} + 219 \, b^{2} c^{3} d^{2} e^{3} - 68 \, b^{3} c^{2} d e^{4} + 8 \, b^{4} c e^{5}\right)} f + 2 \, {\left(211 \, c^{5} d^{5} - 769 \, b c^{4} d^{4} e + 1065 \, b^{2} c^{3} d^{3} e^{2} - 691 \, b^{3} c^{2} d^{2} e^{3} + 208 \, b^{4} c d e^{4} - 24 \, b^{5} e^{5}\right)} g - {\left(22 \, {\left(52 \, c^{5} d^{3} e^{2} - 39 \, b c^{4} d^{2} e^{3} - 15 \, b^{2} c^{3} d e^{4} + 2 \, b^{3} c^{2} e^{5}\right)} f - {\left(211 \, c^{5} d^{4} e - 558 \, b c^{4} d^{3} e^{2} + 507 \, b^{2} c^{3} d^{2} e^{3} - 184 \, b^{3} c^{2} d e^{4} + 24 \, b^{4} c e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{3465 \, {\left(c^{4} e^{3} x + c^{4} d e^{2}\right)}}"," ",0,"-2/3465*(315*c^5*e^5*g*x^5 + 35*(11*c^5*e^5*f + 2*(5*c^5*d*e^4 + 6*b*c^4*e^5)*g)*x^4 + 5*(22*(4*c^5*d*e^4 + 5*b*c^4*e^5)*f - (118*c^5*d^2*e^3 - 214*b*c^4*d*e^4 - 3*b^2*c^3*e^5)*g)*x^3 - 3*(11*(26*c^5*d^2*e^3 - 46*b*c^4*d*e^4 - b^2*c^3*e^5)*f + 2*(118*c^5*d^3*e^2 - 101*b*c^4*d^2*e^3 - 20*b^2*c^3*d*e^4 + 3*b^3*c^2*e^5)*g)*x^2 + 11*(107*c^5*d^4*e - 266*b*c^4*d^3*e^2 + 219*b^2*c^3*d^2*e^3 - 68*b^3*c^2*d*e^4 + 8*b^4*c*e^5)*f + 2*(211*c^5*d^5 - 769*b*c^4*d^4*e + 1065*b^2*c^3*d^3*e^2 - 691*b^3*c^2*d^2*e^3 + 208*b^4*c*d*e^4 - 24*b^5*e^5)*g - (22*(52*c^5*d^3*e^2 - 39*b*c^4*d^2*e^3 - 15*b^2*c^3*d*e^4 + 2*b^3*c^2*e^5)*f - (211*c^5*d^4*e - 558*b*c^4*d^3*e^2 + 507*b^2*c^3*d^2*e^3 - 184*b^3*c^2*d*e^4 + 24*b^4*c*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^4*e^3*x + c^4*d*e^2)","B",0
2243,1,354,0,0.411403," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, c^{4} e^{4} g x^{4} + 5 \, {\left(9 \, c^{4} e^{4} f - {\left(c^{4} d e^{3} - 10 \, b c^{3} e^{4}\right)} g\right)} x^{3} - 3 \, {\left(3 \, {\left(c^{4} d e^{3} - 8 \, b c^{3} e^{4}\right)} f + {\left(23 \, c^{4} d^{2} e^{2} - 22 \, b c^{3} d e^{3} - b^{2} c^{2} e^{4}\right)} g\right)} x^{2} + 9 \, {\left(9 \, c^{4} d^{3} e - 20 \, b c^{3} d^{2} e^{2} + 13 \, b^{2} c^{2} d e^{3} - 2 \, b^{3} c e^{4}\right)} f + 2 \, {\left(13 \, c^{4} d^{4} - 43 \, b c^{3} d^{3} e + 51 \, b^{2} c^{2} d^{2} e^{2} - 25 \, b^{3} c d e^{3} + 4 \, b^{4} e^{4}\right)} g - {\left(9 \, {\left(13 \, c^{4} d^{2} e^{2} - 12 \, b c^{3} d e^{3} - b^{2} c^{2} e^{4}\right)} f - {\left(13 \, c^{4} d^{3} e - 30 \, b c^{3} d^{2} e^{2} + 21 \, b^{2} c^{2} d e^{3} - 4 \, b^{3} c e^{4}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{315 \, {\left(c^{3} e^{3} x + c^{3} d e^{2}\right)}}"," ",0,"-2/315*(35*c^4*e^4*g*x^4 + 5*(9*c^4*e^4*f - (c^4*d*e^3 - 10*b*c^3*e^4)*g)*x^3 - 3*(3*(c^4*d*e^3 - 8*b*c^3*e^4)*f + (23*c^4*d^2*e^2 - 22*b*c^3*d*e^3 - b^2*c^2*e^4)*g)*x^2 + 9*(9*c^4*d^3*e - 20*b*c^3*d^2*e^2 + 13*b^2*c^2*d*e^3 - 2*b^3*c*e^4)*f + 2*(13*c^4*d^4 - 43*b*c^3*d^3*e + 51*b^2*c^2*d^2*e^2 - 25*b^3*c*d*e^3 + 4*b^4*e^4)*g - (9*(13*c^4*d^2*e^2 - 12*b*c^3*d*e^3 - b^2*c^2*e^4)*f - (13*c^4*d^3*e - 30*b*c^3*d^2*e^2 + 21*b^2*c^2*d*e^3 - 4*b^3*c*e^4)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^3*e^3*x + c^3*d*e^2)","B",0
2244,1,229,0,0.403723," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, c^{3} e^{3} g x^{3} + {\left(7 \, c^{3} e^{3} f - 8 \, {\left(c^{3} d e^{2} - b c^{2} e^{3}\right)} g\right)} x^{2} + 7 \, {\left(c^{3} d^{2} e - 2 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} f + 2 \, {\left(c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} g - {\left(14 \, {\left(c^{3} d e^{2} - b c^{2} e^{3}\right)} f - {\left(c^{3} d^{2} e - 2 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{35 \, {\left(c^{2} e^{3} x + c^{2} d e^{2}\right)}}"," ",0,"-2/35*(5*c^3*e^3*g*x^3 + (7*c^3*e^3*f - 8*(c^3*d*e^2 - b*c^2*e^3)*g)*x^2 + 7*(c^3*d^2*e - 2*b*c^2*d*e^2 + b^2*c*e^3)*f + 2*(c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3)*g - (14*(c^3*d*e^2 - b*c^2*e^3)*f - (c^3*d^2*e - 2*b*c^2*d*e^2 + b^2*c*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^2*e^3*x + c^2*d*e^2)","B",0
2245,1,656,0,0.439199," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2 \, c d - b e} {\left({\left(2 \, c^{2} d^{2} e - b c d e^{2}\right)} f - {\left(2 \, c^{2} d^{3} - b c d^{2} e\right)} g + {\left({\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f - {\left(2 \, c^{2} d^{2} e - b c d e^{2}\right)} g\right)} x\right)} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(3 \, c^{2} e^{2} g x^{2} - 5 \, {\left(7 \, c^{2} d e - 4 \, b c e^{2}\right)} f + {\left(38 \, c^{2} d^{2} - 26 \, b c d e + 3 \, b^{2} e^{2}\right)} g + {\left(5 \, c^{2} e^{2} f - {\left(11 \, c^{2} d e - 6 \, b c e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{15 \, {\left(c e^{3} x + c d e^{2}\right)}}, -\frac{2 \, {\left(15 \, \sqrt{-2 \, c d + b e} {\left({\left(2 \, c^{2} d^{2} e - b c d e^{2}\right)} f - {\left(2 \, c^{2} d^{3} - b c d^{2} e\right)} g + {\left({\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f - {\left(2 \, c^{2} d^{2} e - b c d e^{2}\right)} g\right)} x\right)} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + {\left(3 \, c^{2} e^{2} g x^{2} - 5 \, {\left(7 \, c^{2} d e - 4 \, b c e^{2}\right)} f + {\left(38 \, c^{2} d^{2} - 26 \, b c d e + 3 \, b^{2} e^{2}\right)} g + {\left(5 \, c^{2} e^{2} f - {\left(11 \, c^{2} d e - 6 \, b c e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}\right)}}{15 \, {\left(c e^{3} x + c d e^{2}\right)}}\right]"," ",0,"[1/15*(15*sqrt(2*c*d - b*e)*((2*c^2*d^2*e - b*c*d*e^2)*f - (2*c^2*d^3 - b*c*d^2*e)*g + ((2*c^2*d*e^2 - b*c*e^3)*f - (2*c^2*d^2*e - b*c*d*e^2)*g)*x)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(3*c^2*e^2*g*x^2 - 5*(7*c^2*d*e - 4*b*c*e^2)*f + (38*c^2*d^2 - 26*b*c*d*e + 3*b^2*e^2)*g + (5*c^2*e^2*f - (11*c^2*d*e - 6*b*c*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(c*e^3*x + c*d*e^2), -2/15*(15*sqrt(-2*c*d + b*e)*((2*c^2*d^2*e - b*c*d*e^2)*f - (2*c^2*d^3 - b*c*d^2*e)*g + ((2*c^2*d*e^2 - b*c*e^3)*f - (2*c^2*d^2*e - b*c*d*e^2)*g)*x)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + (3*c^2*e^2*g*x^2 - 5*(7*c^2*d*e - 4*b*c*e^2)*f + (38*c^2*d^2 - 26*b*c*d*e + 3*b^2*e^2)*g + (5*c^2*e^2*f - (11*c^2*d*e - 6*b*c*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(c*e^3*x + c*d*e^2)]","A",0
2246,1,639,0,0.438224," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, c d^{2} e f + {\left(3 \, c e^{3} f - {\left(7 \, c d e^{2} - 2 \, b e^{3}\right)} g\right)} x^{2} - {\left(7 \, c d^{3} - 2 \, b d^{2} e\right)} g + 2 \, {\left(3 \, c d e^{2} f - {\left(7 \, c d^{2} e - 2 \, b d e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(2 \, c e^{2} g x^{2} + 3 \, {\left(4 \, c d e - b e^{2}\right)} f - {\left(26 \, c d^{2} - 11 \, b d e\right)} g + 2 \, {\left(3 \, c e^{2} f - {\left(9 \, c d e - 4 \, b e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{6 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}, \frac{3 \, {\left(3 \, c d^{2} e f + {\left(3 \, c e^{3} f - {\left(7 \, c d e^{2} - 2 \, b e^{3}\right)} g\right)} x^{2} - {\left(7 \, c d^{3} - 2 \, b d^{2} e\right)} g + 2 \, {\left(3 \, c d e^{2} f - {\left(7 \, c d^{2} e - 2 \, b d e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) - {\left(2 \, c e^{2} g x^{2} + 3 \, {\left(4 \, c d e - b e^{2}\right)} f - {\left(26 \, c d^{2} - 11 \, b d e\right)} g + 2 \, {\left(3 \, c e^{2} f - {\left(9 \, c d e - 4 \, b e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{3 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}\right]"," ",0,"[1/6*(3*(3*c*d^2*e*f + (3*c*e^3*f - (7*c*d*e^2 - 2*b*e^3)*g)*x^2 - (7*c*d^3 - 2*b*d^2*e)*g + 2*(3*c*d*e^2*f - (7*c*d^2*e - 2*b*d*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(2*c*e^2*g*x^2 + 3*(4*c*d*e - b*e^2)*f - (26*c*d^2 - 11*b*d*e)*g + 2*(3*c*e^2*f - (9*c*d*e - 4*b*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2), 1/3*(3*(3*c*d^2*e*f + (3*c*e^3*f - (7*c*d*e^2 - 2*b*e^3)*g)*x^2 - (7*c*d^3 - 2*b*d^2*e)*g + 2*(3*c*d*e^2*f - (7*c*d^2*e - 2*b*d*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) - (2*c*e^2*g*x^2 + 3*(4*c*d*e - b*e^2)*f - (26*c*d^2 - 11*b*d*e)*g + 2*(3*c*e^2*f - (9*c*d*e - 4*b*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)]","A",0
2247,1,998,0,0.463519," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{3} e f + {\left(c^{2} e^{4} f - {\left(9 \, c^{2} d e^{3} - 4 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(c^{2} d e^{3} f - {\left(9 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3}\right)} g\right)} x^{2} - {\left(9 \, c^{2} d^{4} - 4 \, b c d^{3} e\right)} g + 3 \, {\left(c^{2} d^{2} e^{2} f - {\left(9 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(8 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} g x^{2} - {\left(2 \, c^{2} d^{2} e + 3 \, b c d e^{2} - 2 \, b^{2} e^{3}\right)} f + {\left(34 \, c^{2} d^{3} - 21 \, b c d^{2} e + 2 \, b^{2} d e^{2}\right)} g - {\left(5 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f - {\left(58 \, c^{2} d^{2} e - 37 \, b c d e^{2} + 4 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(2 \, c d^{4} e^{2} - b d^{3} e^{3} + {\left(2 \, c d e^{5} - b e^{6}\right)} x^{3} + 3 \, {\left(2 \, c d^{2} e^{4} - b d e^{5}\right)} x^{2} + 3 \, {\left(2 \, c d^{3} e^{3} - b d^{2} e^{4}\right)} x\right)}}, -\frac{3 \, {\left(c^{2} d^{3} e f + {\left(c^{2} e^{4} f - {\left(9 \, c^{2} d e^{3} - 4 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(c^{2} d e^{3} f - {\left(9 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3}\right)} g\right)} x^{2} - {\left(9 \, c^{2} d^{4} - 4 \, b c d^{3} e\right)} g + 3 \, {\left(c^{2} d^{2} e^{2} f - {\left(9 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(8 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} g x^{2} - {\left(2 \, c^{2} d^{2} e + 3 \, b c d e^{2} - 2 \, b^{2} e^{3}\right)} f + {\left(34 \, c^{2} d^{3} - 21 \, b c d^{2} e + 2 \, b^{2} d e^{2}\right)} g - {\left(5 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f - {\left(58 \, c^{2} d^{2} e - 37 \, b c d e^{2} + 4 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(2 \, c d^{4} e^{2} - b d^{3} e^{3} + {\left(2 \, c d e^{5} - b e^{6}\right)} x^{3} + 3 \, {\left(2 \, c d^{2} e^{4} - b d e^{5}\right)} x^{2} + 3 \, {\left(2 \, c d^{3} e^{3} - b d^{2} e^{4}\right)} x\right)}}\right]"," ",0,"[1/8*(3*(c^2*d^3*e*f + (c^2*e^4*f - (9*c^2*d*e^3 - 4*b*c*e^4)*g)*x^3 + 3*(c^2*d*e^3*f - (9*c^2*d^2*e^2 - 4*b*c*d*e^3)*g)*x^2 - (9*c^2*d^4 - 4*b*c*d^3*e)*g + 3*(c^2*d^2*e^2*f - (9*c^2*d^3*e - 4*b*c*d^2*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(8*(2*c^2*d*e^2 - b*c*e^3)*g*x^2 - (2*c^2*d^2*e + 3*b*c*d*e^2 - 2*b^2*e^3)*f + (34*c^2*d^3 - 21*b*c*d^2*e + 2*b^2*d*e^2)*g - (5*(2*c^2*d*e^2 - b*c*e^3)*f - (58*c^2*d^2*e - 37*b*c*d*e^2 + 4*b^2*e^3)*g)*x)*sqrt(e*x + d))/(2*c*d^4*e^2 - b*d^3*e^3 + (2*c*d*e^5 - b*e^6)*x^3 + 3*(2*c*d^2*e^4 - b*d*e^5)*x^2 + 3*(2*c*d^3*e^3 - b*d^2*e^4)*x), -1/4*(3*(c^2*d^3*e*f + (c^2*e^4*f - (9*c^2*d*e^3 - 4*b*c*e^4)*g)*x^3 + 3*(c^2*d*e^3*f - (9*c^2*d^2*e^2 - 4*b*c*d*e^3)*g)*x^2 - (9*c^2*d^4 - 4*b*c*d^3*e)*g + 3*(c^2*d^2*e^2*f - (9*c^2*d^3*e - 4*b*c*d^2*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(8*(2*c^2*d*e^2 - b*c*e^3)*g*x^2 - (2*c^2*d^2*e + 3*b*c*d*e^2 - 2*b^2*e^3)*f + (34*c^2*d^3 - 21*b*c*d^2*e + 2*b^2*d*e^2)*g - (5*(2*c^2*d*e^2 - b*c*e^3)*f - (58*c^2*d^2*e - 37*b*c*d*e^2 + 4*b^2*e^3)*g)*x)*sqrt(e*x + d))/(2*c*d^4*e^2 - b*d^3*e^3 + (2*c*d*e^5 - b*e^6)*x^3 + 3*(2*c*d^2*e^4 - b*d*e^5)*x^2 + 3*(2*c*d^3*e^3 - b*d^2*e^4)*x)]","A",0
2248,1,1454,0,0.448377," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{3} d^{4} e f + {\left(c^{3} e^{5} f + {\left(11 \, c^{3} d e^{4} - 6 \, b c^{2} e^{5}\right)} g\right)} x^{4} + 4 \, {\left(c^{3} d e^{4} f + {\left(11 \, c^{3} d^{2} e^{3} - 6 \, b c^{2} d e^{4}\right)} g\right)} x^{3} + 6 \, {\left(c^{3} d^{2} e^{3} f + {\left(11 \, c^{3} d^{3} e^{2} - 6 \, b c^{2} d^{2} e^{3}\right)} g\right)} x^{2} + {\left(11 \, c^{3} d^{5} - 6 \, b c^{2} d^{4} e\right)} g + 4 \, {\left(c^{3} d^{3} e^{2} f + {\left(11 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left({\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f - {\left(42 \, c^{3} d^{2} e^{2} - 41 \, b c^{2} d e^{3} + 10 \, b^{2} c e^{4}\right)} g\right)} x^{2} + {\left(14 \, c^{3} d^{3} e - 43 \, b c^{2} d^{2} e^{2} + 34 \, b^{2} c d e^{3} - 8 \, b^{3} e^{4}\right)} f - {\left(38 \, c^{3} d^{4} - 19 \, b c^{2} d^{3} e - 8 \, b^{2} c d^{2} e^{2} + 4 \, b^{3} d e^{3}\right)} g - 2 \, {\left({\left(22 \, c^{3} d^{2} e^{2} - 25 \, b c^{2} d e^{3} + 7 \, b^{2} c e^{4}\right)} f + {\left(50 \, c^{3} d^{3} e - 23 \, b c^{2} d^{2} e^{2} - 13 \, b^{2} c d e^{3} + 6 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(4 \, c^{2} d^{6} e^{2} - 4 \, b c d^{5} e^{3} + b^{2} d^{4} e^{4} + {\left(4 \, c^{2} d^{2} e^{6} - 4 \, b c d e^{7} + b^{2} e^{8}\right)} x^{4} + 4 \, {\left(4 \, c^{2} d^{3} e^{5} - 4 \, b c d^{2} e^{6} + b^{2} d e^{7}\right)} x^{3} + 6 \, {\left(4 \, c^{2} d^{4} e^{4} - 4 \, b c d^{3} e^{5} + b^{2} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(4 \, c^{2} d^{5} e^{3} - 4 \, b c d^{4} e^{4} + b^{2} d^{3} e^{5}\right)} x\right)}}, -\frac{3 \, {\left(c^{3} d^{4} e f + {\left(c^{3} e^{5} f + {\left(11 \, c^{3} d e^{4} - 6 \, b c^{2} e^{5}\right)} g\right)} x^{4} + 4 \, {\left(c^{3} d e^{4} f + {\left(11 \, c^{3} d^{2} e^{3} - 6 \, b c^{2} d e^{4}\right)} g\right)} x^{3} + 6 \, {\left(c^{3} d^{2} e^{3} f + {\left(11 \, c^{3} d^{3} e^{2} - 6 \, b c^{2} d^{2} e^{3}\right)} g\right)} x^{2} + {\left(11 \, c^{3} d^{5} - 6 \, b c^{2} d^{4} e\right)} g + 4 \, {\left(c^{3} d^{3} e^{2} f + {\left(11 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left({\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f - {\left(42 \, c^{3} d^{2} e^{2} - 41 \, b c^{2} d e^{3} + 10 \, b^{2} c e^{4}\right)} g\right)} x^{2} + {\left(14 \, c^{3} d^{3} e - 43 \, b c^{2} d^{2} e^{2} + 34 \, b^{2} c d e^{3} - 8 \, b^{3} e^{4}\right)} f - {\left(38 \, c^{3} d^{4} - 19 \, b c^{2} d^{3} e - 8 \, b^{2} c d^{2} e^{2} + 4 \, b^{3} d e^{3}\right)} g - 2 \, {\left({\left(22 \, c^{3} d^{2} e^{2} - 25 \, b c^{2} d e^{3} + 7 \, b^{2} c e^{4}\right)} f + {\left(50 \, c^{3} d^{3} e - 23 \, b c^{2} d^{2} e^{2} - 13 \, b^{2} c d e^{3} + 6 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(4 \, c^{2} d^{6} e^{2} - 4 \, b c d^{5} e^{3} + b^{2} d^{4} e^{4} + {\left(4 \, c^{2} d^{2} e^{6} - 4 \, b c d e^{7} + b^{2} e^{8}\right)} x^{4} + 4 \, {\left(4 \, c^{2} d^{3} e^{5} - 4 \, b c d^{2} e^{6} + b^{2} d e^{7}\right)} x^{3} + 6 \, {\left(4 \, c^{2} d^{4} e^{4} - 4 \, b c d^{3} e^{5} + b^{2} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(4 \, c^{2} d^{5} e^{3} - 4 \, b c d^{4} e^{4} + b^{2} d^{3} e^{5}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(c^3*d^4*e*f + (c^3*e^5*f + (11*c^3*d*e^4 - 6*b*c^2*e^5)*g)*x^4 + 4*(c^3*d*e^4*f + (11*c^3*d^2*e^3 - 6*b*c^2*d*e^4)*g)*x^3 + 6*(c^3*d^2*e^3*f + (11*c^3*d^3*e^2 - 6*b*c^2*d^2*e^3)*g)*x^2 + (11*c^3*d^5 - 6*b*c^2*d^4*e)*g + 4*(c^3*d^3*e^2*f + (11*c^3*d^4*e - 6*b*c^2*d^3*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*((2*c^3*d*e^3 - b*c^2*e^4)*f - (42*c^3*d^2*e^2 - 41*b*c^2*d*e^3 + 10*b^2*c*e^4)*g)*x^2 + (14*c^3*d^3*e - 43*b*c^2*d^2*e^2 + 34*b^2*c*d*e^3 - 8*b^3*e^4)*f - (38*c^3*d^4 - 19*b*c^2*d^3*e - 8*b^2*c*d^2*e^2 + 4*b^3*d*e^3)*g - 2*((22*c^3*d^2*e^2 - 25*b*c^2*d*e^3 + 7*b^2*c*e^4)*f + (50*c^3*d^3*e - 23*b*c^2*d^2*e^2 - 13*b^2*c*d*e^3 + 6*b^3*e^4)*g)*x)*sqrt(e*x + d))/(4*c^2*d^6*e^2 - 4*b*c*d^5*e^3 + b^2*d^4*e^4 + (4*c^2*d^2*e^6 - 4*b*c*d*e^7 + b^2*e^8)*x^4 + 4*(4*c^2*d^3*e^5 - 4*b*c*d^2*e^6 + b^2*d*e^7)*x^3 + 6*(4*c^2*d^4*e^4 - 4*b*c*d^3*e^5 + b^2*d^2*e^6)*x^2 + 4*(4*c^2*d^5*e^3 - 4*b*c*d^4*e^4 + b^2*d^3*e^5)*x), -1/24*(3*(c^3*d^4*e*f + (c^3*e^5*f + (11*c^3*d*e^4 - 6*b*c^2*e^5)*g)*x^4 + 4*(c^3*d*e^4*f + (11*c^3*d^2*e^3 - 6*b*c^2*d*e^4)*g)*x^3 + 6*(c^3*d^2*e^3*f + (11*c^3*d^3*e^2 - 6*b*c^2*d^2*e^3)*g)*x^2 + (11*c^3*d^5 - 6*b*c^2*d^4*e)*g + 4*(c^3*d^3*e^2*f + (11*c^3*d^4*e - 6*b*c^2*d^3*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*((2*c^3*d*e^3 - b*c^2*e^4)*f - (42*c^3*d^2*e^2 - 41*b*c^2*d*e^3 + 10*b^2*c*e^4)*g)*x^2 + (14*c^3*d^3*e - 43*b*c^2*d^2*e^2 + 34*b^2*c*d*e^3 - 8*b^3*e^4)*f - (38*c^3*d^4 - 19*b*c^2*d^3*e - 8*b^2*c*d^2*e^2 + 4*b^3*d*e^3)*g - 2*((22*c^3*d^2*e^2 - 25*b*c^2*d*e^3 + 7*b^2*c*e^4)*f + (50*c^3*d^3*e - 23*b*c^2*d^2*e^2 - 13*b^2*c*d*e^3 + 6*b^3*e^4)*g)*x)*sqrt(e*x + d))/(4*c^2*d^6*e^2 - 4*b*c*d^5*e^3 + b^2*d^4*e^4 + (4*c^2*d^2*e^6 - 4*b*c*d*e^7 + b^2*e^8)*x^4 + 4*(4*c^2*d^3*e^5 - 4*b*c*d^2*e^6 + b^2*d*e^7)*x^3 + 6*(4*c^2*d^4*e^4 - 4*b*c*d^3*e^5 + b^2*d^2*e^6)*x^2 + 4*(4*c^2*d^5*e^3 - 4*b*c*d^4*e^4 + b^2*d^3*e^5)*x)]","B",0
2249,1,2104,0,0.503102," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2)/(e*x+d)^(13/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, c^{4} d^{5} e f + {\left(3 \, c^{4} e^{6} f + {\left(13 \, c^{4} d e^{5} - 8 \, b c^{3} e^{6}\right)} g\right)} x^{5} + 5 \, {\left(3 \, c^{4} d e^{5} f + {\left(13 \, c^{4} d^{2} e^{4} - 8 \, b c^{3} d e^{5}\right)} g\right)} x^{4} + 10 \, {\left(3 \, c^{4} d^{2} e^{4} f + {\left(13 \, c^{4} d^{3} e^{3} - 8 \, b c^{3} d^{2} e^{4}\right)} g\right)} x^{3} + 10 \, {\left(3 \, c^{4} d^{3} e^{3} f + {\left(13 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3}\right)} g\right)} x^{2} + {\left(13 \, c^{4} d^{6} - 8 \, b c^{3} d^{5} e\right)} g + 5 \, {\left(3 \, c^{4} d^{4} e^{2} f + {\left(13 \, c^{4} d^{5} e - 8 \, b c^{3} d^{4} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(3 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f + {\left(26 \, c^{4} d^{2} e^{3} - 29 \, b c^{3} d e^{4} + 8 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} + {\left(3 \, {\left(26 \, c^{4} d^{2} e^{3} - 17 \, b c^{3} d e^{4} + 2 \, b^{2} c^{2} e^{5}\right)} f - {\left(686 \, c^{4} d^{3} e^{2} - 1107 \, b c^{3} d^{2} e^{3} + 606 \, b^{2} c^{2} d e^{4} - 112 \, b^{3} c e^{5}\right)} g\right)} x^{2} + 3 \, {\left(78 \, c^{4} d^{4} e - 235 \, b c^{3} d^{3} e^{2} + 242 \, b^{2} c^{2} d^{2} e^{3} - 104 \, b^{3} c d e^{4} + 16 \, b^{4} e^{5}\right)} f - {\left(10 \, c^{4} d^{5} + 95 \, b c^{3} d^{4} e - 162 \, b^{2} c^{2} d^{3} e^{2} + 88 \, b^{3} c d^{2} e^{3} - 16 \, b^{4} d e^{4}\right)} g - {\left(3 \, {\left(158 \, c^{4} d^{3} e^{2} - 263 \, b c^{3} d^{2} e^{3} + 140 \, b^{2} c^{2} d e^{4} - 24 \, b^{3} c e^{5}\right)} f + {\left(6 \, c^{4} d^{4} e + 437 \, b c^{3} d^{3} e^{2} - 684 \, b^{2} c^{2} d^{2} e^{3} + 360 \, b^{3} c d e^{4} - 64 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(8 \, c^{3} d^{8} e^{2} - 12 \, b c^{2} d^{7} e^{3} + 6 \, b^{2} c d^{6} e^{4} - b^{3} d^{5} e^{5} + {\left(8 \, c^{3} d^{3} e^{7} - 12 \, b c^{2} d^{2} e^{8} + 6 \, b^{2} c d e^{9} - b^{3} e^{10}\right)} x^{5} + 5 \, {\left(8 \, c^{3} d^{4} e^{6} - 12 \, b c^{2} d^{3} e^{7} + 6 \, b^{2} c d^{2} e^{8} - b^{3} d e^{9}\right)} x^{4} + 10 \, {\left(8 \, c^{3} d^{5} e^{5} - 12 \, b c^{2} d^{4} e^{6} + 6 \, b^{2} c d^{3} e^{7} - b^{3} d^{2} e^{8}\right)} x^{3} + 10 \, {\left(8 \, c^{3} d^{6} e^{4} - 12 \, b c^{2} d^{5} e^{5} + 6 \, b^{2} c d^{4} e^{6} - b^{3} d^{3} e^{7}\right)} x^{2} + 5 \, {\left(8 \, c^{3} d^{7} e^{3} - 12 \, b c^{2} d^{6} e^{4} + 6 \, b^{2} c d^{5} e^{5} - b^{3} d^{4} e^{6}\right)} x\right)}}, -\frac{3 \, {\left(3 \, c^{4} d^{5} e f + {\left(3 \, c^{4} e^{6} f + {\left(13 \, c^{4} d e^{5} - 8 \, b c^{3} e^{6}\right)} g\right)} x^{5} + 5 \, {\left(3 \, c^{4} d e^{5} f + {\left(13 \, c^{4} d^{2} e^{4} - 8 \, b c^{3} d e^{5}\right)} g\right)} x^{4} + 10 \, {\left(3 \, c^{4} d^{2} e^{4} f + {\left(13 \, c^{4} d^{3} e^{3} - 8 \, b c^{3} d^{2} e^{4}\right)} g\right)} x^{3} + 10 \, {\left(3 \, c^{4} d^{3} e^{3} f + {\left(13 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3}\right)} g\right)} x^{2} + {\left(13 \, c^{4} d^{6} - 8 \, b c^{3} d^{5} e\right)} g + 5 \, {\left(3 \, c^{4} d^{4} e^{2} f + {\left(13 \, c^{4} d^{5} e - 8 \, b c^{3} d^{4} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(3 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f + {\left(26 \, c^{4} d^{2} e^{3} - 29 \, b c^{3} d e^{4} + 8 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} + {\left(3 \, {\left(26 \, c^{4} d^{2} e^{3} - 17 \, b c^{3} d e^{4} + 2 \, b^{2} c^{2} e^{5}\right)} f - {\left(686 \, c^{4} d^{3} e^{2} - 1107 \, b c^{3} d^{2} e^{3} + 606 \, b^{2} c^{2} d e^{4} - 112 \, b^{3} c e^{5}\right)} g\right)} x^{2} + 3 \, {\left(78 \, c^{4} d^{4} e - 235 \, b c^{3} d^{3} e^{2} + 242 \, b^{2} c^{2} d^{2} e^{3} - 104 \, b^{3} c d e^{4} + 16 \, b^{4} e^{5}\right)} f - {\left(10 \, c^{4} d^{5} + 95 \, b c^{3} d^{4} e - 162 \, b^{2} c^{2} d^{3} e^{2} + 88 \, b^{3} c d^{2} e^{3} - 16 \, b^{4} d e^{4}\right)} g - {\left(3 \, {\left(158 \, c^{4} d^{3} e^{2} - 263 \, b c^{3} d^{2} e^{3} + 140 \, b^{2} c^{2} d e^{4} - 24 \, b^{3} c e^{5}\right)} f + {\left(6 \, c^{4} d^{4} e + 437 \, b c^{3} d^{3} e^{2} - 684 \, b^{2} c^{2} d^{2} e^{3} + 360 \, b^{3} c d e^{4} - 64 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(8 \, c^{3} d^{8} e^{2} - 12 \, b c^{2} d^{7} e^{3} + 6 \, b^{2} c d^{6} e^{4} - b^{3} d^{5} e^{5} + {\left(8 \, c^{3} d^{3} e^{7} - 12 \, b c^{2} d^{2} e^{8} + 6 \, b^{2} c d e^{9} - b^{3} e^{10}\right)} x^{5} + 5 \, {\left(8 \, c^{3} d^{4} e^{6} - 12 \, b c^{2} d^{3} e^{7} + 6 \, b^{2} c d^{2} e^{8} - b^{3} d e^{9}\right)} x^{4} + 10 \, {\left(8 \, c^{3} d^{5} e^{5} - 12 \, b c^{2} d^{4} e^{6} + 6 \, b^{2} c d^{3} e^{7} - b^{3} d^{2} e^{8}\right)} x^{3} + 10 \, {\left(8 \, c^{3} d^{6} e^{4} - 12 \, b c^{2} d^{5} e^{5} + 6 \, b^{2} c d^{4} e^{6} - b^{3} d^{3} e^{7}\right)} x^{2} + 5 \, {\left(8 \, c^{3} d^{7} e^{3} - 12 \, b c^{2} d^{6} e^{4} + 6 \, b^{2} c d^{5} e^{5} - b^{3} d^{4} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/384*(3*(3*c^4*d^5*e*f + (3*c^4*e^6*f + (13*c^4*d*e^5 - 8*b*c^3*e^6)*g)*x^5 + 5*(3*c^4*d*e^5*f + (13*c^4*d^2*e^4 - 8*b*c^3*d*e^5)*g)*x^4 + 10*(3*c^4*d^2*e^4*f + (13*c^4*d^3*e^3 - 8*b*c^3*d^2*e^4)*g)*x^3 + 10*(3*c^4*d^3*e^3*f + (13*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3)*g)*x^2 + (13*c^4*d^6 - 8*b*c^3*d^5*e)*g + 5*(3*c^4*d^4*e^2*f + (13*c^4*d^5*e - 8*b*c^3*d^4*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(3*(2*c^4*d*e^4 - b*c^3*e^5)*f + (26*c^4*d^2*e^3 - 29*b*c^3*d*e^4 + 8*b^2*c^2*e^5)*g)*x^3 + (3*(26*c^4*d^2*e^3 - 17*b*c^3*d*e^4 + 2*b^2*c^2*e^5)*f - (686*c^4*d^3*e^2 - 1107*b*c^3*d^2*e^3 + 606*b^2*c^2*d*e^4 - 112*b^3*c*e^5)*g)*x^2 + 3*(78*c^4*d^4*e - 235*b*c^3*d^3*e^2 + 242*b^2*c^2*d^2*e^3 - 104*b^3*c*d*e^4 + 16*b^4*e^5)*f - (10*c^4*d^5 + 95*b*c^3*d^4*e - 162*b^2*c^2*d^3*e^2 + 88*b^3*c*d^2*e^3 - 16*b^4*d*e^4)*g - (3*(158*c^4*d^3*e^2 - 263*b*c^3*d^2*e^3 + 140*b^2*c^2*d*e^4 - 24*b^3*c*e^5)*f + (6*c^4*d^4*e + 437*b*c^3*d^3*e^2 - 684*b^2*c^2*d^2*e^3 + 360*b^3*c*d*e^4 - 64*b^4*e^5)*g)*x)*sqrt(e*x + d))/(8*c^3*d^8*e^2 - 12*b*c^2*d^7*e^3 + 6*b^2*c*d^6*e^4 - b^3*d^5*e^5 + (8*c^3*d^3*e^7 - 12*b*c^2*d^2*e^8 + 6*b^2*c*d*e^9 - b^3*e^10)*x^5 + 5*(8*c^3*d^4*e^6 - 12*b*c^2*d^3*e^7 + 6*b^2*c*d^2*e^8 - b^3*d*e^9)*x^4 + 10*(8*c^3*d^5*e^5 - 12*b*c^2*d^4*e^6 + 6*b^2*c*d^3*e^7 - b^3*d^2*e^8)*x^3 + 10*(8*c^3*d^6*e^4 - 12*b*c^2*d^5*e^5 + 6*b^2*c*d^4*e^6 - b^3*d^3*e^7)*x^2 + 5*(8*c^3*d^7*e^3 - 12*b*c^2*d^6*e^4 + 6*b^2*c*d^5*e^5 - b^3*d^4*e^6)*x), -1/192*(3*(3*c^4*d^5*e*f + (3*c^4*e^6*f + (13*c^4*d*e^5 - 8*b*c^3*e^6)*g)*x^5 + 5*(3*c^4*d*e^5*f + (13*c^4*d^2*e^4 - 8*b*c^3*d*e^5)*g)*x^4 + 10*(3*c^4*d^2*e^4*f + (13*c^4*d^3*e^3 - 8*b*c^3*d^2*e^4)*g)*x^3 + 10*(3*c^4*d^3*e^3*f + (13*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3)*g)*x^2 + (13*c^4*d^6 - 8*b*c^3*d^5*e)*g + 5*(3*c^4*d^4*e^2*f + (13*c^4*d^5*e - 8*b*c^3*d^4*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(3*(2*c^4*d*e^4 - b*c^3*e^5)*f + (26*c^4*d^2*e^3 - 29*b*c^3*d*e^4 + 8*b^2*c^2*e^5)*g)*x^3 + (3*(26*c^4*d^2*e^3 - 17*b*c^3*d*e^4 + 2*b^2*c^2*e^5)*f - (686*c^4*d^3*e^2 - 1107*b*c^3*d^2*e^3 + 606*b^2*c^2*d*e^4 - 112*b^3*c*e^5)*g)*x^2 + 3*(78*c^4*d^4*e - 235*b*c^3*d^3*e^2 + 242*b^2*c^2*d^2*e^3 - 104*b^3*c*d*e^4 + 16*b^4*e^5)*f - (10*c^4*d^5 + 95*b*c^3*d^4*e - 162*b^2*c^2*d^3*e^2 + 88*b^3*c*d^2*e^3 - 16*b^4*d*e^4)*g - (3*(158*c^4*d^3*e^2 - 263*b*c^3*d^2*e^3 + 140*b^2*c^2*d*e^4 - 24*b^3*c*e^5)*f + (6*c^4*d^4*e + 437*b*c^3*d^3*e^2 - 684*b^2*c^2*d^2*e^3 + 360*b^3*c*d*e^4 - 64*b^4*e^5)*g)*x)*sqrt(e*x + d))/(8*c^3*d^8*e^2 - 12*b*c^2*d^7*e^3 + 6*b^2*c*d^6*e^4 - b^3*d^5*e^5 + (8*c^3*d^3*e^7 - 12*b*c^2*d^2*e^8 + 6*b^2*c*d*e^9 - b^3*e^10)*x^5 + 5*(8*c^3*d^4*e^6 - 12*b*c^2*d^3*e^7 + 6*b^2*c*d^2*e^8 - b^3*d*e^9)*x^4 + 10*(8*c^3*d^5*e^5 - 12*b*c^2*d^4*e^6 + 6*b^2*c*d^3*e^7 - b^3*d^2*e^8)*x^3 + 10*(8*c^3*d^6*e^4 - 12*b*c^2*d^5*e^5 + 6*b^2*c*d^4*e^6 - b^3*d^3*e^7)*x^2 + 5*(8*c^3*d^7*e^3 - 12*b*c^2*d^6*e^4 + 6*b^2*c*d^5*e^5 - b^3*d^4*e^6)*x)]","B",0
2250,1,1370,0,0.497238," ","integrate((e*x+d)^(5/2)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(153153 \, c^{9} e^{9} g x^{9} + 9009 \, {\left(19 \, c^{9} e^{9} f + {\left(56 \, c^{9} d e^{8} + 39 \, b c^{8} e^{9}\right)} g\right)} x^{8} + 3003 \, {\left(19 \, {\left(10 \, c^{9} d e^{8} + 7 \, b c^{8} e^{9}\right)} f + {\left(50 \, c^{9} d^{2} e^{7} + 527 \, b c^{8} d e^{8} + 69 \, b^{2} c^{7} e^{9}\right)} g\right)} x^{7} + 231 \, {\left(19 \, {\left(38 \, c^{9} d^{2} e^{7} + 417 \, b c^{8} d e^{8} + 55 \, b^{2} c^{7} e^{9}\right)} f - {\left(5114 \, c^{9} d^{3} e^{6} - 9585 \, b c^{8} d^{2} e^{7} - 5216 \, b^{2} c^{7} d e^{8} - 3 \, b^{3} c^{6} e^{9}\right)} g\right)} x^{6} - 63 \, {\left(19 \, {\left(1174 \, c^{9} d^{3} e^{6} - 2179 \, b c^{8} d^{2} e^{7} - 1204 \, b^{2} c^{7} d e^{8} - b^{3} c^{6} e^{9}\right)} f + {\left(20456 \, c^{9} d^{4} e^{5} + 4189 \, b c^{8} d^{3} e^{6} - 45509 \, b^{2} c^{7} d^{2} e^{7} - 143 \, b^{3} c^{6} d e^{8} + 12 \, b^{4} c^{5} e^{9}\right)} g\right)} x^{5} - 7 \, {\left(95 \, {\left(2348 \, c^{9} d^{4} e^{5} + 587 \, b c^{8} d^{3} e^{6} - 5343 \, b^{2} c^{7} d^{2} e^{7} - 25 \, b^{3} c^{6} d e^{8} + 2 \, b^{4} c^{5} e^{9}\right)} f - {\left(72574 \, c^{9} d^{5} e^{4} - 530165 \, b c^{8} d^{4} e^{5} + 496980 \, b^{2} c^{7} d^{3} e^{6} + 8230 \, b^{3} c^{6} d^{2} e^{7} - 1550 \, b^{4} c^{5} d e^{8} + 120 \, b^{5} c^{4} e^{9}\right)} g\right)} x^{4} + {\left(19 \, {\left(37354 \, c^{9} d^{5} e^{4} - 257745 \, b c^{8} d^{4} e^{5} + 237200 \, b^{2} c^{7} d^{3} e^{6} + 6070 \, b^{3} c^{6} d^{2} e^{7} - 1080 \, b^{4} c^{5} d e^{8} + 80 \, b^{5} c^{4} e^{9}\right)} f + {\left(1411994 \, c^{9} d^{6} e^{3} - 3574809 \, b c^{8} d^{5} e^{4} + 1981645 \, b^{2} c^{7} d^{4} e^{5} + 247010 \, b^{3} c^{6} d^{3} e^{6} - 78240 \, b^{4} c^{5} d^{2} e^{7} + 13360 \, b^{5} c^{4} d e^{8} - 960 \, b^{6} c^{3} e^{9}\right)} g\right)} x^{3} + 3 \, {\left(19 \, {\left(35362 \, c^{9} d^{6} e^{3} - 87409 \, b c^{8} d^{5} e^{4} + 44825 \, b^{2} c^{7} d^{4} e^{5} + 9650 \, b^{3} c^{6} d^{3} e^{6} - 2860 \, b^{4} c^{5} d^{2} e^{7} + 464 \, b^{5} c^{4} d e^{8} - 32 \, b^{6} c^{3} e^{9}\right)} f + {\left(176810 \, c^{9} d^{7} e^{2} - 248777 \, b c^{8} d^{6} e^{3} - 105344 \, b^{2} c^{7} d^{5} e^{4} + 276115 \, b^{3} c^{6} d^{4} e^{5} - 130100 \, b^{4} c^{5} d^{3} e^{6} + 36640 \, b^{5} c^{4} d^{2} e^{7} - 5728 \, b^{6} c^{3} d e^{8} + 384 \, b^{7} c^{2} e^{9}\right)} g\right)} x^{2} - 19 \, {\left(74461 \, c^{9} d^{8} e - 317517 \, b c^{8} d^{7} e^{2} + 563561 \, b^{2} c^{7} d^{6} e^{3} - 549615 \, b^{3} c^{6} d^{5} e^{4} + 329190 \, b^{4} c^{5} d^{4} e^{5} - 126672 \, b^{5} c^{4} d^{3} e^{6} + 30560 \, b^{6} c^{3} d^{2} e^{7} - 4224 \, b^{7} c^{2} d e^{8} + 256 \, b^{8} c e^{9}\right)} f - 2 \, {\left(262729 \, c^{9} d^{9} - 1470288 \, b c^{8} d^{8} e + 3543734 \, b^{2} c^{7} d^{7} e^{2} - 4831980 \, b^{3} c^{6} d^{6} e^{3} + 4120665 \, b^{4} c^{5} d^{5} e^{4} - 2291820 \, b^{5} c^{4} d^{4} e^{5} + 836432 \, b^{6} c^{3} d^{3} e^{6} - 193920 \, b^{7} c^{2} d^{2} e^{7} + 25984 \, b^{8} c d e^{8} - 1536 \, b^{9} e^{9}\right)} g + {\left(19 \, {\left(39346 \, c^{9} d^{7} e^{2} - 31625 \, b c^{8} d^{6} e^{3} - 83676 \, b^{2} c^{7} d^{5} e^{4} + 114555 \, b^{3} c^{6} d^{4} e^{5} - 50040 \, b^{4} c^{5} d^{3} e^{6} + 13296 \, b^{5} c^{4} d^{2} e^{7} - 1984 \, b^{6} c^{3} d e^{8} + 128 \, b^{7} c^{2} e^{9}\right)} f - {\left(262729 \, c^{9} d^{8} e - 1207559 \, b c^{8} d^{7} e^{2} + 2336175 \, b^{2} c^{7} d^{6} e^{3} - 2495805 \, b^{3} c^{6} d^{5} e^{4} + 1624860 \, b^{4} c^{5} d^{4} e^{5} - 666960 \, b^{5} c^{4} d^{3} e^{6} + 169472 \, b^{6} c^{3} d^{2} e^{7} - 24448 \, b^{7} c^{2} d e^{8} + 1536 \, b^{8} c e^{9}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{2909907 \, {\left(c^{7} e^{3} x + c^{7} d e^{2}\right)}}"," ",0,"2/2909907*(153153*c^9*e^9*g*x^9 + 9009*(19*c^9*e^9*f + (56*c^9*d*e^8 + 39*b*c^8*e^9)*g)*x^8 + 3003*(19*(10*c^9*d*e^8 + 7*b*c^8*e^9)*f + (50*c^9*d^2*e^7 + 527*b*c^8*d*e^8 + 69*b^2*c^7*e^9)*g)*x^7 + 231*(19*(38*c^9*d^2*e^7 + 417*b*c^8*d*e^8 + 55*b^2*c^7*e^9)*f - (5114*c^9*d^3*e^6 - 9585*b*c^8*d^2*e^7 - 5216*b^2*c^7*d*e^8 - 3*b^3*c^6*e^9)*g)*x^6 - 63*(19*(1174*c^9*d^3*e^6 - 2179*b*c^8*d^2*e^7 - 1204*b^2*c^7*d*e^8 - b^3*c^6*e^9)*f + (20456*c^9*d^4*e^5 + 4189*b*c^8*d^3*e^6 - 45509*b^2*c^7*d^2*e^7 - 143*b^3*c^6*d*e^8 + 12*b^4*c^5*e^9)*g)*x^5 - 7*(95*(2348*c^9*d^4*e^5 + 587*b*c^8*d^3*e^6 - 5343*b^2*c^7*d^2*e^7 - 25*b^3*c^6*d*e^8 + 2*b^4*c^5*e^9)*f - (72574*c^9*d^5*e^4 - 530165*b*c^8*d^4*e^5 + 496980*b^2*c^7*d^3*e^6 + 8230*b^3*c^6*d^2*e^7 - 1550*b^4*c^5*d*e^8 + 120*b^5*c^4*e^9)*g)*x^4 + (19*(37354*c^9*d^5*e^4 - 257745*b*c^8*d^4*e^5 + 237200*b^2*c^7*d^3*e^6 + 6070*b^3*c^6*d^2*e^7 - 1080*b^4*c^5*d*e^8 + 80*b^5*c^4*e^9)*f + (1411994*c^9*d^6*e^3 - 3574809*b*c^8*d^5*e^4 + 1981645*b^2*c^7*d^4*e^5 + 247010*b^3*c^6*d^3*e^6 - 78240*b^4*c^5*d^2*e^7 + 13360*b^5*c^4*d*e^8 - 960*b^6*c^3*e^9)*g)*x^3 + 3*(19*(35362*c^9*d^6*e^3 - 87409*b*c^8*d^5*e^4 + 44825*b^2*c^7*d^4*e^5 + 9650*b^3*c^6*d^3*e^6 - 2860*b^4*c^5*d^2*e^7 + 464*b^5*c^4*d*e^8 - 32*b^6*c^3*e^9)*f + (176810*c^9*d^7*e^2 - 248777*b*c^8*d^6*e^3 - 105344*b^2*c^7*d^5*e^4 + 276115*b^3*c^6*d^4*e^5 - 130100*b^4*c^5*d^3*e^6 + 36640*b^5*c^4*d^2*e^7 - 5728*b^6*c^3*d*e^8 + 384*b^7*c^2*e^9)*g)*x^2 - 19*(74461*c^9*d^8*e - 317517*b*c^8*d^7*e^2 + 563561*b^2*c^7*d^6*e^3 - 549615*b^3*c^6*d^5*e^4 + 329190*b^4*c^5*d^4*e^5 - 126672*b^5*c^4*d^3*e^6 + 30560*b^6*c^3*d^2*e^7 - 4224*b^7*c^2*d*e^8 + 256*b^8*c*e^9)*f - 2*(262729*c^9*d^9 - 1470288*b*c^8*d^8*e + 3543734*b^2*c^7*d^7*e^2 - 4831980*b^3*c^6*d^6*e^3 + 4120665*b^4*c^5*d^5*e^4 - 2291820*b^5*c^4*d^4*e^5 + 836432*b^6*c^3*d^3*e^6 - 193920*b^7*c^2*d^2*e^7 + 25984*b^8*c*d*e^8 - 1536*b^9*e^9)*g + (19*(39346*c^9*d^7*e^2 - 31625*b*c^8*d^6*e^3 - 83676*b^2*c^7*d^5*e^4 + 114555*b^3*c^6*d^4*e^5 - 50040*b^4*c^5*d^3*e^6 + 13296*b^5*c^4*d^2*e^7 - 1984*b^6*c^3*d*e^8 + 128*b^7*c^2*e^9)*f - (262729*c^9*d^8*e - 1207559*b*c^8*d^7*e^2 + 2336175*b^2*c^7*d^6*e^3 - 2495805*b^3*c^6*d^5*e^4 + 1624860*b^4*c^5*d^4*e^5 - 666960*b^5*c^4*d^3*e^6 + 169472*b^6*c^3*d^2*e^7 - 24448*b^7*c^2*d*e^8 + 1536*b^8*c*e^9)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^7*e^3*x + c^7*d*e^2)","B",0
2251,1,1112,0,0.466438," ","integrate((e*x+d)^(3/2)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(45045 \, c^{8} e^{8} g x^{8} + 3003 \, {\left(17 \, c^{8} e^{8} f + {\left(33 \, c^{8} d e^{7} + 35 \, b c^{7} e^{8}\right)} g\right)} x^{7} + 231 \, {\left(17 \, {\left(29 \, c^{8} d e^{7} + 31 \, b c^{7} e^{8}\right)} f - {\left(303 \, c^{8} d^{2} e^{6} - 1558 \, b c^{7} d e^{7} - 275 \, b^{2} c^{6} e^{8}\right)} g\right)} x^{6} - 63 \, {\left(17 \, {\left(79 \, c^{8} d^{2} e^{6} - 398 \, b c^{7} d e^{7} - 71 \, b^{2} c^{6} e^{8}\right)} f + {\left(4527 \, c^{8} d^{3} e^{5} - 4129 \, b c^{7} d^{2} e^{6} - 4813 \, b^{2} c^{6} d e^{7} - 5 \, b^{3} c^{5} e^{8}\right)} g\right)} x^{5} - 35 \, {\left(17 \, {\left(587 \, c^{8} d^{3} e^{5} - 525 \, b c^{7} d^{2} e^{6} - 633 \, b^{2} c^{6} d e^{7} - b^{3} c^{5} e^{8}\right)} f + {\left(1761 \, c^{8} d^{4} e^{4} + 11860 \, b c^{7} d^{3} e^{5} - 15954 \, b^{2} c^{6} d^{2} e^{6} - 108 \, b^{3} c^{5} d e^{7} + 10 \, b^{4} c^{4} e^{8}\right)} g\right)} x^{4} - 5 \, {\left(17 \, {\left(835 \, c^{8} d^{4} e^{4} + 6548 \, b c^{7} d^{3} e^{5} - 8586 \, b^{2} c^{6} d^{2} e^{6} - 92 \, b^{3} c^{5} d e^{7} + 8 \, b^{4} c^{4} e^{8}\right)} f - {\left(51549 \, c^{8} d^{5} e^{3} - 146429 \, b c^{7} d^{4} e^{4} + 91238 \, b^{2} c^{6} d^{3} e^{5} + 4506 \, b^{3} c^{5} d^{2} e^{6} - 944 \, b^{4} c^{4} d e^{7} + 80 \, b^{5} c^{3} e^{8}\right)} g\right)} x^{3} + 3 \, {\left(17 \, {\left(7339 \, c^{8} d^{5} e^{3} - 20435 \, b c^{7} d^{4} e^{4} + 12250 \, b^{2} c^{6} d^{3} e^{5} + 1030 \, b^{3} c^{5} d^{2} e^{6} - 200 \, b^{4} c^{4} d e^{7} + 16 \, b^{5} c^{3} e^{8}\right)} f + {\left(52047 \, c^{8} d^{6} e^{2} - 89650 \, b c^{7} d^{5} e^{3} + 15875 \, b^{2} c^{6} d^{4} e^{4} + 30740 \, b^{3} c^{5} d^{3} e^{5} - 10900 \, b^{4} c^{4} d^{2} e^{6} + 2048 \, b^{5} c^{3} d e^{7} - 160 \, b^{6} c^{2} e^{8}\right)} g\right)} x^{2} - 17 \, {\left(16363 \, c^{8} d^{7} e - 64441 \, b c^{7} d^{6} e^{2} + 101913 \, b^{2} c^{6} d^{5} e^{3} - 84195 \, b^{3} c^{5} d^{4} e^{4} + 40200 \, b^{4} c^{4} d^{3} e^{5} - 11568 \, b^{5} c^{3} d^{2} e^{6} + 1856 \, b^{6} c^{2} d e^{7} - 128 \, b^{7} c e^{8}\right)} f - 2 \, {\left(47067 \, c^{8} d^{8} - 246044 \, b c^{7} d^{7} e + 542642 \, b^{2} c^{6} d^{6} e^{2} - 658380 \, b^{3} c^{5} d^{5} e^{3} + 481275 \, b^{4} c^{4} d^{4} e^{4} - 218352 \, b^{5} c^{3} d^{3} e^{5} + 60624 \, b^{6} c^{2} d^{2} e^{6} - 9472 \, b^{7} c d e^{7} + 640 \, b^{8} e^{8}\right)} g + {\left(17 \, {\left(14341 \, c^{8} d^{6} e^{2} - 21006 \, b c^{7} d^{5} e^{3} - 4395 \, b^{2} c^{6} d^{4} e^{4} + 15180 \, b^{3} c^{5} d^{3} e^{5} - 4920 \, b^{4} c^{4} d^{2} e^{6} + 864 \, b^{5} c^{3} d e^{7} - 64 \, b^{6} c^{2} e^{8}\right)} f - {\left(47067 \, c^{8} d^{7} e - 198977 \, b c^{7} d^{6} e^{2} + 343665 \, b^{2} c^{6} d^{5} e^{3} - 314715 \, b^{3} c^{5} d^{4} e^{4} + 166560 \, b^{4} c^{4} d^{3} e^{5} - 51792 \, b^{5} c^{3} d^{2} e^{6} + 8832 \, b^{6} c^{2} d e^{7} - 640 \, b^{7} c e^{8}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{765765 \, {\left(c^{6} e^{3} x + c^{6} d e^{2}\right)}}"," ",0,"2/765765*(45045*c^8*e^8*g*x^8 + 3003*(17*c^8*e^8*f + (33*c^8*d*e^7 + 35*b*c^7*e^8)*g)*x^7 + 231*(17*(29*c^8*d*e^7 + 31*b*c^7*e^8)*f - (303*c^8*d^2*e^6 - 1558*b*c^7*d*e^7 - 275*b^2*c^6*e^8)*g)*x^6 - 63*(17*(79*c^8*d^2*e^6 - 398*b*c^7*d*e^7 - 71*b^2*c^6*e^8)*f + (4527*c^8*d^3*e^5 - 4129*b*c^7*d^2*e^6 - 4813*b^2*c^6*d*e^7 - 5*b^3*c^5*e^8)*g)*x^5 - 35*(17*(587*c^8*d^3*e^5 - 525*b*c^7*d^2*e^6 - 633*b^2*c^6*d*e^7 - b^3*c^5*e^8)*f + (1761*c^8*d^4*e^4 + 11860*b*c^7*d^3*e^5 - 15954*b^2*c^6*d^2*e^6 - 108*b^3*c^5*d*e^7 + 10*b^4*c^4*e^8)*g)*x^4 - 5*(17*(835*c^8*d^4*e^4 + 6548*b*c^7*d^3*e^5 - 8586*b^2*c^6*d^2*e^6 - 92*b^3*c^5*d*e^7 + 8*b^4*c^4*e^8)*f - (51549*c^8*d^5*e^3 - 146429*b*c^7*d^4*e^4 + 91238*b^2*c^6*d^3*e^5 + 4506*b^3*c^5*d^2*e^6 - 944*b^4*c^4*d*e^7 + 80*b^5*c^3*e^8)*g)*x^3 + 3*(17*(7339*c^8*d^5*e^3 - 20435*b*c^7*d^4*e^4 + 12250*b^2*c^6*d^3*e^5 + 1030*b^3*c^5*d^2*e^6 - 200*b^4*c^4*d*e^7 + 16*b^5*c^3*e^8)*f + (52047*c^8*d^6*e^2 - 89650*b*c^7*d^5*e^3 + 15875*b^2*c^6*d^4*e^4 + 30740*b^3*c^5*d^3*e^5 - 10900*b^4*c^4*d^2*e^6 + 2048*b^5*c^3*d*e^7 - 160*b^6*c^2*e^8)*g)*x^2 - 17*(16363*c^8*d^7*e - 64441*b*c^7*d^6*e^2 + 101913*b^2*c^6*d^5*e^3 - 84195*b^3*c^5*d^4*e^4 + 40200*b^4*c^4*d^3*e^5 - 11568*b^5*c^3*d^2*e^6 + 1856*b^6*c^2*d*e^7 - 128*b^7*c*e^8)*f - 2*(47067*c^8*d^8 - 246044*b*c^7*d^7*e + 542642*b^2*c^6*d^6*e^2 - 658380*b^3*c^5*d^5*e^3 + 481275*b^4*c^4*d^4*e^4 - 218352*b^5*c^3*d^3*e^5 + 60624*b^6*c^2*d^2*e^6 - 9472*b^7*c*d*e^7 + 640*b^8*e^8)*g + (17*(14341*c^8*d^6*e^2 - 21006*b*c^7*d^5*e^3 - 4395*b^2*c^6*d^4*e^4 + 15180*b^3*c^5*d^3*e^5 - 4920*b^4*c^4*d^2*e^6 + 864*b^5*c^3*d*e^7 - 64*b^6*c^2*e^8)*f - (47067*c^8*d^7*e - 198977*b*c^7*d^6*e^2 + 343665*b^2*c^6*d^5*e^3 - 314715*b^3*c^5*d^4*e^4 + 166560*b^4*c^4*d^3*e^5 - 51792*b^5*c^3*d^2*e^6 + 8832*b^6*c^2*d*e^7 - 640*b^7*c*e^8)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^6*e^3*x + c^6*d*e^2)","B",0
2252,1,881,0,0.432037," ","integrate((e*x+d)^(1/2)*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, c^{7} e^{7} g x^{7} + 231 \, {\left(15 \, c^{7} e^{7} f + {\left(14 \, c^{7} d e^{6} + 31 \, b c^{6} e^{7}\right)} g\right)} x^{6} + 63 \, {\left(15 \, {\left(4 \, c^{7} d e^{6} + 9 \, b c^{6} e^{7}\right)} f - {\left(139 \, c^{7} d^{2} e^{5} - 263 \, b c^{6} d e^{6} - 71 \, b^{2} c^{5} e^{7}\right)} g\right)} x^{5} - 35 \, {\left(3 \, {\left(103 \, c^{7} d^{2} e^{5} - 193 \, b c^{6} d e^{6} - 53 \, b^{2} c^{5} e^{7}\right)} f + {\left(278 \, c^{7} d^{3} e^{4} + 54 \, b c^{6} d^{2} e^{5} - 474 \, b^{2} c^{5} d e^{6} - b^{3} c^{4} e^{7}\right)} g\right)} x^{4} - 5 \, {\left(3 \, {\left(824 \, c^{7} d^{3} e^{4} + 206 \, b c^{6} d^{2} e^{5} - 1454 \, b^{2} c^{5} d e^{6} - 5 \, b^{3} c^{4} e^{7}\right)} f - {\left(1637 \, c^{7} d^{4} e^{3} - 5930 \, b c^{6} d^{3} e^{4} + 4224 \, b^{2} c^{5} d^{2} e^{5} + 77 \, b^{3} c^{4} d e^{6} - 8 \, b^{4} c^{3} e^{7}\right)} g\right)} x^{3} + 3 \, {\left(15 \, {\left(271 \, c^{7} d^{4} e^{3} - 954 \, b c^{6} d^{3} e^{4} + 664 \, b^{2} c^{5} d^{2} e^{5} + 21 \, b^{3} c^{4} d e^{6} - 2 \, b^{4} c^{3} e^{7}\right)} f + {\left(3274 \, c^{7} d^{5} e^{2} - 6125 \, b c^{6} d^{4} e^{3} + 2290 \, b^{2} c^{5} d^{3} e^{4} + 715 \, b^{3} c^{4} d^{2} e^{5} - 170 \, b^{4} c^{3} d e^{6} + 16 \, b^{5} c^{2} e^{7}\right)} g\right)} x^{2} - 15 \, {\left(835 \, c^{7} d^{6} e - 3047 \, b c^{6} d^{5} e^{2} + 4283 \, b^{2} c^{5} d^{4} e^{3} - 2933 \, b^{3} c^{4} d^{3} e^{4} + 1046 \, b^{4} c^{3} d^{2} e^{5} - 200 \, b^{5} c^{2} d e^{6} + 16 \, b^{6} c e^{7}\right)} f - 2 \, {\left(1919 \, c^{7} d^{7} - 9368 \, b c^{6} d^{6} e + 18834 \, b^{2} c^{5} d^{5} e^{2} - 20100 \, b^{3} c^{4} d^{4} e^{3} + 12255 \, b^{4} c^{3} d^{3} e^{4} - 4284 \, b^{5} c^{2} d^{2} e^{5} + 808 \, b^{6} c d e^{6} - 64 \, b^{7} e^{7}\right)} g + {\left(15 \, {\left(1084 \, c^{7} d^{5} e^{2} - 1897 \, b c^{6} d^{4} e^{3} + 466 \, b^{2} c^{5} d^{3} e^{4} + 431 \, b^{3} c^{4} d^{2} e^{5} - 92 \, b^{4} c^{3} d e^{6} + 8 \, b^{5} c^{2} e^{7}\right)} f - {\left(1919 \, c^{7} d^{6} e - 7449 \, b c^{6} d^{5} e^{2} + 11385 \, b^{2} c^{5} d^{4} e^{3} - 8715 \, b^{3} c^{4} d^{3} e^{4} + 3540 \, b^{4} c^{3} d^{2} e^{5} - 744 \, b^{5} c^{2} d e^{6} + 64 \, b^{6} c e^{7}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{45045 \, {\left(c^{5} e^{3} x + c^{5} d e^{2}\right)}}"," ",0,"2/45045*(3003*c^7*e^7*g*x^7 + 231*(15*c^7*e^7*f + (14*c^7*d*e^6 + 31*b*c^6*e^7)*g)*x^6 + 63*(15*(4*c^7*d*e^6 + 9*b*c^6*e^7)*f - (139*c^7*d^2*e^5 - 263*b*c^6*d*e^6 - 71*b^2*c^5*e^7)*g)*x^5 - 35*(3*(103*c^7*d^2*e^5 - 193*b*c^6*d*e^6 - 53*b^2*c^5*e^7)*f + (278*c^7*d^3*e^4 + 54*b*c^6*d^2*e^5 - 474*b^2*c^5*d*e^6 - b^3*c^4*e^7)*g)*x^4 - 5*(3*(824*c^7*d^3*e^4 + 206*b*c^6*d^2*e^5 - 1454*b^2*c^5*d*e^6 - 5*b^3*c^4*e^7)*f - (1637*c^7*d^4*e^3 - 5930*b*c^6*d^3*e^4 + 4224*b^2*c^5*d^2*e^5 + 77*b^3*c^4*d*e^6 - 8*b^4*c^3*e^7)*g)*x^3 + 3*(15*(271*c^7*d^4*e^3 - 954*b*c^6*d^3*e^4 + 664*b^2*c^5*d^2*e^5 + 21*b^3*c^4*d*e^6 - 2*b^4*c^3*e^7)*f + (3274*c^7*d^5*e^2 - 6125*b*c^6*d^4*e^3 + 2290*b^2*c^5*d^3*e^4 + 715*b^3*c^4*d^2*e^5 - 170*b^4*c^3*d*e^6 + 16*b^5*c^2*e^7)*g)*x^2 - 15*(835*c^7*d^6*e - 3047*b*c^6*d^5*e^2 + 4283*b^2*c^5*d^4*e^3 - 2933*b^3*c^4*d^3*e^4 + 1046*b^4*c^3*d^2*e^5 - 200*b^5*c^2*d*e^6 + 16*b^6*c*e^7)*f - 2*(1919*c^7*d^7 - 9368*b*c^6*d^6*e + 18834*b^2*c^5*d^5*e^2 - 20100*b^3*c^4*d^4*e^3 + 12255*b^4*c^3*d^3*e^4 - 4284*b^5*c^2*d^2*e^5 + 808*b^6*c*d*e^6 - 64*b^7*e^7)*g + (15*(1084*c^7*d^5*e^2 - 1897*b*c^6*d^4*e^3 + 466*b^2*c^5*d^3*e^4 + 431*b^3*c^4*d^2*e^5 - 92*b^4*c^3*d*e^6 + 8*b^5*c^2*e^7)*f - (1919*c^7*d^6*e - 7449*b*c^6*d^5*e^2 + 11385*b^2*c^5*d^4*e^3 - 8715*b^3*c^4*d^3*e^4 + 3540*b^4*c^3*d^2*e^5 - 744*b^5*c^2*d*e^6 + 64*b^6*c*e^7)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^5*e^3*x + c^5*d*e^2)","B",0
2253,1,675,0,0.421969," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, c^{6} e^{6} g x^{6} + 63 \, {\left(13 \, c^{6} e^{6} f - {\left(c^{6} d e^{5} - 27 \, b c^{5} e^{6}\right)} g\right)} x^{5} - 7 \, {\left(13 \, {\left(c^{6} d e^{5} - 23 \, b c^{5} e^{6}\right)} f + {\left(296 \, c^{6} d^{2} e^{4} - 280 \, b c^{5} d e^{5} - 159 \, b^{2} c^{4} e^{6}\right)} g\right)} x^{4} - {\left(13 \, {\left(206 \, c^{6} d^{2} e^{4} - 192 \, b c^{5} d e^{5} - 113 \, b^{2} c^{4} e^{6}\right)} f - {\left(206 \, c^{6} d^{3} e^{3} - 3114 \, b c^{5} d^{2} e^{4} + 2893 \, b^{2} c^{4} d e^{5} + 15 \, b^{3} c^{3} e^{6}\right)} g\right)} x^{3} + 3 \, {\left(13 \, {\left(10 \, c^{6} d^{3} e^{3} - 118 \, b c^{5} d^{2} e^{4} + 107 \, b^{2} c^{4} d e^{5} + b^{3} c^{3} e^{6}\right)} f + {\left(683 \, c^{6} d^{4} e^{2} - 1328 \, b c^{5} d^{3} e^{3} + 601 \, b^{2} c^{4} d^{2} e^{4} + 50 \, b^{3} c^{3} d e^{5} - 6 \, b^{4} c^{2} e^{6}\right)} g\right)} x^{2} - 13 \, {\left(151 \, c^{6} d^{5} e - 513 \, b c^{5} d^{4} e^{2} + 641 \, b^{2} c^{4} d^{3} e^{3} - 355 \, b^{3} c^{3} d^{2} e^{4} + 84 \, b^{4} c^{2} d e^{5} - 8 \, b^{5} c e^{6}\right)} f - 2 \, {\left(271 \, c^{6} d^{6} - 1236 \, b c^{5} d^{5} e + 2258 \, b^{2} c^{4} d^{4} e^{2} - 2092 \, b^{3} c^{3} d^{3} e^{3} + 1023 \, b^{4} c^{2} d^{2} e^{4} - 248 \, b^{5} c d e^{5} + 24 \, b^{6} e^{6}\right)} g + {\left(13 \, {\left(271 \, c^{6} d^{4} e^{2} - 512 \, b c^{5} d^{3} e^{3} + 207 \, b^{2} c^{4} d^{2} e^{4} + 38 \, b^{3} c^{3} d e^{5} - 4 \, b^{4} c^{2} e^{6}\right)} f - {\left(271 \, c^{6} d^{5} e - 965 \, b c^{5} d^{4} e^{2} + 1293 \, b^{2} c^{4} d^{3} e^{3} - 799 \, b^{3} c^{3} d^{2} e^{4} + 224 \, b^{4} c^{2} d e^{5} - 24 \, b^{5} c e^{6}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{9009 \, {\left(c^{4} e^{3} x + c^{4} d e^{2}\right)}}"," ",0,"2/9009*(693*c^6*e^6*g*x^6 + 63*(13*c^6*e^6*f - (c^6*d*e^5 - 27*b*c^5*e^6)*g)*x^5 - 7*(13*(c^6*d*e^5 - 23*b*c^5*e^6)*f + (296*c^6*d^2*e^4 - 280*b*c^5*d*e^5 - 159*b^2*c^4*e^6)*g)*x^4 - (13*(206*c^6*d^2*e^4 - 192*b*c^5*d*e^5 - 113*b^2*c^4*e^6)*f - (206*c^6*d^3*e^3 - 3114*b*c^5*d^2*e^4 + 2893*b^2*c^4*d*e^5 + 15*b^3*c^3*e^6)*g)*x^3 + 3*(13*(10*c^6*d^3*e^3 - 118*b*c^5*d^2*e^4 + 107*b^2*c^4*d*e^5 + b^3*c^3*e^6)*f + (683*c^6*d^4*e^2 - 1328*b*c^5*d^3*e^3 + 601*b^2*c^4*d^2*e^4 + 50*b^3*c^3*d*e^5 - 6*b^4*c^2*e^6)*g)*x^2 - 13*(151*c^6*d^5*e - 513*b*c^5*d^4*e^2 + 641*b^2*c^4*d^3*e^3 - 355*b^3*c^3*d^2*e^4 + 84*b^4*c^2*d*e^5 - 8*b^5*c*e^6)*f - 2*(271*c^6*d^6 - 1236*b*c^5*d^5*e + 2258*b^2*c^4*d^4*e^2 - 2092*b^3*c^3*d^3*e^3 + 1023*b^4*c^2*d^2*e^4 - 248*b^5*c*d*e^5 + 24*b^6*e^6)*g + (13*(271*c^6*d^4*e^2 - 512*b*c^5*d^3*e^3 + 207*b^2*c^4*d^2*e^4 + 38*b^3*c^3*d*e^5 - 4*b^4*c^2*e^6)*f - (271*c^6*d^5*e - 965*b*c^5*d^4*e^2 + 1293*b^2*c^4*d^3*e^3 - 799*b^3*c^3*d^2*e^4 + 224*b^4*c^2*d*e^5 - 24*b^5*c*e^6)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^4*e^3*x + c^4*d*e^2)","B",0
2254,1,500,0,0.405215," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, c^{5} e^{5} g x^{5} + 7 \, {\left(11 \, c^{5} e^{5} f - {\left(12 \, c^{5} d e^{4} - 23 \, b c^{4} e^{5}\right)} g\right)} x^{4} - {\left(11 \, {\left(10 \, c^{5} d e^{4} - 19 \, b c^{4} e^{5}\right)} f + {\left(96 \, c^{5} d^{2} e^{3} + 17 \, b c^{4} d e^{4} - 113 \, b^{2} c^{3} e^{5}\right)} g\right)} x^{3} - 3 \, {\left(11 \, {\left(4 \, c^{5} d^{2} e^{3} + b c^{4} d e^{4} - 5 \, b^{2} c^{3} e^{5}\right)} f - {\left(54 \, c^{5} d^{3} e^{2} - 107 \, b c^{4} d^{2} e^{3} + 52 \, b^{2} c^{3} d e^{4} + b^{3} c^{2} e^{5}\right)} g\right)} x^{2} - 11 \, {\left(11 \, c^{5} d^{4} e - 35 \, b c^{4} d^{3} e^{2} + 39 \, b^{2} c^{3} d^{2} e^{3} - 17 \, b^{3} c^{2} d e^{4} + 2 \, b^{4} c e^{5}\right)} f - 2 \, {\left(15 \, c^{5} d^{5} - 64 \, b c^{4} d^{4} e + 106 \, b^{2} c^{3} d^{3} e^{2} - 84 \, b^{3} c^{2} d^{2} e^{3} + 31 \, b^{4} c d e^{4} - 4 \, b^{5} e^{5}\right)} g + {\left(11 \, {\left(26 \, c^{5} d^{3} e^{2} - 51 \, b c^{4} d^{2} e^{3} + 24 \, b^{2} c^{3} d e^{4} + b^{3} c^{2} e^{5}\right)} f - {\left(15 \, c^{5} d^{4} e - 49 \, b c^{4} d^{3} e^{2} + 57 \, b^{2} c^{3} d^{2} e^{3} - 27 \, b^{3} c^{2} d e^{4} + 4 \, b^{4} c e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{693 \, {\left(c^{3} e^{3} x + c^{3} d e^{2}\right)}}"," ",0,"2/693*(63*c^5*e^5*g*x^5 + 7*(11*c^5*e^5*f - (12*c^5*d*e^4 - 23*b*c^4*e^5)*g)*x^4 - (11*(10*c^5*d*e^4 - 19*b*c^4*e^5)*f + (96*c^5*d^2*e^3 + 17*b*c^4*d*e^4 - 113*b^2*c^3*e^5)*g)*x^3 - 3*(11*(4*c^5*d^2*e^3 + b*c^4*d*e^4 - 5*b^2*c^3*e^5)*f - (54*c^5*d^3*e^2 - 107*b*c^4*d^2*e^3 + 52*b^2*c^3*d*e^4 + b^3*c^2*e^5)*g)*x^2 - 11*(11*c^5*d^4*e - 35*b*c^4*d^3*e^2 + 39*b^2*c^3*d^2*e^3 - 17*b^3*c^2*d*e^4 + 2*b^4*c*e^5)*f - 2*(15*c^5*d^5 - 64*b*c^4*d^4*e + 106*b^2*c^3*d^3*e^2 - 84*b^3*c^2*d^2*e^3 + 31*b^4*c*d*e^4 - 4*b^5*e^5)*g + (11*(26*c^5*d^3*e^2 - 51*b*c^4*d^2*e^3 + 24*b^2*c^3*d*e^4 + b^3*c^2*e^5)*f - (15*c^5*d^4*e - 49*b*c^4*d^3*e^2 + 57*b^2*c^3*d^2*e^3 - 27*b^3*c^2*d*e^4 + 4*b^4*c*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^3*e^3*x + c^3*d*e^2)","B",0
2255,1,345,0,0.408226," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, c^{4} e^{4} g x^{4} + {\left(9 \, c^{4} e^{4} f - 19 \, {\left(c^{4} d e^{3} - b c^{3} e^{4}\right)} g\right)} x^{3} - 3 \, {\left(9 \, {\left(c^{4} d e^{3} - b c^{3} e^{4}\right)} f - 5 \, {\left(c^{4} d^{2} e^{2} - 2 \, b c^{3} d e^{3} + b^{2} c^{2} e^{4}\right)} g\right)} x^{2} - 9 \, {\left(c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + 3 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} f - 2 \, {\left(c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, b^{2} c^{2} d^{2} e^{2} - 4 \, b^{3} c d e^{3} + b^{4} e^{4}\right)} g + {\left(27 \, {\left(c^{4} d^{2} e^{2} - 2 \, b c^{3} d e^{3} + b^{2} c^{2} e^{4}\right)} f - {\left(c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + 3 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{63 \, {\left(c^{2} e^{3} x + c^{2} d e^{2}\right)}}"," ",0,"2/63*(7*c^4*e^4*g*x^4 + (9*c^4*e^4*f - 19*(c^4*d*e^3 - b*c^3*e^4)*g)*x^3 - 3*(9*(c^4*d*e^3 - b*c^3*e^4)*f - 5*(c^4*d^2*e^2 - 2*b*c^3*d*e^3 + b^2*c^2*e^4)*g)*x^2 - 9*(c^4*d^3*e - 3*b*c^3*d^2*e^2 + 3*b^2*c^2*d*e^3 - b^3*c*e^4)*f - 2*(c^4*d^4 - 4*b*c^3*d^3*e + 6*b^2*c^2*d^2*e^2 - 4*b^3*c*d*e^3 + b^4*e^4)*g + (27*(c^4*d^2*e^2 - 2*b*c^3*d*e^3 + b^2*c^2*e^4)*f - (c^4*d^3*e - 3*b*c^3*d^2*e^2 + 3*b^2*c^2*d*e^3 - b^3*c*e^4)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^2*e^3*x + c^2*d*e^2)","B",0
2256,1,949,0,0.428829," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[-\frac{105 \, \sqrt{2 \, c d - b e} {\left({\left(4 \, c^{3} d^{3} e - 4 \, b c^{2} d^{2} e^{2} + b^{2} c d e^{3}\right)} f - {\left(4 \, c^{3} d^{4} - 4 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2}\right)} g + {\left({\left(4 \, c^{3} d^{2} e^{2} - 4 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} f - {\left(4 \, c^{3} d^{3} e - 4 \, b c^{2} d^{2} e^{2} + b^{2} c d e^{3}\right)} g\right)} x\right)} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(15 \, c^{3} e^{3} g x^{3} + 3 \, {\left(7 \, c^{3} e^{3} f - {\left(22 \, c^{3} d e^{2} - 15 \, b c^{2} e^{3}\right)} g\right)} x^{2} + 7 \, {\left(73 \, c^{3} d^{2} e - 81 \, b c^{2} d e^{2} + 23 \, b^{2} c e^{3}\right)} f - {\left(526 \, c^{3} d^{3} - 612 \, b c^{2} d^{2} e + 206 \, b^{2} c d e^{2} - 15 \, b^{3} e^{3}\right)} g - {\left(7 \, {\left(16 \, c^{3} d e^{2} - 11 \, b c^{2} e^{3}\right)} f - {\left(157 \, c^{3} d^{2} e - 167 \, b c^{2} d e^{2} + 45 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{105 \, {\left(c e^{3} x + c d e^{2}\right)}}, -\frac{2 \, {\left(105 \, \sqrt{-2 \, c d + b e} {\left({\left(4 \, c^{3} d^{3} e - 4 \, b c^{2} d^{2} e^{2} + b^{2} c d e^{3}\right)} f - {\left(4 \, c^{3} d^{4} - 4 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2}\right)} g + {\left({\left(4 \, c^{3} d^{2} e^{2} - 4 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} f - {\left(4 \, c^{3} d^{3} e - 4 \, b c^{2} d^{2} e^{2} + b^{2} c d e^{3}\right)} g\right)} x\right)} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) - {\left(15 \, c^{3} e^{3} g x^{3} + 3 \, {\left(7 \, c^{3} e^{3} f - {\left(22 \, c^{3} d e^{2} - 15 \, b c^{2} e^{3}\right)} g\right)} x^{2} + 7 \, {\left(73 \, c^{3} d^{2} e - 81 \, b c^{2} d e^{2} + 23 \, b^{2} c e^{3}\right)} f - {\left(526 \, c^{3} d^{3} - 612 \, b c^{2} d^{2} e + 206 \, b^{2} c d e^{2} - 15 \, b^{3} e^{3}\right)} g - {\left(7 \, {\left(16 \, c^{3} d e^{2} - 11 \, b c^{2} e^{3}\right)} f - {\left(157 \, c^{3} d^{2} e - 167 \, b c^{2} d e^{2} + 45 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}\right)}}{105 \, {\left(c e^{3} x + c d e^{2}\right)}}\right]"," ",0,"[-1/105*(105*sqrt(2*c*d - b*e)*((4*c^3*d^3*e - 4*b*c^2*d^2*e^2 + b^2*c*d*e^3)*f - (4*c^3*d^4 - 4*b*c^2*d^3*e + b^2*c*d^2*e^2)*g + ((4*c^3*d^2*e^2 - 4*b*c^2*d*e^3 + b^2*c*e^4)*f - (4*c^3*d^3*e - 4*b*c^2*d^2*e^2 + b^2*c*d*e^3)*g)*x)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(15*c^3*e^3*g*x^3 + 3*(7*c^3*e^3*f - (22*c^3*d*e^2 - 15*b*c^2*e^3)*g)*x^2 + 7*(73*c^3*d^2*e - 81*b*c^2*d*e^2 + 23*b^2*c*e^3)*f - (526*c^3*d^3 - 612*b*c^2*d^2*e + 206*b^2*c*d*e^2 - 15*b^3*e^3)*g - (7*(16*c^3*d*e^2 - 11*b*c^2*e^3)*f - (157*c^3*d^2*e - 167*b*c^2*d*e^2 + 45*b^2*c*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(c*e^3*x + c*d*e^2), -2/105*(105*sqrt(-2*c*d + b*e)*((4*c^3*d^3*e - 4*b*c^2*d^2*e^2 + b^2*c*d*e^3)*f - (4*c^3*d^4 - 4*b*c^2*d^3*e + b^2*c*d^2*e^2)*g + ((4*c^3*d^2*e^2 - 4*b*c^2*d*e^3 + b^2*c*e^4)*f - (4*c^3*d^3*e - 4*b*c^2*d^2*e^2 + b^2*c*d*e^3)*g)*x)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) - (15*c^3*e^3*g*x^3 + 3*(7*c^3*e^3*f - (22*c^3*d*e^2 - 15*b*c^2*e^3)*g)*x^2 + 7*(73*c^3*d^2*e - 81*b*c^2*d*e^2 + 23*b^2*c*e^3)*f - (526*c^3*d^3 - 612*b*c^2*d^2*e + 206*b^2*c*d*e^2 - 15*b^3*e^3)*g - (7*(16*c^3*d*e^2 - 11*b*c^2*e^3)*f - (157*c^3*d^2*e - 167*b*c^2*d*e^2 + 45*b^2*c*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(c*e^3*x + c*d*e^2)]","A",0
2257,1,990,0,0.431934," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(5 \, {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} f - {\left(18 \, c^{2} d^{2} e^{2} - 13 \, b c d e^{3} + 2 \, b^{2} e^{4}\right)} g\right)} x^{2} + 5 \, {\left(2 \, c^{2} d^{3} e - b c d^{2} e^{2}\right)} f - {\left(18 \, c^{2} d^{4} - 13 \, b c d^{3} e + 2 \, b^{2} d^{2} e^{2}\right)} g + 2 \, {\left(5 \, {\left(2 \, c^{2} d^{2} e^{2} - b c d e^{3}\right)} f - {\left(18 \, c^{2} d^{3} e - 13 \, b c d^{2} e^{2} + 2 \, b^{2} d e^{3}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(6 \, c^{2} e^{3} g x^{3} + 2 \, {\left(5 \, c^{2} e^{3} f - {\left(18 \, c^{2} d e^{2} - 11 \, b c e^{3}\right)} g\right)} x^{2} - 5 \, {\left(38 \, c^{2} d^{2} e - 26 \, b c d e^{2} + 3 \, b^{2} e^{3}\right)} f + {\left(336 \, c^{2} d^{3} - 292 \, b c d^{2} e + 61 \, b^{2} d e^{2}\right)} g - 2 \, {\left(5 \, {\left(12 \, c^{2} d e^{2} - 7 \, b c e^{3}\right)} f - {\left(117 \, c^{2} d^{2} e - 105 \, b c d e^{2} + 23 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{30 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}, \frac{15 \, {\left({\left(5 \, {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} f - {\left(18 \, c^{2} d^{2} e^{2} - 13 \, b c d e^{3} + 2 \, b^{2} e^{4}\right)} g\right)} x^{2} + 5 \, {\left(2 \, c^{2} d^{3} e - b c d^{2} e^{2}\right)} f - {\left(18 \, c^{2} d^{4} - 13 \, b c d^{3} e + 2 \, b^{2} d^{2} e^{2}\right)} g + 2 \, {\left(5 \, {\left(2 \, c^{2} d^{2} e^{2} - b c d e^{3}\right)} f - {\left(18 \, c^{2} d^{3} e - 13 \, b c d^{2} e^{2} + 2 \, b^{2} d e^{3}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + {\left(6 \, c^{2} e^{3} g x^{3} + 2 \, {\left(5 \, c^{2} e^{3} f - {\left(18 \, c^{2} d e^{2} - 11 \, b c e^{3}\right)} g\right)} x^{2} - 5 \, {\left(38 \, c^{2} d^{2} e - 26 \, b c d e^{2} + 3 \, b^{2} e^{3}\right)} f + {\left(336 \, c^{2} d^{3} - 292 \, b c d^{2} e + 61 \, b^{2} d e^{2}\right)} g - 2 \, {\left(5 \, {\left(12 \, c^{2} d e^{2} - 7 \, b c e^{3}\right)} f - {\left(117 \, c^{2} d^{2} e - 105 \, b c d e^{2} + 23 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{15 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}\right]"," ",0,"[-1/30*(15*((5*(2*c^2*d*e^3 - b*c*e^4)*f - (18*c^2*d^2*e^2 - 13*b*c*d*e^3 + 2*b^2*e^4)*g)*x^2 + 5*(2*c^2*d^3*e - b*c*d^2*e^2)*f - (18*c^2*d^4 - 13*b*c*d^3*e + 2*b^2*d^2*e^2)*g + 2*(5*(2*c^2*d^2*e^2 - b*c*d*e^3)*f - (18*c^2*d^3*e - 13*b*c*d^2*e^2 + 2*b^2*d*e^3)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(6*c^2*e^3*g*x^3 + 2*(5*c^2*e^3*f - (18*c^2*d*e^2 - 11*b*c*e^3)*g)*x^2 - 5*(38*c^2*d^2*e - 26*b*c*d*e^2 + 3*b^2*e^3)*f + (336*c^2*d^3 - 292*b*c*d^2*e + 61*b^2*d*e^2)*g - 2*(5*(12*c^2*d*e^2 - 7*b*c*e^3)*f - (117*c^2*d^2*e - 105*b*c*d*e^2 + 23*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2), 1/15*(15*((5*(2*c^2*d*e^3 - b*c*e^4)*f - (18*c^2*d^2*e^2 - 13*b*c*d*e^3 + 2*b^2*e^4)*g)*x^2 + 5*(2*c^2*d^3*e - b*c*d^2*e^2)*f - (18*c^2*d^4 - 13*b*c*d^3*e + 2*b^2*d^2*e^2)*g + 2*(5*(2*c^2*d^2*e^2 - b*c*d*e^3)*f - (18*c^2*d^3*e - 13*b*c*d^2*e^2 + 2*b^2*d*e^3)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + (6*c^2*e^3*g*x^3 + 2*(5*c^2*e^3*f - (18*c^2*d*e^2 - 11*b*c*e^3)*g)*x^2 - 5*(38*c^2*d^2*e - 26*b*c*d*e^2 + 3*b^2*e^3)*f + (336*c^2*d^3 - 292*b*c*d^2*e + 61*b^2*d*e^2)*g - 2*(5*(12*c^2*d*e^2 - 7*b*c*e^3)*f - (117*c^2*d^2*e - 105*b*c*d*e^2 + 23*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)]","A",0
2258,1,959,0,0.450776," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, c^{2} d^{3} e f + {\left(3 \, c^{2} e^{4} f - {\left(11 \, c^{2} d e^{3} - 4 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(3 \, c^{2} d e^{3} f - {\left(11 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3}\right)} g\right)} x^{2} - {\left(11 \, c^{2} d^{4} - 4 \, b c d^{3} e\right)} g + 3 \, {\left(3 \, c^{2} d^{2} e^{2} f - {\left(11 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(8 \, c^{2} e^{3} g x^{3} + 8 \, {\left(3 \, c^{2} e^{3} f - 7 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} g\right)} x^{2} + 3 \, {\left(18 \, c^{2} d^{2} e - b c d e^{2} - 2 \, b^{2} e^{3}\right)} f - {\left(206 \, c^{2} d^{3} - 107 \, b c d^{2} e + 6 \, b^{2} d e^{2}\right)} g + {\left(3 \, {\left(34 \, c^{2} d e^{2} - 9 \, b c e^{3}\right)} f - {\left(350 \, c^{2} d^{2} e - 187 \, b c d e^{2} + 12 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{24 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}}, -\frac{15 \, {\left(3 \, c^{2} d^{3} e f + {\left(3 \, c^{2} e^{4} f - {\left(11 \, c^{2} d e^{3} - 4 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(3 \, c^{2} d e^{3} f - {\left(11 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3}\right)} g\right)} x^{2} - {\left(11 \, c^{2} d^{4} - 4 \, b c d^{3} e\right)} g + 3 \, {\left(3 \, c^{2} d^{2} e^{2} f - {\left(11 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) - {\left(8 \, c^{2} e^{3} g x^{3} + 8 \, {\left(3 \, c^{2} e^{3} f - 7 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} g\right)} x^{2} + 3 \, {\left(18 \, c^{2} d^{2} e - b c d e^{2} - 2 \, b^{2} e^{3}\right)} f - {\left(206 \, c^{2} d^{3} - 107 \, b c d^{2} e + 6 \, b^{2} d e^{2}\right)} g + {\left(3 \, {\left(34 \, c^{2} d e^{2} - 9 \, b c e^{3}\right)} f - {\left(350 \, c^{2} d^{2} e - 187 \, b c d e^{2} + 12 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{12 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}}\right]"," ",0,"[1/24*(15*(3*c^2*d^3*e*f + (3*c^2*e^4*f - (11*c^2*d*e^3 - 4*b*c*e^4)*g)*x^3 + 3*(3*c^2*d*e^3*f - (11*c^2*d^2*e^2 - 4*b*c*d*e^3)*g)*x^2 - (11*c^2*d^4 - 4*b*c*d^3*e)*g + 3*(3*c^2*d^2*e^2*f - (11*c^2*d^3*e - 4*b*c*d^2*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(8*c^2*e^3*g*x^3 + 8*(3*c^2*e^3*f - 7*(2*c^2*d*e^2 - b*c*e^3)*g)*x^2 + 3*(18*c^2*d^2*e - b*c*d*e^2 - 2*b^2*e^3)*f - (206*c^2*d^3 - 107*b*c*d^2*e + 6*b^2*d*e^2)*g + (3*(34*c^2*d*e^2 - 9*b*c*e^3)*f - (350*c^2*d^2*e - 187*b*c*d*e^2 + 12*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2), -1/12*(15*(3*c^2*d^3*e*f + (3*c^2*e^4*f - (11*c^2*d*e^3 - 4*b*c*e^4)*g)*x^3 + 3*(3*c^2*d*e^3*f - (11*c^2*d^2*e^2 - 4*b*c*d*e^3)*g)*x^2 - (11*c^2*d^4 - 4*b*c*d^3*e)*g + 3*(3*c^2*d^2*e^2*f - (11*c^2*d^3*e - 4*b*c*d^2*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) - (8*c^2*e^3*g*x^3 + 8*(3*c^2*e^3*f - 7*(2*c^2*d*e^2 - b*c*e^3)*g)*x^2 + 3*(18*c^2*d^2*e - b*c*d*e^2 - 2*b^2*e^3)*f - (206*c^2*d^3 - 107*b*c*d^2*e + 6*b^2*d*e^2)*g + (3*(34*c^2*d*e^2 - 9*b*c*e^3)*f - (350*c^2*d^2*e - 187*b*c*d*e^2 + 12*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2)]","A",0
2259,1,1388,0,0.510167," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(13/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{3} d^{4} e f + {\left(c^{3} e^{5} f - {\left(13 \, c^{3} d e^{4} - 6 \, b c^{2} e^{5}\right)} g\right)} x^{4} + 4 \, {\left(c^{3} d e^{4} f - {\left(13 \, c^{3} d^{2} e^{3} - 6 \, b c^{2} d e^{4}\right)} g\right)} x^{3} + 6 \, {\left(c^{3} d^{2} e^{3} f - {\left(13 \, c^{3} d^{3} e^{2} - 6 \, b c^{2} d^{2} e^{3}\right)} g\right)} x^{2} - {\left(13 \, c^{3} d^{5} - 6 \, b c^{2} d^{4} e\right)} g + 4 \, {\left(c^{3} d^{3} e^{2} f - {\left(13 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(48 \, {\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} g x^{3} - 3 \, {\left(11 \, {\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f - {\left(190 \, c^{3} d^{2} e^{2} - 131 \, b c^{2} d e^{3} + 18 \, b^{2} c e^{4}\right)} g\right)} x^{2} - {\left(26 \, c^{3} d^{3} e - 25 \, b c^{2} d^{2} e^{2} + 22 \, b^{2} c d e^{3} - 8 \, b^{3} e^{4}\right)} f + {\left(242 \, c^{3} d^{4} - 145 \, b c^{2} d^{3} e + 4 \, b^{2} c d^{2} e^{2} + 4 \, b^{3} d e^{3}\right)} g - 2 \, {\left({\left(14 \, c^{3} d^{2} e^{2} + 19 \, b c^{2} d e^{3} - 13 \, b^{2} c e^{4}\right)} f - {\left(326 \, c^{3} d^{3} e - 197 \, b c^{2} d^{2} e^{2} + 5 \, b^{2} c d e^{3} + 6 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(2 \, c d^{5} e^{2} - b d^{4} e^{3} + {\left(2 \, c d e^{6} - b e^{7}\right)} x^{4} + 4 \, {\left(2 \, c d^{2} e^{5} - b d e^{6}\right)} x^{3} + 6 \, {\left(2 \, c d^{3} e^{4} - b d^{2} e^{5}\right)} x^{2} + 4 \, {\left(2 \, c d^{4} e^{3} - b d^{3} e^{4}\right)} x\right)}}, \frac{15 \, {\left(c^{3} d^{4} e f + {\left(c^{3} e^{5} f - {\left(13 \, c^{3} d e^{4} - 6 \, b c^{2} e^{5}\right)} g\right)} x^{4} + 4 \, {\left(c^{3} d e^{4} f - {\left(13 \, c^{3} d^{2} e^{3} - 6 \, b c^{2} d e^{4}\right)} g\right)} x^{3} + 6 \, {\left(c^{3} d^{2} e^{3} f - {\left(13 \, c^{3} d^{3} e^{2} - 6 \, b c^{2} d^{2} e^{3}\right)} g\right)} x^{2} - {\left(13 \, c^{3} d^{5} - 6 \, b c^{2} d^{4} e\right)} g + 4 \, {\left(c^{3} d^{3} e^{2} f - {\left(13 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(48 \, {\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} g x^{3} - 3 \, {\left(11 \, {\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f - {\left(190 \, c^{3} d^{2} e^{2} - 131 \, b c^{2} d e^{3} + 18 \, b^{2} c e^{4}\right)} g\right)} x^{2} - {\left(26 \, c^{3} d^{3} e - 25 \, b c^{2} d^{2} e^{2} + 22 \, b^{2} c d e^{3} - 8 \, b^{3} e^{4}\right)} f + {\left(242 \, c^{3} d^{4} - 145 \, b c^{2} d^{3} e + 4 \, b^{2} c d^{2} e^{2} + 4 \, b^{3} d e^{3}\right)} g - 2 \, {\left({\left(14 \, c^{3} d^{2} e^{2} + 19 \, b c^{2} d e^{3} - 13 \, b^{2} c e^{4}\right)} f - {\left(326 \, c^{3} d^{3} e - 197 \, b c^{2} d^{2} e^{2} + 5 \, b^{2} c d e^{3} + 6 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(2 \, c d^{5} e^{2} - b d^{4} e^{3} + {\left(2 \, c d e^{6} - b e^{7}\right)} x^{4} + 4 \, {\left(2 \, c d^{2} e^{5} - b d e^{6}\right)} x^{3} + 6 \, {\left(2 \, c d^{3} e^{4} - b d^{2} e^{5}\right)} x^{2} + 4 \, {\left(2 \, c d^{4} e^{3} - b d^{3} e^{4}\right)} x\right)}}\right]"," ",0,"[1/48*(15*(c^3*d^4*e*f + (c^3*e^5*f - (13*c^3*d*e^4 - 6*b*c^2*e^5)*g)*x^4 + 4*(c^3*d*e^4*f - (13*c^3*d^2*e^3 - 6*b*c^2*d*e^4)*g)*x^3 + 6*(c^3*d^2*e^3*f - (13*c^3*d^3*e^2 - 6*b*c^2*d^2*e^3)*g)*x^2 - (13*c^3*d^5 - 6*b*c^2*d^4*e)*g + 4*(c^3*d^3*e^2*f - (13*c^3*d^4*e - 6*b*c^2*d^3*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(48*(2*c^3*d*e^3 - b*c^2*e^4)*g*x^3 - 3*(11*(2*c^3*d*e^3 - b*c^2*e^4)*f - (190*c^3*d^2*e^2 - 131*b*c^2*d*e^3 + 18*b^2*c*e^4)*g)*x^2 - (26*c^3*d^3*e - 25*b*c^2*d^2*e^2 + 22*b^2*c*d*e^3 - 8*b^3*e^4)*f + (242*c^3*d^4 - 145*b*c^2*d^3*e + 4*b^2*c*d^2*e^2 + 4*b^3*d*e^3)*g - 2*((14*c^3*d^2*e^2 + 19*b*c^2*d*e^3 - 13*b^2*c*e^4)*f - (326*c^3*d^3*e - 197*b*c^2*d^2*e^2 + 5*b^2*c*d*e^3 + 6*b^3*e^4)*g)*x)*sqrt(e*x + d))/(2*c*d^5*e^2 - b*d^4*e^3 + (2*c*d*e^6 - b*e^7)*x^4 + 4*(2*c*d^2*e^5 - b*d*e^6)*x^3 + 6*(2*c*d^3*e^4 - b*d^2*e^5)*x^2 + 4*(2*c*d^4*e^3 - b*d^3*e^4)*x), 1/24*(15*(c^3*d^4*e*f + (c^3*e^5*f - (13*c^3*d*e^4 - 6*b*c^2*e^5)*g)*x^4 + 4*(c^3*d*e^4*f - (13*c^3*d^2*e^3 - 6*b*c^2*d*e^4)*g)*x^3 + 6*(c^3*d^2*e^3*f - (13*c^3*d^3*e^2 - 6*b*c^2*d^2*e^3)*g)*x^2 - (13*c^3*d^5 - 6*b*c^2*d^4*e)*g + 4*(c^3*d^3*e^2*f - (13*c^3*d^4*e - 6*b*c^2*d^3*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(48*(2*c^3*d*e^3 - b*c^2*e^4)*g*x^3 - 3*(11*(2*c^3*d*e^3 - b*c^2*e^4)*f - (190*c^3*d^2*e^2 - 131*b*c^2*d*e^3 + 18*b^2*c*e^4)*g)*x^2 - (26*c^3*d^3*e - 25*b*c^2*d^2*e^2 + 22*b^2*c*d*e^3 - 8*b^3*e^4)*f + (242*c^3*d^4 - 145*b*c^2*d^3*e + 4*b^2*c*d^2*e^2 + 4*b^3*d*e^3)*g - 2*((14*c^3*d^2*e^2 + 19*b*c^2*d*e^3 - 13*b^2*c*e^4)*f - (326*c^3*d^3*e - 197*b*c^2*d^2*e^2 + 5*b^2*c*d*e^3 + 6*b^3*e^4)*g)*x)*sqrt(e*x + d))/(2*c*d^5*e^2 - b*d^4*e^3 + (2*c*d*e^6 - b*e^7)*x^4 + 4*(2*c*d^2*e^5 - b*d*e^6)*x^3 + 6*(2*c*d^3*e^4 - b*d^2*e^5)*x^2 + 4*(2*c*d^4*e^3 - b*d^3*e^4)*x)]","A",0
2260,1,1910,0,0.495942," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(15/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{4} d^{5} e f + {\left(c^{4} e^{6} f + {\left(15 \, c^{4} d e^{5} - 8 \, b c^{3} e^{6}\right)} g\right)} x^{5} + 5 \, {\left(c^{4} d e^{5} f + {\left(15 \, c^{4} d^{2} e^{4} - 8 \, b c^{3} d e^{5}\right)} g\right)} x^{4} + 10 \, {\left(c^{4} d^{2} e^{4} f + {\left(15 \, c^{4} d^{3} e^{3} - 8 \, b c^{3} d^{2} e^{4}\right)} g\right)} x^{3} + 10 \, {\left(c^{4} d^{3} e^{3} f + {\left(15 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3}\right)} g\right)} x^{2} + {\left(15 \, c^{4} d^{6} - 8 \, b c^{3} d^{5} e\right)} g + 5 \, {\left(c^{4} d^{4} e^{2} f + {\left(15 \, c^{4} d^{5} e - 8 \, b c^{3} d^{4} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(5 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f - {\left(362 \, c^{4} d^{2} e^{3} - 357 \, b c^{3} d e^{4} + 88 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} - {\left({\left(382 \, c^{4} d^{2} e^{3} - 427 \, b c^{3} d e^{4} + 118 \, b^{2} c^{2} e^{5}\right)} f + {\left(1122 \, c^{4} d^{3} e^{2} - 245 \, b c^{3} d^{2} e^{3} - 574 \, b^{2} c^{2} d e^{4} + 208 \, b^{3} c e^{5}\right)} g\right)} x^{2} - {\left(122 \, c^{4} d^{4} e - 361 \, b c^{3} d^{3} e^{2} + 454 \, b^{2} c^{2} d^{2} e^{3} - 248 \, b^{3} c d e^{4} + 48 \, b^{4} e^{5}\right)} f - {\left(294 \, c^{4} d^{5} - 247 \, b c^{3} d^{4} e + 98 \, b^{2} c^{2} d^{3} e^{2} - 56 \, b^{3} c d^{2} e^{3} + 16 \, b^{4} d e^{4}\right)} g + {\left({\left(234 \, c^{4} d^{3} e^{2} - 733 \, b c^{3} d^{2} e^{3} + 580 \, b^{2} c^{2} d e^{4} - 136 \, b^{3} c e^{5}\right)} f - {\left(1098 \, c^{4} d^{4} e - 957 \, b c^{3} d^{3} e^{2} + 412 \, b^{2} c^{2} d^{2} e^{3} - 232 \, b^{3} c d e^{4} + 64 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(4 \, c^{2} d^{7} e^{2} - 4 \, b c d^{6} e^{3} + b^{2} d^{5} e^{4} + {\left(4 \, c^{2} d^{2} e^{7} - 4 \, b c d e^{8} + b^{2} e^{9}\right)} x^{5} + 5 \, {\left(4 \, c^{2} d^{3} e^{6} - 4 \, b c d^{2} e^{7} + b^{2} d e^{8}\right)} x^{4} + 10 \, {\left(4 \, c^{2} d^{4} e^{5} - 4 \, b c d^{3} e^{6} + b^{2} d^{2} e^{7}\right)} x^{3} + 10 \, {\left(4 \, c^{2} d^{5} e^{4} - 4 \, b c d^{4} e^{5} + b^{2} d^{3} e^{6}\right)} x^{2} + 5 \, {\left(4 \, c^{2} d^{6} e^{3} - 4 \, b c d^{5} e^{4} + b^{2} d^{4} e^{5}\right)} x\right)}}, \frac{15 \, {\left(c^{4} d^{5} e f + {\left(c^{4} e^{6} f + {\left(15 \, c^{4} d e^{5} - 8 \, b c^{3} e^{6}\right)} g\right)} x^{5} + 5 \, {\left(c^{4} d e^{5} f + {\left(15 \, c^{4} d^{2} e^{4} - 8 \, b c^{3} d e^{5}\right)} g\right)} x^{4} + 10 \, {\left(c^{4} d^{2} e^{4} f + {\left(15 \, c^{4} d^{3} e^{3} - 8 \, b c^{3} d^{2} e^{4}\right)} g\right)} x^{3} + 10 \, {\left(c^{4} d^{3} e^{3} f + {\left(15 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3}\right)} g\right)} x^{2} + {\left(15 \, c^{4} d^{6} - 8 \, b c^{3} d^{5} e\right)} g + 5 \, {\left(c^{4} d^{4} e^{2} f + {\left(15 \, c^{4} d^{5} e - 8 \, b c^{3} d^{4} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(5 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f - {\left(362 \, c^{4} d^{2} e^{3} - 357 \, b c^{3} d e^{4} + 88 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} - {\left({\left(382 \, c^{4} d^{2} e^{3} - 427 \, b c^{3} d e^{4} + 118 \, b^{2} c^{2} e^{5}\right)} f + {\left(1122 \, c^{4} d^{3} e^{2} - 245 \, b c^{3} d^{2} e^{3} - 574 \, b^{2} c^{2} d e^{4} + 208 \, b^{3} c e^{5}\right)} g\right)} x^{2} - {\left(122 \, c^{4} d^{4} e - 361 \, b c^{3} d^{3} e^{2} + 454 \, b^{2} c^{2} d^{2} e^{3} - 248 \, b^{3} c d e^{4} + 48 \, b^{4} e^{5}\right)} f - {\left(294 \, c^{4} d^{5} - 247 \, b c^{3} d^{4} e + 98 \, b^{2} c^{2} d^{3} e^{2} - 56 \, b^{3} c d^{2} e^{3} + 16 \, b^{4} d e^{4}\right)} g + {\left({\left(234 \, c^{4} d^{3} e^{2} - 733 \, b c^{3} d^{2} e^{3} + 580 \, b^{2} c^{2} d e^{4} - 136 \, b^{3} c e^{5}\right)} f - {\left(1098 \, c^{4} d^{4} e - 957 \, b c^{3} d^{3} e^{2} + 412 \, b^{2} c^{2} d^{2} e^{3} - 232 \, b^{3} c d e^{4} + 64 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(4 \, c^{2} d^{7} e^{2} - 4 \, b c d^{6} e^{3} + b^{2} d^{5} e^{4} + {\left(4 \, c^{2} d^{2} e^{7} - 4 \, b c d e^{8} + b^{2} e^{9}\right)} x^{5} + 5 \, {\left(4 \, c^{2} d^{3} e^{6} - 4 \, b c d^{2} e^{7} + b^{2} d e^{8}\right)} x^{4} + 10 \, {\left(4 \, c^{2} d^{4} e^{5} - 4 \, b c d^{3} e^{6} + b^{2} d^{2} e^{7}\right)} x^{3} + 10 \, {\left(4 \, c^{2} d^{5} e^{4} - 4 \, b c d^{4} e^{5} + b^{2} d^{3} e^{6}\right)} x^{2} + 5 \, {\left(4 \, c^{2} d^{6} e^{3} - 4 \, b c d^{5} e^{4} + b^{2} d^{4} e^{5}\right)} x\right)}}\right]"," ",0,"[1/384*(15*(c^4*d^5*e*f + (c^4*e^6*f + (15*c^4*d*e^5 - 8*b*c^3*e^6)*g)*x^5 + 5*(c^4*d*e^5*f + (15*c^4*d^2*e^4 - 8*b*c^3*d*e^5)*g)*x^4 + 10*(c^4*d^2*e^4*f + (15*c^4*d^3*e^3 - 8*b*c^3*d^2*e^4)*g)*x^3 + 10*(c^4*d^3*e^3*f + (15*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3)*g)*x^2 + (15*c^4*d^6 - 8*b*c^3*d^5*e)*g + 5*(c^4*d^4*e^2*f + (15*c^4*d^5*e - 8*b*c^3*d^4*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(5*(2*c^4*d*e^4 - b*c^3*e^5)*f - (362*c^4*d^2*e^3 - 357*b*c^3*d*e^4 + 88*b^2*c^2*e^5)*g)*x^3 - ((382*c^4*d^2*e^3 - 427*b*c^3*d*e^4 + 118*b^2*c^2*e^5)*f + (1122*c^4*d^3*e^2 - 245*b*c^3*d^2*e^3 - 574*b^2*c^2*d*e^4 + 208*b^3*c*e^5)*g)*x^2 - (122*c^4*d^4*e - 361*b*c^3*d^3*e^2 + 454*b^2*c^2*d^2*e^3 - 248*b^3*c*d*e^4 + 48*b^4*e^5)*f - (294*c^4*d^5 - 247*b*c^3*d^4*e + 98*b^2*c^2*d^3*e^2 - 56*b^3*c*d^2*e^3 + 16*b^4*d*e^4)*g + ((234*c^4*d^3*e^2 - 733*b*c^3*d^2*e^3 + 580*b^2*c^2*d*e^4 - 136*b^3*c*e^5)*f - (1098*c^4*d^4*e - 957*b*c^3*d^3*e^2 + 412*b^2*c^2*d^2*e^3 - 232*b^3*c*d*e^4 + 64*b^4*e^5)*g)*x)*sqrt(e*x + d))/(4*c^2*d^7*e^2 - 4*b*c*d^6*e^3 + b^2*d^5*e^4 + (4*c^2*d^2*e^7 - 4*b*c*d*e^8 + b^2*e^9)*x^5 + 5*(4*c^2*d^3*e^6 - 4*b*c*d^2*e^7 + b^2*d*e^8)*x^4 + 10*(4*c^2*d^4*e^5 - 4*b*c*d^3*e^6 + b^2*d^2*e^7)*x^3 + 10*(4*c^2*d^5*e^4 - 4*b*c*d^4*e^5 + b^2*d^3*e^6)*x^2 + 5*(4*c^2*d^6*e^3 - 4*b*c*d^5*e^4 + b^2*d^4*e^5)*x), 1/192*(15*(c^4*d^5*e*f + (c^4*e^6*f + (15*c^4*d*e^5 - 8*b*c^3*e^6)*g)*x^5 + 5*(c^4*d*e^5*f + (15*c^4*d^2*e^4 - 8*b*c^3*d*e^5)*g)*x^4 + 10*(c^4*d^2*e^4*f + (15*c^4*d^3*e^3 - 8*b*c^3*d^2*e^4)*g)*x^3 + 10*(c^4*d^3*e^3*f + (15*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3)*g)*x^2 + (15*c^4*d^6 - 8*b*c^3*d^5*e)*g + 5*(c^4*d^4*e^2*f + (15*c^4*d^5*e - 8*b*c^3*d^4*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(5*(2*c^4*d*e^4 - b*c^3*e^5)*f - (362*c^4*d^2*e^3 - 357*b*c^3*d*e^4 + 88*b^2*c^2*e^5)*g)*x^3 - ((382*c^4*d^2*e^3 - 427*b*c^3*d*e^4 + 118*b^2*c^2*e^5)*f + (1122*c^4*d^3*e^2 - 245*b*c^3*d^2*e^3 - 574*b^2*c^2*d*e^4 + 208*b^3*c*e^5)*g)*x^2 - (122*c^4*d^4*e - 361*b*c^3*d^3*e^2 + 454*b^2*c^2*d^2*e^3 - 248*b^3*c*d*e^4 + 48*b^4*e^5)*f - (294*c^4*d^5 - 247*b*c^3*d^4*e + 98*b^2*c^2*d^3*e^2 - 56*b^3*c*d^2*e^3 + 16*b^4*d*e^4)*g + ((234*c^4*d^3*e^2 - 733*b*c^3*d^2*e^3 + 580*b^2*c^2*d*e^4 - 136*b^3*c*e^5)*f - (1098*c^4*d^4*e - 957*b*c^3*d^3*e^2 + 412*b^2*c^2*d^2*e^3 - 232*b^3*c*d*e^4 + 64*b^4*e^5)*g)*x)*sqrt(e*x + d))/(4*c^2*d^7*e^2 - 4*b*c*d^6*e^3 + b^2*d^5*e^4 + (4*c^2*d^2*e^7 - 4*b*c*d*e^8 + b^2*e^9)*x^5 + 5*(4*c^2*d^3*e^6 - 4*b*c*d^2*e^7 + b^2*d*e^8)*x^4 + 10*(4*c^2*d^4*e^5 - 4*b*c*d^3*e^6 + b^2*d^2*e^7)*x^3 + 10*(4*c^2*d^5*e^4 - 4*b*c*d^4*e^5 + b^2*d^3*e^6)*x^2 + 5*(4*c^2*d^6*e^3 - 4*b*c*d^5*e^4 + b^2*d^4*e^5)*x)]","B",0
2261,1,2650,0,0.532771," ","integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(17/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, c^{5} d^{6} e f + {\left(3 \, c^{5} e^{7} f + {\left(17 \, c^{5} d e^{6} - 10 \, b c^{4} e^{7}\right)} g\right)} x^{6} + 6 \, {\left(3 \, c^{5} d e^{6} f + {\left(17 \, c^{5} d^{2} e^{5} - 10 \, b c^{4} d e^{6}\right)} g\right)} x^{5} + 15 \, {\left(3 \, c^{5} d^{2} e^{5} f + {\left(17 \, c^{5} d^{3} e^{4} - 10 \, b c^{4} d^{2} e^{5}\right)} g\right)} x^{4} + 20 \, {\left(3 \, c^{5} d^{3} e^{4} f + {\left(17 \, c^{5} d^{4} e^{3} - 10 \, b c^{4} d^{3} e^{4}\right)} g\right)} x^{3} + 15 \, {\left(3 \, c^{5} d^{4} e^{3} f + {\left(17 \, c^{5} d^{5} e^{2} - 10 \, b c^{4} d^{4} e^{3}\right)} g\right)} x^{2} + {\left(17 \, c^{5} d^{7} - 10 \, b c^{4} d^{6} e\right)} g + 6 \, {\left(3 \, c^{5} d^{5} e^{2} f + {\left(17 \, c^{5} d^{6} e - 10 \, b c^{4} d^{5} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(15 \, {\left(3 \, {\left(2 \, c^{5} d e^{5} - b c^{4} e^{6}\right)} f + {\left(34 \, c^{5} d^{2} e^{4} - 37 \, b c^{4} d e^{5} + 10 \, b^{2} c^{3} e^{6}\right)} g\right)} x^{4} + 10 \, {\left(3 \, {\left(16 \, c^{5} d^{2} e^{4} - 10 \, b c^{4} d e^{5} + b^{2} c^{3} e^{6}\right)} f - {\left(752 \, c^{5} d^{3} e^{3} - 1206 \, b c^{4} d^{2} e^{4} + 651 \, b^{2} c^{3} d e^{5} - 118 \, b^{3} c^{2} e^{6}\right)} g\right)} x^{3} - 2 \, {\left(3 \, {\left(842 \, c^{5} d^{3} e^{3} - 1383 \, b c^{4} d^{2} e^{4} + 729 \, b^{2} c^{3} d e^{5} - 124 \, b^{3} c^{2} e^{6}\right)} f - {\left(1046 \, c^{5} d^{4} e^{2} - 6469 \, b c^{4} d^{3} e^{3} + 8337 \, b^{2} c^{3} d^{2} e^{4} - 4042 \, b^{3} c^{2} d e^{5} + 680 \, b^{4} c e^{6}\right)} g\right)} x^{2} - 3 \, {\left(634 \, c^{5} d^{5} e - 2409 \, b c^{4} d^{4} e^{2} + 3654 \, b^{2} c^{3} d^{3} e^{3} - 2680 \, b^{3} c^{2} d^{2} e^{4} + 944 \, b^{4} c d e^{5} - 128 \, b^{5} e^{6}\right)} f - {\left(538 \, c^{5} d^{6} - 1213 \, b c^{4} d^{5} e + 1728 \, b^{2} c^{3} d^{4} e^{2} - 1460 \, b^{3} c^{2} d^{3} e^{3} + 608 \, b^{4} c d^{2} e^{4} - 96 \, b^{5} d e^{5}\right)} g + 2 \, {\left(3 \, {\left(824 \, c^{5} d^{4} e^{2} - 2490 \, b c^{4} d^{3} e^{3} + 2559 \, b^{2} c^{3} d^{2} e^{4} - 1096 \, b^{3} c^{2} d e^{5} + 168 \, b^{4} c e^{6}\right)} f - {\left(1352 \, c^{5} d^{5} e - 3190 \, b c^{4} d^{4} e^{2} + 4557 \, b^{2} c^{3} d^{3} e^{3} - 3778 \, b^{3} c^{2} d^{2} e^{4} + 1544 \, b^{4} c d e^{5} - 240 \, b^{5} e^{6}\right)} g\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(8 \, c^{3} d^{9} e^{2} - 12 \, b c^{2} d^{8} e^{3} + 6 \, b^{2} c d^{7} e^{4} - b^{3} d^{6} e^{5} + {\left(8 \, c^{3} d^{3} e^{8} - 12 \, b c^{2} d^{2} e^{9} + 6 \, b^{2} c d e^{10} - b^{3} e^{11}\right)} x^{6} + 6 \, {\left(8 \, c^{3} d^{4} e^{7} - 12 \, b c^{2} d^{3} e^{8} + 6 \, b^{2} c d^{2} e^{9} - b^{3} d e^{10}\right)} x^{5} + 15 \, {\left(8 \, c^{3} d^{5} e^{6} - 12 \, b c^{2} d^{4} e^{7} + 6 \, b^{2} c d^{3} e^{8} - b^{3} d^{2} e^{9}\right)} x^{4} + 20 \, {\left(8 \, c^{3} d^{6} e^{5} - 12 \, b c^{2} d^{5} e^{6} + 6 \, b^{2} c d^{4} e^{7} - b^{3} d^{3} e^{8}\right)} x^{3} + 15 \, {\left(8 \, c^{3} d^{7} e^{4} - 12 \, b c^{2} d^{6} e^{5} + 6 \, b^{2} c d^{5} e^{6} - b^{3} d^{4} e^{7}\right)} x^{2} + 6 \, {\left(8 \, c^{3} d^{8} e^{3} - 12 \, b c^{2} d^{7} e^{4} + 6 \, b^{2} c d^{6} e^{5} - b^{3} d^{5} e^{6}\right)} x\right)}}, \frac{15 \, {\left(3 \, c^{5} d^{6} e f + {\left(3 \, c^{5} e^{7} f + {\left(17 \, c^{5} d e^{6} - 10 \, b c^{4} e^{7}\right)} g\right)} x^{6} + 6 \, {\left(3 \, c^{5} d e^{6} f + {\left(17 \, c^{5} d^{2} e^{5} - 10 \, b c^{4} d e^{6}\right)} g\right)} x^{5} + 15 \, {\left(3 \, c^{5} d^{2} e^{5} f + {\left(17 \, c^{5} d^{3} e^{4} - 10 \, b c^{4} d^{2} e^{5}\right)} g\right)} x^{4} + 20 \, {\left(3 \, c^{5} d^{3} e^{4} f + {\left(17 \, c^{5} d^{4} e^{3} - 10 \, b c^{4} d^{3} e^{4}\right)} g\right)} x^{3} + 15 \, {\left(3 \, c^{5} d^{4} e^{3} f + {\left(17 \, c^{5} d^{5} e^{2} - 10 \, b c^{4} d^{4} e^{3}\right)} g\right)} x^{2} + {\left(17 \, c^{5} d^{7} - 10 \, b c^{4} d^{6} e\right)} g + 6 \, {\left(3 \, c^{5} d^{5} e^{2} f + {\left(17 \, c^{5} d^{6} e - 10 \, b c^{4} d^{5} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(15 \, {\left(3 \, {\left(2 \, c^{5} d e^{5} - b c^{4} e^{6}\right)} f + {\left(34 \, c^{5} d^{2} e^{4} - 37 \, b c^{4} d e^{5} + 10 \, b^{2} c^{3} e^{6}\right)} g\right)} x^{4} + 10 \, {\left(3 \, {\left(16 \, c^{5} d^{2} e^{4} - 10 \, b c^{4} d e^{5} + b^{2} c^{3} e^{6}\right)} f - {\left(752 \, c^{5} d^{3} e^{3} - 1206 \, b c^{4} d^{2} e^{4} + 651 \, b^{2} c^{3} d e^{5} - 118 \, b^{3} c^{2} e^{6}\right)} g\right)} x^{3} - 2 \, {\left(3 \, {\left(842 \, c^{5} d^{3} e^{3} - 1383 \, b c^{4} d^{2} e^{4} + 729 \, b^{2} c^{3} d e^{5} - 124 \, b^{3} c^{2} e^{6}\right)} f - {\left(1046 \, c^{5} d^{4} e^{2} - 6469 \, b c^{4} d^{3} e^{3} + 8337 \, b^{2} c^{3} d^{2} e^{4} - 4042 \, b^{3} c^{2} d e^{5} + 680 \, b^{4} c e^{6}\right)} g\right)} x^{2} - 3 \, {\left(634 \, c^{5} d^{5} e - 2409 \, b c^{4} d^{4} e^{2} + 3654 \, b^{2} c^{3} d^{3} e^{3} - 2680 \, b^{3} c^{2} d^{2} e^{4} + 944 \, b^{4} c d e^{5} - 128 \, b^{5} e^{6}\right)} f - {\left(538 \, c^{5} d^{6} - 1213 \, b c^{4} d^{5} e + 1728 \, b^{2} c^{3} d^{4} e^{2} - 1460 \, b^{3} c^{2} d^{3} e^{3} + 608 \, b^{4} c d^{2} e^{4} - 96 \, b^{5} d e^{5}\right)} g + 2 \, {\left(3 \, {\left(824 \, c^{5} d^{4} e^{2} - 2490 \, b c^{4} d^{3} e^{3} + 2559 \, b^{2} c^{3} d^{2} e^{4} - 1096 \, b^{3} c^{2} d e^{5} + 168 \, b^{4} c e^{6}\right)} f - {\left(1352 \, c^{5} d^{5} e - 3190 \, b c^{4} d^{4} e^{2} + 4557 \, b^{2} c^{3} d^{3} e^{3} - 3778 \, b^{3} c^{2} d^{2} e^{4} + 1544 \, b^{4} c d e^{5} - 240 \, b^{5} e^{6}\right)} g\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(8 \, c^{3} d^{9} e^{2} - 12 \, b c^{2} d^{8} e^{3} + 6 \, b^{2} c d^{7} e^{4} - b^{3} d^{6} e^{5} + {\left(8 \, c^{3} d^{3} e^{8} - 12 \, b c^{2} d^{2} e^{9} + 6 \, b^{2} c d e^{10} - b^{3} e^{11}\right)} x^{6} + 6 \, {\left(8 \, c^{3} d^{4} e^{7} - 12 \, b c^{2} d^{3} e^{8} + 6 \, b^{2} c d^{2} e^{9} - b^{3} d e^{10}\right)} x^{5} + 15 \, {\left(8 \, c^{3} d^{5} e^{6} - 12 \, b c^{2} d^{4} e^{7} + 6 \, b^{2} c d^{3} e^{8} - b^{3} d^{2} e^{9}\right)} x^{4} + 20 \, {\left(8 \, c^{3} d^{6} e^{5} - 12 \, b c^{2} d^{5} e^{6} + 6 \, b^{2} c d^{4} e^{7} - b^{3} d^{3} e^{8}\right)} x^{3} + 15 \, {\left(8 \, c^{3} d^{7} e^{4} - 12 \, b c^{2} d^{6} e^{5} + 6 \, b^{2} c d^{5} e^{6} - b^{3} d^{4} e^{7}\right)} x^{2} + 6 \, {\left(8 \, c^{3} d^{8} e^{3} - 12 \, b c^{2} d^{7} e^{4} + 6 \, b^{2} c d^{6} e^{5} - b^{3} d^{5} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/3840*(15*(3*c^5*d^6*e*f + (3*c^5*e^7*f + (17*c^5*d*e^6 - 10*b*c^4*e^7)*g)*x^6 + 6*(3*c^5*d*e^6*f + (17*c^5*d^2*e^5 - 10*b*c^4*d*e^6)*g)*x^5 + 15*(3*c^5*d^2*e^5*f + (17*c^5*d^3*e^4 - 10*b*c^4*d^2*e^5)*g)*x^4 + 20*(3*c^5*d^3*e^4*f + (17*c^5*d^4*e^3 - 10*b*c^4*d^3*e^4)*g)*x^3 + 15*(3*c^5*d^4*e^3*f + (17*c^5*d^5*e^2 - 10*b*c^4*d^4*e^3)*g)*x^2 + (17*c^5*d^7 - 10*b*c^4*d^6*e)*g + 6*(3*c^5*d^5*e^2*f + (17*c^5*d^6*e - 10*b*c^4*d^5*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(15*(3*(2*c^5*d*e^5 - b*c^4*e^6)*f + (34*c^5*d^2*e^4 - 37*b*c^4*d*e^5 + 10*b^2*c^3*e^6)*g)*x^4 + 10*(3*(16*c^5*d^2*e^4 - 10*b*c^4*d*e^5 + b^2*c^3*e^6)*f - (752*c^5*d^3*e^3 - 1206*b*c^4*d^2*e^4 + 651*b^2*c^3*d*e^5 - 118*b^3*c^2*e^6)*g)*x^3 - 2*(3*(842*c^5*d^3*e^3 - 1383*b*c^4*d^2*e^4 + 729*b^2*c^3*d*e^5 - 124*b^3*c^2*e^6)*f - (1046*c^5*d^4*e^2 - 6469*b*c^4*d^3*e^3 + 8337*b^2*c^3*d^2*e^4 - 4042*b^3*c^2*d*e^5 + 680*b^4*c*e^6)*g)*x^2 - 3*(634*c^5*d^5*e - 2409*b*c^4*d^4*e^2 + 3654*b^2*c^3*d^3*e^3 - 2680*b^3*c^2*d^2*e^4 + 944*b^4*c*d*e^5 - 128*b^5*e^6)*f - (538*c^5*d^6 - 1213*b*c^4*d^5*e + 1728*b^2*c^3*d^4*e^2 - 1460*b^3*c^2*d^3*e^3 + 608*b^4*c*d^2*e^4 - 96*b^5*d*e^5)*g + 2*(3*(824*c^5*d^4*e^2 - 2490*b*c^4*d^3*e^3 + 2559*b^2*c^3*d^2*e^4 - 1096*b^3*c^2*d*e^5 + 168*b^4*c*e^6)*f - (1352*c^5*d^5*e - 3190*b*c^4*d^4*e^2 + 4557*b^2*c^3*d^3*e^3 - 3778*b^3*c^2*d^2*e^4 + 1544*b^4*c*d*e^5 - 240*b^5*e^6)*g)*x)*sqrt(e*x + d))/(8*c^3*d^9*e^2 - 12*b*c^2*d^8*e^3 + 6*b^2*c*d^7*e^4 - b^3*d^6*e^5 + (8*c^3*d^3*e^8 - 12*b*c^2*d^2*e^9 + 6*b^2*c*d*e^10 - b^3*e^11)*x^6 + 6*(8*c^3*d^4*e^7 - 12*b*c^2*d^3*e^8 + 6*b^2*c*d^2*e^9 - b^3*d*e^10)*x^5 + 15*(8*c^3*d^5*e^6 - 12*b*c^2*d^4*e^7 + 6*b^2*c*d^3*e^8 - b^3*d^2*e^9)*x^4 + 20*(8*c^3*d^6*e^5 - 12*b*c^2*d^5*e^6 + 6*b^2*c*d^4*e^7 - b^3*d^3*e^8)*x^3 + 15*(8*c^3*d^7*e^4 - 12*b*c^2*d^6*e^5 + 6*b^2*c*d^5*e^6 - b^3*d^4*e^7)*x^2 + 6*(8*c^3*d^8*e^3 - 12*b*c^2*d^7*e^4 + 6*b^2*c*d^6*e^5 - b^3*d^5*e^6)*x), 1/1920*(15*(3*c^5*d^6*e*f + (3*c^5*e^7*f + (17*c^5*d*e^6 - 10*b*c^4*e^7)*g)*x^6 + 6*(3*c^5*d*e^6*f + (17*c^5*d^2*e^5 - 10*b*c^4*d*e^6)*g)*x^5 + 15*(3*c^5*d^2*e^5*f + (17*c^5*d^3*e^4 - 10*b*c^4*d^2*e^5)*g)*x^4 + 20*(3*c^5*d^3*e^4*f + (17*c^5*d^4*e^3 - 10*b*c^4*d^3*e^4)*g)*x^3 + 15*(3*c^5*d^4*e^3*f + (17*c^5*d^5*e^2 - 10*b*c^4*d^4*e^3)*g)*x^2 + (17*c^5*d^7 - 10*b*c^4*d^6*e)*g + 6*(3*c^5*d^5*e^2*f + (17*c^5*d^6*e - 10*b*c^4*d^5*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(15*(3*(2*c^5*d*e^5 - b*c^4*e^6)*f + (34*c^5*d^2*e^4 - 37*b*c^4*d*e^5 + 10*b^2*c^3*e^6)*g)*x^4 + 10*(3*(16*c^5*d^2*e^4 - 10*b*c^4*d*e^5 + b^2*c^3*e^6)*f - (752*c^5*d^3*e^3 - 1206*b*c^4*d^2*e^4 + 651*b^2*c^3*d*e^5 - 118*b^3*c^2*e^6)*g)*x^3 - 2*(3*(842*c^5*d^3*e^3 - 1383*b*c^4*d^2*e^4 + 729*b^2*c^3*d*e^5 - 124*b^3*c^2*e^6)*f - (1046*c^5*d^4*e^2 - 6469*b*c^4*d^3*e^3 + 8337*b^2*c^3*d^2*e^4 - 4042*b^3*c^2*d*e^5 + 680*b^4*c*e^6)*g)*x^2 - 3*(634*c^5*d^5*e - 2409*b*c^4*d^4*e^2 + 3654*b^2*c^3*d^3*e^3 - 2680*b^3*c^2*d^2*e^4 + 944*b^4*c*d*e^5 - 128*b^5*e^6)*f - (538*c^5*d^6 - 1213*b*c^4*d^5*e + 1728*b^2*c^3*d^4*e^2 - 1460*b^3*c^2*d^3*e^3 + 608*b^4*c*d^2*e^4 - 96*b^5*d*e^5)*g + 2*(3*(824*c^5*d^4*e^2 - 2490*b*c^4*d^3*e^3 + 2559*b^2*c^3*d^2*e^4 - 1096*b^3*c^2*d*e^5 + 168*b^4*c*e^6)*f - (1352*c^5*d^5*e - 3190*b*c^4*d^4*e^2 + 4557*b^2*c^3*d^3*e^3 - 3778*b^3*c^2*d^2*e^4 + 1544*b^4*c*d*e^5 - 240*b^5*e^6)*g)*x)*sqrt(e*x + d))/(8*c^3*d^9*e^2 - 12*b*c^2*d^8*e^3 + 6*b^2*c*d^7*e^4 - b^3*d^6*e^5 + (8*c^3*d^3*e^8 - 12*b*c^2*d^2*e^9 + 6*b^2*c*d*e^10 - b^3*e^11)*x^6 + 6*(8*c^3*d^4*e^7 - 12*b*c^2*d^3*e^8 + 6*b^2*c*d^2*e^9 - b^3*d*e^10)*x^5 + 15*(8*c^3*d^5*e^6 - 12*b*c^2*d^4*e^7 + 6*b^2*c*d^3*e^8 - b^3*d^2*e^9)*x^4 + 20*(8*c^3*d^6*e^5 - 12*b*c^2*d^5*e^6 + 6*b^2*c*d^4*e^7 - b^3*d^3*e^8)*x^3 + 15*(8*c^3*d^7*e^4 - 12*b*c^2*d^6*e^5 + 6*b^2*c*d^5*e^6 - b^3*d^4*e^7)*x^2 + 6*(8*c^3*d^8*e^3 - 12*b*c^2*d^7*e^4 + 6*b^2*c*d^6*e^5 - b^3*d^5*e^6)*x)]","B",0
2262,1,235,0,0.404771," ","integrate((e*x+d)^(5/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, c^{3} e^{3} g x^{3} + 3 \, {\left(7 \, c^{3} e^{3} f + 2 \, {\left(10 \, c^{3} d e^{2} - 3 \, b c^{2} e^{3}\right)} g\right)} x^{2} + 7 \, {\left(43 \, c^{3} d^{2} e - 36 \, b c^{2} d e^{2} + 8 \, b^{2} c e^{3}\right)} f + 2 \, {\left(115 \, c^{3} d^{3} - 219 \, b c^{2} d^{2} e + 128 \, b^{2} c d e^{2} - 24 \, b^{3} e^{3}\right)} g + {\left(14 \, {\left(7 \, c^{3} d e^{2} - 2 \, b c^{2} e^{3}\right)} f + {\left(115 \, c^{3} d^{2} e - 104 \, b c^{2} d e^{2} + 24 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{105 \, {\left(c^{4} e^{3} x + c^{4} d e^{2}\right)}}"," ",0,"-2/105*(15*c^3*e^3*g*x^3 + 3*(7*c^3*e^3*f + 2*(10*c^3*d*e^2 - 3*b*c^2*e^3)*g)*x^2 + 7*(43*c^3*d^2*e - 36*b*c^2*d*e^2 + 8*b^2*c*e^3)*f + 2*(115*c^3*d^3 - 219*b*c^2*d^2*e + 128*b^2*c*d*e^2 - 24*b^3*e^3)*g + (14*(7*c^3*d*e^2 - 2*b*c^2*e^3)*f + (115*c^3*d^2*e - 104*b*c^2*d*e^2 + 24*b^2*c*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^4*e^3*x + c^4*d*e^2)","A",0
2263,1,143,0,0.402369," ","integrate((e*x+d)^(3/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, c^{2} e^{2} g x^{2} + 5 \, {\left(5 \, c^{2} d e - 2 \, b c e^{2}\right)} f + 2 \, {\left(9 \, c^{2} d^{2} - 13 \, b c d e + 4 \, b^{2} e^{2}\right)} g + {\left(5 \, c^{2} e^{2} f + {\left(9 \, c^{2} d e - 4 \, b c e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{15 \, {\left(c^{3} e^{3} x + c^{3} d e^{2}\right)}}"," ",0,"-2/15*(3*c^2*e^2*g*x^2 + 5*(5*c^2*d*e - 2*b*c*e^2)*f + 2*(9*c^2*d^2 - 13*b*c*d*e + 4*b^2*e^2)*g + (5*c^2*e^2*f + (9*c^2*d*e - 4*b*c*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^3*e^3*x + c^3*d*e^2)","A",0
2264,1,79,0,0.389028," ","integrate((e*x+d)^(1/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c e g x + 3 \, c e f + 2 \, {\left(c d - b e\right)} g\right)} \sqrt{e x + d}}{3 \, {\left(c^{2} e^{3} x + c^{2} d e^{2}\right)}}"," ",0,"-2/3*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c*e*g*x + 3*c*e*f + 2*(c*d - b*e)*g)*sqrt(e*x + d)/(c^2*e^3*x + c^2*d*e^2)","A",0
2265,1,442,0,0.427245," ","integrate((g*x+f)/(e*x+d)^(1/2)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c d - b e\right)} \sqrt{e x + d} g + {\left(c d e f - c d^{2} g + {\left(c e^{2} f - c d e g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, c^{2} d^{2} e^{2} - b c d e^{3} + {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} x}, -\frac{2 \, {\left(\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(2 \, c d - b e\right)} \sqrt{e x + d} g + {\left(c d e f - c d^{2} g + {\left(c e^{2} f - c d e g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right)\right)}}{2 \, c^{2} d^{2} e^{2} - b c d e^{3} + {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} x}\right]"," ",0,"[-(2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*d - b*e)*sqrt(e*x + d)*g + (c*d*e*f - c*d^2*g + (c*e^2*f - c*d*e*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)))/(2*c^2*d^2*e^2 - b*c*d*e^3 + (2*c^2*d*e^3 - b*c*e^4)*x), -2*(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(2*c*d - b*e)*sqrt(e*x + d)*g + (c*d*e*f - c*d^2*g + (c*e^2*f - c*d*e*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)))/(2*c^2*d^2*e^2 - b*c*d*e^3 + (2*c^2*d*e^3 - b*c*e^4)*x)]","A",0
2266,1,698,0,0.442030," ","integrate((g*x+f)/(e*x+d)^(3/2)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d^{2} e f + {\left(c e^{3} f + {\left(3 \, c d e^{2} - 2 \, b e^{3}\right)} g\right)} x^{2} + {\left(3 \, c d^{3} - 2 \, b d^{2} e\right)} g + 2 \, {\left(c d e^{2} f + {\left(3 \, c d^{2} e - 2 \, b d e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(2 \, c d e - b e^{2}\right)} f - {\left(2 \, c d^{2} - b d e\right)} g\right)} \sqrt{e x + d}}{2 \, {\left(4 \, c^{2} d^{4} e^{2} - 4 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4} + {\left(4 \, c^{2} d^{2} e^{4} - 4 \, b c d e^{5} + b^{2} e^{6}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{3} e^{3} - 4 \, b c d^{2} e^{4} + b^{2} d e^{5}\right)} x\right)}}, -\frac{{\left(c d^{2} e f + {\left(c e^{3} f + {\left(3 \, c d e^{2} - 2 \, b e^{3}\right)} g\right)} x^{2} + {\left(3 \, c d^{3} - 2 \, b d^{2} e\right)} g + 2 \, {\left(c d e^{2} f + {\left(3 \, c d^{2} e - 2 \, b d e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(2 \, c d e - b e^{2}\right)} f - {\left(2 \, c d^{2} - b d e\right)} g\right)} \sqrt{e x + d}}{4 \, c^{2} d^{4} e^{2} - 4 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4} + {\left(4 \, c^{2} d^{2} e^{4} - 4 \, b c d e^{5} + b^{2} e^{6}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{3} e^{3} - 4 \, b c d^{2} e^{4} + b^{2} d e^{5}\right)} x}\right]"," ",0,"[1/2*((c*d^2*e*f + (c*e^3*f + (3*c*d*e^2 - 2*b*e^3)*g)*x^2 + (3*c*d^3 - 2*b*d^2*e)*g + 2*(c*d*e^2*f + (3*c*d^2*e - 2*b*d*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((2*c*d*e - b*e^2)*f - (2*c*d^2 - b*d*e)*g)*sqrt(e*x + d))/(4*c^2*d^4*e^2 - 4*b*c*d^3*e^3 + b^2*d^2*e^4 + (4*c^2*d^2*e^4 - 4*b*c*d*e^5 + b^2*e^6)*x^2 + 2*(4*c^2*d^3*e^3 - 4*b*c*d^2*e^4 + b^2*d*e^5)*x), -((c*d^2*e*f + (c*e^3*f + (3*c*d*e^2 - 2*b*e^3)*g)*x^2 + (3*c*d^3 - 2*b*d^2*e)*g + 2*(c*d*e^2*f + (3*c*d^2*e - 2*b*d*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((2*c*d*e - b*e^2)*f - (2*c*d^2 - b*d*e)*g)*sqrt(e*x + d))/(4*c^2*d^4*e^2 - 4*b*c*d^3*e^3 + b^2*d^2*e^4 + (4*c^2*d^2*e^4 - 4*b*c*d*e^5 + b^2*e^6)*x^2 + 2*(4*c^2*d^3*e^3 - 4*b*c*d^2*e^4 + b^2*d*e^5)*x)]","B",0
2267,1,1168,0,0.447179," ","integrate((g*x+f)/(e*x+d)^(5/2)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, c^{2} d^{3} e f + {\left(3 \, c^{2} e^{4} f + {\left(5 \, c^{2} d e^{3} - 4 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(3 \, c^{2} d e^{3} f + {\left(5 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3}\right)} g\right)} x^{2} + {\left(5 \, c^{2} d^{4} - 4 \, b c d^{3} e\right)} g + 3 \, {\left(3 \, c^{2} d^{2} e^{2} f + {\left(5 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(14 \, c^{2} d^{2} e - 11 \, b c d e^{2} + 2 \, b^{2} e^{3}\right)} f + {\left(2 \, c^{2} d^{3} - 5 \, b c d^{2} e + 2 \, b^{2} d e^{2}\right)} g + {\left(3 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f + {\left(10 \, c^{2} d^{2} e - 13 \, b c d e^{2} + 4 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(8 \, c^{3} d^{6} e^{2} - 12 \, b c^{2} d^{5} e^{3} + 6 \, b^{2} c d^{4} e^{4} - b^{3} d^{3} e^{5} + {\left(8 \, c^{3} d^{3} e^{5} - 12 \, b c^{2} d^{2} e^{6} + 6 \, b^{2} c d e^{7} - b^{3} e^{8}\right)} x^{3} + 3 \, {\left(8 \, c^{3} d^{4} e^{4} - 12 \, b c^{2} d^{3} e^{5} + 6 \, b^{2} c d^{2} e^{6} - b^{3} d e^{7}\right)} x^{2} + 3 \, {\left(8 \, c^{3} d^{5} e^{3} - 12 \, b c^{2} d^{4} e^{4} + 6 \, b^{2} c d^{3} e^{5} - b^{3} d^{2} e^{6}\right)} x\right)}}, -\frac{{\left(3 \, c^{2} d^{3} e f + {\left(3 \, c^{2} e^{4} f + {\left(5 \, c^{2} d e^{3} - 4 \, b c e^{4}\right)} g\right)} x^{3} + 3 \, {\left(3 \, c^{2} d e^{3} f + {\left(5 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3}\right)} g\right)} x^{2} + {\left(5 \, c^{2} d^{4} - 4 \, b c d^{3} e\right)} g + 3 \, {\left(3 \, c^{2} d^{2} e^{2} f + {\left(5 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(14 \, c^{2} d^{2} e - 11 \, b c d e^{2} + 2 \, b^{2} e^{3}\right)} f + {\left(2 \, c^{2} d^{3} - 5 \, b c d^{2} e + 2 \, b^{2} d e^{2}\right)} g + {\left(3 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f + {\left(10 \, c^{2} d^{2} e - 13 \, b c d e^{2} + 4 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(8 \, c^{3} d^{6} e^{2} - 12 \, b c^{2} d^{5} e^{3} + 6 \, b^{2} c d^{4} e^{4} - b^{3} d^{3} e^{5} + {\left(8 \, c^{3} d^{3} e^{5} - 12 \, b c^{2} d^{2} e^{6} + 6 \, b^{2} c d e^{7} - b^{3} e^{8}\right)} x^{3} + 3 \, {\left(8 \, c^{3} d^{4} e^{4} - 12 \, b c^{2} d^{3} e^{5} + 6 \, b^{2} c d^{2} e^{6} - b^{3} d e^{7}\right)} x^{2} + 3 \, {\left(8 \, c^{3} d^{5} e^{3} - 12 \, b c^{2} d^{4} e^{4} + 6 \, b^{2} c d^{3} e^{5} - b^{3} d^{2} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/8*((3*c^2*d^3*e*f + (3*c^2*e^4*f + (5*c^2*d*e^3 - 4*b*c*e^4)*g)*x^3 + 3*(3*c^2*d*e^3*f + (5*c^2*d^2*e^2 - 4*b*c*d*e^3)*g)*x^2 + (5*c^2*d^4 - 4*b*c*d^3*e)*g + 3*(3*c^2*d^2*e^2*f + (5*c^2*d^3*e - 4*b*c*d^2*e^2)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((14*c^2*d^2*e - 11*b*c*d*e^2 + 2*b^2*e^3)*f + (2*c^2*d^3 - 5*b*c*d^2*e + 2*b^2*d*e^2)*g + (3*(2*c^2*d*e^2 - b*c*e^3)*f + (10*c^2*d^2*e - 13*b*c*d*e^2 + 4*b^2*e^3)*g)*x)*sqrt(e*x + d))/(8*c^3*d^6*e^2 - 12*b*c^2*d^5*e^3 + 6*b^2*c*d^4*e^4 - b^3*d^3*e^5 + (8*c^3*d^3*e^5 - 12*b*c^2*d^2*e^6 + 6*b^2*c*d*e^7 - b^3*e^8)*x^3 + 3*(8*c^3*d^4*e^4 - 12*b*c^2*d^3*e^5 + 6*b^2*c*d^2*e^6 - b^3*d*e^7)*x^2 + 3*(8*c^3*d^5*e^3 - 12*b*c^2*d^4*e^4 + 6*b^2*c*d^3*e^5 - b^3*d^2*e^6)*x), -1/4*((3*c^2*d^3*e*f + (3*c^2*e^4*f + (5*c^2*d*e^3 - 4*b*c*e^4)*g)*x^3 + 3*(3*c^2*d*e^3*f + (5*c^2*d^2*e^2 - 4*b*c*d*e^3)*g)*x^2 + (5*c^2*d^4 - 4*b*c*d^3*e)*g + 3*(3*c^2*d^2*e^2*f + (5*c^2*d^3*e - 4*b*c*d^2*e^2)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((14*c^2*d^2*e - 11*b*c*d*e^2 + 2*b^2*e^3)*f + (2*c^2*d^3 - 5*b*c*d^2*e + 2*b^2*d*e^2)*g + (3*(2*c^2*d*e^2 - b*c*e^3)*f + (10*c^2*d^2*e - 13*b*c*d*e^2 + 4*b^2*e^3)*g)*x)*sqrt(e*x + d))/(8*c^3*d^6*e^2 - 12*b*c^2*d^5*e^3 + 6*b^2*c*d^4*e^4 - b^3*d^3*e^5 + (8*c^3*d^3*e^5 - 12*b*c^2*d^2*e^6 + 6*b^2*c*d*e^7 - b^3*e^8)*x^3 + 3*(8*c^3*d^4*e^4 - 12*b*c^2*d^3*e^5 + 6*b^2*c*d^2*e^6 - b^3*d*e^7)*x^2 + 3*(8*c^3*d^5*e^3 - 12*b*c^2*d^4*e^4 + 6*b^2*c*d^3*e^5 - b^3*d^2*e^6)*x)]","B",0
2268,1,374,0,0.409671," ","integrate((e*x+d)^(9/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{4} e^{4} g x^{4} + {\left(7 \, c^{4} e^{4} f + {\left(29 \, c^{4} d e^{3} - 8 \, b c^{3} e^{4}\right)} g\right)} x^{3} + {\left(7 \, {\left(7 \, c^{4} d e^{3} - 2 \, b c^{3} e^{4}\right)} f + {\left(93 \, c^{4} d^{2} e^{2} - 74 \, b c^{3} d e^{3} + 16 \, b^{2} c^{2} e^{4}\right)} g\right)} x^{2} - 7 \, {\left(91 \, c^{4} d^{3} e - 158 \, b c^{3} d^{2} e^{2} + 88 \, b^{2} c^{2} d e^{3} - 16 \, b^{3} c e^{4}\right)} f - 2 \, {\left(407 \, c^{4} d^{4} - 1075 \, b c^{3} d^{3} e + 1028 \, b^{2} c^{2} d^{2} e^{2} - 424 \, b^{3} c d e^{3} + 64 \, b^{4} e^{4}\right)} g + {\left(7 \, {\left(43 \, c^{4} d^{2} e^{2} - 36 \, b c^{3} d e^{3} + 8 \, b^{2} c^{2} e^{4}\right)} f + {\left(407 \, c^{4} d^{3} e - 668 \, b c^{3} d^{2} e^{2} + 360 \, b^{2} c^{2} d e^{3} - 64 \, b^{3} c e^{4}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{35 \, {\left(c^{6} e^{4} x^{2} + b c^{5} e^{4} x - c^{6} d^{2} e^{2} + b c^{5} d e^{3}\right)}}"," ",0,"2/35*(5*c^4*e^4*g*x^4 + (7*c^4*e^4*f + (29*c^4*d*e^3 - 8*b*c^3*e^4)*g)*x^3 + (7*(7*c^4*d*e^3 - 2*b*c^3*e^4)*f + (93*c^4*d^2*e^2 - 74*b*c^3*d*e^3 + 16*b^2*c^2*e^4)*g)*x^2 - 7*(91*c^4*d^3*e - 158*b*c^3*d^2*e^2 + 88*b^2*c^2*d*e^3 - 16*b^3*c*e^4)*f - 2*(407*c^4*d^4 - 1075*b*c^3*d^3*e + 1028*b^2*c^2*d^2*e^2 - 424*b^3*c*d*e^3 + 64*b^4*e^4)*g + (7*(43*c^4*d^2*e^2 - 36*b*c^3*d*e^3 + 8*b^2*c^2*e^4)*f + (407*c^4*d^3*e - 668*b*c^3*d^2*e^2 + 360*b^2*c^2*d*e^3 - 64*b^3*c*e^4)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^6*e^4*x^2 + b*c^5*e^4*x - c^6*d^2*e^2 + b*c^5*d*e^3)","A",0
2269,1,257,0,0.407639," ","integrate((e*x+d)^(7/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{3} e^{3} g x^{3} + {\left(5 \, c^{3} e^{3} f + 2 \, {\left(8 \, c^{3} d e^{2} - 3 \, b c^{2} e^{3}\right)} g\right)} x^{2} - 5 \, {\left(23 \, c^{3} d^{2} e - 28 \, b c^{2} d e^{2} + 8 \, b^{2} c e^{3}\right)} f - 2 \, {\left(79 \, c^{3} d^{3} - 167 \, b c^{2} d^{2} e + 112 \, b^{2} c d e^{2} - 24 \, b^{3} e^{3}\right)} g + {\left(10 \, {\left(5 \, c^{3} d e^{2} - 2 \, b c^{2} e^{3}\right)} f + {\left(79 \, c^{3} d^{2} e - 88 \, b c^{2} d e^{2} + 24 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{15 \, {\left(c^{5} e^{4} x^{2} + b c^{4} e^{4} x - c^{5} d^{2} e^{2} + b c^{4} d e^{3}\right)}}"," ",0,"2/15*(3*c^3*e^3*g*x^3 + (5*c^3*e^3*f + 2*(8*c^3*d*e^2 - 3*b*c^2*e^3)*g)*x^2 - 5*(23*c^3*d^2*e - 28*b*c^2*d*e^2 + 8*b^2*c*e^3)*f - 2*(79*c^3*d^3 - 167*b*c^2*d^2*e + 112*b^2*c*d*e^2 - 24*b^3*e^3)*g + (10*(5*c^3*d*e^2 - 2*b*c^2*e^3)*f + (79*c^3*d^2*e - 88*b*c^2*d*e^2 + 24*b^2*c*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^5*e^4*x^2 + b*c^4*e^4*x - c^5*d^2*e^2 + b*c^4*d*e^3)","A",0
2270,1,165,0,0.410957," ","integrate((e*x+d)^(5/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{2} e^{2} g x^{2} - 3 \, {\left(3 \, c^{2} d e - 2 \, b c e^{2}\right)} f - 2 \, {\left(7 \, c^{2} d^{2} - 11 \, b c d e + 4 \, b^{2} e^{2}\right)} g + {\left(3 \, c^{2} e^{2} f + {\left(7 \, c^{2} d e - 4 \, b c e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{3 \, {\left(c^{4} e^{4} x^{2} + b c^{3} e^{4} x - c^{4} d^{2} e^{2} + b c^{3} d e^{3}\right)}}"," ",0,"2/3*(c^2*e^2*g*x^2 - 3*(3*c^2*d*e - 2*b*c*e^2)*f - 2*(7*c^2*d^2 - 11*b*c*d*e + 4*b^2*e^2)*g + (3*c^2*e^2*f + (7*c^2*d*e - 4*b*c*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^4*e^4*x^2 + b*c^3*e^4*x - c^4*d^2*e^2 + b*c^3*d*e^3)","A",0
2271,1,102,0,0.411560," ","integrate((e*x+d)^(3/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(c e g x - c e f - 2 \, {\left(c d - b e\right)} g\right)} \sqrt{e x + d}}{c^{3} e^{4} x^{2} + b c^{2} e^{4} x - c^{3} d^{2} e^{2} + b c^{2} d e^{3}}"," ",0,"2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(c*e*g*x - c*e*f - 2*(c*d - b*e)*g)*sqrt(e*x + d)/(c^3*e^4*x^2 + b*c^2*e^4*x - c^3*d^2*e^2 + b*c^2*d*e^3)","A",0
2272,1,776,0,0.423955," ","integrate((e*x+d)^(1/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(c^{2} e^{3} f - c^{2} d e^{2} g\right)} x^{2} - {\left(c^{2} d^{2} e - b c d e^{2}\right)} f + {\left(c^{2} d^{3} - b c d^{2} e\right)} g + {\left(b c e^{3} f - b c d e^{2} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(2 \, c^{2} d e - b c e^{2}\right)} f + {\left(2 \, c^{2} d^{2} - 3 \, b c d e + b^{2} e^{2}\right)} g\right)} \sqrt{e x + d}}{4 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3} + 5 \, b^{2} c^{2} d^{2} e^{4} - b^{3} c d e^{5} - {\left(4 \, c^{4} d^{2} e^{4} - 4 \, b c^{3} d e^{5} + b^{2} c^{2} e^{6}\right)} x^{2} - {\left(4 \, b c^{3} d^{2} e^{4} - 4 \, b^{2} c^{2} d e^{5} + b^{3} c e^{6}\right)} x}, \frac{2 \, {\left({\left({\left(c^{2} e^{3} f - c^{2} d e^{2} g\right)} x^{2} - {\left(c^{2} d^{2} e - b c d e^{2}\right)} f + {\left(c^{2} d^{3} - b c d^{2} e\right)} g + {\left(b c e^{3} f - b c d e^{2} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(2 \, c^{2} d e - b c e^{2}\right)} f + {\left(2 \, c^{2} d^{2} - 3 \, b c d e + b^{2} e^{2}\right)} g\right)} \sqrt{e x + d}\right)}}{4 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3} + 5 \, b^{2} c^{2} d^{2} e^{4} - b^{3} c d e^{5} - {\left(4 \, c^{4} d^{2} e^{4} - 4 \, b c^{3} d e^{5} + b^{2} c^{2} e^{6}\right)} x^{2} - {\left(4 \, b c^{3} d^{2} e^{4} - 4 \, b^{2} c^{2} d e^{5} + b^{3} c e^{6}\right)} x}\right]"," ",0,"[-(((c^2*e^3*f - c^2*d*e^2*g)*x^2 - (c^2*d^2*e - b*c*d*e^2)*f + (c^2*d^3 - b*c*d^2*e)*g + (b*c*e^3*f - b*c*d*e^2*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((2*c^2*d*e - b*c*e^2)*f + (2*c^2*d^2 - 3*b*c*d*e + b^2*e^2)*g)*sqrt(e*x + d))/(4*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3 + 5*b^2*c^2*d^2*e^4 - b^3*c*d*e^5 - (4*c^4*d^2*e^4 - 4*b*c^3*d*e^5 + b^2*c^2*e^6)*x^2 - (4*b*c^3*d^2*e^4 - 4*b^2*c^2*d*e^5 + b^3*c*e^6)*x), 2*(((c^2*e^3*f - c^2*d*e^2*g)*x^2 - (c^2*d^2*e - b*c*d*e^2)*f + (c^2*d^3 - b*c*d^2*e)*g + (b*c*e^3*f - b*c*d*e^2*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((2*c^2*d*e - b*c*e^2)*f + (2*c^2*d^2 - 3*b*c*d*e + b^2*e^2)*g)*sqrt(e*x + d))/(4*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3 + 5*b^2*c^2*d^2*e^4 - b^3*c*d*e^5 - (4*c^4*d^2*e^4 - 4*b*c^3*d*e^5 + b^2*c^2*e^6)*x^2 - (4*b*c^3*d^2*e^4 - 4*b^2*c^2*d*e^5 + b^3*c*e^6)*x)]","B",0
2273,1,1351,0,0.455204," ","integrate((g*x+f)/(e*x+d)^(1/2)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, c^{2} e^{4} f + {\left(c^{2} d e^{3} - 2 \, b c e^{4}\right)} g\right)} x^{3} + {\left(3 \, {\left(c^{2} d e^{3} + b c e^{4}\right)} f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} - 2 \, b^{2} e^{4}\right)} g\right)} x^{2} - 3 \, {\left(c^{2} d^{3} e - b c d^{2} e^{2}\right)} f - {\left(c^{2} d^{4} - 3 \, b c d^{3} e + 2 \, b^{2} d^{2} e^{2}\right)} g - {\left(3 \, {\left(c^{2} d^{2} e^{2} - 2 \, b c d e^{3}\right)} f + {\left(c^{2} d^{3} e - 4 \, b c d^{2} e^{2} + 4 \, b^{2} d e^{3}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(2 \, c^{2} d^{2} e + b c d e^{2} - b^{2} e^{3}\right)} f + 3 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2}\right)} g + {\left(3 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f + {\left(2 \, c^{2} d^{2} e - 5 \, b c d e^{2} + 2 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(8 \, c^{4} d^{6} e^{2} - 20 \, b c^{3} d^{5} e^{3} + 18 \, b^{2} c^{2} d^{4} e^{4} - 7 \, b^{3} c d^{3} e^{5} + b^{4} d^{2} e^{6} - {\left(8 \, c^{4} d^{3} e^{5} - 12 \, b c^{3} d^{2} e^{6} + 6 \, b^{2} c^{2} d e^{7} - b^{3} c e^{8}\right)} x^{3} - {\left(8 \, c^{4} d^{4} e^{4} - 4 \, b c^{3} d^{3} e^{5} - 6 \, b^{2} c^{2} d^{2} e^{6} + 5 \, b^{3} c d e^{7} - b^{4} e^{8}\right)} x^{2} + {\left(8 \, c^{4} d^{5} e^{3} - 28 \, b c^{3} d^{4} e^{4} + 30 \, b^{2} c^{2} d^{3} e^{5} - 13 \, b^{3} c d^{2} e^{6} + 2 \, b^{4} d e^{7}\right)} x\right)}}, \frac{{\left({\left(3 \, c^{2} e^{4} f + {\left(c^{2} d e^{3} - 2 \, b c e^{4}\right)} g\right)} x^{3} + {\left(3 \, {\left(c^{2} d e^{3} + b c e^{4}\right)} f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} - 2 \, b^{2} e^{4}\right)} g\right)} x^{2} - 3 \, {\left(c^{2} d^{3} e - b c d^{2} e^{2}\right)} f - {\left(c^{2} d^{4} - 3 \, b c d^{3} e + 2 \, b^{2} d^{2} e^{2}\right)} g - {\left(3 \, {\left(c^{2} d^{2} e^{2} - 2 \, b c d e^{3}\right)} f + {\left(c^{2} d^{3} e - 4 \, b c d^{2} e^{2} + 4 \, b^{2} d e^{3}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(2 \, c^{2} d^{2} e + b c d e^{2} - b^{2} e^{3}\right)} f + 3 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2}\right)} g + {\left(3 \, {\left(2 \, c^{2} d e^{2} - b c e^{3}\right)} f + {\left(2 \, c^{2} d^{2} e - 5 \, b c d e^{2} + 2 \, b^{2} e^{3}\right)} g\right)} x\right)} \sqrt{e x + d}}{8 \, c^{4} d^{6} e^{2} - 20 \, b c^{3} d^{5} e^{3} + 18 \, b^{2} c^{2} d^{4} e^{4} - 7 \, b^{3} c d^{3} e^{5} + b^{4} d^{2} e^{6} - {\left(8 \, c^{4} d^{3} e^{5} - 12 \, b c^{3} d^{2} e^{6} + 6 \, b^{2} c^{2} d e^{7} - b^{3} c e^{8}\right)} x^{3} - {\left(8 \, c^{4} d^{4} e^{4} - 4 \, b c^{3} d^{3} e^{5} - 6 \, b^{2} c^{2} d^{2} e^{6} + 5 \, b^{3} c d e^{7} - b^{4} e^{8}\right)} x^{2} + {\left(8 \, c^{4} d^{5} e^{3} - 28 \, b c^{3} d^{4} e^{4} + 30 \, b^{2} c^{2} d^{3} e^{5} - 13 \, b^{3} c d^{2} e^{6} + 2 \, b^{4} d e^{7}\right)} x}\right]"," ",0,"[1/2*(((3*c^2*e^4*f + (c^2*d*e^3 - 2*b*c*e^4)*g)*x^3 + (3*(c^2*d*e^3 + b*c*e^4)*f + (c^2*d^2*e^2 - b*c*d*e^3 - 2*b^2*e^4)*g)*x^2 - 3*(c^2*d^3*e - b*c*d^2*e^2)*f - (c^2*d^4 - 3*b*c*d^3*e + 2*b^2*d^2*e^2)*g - (3*(c^2*d^2*e^2 - 2*b*c*d*e^3)*f + (c^2*d^3*e - 4*b*c*d^2*e^2 + 4*b^2*d*e^3)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((2*c^2*d^2*e + b*c*d*e^2 - b^2*e^3)*f + 3*(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2)*g + (3*(2*c^2*d*e^2 - b*c*e^3)*f + (2*c^2*d^2*e - 5*b*c*d*e^2 + 2*b^2*e^3)*g)*x)*sqrt(e*x + d))/(8*c^4*d^6*e^2 - 20*b*c^3*d^5*e^3 + 18*b^2*c^2*d^4*e^4 - 7*b^3*c*d^3*e^5 + b^4*d^2*e^6 - (8*c^4*d^3*e^5 - 12*b*c^3*d^2*e^6 + 6*b^2*c^2*d*e^7 - b^3*c*e^8)*x^3 - (8*c^4*d^4*e^4 - 4*b*c^3*d^3*e^5 - 6*b^2*c^2*d^2*e^6 + 5*b^3*c*d*e^7 - b^4*e^8)*x^2 + (8*c^4*d^5*e^3 - 28*b*c^3*d^4*e^4 + 30*b^2*c^2*d^3*e^5 - 13*b^3*c*d^2*e^6 + 2*b^4*d*e^7)*x), (((3*c^2*e^4*f + (c^2*d*e^3 - 2*b*c*e^4)*g)*x^3 + (3*(c^2*d*e^3 + b*c*e^4)*f + (c^2*d^2*e^2 - b*c*d*e^3 - 2*b^2*e^4)*g)*x^2 - 3*(c^2*d^3*e - b*c*d^2*e^2)*f - (c^2*d^4 - 3*b*c*d^3*e + 2*b^2*d^2*e^2)*g - (3*(c^2*d^2*e^2 - 2*b*c*d*e^3)*f + (c^2*d^3*e - 4*b*c*d^2*e^2 + 4*b^2*d*e^3)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((2*c^2*d^2*e + b*c*d*e^2 - b^2*e^3)*f + 3*(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2)*g + (3*(2*c^2*d*e^2 - b*c*e^3)*f + (2*c^2*d^2*e - 5*b*c*d*e^2 + 2*b^2*e^3)*g)*x)*sqrt(e*x + d))/(8*c^4*d^6*e^2 - 20*b*c^3*d^5*e^3 + 18*b^2*c^2*d^4*e^4 - 7*b^3*c*d^3*e^5 + b^4*d^2*e^6 - (8*c^4*d^3*e^5 - 12*b*c^3*d^2*e^6 + 6*b^2*c^2*d*e^7 - b^3*c*e^8)*x^3 - (8*c^4*d^4*e^4 - 4*b*c^3*d^3*e^5 - 6*b^2*c^2*d^2*e^6 + 5*b^3*c*d*e^7 - b^4*e^8)*x^2 + (8*c^4*d^5*e^3 - 28*b*c^3*d^4*e^4 + 30*b^2*c^2*d^3*e^5 - 13*b^3*c*d^2*e^6 + 2*b^4*d*e^7)*x)]","B",0
2274,1,1976,0,0.480895," ","integrate((g*x+f)/(e*x+d)^(3/2)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, c^{3} e^{5} f + {\left(3 \, c^{3} d e^{4} - 4 \, b c^{2} e^{5}\right)} g\right)} x^{4} + {\left(5 \, {\left(2 \, c^{3} d e^{4} + b c^{2} e^{5}\right)} f + {\left(6 \, c^{3} d^{2} e^{3} - 5 \, b c^{2} d e^{4} - 4 \, b^{2} c e^{5}\right)} g\right)} x^{3} + 3 \, {\left(5 \, b c^{2} d e^{4} f + {\left(3 \, b c^{2} d^{2} e^{3} - 4 \, b^{2} c d e^{4}\right)} g\right)} x^{2} - 5 \, {\left(c^{3} d^{4} e - b c^{2} d^{3} e^{2}\right)} f - {\left(3 \, c^{3} d^{5} - 7 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2}\right)} g - {\left(5 \, {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3}\right)} f + {\left(6 \, c^{3} d^{4} e - 17 \, b c^{2} d^{3} e^{2} + 12 \, b^{2} c d^{2} e^{3}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(5 \, {\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f + {\left(6 \, c^{3} d^{2} e^{2} - 11 \, b c^{2} d e^{3} + 4 \, b^{2} c e^{4}\right)} g\right)} x^{2} - {\left(6 \, c^{3} d^{3} e - 29 \, b c^{2} d^{2} e^{2} + 17 \, b^{2} c d e^{3} - 2 \, b^{3} e^{4}\right)} f + {\left(22 \, c^{3} d^{4} - 29 \, b c^{2} d^{3} e + 5 \, b^{2} c d^{2} e^{2} + 2 \, b^{3} d e^{3}\right)} g + {\left(5 \, {\left(8 \, c^{3} d^{2} e^{2} - 2 \, b c^{2} d e^{3} - b^{2} c e^{4}\right)} f + {\left(24 \, c^{3} d^{3} e - 38 \, b c^{2} d^{2} e^{2} + 5 \, b^{2} c d e^{3} + 4 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(16 \, c^{5} d^{8} e^{2} - 48 \, b c^{4} d^{7} e^{3} + 56 \, b^{2} c^{3} d^{6} e^{4} - 32 \, b^{3} c^{2} d^{5} e^{5} + 9 \, b^{4} c d^{4} e^{6} - b^{5} d^{3} e^{7} - {\left(16 \, c^{5} d^{4} e^{6} - 32 \, b c^{4} d^{3} e^{7} + 24 \, b^{2} c^{3} d^{2} e^{8} - 8 \, b^{3} c^{2} d e^{9} + b^{4} c e^{10}\right)} x^{4} - {\left(32 \, c^{5} d^{5} e^{5} - 48 \, b c^{4} d^{4} e^{6} + 16 \, b^{2} c^{3} d^{3} e^{7} + 8 \, b^{3} c^{2} d^{2} e^{8} - 6 \, b^{4} c d e^{9} + b^{5} e^{10}\right)} x^{3} - 3 \, {\left(16 \, b c^{4} d^{5} e^{5} - 32 \, b^{2} c^{3} d^{4} e^{6} + 24 \, b^{3} c^{2} d^{3} e^{7} - 8 \, b^{4} c d^{2} e^{8} + b^{5} d e^{9}\right)} x^{2} + {\left(32 \, c^{5} d^{7} e^{3} - 112 \, b c^{4} d^{6} e^{4} + 144 \, b^{2} c^{3} d^{5} e^{5} - 88 \, b^{3} c^{2} d^{4} e^{6} + 26 \, b^{4} c d^{3} e^{7} - 3 \, b^{5} d^{2} e^{8}\right)} x\right)}}, \frac{3 \, {\left({\left(5 \, c^{3} e^{5} f + {\left(3 \, c^{3} d e^{4} - 4 \, b c^{2} e^{5}\right)} g\right)} x^{4} + {\left(5 \, {\left(2 \, c^{3} d e^{4} + b c^{2} e^{5}\right)} f + {\left(6 \, c^{3} d^{2} e^{3} - 5 \, b c^{2} d e^{4} - 4 \, b^{2} c e^{5}\right)} g\right)} x^{3} + 3 \, {\left(5 \, b c^{2} d e^{4} f + {\left(3 \, b c^{2} d^{2} e^{3} - 4 \, b^{2} c d e^{4}\right)} g\right)} x^{2} - 5 \, {\left(c^{3} d^{4} e - b c^{2} d^{3} e^{2}\right)} f - {\left(3 \, c^{3} d^{5} - 7 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2}\right)} g - {\left(5 \, {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3}\right)} f + {\left(6 \, c^{3} d^{4} e - 17 \, b c^{2} d^{3} e^{2} + 12 \, b^{2} c d^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(5 \, {\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f + {\left(6 \, c^{3} d^{2} e^{2} - 11 \, b c^{2} d e^{3} + 4 \, b^{2} c e^{4}\right)} g\right)} x^{2} - {\left(6 \, c^{3} d^{3} e - 29 \, b c^{2} d^{2} e^{2} + 17 \, b^{2} c d e^{3} - 2 \, b^{3} e^{4}\right)} f + {\left(22 \, c^{3} d^{4} - 29 \, b c^{2} d^{3} e + 5 \, b^{2} c d^{2} e^{2} + 2 \, b^{3} d e^{3}\right)} g + {\left(5 \, {\left(8 \, c^{3} d^{2} e^{2} - 2 \, b c^{2} d e^{3} - b^{2} c e^{4}\right)} f + {\left(24 \, c^{3} d^{3} e - 38 \, b c^{2} d^{2} e^{2} + 5 \, b^{2} c d e^{3} + 4 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(16 \, c^{5} d^{8} e^{2} - 48 \, b c^{4} d^{7} e^{3} + 56 \, b^{2} c^{3} d^{6} e^{4} - 32 \, b^{3} c^{2} d^{5} e^{5} + 9 \, b^{4} c d^{4} e^{6} - b^{5} d^{3} e^{7} - {\left(16 \, c^{5} d^{4} e^{6} - 32 \, b c^{4} d^{3} e^{7} + 24 \, b^{2} c^{3} d^{2} e^{8} - 8 \, b^{3} c^{2} d e^{9} + b^{4} c e^{10}\right)} x^{4} - {\left(32 \, c^{5} d^{5} e^{5} - 48 \, b c^{4} d^{4} e^{6} + 16 \, b^{2} c^{3} d^{3} e^{7} + 8 \, b^{3} c^{2} d^{2} e^{8} - 6 \, b^{4} c d e^{9} + b^{5} e^{10}\right)} x^{3} - 3 \, {\left(16 \, b c^{4} d^{5} e^{5} - 32 \, b^{2} c^{3} d^{4} e^{6} + 24 \, b^{3} c^{2} d^{3} e^{7} - 8 \, b^{4} c d^{2} e^{8} + b^{5} d e^{9}\right)} x^{2} + {\left(32 \, c^{5} d^{7} e^{3} - 112 \, b c^{4} d^{6} e^{4} + 144 \, b^{2} c^{3} d^{5} e^{5} - 88 \, b^{3} c^{2} d^{4} e^{6} + 26 \, b^{4} c d^{3} e^{7} - 3 \, b^{5} d^{2} e^{8}\right)} x\right)}}\right]"," ",0,"[-1/8*(3*((5*c^3*e^5*f + (3*c^3*d*e^4 - 4*b*c^2*e^5)*g)*x^4 + (5*(2*c^3*d*e^4 + b*c^2*e^5)*f + (6*c^3*d^2*e^3 - 5*b*c^2*d*e^4 - 4*b^2*c*e^5)*g)*x^3 + 3*(5*b*c^2*d*e^4*f + (3*b*c^2*d^2*e^3 - 4*b^2*c*d*e^4)*g)*x^2 - 5*(c^3*d^4*e - b*c^2*d^3*e^2)*f - (3*c^3*d^5 - 7*b*c^2*d^4*e + 4*b^2*c*d^3*e^2)*g - (5*(2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3)*f + (6*c^3*d^4*e - 17*b*c^2*d^3*e^2 + 12*b^2*c*d^2*e^3)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(5*(2*c^3*d*e^3 - b*c^2*e^4)*f + (6*c^3*d^2*e^2 - 11*b*c^2*d*e^3 + 4*b^2*c*e^4)*g)*x^2 - (6*c^3*d^3*e - 29*b*c^2*d^2*e^2 + 17*b^2*c*d*e^3 - 2*b^3*e^4)*f + (22*c^3*d^4 - 29*b*c^2*d^3*e + 5*b^2*c*d^2*e^2 + 2*b^3*d*e^3)*g + (5*(8*c^3*d^2*e^2 - 2*b*c^2*d*e^3 - b^2*c*e^4)*f + (24*c^3*d^3*e - 38*b*c^2*d^2*e^2 + 5*b^2*c*d*e^3 + 4*b^3*e^4)*g)*x)*sqrt(e*x + d))/(16*c^5*d^8*e^2 - 48*b*c^4*d^7*e^3 + 56*b^2*c^3*d^6*e^4 - 32*b^3*c^2*d^5*e^5 + 9*b^4*c*d^4*e^6 - b^5*d^3*e^7 - (16*c^5*d^4*e^6 - 32*b*c^4*d^3*e^7 + 24*b^2*c^3*d^2*e^8 - 8*b^3*c^2*d*e^9 + b^4*c*e^10)*x^4 - (32*c^5*d^5*e^5 - 48*b*c^4*d^4*e^6 + 16*b^2*c^3*d^3*e^7 + 8*b^3*c^2*d^2*e^8 - 6*b^4*c*d*e^9 + b^5*e^10)*x^3 - 3*(16*b*c^4*d^5*e^5 - 32*b^2*c^3*d^4*e^6 + 24*b^3*c^2*d^3*e^7 - 8*b^4*c*d^2*e^8 + b^5*d*e^9)*x^2 + (32*c^5*d^7*e^3 - 112*b*c^4*d^6*e^4 + 144*b^2*c^3*d^5*e^5 - 88*b^3*c^2*d^4*e^6 + 26*b^4*c*d^3*e^7 - 3*b^5*d^2*e^8)*x), 1/4*(3*((5*c^3*e^5*f + (3*c^3*d*e^4 - 4*b*c^2*e^5)*g)*x^4 + (5*(2*c^3*d*e^4 + b*c^2*e^5)*f + (6*c^3*d^2*e^3 - 5*b*c^2*d*e^4 - 4*b^2*c*e^5)*g)*x^3 + 3*(5*b*c^2*d*e^4*f + (3*b*c^2*d^2*e^3 - 4*b^2*c*d*e^4)*g)*x^2 - 5*(c^3*d^4*e - b*c^2*d^3*e^2)*f - (3*c^3*d^5 - 7*b*c^2*d^4*e + 4*b^2*c*d^3*e^2)*g - (5*(2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3)*f + (6*c^3*d^4*e - 17*b*c^2*d^3*e^2 + 12*b^2*c*d^2*e^3)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(5*(2*c^3*d*e^3 - b*c^2*e^4)*f + (6*c^3*d^2*e^2 - 11*b*c^2*d*e^3 + 4*b^2*c*e^4)*g)*x^2 - (6*c^3*d^3*e - 29*b*c^2*d^2*e^2 + 17*b^2*c*d*e^3 - 2*b^3*e^4)*f + (22*c^3*d^4 - 29*b*c^2*d^3*e + 5*b^2*c*d^2*e^2 + 2*b^3*d*e^3)*g + (5*(8*c^3*d^2*e^2 - 2*b*c^2*d*e^3 - b^2*c*e^4)*f + (24*c^3*d^3*e - 38*b*c^2*d^2*e^2 + 5*b^2*c*d*e^3 + 4*b^3*e^4)*g)*x)*sqrt(e*x + d))/(16*c^5*d^8*e^2 - 48*b*c^4*d^7*e^3 + 56*b^2*c^3*d^6*e^4 - 32*b^3*c^2*d^5*e^5 + 9*b^4*c*d^4*e^6 - b^5*d^3*e^7 - (16*c^5*d^4*e^6 - 32*b*c^4*d^3*e^7 + 24*b^2*c^3*d^2*e^8 - 8*b^3*c^2*d*e^9 + b^4*c*e^10)*x^4 - (32*c^5*d^5*e^5 - 48*b*c^4*d^4*e^6 + 16*b^2*c^3*d^3*e^7 + 8*b^3*c^2*d^2*e^8 - 6*b^4*c*d*e^9 + b^5*e^10)*x^3 - 3*(16*b*c^4*d^5*e^5 - 32*b^2*c^3*d^4*e^6 + 24*b^3*c^2*d^3*e^7 - 8*b^4*c*d^2*e^8 + b^5*d*e^9)*x^2 + (32*c^5*d^7*e^3 - 112*b*c^4*d^6*e^4 + 144*b^2*c^3*d^5*e^5 - 88*b^3*c^2*d^4*e^6 + 26*b^4*c*d^3*e^7 - 3*b^5*d^2*e^8)*x)]","B",0
2275,1,2832,0,0.544477," ","integrate((g*x+f)/(e*x+d)^(5/2)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(7 \, c^{4} e^{6} f + {\left(5 \, c^{4} d e^{5} - 6 \, b c^{3} e^{6}\right)} g\right)} x^{5} + {\left(7 \, {\left(3 \, c^{4} d e^{5} + b c^{3} e^{6}\right)} f + {\left(15 \, c^{4} d^{2} e^{4} - 13 \, b c^{3} d e^{5} - 6 \, b^{2} c^{2} e^{6}\right)} g\right)} x^{4} + 2 \, {\left(7 \, {\left(c^{4} d^{2} e^{4} + 2 \, b c^{3} d e^{5}\right)} f + {\left(5 \, c^{4} d^{3} e^{3} + 4 \, b c^{3} d^{2} e^{4} - 12 \, b^{2} c^{2} d e^{5}\right)} g\right)} x^{3} - 2 \, {\left(7 \, {\left(c^{4} d^{3} e^{3} - 3 \, b c^{3} d^{2} e^{4}\right)} f + {\left(5 \, c^{4} d^{4} e^{2} - 21 \, b c^{3} d^{3} e^{3} + 18 \, b^{2} c^{2} d^{2} e^{4}\right)} g\right)} x^{2} - 7 \, {\left(c^{4} d^{5} e - b c^{3} d^{4} e^{2}\right)} f - {\left(5 \, c^{4} d^{6} - 11 \, b c^{3} d^{5} e + 6 \, b^{2} c^{2} d^{4} e^{2}\right)} g - {\left(7 \, {\left(3 \, c^{4} d^{4} e^{2} - 4 \, b c^{3} d^{3} e^{3}\right)} f + {\left(15 \, c^{4} d^{5} e - 38 \, b c^{3} d^{4} e^{2} + 24 \, b^{2} c^{2} d^{3} e^{3}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(15 \, {\left(7 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f + {\left(10 \, c^{4} d^{2} e^{3} - 17 \, b c^{3} d e^{4} + 6 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} + 5 \, {\left(7 \, {\left(14 \, c^{4} d^{2} e^{3} - 5 \, b c^{3} d e^{4} - b^{2} c^{2} e^{5}\right)} f + {\left(70 \, c^{4} d^{3} e^{2} - 109 \, b c^{3} d^{2} e^{3} + 25 \, b^{2} c^{2} d e^{4} + 6 \, b^{3} c e^{5}\right)} g\right)} x^{2} - {\left(170 \, c^{4} d^{4} e - 459 \, b c^{3} d^{3} e^{2} + 311 \, b^{2} c^{2} d^{2} e^{3} - 78 \, b^{3} c d e^{4} + 8 \, b^{4} e^{5}\right)} f + {\left(98 \, c^{4} d^{5} - 75 \, b c^{3} d^{4} e - 67 \, b^{2} c^{2} d^{3} e^{2} + 48 \, b^{3} c d^{2} e^{3} - 4 \, b^{4} d e^{4}\right)} g + {\left(7 \, {\left(34 \, c^{4} d^{3} e^{2} + 19 \, b c^{3} d^{2} e^{3} - 22 \, b^{2} c^{2} d e^{4} + 2 \, b^{3} c e^{5}\right)} f + {\left(170 \, c^{4} d^{4} e - 109 \, b c^{3} d^{3} e^{2} - 224 \, b^{2} c^{2} d^{2} e^{3} + 142 \, b^{3} c d e^{4} - 12 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(32 \, c^{6} d^{10} e^{2} - 112 \, b c^{5} d^{9} e^{3} + 160 \, b^{2} c^{4} d^{8} e^{4} - 120 \, b^{3} c^{3} d^{7} e^{5} + 50 \, b^{4} c^{2} d^{6} e^{6} - 11 \, b^{5} c d^{5} e^{7} + b^{6} d^{4} e^{8} - {\left(32 \, c^{6} d^{5} e^{7} - 80 \, b c^{5} d^{4} e^{8} + 80 \, b^{2} c^{4} d^{3} e^{9} - 40 \, b^{3} c^{3} d^{2} e^{10} + 10 \, b^{4} c^{2} d e^{11} - b^{5} c e^{12}\right)} x^{5} - {\left(96 \, c^{6} d^{6} e^{6} - 208 \, b c^{5} d^{5} e^{7} + 160 \, b^{2} c^{4} d^{4} e^{8} - 40 \, b^{3} c^{3} d^{3} e^{9} - 10 \, b^{4} c^{2} d^{2} e^{10} + 7 \, b^{5} c d e^{11} - b^{6} e^{12}\right)} x^{4} - 2 \, {\left(32 \, c^{6} d^{7} e^{5} - 16 \, b c^{5} d^{6} e^{6} - 80 \, b^{2} c^{4} d^{5} e^{7} + 120 \, b^{3} c^{3} d^{4} e^{8} - 70 \, b^{4} c^{2} d^{3} e^{9} + 19 \, b^{5} c d^{2} e^{10} - 2 \, b^{6} d e^{11}\right)} x^{3} + 2 \, {\left(32 \, c^{6} d^{8} e^{4} - 176 \, b c^{5} d^{7} e^{5} + 320 \, b^{2} c^{4} d^{6} e^{6} - 280 \, b^{3} c^{3} d^{5} e^{7} + 130 \, b^{4} c^{2} d^{4} e^{8} - 31 \, b^{5} c d^{3} e^{9} + 3 \, b^{6} d^{2} e^{10}\right)} x^{2} + {\left(96 \, c^{6} d^{9} e^{3} - 368 \, b c^{5} d^{8} e^{4} + 560 \, b^{2} c^{4} d^{7} e^{5} - 440 \, b^{3} c^{3} d^{6} e^{6} + 190 \, b^{4} c^{2} d^{5} e^{7} - 43 \, b^{5} c d^{4} e^{8} + 4 \, b^{6} d^{3} e^{9}\right)} x\right)}}, \frac{15 \, {\left({\left(7 \, c^{4} e^{6} f + {\left(5 \, c^{4} d e^{5} - 6 \, b c^{3} e^{6}\right)} g\right)} x^{5} + {\left(7 \, {\left(3 \, c^{4} d e^{5} + b c^{3} e^{6}\right)} f + {\left(15 \, c^{4} d^{2} e^{4} - 13 \, b c^{3} d e^{5} - 6 \, b^{2} c^{2} e^{6}\right)} g\right)} x^{4} + 2 \, {\left(7 \, {\left(c^{4} d^{2} e^{4} + 2 \, b c^{3} d e^{5}\right)} f + {\left(5 \, c^{4} d^{3} e^{3} + 4 \, b c^{3} d^{2} e^{4} - 12 \, b^{2} c^{2} d e^{5}\right)} g\right)} x^{3} - 2 \, {\left(7 \, {\left(c^{4} d^{3} e^{3} - 3 \, b c^{3} d^{2} e^{4}\right)} f + {\left(5 \, c^{4} d^{4} e^{2} - 21 \, b c^{3} d^{3} e^{3} + 18 \, b^{2} c^{2} d^{2} e^{4}\right)} g\right)} x^{2} - 7 \, {\left(c^{4} d^{5} e - b c^{3} d^{4} e^{2}\right)} f - {\left(5 \, c^{4} d^{6} - 11 \, b c^{3} d^{5} e + 6 \, b^{2} c^{2} d^{4} e^{2}\right)} g - {\left(7 \, {\left(3 \, c^{4} d^{4} e^{2} - 4 \, b c^{3} d^{3} e^{3}\right)} f + {\left(15 \, c^{4} d^{5} e - 38 \, b c^{3} d^{4} e^{2} + 24 \, b^{2} c^{2} d^{3} e^{3}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(15 \, {\left(7 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f + {\left(10 \, c^{4} d^{2} e^{3} - 17 \, b c^{3} d e^{4} + 6 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} + 5 \, {\left(7 \, {\left(14 \, c^{4} d^{2} e^{3} - 5 \, b c^{3} d e^{4} - b^{2} c^{2} e^{5}\right)} f + {\left(70 \, c^{4} d^{3} e^{2} - 109 \, b c^{3} d^{2} e^{3} + 25 \, b^{2} c^{2} d e^{4} + 6 \, b^{3} c e^{5}\right)} g\right)} x^{2} - {\left(170 \, c^{4} d^{4} e - 459 \, b c^{3} d^{3} e^{2} + 311 \, b^{2} c^{2} d^{2} e^{3} - 78 \, b^{3} c d e^{4} + 8 \, b^{4} e^{5}\right)} f + {\left(98 \, c^{4} d^{5} - 75 \, b c^{3} d^{4} e - 67 \, b^{2} c^{2} d^{3} e^{2} + 48 \, b^{3} c d^{2} e^{3} - 4 \, b^{4} d e^{4}\right)} g + {\left(7 \, {\left(34 \, c^{4} d^{3} e^{2} + 19 \, b c^{3} d^{2} e^{3} - 22 \, b^{2} c^{2} d e^{4} + 2 \, b^{3} c e^{5}\right)} f + {\left(170 \, c^{4} d^{4} e - 109 \, b c^{3} d^{3} e^{2} - 224 \, b^{2} c^{2} d^{2} e^{3} + 142 \, b^{3} c d e^{4} - 12 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(32 \, c^{6} d^{10} e^{2} - 112 \, b c^{5} d^{9} e^{3} + 160 \, b^{2} c^{4} d^{8} e^{4} - 120 \, b^{3} c^{3} d^{7} e^{5} + 50 \, b^{4} c^{2} d^{6} e^{6} - 11 \, b^{5} c d^{5} e^{7} + b^{6} d^{4} e^{8} - {\left(32 \, c^{6} d^{5} e^{7} - 80 \, b c^{5} d^{4} e^{8} + 80 \, b^{2} c^{4} d^{3} e^{9} - 40 \, b^{3} c^{3} d^{2} e^{10} + 10 \, b^{4} c^{2} d e^{11} - b^{5} c e^{12}\right)} x^{5} - {\left(96 \, c^{6} d^{6} e^{6} - 208 \, b c^{5} d^{5} e^{7} + 160 \, b^{2} c^{4} d^{4} e^{8} - 40 \, b^{3} c^{3} d^{3} e^{9} - 10 \, b^{4} c^{2} d^{2} e^{10} + 7 \, b^{5} c d e^{11} - b^{6} e^{12}\right)} x^{4} - 2 \, {\left(32 \, c^{6} d^{7} e^{5} - 16 \, b c^{5} d^{6} e^{6} - 80 \, b^{2} c^{4} d^{5} e^{7} + 120 \, b^{3} c^{3} d^{4} e^{8} - 70 \, b^{4} c^{2} d^{3} e^{9} + 19 \, b^{5} c d^{2} e^{10} - 2 \, b^{6} d e^{11}\right)} x^{3} + 2 \, {\left(32 \, c^{6} d^{8} e^{4} - 176 \, b c^{5} d^{7} e^{5} + 320 \, b^{2} c^{4} d^{6} e^{6} - 280 \, b^{3} c^{3} d^{5} e^{7} + 130 \, b^{4} c^{2} d^{4} e^{8} - 31 \, b^{5} c d^{3} e^{9} + 3 \, b^{6} d^{2} e^{10}\right)} x^{2} + {\left(96 \, c^{6} d^{9} e^{3} - 368 \, b c^{5} d^{8} e^{4} + 560 \, b^{2} c^{4} d^{7} e^{5} - 440 \, b^{3} c^{3} d^{6} e^{6} + 190 \, b^{4} c^{2} d^{5} e^{7} - 43 \, b^{5} c d^{4} e^{8} + 4 \, b^{6} d^{3} e^{9}\right)} x\right)}}\right]"," ",0,"[1/48*(15*((7*c^4*e^6*f + (5*c^4*d*e^5 - 6*b*c^3*e^6)*g)*x^5 + (7*(3*c^4*d*e^5 + b*c^3*e^6)*f + (15*c^4*d^2*e^4 - 13*b*c^3*d*e^5 - 6*b^2*c^2*e^6)*g)*x^4 + 2*(7*(c^4*d^2*e^4 + 2*b*c^3*d*e^5)*f + (5*c^4*d^3*e^3 + 4*b*c^3*d^2*e^4 - 12*b^2*c^2*d*e^5)*g)*x^3 - 2*(7*(c^4*d^3*e^3 - 3*b*c^3*d^2*e^4)*f + (5*c^4*d^4*e^2 - 21*b*c^3*d^3*e^3 + 18*b^2*c^2*d^2*e^4)*g)*x^2 - 7*(c^4*d^5*e - b*c^3*d^4*e^2)*f - (5*c^4*d^6 - 11*b*c^3*d^5*e + 6*b^2*c^2*d^4*e^2)*g - (7*(3*c^4*d^4*e^2 - 4*b*c^3*d^3*e^3)*f + (15*c^4*d^5*e - 38*b*c^3*d^4*e^2 + 24*b^2*c^2*d^3*e^3)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(15*(7*(2*c^4*d*e^4 - b*c^3*e^5)*f + (10*c^4*d^2*e^3 - 17*b*c^3*d*e^4 + 6*b^2*c^2*e^5)*g)*x^3 + 5*(7*(14*c^4*d^2*e^3 - 5*b*c^3*d*e^4 - b^2*c^2*e^5)*f + (70*c^4*d^3*e^2 - 109*b*c^3*d^2*e^3 + 25*b^2*c^2*d*e^4 + 6*b^3*c*e^5)*g)*x^2 - (170*c^4*d^4*e - 459*b*c^3*d^3*e^2 + 311*b^2*c^2*d^2*e^3 - 78*b^3*c*d*e^4 + 8*b^4*e^5)*f + (98*c^4*d^5 - 75*b*c^3*d^4*e - 67*b^2*c^2*d^3*e^2 + 48*b^3*c*d^2*e^3 - 4*b^4*d*e^4)*g + (7*(34*c^4*d^3*e^2 + 19*b*c^3*d^2*e^3 - 22*b^2*c^2*d*e^4 + 2*b^3*c*e^5)*f + (170*c^4*d^4*e - 109*b*c^3*d^3*e^2 - 224*b^2*c^2*d^2*e^3 + 142*b^3*c*d*e^4 - 12*b^4*e^5)*g)*x)*sqrt(e*x + d))/(32*c^6*d^10*e^2 - 112*b*c^5*d^9*e^3 + 160*b^2*c^4*d^8*e^4 - 120*b^3*c^3*d^7*e^5 + 50*b^4*c^2*d^6*e^6 - 11*b^5*c*d^5*e^7 + b^6*d^4*e^8 - (32*c^6*d^5*e^7 - 80*b*c^5*d^4*e^8 + 80*b^2*c^4*d^3*e^9 - 40*b^3*c^3*d^2*e^10 + 10*b^4*c^2*d*e^11 - b^5*c*e^12)*x^5 - (96*c^6*d^6*e^6 - 208*b*c^5*d^5*e^7 + 160*b^2*c^4*d^4*e^8 - 40*b^3*c^3*d^3*e^9 - 10*b^4*c^2*d^2*e^10 + 7*b^5*c*d*e^11 - b^6*e^12)*x^4 - 2*(32*c^6*d^7*e^5 - 16*b*c^5*d^6*e^6 - 80*b^2*c^4*d^5*e^7 + 120*b^3*c^3*d^4*e^8 - 70*b^4*c^2*d^3*e^9 + 19*b^5*c*d^2*e^10 - 2*b^6*d*e^11)*x^3 + 2*(32*c^6*d^8*e^4 - 176*b*c^5*d^7*e^5 + 320*b^2*c^4*d^6*e^6 - 280*b^3*c^3*d^5*e^7 + 130*b^4*c^2*d^4*e^8 - 31*b^5*c*d^3*e^9 + 3*b^6*d^2*e^10)*x^2 + (96*c^6*d^9*e^3 - 368*b*c^5*d^8*e^4 + 560*b^2*c^4*d^7*e^5 - 440*b^3*c^3*d^6*e^6 + 190*b^4*c^2*d^5*e^7 - 43*b^5*c*d^4*e^8 + 4*b^6*d^3*e^9)*x), 1/24*(15*((7*c^4*e^6*f + (5*c^4*d*e^5 - 6*b*c^3*e^6)*g)*x^5 + (7*(3*c^4*d*e^5 + b*c^3*e^6)*f + (15*c^4*d^2*e^4 - 13*b*c^3*d*e^5 - 6*b^2*c^2*e^6)*g)*x^4 + 2*(7*(c^4*d^2*e^4 + 2*b*c^3*d*e^5)*f + (5*c^4*d^3*e^3 + 4*b*c^3*d^2*e^4 - 12*b^2*c^2*d*e^5)*g)*x^3 - 2*(7*(c^4*d^3*e^3 - 3*b*c^3*d^2*e^4)*f + (5*c^4*d^4*e^2 - 21*b*c^3*d^3*e^3 + 18*b^2*c^2*d^2*e^4)*g)*x^2 - 7*(c^4*d^5*e - b*c^3*d^4*e^2)*f - (5*c^4*d^6 - 11*b*c^3*d^5*e + 6*b^2*c^2*d^4*e^2)*g - (7*(3*c^4*d^4*e^2 - 4*b*c^3*d^3*e^3)*f + (15*c^4*d^5*e - 38*b*c^3*d^4*e^2 + 24*b^2*c^2*d^3*e^3)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(15*(7*(2*c^4*d*e^4 - b*c^3*e^5)*f + (10*c^4*d^2*e^3 - 17*b*c^3*d*e^4 + 6*b^2*c^2*e^5)*g)*x^3 + 5*(7*(14*c^4*d^2*e^3 - 5*b*c^3*d*e^4 - b^2*c^2*e^5)*f + (70*c^4*d^3*e^2 - 109*b*c^3*d^2*e^3 + 25*b^2*c^2*d*e^4 + 6*b^3*c*e^5)*g)*x^2 - (170*c^4*d^4*e - 459*b*c^3*d^3*e^2 + 311*b^2*c^2*d^2*e^3 - 78*b^3*c*d*e^4 + 8*b^4*e^5)*f + (98*c^4*d^5 - 75*b*c^3*d^4*e - 67*b^2*c^2*d^3*e^2 + 48*b^3*c*d^2*e^3 - 4*b^4*d*e^4)*g + (7*(34*c^4*d^3*e^2 + 19*b*c^3*d^2*e^3 - 22*b^2*c^2*d*e^4 + 2*b^3*c*e^5)*f + (170*c^4*d^4*e - 109*b*c^3*d^3*e^2 - 224*b^2*c^2*d^2*e^3 + 142*b^3*c*d*e^4 - 12*b^4*e^5)*g)*x)*sqrt(e*x + d))/(32*c^6*d^10*e^2 - 112*b*c^5*d^9*e^3 + 160*b^2*c^4*d^8*e^4 - 120*b^3*c^3*d^7*e^5 + 50*b^4*c^2*d^6*e^6 - 11*b^5*c*d^5*e^7 + b^6*d^4*e^8 - (32*c^6*d^5*e^7 - 80*b*c^5*d^4*e^8 + 80*b^2*c^4*d^3*e^9 - 40*b^3*c^3*d^2*e^10 + 10*b^4*c^2*d*e^11 - b^5*c*e^12)*x^5 - (96*c^6*d^6*e^6 - 208*b*c^5*d^5*e^7 + 160*b^2*c^4*d^4*e^8 - 40*b^3*c^3*d^3*e^9 - 10*b^4*c^2*d^2*e^10 + 7*b^5*c*d*e^11 - b^6*e^12)*x^4 - 2*(32*c^6*d^7*e^5 - 16*b*c^5*d^6*e^6 - 80*b^2*c^4*d^5*e^7 + 120*b^3*c^3*d^4*e^8 - 70*b^4*c^2*d^3*e^9 + 19*b^5*c*d^2*e^10 - 2*b^6*d*e^11)*x^3 + 2*(32*c^6*d^8*e^4 - 176*b*c^5*d^7*e^5 + 320*b^2*c^4*d^6*e^6 - 280*b^3*c^3*d^5*e^7 + 130*b^4*c^2*d^4*e^8 - 31*b^5*c*d^3*e^9 + 3*b^6*d^2*e^10)*x^2 + (96*c^6*d^9*e^3 - 368*b*c^5*d^8*e^4 + 560*b^2*c^4*d^7*e^5 - 440*b^3*c^3*d^6*e^6 + 190*b^4*c^2*d^5*e^7 - 43*b^5*c*d^4*e^8 + 4*b^6*d^3*e^9)*x)]","B",0
2276,1,578,0,0.418887," ","integrate((e*x+d)^(13/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, c^{5} e^{5} g x^{5} + 3 \, {\left(7 \, c^{5} e^{5} f + 2 \, {\left(19 \, c^{5} d e^{4} - 5 \, b c^{4} e^{5}\right)} g\right)} x^{4} + 2 \, {\left(14 \, {\left(7 \, c^{5} d e^{4} - 2 \, b c^{4} e^{5}\right)} f + {\left(257 \, c^{5} d^{2} e^{3} - 192 \, b c^{4} d e^{4} + 40 \, b^{2} c^{3} e^{5}\right)} g\right)} x^{3} + 6 \, {\left(7 \, {\left(43 \, c^{5} d^{2} e^{3} - 36 \, b c^{4} d e^{4} + 8 \, b^{2} c^{3} e^{5}\right)} f + 2 \, {\left(292 \, c^{5} d^{3} e^{2} - 449 \, b c^{4} d^{2} e^{3} + 232 \, b^{2} c^{3} d e^{4} - 40 \, b^{3} c^{2} e^{5}\right)} g\right)} x^{2} + 7 \, {\left(723 \, c^{5} d^{4} e - 1992 \, b c^{4} d^{3} e^{2} + 1968 \, b^{2} c^{3} d^{2} e^{3} - 832 \, b^{3} c^{2} d e^{4} + 128 \, b^{4} c e^{5}\right)} f + 2 \, {\left(4707 \, c^{5} d^{5} - 16563 \, b c^{4} d^{4} e + 22752 \, b^{2} c^{3} d^{3} e^{2} - 15248 \, b^{3} c^{2} d^{2} e^{3} + 4992 \, b^{4} c d e^{4} - 640 \, b^{5} e^{5}\right)} g - 3 \, {\left(28 \, {\left(91 \, c^{5} d^{3} e^{2} - 158 \, b c^{4} d^{2} e^{3} + 88 \, b^{2} c^{3} d e^{4} - 16 \, b^{3} c^{2} e^{5}\right)} f + {\left(4707 \, c^{5} d^{4} e - 11856 \, b c^{4} d^{3} e^{2} + 10896 \, b^{2} c^{3} d^{2} e^{3} - 4352 \, b^{3} c^{2} d e^{4} + 640 \, b^{4} c e^{5}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{105 \, {\left(c^{8} e^{5} x^{3} + c^{8} d^{3} e^{2} - 2 \, b c^{7} d^{2} e^{3} + b^{2} c^{6} d e^{4} - {\left(c^{8} d e^{4} - 2 \, b c^{7} e^{5}\right)} x^{2} - {\left(c^{8} d^{2} e^{3} - b^{2} c^{6} e^{5}\right)} x\right)}}"," ",0,"-2/105*(15*c^5*e^5*g*x^5 + 3*(7*c^5*e^5*f + 2*(19*c^5*d*e^4 - 5*b*c^4*e^5)*g)*x^4 + 2*(14*(7*c^5*d*e^4 - 2*b*c^4*e^5)*f + (257*c^5*d^2*e^3 - 192*b*c^4*d*e^4 + 40*b^2*c^3*e^5)*g)*x^3 + 6*(7*(43*c^5*d^2*e^3 - 36*b*c^4*d*e^4 + 8*b^2*c^3*e^5)*f + 2*(292*c^5*d^3*e^2 - 449*b*c^4*d^2*e^3 + 232*b^2*c^3*d*e^4 - 40*b^3*c^2*e^5)*g)*x^2 + 7*(723*c^5*d^4*e - 1992*b*c^4*d^3*e^2 + 1968*b^2*c^3*d^2*e^3 - 832*b^3*c^2*d*e^4 + 128*b^4*c*e^5)*f + 2*(4707*c^5*d^5 - 16563*b*c^4*d^4*e + 22752*b^2*c^3*d^3*e^2 - 15248*b^3*c^2*d^2*e^3 + 4992*b^4*c*d*e^4 - 640*b^5*e^5)*g - 3*(28*(91*c^5*d^3*e^2 - 158*b*c^4*d^2*e^3 + 88*b^2*c^3*d*e^4 - 16*b^3*c^2*e^5)*f + (4707*c^5*d^4*e - 11856*b*c^4*d^3*e^2 + 10896*b^2*c^3*d^2*e^3 - 4352*b^3*c^2*d*e^4 + 640*b^4*c*e^5)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^8*e^5*x^3 + c^8*d^3*e^2 - 2*b*c^7*d^2*e^3 + b^2*c^6*d*e^4 - (c^8*d*e^4 - 2*b*c^7*e^5)*x^2 - (c^8*d^2*e^3 - b^2*c^6*e^5)*x)","A",0
2277,1,428,0,0.429145," ","integrate((e*x+d)^(11/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, c^{4} e^{4} g x^{4} + {\left(5 \, c^{4} e^{4} f + {\left(23 \, c^{4} d e^{3} - 8 \, b c^{3} e^{4}\right)} g\right)} x^{3} + 3 \, {\left(5 \, {\left(5 \, c^{4} d e^{3} - 2 \, b c^{3} e^{4}\right)} f + {\left(61 \, c^{4} d^{2} e^{2} - 62 \, b c^{3} d e^{3} + 16 \, b^{2} c^{2} e^{4}\right)} g\right)} x^{2} + 5 \, {\left(45 \, c^{4} d^{3} e - 102 \, b c^{3} d^{2} e^{2} + 72 \, b^{2} c^{2} d e^{3} - 16 \, b^{3} c e^{4}\right)} f + 2 \, {\left(249 \, c^{4} d^{4} - 741 \, b c^{3} d^{3} e + 804 \, b^{2} c^{2} d^{2} e^{2} - 376 \, b^{3} c d e^{3} + 64 \, b^{4} e^{4}\right)} g - 3 \, {\left(5 \, {\left(23 \, c^{4} d^{2} e^{2} - 28 \, b c^{3} d e^{3} + 8 \, b^{2} c^{2} e^{4}\right)} f + {\left(249 \, c^{4} d^{3} e - 492 \, b c^{3} d^{2} e^{2} + 312 \, b^{2} c^{2} d e^{3} - 64 \, b^{3} c e^{4}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{15 \, {\left(c^{7} e^{5} x^{3} + c^{7} d^{3} e^{2} - 2 \, b c^{6} d^{2} e^{3} + b^{2} c^{5} d e^{4} - {\left(c^{7} d e^{4} - 2 \, b c^{6} e^{5}\right)} x^{2} - {\left(c^{7} d^{2} e^{3} - b^{2} c^{5} e^{5}\right)} x\right)}}"," ",0,"-2/15*(3*c^4*e^4*g*x^4 + (5*c^4*e^4*f + (23*c^4*d*e^3 - 8*b*c^3*e^4)*g)*x^3 + 3*(5*(5*c^4*d*e^3 - 2*b*c^3*e^4)*f + (61*c^4*d^2*e^2 - 62*b*c^3*d*e^3 + 16*b^2*c^2*e^4)*g)*x^2 + 5*(45*c^4*d^3*e - 102*b*c^3*d^2*e^2 + 72*b^2*c^2*d*e^3 - 16*b^3*c*e^4)*f + 2*(249*c^4*d^4 - 741*b*c^3*d^3*e + 804*b^2*c^2*d^2*e^2 - 376*b^3*c*d*e^3 + 64*b^4*e^4)*g - 3*(5*(23*c^4*d^2*e^2 - 28*b*c^3*d*e^3 + 8*b^2*c^2*e^4)*f + (249*c^4*d^3*e - 492*b*c^3*d^2*e^2 + 312*b^2*c^2*d*e^3 - 64*b^3*c*e^4)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^7*e^5*x^3 + c^7*d^3*e^2 - 2*b*c^6*d^2*e^3 + b^2*c^5*d*e^4 - (c^7*d*e^4 - 2*b*c^6*e^5)*x^2 - (c^7*d^2*e^3 - b^2*c^5*e^5)*x)","A",0
2278,1,308,0,0.413499," ","integrate((e*x+d)^(9/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(c^{3} e^{3} g x^{3} + 3 \, {\left(c^{3} e^{3} f + 2 \, {\left(2 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} g\right)} x^{2} + {\left(11 \, c^{3} d^{2} e - 20 \, b c^{2} d e^{2} + 8 \, b^{2} c e^{3}\right)} f + 2 \, {\left(17 \, c^{3} d^{3} - 41 \, b c^{2} d^{2} e + 32 \, b^{2} c d e^{2} - 8 \, b^{3} e^{3}\right)} g - 3 \, {\left(2 \, {\left(3 \, c^{3} d e^{2} - 2 \, b c^{2} e^{3}\right)} f + {\left(17 \, c^{3} d^{2} e - 24 \, b c^{2} d e^{2} + 8 \, b^{2} c e^{3}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{3 \, {\left(c^{6} e^{5} x^{3} + c^{6} d^{3} e^{2} - 2 \, b c^{5} d^{2} e^{3} + b^{2} c^{4} d e^{4} - {\left(c^{6} d e^{4} - 2 \, b c^{5} e^{5}\right)} x^{2} - {\left(c^{6} d^{2} e^{3} - b^{2} c^{4} e^{5}\right)} x\right)}}"," ",0,"-2/3*(c^3*e^3*g*x^3 + 3*(c^3*e^3*f + 2*(2*c^3*d*e^2 - b*c^2*e^3)*g)*x^2 + (11*c^3*d^2*e - 20*b*c^2*d*e^2 + 8*b^2*c*e^3)*f + 2*(17*c^3*d^3 - 41*b*c^2*d^2*e + 32*b^2*c*d*e^2 - 8*b^3*e^3)*g - 3*(2*(3*c^3*d*e^2 - 2*b*c^2*e^3)*f + (17*c^3*d^2*e - 24*b*c^2*d*e^2 + 8*b^2*c*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^6*e^5*x^3 + c^6*d^3*e^2 - 2*b*c^5*d^2*e^3 + b^2*c^4*d*e^4 - (c^6*d*e^4 - 2*b*c^5*e^5)*x^2 - (c^6*d^2*e^3 - b^2*c^4*e^5)*x)","A",0
2279,1,216,0,0.398877," ","integrate((e*x+d)^(7/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, c^{2} e^{2} g x^{2} + {\left(c^{2} d e - 2 \, b c e^{2}\right)} f + 2 \, {\left(5 \, c^{2} d^{2} - 9 \, b c d e + 4 \, b^{2} e^{2}\right)} g - 3 \, {\left(c^{2} e^{2} f + {\left(5 \, c^{2} d e - 4 \, b c e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{e x + d}}{3 \, {\left(c^{5} e^{5} x^{3} + c^{5} d^{3} e^{2} - 2 \, b c^{4} d^{2} e^{3} + b^{2} c^{3} d e^{4} - {\left(c^{5} d e^{4} - 2 \, b c^{4} e^{5}\right)} x^{2} - {\left(c^{5} d^{2} e^{3} - b^{2} c^{3} e^{5}\right)} x\right)}}"," ",0,"-2/3*(3*c^2*e^2*g*x^2 + (c^2*d*e - 2*b*c*e^2)*f + 2*(5*c^2*d^2 - 9*b*c*d*e + 4*b^2*e^2)*g - 3*(c^2*e^2*f + (5*c^2*d*e - 4*b*c*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d)/(c^5*e^5*x^3 + c^5*d^3*e^2 - 2*b*c^4*d^2*e^3 + b^2*c^3*d*e^4 - (c^5*d*e^4 - 2*b*c^4*e^5)*x^2 - (c^5*d^2*e^3 - b^2*c^3*e^5)*x)","A",0
2280,1,154,0,0.400470," ","integrate((e*x+d)^(5/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, c e g x + c e f - 2 \, {\left(c d - b e\right)} g\right)} \sqrt{e x + d}}{3 \, {\left(c^{4} e^{5} x^{3} + c^{4} d^{3} e^{2} - 2 \, b c^{3} d^{2} e^{3} + b^{2} c^{2} d e^{4} - {\left(c^{4} d e^{4} - 2 \, b c^{3} e^{5}\right)} x^{2} - {\left(c^{4} d^{2} e^{3} - b^{2} c^{2} e^{5}\right)} x\right)}}"," ",0,"2/3*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*c*e*g*x + c*e*f - 2*(c*d - b*e)*g)*sqrt(e*x + d)/(c^4*e^5*x^3 + c^4*d^3*e^2 - 2*b*c^3*d^2*e^3 + b^2*c^2*d*e^4 - (c^4*d*e^4 - 2*b*c^3*e^5)*x^2 - (c^4*d^2*e^3 - b^2*c^2*e^5)*x)","A",0
2281,1,1437,0,0.439440," ","integrate((e*x+d)^(3/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(c^{3} e^{4} f - c^{3} d e^{3} g\right)} x^{3} - {\left({\left(c^{3} d e^{3} - 2 \, b c^{2} e^{4}\right)} f - {\left(c^{3} d^{2} e^{2} - 2 \, b c^{2} d e^{3}\right)} g\right)} x^{2} + {\left(c^{3} d^{3} e - 2 \, b c^{2} d^{2} e^{2} + b^{2} c d e^{3}\right)} f - {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2}\right)} g - {\left({\left(c^{3} d^{2} e^{2} - b^{2} c e^{4}\right)} f - {\left(c^{3} d^{3} e - b^{2} c d e^{3}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(10 \, c^{3} d^{2} e - 13 \, b c^{2} d e^{2} + 4 \, b^{2} c e^{3}\right)} f - {\left(2 \, c^{3} d^{3} - b c^{2} d^{2} e - 2 \, b^{2} c d e^{2} + b^{3} e^{3}\right)} g - 3 \, {\left({\left(2 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} f - {\left(2 \, c^{3} d^{2} e - b c^{2} d e^{2}\right)} g\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(8 \, c^{6} d^{6} e^{2} - 28 \, b c^{5} d^{5} e^{3} + 38 \, b^{2} c^{4} d^{4} e^{4} - 25 \, b^{3} c^{3} d^{3} e^{5} + 8 \, b^{4} c^{2} d^{2} e^{6} - b^{5} c d e^{7} + {\left(8 \, c^{6} d^{3} e^{5} - 12 \, b c^{5} d^{2} e^{6} + 6 \, b^{2} c^{4} d e^{7} - b^{3} c^{3} e^{8}\right)} x^{3} - {\left(8 \, c^{6} d^{4} e^{4} - 28 \, b c^{5} d^{3} e^{5} + 30 \, b^{2} c^{4} d^{2} e^{6} - 13 \, b^{3} c^{3} d e^{7} + 2 \, b^{4} c^{2} e^{8}\right)} x^{2} - {\left(8 \, c^{6} d^{5} e^{3} - 12 \, b c^{5} d^{4} e^{4} - 2 \, b^{2} c^{4} d^{3} e^{5} + 11 \, b^{3} c^{3} d^{2} e^{6} - 6 \, b^{4} c^{2} d e^{7} + b^{5} c e^{8}\right)} x\right)}}, -\frac{2 \, {\left(3 \, {\left({\left(c^{3} e^{4} f - c^{3} d e^{3} g\right)} x^{3} - {\left({\left(c^{3} d e^{3} - 2 \, b c^{2} e^{4}\right)} f - {\left(c^{3} d^{2} e^{2} - 2 \, b c^{2} d e^{3}\right)} g\right)} x^{2} + {\left(c^{3} d^{3} e - 2 \, b c^{2} d^{2} e^{2} + b^{2} c d e^{3}\right)} f - {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2}\right)} g - {\left({\left(c^{3} d^{2} e^{2} - b^{2} c e^{4}\right)} f - {\left(c^{3} d^{3} e - b^{2} c d e^{3}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) - \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left({\left(10 \, c^{3} d^{2} e - 13 \, b c^{2} d e^{2} + 4 \, b^{2} c e^{3}\right)} f - {\left(2 \, c^{3} d^{3} - b c^{2} d^{2} e - 2 \, b^{2} c d e^{2} + b^{3} e^{3}\right)} g - 3 \, {\left({\left(2 \, c^{3} d e^{2} - b c^{2} e^{3}\right)} f - {\left(2 \, c^{3} d^{2} e - b c^{2} d e^{2}\right)} g\right)} x\right)} \sqrt{e x + d}\right)}}{3 \, {\left(8 \, c^{6} d^{6} e^{2} - 28 \, b c^{5} d^{5} e^{3} + 38 \, b^{2} c^{4} d^{4} e^{4} - 25 \, b^{3} c^{3} d^{3} e^{5} + 8 \, b^{4} c^{2} d^{2} e^{6} - b^{5} c d e^{7} + {\left(8 \, c^{6} d^{3} e^{5} - 12 \, b c^{5} d^{2} e^{6} + 6 \, b^{2} c^{4} d e^{7} - b^{3} c^{3} e^{8}\right)} x^{3} - {\left(8 \, c^{6} d^{4} e^{4} - 28 \, b c^{5} d^{3} e^{5} + 30 \, b^{2} c^{4} d^{2} e^{6} - 13 \, b^{3} c^{3} d e^{7} + 2 \, b^{4} c^{2} e^{8}\right)} x^{2} - {\left(8 \, c^{6} d^{5} e^{3} - 12 \, b c^{5} d^{4} e^{4} - 2 \, b^{2} c^{4} d^{3} e^{5} + 11 \, b^{3} c^{3} d^{2} e^{6} - 6 \, b^{4} c^{2} d e^{7} + b^{5} c e^{8}\right)} x\right)}}\right]"," ",0,"[-1/3*(3*((c^3*e^4*f - c^3*d*e^3*g)*x^3 - ((c^3*d*e^3 - 2*b*c^2*e^4)*f - (c^3*d^2*e^2 - 2*b*c^2*d*e^3)*g)*x^2 + (c^3*d^3*e - 2*b*c^2*d^2*e^2 + b^2*c*d*e^3)*f - (c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2)*g - ((c^3*d^2*e^2 - b^2*c*e^4)*f - (c^3*d^3*e - b^2*c*d*e^3)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((10*c^3*d^2*e - 13*b*c^2*d*e^2 + 4*b^2*c*e^3)*f - (2*c^3*d^3 - b*c^2*d^2*e - 2*b^2*c*d*e^2 + b^3*e^3)*g - 3*((2*c^3*d*e^2 - b*c^2*e^3)*f - (2*c^3*d^2*e - b*c^2*d*e^2)*g)*x)*sqrt(e*x + d))/(8*c^6*d^6*e^2 - 28*b*c^5*d^5*e^3 + 38*b^2*c^4*d^4*e^4 - 25*b^3*c^3*d^3*e^5 + 8*b^4*c^2*d^2*e^6 - b^5*c*d*e^7 + (8*c^6*d^3*e^5 - 12*b*c^5*d^2*e^6 + 6*b^2*c^4*d*e^7 - b^3*c^3*e^8)*x^3 - (8*c^6*d^4*e^4 - 28*b*c^5*d^3*e^5 + 30*b^2*c^4*d^2*e^6 - 13*b^3*c^3*d*e^7 + 2*b^4*c^2*e^8)*x^2 - (8*c^6*d^5*e^3 - 12*b*c^5*d^4*e^4 - 2*b^2*c^4*d^3*e^5 + 11*b^3*c^3*d^2*e^6 - 6*b^4*c^2*d*e^7 + b^5*c*e^8)*x), -2/3*(3*((c^3*e^4*f - c^3*d*e^3*g)*x^3 - ((c^3*d*e^3 - 2*b*c^2*e^4)*f - (c^3*d^2*e^2 - 2*b*c^2*d*e^3)*g)*x^2 + (c^3*d^3*e - 2*b*c^2*d^2*e^2 + b^2*c*d*e^3)*f - (c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2)*g - ((c^3*d^2*e^2 - b^2*c*e^4)*f - (c^3*d^3*e - b^2*c*d*e^3)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) - sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*((10*c^3*d^2*e - 13*b*c^2*d*e^2 + 4*b^2*c*e^3)*f - (2*c^3*d^3 - b*c^2*d^2*e - 2*b^2*c*d*e^2 + b^3*e^3)*g - 3*((2*c^3*d*e^2 - b*c^2*e^3)*f - (2*c^3*d^2*e - b*c^2*d*e^2)*g)*x)*sqrt(e*x + d))/(8*c^6*d^6*e^2 - 28*b*c^5*d^5*e^3 + 38*b^2*c^4*d^4*e^4 - 25*b^3*c^3*d^3*e^5 + 8*b^4*c^2*d^2*e^6 - b^5*c*d*e^7 + (8*c^6*d^3*e^5 - 12*b*c^5*d^2*e^6 + 6*b^2*c^4*d*e^7 - b^3*c^3*e^8)*x^3 - (8*c^6*d^4*e^4 - 28*b*c^5*d^3*e^5 + 30*b^2*c^4*d^2*e^6 - 13*b^3*c^3*d*e^7 + 2*b^4*c^2*e^8)*x^2 - (8*c^6*d^5*e^3 - 12*b*c^5*d^4*e^4 - 2*b^2*c^4*d^3*e^5 + 11*b^3*c^3*d^2*e^6 - 6*b^4*c^2*d*e^7 + b^5*c*e^8)*x)]","B",0
2282,1,2106,0,0.459412," ","integrate((e*x+d)^(1/2)*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, c^{3} e^{5} f - {\left(c^{3} d e^{4} + 2 \, b c^{2} e^{5}\right)} g\right)} x^{4} + 2 \, {\left(5 \, b c^{2} e^{5} f - {\left(b c^{2} d e^{4} + 2 \, b^{2} c e^{5}\right)} g\right)} x^{3} - {\left(5 \, {\left(2 \, c^{3} d^{2} e^{3} - 2 \, b c^{2} d e^{4} - b^{2} c e^{5}\right)} f - {\left(2 \, c^{3} d^{3} e^{2} + 2 \, b c^{2} d^{2} e^{3} - 5 \, b^{2} c d e^{4} - 2 \, b^{3} e^{5}\right)} g\right)} x^{2} + 5 \, {\left(c^{3} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + b^{2} c d^{2} e^{3}\right)} f - {\left(c^{3} d^{5} - 3 \, b^{2} c d^{3} e^{2} + 2 \, b^{3} d^{2} e^{3}\right)} g - 2 \, {\left(5 \, {\left(b c^{2} d^{2} e^{3} - b^{2} c d e^{4}\right)} f - {\left(b c^{2} d^{3} e^{2} + b^{2} c d^{2} e^{3} - 2 \, b^{3} d e^{4}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(5 \, {\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f - {\left(2 \, c^{3} d^{2} e^{2} + 3 \, b c^{2} d e^{3} - 2 \, b^{2} c e^{4}\right)} g\right)} x^{2} - {\left(26 \, c^{3} d^{3} e - 29 \, b c^{2} d^{2} e^{2} + 2 \, b^{2} c d e^{3} + 3 \, b^{3} e^{4}\right)} f - {\left(14 \, c^{3} d^{4} - 43 \, b c^{2} d^{3} e + 40 \, b^{2} c d^{2} e^{2} - 11 \, b^{3} d e^{3}\right)} g - 2 \, {\left(5 \, {\left(2 \, c^{3} d^{2} e^{2} - 5 \, b c^{2} d e^{3} + 2 \, b^{2} c e^{4}\right)} f - {\left(2 \, c^{3} d^{3} e - b c^{2} d^{2} e^{2} - 8 \, b^{2} c d e^{3} + 4 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(16 \, c^{6} d^{8} e^{2} - 64 \, b c^{5} d^{7} e^{3} + 104 \, b^{2} c^{4} d^{6} e^{4} - 88 \, b^{3} c^{3} d^{5} e^{5} + 41 \, b^{4} c^{2} d^{4} e^{6} - 10 \, b^{5} c d^{3} e^{7} + b^{6} d^{2} e^{8} + {\left(16 \, c^{6} d^{4} e^{6} - 32 \, b c^{5} d^{3} e^{7} + 24 \, b^{2} c^{4} d^{2} e^{8} - 8 \, b^{3} c^{3} d e^{9} + b^{4} c^{2} e^{10}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} e^{6} - 32 \, b^{2} c^{4} d^{3} e^{7} + 24 \, b^{3} c^{3} d^{2} e^{8} - 8 \, b^{4} c^{2} d e^{9} + b^{5} c e^{10}\right)} x^{3} - {\left(32 \, c^{6} d^{6} e^{4} - 96 \, b c^{5} d^{5} e^{5} + 96 \, b^{2} c^{4} d^{4} e^{6} - 32 \, b^{3} c^{3} d^{3} e^{7} - 6 \, b^{4} c^{2} d^{2} e^{8} + 6 \, b^{5} c d e^{9} - b^{6} e^{10}\right)} x^{2} - 2 \, {\left(16 \, b c^{5} d^{6} e^{4} - 48 \, b^{2} c^{4} d^{5} e^{5} + 56 \, b^{3} c^{3} d^{4} e^{6} - 32 \, b^{4} c^{2} d^{3} e^{7} + 9 \, b^{5} c d^{2} e^{8} - b^{6} d e^{9}\right)} x\right)}}, -\frac{3 \, {\left({\left(5 \, c^{3} e^{5} f - {\left(c^{3} d e^{4} + 2 \, b c^{2} e^{5}\right)} g\right)} x^{4} + 2 \, {\left(5 \, b c^{2} e^{5} f - {\left(b c^{2} d e^{4} + 2 \, b^{2} c e^{5}\right)} g\right)} x^{3} - {\left(5 \, {\left(2 \, c^{3} d^{2} e^{3} - 2 \, b c^{2} d e^{4} - b^{2} c e^{5}\right)} f - {\left(2 \, c^{3} d^{3} e^{2} + 2 \, b c^{2} d^{2} e^{3} - 5 \, b^{2} c d e^{4} - 2 \, b^{3} e^{5}\right)} g\right)} x^{2} + 5 \, {\left(c^{3} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + b^{2} c d^{2} e^{3}\right)} f - {\left(c^{3} d^{5} - 3 \, b^{2} c d^{3} e^{2} + 2 \, b^{3} d^{2} e^{3}\right)} g - 2 \, {\left(5 \, {\left(b c^{2} d^{2} e^{3} - b^{2} c d e^{4}\right)} f - {\left(b c^{2} d^{3} e^{2} + b^{2} c d^{2} e^{3} - 2 \, b^{3} d e^{4}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(3 \, {\left(5 \, {\left(2 \, c^{3} d e^{3} - b c^{2} e^{4}\right)} f - {\left(2 \, c^{3} d^{2} e^{2} + 3 \, b c^{2} d e^{3} - 2 \, b^{2} c e^{4}\right)} g\right)} x^{2} - {\left(26 \, c^{3} d^{3} e - 29 \, b c^{2} d^{2} e^{2} + 2 \, b^{2} c d e^{3} + 3 \, b^{3} e^{4}\right)} f - {\left(14 \, c^{3} d^{4} - 43 \, b c^{2} d^{3} e + 40 \, b^{2} c d^{2} e^{2} - 11 \, b^{3} d e^{3}\right)} g - 2 \, {\left(5 \, {\left(2 \, c^{3} d^{2} e^{2} - 5 \, b c^{2} d e^{3} + 2 \, b^{2} c e^{4}\right)} f - {\left(2 \, c^{3} d^{3} e - b c^{2} d^{2} e^{2} - 8 \, b^{2} c d e^{3} + 4 \, b^{3} e^{4}\right)} g\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(16 \, c^{6} d^{8} e^{2} - 64 \, b c^{5} d^{7} e^{3} + 104 \, b^{2} c^{4} d^{6} e^{4} - 88 \, b^{3} c^{3} d^{5} e^{5} + 41 \, b^{4} c^{2} d^{4} e^{6} - 10 \, b^{5} c d^{3} e^{7} + b^{6} d^{2} e^{8} + {\left(16 \, c^{6} d^{4} e^{6} - 32 \, b c^{5} d^{3} e^{7} + 24 \, b^{2} c^{4} d^{2} e^{8} - 8 \, b^{3} c^{3} d e^{9} + b^{4} c^{2} e^{10}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} e^{6} - 32 \, b^{2} c^{4} d^{3} e^{7} + 24 \, b^{3} c^{3} d^{2} e^{8} - 8 \, b^{4} c^{2} d e^{9} + b^{5} c e^{10}\right)} x^{3} - {\left(32 \, c^{6} d^{6} e^{4} - 96 \, b c^{5} d^{5} e^{5} + 96 \, b^{2} c^{4} d^{4} e^{6} - 32 \, b^{3} c^{3} d^{3} e^{7} - 6 \, b^{4} c^{2} d^{2} e^{8} + 6 \, b^{5} c d e^{9} - b^{6} e^{10}\right)} x^{2} - 2 \, {\left(16 \, b c^{5} d^{6} e^{4} - 48 \, b^{2} c^{4} d^{5} e^{5} + 56 \, b^{3} c^{3} d^{4} e^{6} - 32 \, b^{4} c^{2} d^{3} e^{7} + 9 \, b^{5} c d^{2} e^{8} - b^{6} d e^{9}\right)} x\right)}}\right]"," ",0,"[1/6*(3*((5*c^3*e^5*f - (c^3*d*e^4 + 2*b*c^2*e^5)*g)*x^4 + 2*(5*b*c^2*e^5*f - (b*c^2*d*e^4 + 2*b^2*c*e^5)*g)*x^3 - (5*(2*c^3*d^2*e^3 - 2*b*c^2*d*e^4 - b^2*c*e^5)*f - (2*c^3*d^3*e^2 + 2*b*c^2*d^2*e^3 - 5*b^2*c*d*e^4 - 2*b^3*e^5)*g)*x^2 + 5*(c^3*d^4*e - 2*b*c^2*d^3*e^2 + b^2*c*d^2*e^3)*f - (c^3*d^5 - 3*b^2*c*d^3*e^2 + 2*b^3*d^2*e^3)*g - 2*(5*(b*c^2*d^2*e^3 - b^2*c*d*e^4)*f - (b*c^2*d^3*e^2 + b^2*c*d^2*e^3 - 2*b^3*d*e^4)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(5*(2*c^3*d*e^3 - b*c^2*e^4)*f - (2*c^3*d^2*e^2 + 3*b*c^2*d*e^3 - 2*b^2*c*e^4)*g)*x^2 - (26*c^3*d^3*e - 29*b*c^2*d^2*e^2 + 2*b^2*c*d*e^3 + 3*b^3*e^4)*f - (14*c^3*d^4 - 43*b*c^2*d^3*e + 40*b^2*c*d^2*e^2 - 11*b^3*d*e^3)*g - 2*(5*(2*c^3*d^2*e^2 - 5*b*c^2*d*e^3 + 2*b^2*c*e^4)*f - (2*c^3*d^3*e - b*c^2*d^2*e^2 - 8*b^2*c*d*e^3 + 4*b^3*e^4)*g)*x)*sqrt(e*x + d))/(16*c^6*d^8*e^2 - 64*b*c^5*d^7*e^3 + 104*b^2*c^4*d^6*e^4 - 88*b^3*c^3*d^5*e^5 + 41*b^4*c^2*d^4*e^6 - 10*b^5*c*d^3*e^7 + b^6*d^2*e^8 + (16*c^6*d^4*e^6 - 32*b*c^5*d^3*e^7 + 24*b^2*c^4*d^2*e^8 - 8*b^3*c^3*d*e^9 + b^4*c^2*e^10)*x^4 + 2*(16*b*c^5*d^4*e^6 - 32*b^2*c^4*d^3*e^7 + 24*b^3*c^3*d^2*e^8 - 8*b^4*c^2*d*e^9 + b^5*c*e^10)*x^3 - (32*c^6*d^6*e^4 - 96*b*c^5*d^5*e^5 + 96*b^2*c^4*d^4*e^6 - 32*b^3*c^3*d^3*e^7 - 6*b^4*c^2*d^2*e^8 + 6*b^5*c*d*e^9 - b^6*e^10)*x^2 - 2*(16*b*c^5*d^6*e^4 - 48*b^2*c^4*d^5*e^5 + 56*b^3*c^3*d^4*e^6 - 32*b^4*c^2*d^3*e^7 + 9*b^5*c*d^2*e^8 - b^6*d*e^9)*x), -1/3*(3*((5*c^3*e^5*f - (c^3*d*e^4 + 2*b*c^2*e^5)*g)*x^4 + 2*(5*b*c^2*e^5*f - (b*c^2*d*e^4 + 2*b^2*c*e^5)*g)*x^3 - (5*(2*c^3*d^2*e^3 - 2*b*c^2*d*e^4 - b^2*c*e^5)*f - (2*c^3*d^3*e^2 + 2*b*c^2*d^2*e^3 - 5*b^2*c*d*e^4 - 2*b^3*e^5)*g)*x^2 + 5*(c^3*d^4*e - 2*b*c^2*d^3*e^2 + b^2*c*d^2*e^3)*f - (c^3*d^5 - 3*b^2*c*d^3*e^2 + 2*b^3*d^2*e^3)*g - 2*(5*(b*c^2*d^2*e^3 - b^2*c*d*e^4)*f - (b*c^2*d^3*e^2 + b^2*c*d^2*e^3 - 2*b^3*d*e^4)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(3*(5*(2*c^3*d*e^3 - b*c^2*e^4)*f - (2*c^3*d^2*e^2 + 3*b*c^2*d*e^3 - 2*b^2*c*e^4)*g)*x^2 - (26*c^3*d^3*e - 29*b*c^2*d^2*e^2 + 2*b^2*c*d*e^3 + 3*b^3*e^4)*f - (14*c^3*d^4 - 43*b*c^2*d^3*e + 40*b^2*c*d^2*e^2 - 11*b^3*d*e^3)*g - 2*(5*(2*c^3*d^2*e^2 - 5*b*c^2*d*e^3 + 2*b^2*c*e^4)*f - (2*c^3*d^3*e - b*c^2*d^2*e^2 - 8*b^2*c*d*e^3 + 4*b^3*e^4)*g)*x)*sqrt(e*x + d))/(16*c^6*d^8*e^2 - 64*b*c^5*d^7*e^3 + 104*b^2*c^4*d^6*e^4 - 88*b^3*c^3*d^5*e^5 + 41*b^4*c^2*d^4*e^6 - 10*b^5*c*d^3*e^7 + b^6*d^2*e^8 + (16*c^6*d^4*e^6 - 32*b*c^5*d^3*e^7 + 24*b^2*c^4*d^2*e^8 - 8*b^3*c^3*d*e^9 + b^4*c^2*e^10)*x^4 + 2*(16*b*c^5*d^4*e^6 - 32*b^2*c^4*d^3*e^7 + 24*b^3*c^3*d^2*e^8 - 8*b^4*c^2*d*e^9 + b^5*c*e^10)*x^3 - (32*c^6*d^6*e^4 - 96*b*c^5*d^5*e^5 + 96*b^2*c^4*d^4*e^6 - 32*b^3*c^3*d^3*e^7 - 6*b^4*c^2*d^2*e^8 + 6*b^5*c*d*e^9 - b^6*e^10)*x^2 - 2*(16*b*c^5*d^6*e^4 - 48*b^2*c^4*d^5*e^5 + 56*b^3*c^3*d^4*e^6 - 32*b^4*c^2*d^3*e^7 + 9*b^5*c*d^2*e^8 - b^6*d*e^9)*x)]","B",0
2283,1,3096,0,0.562544," ","integrate((g*x+f)/(e*x+d)^(1/2)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(7 \, c^{4} e^{6} f + {\left(c^{4} d e^{5} - 4 \, b c^{3} e^{6}\right)} g\right)} x^{5} + {\left(7 \, {\left(c^{4} d e^{5} + 2 \, b c^{3} e^{6}\right)} f + {\left(c^{4} d^{2} e^{4} - 2 \, b c^{3} d e^{5} - 8 \, b^{2} c^{2} e^{6}\right)} g\right)} x^{4} - {\left(7 \, {\left(2 \, c^{4} d^{2} e^{4} - 4 \, b c^{3} d e^{5} - b^{2} c^{2} e^{6}\right)} f + {\left(2 \, c^{4} d^{3} e^{3} - 12 \, b c^{3} d^{2} e^{4} + 15 \, b^{2} c^{2} d e^{5} + 4 \, b^{3} c e^{6}\right)} g\right)} x^{3} - {\left(7 \, {\left(2 \, c^{4} d^{3} e^{3} - 3 \, b^{2} c^{2} d e^{5}\right)} f + {\left(2 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3} - 3 \, b^{2} c^{2} d^{2} e^{4} + 12 \, b^{3} c d e^{5}\right)} g\right)} x^{2} + 7 \, {\left(c^{4} d^{5} e - 2 \, b c^{3} d^{4} e^{2} + b^{2} c^{2} d^{3} e^{3}\right)} f + {\left(c^{4} d^{6} - 6 \, b c^{3} d^{5} e + 9 \, b^{2} c^{2} d^{4} e^{2} - 4 \, b^{3} c d^{3} e^{3}\right)} g + {\left(7 \, {\left(c^{4} d^{4} e^{2} - 4 \, b c^{3} d^{3} e^{3} + 3 \, b^{2} c^{2} d^{2} e^{4}\right)} f + {\left(c^{4} d^{5} e - 8 \, b c^{3} d^{4} e^{2} + 19 \, b^{2} c^{2} d^{3} e^{3} - 12 \, b^{3} c d^{2} e^{4}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(15 \, {\left(7 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f + {\left(2 \, c^{4} d^{2} e^{3} - 9 \, b c^{3} d e^{4} + 4 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} + 5 \, {\left(7 \, {\left(2 \, c^{4} d^{2} e^{3} + 7 \, b c^{3} d e^{4} - 4 \, b^{2} c^{2} e^{5}\right)} f + {\left(2 \, c^{4} d^{3} e^{2} - b c^{3} d^{2} e^{3} - 32 \, b^{2} c^{2} d e^{4} + 16 \, b^{3} c e^{5}\right)} g\right)} x^{2} - {\left(86 \, c^{4} d^{4} e - 11 \, b c^{3} d^{3} e^{2} - 130 \, b^{2} c^{2} d^{2} e^{3} + 69 \, b^{3} c d e^{4} - 6 \, b^{4} e^{5}\right)} f - {\left(122 \, c^{4} d^{5} - 325 \, b c^{3} d^{4} e + 262 \, b^{2} c^{2} d^{3} e^{2} - 53 \, b^{3} c d^{2} e^{3} - 6 \, b^{4} d e^{4}\right)} g - {\left(7 \, {\left(46 \, c^{4} d^{3} e^{2} - 79 \, b c^{3} d^{2} e^{3} + 22 \, b^{2} c^{2} d e^{4} + 3 \, b^{3} c e^{5}\right)} f + {\left(46 \, c^{4} d^{4} e - 263 \, b c^{3} d^{3} e^{2} + 338 \, b^{2} c^{2} d^{2} e^{3} - 85 \, b^{3} c d e^{4} - 12 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(32 \, c^{7} d^{10} e^{2} - 144 \, b c^{6} d^{9} e^{3} + 272 \, b^{2} c^{5} d^{8} e^{4} - 280 \, b^{3} c^{4} d^{7} e^{5} + 170 \, b^{4} c^{3} d^{6} e^{6} - 61 \, b^{5} c^{2} d^{5} e^{7} + 12 \, b^{6} c d^{4} e^{8} - b^{7} d^{3} e^{9} + {\left(32 \, c^{7} d^{5} e^{7} - 80 \, b c^{6} d^{4} e^{8} + 80 \, b^{2} c^{5} d^{3} e^{9} - 40 \, b^{3} c^{4} d^{2} e^{10} + 10 \, b^{4} c^{3} d e^{11} - b^{5} c^{2} e^{12}\right)} x^{5} + {\left(32 \, c^{7} d^{6} e^{6} - 16 \, b c^{6} d^{5} e^{7} - 80 \, b^{2} c^{5} d^{4} e^{8} + 120 \, b^{3} c^{4} d^{3} e^{9} - 70 \, b^{4} c^{3} d^{2} e^{10} + 19 \, b^{5} c^{2} d e^{11} - 2 \, b^{6} c e^{12}\right)} x^{4} - {\left(64 \, c^{7} d^{7} e^{5} - 288 \, b c^{6} d^{6} e^{6} + 448 \, b^{2} c^{5} d^{5} e^{7} - 320 \, b^{3} c^{4} d^{4} e^{8} + 100 \, b^{4} c^{3} d^{3} e^{9} - 2 \, b^{5} c^{2} d^{2} e^{10} - 6 \, b^{6} c d e^{11} + b^{7} e^{12}\right)} x^{3} - {\left(64 \, c^{7} d^{8} e^{4} - 160 \, b c^{6} d^{7} e^{5} + 64 \, b^{2} c^{5} d^{6} e^{6} + 160 \, b^{3} c^{4} d^{5} e^{7} - 220 \, b^{4} c^{3} d^{4} e^{8} + 118 \, b^{5} c^{2} d^{3} e^{9} - 30 \, b^{6} c d^{2} e^{10} + 3 \, b^{7} d e^{11}\right)} x^{2} + {\left(32 \, c^{7} d^{9} e^{3} - 208 \, b c^{6} d^{8} e^{4} + 496 \, b^{2} c^{5} d^{7} e^{5} - 600 \, b^{3} c^{4} d^{6} e^{6} + 410 \, b^{4} c^{3} d^{5} e^{7} - 161 \, b^{5} c^{2} d^{4} e^{8} + 34 \, b^{6} c d^{3} e^{9} - 3 \, b^{7} d^{2} e^{10}\right)} x\right)}}, -\frac{15 \, {\left({\left(7 \, c^{4} e^{6} f + {\left(c^{4} d e^{5} - 4 \, b c^{3} e^{6}\right)} g\right)} x^{5} + {\left(7 \, {\left(c^{4} d e^{5} + 2 \, b c^{3} e^{6}\right)} f + {\left(c^{4} d^{2} e^{4} - 2 \, b c^{3} d e^{5} - 8 \, b^{2} c^{2} e^{6}\right)} g\right)} x^{4} - {\left(7 \, {\left(2 \, c^{4} d^{2} e^{4} - 4 \, b c^{3} d e^{5} - b^{2} c^{2} e^{6}\right)} f + {\left(2 \, c^{4} d^{3} e^{3} - 12 \, b c^{3} d^{2} e^{4} + 15 \, b^{2} c^{2} d e^{5} + 4 \, b^{3} c e^{6}\right)} g\right)} x^{3} - {\left(7 \, {\left(2 \, c^{4} d^{3} e^{3} - 3 \, b^{2} c^{2} d e^{5}\right)} f + {\left(2 \, c^{4} d^{4} e^{2} - 8 \, b c^{3} d^{3} e^{3} - 3 \, b^{2} c^{2} d^{2} e^{4} + 12 \, b^{3} c d e^{5}\right)} g\right)} x^{2} + 7 \, {\left(c^{4} d^{5} e - 2 \, b c^{3} d^{4} e^{2} + b^{2} c^{2} d^{3} e^{3}\right)} f + {\left(c^{4} d^{6} - 6 \, b c^{3} d^{5} e + 9 \, b^{2} c^{2} d^{4} e^{2} - 4 \, b^{3} c d^{3} e^{3}\right)} g + {\left(7 \, {\left(c^{4} d^{4} e^{2} - 4 \, b c^{3} d^{3} e^{3} + 3 \, b^{2} c^{2} d^{2} e^{4}\right)} f + {\left(c^{4} d^{5} e - 8 \, b c^{3} d^{4} e^{2} + 19 \, b^{2} c^{2} d^{3} e^{3} - 12 \, b^{3} c d^{2} e^{4}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(15 \, {\left(7 \, {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)} f + {\left(2 \, c^{4} d^{2} e^{3} - 9 \, b c^{3} d e^{4} + 4 \, b^{2} c^{2} e^{5}\right)} g\right)} x^{3} + 5 \, {\left(7 \, {\left(2 \, c^{4} d^{2} e^{3} + 7 \, b c^{3} d e^{4} - 4 \, b^{2} c^{2} e^{5}\right)} f + {\left(2 \, c^{4} d^{3} e^{2} - b c^{3} d^{2} e^{3} - 32 \, b^{2} c^{2} d e^{4} + 16 \, b^{3} c e^{5}\right)} g\right)} x^{2} - {\left(86 \, c^{4} d^{4} e - 11 \, b c^{3} d^{3} e^{2} - 130 \, b^{2} c^{2} d^{2} e^{3} + 69 \, b^{3} c d e^{4} - 6 \, b^{4} e^{5}\right)} f - {\left(122 \, c^{4} d^{5} - 325 \, b c^{3} d^{4} e + 262 \, b^{2} c^{2} d^{3} e^{2} - 53 \, b^{3} c d^{2} e^{3} - 6 \, b^{4} d e^{4}\right)} g - {\left(7 \, {\left(46 \, c^{4} d^{3} e^{2} - 79 \, b c^{3} d^{2} e^{3} + 22 \, b^{2} c^{2} d e^{4} + 3 \, b^{3} c e^{5}\right)} f + {\left(46 \, c^{4} d^{4} e - 263 \, b c^{3} d^{3} e^{2} + 338 \, b^{2} c^{2} d^{2} e^{3} - 85 \, b^{3} c d e^{4} - 12 \, b^{4} e^{5}\right)} g\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(32 \, c^{7} d^{10} e^{2} - 144 \, b c^{6} d^{9} e^{3} + 272 \, b^{2} c^{5} d^{8} e^{4} - 280 \, b^{3} c^{4} d^{7} e^{5} + 170 \, b^{4} c^{3} d^{6} e^{6} - 61 \, b^{5} c^{2} d^{5} e^{7} + 12 \, b^{6} c d^{4} e^{8} - b^{7} d^{3} e^{9} + {\left(32 \, c^{7} d^{5} e^{7} - 80 \, b c^{6} d^{4} e^{8} + 80 \, b^{2} c^{5} d^{3} e^{9} - 40 \, b^{3} c^{4} d^{2} e^{10} + 10 \, b^{4} c^{3} d e^{11} - b^{5} c^{2} e^{12}\right)} x^{5} + {\left(32 \, c^{7} d^{6} e^{6} - 16 \, b c^{6} d^{5} e^{7} - 80 \, b^{2} c^{5} d^{4} e^{8} + 120 \, b^{3} c^{4} d^{3} e^{9} - 70 \, b^{4} c^{3} d^{2} e^{10} + 19 \, b^{5} c^{2} d e^{11} - 2 \, b^{6} c e^{12}\right)} x^{4} - {\left(64 \, c^{7} d^{7} e^{5} - 288 \, b c^{6} d^{6} e^{6} + 448 \, b^{2} c^{5} d^{5} e^{7} - 320 \, b^{3} c^{4} d^{4} e^{8} + 100 \, b^{4} c^{3} d^{3} e^{9} - 2 \, b^{5} c^{2} d^{2} e^{10} - 6 \, b^{6} c d e^{11} + b^{7} e^{12}\right)} x^{3} - {\left(64 \, c^{7} d^{8} e^{4} - 160 \, b c^{6} d^{7} e^{5} + 64 \, b^{2} c^{5} d^{6} e^{6} + 160 \, b^{3} c^{4} d^{5} e^{7} - 220 \, b^{4} c^{3} d^{4} e^{8} + 118 \, b^{5} c^{2} d^{3} e^{9} - 30 \, b^{6} c d^{2} e^{10} + 3 \, b^{7} d e^{11}\right)} x^{2} + {\left(32 \, c^{7} d^{9} e^{3} - 208 \, b c^{6} d^{8} e^{4} + 496 \, b^{2} c^{5} d^{7} e^{5} - 600 \, b^{3} c^{4} d^{6} e^{6} + 410 \, b^{4} c^{3} d^{5} e^{7} - 161 \, b^{5} c^{2} d^{4} e^{8} + 34 \, b^{6} c d^{3} e^{9} - 3 \, b^{7} d^{2} e^{10}\right)} x\right)}}\right]"," ",0,"[-1/24*(15*((7*c^4*e^6*f + (c^4*d*e^5 - 4*b*c^3*e^6)*g)*x^5 + (7*(c^4*d*e^5 + 2*b*c^3*e^6)*f + (c^4*d^2*e^4 - 2*b*c^3*d*e^5 - 8*b^2*c^2*e^6)*g)*x^4 - (7*(2*c^4*d^2*e^4 - 4*b*c^3*d*e^5 - b^2*c^2*e^6)*f + (2*c^4*d^3*e^3 - 12*b*c^3*d^2*e^4 + 15*b^2*c^2*d*e^5 + 4*b^3*c*e^6)*g)*x^3 - (7*(2*c^4*d^3*e^3 - 3*b^2*c^2*d*e^5)*f + (2*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3 - 3*b^2*c^2*d^2*e^4 + 12*b^3*c*d*e^5)*g)*x^2 + 7*(c^4*d^5*e - 2*b*c^3*d^4*e^2 + b^2*c^2*d^3*e^3)*f + (c^4*d^6 - 6*b*c^3*d^5*e + 9*b^2*c^2*d^4*e^2 - 4*b^3*c*d^3*e^3)*g + (7*(c^4*d^4*e^2 - 4*b*c^3*d^3*e^3 + 3*b^2*c^2*d^2*e^4)*f + (c^4*d^5*e - 8*b*c^3*d^4*e^2 + 19*b^2*c^2*d^3*e^3 - 12*b^3*c*d^2*e^4)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(15*(7*(2*c^4*d*e^4 - b*c^3*e^5)*f + (2*c^4*d^2*e^3 - 9*b*c^3*d*e^4 + 4*b^2*c^2*e^5)*g)*x^3 + 5*(7*(2*c^4*d^2*e^3 + 7*b*c^3*d*e^4 - 4*b^2*c^2*e^5)*f + (2*c^4*d^3*e^2 - b*c^3*d^2*e^3 - 32*b^2*c^2*d*e^4 + 16*b^3*c*e^5)*g)*x^2 - (86*c^4*d^4*e - 11*b*c^3*d^3*e^2 - 130*b^2*c^2*d^2*e^3 + 69*b^3*c*d*e^4 - 6*b^4*e^5)*f - (122*c^4*d^5 - 325*b*c^3*d^4*e + 262*b^2*c^2*d^3*e^2 - 53*b^3*c*d^2*e^3 - 6*b^4*d*e^4)*g - (7*(46*c^4*d^3*e^2 - 79*b*c^3*d^2*e^3 + 22*b^2*c^2*d*e^4 + 3*b^3*c*e^5)*f + (46*c^4*d^4*e - 263*b*c^3*d^3*e^2 + 338*b^2*c^2*d^2*e^3 - 85*b^3*c*d*e^4 - 12*b^4*e^5)*g)*x)*sqrt(e*x + d))/(32*c^7*d^10*e^2 - 144*b*c^6*d^9*e^3 + 272*b^2*c^5*d^8*e^4 - 280*b^3*c^4*d^7*e^5 + 170*b^4*c^3*d^6*e^6 - 61*b^5*c^2*d^5*e^7 + 12*b^6*c*d^4*e^8 - b^7*d^3*e^9 + (32*c^7*d^5*e^7 - 80*b*c^6*d^4*e^8 + 80*b^2*c^5*d^3*e^9 - 40*b^3*c^4*d^2*e^10 + 10*b^4*c^3*d*e^11 - b^5*c^2*e^12)*x^5 + (32*c^7*d^6*e^6 - 16*b*c^6*d^5*e^7 - 80*b^2*c^5*d^4*e^8 + 120*b^3*c^4*d^3*e^9 - 70*b^4*c^3*d^2*e^10 + 19*b^5*c^2*d*e^11 - 2*b^6*c*e^12)*x^4 - (64*c^7*d^7*e^5 - 288*b*c^6*d^6*e^6 + 448*b^2*c^5*d^5*e^7 - 320*b^3*c^4*d^4*e^8 + 100*b^4*c^3*d^3*e^9 - 2*b^5*c^2*d^2*e^10 - 6*b^6*c*d*e^11 + b^7*e^12)*x^3 - (64*c^7*d^8*e^4 - 160*b*c^6*d^7*e^5 + 64*b^2*c^5*d^6*e^6 + 160*b^3*c^4*d^5*e^7 - 220*b^4*c^3*d^4*e^8 + 118*b^5*c^2*d^3*e^9 - 30*b^6*c*d^2*e^10 + 3*b^7*d*e^11)*x^2 + (32*c^7*d^9*e^3 - 208*b*c^6*d^8*e^4 + 496*b^2*c^5*d^7*e^5 - 600*b^3*c^4*d^6*e^6 + 410*b^4*c^3*d^5*e^7 - 161*b^5*c^2*d^4*e^8 + 34*b^6*c*d^3*e^9 - 3*b^7*d^2*e^10)*x), -1/12*(15*((7*c^4*e^6*f + (c^4*d*e^5 - 4*b*c^3*e^6)*g)*x^5 + (7*(c^4*d*e^5 + 2*b*c^3*e^6)*f + (c^4*d^2*e^4 - 2*b*c^3*d*e^5 - 8*b^2*c^2*e^6)*g)*x^4 - (7*(2*c^4*d^2*e^4 - 4*b*c^3*d*e^5 - b^2*c^2*e^6)*f + (2*c^4*d^3*e^3 - 12*b*c^3*d^2*e^4 + 15*b^2*c^2*d*e^5 + 4*b^3*c*e^6)*g)*x^3 - (7*(2*c^4*d^3*e^3 - 3*b^2*c^2*d*e^5)*f + (2*c^4*d^4*e^2 - 8*b*c^3*d^3*e^3 - 3*b^2*c^2*d^2*e^4 + 12*b^3*c*d*e^5)*g)*x^2 + 7*(c^4*d^5*e - 2*b*c^3*d^4*e^2 + b^2*c^2*d^3*e^3)*f + (c^4*d^6 - 6*b*c^3*d^5*e + 9*b^2*c^2*d^4*e^2 - 4*b^3*c*d^3*e^3)*g + (7*(c^4*d^4*e^2 - 4*b*c^3*d^3*e^3 + 3*b^2*c^2*d^2*e^4)*f + (c^4*d^5*e - 8*b*c^3*d^4*e^2 + 19*b^2*c^2*d^3*e^3 - 12*b^3*c*d^2*e^4)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(15*(7*(2*c^4*d*e^4 - b*c^3*e^5)*f + (2*c^4*d^2*e^3 - 9*b*c^3*d*e^4 + 4*b^2*c^2*e^5)*g)*x^3 + 5*(7*(2*c^4*d^2*e^3 + 7*b*c^3*d*e^4 - 4*b^2*c^2*e^5)*f + (2*c^4*d^3*e^2 - b*c^3*d^2*e^3 - 32*b^2*c^2*d*e^4 + 16*b^3*c*e^5)*g)*x^2 - (86*c^4*d^4*e - 11*b*c^3*d^3*e^2 - 130*b^2*c^2*d^2*e^3 + 69*b^3*c*d*e^4 - 6*b^4*e^5)*f - (122*c^4*d^5 - 325*b*c^3*d^4*e + 262*b^2*c^2*d^3*e^2 - 53*b^3*c*d^2*e^3 - 6*b^4*d*e^4)*g - (7*(46*c^4*d^3*e^2 - 79*b*c^3*d^2*e^3 + 22*b^2*c^2*d*e^4 + 3*b^3*c*e^5)*f + (46*c^4*d^4*e - 263*b*c^3*d^3*e^2 + 338*b^2*c^2*d^2*e^3 - 85*b^3*c*d*e^4 - 12*b^4*e^5)*g)*x)*sqrt(e*x + d))/(32*c^7*d^10*e^2 - 144*b*c^6*d^9*e^3 + 272*b^2*c^5*d^8*e^4 - 280*b^3*c^4*d^7*e^5 + 170*b^4*c^3*d^6*e^6 - 61*b^5*c^2*d^5*e^7 + 12*b^6*c*d^4*e^8 - b^7*d^3*e^9 + (32*c^7*d^5*e^7 - 80*b*c^6*d^4*e^8 + 80*b^2*c^5*d^3*e^9 - 40*b^3*c^4*d^2*e^10 + 10*b^4*c^3*d*e^11 - b^5*c^2*e^12)*x^5 + (32*c^7*d^6*e^6 - 16*b*c^6*d^5*e^7 - 80*b^2*c^5*d^4*e^8 + 120*b^3*c^4*d^3*e^9 - 70*b^4*c^3*d^2*e^10 + 19*b^5*c^2*d*e^11 - 2*b^6*c*e^12)*x^4 - (64*c^7*d^7*e^5 - 288*b*c^6*d^6*e^6 + 448*b^2*c^5*d^5*e^7 - 320*b^3*c^4*d^4*e^8 + 100*b^4*c^3*d^3*e^9 - 2*b^5*c^2*d^2*e^10 - 6*b^6*c*d*e^11 + b^7*e^12)*x^3 - (64*c^7*d^8*e^4 - 160*b*c^6*d^7*e^5 + 64*b^2*c^5*d^6*e^6 + 160*b^3*c^4*d^5*e^7 - 220*b^4*c^3*d^4*e^8 + 118*b^5*c^2*d^3*e^9 - 30*b^6*c*d^2*e^10 + 3*b^7*d*e^11)*x^2 + (32*c^7*d^9*e^3 - 208*b*c^6*d^8*e^4 + 496*b^2*c^5*d^7*e^5 - 600*b^3*c^4*d^6*e^6 + 410*b^4*c^3*d^5*e^7 - 161*b^5*c^2*d^4*e^8 + 34*b^6*c*d^3*e^9 - 3*b^7*d^2*e^10)*x)]","B",0
2284,1,4084,0,0.710911," ","integrate((g*x+f)/(e*x+d)^(3/2)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(3 \, c^{5} e^{7} f + {\left(c^{5} d e^{6} - 2 \, b c^{4} e^{7}\right)} g\right)} x^{6} + 2 \, {\left(3 \, {\left(c^{5} d e^{6} + b c^{4} e^{7}\right)} f + {\left(c^{5} d^{2} e^{5} - b c^{4} d e^{6} - 2 \, b^{2} c^{3} e^{7}\right)} g\right)} x^{5} - {\left(3 \, {\left(c^{5} d^{2} e^{5} - 6 \, b c^{4} d e^{6} - b^{2} c^{3} e^{7}\right)} f + {\left(c^{5} d^{3} e^{4} - 8 \, b c^{4} d^{2} e^{5} + 11 \, b^{2} c^{3} d e^{6} + 2 \, b^{3} c^{2} e^{7}\right)} g\right)} x^{4} - 4 \, {\left(3 \, {\left(c^{5} d^{3} e^{4} - b c^{4} d^{2} e^{5} - b^{2} c^{3} d e^{6}\right)} f + {\left(c^{5} d^{4} e^{3} - 3 \, b c^{4} d^{3} e^{4} + b^{2} c^{3} d^{2} e^{5} + 2 \, b^{3} c^{2} d e^{6}\right)} g\right)} x^{3} - {\left(3 \, {\left(c^{5} d^{4} e^{3} + 4 \, b c^{4} d^{3} e^{4} - 6 \, b^{2} c^{3} d^{2} e^{5}\right)} f + {\left(c^{5} d^{5} e^{2} + 2 \, b c^{4} d^{4} e^{3} - 14 \, b^{2} c^{3} d^{3} e^{4} + 12 \, b^{3} c^{2} d^{2} e^{5}\right)} g\right)} x^{2} + 3 \, {\left(c^{5} d^{6} e - 2 \, b c^{4} d^{5} e^{2} + b^{2} c^{3} d^{4} e^{3}\right)} f + {\left(c^{5} d^{7} - 4 \, b c^{4} d^{6} e + 5 \, b^{2} c^{3} d^{5} e^{2} - 2 \, b^{3} c^{2} d^{4} e^{3}\right)} g + 2 \, {\left(3 \, {\left(c^{5} d^{5} e^{2} - 3 \, b c^{4} d^{4} e^{3} + 2 \, b^{2} c^{3} d^{3} e^{4}\right)} f + {\left(c^{5} d^{6} e - 5 \, b c^{4} d^{5} e^{2} + 8 \, b^{2} c^{3} d^{4} e^{3} - 4 \, b^{3} c^{2} d^{3} e^{4}\right)} g\right)} x\right)} \sqrt{2 \, c d - b e} \log\left(-\frac{c e^{2} x^{2} - 3 \, c d^{2} + 2 \, b d e - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{2 \, c d - b e} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(105 \, {\left(3 \, {\left(2 \, c^{5} d e^{5} - b c^{4} e^{6}\right)} f + {\left(2 \, c^{5} d^{2} e^{4} - 5 \, b c^{4} d e^{5} + 2 \, b^{2} c^{3} e^{6}\right)} g\right)} x^{4} + 140 \, {\left(3 \, {\left(2 \, c^{5} d^{2} e^{4} + b c^{4} d e^{5} - b^{2} c^{3} e^{6}\right)} f + {\left(2 \, c^{5} d^{3} e^{3} - 3 \, b c^{4} d^{2} e^{4} - 3 \, b^{2} c^{3} d e^{5} + 2 \, b^{3} c^{2} e^{6}\right)} g\right)} x^{3} - 21 \, {\left(3 \, {\left(12 \, c^{5} d^{3} e^{3} - 38 \, b c^{4} d^{2} e^{4} + 14 \, b^{2} c^{3} d e^{5} + b^{3} c^{2} e^{6}\right)} f + {\left(12 \, c^{5} d^{4} e^{2} - 62 \, b c^{4} d^{3} e^{3} + 90 \, b^{2} c^{3} d^{2} e^{4} - 27 \, b^{3} c^{2} d e^{5} - 2 \, b^{4} c e^{6}\right)} g\right)} x^{2} - {\left(2 \, c^{5} d^{5} e + 607 \, b c^{4} d^{4} e^{2} - 1030 \, b^{2} c^{3} d^{3} e^{3} + 527 \, b^{3} c^{2} d^{2} e^{4} - 98 \, b^{4} c d e^{5} + 8 \, b^{5} e^{6}\right)} f - {\left(342 \, c^{5} d^{6} - 823 \, b c^{4} d^{5} e + 532 \, b^{2} c^{3} d^{4} e^{2} + 9 \, b^{3} c^{2} d^{3} e^{3} - 64 \, b^{4} c d^{2} e^{4} + 4 \, b^{5} d e^{5}\right)} g - 6 \, {\left(3 \, {\left(68 \, c^{5} d^{4} e^{2} - 94 \, b c^{4} d^{3} e^{3} + 4 \, b^{2} c^{3} d^{2} e^{4} + 15 \, b^{3} c^{2} d e^{5} - b^{4} c e^{6}\right)} f + {\left(68 \, c^{5} d^{5} e - 230 \, b c^{4} d^{4} e^{2} + 192 \, b^{2} c^{3} d^{3} e^{3} + 7 \, b^{3} c^{2} d^{2} e^{4} - 31 \, b^{4} c d e^{5} + 2 \, b^{5} e^{6}\right)} g\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(64 \, c^{8} d^{12} e^{2} - 320 \, b c^{7} d^{11} e^{3} + 688 \, b^{2} c^{6} d^{10} e^{4} - 832 \, b^{3} c^{5} d^{9} e^{5} + 620 \, b^{4} c^{4} d^{8} e^{6} - 292 \, b^{5} c^{3} d^{7} e^{7} + 85 \, b^{6} c^{2} d^{6} e^{8} - 14 \, b^{7} c d^{5} e^{9} + b^{8} d^{4} e^{10} + {\left(64 \, c^{8} d^{6} e^{8} - 192 \, b c^{7} d^{5} e^{9} + 240 \, b^{2} c^{6} d^{4} e^{10} - 160 \, b^{3} c^{5} d^{3} e^{11} + 60 \, b^{4} c^{4} d^{2} e^{12} - 12 \, b^{5} c^{3} d e^{13} + b^{6} c^{2} e^{14}\right)} x^{6} + 2 \, {\left(64 \, c^{8} d^{7} e^{7} - 128 \, b c^{7} d^{6} e^{8} + 48 \, b^{2} c^{6} d^{5} e^{9} + 80 \, b^{3} c^{5} d^{4} e^{10} - 100 \, b^{4} c^{4} d^{3} e^{11} + 48 \, b^{5} c^{3} d^{2} e^{12} - 11 \, b^{6} c^{2} d e^{13} + b^{7} c e^{14}\right)} x^{5} - {\left(64 \, c^{8} d^{8} e^{6} - 576 \, b c^{7} d^{7} e^{7} + 1328 \, b^{2} c^{6} d^{6} e^{8} - 1408 \, b^{3} c^{5} d^{5} e^{9} + 780 \, b^{4} c^{4} d^{4} e^{10} - 212 \, b^{5} c^{3} d^{3} e^{11} + 13 \, b^{6} c^{2} d^{2} e^{12} + 6 \, b^{7} c d e^{13} - b^{8} e^{14}\right)} x^{4} - 4 \, {\left(64 \, c^{8} d^{9} e^{5} - 256 \, b c^{7} d^{8} e^{6} + 368 \, b^{2} c^{6} d^{7} e^{7} - 208 \, b^{3} c^{5} d^{6} e^{8} - 20 \, b^{4} c^{4} d^{5} e^{9} + 88 \, b^{5} c^{3} d^{4} e^{10} - 47 \, b^{6} c^{2} d^{3} e^{11} + 11 \, b^{7} c d^{2} e^{12} - b^{8} d e^{13}\right)} x^{3} - {\left(64 \, c^{8} d^{10} e^{4} + 64 \, b c^{7} d^{9} e^{5} - 912 \, b^{2} c^{6} d^{8} e^{6} + 1952 \, b^{3} c^{5} d^{7} e^{7} - 2020 \, b^{4} c^{4} d^{6} e^{8} + 1188 \, b^{5} c^{3} d^{5} e^{9} - 407 \, b^{6} c^{2} d^{4} e^{10} + 76 \, b^{7} c d^{3} e^{11} - 6 \, b^{8} d^{2} e^{12}\right)} x^{2} + 2 \, {\left(64 \, c^{8} d^{11} e^{3} - 384 \, b c^{7} d^{10} e^{4} + 944 \, b^{2} c^{6} d^{9} e^{5} - 1264 \, b^{3} c^{5} d^{8} e^{6} + 1020 \, b^{4} c^{4} d^{7} e^{7} - 512 \, b^{5} c^{3} d^{6} e^{8} + 157 \, b^{6} c^{2} d^{5} e^{9} - 27 \, b^{7} c d^{4} e^{10} + 2 \, b^{8} d^{3} e^{11}\right)} x\right)}}, -\frac{105 \, {\left({\left(3 \, c^{5} e^{7} f + {\left(c^{5} d e^{6} - 2 \, b c^{4} e^{7}\right)} g\right)} x^{6} + 2 \, {\left(3 \, {\left(c^{5} d e^{6} + b c^{4} e^{7}\right)} f + {\left(c^{5} d^{2} e^{5} - b c^{4} d e^{6} - 2 \, b^{2} c^{3} e^{7}\right)} g\right)} x^{5} - {\left(3 \, {\left(c^{5} d^{2} e^{5} - 6 \, b c^{4} d e^{6} - b^{2} c^{3} e^{7}\right)} f + {\left(c^{5} d^{3} e^{4} - 8 \, b c^{4} d^{2} e^{5} + 11 \, b^{2} c^{3} d e^{6} + 2 \, b^{3} c^{2} e^{7}\right)} g\right)} x^{4} - 4 \, {\left(3 \, {\left(c^{5} d^{3} e^{4} - b c^{4} d^{2} e^{5} - b^{2} c^{3} d e^{6}\right)} f + {\left(c^{5} d^{4} e^{3} - 3 \, b c^{4} d^{3} e^{4} + b^{2} c^{3} d^{2} e^{5} + 2 \, b^{3} c^{2} d e^{6}\right)} g\right)} x^{3} - {\left(3 \, {\left(c^{5} d^{4} e^{3} + 4 \, b c^{4} d^{3} e^{4} - 6 \, b^{2} c^{3} d^{2} e^{5}\right)} f + {\left(c^{5} d^{5} e^{2} + 2 \, b c^{4} d^{4} e^{3} - 14 \, b^{2} c^{3} d^{3} e^{4} + 12 \, b^{3} c^{2} d^{2} e^{5}\right)} g\right)} x^{2} + 3 \, {\left(c^{5} d^{6} e - 2 \, b c^{4} d^{5} e^{2} + b^{2} c^{3} d^{4} e^{3}\right)} f + {\left(c^{5} d^{7} - 4 \, b c^{4} d^{6} e + 5 \, b^{2} c^{3} d^{5} e^{2} - 2 \, b^{3} c^{2} d^{4} e^{3}\right)} g + 2 \, {\left(3 \, {\left(c^{5} d^{5} e^{2} - 3 \, b c^{4} d^{4} e^{3} + 2 \, b^{2} c^{3} d^{3} e^{4}\right)} f + {\left(c^{5} d^{6} e - 5 \, b c^{4} d^{5} e^{2} + 8 \, b^{2} c^{3} d^{4} e^{3} - 4 \, b^{3} c^{2} d^{3} e^{4}\right)} g\right)} x\right)} \sqrt{-2 \, c d + b e} \arctan\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt{-2 \, c d + b e} \sqrt{e x + d}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}\right) + \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(105 \, {\left(3 \, {\left(2 \, c^{5} d e^{5} - b c^{4} e^{6}\right)} f + {\left(2 \, c^{5} d^{2} e^{4} - 5 \, b c^{4} d e^{5} + 2 \, b^{2} c^{3} e^{6}\right)} g\right)} x^{4} + 140 \, {\left(3 \, {\left(2 \, c^{5} d^{2} e^{4} + b c^{4} d e^{5} - b^{2} c^{3} e^{6}\right)} f + {\left(2 \, c^{5} d^{3} e^{3} - 3 \, b c^{4} d^{2} e^{4} - 3 \, b^{2} c^{3} d e^{5} + 2 \, b^{3} c^{2} e^{6}\right)} g\right)} x^{3} - 21 \, {\left(3 \, {\left(12 \, c^{5} d^{3} e^{3} - 38 \, b c^{4} d^{2} e^{4} + 14 \, b^{2} c^{3} d e^{5} + b^{3} c^{2} e^{6}\right)} f + {\left(12 \, c^{5} d^{4} e^{2} - 62 \, b c^{4} d^{3} e^{3} + 90 \, b^{2} c^{3} d^{2} e^{4} - 27 \, b^{3} c^{2} d e^{5} - 2 \, b^{4} c e^{6}\right)} g\right)} x^{2} - {\left(2 \, c^{5} d^{5} e + 607 \, b c^{4} d^{4} e^{2} - 1030 \, b^{2} c^{3} d^{3} e^{3} + 527 \, b^{3} c^{2} d^{2} e^{4} - 98 \, b^{4} c d e^{5} + 8 \, b^{5} e^{6}\right)} f - {\left(342 \, c^{5} d^{6} - 823 \, b c^{4} d^{5} e + 532 \, b^{2} c^{3} d^{4} e^{2} + 9 \, b^{3} c^{2} d^{3} e^{3} - 64 \, b^{4} c d^{2} e^{4} + 4 \, b^{5} d e^{5}\right)} g - 6 \, {\left(3 \, {\left(68 \, c^{5} d^{4} e^{2} - 94 \, b c^{4} d^{3} e^{3} + 4 \, b^{2} c^{3} d^{2} e^{4} + 15 \, b^{3} c^{2} d e^{5} - b^{4} c e^{6}\right)} f + {\left(68 \, c^{5} d^{5} e - 230 \, b c^{4} d^{4} e^{2} + 192 \, b^{2} c^{3} d^{3} e^{3} + 7 \, b^{3} c^{2} d^{2} e^{4} - 31 \, b^{4} c d e^{5} + 2 \, b^{5} e^{6}\right)} g\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(64 \, c^{8} d^{12} e^{2} - 320 \, b c^{7} d^{11} e^{3} + 688 \, b^{2} c^{6} d^{10} e^{4} - 832 \, b^{3} c^{5} d^{9} e^{5} + 620 \, b^{4} c^{4} d^{8} e^{6} - 292 \, b^{5} c^{3} d^{7} e^{7} + 85 \, b^{6} c^{2} d^{6} e^{8} - 14 \, b^{7} c d^{5} e^{9} + b^{8} d^{4} e^{10} + {\left(64 \, c^{8} d^{6} e^{8} - 192 \, b c^{7} d^{5} e^{9} + 240 \, b^{2} c^{6} d^{4} e^{10} - 160 \, b^{3} c^{5} d^{3} e^{11} + 60 \, b^{4} c^{4} d^{2} e^{12} - 12 \, b^{5} c^{3} d e^{13} + b^{6} c^{2} e^{14}\right)} x^{6} + 2 \, {\left(64 \, c^{8} d^{7} e^{7} - 128 \, b c^{7} d^{6} e^{8} + 48 \, b^{2} c^{6} d^{5} e^{9} + 80 \, b^{3} c^{5} d^{4} e^{10} - 100 \, b^{4} c^{4} d^{3} e^{11} + 48 \, b^{5} c^{3} d^{2} e^{12} - 11 \, b^{6} c^{2} d e^{13} + b^{7} c e^{14}\right)} x^{5} - {\left(64 \, c^{8} d^{8} e^{6} - 576 \, b c^{7} d^{7} e^{7} + 1328 \, b^{2} c^{6} d^{6} e^{8} - 1408 \, b^{3} c^{5} d^{5} e^{9} + 780 \, b^{4} c^{4} d^{4} e^{10} - 212 \, b^{5} c^{3} d^{3} e^{11} + 13 \, b^{6} c^{2} d^{2} e^{12} + 6 \, b^{7} c d e^{13} - b^{8} e^{14}\right)} x^{4} - 4 \, {\left(64 \, c^{8} d^{9} e^{5} - 256 \, b c^{7} d^{8} e^{6} + 368 \, b^{2} c^{6} d^{7} e^{7} - 208 \, b^{3} c^{5} d^{6} e^{8} - 20 \, b^{4} c^{4} d^{5} e^{9} + 88 \, b^{5} c^{3} d^{4} e^{10} - 47 \, b^{6} c^{2} d^{3} e^{11} + 11 \, b^{7} c d^{2} e^{12} - b^{8} d e^{13}\right)} x^{3} - {\left(64 \, c^{8} d^{10} e^{4} + 64 \, b c^{7} d^{9} e^{5} - 912 \, b^{2} c^{6} d^{8} e^{6} + 1952 \, b^{3} c^{5} d^{7} e^{7} - 2020 \, b^{4} c^{4} d^{6} e^{8} + 1188 \, b^{5} c^{3} d^{5} e^{9} - 407 \, b^{6} c^{2} d^{4} e^{10} + 76 \, b^{7} c d^{3} e^{11} - 6 \, b^{8} d^{2} e^{12}\right)} x^{2} + 2 \, {\left(64 \, c^{8} d^{11} e^{3} - 384 \, b c^{7} d^{10} e^{4} + 944 \, b^{2} c^{6} d^{9} e^{5} - 1264 \, b^{3} c^{5} d^{8} e^{6} + 1020 \, b^{4} c^{4} d^{7} e^{7} - 512 \, b^{5} c^{3} d^{6} e^{8} + 157 \, b^{6} c^{2} d^{5} e^{9} - 27 \, b^{7} c d^{4} e^{10} + 2 \, b^{8} d^{3} e^{11}\right)} x\right)}}\right]"," ",0,"[1/48*(105*((3*c^5*e^7*f + (c^5*d*e^6 - 2*b*c^4*e^7)*g)*x^6 + 2*(3*(c^5*d*e^6 + b*c^4*e^7)*f + (c^5*d^2*e^5 - b*c^4*d*e^6 - 2*b^2*c^3*e^7)*g)*x^5 - (3*(c^5*d^2*e^5 - 6*b*c^4*d*e^6 - b^2*c^3*e^7)*f + (c^5*d^3*e^4 - 8*b*c^4*d^2*e^5 + 11*b^2*c^3*d*e^6 + 2*b^3*c^2*e^7)*g)*x^4 - 4*(3*(c^5*d^3*e^4 - b*c^4*d^2*e^5 - b^2*c^3*d*e^6)*f + (c^5*d^4*e^3 - 3*b*c^4*d^3*e^4 + b^2*c^3*d^2*e^5 + 2*b^3*c^2*d*e^6)*g)*x^3 - (3*(c^5*d^4*e^3 + 4*b*c^4*d^3*e^4 - 6*b^2*c^3*d^2*e^5)*f + (c^5*d^5*e^2 + 2*b*c^4*d^4*e^3 - 14*b^2*c^3*d^3*e^4 + 12*b^3*c^2*d^2*e^5)*g)*x^2 + 3*(c^5*d^6*e - 2*b*c^4*d^5*e^2 + b^2*c^3*d^4*e^3)*f + (c^5*d^7 - 4*b*c^4*d^6*e + 5*b^2*c^3*d^5*e^2 - 2*b^3*c^2*d^4*e^3)*g + 2*(3*(c^5*d^5*e^2 - 3*b*c^4*d^4*e^3 + 2*b^2*c^3*d^3*e^4)*f + (c^5*d^6*e - 5*b*c^4*d^5*e^2 + 8*b^2*c^3*d^4*e^3 - 4*b^3*c^2*d^3*e^4)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(105*(3*(2*c^5*d*e^5 - b*c^4*e^6)*f + (2*c^5*d^2*e^4 - 5*b*c^4*d*e^5 + 2*b^2*c^3*e^6)*g)*x^4 + 140*(3*(2*c^5*d^2*e^4 + b*c^4*d*e^5 - b^2*c^3*e^6)*f + (2*c^5*d^3*e^3 - 3*b*c^4*d^2*e^4 - 3*b^2*c^3*d*e^5 + 2*b^3*c^2*e^6)*g)*x^3 - 21*(3*(12*c^5*d^3*e^3 - 38*b*c^4*d^2*e^4 + 14*b^2*c^3*d*e^5 + b^3*c^2*e^6)*f + (12*c^5*d^4*e^2 - 62*b*c^4*d^3*e^3 + 90*b^2*c^3*d^2*e^4 - 27*b^3*c^2*d*e^5 - 2*b^4*c*e^6)*g)*x^2 - (2*c^5*d^5*e + 607*b*c^4*d^4*e^2 - 1030*b^2*c^3*d^3*e^3 + 527*b^3*c^2*d^2*e^4 - 98*b^4*c*d*e^5 + 8*b^5*e^6)*f - (342*c^5*d^6 - 823*b*c^4*d^5*e + 532*b^2*c^3*d^4*e^2 + 9*b^3*c^2*d^3*e^3 - 64*b^4*c*d^2*e^4 + 4*b^5*d*e^5)*g - 6*(3*(68*c^5*d^4*e^2 - 94*b*c^4*d^3*e^3 + 4*b^2*c^3*d^2*e^4 + 15*b^3*c^2*d*e^5 - b^4*c*e^6)*f + (68*c^5*d^5*e - 230*b*c^4*d^4*e^2 + 192*b^2*c^3*d^3*e^3 + 7*b^3*c^2*d^2*e^4 - 31*b^4*c*d*e^5 + 2*b^5*e^6)*g)*x)*sqrt(e*x + d))/(64*c^8*d^12*e^2 - 320*b*c^7*d^11*e^3 + 688*b^2*c^6*d^10*e^4 - 832*b^3*c^5*d^9*e^5 + 620*b^4*c^4*d^8*e^6 - 292*b^5*c^3*d^7*e^7 + 85*b^6*c^2*d^6*e^8 - 14*b^7*c*d^5*e^9 + b^8*d^4*e^10 + (64*c^8*d^6*e^8 - 192*b*c^7*d^5*e^9 + 240*b^2*c^6*d^4*e^10 - 160*b^3*c^5*d^3*e^11 + 60*b^4*c^4*d^2*e^12 - 12*b^5*c^3*d*e^13 + b^6*c^2*e^14)*x^6 + 2*(64*c^8*d^7*e^7 - 128*b*c^7*d^6*e^8 + 48*b^2*c^6*d^5*e^9 + 80*b^3*c^5*d^4*e^10 - 100*b^4*c^4*d^3*e^11 + 48*b^5*c^3*d^2*e^12 - 11*b^6*c^2*d*e^13 + b^7*c*e^14)*x^5 - (64*c^8*d^8*e^6 - 576*b*c^7*d^7*e^7 + 1328*b^2*c^6*d^6*e^8 - 1408*b^3*c^5*d^5*e^9 + 780*b^4*c^4*d^4*e^10 - 212*b^5*c^3*d^3*e^11 + 13*b^6*c^2*d^2*e^12 + 6*b^7*c*d*e^13 - b^8*e^14)*x^4 - 4*(64*c^8*d^9*e^5 - 256*b*c^7*d^8*e^6 + 368*b^2*c^6*d^7*e^7 - 208*b^3*c^5*d^6*e^8 - 20*b^4*c^4*d^5*e^9 + 88*b^5*c^3*d^4*e^10 - 47*b^6*c^2*d^3*e^11 + 11*b^7*c*d^2*e^12 - b^8*d*e^13)*x^3 - (64*c^8*d^10*e^4 + 64*b*c^7*d^9*e^5 - 912*b^2*c^6*d^8*e^6 + 1952*b^3*c^5*d^7*e^7 - 2020*b^4*c^4*d^6*e^8 + 1188*b^5*c^3*d^5*e^9 - 407*b^6*c^2*d^4*e^10 + 76*b^7*c*d^3*e^11 - 6*b^8*d^2*e^12)*x^2 + 2*(64*c^8*d^11*e^3 - 384*b*c^7*d^10*e^4 + 944*b^2*c^6*d^9*e^5 - 1264*b^3*c^5*d^8*e^6 + 1020*b^4*c^4*d^7*e^7 - 512*b^5*c^3*d^6*e^8 + 157*b^6*c^2*d^5*e^9 - 27*b^7*c*d^4*e^10 + 2*b^8*d^3*e^11)*x), -1/24*(105*((3*c^5*e^7*f + (c^5*d*e^6 - 2*b*c^4*e^7)*g)*x^6 + 2*(3*(c^5*d*e^6 + b*c^4*e^7)*f + (c^5*d^2*e^5 - b*c^4*d*e^6 - 2*b^2*c^3*e^7)*g)*x^5 - (3*(c^5*d^2*e^5 - 6*b*c^4*d*e^6 - b^2*c^3*e^7)*f + (c^5*d^3*e^4 - 8*b*c^4*d^2*e^5 + 11*b^2*c^3*d*e^6 + 2*b^3*c^2*e^7)*g)*x^4 - 4*(3*(c^5*d^3*e^4 - b*c^4*d^2*e^5 - b^2*c^3*d*e^6)*f + (c^5*d^4*e^3 - 3*b*c^4*d^3*e^4 + b^2*c^3*d^2*e^5 + 2*b^3*c^2*d*e^6)*g)*x^3 - (3*(c^5*d^4*e^3 + 4*b*c^4*d^3*e^4 - 6*b^2*c^3*d^2*e^5)*f + (c^5*d^5*e^2 + 2*b*c^4*d^4*e^3 - 14*b^2*c^3*d^3*e^4 + 12*b^3*c^2*d^2*e^5)*g)*x^2 + 3*(c^5*d^6*e - 2*b*c^4*d^5*e^2 + b^2*c^3*d^4*e^3)*f + (c^5*d^7 - 4*b*c^4*d^6*e + 5*b^2*c^3*d^5*e^2 - 2*b^3*c^2*d^4*e^3)*g + 2*(3*(c^5*d^5*e^2 - 3*b*c^4*d^4*e^3 + 2*b^2*c^3*d^3*e^4)*f + (c^5*d^6*e - 5*b*c^4*d^5*e^2 + 8*b^2*c^3*d^4*e^3 - 4*b^3*c^2*d^3*e^4)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) + sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(105*(3*(2*c^5*d*e^5 - b*c^4*e^6)*f + (2*c^5*d^2*e^4 - 5*b*c^4*d*e^5 + 2*b^2*c^3*e^6)*g)*x^4 + 140*(3*(2*c^5*d^2*e^4 + b*c^4*d*e^5 - b^2*c^3*e^6)*f + (2*c^5*d^3*e^3 - 3*b*c^4*d^2*e^4 - 3*b^2*c^3*d*e^5 + 2*b^3*c^2*e^6)*g)*x^3 - 21*(3*(12*c^5*d^3*e^3 - 38*b*c^4*d^2*e^4 + 14*b^2*c^3*d*e^5 + b^3*c^2*e^6)*f + (12*c^5*d^4*e^2 - 62*b*c^4*d^3*e^3 + 90*b^2*c^3*d^2*e^4 - 27*b^3*c^2*d*e^5 - 2*b^4*c*e^6)*g)*x^2 - (2*c^5*d^5*e + 607*b*c^4*d^4*e^2 - 1030*b^2*c^3*d^3*e^3 + 527*b^3*c^2*d^2*e^4 - 98*b^4*c*d*e^5 + 8*b^5*e^6)*f - (342*c^5*d^6 - 823*b*c^4*d^5*e + 532*b^2*c^3*d^4*e^2 + 9*b^3*c^2*d^3*e^3 - 64*b^4*c*d^2*e^4 + 4*b^5*d*e^5)*g - 6*(3*(68*c^5*d^4*e^2 - 94*b*c^4*d^3*e^3 + 4*b^2*c^3*d^2*e^4 + 15*b^3*c^2*d*e^5 - b^4*c*e^6)*f + (68*c^5*d^5*e - 230*b*c^4*d^4*e^2 + 192*b^2*c^3*d^3*e^3 + 7*b^3*c^2*d^2*e^4 - 31*b^4*c*d*e^5 + 2*b^5*e^6)*g)*x)*sqrt(e*x + d))/(64*c^8*d^12*e^2 - 320*b*c^7*d^11*e^3 + 688*b^2*c^6*d^10*e^4 - 832*b^3*c^5*d^9*e^5 + 620*b^4*c^4*d^8*e^6 - 292*b^5*c^3*d^7*e^7 + 85*b^6*c^2*d^6*e^8 - 14*b^7*c*d^5*e^9 + b^8*d^4*e^10 + (64*c^8*d^6*e^8 - 192*b*c^7*d^5*e^9 + 240*b^2*c^6*d^4*e^10 - 160*b^3*c^5*d^3*e^11 + 60*b^4*c^4*d^2*e^12 - 12*b^5*c^3*d*e^13 + b^6*c^2*e^14)*x^6 + 2*(64*c^8*d^7*e^7 - 128*b*c^7*d^6*e^8 + 48*b^2*c^6*d^5*e^9 + 80*b^3*c^5*d^4*e^10 - 100*b^4*c^4*d^3*e^11 + 48*b^5*c^3*d^2*e^12 - 11*b^6*c^2*d*e^13 + b^7*c*e^14)*x^5 - (64*c^8*d^8*e^6 - 576*b*c^7*d^7*e^7 + 1328*b^2*c^6*d^6*e^8 - 1408*b^3*c^5*d^5*e^9 + 780*b^4*c^4*d^4*e^10 - 212*b^5*c^3*d^3*e^11 + 13*b^6*c^2*d^2*e^12 + 6*b^7*c*d*e^13 - b^8*e^14)*x^4 - 4*(64*c^8*d^9*e^5 - 256*b*c^7*d^8*e^6 + 368*b^2*c^6*d^7*e^7 - 208*b^3*c^5*d^6*e^8 - 20*b^4*c^4*d^5*e^9 + 88*b^5*c^3*d^4*e^10 - 47*b^6*c^2*d^3*e^11 + 11*b^7*c*d^2*e^12 - b^8*d*e^13)*x^3 - (64*c^8*d^10*e^4 + 64*b*c^7*d^9*e^5 - 912*b^2*c^6*d^8*e^6 + 1952*b^3*c^5*d^7*e^7 - 2020*b^4*c^4*d^6*e^8 + 1188*b^5*c^3*d^5*e^9 - 407*b^6*c^2*d^4*e^10 + 76*b^7*c*d^3*e^11 - 6*b^8*d^2*e^12)*x^2 + 2*(64*c^8*d^11*e^3 - 384*b*c^7*d^10*e^4 + 944*b^2*c^6*d^9*e^5 - 1264*b^3*c^5*d^8*e^6 + 1020*b^4*c^4*d^7*e^7 - 512*b^5*c^3*d^6*e^8 + 157*b^6*c^2*d^5*e^9 - 27*b^7*c*d^4*e^10 + 2*b^8*d^3*e^11)*x)]","B",0
2285,0,0,0,0.451973," ","integrate((e*x+d)^m*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} e^{4} g x^{5} + {\left(c^{2} e^{4} f + 2 \, b c e^{4} g\right)} x^{4} + {\left(2 \, b c e^{4} f - {\left(2 \, c^{2} d^{2} e^{2} - 2 \, b c d e^{3} - b^{2} e^{4}\right)} g\right)} x^{3} - {\left({\left(2 \, c^{2} d^{2} e^{2} - 2 \, b c d e^{3} - b^{2} e^{4}\right)} f + 2 \, {\left(b c d^{2} e^{2} - b^{2} d e^{3}\right)} g\right)} x^{2} + {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} f - {\left(2 \, {\left(b c d^{2} e^{2} - b^{2} d e^{3}\right)} f - {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c^2*e^4*g*x^5 + (c^2*e^4*f + 2*b*c*e^4*g)*x^4 + (2*b*c*e^4*f - (2*c^2*d^2*e^2 - 2*b*c*d*e^3 - b^2*e^4)*g)*x^3 - ((2*c^2*d^2*e^2 - 2*b*c*d*e^3 - b^2*e^4)*f + 2*(b*c*d^2*e^2 - b^2*d*e^3)*g)*x^2 + (c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*f - (2*(b*c*d^2*e^2 - b^2*d*e^3)*f - (c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(e*x + d)^m, x)","F",0
2286,0,0,0,0.443033," ","integrate((e*x+d)^m*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c e^{2} g x^{3} + {\left(c e^{2} f + b e^{2} g\right)} x^{2} - {\left(c d^{2} - b d e\right)} f + {\left(b e^{2} f - {\left(c d^{2} - b d e\right)} g\right)} x\right)} \sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(-(c*e^2*g*x^3 + (c*e^2*f + b*e^2*g)*x^2 - (c*d^2 - b*d*e)*f + (b*e^2*f - (c*d^2 - b*d*e)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(e*x + d)^m, x)","F",0
2287,0,0,0,0.431396," ","integrate((e*x+d)^m*(g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(g x + f\right)} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(g*x + f)*(e*x + d)^m, x)","F",0
2288,0,0,0,0.428319," ","integrate((e*x+d)^m*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(g x + f\right)} {\left(e x + d\right)}^{m}}{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}, x\right)"," ",0,"integral(-sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(g*x + f)*(e*x + d)^m/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e), x)","F",0
2289,0,0,0,0.438963," ","integrate((e*x+d)^m*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(g x + f\right)} {\left(e x + d\right)}^{m}}{c^{2} e^{4} x^{4} + 2 \, b c e^{4} x^{3} + c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} - {\left(2 \, c^{2} d^{2} e^{2} - 2 \, b c d e^{3} - b^{2} e^{4}\right)} x^{2} - 2 \, {\left(b c d^{2} e^{2} - b^{2} d e^{3}\right)} x}, x\right)"," ",0,"integral(sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(g*x + f)*(e*x + d)^m/(c^2*e^4*x^4 + 2*b*c*e^4*x^3 + c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 - (2*c^2*d^2*e^2 - 2*b*c*d*e^3 - b^2*e^4)*x^2 - 2*(b*c*d^2*e^2 - b^2*d*e^3)*x), x)","F",0
2290,0,0,0,0.488355," ","integrate((e*x+d)^m*(g*x+f)/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} {\left(g x + f\right)} {\left(e x + d\right)}^{m}}{c^{3} e^{6} x^{6} + 3 \, b c^{2} e^{6} x^{5} - c^{3} d^{6} + 3 \, b c^{2} d^{5} e - 3 \, b^{2} c d^{4} e^{2} + b^{3} d^{3} e^{3} - 3 \, {\left(c^{3} d^{2} e^{4} - b c^{2} d e^{5} - b^{2} c e^{6}\right)} x^{4} - {\left(6 \, b c^{2} d^{2} e^{4} - 6 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{3} d^{4} e^{2} - 2 \, b c^{2} d^{3} e^{3} + b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(b c^{2} d^{4} e^{2} - 2 \, b^{2} c d^{3} e^{3} + b^{3} d^{2} e^{4}\right)} x}, x\right)"," ",0,"integral(-sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*(g*x + f)*(e*x + d)^m/(c^3*e^6*x^6 + 3*b*c^2*e^6*x^5 - c^3*d^6 + 3*b*c^2*d^5*e - 3*b^2*c*d^4*e^2 + b^3*d^3*e^3 - 3*(c^3*d^2*e^4 - b*c^2*d*e^5 - b^2*c*e^6)*x^4 - (6*b*c^2*d^2*e^4 - 6*b^2*c*d*e^5 - b^3*e^6)*x^3 + 3*(c^3*d^4*e^2 - 2*b*c^2*d^3*e^3 + b^3*d*e^5)*x^2 + 3*(b*c^2*d^4*e^2 - 2*b^2*c*d^3*e^3 + b^3*d^2*e^4)*x), x)","F",0
2291,1,66,0,0.440353," ","integrate((e*x+d)^m*(c*d*m-b*e*(1+m+p)-c*e*(2+m+2*p)*x)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^p,x, algorithm=""fricas"")","-\frac{{\left(c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e\right)} {\left(-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right)}^{p} {\left(e x + d\right)}^{m}}{e}"," ",0,"-(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)*(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^p*(e*x + d)^m/e","A",0
2292,1,132,0,0.441213," ","integrate((e*x+d)^(-3-2*p)*(g*x+f)*(d*(d*g*p+d*g+e*f)+e*(2*d*g*p+3*d*g+e*f)*x+e^2*g*(2+p)*x^2)^p,x, algorithm=""fricas"")","-\frac{{\left(d^{2} g p + d e f + d^{2} g + {\left(e^{2} g p + 2 \, e^{2} g\right)} x^{2} + {\left(2 \, d e g p + e^{2} f + 3 \, d e g\right)} x\right)} {\left(d^{2} g p + d e f + d^{2} g + {\left(e^{2} g p + 2 \, e^{2} g\right)} x^{2} + {\left(2 \, d e g p + e^{2} f + 3 \, d e g\right)} x\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}}{e^{2} p + 2 \, e^{2}}"," ",0,"-(d^2*g*p + d*e*f + d^2*g + (e^2*g*p + 2*e^2*g)*x^2 + (2*d*e*g*p + e^2*f + 3*d*e*g)*x)*(d^2*g*p + d*e*f + d^2*g + (e^2*g*p + 2*e^2*g)*x^2 + (2*d*e*g*p + e^2*f + 3*d*e*g)*x)^p*(e*x + d)^(-2*p - 3)/(e^2*p + 2*e^2)","B",0
2293,1,448,0,0.438375," ","integrate((e*x+d)^2*(g*x+f)/(-c*g^2*x^2-b*g^2*x-b*f*g+c*f^2)^2,x, algorithm=""fricas"")","\frac{2 \, c^{3} e^{2} f^{3} + {\left(4 \, c^{3} d e - 5 \, b c^{2} e^{2}\right)} f^{2} g + 2 \, {\left(c^{3} d^{2} - 3 \, b c^{2} d e + 2 \, b^{2} c e^{2}\right)} f g^{2} - {\left(b c^{2} d^{2} - 2 \, b^{2} c d e + b^{3} e^{2}\right)} g^{3} + {\left(3 \, c^{3} e^{2} f^{3} + {\left(2 \, c^{3} d e - 7 \, b c^{2} e^{2}\right)} f^{2} g - {\left(c^{3} d^{2} + 2 \, b c^{2} d e - 5 \, b^{2} c e^{2}\right)} f g^{2} + {\left(b c^{2} d^{2} - b^{3} e^{2}\right)} g^{3} - {\left(3 \, c^{3} e^{2} f^{2} g + 2 \, {\left(c^{3} d e - 2 \, b c^{2} e^{2}\right)} f g^{2} - {\left(c^{3} d^{2} - b^{2} c e^{2}\right)} g^{3}\right)} x\right)} \log\left(c g x - c f + b g\right) + {\left(c^{3} e^{2} f^{3} - b c^{2} d^{2} g^{3} - {\left(2 \, c^{3} d e + b c^{2} e^{2}\right)} f^{2} g + {\left(c^{3} d^{2} + 2 \, b c^{2} d e\right)} f g^{2} - {\left(c^{3} e^{2} f^{2} g - 2 \, c^{3} d e f g^{2} + c^{3} d^{2} g^{3}\right)} x\right)} \log\left(g x + f\right)}{4 \, c^{5} f^{3} g^{3} - 8 \, b c^{4} f^{2} g^{4} + 5 \, b^{2} c^{3} f g^{5} - b^{3} c^{2} g^{6} - {\left(4 \, c^{5} f^{2} g^{4} - 4 \, b c^{4} f g^{5} + b^{2} c^{3} g^{6}\right)} x}"," ",0,"(2*c^3*e^2*f^3 + (4*c^3*d*e - 5*b*c^2*e^2)*f^2*g + 2*(c^3*d^2 - 3*b*c^2*d*e + 2*b^2*c*e^2)*f*g^2 - (b*c^2*d^2 - 2*b^2*c*d*e + b^3*e^2)*g^3 + (3*c^3*e^2*f^3 + (2*c^3*d*e - 7*b*c^2*e^2)*f^2*g - (c^3*d^2 + 2*b*c^2*d*e - 5*b^2*c*e^2)*f*g^2 + (b*c^2*d^2 - b^3*e^2)*g^3 - (3*c^3*e^2*f^2*g + 2*(c^3*d*e - 2*b*c^2*e^2)*f*g^2 - (c^3*d^2 - b^2*c*e^2)*g^3)*x)*log(c*g*x - c*f + b*g) + (c^3*e^2*f^3 - b*c^2*d^2*g^3 - (2*c^3*d*e + b*c^2*e^2)*f^2*g + (c^3*d^2 + 2*b*c^2*d*e)*f*g^2 - (c^3*e^2*f^2*g - 2*c^3*d*e*f*g^2 + c^3*d^2*g^3)*x)*log(g*x + f))/(4*c^5*f^3*g^3 - 8*b*c^4*f^2*g^4 + 5*b^2*c^3*f*g^5 - b^3*c^2*g^6 - (4*c^5*f^2*g^4 - 4*b*c^4*f*g^5 + b^2*c^3*g^6)*x)","B",0
2294,1,57,0,0.347603," ","integrate((1+x)^4*(b*x+a)*(x^2-x+1)^4,x, algorithm=""fricas"")","\frac{1}{14} x^{14} b + \frac{1}{13} x^{13} a + \frac{4}{11} x^{11} b + \frac{2}{5} x^{10} a + \frac{3}{4} x^{8} b + \frac{6}{7} x^{7} a + \frac{4}{5} x^{5} b + x^{4} a + \frac{1}{2} x^{2} b + x a"," ",0,"1/14*x^14*b + 1/13*x^13*a + 4/11*x^11*b + 2/5*x^10*a + 3/4*x^8*b + 6/7*x^7*a + 4/5*x^5*b + x^4*a + 1/2*x^2*b + x*a","A",0
2295,1,46,0,0.345216," ","integrate((1+x)^3*(b*x+a)*(x^2-x+1)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} b + \frac{1}{10} x^{10} a + \frac{3}{8} x^{8} b + \frac{3}{7} x^{7} a + \frac{3}{5} x^{5} b + \frac{3}{4} x^{4} a + \frac{1}{2} x^{2} b + x a"," ",0,"1/11*x^11*b + 1/10*x^10*a + 3/8*x^8*b + 3/7*x^7*a + 3/5*x^5*b + 3/4*x^4*a + 1/2*x^2*b + x*a","A",0
2296,1,34,0,0.347497," ","integrate((1+x)^2*(b*x+a)*(x^2-x+1)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} b + \frac{1}{7} x^{7} a + \frac{2}{5} x^{5} b + \frac{1}{2} x^{4} a + \frac{1}{2} x^{2} b + x a"," ",0,"1/8*x^8*b + 1/7*x^7*a + 2/5*x^5*b + 1/2*x^4*a + 1/2*x^2*b + x*a","A",0
2297,1,22,0,0.342505," ","integrate((1+x)*(b*x+a)*(x^2-x+1),x, algorithm=""fricas"")","\frac{1}{5} x^{5} b + \frac{1}{4} x^{4} a + \frac{1}{2} x^{2} b + x a"," ",0,"1/5*x^5*b + 1/4*x^4*a + 1/2*x^2*b + x*a","A",0
2298,1,47,0,0.402639," ","integrate((b*x+a)/(1+x)/(x^2-x+1),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} {\left(a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{6} \, {\left(a - b\right)} \log\left(x^{2} - x + 1\right) + \frac{1}{3} \, {\left(a - b\right)} \log\left(x + 1\right)"," ",0,"1/3*sqrt(3)*(a + b)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/6*(a - b)*log(x^2 - x + 1) + 1/3*(a - b)*log(x + 1)","A",0
2299,1,103,0,0.401988," ","integrate((b*x+a)/(1+x)^2/(x^2-x+1)^2,x, algorithm=""fricas"")","\frac{6 \, b x^{2} + 2 \, \sqrt{3} {\left({\left(2 \, a + b\right)} x^{3} + 2 \, a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 6 \, a x - {\left({\left(2 \, a - b\right)} x^{3} + 2 \, a - b\right)} \log\left(x^{2} - x + 1\right) + 2 \, {\left({\left(2 \, a - b\right)} x^{3} + 2 \, a - b\right)} \log\left(x + 1\right)}{18 \, {\left(x^{3} + 1\right)}}"," ",0,"1/18*(6*b*x^2 + 2*sqrt(3)*((2*a + b)*x^3 + 2*a + b)*arctan(1/3*sqrt(3)*(2*x - 1)) + 6*a*x - ((2*a - b)*x^3 + 2*a - b)*log(x^2 - x + 1) + 2*((2*a - b)*x^3 + 2*a - b)*log(x + 1))/(x^3 + 1)","A",0
2300,1,160,0,0.407682," ","integrate((b*x+a)/(1+x)^3/(x^2-x+1)^3,x, algorithm=""fricas"")","\frac{12 \, b x^{5} + 15 \, a x^{4} + 21 \, b x^{2} + 2 \, \sqrt{3} {\left({\left(5 \, a + 2 \, b\right)} x^{6} + 2 \, {\left(5 \, a + 2 \, b\right)} x^{3} + 5 \, a + 2 \, b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 24 \, a x - {\left({\left(5 \, a - 2 \, b\right)} x^{6} + 2 \, {\left(5 \, a - 2 \, b\right)} x^{3} + 5 \, a - 2 \, b\right)} \log\left(x^{2} - x + 1\right) + 2 \, {\left({\left(5 \, a - 2 \, b\right)} x^{6} + 2 \, {\left(5 \, a - 2 \, b\right)} x^{3} + 5 \, a - 2 \, b\right)} \log\left(x + 1\right)}{54 \, {\left(x^{6} + 2 \, x^{3} + 1\right)}}"," ",0,"1/54*(12*b*x^5 + 15*a*x^4 + 21*b*x^2 + 2*sqrt(3)*((5*a + 2*b)*x^6 + 2*(5*a + 2*b)*x^3 + 5*a + 2*b)*arctan(1/3*sqrt(3)*(2*x - 1)) + 24*a*x - ((5*a - 2*b)*x^6 + 2*(5*a - 2*b)*x^3 + 5*a - 2*b)*log(x^2 - x + 1) + 2*((5*a - 2*b)*x^6 + 2*(5*a - 2*b)*x^3 + 5*a - 2*b)*log(x + 1))/(x^6 + 2*x^3 + 1)","A",0
2301,0,0,0,0.414085," ","integrate((1+x)^(3/2)*(b*x+a)*(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a x^{3} + b x + a\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}, x\right)"," ",0,"integral((b*x^4 + a*x^3 + b*x + a)*sqrt(x^2 - x + 1)*sqrt(x + 1), x)","F",0
2302,0,0,0,0.412454," ","integrate((1+x)^(1/2)*(b*x+a)*(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}, x\right)"," ",0,"integral((b*x + a)*sqrt(x^2 - x + 1)*sqrt(x + 1), x)","F",0
2303,0,0,0,0.411575," ","integrate((b*x+a)/(1+x)^(1/2)/(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{3} + 1}, x\right)"," ",0,"integral((b*x + a)*sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^3 + 1), x)","F",0
2304,0,0,0,0.402710," ","integrate((b*x+a)/(1+x)^(3/2)/(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{6} + 2 \, x^{3} + 1}, x\right)"," ",0,"integral((b*x + a)*sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^6 + 2*x^3 + 1), x)","F",0
2305,0,0,0,0.401147," ","integrate((b*x+a)/(1+x)^(5/2)/(x^2-x+1)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{9} + 3 \, x^{6} + 3 \, x^{3} + 1}, x\right)"," ",0,"integral((b*x + a)*sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^9 + 3*x^6 + 3*x^3 + 1), x)","F",0
2306,1,324,0,0.331221," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{4} c B + \frac{4}{7} x^{7} e^{3} d c B + \frac{1}{7} x^{7} e^{4} b B + \frac{1}{7} x^{7} e^{4} c A + x^{6} e^{2} d^{2} c B + \frac{2}{3} x^{6} e^{3} d b B + \frac{1}{6} x^{6} e^{4} a B + \frac{2}{3} x^{6} e^{3} d c A + \frac{1}{6} x^{6} e^{4} b A + \frac{4}{5} x^{5} e d^{3} c B + \frac{6}{5} x^{5} e^{2} d^{2} b B + \frac{4}{5} x^{5} e^{3} d a B + \frac{6}{5} x^{5} e^{2} d^{2} c A + \frac{4}{5} x^{5} e^{3} d b A + \frac{1}{5} x^{5} e^{4} a A + \frac{1}{4} x^{4} d^{4} c B + x^{4} e d^{3} b B + \frac{3}{2} x^{4} e^{2} d^{2} a B + x^{4} e d^{3} c A + \frac{3}{2} x^{4} e^{2} d^{2} b A + x^{4} e^{3} d a A + \frac{1}{3} x^{3} d^{4} b B + \frac{4}{3} x^{3} e d^{3} a B + \frac{1}{3} x^{3} d^{4} c A + \frac{4}{3} x^{3} e d^{3} b A + 2 x^{3} e^{2} d^{2} a A + \frac{1}{2} x^{2} d^{4} a B + \frac{1}{2} x^{2} d^{4} b A + 2 x^{2} e d^{3} a A + x d^{4} a A"," ",0,"1/8*x^8*e^4*c*B + 4/7*x^7*e^3*d*c*B + 1/7*x^7*e^4*b*B + 1/7*x^7*e^4*c*A + x^6*e^2*d^2*c*B + 2/3*x^6*e^3*d*b*B + 1/6*x^6*e^4*a*B + 2/3*x^6*e^3*d*c*A + 1/6*x^6*e^4*b*A + 4/5*x^5*e*d^3*c*B + 6/5*x^5*e^2*d^2*b*B + 4/5*x^5*e^3*d*a*B + 6/5*x^5*e^2*d^2*c*A + 4/5*x^5*e^3*d*b*A + 1/5*x^5*e^4*a*A + 1/4*x^4*d^4*c*B + x^4*e*d^3*b*B + 3/2*x^4*e^2*d^2*a*B + x^4*e*d^3*c*A + 3/2*x^4*e^2*d^2*b*A + x^4*e^3*d*a*A + 1/3*x^3*d^4*b*B + 4/3*x^3*e*d^3*a*B + 1/3*x^3*d^4*c*A + 4/3*x^3*e*d^3*b*A + 2*x^3*e^2*d^2*a*A + 1/2*x^2*d^4*a*B + 1/2*x^2*d^4*b*A + 2*x^2*e*d^3*a*A + x*d^4*a*A","B",0
2307,1,247,0,0.343104," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{3} c B + \frac{1}{2} x^{6} e^{2} d c B + \frac{1}{6} x^{6} e^{3} b B + \frac{1}{6} x^{6} e^{3} c A + \frac{3}{5} x^{5} e d^{2} c B + \frac{3}{5} x^{5} e^{2} d b B + \frac{1}{5} x^{5} e^{3} a B + \frac{3}{5} x^{5} e^{2} d c A + \frac{1}{5} x^{5} e^{3} b A + \frac{1}{4} x^{4} d^{3} c B + \frac{3}{4} x^{4} e d^{2} b B + \frac{3}{4} x^{4} e^{2} d a B + \frac{3}{4} x^{4} e d^{2} c A + \frac{3}{4} x^{4} e^{2} d b A + \frac{1}{4} x^{4} e^{3} a A + \frac{1}{3} x^{3} d^{3} b B + x^{3} e d^{2} a B + \frac{1}{3} x^{3} d^{3} c A + x^{3} e d^{2} b A + x^{3} e^{2} d a A + \frac{1}{2} x^{2} d^{3} a B + \frac{1}{2} x^{2} d^{3} b A + \frac{3}{2} x^{2} e d^{2} a A + x d^{3} a A"," ",0,"1/7*x^7*e^3*c*B + 1/2*x^6*e^2*d*c*B + 1/6*x^6*e^3*b*B + 1/6*x^6*e^3*c*A + 3/5*x^5*e*d^2*c*B + 3/5*x^5*e^2*d*b*B + 1/5*x^5*e^3*a*B + 3/5*x^5*e^2*d*c*A + 1/5*x^5*e^3*b*A + 1/4*x^4*d^3*c*B + 3/4*x^4*e*d^2*b*B + 3/4*x^4*e^2*d*a*B + 3/4*x^4*e*d^2*c*A + 3/4*x^4*e^2*d*b*A + 1/4*x^4*e^3*a*A + 1/3*x^3*d^3*b*B + x^3*e*d^2*a*B + 1/3*x^3*d^3*c*A + x^3*e*d^2*b*A + x^3*e^2*d*a*A + 1/2*x^2*d^3*a*B + 1/2*x^2*d^3*b*A + 3/2*x^2*e*d^2*a*A + x*d^3*a*A","A",0
2308,1,171,0,0.340750," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{2} c B + \frac{2}{5} x^{5} e d c B + \frac{1}{5} x^{5} e^{2} b B + \frac{1}{5} x^{5} e^{2} c A + \frac{1}{4} x^{4} d^{2} c B + \frac{1}{2} x^{4} e d b B + \frac{1}{4} x^{4} e^{2} a B + \frac{1}{2} x^{4} e d c A + \frac{1}{4} x^{4} e^{2} b A + \frac{1}{3} x^{3} d^{2} b B + \frac{2}{3} x^{3} e d a B + \frac{1}{3} x^{3} d^{2} c A + \frac{2}{3} x^{3} e d b A + \frac{1}{3} x^{3} e^{2} a A + \frac{1}{2} x^{2} d^{2} a B + \frac{1}{2} x^{2} d^{2} b A + x^{2} e d a A + x d^{2} a A"," ",0,"1/6*x^6*e^2*c*B + 2/5*x^5*e*d*c*B + 1/5*x^5*e^2*b*B + 1/5*x^5*e^2*c*A + 1/4*x^4*d^2*c*B + 1/2*x^4*e*d*b*B + 1/4*x^4*e^2*a*B + 1/2*x^4*e*d*c*A + 1/4*x^4*e^2*b*A + 1/3*x^3*d^2*b*B + 2/3*x^3*e*d*a*B + 1/3*x^3*d^2*c*A + 2/3*x^3*e*d*b*A + 1/3*x^3*e^2*a*A + 1/2*x^2*d^2*a*B + 1/2*x^2*d^2*b*A + x^2*e*d*a*A + x*d^2*a*A","A",0
2309,1,94,0,0.346406," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e c B + \frac{1}{4} x^{4} d c B + \frac{1}{4} x^{4} e b B + \frac{1}{4} x^{4} e c A + \frac{1}{3} x^{3} d b B + \frac{1}{3} x^{3} e a B + \frac{1}{3} x^{3} d c A + \frac{1}{3} x^{3} e b A + \frac{1}{2} x^{2} d a B + \frac{1}{2} x^{2} d b A + \frac{1}{2} x^{2} e a A + x d a A"," ",0,"1/5*x^5*e*c*B + 1/4*x^4*d*c*B + 1/4*x^4*e*b*B + 1/4*x^4*e*c*A + 1/3*x^3*d*b*B + 1/3*x^3*e*a*B + 1/3*x^3*d*c*A + 1/3*x^3*e*b*A + 1/2*x^2*d*a*B + 1/2*x^2*d*b*A + 1/2*x^2*e*a*A + x*d*a*A","A",0
2310,1,40,0,0.339220," ","integrate((B*x+A)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} b B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} a B + \frac{1}{2} x^{2} b A + x a A"," ",0,"1/4*x^4*c*B + 1/3*x^3*b*B + 1/3*x^3*c*A + 1/2*x^2*a*B + 1/2*x^2*b*A + x*a*A","A",0
2311,1,123,0,0.386490," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d),x, algorithm=""fricas"")","\frac{2 \, B c e^{3} x^{3} - 3 \, {\left(B c d e^{2} - {\left(B b + A c\right)} e^{3}\right)} x^{2} + 6 \, {\left(B c d^{2} e - {\left(B b + A c\right)} d e^{2} + {\left(B a + A b\right)} e^{3}\right)} x - 6 \, {\left(B c d^{3} - A a e^{3} - {\left(B b + A c\right)} d^{2} e + {\left(B a + A b\right)} d e^{2}\right)} \log\left(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(2*B*c*e^3*x^3 - 3*(B*c*d*e^2 - (B*b + A*c)*e^3)*x^2 + 6*(B*c*d^2*e - (B*b + A*c)*d*e^2 + (B*a + A*b)*e^3)*x - 6*(B*c*d^3 - A*a*e^3 - (B*b + A*c)*d^2*e + (B*a + A*b)*d*e^2)*log(e*x + d))/e^4","A",0
2312,1,192,0,0.375348," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{B c e^{3} x^{3} + 2 \, B c d^{3} - 2 \, A a e^{3} - 2 \, {\left(B b + A c\right)} d^{2} e + 2 \, {\left(B a + A b\right)} d e^{2} - {\left(3 \, B c d e^{2} - 2 \, {\left(B b + A c\right)} e^{3}\right)} x^{2} - 2 \, {\left(2 \, B c d^{2} e - {\left(B b + A c\right)} d e^{2}\right)} x + 2 \, {\left(3 \, B c d^{3} - 2 \, {\left(B b + A c\right)} d^{2} e + {\left(B a + A b\right)} d e^{2} + {\left(3 \, B c d^{2} e - 2 \, {\left(B b + A c\right)} d e^{2} + {\left(B a + A b\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(B*c*e^3*x^3 + 2*B*c*d^3 - 2*A*a*e^3 - 2*(B*b + A*c)*d^2*e + 2*(B*a + A*b)*d*e^2 - (3*B*c*d*e^2 - 2*(B*b + A*c)*e^3)*x^2 - 2*(2*B*c*d^2*e - (B*b + A*c)*d*e^2)*x + 2*(3*B*c*d^3 - 2*(B*b + A*c)*d^2*e + (B*a + A*b)*d*e^2 + (3*B*c*d^2*e - 2*(B*b + A*c)*d*e^2 + (B*a + A*b)*e^3)*x)*log(e*x + d))/(e^5*x + d*e^4)","A",0
2313,1,203,0,0.388753," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, B c e^{3} x^{3} + 4 \, B c d e^{2} x^{2} - 5 \, B c d^{3} - A a e^{3} + 3 \, {\left(B b + A c\right)} d^{2} e - {\left(B a + A b\right)} d e^{2} - 2 \, {\left(2 \, B c d^{2} e - 2 \, {\left(B b + A c\right)} d e^{2} + {\left(B a + A b\right)} e^{3}\right)} x - 2 \, {\left(3 \, B c d^{3} - {\left(B b + A c\right)} d^{2} e + {\left(3 \, B c d e^{2} - {\left(B b + A c\right)} e^{3}\right)} x^{2} + 2 \, {\left(3 \, B c d^{2} e - {\left(B b + A c\right)} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(2*B*c*e^3*x^3 + 4*B*c*d*e^2*x^2 - 5*B*c*d^3 - A*a*e^3 + 3*(B*b + A*c)*d^2*e - (B*a + A*b)*d*e^2 - 2*(2*B*c*d^2*e - 2*(B*b + A*c)*d*e^2 + (B*a + A*b)*e^3)*x - 2*(3*B*c*d^3 - (B*b + A*c)*d^2*e + (3*B*c*d*e^2 - (B*b + A*c)*e^3)*x^2 + 2*(3*B*c*d^2*e - (B*b + A*c)*d*e^2)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
2314,1,185,0,0.390827," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{11 \, B c d^{3} - 2 \, A a e^{3} - 2 \, {\left(B b + A c\right)} d^{2} e - {\left(B a + A b\right)} d e^{2} + 6 \, {\left(3 \, B c d e^{2} - {\left(B b + A c\right)} e^{3}\right)} x^{2} + 3 \, {\left(9 \, B c d^{2} e - 2 \, {\left(B b + A c\right)} d e^{2} - {\left(B a + A b\right)} e^{3}\right)} x + 6 \, {\left(B c e^{3} x^{3} + 3 \, B c d e^{2} x^{2} + 3 \, B c d^{2} e x + B c d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(11*B*c*d^3 - 2*A*a*e^3 - 2*(B*b + A*c)*d^2*e - (B*a + A*b)*d*e^2 + 6*(3*B*c*d*e^2 - (B*b + A*c)*e^3)*x^2 + 3*(9*B*c*d^2*e - 2*(B*b + A*c)*d*e^2 - (B*a + A*b)*e^3)*x + 6*(B*c*e^3*x^3 + 3*B*c*d*e^2*x^2 + 3*B*c*d^2*e*x + B*c*d^3)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
2315,1,157,0,0.370495," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{12 \, B c e^{3} x^{3} + 3 \, B c d^{3} + 3 \, A a e^{3} + {\left(B b + A c\right)} d^{2} e + {\left(B a + A b\right)} d e^{2} + 6 \, {\left(3 \, B c d e^{2} + {\left(B b + A c\right)} e^{3}\right)} x^{2} + 4 \, {\left(3 \, B c d^{2} e + {\left(B b + A c\right)} d e^{2} + {\left(B a + A b\right)} e^{3}\right)} x}{12 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-1/12*(12*B*c*e^3*x^3 + 3*B*c*d^3 + 3*A*a*e^3 + (B*b + A*c)*d^2*e + (B*a + A*b)*d*e^2 + 6*(3*B*c*d*e^2 + (B*b + A*c)*e^3)*x^2 + 4*(3*B*c*d^2*e + (B*b + A*c)*d*e^2 + (B*a + A*b)*e^3)*x)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","A",0
2316,1,173,0,0.372069," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{30 \, B c e^{3} x^{3} + 3 \, B c d^{3} + 12 \, A a e^{3} + 2 \, {\left(B b + A c\right)} d^{2} e + 3 \, {\left(B a + A b\right)} d e^{2} + 10 \, {\left(3 \, B c d e^{2} + 2 \, {\left(B b + A c\right)} e^{3}\right)} x^{2} + 5 \, {\left(3 \, B c d^{2} e + 2 \, {\left(B b + A c\right)} d e^{2} + 3 \, {\left(B a + A b\right)} e^{3}\right)} x}{60 \, {\left(e^{9} x^{5} + 5 \, d e^{8} x^{4} + 10 \, d^{2} e^{7} x^{3} + 10 \, d^{3} e^{6} x^{2} + 5 \, d^{4} e^{5} x + d^{5} e^{4}\right)}}"," ",0,"-1/60*(30*B*c*e^3*x^3 + 3*B*c*d^3 + 12*A*a*e^3 + 2*(B*b + A*c)*d^2*e + 3*(B*a + A*b)*d*e^2 + 10*(3*B*c*d*e^2 + 2*(B*b + A*c)*e^3)*x^2 + 5*(3*B*c*d^2*e + 2*(B*b + A*c)*d*e^2 + 3*(B*a + A*b)*e^3)*x)/(e^9*x^5 + 5*d*e^8*x^4 + 10*d^2*e^7*x^3 + 10*d^3*e^6*x^2 + 5*d^4*e^5*x + d^5*e^4)","A",0
2317,1,178,0,0.363658," ","integrate((B*x+A)*(c*x^2+b*x+a)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{20 \, B c e^{3} x^{3} + B c d^{3} + 10 \, A a e^{3} + {\left(B b + A c\right)} d^{2} e + 2 \, {\left(B a + A b\right)} d e^{2} + 15 \, {\left(B c d e^{2} + {\left(B b + A c\right)} e^{3}\right)} x^{2} + 6 \, {\left(B c d^{2} e + {\left(B b + A c\right)} d e^{2} + 2 \, {\left(B a + A b\right)} e^{3}\right)} x}{60 \, {\left(e^{10} x^{6} + 6 \, d e^{9} x^{5} + 15 \, d^{2} e^{8} x^{4} + 20 \, d^{3} e^{7} x^{3} + 15 \, d^{4} e^{6} x^{2} + 6 \, d^{5} e^{5} x + d^{6} e^{4}\right)}}"," ",0,"-1/60*(20*B*c*e^3*x^3 + B*c*d^3 + 10*A*a*e^3 + (B*b + A*c)*d^2*e + 2*(B*a + A*b)*d*e^2 + 15*(B*c*d*e^2 + (B*b + A*c)*e^3)*x^2 + 6*(B*c*d^2*e + (B*b + A*c)*d*e^2 + 2*(B*a + A*b)*e^3)*x)/(e^10*x^6 + 6*d*e^9*x^5 + 15*d^2*e^8*x^4 + 20*d^3*e^7*x^3 + 15*d^4*e^6*x^2 + 6*d^5*e^5*x + d^6*e^4)","A",0
2318,1,919,0,0.343696," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{5} c^{2} B + \frac{1}{2} x^{10} e^{4} d c^{2} B + \frac{1}{5} x^{10} e^{5} c b B + \frac{1}{10} x^{10} e^{5} c^{2} A + \frac{10}{9} x^{9} e^{3} d^{2} c^{2} B + \frac{10}{9} x^{9} e^{4} d c b B + \frac{1}{9} x^{9} e^{5} b^{2} B + \frac{2}{9} x^{9} e^{5} c a B + \frac{5}{9} x^{9} e^{4} d c^{2} A + \frac{2}{9} x^{9} e^{5} c b A + \frac{5}{4} x^{8} e^{2} d^{3} c^{2} B + \frac{5}{2} x^{8} e^{3} d^{2} c b B + \frac{5}{8} x^{8} e^{4} d b^{2} B + \frac{5}{4} x^{8} e^{4} d c a B + \frac{1}{4} x^{8} e^{5} b a B + \frac{5}{4} x^{8} e^{3} d^{2} c^{2} A + \frac{5}{4} x^{8} e^{4} d c b A + \frac{1}{8} x^{8} e^{5} b^{2} A + \frac{1}{4} x^{8} e^{5} c a A + \frac{5}{7} x^{7} e d^{4} c^{2} B + \frac{20}{7} x^{7} e^{2} d^{3} c b B + \frac{10}{7} x^{7} e^{3} d^{2} b^{2} B + \frac{20}{7} x^{7} e^{3} d^{2} c a B + \frac{10}{7} x^{7} e^{4} d b a B + \frac{1}{7} x^{7} e^{5} a^{2} B + \frac{10}{7} x^{7} e^{2} d^{3} c^{2} A + \frac{20}{7} x^{7} e^{3} d^{2} c b A + \frac{5}{7} x^{7} e^{4} d b^{2} A + \frac{10}{7} x^{7} e^{4} d c a A + \frac{2}{7} x^{7} e^{5} b a A + \frac{1}{6} x^{6} d^{5} c^{2} B + \frac{5}{3} x^{6} e d^{4} c b B + \frac{5}{3} x^{6} e^{2} d^{3} b^{2} B + \frac{10}{3} x^{6} e^{2} d^{3} c a B + \frac{10}{3} x^{6} e^{3} d^{2} b a B + \frac{5}{6} x^{6} e^{4} d a^{2} B + \frac{5}{6} x^{6} e d^{4} c^{2} A + \frac{10}{3} x^{6} e^{2} d^{3} c b A + \frac{5}{3} x^{6} e^{3} d^{2} b^{2} A + \frac{10}{3} x^{6} e^{3} d^{2} c a A + \frac{5}{3} x^{6} e^{4} d b a A + \frac{1}{6} x^{6} e^{5} a^{2} A + \frac{2}{5} x^{5} d^{5} c b B + x^{5} e d^{4} b^{2} B + 2 x^{5} e d^{4} c a B + 4 x^{5} e^{2} d^{3} b a B + 2 x^{5} e^{3} d^{2} a^{2} B + \frac{1}{5} x^{5} d^{5} c^{2} A + 2 x^{5} e d^{4} c b A + 2 x^{5} e^{2} d^{3} b^{2} A + 4 x^{5} e^{2} d^{3} c a A + 4 x^{5} e^{3} d^{2} b a A + x^{5} e^{4} d a^{2} A + \frac{1}{4} x^{4} d^{5} b^{2} B + \frac{1}{2} x^{4} d^{5} c a B + \frac{5}{2} x^{4} e d^{4} b a B + \frac{5}{2} x^{4} e^{2} d^{3} a^{2} B + \frac{1}{2} x^{4} d^{5} c b A + \frac{5}{4} x^{4} e d^{4} b^{2} A + \frac{5}{2} x^{4} e d^{4} c a A + 5 x^{4} e^{2} d^{3} b a A + \frac{5}{2} x^{4} e^{3} d^{2} a^{2} A + \frac{2}{3} x^{3} d^{5} b a B + \frac{5}{3} x^{3} e d^{4} a^{2} B + \frac{1}{3} x^{3} d^{5} b^{2} A + \frac{2}{3} x^{3} d^{5} c a A + \frac{10}{3} x^{3} e d^{4} b a A + \frac{10}{3} x^{3} e^{2} d^{3} a^{2} A + \frac{1}{2} x^{2} d^{5} a^{2} B + x^{2} d^{5} b a A + \frac{5}{2} x^{2} e d^{4} a^{2} A + x d^{5} a^{2} A"," ",0,"1/11*x^11*e^5*c^2*B + 1/2*x^10*e^4*d*c^2*B + 1/5*x^10*e^5*c*b*B + 1/10*x^10*e^5*c^2*A + 10/9*x^9*e^3*d^2*c^2*B + 10/9*x^9*e^4*d*c*b*B + 1/9*x^9*e^5*b^2*B + 2/9*x^9*e^5*c*a*B + 5/9*x^9*e^4*d*c^2*A + 2/9*x^9*e^5*c*b*A + 5/4*x^8*e^2*d^3*c^2*B + 5/2*x^8*e^3*d^2*c*b*B + 5/8*x^8*e^4*d*b^2*B + 5/4*x^8*e^4*d*c*a*B + 1/4*x^8*e^5*b*a*B + 5/4*x^8*e^3*d^2*c^2*A + 5/4*x^8*e^4*d*c*b*A + 1/8*x^8*e^5*b^2*A + 1/4*x^8*e^5*c*a*A + 5/7*x^7*e*d^4*c^2*B + 20/7*x^7*e^2*d^3*c*b*B + 10/7*x^7*e^3*d^2*b^2*B + 20/7*x^7*e^3*d^2*c*a*B + 10/7*x^7*e^4*d*b*a*B + 1/7*x^7*e^5*a^2*B + 10/7*x^7*e^2*d^3*c^2*A + 20/7*x^7*e^3*d^2*c*b*A + 5/7*x^7*e^4*d*b^2*A + 10/7*x^7*e^4*d*c*a*A + 2/7*x^7*e^5*b*a*A + 1/6*x^6*d^5*c^2*B + 5/3*x^6*e*d^4*c*b*B + 5/3*x^6*e^2*d^3*b^2*B + 10/3*x^6*e^2*d^3*c*a*B + 10/3*x^6*e^3*d^2*b*a*B + 5/6*x^6*e^4*d*a^2*B + 5/6*x^6*e*d^4*c^2*A + 10/3*x^6*e^2*d^3*c*b*A + 5/3*x^6*e^3*d^2*b^2*A + 10/3*x^6*e^3*d^2*c*a*A + 5/3*x^6*e^4*d*b*a*A + 1/6*x^6*e^5*a^2*A + 2/5*x^5*d^5*c*b*B + x^5*e*d^4*b^2*B + 2*x^5*e*d^4*c*a*B + 4*x^5*e^2*d^3*b*a*B + 2*x^5*e^3*d^2*a^2*B + 1/5*x^5*d^5*c^2*A + 2*x^5*e*d^4*c*b*A + 2*x^5*e^2*d^3*b^2*A + 4*x^5*e^2*d^3*c*a*A + 4*x^5*e^3*d^2*b*a*A + x^5*e^4*d*a^2*A + 1/4*x^4*d^5*b^2*B + 1/2*x^4*d^5*c*a*B + 5/2*x^4*e*d^4*b*a*B + 5/2*x^4*e^2*d^3*a^2*B + 1/2*x^4*d^5*c*b*A + 5/4*x^4*e*d^4*b^2*A + 5/2*x^4*e*d^4*c*a*A + 5*x^4*e^2*d^3*b*a*A + 5/2*x^4*e^3*d^2*a^2*A + 2/3*x^3*d^5*b*a*B + 5/3*x^3*e*d^4*a^2*B + 1/3*x^3*d^5*b^2*A + 2/3*x^3*d^5*c*a*A + 10/3*x^3*e*d^4*b*a*A + 10/3*x^3*e^2*d^3*a^2*A + 1/2*x^2*d^5*a^2*B + x^2*d^5*b*a*A + 5/2*x^2*e*d^4*a^2*A + x*d^5*a^2*A","B",0
2319,1,743,0,0.357358," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{4} c^{2} B + \frac{4}{9} x^{9} e^{3} d c^{2} B + \frac{2}{9} x^{9} e^{4} c b B + \frac{1}{9} x^{9} e^{4} c^{2} A + \frac{3}{4} x^{8} e^{2} d^{2} c^{2} B + x^{8} e^{3} d c b B + \frac{1}{8} x^{8} e^{4} b^{2} B + \frac{1}{4} x^{8} e^{4} c a B + \frac{1}{2} x^{8} e^{3} d c^{2} A + \frac{1}{4} x^{8} e^{4} c b A + \frac{4}{7} x^{7} e d^{3} c^{2} B + \frac{12}{7} x^{7} e^{2} d^{2} c b B + \frac{4}{7} x^{7} e^{3} d b^{2} B + \frac{8}{7} x^{7} e^{3} d c a B + \frac{2}{7} x^{7} e^{4} b a B + \frac{6}{7} x^{7} e^{2} d^{2} c^{2} A + \frac{8}{7} x^{7} e^{3} d c b A + \frac{1}{7} x^{7} e^{4} b^{2} A + \frac{2}{7} x^{7} e^{4} c a A + \frac{1}{6} x^{6} d^{4} c^{2} B + \frac{4}{3} x^{6} e d^{3} c b B + x^{6} e^{2} d^{2} b^{2} B + 2 x^{6} e^{2} d^{2} c a B + \frac{4}{3} x^{6} e^{3} d b a B + \frac{1}{6} x^{6} e^{4} a^{2} B + \frac{2}{3} x^{6} e d^{3} c^{2} A + 2 x^{6} e^{2} d^{2} c b A + \frac{2}{3} x^{6} e^{3} d b^{2} A + \frac{4}{3} x^{6} e^{3} d c a A + \frac{1}{3} x^{6} e^{4} b a A + \frac{2}{5} x^{5} d^{4} c b B + \frac{4}{5} x^{5} e d^{3} b^{2} B + \frac{8}{5} x^{5} e d^{3} c a B + \frac{12}{5} x^{5} e^{2} d^{2} b a B + \frac{4}{5} x^{5} e^{3} d a^{2} B + \frac{1}{5} x^{5} d^{4} c^{2} A + \frac{8}{5} x^{5} e d^{3} c b A + \frac{6}{5} x^{5} e^{2} d^{2} b^{2} A + \frac{12}{5} x^{5} e^{2} d^{2} c a A + \frac{8}{5} x^{5} e^{3} d b a A + \frac{1}{5} x^{5} e^{4} a^{2} A + \frac{1}{4} x^{4} d^{4} b^{2} B + \frac{1}{2} x^{4} d^{4} c a B + 2 x^{4} e d^{3} b a B + \frac{3}{2} x^{4} e^{2} d^{2} a^{2} B + \frac{1}{2} x^{4} d^{4} c b A + x^{4} e d^{3} b^{2} A + 2 x^{4} e d^{3} c a A + 3 x^{4} e^{2} d^{2} b a A + x^{4} e^{3} d a^{2} A + \frac{2}{3} x^{3} d^{4} b a B + \frac{4}{3} x^{3} e d^{3} a^{2} B + \frac{1}{3} x^{3} d^{4} b^{2} A + \frac{2}{3} x^{3} d^{4} c a A + \frac{8}{3} x^{3} e d^{3} b a A + 2 x^{3} e^{2} d^{2} a^{2} A + \frac{1}{2} x^{2} d^{4} a^{2} B + x^{2} d^{4} b a A + 2 x^{2} e d^{3} a^{2} A + x d^{4} a^{2} A"," ",0,"1/10*x^10*e^4*c^2*B + 4/9*x^9*e^3*d*c^2*B + 2/9*x^9*e^4*c*b*B + 1/9*x^9*e^4*c^2*A + 3/4*x^8*e^2*d^2*c^2*B + x^8*e^3*d*c*b*B + 1/8*x^8*e^4*b^2*B + 1/4*x^8*e^4*c*a*B + 1/2*x^8*e^3*d*c^2*A + 1/4*x^8*e^4*c*b*A + 4/7*x^7*e*d^3*c^2*B + 12/7*x^7*e^2*d^2*c*b*B + 4/7*x^7*e^3*d*b^2*B + 8/7*x^7*e^3*d*c*a*B + 2/7*x^7*e^4*b*a*B + 6/7*x^7*e^2*d^2*c^2*A + 8/7*x^7*e^3*d*c*b*A + 1/7*x^7*e^4*b^2*A + 2/7*x^7*e^4*c*a*A + 1/6*x^6*d^4*c^2*B + 4/3*x^6*e*d^3*c*b*B + x^6*e^2*d^2*b^2*B + 2*x^6*e^2*d^2*c*a*B + 4/3*x^6*e^3*d*b*a*B + 1/6*x^6*e^4*a^2*B + 2/3*x^6*e*d^3*c^2*A + 2*x^6*e^2*d^2*c*b*A + 2/3*x^6*e^3*d*b^2*A + 4/3*x^6*e^3*d*c*a*A + 1/3*x^6*e^4*b*a*A + 2/5*x^5*d^4*c*b*B + 4/5*x^5*e*d^3*b^2*B + 8/5*x^5*e*d^3*c*a*B + 12/5*x^5*e^2*d^2*b*a*B + 4/5*x^5*e^3*d*a^2*B + 1/5*x^5*d^4*c^2*A + 8/5*x^5*e*d^3*c*b*A + 6/5*x^5*e^2*d^2*b^2*A + 12/5*x^5*e^2*d^2*c*a*A + 8/5*x^5*e^3*d*b*a*A + 1/5*x^5*e^4*a^2*A + 1/4*x^4*d^4*b^2*B + 1/2*x^4*d^4*c*a*B + 2*x^4*e*d^3*b*a*B + 3/2*x^4*e^2*d^2*a^2*B + 1/2*x^4*d^4*c*b*A + x^4*e*d^3*b^2*A + 2*x^4*e*d^3*c*a*A + 3*x^4*e^2*d^2*b*a*A + x^4*e^3*d*a^2*A + 2/3*x^3*d^4*b*a*B + 4/3*x^3*e*d^3*a^2*B + 1/3*x^3*d^4*b^2*A + 2/3*x^3*d^4*c*a*A + 8/3*x^3*e*d^3*b*a*A + 2*x^3*e^2*d^2*a^2*A + 1/2*x^2*d^4*a^2*B + x^2*d^4*b*a*A + 2*x^2*e*d^3*a^2*A + x*d^4*a^2*A","B",0
2320,1,568,0,0.356158," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{3} c^{2} B + \frac{3}{8} x^{8} e^{2} d c^{2} B + \frac{1}{4} x^{8} e^{3} c b B + \frac{1}{8} x^{8} e^{3} c^{2} A + \frac{3}{7} x^{7} e d^{2} c^{2} B + \frac{6}{7} x^{7} e^{2} d c b B + \frac{1}{7} x^{7} e^{3} b^{2} B + \frac{2}{7} x^{7} e^{3} c a B + \frac{3}{7} x^{7} e^{2} d c^{2} A + \frac{2}{7} x^{7} e^{3} c b A + \frac{1}{6} x^{6} d^{3} c^{2} B + x^{6} e d^{2} c b B + \frac{1}{2} x^{6} e^{2} d b^{2} B + x^{6} e^{2} d c a B + \frac{1}{3} x^{6} e^{3} b a B + \frac{1}{2} x^{6} e d^{2} c^{2} A + x^{6} e^{2} d c b A + \frac{1}{6} x^{6} e^{3} b^{2} A + \frac{1}{3} x^{6} e^{3} c a A + \frac{2}{5} x^{5} d^{3} c b B + \frac{3}{5} x^{5} e d^{2} b^{2} B + \frac{6}{5} x^{5} e d^{2} c a B + \frac{6}{5} x^{5} e^{2} d b a B + \frac{1}{5} x^{5} e^{3} a^{2} B + \frac{1}{5} x^{5} d^{3} c^{2} A + \frac{6}{5} x^{5} e d^{2} c b A + \frac{3}{5} x^{5} e^{2} d b^{2} A + \frac{6}{5} x^{5} e^{2} d c a A + \frac{2}{5} x^{5} e^{3} b a A + \frac{1}{4} x^{4} d^{3} b^{2} B + \frac{1}{2} x^{4} d^{3} c a B + \frac{3}{2} x^{4} e d^{2} b a B + \frac{3}{4} x^{4} e^{2} d a^{2} B + \frac{1}{2} x^{4} d^{3} c b A + \frac{3}{4} x^{4} e d^{2} b^{2} A + \frac{3}{2} x^{4} e d^{2} c a A + \frac{3}{2} x^{4} e^{2} d b a A + \frac{1}{4} x^{4} e^{3} a^{2} A + \frac{2}{3} x^{3} d^{3} b a B + x^{3} e d^{2} a^{2} B + \frac{1}{3} x^{3} d^{3} b^{2} A + \frac{2}{3} x^{3} d^{3} c a A + 2 x^{3} e d^{2} b a A + x^{3} e^{2} d a^{2} A + \frac{1}{2} x^{2} d^{3} a^{2} B + x^{2} d^{3} b a A + \frac{3}{2} x^{2} e d^{2} a^{2} A + x d^{3} a^{2} A"," ",0,"1/9*x^9*e^3*c^2*B + 3/8*x^8*e^2*d*c^2*B + 1/4*x^8*e^3*c*b*B + 1/8*x^8*e^3*c^2*A + 3/7*x^7*e*d^2*c^2*B + 6/7*x^7*e^2*d*c*b*B + 1/7*x^7*e^3*b^2*B + 2/7*x^7*e^3*c*a*B + 3/7*x^7*e^2*d*c^2*A + 2/7*x^7*e^3*c*b*A + 1/6*x^6*d^3*c^2*B + x^6*e*d^2*c*b*B + 1/2*x^6*e^2*d*b^2*B + x^6*e^2*d*c*a*B + 1/3*x^6*e^3*b*a*B + 1/2*x^6*e*d^2*c^2*A + x^6*e^2*d*c*b*A + 1/6*x^6*e^3*b^2*A + 1/3*x^6*e^3*c*a*A + 2/5*x^5*d^3*c*b*B + 3/5*x^5*e*d^2*b^2*B + 6/5*x^5*e*d^2*c*a*B + 6/5*x^5*e^2*d*b*a*B + 1/5*x^5*e^3*a^2*B + 1/5*x^5*d^3*c^2*A + 6/5*x^5*e*d^2*c*b*A + 3/5*x^5*e^2*d*b^2*A + 6/5*x^5*e^2*d*c*a*A + 2/5*x^5*e^3*b*a*A + 1/4*x^4*d^3*b^2*B + 1/2*x^4*d^3*c*a*B + 3/2*x^4*e*d^2*b*a*B + 3/4*x^4*e^2*d*a^2*B + 1/2*x^4*d^3*c*b*A + 3/4*x^4*e*d^2*b^2*A + 3/2*x^4*e*d^2*c*a*A + 3/2*x^4*e^2*d*b*a*A + 1/4*x^4*e^3*a^2*A + 2/3*x^3*d^3*b*a*B + x^3*e*d^2*a^2*B + 1/3*x^3*d^3*b^2*A + 2/3*x^3*d^3*c*a*A + 2*x^3*e*d^2*b*a*A + x^3*e^2*d*a^2*A + 1/2*x^2*d^3*a^2*B + x^2*d^3*b*a*A + 3/2*x^2*e*d^2*a^2*A + x*d^3*a^2*A","A",0
2321,1,396,0,0.361300," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{2} c^{2} B + \frac{2}{7} x^{7} e d c^{2} B + \frac{2}{7} x^{7} e^{2} c b B + \frac{1}{7} x^{7} e^{2} c^{2} A + \frac{1}{6} x^{6} d^{2} c^{2} B + \frac{2}{3} x^{6} e d c b B + \frac{1}{6} x^{6} e^{2} b^{2} B + \frac{1}{3} x^{6} e^{2} c a B + \frac{1}{3} x^{6} e d c^{2} A + \frac{1}{3} x^{6} e^{2} c b A + \frac{2}{5} x^{5} d^{2} c b B + \frac{2}{5} x^{5} e d b^{2} B + \frac{4}{5} x^{5} e d c a B + \frac{2}{5} x^{5} e^{2} b a B + \frac{1}{5} x^{5} d^{2} c^{2} A + \frac{4}{5} x^{5} e d c b A + \frac{1}{5} x^{5} e^{2} b^{2} A + \frac{2}{5} x^{5} e^{2} c a A + \frac{1}{4} x^{4} d^{2} b^{2} B + \frac{1}{2} x^{4} d^{2} c a B + x^{4} e d b a B + \frac{1}{4} x^{4} e^{2} a^{2} B + \frac{1}{2} x^{4} d^{2} c b A + \frac{1}{2} x^{4} e d b^{2} A + x^{4} e d c a A + \frac{1}{2} x^{4} e^{2} b a A + \frac{2}{3} x^{3} d^{2} b a B + \frac{2}{3} x^{3} e d a^{2} B + \frac{1}{3} x^{3} d^{2} b^{2} A + \frac{2}{3} x^{3} d^{2} c a A + \frac{4}{3} x^{3} e d b a A + \frac{1}{3} x^{3} e^{2} a^{2} A + \frac{1}{2} x^{2} d^{2} a^{2} B + x^{2} d^{2} b a A + x^{2} e d a^{2} A + x d^{2} a^{2} A"," ",0,"1/8*x^8*e^2*c^2*B + 2/7*x^7*e*d*c^2*B + 2/7*x^7*e^2*c*b*B + 1/7*x^7*e^2*c^2*A + 1/6*x^6*d^2*c^2*B + 2/3*x^6*e*d*c*b*B + 1/6*x^6*e^2*b^2*B + 1/3*x^6*e^2*c*a*B + 1/3*x^6*e*d*c^2*A + 1/3*x^6*e^2*c*b*A + 2/5*x^5*d^2*c*b*B + 2/5*x^5*e*d*b^2*B + 4/5*x^5*e*d*c*a*B + 2/5*x^5*e^2*b*a*B + 1/5*x^5*d^2*c^2*A + 4/5*x^5*e*d*c*b*A + 1/5*x^5*e^2*b^2*A + 2/5*x^5*e^2*c*a*A + 1/4*x^4*d^2*b^2*B + 1/2*x^4*d^2*c*a*B + x^4*e*d*b*a*B + 1/4*x^4*e^2*a^2*B + 1/2*x^4*d^2*c*b*A + 1/2*x^4*e*d*b^2*A + x^4*e*d*c*a*A + 1/2*x^4*e^2*b*a*A + 2/3*x^3*d^2*b*a*B + 2/3*x^3*e*d*a^2*B + 1/3*x^3*d^2*b^2*A + 2/3*x^3*d^2*c*a*A + 4/3*x^3*e*d*b*a*A + 1/3*x^3*e^2*a^2*A + 1/2*x^2*d^2*a^2*B + x^2*d^2*b*a*A + x^2*e*d*a^2*A + x*d^2*a^2*A","A",0
2322,1,225,0,0.337352," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e c^{2} B + \frac{1}{6} x^{6} d c^{2} B + \frac{1}{3} x^{6} e c b B + \frac{1}{6} x^{6} e c^{2} A + \frac{2}{5} x^{5} d c b B + \frac{1}{5} x^{5} e b^{2} B + \frac{2}{5} x^{5} e c a B + \frac{1}{5} x^{5} d c^{2} A + \frac{2}{5} x^{5} e c b A + \frac{1}{4} x^{4} d b^{2} B + \frac{1}{2} x^{4} d c a B + \frac{1}{2} x^{4} e b a B + \frac{1}{2} x^{4} d c b A + \frac{1}{4} x^{4} e b^{2} A + \frac{1}{2} x^{4} e c a A + \frac{2}{3} x^{3} d b a B + \frac{1}{3} x^{3} e a^{2} B + \frac{1}{3} x^{3} d b^{2} A + \frac{2}{3} x^{3} d c a A + \frac{2}{3} x^{3} e b a A + \frac{1}{2} x^{2} d a^{2} B + x^{2} d b a A + \frac{1}{2} x^{2} e a^{2} A + x d a^{2} A"," ",0,"1/7*x^7*e*c^2*B + 1/6*x^6*d*c^2*B + 1/3*x^6*e*c*b*B + 1/6*x^6*e*c^2*A + 2/5*x^5*d*c*b*B + 1/5*x^5*e*b^2*B + 2/5*x^5*e*c*a*B + 1/5*x^5*d*c^2*A + 2/5*x^5*e*c*b*A + 1/4*x^4*d*b^2*B + 1/2*x^4*d*c*a*B + 1/2*x^4*e*b*a*B + 1/2*x^4*d*c*b*A + 1/4*x^4*e*b^2*A + 1/2*x^4*e*c*a*A + 2/3*x^3*d*b*a*B + 1/3*x^3*e*a^2*B + 1/3*x^3*d*b^2*A + 2/3*x^3*d*c*a*A + 2/3*x^3*e*b*a*A + 1/2*x^2*d*a^2*B + x^2*d*b*a*A + 1/2*x^2*e*a^2*A + x*d*a^2*A","A",0
2323,1,99,0,0.347291," ","integrate((B*x+A)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} c^{2} B + \frac{2}{5} x^{5} c b B + \frac{1}{5} x^{5} c^{2} A + \frac{1}{4} x^{4} b^{2} B + \frac{1}{2} x^{4} c a B + \frac{1}{2} x^{4} c b A + \frac{2}{3} x^{3} b a B + \frac{1}{3} x^{3} b^{2} A + \frac{2}{3} x^{3} c a A + \frac{1}{2} x^{2} a^{2} B + x^{2} b a A + x a^{2} A"," ",0,"1/6*x^6*c^2*B + 2/5*x^5*c*b*B + 1/5*x^5*c^2*A + 1/4*x^4*b^2*B + 1/2*x^4*c*a*B + 1/2*x^4*c*b*A + 2/3*x^3*b*a*B + 1/3*x^3*b^2*A + 2/3*x^3*c*a*A + 1/2*x^2*a^2*B + x^2*b*a*A + x*a^2*A","A",0
2324,1,379,0,0.382981," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d),x, algorithm=""fricas"")","\frac{12 \, B c^{2} e^{5} x^{5} - 15 \, {\left(B c^{2} d e^{4} - {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 20 \, {\left(B c^{2} d^{2} e^{3} - {\left(2 \, B b c + A c^{2}\right)} d e^{4} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{5}\right)} x^{3} - 30 \, {\left(B c^{2} d^{3} e^{2} - {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} + 60 \, {\left(B c^{2} d^{4} e - {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4} + {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x - 60 \, {\left(B c^{2} d^{5} - A a^{2} e^{5} - {\left(2 \, B b c + A c^{2}\right)} d^{4} e + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} + {\left(B a^{2} + 2 \, A a b\right)} d e^{4}\right)} \log\left(e x + d\right)}{60 \, e^{6}}"," ",0,"1/60*(12*B*c^2*e^5*x^5 - 15*(B*c^2*d*e^4 - (2*B*b*c + A*c^2)*e^5)*x^4 + 20*(B*c^2*d^2*e^3 - (2*B*b*c + A*c^2)*d*e^4 + (B*b^2 + 2*(B*a + A*b)*c)*e^5)*x^3 - 30*(B*c^2*d^3*e^2 - (2*B*b*c + A*c^2)*d^2*e^3 + (B*b^2 + 2*(B*a + A*b)*c)*d*e^4 - (2*B*a*b + A*b^2 + 2*A*a*c)*e^5)*x^2 + 60*(B*c^2*d^4*e - (2*B*b*c + A*c^2)*d^3*e^2 + (B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 - (2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4 + (B*a^2 + 2*A*a*b)*e^5)*x - 60*(B*c^2*d^5 - A*a^2*e^5 - (2*B*b*c + A*c^2)*d^4*e + (B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 - (2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 + (B*a^2 + 2*A*a*b)*d*e^4)*log(e*x + d))/e^6","A",0
2325,1,567,0,0.386977," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{3 \, B c^{2} e^{5} x^{5} + 12 \, B c^{2} d^{5} - 12 \, A a^{2} e^{5} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 12 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} - 12 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} + 12 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{4} - {\left(5 \, B c^{2} d e^{4} - 4 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 2 \, {\left(5 \, B c^{2} d^{2} e^{3} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{5}\right)} x^{3} - 6 \, {\left(5 \, B c^{2} d^{3} e^{2} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4} - 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} - 12 \, {\left(4 \, B c^{2} d^{4} e - 3 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 2 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4}\right)} x + 12 \, {\left(5 \, B c^{2} d^{5} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} - 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} + {\left(B a^{2} + 2 \, A a b\right)} d e^{4} + {\left(5 \, B c^{2} d^{4} e - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} - 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4} + {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"1/12*(3*B*c^2*e^5*x^5 + 12*B*c^2*d^5 - 12*A*a^2*e^5 - 12*(2*B*b*c + A*c^2)*d^4*e + 12*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 - 12*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 + 12*(B*a^2 + 2*A*a*b)*d*e^4 - (5*B*c^2*d*e^4 - 4*(2*B*b*c + A*c^2)*e^5)*x^4 + 2*(5*B*c^2*d^2*e^3 - 4*(2*B*b*c + A*c^2)*d*e^4 + 3*(B*b^2 + 2*(B*a + A*b)*c)*e^5)*x^3 - 6*(5*B*c^2*d^3*e^2 - 4*(2*B*b*c + A*c^2)*d^2*e^3 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d*e^4 - 2*(2*B*a*b + A*b^2 + 2*A*a*c)*e^5)*x^2 - 12*(4*B*c^2*d^4*e - 3*(2*B*b*c + A*c^2)*d^3*e^2 + 2*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 - (2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4)*x + 12*(5*B*c^2*d^5 - 4*(2*B*b*c + A*c^2)*d^4*e + 3*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 - 2*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 + (B*a^2 + 2*A*a*b)*d*e^4 + (5*B*c^2*d^4*e - 4*(2*B*b*c + A*c^2)*d^3*e^2 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 - 2*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4 + (B*a^2 + 2*A*a*b)*e^5)*x)*log(e*x + d))/(e^7*x + d*e^6)","B",0
2326,1,620,0,0.398894," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, B c^{2} e^{5} x^{5} - 27 \, B c^{2} d^{5} - 3 \, A a^{2} e^{5} + 21 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e - 15 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} + 9 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{4} - {\left(5 \, B c^{2} d e^{4} - 3 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 2 \, {\left(10 \, B c^{2} d^{2} e^{3} - 6 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{5}\right)} x^{3} + 3 \, {\left(21 \, B c^{2} d^{3} e^{2} - 11 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 4 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4}\right)} x^{2} + 6 \, {\left(B c^{2} d^{4} e + {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} - 2 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} + 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4} - {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x - 6 \, {\left(10 \, B c^{2} d^{5} - 6 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} + {\left(10 \, B c^{2} d^{3} e^{2} - 6 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} + 2 \, {\left(10 \, B c^{2} d^{4} e - 6 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"1/6*(2*B*c^2*e^5*x^5 - 27*B*c^2*d^5 - 3*A*a^2*e^5 + 21*(2*B*b*c + A*c^2)*d^4*e - 15*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 + 9*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 - 3*(B*a^2 + 2*A*a*b)*d*e^4 - (5*B*c^2*d*e^4 - 3*(2*B*b*c + A*c^2)*e^5)*x^4 + 2*(10*B*c^2*d^2*e^3 - 6*(2*B*b*c + A*c^2)*d*e^4 + 3*(B*b^2 + 2*(B*a + A*b)*c)*e^5)*x^3 + 3*(21*B*c^2*d^3*e^2 - 11*(2*B*b*c + A*c^2)*d^2*e^3 + 4*(B*b^2 + 2*(B*a + A*b)*c)*d*e^4)*x^2 + 6*(B*c^2*d^4*e + (2*B*b*c + A*c^2)*d^3*e^2 - 2*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 + 2*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4 - (B*a^2 + 2*A*a*b)*e^5)*x - 6*(10*B*c^2*d^5 - 6*(2*B*b*c + A*c^2)*d^4*e + 3*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 - (2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 + (10*B*c^2*d^3*e^2 - 6*(2*B*b*c + A*c^2)*d^2*e^3 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d*e^4 - (2*B*a*b + A*b^2 + 2*A*a*c)*e^5)*x^2 + 2*(10*B*c^2*d^4*e - 6*(2*B*b*c + A*c^2)*d^3*e^2 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 - (2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4)*x)*log(e*x + d))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","B",0
2327,1,618,0,0.401168," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, B c^{2} e^{5} x^{5} + 47 \, B c^{2} d^{5} - 2 \, A a^{2} e^{5} - 26 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 11 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} - 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} - {\left(B a^{2} + 2 \, A a b\right)} d e^{4} - 3 \, {\left(5 \, B c^{2} d e^{4} - 2 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} - 9 \, {\left(7 \, B c^{2} d^{2} e^{3} - 2 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4}\right)} x^{3} - 3 \, {\left(3 \, B c^{2} d^{3} e^{2} + 6 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} - 6 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4} + 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} + 3 \, {\left(27 \, B c^{2} d^{4} e - 18 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 9 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} - 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4} - {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x + 6 \, {\left(10 \, B c^{2} d^{5} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} + {\left(10 \, B c^{2} d^{2} e^{3} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{5}\right)} x^{3} + 3 \, {\left(10 \, B c^{2} d^{3} e^{2} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4}\right)} x^{2} + 3 \, {\left(10 \, B c^{2} d^{4} e - 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"1/6*(3*B*c^2*e^5*x^5 + 47*B*c^2*d^5 - 2*A*a^2*e^5 - 26*(2*B*b*c + A*c^2)*d^4*e + 11*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 - 2*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 - (B*a^2 + 2*A*a*b)*d*e^4 - 3*(5*B*c^2*d*e^4 - 2*(2*B*b*c + A*c^2)*e^5)*x^4 - 9*(7*B*c^2*d^2*e^3 - 2*(2*B*b*c + A*c^2)*d*e^4)*x^3 - 3*(3*B*c^2*d^3*e^2 + 6*(2*B*b*c + A*c^2)*d^2*e^3 - 6*(B*b^2 + 2*(B*a + A*b)*c)*d*e^4 + 2*(2*B*a*b + A*b^2 + 2*A*a*c)*e^5)*x^2 + 3*(27*B*c^2*d^4*e - 18*(2*B*b*c + A*c^2)*d^3*e^2 + 9*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 - 2*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4 - (B*a^2 + 2*A*a*b)*e^5)*x + 6*(10*B*c^2*d^5 - 4*(2*B*b*c + A*c^2)*d^4*e + (B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 + (10*B*c^2*d^2*e^3 - 4*(2*B*b*c + A*c^2)*d*e^4 + (B*b^2 + 2*(B*a + A*b)*c)*e^5)*x^3 + 3*(10*B*c^2*d^3*e^2 - 4*(2*B*b*c + A*c^2)*d^2*e^3 + (B*b^2 + 2*(B*a + A*b)*c)*d*e^4)*x^2 + 3*(10*B*c^2*d^4*e - 4*(2*B*b*c + A*c^2)*d^3*e^2 + (B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3)*x)*log(e*x + d))/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","B",0
2328,1,572,0,0.380505," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{12 \, B c^{2} e^{5} x^{5} + 48 \, B c^{2} d e^{4} x^{4} - 77 \, B c^{2} d^{5} - 3 \, A a^{2} e^{5} + 25 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e - 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} - {\left(B a^{2} + 2 \, A a b\right)} d e^{4} - 12 \, {\left(4 \, B c^{2} d^{2} e^{3} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{5}\right)} x^{3} - 6 \, {\left(42 \, B c^{2} d^{3} e^{2} - 18 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4} + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} - 4 \, {\left(62 \, B c^{2} d^{4} e - 22 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4} + {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x - 12 \, {\left(5 \, B c^{2} d^{5} - {\left(2 \, B b c + A c^{2}\right)} d^{4} e + {\left(5 \, B c^{2} d e^{4} - {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 4 \, {\left(5 \, B c^{2} d^{2} e^{3} - {\left(2 \, B b c + A c^{2}\right)} d e^{4}\right)} x^{3} + 6 \, {\left(5 \, B c^{2} d^{3} e^{2} - {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3}\right)} x^{2} + 4 \, {\left(5 \, B c^{2} d^{4} e - {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{10} x^{4} + 4 \, d e^{9} x^{3} + 6 \, d^{2} e^{8} x^{2} + 4 \, d^{3} e^{7} x + d^{4} e^{6}\right)}}"," ",0,"1/12*(12*B*c^2*e^5*x^5 + 48*B*c^2*d*e^4*x^4 - 77*B*c^2*d^5 - 3*A*a^2*e^5 + 25*(2*B*b*c + A*c^2)*d^4*e - 3*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 - (2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 - (B*a^2 + 2*A*a*b)*d*e^4 - 12*(4*B*c^2*d^2*e^3 - 4*(2*B*b*c + A*c^2)*d*e^4 + (B*b^2 + 2*(B*a + A*b)*c)*e^5)*x^3 - 6*(42*B*c^2*d^3*e^2 - 18*(2*B*b*c + A*c^2)*d^2*e^3 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d*e^4 + (2*B*a*b + A*b^2 + 2*A*a*c)*e^5)*x^2 - 4*(62*B*c^2*d^4*e - 22*(2*B*b*c + A*c^2)*d^3*e^2 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 + (2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4 + (B*a^2 + 2*A*a*b)*e^5)*x - 12*(5*B*c^2*d^5 - (2*B*b*c + A*c^2)*d^4*e + (5*B*c^2*d*e^4 - (2*B*b*c + A*c^2)*e^5)*x^4 + 4*(5*B*c^2*d^2*e^3 - (2*B*b*c + A*c^2)*d*e^4)*x^3 + 6*(5*B*c^2*d^3*e^2 - (2*B*b*c + A*c^2)*d^2*e^3)*x^2 + 4*(5*B*c^2*d^4*e - (2*B*b*c + A*c^2)*d^3*e^2)*x)*log(e*x + d))/(e^10*x^4 + 4*d*e^9*x^3 + 6*d^2*e^8*x^2 + 4*d^3*e^7*x + d^4*e^6)","B",0
2329,1,505,0,0.393511," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^6,x, algorithm=""fricas"")","\frac{137 \, B c^{2} d^{5} - 12 \, A a^{2} e^{5} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e - 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} - 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{4} + 60 \, {\left(5 \, B c^{2} d e^{4} - {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 30 \, {\left(30 \, B c^{2} d^{2} e^{3} - 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} - {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{5}\right)} x^{3} + 10 \, {\left(110 \, B c^{2} d^{3} e^{2} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} - 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4} - 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} + 5 \, {\left(125 \, B c^{2} d^{4} e - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} - 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} - 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x + 60 \, {\left(B c^{2} e^{5} x^{5} + 5 \, B c^{2} d e^{4} x^{4} + 10 \, B c^{2} d^{2} e^{3} x^{3} + 10 \, B c^{2} d^{3} e^{2} x^{2} + 5 \, B c^{2} d^{4} e x + B c^{2} d^{5}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{11} x^{5} + 5 \, d e^{10} x^{4} + 10 \, d^{2} e^{9} x^{3} + 10 \, d^{3} e^{8} x^{2} + 5 \, d^{4} e^{7} x + d^{5} e^{6}\right)}}"," ",0,"1/60*(137*B*c^2*d^5 - 12*A*a^2*e^5 - 12*(2*B*b*c + A*c^2)*d^4*e - 3*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 - 2*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 - 3*(B*a^2 + 2*A*a*b)*d*e^4 + 60*(5*B*c^2*d*e^4 - (2*B*b*c + A*c^2)*e^5)*x^4 + 30*(30*B*c^2*d^2*e^3 - 4*(2*B*b*c + A*c^2)*d*e^4 - (B*b^2 + 2*(B*a + A*b)*c)*e^5)*x^3 + 10*(110*B*c^2*d^3*e^2 - 12*(2*B*b*c + A*c^2)*d^2*e^3 - 3*(B*b^2 + 2*(B*a + A*b)*c)*d*e^4 - 2*(2*B*a*b + A*b^2 + 2*A*a*c)*e^5)*x^2 + 5*(125*B*c^2*d^4*e - 12*(2*B*b*c + A*c^2)*d^3*e^2 - 3*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 - 2*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4 - 3*(B*a^2 + 2*A*a*b)*e^5)*x + 60*(B*c^2*e^5*x^5 + 5*B*c^2*d*e^4*x^4 + 10*B*c^2*d^2*e^3*x^3 + 10*B*c^2*d^3*e^2*x^2 + 5*B*c^2*d^4*e*x + B*c^2*d^5)*log(e*x + d))/(e^11*x^5 + 5*d*e^10*x^4 + 10*d^2*e^9*x^3 + 10*d^3*e^8*x^2 + 5*d^4*e^7*x + d^5*e^6)","A",0
2330,1,438,0,0.385067," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{60 \, B c^{2} e^{5} x^{5} + 10 \, B c^{2} d^{5} + 10 \, A a^{2} e^{5} + 2 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{4} + 30 \, {\left(5 \, B c^{2} d e^{4} + {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 20 \, {\left(10 \, B c^{2} d^{2} e^{3} + 2 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{5}\right)} x^{3} + 15 \, {\left(10 \, B c^{2} d^{3} e^{2} + 2 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4} + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} + 6 \, {\left(10 \, B c^{2} d^{4} e + 2 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x}{60 \, {\left(e^{12} x^{6} + 6 \, d e^{11} x^{5} + 15 \, d^{2} e^{10} x^{4} + 20 \, d^{3} e^{9} x^{3} + 15 \, d^{4} e^{8} x^{2} + 6 \, d^{5} e^{7} x + d^{6} e^{6}\right)}}"," ",0,"-1/60*(60*B*c^2*e^5*x^5 + 10*B*c^2*d^5 + 10*A*a^2*e^5 + 2*(2*B*b*c + A*c^2)*d^4*e + (B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 + (2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 + 2*(B*a^2 + 2*A*a*b)*d*e^4 + 30*(5*B*c^2*d*e^4 + (2*B*b*c + A*c^2)*e^5)*x^4 + 20*(10*B*c^2*d^2*e^3 + 2*(2*B*b*c + A*c^2)*d*e^4 + (B*b^2 + 2*(B*a + A*b)*c)*e^5)*x^3 + 15*(10*B*c^2*d^3*e^2 + 2*(2*B*b*c + A*c^2)*d^2*e^3 + (B*b^2 + 2*(B*a + A*b)*c)*d*e^4 + (2*B*a*b + A*b^2 + 2*A*a*c)*e^5)*x^2 + 6*(10*B*c^2*d^4*e + 2*(2*B*b*c + A*c^2)*d^3*e^2 + (B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 + (2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4 + 2*(B*a^2 + 2*A*a*b)*e^5)*x)/(e^12*x^6 + 6*d*e^11*x^5 + 15*d^2*e^10*x^4 + 20*d^3*e^9*x^3 + 15*d^4*e^8*x^2 + 6*d^5*e^7*x + d^6*e^6)","A",0
2331,1,457,0,0.390572," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{210 \, B c^{2} e^{5} x^{5} + 10 \, B c^{2} d^{5} + 60 \, A a^{2} e^{5} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} + 4 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} + 10 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{4} + 70 \, {\left(5 \, B c^{2} d e^{4} + 2 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 35 \, {\left(10 \, B c^{2} d^{2} e^{3} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{5}\right)} x^{3} + 21 \, {\left(10 \, B c^{2} d^{3} e^{2} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4} + 4 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} + 7 \, {\left(10 \, B c^{2} d^{4} e + 4 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} + 4 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4} + 10 \, {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x}{420 \, {\left(e^{13} x^{7} + 7 \, d e^{12} x^{6} + 21 \, d^{2} e^{11} x^{5} + 35 \, d^{3} e^{10} x^{4} + 35 \, d^{4} e^{9} x^{3} + 21 \, d^{5} e^{8} x^{2} + 7 \, d^{6} e^{7} x + d^{7} e^{6}\right)}}"," ",0,"-1/420*(210*B*c^2*e^5*x^5 + 10*B*c^2*d^5 + 60*A*a^2*e^5 + 4*(2*B*b*c + A*c^2)*d^4*e + 3*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 + 4*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 + 10*(B*a^2 + 2*A*a*b)*d*e^4 + 70*(5*B*c^2*d*e^4 + 2*(2*B*b*c + A*c^2)*e^5)*x^4 + 35*(10*B*c^2*d^2*e^3 + 4*(2*B*b*c + A*c^2)*d*e^4 + 3*(B*b^2 + 2*(B*a + A*b)*c)*e^5)*x^3 + 21*(10*B*c^2*d^3*e^2 + 4*(2*B*b*c + A*c^2)*d^2*e^3 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d*e^4 + 4*(2*B*a*b + A*b^2 + 2*A*a*c)*e^5)*x^2 + 7*(10*B*c^2*d^4*e + 4*(2*B*b*c + A*c^2)*d^3*e^2 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 + 4*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4 + 10*(B*a^2 + 2*A*a*b)*e^5)*x)/(e^13*x^7 + 7*d*e^12*x^6 + 21*d^2*e^11*x^5 + 35*d^3*e^10*x^4 + 35*d^4*e^9*x^3 + 21*d^5*e^8*x^2 + 7*d^6*e^7*x + d^7*e^6)","A",0
2332,1,468,0,0.394899," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{280 \, B c^{2} e^{5} x^{5} + 5 \, B c^{2} d^{5} + 105 \, A a^{2} e^{5} + 3 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{2} + 5 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{3} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{4} + 70 \, {\left(5 \, B c^{2} d e^{4} + 3 \, {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} x^{4} + 56 \, {\left(5 \, B c^{2} d^{2} e^{3} + 3 \, {\left(2 \, B b c + A c^{2}\right)} d e^{4} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{5}\right)} x^{3} + 28 \, {\left(5 \, B c^{2} d^{3} e^{2} + 3 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{3} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{4} + 5 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} + 8 \, {\left(5 \, B c^{2} d^{4} e + 3 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{2} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{3} + 5 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{4} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x}{840 \, {\left(e^{14} x^{8} + 8 \, d e^{13} x^{7} + 28 \, d^{2} e^{12} x^{6} + 56 \, d^{3} e^{11} x^{5} + 70 \, d^{4} e^{10} x^{4} + 56 \, d^{5} e^{9} x^{3} + 28 \, d^{6} e^{8} x^{2} + 8 \, d^{7} e^{7} x + d^{8} e^{6}\right)}}"," ",0,"-1/840*(280*B*c^2*e^5*x^5 + 5*B*c^2*d^5 + 105*A*a^2*e^5 + 3*(2*B*b*c + A*c^2)*d^4*e + 3*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^2 + 5*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^3 + 15*(B*a^2 + 2*A*a*b)*d*e^4 + 70*(5*B*c^2*d*e^4 + 3*(2*B*b*c + A*c^2)*e^5)*x^4 + 56*(5*B*c^2*d^2*e^3 + 3*(2*B*b*c + A*c^2)*d*e^4 + 3*(B*b^2 + 2*(B*a + A*b)*c)*e^5)*x^3 + 28*(5*B*c^2*d^3*e^2 + 3*(2*B*b*c + A*c^2)*d^2*e^3 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d*e^4 + 5*(2*B*a*b + A*b^2 + 2*A*a*c)*e^5)*x^2 + 8*(5*B*c^2*d^4*e + 3*(2*B*b*c + A*c^2)*d^3*e^2 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^3 + 5*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^4 + 15*(B*a^2 + 2*A*a*b)*e^5)*x)/(e^14*x^8 + 8*d*e^13*x^7 + 28*d^2*e^12*x^6 + 56*d^3*e^11*x^5 + 70*d^4*e^10*x^4 + 56*d^5*e^9*x^3 + 28*d^6*e^8*x^2 + 8*d^7*e^7*x + d^8*e^6)","A",0
2333,1,1663,0,0.348792," ","integrate((B*x+A)*(e*x+d)^5*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{5} c^{3} B + \frac{5}{12} x^{12} e^{4} d c^{3} B + \frac{1}{4} x^{12} e^{5} c^{2} b B + \frac{1}{12} x^{12} e^{5} c^{3} A + \frac{10}{11} x^{11} e^{3} d^{2} c^{3} B + \frac{15}{11} x^{11} e^{4} d c^{2} b B + \frac{3}{11} x^{11} e^{5} c b^{2} B + \frac{3}{11} x^{11} e^{5} c^{2} a B + \frac{5}{11} x^{11} e^{4} d c^{3} A + \frac{3}{11} x^{11} e^{5} c^{2} b A + x^{10} e^{2} d^{3} c^{3} B + 3 x^{10} e^{3} d^{2} c^{2} b B + \frac{3}{2} x^{10} e^{4} d c b^{2} B + \frac{1}{10} x^{10} e^{5} b^{3} B + \frac{3}{2} x^{10} e^{4} d c^{2} a B + \frac{3}{5} x^{10} e^{5} c b a B + x^{10} e^{3} d^{2} c^{3} A + \frac{3}{2} x^{10} e^{4} d c^{2} b A + \frac{3}{10} x^{10} e^{5} c b^{2} A + \frac{3}{10} x^{10} e^{5} c^{2} a A + \frac{5}{9} x^{9} e d^{4} c^{3} B + \frac{10}{3} x^{9} e^{2} d^{3} c^{2} b B + \frac{10}{3} x^{9} e^{3} d^{2} c b^{2} B + \frac{5}{9} x^{9} e^{4} d b^{3} B + \frac{10}{3} x^{9} e^{3} d^{2} c^{2} a B + \frac{10}{3} x^{9} e^{4} d c b a B + \frac{1}{3} x^{9} e^{5} b^{2} a B + \frac{1}{3} x^{9} e^{5} c a^{2} B + \frac{10}{9} x^{9} e^{2} d^{3} c^{3} A + \frac{10}{3} x^{9} e^{3} d^{2} c^{2} b A + \frac{5}{3} x^{9} e^{4} d c b^{2} A + \frac{1}{9} x^{9} e^{5} b^{3} A + \frac{5}{3} x^{9} e^{4} d c^{2} a A + \frac{2}{3} x^{9} e^{5} c b a A + \frac{1}{8} x^{8} d^{5} c^{3} B + \frac{15}{8} x^{8} e d^{4} c^{2} b B + \frac{15}{4} x^{8} e^{2} d^{3} c b^{2} B + \frac{5}{4} x^{8} e^{3} d^{2} b^{3} B + \frac{15}{4} x^{8} e^{2} d^{3} c^{2} a B + \frac{15}{2} x^{8} e^{3} d^{2} c b a B + \frac{15}{8} x^{8} e^{4} d b^{2} a B + \frac{15}{8} x^{8} e^{4} d c a^{2} B + \frac{3}{8} x^{8} e^{5} b a^{2} B + \frac{5}{8} x^{8} e d^{4} c^{3} A + \frac{15}{4} x^{8} e^{2} d^{3} c^{2} b A + \frac{15}{4} x^{8} e^{3} d^{2} c b^{2} A + \frac{5}{8} x^{8} e^{4} d b^{3} A + \frac{15}{4} x^{8} e^{3} d^{2} c^{2} a A + \frac{15}{4} x^{8} e^{4} d c b a A + \frac{3}{8} x^{8} e^{5} b^{2} a A + \frac{3}{8} x^{8} e^{5} c a^{2} A + \frac{3}{7} x^{7} d^{5} c^{2} b B + \frac{15}{7} x^{7} e d^{4} c b^{2} B + \frac{10}{7} x^{7} e^{2} d^{3} b^{3} B + \frac{15}{7} x^{7} e d^{4} c^{2} a B + \frac{60}{7} x^{7} e^{2} d^{3} c b a B + \frac{30}{7} x^{7} e^{3} d^{2} b^{2} a B + \frac{30}{7} x^{7} e^{3} d^{2} c a^{2} B + \frac{15}{7} x^{7} e^{4} d b a^{2} B + \frac{1}{7} x^{7} e^{5} a^{3} B + \frac{1}{7} x^{7} d^{5} c^{3} A + \frac{15}{7} x^{7} e d^{4} c^{2} b A + \frac{30}{7} x^{7} e^{2} d^{3} c b^{2} A + \frac{10}{7} x^{7} e^{3} d^{2} b^{3} A + \frac{30}{7} x^{7} e^{2} d^{3} c^{2} a A + \frac{60}{7} x^{7} e^{3} d^{2} c b a A + \frac{15}{7} x^{7} e^{4} d b^{2} a A + \frac{15}{7} x^{7} e^{4} d c a^{2} A + \frac{3}{7} x^{7} e^{5} b a^{2} A + \frac{1}{2} x^{6} d^{5} c b^{2} B + \frac{5}{6} x^{6} e d^{4} b^{3} B + \frac{1}{2} x^{6} d^{5} c^{2} a B + 5 x^{6} e d^{4} c b a B + 5 x^{6} e^{2} d^{3} b^{2} a B + 5 x^{6} e^{2} d^{3} c a^{2} B + 5 x^{6} e^{3} d^{2} b a^{2} B + \frac{5}{6} x^{6} e^{4} d a^{3} B + \frac{1}{2} x^{6} d^{5} c^{2} b A + \frac{5}{2} x^{6} e d^{4} c b^{2} A + \frac{5}{3} x^{6} e^{2} d^{3} b^{3} A + \frac{5}{2} x^{6} e d^{4} c^{2} a A + 10 x^{6} e^{2} d^{3} c b a A + 5 x^{6} e^{3} d^{2} b^{2} a A + 5 x^{6} e^{3} d^{2} c a^{2} A + \frac{5}{2} x^{6} e^{4} d b a^{2} A + \frac{1}{6} x^{6} e^{5} a^{3} A + \frac{1}{5} x^{5} d^{5} b^{3} B + \frac{6}{5} x^{5} d^{5} c b a B + 3 x^{5} e d^{4} b^{2} a B + 3 x^{5} e d^{4} c a^{2} B + 6 x^{5} e^{2} d^{3} b a^{2} B + 2 x^{5} e^{3} d^{2} a^{3} B + \frac{3}{5} x^{5} d^{5} c b^{2} A + x^{5} e d^{4} b^{3} A + \frac{3}{5} x^{5} d^{5} c^{2} a A + 6 x^{5} e d^{4} c b a A + 6 x^{5} e^{2} d^{3} b^{2} a A + 6 x^{5} e^{2} d^{3} c a^{2} A + 6 x^{5} e^{3} d^{2} b a^{2} A + x^{5} e^{4} d a^{3} A + \frac{3}{4} x^{4} d^{5} b^{2} a B + \frac{3}{4} x^{4} d^{5} c a^{2} B + \frac{15}{4} x^{4} e d^{4} b a^{2} B + \frac{5}{2} x^{4} e^{2} d^{3} a^{3} B + \frac{1}{4} x^{4} d^{5} b^{3} A + \frac{3}{2} x^{4} d^{5} c b a A + \frac{15}{4} x^{4} e d^{4} b^{2} a A + \frac{15}{4} x^{4} e d^{4} c a^{2} A + \frac{15}{2} x^{4} e^{2} d^{3} b a^{2} A + \frac{5}{2} x^{4} e^{3} d^{2} a^{3} A + x^{3} d^{5} b a^{2} B + \frac{5}{3} x^{3} e d^{4} a^{3} B + x^{3} d^{5} b^{2} a A + x^{3} d^{5} c a^{2} A + 5 x^{3} e d^{4} b a^{2} A + \frac{10}{3} x^{3} e^{2} d^{3} a^{3} A + \frac{1}{2} x^{2} d^{5} a^{3} B + \frac{3}{2} x^{2} d^{5} b a^{2} A + \frac{5}{2} x^{2} e d^{4} a^{3} A + x d^{5} a^{3} A"," ",0,"1/13*x^13*e^5*c^3*B + 5/12*x^12*e^4*d*c^3*B + 1/4*x^12*e^5*c^2*b*B + 1/12*x^12*e^5*c^3*A + 10/11*x^11*e^3*d^2*c^3*B + 15/11*x^11*e^4*d*c^2*b*B + 3/11*x^11*e^5*c*b^2*B + 3/11*x^11*e^5*c^2*a*B + 5/11*x^11*e^4*d*c^3*A + 3/11*x^11*e^5*c^2*b*A + x^10*e^2*d^3*c^3*B + 3*x^10*e^3*d^2*c^2*b*B + 3/2*x^10*e^4*d*c*b^2*B + 1/10*x^10*e^5*b^3*B + 3/2*x^10*e^4*d*c^2*a*B + 3/5*x^10*e^5*c*b*a*B + x^10*e^3*d^2*c^3*A + 3/2*x^10*e^4*d*c^2*b*A + 3/10*x^10*e^5*c*b^2*A + 3/10*x^10*e^5*c^2*a*A + 5/9*x^9*e*d^4*c^3*B + 10/3*x^9*e^2*d^3*c^2*b*B + 10/3*x^9*e^3*d^2*c*b^2*B + 5/9*x^9*e^4*d*b^3*B + 10/3*x^9*e^3*d^2*c^2*a*B + 10/3*x^9*e^4*d*c*b*a*B + 1/3*x^9*e^5*b^2*a*B + 1/3*x^9*e^5*c*a^2*B + 10/9*x^9*e^2*d^3*c^3*A + 10/3*x^9*e^3*d^2*c^2*b*A + 5/3*x^9*e^4*d*c*b^2*A + 1/9*x^9*e^5*b^3*A + 5/3*x^9*e^4*d*c^2*a*A + 2/3*x^9*e^5*c*b*a*A + 1/8*x^8*d^5*c^3*B + 15/8*x^8*e*d^4*c^2*b*B + 15/4*x^8*e^2*d^3*c*b^2*B + 5/4*x^8*e^3*d^2*b^3*B + 15/4*x^8*e^2*d^3*c^2*a*B + 15/2*x^8*e^3*d^2*c*b*a*B + 15/8*x^8*e^4*d*b^2*a*B + 15/8*x^8*e^4*d*c*a^2*B + 3/8*x^8*e^5*b*a^2*B + 5/8*x^8*e*d^4*c^3*A + 15/4*x^8*e^2*d^3*c^2*b*A + 15/4*x^8*e^3*d^2*c*b^2*A + 5/8*x^8*e^4*d*b^3*A + 15/4*x^8*e^3*d^2*c^2*a*A + 15/4*x^8*e^4*d*c*b*a*A + 3/8*x^8*e^5*b^2*a*A + 3/8*x^8*e^5*c*a^2*A + 3/7*x^7*d^5*c^2*b*B + 15/7*x^7*e*d^4*c*b^2*B + 10/7*x^7*e^2*d^3*b^3*B + 15/7*x^7*e*d^4*c^2*a*B + 60/7*x^7*e^2*d^3*c*b*a*B + 30/7*x^7*e^3*d^2*b^2*a*B + 30/7*x^7*e^3*d^2*c*a^2*B + 15/7*x^7*e^4*d*b*a^2*B + 1/7*x^7*e^5*a^3*B + 1/7*x^7*d^5*c^3*A + 15/7*x^7*e*d^4*c^2*b*A + 30/7*x^7*e^2*d^3*c*b^2*A + 10/7*x^7*e^3*d^2*b^3*A + 30/7*x^7*e^2*d^3*c^2*a*A + 60/7*x^7*e^3*d^2*c*b*a*A + 15/7*x^7*e^4*d*b^2*a*A + 15/7*x^7*e^4*d*c*a^2*A + 3/7*x^7*e^5*b*a^2*A + 1/2*x^6*d^5*c*b^2*B + 5/6*x^6*e*d^4*b^3*B + 1/2*x^6*d^5*c^2*a*B + 5*x^6*e*d^4*c*b*a*B + 5*x^6*e^2*d^3*b^2*a*B + 5*x^6*e^2*d^3*c*a^2*B + 5*x^6*e^3*d^2*b*a^2*B + 5/6*x^6*e^4*d*a^3*B + 1/2*x^6*d^5*c^2*b*A + 5/2*x^6*e*d^4*c*b^2*A + 5/3*x^6*e^2*d^3*b^3*A + 5/2*x^6*e*d^4*c^2*a*A + 10*x^6*e^2*d^3*c*b*a*A + 5*x^6*e^3*d^2*b^2*a*A + 5*x^6*e^3*d^2*c*a^2*A + 5/2*x^6*e^4*d*b*a^2*A + 1/6*x^6*e^5*a^3*A + 1/5*x^5*d^5*b^3*B + 6/5*x^5*d^5*c*b*a*B + 3*x^5*e*d^4*b^2*a*B + 3*x^5*e*d^4*c*a^2*B + 6*x^5*e^2*d^3*b*a^2*B + 2*x^5*e^3*d^2*a^3*B + 3/5*x^5*d^5*c*b^2*A + x^5*e*d^4*b^3*A + 3/5*x^5*d^5*c^2*a*A + 6*x^5*e*d^4*c*b*a*A + 6*x^5*e^2*d^3*b^2*a*A + 6*x^5*e^2*d^3*c*a^2*A + 6*x^5*e^3*d^2*b*a^2*A + x^5*e^4*d*a^3*A + 3/4*x^4*d^5*b^2*a*B + 3/4*x^4*d^5*c*a^2*B + 15/4*x^4*e*d^4*b*a^2*B + 5/2*x^4*e^2*d^3*a^3*B + 1/4*x^4*d^5*b^3*A + 3/2*x^4*d^5*c*b*a*A + 15/4*x^4*e*d^4*b^2*a*A + 15/4*x^4*e*d^4*c*a^2*A + 15/2*x^4*e^2*d^3*b*a^2*A + 5/2*x^4*e^3*d^2*a^3*A + x^3*d^5*b*a^2*B + 5/3*x^3*e*d^4*a^3*B + x^3*d^5*b^2*a*A + x^3*d^5*c*a^2*A + 5*x^3*e*d^4*b*a^2*A + 10/3*x^3*e^2*d^3*a^3*A + 1/2*x^2*d^5*a^3*B + 3/2*x^2*d^5*b*a^2*A + 5/2*x^2*e*d^4*a^3*A + x*d^5*a^3*A","B",0
2334,1,1353,0,0.329377," ","integrate((B*x+A)*(e*x+d)^4*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{4} c^{3} B + \frac{4}{11} x^{11} e^{3} d c^{3} B + \frac{3}{11} x^{11} e^{4} c^{2} b B + \frac{1}{11} x^{11} e^{4} c^{3} A + \frac{3}{5} x^{10} e^{2} d^{2} c^{3} B + \frac{6}{5} x^{10} e^{3} d c^{2} b B + \frac{3}{10} x^{10} e^{4} c b^{2} B + \frac{3}{10} x^{10} e^{4} c^{2} a B + \frac{2}{5} x^{10} e^{3} d c^{3} A + \frac{3}{10} x^{10} e^{4} c^{2} b A + \frac{4}{9} x^{9} e d^{3} c^{3} B + 2 x^{9} e^{2} d^{2} c^{2} b B + \frac{4}{3} x^{9} e^{3} d c b^{2} B + \frac{1}{9} x^{9} e^{4} b^{3} B + \frac{4}{3} x^{9} e^{3} d c^{2} a B + \frac{2}{3} x^{9} e^{4} c b a B + \frac{2}{3} x^{9} e^{2} d^{2} c^{3} A + \frac{4}{3} x^{9} e^{3} d c^{2} b A + \frac{1}{3} x^{9} e^{4} c b^{2} A + \frac{1}{3} x^{9} e^{4} c^{2} a A + \frac{1}{8} x^{8} d^{4} c^{3} B + \frac{3}{2} x^{8} e d^{3} c^{2} b B + \frac{9}{4} x^{8} e^{2} d^{2} c b^{2} B + \frac{1}{2} x^{8} e^{3} d b^{3} B + \frac{9}{4} x^{8} e^{2} d^{2} c^{2} a B + 3 x^{8} e^{3} d c b a B + \frac{3}{8} x^{8} e^{4} b^{2} a B + \frac{3}{8} x^{8} e^{4} c a^{2} B + \frac{1}{2} x^{8} e d^{3} c^{3} A + \frac{9}{4} x^{8} e^{2} d^{2} c^{2} b A + \frac{3}{2} x^{8} e^{3} d c b^{2} A + \frac{1}{8} x^{8} e^{4} b^{3} A + \frac{3}{2} x^{8} e^{3} d c^{2} a A + \frac{3}{4} x^{8} e^{4} c b a A + \frac{3}{7} x^{7} d^{4} c^{2} b B + \frac{12}{7} x^{7} e d^{3} c b^{2} B + \frac{6}{7} x^{7} e^{2} d^{2} b^{3} B + \frac{12}{7} x^{7} e d^{3} c^{2} a B + \frac{36}{7} x^{7} e^{2} d^{2} c b a B + \frac{12}{7} x^{7} e^{3} d b^{2} a B + \frac{12}{7} x^{7} e^{3} d c a^{2} B + \frac{3}{7} x^{7} e^{4} b a^{2} B + \frac{1}{7} x^{7} d^{4} c^{3} A + \frac{12}{7} x^{7} e d^{3} c^{2} b A + \frac{18}{7} x^{7} e^{2} d^{2} c b^{2} A + \frac{4}{7} x^{7} e^{3} d b^{3} A + \frac{18}{7} x^{7} e^{2} d^{2} c^{2} a A + \frac{24}{7} x^{7} e^{3} d c b a A + \frac{3}{7} x^{7} e^{4} b^{2} a A + \frac{3}{7} x^{7} e^{4} c a^{2} A + \frac{1}{2} x^{6} d^{4} c b^{2} B + \frac{2}{3} x^{6} e d^{3} b^{3} B + \frac{1}{2} x^{6} d^{4} c^{2} a B + 4 x^{6} e d^{3} c b a B + 3 x^{6} e^{2} d^{2} b^{2} a B + 3 x^{6} e^{2} d^{2} c a^{2} B + 2 x^{6} e^{3} d b a^{2} B + \frac{1}{6} x^{6} e^{4} a^{3} B + \frac{1}{2} x^{6} d^{4} c^{2} b A + 2 x^{6} e d^{3} c b^{2} A + x^{6} e^{2} d^{2} b^{3} A + 2 x^{6} e d^{3} c^{2} a A + 6 x^{6} e^{2} d^{2} c b a A + 2 x^{6} e^{3} d b^{2} a A + 2 x^{6} e^{3} d c a^{2} A + \frac{1}{2} x^{6} e^{4} b a^{2} A + \frac{1}{5} x^{5} d^{4} b^{3} B + \frac{6}{5} x^{5} d^{4} c b a B + \frac{12}{5} x^{5} e d^{3} b^{2} a B + \frac{12}{5} x^{5} e d^{3} c a^{2} B + \frac{18}{5} x^{5} e^{2} d^{2} b a^{2} B + \frac{4}{5} x^{5} e^{3} d a^{3} B + \frac{3}{5} x^{5} d^{4} c b^{2} A + \frac{4}{5} x^{5} e d^{3} b^{3} A + \frac{3}{5} x^{5} d^{4} c^{2} a A + \frac{24}{5} x^{5} e d^{3} c b a A + \frac{18}{5} x^{5} e^{2} d^{2} b^{2} a A + \frac{18}{5} x^{5} e^{2} d^{2} c a^{2} A + \frac{12}{5} x^{5} e^{3} d b a^{2} A + \frac{1}{5} x^{5} e^{4} a^{3} A + \frac{3}{4} x^{4} d^{4} b^{2} a B + \frac{3}{4} x^{4} d^{4} c a^{2} B + 3 x^{4} e d^{3} b a^{2} B + \frac{3}{2} x^{4} e^{2} d^{2} a^{3} B + \frac{1}{4} x^{4} d^{4} b^{3} A + \frac{3}{2} x^{4} d^{4} c b a A + 3 x^{4} e d^{3} b^{2} a A + 3 x^{4} e d^{3} c a^{2} A + \frac{9}{2} x^{4} e^{2} d^{2} b a^{2} A + x^{4} e^{3} d a^{3} A + x^{3} d^{4} b a^{2} B + \frac{4}{3} x^{3} e d^{3} a^{3} B + x^{3} d^{4} b^{2} a A + x^{3} d^{4} c a^{2} A + 4 x^{3} e d^{3} b a^{2} A + 2 x^{3} e^{2} d^{2} a^{3} A + \frac{1}{2} x^{2} d^{4} a^{3} B + \frac{3}{2} x^{2} d^{4} b a^{2} A + 2 x^{2} e d^{3} a^{3} A + x d^{4} a^{3} A"," ",0,"1/12*x^12*e^4*c^3*B + 4/11*x^11*e^3*d*c^3*B + 3/11*x^11*e^4*c^2*b*B + 1/11*x^11*e^4*c^3*A + 3/5*x^10*e^2*d^2*c^3*B + 6/5*x^10*e^3*d*c^2*b*B + 3/10*x^10*e^4*c*b^2*B + 3/10*x^10*e^4*c^2*a*B + 2/5*x^10*e^3*d*c^3*A + 3/10*x^10*e^4*c^2*b*A + 4/9*x^9*e*d^3*c^3*B + 2*x^9*e^2*d^2*c^2*b*B + 4/3*x^9*e^3*d*c*b^2*B + 1/9*x^9*e^4*b^3*B + 4/3*x^9*e^3*d*c^2*a*B + 2/3*x^9*e^4*c*b*a*B + 2/3*x^9*e^2*d^2*c^3*A + 4/3*x^9*e^3*d*c^2*b*A + 1/3*x^9*e^4*c*b^2*A + 1/3*x^9*e^4*c^2*a*A + 1/8*x^8*d^4*c^3*B + 3/2*x^8*e*d^3*c^2*b*B + 9/4*x^8*e^2*d^2*c*b^2*B + 1/2*x^8*e^3*d*b^3*B + 9/4*x^8*e^2*d^2*c^2*a*B + 3*x^8*e^3*d*c*b*a*B + 3/8*x^8*e^4*b^2*a*B + 3/8*x^8*e^4*c*a^2*B + 1/2*x^8*e*d^3*c^3*A + 9/4*x^8*e^2*d^2*c^2*b*A + 3/2*x^8*e^3*d*c*b^2*A + 1/8*x^8*e^4*b^3*A + 3/2*x^8*e^3*d*c^2*a*A + 3/4*x^8*e^4*c*b*a*A + 3/7*x^7*d^4*c^2*b*B + 12/7*x^7*e*d^3*c*b^2*B + 6/7*x^7*e^2*d^2*b^3*B + 12/7*x^7*e*d^3*c^2*a*B + 36/7*x^7*e^2*d^2*c*b*a*B + 12/7*x^7*e^3*d*b^2*a*B + 12/7*x^7*e^3*d*c*a^2*B + 3/7*x^7*e^4*b*a^2*B + 1/7*x^7*d^4*c^3*A + 12/7*x^7*e*d^3*c^2*b*A + 18/7*x^7*e^2*d^2*c*b^2*A + 4/7*x^7*e^3*d*b^3*A + 18/7*x^7*e^2*d^2*c^2*a*A + 24/7*x^7*e^3*d*c*b*a*A + 3/7*x^7*e^4*b^2*a*A + 3/7*x^7*e^4*c*a^2*A + 1/2*x^6*d^4*c*b^2*B + 2/3*x^6*e*d^3*b^3*B + 1/2*x^6*d^4*c^2*a*B + 4*x^6*e*d^3*c*b*a*B + 3*x^6*e^2*d^2*b^2*a*B + 3*x^6*e^2*d^2*c*a^2*B + 2*x^6*e^3*d*b*a^2*B + 1/6*x^6*e^4*a^3*B + 1/2*x^6*d^4*c^2*b*A + 2*x^6*e*d^3*c*b^2*A + x^6*e^2*d^2*b^3*A + 2*x^6*e*d^3*c^2*a*A + 6*x^6*e^2*d^2*c*b*a*A + 2*x^6*e^3*d*b^2*a*A + 2*x^6*e^3*d*c*a^2*A + 1/2*x^6*e^4*b*a^2*A + 1/5*x^5*d^4*b^3*B + 6/5*x^5*d^4*c*b*a*B + 12/5*x^5*e*d^3*b^2*a*B + 12/5*x^5*e*d^3*c*a^2*B + 18/5*x^5*e^2*d^2*b*a^2*B + 4/5*x^5*e^3*d*a^3*B + 3/5*x^5*d^4*c*b^2*A + 4/5*x^5*e*d^3*b^3*A + 3/5*x^5*d^4*c^2*a*A + 24/5*x^5*e*d^3*c*b*a*A + 18/5*x^5*e^2*d^2*b^2*a*A + 18/5*x^5*e^2*d^2*c*a^2*A + 12/5*x^5*e^3*d*b*a^2*A + 1/5*x^5*e^4*a^3*A + 3/4*x^4*d^4*b^2*a*B + 3/4*x^4*d^4*c*a^2*B + 3*x^4*e*d^3*b*a^2*B + 3/2*x^4*e^2*d^2*a^3*B + 1/4*x^4*d^4*b^3*A + 3/2*x^4*d^4*c*b*a*A + 3*x^4*e*d^3*b^2*a*A + 3*x^4*e*d^3*c*a^2*A + 9/2*x^4*e^2*d^2*b*a^2*A + x^4*e^3*d*a^3*A + x^3*d^4*b*a^2*B + 4/3*x^3*e*d^3*a^3*B + x^3*d^4*b^2*a*A + x^3*d^4*c*a^2*A + 4*x^3*e*d^3*b*a^2*A + 2*x^3*e^2*d^2*a^3*A + 1/2*x^2*d^4*a^3*B + 3/2*x^2*d^4*b*a^2*A + 2*x^2*e*d^3*a^3*A + x*d^4*a^3*A","B",0
2335,1,1040,0,0.335872," ","integrate((B*x+A)*(e*x+d)^3*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{3} c^{3} B + \frac{3}{10} x^{10} e^{2} d c^{3} B + \frac{3}{10} x^{10} e^{3} c^{2} b B + \frac{1}{10} x^{10} e^{3} c^{3} A + \frac{1}{3} x^{9} e d^{2} c^{3} B + x^{9} e^{2} d c^{2} b B + \frac{1}{3} x^{9} e^{3} c b^{2} B + \frac{1}{3} x^{9} e^{3} c^{2} a B + \frac{1}{3} x^{9} e^{2} d c^{3} A + \frac{1}{3} x^{9} e^{3} c^{2} b A + \frac{1}{8} x^{8} d^{3} c^{3} B + \frac{9}{8} x^{8} e d^{2} c^{2} b B + \frac{9}{8} x^{8} e^{2} d c b^{2} B + \frac{1}{8} x^{8} e^{3} b^{3} B + \frac{9}{8} x^{8} e^{2} d c^{2} a B + \frac{3}{4} x^{8} e^{3} c b a B + \frac{3}{8} x^{8} e d^{2} c^{3} A + \frac{9}{8} x^{8} e^{2} d c^{2} b A + \frac{3}{8} x^{8} e^{3} c b^{2} A + \frac{3}{8} x^{8} e^{3} c^{2} a A + \frac{3}{7} x^{7} d^{3} c^{2} b B + \frac{9}{7} x^{7} e d^{2} c b^{2} B + \frac{3}{7} x^{7} e^{2} d b^{3} B + \frac{9}{7} x^{7} e d^{2} c^{2} a B + \frac{18}{7} x^{7} e^{2} d c b a B + \frac{3}{7} x^{7} e^{3} b^{2} a B + \frac{3}{7} x^{7} e^{3} c a^{2} B + \frac{1}{7} x^{7} d^{3} c^{3} A + \frac{9}{7} x^{7} e d^{2} c^{2} b A + \frac{9}{7} x^{7} e^{2} d c b^{2} A + \frac{1}{7} x^{7} e^{3} b^{3} A + \frac{9}{7} x^{7} e^{2} d c^{2} a A + \frac{6}{7} x^{7} e^{3} c b a A + \frac{1}{2} x^{6} d^{3} c b^{2} B + \frac{1}{2} x^{6} e d^{2} b^{3} B + \frac{1}{2} x^{6} d^{3} c^{2} a B + 3 x^{6} e d^{2} c b a B + \frac{3}{2} x^{6} e^{2} d b^{2} a B + \frac{3}{2} x^{6} e^{2} d c a^{2} B + \frac{1}{2} x^{6} e^{3} b a^{2} B + \frac{1}{2} x^{6} d^{3} c^{2} b A + \frac{3}{2} x^{6} e d^{2} c b^{2} A + \frac{1}{2} x^{6} e^{2} d b^{3} A + \frac{3}{2} x^{6} e d^{2} c^{2} a A + 3 x^{6} e^{2} d c b a A + \frac{1}{2} x^{6} e^{3} b^{2} a A + \frac{1}{2} x^{6} e^{3} c a^{2} A + \frac{1}{5} x^{5} d^{3} b^{3} B + \frac{6}{5} x^{5} d^{3} c b a B + \frac{9}{5} x^{5} e d^{2} b^{2} a B + \frac{9}{5} x^{5} e d^{2} c a^{2} B + \frac{9}{5} x^{5} e^{2} d b a^{2} B + \frac{1}{5} x^{5} e^{3} a^{3} B + \frac{3}{5} x^{5} d^{3} c b^{2} A + \frac{3}{5} x^{5} e d^{2} b^{3} A + \frac{3}{5} x^{5} d^{3} c^{2} a A + \frac{18}{5} x^{5} e d^{2} c b a A + \frac{9}{5} x^{5} e^{2} d b^{2} a A + \frac{9}{5} x^{5} e^{2} d c a^{2} A + \frac{3}{5} x^{5} e^{3} b a^{2} A + \frac{3}{4} x^{4} d^{3} b^{2} a B + \frac{3}{4} x^{4} d^{3} c a^{2} B + \frac{9}{4} x^{4} e d^{2} b a^{2} B + \frac{3}{4} x^{4} e^{2} d a^{3} B + \frac{1}{4} x^{4} d^{3} b^{3} A + \frac{3}{2} x^{4} d^{3} c b a A + \frac{9}{4} x^{4} e d^{2} b^{2} a A + \frac{9}{4} x^{4} e d^{2} c a^{2} A + \frac{9}{4} x^{4} e^{2} d b a^{2} A + \frac{1}{4} x^{4} e^{3} a^{3} A + x^{3} d^{3} b a^{2} B + x^{3} e d^{2} a^{3} B + x^{3} d^{3} b^{2} a A + x^{3} d^{3} c a^{2} A + 3 x^{3} e d^{2} b a^{2} A + x^{3} e^{2} d a^{3} A + \frac{1}{2} x^{2} d^{3} a^{3} B + \frac{3}{2} x^{2} d^{3} b a^{2} A + \frac{3}{2} x^{2} e d^{2} a^{3} A + x d^{3} a^{3} A"," ",0,"1/11*x^11*e^3*c^3*B + 3/10*x^10*e^2*d*c^3*B + 3/10*x^10*e^3*c^2*b*B + 1/10*x^10*e^3*c^3*A + 1/3*x^9*e*d^2*c^3*B + x^9*e^2*d*c^2*b*B + 1/3*x^9*e^3*c*b^2*B + 1/3*x^9*e^3*c^2*a*B + 1/3*x^9*e^2*d*c^3*A + 1/3*x^9*e^3*c^2*b*A + 1/8*x^8*d^3*c^3*B + 9/8*x^8*e*d^2*c^2*b*B + 9/8*x^8*e^2*d*c*b^2*B + 1/8*x^8*e^3*b^3*B + 9/8*x^8*e^2*d*c^2*a*B + 3/4*x^8*e^3*c*b*a*B + 3/8*x^8*e*d^2*c^3*A + 9/8*x^8*e^2*d*c^2*b*A + 3/8*x^8*e^3*c*b^2*A + 3/8*x^8*e^3*c^2*a*A + 3/7*x^7*d^3*c^2*b*B + 9/7*x^7*e*d^2*c*b^2*B + 3/7*x^7*e^2*d*b^3*B + 9/7*x^7*e*d^2*c^2*a*B + 18/7*x^7*e^2*d*c*b*a*B + 3/7*x^7*e^3*b^2*a*B + 3/7*x^7*e^3*c*a^2*B + 1/7*x^7*d^3*c^3*A + 9/7*x^7*e*d^2*c^2*b*A + 9/7*x^7*e^2*d*c*b^2*A + 1/7*x^7*e^3*b^3*A + 9/7*x^7*e^2*d*c^2*a*A + 6/7*x^7*e^3*c*b*a*A + 1/2*x^6*d^3*c*b^2*B + 1/2*x^6*e*d^2*b^3*B + 1/2*x^6*d^3*c^2*a*B + 3*x^6*e*d^2*c*b*a*B + 3/2*x^6*e^2*d*b^2*a*B + 3/2*x^6*e^2*d*c*a^2*B + 1/2*x^6*e^3*b*a^2*B + 1/2*x^6*d^3*c^2*b*A + 3/2*x^6*e*d^2*c*b^2*A + 1/2*x^6*e^2*d*b^3*A + 3/2*x^6*e*d^2*c^2*a*A + 3*x^6*e^2*d*c*b*a*A + 1/2*x^6*e^3*b^2*a*A + 1/2*x^6*e^3*c*a^2*A + 1/5*x^5*d^3*b^3*B + 6/5*x^5*d^3*c*b*a*B + 9/5*x^5*e*d^2*b^2*a*B + 9/5*x^5*e*d^2*c*a^2*B + 9/5*x^5*e^2*d*b*a^2*B + 1/5*x^5*e^3*a^3*B + 3/5*x^5*d^3*c*b^2*A + 3/5*x^5*e*d^2*b^3*A + 3/5*x^5*d^3*c^2*a*A + 18/5*x^5*e*d^2*c*b*a*A + 9/5*x^5*e^2*d*b^2*a*A + 9/5*x^5*e^2*d*c*a^2*A + 3/5*x^5*e^3*b*a^2*A + 3/4*x^4*d^3*b^2*a*B + 3/4*x^4*d^3*c*a^2*B + 9/4*x^4*e*d^2*b*a^2*B + 3/4*x^4*e^2*d*a^3*B + 1/4*x^4*d^3*b^3*A + 3/2*x^4*d^3*c*b*a*A + 9/4*x^4*e*d^2*b^2*a*A + 9/4*x^4*e*d^2*c*a^2*A + 9/4*x^4*e^2*d*b*a^2*A + 1/4*x^4*e^3*a^3*A + x^3*d^3*b*a^2*B + x^3*e*d^2*a^3*B + x^3*d^3*b^2*a*A + x^3*d^3*c*a^2*A + 3*x^3*e*d^2*b*a^2*A + x^3*e^2*d*a^3*A + 1/2*x^2*d^3*a^3*B + 3/2*x^2*d^3*b*a^2*A + 3/2*x^2*e*d^2*a^3*A + x*d^3*a^3*A","A",0
2336,1,727,0,0.328663," ","integrate((B*x+A)*(e*x+d)^2*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{2} c^{3} B + \frac{2}{9} x^{9} e d c^{3} B + \frac{1}{3} x^{9} e^{2} c^{2} b B + \frac{1}{9} x^{9} e^{2} c^{3} A + \frac{1}{8} x^{8} d^{2} c^{3} B + \frac{3}{4} x^{8} e d c^{2} b B + \frac{3}{8} x^{8} e^{2} c b^{2} B + \frac{3}{8} x^{8} e^{2} c^{2} a B + \frac{1}{4} x^{8} e d c^{3} A + \frac{3}{8} x^{8} e^{2} c^{2} b A + \frac{3}{7} x^{7} d^{2} c^{2} b B + \frac{6}{7} x^{7} e d c b^{2} B + \frac{1}{7} x^{7} e^{2} b^{3} B + \frac{6}{7} x^{7} e d c^{2} a B + \frac{6}{7} x^{7} e^{2} c b a B + \frac{1}{7} x^{7} d^{2} c^{3} A + \frac{6}{7} x^{7} e d c^{2} b A + \frac{3}{7} x^{7} e^{2} c b^{2} A + \frac{3}{7} x^{7} e^{2} c^{2} a A + \frac{1}{2} x^{6} d^{2} c b^{2} B + \frac{1}{3} x^{6} e d b^{3} B + \frac{1}{2} x^{6} d^{2} c^{2} a B + 2 x^{6} e d c b a B + \frac{1}{2} x^{6} e^{2} b^{2} a B + \frac{1}{2} x^{6} e^{2} c a^{2} B + \frac{1}{2} x^{6} d^{2} c^{2} b A + x^{6} e d c b^{2} A + \frac{1}{6} x^{6} e^{2} b^{3} A + x^{6} e d c^{2} a A + x^{6} e^{2} c b a A + \frac{1}{5} x^{5} d^{2} b^{3} B + \frac{6}{5} x^{5} d^{2} c b a B + \frac{6}{5} x^{5} e d b^{2} a B + \frac{6}{5} x^{5} e d c a^{2} B + \frac{3}{5} x^{5} e^{2} b a^{2} B + \frac{3}{5} x^{5} d^{2} c b^{2} A + \frac{2}{5} x^{5} e d b^{3} A + \frac{3}{5} x^{5} d^{2} c^{2} a A + \frac{12}{5} x^{5} e d c b a A + \frac{3}{5} x^{5} e^{2} b^{2} a A + \frac{3}{5} x^{5} e^{2} c a^{2} A + \frac{3}{4} x^{4} d^{2} b^{2} a B + \frac{3}{4} x^{4} d^{2} c a^{2} B + \frac{3}{2} x^{4} e d b a^{2} B + \frac{1}{4} x^{4} e^{2} a^{3} B + \frac{1}{4} x^{4} d^{2} b^{3} A + \frac{3}{2} x^{4} d^{2} c b a A + \frac{3}{2} x^{4} e d b^{2} a A + \frac{3}{2} x^{4} e d c a^{2} A + \frac{3}{4} x^{4} e^{2} b a^{2} A + x^{3} d^{2} b a^{2} B + \frac{2}{3} x^{3} e d a^{3} B + x^{3} d^{2} b^{2} a A + x^{3} d^{2} c a^{2} A + 2 x^{3} e d b a^{2} A + \frac{1}{3} x^{3} e^{2} a^{3} A + \frac{1}{2} x^{2} d^{2} a^{3} B + \frac{3}{2} x^{2} d^{2} b a^{2} A + x^{2} e d a^{3} A + x d^{2} a^{3} A"," ",0,"1/10*x^10*e^2*c^3*B + 2/9*x^9*e*d*c^3*B + 1/3*x^9*e^2*c^2*b*B + 1/9*x^9*e^2*c^3*A + 1/8*x^8*d^2*c^3*B + 3/4*x^8*e*d*c^2*b*B + 3/8*x^8*e^2*c*b^2*B + 3/8*x^8*e^2*c^2*a*B + 1/4*x^8*e*d*c^3*A + 3/8*x^8*e^2*c^2*b*A + 3/7*x^7*d^2*c^2*b*B + 6/7*x^7*e*d*c*b^2*B + 1/7*x^7*e^2*b^3*B + 6/7*x^7*e*d*c^2*a*B + 6/7*x^7*e^2*c*b*a*B + 1/7*x^7*d^2*c^3*A + 6/7*x^7*e*d*c^2*b*A + 3/7*x^7*e^2*c*b^2*A + 3/7*x^7*e^2*c^2*a*A + 1/2*x^6*d^2*c*b^2*B + 1/3*x^6*e*d*b^3*B + 1/2*x^6*d^2*c^2*a*B + 2*x^6*e*d*c*b*a*B + 1/2*x^6*e^2*b^2*a*B + 1/2*x^6*e^2*c*a^2*B + 1/2*x^6*d^2*c^2*b*A + x^6*e*d*c*b^2*A + 1/6*x^6*e^2*b^3*A + x^6*e*d*c^2*a*A + x^6*e^2*c*b*a*A + 1/5*x^5*d^2*b^3*B + 6/5*x^5*d^2*c*b*a*B + 6/5*x^5*e*d*b^2*a*B + 6/5*x^5*e*d*c*a^2*B + 3/5*x^5*e^2*b*a^2*B + 3/5*x^5*d^2*c*b^2*A + 2/5*x^5*e*d*b^3*A + 3/5*x^5*d^2*c^2*a*A + 12/5*x^5*e*d*c*b*a*A + 3/5*x^5*e^2*b^2*a*A + 3/5*x^5*e^2*c*a^2*A + 3/4*x^4*d^2*b^2*a*B + 3/4*x^4*d^2*c*a^2*B + 3/2*x^4*e*d*b*a^2*B + 1/4*x^4*e^2*a^3*B + 1/4*x^4*d^2*b^3*A + 3/2*x^4*d^2*c*b*a*A + 3/2*x^4*e*d*b^2*a*A + 3/2*x^4*e*d*c*a^2*A + 3/4*x^4*e^2*b*a^2*A + x^3*d^2*b*a^2*B + 2/3*x^3*e*d*a^3*B + x^3*d^2*b^2*a*A + x^3*d^2*c*a^2*A + 2*x^3*e*d*b*a^2*A + 1/3*x^3*e^2*a^3*A + 1/2*x^2*d^2*a^3*B + 3/2*x^2*d^2*b*a^2*A + x^2*e*d*a^3*A + x*d^2*a^3*A","A",0
2337,1,417,0,0.347588," ","integrate((B*x+A)*(e*x+d)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e c^{3} B + \frac{1}{8} x^{8} d c^{3} B + \frac{3}{8} x^{8} e c^{2} b B + \frac{1}{8} x^{8} e c^{3} A + \frac{3}{7} x^{7} d c^{2} b B + \frac{3}{7} x^{7} e c b^{2} B + \frac{3}{7} x^{7} e c^{2} a B + \frac{1}{7} x^{7} d c^{3} A + \frac{3}{7} x^{7} e c^{2} b A + \frac{1}{2} x^{6} d c b^{2} B + \frac{1}{6} x^{6} e b^{3} B + \frac{1}{2} x^{6} d c^{2} a B + x^{6} e c b a B + \frac{1}{2} x^{6} d c^{2} b A + \frac{1}{2} x^{6} e c b^{2} A + \frac{1}{2} x^{6} e c^{2} a A + \frac{1}{5} x^{5} d b^{3} B + \frac{6}{5} x^{5} d c b a B + \frac{3}{5} x^{5} e b^{2} a B + \frac{3}{5} x^{5} e c a^{2} B + \frac{3}{5} x^{5} d c b^{2} A + \frac{1}{5} x^{5} e b^{3} A + \frac{3}{5} x^{5} d c^{2} a A + \frac{6}{5} x^{5} e c b a A + \frac{3}{4} x^{4} d b^{2} a B + \frac{3}{4} x^{4} d c a^{2} B + \frac{3}{4} x^{4} e b a^{2} B + \frac{1}{4} x^{4} d b^{3} A + \frac{3}{2} x^{4} d c b a A + \frac{3}{4} x^{4} e b^{2} a A + \frac{3}{4} x^{4} e c a^{2} A + x^{3} d b a^{2} B + \frac{1}{3} x^{3} e a^{3} B + x^{3} d b^{2} a A + x^{3} d c a^{2} A + x^{3} e b a^{2} A + \frac{1}{2} x^{2} d a^{3} B + \frac{3}{2} x^{2} d b a^{2} A + \frac{1}{2} x^{2} e a^{3} A + x d a^{3} A"," ",0,"1/9*x^9*e*c^3*B + 1/8*x^8*d*c^3*B + 3/8*x^8*e*c^2*b*B + 1/8*x^8*e*c^3*A + 3/7*x^7*d*c^2*b*B + 3/7*x^7*e*c*b^2*B + 3/7*x^7*e*c^2*a*B + 1/7*x^7*d*c^3*A + 3/7*x^7*e*c^2*b*A + 1/2*x^6*d*c*b^2*B + 1/6*x^6*e*b^3*B + 1/2*x^6*d*c^2*a*B + x^6*e*c*b*a*B + 1/2*x^6*d*c^2*b*A + 1/2*x^6*e*c*b^2*A + 1/2*x^6*e*c^2*a*A + 1/5*x^5*d*b^3*B + 6/5*x^5*d*c*b*a*B + 3/5*x^5*e*b^2*a*B + 3/5*x^5*e*c*a^2*B + 3/5*x^5*d*c*b^2*A + 1/5*x^5*e*b^3*A + 3/5*x^5*d*c^2*a*A + 6/5*x^5*e*c*b*a*A + 3/4*x^4*d*b^2*a*B + 3/4*x^4*d*c*a^2*B + 3/4*x^4*e*b*a^2*B + 1/4*x^4*d*b^3*A + 3/2*x^4*d*c*b*a*A + 3/4*x^4*e*b^2*a*A + 3/4*x^4*e*c*a^2*A + x^3*d*b*a^2*B + 1/3*x^3*e*a^3*B + x^3*d*b^2*a*A + x^3*d*c*a^2*A + x^3*e*b*a^2*A + 1/2*x^2*d*a^3*B + 3/2*x^2*d*b*a^2*A + 1/2*x^2*e*a^3*A + x*d*a^3*A","A",0
2338,1,187,0,0.353740," ","integrate((B*x+A)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{3} B + \frac{3}{7} x^{7} c^{2} b B + \frac{1}{7} x^{7} c^{3} A + \frac{1}{2} x^{6} c b^{2} B + \frac{1}{2} x^{6} c^{2} a B + \frac{1}{2} x^{6} c^{2} b A + \frac{1}{5} x^{5} b^{3} B + \frac{6}{5} x^{5} c b a B + \frac{3}{5} x^{5} c b^{2} A + \frac{3}{5} x^{5} c^{2} a A + \frac{3}{4} x^{4} b^{2} a B + \frac{3}{4} x^{4} c a^{2} B + \frac{1}{4} x^{4} b^{3} A + \frac{3}{2} x^{4} c b a A + x^{3} b a^{2} B + x^{3} b^{2} a A + x^{3} c a^{2} A + \frac{1}{2} x^{2} a^{3} B + \frac{3}{2} x^{2} b a^{2} A + x a^{3} A"," ",0,"1/8*x^8*c^3*B + 3/7*x^7*c^2*b*B + 1/7*x^7*c^3*A + 1/2*x^6*c*b^2*B + 1/2*x^6*c^2*a*B + 1/2*x^6*c^2*b*A + 1/5*x^5*b^3*B + 6/5*x^5*c*b*a*B + 3/5*x^5*c*b^2*A + 3/5*x^5*c^2*a*A + 3/4*x^4*b^2*a*B + 3/4*x^4*c*a^2*B + 1/4*x^4*b^3*A + 3/2*x^4*c*b*a*A + x^3*b*a^2*B + x^3*b^2*a*A + x^3*c*a^2*A + 1/2*x^2*a^3*B + 3/2*x^2*b*a^2*A + x*a^3*A","A",0
2339,1,843,0,0.391516," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d),x, algorithm=""fricas"")","\frac{60 \, B c^{3} e^{7} x^{7} - 70 \, {\left(B c^{3} d e^{6} - {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 84 \, {\left(B c^{3} d^{2} e^{5} - {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} - 105 \, {\left(B c^{3} d^{3} e^{4} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} + 140 \, {\left(B c^{3} d^{4} e^{3} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} - 210 \, {\left(B c^{3} d^{5} e^{2} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} - 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} + 420 \, {\left(B c^{3} d^{6} e - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} - 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x - 420 \, {\left(B c^{3} d^{7} - A a^{3} e^{7} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} - 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6}\right)} \log\left(e x + d\right)}{420 \, e^{8}}"," ",0,"1/420*(60*B*c^3*e^7*x^7 - 70*(B*c^3*d*e^6 - (3*B*b*c^2 + A*c^3)*e^7)*x^6 + 84*(B*c^3*d^2*e^5 - (3*B*b*c^2 + A*c^3)*d*e^6 + 3*(B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 - 105*(B*c^3*d^3*e^4 - (3*B*b*c^2 + A*c^3)*d^2*e^5 + 3*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 140*(B*c^3*d^4*e^3 - (3*B*b*c^2 + A*c^3)*d^3*e^4 + 3*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 - 210*(B*c^3*d^5*e^2 - (3*B*b*c^2 + A*c^3)*d^4*e^3 + 3*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 - 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 420*(B*c^3*d^6*e - (3*B*b*c^2 + A*c^3)*d^5*e^2 + 3*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 - 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 + (B*a^3 + 3*A*a^2*b)*e^7)*x - 420*(B*c^3*d^7 - A*a^3*e^7 - (3*B*b*c^2 + A*c^3)*d^6*e + 3*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 + (B*a^3 + 3*A*a^2*b)*d*e^6)*log(e*x + d))/e^8","A",0
2340,1,1189,0,0.402038," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{10 \, B c^{3} e^{7} x^{7} + 60 \, B c^{3} d^{7} - 60 \, A a^{3} e^{7} - 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 180 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - 60 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + 60 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} - 180 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} + 60 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} - 2 \, {\left(7 \, B c^{3} d e^{6} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 3 \, {\left(7 \, B c^{3} d^{2} e^{5} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} - 5 \, {\left(7 \, B c^{3} d^{3} e^{4} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} + 10 \, {\left(7 \, B c^{3} d^{4} e^{3} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} - 30 \, {\left(7 \, B c^{3} d^{5} e^{2} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} - 6 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} - 60 \, {\left(6 \, B c^{3} d^{6} e - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 12 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - 3 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + 2 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} - 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6}\right)} x + 60 \, {\left(7 \, B c^{3} d^{7} - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} - 6 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} + {\left(7 \, B c^{3} d^{6} e - 6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} - 6 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"1/60*(10*B*c^3*e^7*x^7 + 60*B*c^3*d^7 - 60*A*a^3*e^7 - 60*(3*B*b*c^2 + A*c^3)*d^6*e + 180*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - 60*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + 60*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - 180*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 + 60*(B*a^3 + 3*A*a^2*b)*d*e^6 - 2*(7*B*c^3*d*e^6 - 6*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 3*(7*B*c^3*d^2*e^5 - 6*(3*B*b*c^2 + A*c^3)*d*e^6 + 15*(B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 - 5*(7*B*c^3*d^3*e^4 - 6*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 10*(7*B*c^3*d^4*e^3 - 6*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 - 30*(7*B*c^3*d^5*e^2 - 6*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 - 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 - 60*(6*B*c^3*d^6*e - 5*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 12*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 3*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + 2*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 - 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6)*x + 60*(7*B*c^3*d^7 - 6*(3*B*b*c^2 + A*c^3)*d^6*e + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 + (B*a^3 + 3*A*a^2*b)*d*e^6 + (7*B*c^3*d^6*e - 6*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 - 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 + (B*a^3 + 3*A*a^2*b)*e^7)*x)*log(e*x + d))/(e^9*x + d*e^8)","B",0
2341,1,1311,0,0.403382," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{4 \, B c^{3} e^{7} x^{7} - 130 \, B c^{3} d^{7} - 10 \, A a^{3} e^{7} + 110 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e - 270 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} + 70 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} - 50 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} + 90 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} - 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} - {\left(7 \, B c^{3} d e^{6} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 2 \, {\left(7 \, B c^{3} d^{2} e^{5} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 10 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} - 5 \, {\left(7 \, B c^{3} d^{3} e^{4} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 10 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} - 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} + 20 \, {\left(7 \, B c^{3} d^{4} e^{3} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 10 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} + 10 \, {\left(50 \, B c^{3} d^{5} e^{2} - 34 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 63 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} - 11 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + 4 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6}\right)} x^{2} + 20 \, {\left(8 \, B c^{3} d^{6} e - 4 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} - 2 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} + 6 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x - 60 \, {\left(7 \, B c^{3} d^{7} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 10 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} - {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} + {\left(7 \, B c^{3} d^{5} e^{2} - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 10 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} - 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} - {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} + 2 \, {\left(7 \, B c^{3} d^{6} e - 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 10 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} - {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"1/20*(4*B*c^3*e^7*x^7 - 130*B*c^3*d^7 - 10*A*a^3*e^7 + 110*(3*B*b*c^2 + A*c^3)*d^6*e - 270*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 + 70*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 - 50*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 + 90*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 - 10*(B*a^3 + 3*A*a^2*b)*d*e^6 - (7*B*c^3*d*e^6 - 5*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 2*(7*B*c^3*d^2*e^5 - 5*(3*B*b*c^2 + A*c^3)*d*e^6 + 10*(B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 - 5*(7*B*c^3*d^3*e^4 - 5*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 10*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 - 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 20*(7*B*c^3*d^4*e^3 - 5*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 10*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 + 10*(50*B*c^3*d^5*e^2 - 34*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 63*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - 11*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + 4*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6)*x^2 + 20*(8*B*c^3*d^6*e - 4*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 3*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 - 2*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 + 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 - (B*a^3 + 3*A*a^2*b)*e^7)*x - 60*(7*B*c^3*d^7 - 5*(3*B*b*c^2 + A*c^3)*d^6*e + 10*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - (B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 + (7*B*c^3*d^5*e^2 - 5*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 10*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 - (B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 2*(7*B*c^3*d^6*e - 5*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 10*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 - (B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6)*x)*log(e*x + d))/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","B",0
2342,1,1369,0,0.420139," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, B c^{3} e^{7} x^{7} + 214 \, B c^{3} d^{7} - 4 \, A a^{3} e^{7} - 148 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 282 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - 52 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + 22 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} - 12 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} - 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} - {\left(7 \, B c^{3} d e^{6} - 4 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 3 \, {\left(7 \, B c^{3} d^{2} e^{5} - 4 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 6 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} - 3 \, {\left(35 \, B c^{3} d^{3} e^{4} - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} - 2 \, {\left(278 \, B c^{3} d^{4} e^{3} - 146 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 189 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} - 18 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6}\right)} x^{3} - 6 \, {\left(68 \, B c^{3} d^{5} e^{2} - 26 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 9 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} + 6 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} - 6 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} + 6 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} + 6 \, {\left(37 \, B c^{3} d^{6} e - 34 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 81 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - 18 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + 9 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} - 6 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x + 12 \, {\left(35 \, B c^{3} d^{7} - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} + {\left(35 \, B c^{3} d^{4} e^{3} - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} + 3 \, {\left(35 \, B c^{3} d^{5} e^{2} - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6}\right)} x^{2} + 3 \, {\left(35 \, B c^{3} d^{6} e - 20 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right)}}"," ",0,"1/12*(3*B*c^3*e^7*x^7 + 214*B*c^3*d^7 - 4*A*a^3*e^7 - 148*(3*B*b*c^2 + A*c^3)*d^6*e + 282*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - 52*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + 22*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - 12*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 - 2*(B*a^3 + 3*A*a^2*b)*d*e^6 - (7*B*c^3*d*e^6 - 4*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 3*(7*B*c^3*d^2*e^5 - 4*(3*B*b*c^2 + A*c^3)*d*e^6 + 6*(B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 - 3*(35*B*c^3*d^3*e^4 - 20*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 - 2*(278*B*c^3*d^4*e^3 - 146*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 189*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - 18*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6)*x^3 - 6*(68*B*c^3*d^5*e^2 - 26*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 9*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 + 6*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 - 6*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 + 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 6*(37*B*c^3*d^6*e - 34*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 81*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 18*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + 9*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 - 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 - (B*a^3 + 3*A*a^2*b)*e^7)*x + 12*(35*B*c^3*d^7 - 20*(3*B*b*c^2 + A*c^3)*d^6*e + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 + (35*B*c^3*d^4*e^3 - 20*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 + 3*(35*B*c^3*d^5*e^2 - 20*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6)*x^2 + 3*(35*B*c^3*d^6*e - 20*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5)*x)*log(e*x + d))/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8)","B",0
2343,1,1343,0,0.395675," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^5,x, algorithm=""fricas"")","\frac{4 \, B c^{3} e^{7} x^{7} - 319 \, B c^{3} d^{7} - 3 \, A a^{3} e^{7} + 171 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e - 231 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} + 25 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} - 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} - 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} - 2 \, {\left(7 \, B c^{3} d e^{6} - 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 12 \, {\left(7 \, B c^{3} d^{2} e^{5} - 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} + 4 \, {\left(139 \, B c^{3} d^{3} e^{4} - 51 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 36 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6}\right)} x^{4} + 4 \, {\left(136 \, B c^{3} d^{4} e^{3} - 24 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} - 36 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} + 12 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} - 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} - 6 \, {\left(74 \, B c^{3} d^{5} e^{2} - 66 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 126 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} - 18 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} + 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} - 4 \, {\left(214 \, B c^{3} d^{6} e - 126 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 186 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - 22 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} + 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x - 12 \, {\left(35 \, B c^{3} d^{7} - 15 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + {\left(35 \, B c^{3} d^{3} e^{4} - 15 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} + 4 \, {\left(35 \, B c^{3} d^{4} e^{3} - 15 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6}\right)} x^{3} + 6 \, {\left(35 \, B c^{3} d^{5} e^{2} - 15 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5}\right)} x^{2} + 4 \, {\left(35 \, B c^{3} d^{6} e - 15 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{12} x^{4} + 4 \, d e^{11} x^{3} + 6 \, d^{2} e^{10} x^{2} + 4 \, d^{3} e^{9} x + d^{4} e^{8}\right)}}"," ",0,"1/12*(4*B*c^3*e^7*x^7 - 319*B*c^3*d^7 - 3*A*a^3*e^7 + 171*(3*B*b*c^2 + A*c^3)*d^6*e - 231*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 + 25*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 - 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 - (B*a^3 + 3*A*a^2*b)*d*e^6 - 2*(7*B*c^3*d*e^6 - 3*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 12*(7*B*c^3*d^2*e^5 - 3*(3*B*b*c^2 + A*c^3)*d*e^6 + 3*(B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 + 4*(139*B*c^3*d^3*e^4 - 51*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 36*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6)*x^4 + 4*(136*B*c^3*d^4*e^3 - 24*(3*B*b*c^2 + A*c^3)*d^3*e^4 - 36*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 + 12*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 - 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 - 6*(74*B*c^3*d^5*e^2 - 66*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 126*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - 18*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 + 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 - 4*(214*B*c^3*d^6*e - 126*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 186*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 22*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 + 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 + (B*a^3 + 3*A*a^2*b)*e^7)*x - 12*(35*B*c^3*d^7 - 15*(3*B*b*c^2 + A*c^3)*d^6*e + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + (35*B*c^3*d^3*e^4 - 15*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 4*(35*B*c^3*d^4*e^3 - 15*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6)*x^3 + 6*(35*B*c^3*d^5*e^2 - 15*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5)*x^2 + 4*(35*B*c^3*d^6*e - 15*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4)*x)*log(e*x + d))/(e^12*x^4 + 4*d*e^11*x^3 + 6*d^2*e^10*x^2 + 4*d^3*e^9*x + d^4*e^8)","B",0
2344,1,1247,0,0.401183," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^6,x, algorithm=""fricas"")","\frac{10 \, B c^{3} e^{7} x^{7} + 459 \, B c^{3} d^{7} - 4 \, A a^{3} e^{7} - 174 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 137 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} - {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} - 2 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} - 10 \, {\left(7 \, B c^{3} d e^{6} - 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} - 100 \, {\left(5 \, B c^{3} d^{2} e^{5} - {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6}\right)} x^{5} - 20 \, {\left(20 \, B c^{3} d^{3} e^{4} + 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} - 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} + 10 \, {\left(130 \, B c^{3} d^{4} e^{3} - 80 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 90 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} - {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} + 10 \, {\left(270 \, B c^{3} d^{5} e^{2} - 120 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 110 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} - {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} - 2 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} + 5 \, {\left(375 \, B c^{3} d^{6} e - 150 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 125 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} - {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} - 2 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x + 60 \, {\left(7 \, B c^{3} d^{7} - 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} + {\left(7 \, B c^{3} d^{2} e^{5} - 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} + 5 \, {\left(7 \, B c^{3} d^{3} e^{4} - 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6}\right)} x^{4} + 10 \, {\left(7 \, B c^{3} d^{4} e^{3} - 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5}\right)} x^{3} + 10 \, {\left(7 \, B c^{3} d^{5} e^{2} - 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4}\right)} x^{2} + 5 \, {\left(7 \, B c^{3} d^{6} e - 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{13} x^{5} + 5 \, d e^{12} x^{4} + 10 \, d^{2} e^{11} x^{3} + 10 \, d^{3} e^{10} x^{2} + 5 \, d^{4} e^{9} x + d^{5} e^{8}\right)}}"," ",0,"1/20*(10*B*c^3*e^7*x^7 + 459*B*c^3*d^7 - 4*A*a^3*e^7 - 174*(3*B*b*c^2 + A*c^3)*d^6*e + 137*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 - (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - 2*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 - (B*a^3 + 3*A*a^2*b)*d*e^6 - 10*(7*B*c^3*d*e^6 - 2*(3*B*b*c^2 + A*c^3)*e^7)*x^6 - 100*(5*B*c^3*d^2*e^5 - (3*B*b*c^2 + A*c^3)*d*e^6)*x^5 - 20*(20*B*c^3*d^3*e^4 + 5*(3*B*b*c^2 + A*c^3)*d^2*e^5 - 15*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 10*(130*B*c^3*d^4*e^3 - 80*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 90*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 - (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 + 10*(270*B*c^3*d^5*e^2 - 120*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 110*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 - (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 - 2*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 5*(375*B*c^3*d^6*e - 150*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 125*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 - (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 - 2*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 - (B*a^3 + 3*A*a^2*b)*e^7)*x + 60*(7*B*c^3*d^7 - 2*(3*B*b*c^2 + A*c^3)*d^6*e + (B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 + (7*B*c^3*d^2*e^5 - 2*(3*B*b*c^2 + A*c^3)*d*e^6 + (B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 + 5*(7*B*c^3*d^3*e^4 - 2*(3*B*b*c^2 + A*c^3)*d^2*e^5 + (B*b^2*c + (B*a + A*b)*c^2)*d*e^6)*x^4 + 10*(7*B*c^3*d^4*e^3 - 2*(3*B*b*c^2 + A*c^3)*d^3*e^4 + (B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5)*x^3 + 10*(7*B*c^3*d^5*e^2 - 2*(3*B*b*c^2 + A*c^3)*d^4*e^3 + (B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4)*x^2 + 5*(7*B*c^3*d^6*e - 2*(3*B*b*c^2 + A*c^3)*d^5*e^2 + (B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3)*x)*log(e*x + d))/(e^13*x^5 + 5*d*e^12*x^4 + 10*d^2*e^11*x^3 + 10*d^3*e^10*x^2 + 5*d^4*e^9*x + d^5*e^8)","B",0
2345,1,1145,0,0.393874," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^7,x, algorithm=""fricas"")","\frac{60 \, B c^{3} e^{7} x^{7} + 360 \, B c^{3} d e^{6} x^{6} - 669 \, B c^{3} d^{7} - 10 \, A a^{3} e^{7} + 147 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e - 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} - {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} - 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} - 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} - 180 \, {\left(2 \, B c^{3} d^{2} e^{5} - 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} - 30 \, {\left(135 \, B c^{3} d^{3} e^{4} - 45 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} - 20 \, {\left(410 \, B c^{3} d^{4} e^{3} - 110 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} + 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} - 15 \, {\left(515 \, B c^{3} d^{5} e^{2} - 125 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} + 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} + 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} - 6 \, {\left(599 \, B c^{3} d^{6} e - 137 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} + 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} + 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x - 60 \, {\left(7 \, B c^{3} d^{7} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + {\left(7 \, B c^{3} d e^{6} - {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 6 \, {\left(7 \, B c^{3} d^{2} e^{5} - {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6}\right)} x^{5} + 15 \, {\left(7 \, B c^{3} d^{3} e^{4} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5}\right)} x^{4} + 20 \, {\left(7 \, B c^{3} d^{4} e^{3} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4}\right)} x^{3} + 15 \, {\left(7 \, B c^{3} d^{5} e^{2} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3}\right)} x^{2} + 6 \, {\left(7 \, B c^{3} d^{6} e - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{14} x^{6} + 6 \, d e^{13} x^{5} + 15 \, d^{2} e^{12} x^{4} + 20 \, d^{3} e^{11} x^{3} + 15 \, d^{4} e^{10} x^{2} + 6 \, d^{5} e^{9} x + d^{6} e^{8}\right)}}"," ",0,"1/60*(60*B*c^3*e^7*x^7 + 360*B*c^3*d*e^6*x^6 - 669*B*c^3*d^7 - 10*A*a^3*e^7 + 147*(3*B*b*c^2 + A*c^3)*d^6*e - 30*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 - (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 - 2*(B*a^3 + 3*A*a^2*b)*d*e^6 - 180*(2*B*c^3*d^2*e^5 - 2*(3*B*b*c^2 + A*c^3)*d*e^6 + (B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 - 30*(135*B*c^3*d^3*e^4 - 45*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 - 20*(410*B*c^3*d^4*e^3 - 110*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 + 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 - 15*(515*B*c^3*d^5*e^2 - 125*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 + 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 + 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 - 6*(599*B*c^3*d^6*e - 137*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 30*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 + 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 + 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 + 2*(B*a^3 + 3*A*a^2*b)*e^7)*x - 60*(7*B*c^3*d^7 - (3*B*b*c^2 + A*c^3)*d^6*e + (7*B*c^3*d*e^6 - (3*B*b*c^2 + A*c^3)*e^7)*x^6 + 6*(7*B*c^3*d^2*e^5 - (3*B*b*c^2 + A*c^3)*d*e^6)*x^5 + 15*(7*B*c^3*d^3*e^4 - (3*B*b*c^2 + A*c^3)*d^2*e^5)*x^4 + 20*(7*B*c^3*d^4*e^3 - (3*B*b*c^2 + A*c^3)*d^3*e^4)*x^3 + 15*(7*B*c^3*d^5*e^2 - (3*B*b*c^2 + A*c^3)*d^4*e^3)*x^2 + 6*(7*B*c^3*d^6*e - (3*B*b*c^2 + A*c^3)*d^5*e^2)*x)*log(e*x + d))/(e^14*x^6 + 6*d*e^13*x^5 + 15*d^2*e^12*x^4 + 20*d^3*e^11*x^3 + 15*d^4*e^10*x^2 + 6*d^5*e^9*x + d^6*e^8)","B",0
2346,1,1023,0,0.391474," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^8,x, algorithm=""fricas"")","\frac{1089 \, B c^{3} d^{7} - 60 \, A a^{3} e^{7} - 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e - 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} - 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} - 12 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} - 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} + 420 \, {\left(7 \, B c^{3} d e^{6} - {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 630 \, {\left(21 \, B c^{3} d^{2} e^{5} - 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} - {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} + 70 \, {\left(385 \, B c^{3} d^{3} e^{4} - 30 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} - 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} - 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} + 35 \, {\left(875 \, B c^{3} d^{4} e^{3} - 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} - 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} - 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} + 21 \, {\left(959 \, B c^{3} d^{5} e^{2} - 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} - 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} - 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} - 12 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} + 7 \, {\left(1029 \, B c^{3} d^{6} e - 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} - 30 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} - 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} - 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} - 12 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} - 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x + 420 \, {\left(B c^{3} e^{7} x^{7} + 7 \, B c^{3} d e^{6} x^{6} + 21 \, B c^{3} d^{2} e^{5} x^{5} + 35 \, B c^{3} d^{3} e^{4} x^{4} + 35 \, B c^{3} d^{4} e^{3} x^{3} + 21 \, B c^{3} d^{5} e^{2} x^{2} + 7 \, B c^{3} d^{6} e x + B c^{3} d^{7}\right)} \log\left(e x + d\right)}{420 \, {\left(e^{15} x^{7} + 7 \, d e^{14} x^{6} + 21 \, d^{2} e^{13} x^{5} + 35 \, d^{3} e^{12} x^{4} + 35 \, d^{4} e^{11} x^{3} + 21 \, d^{5} e^{10} x^{2} + 7 \, d^{6} e^{9} x + d^{7} e^{8}\right)}}"," ",0,"1/420*(1089*B*c^3*d^7 - 60*A*a^3*e^7 - 60*(3*B*b*c^2 + A*c^3)*d^6*e - 30*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 - 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 - 12*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 - 10*(B*a^3 + 3*A*a^2*b)*d*e^6 + 420*(7*B*c^3*d*e^6 - (3*B*b*c^2 + A*c^3)*e^7)*x^6 + 630*(21*B*c^3*d^2*e^5 - 2*(3*B*b*c^2 + A*c^3)*d*e^6 - (B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 + 70*(385*B*c^3*d^3*e^4 - 30*(3*B*b*c^2 + A*c^3)*d^2*e^5 - 15*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 - 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 35*(875*B*c^3*d^4*e^3 - 60*(3*B*b*c^2 + A*c^3)*d^3*e^4 - 30*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 - 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 + 21*(959*B*c^3*d^5*e^2 - 60*(3*B*b*c^2 + A*c^3)*d^4*e^3 - 30*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 - 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 - 12*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 7*(1029*B*c^3*d^6*e - 60*(3*B*b*c^2 + A*c^3)*d^5*e^2 - 30*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 - 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 - 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 - 12*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 - 10*(B*a^3 + 3*A*a^2*b)*e^7)*x + 420*(B*c^3*e^7*x^7 + 7*B*c^3*d*e^6*x^6 + 21*B*c^3*d^2*e^5*x^5 + 35*B*c^3*d^3*e^4*x^4 + 35*B*c^3*d^4*e^3*x^3 + 21*B*c^3*d^5*e^2*x^2 + 7*B*c^3*d^6*e*x + B*c^3*d^7)*log(e*x + d))/(e^15*x^7 + 7*d*e^14*x^6 + 21*d^2*e^13*x^5 + 35*d^3*e^12*x^4 + 35*d^4*e^11*x^3 + 21*d^5*e^10*x^2 + 7*d^6*e^9*x + d^7*e^8)","A",0
2347,1,922,0,0.382508," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{280 \, B c^{3} e^{7} x^{7} + 35 \, B c^{3} d^{7} + 35 \, A a^{3} e^{7} + 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 5 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} + 5 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} + 140 \, {\left(7 \, B c^{3} d e^{6} + {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 280 \, {\left(7 \, B c^{3} d^{2} e^{5} + {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} + 70 \, {\left(35 \, B c^{3} d^{3} e^{4} + 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 5 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} + 56 \, {\left(35 \, B c^{3} d^{4} e^{3} + 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 5 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} + 28 \, {\left(35 \, B c^{3} d^{5} e^{2} + 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 5 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} + 5 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} + 8 \, {\left(35 \, B c^{3} d^{6} e + 5 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 5 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} + 5 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x}{280 \, {\left(e^{16} x^{8} + 8 \, d e^{15} x^{7} + 28 \, d^{2} e^{14} x^{6} + 56 \, d^{3} e^{13} x^{5} + 70 \, d^{4} e^{12} x^{4} + 56 \, d^{5} e^{11} x^{3} + 28 \, d^{6} e^{10} x^{2} + 8 \, d^{7} e^{9} x + d^{8} e^{8}\right)}}"," ",0,"-1/280*(280*B*c^3*e^7*x^7 + 35*B*c^3*d^7 + 35*A*a^3*e^7 + 5*(3*B*b*c^2 + A*c^3)*d^6*e + 5*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 + 5*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 + 5*(B*a^3 + 3*A*a^2*b)*d*e^6 + 140*(7*B*c^3*d*e^6 + (3*B*b*c^2 + A*c^3)*e^7)*x^6 + 280*(7*B*c^3*d^2*e^5 + (3*B*b*c^2 + A*c^3)*d*e^6 + (B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 + 70*(35*B*c^3*d^3*e^4 + 5*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 5*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 56*(35*B*c^3*d^4*e^3 + 5*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 5*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 + 28*(35*B*c^3*d^5*e^2 + 5*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 5*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 + 5*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 8*(35*B*c^3*d^6*e + 5*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 5*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 + 5*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 + 5*(B*a^3 + 3*A*a^2*b)*e^7)*x)/(e^16*x^8 + 8*d*e^15*x^7 + 28*d^2*e^14*x^6 + 56*d^3*e^13*x^5 + 70*d^4*e^12*x^4 + 56*d^5*e^11*x^3 + 28*d^6*e^10*x^2 + 8*d^7*e^9*x + d^8*e^8)","A",0
2348,1,945,0,0.388750," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{1260 \, B c^{3} e^{7} x^{7} + 35 \, B c^{3} d^{7} + 280 \, A a^{3} e^{7} + 10 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} + 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + 5 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} + 30 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} + 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} + 420 \, {\left(7 \, B c^{3} d e^{6} + 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 630 \, {\left(7 \, B c^{3} d^{2} e^{5} + 2 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} + 126 \, {\left(35 \, B c^{3} d^{3} e^{4} + 10 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} + 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} + 84 \, {\left(35 \, B c^{3} d^{4} e^{3} + 10 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} + 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} + 5 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} + 36 \, {\left(35 \, B c^{3} d^{5} e^{2} + 10 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} + 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + 5 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} + 30 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} + 9 \, {\left(35 \, B c^{3} d^{6} e + 10 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} + 4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + 5 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} + 30 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} + 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x}{2520 \, {\left(e^{17} x^{9} + 9 \, d e^{16} x^{8} + 36 \, d^{2} e^{15} x^{7} + 84 \, d^{3} e^{14} x^{6} + 126 \, d^{4} e^{13} x^{5} + 126 \, d^{5} e^{12} x^{4} + 84 \, d^{6} e^{11} x^{3} + 36 \, d^{7} e^{10} x^{2} + 9 \, d^{8} e^{9} x + d^{9} e^{8}\right)}}"," ",0,"-1/2520*(1260*B*c^3*e^7*x^7 + 35*B*c^3*d^7 + 280*A*a^3*e^7 + 10*(3*B*b*c^2 + A*c^3)*d^6*e + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 + 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + 5*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 + 30*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 + 35*(B*a^3 + 3*A*a^2*b)*d*e^6 + 420*(7*B*c^3*d*e^6 + 2*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 630*(7*B*c^3*d^2*e^5 + 2*(3*B*b*c^2 + A*c^3)*d*e^6 + 3*(B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 + 126*(35*B*c^3*d^3*e^4 + 10*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 + 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 84*(35*B*c^3*d^4*e^3 + 10*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 + 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 + 5*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 + 36*(35*B*c^3*d^5*e^2 + 10*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 + 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + 5*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 + 30*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 9*(35*B*c^3*d^6*e + 10*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 15*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 + 4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + 5*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 + 30*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 + 35*(B*a^3 + 3*A*a^2*b)*e^7)*x)/(e^17*x^9 + 9*d*e^16*x^8 + 36*d^2*e^15*x^7 + 84*d^3*e^14*x^6 + 126*d^4*e^13*x^5 + 126*d^5*e^12*x^4 + 84*d^6*e^11*x^3 + 36*d^7*e^10*x^2 + 9*d^8*e^9*x + d^9*e^8)","A",0
2349,1,956,0,0.386060," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{840 \, B c^{3} e^{7} x^{7} + 7 \, B c^{3} d^{7} + 252 \, A a^{3} e^{7} + 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e + 6 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{2} + 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{4} + 21 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{5} + 28 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6} + 210 \, {\left(7 \, B c^{3} d e^{6} + 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} + 252 \, {\left(7 \, B c^{3} d^{2} e^{5} + 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{6} + 6 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{7}\right)} x^{5} + 210 \, {\left(7 \, B c^{3} d^{3} e^{4} + 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{5} + 6 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{6} + 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{7}\right)} x^{4} + 120 \, {\left(7 \, B c^{3} d^{4} e^{3} + 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{4} + 6 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{5} + 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{6} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{7}\right)} x^{3} + 45 \, {\left(7 \, B c^{3} d^{5} e^{2} + 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{3} + 6 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{4} + 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{5} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{6} + 21 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{7}\right)} x^{2} + 10 \, {\left(7 \, B c^{3} d^{6} e + 3 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{2} + 6 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{3} + 2 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{4} + 3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{5} + 21 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{6} + 28 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x}{2520 \, {\left(e^{18} x^{10} + 10 \, d e^{17} x^{9} + 45 \, d^{2} e^{16} x^{8} + 120 \, d^{3} e^{15} x^{7} + 210 \, d^{4} e^{14} x^{6} + 252 \, d^{5} e^{13} x^{5} + 210 \, d^{6} e^{12} x^{4} + 120 \, d^{7} e^{11} x^{3} + 45 \, d^{8} e^{10} x^{2} + 10 \, d^{9} e^{9} x + d^{10} e^{8}\right)}}"," ",0,"-1/2520*(840*B*c^3*e^7*x^7 + 7*B*c^3*d^7 + 252*A*a^3*e^7 + 3*(3*B*b*c^2 + A*c^3)*d^6*e + 6*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^2 + 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^3 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^4 + 21*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^5 + 28*(B*a^3 + 3*A*a^2*b)*d*e^6 + 210*(7*B*c^3*d*e^6 + 3*(3*B*b*c^2 + A*c^3)*e^7)*x^6 + 252*(7*B*c^3*d^2*e^5 + 3*(3*B*b*c^2 + A*c^3)*d*e^6 + 6*(B*b^2*c + (B*a + A*b)*c^2)*e^7)*x^5 + 210*(7*B*c^3*d^3*e^4 + 3*(3*B*b*c^2 + A*c^3)*d^2*e^5 + 6*(B*b^2*c + (B*a + A*b)*c^2)*d*e^6 + 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^7)*x^4 + 120*(7*B*c^3*d^4*e^3 + 3*(3*B*b*c^2 + A*c^3)*d^3*e^4 + 6*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^5 + 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^6 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^7)*x^3 + 45*(7*B*c^3*d^5*e^2 + 3*(3*B*b*c^2 + A*c^3)*d^4*e^3 + 6*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^4 + 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^5 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^6 + 21*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^7)*x^2 + 10*(7*B*c^3*d^6*e + 3*(3*B*b*c^2 + A*c^3)*d^5*e^2 + 6*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^3 + 2*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^4 + 3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^5 + 21*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^6 + 28*(B*a^3 + 3*A*a^2*b)*e^7)*x)/(e^18*x^10 + 10*d*e^17*x^9 + 45*d^2*e^16*x^8 + 120*d^3*e^15*x^7 + 210*d^4*e^14*x^6 + 252*d^5*e^13*x^5 + 210*d^6*e^12*x^4 + 120*d^7*e^11*x^3 + 45*d^8*e^10*x^2 + 10*d^9*e^9*x + d^10*e^8)","A",0
2350,1,342,0,0.404112," ","integrate(x*(e*x+d)^m*(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{{\left(a d^{2} e^{2} m^{2} + 6 \, c d^{4} - 8 \, b d^{3} e + 12 \, a d^{2} e^{2} - {\left(c e^{4} m^{3} + 6 \, c e^{4} m^{2} + 11 \, c e^{4} m + 6 \, c e^{4}\right)} x^{4} - {\left(8 \, b e^{4} + {\left(c d e^{3} + b e^{4}\right)} m^{3} + {\left(3 \, c d e^{3} + 7 \, b e^{4}\right)} m^{2} + 2 \, {\left(c d e^{3} + 7 \, b e^{4}\right)} m\right)} x^{3} - {\left(12 \, a e^{4} + {\left(b d e^{3} + a e^{4}\right)} m^{3} - {\left(3 \, c d^{2} e^{2} - 5 \, b d e^{3} - 8 \, a e^{4}\right)} m^{2} - {\left(3 \, c d^{2} e^{2} - 4 \, b d e^{3} - 19 \, a e^{4}\right)} m\right)} x^{2} - {\left(2 \, b d^{3} e - 7 \, a d^{2} e^{2}\right)} m - {\left(a d e^{3} m^{3} - {\left(2 \, b d^{2} e^{2} - 7 \, a d e^{3}\right)} m^{2} + 2 \, {\left(3 \, c d^{3} e - 4 \, b d^{2} e^{2} + 6 \, a d e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"-(a*d^2*e^2*m^2 + 6*c*d^4 - 8*b*d^3*e + 12*a*d^2*e^2 - (c*e^4*m^3 + 6*c*e^4*m^2 + 11*c*e^4*m + 6*c*e^4)*x^4 - (8*b*e^4 + (c*d*e^3 + b*e^4)*m^3 + (3*c*d*e^3 + 7*b*e^4)*m^2 + 2*(c*d*e^3 + 7*b*e^4)*m)*x^3 - (12*a*e^4 + (b*d*e^3 + a*e^4)*m^3 - (3*c*d^2*e^2 - 5*b*d*e^3 - 8*a*e^4)*m^2 - (3*c*d^2*e^2 - 4*b*d*e^3 - 19*a*e^4)*m)*x^2 - (2*b*d^3*e - 7*a*d^2*e^2)*m - (a*d*e^3*m^3 - (2*b*d^2*e^2 - 7*a*d*e^3)*m^2 + 2*(3*c*d^3*e - 4*b*d^2*e^2 + 6*a*d*e^3)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
2351,1,186,0,0.349189," ","integrate(x*(e*x+d)^5*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{5} c + \frac{5}{8} x^{8} e^{4} d c + \frac{1}{8} x^{8} e^{5} b + \frac{10}{7} x^{7} e^{3} d^{2} c + \frac{5}{7} x^{7} e^{4} d b + \frac{1}{7} x^{7} e^{5} a + \frac{5}{3} x^{6} e^{2} d^{3} c + \frac{5}{3} x^{6} e^{3} d^{2} b + \frac{5}{6} x^{6} e^{4} d a + x^{5} e d^{4} c + 2 x^{5} e^{2} d^{3} b + 2 x^{5} e^{3} d^{2} a + \frac{1}{4} x^{4} d^{5} c + \frac{5}{4} x^{4} e d^{4} b + \frac{5}{2} x^{4} e^{2} d^{3} a + \frac{1}{3} x^{3} d^{5} b + \frac{5}{3} x^{3} e d^{4} a + \frac{1}{2} x^{2} d^{5} a"," ",0,"1/9*x^9*e^5*c + 5/8*x^8*e^4*d*c + 1/8*x^8*e^5*b + 10/7*x^7*e^3*d^2*c + 5/7*x^7*e^4*d*b + 1/7*x^7*e^5*a + 5/3*x^6*e^2*d^3*c + 5/3*x^6*e^3*d^2*b + 5/6*x^6*e^4*d*a + x^5*e*d^4*c + 2*x^5*e^2*d^3*b + 2*x^5*e^3*d^2*a + 1/4*x^4*d^5*c + 5/4*x^4*e*d^4*b + 5/2*x^4*e^2*d^3*a + 1/3*x^3*d^5*b + 5/3*x^3*e*d^4*a + 1/2*x^2*d^5*a","A",0
2352,1,149,0,0.345810," ","integrate(x*(e*x+d)^4*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{4} c + \frac{4}{7} x^{7} e^{3} d c + \frac{1}{7} x^{7} e^{4} b + x^{6} e^{2} d^{2} c + \frac{2}{3} x^{6} e^{3} d b + \frac{1}{6} x^{6} e^{4} a + \frac{4}{5} x^{5} e d^{3} c + \frac{6}{5} x^{5} e^{2} d^{2} b + \frac{4}{5} x^{5} e^{3} d a + \frac{1}{4} x^{4} d^{4} c + x^{4} e d^{3} b + \frac{3}{2} x^{4} e^{2} d^{2} a + \frac{1}{3} x^{3} d^{4} b + \frac{4}{3} x^{3} e d^{3} a + \frac{1}{2} x^{2} d^{4} a"," ",0,"1/8*x^8*e^4*c + 4/7*x^7*e^3*d*c + 1/7*x^7*e^4*b + x^6*e^2*d^2*c + 2/3*x^6*e^3*d*b + 1/6*x^6*e^4*a + 4/5*x^5*e*d^3*c + 6/5*x^5*e^2*d^2*b + 4/5*x^5*e^3*d*a + 1/4*x^4*d^4*c + x^4*e*d^3*b + 3/2*x^4*e^2*d^2*a + 1/3*x^3*d^4*b + 4/3*x^3*e*d^3*a + 1/2*x^2*d^4*a","A",0
2353,1,114,0,0.353601," ","integrate(x*(e*x+d)^3*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{3} c + \frac{1}{2} x^{6} e^{2} d c + \frac{1}{6} x^{6} e^{3} b + \frac{3}{5} x^{5} e d^{2} c + \frac{3}{5} x^{5} e^{2} d b + \frac{1}{5} x^{5} e^{3} a + \frac{1}{4} x^{4} d^{3} c + \frac{3}{4} x^{4} e d^{2} b + \frac{3}{4} x^{4} e^{2} d a + \frac{1}{3} x^{3} d^{3} b + x^{3} e d^{2} a + \frac{1}{2} x^{2} d^{3} a"," ",0,"1/7*x^7*e^3*c + 1/2*x^6*e^2*d*c + 1/6*x^6*e^3*b + 3/5*x^5*e*d^2*c + 3/5*x^5*e^2*d*b + 1/5*x^5*e^3*a + 1/4*x^4*d^3*c + 3/4*x^4*e*d^2*b + 3/4*x^4*e^2*d*a + 1/3*x^3*d^3*b + x^3*e*d^2*a + 1/2*x^2*d^3*a","A",0
2354,1,79,0,0.335774," ","integrate(x*(e*x+d)^2*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{2} c + \frac{2}{5} x^{5} e d c + \frac{1}{5} x^{5} e^{2} b + \frac{1}{4} x^{4} d^{2} c + \frac{1}{2} x^{4} e d b + \frac{1}{4} x^{4} e^{2} a + \frac{1}{3} x^{3} d^{2} b + \frac{2}{3} x^{3} e d a + \frac{1}{2} x^{2} d^{2} a"," ",0,"1/6*x^6*e^2*c + 2/5*x^5*e*d*c + 1/5*x^5*e^2*b + 1/4*x^4*d^2*c + 1/2*x^4*e*d*b + 1/4*x^4*e^2*a + 1/3*x^3*d^2*b + 2/3*x^3*e*d*a + 1/2*x^2*d^2*a","A",0
2355,1,43,0,0.323165," ","integrate(x*(e*x+d)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e c + \frac{1}{4} x^{4} d c + \frac{1}{4} x^{4} e b + \frac{1}{3} x^{3} d b + \frac{1}{3} x^{3} e a + \frac{1}{2} x^{2} d a"," ",0,"1/5*x^5*e*c + 1/4*x^4*d*c + 1/4*x^4*e*b + 1/3*x^3*d*b + 1/3*x^3*e*a + 1/2*x^2*d*a","A",0
2356,1,19,0,0.337950," ","integrate(x*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{4} x^{4} c + \frac{1}{3} x^{3} b + \frac{1}{2} x^{2} a"," ",0,"1/4*x^4*c + 1/3*x^3*b + 1/2*x^2*a","A",0
2357,1,82,0,0.390494," ","integrate(x*(c*x^2+b*x+a)/(e*x+d),x, algorithm=""fricas"")","\frac{2 \, c e^{3} x^{3} - 3 \, {\left(c d e^{2} - b e^{3}\right)} x^{2} + 6 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x - 6 \, {\left(c d^{3} - b d^{2} e + a d e^{2}\right)} \log\left(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(2*c*e^3*x^3 - 3*(c*d*e^2 - b*e^3)*x^2 + 6*(c*d^2*e - b*d*e^2 + a*e^3)*x - 6*(c*d^3 - b*d^2*e + a*d*e^2)*log(e*x + d))/e^4","A",0
2358,1,131,0,0.390389," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{c e^{3} x^{3} + 2 \, c d^{3} - 2 \, b d^{2} e + 2 \, a d e^{2} - {\left(3 \, c d e^{2} - 2 \, b e^{3}\right)} x^{2} - 2 \, {\left(2 \, c d^{2} e - b d e^{2}\right)} x + 2 \, {\left(3 \, c d^{3} - 2 \, b d^{2} e + a d e^{2} + {\left(3 \, c d^{2} e - 2 \, b d e^{2} + a e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(c*e^3*x^3 + 2*c*d^3 - 2*b*d^2*e + 2*a*d*e^2 - (3*c*d*e^2 - 2*b*e^3)*x^2 - 2*(2*c*d^2*e - b*d*e^2)*x + 2*(3*c*d^3 - 2*b*d^2*e + a*d*e^2 + (3*c*d^2*e - 2*b*d*e^2 + a*e^3)*x)*log(e*x + d))/(e^5*x + d*e^4)","A",0
2359,1,147,0,0.382787," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, c e^{3} x^{3} + 4 \, c d e^{2} x^{2} - 5 \, c d^{3} + 3 \, b d^{2} e - a d e^{2} - 2 \, {\left(2 \, c d^{2} e - 2 \, b d e^{2} + a e^{3}\right)} x - 2 \, {\left(3 \, c d^{3} - b d^{2} e + {\left(3 \, c d e^{2} - b e^{3}\right)} x^{2} + 2 \, {\left(3 \, c d^{2} e - b d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(2*c*e^3*x^3 + 4*c*d*e^2*x^2 - 5*c*d^3 + 3*b*d^2*e - a*d*e^2 - 2*(2*c*d^2*e - 2*b*d*e^2 + a*e^3)*x - 2*(3*c*d^3 - b*d^2*e + (3*c*d*e^2 - b*e^3)*x^2 + 2*(3*c*d^2*e - b*d*e^2)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
2360,1,141,0,0.394255," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{11 \, c d^{3} - 2 \, b d^{2} e - a d e^{2} + 6 \, {\left(3 \, c d e^{2} - b e^{3}\right)} x^{2} + 3 \, {\left(9 \, c d^{2} e - 2 \, b d e^{2} - a e^{3}\right)} x + 6 \, {\left(c e^{3} x^{3} + 3 \, c d e^{2} x^{2} + 3 \, c d^{2} e x + c d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(11*c*d^3 - 2*b*d^2*e - a*d*e^2 + 6*(3*c*d*e^2 - b*e^3)*x^2 + 3*(9*c*d^2*e - 2*b*d*e^2 - a*e^3)*x + 6*(c*e^3*x^3 + 3*c*d*e^2*x^2 + 3*c*d^2*e*x + c*d^3)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
2361,1,116,0,0.364885," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{12 \, c e^{3} x^{3} + 3 \, c d^{3} + b d^{2} e + a d e^{2} + 6 \, {\left(3 \, c d e^{2} + b e^{3}\right)} x^{2} + 4 \, {\left(3 \, c d^{2} e + b d e^{2} + a e^{3}\right)} x}{12 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-1/12*(12*c*e^3*x^3 + 3*c*d^3 + b*d^2*e + a*d*e^2 + 6*(3*c*d*e^2 + b*e^3)*x^2 + 4*(3*c*d^2*e + b*d*e^2 + a*e^3)*x)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","A",0
2362,1,132,0,0.392146," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{30 \, c e^{3} x^{3} + 3 \, c d^{3} + 2 \, b d^{2} e + 3 \, a d e^{2} + 10 \, {\left(3 \, c d e^{2} + 2 \, b e^{3}\right)} x^{2} + 5 \, {\left(3 \, c d^{2} e + 2 \, b d e^{2} + 3 \, a e^{3}\right)} x}{60 \, {\left(e^{9} x^{5} + 5 \, d e^{8} x^{4} + 10 \, d^{2} e^{7} x^{3} + 10 \, d^{3} e^{6} x^{2} + 5 \, d^{4} e^{5} x + d^{5} e^{4}\right)}}"," ",0,"-1/60*(30*c*e^3*x^3 + 3*c*d^3 + 2*b*d^2*e + 3*a*d*e^2 + 10*(3*c*d*e^2 + 2*b*e^3)*x^2 + 5*(3*c*d^2*e + 2*b*d*e^2 + 3*a*e^3)*x)/(e^9*x^5 + 5*d*e^8*x^4 + 10*d^2*e^7*x^3 + 10*d^3*e^6*x^2 + 5*d^4*e^5*x + d^5*e^4)","A",0
2363,1,137,0,0.371559," ","integrate(x*(c*x^2+b*x+a)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{20 \, c e^{3} x^{3} + c d^{3} + b d^{2} e + 2 \, a d e^{2} + 15 \, {\left(c d e^{2} + b e^{3}\right)} x^{2} + 6 \, {\left(c d^{2} e + b d e^{2} + 2 \, a e^{3}\right)} x}{60 \, {\left(e^{10} x^{6} + 6 \, d e^{9} x^{5} + 15 \, d^{2} e^{8} x^{4} + 20 \, d^{3} e^{7} x^{3} + 15 \, d^{4} e^{6} x^{2} + 6 \, d^{5} e^{5} x + d^{6} e^{4}\right)}}"," ",0,"-1/60*(20*c*e^3*x^3 + c*d^3 + b*d^2*e + 2*a*d*e^2 + 15*(c*d*e^2 + b*e^3)*x^2 + 6*(c*d^2*e + b*d*e^2 + 2*a*e^3)*x)/(e^10*x^6 + 6*d*e^9*x^5 + 15*d^2*e^8*x^4 + 20*d^3*e^7*x^3 + 15*d^4*e^6*x^2 + 6*d^5*e^5*x + d^6*e^4)","A",0
2364,1,1139,0,0.542327," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} e^{3} x^{3} + 3 \, {\left(3 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d e^{2} - {\left(B b^{3} c^{2} + 4 \, A a c^{4} - {\left(4 \, B a b + A b^{2}\right)} c^{3}\right)} e^{3}\right)} x^{2} - 3 \, {\left({\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} - 3 \, {\left(B b^{2} c^{2} - {\left(2 \, B a + A b\right)} c^{3}\right)} d^{2} e + 3 \, {\left(B b^{3} c + 2 \, A a c^{3} - {\left(3 \, B a b + A b^{2}\right)} c^{2}\right)} d e^{2} - {\left(B b^{4} + {\left(2 \, B a^{2} + 3 \, A a b\right)} c^{2} - {\left(4 \, B a b^{2} + A b^{3}\right)} c\right)} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 6 \, {\left(3 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{2} e - 3 \, {\left(B b^{3} c^{2} + 4 \, A a c^{4} - {\left(4 \, B a b + A b^{2}\right)} c^{3}\right)} d e^{2} + {\left(B b^{4} c + 4 \, {\left(B a^{2} + A a b\right)} c^{3} - {\left(5 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} e^{3}\right)} x + 3 \, {\left({\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{3} - 3 \, {\left(B b^{3} c^{2} + 4 \, A a c^{4} - {\left(4 \, B a b + A b^{2}\right)} c^{3}\right)} d^{2} e + 3 \, {\left(B b^{4} c + 4 \, {\left(B a^{2} + A a b\right)} c^{3} - {\left(5 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d e^{2} - {\left(B b^{5} - 4 \, A a^{2} c^{3} + {\left(8 \, B a^{2} b + 5 \, A a b^{2}\right)} c^{2} - {\left(6 \, B a b^{3} + A b^{4}\right)} c\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}, \frac{2 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} e^{3} x^{3} + 3 \, {\left(3 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d e^{2} - {\left(B b^{3} c^{2} + 4 \, A a c^{4} - {\left(4 \, B a b + A b^{2}\right)} c^{3}\right)} e^{3}\right)} x^{2} + 6 \, {\left({\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} - 3 \, {\left(B b^{2} c^{2} - {\left(2 \, B a + A b\right)} c^{3}\right)} d^{2} e + 3 \, {\left(B b^{3} c + 2 \, A a c^{3} - {\left(3 \, B a b + A b^{2}\right)} c^{2}\right)} d e^{2} - {\left(B b^{4} + {\left(2 \, B a^{2} + 3 \, A a b\right)} c^{2} - {\left(4 \, B a b^{2} + A b^{3}\right)} c\right)} e^{3}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 6 \, {\left(3 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{2} e - 3 \, {\left(B b^{3} c^{2} + 4 \, A a c^{4} - {\left(4 \, B a b + A b^{2}\right)} c^{3}\right)} d e^{2} + {\left(B b^{4} c + 4 \, {\left(B a^{2} + A a b\right)} c^{3} - {\left(5 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} e^{3}\right)} x + 3 \, {\left({\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{3} - 3 \, {\left(B b^{3} c^{2} + 4 \, A a c^{4} - {\left(4 \, B a b + A b^{2}\right)} c^{3}\right)} d^{2} e + 3 \, {\left(B b^{4} c + 4 \, {\left(B a^{2} + A a b\right)} c^{3} - {\left(5 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d e^{2} - {\left(B b^{5} - 4 \, A a^{2} c^{3} + {\left(8 \, B a^{2} b + 5 \, A a b^{2}\right)} c^{2} - {\left(6 \, B a b^{3} + A b^{4}\right)} c\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}\right]"," ",0,"[1/6*(2*(B*b^2*c^3 - 4*B*a*c^4)*e^3*x^3 + 3*(3*(B*b^2*c^3 - 4*B*a*c^4)*d*e^2 - (B*b^3*c^2 + 4*A*a*c^4 - (4*B*a*b + A*b^2)*c^3)*e^3)*x^2 - 3*((B*b*c^3 - 2*A*c^4)*d^3 - 3*(B*b^2*c^2 - (2*B*a + A*b)*c^3)*d^2*e + 3*(B*b^3*c + 2*A*a*c^3 - (3*B*a*b + A*b^2)*c^2)*d*e^2 - (B*b^4 + (2*B*a^2 + 3*A*a*b)*c^2 - (4*B*a*b^2 + A*b^3)*c)*e^3)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 6*(3*(B*b^2*c^3 - 4*B*a*c^4)*d^2*e - 3*(B*b^3*c^2 + 4*A*a*c^4 - (4*B*a*b + A*b^2)*c^3)*d*e^2 + (B*b^4*c + 4*(B*a^2 + A*a*b)*c^3 - (5*B*a*b^2 + A*b^3)*c^2)*e^3)*x + 3*((B*b^2*c^3 - 4*B*a*c^4)*d^3 - 3*(B*b^3*c^2 + 4*A*a*c^4 - (4*B*a*b + A*b^2)*c^3)*d^2*e + 3*(B*b^4*c + 4*(B*a^2 + A*a*b)*c^3 - (5*B*a*b^2 + A*b^3)*c^2)*d*e^2 - (B*b^5 - 4*A*a^2*c^3 + (8*B*a^2*b + 5*A*a*b^2)*c^2 - (6*B*a*b^3 + A*b^4)*c)*e^3)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5), 1/6*(2*(B*b^2*c^3 - 4*B*a*c^4)*e^3*x^3 + 3*(3*(B*b^2*c^3 - 4*B*a*c^4)*d*e^2 - (B*b^3*c^2 + 4*A*a*c^4 - (4*B*a*b + A*b^2)*c^3)*e^3)*x^2 + 6*((B*b*c^3 - 2*A*c^4)*d^3 - 3*(B*b^2*c^2 - (2*B*a + A*b)*c^3)*d^2*e + 3*(B*b^3*c + 2*A*a*c^3 - (3*B*a*b + A*b^2)*c^2)*d*e^2 - (B*b^4 + (2*B*a^2 + 3*A*a*b)*c^2 - (4*B*a*b^2 + A*b^3)*c)*e^3)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 6*(3*(B*b^2*c^3 - 4*B*a*c^4)*d^2*e - 3*(B*b^3*c^2 + 4*A*a*c^4 - (4*B*a*b + A*b^2)*c^3)*d*e^2 + (B*b^4*c + 4*(B*a^2 + A*a*b)*c^3 - (5*B*a*b^2 + A*b^3)*c^2)*e^3)*x + 3*((B*b^2*c^3 - 4*B*a*c^4)*d^3 - 3*(B*b^3*c^2 + 4*A*a*c^4 - (4*B*a*b + A*b^2)*c^3)*d^2*e + 3*(B*b^4*c + 4*(B*a^2 + A*a*b)*c^3 - (5*B*a*b^2 + A*b^3)*c^2)*d*e^2 - (B*b^5 - 4*A*a^2*c^3 + (8*B*a^2*b + 5*A*a*b^2)*c^2 - (6*B*a*b^3 + A*b^4)*c)*e^3)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5)]","A",0
2365,1,673,0,0.447564," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{{\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} e^{2} x^{2} + {\left({\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - 2 \, {\left(B b^{2} c - {\left(2 \, B a + A b\right)} c^{2}\right)} d e + {\left(B b^{3} + 2 \, A a c^{2} - {\left(3 \, B a b + A b^{2}\right)} c\right)} e^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(2 \, {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d e - {\left(B b^{3} c + 4 \, A a c^{3} - {\left(4 \, B a b + A b^{2}\right)} c^{2}\right)} e^{2}\right)} x + {\left({\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d^{2} - 2 \, {\left(B b^{3} c + 4 \, A a c^{3} - {\left(4 \, B a b + A b^{2}\right)} c^{2}\right)} d e + {\left(B b^{4} + 4 \, {\left(B a^{2} + A a b\right)} c^{2} - {\left(5 \, B a b^{2} + A b^{3}\right)} c\right)} e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}, \frac{{\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} e^{2} x^{2} + 2 \, {\left({\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - 2 \, {\left(B b^{2} c - {\left(2 \, B a + A b\right)} c^{2}\right)} d e + {\left(B b^{3} + 2 \, A a c^{2} - {\left(3 \, B a b + A b^{2}\right)} c\right)} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(2 \, {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d e - {\left(B b^{3} c + 4 \, A a c^{3} - {\left(4 \, B a b + A b^{2}\right)} c^{2}\right)} e^{2}\right)} x + {\left({\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d^{2} - 2 \, {\left(B b^{3} c + 4 \, A a c^{3} - {\left(4 \, B a b + A b^{2}\right)} c^{2}\right)} d e + {\left(B b^{4} + 4 \, {\left(B a^{2} + A a b\right)} c^{2} - {\left(5 \, B a b^{2} + A b^{3}\right)} c\right)} e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}\right]"," ",0,"[1/2*((B*b^2*c^2 - 4*B*a*c^3)*e^2*x^2 + ((B*b*c^2 - 2*A*c^3)*d^2 - 2*(B*b^2*c - (2*B*a + A*b)*c^2)*d*e + (B*b^3 + 2*A*a*c^2 - (3*B*a*b + A*b^2)*c)*e^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(2*(B*b^2*c^2 - 4*B*a*c^3)*d*e - (B*b^3*c + 4*A*a*c^3 - (4*B*a*b + A*b^2)*c^2)*e^2)*x + ((B*b^2*c^2 - 4*B*a*c^3)*d^2 - 2*(B*b^3*c + 4*A*a*c^3 - (4*B*a*b + A*b^2)*c^2)*d*e + (B*b^4 + 4*(B*a^2 + A*a*b)*c^2 - (5*B*a*b^2 + A*b^3)*c)*e^2)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4), 1/2*((B*b^2*c^2 - 4*B*a*c^3)*e^2*x^2 + 2*((B*b*c^2 - 2*A*c^3)*d^2 - 2*(B*b^2*c - (2*B*a + A*b)*c^2)*d*e + (B*b^3 + 2*A*a*c^2 - (3*B*a*b + A*b^2)*c)*e^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(2*(B*b^2*c^2 - 4*B*a*c^3)*d*e - (B*b^3*c + 4*A*a*c^3 - (4*B*a*b + A*b^2)*c^2)*e^2)*x + ((B*b^2*c^2 - 4*B*a*c^3)*d^2 - 2*(B*b^3*c + 4*A*a*c^3 - (4*B*a*b + A*b^2)*c^2)*d*e + (B*b^4 + 4*(B*a^2 + A*a*b)*c^2 - (5*B*a*b^2 + A*b^3)*c)*e^2)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4)]","A",0
2366,1,369,0,0.424665," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B b^{2} c - 4 \, B a c^{2}\right)} e x + \sqrt{b^{2} - 4 \, a c} {\left({\left(B b c - 2 \, A c^{2}\right)} d - {\left(B b^{2} - {\left(2 \, B a + A b\right)} c\right)} e\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d - {\left(B b^{3} + 4 \, A a c^{2} - {\left(4 \, B a b + A b^{2}\right)} c\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(B b^{2} c - 4 \, B a c^{2}\right)} e x + 2 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(B b c - 2 \, A c^{2}\right)} d - {\left(B b^{2} - {\left(2 \, B a + A b\right)} c\right)} e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d - {\left(B b^{3} + 4 \, A a c^{2} - {\left(4 \, B a b + A b^{2}\right)} c\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/2*(2*(B*b^2*c - 4*B*a*c^2)*e*x + sqrt(b^2 - 4*a*c)*((B*b*c - 2*A*c^2)*d - (B*b^2 - (2*B*a + A*b)*c)*e)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + ((B*b^2*c - 4*B*a*c^2)*d - (B*b^3 + 4*A*a*c^2 - (4*B*a*b + A*b^2)*c)*e)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3), 1/2*(2*(B*b^2*c - 4*B*a*c^2)*e*x + 2*sqrt(-b^2 + 4*a*c)*((B*b*c - 2*A*c^2)*d - (B*b^2 - (2*B*a + A*b)*c)*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + ((B*b^2*c - 4*B*a*c^2)*d - (B*b^3 + 4*A*a*c^2 - (4*B*a*b + A*b^2)*c)*e)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3)]","A",0
2367,1,207,0,0.394814," ","integrate((B*x+A)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[-\frac{{\left(B b - 2 \, A c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(B b^{2} - 4 \, B a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{2 \, {\left(B b - 2 \, A c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(B b^{2} - 4 \, B a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[-1/2*((B*b - 2*A*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (B*b^2 - 4*B*a*c)*log(c*x^2 + b*x + a))/(b^2*c - 4*a*c^2), 1/2*(2*(B*b - 2*A*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (B*b^2 - 4*B*a*c)*log(c*x^2 + b*x + a))/(b^2*c - 4*a*c^2)]","A",0
2368,1,409,0,4.812229," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} {\left({\left(B b - 2 \, A c\right)} d - {\left(2 \, B a - A b\right)} e\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left({\left(B b^{2} - 4 \, B a c\right)} d - {\left(A b^{2} - 4 \, A a c\right)} e\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(B b^{2} - 4 \, B a c\right)} d - {\left(A b^{2} - 4 \, A a c\right)} e\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(B b - 2 \, A c\right)} d - {\left(2 \, B a - A b\right)} e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left({\left(B b^{2} - 4 \, B a c\right)} d - {\left(A b^{2} - 4 \, A a c\right)} e\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(B b^{2} - 4 \, B a c\right)} d - {\left(A b^{2} - 4 \, A a c\right)} e\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}\right]"," ",0,"[1/2*(sqrt(b^2 - 4*a*c)*((B*b - 2*A*c)*d - (2*B*a - A*b)*e)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + ((B*b^2 - 4*B*a*c)*d - (A*b^2 - 4*A*a*c)*e)*log(c*x^2 + b*x + a) - 2*((B*b^2 - 4*B*a*c)*d - (A*b^2 - 4*A*a*c)*e)*log(e*x + d))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2), 1/2*(2*sqrt(-b^2 + 4*a*c)*((B*b - 2*A*c)*d - (2*B*a - A*b)*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + ((B*b^2 - 4*B*a*c)*d - (A*b^2 - 4*A*a*c)*e)*log(c*x^2 + b*x + a) - 2*((B*b^2 - 4*B*a*c)*d - (A*b^2 - 4*A*a*c)*e)*log(e*x + d))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)]","A",0
2369,1,1594,0,62.067222," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{3} - 2 \, {\left(B b^{3} - 4 \, A a c^{2} - {\left(4 \, B a b - A b^{2}\right)} c\right)} d^{2} e + 2 \, {\left(B a b^{2} + A b^{3} - 4 \, {\left(B a^{2} + A a b\right)} c\right)} d e^{2} - 2 \, {\left(A a b^{2} - 4 \, A a^{2} c\right)} e^{3} - {\left(2 \, {\left(2 \, B a - A b\right)} c d^{2} e - {\left(B b c - 2 \, A c^{2}\right)} d^{3} - {\left(B a b - A b^{2} + 2 \, A a c\right)} d e^{2} + {\left(2 \, {\left(2 \, B a - A b\right)} c d e^{2} - {\left(B b c - 2 \, A c^{2}\right)} d^{2} e - {\left(B a b - A b^{2} + 2 \, A a c\right)} e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{3} - 2 \, {\left(A b^{2} c - 4 \, A a c^{2}\right)} d^{2} e - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} d e^{2} + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{2} e - 2 \, {\left(A b^{2} c - 4 \, A a c^{2}\right)} d e^{2} - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} e^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{3} - 2 \, {\left(A b^{2} c - 4 \, A a c^{2}\right)} d^{2} e - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} d e^{2} + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{2} e - 2 \, {\left(A b^{2} c - 4 \, A a c^{2}\right)} d e^{2} - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{4} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{4} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{5}\right)} x\right)}}, \frac{2 \, {\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{3} - 2 \, {\left(B b^{3} - 4 \, A a c^{2} - {\left(4 \, B a b - A b^{2}\right)} c\right)} d^{2} e + 2 \, {\left(B a b^{2} + A b^{3} - 4 \, {\left(B a^{2} + A a b\right)} c\right)} d e^{2} - 2 \, {\left(A a b^{2} - 4 \, A a^{2} c\right)} e^{3} - 2 \, {\left(2 \, {\left(2 \, B a - A b\right)} c d^{2} e - {\left(B b c - 2 \, A c^{2}\right)} d^{3} - {\left(B a b - A b^{2} + 2 \, A a c\right)} d e^{2} + {\left(2 \, {\left(2 \, B a - A b\right)} c d e^{2} - {\left(B b c - 2 \, A c^{2}\right)} d^{2} e - {\left(B a b - A b^{2} + 2 \, A a c\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{3} - 2 \, {\left(A b^{2} c - 4 \, A a c^{2}\right)} d^{2} e - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} d e^{2} + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{2} e - 2 \, {\left(A b^{2} c - 4 \, A a c^{2}\right)} d e^{2} - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} e^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{3} - 2 \, {\left(A b^{2} c - 4 \, A a c^{2}\right)} d^{2} e - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} d e^{2} + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d^{2} e - 2 \, {\left(A b^{2} c - 4 \, A a c^{2}\right)} d e^{2} - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{4} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{4} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{5}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(B*b^2*c - 4*B*a*c^2)*d^3 - 2*(B*b^3 - 4*A*a*c^2 - (4*B*a*b - A*b^2)*c)*d^2*e + 2*(B*a*b^2 + A*b^3 - 4*(B*a^2 + A*a*b)*c)*d*e^2 - 2*(A*a*b^2 - 4*A*a^2*c)*e^3 - (2*(2*B*a - A*b)*c*d^2*e - (B*b*c - 2*A*c^2)*d^3 - (B*a*b - A*b^2 + 2*A*a*c)*d*e^2 + (2*(2*B*a - A*b)*c*d*e^2 - (B*b*c - 2*A*c^2)*d^2*e - (B*a*b - A*b^2 + 2*A*a*c)*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + ((B*b^2*c - 4*B*a*c^2)*d^3 - 2*(A*b^2*c - 4*A*a*c^2)*d^2*e - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*d*e^2 + ((B*b^2*c - 4*B*a*c^2)*d^2*e - 2*(A*b^2*c - 4*A*a*c^2)*d*e^2 - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*e^3)*x)*log(c*x^2 + b*x + a) - 2*((B*b^2*c - 4*B*a*c^2)*d^3 - 2*(A*b^2*c - 4*A*a*c^2)*d^2*e - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*d*e^2 + ((B*b^2*c - 4*B*a*c^2)*d^2*e - 2*(A*b^2*c - 4*A*a*c^2)*d*e^2 - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*e^3)*x)*log(e*x + d))/((b^2*c^2 - 4*a*c^3)*d^5 - 2*(b^3*c - 4*a*b*c^2)*d^4*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e^3 + (a^2*b^2 - 4*a^3*c)*d*e^4 + ((b^2*c^2 - 4*a*c^3)*d^4*e - 2*(b^3*c - 4*a*b*c^2)*d^3*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 2*(a*b^3 - 4*a^2*b*c)*d*e^4 + (a^2*b^2 - 4*a^3*c)*e^5)*x), 1/2*(2*(B*b^2*c - 4*B*a*c^2)*d^3 - 2*(B*b^3 - 4*A*a*c^2 - (4*B*a*b - A*b^2)*c)*d^2*e + 2*(B*a*b^2 + A*b^3 - 4*(B*a^2 + A*a*b)*c)*d*e^2 - 2*(A*a*b^2 - 4*A*a^2*c)*e^3 - 2*(2*(2*B*a - A*b)*c*d^2*e - (B*b*c - 2*A*c^2)*d^3 - (B*a*b - A*b^2 + 2*A*a*c)*d*e^2 + (2*(2*B*a - A*b)*c*d*e^2 - (B*b*c - 2*A*c^2)*d^2*e - (B*a*b - A*b^2 + 2*A*a*c)*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + ((B*b^2*c - 4*B*a*c^2)*d^3 - 2*(A*b^2*c - 4*A*a*c^2)*d^2*e - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*d*e^2 + ((B*b^2*c - 4*B*a*c^2)*d^2*e - 2*(A*b^2*c - 4*A*a*c^2)*d*e^2 - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*e^3)*x)*log(c*x^2 + b*x + a) - 2*((B*b^2*c - 4*B*a*c^2)*d^3 - 2*(A*b^2*c - 4*A*a*c^2)*d^2*e - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*d*e^2 + ((B*b^2*c - 4*B*a*c^2)*d^2*e - 2*(A*b^2*c - 4*A*a*c^2)*d*e^2 - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*e^3)*x)*log(e*x + d))/((b^2*c^2 - 4*a*c^3)*d^5 - 2*(b^3*c - 4*a*b*c^2)*d^4*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e^3 + (a^2*b^2 - 4*a^3*c)*d*e^4 + ((b^2*c^2 - 4*a*c^3)*d^4*e - 2*(b^3*c - 4*a*b*c^2)*d^3*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 2*(a*b^3 - 4*a^2*b*c)*d*e^4 + (a^2*b^2 - 4*a^3*c)*e^5)*x)]","B",0
2370,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2371,1,5676,0,1.205327," ","integrate((e*x+d)^4*(g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(6 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 12 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + 6 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 12 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} - {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} - 40 \, a^{3} c^{5}\right)} e^{4}\right)} f - {\left(3 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{4} - 4 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{3} e + 18 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} e^{2} + 4 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} - 40 \, a^{3} c^{5}\right)} d e^{3} - {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} e^{4}\right)} g\right)} x^{3} + {\left({\left(18 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{4} - 36 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} d^{3} e + 18 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} d^{2} e^{2} - 4 \, {\left(b^{6} c^{2} - 3 \, a b^{4} c^{3} + 12 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{3} - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} + 8 \, a^{3} b c^{4}\right)} e^{4}\right)} f - {\left(9 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} d^{4} - 12 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} d^{3} e + 6 \, {\left(b^{6} c^{2} - 3 \, a b^{4} c^{3} + 12 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{2} + 4 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} + 8 \, a^{3} b c^{4}\right)} d e^{3} - {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{4}\right)} g\right)} x^{2} - {\left({\left(12 \, {\left(c^{7} d^{4} - 2 \, b c^{6} d^{3} e - 2 \, a b c^{5} d e^{3} + a^{2} c^{5} e^{4} + {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{2} e^{2}\right)} f - {\left(6 \, b c^{6} d^{4} + 36 \, a b c^{5} d^{2} e^{2} - 48 \, a^{2} c^{5} d e^{3} - 8 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{3} e + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} e^{4}\right)} g\right)} x^{4} + 2 \, {\left(12 \, {\left(b c^{6} d^{4} - 2 \, b^{2} c^{5} d^{3} e - 2 \, a b^{2} c^{4} d e^{3} + a^{2} b c^{4} e^{4} + {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{2} e^{2}\right)} f - {\left(6 \, b^{2} c^{5} d^{4} + 36 \, a b^{2} c^{4} d^{2} e^{2} - 48 \, a^{2} b c^{4} d e^{3} - 8 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{3} e + {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} e^{4}\right)} g\right)} x^{3} + {\left(12 \, {\left({\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{4} - 2 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{3} e + {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d e^{3} + {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} e^{4}\right)} f - {\left(6 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{4} - 8 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{3} e + 36 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{2} e^{2} - 48 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d e^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} e^{4}\right)} g\right)} x^{2} + 12 \, {\left(a^{2} c^{5} d^{4} - 2 \, a^{2} b c^{4} d^{3} e - 2 \, a^{3} b c^{3} d e^{3} + a^{4} c^{3} e^{4} + {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d^{2} e^{2}\right)} f - {\left(6 \, a^{2} b c^{4} d^{4} + 36 \, a^{3} b c^{3} d^{2} e^{2} - 48 \, a^{4} c^{3} d e^{3} - 8 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d^{3} e + {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2}\right)} e^{4}\right)} g + 2 \, {\left(12 \, {\left(a b c^{5} d^{4} - 2 \, a b^{2} c^{4} d^{3} e - 2 \, a^{2} b^{2} c^{3} d e^{3} + a^{3} b c^{3} e^{4} + {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{2} e^{2}\right)} f - {\left(6 \, a b^{2} c^{4} d^{4} + 36 \, a^{2} b^{2} c^{3} d^{2} e^{2} - 48 \, a^{3} b c^{3} d e^{3} - 8 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{3} e + {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} e^{4}\right)} g\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left({\left(b^{5} c^{3} - 14 \, a b^{3} c^{4} + 40 \, a^{2} b c^{5}\right)} d^{4} + 4 \, {\left(a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5}\right)} d^{3} e - 36 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{2} e^{2} + 4 \, {\left(a^{2} b^{4} c^{2} + 4 \, a^{3} b^{2} c^{3} - 32 \, a^{4} c^{4}\right)} d e^{3} + {\left(a^{2} b^{5} c - 14 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} e^{4}\right)} f - {\left({\left(a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5}\right)} d^{4} - 24 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{3} e + 6 \, {\left(a^{2} b^{4} c^{2} + 4 \, a^{3} b^{2} c^{3} - 32 \, a^{4} c^{4}\right)} d^{2} e^{2} + 4 \, {\left(a^{2} b^{5} c - 14 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} d e^{3} - 3 \, {\left(a^{2} b^{6} - 11 \, a^{3} b^{4} c + 36 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} e^{4}\right)} g + 2 \, {\left({\left(2 \, {\left(b^{4} c^{4} + a b^{2} c^{5} - 20 \, a^{2} c^{6}\right)} d^{4} - 4 \, {\left(b^{5} c^{3} + a b^{3} c^{4} - 20 \, a^{2} b c^{5}\right)} d^{3} e + 6 \, {\left(5 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} + 8 \, a^{3} c^{5}\right)} d^{2} e^{2} - 4 \, {\left(a b^{5} c^{2} + a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d e^{3} - {\left(a b^{6} c - 14 \, a^{2} b^{4} c^{2} + 46 \, a^{3} b^{2} c^{3} - 24 \, a^{4} c^{4}\right)} e^{4}\right)} f - {\left({\left(b^{5} c^{3} + a b^{3} c^{4} - 20 \, a^{2} b c^{5}\right)} d^{4} - 4 \, {\left(5 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} + 8 \, a^{3} c^{5}\right)} d^{3} e + 6 \, {\left(a b^{5} c^{2} + a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{2} e^{2} + 4 \, {\left(a b^{6} c - 14 \, a^{2} b^{4} c^{2} + 46 \, a^{3} b^{2} c^{3} - 24 \, a^{4} c^{4}\right)} d e^{3} - {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} e^{4}\right)} g\right)} x + {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4} g x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{4} g x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{4} g x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} e^{4} g x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4} g\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{4} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{3} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{2} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x\right)}}, \frac{2 \, {\left({\left(6 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 12 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + 6 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 12 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} - {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} - 40 \, a^{3} c^{5}\right)} e^{4}\right)} f - {\left(3 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{4} - 4 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{3} e + 18 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} e^{2} + 4 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} - 40 \, a^{3} c^{5}\right)} d e^{3} - {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} e^{4}\right)} g\right)} x^{3} + {\left({\left(18 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{4} - 36 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} d^{3} e + 18 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} d^{2} e^{2} - 4 \, {\left(b^{6} c^{2} - 3 \, a b^{4} c^{3} + 12 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{3} - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} + 8 \, a^{3} b c^{4}\right)} e^{4}\right)} f - {\left(9 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} d^{4} - 12 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} d^{3} e + 6 \, {\left(b^{6} c^{2} - 3 \, a b^{4} c^{3} + 12 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{2} + 4 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} + 8 \, a^{3} b c^{4}\right)} d e^{3} - {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{4}\right)} g\right)} x^{2} - 2 \, {\left({\left(12 \, {\left(c^{7} d^{4} - 2 \, b c^{6} d^{3} e - 2 \, a b c^{5} d e^{3} + a^{2} c^{5} e^{4} + {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{2} e^{2}\right)} f - {\left(6 \, b c^{6} d^{4} + 36 \, a b c^{5} d^{2} e^{2} - 48 \, a^{2} c^{5} d e^{3} - 8 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{3} e + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} e^{4}\right)} g\right)} x^{4} + 2 \, {\left(12 \, {\left(b c^{6} d^{4} - 2 \, b^{2} c^{5} d^{3} e - 2 \, a b^{2} c^{4} d e^{3} + a^{2} b c^{4} e^{4} + {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{2} e^{2}\right)} f - {\left(6 \, b^{2} c^{5} d^{4} + 36 \, a b^{2} c^{4} d^{2} e^{2} - 48 \, a^{2} b c^{4} d e^{3} - 8 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{3} e + {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} e^{4}\right)} g\right)} x^{3} + {\left(12 \, {\left({\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{4} - 2 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{3} e + {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d e^{3} + {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} e^{4}\right)} f - {\left(6 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{4} - 8 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{3} e + 36 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{2} e^{2} - 48 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d e^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} e^{4}\right)} g\right)} x^{2} + 12 \, {\left(a^{2} c^{5} d^{4} - 2 \, a^{2} b c^{4} d^{3} e - 2 \, a^{3} b c^{3} d e^{3} + a^{4} c^{3} e^{4} + {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d^{2} e^{2}\right)} f - {\left(6 \, a^{2} b c^{4} d^{4} + 36 \, a^{3} b c^{3} d^{2} e^{2} - 48 \, a^{4} c^{3} d e^{3} - 8 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d^{3} e + {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2}\right)} e^{4}\right)} g + 2 \, {\left(12 \, {\left(a b c^{5} d^{4} - 2 \, a b^{2} c^{4} d^{3} e - 2 \, a^{2} b^{2} c^{3} d e^{3} + a^{3} b c^{3} e^{4} + {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{2} e^{2}\right)} f - {\left(6 \, a b^{2} c^{4} d^{4} + 36 \, a^{2} b^{2} c^{3} d^{2} e^{2} - 48 \, a^{3} b c^{3} d e^{3} - 8 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{3} e + {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} e^{4}\right)} g\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{5} c^{3} - 14 \, a b^{3} c^{4} + 40 \, a^{2} b c^{5}\right)} d^{4} + 4 \, {\left(a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5}\right)} d^{3} e - 36 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{2} e^{2} + 4 \, {\left(a^{2} b^{4} c^{2} + 4 \, a^{3} b^{2} c^{3} - 32 \, a^{4} c^{4}\right)} d e^{3} + {\left(a^{2} b^{5} c - 14 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} e^{4}\right)} f - {\left({\left(a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5}\right)} d^{4} - 24 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{3} e + 6 \, {\left(a^{2} b^{4} c^{2} + 4 \, a^{3} b^{2} c^{3} - 32 \, a^{4} c^{4}\right)} d^{2} e^{2} + 4 \, {\left(a^{2} b^{5} c - 14 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} d e^{3} - 3 \, {\left(a^{2} b^{6} - 11 \, a^{3} b^{4} c + 36 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} e^{4}\right)} g + 2 \, {\left({\left(2 \, {\left(b^{4} c^{4} + a b^{2} c^{5} - 20 \, a^{2} c^{6}\right)} d^{4} - 4 \, {\left(b^{5} c^{3} + a b^{3} c^{4} - 20 \, a^{2} b c^{5}\right)} d^{3} e + 6 \, {\left(5 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} + 8 \, a^{3} c^{5}\right)} d^{2} e^{2} - 4 \, {\left(a b^{5} c^{2} + a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d e^{3} - {\left(a b^{6} c - 14 \, a^{2} b^{4} c^{2} + 46 \, a^{3} b^{2} c^{3} - 24 \, a^{4} c^{4}\right)} e^{4}\right)} f - {\left({\left(b^{5} c^{3} + a b^{3} c^{4} - 20 \, a^{2} b c^{5}\right)} d^{4} - 4 \, {\left(5 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} + 8 \, a^{3} c^{5}\right)} d^{3} e + 6 \, {\left(a b^{5} c^{2} + a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{2} e^{2} + 4 \, {\left(a b^{6} c - 14 \, a^{2} b^{4} c^{2} + 46 \, a^{3} b^{2} c^{3} - 24 \, a^{4} c^{4}\right)} d e^{3} - {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} e^{4}\right)} g\right)} x + {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4} g x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{4} g x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{4} g x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} e^{4} g x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4} g\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{4} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{3} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{2} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x\right)}}\right]"," ",0,"[1/2*(2*((6*(b^2*c^6 - 4*a*c^7)*d^4 - 12*(b^3*c^5 - 4*a*b*c^6)*d^3*e + 6*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 12*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 - (b^6*c^2 - 12*a*b^4*c^3 + 42*a^2*b^2*c^4 - 40*a^3*c^5)*e^4)*f - (3*(b^3*c^5 - 4*a*b*c^6)*d^4 - 4*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^3*e + 18*(a*b^3*c^4 - 4*a^2*b*c^5)*d^2*e^2 + 4*(b^6*c^2 - 12*a*b^4*c^3 + 42*a^2*b^2*c^4 - 40*a^3*c^5)*d*e^3 - (2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*e^4)*g)*x^3 + ((18*(b^3*c^5 - 4*a*b*c^6)*d^4 - 36*(b^4*c^4 - 4*a*b^2*c^5)*d^3*e + 18*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*d^2*e^2 - 4*(b^6*c^2 - 3*a*b^4*c^3 + 12*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^3 - (b^7*c - 12*a*b^5*c^2 + 30*a^2*b^3*c^3 + 8*a^3*b*c^4)*e^4)*f - (9*(b^4*c^4 - 4*a*b^2*c^5)*d^4 - 12*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*d^3*e + 6*(b^6*c^2 - 3*a*b^4*c^3 + 12*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^2 + 4*(b^7*c - 12*a*b^5*c^2 + 30*a^2*b^3*c^3 + 8*a^3*b*c^4)*d*e^3 - (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*e^4)*g)*x^2 - ((12*(c^7*d^4 - 2*b*c^6*d^3*e - 2*a*b*c^5*d*e^3 + a^2*c^5*e^4 + (b^2*c^5 + 2*a*c^6)*d^2*e^2)*f - (6*b*c^6*d^4 + 36*a*b*c^5*d^2*e^2 - 48*a^2*c^5*d*e^3 - 8*(b^2*c^5 + 2*a*c^6)*d^3*e + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*e^4)*g)*x^4 + 2*(12*(b*c^6*d^4 - 2*b^2*c^5*d^3*e - 2*a*b^2*c^4*d*e^3 + a^2*b*c^4*e^4 + (b^3*c^4 + 2*a*b*c^5)*d^2*e^2)*f - (6*b^2*c^5*d^4 + 36*a*b^2*c^4*d^2*e^2 - 48*a^2*b*c^4*d*e^3 - 8*(b^3*c^4 + 2*a*b*c^5)*d^3*e + (b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*e^4)*g)*x^3 + (12*((b^2*c^5 + 2*a*c^6)*d^4 - 2*(b^3*c^4 + 2*a*b*c^5)*d^3*e + (b^4*c^3 + 4*a*b^2*c^4 + 4*a^2*c^5)*d^2*e^2 - 2*(a*b^3*c^3 + 2*a^2*b*c^4)*d*e^3 + (a^2*b^2*c^3 + 2*a^3*c^4)*e^4)*f - (6*(b^3*c^4 + 2*a*b*c^5)*d^4 - 8*(b^4*c^3 + 4*a*b^2*c^4 + 4*a^2*c^5)*d^3*e + 36*(a*b^3*c^3 + 2*a^2*b*c^4)*d^2*e^2 - 48*(a^2*b^2*c^3 + 2*a^3*c^4)*d*e^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*e^4)*g)*x^2 + 12*(a^2*c^5*d^4 - 2*a^2*b*c^4*d^3*e - 2*a^3*b*c^3*d*e^3 + a^4*c^3*e^4 + (a^2*b^2*c^3 + 2*a^3*c^4)*d^2*e^2)*f - (6*a^2*b*c^4*d^4 + 36*a^3*b*c^3*d^2*e^2 - 48*a^4*c^3*d*e^3 - 8*(a^2*b^2*c^3 + 2*a^3*c^4)*d^3*e + (a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2)*e^4)*g + 2*(12*(a*b*c^5*d^4 - 2*a*b^2*c^4*d^3*e - 2*a^2*b^2*c^3*d*e^3 + a^3*b*c^3*e^4 + (a*b^3*c^3 + 2*a^2*b*c^4)*d^2*e^2)*f - (6*a*b^2*c^4*d^4 + 36*a^2*b^2*c^3*d^2*e^2 - 48*a^3*b*c^3*d*e^3 - 8*(a*b^3*c^3 + 2*a^2*b*c^4)*d^3*e + (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*e^4)*g)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - ((b^5*c^3 - 14*a*b^3*c^4 + 40*a^2*b*c^5)*d^4 + 4*(a*b^4*c^3 + 4*a^2*b^2*c^4 - 32*a^3*c^5)*d^3*e - 36*(a^2*b^3*c^3 - 4*a^3*b*c^4)*d^2*e^2 + 4*(a^2*b^4*c^2 + 4*a^3*b^2*c^3 - 32*a^4*c^4)*d*e^3 + (a^2*b^5*c - 14*a^3*b^3*c^2 + 40*a^4*b*c^3)*e^4)*f - ((a*b^4*c^3 + 4*a^2*b^2*c^4 - 32*a^3*c^5)*d^4 - 24*(a^2*b^3*c^3 - 4*a^3*b*c^4)*d^3*e + 6*(a^2*b^4*c^2 + 4*a^3*b^2*c^3 - 32*a^4*c^4)*d^2*e^2 + 4*(a^2*b^5*c - 14*a^3*b^3*c^2 + 40*a^4*b*c^3)*d*e^3 - 3*(a^2*b^6 - 11*a^3*b^4*c + 36*a^4*b^2*c^2 - 32*a^5*c^3)*e^4)*g + 2*((2*(b^4*c^4 + a*b^2*c^5 - 20*a^2*c^6)*d^4 - 4*(b^5*c^3 + a*b^3*c^4 - 20*a^2*b*c^5)*d^3*e + 6*(5*a*b^4*c^3 - 22*a^2*b^2*c^4 + 8*a^3*c^5)*d^2*e^2 - 4*(a*b^5*c^2 + a^2*b^3*c^3 - 20*a^3*b*c^4)*d*e^3 - (a*b^6*c - 14*a^2*b^4*c^2 + 46*a^3*b^2*c^3 - 24*a^4*c^4)*e^4)*f - ((b^5*c^3 + a*b^3*c^4 - 20*a^2*b*c^5)*d^4 - 4*(5*a*b^4*c^3 - 22*a^2*b^2*c^4 + 8*a^3*c^5)*d^3*e + 6*(a*b^5*c^2 + a^2*b^3*c^3 - 20*a^3*b*c^4)*d^2*e^2 + 4*(a*b^6*c - 14*a^2*b^4*c^2 + 46*a^3*b^2*c^3 - 24*a^4*c^4)*d*e^3 - (3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*e^4)*g)*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4*g*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^4*g*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*e^4*g*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*e^4*g*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4*g)*log(c*x^2 + b*x + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^4 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^3 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^2 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x), 1/2*(2*((6*(b^2*c^6 - 4*a*c^7)*d^4 - 12*(b^3*c^5 - 4*a*b*c^6)*d^3*e + 6*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 12*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 - (b^6*c^2 - 12*a*b^4*c^3 + 42*a^2*b^2*c^4 - 40*a^3*c^5)*e^4)*f - (3*(b^3*c^5 - 4*a*b*c^6)*d^4 - 4*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^3*e + 18*(a*b^3*c^4 - 4*a^2*b*c^5)*d^2*e^2 + 4*(b^6*c^2 - 12*a*b^4*c^3 + 42*a^2*b^2*c^4 - 40*a^3*c^5)*d*e^3 - (2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*e^4)*g)*x^3 + ((18*(b^3*c^5 - 4*a*b*c^6)*d^4 - 36*(b^4*c^4 - 4*a*b^2*c^5)*d^3*e + 18*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*d^2*e^2 - 4*(b^6*c^2 - 3*a*b^4*c^3 + 12*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^3 - (b^7*c - 12*a*b^5*c^2 + 30*a^2*b^3*c^3 + 8*a^3*b*c^4)*e^4)*f - (9*(b^4*c^4 - 4*a*b^2*c^5)*d^4 - 12*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*d^3*e + 6*(b^6*c^2 - 3*a*b^4*c^3 + 12*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^2 + 4*(b^7*c - 12*a*b^5*c^2 + 30*a^2*b^3*c^3 + 8*a^3*b*c^4)*d*e^3 - (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*e^4)*g)*x^2 - 2*((12*(c^7*d^4 - 2*b*c^6*d^3*e - 2*a*b*c^5*d*e^3 + a^2*c^5*e^4 + (b^2*c^5 + 2*a*c^6)*d^2*e^2)*f - (6*b*c^6*d^4 + 36*a*b*c^5*d^2*e^2 - 48*a^2*c^5*d*e^3 - 8*(b^2*c^5 + 2*a*c^6)*d^3*e + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*e^4)*g)*x^4 + 2*(12*(b*c^6*d^4 - 2*b^2*c^5*d^3*e - 2*a*b^2*c^4*d*e^3 + a^2*b*c^4*e^4 + (b^3*c^4 + 2*a*b*c^5)*d^2*e^2)*f - (6*b^2*c^5*d^4 + 36*a*b^2*c^4*d^2*e^2 - 48*a^2*b*c^4*d*e^3 - 8*(b^3*c^4 + 2*a*b*c^5)*d^3*e + (b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*e^4)*g)*x^3 + (12*((b^2*c^5 + 2*a*c^6)*d^4 - 2*(b^3*c^4 + 2*a*b*c^5)*d^3*e + (b^4*c^3 + 4*a*b^2*c^4 + 4*a^2*c^5)*d^2*e^2 - 2*(a*b^3*c^3 + 2*a^2*b*c^4)*d*e^3 + (a^2*b^2*c^3 + 2*a^3*c^4)*e^4)*f - (6*(b^3*c^4 + 2*a*b*c^5)*d^4 - 8*(b^4*c^3 + 4*a*b^2*c^4 + 4*a^2*c^5)*d^3*e + 36*(a*b^3*c^3 + 2*a^2*b*c^4)*d^2*e^2 - 48*(a^2*b^2*c^3 + 2*a^3*c^4)*d*e^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*e^4)*g)*x^2 + 12*(a^2*c^5*d^4 - 2*a^2*b*c^4*d^3*e - 2*a^3*b*c^3*d*e^3 + a^4*c^3*e^4 + (a^2*b^2*c^3 + 2*a^3*c^4)*d^2*e^2)*f - (6*a^2*b*c^4*d^4 + 36*a^3*b*c^3*d^2*e^2 - 48*a^4*c^3*d*e^3 - 8*(a^2*b^2*c^3 + 2*a^3*c^4)*d^3*e + (a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2)*e^4)*g + 2*(12*(a*b*c^5*d^4 - 2*a*b^2*c^4*d^3*e - 2*a^2*b^2*c^3*d*e^3 + a^3*b*c^3*e^4 + (a*b^3*c^3 + 2*a^2*b*c^4)*d^2*e^2)*f - (6*a*b^2*c^4*d^4 + 36*a^2*b^2*c^3*d^2*e^2 - 48*a^3*b*c^3*d*e^3 - 8*(a*b^3*c^3 + 2*a^2*b*c^4)*d^3*e + (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*e^4)*g)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - ((b^5*c^3 - 14*a*b^3*c^4 + 40*a^2*b*c^5)*d^4 + 4*(a*b^4*c^3 + 4*a^2*b^2*c^4 - 32*a^3*c^5)*d^3*e - 36*(a^2*b^3*c^3 - 4*a^3*b*c^4)*d^2*e^2 + 4*(a^2*b^4*c^2 + 4*a^3*b^2*c^3 - 32*a^4*c^4)*d*e^3 + (a^2*b^5*c - 14*a^3*b^3*c^2 + 40*a^4*b*c^3)*e^4)*f - ((a*b^4*c^3 + 4*a^2*b^2*c^4 - 32*a^3*c^5)*d^4 - 24*(a^2*b^3*c^3 - 4*a^3*b*c^4)*d^3*e + 6*(a^2*b^4*c^2 + 4*a^3*b^2*c^3 - 32*a^4*c^4)*d^2*e^2 + 4*(a^2*b^5*c - 14*a^3*b^3*c^2 + 40*a^4*b*c^3)*d*e^3 - 3*(a^2*b^6 - 11*a^3*b^4*c + 36*a^4*b^2*c^2 - 32*a^5*c^3)*e^4)*g + 2*((2*(b^4*c^4 + a*b^2*c^5 - 20*a^2*c^6)*d^4 - 4*(b^5*c^3 + a*b^3*c^4 - 20*a^2*b*c^5)*d^3*e + 6*(5*a*b^4*c^3 - 22*a^2*b^2*c^4 + 8*a^3*c^5)*d^2*e^2 - 4*(a*b^5*c^2 + a^2*b^3*c^3 - 20*a^3*b*c^4)*d*e^3 - (a*b^6*c - 14*a^2*b^4*c^2 + 46*a^3*b^2*c^3 - 24*a^4*c^4)*e^4)*f - ((b^5*c^3 + a*b^3*c^4 - 20*a^2*b*c^5)*d^4 - 4*(5*a*b^4*c^3 - 22*a^2*b^2*c^4 + 8*a^3*c^5)*d^3*e + 6*(a*b^5*c^2 + a^2*b^3*c^3 - 20*a^3*b*c^4)*d^2*e^2 + 4*(a*b^6*c - 14*a^2*b^4*c^2 + 46*a^3*b^2*c^3 - 24*a^4*c^4)*d*e^3 - (3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*e^4)*g)*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4*g*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^4*g*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*e^4*g*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*e^4*g*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4*g)*log(c*x^2 + b*x + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^4 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^3 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^2 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x)]","B",0
2372,1,3941,0,0.514679," ","integrate((e*x+d)^3*(g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{3} - 3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{2} e + {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d e^{2} - {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} e^{3}\right)} f - {\left(3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} - 3 \, {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{2} e + 9 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{2} + {\left(b^{6} c - 12 \, a b^{4} c^{2} + 42 \, a^{2} b^{2} c^{3} - 40 \, a^{3} c^{4}\right)} e^{3}\right)} g\right)} x^{3} + {\left({\left(18 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} - 27 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{2} e + 9 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d e^{2} - {\left(b^{6} c - 3 \, a b^{4} c^{2} + 12 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{3}\right)} f - {\left(9 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{3} - 9 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 3 \, a b^{4} c^{2} + 12 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{2} + {\left(b^{7} - 12 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} e^{3}\right)} g\right)} x^{2} + 6 \, {\left({\left({\left(2 \, c^{6} d^{3} - 3 \, b c^{5} d^{2} e - a b c^{4} e^{3} + {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d e^{2}\right)} f - {\left(b c^{5} d^{3} + 3 \, a b c^{4} d e^{2} - 2 \, a^{2} c^{4} e^{3} - {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{2} e\right)} g\right)} x^{4} + 2 \, {\left({\left(2 \, b c^{5} d^{3} - 3 \, b^{2} c^{4} d^{2} e - a b^{2} c^{3} e^{3} + {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d e^{2}\right)} f - {\left(b^{2} c^{4} d^{3} + 3 \, a b^{2} c^{3} d e^{2} - 2 \, a^{2} b c^{3} e^{3} - {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{2} e\right)} g\right)} x^{3} + {\left({\left(2 \, {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{3} - 3 \, {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{2} e + {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e^{2} - {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} e^{3}\right)} f - {\left({\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{3} - {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{2} e + 3 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e^{2} - 2 \, {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} e^{3}\right)} g\right)} x^{2} + {\left(2 \, a^{2} c^{4} d^{3} - 3 \, a^{2} b c^{3} d^{2} e - a^{3} b c^{2} e^{3} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{2}\right)} f - {\left(a^{2} b c^{3} d^{3} + 3 \, a^{3} b c^{2} d e^{2} - 2 \, a^{4} c^{2} e^{3} - {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{2} e\right)} g + 2 \, {\left({\left(2 \, a b c^{4} d^{3} - 3 \, a b^{2} c^{3} d^{2} e - a^{2} b^{2} c^{2} e^{3} + {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e^{2}\right)} f - {\left(a b^{2} c^{3} d^{3} + 3 \, a^{2} b^{2} c^{2} d e^{2} - 2 \, a^{3} b c^{2} e^{3} - {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d^{2} e\right)} g\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left({\left(b^{5} c^{2} - 14 \, a b^{3} c^{3} + 40 \, a^{2} b c^{4}\right)} d^{3} + 3 \, {\left(a b^{4} c^{2} + 4 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d^{2} e - 18 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d e^{2} + {\left(a^{2} b^{4} c + 4 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} e^{3}\right)} f - {\left({\left(a b^{4} c^{2} + 4 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d^{3} - 18 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{2} e + 3 \, {\left(a^{2} b^{4} c + 4 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d e^{2} + {\left(a^{2} b^{5} - 14 \, a^{3} b^{3} c + 40 \, a^{4} b c^{2}\right)} e^{3}\right)} g + 2 \, {\left({\left(2 \, {\left(b^{4} c^{3} + a b^{2} c^{4} - 20 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} + a b^{3} c^{3} - 20 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(5 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d e^{2} - {\left(a b^{5} c + a^{2} b^{3} c^{2} - 20 \, a^{3} b c^{3}\right)} e^{3}\right)} f - {\left({\left(b^{5} c^{2} + a b^{3} c^{3} - 20 \, a^{2} b c^{4}\right)} d^{3} - 3 \, {\left(5 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{2} e + 3 \, {\left(a b^{5} c + a^{2} b^{3} c^{2} - 20 \, a^{3} b c^{3}\right)} d e^{2} + {\left(a b^{6} - 14 \, a^{2} b^{4} c + 46 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} e^{3}\right)} g\right)} x}{2 \, {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{3} + {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} + 24 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} - 128 \, a^{4} c^{6}\right)} x^{2} + 2 \, {\left(a b^{7} c^{2} - 12 \, a^{2} b^{5} c^{3} + 48 \, a^{3} b^{3} c^{4} - 64 \, a^{4} b c^{5}\right)} x\right)}}, \frac{2 \, {\left(3 \, {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{3} - 3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{2} e + {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d e^{2} - {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} e^{3}\right)} f - {\left(3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} - 3 \, {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{2} e + 9 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{2} + {\left(b^{6} c - 12 \, a b^{4} c^{2} + 42 \, a^{2} b^{2} c^{3} - 40 \, a^{3} c^{4}\right)} e^{3}\right)} g\right)} x^{3} + {\left({\left(18 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} - 27 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{2} e + 9 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d e^{2} - {\left(b^{6} c - 3 \, a b^{4} c^{2} + 12 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{3}\right)} f - {\left(9 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{3} - 9 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 3 \, a b^{4} c^{2} + 12 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{2} + {\left(b^{7} - 12 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} e^{3}\right)} g\right)} x^{2} - 12 \, {\left({\left({\left(2 \, c^{6} d^{3} - 3 \, b c^{5} d^{2} e - a b c^{4} e^{3} + {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d e^{2}\right)} f - {\left(b c^{5} d^{3} + 3 \, a b c^{4} d e^{2} - 2 \, a^{2} c^{4} e^{3} - {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{2} e\right)} g\right)} x^{4} + 2 \, {\left({\left(2 \, b c^{5} d^{3} - 3 \, b^{2} c^{4} d^{2} e - a b^{2} c^{3} e^{3} + {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d e^{2}\right)} f - {\left(b^{2} c^{4} d^{3} + 3 \, a b^{2} c^{3} d e^{2} - 2 \, a^{2} b c^{3} e^{3} - {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{2} e\right)} g\right)} x^{3} + {\left({\left(2 \, {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{3} - 3 \, {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{2} e + {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e^{2} - {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} e^{3}\right)} f - {\left({\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{3} - {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{2} e + 3 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e^{2} - 2 \, {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} e^{3}\right)} g\right)} x^{2} + {\left(2 \, a^{2} c^{4} d^{3} - 3 \, a^{2} b c^{3} d^{2} e - a^{3} b c^{2} e^{3} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{2}\right)} f - {\left(a^{2} b c^{3} d^{3} + 3 \, a^{3} b c^{2} d e^{2} - 2 \, a^{4} c^{2} e^{3} - {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{2} e\right)} g + 2 \, {\left({\left(2 \, a b c^{4} d^{3} - 3 \, a b^{2} c^{3} d^{2} e - a^{2} b^{2} c^{2} e^{3} + {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e^{2}\right)} f - {\left(a b^{2} c^{3} d^{3} + 3 \, a^{2} b^{2} c^{2} d e^{2} - 2 \, a^{3} b c^{2} e^{3} - {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d^{2} e\right)} g\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{5} c^{2} - 14 \, a b^{3} c^{3} + 40 \, a^{2} b c^{4}\right)} d^{3} + 3 \, {\left(a b^{4} c^{2} + 4 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d^{2} e - 18 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d e^{2} + {\left(a^{2} b^{4} c + 4 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} e^{3}\right)} f - {\left({\left(a b^{4} c^{2} + 4 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d^{3} - 18 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{2} e + 3 \, {\left(a^{2} b^{4} c + 4 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d e^{2} + {\left(a^{2} b^{5} - 14 \, a^{3} b^{3} c + 40 \, a^{4} b c^{2}\right)} e^{3}\right)} g + 2 \, {\left({\left(2 \, {\left(b^{4} c^{3} + a b^{2} c^{4} - 20 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} + a b^{3} c^{3} - 20 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(5 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d e^{2} - {\left(a b^{5} c + a^{2} b^{3} c^{2} - 20 \, a^{3} b c^{3}\right)} e^{3}\right)} f - {\left({\left(b^{5} c^{2} + a b^{3} c^{3} - 20 \, a^{2} b c^{4}\right)} d^{3} - 3 \, {\left(5 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{2} e + 3 \, {\left(a b^{5} c + a^{2} b^{3} c^{2} - 20 \, a^{3} b c^{3}\right)} d e^{2} + {\left(a b^{6} - 14 \, a^{2} b^{4} c + 46 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} e^{3}\right)} g\right)} x}{2 \, {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{3} + {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} + 24 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} - 128 \, a^{4} c^{6}\right)} x^{2} + 2 \, {\left(a b^{7} c^{2} - 12 \, a^{2} b^{5} c^{3} + 48 \, a^{3} b^{3} c^{4} - 64 \, a^{4} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(3*(2*(b^2*c^5 - 4*a*c^6)*d^3 - 3*(b^3*c^4 - 4*a*b*c^5)*d^2*e + (b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d*e^2 - (a*b^3*c^3 - 4*a^2*b*c^4)*e^3)*f - (3*(b^3*c^4 - 4*a*b*c^5)*d^3 - 3*(b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^2*e + 9*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e^2 + (b^6*c - 12*a*b^4*c^2 + 42*a^2*b^2*c^3 - 40*a^3*c^4)*e^3)*g)*x^3 + ((18*(b^3*c^4 - 4*a*b*c^5)*d^3 - 27*(b^4*c^3 - 4*a*b^2*c^4)*d^2*e + 9*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d*e^2 - (b^6*c - 3*a*b^4*c^2 + 12*a^2*b^2*c^3 - 64*a^3*c^4)*e^3)*f - (9*(b^4*c^3 - 4*a*b^2*c^4)*d^3 - 9*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^2*e + 3*(b^6*c - 3*a*b^4*c^2 + 12*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^2 + (b^7 - 12*a*b^5*c + 30*a^2*b^3*c^2 + 8*a^3*b*c^3)*e^3)*g)*x^2 + 6*(((2*c^6*d^3 - 3*b*c^5*d^2*e - a*b*c^4*e^3 + (b^2*c^4 + 2*a*c^5)*d*e^2)*f - (b*c^5*d^3 + 3*a*b*c^4*d*e^2 - 2*a^2*c^4*e^3 - (b^2*c^4 + 2*a*c^5)*d^2*e)*g)*x^4 + 2*((2*b*c^5*d^3 - 3*b^2*c^4*d^2*e - a*b^2*c^3*e^3 + (b^3*c^3 + 2*a*b*c^4)*d*e^2)*f - (b^2*c^4*d^3 + 3*a*b^2*c^3*d*e^2 - 2*a^2*b*c^3*e^3 - (b^3*c^3 + 2*a*b*c^4)*d^2*e)*g)*x^3 + ((2*(b^2*c^4 + 2*a*c^5)*d^3 - 3*(b^3*c^3 + 2*a*b*c^4)*d^2*e + (b^4*c^2 + 4*a*b^2*c^3 + 4*a^2*c^4)*d*e^2 - (a*b^3*c^2 + 2*a^2*b*c^3)*e^3)*f - ((b^3*c^3 + 2*a*b*c^4)*d^3 - (b^4*c^2 + 4*a*b^2*c^3 + 4*a^2*c^4)*d^2*e + 3*(a*b^3*c^2 + 2*a^2*b*c^3)*d*e^2 - 2*(a^2*b^2*c^2 + 2*a^3*c^3)*e^3)*g)*x^2 + (2*a^2*c^4*d^3 - 3*a^2*b*c^3*d^2*e - a^3*b*c^2*e^3 + (a^2*b^2*c^2 + 2*a^3*c^3)*d*e^2)*f - (a^2*b*c^3*d^3 + 3*a^3*b*c^2*d*e^2 - 2*a^4*c^2*e^3 - (a^2*b^2*c^2 + 2*a^3*c^3)*d^2*e)*g + 2*((2*a*b*c^4*d^3 - 3*a*b^2*c^3*d^2*e - a^2*b^2*c^2*e^3 + (a*b^3*c^2 + 2*a^2*b*c^3)*d*e^2)*f - (a*b^2*c^3*d^3 + 3*a^2*b^2*c^2*d*e^2 - 2*a^3*b*c^2*e^3 - (a*b^3*c^2 + 2*a^2*b*c^3)*d^2*e)*g)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - ((b^5*c^2 - 14*a*b^3*c^3 + 40*a^2*b*c^4)*d^3 + 3*(a*b^4*c^2 + 4*a^2*b^2*c^3 - 32*a^3*c^4)*d^2*e - 18*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d*e^2 + (a^2*b^4*c + 4*a^3*b^2*c^2 - 32*a^4*c^3)*e^3)*f - ((a*b^4*c^2 + 4*a^2*b^2*c^3 - 32*a^3*c^4)*d^3 - 18*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^2*e + 3*(a^2*b^4*c + 4*a^3*b^2*c^2 - 32*a^4*c^3)*d*e^2 + (a^2*b^5 - 14*a^3*b^3*c + 40*a^4*b*c^2)*e^3)*g + 2*((2*(b^4*c^3 + a*b^2*c^4 - 20*a^2*c^5)*d^3 - 3*(b^5*c^2 + a*b^3*c^3 - 20*a^2*b*c^4)*d^2*e + 3*(5*a*b^4*c^2 - 22*a^2*b^2*c^3 + 8*a^3*c^4)*d*e^2 - (a*b^5*c + a^2*b^3*c^2 - 20*a^3*b*c^3)*e^3)*f - ((b^5*c^2 + a*b^3*c^3 - 20*a^2*b*c^4)*d^3 - 3*(5*a*b^4*c^2 - 22*a^2*b^2*c^3 + 8*a^3*c^4)*d^2*e + 3*(a*b^5*c + a^2*b^3*c^2 - 20*a^3*b*c^3)*d*e^2 + (a*b^6 - 14*a^2*b^4*c + 46*a^3*b^2*c^2 - 24*a^4*c^3)*e^3)*g)*x)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^4 + 2*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^3 + (b^8*c^2 - 10*a*b^6*c^3 + 24*a^2*b^4*c^4 + 32*a^3*b^2*c^5 - 128*a^4*c^6)*x^2 + 2*(a*b^7*c^2 - 12*a^2*b^5*c^3 + 48*a^3*b^3*c^4 - 64*a^4*b*c^5)*x), 1/2*(2*(3*(2*(b^2*c^5 - 4*a*c^6)*d^3 - 3*(b^3*c^4 - 4*a*b*c^5)*d^2*e + (b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d*e^2 - (a*b^3*c^3 - 4*a^2*b*c^4)*e^3)*f - (3*(b^3*c^4 - 4*a*b*c^5)*d^3 - 3*(b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^2*e + 9*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e^2 + (b^6*c - 12*a*b^4*c^2 + 42*a^2*b^2*c^3 - 40*a^3*c^4)*e^3)*g)*x^3 + ((18*(b^3*c^4 - 4*a*b*c^5)*d^3 - 27*(b^4*c^3 - 4*a*b^2*c^4)*d^2*e + 9*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d*e^2 - (b^6*c - 3*a*b^4*c^2 + 12*a^2*b^2*c^3 - 64*a^3*c^4)*e^3)*f - (9*(b^4*c^3 - 4*a*b^2*c^4)*d^3 - 9*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^2*e + 3*(b^6*c - 3*a*b^4*c^2 + 12*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^2 + (b^7 - 12*a*b^5*c + 30*a^2*b^3*c^2 + 8*a^3*b*c^3)*e^3)*g)*x^2 - 12*(((2*c^6*d^3 - 3*b*c^5*d^2*e - a*b*c^4*e^3 + (b^2*c^4 + 2*a*c^5)*d*e^2)*f - (b*c^5*d^3 + 3*a*b*c^4*d*e^2 - 2*a^2*c^4*e^3 - (b^2*c^4 + 2*a*c^5)*d^2*e)*g)*x^4 + 2*((2*b*c^5*d^3 - 3*b^2*c^4*d^2*e - a*b^2*c^3*e^3 + (b^3*c^3 + 2*a*b*c^4)*d*e^2)*f - (b^2*c^4*d^3 + 3*a*b^2*c^3*d*e^2 - 2*a^2*b*c^3*e^3 - (b^3*c^3 + 2*a*b*c^4)*d^2*e)*g)*x^3 + ((2*(b^2*c^4 + 2*a*c^5)*d^3 - 3*(b^3*c^3 + 2*a*b*c^4)*d^2*e + (b^4*c^2 + 4*a*b^2*c^3 + 4*a^2*c^4)*d*e^2 - (a*b^3*c^2 + 2*a^2*b*c^3)*e^3)*f - ((b^3*c^3 + 2*a*b*c^4)*d^3 - (b^4*c^2 + 4*a*b^2*c^3 + 4*a^2*c^4)*d^2*e + 3*(a*b^3*c^2 + 2*a^2*b*c^3)*d*e^2 - 2*(a^2*b^2*c^2 + 2*a^3*c^3)*e^3)*g)*x^2 + (2*a^2*c^4*d^3 - 3*a^2*b*c^3*d^2*e - a^3*b*c^2*e^3 + (a^2*b^2*c^2 + 2*a^3*c^3)*d*e^2)*f - (a^2*b*c^3*d^3 + 3*a^3*b*c^2*d*e^2 - 2*a^4*c^2*e^3 - (a^2*b^2*c^2 + 2*a^3*c^3)*d^2*e)*g + 2*((2*a*b*c^4*d^3 - 3*a*b^2*c^3*d^2*e - a^2*b^2*c^2*e^3 + (a*b^3*c^2 + 2*a^2*b*c^3)*d*e^2)*f - (a*b^2*c^3*d^3 + 3*a^2*b^2*c^2*d*e^2 - 2*a^3*b*c^2*e^3 - (a*b^3*c^2 + 2*a^2*b*c^3)*d^2*e)*g)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - ((b^5*c^2 - 14*a*b^3*c^3 + 40*a^2*b*c^4)*d^3 + 3*(a*b^4*c^2 + 4*a^2*b^2*c^3 - 32*a^3*c^4)*d^2*e - 18*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d*e^2 + (a^2*b^4*c + 4*a^3*b^2*c^2 - 32*a^4*c^3)*e^3)*f - ((a*b^4*c^2 + 4*a^2*b^2*c^3 - 32*a^3*c^4)*d^3 - 18*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^2*e + 3*(a^2*b^4*c + 4*a^3*b^2*c^2 - 32*a^4*c^3)*d*e^2 + (a^2*b^5 - 14*a^3*b^3*c + 40*a^4*b*c^2)*e^3)*g + 2*((2*(b^4*c^3 + a*b^2*c^4 - 20*a^2*c^5)*d^3 - 3*(b^5*c^2 + a*b^3*c^3 - 20*a^2*b*c^4)*d^2*e + 3*(5*a*b^4*c^2 - 22*a^2*b^2*c^3 + 8*a^3*c^4)*d*e^2 - (a*b^5*c + a^2*b^3*c^2 - 20*a^3*b*c^3)*e^3)*f - ((b^5*c^2 + a*b^3*c^3 - 20*a^2*b*c^4)*d^3 - 3*(5*a*b^4*c^2 - 22*a^2*b^2*c^3 + 8*a^3*c^4)*d^2*e + 3*(a*b^5*c + a^2*b^3*c^2 - 20*a^3*b*c^3)*d*e^2 + (a*b^6 - 14*a^2*b^4*c + 46*a^3*b^2*c^2 - 24*a^4*c^3)*e^3)*g)*x)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^4 + 2*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^3 + (b^8*c^2 - 10*a*b^6*c^3 + 24*a^2*b^4*c^4 + 32*a^3*b^2*c^5 - 128*a^4*c^6)*x^2 + 2*(a*b^7*c^2 - 12*a^2*b^5*c^3 + 48*a^3*b^3*c^4 - 64*a^4*b*c^5)*x)]","B",0
2373,1,2906,0,0.456581," ","integrate((e*x+d)^2*(g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} - 6 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e + {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} e^{2}\right)} f - {\left(3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} - 2 \, {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d e + 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} e^{2}\right)} g\right)} x^{3} + {\left(3 \, {\left(6 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} - 6 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d e + {\left(b^{5} c - 2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} e^{2}\right)} f - {\left(9 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{2} - 6 \, {\left(b^{5} c - 2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 3 \, a b^{4} c + 12 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{2}\right)} g\right)} x^{2} - 2 \, {\left({\left({\left(6 \, c^{5} d^{2} - 6 \, b c^{4} d e + {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} e^{2}\right)} f - {\left(3 \, b c^{4} d^{2} + 3 \, a b c^{3} e^{2} - 2 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d e\right)} g\right)} x^{4} + 2 \, {\left({\left(6 \, b c^{4} d^{2} - 6 \, b^{2} c^{3} d e + {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} e^{2}\right)} f - {\left(3 \, b^{2} c^{3} d^{2} + 3 \, a b^{2} c^{2} e^{2} - 2 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d e\right)} g\right)} x^{3} + {\left({\left(6 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d^{2} - 6 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d e + {\left(b^{4} c + 4 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{2}\right)} f - {\left(3 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{2} - 2 \, {\left(b^{4} c + 4 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e + 3 \, {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} e^{2}\right)} g\right)} x^{2} + {\left(6 \, a^{2} c^{3} d^{2} - 6 \, a^{2} b c^{2} d e + {\left(a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e^{2}\right)} f - {\left(3 \, a^{2} b c^{2} d^{2} + 3 \, a^{3} b c e^{2} - 2 \, {\left(a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d e\right)} g + 2 \, {\left({\left(6 \, a b c^{3} d^{2} - 6 \, a b^{2} c^{2} d e + {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} e^{2}\right)} f - {\left(3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b^{2} c e^{2} - 2 \, {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} d e\right)} g\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left({\left(b^{5} c - 14 \, a b^{3} c^{2} + 40 \, a^{2} b c^{3}\right)} d^{2} + 2 \, {\left(a b^{4} c + 4 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d e - 6 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} e^{2}\right)} f - {\left({\left(a b^{4} c + 4 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d^{2} - 12 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c - 32 \, a^{4} c^{2}\right)} e^{2}\right)} g + 2 \, {\left({\left(2 \, {\left(b^{4} c^{2} + a b^{2} c^{3} - 20 \, a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c + a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} d e + {\left(5 \, a b^{4} c - 22 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} e^{2}\right)} f - {\left({\left(b^{5} c + a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} d^{2} - 2 \, {\left(5 \, a b^{4} c - 22 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d e + {\left(a b^{5} + a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} e^{2}\right)} g\right)} x}{2 \, {\left(a^{2} b^{6} c - 12 \, a^{3} b^{4} c^{2} + 48 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{4} + 2 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{3} + {\left(b^{8} c - 10 \, a b^{6} c^{2} + 24 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} - 128 \, a^{4} c^{5}\right)} x^{2} + 2 \, {\left(a b^{7} c - 12 \, a^{2} b^{5} c^{2} + 48 \, a^{3} b^{3} c^{3} - 64 \, a^{4} b c^{4}\right)} x\right)}}, \frac{2 \, {\left({\left(6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} - 6 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e + {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} e^{2}\right)} f - {\left(3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} - 2 \, {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d e + 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} e^{2}\right)} g\right)} x^{3} + {\left(3 \, {\left(6 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} - 6 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d e + {\left(b^{5} c - 2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} e^{2}\right)} f - {\left(9 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{2} - 6 \, {\left(b^{5} c - 2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 3 \, a b^{4} c + 12 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{2}\right)} g\right)} x^{2} - 4 \, {\left({\left({\left(6 \, c^{5} d^{2} - 6 \, b c^{4} d e + {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} e^{2}\right)} f - {\left(3 \, b c^{4} d^{2} + 3 \, a b c^{3} e^{2} - 2 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d e\right)} g\right)} x^{4} + 2 \, {\left({\left(6 \, b c^{4} d^{2} - 6 \, b^{2} c^{3} d e + {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} e^{2}\right)} f - {\left(3 \, b^{2} c^{3} d^{2} + 3 \, a b^{2} c^{2} e^{2} - 2 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d e\right)} g\right)} x^{3} + {\left({\left(6 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d^{2} - 6 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d e + {\left(b^{4} c + 4 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{2}\right)} f - {\left(3 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{2} - 2 \, {\left(b^{4} c + 4 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e + 3 \, {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} e^{2}\right)} g\right)} x^{2} + {\left(6 \, a^{2} c^{3} d^{2} - 6 \, a^{2} b c^{2} d e + {\left(a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e^{2}\right)} f - {\left(3 \, a^{2} b c^{2} d^{2} + 3 \, a^{3} b c e^{2} - 2 \, {\left(a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d e\right)} g + 2 \, {\left({\left(6 \, a b c^{3} d^{2} - 6 \, a b^{2} c^{2} d e + {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} e^{2}\right)} f - {\left(3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b^{2} c e^{2} - 2 \, {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} d e\right)} g\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{5} c - 14 \, a b^{3} c^{2} + 40 \, a^{2} b c^{3}\right)} d^{2} + 2 \, {\left(a b^{4} c + 4 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d e - 6 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} e^{2}\right)} f - {\left({\left(a b^{4} c + 4 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d^{2} - 12 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c - 32 \, a^{4} c^{2}\right)} e^{2}\right)} g + 2 \, {\left({\left(2 \, {\left(b^{4} c^{2} + a b^{2} c^{3} - 20 \, a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c + a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} d e + {\left(5 \, a b^{4} c - 22 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} e^{2}\right)} f - {\left({\left(b^{5} c + a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} d^{2} - 2 \, {\left(5 \, a b^{4} c - 22 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d e + {\left(a b^{5} + a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} e^{2}\right)} g\right)} x}{2 \, {\left(a^{2} b^{6} c - 12 \, a^{3} b^{4} c^{2} + 48 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{4} + 2 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{3} + {\left(b^{8} c - 10 \, a b^{6} c^{2} + 24 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} - 128 \, a^{4} c^{5}\right)} x^{2} + 2 \, {\left(a b^{7} c - 12 \, a^{2} b^{5} c^{2} + 48 \, a^{3} b^{3} c^{3} - 64 \, a^{4} b c^{4}\right)} x\right)}}\right]"," ",0,"[1/2*(2*((6*(b^2*c^4 - 4*a*c^5)*d^2 - 6*(b^3*c^3 - 4*a*b*c^4)*d*e + (b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*e^2)*f - (3*(b^3*c^3 - 4*a*b*c^4)*d^2 - 2*(b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*d*e + 3*(a*b^3*c^2 - 4*a^2*b*c^3)*e^2)*g)*x^3 + (3*(6*(b^3*c^3 - 4*a*b*c^4)*d^2 - 6*(b^4*c^2 - 4*a*b^2*c^3)*d*e + (b^5*c - 2*a*b^3*c^2 - 8*a^2*b*c^3)*e^2)*f - (9*(b^4*c^2 - 4*a*b^2*c^3)*d^2 - 6*(b^5*c - 2*a*b^3*c^2 - 8*a^2*b*c^3)*d*e + (b^6 - 3*a*b^4*c + 12*a^2*b^2*c^2 - 64*a^3*c^3)*e^2)*g)*x^2 - 2*(((6*c^5*d^2 - 6*b*c^4*d*e + (b^2*c^3 + 2*a*c^4)*e^2)*f - (3*b*c^4*d^2 + 3*a*b*c^3*e^2 - 2*(b^2*c^3 + 2*a*c^4)*d*e)*g)*x^4 + 2*((6*b*c^4*d^2 - 6*b^2*c^3*d*e + (b^3*c^2 + 2*a*b*c^3)*e^2)*f - (3*b^2*c^3*d^2 + 3*a*b^2*c^2*e^2 - 2*(b^3*c^2 + 2*a*b*c^3)*d*e)*g)*x^3 + ((6*(b^2*c^3 + 2*a*c^4)*d^2 - 6*(b^3*c^2 + 2*a*b*c^3)*d*e + (b^4*c + 4*a*b^2*c^2 + 4*a^2*c^3)*e^2)*f - (3*(b^3*c^2 + 2*a*b*c^3)*d^2 - 2*(b^4*c + 4*a*b^2*c^2 + 4*a^2*c^3)*d*e + 3*(a*b^3*c + 2*a^2*b*c^2)*e^2)*g)*x^2 + (6*a^2*c^3*d^2 - 6*a^2*b*c^2*d*e + (a^2*b^2*c + 2*a^3*c^2)*e^2)*f - (3*a^2*b*c^2*d^2 + 3*a^3*b*c*e^2 - 2*(a^2*b^2*c + 2*a^3*c^2)*d*e)*g + 2*((6*a*b*c^3*d^2 - 6*a*b^2*c^2*d*e + (a*b^3*c + 2*a^2*b*c^2)*e^2)*f - (3*a*b^2*c^2*d^2 + 3*a^2*b^2*c*e^2 - 2*(a*b^3*c + 2*a^2*b*c^2)*d*e)*g)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - ((b^5*c - 14*a*b^3*c^2 + 40*a^2*b*c^3)*d^2 + 2*(a*b^4*c + 4*a^2*b^2*c^2 - 32*a^3*c^3)*d*e - 6*(a^2*b^3*c - 4*a^3*b*c^2)*e^2)*f - ((a*b^4*c + 4*a^2*b^2*c^2 - 32*a^3*c^3)*d^2 - 12*(a^2*b^3*c - 4*a^3*b*c^2)*d*e + (a^2*b^4 + 4*a^3*b^2*c - 32*a^4*c^2)*e^2)*g + 2*((2*(b^4*c^2 + a*b^2*c^3 - 20*a^2*c^4)*d^2 - 2*(b^5*c + a*b^3*c^2 - 20*a^2*b*c^3)*d*e + (5*a*b^4*c - 22*a^2*b^2*c^2 + 8*a^3*c^3)*e^2)*f - ((b^5*c + a*b^3*c^2 - 20*a^2*b*c^3)*d^2 - 2*(5*a*b^4*c - 22*a^2*b^2*c^2 + 8*a^3*c^3)*d*e + (a*b^5 + a^2*b^3*c - 20*a^3*b*c^2)*e^2)*g)*x)/(a^2*b^6*c - 12*a^3*b^4*c^2 + 48*a^4*b^2*c^3 - 64*a^5*c^4 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^4 + 2*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^3 + (b^8*c - 10*a*b^6*c^2 + 24*a^2*b^4*c^3 + 32*a^3*b^2*c^4 - 128*a^4*c^5)*x^2 + 2*(a*b^7*c - 12*a^2*b^5*c^2 + 48*a^3*b^3*c^3 - 64*a^4*b*c^4)*x), 1/2*(2*((6*(b^2*c^4 - 4*a*c^5)*d^2 - 6*(b^3*c^3 - 4*a*b*c^4)*d*e + (b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*e^2)*f - (3*(b^3*c^3 - 4*a*b*c^4)*d^2 - 2*(b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*d*e + 3*(a*b^3*c^2 - 4*a^2*b*c^3)*e^2)*g)*x^3 + (3*(6*(b^3*c^3 - 4*a*b*c^4)*d^2 - 6*(b^4*c^2 - 4*a*b^2*c^3)*d*e + (b^5*c - 2*a*b^3*c^2 - 8*a^2*b*c^3)*e^2)*f - (9*(b^4*c^2 - 4*a*b^2*c^3)*d^2 - 6*(b^5*c - 2*a*b^3*c^2 - 8*a^2*b*c^3)*d*e + (b^6 - 3*a*b^4*c + 12*a^2*b^2*c^2 - 64*a^3*c^3)*e^2)*g)*x^2 - 4*(((6*c^5*d^2 - 6*b*c^4*d*e + (b^2*c^3 + 2*a*c^4)*e^2)*f - (3*b*c^4*d^2 + 3*a*b*c^3*e^2 - 2*(b^2*c^3 + 2*a*c^4)*d*e)*g)*x^4 + 2*((6*b*c^4*d^2 - 6*b^2*c^3*d*e + (b^3*c^2 + 2*a*b*c^3)*e^2)*f - (3*b^2*c^3*d^2 + 3*a*b^2*c^2*e^2 - 2*(b^3*c^2 + 2*a*b*c^3)*d*e)*g)*x^3 + ((6*(b^2*c^3 + 2*a*c^4)*d^2 - 6*(b^3*c^2 + 2*a*b*c^3)*d*e + (b^4*c + 4*a*b^2*c^2 + 4*a^2*c^3)*e^2)*f - (3*(b^3*c^2 + 2*a*b*c^3)*d^2 - 2*(b^4*c + 4*a*b^2*c^2 + 4*a^2*c^3)*d*e + 3*(a*b^3*c + 2*a^2*b*c^2)*e^2)*g)*x^2 + (6*a^2*c^3*d^2 - 6*a^2*b*c^2*d*e + (a^2*b^2*c + 2*a^3*c^2)*e^2)*f - (3*a^2*b*c^2*d^2 + 3*a^3*b*c*e^2 - 2*(a^2*b^2*c + 2*a^3*c^2)*d*e)*g + 2*((6*a*b*c^3*d^2 - 6*a*b^2*c^2*d*e + (a*b^3*c + 2*a^2*b*c^2)*e^2)*f - (3*a*b^2*c^2*d^2 + 3*a^2*b^2*c*e^2 - 2*(a*b^3*c + 2*a^2*b*c^2)*d*e)*g)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - ((b^5*c - 14*a*b^3*c^2 + 40*a^2*b*c^3)*d^2 + 2*(a*b^4*c + 4*a^2*b^2*c^2 - 32*a^3*c^3)*d*e - 6*(a^2*b^3*c - 4*a^3*b*c^2)*e^2)*f - ((a*b^4*c + 4*a^2*b^2*c^2 - 32*a^3*c^3)*d^2 - 12*(a^2*b^3*c - 4*a^3*b*c^2)*d*e + (a^2*b^4 + 4*a^3*b^2*c - 32*a^4*c^2)*e^2)*g + 2*((2*(b^4*c^2 + a*b^2*c^3 - 20*a^2*c^4)*d^2 - 2*(b^5*c + a*b^3*c^2 - 20*a^2*b*c^3)*d*e + (5*a*b^4*c - 22*a^2*b^2*c^2 + 8*a^3*c^3)*e^2)*f - ((b^5*c + a*b^3*c^2 - 20*a^2*b*c^3)*d^2 - 2*(5*a*b^4*c - 22*a^2*b^2*c^2 + 8*a^3*c^3)*d*e + (a*b^5 + a^2*b^3*c - 20*a^3*b*c^2)*e^2)*g)*x)/(a^2*b^6*c - 12*a^3*b^4*c^2 + 48*a^4*b^2*c^3 - 64*a^5*c^4 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^4 + 2*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^3 + (b^8*c - 10*a*b^6*c^2 + 24*a^2*b^4*c^3 + 32*a^3*b^2*c^4 - 128*a^4*c^5)*x^2 + 2*(a*b^7*c - 12*a^2*b^5*c^2 + 48*a^3*b^3*c^3 - 64*a^4*b*c^4)*x)]","B",0
2374,1,1879,0,0.470026," ","integrate((e*x+d)*(g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} f - {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e\right)} g\right)} x^{3} + 3 \, {\left(3 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e\right)} f - {\left(3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d - {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} e\right)} g\right)} x^{2} + 2 \, {\left({\left(3 \, {\left(2 \, c^{4} d - b c^{3} e\right)} f - {\left(3 \, b c^{3} d - {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} e\right)} g\right)} x^{4} + 2 \, {\left(3 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} f - {\left(3 \, b^{2} c^{2} d - {\left(b^{3} c + 2 \, a b c^{2}\right)} e\right)} g\right)} x^{3} + {\left(3 \, {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d - {\left(b^{3} c + 2 \, a b c^{2}\right)} e\right)} f - {\left(3 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} d - {\left(b^{4} + 4 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} g\right)} x^{2} + 3 \, {\left(2 \, a^{2} c^{2} d - a^{2} b c e\right)} f - {\left(3 \, a^{2} b c d - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e\right)} g + 2 \, {\left(3 \, {\left(2 \, a b c^{2} d - a b^{2} c e\right)} f - {\left(3 \, a b^{2} c d - {\left(a b^{3} + 2 \, a^{2} b c\right)} e\right)} g\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left({\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} d + {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} e\right)} f - {\left({\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} d - 6 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e\right)} g + 2 \, {\left({\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} e\right)} f - {\left({\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d - {\left(5 \, a b^{4} - 22 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e\right)} g\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}, \frac{2 \, {\left(3 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} f - {\left(3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e\right)} g\right)} x^{3} + 3 \, {\left(3 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e\right)} f - {\left(3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d - {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} e\right)} g\right)} x^{2} - 4 \, {\left({\left(3 \, {\left(2 \, c^{4} d - b c^{3} e\right)} f - {\left(3 \, b c^{3} d - {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} e\right)} g\right)} x^{4} + 2 \, {\left(3 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} f - {\left(3 \, b^{2} c^{2} d - {\left(b^{3} c + 2 \, a b c^{2}\right)} e\right)} g\right)} x^{3} + {\left(3 \, {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d - {\left(b^{3} c + 2 \, a b c^{2}\right)} e\right)} f - {\left(3 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} d - {\left(b^{4} + 4 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} g\right)} x^{2} + 3 \, {\left(2 \, a^{2} c^{2} d - a^{2} b c e\right)} f - {\left(3 \, a^{2} b c d - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e\right)} g + 2 \, {\left(3 \, {\left(2 \, a b c^{2} d - a b^{2} c e\right)} f - {\left(3 \, a b^{2} c d - {\left(a b^{3} + 2 \, a^{2} b c\right)} e\right)} g\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} d + {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} e\right)} f - {\left({\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} d - 6 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e\right)} g + 2 \, {\left({\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} e\right)} f - {\left({\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d - {\left(5 \, a b^{4} - 22 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e\right)} g\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(3*(2*(b^2*c^3 - 4*a*c^4)*d - (b^3*c^2 - 4*a*b*c^3)*e)*f - (3*(b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*e)*g)*x^3 + 3*(3*(2*(b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 4*a*b^2*c^2)*e)*f - (3*(b^4*c - 4*a*b^2*c^2)*d - (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*e)*g)*x^2 + 2*((3*(2*c^4*d - b*c^3*e)*f - (3*b*c^3*d - (b^2*c^2 + 2*a*c^3)*e)*g)*x^4 + 2*(3*(2*b*c^3*d - b^2*c^2*e)*f - (3*b^2*c^2*d - (b^3*c + 2*a*b*c^2)*e)*g)*x^3 + (3*(2*(b^2*c^2 + 2*a*c^3)*d - (b^3*c + 2*a*b*c^2)*e)*f - (3*(b^3*c + 2*a*b*c^2)*d - (b^4 + 4*a*b^2*c + 4*a^2*c^2)*e)*g)*x^2 + 3*(2*a^2*c^2*d - a^2*b*c*e)*f - (3*a^2*b*c*d - (a^2*b^2 + 2*a^3*c)*e)*g + 2*(3*(2*a*b*c^2*d - a*b^2*c*e)*f - (3*a*b^2*c*d - (a*b^3 + 2*a^2*b*c)*e)*g)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - ((b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*d + (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*e)*f - ((a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*d - 6*(a^2*b^3 - 4*a^3*b*c)*e)*g + 2*((2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d - (b^5 + a*b^3*c - 20*a^2*b*c^2)*e)*f - ((b^5 + a*b^3*c - 20*a^2*b*c^2)*d - (5*a*b^4 - 22*a^2*b^2*c + 8*a^3*c^2)*e)*g)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x), 1/2*(2*(3*(2*(b^2*c^3 - 4*a*c^4)*d - (b^3*c^2 - 4*a*b*c^3)*e)*f - (3*(b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*e)*g)*x^3 + 3*(3*(2*(b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 4*a*b^2*c^2)*e)*f - (3*(b^4*c - 4*a*b^2*c^2)*d - (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*e)*g)*x^2 - 4*((3*(2*c^4*d - b*c^3*e)*f - (3*b*c^3*d - (b^2*c^2 + 2*a*c^3)*e)*g)*x^4 + 2*(3*(2*b*c^3*d - b^2*c^2*e)*f - (3*b^2*c^2*d - (b^3*c + 2*a*b*c^2)*e)*g)*x^3 + (3*(2*(b^2*c^2 + 2*a*c^3)*d - (b^3*c + 2*a*b*c^2)*e)*f - (3*(b^3*c + 2*a*b*c^2)*d - (b^4 + 4*a*b^2*c + 4*a^2*c^2)*e)*g)*x^2 + 3*(2*a^2*c^2*d - a^2*b*c*e)*f - (3*a^2*b*c*d - (a^2*b^2 + 2*a^3*c)*e)*g + 2*(3*(2*a*b*c^2*d - a*b^2*c*e)*f - (3*a*b^2*c*d - (a*b^3 + 2*a^2*b*c)*e)*g)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - ((b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*d + (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*e)*f - ((a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*d - 6*(a^2*b^3 - 4*a^3*b*c)*e)*g + 2*((2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d - (b^5 + a*b^3*c - 20*a^2*b*c^2)*e)*f - ((b^5 + a*b^3*c - 20*a^2*b*c^2)*d - (5*a*b^4 - 22*a^2*b^2*c + 8*a^3*c^2)*e)*g)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)]","B",0
2375,1,1116,0,0.453248," ","integrate((g*x+f)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g\right)} x^{3} + 9 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} g\right)} x^{2} - 6 \, {\left(2 \, a^{2} c^{2} f - a^{2} b c g + {\left(2 \, c^{4} f - b c^{3} g\right)} x^{4} + 2 \, {\left(2 \, b c^{3} f - b^{2} c^{2} g\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} f - {\left(b^{3} c + 2 \, a b c^{2}\right)} g\right)} x^{2} + 2 \, {\left(2 \, a b c^{2} f - a b^{2} c g\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} f - {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} g + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} f - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} g\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}, \frac{6 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g\right)} x^{3} + 9 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} g\right)} x^{2} - 12 \, {\left(2 \, a^{2} c^{2} f - a^{2} b c g + {\left(2 \, c^{4} f - b c^{3} g\right)} x^{4} + 2 \, {\left(2 \, b c^{3} f - b^{2} c^{2} g\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} f - {\left(b^{3} c + 2 \, a b c^{2}\right)} g\right)} x^{2} + 2 \, {\left(2 \, a b c^{2} f - a b^{2} c g\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} f - {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} g + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} f - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} g\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}\right]"," ",0,"[1/2*(6*(2*(b^2*c^3 - 4*a*c^4)*f - (b^3*c^2 - 4*a*b*c^3)*g)*x^3 + 9*(2*(b^3*c^2 - 4*a*b*c^3)*f - (b^4*c - 4*a*b^2*c^2)*g)*x^2 - 6*(2*a^2*c^2*f - a^2*b*c*g + (2*c^4*f - b*c^3*g)*x^4 + 2*(2*b*c^3*f - b^2*c^2*g)*x^3 + (2*(b^2*c^2 + 2*a*c^3)*f - (b^3*c + 2*a*b*c^2)*g)*x^2 + 2*(2*a*b*c^2*f - a*b^2*c*g)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*f - (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*g + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*f - (b^5 + a*b^3*c - 20*a^2*b*c^2)*g)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x), 1/2*(6*(2*(b^2*c^3 - 4*a*c^4)*f - (b^3*c^2 - 4*a*b*c^3)*g)*x^3 + 9*(2*(b^3*c^2 - 4*a*b*c^3)*f - (b^4*c - 4*a*b^2*c^2)*g)*x^2 - 12*(2*a^2*c^2*f - a^2*b*c*g + (2*c^4*f - b*c^3*g)*x^4 + 2*(2*b*c^3*f - b^2*c^2*g)*x^3 + (2*(b^2*c^2 + 2*a*c^3)*f - (b^3*c + 2*a*b*c^2)*g)*x^2 + 2*(2*a*b*c^2*f - a*b^2*c*g)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*f - (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*g + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*f - (b^5 + a*b^3*c - 20*a^2*b*c^2)*g)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)]","B",0
2376,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2377,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2378,1,33,0,0.596150," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2),x, algorithm=""fricas"")","-\frac{4}{3} \, x^{4} + \frac{32}{27} \, x^{3} + \frac{1156}{27} \, x^{2} + \frac{11576}{81} \, x + \frac{10625}{243} \, \log\left(3 \, x + 2\right) - 6 \, \log\left(x + 1\right)"," ",0,"-4/3*x^4 + 32/27*x^3 + 1156/27*x^2 + 11576/81*x + 10625/243*log(3*x + 2) - 6*log(x + 1)","A",0
2379,1,28,0,0.499319," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2),x, algorithm=""fricas"")","-\frac{8}{9} \, x^{3} + \frac{26}{9} \, x^{2} + \frac{922}{27} \, x + \frac{2125}{81} \, \log\left(3 \, x + 2\right) - 6 \, \log\left(x + 1\right)"," ",0,"-8/9*x^3 + 26/9*x^2 + 922/27*x + 2125/81*log(3*x + 2) - 6*log(x + 1)","A",0
2380,1,23,0,0.474283," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2),x, algorithm=""fricas"")","-\frac{2}{3} \, x^{2} + \frac{44}{9} \, x + \frac{425}{27} \, \log\left(3 \, x + 2\right) - 6 \, \log\left(x + 1\right)"," ",0,"-2/3*x^2 + 44/9*x + 425/27*log(3*x + 2) - 6*log(x + 1)","A",0
2381,1,18,0,0.384273," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2),x, algorithm=""fricas"")","-\frac{2}{3} \, x + \frac{85}{9} \, \log\left(3 \, x + 2\right) - 6 \, \log\left(x + 1\right)"," ",0,"-2/3*x + 85/9*log(3*x + 2) - 6*log(x + 1)","A",0
2382,1,15,0,0.376221," ","integrate((5-x)/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{17}{3} \, \log\left(3 \, x + 2\right) - 6 \, \log\left(x + 1\right)"," ",0,"17/3*log(3*x + 2) - 6*log(x + 1)","A",0
2383,1,23,0,0.377933," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{17}{5} \, \log\left(3 \, x + 2\right) + \frac{13}{5} \, \log\left(2 \, x + 3\right) - 6 \, \log\left(x + 1\right)"," ",0,"17/5*log(3*x + 2) + 13/5*log(2*x + 3) - 6*log(x + 1)","A",0
2384,1,48,0,0.394972," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{51 \, {\left(2 \, x + 3\right)} \log\left(3 \, x + 2\right) + 99 \, {\left(2 \, x + 3\right)} \log\left(2 \, x + 3\right) - 150 \, {\left(2 \, x + 3\right)} \log\left(x + 1\right) - 65}{25 \, {\left(2 \, x + 3\right)}}"," ",0,"1/25*(51*(2*x + 3)*log(3*x + 2) + 99*(2*x + 3)*log(2*x + 3) - 150*(2*x + 3)*log(x + 1) - 65)/(2*x + 3)","A",0
2385,1,71,0,0.393703," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{306 \, {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(3 \, x + 2\right) + 1194 \, {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(2 \, x + 3\right) - 1500 \, {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(x + 1\right) - 1980 \, x - 3295}{250 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/250*(306*(4*x^2 + 12*x + 9)*log(3*x + 2) + 1194*(4*x^2 + 12*x + 9)*log(2*x + 3) - 1500*(4*x^2 + 12*x + 9)*log(x + 1) - 1980*x - 3295)/(4*x^2 + 12*x + 9)","A",0
2386,1,96,0,0.393198," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2),x, algorithm=""fricas"")","-\frac{71640 \, x^{2} - 2754 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(3 \, x + 2\right) - 19746 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(2 \, x + 3\right) + 22500 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(x + 1\right) + 229770 \, x + 186715}{3750 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"-1/3750*(71640*x^2 - 2754*(8*x^3 + 36*x^2 + 54*x + 27)*log(3*x + 2) - 19746*(8*x^3 + 36*x^2 + 54*x + 27)*log(2*x + 3) + 22500*(8*x^3 + 36*x^2 + 54*x + 27)*log(x + 1) + 229770*x + 186715)/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
2387,1,68,0,0.387238," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{216 \, x^{4} - 648 \, x^{3} - 1536 \, x^{2} + 4875 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(3 \, x + 2\right) - 6723 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(x + 1\right) + 11411 \, x + 11597}{81 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"-1/81*(216*x^4 - 648*x^3 - 1536*x^2 + 4875*(3*x^2 + 5*x + 2)*log(3*x + 2) - 6723*(3*x^2 + 5*x + 2)*log(x + 1) + 11411*x + 11597)/(3*x^2 + 5*x + 2)","A",0
2388,1,63,0,0.383802," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{72 \, x^{3} + 120 \, x^{2} + 1825 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(3 \, x + 2\right) - 1917 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(x + 1\right) + 2659 \, x + 2449}{27 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"-1/27*(72*x^3 + 120*x^2 + 1825*(3*x^2 + 5*x + 2)*log(3*x + 2) - 1917*(3*x^2 + 5*x + 2)*log(x + 1) + 2659*x + 2449)/(3*x^2 + 5*x + 2)","A",0
2389,1,53,0,0.386842," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{535 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(3 \, x + 2\right) - 531 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(x + 1\right) + 587 \, x + 533}{9 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"-1/9*(535*(3*x^2 + 5*x + 2)*log(3*x + 2) - 531*(3*x^2 + 5*x + 2)*log(x + 1) + 587*x + 533)/(3*x^2 + 5*x + 2)","A",0
2390,1,53,0,0.377354," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{141 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(3 \, x + 2\right) - 141 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(x + 1\right) + 139 \, x + 121}{3 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"-1/3*(141*(3*x^2 + 5*x + 2)*log(3*x + 2) - 141*(3*x^2 + 5*x + 2)*log(x + 1) + 139*x + 121)/(3*x^2 + 5*x + 2)","A",0
2391,1,53,0,0.379953," ","integrate((5-x)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{35 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(3 \, x + 2\right) - 35 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(x + 1\right) + 35 \, x + 29}{3 \, x^{2} + 5 \, x + 2}"," ",0,"-(35*(3*x^2 + 5*x + 2)*log(3*x + 2) - 35*(3*x^2 + 5*x + 2)*log(x + 1) + 35*x + 29)/(3*x^2 + 5*x + 2)","A",0
2392,1,71,0,0.381058," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{627 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(3 \, x + 2\right) - 52 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(2 \, x + 3\right) - 575 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(x + 1\right) + 705 \, x + 555}{25 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"-1/25*(627*(3*x^2 + 5*x + 2)*log(3*x + 2) - 52*(3*x^2 + 5*x + 2)*log(2*x + 3) - 575*(3*x^2 + 5*x + 2)*log(x + 1) + 705*x + 555)/(3*x^2 + 5*x + 2)","A",0
2393,1,96,0,0.382147," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{6810 \, x^{2} + 2187 \, {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)} \log\left(3 \, x + 2\right) - 812 \, {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)} \log\left(2 \, x + 3\right) - 1375 \, {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)} \log\left(x + 1\right) + 14875 \, x + 7315}{125 \, {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"-1/125*(6810*x^2 + 2187*(6*x^3 + 19*x^2 + 19*x + 6)*log(3*x + 2) - 812*(6*x^3 + 19*x^2 + 19*x + 6)*log(2*x + 3) - 1375*(6*x^3 + 19*x^2 + 19*x + 6)*log(x + 1) + 14875*x + 7315)/(6*x^3 + 19*x^2 + 19*x + 6)","A",0
2394,1,121,0,0.392682," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{78540 \, x^{3} + 280810 \, x^{2} + 7479 \, {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)} \log\left(3 \, x + 2\right) - 8104 \, {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)} \log\left(2 \, x + 3\right) + 625 \, {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)} \log\left(x + 1\right) + 319835 \, x + 113815}{625 \, {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)}}"," ",0,"-1/625*(78540*x^3 + 280810*x^2 + 7479*(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log(3*x + 2) - 8104*(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log(2*x + 3) + 625*(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log(x + 1) + 319835*x + 113815)/(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)","A",0
2395,1,146,0,0.390741," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{2973960 \, x^{4} + 14873880 \, x^{3} + 27167700 \, x^{2} + 75573 \, {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)} \log\left(3 \, x + 2\right) - 197448 \, {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)} \log\left(2 \, x + 3\right) + 121875 \, {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)} \log\left(x + 1\right) + 21302995 \, x + 5978965}{9375 \, {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)}}"," ",0,"-1/9375*(2973960*x^4 + 14873880*x^3 + 27167700*x^2 + 75573*(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)*log(3*x + 2) - 197448*(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)*log(2*x + 3) + 121875*(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)*log(x + 1) + 21302995*x + 5978965)/(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)","A",0
2396,1,103,0,0.393174," ","integrate((5-x)*(3+2*x)^5/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","-\frac{1728 \, x^{5} + 5760 \, x^{4} - 495150 \, x^{3} - 1231835 \, x^{2} - 176250 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(3 \, x + 2\right) + 175770 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(x + 1\right) - 979210 \, x - 247043}{162 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"-1/162*(1728*x^5 + 5760*x^4 - 495150*x^3 - 1231835*x^2 - 176250*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(3*x + 2) + 175770*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(x + 1) - 979210*x - 247043)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2397,1,93,0,0.382707," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{142086 \, x^{3} + 353367 \, x^{2} + 47650 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(3 \, x + 2\right) - 47682 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(x + 1\right) + 284958 \, x + 73839}{54 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/54*(142086*x^3 + 353367*x^2 + 47650*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(3*x + 2) - 47682*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(x + 1) + 284958*x + 73839)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2398,1,93,0,0.384908," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{38118 \, x^{3} + 95203 \, x^{2} + 12690 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(3 \, x + 2\right) - 12690 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(x + 1\right) + 77330 \, x + 20299}{18 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/18*(38118*x^3 + 95203*x^2 + 12690*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(3*x + 2) - 12690*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(x + 1) + 77330*x + 20299)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2399,1,93,0,0.377294," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{9918 \, x^{3} + 24799 \, x^{2} + 3306 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(3 \, x + 2\right) - 3306 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(x + 1\right) + 20198 \, x + 5335}{6 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/6*(9918*x^3 + 24799*x^2 + 3306*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(3*x + 2) - 3306*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(x + 1) + 20198*x + 5335)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2400,1,93,0,0.374434," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{2526 \, x^{3} + 6315 \, x^{2} + 842 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(3 \, x + 2\right) - 842 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(x + 1\right) + 5146 \, x + 1363}{2 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/2*(2526*x^3 + 6315*x^2 + 842*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(3*x + 2) - 842*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(x + 1) + 5146*x + 1363)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2401,1,93,0,0.386254," ","integrate((5-x)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{1890 \, x^{3} + 4725 \, x^{2} + 630 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(3 \, x + 2\right) - 630 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(x + 1\right) + 3850 \, x + 1021}{2 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/2*(1890*x^3 + 4725*x^2 + 630*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(3*x + 2) - 630*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(x + 1) + 3850*x + 1021)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2402,1,121,0,0.396883," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{171630 \, x^{3} + 429855 \, x^{2} + 57834 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(3 \, x + 2\right) + 416 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(2 \, x + 3\right) - 58250 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(x + 1\right) + 350570 \, x + 93095}{250 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/250*(171630*x^3 + 429855*x^2 + 57834*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(3*x + 2) + 416*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(2*x + 3) - 58250*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(x + 1) + 350570*x + 93095)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2403,1,146,0,0.395807," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{1165140 \, x^{4} + 4697400 \, x^{3} + 6842995 \, x^{2} + 208926 \, {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)} \log\left(3 \, x + 2\right) + 9824 \, {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)} \log\left(2 \, x + 3\right) - 218750 \, {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)} \log\left(x + 1\right) + 4275600 \, x + 968615}{1250 \, {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)}}"," ",0,"1/1250*(1165140*x^4 + 4697400*x^3 + 6842995*x^2 + 208926*(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)*log(3*x + 2) + 9824*(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)*log(2*x + 3) - 218750*(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)*log(x + 1) + 4275600*x + 968615)/(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)","A",0
2404,1,171,0,0.394442," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{6459480 \, x^{5} + 36556020 \, x^{4} + 80482290 \, x^{3} + 85904835 \, x^{2} + 744066 \, {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)} \log\left(3 \, x + 2\right) + 137184 \, {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)} \log\left(2 \, x + 3\right) - 881250 \, {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)} \log\left(x + 1\right) + 44358230 \, x + 8857895}{6250 \, {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/6250*(6459480*x^5 + 36556020*x^4 + 80482290*x^3 + 85904835*x^2 + 744066*(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)*log(3*x + 2) + 137184*(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)*log(2*x + 3) - 881250*(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)*log(x + 1) + 44358230*x + 8857895)/(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)","A",0
2405,1,32,0,0.366585," ","integrate(x*(1+x)^2/(x^2+x+1)^3,x, algorithm=""fricas"")","-\frac{3 \, x^{2} + 4 \, x + 2}{6 \, {\left(x^{4} + 2 \, x^{3} + 3 \, x^{2} + 2 \, x + 1\right)}}"," ",0,"-1/6*(3*x^2 + 4*x + 2)/(x^4 + 2*x^3 + 3*x^2 + 2*x + 1)","A",0
2406,1,83,0,0.418001," ","integrate((5-x)*(3+2*x)^4*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{544320} \, {\left(1244160 \, x^{6} + 1624320 \, x^{5} - 28649088 \, x^{4} - 123633360 \, x^{3} - 208601544 \, x^{2} - 161915450 \, x - 47009103\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{25969}{186624} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/544320*(1244160*x^6 + 1624320*x^5 - 28649088*x^4 - 123633360*x^3 - 208601544*x^2 - 161915450*x - 47009103)*sqrt(3*x^2 + 5*x + 2) + 25969/186624*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2407,1,78,0,0.410512," ","integrate((5-x)*(3+2*x)^3*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{25920} \, {\left(34560 \, x^{5} - 14976 \, x^{4} - 825840 \, x^{3} - 2317848 \, x^{2} - 2432350 \, x - 859701\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{6221}{62208} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/25920*(34560*x^5 - 14976*x^4 - 825840*x^3 - 2317848*x^2 - 2432350*x - 859701)*sqrt(3*x^2 + 5*x + 2) + 6221/62208*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2408,1,73,0,0.398844," ","integrate((5-x)*(3+2*x)^2*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{12960} \, {\left(10368 \, x^{4} - 23760 \, x^{3} - 229416 \, x^{2} - 375250 \, x - 168627\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{2267}{31104} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/12960*(10368*x^4 - 23760*x^3 - 229416*x^2 - 375250*x - 168627)*sqrt(3*x^2 + 5*x + 2) + 2267/31104*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2409,1,68,0,0.404775," ","integrate((5-x)*(3+2*x)*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{864} \, {\left(432 \, x^{3} - 1896 \, x^{2} - 7426 \, x - 4539\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{559}{10368} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/864*(432*x^3 - 1896*x^2 - 7426*x - 4539)*sqrt(3*x^2 + 5*x + 2) + 559/10368*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2410,1,63,0,0.383312," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{72} \, {\left(24 \, x^{2} - 170 \, x - 159\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{35}{864} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/72*(24*x^2 - 170*x - 159)*sqrt(3*x^2 + 5*x + 2) + 35/864*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2411,1,109,0,0.411651," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x),x, algorithm=""fricas"")","-\frac{1}{24} \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x - 73\right)} + \frac{311}{288} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + \frac{13}{16} \, \sqrt{5} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right)"," ",0,"-1/24*sqrt(3*x^2 + 5*x + 2)*(6*x - 73) + 311/288*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 13/16*sqrt(5)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9))","A",0
2412,1,127,0,0.416292," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^2,x, algorithm=""fricas"")","\frac{215 \, \sqrt{3} {\left(2 \, x + 3\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 171 \, \sqrt{5} {\left(2 \, x + 3\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 120 \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(x + 8\right)}}{240 \, {\left(2 \, x + 3\right)}}"," ",0,"1/240*(215*sqrt(3)*(2*x + 3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 171*sqrt(5)*(2*x + 3)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 120*sqrt(3*x^2 + 5*x + 2)*(x + 8))/(2*x + 3)","A",0
2413,1,143,0,0.402819," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^3,x, algorithm=""fricas"")","\frac{50 \, \sqrt{3} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 27 \, \sqrt{5} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(124 \, x + 121\right)}}{800 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/800*(50*sqrt(3)*(4*x^2 + 12*x + 9)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 27*sqrt(5)*(4*x^2 + 12*x + 9)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*sqrt(3*x^2 + 5*x + 2)*(124*x + 121))/(4*x^2 + 12*x + 9)","A",0
2414,1,111,0,0.413020," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^4,x, algorithm=""fricas"")","\frac{141 \, \sqrt{5} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(696 \, x^{2} + 2758 \, x + 1921\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{12000 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/12000*(141*sqrt(5)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) + 20*(696*x^2 + 2758*x + 1921)*sqrt(3*x^2 + 5*x + 2))/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
2415,1,126,0,0.412810," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^5,x, algorithm=""fricas"")","\frac{153 \, \sqrt{5} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(1056 \, x^{3} + 5252 \, x^{2} + 9108 \, x + 4759\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{16000 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"1/16000*(153*sqrt(5)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) + 20*(1056*x^3 + 5252*x^2 + 9108*x + 4759)*sqrt(3*x^2 + 5*x + 2))/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
2416,1,141,0,0.418090," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^6,x, algorithm=""fricas"")","\frac{3159 \, \sqrt{5} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(35136 \, x^{4} + 225816 \, x^{3} + 549516 \, x^{2} + 606326 \, x + 244331\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{400000 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"1/400000*(3159*sqrt(5)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) + 20*(35136*x^4 + 225816*x^3 + 549516*x^2 + 606326*x + 244331)*sqrt(3*x^2 + 5*x + 2))/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
2417,1,156,0,0.409550," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^7,x, algorithm=""fricas"")","\frac{79359 \, \sqrt{5} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(1567872 \, x^{5} + 12381040 \, x^{4} + 39304480 \, x^{3} + 62797200 \, x^{2} + 50707640 \, x + 16322393\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{12000000 \, {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)}}"," ",0,"1/12000000*(79359*sqrt(5)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) + 20*(1567872*x^5 + 12381040*x^4 + 39304480*x^3 + 62797200*x^2 + 50707640*x + 16322393)*sqrt(3*x^2 + 5*x + 2))/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)","A",0
2418,1,93,0,0.410036," ","integrate((5-x)*(3+2*x)^4*(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{22394880} \, {\left(119439360 \, x^{8} + 370759680 \, x^{7} - 2143687680 \, x^{6} - 14811482880 \, x^{5} - 37262745216 \, x^{4} - 49917376080 \, x^{3} - 37650690888 \, x^{2} - 15049298650 \, x - 2471988351\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{454969}{53747712} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/22394880*(119439360*x^8 + 370759680*x^7 - 2143687680*x^6 - 14811482880*x^5 - 37262745216*x^4 - 49917376080*x^3 - 37650690888*x^2 - 15049298650*x - 2471988351)*sqrt(3*x^2 + 5*x + 2) + 454969/53747712*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2419,1,88,0,0.401716," ","integrate((5-x)*(3+2*x)^3*(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{5806080} \, {\left(17418240 \, x^{7} + 25297920 \, x^{6} - 368236800 \, x^{5} - 1650151296 \, x^{4} - 2993047920 \, x^{3} - 2762417688 \, x^{2} - 1276112350 \, x - 233137461\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{12277}{1990656} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/5806080*(17418240*x^7 + 25297920*x^6 - 368236800*x^5 - 1650151296*x^4 - 2993047920*x^3 - 2762417688*x^2 - 1276112350*x - 233137461)*sqrt(3*x^2 + 5*x + 2) + 12277/1990656*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2420,1,83,0,0.411129," ","integrate((5-x)*(3+2*x)^2*(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{725760} \, {\left(1244160 \, x^{6} - 311040 \, x^{5} - 27084672 \, x^{4} - 79049520 \, x^{3} - 94861176 \, x^{2} - 51971350 \, x - 10669737\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{1129}{248832} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/725760*(1244160*x^6 - 311040*x^5 - 27084672*x^4 - 79049520*x^3 - 94861176*x^2 - 51971350*x - 10669737)*sqrt(3*x^2 + 5*x + 2) + 1129/248832*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2421,1,78,0,0.398855," ","integrate((5-x)*(3+2*x)*(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{103680} \, {\left(103680 \, x^{5} - 210816 \, x^{4} - 2032560 \, x^{3} - 3567288 \, x^{2} - 2406950 \, x - 561921\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{839}{248832} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/103680*(103680*x^5 - 210816*x^4 - 2032560*x^3 - 3567288*x^2 - 2406950*x - 561921)*sqrt(3*x^2 + 5*x + 2) + 839/248832*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2422,1,73,0,0.398494," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{5760} \, {\left(3456 \, x^{4} - 13680 \, x^{3} - 48792 \, x^{2} - 43070 \, x - 11589\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{35}{13824} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/5760*(3456*x^4 - 13680*x^3 - 48792*x^2 - 43070*x - 11589)*sqrt(3*x^2 + 5*x + 2) + 35/13824*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2423,1,119,0,0.419569," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x),x, algorithm=""fricas"")","-\frac{1}{384} \, {\left(144 \, x^{3} - 888 \, x^{2} - 542 \, x - 1277\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{2011}{1536} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + \frac{65}{64} \, \sqrt{5} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right)"," ",0,"-1/384*(144*x^3 - 888*x^2 - 542*x - 1277)*sqrt(3*x^2 + 5*x + 2) + 2011/1536*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 65/64*sqrt(5)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9))","A",0
2424,1,139,0,0.417030," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^2,x, algorithm=""fricas"")","\frac{3743 \, \sqrt{3} {\left(2 \, x + 3\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 2898 \, \sqrt{5} {\left(2 \, x + 3\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 12 \, {\left(48 \, x^{3} - 364 \, x^{2} + 256 \, x + 1755\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{1152 \, {\left(2 \, x + 3\right)}}"," ",0,"1/1152*(3743*sqrt(3)*(2*x + 3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 2898*sqrt(5)*(2*x + 3)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 12*(48*x^3 - 364*x^2 + 256*x + 1755)*sqrt(3*x^2 + 5*x + 2))/(2*x + 3)","A",0
2425,1,153,0,0.421404," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^3,x, algorithm=""fricas"")","\frac{1715 \, \sqrt{3} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 1329 \, \sqrt{5} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 40 \, {\left(12 \, x^{3} - 142 \, x^{2} - 777 \, x - 773\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{640 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/640*(1715*sqrt(3)*(4*x^2 + 12*x + 9)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 1329*sqrt(5)*(4*x^2 + 12*x + 9)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 40*(12*x^3 - 142*x^2 - 777*x - 773)*sqrt(3*x^2 + 5*x + 2))/(4*x^2 + 12*x + 9)","A",0
2426,1,169,0,0.419679," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^4,x, algorithm=""fricas"")","\frac{7650 \, \sqrt{3} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 5919 \, \sqrt{5} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(720 \, x^{3} + 13176 \, x^{2} + 30878 \, x + 19751\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{9600 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/9600*(7650*sqrt(3)*(8*x^3 + 36*x^2 + 54*x + 27)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 5919*sqrt(5)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 20*(720*x^3 + 13176*x^2 + 30878*x + 19751)*sqrt(3*x^2 + 5*x + 2))/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
2427,1,183,0,0.425115," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^5,x, algorithm=""fricas"")","\frac{9000 \, \sqrt{3} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 7077 \, \sqrt{5} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(60576 \, x^{3} + 190412 \, x^{2} + 211148 \, x + 82989\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{192000 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"1/192000*(9000*sqrt(3)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 7077*sqrt(5)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(60576*x^3 + 190412*x^2 + 211148*x + 82989)*sqrt(3*x^2 + 5*x + 2))/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
2428,1,140,0,0.422778," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^6,x, algorithm=""fricas"")","\frac{141 \, \sqrt{5} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(6336 \, x^{4} + 66616 \, x^{3} + 131516 \, x^{2} + 90126 \, x + 19031\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{320000 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"1/320000*(141*sqrt(5)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(6336*x^4 + 66616*x^3 + 131516*x^2 + 90126*x + 19031)*sqrt(3*x^2 + 5*x + 2))/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
2429,1,155,0,0.415945," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^7,x, algorithm=""fricas"")","\frac{3423 \, \sqrt{5} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(95616 \, x^{5} + 799120 \, x^{4} + 3065440 \, x^{3} + 4479600 \, x^{2} + 2526920 \, x + 412679\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{9600000 \, {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)}}"," ",0,"1/9600000*(3423*sqrt(5)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(95616*x^5 + 799120*x^4 + 3065440*x^3 + 4479600*x^2 + 2526920*x + 412679)*sqrt(3*x^2 + 5*x + 2))/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)","A",0
2430,1,170,0,0.419797," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^8,x, algorithm=""fricas"")","\frac{97923 \, \sqrt{5} {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(191232 \, x^{6} + 2893088 \, x^{5} + 16376240 \, x^{4} + 55403520 \, x^{3} + 64140640 \, x^{2} + 15759118 \, x - 6554463\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{336000000 \, {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)}}"," ",0,"1/336000000*(97923*sqrt(5)*(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(191232*x^6 + 2893088*x^5 + 16376240*x^4 + 55403520*x^3 + 64140640*x^2 + 15759118*x - 6554463)*sqrt(3*x^2 + 5*x + 2))/(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)","A",0
2431,1,185,0,0.422386," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^9,x, algorithm=""fricas"")","\frac{153927 \, \sqrt{5} {\left(256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(5681664 \, x^{7} + 60161472 \, x^{6} + 272314944 \, x^{5} + 682163760 \, x^{4} + 1007243840 \, x^{3} + 924451956 \, x^{2} + 512781828 \, x + 131091161\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{640000000 \, {\left(256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561\right)}}"," ",0,"1/640000000*(153927*sqrt(5)*(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*(5681664*x^7 + 60161472*x^6 + 272314944*x^5 + 682163760*x^4 + 1007243840*x^3 + 924451956*x^2 + 512781828*x + 131091161)*sqrt(3*x^2 + 5*x + 2))/(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561)","A",0
2432,1,103,0,0.412131," ","integrate((5-x)*(3+2*x)^4*(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{13795246080} \, {\left(180592312320 \, x^{10} + 875872714752 \, x^{9} - 1932170526720 \, x^{8} - 25759323039744 \, x^{7} - 90095929758720 \, x^{6} - 172473366866688 \, x^{5} - 204855126595200 \, x^{4} - 155155370878800 \, x^{3} - 73069860056520 \, x^{2} - 19521700361210 \, x - 2261297826735\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{249299}{429981696} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/13795246080*(180592312320*x^10 + 875872714752*x^9 - 1932170526720*x^8 - 25759323039744*x^7 - 90095929758720*x^6 - 172473366866688*x^5 - 204855126595200*x^4 - 155155370878800*x^3 - 73069860056520*x^2 - 19521700361210*x - 2261297826735)*sqrt(3*x^2 + 5*x + 2) + 249299/429981696*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2433,1,98,0,0.414679," ","integrate((5-x)*(3+2*x)^3*(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{1254113280} \, {\left(9029615616 \, x^{9} + 29262643200 \, x^{8} - 147947046912 \, x^{7} - 1086687912960 \, x^{6} - 2893044950784 \, x^{5} - 4253933381760 \, x^{4} - 3762746217360 \, x^{3} - 1995914277480 \, x^{2} - 585749416130 \, x - 73178684475\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{182917}{429981696} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/1254113280*(9029615616*x^9 + 29262643200*x^8 - 147947046912*x^7 - 1086687912960*x^6 - 2893044950784*x^5 - 4253933381760*x^4 - 3762746217360*x^3 - 1995914277480*x^2 - 585749416130*x - 73178684475)*sqrt(3*x^2 + 5*x + 2) + 182917/429981696*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2434,1,93,0,0.404720," ","integrate((5-x)*(3+2*x)^2*(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{41803776} \, {\left(167215104 \, x^{8} + 268240896 \, x^{7} - 3275873280 \, x^{6} - 15455860992 \, x^{5} - 30355761024 \, x^{4} - 32476001904 \, x^{3} - 19762157208 \, x^{2} - 6434937470 \, x - 871825317\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{22535}{71663616} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/41803776*(167215104*x^8 + 268240896*x^7 - 3275873280*x^6 - 15455860992*x^5 - 30355761024*x^4 - 32476001904*x^3 - 19762157208*x^2 - 6434937470*x - 871825317)*sqrt(3*x^2 + 5*x + 2) + 22535/71663616*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2435,1,88,0,0.407156," ","integrate((5-x)*(3+2*x)*(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{4644864} \, {\left(10450944 \, x^{7} - 746496 \, x^{6} - 211154688 \, x^{5} - 655212672 \, x^{4} - 897818256 \, x^{3} - 642995688 \, x^{2} - 235223330 \, x - 34777419\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{1865}{7962624} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/4644864*(10450944*x^7 - 746496*x^6 - 211154688*x^5 - 655212672*x^4 - 897818256*x^3 - 642995688*x^2 - 235223330*x - 34777419)*sqrt(3*x^2 + 5*x + 2) + 1865/7962624*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2436,1,83,0,0.399830," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{580608} \, {\left(746496 \, x^{6} - 1347840 \, x^{5} - 13454208 \, x^{4} - 26388720 \, x^{3} - 23110872 \, x^{2} - 9651790 \, x - 1568541\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{175}{995328} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/580608*(746496*x^6 - 1347840*x^5 - 13454208*x^4 - 26388720*x^3 - 23110872*x^2 - 9651790*x - 1568541)*sqrt(3*x^2 + 5*x + 2) + 175/995328*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2437,1,129,0,0.410385," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x),x, algorithm=""fricas"")","-\frac{1}{138240} \, {\left(103680 \, x^{5} - 376704 \, x^{4} - 1311120 \, x^{3} - 1624872 \, x^{2} - 583490 \, x - 580299\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{543811}{331776} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + \frac{325}{256} \, \sqrt{5} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right)"," ",0,"-1/138240*(103680*x^5 - 376704*x^4 - 1311120*x^3 - 1624872*x^2 - 583490*x - 580299)*sqrt(3*x^2 + 5*x + 2) + 543811/331776*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 325/256*sqrt(5)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9))","A",0
2438,1,149,0,0.430959," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^2,x, algorithm=""fricas"")","\frac{205265 \, \sqrt{3} {\left(2 \, x + 3\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 159000 \, \sqrt{5} {\left(2 \, x + 3\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 4 \, {\left(6912 \, x^{5} - 28512 \, x^{4} - 80064 \, x^{3} - 118996 \, x^{2} + 40412 \, x + 293973\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{30720 \, {\left(2 \, x + 3\right)}}"," ",0,"1/30720*(205265*sqrt(3)*(2*x + 3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 159000*sqrt(5)*(2*x + 3)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 4*(6912*x^5 - 28512*x^4 - 80064*x^3 - 118996*x^2 + 40412*x + 293973)*sqrt(3*x^2 + 5*x + 2))/(2*x + 3)","A",0
2439,1,163,0,0.419930," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^3,x, algorithm=""fricas"")","\frac{199615 \, \sqrt{3} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 154620 \, \sqrt{5} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 12 \, {\left(1728 \, x^{5} - 8544 \, x^{4} - 14456 \, x^{3} - 57292 \, x^{2} - 290742 \, x - 295719\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{18432 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/18432*(199615*sqrt(3)*(4*x^2 + 12*x + 9)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 154620*sqrt(5)*(4*x^2 + 12*x + 9)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 12*(1728*x^5 - 8544*x^4 - 14456*x^3 - 57292*x^2 - 290742*x - 295719)*sqrt(3*x^2 + 5*x + 2))/(4*x^2 + 12*x + 9)","A",0
2440,1,179,0,0.421635," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^4,x, algorithm=""fricas"")","\frac{13505 \, \sqrt{3} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 10461 \, \sqrt{5} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 8 \, {\left(288 \, x^{5} - 1896 \, x^{4} + 1944 \, x^{3} + 64332 \, x^{2} + 143533 \, x + 89224\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{1536 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/1536*(13505*sqrt(3)*(8*x^3 + 36*x^2 + 54*x + 27)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 10461*sqrt(5)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 8*(288*x^5 - 1896*x^4 + 1944*x^3 + 64332*x^2 + 143533*x + 89224)*sqrt(3*x^2 + 5*x + 2))/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
2441,1,193,0,0.425234," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^5,x, algorithm=""fricas"")","\frac{112500 \, \sqrt{3} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 87141 \, \sqrt{5} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(3456 \, x^{5} - 39744 \, x^{4} - 533280 \, x^{3} - 1672268 \, x^{2} - 2059268 \, x - 896721\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{30720 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"1/30720*(112500*sqrt(3)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 87141*sqrt(5)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*(3456*x^5 - 39744*x^4 - 533280*x^3 - 1672268*x^2 - 2059268*x - 896721)*sqrt(3*x^2 + 5*x + 2))/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
2442,1,209,0,0.426123," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^6,x, algorithm=""fricas"")","\frac{531000 \, \sqrt{3} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 411333 \, \sqrt{5} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(172800 \, x^{5} + 4630848 \, x^{4} + 21586808 \, x^{3} + 41641148 \, x^{2} + 37019838 \, x + 12600183\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{768000 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"1/768000*(531000*sqrt(3)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 411333*sqrt(5)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 20*(172800*x^5 + 4630848*x^4 + 21586808*x^3 + 41641148*x^2 + 37019838*x + 12600183)*sqrt(3*x^2 + 5*x + 2))/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
2443,1,223,0,0.435032," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^7,x, algorithm=""fricas"")","\frac{54000 \, \sqrt{3} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 41793 \, \sqrt{5} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(1351296 \, x^{5} + 7629680 \, x^{4} + 18217760 \, x^{3} + 22854480 \, x^{2} + 14921560 \, x + 4015849\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{1536000 \, {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)}}"," ",0,"1/1536000*(54000*sqrt(3)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 41793*sqrt(5)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(1351296*x^5 + 7629680*x^4 + 18217760*x^3 + 22854480*x^2 + 14921560*x + 4015849)*sqrt(3*x^2 + 5*x + 2))/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)","A",0
2444,1,171,0,0.419972," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^8,x, algorithm=""fricas"")","\frac{987 \, \sqrt{5} {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(1089792 \, x^{6} + 22620128 \, x^{5} + 81951440 \, x^{4} + 127557120 \, x^{3} + 100711840 \, x^{2} + 39981058 \, x + 6404247\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{53760000 \, {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)}}"," ",0,"1/53760000*(987*sqrt(5)*(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) + 20*(1089792*x^6 + 22620128*x^5 + 81951440*x^4 + 127557120*x^3 + 100711840*x^2 + 39981058*x + 6404247)*sqrt(3*x^2 + 5*x + 2))/(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)","A",0
2445,1,186,0,0.433598," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^9,x, algorithm=""fricas"")","\frac{31857 \, \sqrt{5} {\left(256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(35495424 \, x^{7} + 395685952 \, x^{6} + 2141523904 \, x^{5} + 5486222160 \, x^{4} + 7363989440 \, x^{3} + 5395613996 \, x^{2} + 2061624348 \, x + 325079151\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{2150400000 \, {\left(256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561\right)}}"," ",0,"1/2150400000*(31857*sqrt(5)*(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) + 20*(35495424*x^7 + 395685952*x^6 + 2141523904*x^5 + 5486222160*x^4 + 7363989440*x^3 + 5395613996*x^2 + 2061624348*x + 325079151)*sqrt(3*x^2 + 5*x + 2))/(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561)","A",0
2446,1,201,0,0.428958," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^10,x, algorithm=""fricas"")","\frac{388521 \, \sqrt{5} {\left(512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(333241344 \, x^{8} + 4204480128 \, x^{7} + 23288995392 \, x^{6} + 76435267296 \, x^{5} + 149661252080 \, x^{4} + 173974546136 \, x^{3} + 117870367452 \, x^{2} + 43246799138 \, x + 6706847909\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{32256000000 \, {\left(512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right)}}"," ",0,"1/32256000000*(388521*sqrt(5)*(512*x^9 + 6912*x^8 + 41472*x^7 + 145152*x^6 + 326592*x^5 + 489888*x^4 + 489888*x^3 + 314928*x^2 + 118098*x + 19683)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) + 20*(333241344*x^8 + 4204480128*x^7 + 23288995392*x^6 + 76435267296*x^5 + 149661252080*x^4 + 173974546136*x^3 + 117870367452*x^2 + 43246799138*x + 6706847909)*sqrt(3*x^2 + 5*x + 2))/(512*x^9 + 6912*x^8 + 41472*x^7 + 145152*x^6 + 326592*x^5 + 489888*x^4 + 489888*x^3 + 314928*x^2 + 118098*x + 19683)","A",0
2447,1,113,0,0.415458," ","integrate((5-x)*(3+2*x)^4*(3*x^2+5*x+2)^(7/2),x, algorithm=""fricas"")","-\frac{1}{67077144576} \, {\left(2229025112064 \, x^{12} + 14643456638976 \, x^{11} - 2110350163968 \, x^{10} - 333952593887232 \, x^{9} - 1590604366381056 \, x^{8} - 4022427759003648 \, x^{7} - 6524509131334656 \, x^{6} - 7203650864723712 \, x^{5} - 5499074981552256 \, x^{4} - 2865856228323984 \, x^{3} - 975104480077800 \, x^{2} - 195441229635490 \, x - 17510968283403\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{2595845}{61917364224} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/67077144576*(2229025112064*x^12 + 14643456638976*x^11 - 2110350163968*x^10 - 333952593887232*x^9 - 1590604366381056*x^8 - 4022427759003648*x^7 - 6524509131334656*x^6 - 7203650864723712*x^5 - 5499074981552256*x^4 - 2865856228323984*x^3 - 975104480077800*x^2 - 195441229635490*x - 17510968283403)*sqrt(3*x^2 + 5*x + 2) + 2595845/61917364224*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2448,1,108,0,0.412037," ","integrate((5-x)*(3+2*x)^3*(3*x^2+5*x+2)^(7/2),x, algorithm=""fricas"")","-\frac{1}{94595973120} \, {\left(1702727516160 \, x^{11} + 8487838679040 \, x^{10} - 15591566278656 \, x^{9} - 235832896880640 \, x^{8} - 866110416795648 \, x^{7} - 1766184385305600 \, x^{6} - 2298912734198016 \, x^{5} - 1992318117275520 \, x^{4} - 1149328734822000 \, x^{3} - 425035984788120 \, x^{2} - 91318722047870 \, x - 8675936123685\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{637609}{20639121408} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/94595973120*(1702727516160*x^11 + 8487838679040*x^10 - 15591566278656*x^9 - 235832896880640*x^8 - 866110416795648*x^7 - 1766184385305600*x^6 - 2298912734198016*x^5 - 1992318117275520*x^4 - 1149328734822000*x^3 - 425035984788120*x^2 - 91318722047870*x - 8675936123685)*sqrt(3*x^2 + 5*x + 2) + 637609/20639121408*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2449,1,103,0,0.418406," ","integrate((5-x)*(3+2*x)^2*(3*x^2+5*x+2)^(7/2),x, algorithm=""fricas"")","-\frac{1}{7882997760} \, {\left(77396705280 \, x^{10} + 261858852864 \, x^{9} - 1156531322880 \, x^{8} - 9116575930368 \, x^{7} - 25723491978240 \, x^{6} - 41190616509696 \, x^{5} - 41472321125760 \, x^{4} - 26847121235760 \, x^{3} - 10882383306360 \, x^{2} - 2519542755670 \, x - 254668717065\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{39389}{1719926784} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/7882997760*(77396705280*x^10 + 261858852864*x^9 - 1156531322880*x^8 - 9116575930368*x^7 - 25723491978240*x^6 - 41190616509696*x^5 - 41472321125760*x^4 - 26847121235760*x^3 - 10882383306360*x^2 - 2519542755670*x - 254668717065)*sqrt(3*x^2 + 5*x + 2) + 39389/1719926784*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2450,1,98,0,0.408734," ","integrate((5-x)*(3+2*x)*(3*x^2+5*x+2)^(7/2),x, algorithm=""fricas"")","-\frac{1}{238878720} \, {\left(1289945088 \, x^{9} + 2269347840 \, x^{8} - 23529056256 \, x^{7} - 117850567680 \, x^{6} - 250227954432 \, x^{5} - 302902600320 \, x^{4} - 224097754320 \, x^{3} - 100612822920 \, x^{2} - 25257845290 \, x - 2726071095\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{9793}{573308928} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/238878720*(1289945088*x^9 + 2269347840*x^8 - 23529056256*x^7 - 117850567680*x^6 - 250227954432*x^5 - 302902600320*x^4 - 224097754320*x^3 - 100612822920*x^2 - 25257845290*x - 2726071095)*sqrt(3*x^2 + 5*x + 2) + 9793/573308928*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2451,1,93,0,0.391529," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2),x, algorithm=""fricas"")","-\frac{1}{7962624} \, {\left(23887872 \, x^{8} + 2488320 \, x^{7} - 452625408 \, x^{6} - 1507127040 \, x^{5} - 2320737408 \, x^{4} - 2013572880 \, x^{3} - 1014795048 \, x^{2} - 278256050 \, x - 32198883\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{1225}{95551488} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/7962624*(23887872*x^8 + 2488320*x^7 - 452625408*x^6 - 1507127040*x^5 - 2320737408*x^4 - 2013572880*x^3 - 1014795048*x^2 - 278256050*x - 32198883)*sqrt(3*x^2 + 5*x + 2) + 1225/95551488*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2452,1,139,0,0.424470," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x),x, algorithm=""fricas"")","-\frac{1}{18579456} \, {\left(31352832 \, x^{7} - 50015232 \, x^{6} - 529784064 \, x^{5} - 1167854976 \, x^{4} - 1224844848 \, x^{3} - 722869752 \, x^{2} - 185981750 \, x - 101435865\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{65251715}{31850496} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + \frac{1625}{1024} \, \sqrt{5} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right)"," ",0,"-1/18579456*(31352832*x^7 - 50015232*x^6 - 529784064*x^5 - 1167854976*x^4 - 1224844848*x^3 - 722869752*x^2 - 185981750*x - 101435865)*sqrt(3*x^2 + 5*x + 2) + 65251715/31850496*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 1625/1024*sqrt(5)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9))","A",0
2453,1,159,0,0.427449," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^2,x, algorithm=""fricas"")","\frac{540211805 \, \sqrt{3} {\left(2 \, x + 3\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 418446000 \, \sqrt{5} {\left(2 \, x + 3\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 12 \, {\left(7464960 \, x^{7} - 13893120 \, x^{6} - 125632512 \, x^{5} - 273531168 \, x^{4} - 275126016 \, x^{3} - 179819084 \, x^{2} + 28017108 \, x + 259165107\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{46448640 \, {\left(2 \, x + 3\right)}}"," ",0,"1/46448640*(540211805*sqrt(3)*(2*x + 3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 418446000*sqrt(5)*(2*x + 3)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 12*(7464960*x^7 - 13893120*x^6 - 125632512*x^5 - 273531168*x^4 - 275126016*x^3 - 179819084*x^2 + 28017108*x + 259165107)*sqrt(3*x^2 + 5*x + 2))/(2*x + 3)","A",0
2454,1,173,0,0.438565," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^3,x, algorithm=""fricas"")","\frac{62219465 \, \sqrt{3} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 48195000 \, \sqrt{5} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 12 \, {\left(414720 \, x^{7} - 926208 \, x^{6} - 6830784 \, x^{5} - 15112992 \, x^{4} - 12848072 \, x^{3} - 19284852 \, x^{2} - 89867034 \, x - 91912653\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{2211840 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/2211840*(62219465*sqrt(3)*(4*x^2 + 12*x + 9)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 48195000*sqrt(5)*(4*x^2 + 12*x + 9)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 12*(414720*x^7 - 926208*x^6 - 6830784*x^5 - 15112992*x^4 - 12848072*x^3 - 19284852*x^2 - 89867034*x - 91912653)*sqrt(3*x^2 + 5*x + 2))/(4*x^2 + 12*x + 9)","A",0
2455,1,189,0,0.421187," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^4,x, algorithm=""fricas"")","\frac{13883485 \, \sqrt{3} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 10754100 \, \sqrt{5} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 12 \, {\left(82944 \, x^{7} - 231552 \, x^{6} - 1266816 \, x^{5} - 3277520 \, x^{4} + 746240 \, x^{3} + 44770416 \, x^{2} + 98927312 \, x + 61268351\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{368640 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/368640*(13883485*sqrt(3)*(8*x^3 + 36*x^2 + 54*x + 27)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 10754100*sqrt(5)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 12*(82944*x^7 - 231552*x^6 - 1266816*x^5 - 3277520*x^4 + 746240*x^3 + 44770416*x^2 + 98927312*x + 61268351)*sqrt(3*x^2 + 5*x + 2))/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
2456,1,203,0,0.440312," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^5,x, algorithm=""fricas"")","\frac{744275 \, \sqrt{3} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 576513 \, \sqrt{5} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 24 \, {\left(3456 \, x^{7} - 12864 \, x^{6} - 38288 \, x^{5} - 253688 \, x^{4} - 2869312 \, x^{3} - 9107922 \, x^{2} - 11295211 \, x - 4933171\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{24576 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"1/24576*(744275*sqrt(3)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 576513*sqrt(5)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 24*(3456*x^7 - 12864*x^6 - 38288*x^5 - 253688*x^4 - 2869312*x^3 - 9107922*x^2 - 11295211*x - 4933171)*sqrt(3*x^2 + 5*x + 2))/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
2457,1,219,0,0.422720," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^6,x, algorithm=""fricas"")","\frac{3027500 \, \sqrt{3} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 2345091 \, \sqrt{5} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(46080 \, x^{7} - 257280 \, x^{6} + 483840 \, x^{5} + 27897856 \, x^{4} + 127665096 \, x^{3} + 242016116 \, x^{2} + 213122626 \, x + 72189541\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{204800 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"1/204800*(3027500*sqrt(3)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 2345091*sqrt(5)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 20*(46080*x^7 - 257280*x^6 + 483840*x^5 + 27897856*x^4 + 127665096*x^3 + 242016116*x^2 + 213122626*x + 72189541)*sqrt(3*x^2 + 5*x + 2))/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
2458,1,233,0,0.450651," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^7,x, algorithm=""fricas"")","\frac{25641000 \, \sqrt{3} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 19861443 \, \sqrt{5} {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(2073600 \, x^{7} - 23155200 \, x^{6} - 550079616 \, x^{5} - 2968126160 \, x^{4} - 7425343520 \, x^{3} - 9799959120 \, x^{2} - 6648875480 \, x - 1835461379\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{6144000 \, {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)}}"," ",0,"1/6144000*(25641000*sqrt(3)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 19861443*sqrt(5)*(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*(2073600*x^7 - 23155200*x^6 - 550079616*x^5 - 2968126160*x^4 - 7425343520*x^3 - 9799959120*x^2 - 6648875480*x - 1835461379)*sqrt(3*x^2 + 5*x + 2))/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)","A",0
2459,1,249,0,0.444026," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^8,x, algorithm=""fricas"")","\frac{8442000 \, \sqrt{3} {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 6539127 \, \sqrt{5} {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)} \log\left(-\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} - 124 \, x^{2} - 212 \, x - 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(9676800 \, x^{7} + 338443008 \, x^{6} + 2361590432 \, x^{5} + 7622049520 \, x^{4} + 13619671040 \, x^{3} + 13975079520 \, x^{2} + 7753535702 \, x + 1810375853\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{14336000 \, {\left(128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right)}}"," ",0,"1/14336000*(8442000*sqrt(3)*(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 6539127*sqrt(5)*(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)*log(-(4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) - 124*x^2 - 212*x - 89)/(4*x^2 + 12*x + 9)) - 20*(9676800*x^7 + 338443008*x^6 + 2361590432*x^5 + 7622049520*x^4 + 13619671040*x^3 + 13975079520*x^2 + 7753535702*x + 1810375853)*sqrt(3*x^2 + 5*x + 2))/(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)","A",0
2460,1,263,0,0.445322," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^9,x, algorithm=""fricas"")","\frac{15120000 \, \sqrt{3} {\left(256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 11712477 \, \sqrt{5} {\left(256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(1478785536 \, x^{7} + 12182619328 \, x^{6} + 45214440256 \, x^{5} + 97176896240 \, x^{4} + 129405924160 \, x^{3} + 105874603844 \, x^{2} + 48950756372 \, x + 9818427389\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{573440000 \, {\left(256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561\right)}}"," ",0,"1/573440000*(15120000*sqrt(3)*(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 11712477*sqrt(5)*(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(1478785536*x^7 + 12182619328*x^6 + 45214440256*x^5 + 97176896240*x^4 + 129405924160*x^3 + 105874603844*x^2 + 48950756372*x + 9818427389)*sqrt(3*x^2 + 5*x + 2))/(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561)","A",0
2461,1,200,0,0.430867," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^10,x, algorithm=""fricas"")","\frac{2961 \, \sqrt{5} {\left(512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(28394496 \, x^{8} + 2848109952 \, x^{7} + 15895201728 \, x^{6} + 38558367264 \, x^{5} + 51825176720 \, x^{4} + 41530110824 \, x^{3} + 19810691268 \, x^{2} + 5201574542 \, x + 578701331\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{3686400000 \, {\left(512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right)}}"," ",0,"1/3686400000*(2961*sqrt(5)*(512*x^9 + 6912*x^8 + 41472*x^7 + 145152*x^6 + 326592*x^5 + 489888*x^4 + 489888*x^3 + 314928*x^2 + 118098*x + 19683)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(28394496*x^8 + 2848109952*x^7 + 15895201728*x^6 + 38558367264*x^5 + 51825176720*x^4 + 41530110824*x^3 + 19810691268*x^2 + 5201574542*x + 578701331)*sqrt(3*x^2 + 5*x + 2))/(512*x^9 + 6912*x^8 + 41472*x^7 + 145152*x^6 + 326592*x^5 + 489888*x^4 + 489888*x^3 + 314928*x^2 + 118098*x + 19683)","A",0
2462,1,215,0,0.441962," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^11,x, algorithm=""fricas"")","\frac{13251 \, \sqrt{5} {\left(1024 \, x^{10} + 15360 \, x^{9} + 103680 \, x^{8} + 414720 \, x^{7} + 1088640 \, x^{6} + 1959552 \, x^{5} + 2449440 \, x^{4} + 2099520 \, x^{3} + 1180980 \, x^{2} + 393660 \, x + 59049\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(371791872 \, x^{9} + 5268182272 \, x^{8} + 40186580992 \, x^{7} + 148740043392 \, x^{6} + 304078211712 \, x^{5} + 372602220928 \, x^{4} + 281702072128 \, x^{3} + 128970753208 \, x^{2} + 32786922608 \, x + 3544392763\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{20480000000 \, {\left(1024 \, x^{10} + 15360 \, x^{9} + 103680 \, x^{8} + 414720 \, x^{7} + 1088640 \, x^{6} + 1959552 \, x^{5} + 2449440 \, x^{4} + 2099520 \, x^{3} + 1180980 \, x^{2} + 393660 \, x + 59049\right)}}"," ",0,"1/20480000000*(13251*sqrt(5)*(1024*x^10 + 15360*x^9 + 103680*x^8 + 414720*x^7 + 1088640*x^6 + 1959552*x^5 + 2449440*x^4 + 2099520*x^3 + 1180980*x^2 + 393660*x + 59049)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(371791872*x^9 + 5268182272*x^8 + 40186580992*x^7 + 148740043392*x^6 + 304078211712*x^5 + 372602220928*x^4 + 281702072128*x^3 + 128970753208*x^2 + 32786922608*x + 3544392763)*sqrt(3*x^2 + 5*x + 2))/(1024*x^10 + 15360*x^9 + 103680*x^8 + 414720*x^7 + 1088640*x^6 + 1959552*x^5 + 2449440*x^4 + 2099520*x^3 + 1180980*x^2 + 393660*x + 59049)","A",0
2463,1,230,0,0.446400," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^12,x, algorithm=""fricas"")","\frac{1772001 \, \sqrt{5} {\left(2048 \, x^{11} + 33792 \, x^{10} + 253440 \, x^{9} + 1140480 \, x^{8} + 3421440 \, x^{7} + 7185024 \, x^{6} + 10777536 \, x^{5} + 11547360 \, x^{4} + 8660520 \, x^{3} + 4330260 \, x^{2} + 1299078 \, x + 177147\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(30557343744 \, x^{10} + 479034140160 \, x^{9} + 3387337708800 \, x^{8} + 14992486229760 \, x^{7} + 41485308553600 \, x^{6} + 72251114756992 \, x^{5} + 80329740407040 \, x^{4} + 56898923222800 \, x^{3} + 24817198954840 \, x^{2} + 6058472990850 \, x + 629890144539\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{3379200000000 \, {\left(2048 \, x^{11} + 33792 \, x^{10} + 253440 \, x^{9} + 1140480 \, x^{8} + 3421440 \, x^{7} + 7185024 \, x^{6} + 10777536 \, x^{5} + 11547360 \, x^{4} + 8660520 \, x^{3} + 4330260 \, x^{2} + 1299078 \, x + 177147\right)}}"," ",0,"1/3379200000000*(1772001*sqrt(5)*(2048*x^11 + 33792*x^10 + 253440*x^9 + 1140480*x^8 + 3421440*x^7 + 7185024*x^6 + 10777536*x^5 + 11547360*x^4 + 8660520*x^3 + 4330260*x^2 + 1299078*x + 177147)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(30557343744*x^10 + 479034140160*x^9 + 3387337708800*x^8 + 14992486229760*x^7 + 41485308553600*x^6 + 72251114756992*x^5 + 80329740407040*x^4 + 56898923222800*x^3 + 24817198954840*x^2 + 6058472990850*x + 629890144539)*sqrt(3*x^2 + 5*x + 2))/(2048*x^11 + 33792*x^10 + 253440*x^9 + 1140480*x^8 + 3421440*x^7 + 7185024*x^6 + 10777536*x^5 + 11547360*x^4 + 8660520*x^3 + 4330260*x^2 + 1299078*x + 177147)","A",0
2464,1,245,0,0.460970," ","integrate((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^13,x, algorithm=""fricas"")","\frac{5778927 \, \sqrt{5} {\left(4096 \, x^{12} + 73728 \, x^{11} + 608256 \, x^{10} + 3041280 \, x^{9} + 10264320 \, x^{8} + 24634368 \, x^{7} + 43110144 \, x^{6} + 55427328 \, x^{5} + 51963120 \, x^{4} + 34642080 \, x^{3} + 15588936 \, x^{2} + 4251528 \, x + 531441\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 20 \, {\left(60734693376 \, x^{11} + 1044584776704 \, x^{10} + 8182662620160 \, x^{9} + 38544695427840 \, x^{8} + 123629135656960 \, x^{7} + 273282692080768 \, x^{6} + 410468875350912 \, x^{5} + 412855931529440 \, x^{4} + 271870111600160 \, x^{3} + 111795175925940 \, x^{2} + 25843081681156 \, x + 2531527640959\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{13516800000000 \, {\left(4096 \, x^{12} + 73728 \, x^{11} + 608256 \, x^{10} + 3041280 \, x^{9} + 10264320 \, x^{8} + 24634368 \, x^{7} + 43110144 \, x^{6} + 55427328 \, x^{5} + 51963120 \, x^{4} + 34642080 \, x^{3} + 15588936 \, x^{2} + 4251528 \, x + 531441\right)}}"," ",0,"1/13516800000000*(5778927*sqrt(5)*(4096*x^12 + 73728*x^11 + 608256*x^10 + 3041280*x^9 + 10264320*x^8 + 24634368*x^7 + 43110144*x^6 + 55427328*x^5 + 51963120*x^4 + 34642080*x^3 + 15588936*x^2 + 4251528*x + 531441)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 20*(60734693376*x^11 + 1044584776704*x^10 + 8182662620160*x^9 + 38544695427840*x^8 + 123629135656960*x^7 + 273282692080768*x^6 + 410468875350912*x^5 + 412855931529440*x^4 + 271870111600160*x^3 + 111795175925940*x^2 + 25843081681156*x + 2531527640959)*sqrt(3*x^2 + 5*x + 2))/(4096*x^12 + 73728*x^11 + 608256*x^10 + 3041280*x^9 + 10264320*x^8 + 24634368*x^7 + 43110144*x^6 + 55427328*x^5 + 51963120*x^4 + 34642080*x^3 + 15588936*x^2 + 4251528*x + 531441)","A",0
2465,1,811,0,0.656899," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(64 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} - 48 \, {\left(3 \, B b^{2} c^{2} - 4 \, {\left(B a + A b\right)} c^{3}\right)} d^{2} e + 24 \, {\left(5 \, B b^{3} c + 8 \, A a c^{3} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c^{2}\right)} d e^{2} - {\left(35 \, B b^{4} + 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 40 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(48 \, B c^{4} e^{3} x^{3} + 192 \, B c^{4} d^{3} - 144 \, {\left(3 \, B b c^{3} - 4 \, A c^{4}\right)} d^{2} e + 24 \, {\left(15 \, B b^{2} c^{2} - 2 \, {\left(8 \, B a + 9 \, A b\right)} c^{3}\right)} d e^{2} - {\left(105 \, B b^{3} c + 128 \, A a c^{3} - 20 \, {\left(11 \, B a b + 6 \, A b^{2}\right)} c^{2}\right)} e^{3} + 8 \, {\left(24 \, B c^{4} d e^{2} - {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(144 \, B c^{4} d^{2} e - 24 \, {\left(5 \, B b c^{3} - 6 \, A c^{4}\right)} d e^{2} + {\left(35 \, B b^{2} c^{2} - 4 \, {\left(9 \, B a + 10 \, A b\right)} c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{5}}, \frac{3 \, {\left(64 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{3} - 48 \, {\left(3 \, B b^{2} c^{2} - 4 \, {\left(B a + A b\right)} c^{3}\right)} d^{2} e + 24 \, {\left(5 \, B b^{3} c + 8 \, A a c^{3} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c^{2}\right)} d e^{2} - {\left(35 \, B b^{4} + 48 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} - 40 \, {\left(3 \, B a b^{2} + A b^{3}\right)} c\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(48 \, B c^{4} e^{3} x^{3} + 192 \, B c^{4} d^{3} - 144 \, {\left(3 \, B b c^{3} - 4 \, A c^{4}\right)} d^{2} e + 24 \, {\left(15 \, B b^{2} c^{2} - 2 \, {\left(8 \, B a + 9 \, A b\right)} c^{3}\right)} d e^{2} - {\left(105 \, B b^{3} c + 128 \, A a c^{3} - 20 \, {\left(11 \, B a b + 6 \, A b^{2}\right)} c^{2}\right)} e^{3} + 8 \, {\left(24 \, B c^{4} d e^{2} - {\left(7 \, B b c^{3} - 8 \, A c^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(144 \, B c^{4} d^{2} e - 24 \, {\left(5 \, B b c^{3} - 6 \, A c^{4}\right)} d e^{2} + {\left(35 \, B b^{2} c^{2} - 4 \, {\left(9 \, B a + 10 \, A b\right)} c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{5}}\right]"," ",0,"[-1/768*(3*(64*(B*b*c^3 - 2*A*c^4)*d^3 - 48*(3*B*b^2*c^2 - 4*(B*a + A*b)*c^3)*d^2*e + 24*(5*B*b^3*c + 8*A*a*c^3 - 6*(2*B*a*b + A*b^2)*c^2)*d*e^2 - (35*B*b^4 + 48*(B*a^2 + 2*A*a*b)*c^2 - 40*(3*B*a*b^2 + A*b^3)*c)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(48*B*c^4*e^3*x^3 + 192*B*c^4*d^3 - 144*(3*B*b*c^3 - 4*A*c^4)*d^2*e + 24*(15*B*b^2*c^2 - 2*(8*B*a + 9*A*b)*c^3)*d*e^2 - (105*B*b^3*c + 128*A*a*c^3 - 20*(11*B*a*b + 6*A*b^2)*c^2)*e^3 + 8*(24*B*c^4*d*e^2 - (7*B*b*c^3 - 8*A*c^4)*e^3)*x^2 + 2*(144*B*c^4*d^2*e - 24*(5*B*b*c^3 - 6*A*c^4)*d*e^2 + (35*B*b^2*c^2 - 4*(9*B*a + 10*A*b)*c^3)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^5, 1/384*(3*(64*(B*b*c^3 - 2*A*c^4)*d^3 - 48*(3*B*b^2*c^2 - 4*(B*a + A*b)*c^3)*d^2*e + 24*(5*B*b^3*c + 8*A*a*c^3 - 6*(2*B*a*b + A*b^2)*c^2)*d*e^2 - (35*B*b^4 + 48*(B*a^2 + 2*A*a*b)*c^2 - 40*(3*B*a*b^2 + A*b^3)*c)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(48*B*c^4*e^3*x^3 + 192*B*c^4*d^3 - 144*(3*B*b*c^3 - 4*A*c^4)*d^2*e + 24*(15*B*b^2*c^2 - 2*(8*B*a + 9*A*b)*c^3)*d*e^2 - (105*B*b^3*c + 128*A*a*c^3 - 20*(11*B*a*b + 6*A*b^2)*c^2)*e^3 + 8*(24*B*c^4*d*e^2 - (7*B*b*c^3 - 8*A*c^4)*e^3)*x^2 + 2*(144*B*c^4*d^2*e - 24*(5*B*b*c^3 - 6*A*c^4)*d*e^2 + (35*B*b^2*c^2 - 4*(9*B*a + 10*A*b)*c^3)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
2466,1,487,0,0.513284," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - 4 \, {\left(3 \, B b^{2} c - 4 \, {\left(B a + A b\right)} c^{2}\right)} d e + {\left(5 \, B b^{3} + 8 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, B c^{3} e^{2} x^{2} + 24 \, B c^{3} d^{2} - 12 \, {\left(3 \, B b c^{2} - 4 \, A c^{3}\right)} d e + {\left(15 \, B b^{2} c - 2 \, {\left(8 \, B a + 9 \, A b\right)} c^{2}\right)} e^{2} + 2 \, {\left(12 \, B c^{3} d e - {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{4}}, \frac{3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - 4 \, {\left(3 \, B b^{2} c - 4 \, {\left(B a + A b\right)} c^{2}\right)} d e + {\left(5 \, B b^{3} + 8 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(8 \, B c^{3} e^{2} x^{2} + 24 \, B c^{3} d^{2} - 12 \, {\left(3 \, B b c^{2} - 4 \, A c^{3}\right)} d e + {\left(15 \, B b^{2} c - 2 \, {\left(8 \, B a + 9 \, A b\right)} c^{2}\right)} e^{2} + 2 \, {\left(12 \, B c^{3} d e - {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{4}}\right]"," ",0,"[1/96*(3*(8*(B*b*c^2 - 2*A*c^3)*d^2 - 4*(3*B*b^2*c - 4*(B*a + A*b)*c^2)*d*e + (5*B*b^3 + 8*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*B*c^3*e^2*x^2 + 24*B*c^3*d^2 - 12*(3*B*b*c^2 - 4*A*c^3)*d*e + (15*B*b^2*c - 2*(8*B*a + 9*A*b)*c^2)*e^2 + 2*(12*B*c^3*d*e - (5*B*b*c^2 - 6*A*c^3)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/48*(3*(8*(B*b*c^2 - 2*A*c^3)*d^2 - 4*(3*B*b^2*c - 4*(B*a + A*b)*c^2)*d*e + (5*B*b^3 + 8*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(8*B*c^3*e^2*x^2 + 24*B*c^3*d^2 - 12*(3*B*b*c^2 - 4*A*c^3)*d*e + (15*B*b^2*c - 2*(8*B*a + 9*A*b)*c^2)*e^2 + 2*(12*B*c^3*d*e - (5*B*b*c^2 - 6*A*c^3)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
2467,1,273,0,0.464196," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d - {\left(3 \, B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, B c^{2} e x + 4 \, B c^{2} d - {\left(3 \, B b c - 4 \, A c^{2}\right)} e\right)} \sqrt{c x^{2} + b x + a}}{16 \, c^{3}}, \frac{{\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d - {\left(3 \, B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(2 \, B c^{2} e x + 4 \, B c^{2} d - {\left(3 \, B b c - 4 \, A c^{2}\right)} e\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{3}}\right]"," ",0,"[1/16*((4*(B*b*c - 2*A*c^2)*d - (3*B*b^2 - 4*(B*a + A*b)*c)*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(2*B*c^2*e*x + 4*B*c^2*d - (3*B*b*c - 4*A*c^2)*e)*sqrt(c*x^2 + b*x + a))/c^3, 1/8*((4*(B*b*c - 2*A*c^2)*d - (3*B*b^2 - 4*(B*a + A*b)*c)*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(2*B*c^2*e*x + 4*B*c^2*d - (3*B*b*c - 4*A*c^2)*e)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
2468,1,162,0,0.419359," ","integrate((B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c x^{2} + b x + a} B c - {\left(B b - 2 \, A c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, c^{2}}, \frac{2 \, \sqrt{c x^{2} + b x + a} B c + {\left(B b - 2 \, A c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{2 \, c^{2}}\right]"," ",0,"[1/4*(4*sqrt(c*x^2 + b*x + a)*B*c - (B*b - 2*A*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c))/c^2, 1/2*(2*sqrt(c*x^2 + b*x + a)*B*c + (B*b - 2*A*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)))/c^2]","A",0
2469,1,1079,0,42.737900," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(B c d^{2} - B b d e + B a e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - {\left(B c d - A c e\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}, -\frac{2 \, {\left(B c d^{2} - B b d e + B a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(B c d - A c e\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}, -\frac{2 \, {\left(B c d - A c e\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - {\left(B c d^{2} - B b d e + B a e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{2 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}, -\frac{{\left(B c d - A c e\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + {\left(B c d^{2} - B b d e + B a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{c^{2} d^{2} e - b c d e^{2} + a c e^{3}}\right]"," ",0,"[1/2*((B*c*d^2 - B*b*d*e + B*a*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - (B*c*d - A*c*e)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3), -1/2*(2*(B*c*d^2 - B*b*d*e + B*a*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + (B*c*d - A*c*e)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3), -1/2*(2*(B*c*d - A*c*e)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - (B*c*d^2 - B*b*d*e + B*a*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3), -((B*c*d - A*c*e)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + (B*c*d^2 - B*b*d*e + B*a*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3)]","B",0
2470,1,748,0,2.187172," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(B b - 2 \, A c\right)} d^{2} - {\left(2 \, B a - A b\right)} d e + {\left({\left(B b - 2 \, A c\right)} d e - {\left(2 \, B a - A b\right)} e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(B c d^{3} - A a e^{3} - {\left(B b + A c\right)} d^{2} e + {\left(B a + A b\right)} d e^{2}\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e - 2 \, a b d^{2} e^{3} + a^{2} d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + a^{2} e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)}}, -\frac{{\left({\left(B b - 2 \, A c\right)} d^{2} - {\left(2 \, B a - A b\right)} d e + {\left({\left(B b - 2 \, A c\right)} d e - {\left(2 \, B a - A b\right)} e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(B c d^{3} - A a e^{3} - {\left(B b + A c\right)} d^{2} e + {\left(B a + A b\right)} d e^{2}\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e - 2 \, a b d^{2} e^{3} + a^{2} d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + a^{2} e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)}}\right]"," ",0,"[1/4*(((B*b - 2*A*c)*d^2 - (2*B*a - A*b)*d*e + ((B*b - 2*A*c)*d*e - (2*B*a - A*b)*e^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(B*c*d^3 - A*a*e^3 - (B*b + A*c)*d^2*e + (B*a + A*b)*d*e^2)*sqrt(c*x^2 + b*x + a))/(c^2*d^5 - 2*b*c*d^4*e - 2*a*b*d^2*e^3 + a^2*d*e^4 + (b^2 + 2*a*c)*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + a^2*e^5 + (b^2 + 2*a*c)*d^2*e^3)*x), -1/2*(((B*b - 2*A*c)*d^2 - (2*B*a - A*b)*d*e + ((B*b - 2*A*c)*d*e - (2*B*a - A*b)*e^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(B*c*d^3 - A*a*e^3 - (B*b + A*c)*d^2*e + (B*a + A*b)*d*e^2)*sqrt(c*x^2 + b*x + a))/(c^2*d^5 - 2*b*c*d^4*e - 2*a*b*d^2*e^3 + a^2*d*e^4 + (b^2 + 2*a*c)*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + a^2*e^5 + (b^2 + 2*a*c)*d^2*e^3)*x)]","B",0
2471,1,1750,0,15.986414," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{4} - {\left(B b^{2} + 4 \, {\left(3 \, B a - 2 \, A b\right)} c\right)} d^{3} e + {\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} d^{2} e^{2} + {\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{2} e^{2} - {\left(B b^{2} + 4 \, {\left(3 \, B a - 2 \, A b\right)} c\right)} d e^{3} + {\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} e^{4}\right)} x^{2} + 2 \, {\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{3} e - {\left(B b^{2} + 4 \, {\left(3 \, B a - 2 \, A b\right)} c\right)} d^{2} e^{2} + {\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(4 \, B c^{2} d^{5} - 2 \, A a^{2} e^{5} - {\left(5 \, B b c + 8 \, A c^{2}\right)} d^{4} e + {\left(B b^{2} + {\left(2 \, B a + 13 \, A b\right)} c\right)} d^{3} e^{2} + {\left(B a b - 5 \, A b^{2} - 10 \, A a c\right)} d^{2} e^{3} - {\left(2 \, B a^{2} - 7 \, A a b\right)} d e^{4} + {\left(2 \, B c^{2} d^{4} e - {\left(B b c + 6 \, A c^{2}\right)} d^{3} e^{2} - {\left(B b^{2} + {\left(2 \, B a - 9 \, A b\right)} c\right)} d^{2} e^{3} + {\left(5 \, B a b - 3 \, A b^{2} - 6 \, A a c\right)} d e^{4} - {\left(4 \, B a^{2} - 3 \, A a b\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e - 3 \, a^{2} b d^{3} e^{5} + a^{3} d^{2} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} - 3 \, a^{2} b d e^{7} + a^{3} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} - 3 \, a^{2} b d^{2} e^{6} + a^{3} d e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)}}, -\frac{{\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{4} - {\left(B b^{2} + 4 \, {\left(3 \, B a - 2 \, A b\right)} c\right)} d^{3} e + {\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} d^{2} e^{2} + {\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{2} e^{2} - {\left(B b^{2} + 4 \, {\left(3 \, B a - 2 \, A b\right)} c\right)} d e^{3} + {\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} e^{4}\right)} x^{2} + 2 \, {\left(4 \, {\left(B b c - 2 \, A c^{2}\right)} d^{3} e - {\left(B b^{2} + 4 \, {\left(3 \, B a - 2 \, A b\right)} c\right)} d^{2} e^{2} + {\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(4 \, B c^{2} d^{5} - 2 \, A a^{2} e^{5} - {\left(5 \, B b c + 8 \, A c^{2}\right)} d^{4} e + {\left(B b^{2} + {\left(2 \, B a + 13 \, A b\right)} c\right)} d^{3} e^{2} + {\left(B a b - 5 \, A b^{2} - 10 \, A a c\right)} d^{2} e^{3} - {\left(2 \, B a^{2} - 7 \, A a b\right)} d e^{4} + {\left(2 \, B c^{2} d^{4} e - {\left(B b c + 6 \, A c^{2}\right)} d^{3} e^{2} - {\left(B b^{2} + {\left(2 \, B a - 9 \, A b\right)} c\right)} d^{2} e^{3} + {\left(5 \, B a b - 3 \, A b^{2} - 6 \, A a c\right)} d e^{4} - {\left(4 \, B a^{2} - 3 \, A a b\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e - 3 \, a^{2} b d^{3} e^{5} + a^{3} d^{2} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} - 3 \, a^{2} b d e^{7} + a^{3} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} - 3 \, a^{2} b d^{2} e^{6} + a^{3} d e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)}}\right]"," ",0,"[1/16*((4*(B*b*c - 2*A*c^2)*d^4 - (B*b^2 + 4*(3*B*a - 2*A*b)*c)*d^3*e + (4*B*a*b - 3*A*b^2 + 4*A*a*c)*d^2*e^2 + (4*(B*b*c - 2*A*c^2)*d^2*e^2 - (B*b^2 + 4*(3*B*a - 2*A*b)*c)*d*e^3 + (4*B*a*b - 3*A*b^2 + 4*A*a*c)*e^4)*x^2 + 2*(4*(B*b*c - 2*A*c^2)*d^3*e - (B*b^2 + 4*(3*B*a - 2*A*b)*c)*d^2*e^2 + (4*B*a*b - 3*A*b^2 + 4*A*a*c)*d*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(4*B*c^2*d^5 - 2*A*a^2*e^5 - (5*B*b*c + 8*A*c^2)*d^4*e + (B*b^2 + (2*B*a + 13*A*b)*c)*d^3*e^2 + (B*a*b - 5*A*b^2 - 10*A*a*c)*d^2*e^3 - (2*B*a^2 - 7*A*a*b)*d*e^4 + (2*B*c^2*d^4*e - (B*b*c + 6*A*c^2)*d^3*e^2 - (B*b^2 + (2*B*a - 9*A*b)*c)*d^2*e^3 + (5*B*a*b - 3*A*b^2 - 6*A*a*c)*d*e^4 - (4*B*a^2 - 3*A*a*b)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^8 - 3*b*c^2*d^7*e - 3*a^2*b*d^3*e^5 + a^3*d^2*e^6 + 3*(b^2*c + a*c^2)*d^6*e^2 - (b^3 + 6*a*b*c)*d^5*e^3 + 3*(a*b^2 + a^2*c)*d^4*e^4 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 - 3*a^2*b*d*e^7 + a^3*e^8 + 3*(b^2*c + a*c^2)*d^4*e^4 - (b^3 + 6*a*b*c)*d^3*e^5 + 3*(a*b^2 + a^2*c)*d^2*e^6)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 - 3*a^2*b*d^2*e^6 + a^3*d*e^7 + 3*(b^2*c + a*c^2)*d^5*e^3 - (b^3 + 6*a*b*c)*d^4*e^4 + 3*(a*b^2 + a^2*c)*d^3*e^5)*x), -1/8*((4*(B*b*c - 2*A*c^2)*d^4 - (B*b^2 + 4*(3*B*a - 2*A*b)*c)*d^3*e + (4*B*a*b - 3*A*b^2 + 4*A*a*c)*d^2*e^2 + (4*(B*b*c - 2*A*c^2)*d^2*e^2 - (B*b^2 + 4*(3*B*a - 2*A*b)*c)*d*e^3 + (4*B*a*b - 3*A*b^2 + 4*A*a*c)*e^4)*x^2 + 2*(4*(B*b*c - 2*A*c^2)*d^3*e - (B*b^2 + 4*(3*B*a - 2*A*b)*c)*d^2*e^2 + (4*B*a*b - 3*A*b^2 + 4*A*a*c)*d*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(4*B*c^2*d^5 - 2*A*a^2*e^5 - (5*B*b*c + 8*A*c^2)*d^4*e + (B*b^2 + (2*B*a + 13*A*b)*c)*d^3*e^2 + (B*a*b - 5*A*b^2 - 10*A*a*c)*d^2*e^3 - (2*B*a^2 - 7*A*a*b)*d*e^4 + (2*B*c^2*d^4*e - (B*b*c + 6*A*c^2)*d^3*e^2 - (B*b^2 + (2*B*a - 9*A*b)*c)*d^2*e^3 + (5*B*a*b - 3*A*b^2 - 6*A*a*c)*d*e^4 - (4*B*a^2 - 3*A*a*b)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^8 - 3*b*c^2*d^7*e - 3*a^2*b*d^3*e^5 + a^3*d^2*e^6 + 3*(b^2*c + a*c^2)*d^6*e^2 - (b^3 + 6*a*b*c)*d^5*e^3 + 3*(a*b^2 + a^2*c)*d^4*e^4 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 - 3*a^2*b*d*e^7 + a^3*e^8 + 3*(b^2*c + a*c^2)*d^4*e^4 - (b^3 + 6*a*b*c)*d^3*e^5 + 3*(a*b^2 + a^2*c)*d^2*e^6)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 - 3*a^2*b*d^2*e^6 + a^3*d*e^7 + 3*(b^2*c + a*c^2)*d^5*e^3 - (b^3 + 6*a*b*c)*d^4*e^4 + 3*(a*b^2 + a^2*c)*d^3*e^5)*x)]","B",0
2472,1,3684,0,85.512312," ","integrate((B*x+A)/(e*x+d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{6} - 4 \, {\left(B b^{2} c + 2 \, {\left(4 \, B a - 3 \, A b\right)} c^{2}\right)} d^{5} e + {\left(B b^{3} + 24 \, A a c^{2} + 2 \, {\left(10 \, B a b - 9 \, A b^{2}\right)} c\right)} d^{4} e^{2} - {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} d^{3} e^{3} + {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} e^{3} - 4 \, {\left(B b^{2} c + 2 \, {\left(4 \, B a - 3 \, A b\right)} c^{2}\right)} d^{2} e^{4} + {\left(B b^{3} + 24 \, A a c^{2} + 2 \, {\left(10 \, B a b - 9 \, A b^{2}\right)} c\right)} d e^{5} - {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} e^{6}\right)} x^{3} + 3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{4} e^{2} - 4 \, {\left(B b^{2} c + 2 \, {\left(4 \, B a - 3 \, A b\right)} c^{2}\right)} d^{3} e^{3} + {\left(B b^{3} + 24 \, A a c^{2} + 2 \, {\left(10 \, B a b - 9 \, A b^{2}\right)} c\right)} d^{2} e^{4} - {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} d e^{5}\right)} x^{2} + 3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{5} e - 4 \, {\left(B b^{2} c + 2 \, {\left(4 \, B a - 3 \, A b\right)} c^{2}\right)} d^{4} e^{2} + {\left(B b^{3} + 24 \, A a c^{2} + 2 \, {\left(10 \, B a b - 9 \, A b^{2}\right)} c\right)} d^{3} e^{3} - {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(24 \, B c^{3} d^{7} - 8 \, A a^{3} e^{7} - 36 \, {\left(B b c^{2} + 2 \, A c^{3}\right)} d^{6} e + {\left(15 \, B b^{2} c - 2 \, {\left(8 \, B a - 81 \, A b\right)} c^{2}\right)} d^{5} e^{2} - {\left(3 \, B b^{3} + 92 \, A a c^{2} - {\left(44 \, B a b - 123 \, A b^{2}\right)} c\right)} d^{4} e^{3} - {\left(13 \, B a b^{2} - 33 \, A b^{3} + 4 \, {\left(11 \, B a^{2} - 34 \, A a b\right)} c\right)} d^{3} e^{4} + {\left(20 \, B a^{2} b - 59 \, A a b^{2} - 28 \, A a^{2} c\right)} d^{2} e^{5} - 2 \, {\left(2 \, B a^{3} - 17 \, A a^{2} b\right)} d e^{6} + {\left(8 \, B c^{3} d^{5} e^{2} + 2 \, {\left(B b c^{2} - 22 \, A c^{3}\right)} d^{4} e^{3} - {\left(13 \, B b^{2} c + 44 \, {\left(B a - 2 \, A b\right)} c^{2}\right)} d^{3} e^{4} + {\left(3 \, B b^{3} - 28 \, A a c^{2} + {\left(80 \, B a b - 59 \, A b^{2}\right)} c\right)} d^{2} e^{5} - {\left(21 \, B a b^{2} - 15 \, A b^{3} + 4 \, {\left(13 \, B a^{2} - 7 \, A a b\right)} c\right)} d e^{6} + {\left(18 \, B a^{2} b - 15 \, A a b^{2} + 16 \, A a^{2} c\right)} e^{7}\right)} x^{2} + 2 \, {\left(12 \, B c^{3} d^{6} e - {\left(5 \, B b c^{2} + 54 \, A c^{3}\right)} d^{5} e^{2} - {\left(11 \, B b^{2} c + {\left(42 \, B a - 113 \, A b\right)} c^{2}\right)} d^{4} e^{3} + {\left(4 \, B b^{3} - 48 \, A a c^{2} + {\left(86 \, B a b - 79 \, A b^{2}\right)} c\right)} d^{3} e^{4} - {\left(29 \, B a b^{2} - 20 \, A b^{3} + 2 \, {\left(30 \, B a^{2} - 29 \, A a b\right)} c\right)} d^{2} e^{5} + {\left(31 \, B a^{2} b - 25 \, A a b^{2} + 6 \, A a^{2} c\right)} d e^{6} - {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(c^{4} d^{11} - 4 \, b c^{3} d^{10} e - 4 \, a^{3} b d^{4} e^{7} + a^{4} d^{3} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{6} + {\left(c^{4} d^{8} e^{3} - 4 \, b c^{3} d^{7} e^{4} - 4 \, a^{3} b d e^{10} + a^{4} e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{9}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} - 4 \, b c^{3} d^{8} e^{3} - 4 \, a^{3} b d^{2} e^{9} + a^{4} d e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{8}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e - 4 \, b c^{3} d^{9} e^{2} - 4 \, a^{3} b d^{3} e^{8} + a^{4} d^{2} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{7}\right)} x\right)}}, -\frac{3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{6} - 4 \, {\left(B b^{2} c + 2 \, {\left(4 \, B a - 3 \, A b\right)} c^{2}\right)} d^{5} e + {\left(B b^{3} + 24 \, A a c^{2} + 2 \, {\left(10 \, B a b - 9 \, A b^{2}\right)} c\right)} d^{4} e^{2} - {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} d^{3} e^{3} + {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} e^{3} - 4 \, {\left(B b^{2} c + 2 \, {\left(4 \, B a - 3 \, A b\right)} c^{2}\right)} d^{2} e^{4} + {\left(B b^{3} + 24 \, A a c^{2} + 2 \, {\left(10 \, B a b - 9 \, A b^{2}\right)} c\right)} d e^{5} - {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} e^{6}\right)} x^{3} + 3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{4} e^{2} - 4 \, {\left(B b^{2} c + 2 \, {\left(4 \, B a - 3 \, A b\right)} c^{2}\right)} d^{3} e^{3} + {\left(B b^{3} + 24 \, A a c^{2} + 2 \, {\left(10 \, B a b - 9 \, A b^{2}\right)} c\right)} d^{2} e^{4} - {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} d e^{5}\right)} x^{2} + 3 \, {\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{5} e - 4 \, {\left(B b^{2} c + 2 \, {\left(4 \, B a - 3 \, A b\right)} c^{2}\right)} d^{4} e^{2} + {\left(B b^{3} + 24 \, A a c^{2} + 2 \, {\left(10 \, B a b - 9 \, A b^{2}\right)} c\right)} d^{3} e^{3} - {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(24 \, B c^{3} d^{7} - 8 \, A a^{3} e^{7} - 36 \, {\left(B b c^{2} + 2 \, A c^{3}\right)} d^{6} e + {\left(15 \, B b^{2} c - 2 \, {\left(8 \, B a - 81 \, A b\right)} c^{2}\right)} d^{5} e^{2} - {\left(3 \, B b^{3} + 92 \, A a c^{2} - {\left(44 \, B a b - 123 \, A b^{2}\right)} c\right)} d^{4} e^{3} - {\left(13 \, B a b^{2} - 33 \, A b^{3} + 4 \, {\left(11 \, B a^{2} - 34 \, A a b\right)} c\right)} d^{3} e^{4} + {\left(20 \, B a^{2} b - 59 \, A a b^{2} - 28 \, A a^{2} c\right)} d^{2} e^{5} - 2 \, {\left(2 \, B a^{3} - 17 \, A a^{2} b\right)} d e^{6} + {\left(8 \, B c^{3} d^{5} e^{2} + 2 \, {\left(B b c^{2} - 22 \, A c^{3}\right)} d^{4} e^{3} - {\left(13 \, B b^{2} c + 44 \, {\left(B a - 2 \, A b\right)} c^{2}\right)} d^{3} e^{4} + {\left(3 \, B b^{3} - 28 \, A a c^{2} + {\left(80 \, B a b - 59 \, A b^{2}\right)} c\right)} d^{2} e^{5} - {\left(21 \, B a b^{2} - 15 \, A b^{3} + 4 \, {\left(13 \, B a^{2} - 7 \, A a b\right)} c\right)} d e^{6} + {\left(18 \, B a^{2} b - 15 \, A a b^{2} + 16 \, A a^{2} c\right)} e^{7}\right)} x^{2} + 2 \, {\left(12 \, B c^{3} d^{6} e - {\left(5 \, B b c^{2} + 54 \, A c^{3}\right)} d^{5} e^{2} - {\left(11 \, B b^{2} c + {\left(42 \, B a - 113 \, A b\right)} c^{2}\right)} d^{4} e^{3} + {\left(4 \, B b^{3} - 48 \, A a c^{2} + {\left(86 \, B a b - 79 \, A b^{2}\right)} c\right)} d^{3} e^{4} - {\left(29 \, B a b^{2} - 20 \, A b^{3} + 2 \, {\left(30 \, B a^{2} - 29 \, A a b\right)} c\right)} d^{2} e^{5} + {\left(31 \, B a^{2} b - 25 \, A a b^{2} + 6 \, A a^{2} c\right)} d e^{6} - {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(c^{4} d^{11} - 4 \, b c^{3} d^{10} e - 4 \, a^{3} b d^{4} e^{7} + a^{4} d^{3} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{6} + {\left(c^{4} d^{8} e^{3} - 4 \, b c^{3} d^{7} e^{4} - 4 \, a^{3} b d e^{10} + a^{4} e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{9}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} - 4 \, b c^{3} d^{8} e^{3} - 4 \, a^{3} b d^{2} e^{9} + a^{4} d e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{8}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e - 4 \, b c^{3} d^{9} e^{2} - 4 \, a^{3} b d^{3} e^{8} + a^{4} d^{2} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{7}\right)} x\right)}}\right]"," ",0,"[-1/96*(3*(8*(B*b*c^2 - 2*A*c^3)*d^6 - 4*(B*b^2*c + 2*(4*B*a - 3*A*b)*c^2)*d^5*e + (B*b^3 + 24*A*a*c^2 + 2*(10*B*a*b - 9*A*b^2)*c)*d^4*e^2 - (6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*d^3*e^3 + (8*(B*b*c^2 - 2*A*c^3)*d^3*e^3 - 4*(B*b^2*c + 2*(4*B*a - 3*A*b)*c^2)*d^2*e^4 + (B*b^3 + 24*A*a*c^2 + 2*(10*B*a*b - 9*A*b^2)*c)*d*e^5 - (6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*e^6)*x^3 + 3*(8*(B*b*c^2 - 2*A*c^3)*d^4*e^2 - 4*(B*b^2*c + 2*(4*B*a - 3*A*b)*c^2)*d^3*e^3 + (B*b^3 + 24*A*a*c^2 + 2*(10*B*a*b - 9*A*b^2)*c)*d^2*e^4 - (6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*d*e^5)*x^2 + 3*(8*(B*b*c^2 - 2*A*c^3)*d^5*e - 4*(B*b^2*c + 2*(4*B*a - 3*A*b)*c^2)*d^4*e^2 + (B*b^3 + 24*A*a*c^2 + 2*(10*B*a*b - 9*A*b^2)*c)*d^3*e^3 - (6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*d^2*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(24*B*c^3*d^7 - 8*A*a^3*e^7 - 36*(B*b*c^2 + 2*A*c^3)*d^6*e + (15*B*b^2*c - 2*(8*B*a - 81*A*b)*c^2)*d^5*e^2 - (3*B*b^3 + 92*A*a*c^2 - (44*B*a*b - 123*A*b^2)*c)*d^4*e^3 - (13*B*a*b^2 - 33*A*b^3 + 4*(11*B*a^2 - 34*A*a*b)*c)*d^3*e^4 + (20*B*a^2*b - 59*A*a*b^2 - 28*A*a^2*c)*d^2*e^5 - 2*(2*B*a^3 - 17*A*a^2*b)*d*e^6 + (8*B*c^3*d^5*e^2 + 2*(B*b*c^2 - 22*A*c^3)*d^4*e^3 - (13*B*b^2*c + 44*(B*a - 2*A*b)*c^2)*d^3*e^4 + (3*B*b^3 - 28*A*a*c^2 + (80*B*a*b - 59*A*b^2)*c)*d^2*e^5 - (21*B*a*b^2 - 15*A*b^3 + 4*(13*B*a^2 - 7*A*a*b)*c)*d*e^6 + (18*B*a^2*b - 15*A*a*b^2 + 16*A*a^2*c)*e^7)*x^2 + 2*(12*B*c^3*d^6*e - (5*B*b*c^2 + 54*A*c^3)*d^5*e^2 - (11*B*b^2*c + (42*B*a - 113*A*b)*c^2)*d^4*e^3 + (4*B*b^3 - 48*A*a*c^2 + (86*B*a*b - 79*A*b^2)*c)*d^3*e^4 - (29*B*a*b^2 - 20*A*b^3 + 2*(30*B*a^2 - 29*A*a*b)*c)*d^2*e^5 + (31*B*a^2*b - 25*A*a*b^2 + 6*A*a^2*c)*d*e^6 - (6*B*a^3 - 5*A*a^2*b)*e^7)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^11 - 4*b*c^3*d^10*e - 4*a^3*b*d^4*e^7 + a^4*d^3*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^6 + (c^4*d^8*e^3 - 4*b*c^3*d^7*e^4 - 4*a^3*b*d*e^10 + a^4*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^9)*x^3 + 3*(c^4*d^9*e^2 - 4*b*c^3*d^8*e^3 - 4*a^3*b*d^2*e^9 + a^4*d*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^8)*x^2 + 3*(c^4*d^10*e - 4*b*c^3*d^9*e^2 - 4*a^3*b*d^3*e^8 + a^4*d^2*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^7)*x), -1/48*(3*(8*(B*b*c^2 - 2*A*c^3)*d^6 - 4*(B*b^2*c + 2*(4*B*a - 3*A*b)*c^2)*d^5*e + (B*b^3 + 24*A*a*c^2 + 2*(10*B*a*b - 9*A*b^2)*c)*d^4*e^2 - (6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*d^3*e^3 + (8*(B*b*c^2 - 2*A*c^3)*d^3*e^3 - 4*(B*b^2*c + 2*(4*B*a - 3*A*b)*c^2)*d^2*e^4 + (B*b^3 + 24*A*a*c^2 + 2*(10*B*a*b - 9*A*b^2)*c)*d*e^5 - (6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*e^6)*x^3 + 3*(8*(B*b*c^2 - 2*A*c^3)*d^4*e^2 - 4*(B*b^2*c + 2*(4*B*a - 3*A*b)*c^2)*d^3*e^3 + (B*b^3 + 24*A*a*c^2 + 2*(10*B*a*b - 9*A*b^2)*c)*d^2*e^4 - (6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*d*e^5)*x^2 + 3*(8*(B*b*c^2 - 2*A*c^3)*d^5*e - 4*(B*b^2*c + 2*(4*B*a - 3*A*b)*c^2)*d^4*e^2 + (B*b^3 + 24*A*a*c^2 + 2*(10*B*a*b - 9*A*b^2)*c)*d^3*e^3 - (6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*d^2*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(24*B*c^3*d^7 - 8*A*a^3*e^7 - 36*(B*b*c^2 + 2*A*c^3)*d^6*e + (15*B*b^2*c - 2*(8*B*a - 81*A*b)*c^2)*d^5*e^2 - (3*B*b^3 + 92*A*a*c^2 - (44*B*a*b - 123*A*b^2)*c)*d^4*e^3 - (13*B*a*b^2 - 33*A*b^3 + 4*(11*B*a^2 - 34*A*a*b)*c)*d^3*e^4 + (20*B*a^2*b - 59*A*a*b^2 - 28*A*a^2*c)*d^2*e^5 - 2*(2*B*a^3 - 17*A*a^2*b)*d*e^6 + (8*B*c^3*d^5*e^2 + 2*(B*b*c^2 - 22*A*c^3)*d^4*e^3 - (13*B*b^2*c + 44*(B*a - 2*A*b)*c^2)*d^3*e^4 + (3*B*b^3 - 28*A*a*c^2 + (80*B*a*b - 59*A*b^2)*c)*d^2*e^5 - (21*B*a*b^2 - 15*A*b^3 + 4*(13*B*a^2 - 7*A*a*b)*c)*d*e^6 + (18*B*a^2*b - 15*A*a*b^2 + 16*A*a^2*c)*e^7)*x^2 + 2*(12*B*c^3*d^6*e - (5*B*b*c^2 + 54*A*c^3)*d^5*e^2 - (11*B*b^2*c + (42*B*a - 113*A*b)*c^2)*d^4*e^3 + (4*B*b^3 - 48*A*a*c^2 + (86*B*a*b - 79*A*b^2)*c)*d^3*e^4 - (29*B*a*b^2 - 20*A*b^3 + 2*(30*B*a^2 - 29*A*a*b)*c)*d^2*e^5 + (31*B*a^2*b - 25*A*a*b^2 + 6*A*a^2*c)*d*e^6 - (6*B*a^3 - 5*A*a^2*b)*e^7)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^11 - 4*b*c^3*d^10*e - 4*a^3*b*d^4*e^7 + a^4*d^3*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^6 + (c^4*d^8*e^3 - 4*b*c^3*d^7*e^4 - 4*a^3*b*d*e^10 + a^4*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^9)*x^3 + 3*(c^4*d^9*e^2 - 4*b*c^3*d^8*e^3 - 4*a^3*b*d^2*e^9 + a^4*d*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^8)*x^2 + 3*(c^4*d^10*e - 4*b*c^3*d^9*e^2 - 4*a^3*b*d^3*e^8 + a^4*d^2*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^7)*x)]","B",0
2473,1,1605,0,3.120511," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, {\left(B a b^{2} c^{2} - 4 \, B a^{2} c^{3}\right)} d^{2} e - 4 \, {\left(3 \, B a b^{3} c + 8 \, A a^{2} c^{3} - 2 \, {\left(6 \, B a^{2} b + A a b^{2}\right)} c^{2}\right)} d e^{2} + {\left(5 \, B a b^{4} + 16 \, {\left(B a^{3} + A a^{2} b\right)} c^{2} - 4 \, {\left(6 \, B a^{2} b^{2} + A a b^{3}\right)} c\right)} e^{3} + {\left(8 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{2} e - 4 \, {\left(3 \, B b^{3} c^{2} + 8 \, A a c^{4} - 2 \, {\left(6 \, B a b + A b^{2}\right)} c^{3}\right)} d e^{2} + {\left(5 \, B b^{4} c + 16 \, {\left(B a^{2} + A a b\right)} c^{3} - 4 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, {\left(B b^{3} c^{2} - 4 \, B a b c^{3}\right)} d^{2} e - 4 \, {\left(3 \, B b^{4} c + 8 \, A a b c^{3} - 2 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d e^{2} + {\left(5 \, B b^{5} + 16 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 4 \, {\left(6 \, B a b^{3} + A b^{4}\right)} c\right)} e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(8 \, {\left(2 \, B a - A b\right)} c^{4} d^{3} + 2 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} e^{3} x^{3} - 24 \, {\left(B a b c^{3} - 2 \, A a c^{4}\right)} d^{2} e + 12 \, {\left(3 \, B a b^{2} c^{2} - 2 \, {\left(4 \, B a^{2} + A a b\right)} c^{3}\right)} d e^{2} - {\left(15 \, B a b^{3} c + 32 \, A a^{2} c^{3} - 4 \, {\left(13 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2}\right)} e^{3} + {\left(12 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d e^{2} - {\left(5 \, B b^{3} c^{2} + 16 \, A a c^{4} - 4 \, {\left(5 \, B a b + A b^{2}\right)} c^{3}\right)} e^{3}\right)} x^{2} + {\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} - 24 \, {\left(B b^{2} c^{3} - {\left(2 \, B a + A b\right)} c^{4}\right)} d^{2} e + 12 \, {\left(3 \, B b^{3} c^{2} + 4 \, A a c^{4} - 2 \, {\left(5 \, B a b + A b^{2}\right)} c^{3}\right)} d e^{2} - {\left(15 \, B b^{4} c + 8 \, {\left(3 \, B a^{2} + 5 \, A a b\right)} c^{3} - 2 \, {\left(31 \, B a b^{2} + 6 \, A b^{3}\right)} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}, -\frac{3 \, {\left(8 \, {\left(B a b^{2} c^{2} - 4 \, B a^{2} c^{3}\right)} d^{2} e - 4 \, {\left(3 \, B a b^{3} c + 8 \, A a^{2} c^{3} - 2 \, {\left(6 \, B a^{2} b + A a b^{2}\right)} c^{2}\right)} d e^{2} + {\left(5 \, B a b^{4} + 16 \, {\left(B a^{3} + A a^{2} b\right)} c^{2} - 4 \, {\left(6 \, B a^{2} b^{2} + A a b^{3}\right)} c\right)} e^{3} + {\left(8 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{2} e - 4 \, {\left(3 \, B b^{3} c^{2} + 8 \, A a c^{4} - 2 \, {\left(6 \, B a b + A b^{2}\right)} c^{3}\right)} d e^{2} + {\left(5 \, B b^{4} c + 16 \, {\left(B a^{2} + A a b\right)} c^{3} - 4 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, {\left(B b^{3} c^{2} - 4 \, B a b c^{3}\right)} d^{2} e - 4 \, {\left(3 \, B b^{4} c + 8 \, A a b c^{3} - 2 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d e^{2} + {\left(5 \, B b^{5} + 16 \, {\left(B a^{2} b + A a b^{2}\right)} c^{2} - 4 \, {\left(6 \, B a b^{3} + A b^{4}\right)} c\right)} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(8 \, {\left(2 \, B a - A b\right)} c^{4} d^{3} + 2 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} e^{3} x^{3} - 24 \, {\left(B a b c^{3} - 2 \, A a c^{4}\right)} d^{2} e + 12 \, {\left(3 \, B a b^{2} c^{2} - 2 \, {\left(4 \, B a^{2} + A a b\right)} c^{3}\right)} d e^{2} - {\left(15 \, B a b^{3} c + 32 \, A a^{2} c^{3} - 4 \, {\left(13 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2}\right)} e^{3} + {\left(12 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d e^{2} - {\left(5 \, B b^{3} c^{2} + 16 \, A a c^{4} - 4 \, {\left(5 \, B a b + A b^{2}\right)} c^{3}\right)} e^{3}\right)} x^{2} + {\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} - 24 \, {\left(B b^{2} c^{3} - {\left(2 \, B a + A b\right)} c^{4}\right)} d^{2} e + 12 \, {\left(3 \, B b^{3} c^{2} + 4 \, A a c^{4} - 2 \, {\left(5 \, B a b + A b^{2}\right)} c^{3}\right)} d e^{2} - {\left(15 \, B b^{4} c + 8 \, {\left(3 \, B a^{2} + 5 \, A a b\right)} c^{3} - 2 \, {\left(31 \, B a b^{2} + 6 \, A b^{3}\right)} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}\right]"," ",0,"[-1/16*(3*(8*(B*a*b^2*c^2 - 4*B*a^2*c^3)*d^2*e - 4*(3*B*a*b^3*c + 8*A*a^2*c^3 - 2*(6*B*a^2*b + A*a*b^2)*c^2)*d*e^2 + (5*B*a*b^4 + 16*(B*a^3 + A*a^2*b)*c^2 - 4*(6*B*a^2*b^2 + A*a*b^3)*c)*e^3 + (8*(B*b^2*c^3 - 4*B*a*c^4)*d^2*e - 4*(3*B*b^3*c^2 + 8*A*a*c^4 - 2*(6*B*a*b + A*b^2)*c^3)*d*e^2 + (5*B*b^4*c + 16*(B*a^2 + A*a*b)*c^3 - 4*(6*B*a*b^2 + A*b^3)*c^2)*e^3)*x^2 + (8*(B*b^3*c^2 - 4*B*a*b*c^3)*d^2*e - 4*(3*B*b^4*c + 8*A*a*b*c^3 - 2*(6*B*a*b^2 + A*b^3)*c^2)*d*e^2 + (5*B*b^5 + 16*(B*a^2*b + A*a*b^2)*c^2 - 4*(6*B*a*b^3 + A*b^4)*c)*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(8*(2*B*a - A*b)*c^4*d^3 + 2*(B*b^2*c^3 - 4*B*a*c^4)*e^3*x^3 - 24*(B*a*b*c^3 - 2*A*a*c^4)*d^2*e + 12*(3*B*a*b^2*c^2 - 2*(4*B*a^2 + A*a*b)*c^3)*d*e^2 - (15*B*a*b^3*c + 32*A*a^2*c^3 - 4*(13*B*a^2*b + 3*A*a*b^2)*c^2)*e^3 + (12*(B*b^2*c^3 - 4*B*a*c^4)*d*e^2 - (5*B*b^3*c^2 + 16*A*a*c^4 - 4*(5*B*a*b + A*b^2)*c^3)*e^3)*x^2 + (8*(B*b*c^4 - 2*A*c^5)*d^3 - 24*(B*b^2*c^3 - (2*B*a + A*b)*c^4)*d^2*e + 12*(3*B*b^3*c^2 + 4*A*a*c^4 - 2*(5*B*a*b + A*b^2)*c^3)*d*e^2 - (15*B*b^4*c + 8*(3*B*a^2 + 5*A*a*b)*c^3 - 2*(31*B*a*b^2 + 6*A*b^3)*c^2)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x), -1/8*(3*(8*(B*a*b^2*c^2 - 4*B*a^2*c^3)*d^2*e - 4*(3*B*a*b^3*c + 8*A*a^2*c^3 - 2*(6*B*a^2*b + A*a*b^2)*c^2)*d*e^2 + (5*B*a*b^4 + 16*(B*a^3 + A*a^2*b)*c^2 - 4*(6*B*a^2*b^2 + A*a*b^3)*c)*e^3 + (8*(B*b^2*c^3 - 4*B*a*c^4)*d^2*e - 4*(3*B*b^3*c^2 + 8*A*a*c^4 - 2*(6*B*a*b + A*b^2)*c^3)*d*e^2 + (5*B*b^4*c + 16*(B*a^2 + A*a*b)*c^3 - 4*(6*B*a*b^2 + A*b^3)*c^2)*e^3)*x^2 + (8*(B*b^3*c^2 - 4*B*a*b*c^3)*d^2*e - 4*(3*B*b^4*c + 8*A*a*b*c^3 - 2*(6*B*a*b^2 + A*b^3)*c^2)*d*e^2 + (5*B*b^5 + 16*(B*a^2*b + A*a*b^2)*c^2 - 4*(6*B*a*b^3 + A*b^4)*c)*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(8*(2*B*a - A*b)*c^4*d^3 + 2*(B*b^2*c^3 - 4*B*a*c^4)*e^3*x^3 - 24*(B*a*b*c^3 - 2*A*a*c^4)*d^2*e + 12*(3*B*a*b^2*c^2 - 2*(4*B*a^2 + A*a*b)*c^3)*d*e^2 - (15*B*a*b^3*c + 32*A*a^2*c^3 - 4*(13*B*a^2*b + 3*A*a*b^2)*c^2)*e^3 + (12*(B*b^2*c^3 - 4*B*a*c^4)*d*e^2 - (5*B*b^3*c^2 + 16*A*a*c^4 - 4*(5*B*a*b + A*b^2)*c^3)*e^3)*x^2 + (8*(B*b*c^4 - 2*A*c^5)*d^3 - 24*(B*b^2*c^3 - (2*B*a + A*b)*c^4)*d^2*e + 12*(3*B*b^3*c^2 + 4*A*a*c^4 - 2*(5*B*a*b + A*b^2)*c^3)*d*e^2 - (15*B*b^4*c + 8*(3*B*a^2 + 5*A*a*b)*c^3 - 2*(31*B*a*b^2 + 6*A*b^3)*c^2)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x)]","B",0
2474,1,945,0,2.511328," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, {\left(B a b^{2} c - 4 \, B a^{2} c^{2}\right)} d e - {\left(3 \, B a b^{3} + 8 \, A a^{2} c^{2} - 2 \, {\left(6 \, B a^{2} b + A a b^{2}\right)} c\right)} e^{2} + {\left(4 \, {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d e - {\left(3 \, B b^{3} c + 8 \, A a c^{3} - 2 \, {\left(6 \, B a b + A b^{2}\right)} c^{2}\right)} e^{2}\right)} x^{2} + {\left(4 \, {\left(B b^{3} c - 4 \, B a b c^{2}\right)} d e - {\left(3 \, B b^{4} + 8 \, A a b c^{2} - 2 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} e^{2}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, {\left(2 \, B a - A b\right)} c^{3} d^{2} + {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} e^{2} x^{2} - 4 \, {\left(B a b c^{2} - 2 \, A a c^{3}\right)} d e + {\left(3 \, B a b^{2} c - 2 \, {\left(4 \, B a^{2} + A a b\right)} c^{2}\right)} e^{2} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} - 4 \, {\left(B b^{2} c^{2} - {\left(2 \, B a + A b\right)} c^{3}\right)} d e + {\left(3 \, B b^{3} c + 4 \, A a c^{3} - 2 \, {\left(5 \, B a b + A b^{2}\right)} c^{2}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x\right)}}, -\frac{{\left(4 \, {\left(B a b^{2} c - 4 \, B a^{2} c^{2}\right)} d e - {\left(3 \, B a b^{3} + 8 \, A a^{2} c^{2} - 2 \, {\left(6 \, B a^{2} b + A a b^{2}\right)} c\right)} e^{2} + {\left(4 \, {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d e - {\left(3 \, B b^{3} c + 8 \, A a c^{3} - 2 \, {\left(6 \, B a b + A b^{2}\right)} c^{2}\right)} e^{2}\right)} x^{2} + {\left(4 \, {\left(B b^{3} c - 4 \, B a b c^{2}\right)} d e - {\left(3 \, B b^{4} + 8 \, A a b c^{2} - 2 \, {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} e^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2 \, {\left(2 \, B a - A b\right)} c^{3} d^{2} + {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} e^{2} x^{2} - 4 \, {\left(B a b c^{2} - 2 \, A a c^{3}\right)} d e + {\left(3 \, B a b^{2} c - 2 \, {\left(4 \, B a^{2} + A a b\right)} c^{2}\right)} e^{2} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{2} - 4 \, {\left(B b^{2} c^{2} - {\left(2 \, B a + A b\right)} c^{3}\right)} d e + {\left(3 \, B b^{3} c + 4 \, A a c^{3} - 2 \, {\left(5 \, B a b + A b^{2}\right)} c^{2}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x\right)}}\right]"," ",0,"[1/4*((4*(B*a*b^2*c - 4*B*a^2*c^2)*d*e - (3*B*a*b^3 + 8*A*a^2*c^2 - 2*(6*B*a^2*b + A*a*b^2)*c)*e^2 + (4*(B*b^2*c^2 - 4*B*a*c^3)*d*e - (3*B*b^3*c + 8*A*a*c^3 - 2*(6*B*a*b + A*b^2)*c^2)*e^2)*x^2 + (4*(B*b^3*c - 4*B*a*b*c^2)*d*e - (3*B*b^4 + 8*A*a*b*c^2 - 2*(6*B*a*b^2 + A*b^3)*c)*e^2)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(2*(2*B*a - A*b)*c^3*d^2 + (B*b^2*c^2 - 4*B*a*c^3)*e^2*x^2 - 4*(B*a*b*c^2 - 2*A*a*c^3)*d*e + (3*B*a*b^2*c - 2*(4*B*a^2 + A*a*b)*c^2)*e^2 + (2*(B*b*c^3 - 2*A*c^4)*d^2 - 4*(B*b^2*c^2 - (2*B*a + A*b)*c^3)*d*e + (3*B*b^3*c + 4*A*a*c^3 - 2*(5*B*a*b + A*b^2)*c^2)*e^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x), -1/2*((4*(B*a*b^2*c - 4*B*a^2*c^2)*d*e - (3*B*a*b^3 + 8*A*a^2*c^2 - 2*(6*B*a^2*b + A*a*b^2)*c)*e^2 + (4*(B*b^2*c^2 - 4*B*a*c^3)*d*e - (3*B*b^3*c + 8*A*a*c^3 - 2*(6*B*a*b + A*b^2)*c^2)*e^2)*x^2 + (4*(B*b^3*c - 4*B*a*b*c^2)*d*e - (3*B*b^4 + 8*A*a*b*c^2 - 2*(6*B*a*b^2 + A*b^3)*c)*e^2)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2*(2*B*a - A*b)*c^3*d^2 + (B*b^2*c^2 - 4*B*a*c^3)*e^2*x^2 - 4*(B*a*b*c^2 - 2*A*a*c^3)*d*e + (3*B*a*b^2*c - 2*(4*B*a^2 + A*a*b)*c^2)*e^2 + (2*(B*b*c^3 - 2*A*c^4)*d^2 - 4*(B*b^2*c^2 - (2*B*a + A*b)*c^3)*d*e + (3*B*b^3*c + 4*A*a*c^3 - 2*(5*B*a*b + A*b^2)*c^2)*e^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x)]","B",0
2475,1,489,0,1.649119," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} e x^{2} + {\left(B b^{3} - 4 \, B a b c\right)} e x + {\left(B a b^{2} - 4 \, B a^{2} c\right)} e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left({\left(2 \, B a - A b\right)} c^{2} d - {\left(B a b c - 2 \, A a c^{2}\right)} e + {\left({\left(B b c^{2} - 2 \, A c^{3}\right)} d - {\left(B b^{2} c - {\left(2 \, B a + A b\right)} c^{2}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}, -\frac{{\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} e x^{2} + {\left(B b^{3} - 4 \, B a b c\right)} e x + {\left(B a b^{2} - 4 \, B a^{2} c\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left({\left(2 \, B a - A b\right)} c^{2} d - {\left(B a b c - 2 \, A a c^{2}\right)} e + {\left({\left(B b c^{2} - 2 \, A c^{3}\right)} d - {\left(B b^{2} c - {\left(2 \, B a + A b\right)} c^{2}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x}\right]"," ",0,"[1/2*(((B*b^2*c - 4*B*a*c^2)*e*x^2 + (B*b^3 - 4*B*a*b*c)*e*x + (B*a*b^2 - 4*B*a^2*c)*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*((2*B*a - A*b)*c^2*d - (B*a*b*c - 2*A*a*c^2)*e + ((B*b*c^2 - 2*A*c^3)*d - (B*b^2*c - (2*B*a + A*b)*c^2)*e)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x), -(((B*b^2*c - 4*B*a*c^2)*e*x^2 + (B*b^3 - 4*B*a*b*c)*e*x + (B*a*b^2 - 4*B*a^2*c)*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*((2*B*a - A*b)*c^2*d - (B*a*b*c - 2*A*a*c^2)*e + ((B*b*c^2 - 2*A*c^3)*d - (B*b^2*c - (2*B*a + A*b)*c^2)*e)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)]","B",0
2476,1,74,0,0.474209," ","integrate((B*x+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x + a} {\left(2 \, B a - A b + {\left(B b - 2 \, A c\right)} x\right)}}{a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x}"," ",0,"2*sqrt(c*x^2 + b*x + a)*(2*B*a - A*b + (B*b - 2*A*c)*x)/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)","A",0
2477,1,1656,0,4.950052," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(B a b^{2} - 4 \, B a^{2} c\right)} d e - {\left(A a b^{2} - 4 \, A a^{2} c\right)} e^{2} + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d e - {\left(A b^{2} c - 4 \, A a c^{2}\right)} e^{2}\right)} x^{2} + {\left({\left(B b^{3} - 4 \, B a b c\right)} d e - {\left(A b^{3} - 4 \, A a b c\right)} e^{2}\right)} x\right)} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left({\left(2 \, B a - A b\right)} c^{2} d^{3} - {\left(2 \, A a c^{2} + {\left(3 \, B a b - 2 \, A b^{2}\right)} c\right)} d^{2} e + {\left(B a b^{2} - A b^{3} + {\left(2 \, B a^{2} + A a b\right)} c\right)} d e^{2} - {\left(B a^{2} b - A a b^{2} + 2 \, A a^{2} c\right)} e^{3} - {\left({\left(2 \, B a^{2} - A a b\right)} c e^{3} - {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} + {\left(B b^{2} c + {\left(2 \, B a - 3 \, A b\right)} c^{2}\right)} d^{2} e + {\left(2 \, A a c^{2} - {\left(3 \, B a b - A b^{2}\right)} c\right)} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)}}, -\frac{\sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(B a b^{2} - 4 \, B a^{2} c\right)} d e - {\left(A a b^{2} - 4 \, A a^{2} c\right)} e^{2} + {\left({\left(B b^{2} c - 4 \, B a c^{2}\right)} d e - {\left(A b^{2} c - 4 \, A a c^{2}\right)} e^{2}\right)} x^{2} + {\left({\left(B b^{3} - 4 \, B a b c\right)} d e - {\left(A b^{3} - 4 \, A a b c\right)} e^{2}\right)} x\right)} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left({\left(2 \, B a - A b\right)} c^{2} d^{3} - {\left(2 \, A a c^{2} + {\left(3 \, B a b - 2 \, A b^{2}\right)} c\right)} d^{2} e + {\left(B a b^{2} - A b^{3} + {\left(2 \, B a^{2} + A a b\right)} c\right)} d e^{2} - {\left(B a^{2} b - A a b^{2} + 2 \, A a^{2} c\right)} e^{3} - {\left({\left(2 \, B a^{2} - A a b\right)} c e^{3} - {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{3} + {\left(B b^{2} c + {\left(2 \, B a - 3 \, A b\right)} c^{2}\right)} d^{2} e + {\left(2 \, A a c^{2} - {\left(3 \, B a b - A b^{2}\right)} c\right)} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{{\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x}\right]"," ",0,"[-1/2*(sqrt(c*d^2 - b*d*e + a*e^2)*((B*a*b^2 - 4*B*a^2*c)*d*e - (A*a*b^2 - 4*A*a^2*c)*e^2 + ((B*b^2*c - 4*B*a*c^2)*d*e - (A*b^2*c - 4*A*a*c^2)*e^2)*x^2 + ((B*b^3 - 4*B*a*b*c)*d*e - (A*b^3 - 4*A*a*b*c)*e^2)*x)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*((2*B*a - A*b)*c^2*d^3 - (2*A*a*c^2 + (3*B*a*b - 2*A*b^2)*c)*d^2*e + (B*a*b^2 - A*b^3 + (2*B*a^2 + A*a*b)*c)*d*e^2 - (B*a^2*b - A*a*b^2 + 2*A*a^2*c)*e^3 - ((2*B*a^2 - A*a*b)*c*e^3 - (B*b*c^2 - 2*A*c^3)*d^3 + (B*b^2*c + (2*B*a - 3*A*b)*c^2)*d^2*e + (2*A*a*c^2 - (3*B*a*b - A*b^2)*c)*d*e^2)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x), -(sqrt(-c*d^2 + b*d*e - a*e^2)*((B*a*b^2 - 4*B*a^2*c)*d*e - (A*a*b^2 - 4*A*a^2*c)*e^2 + ((B*b^2*c - 4*B*a*c^2)*d*e - (A*b^2*c - 4*A*a*c^2)*e^2)*x^2 + ((B*b^3 - 4*B*a*b*c)*d*e - (A*b^3 - 4*A*a*b*c)*e^2)*x)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*((2*B*a - A*b)*c^2*d^3 - (2*A*a*c^2 + (3*B*a*b - 2*A*b^2)*c)*d^2*e + (B*a*b^2 - A*b^3 + (2*B*a^2 + A*a*b)*c)*d*e^2 - (B*a^2*b - A*a*b^2 + 2*A*a^2*c)*e^3 - ((2*B*a^2 - A*a*b)*c*e^3 - (B*b*c^2 - 2*A*c^3)*d^3 + (B*b^2*c + (2*B*a - 3*A*b)*c^2)*d^2*e + (2*A*a*c^2 - (3*B*a*b - A*b^2)*c)*d*e^2)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)]","B",0
2478,1,4122,0,19.051058," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, {\left(B a b^{2} c - 4 \, B a^{2} c^{2}\right)} d^{3} e - {\left(B a b^{3} - 24 \, A a^{2} c^{2} - 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} d^{2} e^{2} - {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 4 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} d e^{3} + {\left(4 \, {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d^{2} e^{2} - {\left(B b^{3} c - 24 \, A a c^{3} - 2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{2}\right)} d e^{3} + {\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2} - {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} e^{4}\right)} x^{3} + {\left(4 \, {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d^{3} e + 3 \, {\left(B b^{3} c + 8 \, A a c^{3} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{2}\right)} d^{2} e^{2} - {\left(B b^{4} - 4 \, {\left(2 \, B a^{2} + 3 \, A a b\right)} c^{2} - {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} d e^{3} - {\left(2 \, B a b^{3} - 3 \, A b^{4} - 4 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} e^{4}\right)} x^{2} + {\left(4 \, {\left(B b^{3} c - 4 \, B a b c^{2}\right)} d^{3} e - {\left(B b^{4} + 8 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2} - 2 \, {\left(4 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} d^{2} e^{2} - 3 \, {\left(B a b^{3} - A b^{4} - 8 \, A a^{2} c^{2} - 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} d e^{3} - {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 4 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(2 \, {\left(2 \, B a - A b\right)} c^{3} d^{5} - 2 \, {\left(4 \, A a c^{3} + {\left(4 \, B a b - 3 \, A b^{2}\right)} c^{2}\right)} d^{4} e - {\left(4 \, {\left(B a^{2} - 3 \, A a b\right)} c^{2} - {\left(7 \, B a b^{2} - 6 \, A b^{3}\right)} c\right)} d^{3} e^{2} - {\left(3 \, B a b^{3} - 2 \, A b^{4} + 4 \, A a^{2} c^{2} - {\left(4 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} d^{2} e^{3} + {\left(3 \, B a^{2} b^{2} - A a b^{3} - 2 \, {\left(4 \, B a^{3} - A a^{2} b\right)} c\right)} d e^{4} - {\left(A a^{2} b^{2} - 4 \, A a^{3} c\right)} e^{5} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} e - {\left(B b^{2} c^{2} + 4 \, {\left(3 \, B a - 2 \, A b\right)} c^{3}\right)} d^{3} e^{2} - {\left(B b^{3} c - 4 \, A a c^{3} - {\left(16 \, B a b - 7 \, A b^{2}\right)} c^{2}\right)} d^{2} e^{3} - {\left(4 \, {\left(3 \, B a^{2} + A a b\right)} c^{2} + {\left(B a b^{2} - 3 \, A b^{3}\right)} c\right)} d e^{4} + {\left(8 \, A a^{2} c^{2} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} e^{5}\right)} x^{2} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{5} - 2 \, {\left(B b^{2} c^{2} + {\left(2 \, B a - 3 \, A b\right)} c^{3}\right)} d^{4} e + {\left(B b^{3} c - 8 \, A a c^{3}\right)} d^{3} e^{2} - {\left(B b^{4} + 8 \, {\left(B a^{2} - 2 \, A a b\right)} c^{2} - {\left(8 \, B a b^{2} - 5 \, A b^{3}\right)} c\right)} d^{2} e^{3} - {\left(B a b^{3} - 3 \, A b^{4} + 4 \, A a^{2} c^{2} + 2 \, {\left(B a^{2} b + 4 \, A a b^{2}\right)} c\right)} d e^{4} + {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 2 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{7} - 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{6} e + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} e^{2} - {\left(a b^{5} + 2 \, a^{2} b^{3} c - 24 \, a^{3} b c^{2}\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{6} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} e^{2} + 3 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{3} - {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{5} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{6} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{7}\right)} x^{3} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} e + 3 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{5} e^{2} + {\left(2 \, b^{5} c - 11 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d^{4} e^{3} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{5} - 4 \, a^{2} b^{3} c\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{4} - 13 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{7}\right)} x^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} - {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} e + 3 \, {\left(b^{5} c - 4 \, a b^{3} c^{2}\right)} d^{5} e^{2} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} e^{3} + {\left(2 \, a b^{5} - 11 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{6} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{7}\right)} x\right)}}, -\frac{{\left(4 \, {\left(B a b^{2} c - 4 \, B a^{2} c^{2}\right)} d^{3} e - {\left(B a b^{3} - 24 \, A a^{2} c^{2} - 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} d^{2} e^{2} - {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 4 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} d e^{3} + {\left(4 \, {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d^{2} e^{2} - {\left(B b^{3} c - 24 \, A a c^{3} - 2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{2}\right)} d e^{3} + {\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2} - {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} e^{4}\right)} x^{3} + {\left(4 \, {\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} d^{3} e + 3 \, {\left(B b^{3} c + 8 \, A a c^{3} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{2}\right)} d^{2} e^{2} - {\left(B b^{4} - 4 \, {\left(2 \, B a^{2} + 3 \, A a b\right)} c^{2} - {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} d e^{3} - {\left(2 \, B a b^{3} - 3 \, A b^{4} - 4 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} e^{4}\right)} x^{2} + {\left(4 \, {\left(B b^{3} c - 4 \, B a b c^{2}\right)} d^{3} e - {\left(B b^{4} + 8 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2} - 2 \, {\left(4 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} d^{2} e^{2} - 3 \, {\left(B a b^{3} - A b^{4} - 8 \, A a^{2} c^{2} - 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} d e^{3} - {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 4 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, {\left(2 \, B a - A b\right)} c^{3} d^{5} - 2 \, {\left(4 \, A a c^{3} + {\left(4 \, B a b - 3 \, A b^{2}\right)} c^{2}\right)} d^{4} e - {\left(4 \, {\left(B a^{2} - 3 \, A a b\right)} c^{2} - {\left(7 \, B a b^{2} - 6 \, A b^{3}\right)} c\right)} d^{3} e^{2} - {\left(3 \, B a b^{3} - 2 \, A b^{4} + 4 \, A a^{2} c^{2} - {\left(4 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} d^{2} e^{3} + {\left(3 \, B a^{2} b^{2} - A a b^{3} - 2 \, {\left(4 \, B a^{3} - A a^{2} b\right)} c\right)} d e^{4} - {\left(A a^{2} b^{2} - 4 \, A a^{3} c\right)} e^{5} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{4} e - {\left(B b^{2} c^{2} + 4 \, {\left(3 \, B a - 2 \, A b\right)} c^{3}\right)} d^{3} e^{2} - {\left(B b^{3} c - 4 \, A a c^{3} - {\left(16 \, B a b - 7 \, A b^{2}\right)} c^{2}\right)} d^{2} e^{3} - {\left(4 \, {\left(3 \, B a^{2} + A a b\right)} c^{2} + {\left(B a b^{2} - 3 \, A b^{3}\right)} c\right)} d e^{4} + {\left(8 \, A a^{2} c^{2} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} e^{5}\right)} x^{2} + {\left(2 \, {\left(B b c^{3} - 2 \, A c^{4}\right)} d^{5} - 2 \, {\left(B b^{2} c^{2} + {\left(2 \, B a - 3 \, A b\right)} c^{3}\right)} d^{4} e + {\left(B b^{3} c - 8 \, A a c^{3}\right)} d^{3} e^{2} - {\left(B b^{4} + 8 \, {\left(B a^{2} - 2 \, A a b\right)} c^{2} - {\left(8 \, B a b^{2} - 5 \, A b^{3}\right)} c\right)} d^{2} e^{3} - {\left(B a b^{3} - 3 \, A b^{4} + 4 \, A a^{2} c^{2} + 2 \, {\left(B a^{2} b + 4 \, A a b^{2}\right)} c\right)} d e^{4} + {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3} - 2 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{7} - 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{6} e + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} e^{2} - {\left(a b^{5} + 2 \, a^{2} b^{3} c - 24 \, a^{3} b c^{2}\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{6} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} e^{2} + 3 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{3} - {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{5} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{6} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{7}\right)} x^{3} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} e + 3 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{5} e^{2} + {\left(2 \, b^{5} c - 11 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d^{4} e^{3} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{5} - 4 \, a^{2} b^{3} c\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{4} - 13 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{7}\right)} x^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} - {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} e + 3 \, {\left(b^{5} c - 4 \, a b^{3} c^{2}\right)} d^{5} e^{2} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} e^{3} + {\left(2 \, a b^{5} - 11 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{6} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{7}\right)} x\right)}}\right]"," ",0,"[1/4*((4*(B*a*b^2*c - 4*B*a^2*c^2)*d^3*e - (B*a*b^3 - 24*A*a^2*c^2 - 2*(2*B*a^2*b - 3*A*a*b^2)*c)*d^2*e^2 - (2*B*a^2*b^2 - 3*A*a*b^3 - 4*(2*B*a^3 - 3*A*a^2*b)*c)*d*e^3 + (4*(B*b^2*c^2 - 4*B*a*c^3)*d^2*e^2 - (B*b^3*c - 24*A*a*c^3 - 2*(2*B*a*b - 3*A*b^2)*c^2)*d*e^3 + (4*(2*B*a^2 - 3*A*a*b)*c^2 - (2*B*a*b^2 - 3*A*b^3)*c)*e^4)*x^3 + (4*(B*b^2*c^2 - 4*B*a*c^3)*d^3*e + 3*(B*b^3*c + 8*A*a*c^3 - 2*(2*B*a*b + A*b^2)*c^2)*d^2*e^2 - (B*b^4 - 4*(2*B*a^2 + 3*A*a*b)*c^2 - (2*B*a*b^2 - 3*A*b^3)*c)*d*e^3 - (2*B*a*b^3 - 3*A*b^4 - 4*(2*B*a^2*b - 3*A*a*b^2)*c)*e^4)*x^2 + (4*(B*b^3*c - 4*B*a*b*c^2)*d^3*e - (B*b^4 + 8*(2*B*a^2 - 3*A*a*b)*c^2 - 2*(4*B*a*b^2 - 3*A*b^3)*c)*d^2*e^2 - 3*(B*a*b^3 - A*b^4 - 8*A*a^2*c^2 - 2*(2*B*a^2*b - 3*A*a*b^2)*c)*d*e^3 - (2*B*a^2*b^2 - 3*A*a*b^3 - 4*(2*B*a^3 - 3*A*a^2*b)*c)*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(2*(2*B*a - A*b)*c^3*d^5 - 2*(4*A*a*c^3 + (4*B*a*b - 3*A*b^2)*c^2)*d^4*e - (4*(B*a^2 - 3*A*a*b)*c^2 - (7*B*a*b^2 - 6*A*b^3)*c)*d^3*e^2 - (3*B*a*b^3 - 2*A*b^4 + 4*A*a^2*c^2 - (4*B*a^2*b - 3*A*a*b^2)*c)*d^2*e^3 + (3*B*a^2*b^2 - A*a*b^3 - 2*(4*B*a^3 - A*a^2*b)*c)*d*e^4 - (A*a^2*b^2 - 4*A*a^3*c)*e^5 + (2*(B*b*c^3 - 2*A*c^4)*d^4*e - (B*b^2*c^2 + 4*(3*B*a - 2*A*b)*c^3)*d^3*e^2 - (B*b^3*c - 4*A*a*c^3 - (16*B*a*b - 7*A*b^2)*c^2)*d^2*e^3 - (4*(3*B*a^2 + A*a*b)*c^2 + (B*a*b^2 - 3*A*b^3)*c)*d*e^4 + (8*A*a^2*c^2 + (2*B*a^2*b - 3*A*a*b^2)*c)*e^5)*x^2 + (2*(B*b*c^3 - 2*A*c^4)*d^5 - 2*(B*b^2*c^2 + (2*B*a - 3*A*b)*c^3)*d^4*e + (B*b^3*c - 8*A*a*c^3)*d^3*e^2 - (B*b^4 + 8*(B*a^2 - 2*A*a*b)*c^2 - (8*B*a*b^2 - 5*A*b^3)*c)*d^2*e^3 - (B*a*b^3 - 3*A*b^4 + 4*A*a^2*c^2 + 2*(B*a^2*b + 4*A*a*b^2)*c)*d*e^4 + (2*B*a^2*b^2 - 3*A*a*b^3 - 2*(2*B*a^3 - 5*A*a^2*b)*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^3 - 4*a^2*c^4)*d^7 - 3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^6*e + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^5*e^2 - (a*b^5 + 2*a^2*b^3*c - 24*a^3*b*c^2)*d^4*e^3 + 3*(a^2*b^4 - 3*a^3*b^2*c - 4*a^4*c^2)*d^3*e^4 - 3*(a^3*b^3 - 4*a^4*b*c)*d^2*e^5 + (a^4*b^2 - 4*a^5*c)*d*e^6 + ((b^2*c^4 - 4*a*c^5)*d^6*e - 3*(b^3*c^3 - 4*a*b*c^4)*d^5*e^2 + 3*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e^3 - (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^4 + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^5 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^6 + (a^3*b^2*c - 4*a^4*c^2)*e^7)*x^3 + ((b^2*c^4 - 4*a*c^5)*d^7 - 2*(b^3*c^3 - 4*a*b*c^4)*d^6*e + 3*(a*b^2*c^3 - 4*a^2*c^4)*d^5*e^2 + (2*b^5*c - 11*a*b^3*c^2 + 12*a^2*b*c^3)*d^4*e^3 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^3*e^4 + 3*(a*b^5 - 4*a^2*b^3*c)*d^2*e^5 - (3*a^2*b^4 - 13*a^3*b^2*c + 4*a^4*c^2)*d*e^6 + (a^3*b^3 - 4*a^4*b*c)*e^7)*x^2 + ((b^3*c^3 - 4*a*b*c^4)*d^7 - (3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^6*e + 3*(b^5*c - 4*a*b^3*c^2)*d^5*e^2 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^4*e^3 + (2*a*b^5 - 11*a^2*b^3*c + 12*a^3*b*c^2)*d^3*e^4 + 3*(a^3*b^2*c - 4*a^4*c^2)*d^2*e^5 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^6 + (a^4*b^2 - 4*a^5*c)*e^7)*x), -1/2*((4*(B*a*b^2*c - 4*B*a^2*c^2)*d^3*e - (B*a*b^3 - 24*A*a^2*c^2 - 2*(2*B*a^2*b - 3*A*a*b^2)*c)*d^2*e^2 - (2*B*a^2*b^2 - 3*A*a*b^3 - 4*(2*B*a^3 - 3*A*a^2*b)*c)*d*e^3 + (4*(B*b^2*c^2 - 4*B*a*c^3)*d^2*e^2 - (B*b^3*c - 24*A*a*c^3 - 2*(2*B*a*b - 3*A*b^2)*c^2)*d*e^3 + (4*(2*B*a^2 - 3*A*a*b)*c^2 - (2*B*a*b^2 - 3*A*b^3)*c)*e^4)*x^3 + (4*(B*b^2*c^2 - 4*B*a*c^3)*d^3*e + 3*(B*b^3*c + 8*A*a*c^3 - 2*(2*B*a*b + A*b^2)*c^2)*d^2*e^2 - (B*b^4 - 4*(2*B*a^2 + 3*A*a*b)*c^2 - (2*B*a*b^2 - 3*A*b^3)*c)*d*e^3 - (2*B*a*b^3 - 3*A*b^4 - 4*(2*B*a^2*b - 3*A*a*b^2)*c)*e^4)*x^2 + (4*(B*b^3*c - 4*B*a*b*c^2)*d^3*e - (B*b^4 + 8*(2*B*a^2 - 3*A*a*b)*c^2 - 2*(4*B*a*b^2 - 3*A*b^3)*c)*d^2*e^2 - 3*(B*a*b^3 - A*b^4 - 8*A*a^2*c^2 - 2*(2*B*a^2*b - 3*A*a*b^2)*c)*d*e^3 - (2*B*a^2*b^2 - 3*A*a*b^3 - 4*(2*B*a^3 - 3*A*a^2*b)*c)*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(2*(2*B*a - A*b)*c^3*d^5 - 2*(4*A*a*c^3 + (4*B*a*b - 3*A*b^2)*c^2)*d^4*e - (4*(B*a^2 - 3*A*a*b)*c^2 - (7*B*a*b^2 - 6*A*b^3)*c)*d^3*e^2 - (3*B*a*b^3 - 2*A*b^4 + 4*A*a^2*c^2 - (4*B*a^2*b - 3*A*a*b^2)*c)*d^2*e^3 + (3*B*a^2*b^2 - A*a*b^3 - 2*(4*B*a^3 - A*a^2*b)*c)*d*e^4 - (A*a^2*b^2 - 4*A*a^3*c)*e^5 + (2*(B*b*c^3 - 2*A*c^4)*d^4*e - (B*b^2*c^2 + 4*(3*B*a - 2*A*b)*c^3)*d^3*e^2 - (B*b^3*c - 4*A*a*c^3 - (16*B*a*b - 7*A*b^2)*c^2)*d^2*e^3 - (4*(3*B*a^2 + A*a*b)*c^2 + (B*a*b^2 - 3*A*b^3)*c)*d*e^4 + (8*A*a^2*c^2 + (2*B*a^2*b - 3*A*a*b^2)*c)*e^5)*x^2 + (2*(B*b*c^3 - 2*A*c^4)*d^5 - 2*(B*b^2*c^2 + (2*B*a - 3*A*b)*c^3)*d^4*e + (B*b^3*c - 8*A*a*c^3)*d^3*e^2 - (B*b^4 + 8*(B*a^2 - 2*A*a*b)*c^2 - (8*B*a*b^2 - 5*A*b^3)*c)*d^2*e^3 - (B*a*b^3 - 3*A*b^4 + 4*A*a^2*c^2 + 2*(B*a^2*b + 4*A*a*b^2)*c)*d*e^4 + (2*B*a^2*b^2 - 3*A*a*b^3 - 2*(2*B*a^3 - 5*A*a^2*b)*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^3 - 4*a^2*c^4)*d^7 - 3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^6*e + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^5*e^2 - (a*b^5 + 2*a^2*b^3*c - 24*a^3*b*c^2)*d^4*e^3 + 3*(a^2*b^4 - 3*a^3*b^2*c - 4*a^4*c^2)*d^3*e^4 - 3*(a^3*b^3 - 4*a^4*b*c)*d^2*e^5 + (a^4*b^2 - 4*a^5*c)*d*e^6 + ((b^2*c^4 - 4*a*c^5)*d^6*e - 3*(b^3*c^3 - 4*a*b*c^4)*d^5*e^2 + 3*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e^3 - (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^4 + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^5 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^6 + (a^3*b^2*c - 4*a^4*c^2)*e^7)*x^3 + ((b^2*c^4 - 4*a*c^5)*d^7 - 2*(b^3*c^3 - 4*a*b*c^4)*d^6*e + 3*(a*b^2*c^3 - 4*a^2*c^4)*d^5*e^2 + (2*b^5*c - 11*a*b^3*c^2 + 12*a^2*b*c^3)*d^4*e^3 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^3*e^4 + 3*(a*b^5 - 4*a^2*b^3*c)*d^2*e^5 - (3*a^2*b^4 - 13*a^3*b^2*c + 4*a^4*c^2)*d*e^6 + (a^3*b^3 - 4*a^4*b*c)*e^7)*x^2 + ((b^3*c^3 - 4*a*b*c^4)*d^7 - (3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^6*e + 3*(b^5*c - 4*a*b^3*c^2)*d^5*e^2 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^4*e^3 + (2*a*b^5 - 11*a^2*b^3*c + 12*a^3*b*c^2)*d^3*e^4 + 3*(a^3*b^2*c - 4*a^4*c^2)*d^2*e^5 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^6 + (a^4*b^2 - 4*a^5*c)*e^7)*x)]","B",0
2479,1,8054,0,88.929695," ","integrate((B*x+A)/(e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, {\left(B a b^{2} c^{2} - 4 \, B a^{2} c^{3}\right)} d^{5} e - 4 \, {\left(B a b^{3} c - 16 \, A a^{2} c^{3} - 4 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2}\right)} d^{4} e^{2} + {\left(B a b^{4} + 16 \, {\left(3 \, B a^{3} - 4 \, A a^{2} b\right)} c^{2} - 16 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} c\right)} d^{3} e^{3} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4} - 16 \, A a^{3} c^{2} - 8 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} d^{2} e^{4} + {\left(8 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{3} e^{3} - 4 \, {\left(B b^{3} c^{2} - 16 \, A a c^{4} - 4 \, {\left(B a b - A b^{2}\right)} c^{3}\right)} d^{2} e^{4} + {\left(B b^{4} c + 16 \, {\left(3 \, B a^{2} - 4 \, A a b\right)} c^{3} - 16 \, {\left(B a b^{2} - A b^{3}\right)} c^{2}\right)} d e^{5} - {\left(16 \, A a^{2} c^{3} + 8 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c^{2} - {\left(4 \, B a b^{3} - 5 \, A b^{4}\right)} c\right)} e^{6}\right)} x^{4} + {\left(16 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{4} e^{2} - 32 \, {\left(A b^{2} c^{3} - 4 \, A a c^{4}\right)} d^{3} e^{3} - 2 \, {\left(B b^{4} c - 16 \, {\left(3 \, B a^{2} - 2 \, A a b\right)} c^{3} + 8 \, {\left(B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{2} e^{4} + {\left(B b^{5} - 32 \, A a^{2} c^{3} + 16 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} - 2 \, {\left(4 \, B a b^{3} - 3 \, A b^{4}\right)} c\right)} d e^{5} + {\left(4 \, B a b^{4} - 5 \, A b^{5} - 16 \, A a^{2} b c^{2} - 8 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} c\right)} e^{6}\right)} x^{3} + {\left(8 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{5} e + 4 \, {\left(3 \, B b^{3} c^{2} + 16 \, A a c^{4} - 4 \, {\left(3 \, B a b + A b^{2}\right)} c^{3}\right)} d^{4} e^{2} - {\left(7 \, B b^{4} c - 16 \, {\left(B a^{2} + 4 \, A a b\right)} c^{3} - 8 \, {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} c^{2}\right)} d^{3} e^{3} + {\left(2 \, B b^{5} + 48 \, A a^{2} c^{3} + 24 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} c^{2} - {\left(32 \, B a b^{3} - 27 \, A b^{4}\right)} c\right)} d^{2} e^{4} + {\left(9 \, B a b^{4} - 10 \, A b^{5} + 48 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} c^{2} - 16 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} c\right)} d e^{5} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4} - 16 \, A a^{3} c^{2} - 8 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} e^{6}\right)} x^{2} + {\left(8 \, {\left(B b^{3} c^{2} - 4 \, B a b c^{3}\right)} d^{5} e - 4 \, {\left(B b^{4} c + 16 \, {\left(B a^{2} - A a b\right)} c^{3} - 4 \, {\left(2 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{4} e^{2} + {\left(B b^{5} + 128 \, A a^{2} c^{3} + 16 \, {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} c^{2} - 8 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} c\right)} d^{3} e^{3} + {\left(6 \, B a b^{4} - 5 \, A b^{5} + 48 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{2} - 8 \, {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} c\right)} d^{2} e^{4} + 2 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4} - 16 \, A a^{3} c^{2} - 8 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} d e^{5}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(8 \, {\left(2 \, B a - A b\right)} c^{4} d^{7} - 8 \, {\left(6 \, A a c^{4} + {\left(5 \, B a b - 4 \, A b^{2}\right)} c^{3}\right)} d^{6} e - 4 \, {\left(4 \, {\left(5 \, B a^{2} - 7 \, A a b\right)} c^{3} - 3 \, {\left(5 \, B a b^{2} - 4 \, A b^{3}\right)} c^{2}\right)} d^{5} e^{2} + {\left(32 \, A a^{2} c^{3} + 4 \, {\left(29 \, B a^{2} b - 24 \, A a b^{2}\right)} c^{2} - {\left(49 \, B a b^{3} - 32 \, A b^{4}\right)} c\right)} d^{4} e^{3} + {\left(13 \, B a b^{4} - 8 \, A b^{5} - 44 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} - {\left(10 \, B a^{2} b^{2} - 33 \, A a b^{3}\right)} c\right)} d^{3} e^{4} - {\left(11 \, B a^{2} b^{3} + A a b^{4} - 88 \, A a^{3} c^{2} - 2 \, {\left(18 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} c\right)} d^{2} e^{5} - {\left(2 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3} - 4 \, {\left(2 \, B a^{4} - 11 \, A a^{3} b\right)} c\right)} d e^{6} - 2 \, {\left(A a^{3} b^{2} - 4 \, A a^{4} c\right)} e^{7} + {\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e^{2} + 2 \, {\left(B b^{2} c^{3} - 4 \, {\left(11 \, B a - 5 \, A b\right)} c^{4}\right)} d^{4} e^{3} - {\left(13 \, B b^{3} c^{2} - 88 \, A a c^{4} - 2 \, {\left(66 \, B a b - 31 \, A b^{2}\right)} c^{3}\right)} d^{3} e^{4} + {\left(3 \, B b^{4} c - 4 \, {\left(14 \, B a^{2} + 33 \, A a b\right)} c^{3} - {\left(38 \, B a b^{2} - 53 \, A b^{3}\right)} c^{2}\right)} d^{2} e^{5} + {\left(104 \, A a^{2} c^{3} + 2 \, {\left(2 \, B a^{2} b + 7 \, A a b^{2}\right)} c^{2} + 3 \, {\left(3 \, B a b^{3} - 5 \, A b^{4}\right)} c\right)} d e^{6} + {\left(4 \, {\left(8 \, B a^{3} - 13 \, A a^{2} b\right)} c^{2} - 3 \, {\left(4 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} e^{7}\right)} x^{3} + {\left(16 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} e - 4 \, {\left(B b^{2} c^{3} + 2 \, {\left(16 \, B a - 9 \, A b\right)} c^{4}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c^{2} - 80 \, A a c^{4} - 4 \, {\left(37 \, B a b - 20 \, A b^{2}\right)} c^{3}\right)} d^{4} e^{3} - {\left(8 \, B b^{4} c + 4 \, {\left(34 \, B a^{2} + 7 \, A a b\right)} c^{3} - {\left(26 \, B a b^{2} + 27 \, A b^{3}\right)} c^{2}\right)} d^{3} e^{4} + {\left(3 \, B b^{5} + 136 \, A a^{2} c^{3} + 2 \, {\left(26 \, B a^{2} b - 73 \, A a b^{2}\right)} c^{2} - {\left(25 \, B a b^{3} - 28 \, A b^{4}\right)} c\right)} d^{2} e^{5} + {\left(9 \, B a b^{4} - 15 \, A b^{5} - 4 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} - {\left(22 \, B a^{2} b^{2} - 49 \, A a b^{3}\right)} c\right)} d e^{6} - {\left(12 \, B a^{2} b^{3} - 15 \, A a b^{4} - 24 \, A a^{3} c^{2} - 2 \, {\left(20 \, B a^{3} b - 31 \, A a^{2} b^{2}\right)} c\right)} e^{7}\right)} x^{2} + {\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{7} - 8 \, {\left(B b^{2} c^{3} + {\left(2 \, B a - 3 \, A b\right)} c^{4}\right)} d^{6} e + 4 \, {\left(3 \, B b^{3} c^{2} - 16 \, A a c^{4} - 4 \, {\left(3 \, B a b - A b^{2}\right)} c^{3}\right)} d^{5} e^{2} - {\left(17 \, B b^{4} c + 8 \, {\left(17 \, B a^{2} - 30 \, A a b\right)} c^{3} - 2 \, {\left(71 \, B a b^{2} - 40 \, A b^{3}\right)} c^{2}\right)} d^{4} e^{3} + {\left(5 \, B b^{5} + 40 \, A a^{2} c^{3} + 2 \, {\left(58 \, B a^{2} b - 137 \, A a b^{2}\right)} c^{2} - {\left(79 \, B a b^{3} - 81 \, A b^{4}\right)} c\right)} d^{3} e^{4} + {\left(16 \, B a b^{4} - 25 \, A b^{5} - 4 \, {\left(26 \, B a^{3} - 19 \, A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - 63 \, A a b^{3}\right)} c\right)} d^{2} e^{5} - {\left(17 \, B a^{2} b^{3} - 20 \, A a b^{4} - 88 \, A a^{3} c^{2} - 2 \, {\left(26 \, B a^{3} b - 47 \, A a^{2} b^{2}\right)} c\right)} d e^{6} - {\left(4 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3} - 4 \, {\left(4 \, B a^{4} - 5 \, A a^{3} b\right)} c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left({\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{10} - 4 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{9} e + 2 \, {\left(3 \, a b^{4} c^{2} - 10 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{8} e^{2} - 4 \, {\left(a b^{5} c - a^{2} b^{3} c^{2} - 12 \, a^{3} b c^{3}\right)} d^{7} e^{3} + {\left(a b^{6} + 8 \, a^{2} b^{4} c - 42 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} d^{6} e^{4} - 4 \, {\left(a^{2} b^{5} - a^{3} b^{3} c - 12 \, a^{4} b c^{2}\right)} d^{5} e^{5} + 2 \, {\left(3 \, a^{3} b^{4} - 10 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} d^{4} e^{6} - 4 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{3} e^{7} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d^{2} e^{8} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} e^{2} - 4 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e^{3} + 2 \, {\left(3 \, b^{4} c^{3} - 10 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{6} e^{4} - 4 \, {\left(b^{5} c^{2} - a b^{3} c^{3} - 12 \, a^{2} b c^{4}\right)} d^{5} e^{5} + {\left(b^{6} c + 8 \, a b^{4} c^{2} - 42 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{4} e^{6} - 4 \, {\left(a b^{5} c - a^{2} b^{3} c^{2} - 12 \, a^{3} b c^{3}\right)} d^{3} e^{7} + 2 \, {\left(3 \, a^{2} b^{4} c - 10 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{2} e^{8} - 4 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d e^{9} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} e^{10}\right)} x^{4} + {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{9} e - 7 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{8} e^{2} + 8 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{7} e^{3} - 2 \, {\left(b^{5} c^{2} + 6 \, a b^{3} c^{3} - 40 \, a^{2} b c^{4}\right)} d^{6} e^{4} - 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 18 \, a^{2} b^{2} c^{3} + 24 \, a^{3} c^{4}\right)} d^{5} e^{5} + {\left(b^{7} - 34 \, a^{2} b^{3} c^{2} + 72 \, a^{3} b c^{3}\right)} d^{4} e^{6} - 4 \, {\left(a b^{6} - 4 \, a^{2} b^{4} c - 2 \, a^{3} b^{2} c^{2} + 8 \, a^{4} c^{3}\right)} d^{3} e^{7} + 2 \, {\left(3 \, a^{2} b^{5} - 14 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} d^{2} e^{8} - 2 \, {\left(2 \, a^{3} b^{4} - 9 \, a^{4} b^{2} c + 4 \, a^{5} c^{2}\right)} d e^{9} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{10}\right)} x^{3} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{10} - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{9} e - {\left(2 \, b^{4} c^{3} - 13 \, a b^{2} c^{4} + 20 \, a^{2} c^{5}\right)} d^{8} e^{2} + 8 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{7} e^{3} - {\left(7 \, b^{6} c - 22 \, a b^{4} c^{2} - 34 \, a^{2} b^{2} c^{3} + 40 \, a^{3} c^{4}\right)} d^{6} e^{4} + 2 \, {\left(b^{7} + 4 \, a b^{5} c - 38 \, a^{2} b^{3} c^{2} + 24 \, a^{3} b c^{3}\right)} d^{5} e^{5} - {\left(7 \, a b^{6} - 22 \, a^{2} b^{4} c - 34 \, a^{3} b^{2} c^{2} + 40 \, a^{4} c^{3}\right)} d^{4} e^{6} + 8 \, {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 4 \, a^{4} b c^{2}\right)} d^{3} e^{7} - {\left(2 \, a^{3} b^{4} - 13 \, a^{4} b^{2} c + 20 \, a^{5} c^{2}\right)} d^{2} e^{8} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{10}\right)} x^{2} + {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{10} - 2 \, {\left(2 \, b^{4} c^{3} - 9 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{9} e + 2 \, {\left(3 \, b^{5} c^{2} - 14 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{8} e^{2} - 4 \, {\left(b^{6} c - 4 \, a b^{4} c^{2} - 2 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{7} e^{3} + {\left(b^{7} - 34 \, a^{2} b^{3} c^{2} + 72 \, a^{3} b c^{3}\right)} d^{6} e^{4} - 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} + 24 \, a^{4} c^{3}\right)} d^{5} e^{5} - 2 \, {\left(a^{2} b^{5} + 6 \, a^{3} b^{3} c - 40 \, a^{4} b c^{2}\right)} d^{4} e^{6} + 8 \, {\left(a^{3} b^{4} - 3 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d^{3} e^{7} - 7 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{2} e^{8} + 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d e^{9}\right)} x\right)}}, -\frac{3 \, {\left(8 \, {\left(B a b^{2} c^{2} - 4 \, B a^{2} c^{3}\right)} d^{5} e - 4 \, {\left(B a b^{3} c - 16 \, A a^{2} c^{3} - 4 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2}\right)} d^{4} e^{2} + {\left(B a b^{4} + 16 \, {\left(3 \, B a^{3} - 4 \, A a^{2} b\right)} c^{2} - 16 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} c\right)} d^{3} e^{3} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4} - 16 \, A a^{3} c^{2} - 8 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} d^{2} e^{4} + {\left(8 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{3} e^{3} - 4 \, {\left(B b^{3} c^{2} - 16 \, A a c^{4} - 4 \, {\left(B a b - A b^{2}\right)} c^{3}\right)} d^{2} e^{4} + {\left(B b^{4} c + 16 \, {\left(3 \, B a^{2} - 4 \, A a b\right)} c^{3} - 16 \, {\left(B a b^{2} - A b^{3}\right)} c^{2}\right)} d e^{5} - {\left(16 \, A a^{2} c^{3} + 8 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c^{2} - {\left(4 \, B a b^{3} - 5 \, A b^{4}\right)} c\right)} e^{6}\right)} x^{4} + {\left(16 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{4} e^{2} - 32 \, {\left(A b^{2} c^{3} - 4 \, A a c^{4}\right)} d^{3} e^{3} - 2 \, {\left(B b^{4} c - 16 \, {\left(3 \, B a^{2} - 2 \, A a b\right)} c^{3} + 8 \, {\left(B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{2} e^{4} + {\left(B b^{5} - 32 \, A a^{2} c^{3} + 16 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} - 2 \, {\left(4 \, B a b^{3} - 3 \, A b^{4}\right)} c\right)} d e^{5} + {\left(4 \, B a b^{4} - 5 \, A b^{5} - 16 \, A a^{2} b c^{2} - 8 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} c\right)} e^{6}\right)} x^{3} + {\left(8 \, {\left(B b^{2} c^{3} - 4 \, B a c^{4}\right)} d^{5} e + 4 \, {\left(3 \, B b^{3} c^{2} + 16 \, A a c^{4} - 4 \, {\left(3 \, B a b + A b^{2}\right)} c^{3}\right)} d^{4} e^{2} - {\left(7 \, B b^{4} c - 16 \, {\left(B a^{2} + 4 \, A a b\right)} c^{3} - 8 \, {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} c^{2}\right)} d^{3} e^{3} + {\left(2 \, B b^{5} + 48 \, A a^{2} c^{3} + 24 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} c^{2} - {\left(32 \, B a b^{3} - 27 \, A b^{4}\right)} c\right)} d^{2} e^{4} + {\left(9 \, B a b^{4} - 10 \, A b^{5} + 48 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} c^{2} - 16 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} c\right)} d e^{5} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4} - 16 \, A a^{3} c^{2} - 8 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} e^{6}\right)} x^{2} + {\left(8 \, {\left(B b^{3} c^{2} - 4 \, B a b c^{3}\right)} d^{5} e - 4 \, {\left(B b^{4} c + 16 \, {\left(B a^{2} - A a b\right)} c^{3} - 4 \, {\left(2 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{4} e^{2} + {\left(B b^{5} + 128 \, A a^{2} c^{3} + 16 \, {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} c^{2} - 8 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} c\right)} d^{3} e^{3} + {\left(6 \, B a b^{4} - 5 \, A b^{5} + 48 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{2} - 8 \, {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} c\right)} d^{2} e^{4} + 2 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4} - 16 \, A a^{3} c^{2} - 8 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} d e^{5}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, {\left(2 \, B a - A b\right)} c^{4} d^{7} - 8 \, {\left(6 \, A a c^{4} + {\left(5 \, B a b - 4 \, A b^{2}\right)} c^{3}\right)} d^{6} e - 4 \, {\left(4 \, {\left(5 \, B a^{2} - 7 \, A a b\right)} c^{3} - 3 \, {\left(5 \, B a b^{2} - 4 \, A b^{3}\right)} c^{2}\right)} d^{5} e^{2} + {\left(32 \, A a^{2} c^{3} + 4 \, {\left(29 \, B a^{2} b - 24 \, A a b^{2}\right)} c^{2} - {\left(49 \, B a b^{3} - 32 \, A b^{4}\right)} c\right)} d^{4} e^{3} + {\left(13 \, B a b^{4} - 8 \, A b^{5} - 44 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} - {\left(10 \, B a^{2} b^{2} - 33 \, A a b^{3}\right)} c\right)} d^{3} e^{4} - {\left(11 \, B a^{2} b^{3} + A a b^{4} - 88 \, A a^{3} c^{2} - 2 \, {\left(18 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} c\right)} d^{2} e^{5} - {\left(2 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3} - 4 \, {\left(2 \, B a^{4} - 11 \, A a^{3} b\right)} c\right)} d e^{6} - 2 \, {\left(A a^{3} b^{2} - 4 \, A a^{4} c\right)} e^{7} + {\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{5} e^{2} + 2 \, {\left(B b^{2} c^{3} - 4 \, {\left(11 \, B a - 5 \, A b\right)} c^{4}\right)} d^{4} e^{3} - {\left(13 \, B b^{3} c^{2} - 88 \, A a c^{4} - 2 \, {\left(66 \, B a b - 31 \, A b^{2}\right)} c^{3}\right)} d^{3} e^{4} + {\left(3 \, B b^{4} c - 4 \, {\left(14 \, B a^{2} + 33 \, A a b\right)} c^{3} - {\left(38 \, B a b^{2} - 53 \, A b^{3}\right)} c^{2}\right)} d^{2} e^{5} + {\left(104 \, A a^{2} c^{3} + 2 \, {\left(2 \, B a^{2} b + 7 \, A a b^{2}\right)} c^{2} + 3 \, {\left(3 \, B a b^{3} - 5 \, A b^{4}\right)} c\right)} d e^{6} + {\left(4 \, {\left(8 \, B a^{3} - 13 \, A a^{2} b\right)} c^{2} - 3 \, {\left(4 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} e^{7}\right)} x^{3} + {\left(16 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{6} e - 4 \, {\left(B b^{2} c^{3} + 2 \, {\left(16 \, B a - 9 \, A b\right)} c^{4}\right)} d^{5} e^{2} - {\left(7 \, B b^{3} c^{2} - 80 \, A a c^{4} - 4 \, {\left(37 \, B a b - 20 \, A b^{2}\right)} c^{3}\right)} d^{4} e^{3} - {\left(8 \, B b^{4} c + 4 \, {\left(34 \, B a^{2} + 7 \, A a b\right)} c^{3} - {\left(26 \, B a b^{2} + 27 \, A b^{3}\right)} c^{2}\right)} d^{3} e^{4} + {\left(3 \, B b^{5} + 136 \, A a^{2} c^{3} + 2 \, {\left(26 \, B a^{2} b - 73 \, A a b^{2}\right)} c^{2} - {\left(25 \, B a b^{3} - 28 \, A b^{4}\right)} c\right)} d^{2} e^{5} + {\left(9 \, B a b^{4} - 15 \, A b^{5} - 4 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} - {\left(22 \, B a^{2} b^{2} - 49 \, A a b^{3}\right)} c\right)} d e^{6} - {\left(12 \, B a^{2} b^{3} - 15 \, A a b^{4} - 24 \, A a^{3} c^{2} - 2 \, {\left(20 \, B a^{3} b - 31 \, A a^{2} b^{2}\right)} c\right)} e^{7}\right)} x^{2} + {\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{7} - 8 \, {\left(B b^{2} c^{3} + {\left(2 \, B a - 3 \, A b\right)} c^{4}\right)} d^{6} e + 4 \, {\left(3 \, B b^{3} c^{2} - 16 \, A a c^{4} - 4 \, {\left(3 \, B a b - A b^{2}\right)} c^{3}\right)} d^{5} e^{2} - {\left(17 \, B b^{4} c + 8 \, {\left(17 \, B a^{2} - 30 \, A a b\right)} c^{3} - 2 \, {\left(71 \, B a b^{2} - 40 \, A b^{3}\right)} c^{2}\right)} d^{4} e^{3} + {\left(5 \, B b^{5} + 40 \, A a^{2} c^{3} + 2 \, {\left(58 \, B a^{2} b - 137 \, A a b^{2}\right)} c^{2} - {\left(79 \, B a b^{3} - 81 \, A b^{4}\right)} c\right)} d^{3} e^{4} + {\left(16 \, B a b^{4} - 25 \, A b^{5} - 4 \, {\left(26 \, B a^{3} - 19 \, A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - 63 \, A a b^{3}\right)} c\right)} d^{2} e^{5} - {\left(17 \, B a^{2} b^{3} - 20 \, A a b^{4} - 88 \, A a^{3} c^{2} - 2 \, {\left(26 \, B a^{3} b - 47 \, A a^{2} b^{2}\right)} c\right)} d e^{6} - {\left(4 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3} - 4 \, {\left(4 \, B a^{4} - 5 \, A a^{3} b\right)} c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left({\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{10} - 4 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{9} e + 2 \, {\left(3 \, a b^{4} c^{2} - 10 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{8} e^{2} - 4 \, {\left(a b^{5} c - a^{2} b^{3} c^{2} - 12 \, a^{3} b c^{3}\right)} d^{7} e^{3} + {\left(a b^{6} + 8 \, a^{2} b^{4} c - 42 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} d^{6} e^{4} - 4 \, {\left(a^{2} b^{5} - a^{3} b^{3} c - 12 \, a^{4} b c^{2}\right)} d^{5} e^{5} + 2 \, {\left(3 \, a^{3} b^{4} - 10 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} d^{4} e^{6} - 4 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{3} e^{7} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d^{2} e^{8} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} e^{2} - 4 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e^{3} + 2 \, {\left(3 \, b^{4} c^{3} - 10 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{6} e^{4} - 4 \, {\left(b^{5} c^{2} - a b^{3} c^{3} - 12 \, a^{2} b c^{4}\right)} d^{5} e^{5} + {\left(b^{6} c + 8 \, a b^{4} c^{2} - 42 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{4} e^{6} - 4 \, {\left(a b^{5} c - a^{2} b^{3} c^{2} - 12 \, a^{3} b c^{3}\right)} d^{3} e^{7} + 2 \, {\left(3 \, a^{2} b^{4} c - 10 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{2} e^{8} - 4 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d e^{9} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} e^{10}\right)} x^{4} + {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{9} e - 7 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{8} e^{2} + 8 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{7} e^{3} - 2 \, {\left(b^{5} c^{2} + 6 \, a b^{3} c^{3} - 40 \, a^{2} b c^{4}\right)} d^{6} e^{4} - 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 18 \, a^{2} b^{2} c^{3} + 24 \, a^{3} c^{4}\right)} d^{5} e^{5} + {\left(b^{7} - 34 \, a^{2} b^{3} c^{2} + 72 \, a^{3} b c^{3}\right)} d^{4} e^{6} - 4 \, {\left(a b^{6} - 4 \, a^{2} b^{4} c - 2 \, a^{3} b^{2} c^{2} + 8 \, a^{4} c^{3}\right)} d^{3} e^{7} + 2 \, {\left(3 \, a^{2} b^{5} - 14 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} d^{2} e^{8} - 2 \, {\left(2 \, a^{3} b^{4} - 9 \, a^{4} b^{2} c + 4 \, a^{5} c^{2}\right)} d e^{9} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{10}\right)} x^{3} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{10} - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{9} e - {\left(2 \, b^{4} c^{3} - 13 \, a b^{2} c^{4} + 20 \, a^{2} c^{5}\right)} d^{8} e^{2} + 8 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{7} e^{3} - {\left(7 \, b^{6} c - 22 \, a b^{4} c^{2} - 34 \, a^{2} b^{2} c^{3} + 40 \, a^{3} c^{4}\right)} d^{6} e^{4} + 2 \, {\left(b^{7} + 4 \, a b^{5} c - 38 \, a^{2} b^{3} c^{2} + 24 \, a^{3} b c^{3}\right)} d^{5} e^{5} - {\left(7 \, a b^{6} - 22 \, a^{2} b^{4} c - 34 \, a^{3} b^{2} c^{2} + 40 \, a^{4} c^{3}\right)} d^{4} e^{6} + 8 \, {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 4 \, a^{4} b c^{2}\right)} d^{3} e^{7} - {\left(2 \, a^{3} b^{4} - 13 \, a^{4} b^{2} c + 20 \, a^{5} c^{2}\right)} d^{2} e^{8} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{10}\right)} x^{2} + {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{10} - 2 \, {\left(2 \, b^{4} c^{3} - 9 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{9} e + 2 \, {\left(3 \, b^{5} c^{2} - 14 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{8} e^{2} - 4 \, {\left(b^{6} c - 4 \, a b^{4} c^{2} - 2 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{7} e^{3} + {\left(b^{7} - 34 \, a^{2} b^{3} c^{2} + 72 \, a^{3} b c^{3}\right)} d^{6} e^{4} - 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} + 24 \, a^{4} c^{3}\right)} d^{5} e^{5} - 2 \, {\left(a^{2} b^{5} + 6 \, a^{3} b^{3} c - 40 \, a^{4} b c^{2}\right)} d^{4} e^{6} + 8 \, {\left(a^{3} b^{4} - 3 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d^{3} e^{7} - 7 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{2} e^{8} + 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d e^{9}\right)} x\right)}}\right]"," ",0,"[1/16*(3*(8*(B*a*b^2*c^2 - 4*B*a^2*c^3)*d^5*e - 4*(B*a*b^3*c - 16*A*a^2*c^3 - 4*(B*a^2*b - A*a*b^2)*c^2)*d^4*e^2 + (B*a*b^4 + 16*(3*B*a^3 - 4*A*a^2*b)*c^2 - 16*(B*a^2*b^2 - A*a*b^3)*c)*d^3*e^3 + (4*B*a^2*b^3 - 5*A*a*b^4 - 16*A*a^3*c^2 - 8*(2*B*a^3*b - 3*A*a^2*b^2)*c)*d^2*e^4 + (8*(B*b^2*c^3 - 4*B*a*c^4)*d^3*e^3 - 4*(B*b^3*c^2 - 16*A*a*c^4 - 4*(B*a*b - A*b^2)*c^3)*d^2*e^4 + (B*b^4*c + 16*(3*B*a^2 - 4*A*a*b)*c^3 - 16*(B*a*b^2 - A*b^3)*c^2)*d*e^5 - (16*A*a^2*c^3 + 8*(2*B*a^2*b - 3*A*a*b^2)*c^2 - (4*B*a*b^3 - 5*A*b^4)*c)*e^6)*x^4 + (16*(B*b^2*c^3 - 4*B*a*c^4)*d^4*e^2 - 32*(A*b^2*c^3 - 4*A*a*c^4)*d^3*e^3 - 2*(B*b^4*c - 16*(3*B*a^2 - 2*A*a*b)*c^3 + 8*(B*a*b^2 - A*b^3)*c^2)*d^2*e^4 + (B*b^5 - 32*A*a^2*c^3 + 16*(B*a^2*b - A*a*b^2)*c^2 - 2*(4*B*a*b^3 - 3*A*b^4)*c)*d*e^5 + (4*B*a*b^4 - 5*A*b^5 - 16*A*a^2*b*c^2 - 8*(2*B*a^2*b^2 - 3*A*a*b^3)*c)*e^6)*x^3 + (8*(B*b^2*c^3 - 4*B*a*c^4)*d^5*e + 4*(3*B*b^3*c^2 + 16*A*a*c^4 - 4*(3*B*a*b + A*b^2)*c^3)*d^4*e^2 - (7*B*b^4*c - 16*(B*a^2 + 4*A*a*b)*c^3 - 8*(3*B*a*b^2 - 2*A*b^3)*c^2)*d^3*e^3 + (2*B*b^5 + 48*A*a^2*c^3 + 24*(4*B*a^2*b - 5*A*a*b^2)*c^2 - (32*B*a*b^3 - 27*A*b^4)*c)*d^2*e^4 + (9*B*a*b^4 - 10*A*b^5 + 48*(B*a^3 - 2*A*a^2*b)*c^2 - 16*(3*B*a^2*b^2 - 4*A*a*b^3)*c)*d*e^5 + (4*B*a^2*b^3 - 5*A*a*b^4 - 16*A*a^3*c^2 - 8*(2*B*a^3*b - 3*A*a^2*b^2)*c)*e^6)*x^2 + (8*(B*b^3*c^2 - 4*B*a*b*c^3)*d^5*e - 4*(B*b^4*c + 16*(B*a^2 - A*a*b)*c^3 - 4*(2*B*a*b^2 - A*b^3)*c^2)*d^4*e^2 + (B*b^5 + 128*A*a^2*c^3 + 16*(5*B*a^2*b - 6*A*a*b^2)*c^2 - 8*(3*B*a*b^3 - 2*A*b^4)*c)*d^3*e^3 + (6*B*a*b^4 - 5*A*b^5 + 48*(2*B*a^3 - 3*A*a^2*b)*c^2 - 8*(6*B*a^2*b^2 - 7*A*a*b^3)*c)*d^2*e^4 + 2*(4*B*a^2*b^3 - 5*A*a*b^4 - 16*A*a^3*c^2 - 8*(2*B*a^3*b - 3*A*a^2*b^2)*c)*d*e^5)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(8*(2*B*a - A*b)*c^4*d^7 - 8*(6*A*a*c^4 + (5*B*a*b - 4*A*b^2)*c^3)*d^6*e - 4*(4*(5*B*a^2 - 7*A*a*b)*c^3 - 3*(5*B*a*b^2 - 4*A*b^3)*c^2)*d^5*e^2 + (32*A*a^2*c^3 + 4*(29*B*a^2*b - 24*A*a*b^2)*c^2 - (49*B*a*b^3 - 32*A*b^4)*c)*d^4*e^3 + (13*B*a*b^4 - 8*A*b^5 - 44*(2*B*a^3 + A*a^2*b)*c^2 - (10*B*a^2*b^2 - 33*A*a*b^3)*c)*d^3*e^4 - (11*B*a^2*b^3 + A*a*b^4 - 88*A*a^3*c^2 - 2*(18*B*a^3*b - 7*A*a^2*b^2)*c)*d^2*e^5 - (2*B*a^3*b^2 - 11*A*a^2*b^3 - 4*(2*B*a^4 - 11*A*a^3*b)*c)*d*e^6 - 2*(A*a^3*b^2 - 4*A*a^4*c)*e^7 + (8*(B*b*c^4 - 2*A*c^5)*d^5*e^2 + 2*(B*b^2*c^3 - 4*(11*B*a - 5*A*b)*c^4)*d^4*e^3 - (13*B*b^3*c^2 - 88*A*a*c^4 - 2*(66*B*a*b - 31*A*b^2)*c^3)*d^3*e^4 + (3*B*b^4*c - 4*(14*B*a^2 + 33*A*a*b)*c^3 - (38*B*a*b^2 - 53*A*b^3)*c^2)*d^2*e^5 + (104*A*a^2*c^3 + 2*(2*B*a^2*b + 7*A*a*b^2)*c^2 + 3*(3*B*a*b^3 - 5*A*b^4)*c)*d*e^6 + (4*(8*B*a^3 - 13*A*a^2*b)*c^2 - 3*(4*B*a^2*b^2 - 5*A*a*b^3)*c)*e^7)*x^3 + (16*(B*b*c^4 - 2*A*c^5)*d^6*e - 4*(B*b^2*c^3 + 2*(16*B*a - 9*A*b)*c^4)*d^5*e^2 - (7*B*b^3*c^2 - 80*A*a*c^4 - 4*(37*B*a*b - 20*A*b^2)*c^3)*d^4*e^3 - (8*B*b^4*c + 4*(34*B*a^2 + 7*A*a*b)*c^3 - (26*B*a*b^2 + 27*A*b^3)*c^2)*d^3*e^4 + (3*B*b^5 + 136*A*a^2*c^3 + 2*(26*B*a^2*b - 73*A*a*b^2)*c^2 - (25*B*a*b^3 - 28*A*b^4)*c)*d^2*e^5 + (9*B*a*b^4 - 15*A*b^5 - 4*(2*B*a^3 - 5*A*a^2*b)*c^2 - (22*B*a^2*b^2 - 49*A*a*b^3)*c)*d*e^6 - (12*B*a^2*b^3 - 15*A*a*b^4 - 24*A*a^3*c^2 - 2*(20*B*a^3*b - 31*A*a^2*b^2)*c)*e^7)*x^2 + (8*(B*b*c^4 - 2*A*c^5)*d^7 - 8*(B*b^2*c^3 + (2*B*a - 3*A*b)*c^4)*d^6*e + 4*(3*B*b^3*c^2 - 16*A*a*c^4 - 4*(3*B*a*b - A*b^2)*c^3)*d^5*e^2 - (17*B*b^4*c + 8*(17*B*a^2 - 30*A*a*b)*c^3 - 2*(71*B*a*b^2 - 40*A*b^3)*c^2)*d^4*e^3 + (5*B*b^5 + 40*A*a^2*c^3 + 2*(58*B*a^2*b - 137*A*a*b^2)*c^2 - (79*B*a*b^3 - 81*A*b^4)*c)*d^3*e^4 + (16*B*a*b^4 - 25*A*b^5 - 4*(26*B*a^3 - 19*A*a^2*b)*c^2 - (2*B*a^2*b^2 - 63*A*a*b^3)*c)*d^2*e^5 - (17*B*a^2*b^3 - 20*A*a*b^4 - 88*A*a^3*c^2 - 2*(26*B*a^3*b - 47*A*a^2*b^2)*c)*d*e^6 - (4*B*a^3*b^2 - 5*A*a^2*b^3 - 4*(4*B*a^4 - 5*A*a^3*b)*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^4 - 4*a^2*c^5)*d^10 - 4*(a*b^3*c^3 - 4*a^2*b*c^4)*d^9*e + 2*(3*a*b^4*c^2 - 10*a^2*b^2*c^3 - 8*a^3*c^4)*d^8*e^2 - 4*(a*b^5*c - a^2*b^3*c^2 - 12*a^3*b*c^3)*d^7*e^3 + (a*b^6 + 8*a^2*b^4*c - 42*a^3*b^2*c^2 - 24*a^4*c^3)*d^6*e^4 - 4*(a^2*b^5 - a^3*b^3*c - 12*a^4*b*c^2)*d^5*e^5 + 2*(3*a^3*b^4 - 10*a^4*b^2*c - 8*a^5*c^2)*d^4*e^6 - 4*(a^4*b^3 - 4*a^5*b*c)*d^3*e^7 + (a^5*b^2 - 4*a^6*c)*d^2*e^8 + ((b^2*c^5 - 4*a*c^6)*d^8*e^2 - 4*(b^3*c^4 - 4*a*b*c^5)*d^7*e^3 + 2*(3*b^4*c^3 - 10*a*b^2*c^4 - 8*a^2*c^5)*d^6*e^4 - 4*(b^5*c^2 - a*b^3*c^3 - 12*a^2*b*c^4)*d^5*e^5 + (b^6*c + 8*a*b^4*c^2 - 42*a^2*b^2*c^3 - 24*a^3*c^4)*d^4*e^6 - 4*(a*b^5*c - a^2*b^3*c^2 - 12*a^3*b*c^3)*d^3*e^7 + 2*(3*a^2*b^4*c - 10*a^3*b^2*c^2 - 8*a^4*c^3)*d^2*e^8 - 4*(a^3*b^3*c - 4*a^4*b*c^2)*d*e^9 + (a^4*b^2*c - 4*a^5*c^2)*e^10)*x^4 + (2*(b^2*c^5 - 4*a*c^6)*d^9*e - 7*(b^3*c^4 - 4*a*b*c^5)*d^8*e^2 + 8*(b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*d^7*e^3 - 2*(b^5*c^2 + 6*a*b^3*c^3 - 40*a^2*b*c^4)*d^6*e^4 - 2*(b^6*c - 10*a*b^4*c^2 + 18*a^2*b^2*c^3 + 24*a^3*c^4)*d^5*e^5 + (b^7 - 34*a^2*b^3*c^2 + 72*a^3*b*c^3)*d^4*e^6 - 4*(a*b^6 - 4*a^2*b^4*c - 2*a^3*b^2*c^2 + 8*a^4*c^3)*d^3*e^7 + 2*(3*a^2*b^5 - 14*a^3*b^3*c + 8*a^4*b*c^2)*d^2*e^8 - 2*(2*a^3*b^4 - 9*a^4*b^2*c + 4*a^5*c^2)*d*e^9 + (a^4*b^3 - 4*a^5*b*c)*e^10)*x^3 + ((b^2*c^5 - 4*a*c^6)*d^10 - 2*(b^3*c^4 - 4*a*b*c^5)*d^9*e - (2*b^4*c^3 - 13*a*b^2*c^4 + 20*a^2*c^5)*d^8*e^2 + 8*(b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^7*e^3 - (7*b^6*c - 22*a*b^4*c^2 - 34*a^2*b^2*c^3 + 40*a^3*c^4)*d^6*e^4 + 2*(b^7 + 4*a*b^5*c - 38*a^2*b^3*c^2 + 24*a^3*b*c^3)*d^5*e^5 - (7*a*b^6 - 22*a^2*b^4*c - 34*a^3*b^2*c^2 + 40*a^4*c^3)*d^4*e^6 + 8*(a^2*b^5 - 5*a^3*b^3*c + 4*a^4*b*c^2)*d^3*e^7 - (2*a^3*b^4 - 13*a^4*b^2*c + 20*a^5*c^2)*d^2*e^8 - 2*(a^4*b^3 - 4*a^5*b*c)*d*e^9 + (a^5*b^2 - 4*a^6*c)*e^10)*x^2 + ((b^3*c^4 - 4*a*b*c^5)*d^10 - 2*(2*b^4*c^3 - 9*a*b^2*c^4 + 4*a^2*c^5)*d^9*e + 2*(3*b^5*c^2 - 14*a*b^3*c^3 + 8*a^2*b*c^4)*d^8*e^2 - 4*(b^6*c - 4*a*b^4*c^2 - 2*a^2*b^2*c^3 + 8*a^3*c^4)*d^7*e^3 + (b^7 - 34*a^2*b^3*c^2 + 72*a^3*b*c^3)*d^6*e^4 - 2*(a*b^6 - 10*a^2*b^4*c + 18*a^3*b^2*c^2 + 24*a^4*c^3)*d^5*e^5 - 2*(a^2*b^5 + 6*a^3*b^3*c - 40*a^4*b*c^2)*d^4*e^6 + 8*(a^3*b^4 - 3*a^4*b^2*c - 4*a^5*c^2)*d^3*e^7 - 7*(a^4*b^3 - 4*a^5*b*c)*d^2*e^8 + 2*(a^5*b^2 - 4*a^6*c)*d*e^9)*x), -1/8*(3*(8*(B*a*b^2*c^2 - 4*B*a^2*c^3)*d^5*e - 4*(B*a*b^3*c - 16*A*a^2*c^3 - 4*(B*a^2*b - A*a*b^2)*c^2)*d^4*e^2 + (B*a*b^4 + 16*(3*B*a^3 - 4*A*a^2*b)*c^2 - 16*(B*a^2*b^2 - A*a*b^3)*c)*d^3*e^3 + (4*B*a^2*b^3 - 5*A*a*b^4 - 16*A*a^3*c^2 - 8*(2*B*a^3*b - 3*A*a^2*b^2)*c)*d^2*e^4 + (8*(B*b^2*c^3 - 4*B*a*c^4)*d^3*e^3 - 4*(B*b^3*c^2 - 16*A*a*c^4 - 4*(B*a*b - A*b^2)*c^3)*d^2*e^4 + (B*b^4*c + 16*(3*B*a^2 - 4*A*a*b)*c^3 - 16*(B*a*b^2 - A*b^3)*c^2)*d*e^5 - (16*A*a^2*c^3 + 8*(2*B*a^2*b - 3*A*a*b^2)*c^2 - (4*B*a*b^3 - 5*A*b^4)*c)*e^6)*x^4 + (16*(B*b^2*c^3 - 4*B*a*c^4)*d^4*e^2 - 32*(A*b^2*c^3 - 4*A*a*c^4)*d^3*e^3 - 2*(B*b^4*c - 16*(3*B*a^2 - 2*A*a*b)*c^3 + 8*(B*a*b^2 - A*b^3)*c^2)*d^2*e^4 + (B*b^5 - 32*A*a^2*c^3 + 16*(B*a^2*b - A*a*b^2)*c^2 - 2*(4*B*a*b^3 - 3*A*b^4)*c)*d*e^5 + (4*B*a*b^4 - 5*A*b^5 - 16*A*a^2*b*c^2 - 8*(2*B*a^2*b^2 - 3*A*a*b^3)*c)*e^6)*x^3 + (8*(B*b^2*c^3 - 4*B*a*c^4)*d^5*e + 4*(3*B*b^3*c^2 + 16*A*a*c^4 - 4*(3*B*a*b + A*b^2)*c^3)*d^4*e^2 - (7*B*b^4*c - 16*(B*a^2 + 4*A*a*b)*c^3 - 8*(3*B*a*b^2 - 2*A*b^3)*c^2)*d^3*e^3 + (2*B*b^5 + 48*A*a^2*c^3 + 24*(4*B*a^2*b - 5*A*a*b^2)*c^2 - (32*B*a*b^3 - 27*A*b^4)*c)*d^2*e^4 + (9*B*a*b^4 - 10*A*b^5 + 48*(B*a^3 - 2*A*a^2*b)*c^2 - 16*(3*B*a^2*b^2 - 4*A*a*b^3)*c)*d*e^5 + (4*B*a^2*b^3 - 5*A*a*b^4 - 16*A*a^3*c^2 - 8*(2*B*a^3*b - 3*A*a^2*b^2)*c)*e^6)*x^2 + (8*(B*b^3*c^2 - 4*B*a*b*c^3)*d^5*e - 4*(B*b^4*c + 16*(B*a^2 - A*a*b)*c^3 - 4*(2*B*a*b^2 - A*b^3)*c^2)*d^4*e^2 + (B*b^5 + 128*A*a^2*c^3 + 16*(5*B*a^2*b - 6*A*a*b^2)*c^2 - 8*(3*B*a*b^3 - 2*A*b^4)*c)*d^3*e^3 + (6*B*a*b^4 - 5*A*b^5 + 48*(2*B*a^3 - 3*A*a^2*b)*c^2 - 8*(6*B*a^2*b^2 - 7*A*a*b^3)*c)*d^2*e^4 + 2*(4*B*a^2*b^3 - 5*A*a*b^4 - 16*A*a^3*c^2 - 8*(2*B*a^3*b - 3*A*a^2*b^2)*c)*d*e^5)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(8*(2*B*a - A*b)*c^4*d^7 - 8*(6*A*a*c^4 + (5*B*a*b - 4*A*b^2)*c^3)*d^6*e - 4*(4*(5*B*a^2 - 7*A*a*b)*c^3 - 3*(5*B*a*b^2 - 4*A*b^3)*c^2)*d^5*e^2 + (32*A*a^2*c^3 + 4*(29*B*a^2*b - 24*A*a*b^2)*c^2 - (49*B*a*b^3 - 32*A*b^4)*c)*d^4*e^3 + (13*B*a*b^4 - 8*A*b^5 - 44*(2*B*a^3 + A*a^2*b)*c^2 - (10*B*a^2*b^2 - 33*A*a*b^3)*c)*d^3*e^4 - (11*B*a^2*b^3 + A*a*b^4 - 88*A*a^3*c^2 - 2*(18*B*a^3*b - 7*A*a^2*b^2)*c)*d^2*e^5 - (2*B*a^3*b^2 - 11*A*a^2*b^3 - 4*(2*B*a^4 - 11*A*a^3*b)*c)*d*e^6 - 2*(A*a^3*b^2 - 4*A*a^4*c)*e^7 + (8*(B*b*c^4 - 2*A*c^5)*d^5*e^2 + 2*(B*b^2*c^3 - 4*(11*B*a - 5*A*b)*c^4)*d^4*e^3 - (13*B*b^3*c^2 - 88*A*a*c^4 - 2*(66*B*a*b - 31*A*b^2)*c^3)*d^3*e^4 + (3*B*b^4*c - 4*(14*B*a^2 + 33*A*a*b)*c^3 - (38*B*a*b^2 - 53*A*b^3)*c^2)*d^2*e^5 + (104*A*a^2*c^3 + 2*(2*B*a^2*b + 7*A*a*b^2)*c^2 + 3*(3*B*a*b^3 - 5*A*b^4)*c)*d*e^6 + (4*(8*B*a^3 - 13*A*a^2*b)*c^2 - 3*(4*B*a^2*b^2 - 5*A*a*b^3)*c)*e^7)*x^3 + (16*(B*b*c^4 - 2*A*c^5)*d^6*e - 4*(B*b^2*c^3 + 2*(16*B*a - 9*A*b)*c^4)*d^5*e^2 - (7*B*b^3*c^2 - 80*A*a*c^4 - 4*(37*B*a*b - 20*A*b^2)*c^3)*d^4*e^3 - (8*B*b^4*c + 4*(34*B*a^2 + 7*A*a*b)*c^3 - (26*B*a*b^2 + 27*A*b^3)*c^2)*d^3*e^4 + (3*B*b^5 + 136*A*a^2*c^3 + 2*(26*B*a^2*b - 73*A*a*b^2)*c^2 - (25*B*a*b^3 - 28*A*b^4)*c)*d^2*e^5 + (9*B*a*b^4 - 15*A*b^5 - 4*(2*B*a^3 - 5*A*a^2*b)*c^2 - (22*B*a^2*b^2 - 49*A*a*b^3)*c)*d*e^6 - (12*B*a^2*b^3 - 15*A*a*b^4 - 24*A*a^3*c^2 - 2*(20*B*a^3*b - 31*A*a^2*b^2)*c)*e^7)*x^2 + (8*(B*b*c^4 - 2*A*c^5)*d^7 - 8*(B*b^2*c^3 + (2*B*a - 3*A*b)*c^4)*d^6*e + 4*(3*B*b^3*c^2 - 16*A*a*c^4 - 4*(3*B*a*b - A*b^2)*c^3)*d^5*e^2 - (17*B*b^4*c + 8*(17*B*a^2 - 30*A*a*b)*c^3 - 2*(71*B*a*b^2 - 40*A*b^3)*c^2)*d^4*e^3 + (5*B*b^5 + 40*A*a^2*c^3 + 2*(58*B*a^2*b - 137*A*a*b^2)*c^2 - (79*B*a*b^3 - 81*A*b^4)*c)*d^3*e^4 + (16*B*a*b^4 - 25*A*b^5 - 4*(26*B*a^3 - 19*A*a^2*b)*c^2 - (2*B*a^2*b^2 - 63*A*a*b^3)*c)*d^2*e^5 - (17*B*a^2*b^3 - 20*A*a*b^4 - 88*A*a^3*c^2 - 2*(26*B*a^3*b - 47*A*a^2*b^2)*c)*d*e^6 - (4*B*a^3*b^2 - 5*A*a^2*b^3 - 4*(4*B*a^4 - 5*A*a^3*b)*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^4 - 4*a^2*c^5)*d^10 - 4*(a*b^3*c^3 - 4*a^2*b*c^4)*d^9*e + 2*(3*a*b^4*c^2 - 10*a^2*b^2*c^3 - 8*a^3*c^4)*d^8*e^2 - 4*(a*b^5*c - a^2*b^3*c^2 - 12*a^3*b*c^3)*d^7*e^3 + (a*b^6 + 8*a^2*b^4*c - 42*a^3*b^2*c^2 - 24*a^4*c^3)*d^6*e^4 - 4*(a^2*b^5 - a^3*b^3*c - 12*a^4*b*c^2)*d^5*e^5 + 2*(3*a^3*b^4 - 10*a^4*b^2*c - 8*a^5*c^2)*d^4*e^6 - 4*(a^4*b^3 - 4*a^5*b*c)*d^3*e^7 + (a^5*b^2 - 4*a^6*c)*d^2*e^8 + ((b^2*c^5 - 4*a*c^6)*d^8*e^2 - 4*(b^3*c^4 - 4*a*b*c^5)*d^7*e^3 + 2*(3*b^4*c^3 - 10*a*b^2*c^4 - 8*a^2*c^5)*d^6*e^4 - 4*(b^5*c^2 - a*b^3*c^3 - 12*a^2*b*c^4)*d^5*e^5 + (b^6*c + 8*a*b^4*c^2 - 42*a^2*b^2*c^3 - 24*a^3*c^4)*d^4*e^6 - 4*(a*b^5*c - a^2*b^3*c^2 - 12*a^3*b*c^3)*d^3*e^7 + 2*(3*a^2*b^4*c - 10*a^3*b^2*c^2 - 8*a^4*c^3)*d^2*e^8 - 4*(a^3*b^3*c - 4*a^4*b*c^2)*d*e^9 + (a^4*b^2*c - 4*a^5*c^2)*e^10)*x^4 + (2*(b^2*c^5 - 4*a*c^6)*d^9*e - 7*(b^3*c^4 - 4*a*b*c^5)*d^8*e^2 + 8*(b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*d^7*e^3 - 2*(b^5*c^2 + 6*a*b^3*c^3 - 40*a^2*b*c^4)*d^6*e^4 - 2*(b^6*c - 10*a*b^4*c^2 + 18*a^2*b^2*c^3 + 24*a^3*c^4)*d^5*e^5 + (b^7 - 34*a^2*b^3*c^2 + 72*a^3*b*c^3)*d^4*e^6 - 4*(a*b^6 - 4*a^2*b^4*c - 2*a^3*b^2*c^2 + 8*a^4*c^3)*d^3*e^7 + 2*(3*a^2*b^5 - 14*a^3*b^3*c + 8*a^4*b*c^2)*d^2*e^8 - 2*(2*a^3*b^4 - 9*a^4*b^2*c + 4*a^5*c^2)*d*e^9 + (a^4*b^3 - 4*a^5*b*c)*e^10)*x^3 + ((b^2*c^5 - 4*a*c^6)*d^10 - 2*(b^3*c^4 - 4*a*b*c^5)*d^9*e - (2*b^4*c^3 - 13*a*b^2*c^4 + 20*a^2*c^5)*d^8*e^2 + 8*(b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^7*e^3 - (7*b^6*c - 22*a*b^4*c^2 - 34*a^2*b^2*c^3 + 40*a^3*c^4)*d^6*e^4 + 2*(b^7 + 4*a*b^5*c - 38*a^2*b^3*c^2 + 24*a^3*b*c^3)*d^5*e^5 - (7*a*b^6 - 22*a^2*b^4*c - 34*a^3*b^2*c^2 + 40*a^4*c^3)*d^4*e^6 + 8*(a^2*b^5 - 5*a^3*b^3*c + 4*a^4*b*c^2)*d^3*e^7 - (2*a^3*b^4 - 13*a^4*b^2*c + 20*a^5*c^2)*d^2*e^8 - 2*(a^4*b^3 - 4*a^5*b*c)*d*e^9 + (a^5*b^2 - 4*a^6*c)*e^10)*x^2 + ((b^3*c^4 - 4*a*b*c^5)*d^10 - 2*(2*b^4*c^3 - 9*a*b^2*c^4 + 4*a^2*c^5)*d^9*e + 2*(3*b^5*c^2 - 14*a*b^3*c^3 + 8*a^2*b*c^4)*d^8*e^2 - 4*(b^6*c - 4*a*b^4*c^2 - 2*a^2*b^2*c^3 + 8*a^3*c^4)*d^7*e^3 + (b^7 - 34*a^2*b^3*c^2 + 72*a^3*b*c^3)*d^6*e^4 - 2*(a*b^6 - 10*a^2*b^4*c + 18*a^3*b^2*c^2 + 24*a^4*c^3)*d^5*e^5 - 2*(a^2*b^5 + 6*a^3*b^3*c - 40*a^4*b*c^2)*d^4*e^6 + 8*(a^3*b^4 - 3*a^4*b^2*c - 4*a^5*c^2)*d^3*e^7 - 7*(a^4*b^3 - 4*a^5*b*c)*d^2*e^8 + 2*(a^5*b^2 - 4*a^6*c)*d*e^9)*x)]","B",0
2480,1,3181,0,14.413622," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, {\left(B a^{2} b^{4} c - 8 \, B a^{3} b^{2} c^{2} + 16 \, B a^{4} c^{3}\right)} d e^{3} - {\left(5 \, B a^{2} b^{5} - 32 \, A a^{4} c^{3} + 16 \, {\left(5 \, B a^{4} b + A a^{3} b^{2}\right)} c^{2} - 2 \, {\left(20 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c\right)} e^{4} + {\left(8 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} d e^{3} - {\left(5 \, B b^{5} c^{2} - 32 \, A a^{2} c^{5} + 16 \, {\left(5 \, B a^{2} b + A a b^{2}\right)} c^{4} - 2 \, {\left(20 \, B a b^{3} + A b^{4}\right)} c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{5} c^{2} - 8 \, B a b^{3} c^{3} + 16 \, B a^{2} b c^{4}\right)} d e^{3} - {\left(5 \, B b^{6} c - 32 \, A a^{2} b c^{4} + 16 \, {\left(5 \, B a^{2} b^{2} + A a b^{3}\right)} c^{3} - 2 \, {\left(20 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, {\left(B b^{6} c - 6 \, B a b^{4} c^{2} + 32 \, B a^{3} c^{4}\right)} d e^{3} - {\left(5 \, B b^{7} + 12 \, A a b^{4} c^{2} + 160 \, B a^{3} b c^{3} - 64 \, A a^{3} c^{4} - 2 \, {\left(15 \, B a b^{5} + A b^{6}\right)} c\right)} e^{4}\right)} x^{2} + 2 \, {\left(8 \, {\left(B a b^{5} c - 8 \, B a^{2} b^{3} c^{2} + 16 \, B a^{3} b c^{3}\right)} d e^{3} - {\left(5 \, B a b^{6} - 32 \, A a^{3} b c^{3} + 16 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{2} - 2 \, {\left(20 \, B a^{2} b^{4} + A a b^{5}\right)} c\right)} e^{4}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(96 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{4} d^{2} e^{2} - 3 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} e^{4} x^{4} + 2 \, {\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{5} + {\left(2 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{4} + 16 \, {\left(4 \, A a^{2} c^{5} - {\left(4 \, B a^{2} b - A a b^{2}\right)} c^{4}\right)} d^{3} e + 8 \, {\left(3 \, B a^{2} b^{3} c^{2} - 20 \, B a^{3} b c^{3} + 16 \, A a^{3} c^{4}\right)} d e^{3} - {\left(15 \, B a^{2} b^{4} c + 8 \, {\left(16 \, B a^{4} + 5 \, A a^{3} b\right)} c^{3} - 2 \, {\left(50 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} c^{2}\right)} e^{4} + 4 \, {\left(4 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} - 4 \, {\left(B b^{2} c^{5} + 4 \, {\left(B a - A b\right)} c^{6}\right)} d^{3} e - 3 \, {\left(B b^{3} c^{4} + 8 \, A a c^{6} - 2 \, {\left(6 \, B a b - A b^{2}\right)} c^{5}\right)} d^{2} e^{2} + 2 \, {\left(4 \, B b^{4} c^{3} + 4 \, {\left(8 \, B a^{2} + 3 \, A a b\right)} c^{5} - {\left(28 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d e^{3} - {\left(5 \, B b^{5} c^{2} - 16 \, A a^{2} c^{5} + 2 \, {\left(32 \, B a^{2} b + 7 \, A a b^{2}\right)} c^{4} - {\left(37 \, B a b^{3} + 2 \, A b^{4}\right)} c^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 8 \, {\left(B b^{3} c^{4} + 4 \, {\left(B a b - A b^{2}\right)} c^{5}\right)} d^{3} e + 12 \, {\left(4 \, {\left(2 \, B a^{2} - A a b\right)} c^{5} + {\left(2 \, B a b^{2} - A b^{3}\right)} c^{4}\right)} d^{2} e^{2} + 8 \, {\left(B b^{5} c^{2} - 6 \, B a b^{3} c^{3} + 2 \, A a b^{2} c^{4} + 8 \, A a^{2} c^{5}\right)} d e^{3} - {\left(5 \, B b^{6} c + 64 \, B a^{3} c^{4} + 4 \, {\left(4 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} c^{3} - 2 \, {\left(15 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} e^{4}\right)} x^{2} + 6 \, {\left(24 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} c^{4} d^{2} e^{2} + {\left(B b^{3} c^{4} - 8 \, A a c^{6} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c^{5}\right)} d^{4} + 4 \, {\left(4 \, A a b c^{5} - {\left(4 \, B a b^{2} - A b^{3}\right)} c^{4}\right)} d^{3} e + 8 \, {\left(B a b^{4} c^{2} - 7 \, B a^{2} b^{2} c^{3} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c^{4}\right)} d e^{3} - {\left(5 \, B a b^{5} c - 8 \, A a^{3} c^{4} + 2 \, {\left(26 \, B a^{3} b + 7 \, A a^{2} b^{2}\right)} c^{3} - {\left(35 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6} + {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} x^{4} + 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} x^{3} + {\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} x^{2} + 2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x\right)}}, -\frac{3 \, {\left(8 \, {\left(B a^{2} b^{4} c - 8 \, B a^{3} b^{2} c^{2} + 16 \, B a^{4} c^{3}\right)} d e^{3} - {\left(5 \, B a^{2} b^{5} - 32 \, A a^{4} c^{3} + 16 \, {\left(5 \, B a^{4} b + A a^{3} b^{2}\right)} c^{2} - 2 \, {\left(20 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c\right)} e^{4} + {\left(8 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} d e^{3} - {\left(5 \, B b^{5} c^{2} - 32 \, A a^{2} c^{5} + 16 \, {\left(5 \, B a^{2} b + A a b^{2}\right)} c^{4} - 2 \, {\left(20 \, B a b^{3} + A b^{4}\right)} c^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b^{5} c^{2} - 8 \, B a b^{3} c^{3} + 16 \, B a^{2} b c^{4}\right)} d e^{3} - {\left(5 \, B b^{6} c - 32 \, A a^{2} b c^{4} + 16 \, {\left(5 \, B a^{2} b^{2} + A a b^{3}\right)} c^{3} - 2 \, {\left(20 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} e^{4}\right)} x^{3} + {\left(8 \, {\left(B b^{6} c - 6 \, B a b^{4} c^{2} + 32 \, B a^{3} c^{4}\right)} d e^{3} - {\left(5 \, B b^{7} + 12 \, A a b^{4} c^{2} + 160 \, B a^{3} b c^{3} - 64 \, A a^{3} c^{4} - 2 \, {\left(15 \, B a b^{5} + A b^{6}\right)} c\right)} e^{4}\right)} x^{2} + 2 \, {\left(8 \, {\left(B a b^{5} c - 8 \, B a^{2} b^{3} c^{2} + 16 \, B a^{3} b c^{3}\right)} d e^{3} - {\left(5 \, B a b^{6} - 32 \, A a^{3} b c^{3} + 16 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{2} - 2 \, {\left(20 \, B a^{2} b^{4} + A a b^{5}\right)} c\right)} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(96 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{4} d^{2} e^{2} - 3 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} e^{4} x^{4} + 2 \, {\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{5} + {\left(2 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{4} + 16 \, {\left(4 \, A a^{2} c^{5} - {\left(4 \, B a^{2} b - A a b^{2}\right)} c^{4}\right)} d^{3} e + 8 \, {\left(3 \, B a^{2} b^{3} c^{2} - 20 \, B a^{3} b c^{3} + 16 \, A a^{3} c^{4}\right)} d e^{3} - {\left(15 \, B a^{2} b^{4} c + 8 \, {\left(16 \, B a^{4} + 5 \, A a^{3} b\right)} c^{3} - 2 \, {\left(50 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} c^{2}\right)} e^{4} + 4 \, {\left(4 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{4} - 4 \, {\left(B b^{2} c^{5} + 4 \, {\left(B a - A b\right)} c^{6}\right)} d^{3} e - 3 \, {\left(B b^{3} c^{4} + 8 \, A a c^{6} - 2 \, {\left(6 \, B a b - A b^{2}\right)} c^{5}\right)} d^{2} e^{2} + 2 \, {\left(4 \, B b^{4} c^{3} + 4 \, {\left(8 \, B a^{2} + 3 \, A a b\right)} c^{5} - {\left(28 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d e^{3} - {\left(5 \, B b^{5} c^{2} - 16 \, A a^{2} c^{5} + 2 \, {\left(32 \, B a^{2} b + 7 \, A a b^{2}\right)} c^{4} - {\left(37 \, B a b^{3} + 2 \, A b^{4}\right)} c^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{4} - 8 \, {\left(B b^{3} c^{4} + 4 \, {\left(B a b - A b^{2}\right)} c^{5}\right)} d^{3} e + 12 \, {\left(4 \, {\left(2 \, B a^{2} - A a b\right)} c^{5} + {\left(2 \, B a b^{2} - A b^{3}\right)} c^{4}\right)} d^{2} e^{2} + 8 \, {\left(B b^{5} c^{2} - 6 \, B a b^{3} c^{3} + 2 \, A a b^{2} c^{4} + 8 \, A a^{2} c^{5}\right)} d e^{3} - {\left(5 \, B b^{6} c + 64 \, B a^{3} c^{4} + 4 \, {\left(4 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} c^{3} - 2 \, {\left(15 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} e^{4}\right)} x^{2} + 6 \, {\left(24 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} c^{4} d^{2} e^{2} + {\left(B b^{3} c^{4} - 8 \, A a c^{6} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c^{5}\right)} d^{4} + 4 \, {\left(4 \, A a b c^{5} - {\left(4 \, B a b^{2} - A b^{3}\right)} c^{4}\right)} d^{3} e + 8 \, {\left(B a b^{4} c^{2} - 7 \, B a^{2} b^{2} c^{3} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c^{4}\right)} d e^{3} - {\left(5 \, B a b^{5} c - 8 \, A a^{3} c^{4} + 2 \, {\left(26 \, B a^{3} b + 7 \, A a^{2} b^{2}\right)} c^{3} - {\left(35 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6} + {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} x^{4} + 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} x^{3} + {\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} x^{2} + 2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x\right)}}\right]"," ",0,"[1/12*(3*(8*(B*a^2*b^4*c - 8*B*a^3*b^2*c^2 + 16*B*a^4*c^3)*d*e^3 - (5*B*a^2*b^5 - 32*A*a^4*c^3 + 16*(5*B*a^4*b + A*a^3*b^2)*c^2 - 2*(20*B*a^3*b^3 + A*a^2*b^4)*c)*e^4 + (8*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*d*e^3 - (5*B*b^5*c^2 - 32*A*a^2*c^5 + 16*(5*B*a^2*b + A*a*b^2)*c^4 - 2*(20*B*a*b^3 + A*b^4)*c^3)*e^4)*x^4 + 2*(8*(B*b^5*c^2 - 8*B*a*b^3*c^3 + 16*B*a^2*b*c^4)*d*e^3 - (5*B*b^6*c - 32*A*a^2*b*c^4 + 16*(5*B*a^2*b^2 + A*a*b^3)*c^3 - 2*(20*B*a*b^4 + A*b^5)*c^2)*e^4)*x^3 + (8*(B*b^6*c - 6*B*a*b^4*c^2 + 32*B*a^3*c^4)*d*e^3 - (5*B*b^7 + 12*A*a*b^4*c^2 + 160*B*a^3*b*c^3 - 64*A*a^3*c^4 - 2*(15*B*a*b^5 + A*b^6)*c)*e^4)*x^2 + 2*(8*(B*a*b^5*c - 8*B*a^2*b^3*c^2 + 16*B*a^3*b*c^3)*d*e^3 - (5*B*a*b^6 - 32*A*a^3*b*c^3 + 16*(5*B*a^3*b^2 + A*a^2*b^3)*c^2 - 2*(20*B*a^2*b^4 + A*a*b^5)*c)*e^4)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(96*(2*B*a^3 - A*a^2*b)*c^4*d^2*e^2 - 3*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*e^4*x^4 + 2*(4*(2*B*a^2 - 3*A*a*b)*c^5 + (2*B*a*b^2 + A*b^3)*c^4)*d^4 + 16*(4*A*a^2*c^5 - (4*B*a^2*b - A*a*b^2)*c^4)*d^3*e + 8*(3*B*a^2*b^3*c^2 - 20*B*a^3*b*c^3 + 16*A*a^3*c^4)*d*e^3 - (15*B*a^2*b^4*c + 8*(16*B*a^4 + 5*A*a^3*b)*c^3 - 2*(50*B*a^3*b^2 + 3*A*a^2*b^3)*c^2)*e^4 + 4*(4*(B*b*c^6 - 2*A*c^7)*d^4 - 4*(B*b^2*c^5 + 4*(B*a - A*b)*c^6)*d^3*e - 3*(B*b^3*c^4 + 8*A*a*c^6 - 2*(6*B*a*b - A*b^2)*c^5)*d^2*e^2 + 2*(4*B*b^4*c^3 + 4*(8*B*a^2 + 3*A*a*b)*c^5 - (28*B*a*b^2 + A*b^3)*c^4)*d*e^3 - (5*B*b^5*c^2 - 16*A*a^2*c^5 + 2*(32*B*a^2*b + 7*A*a*b^2)*c^4 - (37*B*a*b^3 + 2*A*b^4)*c^3)*e^4)*x^3 + 3*(8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 8*(B*b^3*c^4 + 4*(B*a*b - A*b^2)*c^5)*d^3*e + 12*(4*(2*B*a^2 - A*a*b)*c^5 + (2*B*a*b^2 - A*b^3)*c^4)*d^2*e^2 + 8*(B*b^5*c^2 - 6*B*a*b^3*c^3 + 2*A*a*b^2*c^4 + 8*A*a^2*c^5)*d*e^3 - (5*B*b^6*c + 64*B*a^3*c^4 + 4*(4*B*a^2*b^2 + 3*A*a*b^3)*c^3 - 2*(15*B*a*b^4 + A*b^5)*c^2)*e^4)*x^2 + 6*(24*(2*B*a^2*b - A*a*b^2)*c^4*d^2*e^2 + (B*b^3*c^4 - 8*A*a*c^6 + 2*(2*B*a*b - A*b^2)*c^5)*d^4 + 4*(4*A*a*b*c^5 - (4*B*a*b^2 - A*b^3)*c^4)*d^3*e + 8*(B*a*b^4*c^2 - 7*B*a^2*b^2*c^3 + 4*(B*a^3 + A*a^2*b)*c^4)*d*e^3 - (5*B*a*b^5*c - 8*A*a^3*c^4 + 2*(26*B*a^3*b + 7*A*a^2*b^2)*c^3 - (35*B*a^2*b^3 + 2*A*a*b^4)*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6 + (b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*x^4 + 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*x^3 + (b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*x^2 + 2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x), -1/6*(3*(8*(B*a^2*b^4*c - 8*B*a^3*b^2*c^2 + 16*B*a^4*c^3)*d*e^3 - (5*B*a^2*b^5 - 32*A*a^4*c^3 + 16*(5*B*a^4*b + A*a^3*b^2)*c^2 - 2*(20*B*a^3*b^3 + A*a^2*b^4)*c)*e^4 + (8*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*d*e^3 - (5*B*b^5*c^2 - 32*A*a^2*c^5 + 16*(5*B*a^2*b + A*a*b^2)*c^4 - 2*(20*B*a*b^3 + A*b^4)*c^3)*e^4)*x^4 + 2*(8*(B*b^5*c^2 - 8*B*a*b^3*c^3 + 16*B*a^2*b*c^4)*d*e^3 - (5*B*b^6*c - 32*A*a^2*b*c^4 + 16*(5*B*a^2*b^2 + A*a*b^3)*c^3 - 2*(20*B*a*b^4 + A*b^5)*c^2)*e^4)*x^3 + (8*(B*b^6*c - 6*B*a*b^4*c^2 + 32*B*a^3*c^4)*d*e^3 - (5*B*b^7 + 12*A*a*b^4*c^2 + 160*B*a^3*b*c^3 - 64*A*a^3*c^4 - 2*(15*B*a*b^5 + A*b^6)*c)*e^4)*x^2 + 2*(8*(B*a*b^5*c - 8*B*a^2*b^3*c^2 + 16*B*a^3*b*c^3)*d*e^3 - (5*B*a*b^6 - 32*A*a^3*b*c^3 + 16*(5*B*a^3*b^2 + A*a^2*b^3)*c^2 - 2*(20*B*a^2*b^4 + A*a*b^5)*c)*e^4)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(96*(2*B*a^3 - A*a^2*b)*c^4*d^2*e^2 - 3*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*e^4*x^4 + 2*(4*(2*B*a^2 - 3*A*a*b)*c^5 + (2*B*a*b^2 + A*b^3)*c^4)*d^4 + 16*(4*A*a^2*c^5 - (4*B*a^2*b - A*a*b^2)*c^4)*d^3*e + 8*(3*B*a^2*b^3*c^2 - 20*B*a^3*b*c^3 + 16*A*a^3*c^4)*d*e^3 - (15*B*a^2*b^4*c + 8*(16*B*a^4 + 5*A*a^3*b)*c^3 - 2*(50*B*a^3*b^2 + 3*A*a^2*b^3)*c^2)*e^4 + 4*(4*(B*b*c^6 - 2*A*c^7)*d^4 - 4*(B*b^2*c^5 + 4*(B*a - A*b)*c^6)*d^3*e - 3*(B*b^3*c^4 + 8*A*a*c^6 - 2*(6*B*a*b - A*b^2)*c^5)*d^2*e^2 + 2*(4*B*b^4*c^3 + 4*(8*B*a^2 + 3*A*a*b)*c^5 - (28*B*a*b^2 + A*b^3)*c^4)*d*e^3 - (5*B*b^5*c^2 - 16*A*a^2*c^5 + 2*(32*B*a^2*b + 7*A*a*b^2)*c^4 - (37*B*a*b^3 + 2*A*b^4)*c^3)*e^4)*x^3 + 3*(8*(B*b^2*c^5 - 2*A*b*c^6)*d^4 - 8*(B*b^3*c^4 + 4*(B*a*b - A*b^2)*c^5)*d^3*e + 12*(4*(2*B*a^2 - A*a*b)*c^5 + (2*B*a*b^2 - A*b^3)*c^4)*d^2*e^2 + 8*(B*b^5*c^2 - 6*B*a*b^3*c^3 + 2*A*a*b^2*c^4 + 8*A*a^2*c^5)*d*e^3 - (5*B*b^6*c + 64*B*a^3*c^4 + 4*(4*B*a^2*b^2 + 3*A*a*b^3)*c^3 - 2*(15*B*a*b^4 + A*b^5)*c^2)*e^4)*x^2 + 6*(24*(2*B*a^2*b - A*a*b^2)*c^4*d^2*e^2 + (B*b^3*c^4 - 8*A*a*c^6 + 2*(2*B*a*b - A*b^2)*c^5)*d^4 + 4*(4*A*a*b*c^5 - (4*B*a*b^2 - A*b^3)*c^4)*d^3*e + 8*(B*a*b^4*c^2 - 7*B*a^2*b^2*c^3 + 4*(B*a^3 + A*a^2*b)*c^4)*d*e^3 - (5*B*a*b^5*c - 8*A*a^3*c^4 + 2*(26*B*a^3*b + 7*A*a^2*b^2)*c^3 - (35*B*a^2*b^3 + 2*A*a*b^4)*c^2)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6 + (b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*x^4 + 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*x^3 + (b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*x^2 + 2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x)]","B",0
2481,1,1881,0,11.255941," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right)} e^{3} x^{4} + 2 \, {\left(B b^{5} c - 8 \, B a b^{3} c^{2} + 16 \, B a^{2} b c^{3}\right)} e^{3} x^{3} + {\left(B b^{6} - 6 \, B a b^{4} c + 32 \, B a^{3} c^{3}\right)} e^{3} x^{2} + 2 \, {\left(B a b^{5} - 8 \, B a^{2} b^{3} c + 16 \, B a^{3} b c^{2}\right)} e^{3} x + {\left(B a^{2} b^{4} - 8 \, B a^{3} b^{2} c + 16 \, B a^{4} c^{2}\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(24 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{3} d e^{2} + {\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{4} + {\left(2 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{3} + 6 \, {\left(4 \, A a^{2} c^{4} - {\left(4 \, B a^{2} b - A a b^{2}\right)} c^{3}\right)} d^{2} e + {\left(3 \, B a^{2} b^{3} c - 20 \, B a^{3} b c^{2} + 16 \, A a^{3} c^{3}\right)} e^{3} + {\left(8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 6 \, {\left(B b^{2} c^{4} + 4 \, {\left(B a - A b\right)} c^{5}\right)} d^{2} e - 3 \, {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(6 \, B a b - A b^{2}\right)} c^{4}\right)} d e^{2} + {\left(4 \, B b^{4} c^{2} + 4 \, {\left(8 \, B a^{2} + 3 \, A a b\right)} c^{4} - {\left(28 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} e^{3}\right)} x^{3} + 3 \, {\left(4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 3 \, {\left(B b^{3} c^{3} + 4 \, {\left(B a b - A b^{2}\right)} c^{4}\right)} d^{2} e + 3 \, {\left(4 \, {\left(2 \, B a^{2} - A a b\right)} c^{4} + {\left(2 \, B a b^{2} - A b^{3}\right)} c^{3}\right)} d e^{2} + {\left(B b^{5} c - 6 \, B a b^{3} c^{2} + 2 \, A a b^{2} c^{3} + 8 \, A a^{2} c^{4}\right)} e^{3}\right)} x^{2} + 3 \, {\left(12 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} c^{3} d e^{2} + {\left(B b^{3} c^{3} - 8 \, A a c^{5} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c^{4}\right)} d^{3} + 3 \, {\left(4 \, A a b c^{4} - {\left(4 \, B a b^{2} - A b^{3}\right)} c^{3}\right)} d^{2} e + 2 \, {\left(B a b^{4} c - 7 \, B a^{2} b^{2} c^{2} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}, -\frac{3 \, {\left({\left(B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right)} e^{3} x^{4} + 2 \, {\left(B b^{5} c - 8 \, B a b^{3} c^{2} + 16 \, B a^{2} b c^{3}\right)} e^{3} x^{3} + {\left(B b^{6} - 6 \, B a b^{4} c + 32 \, B a^{3} c^{3}\right)} e^{3} x^{2} + 2 \, {\left(B a b^{5} - 8 \, B a^{2} b^{3} c + 16 \, B a^{3} b c^{2}\right)} e^{3} x + {\left(B a^{2} b^{4} - 8 \, B a^{3} b^{2} c + 16 \, B a^{4} c^{2}\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(24 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{3} d e^{2} + {\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{4} + {\left(2 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{3} + 6 \, {\left(4 \, A a^{2} c^{4} - {\left(4 \, B a^{2} b - A a b^{2}\right)} c^{3}\right)} d^{2} e + {\left(3 \, B a^{2} b^{3} c - 20 \, B a^{3} b c^{2} + 16 \, A a^{3} c^{3}\right)} e^{3} + {\left(8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{3} - 6 \, {\left(B b^{2} c^{4} + 4 \, {\left(B a - A b\right)} c^{5}\right)} d^{2} e - 3 \, {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(6 \, B a b - A b^{2}\right)} c^{4}\right)} d e^{2} + {\left(4 \, B b^{4} c^{2} + 4 \, {\left(8 \, B a^{2} + 3 \, A a b\right)} c^{4} - {\left(28 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} e^{3}\right)} x^{3} + 3 \, {\left(4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{3} - 3 \, {\left(B b^{3} c^{3} + 4 \, {\left(B a b - A b^{2}\right)} c^{4}\right)} d^{2} e + 3 \, {\left(4 \, {\left(2 \, B a^{2} - A a b\right)} c^{4} + {\left(2 \, B a b^{2} - A b^{3}\right)} c^{3}\right)} d e^{2} + {\left(B b^{5} c - 6 \, B a b^{3} c^{2} + 2 \, A a b^{2} c^{3} + 8 \, A a^{2} c^{4}\right)} e^{3}\right)} x^{2} + 3 \, {\left(12 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} c^{3} d e^{2} + {\left(B b^{3} c^{3} - 8 \, A a c^{5} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c^{4}\right)} d^{3} + 3 \, {\left(4 \, A a b c^{4} - {\left(4 \, B a b^{2} - A b^{3}\right)} c^{3}\right)} d^{2} e + 2 \, {\left(B a b^{4} c - 7 \, B a^{2} b^{2} c^{2} + 4 \, {\left(B a^{3} + A a^{2} b\right)} c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/6*(3*((B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*e^3*x^4 + 2*(B*b^5*c - 8*B*a*b^3*c^2 + 16*B*a^2*b*c^3)*e^3*x^3 + (B*b^6 - 6*B*a*b^4*c + 32*B*a^3*c^3)*e^3*x^2 + 2*(B*a*b^5 - 8*B*a^2*b^3*c + 16*B*a^3*b*c^2)*e^3*x + (B*a^2*b^4 - 8*B*a^3*b^2*c + 16*B*a^4*c^2)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(24*(2*B*a^3 - A*a^2*b)*c^3*d*e^2 + (4*(2*B*a^2 - 3*A*a*b)*c^4 + (2*B*a*b^2 + A*b^3)*c^3)*d^3 + 6*(4*A*a^2*c^4 - (4*B*a^2*b - A*a*b^2)*c^3)*d^2*e + (3*B*a^2*b^3*c - 20*B*a^3*b*c^2 + 16*A*a^3*c^3)*e^3 + (8*(B*b*c^5 - 2*A*c^6)*d^3 - 6*(B*b^2*c^4 + 4*(B*a - A*b)*c^5)*d^2*e - 3*(B*b^3*c^3 + 8*A*a*c^5 - 2*(6*B*a*b - A*b^2)*c^4)*d*e^2 + (4*B*b^4*c^2 + 4*(8*B*a^2 + 3*A*a*b)*c^4 - (28*B*a*b^2 + A*b^3)*c^3)*e^3)*x^3 + 3*(4*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 3*(B*b^3*c^3 + 4*(B*a*b - A*b^2)*c^4)*d^2*e + 3*(4*(2*B*a^2 - A*a*b)*c^4 + (2*B*a*b^2 - A*b^3)*c^3)*d*e^2 + (B*b^5*c - 6*B*a*b^3*c^2 + 2*A*a*b^2*c^3 + 8*A*a^2*c^4)*e^3)*x^2 + 3*(12*(2*B*a^2*b - A*a*b^2)*c^3*d*e^2 + (B*b^3*c^3 - 8*A*a*c^5 + 2*(2*B*a*b - A*b^2)*c^4)*d^3 + 3*(4*A*a*b*c^4 - (4*B*a*b^2 - A*b^3)*c^3)*d^2*e + 2*(B*a*b^4*c - 7*B*a^2*b^2*c^2 + 4*(B*a^3 + A*a^2*b)*c^3)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x), -1/3*(3*((B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*e^3*x^4 + 2*(B*b^5*c - 8*B*a*b^3*c^2 + 16*B*a^2*b*c^3)*e^3*x^3 + (B*b^6 - 6*B*a*b^4*c + 32*B*a^3*c^3)*e^3*x^2 + 2*(B*a*b^5 - 8*B*a^2*b^3*c + 16*B*a^3*b*c^2)*e^3*x + (B*a^2*b^4 - 8*B*a^3*b^2*c + 16*B*a^4*c^2)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(24*(2*B*a^3 - A*a^2*b)*c^3*d*e^2 + (4*(2*B*a^2 - 3*A*a*b)*c^4 + (2*B*a*b^2 + A*b^3)*c^3)*d^3 + 6*(4*A*a^2*c^4 - (4*B*a^2*b - A*a*b^2)*c^3)*d^2*e + (3*B*a^2*b^3*c - 20*B*a^3*b*c^2 + 16*A*a^3*c^3)*e^3 + (8*(B*b*c^5 - 2*A*c^6)*d^3 - 6*(B*b^2*c^4 + 4*(B*a - A*b)*c^5)*d^2*e - 3*(B*b^3*c^3 + 8*A*a*c^5 - 2*(6*B*a*b - A*b^2)*c^4)*d*e^2 + (4*B*b^4*c^2 + 4*(8*B*a^2 + 3*A*a*b)*c^4 - (28*B*a*b^2 + A*b^3)*c^3)*e^3)*x^3 + 3*(4*(B*b^2*c^4 - 2*A*b*c^5)*d^3 - 3*(B*b^3*c^3 + 4*(B*a*b - A*b^2)*c^4)*d^2*e + 3*(4*(2*B*a^2 - A*a*b)*c^4 + (2*B*a*b^2 - A*b^3)*c^3)*d*e^2 + (B*b^5*c - 6*B*a*b^3*c^2 + 2*A*a*b^2*c^3 + 8*A*a^2*c^4)*e^3)*x^2 + 3*(12*(2*B*a^2*b - A*a*b^2)*c^3*d*e^2 + (B*b^3*c^3 - 8*A*a*c^5 + 2*(2*B*a*b - A*b^2)*c^4)*d^3 + 3*(4*A*a*b*c^4 - (4*B*a*b^2 - A*b^3)*c^3)*d^2*e + 2*(B*a*b^4*c - 7*B*a^2*b^2*c^2 + 4*(B*a^3 + A*a^2*b)*c^3)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x)]","B",0
2482,1,469,0,9.118904," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d^{2} - 4 \, {\left(B b^{2} c + 4 \, {\left(B a - A b\right)} c^{2}\right)} d e - {\left(B b^{3} + 8 \, A a c^{2} - 2 \, {\left(6 \, B a b - A b^{2}\right)} c\right)} e^{2}\right)} x^{3} + {\left(2 \, B a b^{2} + A b^{3} + 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} d^{2} - 4 \, {\left(4 \, B a^{2} b - A a b^{2} - 4 \, A a^{2} c\right)} d e + 8 \, {\left(2 \, B a^{3} - A a^{2} b\right)} e^{2} + 3 \, {\left(4 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d^{2} - 2 \, {\left(B b^{3} + 4 \, {\left(B a b - A b^{2}\right)} c\right)} d e + {\left(2 \, B a b^{2} - A b^{3} + 4 \, {\left(2 \, B a^{2} - A a b\right)} c\right)} e^{2}\right)} x^{2} + 3 \, {\left({\left(B b^{3} - 8 \, A a c^{2} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c\right)} d^{2} - 2 \, {\left(4 \, B a b^{2} - A b^{3} - 4 \, A a b c\right)} d e + 4 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"-2/3*((8*(B*b*c^2 - 2*A*c^3)*d^2 - 4*(B*b^2*c + 4*(B*a - A*b)*c^2)*d*e - (B*b^3 + 8*A*a*c^2 - 2*(6*B*a*b - A*b^2)*c)*e^2)*x^3 + (2*B*a*b^2 + A*b^3 + 4*(2*B*a^2 - 3*A*a*b)*c)*d^2 - 4*(4*B*a^2*b - A*a*b^2 - 4*A*a^2*c)*d*e + 8*(2*B*a^3 - A*a^2*b)*e^2 + 3*(4*(B*b^2*c - 2*A*b*c^2)*d^2 - 2*(B*b^3 + 4*(B*a*b - A*b^2)*c)*d*e + (2*B*a*b^2 - A*b^3 + 4*(2*B*a^2 - A*a*b)*c)*e^2)*x^2 + 3*((B*b^3 - 8*A*a*c^2 + 2*(2*B*a*b - A*b^2)*c)*d^2 - 2*(4*B*a*b^2 - A*b^3 - 4*A*a*b*c)*d*e + 4*(2*B*a^2*b - A*a*b^2)*e^2)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
2483,1,353,0,8.907516," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, {\left(4 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} d - {\left(B b^{2} c + 4 \, {\left(B a - A b\right)} c^{2}\right)} e\right)} x^{3} + 3 \, {\left(4 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} d - {\left(B b^{3} + 4 \, {\left(B a b - A b^{2}\right)} c\right)} e\right)} x^{2} + {\left(2 \, B a b^{2} + A b^{3} + 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} d - 2 \, {\left(4 \, B a^{2} b - A a b^{2} - 4 \, A a^{2} c\right)} e + 3 \, {\left({\left(B b^{3} - 8 \, A a c^{2} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c\right)} d - {\left(4 \, B a b^{2} - A b^{3} - 4 \, A a b c\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"-2/3*(2*(4*(B*b*c^2 - 2*A*c^3)*d - (B*b^2*c + 4*(B*a - A*b)*c^2)*e)*x^3 + 3*(4*(B*b^2*c - 2*A*b*c^2)*d - (B*b^3 + 4*(B*a*b - A*b^2)*c)*e)*x^2 + (2*B*a*b^2 + A*b^3 + 4*(2*B*a^2 - 3*A*a*b)*c)*d - 2*(4*B*a^2*b - A*a*b^2 - 4*A*a^2*c)*e + 3*((B*b^3 - 8*A*a*c^2 + 2*(2*B*a*b - A*b^2)*c)*d - (4*B*a*b^2 - A*b^3 - 4*A*a*b*c)*e)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
2484,1,245,0,1.096547," ","integrate((B*x+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, B a b^{2} + A b^{3} + 8 \, {\left(B b c^{2} - 2 \, A c^{3}\right)} x^{3} + 12 \, {\left(B b^{2} c - 2 \, A b c^{2}\right)} x^{2} + 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c + 3 \, {\left(B b^{3} - 8 \, A a c^{2} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"-2/3*(2*B*a*b^2 + A*b^3 + 8*(B*b*c^2 - 2*A*c^3)*x^3 + 12*(B*b^2*c - 2*A*b*c^2)*x^2 + 4*(2*B*a^2 - 3*A*a*b)*c + 3*(B*b^3 - 8*A*a*c^2 + 2*(2*B*a*b - A*b^2)*c)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
2485,1,6068,0,24.722414," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(B a^{2} b^{4} - 8 \, B a^{3} b^{2} c + 16 \, B a^{4} c^{2}\right)} d e^{3} - {\left(A a^{2} b^{4} - 8 \, A a^{3} b^{2} c + 16 \, A a^{4} c^{2}\right)} e^{4} + {\left({\left(B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right)} d e^{3} - {\left(A b^{4} c^{2} - 8 \, A a b^{2} c^{3} + 16 \, A a^{2} c^{4}\right)} e^{4}\right)} x^{4} + 2 \, {\left({\left(B b^{5} c - 8 \, B a b^{3} c^{2} + 16 \, B a^{2} b c^{3}\right)} d e^{3} - {\left(A b^{5} c - 8 \, A a b^{3} c^{2} + 16 \, A a^{2} b c^{3}\right)} e^{4}\right)} x^{3} + {\left({\left(B b^{6} - 6 \, B a b^{4} c + 32 \, B a^{3} c^{3}\right)} d e^{3} - {\left(A b^{6} - 6 \, A a b^{4} c + 32 \, A a^{3} c^{3}\right)} e^{4}\right)} x^{2} + 2 \, {\left({\left(B a b^{5} - 8 \, B a^{2} b^{3} c + 16 \, B a^{3} b c^{2}\right)} d e^{3} - {\left(A a b^{5} - 8 \, A a^{2} b^{3} c + 16 \, A a^{3} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left({\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{4} + {\left(2 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{5} - {\left(8 \, A a^{2} c^{4} + 2 \, {\left(8 \, B a^{2} b - 17 \, A a b^{2}\right)} c^{3} + 3 \, {\left(2 \, B a b^{3} + A b^{4}\right)} c^{2}\right)} d^{4} e + {\left(20 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{3} + 3 \, {\left(2 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} c^{2} + 3 \, {\left(2 \, B a b^{4} + A b^{5}\right)} c\right)} d^{3} e^{2} - {\left(2 \, B a b^{5} + A b^{6} - B a^{2} b^{3} c + 40 \, A a^{3} c^{3} + 2 \, {\left(26 \, B a^{3} b - 33 \, A a^{2} b^{2}\right)} c^{2}\right)} d^{2} e^{3} + {\left(B a^{2} b^{4} + 5 \, A a b^{5} + 16 \, {\left(2 \, B a^{4} + A a^{3} b\right)} c^{2} + 2 \, {\left(4 \, B a^{3} b^{2} - 17 \, A a^{2} b^{3}\right)} c\right)} d e^{4} + {\left(B a^{3} b^{3} - 4 \, A a^{2} b^{4} - 32 \, A a^{4} c^{2} - 4 \, {\left(3 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} c\right)} e^{5} + {\left(8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} - 2 \, {\left(11 \, B b^{2} c^{4} - 4 \, {\left(B a + 5 \, A b\right)} c^{5}\right)} d^{4} e + {\left(17 \, B b^{3} c^{3} - 56 \, A a c^{5} + 2 \, {\left(6 \, B a b - 13 \, A b^{2}\right)} c^{4}\right)} d^{3} e^{2} - {\left(3 \, B b^{4} c^{2} + 4 \, {\left(2 \, B a^{2} - 21 \, A a b\right)} c^{4} + {\left(26 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{2} e^{3} - {\left(40 \, A a^{2} c^{4} - 2 \, {\left(14 \, B a^{2} b - 11 \, A a b^{2}\right)} c^{3} - 3 \, {\left(B a b^{3} + A b^{4}\right)} c^{2}\right)} d e^{4} - {\left(3 \, A a b^{3} c^{2} + 4 \, {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} c^{3}\right)} e^{5}\right)} x^{3} + 3 \, {\left(4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} - {\left(11 \, B b^{3} c^{3} - 4 \, {\left(B a b + 5 \, A b^{2}\right)} c^{4}\right)} d^{4} e + {\left(9 \, B b^{4} c^{2} + 4 \, {\left(2 \, B a^{2} - 7 \, A a b\right)} c^{4} + {\left(2 \, B a b^{2} - 13 \, A b^{3}\right)} c^{3}\right)} d^{3} e^{2} - {\left(2 \, B b^{5} c + 8 \, A a^{2} c^{4} + 2 \, {\left(6 \, B a^{2} b - 23 \, A a b^{2}\right)} c^{3} + {\left(9 \, B a b^{3} + A b^{4}\right)} c^{2}\right)} d^{2} e^{3} + {\left(4 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{3} + 5 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} c^{2} + 2 \, {\left(B a b^{4} + A b^{5}\right)} c\right)} d e^{4} - 2 \, {\left(A a b^{4} c + 4 \, A a^{3} c^{3} + {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} c^{2}\right)} e^{5}\right)} x^{2} + 3 \, {\left({\left(B b^{3} c^{3} - 8 \, A a c^{5} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c^{4}\right)} d^{5} - {\left(3 \, B b^{4} c^{2} - 20 \, A a b c^{4} + {\left(8 \, B a b^{2} - 5 \, A b^{3}\right)} c^{3}\right)} d^{4} e + {\left(3 \, B b^{5} c - 24 \, A a^{2} c^{4} + 2 \, {\left(10 \, B a^{2} b - 11 \, A a b^{2}\right)} c^{3} + 3 \, {\left(B a b^{3} - A b^{4}\right)} c^{2}\right)} d^{3} e^{2} - {\left(B b^{6} + A b^{5} c + 4 \, {\left(2 \, B a^{3} - 7 \, A a^{2} b\right)} c^{3} + {\left(22 \, B a^{2} b^{2} - 17 \, A a b^{3}\right)} c^{2}\right)} d^{2} e^{3} + {\left(B a b^{5} + A b^{6} - 6 \, A a b^{4} c - 16 \, A a^{3} c^{3} + 8 \, {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} c^{2}\right)} d e^{4} - {\left(A a b^{5} + 8 \, B a^{4} c^{2} + 2 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left({\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{6} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e + 3 \, {\left(a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} e^{2} - {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 32 \, a^{4} b^{3} c^{2} + 96 \, a^{5} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} b^{6} - 7 \, a^{4} b^{4} c + 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} + {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{6} - 3 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{5} e + 3 \, {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{4} e^{2} - {\left(b^{7} c^{2} - 2 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 96 \, a^{3} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(a b^{6} c^{2} - 7 \, a^{2} b^{4} c^{3} + 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{5} + {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left({\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{6} - 3 \, {\left(b^{6} c^{3} - 8 \, a b^{4} c^{4} + 16 \, a^{2} b^{2} c^{5}\right)} d^{5} e + 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{2} - {\left(b^{8} c - 2 \, a b^{6} c^{2} - 32 \, a^{2} b^{4} c^{3} + 96 \, a^{3} b^{2} c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{6} c - 8 \, a^{3} b^{4} c^{2} + 16 \, a^{4} b^{2} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} e^{6}\right)} x^{3} + {\left({\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} d^{6} - 3 \, {\left(b^{7} c^{2} - 6 \, a b^{5} c^{3} + 32 \, a^{3} b c^{5}\right)} d^{5} e + 3 \, {\left(b^{8} c - 5 \, a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} + 32 \, a^{4} c^{5}\right)} d^{4} e^{2} - {\left(b^{9} - 36 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} + 192 \, a^{4} b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{8} - 5 \, a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{4} b^{2} c^{3} + 32 \, a^{5} c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{7} - 6 \, a^{3} b^{5} c + 32 \, a^{5} b c^{3}\right)} d e^{5} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{6} - 3 \, {\left(a b^{6} c^{2} - 8 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4}\right)} d^{5} e + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{4} e^{2} - {\left(a b^{8} - 2 \, a^{2} b^{6} c - 32 \, a^{3} b^{4} c^{2} + 96 \, a^{4} b^{2} c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{3} b^{6} - 8 \, a^{4} b^{4} c + 16 \, a^{5} b^{2} c^{2}\right)} d e^{5} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} e^{6}\right)} x\right)}}, -\frac{3 \, {\left({\left(B a^{2} b^{4} - 8 \, B a^{3} b^{2} c + 16 \, B a^{4} c^{2}\right)} d e^{3} - {\left(A a^{2} b^{4} - 8 \, A a^{3} b^{2} c + 16 \, A a^{4} c^{2}\right)} e^{4} + {\left({\left(B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right)} d e^{3} - {\left(A b^{4} c^{2} - 8 \, A a b^{2} c^{3} + 16 \, A a^{2} c^{4}\right)} e^{4}\right)} x^{4} + 2 \, {\left({\left(B b^{5} c - 8 \, B a b^{3} c^{2} + 16 \, B a^{2} b c^{3}\right)} d e^{3} - {\left(A b^{5} c - 8 \, A a b^{3} c^{2} + 16 \, A a^{2} b c^{3}\right)} e^{4}\right)} x^{3} + {\left({\left(B b^{6} - 6 \, B a b^{4} c + 32 \, B a^{3} c^{3}\right)} d e^{3} - {\left(A b^{6} - 6 \, A a b^{4} c + 32 \, A a^{3} c^{3}\right)} e^{4}\right)} x^{2} + 2 \, {\left({\left(B a b^{5} - 8 \, B a^{2} b^{3} c + 16 \, B a^{3} b c^{2}\right)} d e^{3} - {\left(A a b^{5} - 8 \, A a^{2} b^{3} c + 16 \, A a^{3} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left({\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{4} + {\left(2 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{5} - {\left(8 \, A a^{2} c^{4} + 2 \, {\left(8 \, B a^{2} b - 17 \, A a b^{2}\right)} c^{3} + 3 \, {\left(2 \, B a b^{3} + A b^{4}\right)} c^{2}\right)} d^{4} e + {\left(20 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{3} + 3 \, {\left(2 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} c^{2} + 3 \, {\left(2 \, B a b^{4} + A b^{5}\right)} c\right)} d^{3} e^{2} - {\left(2 \, B a b^{5} + A b^{6} - B a^{2} b^{3} c + 40 \, A a^{3} c^{3} + 2 \, {\left(26 \, B a^{3} b - 33 \, A a^{2} b^{2}\right)} c^{2}\right)} d^{2} e^{3} + {\left(B a^{2} b^{4} + 5 \, A a b^{5} + 16 \, {\left(2 \, B a^{4} + A a^{3} b\right)} c^{2} + 2 \, {\left(4 \, B a^{3} b^{2} - 17 \, A a^{2} b^{3}\right)} c\right)} d e^{4} + {\left(B a^{3} b^{3} - 4 \, A a^{2} b^{4} - 32 \, A a^{4} c^{2} - 4 \, {\left(3 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} c\right)} e^{5} + {\left(8 \, {\left(B b c^{5} - 2 \, A c^{6}\right)} d^{5} - 2 \, {\left(11 \, B b^{2} c^{4} - 4 \, {\left(B a + 5 \, A b\right)} c^{5}\right)} d^{4} e + {\left(17 \, B b^{3} c^{3} - 56 \, A a c^{5} + 2 \, {\left(6 \, B a b - 13 \, A b^{2}\right)} c^{4}\right)} d^{3} e^{2} - {\left(3 \, B b^{4} c^{2} + 4 \, {\left(2 \, B a^{2} - 21 \, A a b\right)} c^{4} + {\left(26 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{2} e^{3} - {\left(40 \, A a^{2} c^{4} - 2 \, {\left(14 \, B a^{2} b - 11 \, A a b^{2}\right)} c^{3} - 3 \, {\left(B a b^{3} + A b^{4}\right)} c^{2}\right)} d e^{4} - {\left(3 \, A a b^{3} c^{2} + 4 \, {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} c^{3}\right)} e^{5}\right)} x^{3} + 3 \, {\left(4 \, {\left(B b^{2} c^{4} - 2 \, A b c^{5}\right)} d^{5} - {\left(11 \, B b^{3} c^{3} - 4 \, {\left(B a b + 5 \, A b^{2}\right)} c^{4}\right)} d^{4} e + {\left(9 \, B b^{4} c^{2} + 4 \, {\left(2 \, B a^{2} - 7 \, A a b\right)} c^{4} + {\left(2 \, B a b^{2} - 13 \, A b^{3}\right)} c^{3}\right)} d^{3} e^{2} - {\left(2 \, B b^{5} c + 8 \, A a^{2} c^{4} + 2 \, {\left(6 \, B a^{2} b - 23 \, A a b^{2}\right)} c^{3} + {\left(9 \, B a b^{3} + A b^{4}\right)} c^{2}\right)} d^{2} e^{3} + {\left(4 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{3} + 5 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} c^{2} + 2 \, {\left(B a b^{4} + A b^{5}\right)} c\right)} d e^{4} - 2 \, {\left(A a b^{4} c + 4 \, A a^{3} c^{3} + {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} c^{2}\right)} e^{5}\right)} x^{2} + 3 \, {\left({\left(B b^{3} c^{3} - 8 \, A a c^{5} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c^{4}\right)} d^{5} - {\left(3 \, B b^{4} c^{2} - 20 \, A a b c^{4} + {\left(8 \, B a b^{2} - 5 \, A b^{3}\right)} c^{3}\right)} d^{4} e + {\left(3 \, B b^{5} c - 24 \, A a^{2} c^{4} + 2 \, {\left(10 \, B a^{2} b - 11 \, A a b^{2}\right)} c^{3} + 3 \, {\left(B a b^{3} - A b^{4}\right)} c^{2}\right)} d^{3} e^{2} - {\left(B b^{6} + A b^{5} c + 4 \, {\left(2 \, B a^{3} - 7 \, A a^{2} b\right)} c^{3} + {\left(22 \, B a^{2} b^{2} - 17 \, A a b^{3}\right)} c^{2}\right)} d^{2} e^{3} + {\left(B a b^{5} + A b^{6} - 6 \, A a b^{4} c - 16 \, A a^{3} c^{3} + 8 \, {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} c^{2}\right)} d e^{4} - {\left(A a b^{5} + 8 \, B a^{4} c^{2} + 2 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left({\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{6} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e + 3 \, {\left(a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} e^{2} - {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 32 \, a^{4} b^{3} c^{2} + 96 \, a^{5} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} b^{6} - 7 \, a^{4} b^{4} c + 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} + {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{6} - 3 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{5} e + 3 \, {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{4} e^{2} - {\left(b^{7} c^{2} - 2 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 96 \, a^{3} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(a b^{6} c^{2} - 7 \, a^{2} b^{4} c^{3} + 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{5} + {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left({\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{6} - 3 \, {\left(b^{6} c^{3} - 8 \, a b^{4} c^{4} + 16 \, a^{2} b^{2} c^{5}\right)} d^{5} e + 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{2} - {\left(b^{8} c - 2 \, a b^{6} c^{2} - 32 \, a^{2} b^{4} c^{3} + 96 \, a^{3} b^{2} c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{6} c - 8 \, a^{3} b^{4} c^{2} + 16 \, a^{4} b^{2} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} e^{6}\right)} x^{3} + {\left({\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} d^{6} - 3 \, {\left(b^{7} c^{2} - 6 \, a b^{5} c^{3} + 32 \, a^{3} b c^{5}\right)} d^{5} e + 3 \, {\left(b^{8} c - 5 \, a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} + 32 \, a^{4} c^{5}\right)} d^{4} e^{2} - {\left(b^{9} - 36 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} + 192 \, a^{4} b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{8} - 5 \, a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{4} b^{2} c^{3} + 32 \, a^{5} c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{7} - 6 \, a^{3} b^{5} c + 32 \, a^{5} b c^{3}\right)} d e^{5} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{6} - 3 \, {\left(a b^{6} c^{2} - 8 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4}\right)} d^{5} e + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{4} e^{2} - {\left(a b^{8} - 2 \, a^{2} b^{6} c - 32 \, a^{3} b^{4} c^{2} + 96 \, a^{4} b^{2} c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{3} b^{6} - 8 \, a^{4} b^{4} c + 16 \, a^{5} b^{2} c^{2}\right)} d e^{5} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/6*(3*((B*a^2*b^4 - 8*B*a^3*b^2*c + 16*B*a^4*c^2)*d*e^3 - (A*a^2*b^4 - 8*A*a^3*b^2*c + 16*A*a^4*c^2)*e^4 + ((B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*d*e^3 - (A*b^4*c^2 - 8*A*a*b^2*c^3 + 16*A*a^2*c^4)*e^4)*x^4 + 2*((B*b^5*c - 8*B*a*b^3*c^2 + 16*B*a^2*b*c^3)*d*e^3 - (A*b^5*c - 8*A*a*b^3*c^2 + 16*A*a^2*b*c^3)*e^4)*x^3 + ((B*b^6 - 6*B*a*b^4*c + 32*B*a^3*c^3)*d*e^3 - (A*b^6 - 6*A*a*b^4*c + 32*A*a^3*c^3)*e^4)*x^2 + 2*((B*a*b^5 - 8*B*a^2*b^3*c + 16*B*a^3*b*c^2)*d*e^3 - (A*a*b^5 - 8*A*a^2*b^3*c + 16*A*a^3*b*c^2)*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*((4*(2*B*a^2 - 3*A*a*b)*c^4 + (2*B*a*b^2 + A*b^3)*c^3)*d^5 - (8*A*a^2*c^4 + 2*(8*B*a^2*b - 17*A*a*b^2)*c^3 + 3*(2*B*a*b^3 + A*b^4)*c^2)*d^4*e + (20*(2*B*a^3 - A*a^2*b)*c^3 + 3*(2*B*a^2*b^2 - 9*A*a*b^3)*c^2 + 3*(2*B*a*b^4 + A*b^5)*c)*d^3*e^2 - (2*B*a*b^5 + A*b^6 - B*a^2*b^3*c + 40*A*a^3*c^3 + 2*(26*B*a^3*b - 33*A*a^2*b^2)*c^2)*d^2*e^3 + (B*a^2*b^4 + 5*A*a*b^5 + 16*(2*B*a^4 + A*a^3*b)*c^2 + 2*(4*B*a^3*b^2 - 17*A*a^2*b^3)*c)*d*e^4 + (B*a^3*b^3 - 4*A*a^2*b^4 - 32*A*a^4*c^2 - 4*(3*B*a^4*b - 7*A*a^3*b^2)*c)*e^5 + (8*(B*b*c^5 - 2*A*c^6)*d^5 - 2*(11*B*b^2*c^4 - 4*(B*a + 5*A*b)*c^5)*d^4*e + (17*B*b^3*c^3 - 56*A*a*c^5 + 2*(6*B*a*b - 13*A*b^2)*c^4)*d^3*e^2 - (3*B*b^4*c^2 + 4*(2*B*a^2 - 21*A*a*b)*c^4 + (26*B*a*b^2 + A*b^3)*c^3)*d^2*e^3 - (40*A*a^2*c^4 - 2*(14*B*a^2*b - 11*A*a*b^2)*c^3 - 3*(B*a*b^3 + A*b^4)*c^2)*d*e^4 - (3*A*a*b^3*c^2 + 4*(4*B*a^3 - 5*A*a^2*b)*c^3)*e^5)*x^3 + 3*(4*(B*b^2*c^4 - 2*A*b*c^5)*d^5 - (11*B*b^3*c^3 - 4*(B*a*b + 5*A*b^2)*c^4)*d^4*e + (9*B*b^4*c^2 + 4*(2*B*a^2 - 7*A*a*b)*c^4 + (2*B*a*b^2 - 13*A*b^3)*c^3)*d^3*e^2 - (2*B*b^5*c + 8*A*a^2*c^4 + 2*(6*B*a^2*b - 23*A*a*b^2)*c^3 + (9*B*a*b^3 + A*b^4)*c^2)*d^2*e^3 + (4*(2*B*a^3 - 3*A*a^2*b)*c^3 + 5*(2*B*a^2*b^2 - 3*A*a*b^3)*c^2 + 2*(B*a*b^4 + A*b^5)*c)*d*e^4 - 2*(A*a*b^4*c + 4*A*a^3*c^3 + (4*B*a^3*b - 7*A*a^2*b^2)*c^2)*e^5)*x^2 + 3*((B*b^3*c^3 - 8*A*a*c^5 + 2*(2*B*a*b - A*b^2)*c^4)*d^5 - (3*B*b^4*c^2 - 20*A*a*b*c^4 + (8*B*a*b^2 - 5*A*b^3)*c^3)*d^4*e + (3*B*b^5*c - 24*A*a^2*c^4 + 2*(10*B*a^2*b - 11*A*a*b^2)*c^3 + 3*(B*a*b^3 - A*b^4)*c^2)*d^3*e^2 - (B*b^6 + A*b^5*c + 4*(2*B*a^3 - 7*A*a^2*b)*c^3 + (22*B*a^2*b^2 - 17*A*a*b^3)*c^2)*d^2*e^3 + (B*a*b^5 + A*b^6 - 6*A*a*b^4*c - 16*A*a^3*c^3 + 8*(3*B*a^3*b - A*a^2*b^2)*c^2)*d*e^4 - (A*a*b^5 + 8*B*a^4*c^2 + 2*(B*a^3*b^2 - 3*A*a^2*b^3)*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^6 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e + 3*(a^2*b^6*c - 7*a^3*b^4*c^2 + 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4*e^2 - (a^2*b^7 - 2*a^3*b^5*c - 32*a^4*b^3*c^2 + 96*a^5*b*c^3)*d^3*e^3 + 3*(a^3*b^6 - 7*a^4*b^4*c + 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^4 - 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 + ((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^6 - 3*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^5*e + 3*(b^6*c^3 - 7*a*b^4*c^4 + 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^4*e^2 - (b^7*c^2 - 2*a*b^5*c^3 - 32*a^2*b^3*c^4 + 96*a^3*b*c^5)*d^3*e^3 + 3*(a*b^6*c^2 - 7*a^2*b^4*c^3 + 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^2*e^4 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^5 + (a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^6)*x^4 + 2*((b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^6 - 3*(b^6*c^3 - 8*a*b^4*c^4 + 16*a^2*b^2*c^5)*d^5*e + 3*(b^7*c^2 - 7*a*b^5*c^3 + 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^2 - (b^8*c - 2*a*b^6*c^2 - 32*a^2*b^4*c^3 + 96*a^3*b^2*c^4)*d^3*e^3 + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^4 - 3*(a^2*b^6*c - 8*a^3*b^4*c^2 + 16*a^4*b^2*c^3)*d*e^5 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*e^6)*x^3 + ((b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*d^6 - 3*(b^7*c^2 - 6*a*b^5*c^3 + 32*a^3*b*c^5)*d^5*e + 3*(b^8*c - 5*a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^3*b^2*c^4 + 32*a^4*c^5)*d^4*e^2 - (b^9 - 36*a^2*b^5*c^2 + 32*a^3*b^3*c^3 + 192*a^4*b*c^4)*d^3*e^3 + 3*(a*b^8 - 5*a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^4*b^2*c^3 + 32*a^5*c^4)*d^2*e^4 - 3*(a^2*b^7 - 6*a^3*b^5*c + 32*a^5*b*c^3)*d*e^5 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*e^6)*x^2 + 2*((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^6 - 3*(a*b^6*c^2 - 8*a^2*b^4*c^3 + 16*a^3*b^2*c^4)*d^5*e + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^4*e^2 - (a*b^8 - 2*a^2*b^6*c - 32*a^3*b^4*c^2 + 96*a^4*b^2*c^3)*d^3*e^3 + 3*(a^2*b^7 - 7*a^3*b^5*c + 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2*e^4 - 3*(a^3*b^6 - 8*a^4*b^4*c + 16*a^5*b^2*c^2)*d*e^5 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*e^6)*x), -1/3*(3*((B*a^2*b^4 - 8*B*a^3*b^2*c + 16*B*a^4*c^2)*d*e^3 - (A*a^2*b^4 - 8*A*a^3*b^2*c + 16*A*a^4*c^2)*e^4 + ((B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*d*e^3 - (A*b^4*c^2 - 8*A*a*b^2*c^3 + 16*A*a^2*c^4)*e^4)*x^4 + 2*((B*b^5*c - 8*B*a*b^3*c^2 + 16*B*a^2*b*c^3)*d*e^3 - (A*b^5*c - 8*A*a*b^3*c^2 + 16*A*a^2*b*c^3)*e^4)*x^3 + ((B*b^6 - 6*B*a*b^4*c + 32*B*a^3*c^3)*d*e^3 - (A*b^6 - 6*A*a*b^4*c + 32*A*a^3*c^3)*e^4)*x^2 + 2*((B*a*b^5 - 8*B*a^2*b^3*c + 16*B*a^3*b*c^2)*d*e^3 - (A*a*b^5 - 8*A*a^2*b^3*c + 16*A*a^3*b*c^2)*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*((4*(2*B*a^2 - 3*A*a*b)*c^4 + (2*B*a*b^2 + A*b^3)*c^3)*d^5 - (8*A*a^2*c^4 + 2*(8*B*a^2*b - 17*A*a*b^2)*c^3 + 3*(2*B*a*b^3 + A*b^4)*c^2)*d^4*e + (20*(2*B*a^3 - A*a^2*b)*c^3 + 3*(2*B*a^2*b^2 - 9*A*a*b^3)*c^2 + 3*(2*B*a*b^4 + A*b^5)*c)*d^3*e^2 - (2*B*a*b^5 + A*b^6 - B*a^2*b^3*c + 40*A*a^3*c^3 + 2*(26*B*a^3*b - 33*A*a^2*b^2)*c^2)*d^2*e^3 + (B*a^2*b^4 + 5*A*a*b^5 + 16*(2*B*a^4 + A*a^3*b)*c^2 + 2*(4*B*a^3*b^2 - 17*A*a^2*b^3)*c)*d*e^4 + (B*a^3*b^3 - 4*A*a^2*b^4 - 32*A*a^4*c^2 - 4*(3*B*a^4*b - 7*A*a^3*b^2)*c)*e^5 + (8*(B*b*c^5 - 2*A*c^6)*d^5 - 2*(11*B*b^2*c^4 - 4*(B*a + 5*A*b)*c^5)*d^4*e + (17*B*b^3*c^3 - 56*A*a*c^5 + 2*(6*B*a*b - 13*A*b^2)*c^4)*d^3*e^2 - (3*B*b^4*c^2 + 4*(2*B*a^2 - 21*A*a*b)*c^4 + (26*B*a*b^2 + A*b^3)*c^3)*d^2*e^3 - (40*A*a^2*c^4 - 2*(14*B*a^2*b - 11*A*a*b^2)*c^3 - 3*(B*a*b^3 + A*b^4)*c^2)*d*e^4 - (3*A*a*b^3*c^2 + 4*(4*B*a^3 - 5*A*a^2*b)*c^3)*e^5)*x^3 + 3*(4*(B*b^2*c^4 - 2*A*b*c^5)*d^5 - (11*B*b^3*c^3 - 4*(B*a*b + 5*A*b^2)*c^4)*d^4*e + (9*B*b^4*c^2 + 4*(2*B*a^2 - 7*A*a*b)*c^4 + (2*B*a*b^2 - 13*A*b^3)*c^3)*d^3*e^2 - (2*B*b^5*c + 8*A*a^2*c^4 + 2*(6*B*a^2*b - 23*A*a*b^2)*c^3 + (9*B*a*b^3 + A*b^4)*c^2)*d^2*e^3 + (4*(2*B*a^3 - 3*A*a^2*b)*c^3 + 5*(2*B*a^2*b^2 - 3*A*a*b^3)*c^2 + 2*(B*a*b^4 + A*b^5)*c)*d*e^4 - 2*(A*a*b^4*c + 4*A*a^3*c^3 + (4*B*a^3*b - 7*A*a^2*b^2)*c^2)*e^5)*x^2 + 3*((B*b^3*c^3 - 8*A*a*c^5 + 2*(2*B*a*b - A*b^2)*c^4)*d^5 - (3*B*b^4*c^2 - 20*A*a*b*c^4 + (8*B*a*b^2 - 5*A*b^3)*c^3)*d^4*e + (3*B*b^5*c - 24*A*a^2*c^4 + 2*(10*B*a^2*b - 11*A*a*b^2)*c^3 + 3*(B*a*b^3 - A*b^4)*c^2)*d^3*e^2 - (B*b^6 + A*b^5*c + 4*(2*B*a^3 - 7*A*a^2*b)*c^3 + (22*B*a^2*b^2 - 17*A*a*b^3)*c^2)*d^2*e^3 + (B*a*b^5 + A*b^6 - 6*A*a*b^4*c - 16*A*a^3*c^3 + 8*(3*B*a^3*b - A*a^2*b^2)*c^2)*d*e^4 - (A*a*b^5 + 8*B*a^4*c^2 + 2*(B*a^3*b^2 - 3*A*a^2*b^3)*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^6 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e + 3*(a^2*b^6*c - 7*a^3*b^4*c^2 + 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4*e^2 - (a^2*b^7 - 2*a^3*b^5*c - 32*a^4*b^3*c^2 + 96*a^5*b*c^3)*d^3*e^3 + 3*(a^3*b^6 - 7*a^4*b^4*c + 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^4 - 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 + ((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^6 - 3*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^5*e + 3*(b^6*c^3 - 7*a*b^4*c^4 + 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^4*e^2 - (b^7*c^2 - 2*a*b^5*c^3 - 32*a^2*b^3*c^4 + 96*a^3*b*c^5)*d^3*e^3 + 3*(a*b^6*c^2 - 7*a^2*b^4*c^3 + 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^2*e^4 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^5 + (a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^6)*x^4 + 2*((b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^6 - 3*(b^6*c^3 - 8*a*b^4*c^4 + 16*a^2*b^2*c^5)*d^5*e + 3*(b^7*c^2 - 7*a*b^5*c^3 + 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^2 - (b^8*c - 2*a*b^6*c^2 - 32*a^2*b^4*c^3 + 96*a^3*b^2*c^4)*d^3*e^3 + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^4 - 3*(a^2*b^6*c - 8*a^3*b^4*c^2 + 16*a^4*b^2*c^3)*d*e^5 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*e^6)*x^3 + ((b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*d^6 - 3*(b^7*c^2 - 6*a*b^5*c^3 + 32*a^3*b*c^5)*d^5*e + 3*(b^8*c - 5*a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^3*b^2*c^4 + 32*a^4*c^5)*d^4*e^2 - (b^9 - 36*a^2*b^5*c^2 + 32*a^3*b^3*c^3 + 192*a^4*b*c^4)*d^3*e^3 + 3*(a*b^8 - 5*a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^4*b^2*c^3 + 32*a^5*c^4)*d^2*e^4 - 3*(a^2*b^7 - 6*a^3*b^5*c + 32*a^5*b*c^3)*d*e^5 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*e^6)*x^2 + 2*((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^6 - 3*(a*b^6*c^2 - 8*a^2*b^4*c^3 + 16*a^3*b^2*c^4)*d^5*e + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^4*e^2 - (a*b^8 - 2*a^2*b^6*c - 32*a^3*b^4*c^2 + 96*a^4*b^2*c^3)*d^3*e^3 + 3*(a^2*b^7 - 7*a^3*b^5*c + 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2*e^4 - 3*(a^3*b^6 - 8*a^4*b^4*c + 16*a^5*b^2*c^2)*d*e^5 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*e^6)*x)]","B",0
2486,1,12690,0,103.118012," ","integrate((B*x+A)/(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, {\left(B a^{2} b^{4} c - 8 \, B a^{3} b^{2} c^{2} + 16 \, B a^{4} c^{3}\right)} d^{3} e^{3} - {\left(3 \, B a^{2} b^{5} + 160 \, A a^{4} c^{3} + 16 \, {\left(3 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} c^{2} - 2 \, {\left(12 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} d^{2} e^{4} - {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(2 \, B a^{5} - 5 \, A a^{4} b\right)} c^{2} - 8 \, {\left(2 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} c\right)} d e^{5} + {\left(8 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} d^{2} e^{4} - {\left(3 \, B b^{5} c^{2} + 160 \, A a^{2} c^{5} + 16 \, {\left(3 \, B a^{2} b - 5 \, A a b^{2}\right)} c^{4} - 2 \, {\left(12 \, B a b^{3} - 5 \, A b^{4}\right)} c^{3}\right)} d e^{5} - {\left(16 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{4} - 8 \, {\left(2 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{3} + {\left(2 \, B a b^{4} - 5 \, A b^{5}\right)} c^{2}\right)} e^{6}\right)} x^{5} + {\left(8 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} d^{3} e^{3} + {\left(13 \, B b^{5} c^{2} - 160 \, A a^{2} c^{5} + 16 \, {\left(13 \, B a^{2} b + 5 \, A a b^{2}\right)} c^{4} - 2 \, {\left(52 \, B a b^{3} + 5 \, A b^{4}\right)} c^{3}\right)} d^{2} e^{4} - {\left(6 \, B b^{6} c + 16 \, {\left(2 \, B a^{3} + 15 \, A a^{2} b\right)} c^{4} + 40 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} c^{3} - {\left(46 \, B a b^{4} - 15 \, A b^{5}\right)} c^{2}\right)} d e^{5} - 2 \, {\left(16 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3} - 8 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2} + {\left(2 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} e^{6}\right)} x^{4} + {\left(16 \, {\left(B b^{5} c^{2} - 8 \, B a b^{3} c^{3} + 16 \, B a^{2} b c^{4}\right)} d^{3} e^{3} + 2 \, {\left(B b^{6} c - 10 \, A b^{5} c^{2} + 32 \, {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} c^{4} - 16 \, {\left(3 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{3}\right)} d^{2} e^{4} - {\left(3 \, B b^{7} - 14 \, B a b^{5} c + 320 \, A a^{3} c^{4} + 160 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} c^{3} - 4 \, {\left(8 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2}\right)} d e^{5} - {\left(2 \, B a b^{6} - 5 \, A b^{7} + 32 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{3} - 6 \, {\left(2 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} e^{6}\right)} x^{3} + {\left(8 \, {\left(B b^{6} c - 6 \, B a b^{4} c^{2} + 32 \, B a^{3} c^{4}\right)} d^{3} e^{3} - {\left(3 \, B b^{7} - 160 \, B a^{3} b c^{3} + 320 \, A a^{3} c^{4} + 4 \, {\left(32 \, B a^{2} b^{3} - 15 \, A a b^{4}\right)} c^{2} - 2 \, {\left(17 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} d^{2} e^{4} - {\left(8 \, B a b^{6} - 5 \, A b^{7} + 32 \, {\left(2 \, B a^{4} + 5 \, A a^{3} b\right)} c^{3} + 32 \, {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2} - 10 \, {\left(6 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} d e^{5} - 2 \, {\left(2 \, B a^{2} b^{5} - 5 \, A a b^{6} + 16 \, {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} c^{2} - 8 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} e^{6}\right)} x^{2} + {\left(16 \, {\left(B a b^{5} c - 8 \, B a^{2} b^{3} c^{2} + 16 \, B a^{3} b c^{3}\right)} d^{3} e^{3} - 2 \, {\left(3 \, B a b^{6} - 32 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{3} + 80 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{2} - 2 \, {\left(14 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} d^{2} e^{4} - {\left(7 \, B a^{2} b^{5} - 10 \, A a b^{6} + 160 \, A a^{4} c^{3} + 16 \, {\left(7 \, B a^{4} b - 15 \, A a^{3} b^{2}\right)} c^{2} - 2 \, {\left(28 \, B a^{3} b^{3} - 45 \, A a^{2} b^{4}\right)} c\right)} d e^{5} - {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(2 \, B a^{5} - 5 \, A a^{4} b\right)} c^{2} - 8 \, {\left(2 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} c\right)} e^{6}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(2 \, {\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{5} + {\left(2 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{7} - 8 \, {\left(4 \, A a^{2} c^{5} + {\left(4 \, B a^{2} b - 11 \, A a b^{2}\right)} c^{4} + {\left(2 \, B a b^{3} + A b^{4}\right)} c^{3}\right)} d^{6} e + 4 \, {\left(4 \, {\left(10 \, B a^{3} - A a^{2} b\right)} c^{4} - 2 \, {\left(2 \, B a^{2} b^{2} + 13 \, A a b^{3}\right)} c^{3} + 3 \, {\left(2 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} d^{5} e^{2} - 8 \, {\left(32 \, A a^{3} c^{4} + 4 \, {\left(9 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} c^{3} - {\left(7 \, B a^{2} b^{3} + 3 \, A a b^{4}\right)} c^{2} + {\left(2 \, B a b^{5} + A b^{6}\right)} c\right)} d^{4} e^{3} + {\left(4 \, B a b^{6} + 2 \, A b^{7} + 8 \, {\left(4 \, B a^{4} + 45 \, A a^{3} b\right)} c^{3} + 2 \, {\left(86 \, B a^{3} b^{2} - 155 \, A a^{2} b^{3}\right)} c^{2} - {\left(31 \, B a^{2} b^{4} - 32 \, A a b^{5}\right)} c\right)} d^{3} e^{4} + {\left(7 \, B a^{2} b^{5} - 16 \, A a b^{6} - 176 \, A a^{4} c^{3} - 16 \, {\left(B a^{4} b + A a^{3} b^{2}\right)} c^{2} - {\left(48 \, B a^{3} b^{3} - 91 \, A a^{2} b^{4}\right)} c\right)} d^{2} e^{5} - {\left(11 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5} + 112 \, {\left(B a^{5} - A a^{4} b\right)} c^{2} - 4 \, {\left(20 \, B a^{4} b^{2} - 19 \, A a^{3} b^{3}\right)} c\right)} d e^{6} + 3 \, {\left(A a^{3} b^{4} - 8 \, A a^{4} b^{2} c + 16 \, A a^{5} c^{2}\right)} e^{7} + {\left(16 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} e - 8 \, {\left(7 \, B b^{2} c^{5} - 4 \, {\left(B a + 3 \, A b\right)} c^{6}\right)} d^{5} e^{2} + 2 \, {\left(29 \, B b^{3} c^{4} - 88 \, A a c^{6} + 2 \, {\left(2 \, B a b - 19 \, A b^{2}\right)} c^{5}\right)} d^{4} e^{3} - {\left(27 \, B b^{4} c^{3} + 176 \, {\left(B a^{2} - 2 \, A a b\right)} c^{5} + 8 \, {\left(B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{3} e^{4} + {\left(9 \, B b^{5} c^{2} - 16 \, A a^{2} c^{5} + 16 \, {\left(17 \, B a^{2} b - 16 \, A a b^{2}\right)} c^{4} - {\left(44 \, B a b^{3} - 35 \, A b^{4}\right)} c^{3}\right)} d^{2} e^{5} - {\left(16 \, {\left(13 \, B a^{3} - A a^{2} b\right)} c^{4} - 16 \, {\left(B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{3} + 3 \, {\left(B a b^{4} + 5 \, A b^{5}\right)} c^{2}\right)} d e^{6} + {\left(128 \, A a^{3} c^{4} + 20 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3} - 3 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2}\right)} e^{7}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{7} - 8 \, {\left(2 \, B b^{2} c^{5} - {\left(2 \, B a + 3 \, A b\right)} c^{6}\right)} d^{6} e - {\left(13 \, B b^{3} c^{4} + 88 \, A a c^{6} - 2 \, {\left(14 \, B a b + 17 \, A b^{2}\right)} c^{5}\right)} d^{5} e^{2} + {\left(36 \, B b^{4} c^{3} + 4 \, {\left(2 \, B a^{2} + 11 \, A a b\right)} c^{5} - {\left(46 \, B a b^{2} + 61 \, A b^{3}\right)} c^{4}\right)} d^{4} e^{3} - 2 \, {\left(12 \, B b^{5} c^{2} + 64 \, A a^{2} c^{5} + 2 \, {\left(32 \, B a^{2} b - 49 \, A a b^{2}\right)} c^{4} - {\left(19 \, B a b^{3} + 2 \, A b^{4}\right)} c^{3}\right)} d^{3} e^{4} + {\left(9 \, B b^{6} c - 16 \, {\left(2 \, B a^{3} - 11 \, A a^{2} b\right)} c^{4} + 2 \, {\left(106 \, B a^{2} b^{2} - 121 \, A a b^{3}\right)} c^{3} - 6 \, {\left(8 \, B a b^{4} - 5 \, A b^{5}\right)} c^{2}\right)} d^{2} e^{5} - {\left(56 \, A a^{3} c^{4} + 2 \, {\left(74 \, B a^{3} b + 19 \, A a^{2} b^{2}\right)} c^{3} - 15 \, {\left(B a^{2} b^{3} + 6 \, A a b^{4}\right)} c^{2} + 3 \, {\left(B a b^{5} + 5 \, A b^{6}\right)} c\right)} d e^{6} - 3 \, {\left(4 \, {\left(2 \, B a^{4} - 13 \, A a^{3} b\right)} c^{3} - 7 \, {\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2} + {\left(2 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} e^{7}\right)} x^{3} + 3 \, {\left(8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{7} - 2 \, {\left(13 \, B b^{3} c^{4} + 8 \, A a c^{6} - 2 \, {\left(6 \, B a b + 11 \, A b^{2}\right)} c^{5}\right)} d^{6} e + 2 \, {\left(12 \, B b^{4} c^{3} + 4 \, {\left(6 \, B a^{2} - 5 \, A a b\right)} c^{5} - {\left(18 \, B a b^{2} + 13 \, A b^{3}\right)} c^{4}\right)} d^{5} e^{2} - 4 \, {\left(B b^{5} c^{2} + 32 \, A a^{2} c^{5} + 2 \, {\left(6 \, B a^{2} b - 17 \, A a b^{2}\right)} c^{4} - 2 \, {\left(B a b^{3} - 2 \, A b^{4}\right)} c^{3}\right)} d^{4} e^{3} - {\left(5 \, B b^{6} c + 68 \, A a b^{3} c^{3} + 64 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} c^{4} - 14 \, {\left(B a b^{4} + A b^{5}\right)} c^{2}\right)} d^{3} e^{4} + {\left(3 \, B b^{7} - 48 \, A a^{3} c^{4} + 4 \, {\left(22 \, B a^{3} b + 7 \, A a^{2} b^{2}\right)} c^{3} + 2 \, {\left(11 \, B a^{2} b^{3} - 21 \, A a b^{4}\right)} c^{2} - {\left(14 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} d^{2} e^{5} - {\left(B a b^{6} + 5 \, A b^{7} + 8 \, {\left(14 \, B a^{4} + A a^{3} b\right)} c^{3} + 2 \, {\left(2 \, B a^{3} b^{2} + 9 \, A a^{2} b^{3}\right)} c^{2} - 2 \, {\left(B a^{2} b^{4} + 15 \, A a b^{5}\right)} c\right)} d e^{6} - {\left(2 \, B a^{2} b^{5} - 5 \, A a b^{6} - 16 \, A a^{3} b^{2} c^{2} - 64 \, A a^{4} c^{3} - 6 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} e^{7}\right)} x^{2} + 2 \, {\left(3 \, {\left(B b^{3} c^{4} - 8 \, A a c^{6} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c^{5}\right)} d^{7} - {\left(12 \, B b^{4} c^{3} - 4 \, {\left(2 \, B a^{2} + 15 \, A a b\right)} c^{5} + {\left(22 \, B a b^{2} - 19 \, A b^{3}\right)} c^{4}\right)} d^{6} e + 2 \, {\left(9 \, B b^{5} c^{2} - 56 \, A a^{2} c^{5} + 4 \, {\left(13 \, B a^{2} b - 8 \, A a b^{2}\right)} c^{4} - 2 \, {\left(5 \, B a b^{3} + 4 \, A b^{4}\right)} c^{3}\right)} d^{5} e^{2} - 2 \, {\left(6 \, B b^{6} c + 4 \, {\left(2 \, B a^{3} - 11 \, A a^{2} b\right)} c^{4} + 2 \, {\left(44 \, B a^{2} b^{2} - 23 \, A a b^{3}\right)} c^{3} - 3 \, {\left(8 \, B a b^{4} - A b^{5}\right)} c^{2}\right)} d^{4} e^{3} + {\left(3 \, B b^{7} - 152 \, A a^{3} c^{4} + 2 \, {\left(6 \, B a^{3} b + 61 \, A a^{2} b^{2}\right)} c^{3} + {\left(91 \, B a^{2} b^{3} - 102 \, A a b^{4}\right)} c^{2} - {\left(23 \, B a b^{5} - 14 \, A b^{6}\right)} c\right)} d^{3} e^{4} + {\left(5 \, B a b^{6} - 5 \, A b^{7} - 4 \, {\left(14 \, B a^{4} - 39 \, A a^{3} b\right)} c^{3} + {\left(74 \, B a^{3} b^{2} - 125 \, A a^{2} b^{3}\right)} c^{2} - {\left(38 \, B a^{2} b^{4} - 43 \, A a b^{5}\right)} c\right)} d^{2} e^{5} - {\left(4 \, B a^{2} b^{5} + 5 \, A a b^{6} + 64 \, A a^{4} c^{3} + 20 \, {\left(4 \, B a^{4} b + A a^{3} b^{2}\right)} c^{2} - 2 \, {\left(15 \, B a^{3} b^{3} + 16 \, A a^{2} b^{4}\right)} c\right)} d e^{6} - 2 \, {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(B a^{5} - 4 \, A a^{4} b\right)} c^{2} - {\left(14 \, B a^{4} b^{2} - 37 \, A a^{3} b^{3}\right)} c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left({\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6}\right)} d^{9} - 4 \, {\left(a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} d^{8} e + 2 \, {\left(3 \, a^{2} b^{6} c^{2} - 22 \, a^{3} b^{4} c^{3} + 32 \, a^{4} b^{2} c^{4} + 32 \, a^{5} c^{5}\right)} d^{7} e^{2} - 4 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} - 8 \, a^{4} b^{3} c^{3} + 48 \, a^{5} b c^{4}\right)} d^{6} e^{3} + {\left(a^{2} b^{8} + 4 \, a^{3} b^{6} c - 74 \, a^{4} b^{4} c^{2} + 144 \, a^{5} b^{2} c^{3} + 96 \, a^{6} c^{4}\right)} d^{5} e^{4} - 4 \, {\left(a^{3} b^{7} - 5 \, a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 48 \, a^{6} b c^{3}\right)} d^{4} e^{5} + 2 \, {\left(3 \, a^{4} b^{6} - 22 \, a^{5} b^{4} c + 32 \, a^{6} b^{2} c^{2} + 32 \, a^{7} c^{3}\right)} d^{3} e^{6} - 4 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} d^{2} e^{7} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} d e^{8} + {\left({\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{8} e - 4 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{7} e^{2} + 2 \, {\left(3 \, b^{6} c^{4} - 22 \, a b^{4} c^{5} + 32 \, a^{2} b^{2} c^{6} + 32 \, a^{3} c^{7}\right)} d^{6} e^{3} - 4 \, {\left(b^{7} c^{3} - 5 \, a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 48 \, a^{3} b c^{6}\right)} d^{5} e^{4} + {\left(b^{8} c^{2} + 4 \, a b^{6} c^{3} - 74 \, a^{2} b^{4} c^{4} + 144 \, a^{3} b^{2} c^{5} + 96 \, a^{4} c^{6}\right)} d^{4} e^{5} - 4 \, {\left(a b^{7} c^{2} - 5 \, a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} + 48 \, a^{4} b c^{5}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{6} c^{2} - 22 \, a^{3} b^{4} c^{3} + 32 \, a^{4} b^{2} c^{4} + 32 \, a^{5} c^{5}\right)} d^{2} e^{7} - 4 \, {\left(a^{3} b^{5} c^{2} - 8 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4}\right)} d e^{8} + {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)} e^{9}\right)} x^{5} + {\left({\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{9} - 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{8} e - 2 \, {\left(b^{6} c^{4} - 10 \, a b^{4} c^{5} + 32 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{7} e^{2} + 4 \, {\left(2 \, b^{7} c^{3} - 17 \, a b^{5} c^{4} + 40 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{6} e^{3} - {\left(7 \, b^{8} c^{2} - 44 \, a b^{6} c^{3} + 10 \, a^{2} b^{4} c^{4} + 240 \, a^{3} b^{2} c^{5} - 96 \, a^{4} c^{6}\right)} d^{5} e^{4} + 2 \, {\left(b^{9} c + 2 \, a b^{7} c^{2} - 64 \, a^{2} b^{5} c^{3} + 160 \, a^{3} b^{3} c^{4}\right)} d^{4} e^{5} - 2 \, {\left(4 \, a b^{8} c - 23 \, a^{2} b^{6} c^{2} - 10 \, a^{3} b^{4} c^{3} + 160 \, a^{4} b^{2} c^{4} - 32 \, a^{5} c^{5}\right)} d^{3} e^{6} + 4 \, {\left(3 \, a^{2} b^{7} c - 23 \, a^{3} b^{5} c^{2} + 40 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4}\right)} d^{2} e^{7} - {\left(8 \, a^{3} b^{6} c - 65 \, a^{4} b^{4} c^{2} + 136 \, a^{5} b^{2} c^{3} - 16 \, a^{6} c^{4}\right)} d e^{8} + 2 \, {\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)} e^{9}\right)} x^{4} + {\left(2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{9} - {\left(7 \, b^{6} c^{4} - 58 \, a b^{4} c^{5} + 128 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{8} e + 8 \, {\left(b^{7} c^{3} - 8 \, a b^{5} c^{4} + 16 \, a^{2} b^{3} c^{5}\right)} d^{7} e^{2} - 2 \, {\left(b^{8} c^{2} - 4 \, a b^{6} c^{3} - 20 \, a^{2} b^{4} c^{4} + 96 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{6} e^{3} - 2 \, {\left(b^{9} c - 10 \, a b^{7} c^{2} + 38 \, a^{2} b^{5} c^{3} - 80 \, a^{3} b^{3} c^{4} + 96 \, a^{4} b c^{5}\right)} d^{5} e^{4} + {\left(b^{10} - 2 \, a b^{8} c - 26 \, a^{2} b^{6} c^{2} + 60 \, a^{3} b^{4} c^{3} + 192 \, a^{5} c^{5}\right)} d^{4} e^{5} - 4 \, {\left(a b^{9} - 6 \, a^{2} b^{7} c + 4 \, a^{3} b^{5} c^{2} + 64 \, a^{5} b c^{4}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{8} - 20 \, a^{3} b^{6} c + 20 \, a^{4} b^{4} c^{2} + 32 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4}\right)} d^{2} e^{7} - 2 \, {\left(2 \, a^{3} b^{7} - 13 \, a^{4} b^{5} c + 8 \, a^{5} b^{3} c^{2} + 48 \, a^{6} b c^{3}\right)} d e^{8} + {\left(a^{4} b^{6} - 6 \, a^{5} b^{4} c + 32 \, a^{7} c^{3}\right)} e^{9}\right)} x^{3} + {\left({\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} d^{9} - 2 \, {\left(2 \, b^{7} c^{3} - 13 \, a b^{5} c^{4} + 8 \, a^{2} b^{3} c^{5} + 48 \, a^{3} b c^{6}\right)} d^{8} e + 2 \, {\left(3 \, b^{8} c^{2} - 20 \, a b^{6} c^{3} + 20 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} d^{7} e^{2} - 4 \, {\left(b^{9} c - 6 \, a b^{7} c^{2} + 4 \, a^{2} b^{5} c^{3} + 64 \, a^{4} b c^{5}\right)} d^{6} e^{3} + {\left(b^{10} - 2 \, a b^{8} c - 26 \, a^{2} b^{6} c^{2} + 60 \, a^{3} b^{4} c^{3} + 192 \, a^{5} c^{5}\right)} d^{5} e^{4} - 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 38 \, a^{3} b^{5} c^{2} - 80 \, a^{4} b^{3} c^{3} + 96 \, a^{5} b c^{4}\right)} d^{4} e^{5} - 2 \, {\left(a^{2} b^{8} - 4 \, a^{3} b^{6} c - 20 \, a^{4} b^{4} c^{2} + 96 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} d^{3} e^{6} + 8 \, {\left(a^{3} b^{7} - 8 \, a^{4} b^{5} c + 16 \, a^{5} b^{3} c^{2}\right)} d^{2} e^{7} - {\left(7 \, a^{4} b^{6} - 58 \, a^{5} b^{4} c + 128 \, a^{6} b^{2} c^{2} - 32 \, a^{7} c^{3}\right)} d e^{8} + 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} e^{9}\right)} x^{2} + {\left(2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} d^{9} - {\left(8 \, a b^{6} c^{3} - 65 \, a^{2} b^{4} c^{4} + 136 \, a^{3} b^{2} c^{5} - 16 \, a^{4} c^{6}\right)} d^{8} e + 4 \, {\left(3 \, a b^{7} c^{2} - 23 \, a^{2} b^{5} c^{3} + 40 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} d^{7} e^{2} - 2 \, {\left(4 \, a b^{8} c - 23 \, a^{2} b^{6} c^{2} - 10 \, a^{3} b^{4} c^{3} + 160 \, a^{4} b^{2} c^{4} - 32 \, a^{5} c^{5}\right)} d^{6} e^{3} + 2 \, {\left(a b^{9} + 2 \, a^{2} b^{7} c - 64 \, a^{3} b^{5} c^{2} + 160 \, a^{4} b^{3} c^{3}\right)} d^{5} e^{4} - {\left(7 \, a^{2} b^{8} - 44 \, a^{3} b^{6} c + 10 \, a^{4} b^{4} c^{2} + 240 \, a^{5} b^{2} c^{3} - 96 \, a^{6} c^{4}\right)} d^{4} e^{5} + 4 \, {\left(2 \, a^{3} b^{7} - 17 \, a^{4} b^{5} c + 40 \, a^{5} b^{3} c^{2} - 16 \, a^{6} b c^{3}\right)} d^{3} e^{6} - 2 \, {\left(a^{4} b^{6} - 10 \, a^{5} b^{4} c + 32 \, a^{6} b^{2} c^{2} - 32 \, a^{7} c^{3}\right)} d^{2} e^{7} - 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} d e^{8} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} e^{9}\right)} x\right)}}, -\frac{3 \, {\left(8 \, {\left(B a^{2} b^{4} c - 8 \, B a^{3} b^{2} c^{2} + 16 \, B a^{4} c^{3}\right)} d^{3} e^{3} - {\left(3 \, B a^{2} b^{5} + 160 \, A a^{4} c^{3} + 16 \, {\left(3 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} c^{2} - 2 \, {\left(12 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} d^{2} e^{4} - {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(2 \, B a^{5} - 5 \, A a^{4} b\right)} c^{2} - 8 \, {\left(2 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} c\right)} d e^{5} + {\left(8 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} d^{2} e^{4} - {\left(3 \, B b^{5} c^{2} + 160 \, A a^{2} c^{5} + 16 \, {\left(3 \, B a^{2} b - 5 \, A a b^{2}\right)} c^{4} - 2 \, {\left(12 \, B a b^{3} - 5 \, A b^{4}\right)} c^{3}\right)} d e^{5} - {\left(16 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{4} - 8 \, {\left(2 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{3} + {\left(2 \, B a b^{4} - 5 \, A b^{5}\right)} c^{2}\right)} e^{6}\right)} x^{5} + {\left(8 \, {\left(B b^{4} c^{3} - 8 \, B a b^{2} c^{4} + 16 \, B a^{2} c^{5}\right)} d^{3} e^{3} + {\left(13 \, B b^{5} c^{2} - 160 \, A a^{2} c^{5} + 16 \, {\left(13 \, B a^{2} b + 5 \, A a b^{2}\right)} c^{4} - 2 \, {\left(52 \, B a b^{3} + 5 \, A b^{4}\right)} c^{3}\right)} d^{2} e^{4} - {\left(6 \, B b^{6} c + 16 \, {\left(2 \, B a^{3} + 15 \, A a^{2} b\right)} c^{4} + 40 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} c^{3} - {\left(46 \, B a b^{4} - 15 \, A b^{5}\right)} c^{2}\right)} d e^{5} - 2 \, {\left(16 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3} - 8 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2} + {\left(2 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} e^{6}\right)} x^{4} + {\left(16 \, {\left(B b^{5} c^{2} - 8 \, B a b^{3} c^{3} + 16 \, B a^{2} b c^{4}\right)} d^{3} e^{3} + 2 \, {\left(B b^{6} c - 10 \, A b^{5} c^{2} + 32 \, {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} c^{4} - 16 \, {\left(3 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{3}\right)} d^{2} e^{4} - {\left(3 \, B b^{7} - 14 \, B a b^{5} c + 320 \, A a^{3} c^{4} + 160 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} c^{3} - 4 \, {\left(8 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2}\right)} d e^{5} - {\left(2 \, B a b^{6} - 5 \, A b^{7} + 32 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{3} - 6 \, {\left(2 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} e^{6}\right)} x^{3} + {\left(8 \, {\left(B b^{6} c - 6 \, B a b^{4} c^{2} + 32 \, B a^{3} c^{4}\right)} d^{3} e^{3} - {\left(3 \, B b^{7} - 160 \, B a^{3} b c^{3} + 320 \, A a^{3} c^{4} + 4 \, {\left(32 \, B a^{2} b^{3} - 15 \, A a b^{4}\right)} c^{2} - 2 \, {\left(17 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} d^{2} e^{4} - {\left(8 \, B a b^{6} - 5 \, A b^{7} + 32 \, {\left(2 \, B a^{4} + 5 \, A a^{3} b\right)} c^{3} + 32 \, {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2} - 10 \, {\left(6 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} d e^{5} - 2 \, {\left(2 \, B a^{2} b^{5} - 5 \, A a b^{6} + 16 \, {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} c^{2} - 8 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} e^{6}\right)} x^{2} + {\left(16 \, {\left(B a b^{5} c - 8 \, B a^{2} b^{3} c^{2} + 16 \, B a^{3} b c^{3}\right)} d^{3} e^{3} - 2 \, {\left(3 \, B a b^{6} - 32 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{3} + 80 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{2} - 2 \, {\left(14 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} d^{2} e^{4} - {\left(7 \, B a^{2} b^{5} - 10 \, A a b^{6} + 160 \, A a^{4} c^{3} + 16 \, {\left(7 \, B a^{4} b - 15 \, A a^{3} b^{2}\right)} c^{2} - 2 \, {\left(28 \, B a^{3} b^{3} - 45 \, A a^{2} b^{4}\right)} c\right)} d e^{5} - {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(2 \, B a^{5} - 5 \, A a^{4} b\right)} c^{2} - 8 \, {\left(2 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} c\right)} e^{6}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, {\left(4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{5} + {\left(2 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{7} - 8 \, {\left(4 \, A a^{2} c^{5} + {\left(4 \, B a^{2} b - 11 \, A a b^{2}\right)} c^{4} + {\left(2 \, B a b^{3} + A b^{4}\right)} c^{3}\right)} d^{6} e + 4 \, {\left(4 \, {\left(10 \, B a^{3} - A a^{2} b\right)} c^{4} - 2 \, {\left(2 \, B a^{2} b^{2} + 13 \, A a b^{3}\right)} c^{3} + 3 \, {\left(2 \, B a b^{4} + A b^{5}\right)} c^{2}\right)} d^{5} e^{2} - 8 \, {\left(32 \, A a^{3} c^{4} + 4 \, {\left(9 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} c^{3} - {\left(7 \, B a^{2} b^{3} + 3 \, A a b^{4}\right)} c^{2} + {\left(2 \, B a b^{5} + A b^{6}\right)} c\right)} d^{4} e^{3} + {\left(4 \, B a b^{6} + 2 \, A b^{7} + 8 \, {\left(4 \, B a^{4} + 45 \, A a^{3} b\right)} c^{3} + 2 \, {\left(86 \, B a^{3} b^{2} - 155 \, A a^{2} b^{3}\right)} c^{2} - {\left(31 \, B a^{2} b^{4} - 32 \, A a b^{5}\right)} c\right)} d^{3} e^{4} + {\left(7 \, B a^{2} b^{5} - 16 \, A a b^{6} - 176 \, A a^{4} c^{3} - 16 \, {\left(B a^{4} b + A a^{3} b^{2}\right)} c^{2} - {\left(48 \, B a^{3} b^{3} - 91 \, A a^{2} b^{4}\right)} c\right)} d^{2} e^{5} - {\left(11 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5} + 112 \, {\left(B a^{5} - A a^{4} b\right)} c^{2} - 4 \, {\left(20 \, B a^{4} b^{2} - 19 \, A a^{3} b^{3}\right)} c\right)} d e^{6} + 3 \, {\left(A a^{3} b^{4} - 8 \, A a^{4} b^{2} c + 16 \, A a^{5} c^{2}\right)} e^{7} + {\left(16 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{6} e - 8 \, {\left(7 \, B b^{2} c^{5} - 4 \, {\left(B a + 3 \, A b\right)} c^{6}\right)} d^{5} e^{2} + 2 \, {\left(29 \, B b^{3} c^{4} - 88 \, A a c^{6} + 2 \, {\left(2 \, B a b - 19 \, A b^{2}\right)} c^{5}\right)} d^{4} e^{3} - {\left(27 \, B b^{4} c^{3} + 176 \, {\left(B a^{2} - 2 \, A a b\right)} c^{5} + 8 \, {\left(B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{3} e^{4} + {\left(9 \, B b^{5} c^{2} - 16 \, A a^{2} c^{5} + 16 \, {\left(17 \, B a^{2} b - 16 \, A a b^{2}\right)} c^{4} - {\left(44 \, B a b^{3} - 35 \, A b^{4}\right)} c^{3}\right)} d^{2} e^{5} - {\left(16 \, {\left(13 \, B a^{3} - A a^{2} b\right)} c^{4} - 16 \, {\left(B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{3} + 3 \, {\left(B a b^{4} + 5 \, A b^{5}\right)} c^{2}\right)} d e^{6} + {\left(128 \, A a^{3} c^{4} + 20 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3} - 3 \, {\left(2 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} c^{2}\right)} e^{7}\right)} x^{4} + 2 \, {\left(8 \, {\left(B b c^{6} - 2 \, A c^{7}\right)} d^{7} - 8 \, {\left(2 \, B b^{2} c^{5} - {\left(2 \, B a + 3 \, A b\right)} c^{6}\right)} d^{6} e - {\left(13 \, B b^{3} c^{4} + 88 \, A a c^{6} - 2 \, {\left(14 \, B a b + 17 \, A b^{2}\right)} c^{5}\right)} d^{5} e^{2} + {\left(36 \, B b^{4} c^{3} + 4 \, {\left(2 \, B a^{2} + 11 \, A a b\right)} c^{5} - {\left(46 \, B a b^{2} + 61 \, A b^{3}\right)} c^{4}\right)} d^{4} e^{3} - 2 \, {\left(12 \, B b^{5} c^{2} + 64 \, A a^{2} c^{5} + 2 \, {\left(32 \, B a^{2} b - 49 \, A a b^{2}\right)} c^{4} - {\left(19 \, B a b^{3} + 2 \, A b^{4}\right)} c^{3}\right)} d^{3} e^{4} + {\left(9 \, B b^{6} c - 16 \, {\left(2 \, B a^{3} - 11 \, A a^{2} b\right)} c^{4} + 2 \, {\left(106 \, B a^{2} b^{2} - 121 \, A a b^{3}\right)} c^{3} - 6 \, {\left(8 \, B a b^{4} - 5 \, A b^{5}\right)} c^{2}\right)} d^{2} e^{5} - {\left(56 \, A a^{3} c^{4} + 2 \, {\left(74 \, B a^{3} b + 19 \, A a^{2} b^{2}\right)} c^{3} - 15 \, {\left(B a^{2} b^{3} + 6 \, A a b^{4}\right)} c^{2} + 3 \, {\left(B a b^{5} + 5 \, A b^{6}\right)} c\right)} d e^{6} - 3 \, {\left(4 \, {\left(2 \, B a^{4} - 13 \, A a^{3} b\right)} c^{3} - 7 \, {\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2} + {\left(2 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} e^{7}\right)} x^{3} + 3 \, {\left(8 \, {\left(B b^{2} c^{5} - 2 \, A b c^{6}\right)} d^{7} - 2 \, {\left(13 \, B b^{3} c^{4} + 8 \, A a c^{6} - 2 \, {\left(6 \, B a b + 11 \, A b^{2}\right)} c^{5}\right)} d^{6} e + 2 \, {\left(12 \, B b^{4} c^{3} + 4 \, {\left(6 \, B a^{2} - 5 \, A a b\right)} c^{5} - {\left(18 \, B a b^{2} + 13 \, A b^{3}\right)} c^{4}\right)} d^{5} e^{2} - 4 \, {\left(B b^{5} c^{2} + 32 \, A a^{2} c^{5} + 2 \, {\left(6 \, B a^{2} b - 17 \, A a b^{2}\right)} c^{4} - 2 \, {\left(B a b^{3} - 2 \, A b^{4}\right)} c^{3}\right)} d^{4} e^{3} - {\left(5 \, B b^{6} c + 68 \, A a b^{3} c^{3} + 64 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} c^{4} - 14 \, {\left(B a b^{4} + A b^{5}\right)} c^{2}\right)} d^{3} e^{4} + {\left(3 \, B b^{7} - 48 \, A a^{3} c^{4} + 4 \, {\left(22 \, B a^{3} b + 7 \, A a^{2} b^{2}\right)} c^{3} + 2 \, {\left(11 \, B a^{2} b^{3} - 21 \, A a b^{4}\right)} c^{2} - {\left(14 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} d^{2} e^{5} - {\left(B a b^{6} + 5 \, A b^{7} + 8 \, {\left(14 \, B a^{4} + A a^{3} b\right)} c^{3} + 2 \, {\left(2 \, B a^{3} b^{2} + 9 \, A a^{2} b^{3}\right)} c^{2} - 2 \, {\left(B a^{2} b^{4} + 15 \, A a b^{5}\right)} c\right)} d e^{6} - {\left(2 \, B a^{2} b^{5} - 5 \, A a b^{6} - 16 \, A a^{3} b^{2} c^{2} - 64 \, A a^{4} c^{3} - 6 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c\right)} e^{7}\right)} x^{2} + 2 \, {\left(3 \, {\left(B b^{3} c^{4} - 8 \, A a c^{6} + 2 \, {\left(2 \, B a b - A b^{2}\right)} c^{5}\right)} d^{7} - {\left(12 \, B b^{4} c^{3} - 4 \, {\left(2 \, B a^{2} + 15 \, A a b\right)} c^{5} + {\left(22 \, B a b^{2} - 19 \, A b^{3}\right)} c^{4}\right)} d^{6} e + 2 \, {\left(9 \, B b^{5} c^{2} - 56 \, A a^{2} c^{5} + 4 \, {\left(13 \, B a^{2} b - 8 \, A a b^{2}\right)} c^{4} - 2 \, {\left(5 \, B a b^{3} + 4 \, A b^{4}\right)} c^{3}\right)} d^{5} e^{2} - 2 \, {\left(6 \, B b^{6} c + 4 \, {\left(2 \, B a^{3} - 11 \, A a^{2} b\right)} c^{4} + 2 \, {\left(44 \, B a^{2} b^{2} - 23 \, A a b^{3}\right)} c^{3} - 3 \, {\left(8 \, B a b^{4} - A b^{5}\right)} c^{2}\right)} d^{4} e^{3} + {\left(3 \, B b^{7} - 152 \, A a^{3} c^{4} + 2 \, {\left(6 \, B a^{3} b + 61 \, A a^{2} b^{2}\right)} c^{3} + {\left(91 \, B a^{2} b^{3} - 102 \, A a b^{4}\right)} c^{2} - {\left(23 \, B a b^{5} - 14 \, A b^{6}\right)} c\right)} d^{3} e^{4} + {\left(5 \, B a b^{6} - 5 \, A b^{7} - 4 \, {\left(14 \, B a^{4} - 39 \, A a^{3} b\right)} c^{3} + {\left(74 \, B a^{3} b^{2} - 125 \, A a^{2} b^{3}\right)} c^{2} - {\left(38 \, B a^{2} b^{4} - 43 \, A a b^{5}\right)} c\right)} d^{2} e^{5} - {\left(4 \, B a^{2} b^{5} + 5 \, A a b^{6} + 64 \, A a^{4} c^{3} + 20 \, {\left(4 \, B a^{4} b + A a^{3} b^{2}\right)} c^{2} - 2 \, {\left(15 \, B a^{3} b^{3} + 16 \, A a^{2} b^{4}\right)} c\right)} d e^{6} - 2 \, {\left(2 \, B a^{3} b^{4} - 5 \, A a^{2} b^{5} + 16 \, {\left(B a^{5} - 4 \, A a^{4} b\right)} c^{2} - {\left(14 \, B a^{4} b^{2} - 37 \, A a^{3} b^{3}\right)} c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left({\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6}\right)} d^{9} - 4 \, {\left(a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} d^{8} e + 2 \, {\left(3 \, a^{2} b^{6} c^{2} - 22 \, a^{3} b^{4} c^{3} + 32 \, a^{4} b^{2} c^{4} + 32 \, a^{5} c^{5}\right)} d^{7} e^{2} - 4 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} - 8 \, a^{4} b^{3} c^{3} + 48 \, a^{5} b c^{4}\right)} d^{6} e^{3} + {\left(a^{2} b^{8} + 4 \, a^{3} b^{6} c - 74 \, a^{4} b^{4} c^{2} + 144 \, a^{5} b^{2} c^{3} + 96 \, a^{6} c^{4}\right)} d^{5} e^{4} - 4 \, {\left(a^{3} b^{7} - 5 \, a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 48 \, a^{6} b c^{3}\right)} d^{4} e^{5} + 2 \, {\left(3 \, a^{4} b^{6} - 22 \, a^{5} b^{4} c + 32 \, a^{6} b^{2} c^{2} + 32 \, a^{7} c^{3}\right)} d^{3} e^{6} - 4 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} d^{2} e^{7} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} d e^{8} + {\left({\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{8} e - 4 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{7} e^{2} + 2 \, {\left(3 \, b^{6} c^{4} - 22 \, a b^{4} c^{5} + 32 \, a^{2} b^{2} c^{6} + 32 \, a^{3} c^{7}\right)} d^{6} e^{3} - 4 \, {\left(b^{7} c^{3} - 5 \, a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 48 \, a^{3} b c^{6}\right)} d^{5} e^{4} + {\left(b^{8} c^{2} + 4 \, a b^{6} c^{3} - 74 \, a^{2} b^{4} c^{4} + 144 \, a^{3} b^{2} c^{5} + 96 \, a^{4} c^{6}\right)} d^{4} e^{5} - 4 \, {\left(a b^{7} c^{2} - 5 \, a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} + 48 \, a^{4} b c^{5}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{6} c^{2} - 22 \, a^{3} b^{4} c^{3} + 32 \, a^{4} b^{2} c^{4} + 32 \, a^{5} c^{5}\right)} d^{2} e^{7} - 4 \, {\left(a^{3} b^{5} c^{2} - 8 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4}\right)} d e^{8} + {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)} e^{9}\right)} x^{5} + {\left({\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{9} - 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{8} e - 2 \, {\left(b^{6} c^{4} - 10 \, a b^{4} c^{5} + 32 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{7} e^{2} + 4 \, {\left(2 \, b^{7} c^{3} - 17 \, a b^{5} c^{4} + 40 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{6} e^{3} - {\left(7 \, b^{8} c^{2} - 44 \, a b^{6} c^{3} + 10 \, a^{2} b^{4} c^{4} + 240 \, a^{3} b^{2} c^{5} - 96 \, a^{4} c^{6}\right)} d^{5} e^{4} + 2 \, {\left(b^{9} c + 2 \, a b^{7} c^{2} - 64 \, a^{2} b^{5} c^{3} + 160 \, a^{3} b^{3} c^{4}\right)} d^{4} e^{5} - 2 \, {\left(4 \, a b^{8} c - 23 \, a^{2} b^{6} c^{2} - 10 \, a^{3} b^{4} c^{3} + 160 \, a^{4} b^{2} c^{4} - 32 \, a^{5} c^{5}\right)} d^{3} e^{6} + 4 \, {\left(3 \, a^{2} b^{7} c - 23 \, a^{3} b^{5} c^{2} + 40 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4}\right)} d^{2} e^{7} - {\left(8 \, a^{3} b^{6} c - 65 \, a^{4} b^{4} c^{2} + 136 \, a^{5} b^{2} c^{3} - 16 \, a^{6} c^{4}\right)} d e^{8} + 2 \, {\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)} e^{9}\right)} x^{4} + {\left(2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{9} - {\left(7 \, b^{6} c^{4} - 58 \, a b^{4} c^{5} + 128 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{8} e + 8 \, {\left(b^{7} c^{3} - 8 \, a b^{5} c^{4} + 16 \, a^{2} b^{3} c^{5}\right)} d^{7} e^{2} - 2 \, {\left(b^{8} c^{2} - 4 \, a b^{6} c^{3} - 20 \, a^{2} b^{4} c^{4} + 96 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{6} e^{3} - 2 \, {\left(b^{9} c - 10 \, a b^{7} c^{2} + 38 \, a^{2} b^{5} c^{3} - 80 \, a^{3} b^{3} c^{4} + 96 \, a^{4} b c^{5}\right)} d^{5} e^{4} + {\left(b^{10} - 2 \, a b^{8} c - 26 \, a^{2} b^{6} c^{2} + 60 \, a^{3} b^{4} c^{3} + 192 \, a^{5} c^{5}\right)} d^{4} e^{5} - 4 \, {\left(a b^{9} - 6 \, a^{2} b^{7} c + 4 \, a^{3} b^{5} c^{2} + 64 \, a^{5} b c^{4}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{8} - 20 \, a^{3} b^{6} c + 20 \, a^{4} b^{4} c^{2} + 32 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4}\right)} d^{2} e^{7} - 2 \, {\left(2 \, a^{3} b^{7} - 13 \, a^{4} b^{5} c + 8 \, a^{5} b^{3} c^{2} + 48 \, a^{6} b c^{3}\right)} d e^{8} + {\left(a^{4} b^{6} - 6 \, a^{5} b^{4} c + 32 \, a^{7} c^{3}\right)} e^{9}\right)} x^{3} + {\left({\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} d^{9} - 2 \, {\left(2 \, b^{7} c^{3} - 13 \, a b^{5} c^{4} + 8 \, a^{2} b^{3} c^{5} + 48 \, a^{3} b c^{6}\right)} d^{8} e + 2 \, {\left(3 \, b^{8} c^{2} - 20 \, a b^{6} c^{3} + 20 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} d^{7} e^{2} - 4 \, {\left(b^{9} c - 6 \, a b^{7} c^{2} + 4 \, a^{2} b^{5} c^{3} + 64 \, a^{4} b c^{5}\right)} d^{6} e^{3} + {\left(b^{10} - 2 \, a b^{8} c - 26 \, a^{2} b^{6} c^{2} + 60 \, a^{3} b^{4} c^{3} + 192 \, a^{5} c^{5}\right)} d^{5} e^{4} - 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 38 \, a^{3} b^{5} c^{2} - 80 \, a^{4} b^{3} c^{3} + 96 \, a^{5} b c^{4}\right)} d^{4} e^{5} - 2 \, {\left(a^{2} b^{8} - 4 \, a^{3} b^{6} c - 20 \, a^{4} b^{4} c^{2} + 96 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} d^{3} e^{6} + 8 \, {\left(a^{3} b^{7} - 8 \, a^{4} b^{5} c + 16 \, a^{5} b^{3} c^{2}\right)} d^{2} e^{7} - {\left(7 \, a^{4} b^{6} - 58 \, a^{5} b^{4} c + 128 \, a^{6} b^{2} c^{2} - 32 \, a^{7} c^{3}\right)} d e^{8} + 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} e^{9}\right)} x^{2} + {\left(2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} d^{9} - {\left(8 \, a b^{6} c^{3} - 65 \, a^{2} b^{4} c^{4} + 136 \, a^{3} b^{2} c^{5} - 16 \, a^{4} c^{6}\right)} d^{8} e + 4 \, {\left(3 \, a b^{7} c^{2} - 23 \, a^{2} b^{5} c^{3} + 40 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} d^{7} e^{2} - 2 \, {\left(4 \, a b^{8} c - 23 \, a^{2} b^{6} c^{2} - 10 \, a^{3} b^{4} c^{3} + 160 \, a^{4} b^{2} c^{4} - 32 \, a^{5} c^{5}\right)} d^{6} e^{3} + 2 \, {\left(a b^{9} + 2 \, a^{2} b^{7} c - 64 \, a^{3} b^{5} c^{2} + 160 \, a^{4} b^{3} c^{3}\right)} d^{5} e^{4} - {\left(7 \, a^{2} b^{8} - 44 \, a^{3} b^{6} c + 10 \, a^{4} b^{4} c^{2} + 240 \, a^{5} b^{2} c^{3} - 96 \, a^{6} c^{4}\right)} d^{4} e^{5} + 4 \, {\left(2 \, a^{3} b^{7} - 17 \, a^{4} b^{5} c + 40 \, a^{5} b^{3} c^{2} - 16 \, a^{6} b c^{3}\right)} d^{3} e^{6} - 2 \, {\left(a^{4} b^{6} - 10 \, a^{5} b^{4} c + 32 \, a^{6} b^{2} c^{2} - 32 \, a^{7} c^{3}\right)} d^{2} e^{7} - 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} d e^{8} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} e^{9}\right)} x\right)}}\right]"," ",0,"[1/12*(3*(8*(B*a^2*b^4*c - 8*B*a^3*b^2*c^2 + 16*B*a^4*c^3)*d^3*e^3 - (3*B*a^2*b^5 + 160*A*a^4*c^3 + 16*(3*B*a^4*b - 5*A*a^3*b^2)*c^2 - 2*(12*B*a^3*b^3 - 5*A*a^2*b^4)*c)*d^2*e^4 - (2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(2*B*a^5 - 5*A*a^4*b)*c^2 - 8*(2*B*a^4*b^2 - 5*A*a^3*b^3)*c)*d*e^5 + (8*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*d^2*e^4 - (3*B*b^5*c^2 + 160*A*a^2*c^5 + 16*(3*B*a^2*b - 5*A*a*b^2)*c^4 - 2*(12*B*a*b^3 - 5*A*b^4)*c^3)*d*e^5 - (16*(2*B*a^3 - 5*A*a^2*b)*c^4 - 8*(2*B*a^2*b^2 - 5*A*a*b^3)*c^3 + (2*B*a*b^4 - 5*A*b^5)*c^2)*e^6)*x^5 + (8*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*d^3*e^3 + (13*B*b^5*c^2 - 160*A*a^2*c^5 + 16*(13*B*a^2*b + 5*A*a*b^2)*c^4 - 2*(52*B*a*b^3 + 5*A*b^4)*c^3)*d^2*e^4 - (6*B*b^6*c + 16*(2*B*a^3 + 15*A*a^2*b)*c^4 + 40*(2*B*a^2*b^2 - 3*A*a*b^3)*c^3 - (46*B*a*b^4 - 15*A*b^5)*c^2)*d*e^5 - 2*(16*(2*B*a^3*b - 5*A*a^2*b^2)*c^3 - 8*(2*B*a^2*b^3 - 5*A*a*b^4)*c^2 + (2*B*a*b^5 - 5*A*b^6)*c)*e^6)*x^4 + (16*(B*b^5*c^2 - 8*B*a*b^3*c^3 + 16*B*a^2*b*c^4)*d^3*e^3 + 2*(B*b^6*c - 10*A*b^5*c^2 + 32*(4*B*a^3 - 5*A*a^2*b)*c^4 - 16*(3*B*a^2*b^2 - 5*A*a*b^3)*c^3)*d^2*e^4 - (3*B*b^7 - 14*B*a*b^5*c + 320*A*a^3*c^4 + 160*(B*a^3*b - A*a^2*b^2)*c^3 - 4*(8*B*a^2*b^3 - 5*A*a*b^4)*c^2)*d*e^5 - (2*B*a*b^6 - 5*A*b^7 + 32*(2*B*a^4 - 5*A*a^3*b)*c^3 - 6*(2*B*a^2*b^4 - 5*A*a*b^5)*c)*e^6)*x^3 + (8*(B*b^6*c - 6*B*a*b^4*c^2 + 32*B*a^3*c^4)*d^3*e^3 - (3*B*b^7 - 160*B*a^3*b*c^3 + 320*A*a^3*c^4 + 4*(32*B*a^2*b^3 - 15*A*a*b^4)*c^2 - 2*(17*B*a*b^5 - 5*A*b^6)*c)*d^2*e^4 - (8*B*a*b^6 - 5*A*b^7 + 32*(2*B*a^4 + 5*A*a^3*b)*c^3 + 32*(3*B*a^3*b^2 - 5*A*a^2*b^3)*c^2 - 10*(6*B*a^2*b^4 - 5*A*a*b^5)*c)*d*e^5 - 2*(2*B*a^2*b^5 - 5*A*a*b^6 + 16*(2*B*a^4*b - 5*A*a^3*b^2)*c^2 - 8*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c)*e^6)*x^2 + (16*(B*a*b^5*c - 8*B*a^2*b^3*c^2 + 16*B*a^3*b*c^3)*d^3*e^3 - 2*(3*B*a*b^6 - 32*(2*B*a^4 - 5*A*a^3*b)*c^3 + 80*(B*a^3*b^2 - A*a^2*b^3)*c^2 - 2*(14*B*a^2*b^4 - 5*A*a*b^5)*c)*d^2*e^4 - (7*B*a^2*b^5 - 10*A*a*b^6 + 160*A*a^4*c^3 + 16*(7*B*a^4*b - 15*A*a^3*b^2)*c^2 - 2*(28*B*a^3*b^3 - 45*A*a^2*b^4)*c)*d*e^5 - (2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(2*B*a^5 - 5*A*a^4*b)*c^2 - 8*(2*B*a^4*b^2 - 5*A*a^3*b^3)*c)*e^6)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(2*(4*(2*B*a^2 - 3*A*a*b)*c^5 + (2*B*a*b^2 + A*b^3)*c^4)*d^7 - 8*(4*A*a^2*c^5 + (4*B*a^2*b - 11*A*a*b^2)*c^4 + (2*B*a*b^3 + A*b^4)*c^3)*d^6*e + 4*(4*(10*B*a^3 - A*a^2*b)*c^4 - 2*(2*B*a^2*b^2 + 13*A*a*b^3)*c^3 + 3*(2*B*a*b^4 + A*b^5)*c^2)*d^5*e^2 - 8*(32*A*a^3*c^4 + 4*(9*B*a^3*b - 8*A*a^2*b^2)*c^3 - (7*B*a^2*b^3 + 3*A*a*b^4)*c^2 + (2*B*a*b^5 + A*b^6)*c)*d^4*e^3 + (4*B*a*b^6 + 2*A*b^7 + 8*(4*B*a^4 + 45*A*a^3*b)*c^3 + 2*(86*B*a^3*b^2 - 155*A*a^2*b^3)*c^2 - (31*B*a^2*b^4 - 32*A*a*b^5)*c)*d^3*e^4 + (7*B*a^2*b^5 - 16*A*a*b^6 - 176*A*a^4*c^3 - 16*(B*a^4*b + A*a^3*b^2)*c^2 - (48*B*a^3*b^3 - 91*A*a^2*b^4)*c)*d^2*e^5 - (11*B*a^3*b^4 - 11*A*a^2*b^5 + 112*(B*a^5 - A*a^4*b)*c^2 - 4*(20*B*a^4*b^2 - 19*A*a^3*b^3)*c)*d*e^6 + 3*(A*a^3*b^4 - 8*A*a^4*b^2*c + 16*A*a^5*c^2)*e^7 + (16*(B*b*c^6 - 2*A*c^7)*d^6*e - 8*(7*B*b^2*c^5 - 4*(B*a + 3*A*b)*c^6)*d^5*e^2 + 2*(29*B*b^3*c^4 - 88*A*a*c^6 + 2*(2*B*a*b - 19*A*b^2)*c^5)*d^4*e^3 - (27*B*b^4*c^3 + 176*(B*a^2 - 2*A*a*b)*c^5 + 8*(B*a*b^2 + A*b^3)*c^4)*d^3*e^4 + (9*B*b^5*c^2 - 16*A*a^2*c^5 + 16*(17*B*a^2*b - 16*A*a*b^2)*c^4 - (44*B*a*b^3 - 35*A*b^4)*c^3)*d^2*e^5 - (16*(13*B*a^3 - A*a^2*b)*c^4 - 16*(B*a^2*b^2 + 5*A*a*b^3)*c^3 + 3*(B*a*b^4 + 5*A*b^5)*c^2)*d*e^6 + (128*A*a^3*c^4 + 20*(2*B*a^3*b - 5*A*a^2*b^2)*c^3 - 3*(2*B*a^2*b^3 - 5*A*a*b^4)*c^2)*e^7)*x^4 + 2*(8*(B*b*c^6 - 2*A*c^7)*d^7 - 8*(2*B*b^2*c^5 - (2*B*a + 3*A*b)*c^6)*d^6*e - (13*B*b^3*c^4 + 88*A*a*c^6 - 2*(14*B*a*b + 17*A*b^2)*c^5)*d^5*e^2 + (36*B*b^4*c^3 + 4*(2*B*a^2 + 11*A*a*b)*c^5 - (46*B*a*b^2 + 61*A*b^3)*c^4)*d^4*e^3 - 2*(12*B*b^5*c^2 + 64*A*a^2*c^5 + 2*(32*B*a^2*b - 49*A*a*b^2)*c^4 - (19*B*a*b^3 + 2*A*b^4)*c^3)*d^3*e^4 + (9*B*b^6*c - 16*(2*B*a^3 - 11*A*a^2*b)*c^4 + 2*(106*B*a^2*b^2 - 121*A*a*b^3)*c^3 - 6*(8*B*a*b^4 - 5*A*b^5)*c^2)*d^2*e^5 - (56*A*a^3*c^4 + 2*(74*B*a^3*b + 19*A*a^2*b^2)*c^3 - 15*(B*a^2*b^3 + 6*A*a*b^4)*c^2 + 3*(B*a*b^5 + 5*A*b^6)*c)*d*e^6 - 3*(4*(2*B*a^4 - 13*A*a^3*b)*c^3 - 7*(2*B*a^3*b^2 - 5*A*a^2*b^3)*c^2 + (2*B*a^2*b^4 - 5*A*a*b^5)*c)*e^7)*x^3 + 3*(8*(B*b^2*c^5 - 2*A*b*c^6)*d^7 - 2*(13*B*b^3*c^4 + 8*A*a*c^6 - 2*(6*B*a*b + 11*A*b^2)*c^5)*d^6*e + 2*(12*B*b^4*c^3 + 4*(6*B*a^2 - 5*A*a*b)*c^5 - (18*B*a*b^2 + 13*A*b^3)*c^4)*d^5*e^2 - 4*(B*b^5*c^2 + 32*A*a^2*c^5 + 2*(6*B*a^2*b - 17*A*a*b^2)*c^4 - 2*(B*a*b^3 - 2*A*b^4)*c^3)*d^4*e^3 - (5*B*b^6*c + 68*A*a*b^3*c^3 + 64*(B*a^3 - 2*A*a^2*b)*c^4 - 14*(B*a*b^4 + A*b^5)*c^2)*d^3*e^4 + (3*B*b^7 - 48*A*a^3*c^4 + 4*(22*B*a^3*b + 7*A*a^2*b^2)*c^3 + 2*(11*B*a^2*b^3 - 21*A*a*b^4)*c^2 - (14*B*a*b^5 - 5*A*b^6)*c)*d^2*e^5 - (B*a*b^6 + 5*A*b^7 + 8*(14*B*a^4 + A*a^3*b)*c^3 + 2*(2*B*a^3*b^2 + 9*A*a^2*b^3)*c^2 - 2*(B*a^2*b^4 + 15*A*a*b^5)*c)*d*e^6 - (2*B*a^2*b^5 - 5*A*a*b^6 - 16*A*a^3*b^2*c^2 - 64*A*a^4*c^3 - 6*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c)*e^7)*x^2 + 2*(3*(B*b^3*c^4 - 8*A*a*c^6 + 2*(2*B*a*b - A*b^2)*c^5)*d^7 - (12*B*b^4*c^3 - 4*(2*B*a^2 + 15*A*a*b)*c^5 + (22*B*a*b^2 - 19*A*b^3)*c^4)*d^6*e + 2*(9*B*b^5*c^2 - 56*A*a^2*c^5 + 4*(13*B*a^2*b - 8*A*a*b^2)*c^4 - 2*(5*B*a*b^3 + 4*A*b^4)*c^3)*d^5*e^2 - 2*(6*B*b^6*c + 4*(2*B*a^3 - 11*A*a^2*b)*c^4 + 2*(44*B*a^2*b^2 - 23*A*a*b^3)*c^3 - 3*(8*B*a*b^4 - A*b^5)*c^2)*d^4*e^3 + (3*B*b^7 - 152*A*a^3*c^4 + 2*(6*B*a^3*b + 61*A*a^2*b^2)*c^3 + (91*B*a^2*b^3 - 102*A*a*b^4)*c^2 - (23*B*a*b^5 - 14*A*b^6)*c)*d^3*e^4 + (5*B*a*b^6 - 5*A*b^7 - 4*(14*B*a^4 - 39*A*a^3*b)*c^3 + (74*B*a^3*b^2 - 125*A*a^2*b^3)*c^2 - (38*B*a^2*b^4 - 43*A*a*b^5)*c)*d^2*e^5 - (4*B*a^2*b^5 + 5*A*a*b^6 + 64*A*a^4*c^3 + 20*(4*B*a^4*b + A*a^3*b^2)*c^2 - 2*(15*B*a^3*b^3 + 16*A*a^2*b^4)*c)*d*e^6 - 2*(2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(B*a^5 - 4*A*a^4*b)*c^2 - (14*B*a^4*b^2 - 37*A*a^3*b^3)*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6)*d^9 - 4*(a^2*b^5*c^3 - 8*a^3*b^3*c^4 + 16*a^4*b*c^5)*d^8*e + 2*(3*a^2*b^6*c^2 - 22*a^3*b^4*c^3 + 32*a^4*b^2*c^4 + 32*a^5*c^5)*d^7*e^2 - 4*(a^2*b^7*c - 5*a^3*b^5*c^2 - 8*a^4*b^3*c^3 + 48*a^5*b*c^4)*d^6*e^3 + (a^2*b^8 + 4*a^3*b^6*c - 74*a^4*b^4*c^2 + 144*a^5*b^2*c^3 + 96*a^6*c^4)*d^5*e^4 - 4*(a^3*b^7 - 5*a^4*b^5*c - 8*a^5*b^3*c^2 + 48*a^6*b*c^3)*d^4*e^5 + 2*(3*a^4*b^6 - 22*a^5*b^4*c + 32*a^6*b^2*c^2 + 32*a^7*c^3)*d^3*e^6 - 4*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*d^2*e^7 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*d*e^8 + ((b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^8*e - 4*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^7*e^2 + 2*(3*b^6*c^4 - 22*a*b^4*c^5 + 32*a^2*b^2*c^6 + 32*a^3*c^7)*d^6*e^3 - 4*(b^7*c^3 - 5*a*b^5*c^4 - 8*a^2*b^3*c^5 + 48*a^3*b*c^6)*d^5*e^4 + (b^8*c^2 + 4*a*b^6*c^3 - 74*a^2*b^4*c^4 + 144*a^3*b^2*c^5 + 96*a^4*c^6)*d^4*e^5 - 4*(a*b^7*c^2 - 5*a^2*b^5*c^3 - 8*a^3*b^3*c^4 + 48*a^4*b*c^5)*d^3*e^6 + 2*(3*a^2*b^6*c^2 - 22*a^3*b^4*c^3 + 32*a^4*b^2*c^4 + 32*a^5*c^5)*d^2*e^7 - 4*(a^3*b^5*c^2 - 8*a^4*b^3*c^3 + 16*a^5*b*c^4)*d*e^8 + (a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)*e^9)*x^5 + ((b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^9 - 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^8*e - 2*(b^6*c^4 - 10*a*b^4*c^5 + 32*a^2*b^2*c^6 - 32*a^3*c^7)*d^7*e^2 + 4*(2*b^7*c^3 - 17*a*b^5*c^4 + 40*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^6*e^3 - (7*b^8*c^2 - 44*a*b^6*c^3 + 10*a^2*b^4*c^4 + 240*a^3*b^2*c^5 - 96*a^4*c^6)*d^5*e^4 + 2*(b^9*c + 2*a*b^7*c^2 - 64*a^2*b^5*c^3 + 160*a^3*b^3*c^4)*d^4*e^5 - 2*(4*a*b^8*c - 23*a^2*b^6*c^2 - 10*a^3*b^4*c^3 + 160*a^4*b^2*c^4 - 32*a^5*c^5)*d^3*e^6 + 4*(3*a^2*b^7*c - 23*a^3*b^5*c^2 + 40*a^4*b^3*c^3 + 16*a^5*b*c^4)*d^2*e^7 - (8*a^3*b^6*c - 65*a^4*b^4*c^2 + 136*a^5*b^2*c^3 - 16*a^6*c^4)*d*e^8 + 2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)*e^9)*x^4 + (2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^9 - (7*b^6*c^4 - 58*a*b^4*c^5 + 128*a^2*b^2*c^6 - 32*a^3*c^7)*d^8*e + 8*(b^7*c^3 - 8*a*b^5*c^4 + 16*a^2*b^3*c^5)*d^7*e^2 - 2*(b^8*c^2 - 4*a*b^6*c^3 - 20*a^2*b^4*c^4 + 96*a^3*b^2*c^5 - 64*a^4*c^6)*d^6*e^3 - 2*(b^9*c - 10*a*b^7*c^2 + 38*a^2*b^5*c^3 - 80*a^3*b^3*c^4 + 96*a^4*b*c^5)*d^5*e^4 + (b^10 - 2*a*b^8*c - 26*a^2*b^6*c^2 + 60*a^3*b^4*c^3 + 192*a^5*c^5)*d^4*e^5 - 4*(a*b^9 - 6*a^2*b^7*c + 4*a^3*b^5*c^2 + 64*a^5*b*c^4)*d^3*e^6 + 2*(3*a^2*b^8 - 20*a^3*b^6*c + 20*a^4*b^4*c^2 + 32*a^5*b^2*c^3 + 64*a^6*c^4)*d^2*e^7 - 2*(2*a^3*b^7 - 13*a^4*b^5*c + 8*a^5*b^3*c^2 + 48*a^6*b*c^3)*d*e^8 + (a^4*b^6 - 6*a^5*b^4*c + 32*a^7*c^3)*e^9)*x^3 + ((b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*d^9 - 2*(2*b^7*c^3 - 13*a*b^5*c^4 + 8*a^2*b^3*c^5 + 48*a^3*b*c^6)*d^8*e + 2*(3*b^8*c^2 - 20*a*b^6*c^3 + 20*a^2*b^4*c^4 + 32*a^3*b^2*c^5 + 64*a^4*c^6)*d^7*e^2 - 4*(b^9*c - 6*a*b^7*c^2 + 4*a^2*b^5*c^3 + 64*a^4*b*c^5)*d^6*e^3 + (b^10 - 2*a*b^8*c - 26*a^2*b^6*c^2 + 60*a^3*b^4*c^3 + 192*a^5*c^5)*d^5*e^4 - 2*(a*b^9 - 10*a^2*b^7*c + 38*a^3*b^5*c^2 - 80*a^4*b^3*c^3 + 96*a^5*b*c^4)*d^4*e^5 - 2*(a^2*b^8 - 4*a^3*b^6*c - 20*a^4*b^4*c^2 + 96*a^5*b^2*c^3 - 64*a^6*c^4)*d^3*e^6 + 8*(a^3*b^7 - 8*a^4*b^5*c + 16*a^5*b^3*c^2)*d^2*e^7 - (7*a^4*b^6 - 58*a^5*b^4*c + 128*a^6*b^2*c^2 - 32*a^7*c^3)*d*e^8 + 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*e^9)*x^2 + (2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*d^9 - (8*a*b^6*c^3 - 65*a^2*b^4*c^4 + 136*a^3*b^2*c^5 - 16*a^4*c^6)*d^8*e + 4*(3*a*b^7*c^2 - 23*a^2*b^5*c^3 + 40*a^3*b^3*c^4 + 16*a^4*b*c^5)*d^7*e^2 - 2*(4*a*b^8*c - 23*a^2*b^6*c^2 - 10*a^3*b^4*c^3 + 160*a^4*b^2*c^4 - 32*a^5*c^5)*d^6*e^3 + 2*(a*b^9 + 2*a^2*b^7*c - 64*a^3*b^5*c^2 + 160*a^4*b^3*c^3)*d^5*e^4 - (7*a^2*b^8 - 44*a^3*b^6*c + 10*a^4*b^4*c^2 + 240*a^5*b^2*c^3 - 96*a^6*c^4)*d^4*e^5 + 4*(2*a^3*b^7 - 17*a^4*b^5*c + 40*a^5*b^3*c^2 - 16*a^6*b*c^3)*d^3*e^6 - 2*(a^4*b^6 - 10*a^5*b^4*c + 32*a^6*b^2*c^2 - 32*a^7*c^3)*d^2*e^7 - 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*d*e^8 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*e^9)*x), -1/6*(3*(8*(B*a^2*b^4*c - 8*B*a^3*b^2*c^2 + 16*B*a^4*c^3)*d^3*e^3 - (3*B*a^2*b^5 + 160*A*a^4*c^3 + 16*(3*B*a^4*b - 5*A*a^3*b^2)*c^2 - 2*(12*B*a^3*b^3 - 5*A*a^2*b^4)*c)*d^2*e^4 - (2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(2*B*a^5 - 5*A*a^4*b)*c^2 - 8*(2*B*a^4*b^2 - 5*A*a^3*b^3)*c)*d*e^5 + (8*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*d^2*e^4 - (3*B*b^5*c^2 + 160*A*a^2*c^5 + 16*(3*B*a^2*b - 5*A*a*b^2)*c^4 - 2*(12*B*a*b^3 - 5*A*b^4)*c^3)*d*e^5 - (16*(2*B*a^3 - 5*A*a^2*b)*c^4 - 8*(2*B*a^2*b^2 - 5*A*a*b^3)*c^3 + (2*B*a*b^4 - 5*A*b^5)*c^2)*e^6)*x^5 + (8*(B*b^4*c^3 - 8*B*a*b^2*c^4 + 16*B*a^2*c^5)*d^3*e^3 + (13*B*b^5*c^2 - 160*A*a^2*c^5 + 16*(13*B*a^2*b + 5*A*a*b^2)*c^4 - 2*(52*B*a*b^3 + 5*A*b^4)*c^3)*d^2*e^4 - (6*B*b^6*c + 16*(2*B*a^3 + 15*A*a^2*b)*c^4 + 40*(2*B*a^2*b^2 - 3*A*a*b^3)*c^3 - (46*B*a*b^4 - 15*A*b^5)*c^2)*d*e^5 - 2*(16*(2*B*a^3*b - 5*A*a^2*b^2)*c^3 - 8*(2*B*a^2*b^3 - 5*A*a*b^4)*c^2 + (2*B*a*b^5 - 5*A*b^6)*c)*e^6)*x^4 + (16*(B*b^5*c^2 - 8*B*a*b^3*c^3 + 16*B*a^2*b*c^4)*d^3*e^3 + 2*(B*b^6*c - 10*A*b^5*c^2 + 32*(4*B*a^3 - 5*A*a^2*b)*c^4 - 16*(3*B*a^2*b^2 - 5*A*a*b^3)*c^3)*d^2*e^4 - (3*B*b^7 - 14*B*a*b^5*c + 320*A*a^3*c^4 + 160*(B*a^3*b - A*a^2*b^2)*c^3 - 4*(8*B*a^2*b^3 - 5*A*a*b^4)*c^2)*d*e^5 - (2*B*a*b^6 - 5*A*b^7 + 32*(2*B*a^4 - 5*A*a^3*b)*c^3 - 6*(2*B*a^2*b^4 - 5*A*a*b^5)*c)*e^6)*x^3 + (8*(B*b^6*c - 6*B*a*b^4*c^2 + 32*B*a^3*c^4)*d^3*e^3 - (3*B*b^7 - 160*B*a^3*b*c^3 + 320*A*a^3*c^4 + 4*(32*B*a^2*b^3 - 15*A*a*b^4)*c^2 - 2*(17*B*a*b^5 - 5*A*b^6)*c)*d^2*e^4 - (8*B*a*b^6 - 5*A*b^7 + 32*(2*B*a^4 + 5*A*a^3*b)*c^3 + 32*(3*B*a^3*b^2 - 5*A*a^2*b^3)*c^2 - 10*(6*B*a^2*b^4 - 5*A*a*b^5)*c)*d*e^5 - 2*(2*B*a^2*b^5 - 5*A*a*b^6 + 16*(2*B*a^4*b - 5*A*a^3*b^2)*c^2 - 8*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c)*e^6)*x^2 + (16*(B*a*b^5*c - 8*B*a^2*b^3*c^2 + 16*B*a^3*b*c^3)*d^3*e^3 - 2*(3*B*a*b^6 - 32*(2*B*a^4 - 5*A*a^3*b)*c^3 + 80*(B*a^3*b^2 - A*a^2*b^3)*c^2 - 2*(14*B*a^2*b^4 - 5*A*a*b^5)*c)*d^2*e^4 - (7*B*a^2*b^5 - 10*A*a*b^6 + 160*A*a^4*c^3 + 16*(7*B*a^4*b - 15*A*a^3*b^2)*c^2 - 2*(28*B*a^3*b^3 - 45*A*a^2*b^4)*c)*d*e^5 - (2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(2*B*a^5 - 5*A*a^4*b)*c^2 - 8*(2*B*a^4*b^2 - 5*A*a^3*b^3)*c)*e^6)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(2*(4*(2*B*a^2 - 3*A*a*b)*c^5 + (2*B*a*b^2 + A*b^3)*c^4)*d^7 - 8*(4*A*a^2*c^5 + (4*B*a^2*b - 11*A*a*b^2)*c^4 + (2*B*a*b^3 + A*b^4)*c^3)*d^6*e + 4*(4*(10*B*a^3 - A*a^2*b)*c^4 - 2*(2*B*a^2*b^2 + 13*A*a*b^3)*c^3 + 3*(2*B*a*b^4 + A*b^5)*c^2)*d^5*e^2 - 8*(32*A*a^3*c^4 + 4*(9*B*a^3*b - 8*A*a^2*b^2)*c^3 - (7*B*a^2*b^3 + 3*A*a*b^4)*c^2 + (2*B*a*b^5 + A*b^6)*c)*d^4*e^3 + (4*B*a*b^6 + 2*A*b^7 + 8*(4*B*a^4 + 45*A*a^3*b)*c^3 + 2*(86*B*a^3*b^2 - 155*A*a^2*b^3)*c^2 - (31*B*a^2*b^4 - 32*A*a*b^5)*c)*d^3*e^4 + (7*B*a^2*b^5 - 16*A*a*b^6 - 176*A*a^4*c^3 - 16*(B*a^4*b + A*a^3*b^2)*c^2 - (48*B*a^3*b^3 - 91*A*a^2*b^4)*c)*d^2*e^5 - (11*B*a^3*b^4 - 11*A*a^2*b^5 + 112*(B*a^5 - A*a^4*b)*c^2 - 4*(20*B*a^4*b^2 - 19*A*a^3*b^3)*c)*d*e^6 + 3*(A*a^3*b^4 - 8*A*a^4*b^2*c + 16*A*a^5*c^2)*e^7 + (16*(B*b*c^6 - 2*A*c^7)*d^6*e - 8*(7*B*b^2*c^5 - 4*(B*a + 3*A*b)*c^6)*d^5*e^2 + 2*(29*B*b^3*c^4 - 88*A*a*c^6 + 2*(2*B*a*b - 19*A*b^2)*c^5)*d^4*e^3 - (27*B*b^4*c^3 + 176*(B*a^2 - 2*A*a*b)*c^5 + 8*(B*a*b^2 + A*b^3)*c^4)*d^3*e^4 + (9*B*b^5*c^2 - 16*A*a^2*c^5 + 16*(17*B*a^2*b - 16*A*a*b^2)*c^4 - (44*B*a*b^3 - 35*A*b^4)*c^3)*d^2*e^5 - (16*(13*B*a^3 - A*a^2*b)*c^4 - 16*(B*a^2*b^2 + 5*A*a*b^3)*c^3 + 3*(B*a*b^4 + 5*A*b^5)*c^2)*d*e^6 + (128*A*a^3*c^4 + 20*(2*B*a^3*b - 5*A*a^2*b^2)*c^3 - 3*(2*B*a^2*b^3 - 5*A*a*b^4)*c^2)*e^7)*x^4 + 2*(8*(B*b*c^6 - 2*A*c^7)*d^7 - 8*(2*B*b^2*c^5 - (2*B*a + 3*A*b)*c^6)*d^6*e - (13*B*b^3*c^4 + 88*A*a*c^6 - 2*(14*B*a*b + 17*A*b^2)*c^5)*d^5*e^2 + (36*B*b^4*c^3 + 4*(2*B*a^2 + 11*A*a*b)*c^5 - (46*B*a*b^2 + 61*A*b^3)*c^4)*d^4*e^3 - 2*(12*B*b^5*c^2 + 64*A*a^2*c^5 + 2*(32*B*a^2*b - 49*A*a*b^2)*c^4 - (19*B*a*b^3 + 2*A*b^4)*c^3)*d^3*e^4 + (9*B*b^6*c - 16*(2*B*a^3 - 11*A*a^2*b)*c^4 + 2*(106*B*a^2*b^2 - 121*A*a*b^3)*c^3 - 6*(8*B*a*b^4 - 5*A*b^5)*c^2)*d^2*e^5 - (56*A*a^3*c^4 + 2*(74*B*a^3*b + 19*A*a^2*b^2)*c^3 - 15*(B*a^2*b^3 + 6*A*a*b^4)*c^2 + 3*(B*a*b^5 + 5*A*b^6)*c)*d*e^6 - 3*(4*(2*B*a^4 - 13*A*a^3*b)*c^3 - 7*(2*B*a^3*b^2 - 5*A*a^2*b^3)*c^2 + (2*B*a^2*b^4 - 5*A*a*b^5)*c)*e^7)*x^3 + 3*(8*(B*b^2*c^5 - 2*A*b*c^6)*d^7 - 2*(13*B*b^3*c^4 + 8*A*a*c^6 - 2*(6*B*a*b + 11*A*b^2)*c^5)*d^6*e + 2*(12*B*b^4*c^3 + 4*(6*B*a^2 - 5*A*a*b)*c^5 - (18*B*a*b^2 + 13*A*b^3)*c^4)*d^5*e^2 - 4*(B*b^5*c^2 + 32*A*a^2*c^5 + 2*(6*B*a^2*b - 17*A*a*b^2)*c^4 - 2*(B*a*b^3 - 2*A*b^4)*c^3)*d^4*e^3 - (5*B*b^6*c + 68*A*a*b^3*c^3 + 64*(B*a^3 - 2*A*a^2*b)*c^4 - 14*(B*a*b^4 + A*b^5)*c^2)*d^3*e^4 + (3*B*b^7 - 48*A*a^3*c^4 + 4*(22*B*a^3*b + 7*A*a^2*b^2)*c^3 + 2*(11*B*a^2*b^3 - 21*A*a*b^4)*c^2 - (14*B*a*b^5 - 5*A*b^6)*c)*d^2*e^5 - (B*a*b^6 + 5*A*b^7 + 8*(14*B*a^4 + A*a^3*b)*c^3 + 2*(2*B*a^3*b^2 + 9*A*a^2*b^3)*c^2 - 2*(B*a^2*b^4 + 15*A*a*b^5)*c)*d*e^6 - (2*B*a^2*b^5 - 5*A*a*b^6 - 16*A*a^3*b^2*c^2 - 64*A*a^4*c^3 - 6*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c)*e^7)*x^2 + 2*(3*(B*b^3*c^4 - 8*A*a*c^6 + 2*(2*B*a*b - A*b^2)*c^5)*d^7 - (12*B*b^4*c^3 - 4*(2*B*a^2 + 15*A*a*b)*c^5 + (22*B*a*b^2 - 19*A*b^3)*c^4)*d^6*e + 2*(9*B*b^5*c^2 - 56*A*a^2*c^5 + 4*(13*B*a^2*b - 8*A*a*b^2)*c^4 - 2*(5*B*a*b^3 + 4*A*b^4)*c^3)*d^5*e^2 - 2*(6*B*b^6*c + 4*(2*B*a^3 - 11*A*a^2*b)*c^4 + 2*(44*B*a^2*b^2 - 23*A*a*b^3)*c^3 - 3*(8*B*a*b^4 - A*b^5)*c^2)*d^4*e^3 + (3*B*b^7 - 152*A*a^3*c^4 + 2*(6*B*a^3*b + 61*A*a^2*b^2)*c^3 + (91*B*a^2*b^3 - 102*A*a*b^4)*c^2 - (23*B*a*b^5 - 14*A*b^6)*c)*d^3*e^4 + (5*B*a*b^6 - 5*A*b^7 - 4*(14*B*a^4 - 39*A*a^3*b)*c^3 + (74*B*a^3*b^2 - 125*A*a^2*b^3)*c^2 - (38*B*a^2*b^4 - 43*A*a*b^5)*c)*d^2*e^5 - (4*B*a^2*b^5 + 5*A*a*b^6 + 64*A*a^4*c^3 + 20*(4*B*a^4*b + A*a^3*b^2)*c^2 - 2*(15*B*a^3*b^3 + 16*A*a^2*b^4)*c)*d*e^6 - 2*(2*B*a^3*b^4 - 5*A*a^2*b^5 + 16*(B*a^5 - 4*A*a^4*b)*c^2 - (14*B*a^4*b^2 - 37*A*a^3*b^3)*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6)*d^9 - 4*(a^2*b^5*c^3 - 8*a^3*b^3*c^4 + 16*a^4*b*c^5)*d^8*e + 2*(3*a^2*b^6*c^2 - 22*a^3*b^4*c^3 + 32*a^4*b^2*c^4 + 32*a^5*c^5)*d^7*e^2 - 4*(a^2*b^7*c - 5*a^3*b^5*c^2 - 8*a^4*b^3*c^3 + 48*a^5*b*c^4)*d^6*e^3 + (a^2*b^8 + 4*a^3*b^6*c - 74*a^4*b^4*c^2 + 144*a^5*b^2*c^3 + 96*a^6*c^4)*d^5*e^4 - 4*(a^3*b^7 - 5*a^4*b^5*c - 8*a^5*b^3*c^2 + 48*a^6*b*c^3)*d^4*e^5 + 2*(3*a^4*b^6 - 22*a^5*b^4*c + 32*a^6*b^2*c^2 + 32*a^7*c^3)*d^3*e^6 - 4*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*d^2*e^7 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*d*e^8 + ((b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^8*e - 4*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^7*e^2 + 2*(3*b^6*c^4 - 22*a*b^4*c^5 + 32*a^2*b^2*c^6 + 32*a^3*c^7)*d^6*e^3 - 4*(b^7*c^3 - 5*a*b^5*c^4 - 8*a^2*b^3*c^5 + 48*a^3*b*c^6)*d^5*e^4 + (b^8*c^2 + 4*a*b^6*c^3 - 74*a^2*b^4*c^4 + 144*a^3*b^2*c^5 + 96*a^4*c^6)*d^4*e^5 - 4*(a*b^7*c^2 - 5*a^2*b^5*c^3 - 8*a^3*b^3*c^4 + 48*a^4*b*c^5)*d^3*e^6 + 2*(3*a^2*b^6*c^2 - 22*a^3*b^4*c^3 + 32*a^4*b^2*c^4 + 32*a^5*c^5)*d^2*e^7 - 4*(a^3*b^5*c^2 - 8*a^4*b^3*c^3 + 16*a^5*b*c^4)*d*e^8 + (a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)*e^9)*x^5 + ((b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^9 - 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^8*e - 2*(b^6*c^4 - 10*a*b^4*c^5 + 32*a^2*b^2*c^6 - 32*a^3*c^7)*d^7*e^2 + 4*(2*b^7*c^3 - 17*a*b^5*c^4 + 40*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^6*e^3 - (7*b^8*c^2 - 44*a*b^6*c^3 + 10*a^2*b^4*c^4 + 240*a^3*b^2*c^5 - 96*a^4*c^6)*d^5*e^4 + 2*(b^9*c + 2*a*b^7*c^2 - 64*a^2*b^5*c^3 + 160*a^3*b^3*c^4)*d^4*e^5 - 2*(4*a*b^8*c - 23*a^2*b^6*c^2 - 10*a^3*b^4*c^3 + 160*a^4*b^2*c^4 - 32*a^5*c^5)*d^3*e^6 + 4*(3*a^2*b^7*c - 23*a^3*b^5*c^2 + 40*a^4*b^3*c^3 + 16*a^5*b*c^4)*d^2*e^7 - (8*a^3*b^6*c - 65*a^4*b^4*c^2 + 136*a^5*b^2*c^3 - 16*a^6*c^4)*d*e^8 + 2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)*e^9)*x^4 + (2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^9 - (7*b^6*c^4 - 58*a*b^4*c^5 + 128*a^2*b^2*c^6 - 32*a^3*c^7)*d^8*e + 8*(b^7*c^3 - 8*a*b^5*c^4 + 16*a^2*b^3*c^5)*d^7*e^2 - 2*(b^8*c^2 - 4*a*b^6*c^3 - 20*a^2*b^4*c^4 + 96*a^3*b^2*c^5 - 64*a^4*c^6)*d^6*e^3 - 2*(b^9*c - 10*a*b^7*c^2 + 38*a^2*b^5*c^3 - 80*a^3*b^3*c^4 + 96*a^4*b*c^5)*d^5*e^4 + (b^10 - 2*a*b^8*c - 26*a^2*b^6*c^2 + 60*a^3*b^4*c^3 + 192*a^5*c^5)*d^4*e^5 - 4*(a*b^9 - 6*a^2*b^7*c + 4*a^3*b^5*c^2 + 64*a^5*b*c^4)*d^3*e^6 + 2*(3*a^2*b^8 - 20*a^3*b^6*c + 20*a^4*b^4*c^2 + 32*a^5*b^2*c^3 + 64*a^6*c^4)*d^2*e^7 - 2*(2*a^3*b^7 - 13*a^4*b^5*c + 8*a^5*b^3*c^2 + 48*a^6*b*c^3)*d*e^8 + (a^4*b^6 - 6*a^5*b^4*c + 32*a^7*c^3)*e^9)*x^3 + ((b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*d^9 - 2*(2*b^7*c^3 - 13*a*b^5*c^4 + 8*a^2*b^3*c^5 + 48*a^3*b*c^6)*d^8*e + 2*(3*b^8*c^2 - 20*a*b^6*c^3 + 20*a^2*b^4*c^4 + 32*a^3*b^2*c^5 + 64*a^4*c^6)*d^7*e^2 - 4*(b^9*c - 6*a*b^7*c^2 + 4*a^2*b^5*c^3 + 64*a^4*b*c^5)*d^6*e^3 + (b^10 - 2*a*b^8*c - 26*a^2*b^6*c^2 + 60*a^3*b^4*c^3 + 192*a^5*c^5)*d^5*e^4 - 2*(a*b^9 - 10*a^2*b^7*c + 38*a^3*b^5*c^2 - 80*a^4*b^3*c^3 + 96*a^5*b*c^4)*d^4*e^5 - 2*(a^2*b^8 - 4*a^3*b^6*c - 20*a^4*b^4*c^2 + 96*a^5*b^2*c^3 - 64*a^6*c^4)*d^3*e^6 + 8*(a^3*b^7 - 8*a^4*b^5*c + 16*a^5*b^3*c^2)*d^2*e^7 - (7*a^4*b^6 - 58*a^5*b^4*c + 128*a^6*b^2*c^2 - 32*a^7*c^3)*d*e^8 + 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*e^9)*x^2 + (2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*d^9 - (8*a*b^6*c^3 - 65*a^2*b^4*c^4 + 136*a^3*b^2*c^5 - 16*a^4*c^6)*d^8*e + 4*(3*a*b^7*c^2 - 23*a^2*b^5*c^3 + 40*a^3*b^3*c^4 + 16*a^4*b*c^5)*d^7*e^2 - 2*(4*a*b^8*c - 23*a^2*b^6*c^2 - 10*a^3*b^4*c^3 + 160*a^4*b^2*c^4 - 32*a^5*c^5)*d^6*e^3 + 2*(a*b^9 + 2*a^2*b^7*c - 64*a^3*b^5*c^2 + 160*a^4*b^3*c^3)*d^5*e^4 - (7*a^2*b^8 - 44*a^3*b^6*c + 10*a^4*b^4*c^2 + 240*a^5*b^2*c^3 - 96*a^6*c^4)*d^4*e^5 + 4*(2*a^3*b^7 - 17*a^4*b^5*c + 40*a^5*b^3*c^2 - 16*a^6*b*c^3)*d^3*e^6 - 2*(a^4*b^6 - 10*a^5*b^4*c + 32*a^6*b^2*c^2 - 32*a^7*c^3)*d^2*e^7 - 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*d*e^8 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*e^9)*x)]","B",0
2487,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)^6/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2488,1,5253,0,80.935020," ","integrate((B*x+A)*(e*x+d)^5/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(B b^{6} c^{3} - 12 \, B a b^{4} c^{4} + 48 \, B a^{2} b^{2} c^{5} - 64 \, B a^{3} c^{6}\right)} e^{5} x^{6} + 3 \, {\left(B b^{7} c^{2} - 12 \, B a b^{5} c^{3} + 48 \, B a^{2} b^{3} c^{4} - 64 \, B a^{3} b c^{5}\right)} e^{5} x^{5} + 3 \, {\left(B b^{8} c - 11 \, B a b^{6} c^{2} + 36 \, B a^{2} b^{4} c^{3} - 16 \, B a^{3} b^{2} c^{4} - 64 \, B a^{4} c^{5}\right)} e^{5} x^{4} + {\left(B b^{9} - 6 \, B a b^{7} c - 24 \, B a^{2} b^{5} c^{2} + 224 \, B a^{3} b^{3} c^{3} - 384 \, B a^{4} b c^{4}\right)} e^{5} x^{3} + 3 \, {\left(B a b^{8} - 11 \, B a^{2} b^{6} c + 36 \, B a^{3} b^{4} c^{2} - 16 \, B a^{4} b^{2} c^{3} - 64 \, B a^{5} c^{4}\right)} e^{5} x^{2} + 3 \, {\left(B a^{2} b^{7} - 12 \, B a^{3} b^{5} c + 48 \, B a^{4} b^{3} c^{2} - 64 \, B a^{5} b c^{3}\right)} e^{5} x + {\left(B a^{3} b^{6} - 12 \, B a^{4} b^{4} c + 48 \, B a^{5} b^{2} c^{2} - 64 \, B a^{6} c^{3}\right)} e^{5}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(640 \, {\left(2 \, B a^{5} - A a^{4} b\right)} c^{4} d e^{4} + {\left(48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{6} + 8 \, {\left(6 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{5} - {\left(2 \, B a b^{4} + 3 \, A b^{5}\right)} c^{4}\right)} d^{5} + 10 \, {\left(48 \, A a^{3} c^{6} - 24 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c^{5} - {\left(4 \, B a^{2} b^{3} + A a b^{4}\right)} c^{4}\right)} d^{4} e + 80 \, {\left(4 \, {\left(2 \, B a^{4} - 3 \, A a^{3} b\right)} c^{5} + {\left(6 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{4}\right)} d^{3} e^{2} + 160 \, {\left(4 \, A a^{4} c^{5} - {\left(8 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} c^{4}\right)} d^{2} e^{3} - {\left(15 \, B a^{3} b^{5} c - 160 \, B a^{4} b^{3} c^{2} + 528 \, B a^{5} b c^{3} - 256 \, A a^{5} c^{4}\right)} e^{5} + {\left(128 \, {\left(B b c^{8} - 2 \, A c^{9}\right)} d^{5} - 80 \, {\left(3 \, B b^{2} c^{7} + 4 \, {\left(B a - 2 \, A b\right)} c^{8}\right)} d^{4} e + 80 \, {\left(B b^{3} c^{6} - 8 \, A a c^{8} + 6 \, {\left(2 \, B a b - A b^{2}\right)} c^{7}\right)} d^{3} e^{2} + 20 \, {\left(B b^{4} c^{5} - 48 \, {\left(B a^{2} - A a b\right)} c^{7} - 4 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{6}\right)} d^{2} e^{3} + 5 \, {\left(3 \, B b^{5} c^{4} - 96 \, A a^{2} c^{7} + 48 \, {\left(5 \, B a^{2} b - A a b^{2}\right)} c^{6} - 2 \, {\left(20 \, B a b^{3} - A b^{4}\right)} c^{5}\right)} d e^{4} - {\left(23 \, B b^{6} c^{3} - 16 \, {\left(46 \, B a^{3} + 15 \, A a^{2} b\right)} c^{6} + 8 \, {\left(114 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{5} - 3 \, {\left(86 \, B a b^{4} + A b^{5}\right)} c^{4}\right)} e^{5}\right)} x^{5} + 5 \, {\left(64 \, {\left(B b^{2} c^{7} - 2 \, A b c^{8}\right)} d^{5} - 40 \, {\left(3 \, B b^{3} c^{6} + 4 \, {\left(B a b - 2 \, A b^{2}\right)} c^{7}\right)} d^{4} e + 40 \, {\left(B b^{4} c^{5} - 8 \, A a b c^{7} + 6 \, {\left(2 \, B a b^{2} - A b^{3}\right)} c^{6}\right)} d^{3} e^{2} + 10 \, {\left(B b^{5} c^{4} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{6} - 4 \, {\left(6 \, B a b^{3} - A b^{4}\right)} c^{5}\right)} d^{2} e^{3} + 5 \, {\left(48 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{6} + 24 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c^{5} - {\left(2 \, B a b^{4} - A b^{5}\right)} c^{4}\right)} d e^{4} - {\left(7 \, B b^{7} c^{2} - 75 \, B a b^{5} c^{3} - 96 \, A a^{3} c^{6} - 16 \, {\left(5 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{5} + 2 \, {\left(120 \, B a^{2} b^{3} + A a b^{4}\right)} c^{4}\right)} e^{5}\right)} x^{4} + 5 \, {\left(16 \, {\left(3 \, B b^{3} c^{6} - 8 \, A a c^{8} + 2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{7}\right)} d^{5} - 10 \, {\left(9 \, B b^{4} c^{5} + 16 \, {\left(B a^{2} - 2 \, A a b\right)} c^{7} + 24 \, {\left(B a b^{2} - A b^{3}\right)} c^{6}\right)} d^{4} e + 10 \, {\left(3 \, B b^{5} c^{4} - 32 \, A a^{2} c^{7} + 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{6} + 2 \, {\left(20 \, B a b^{3} - 9 \, A b^{4}\right)} c^{5}\right)} d^{3} e^{2} + 10 \, {\left(48 \, A a^{2} b c^{6} - 8 \, {\left(12 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{5} - {\left(8 \, B a b^{4} - 3 \, A b^{5}\right)} c^{4}\right)} d^{2} e^{3} + 40 \, {\left(12 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c^{5} + {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} c^{4}\right)} d e^{4} - {\left(3 \, B b^{8} c - 20 \, B a b^{6} c^{2} - 30 \, B a^{2} b^{4} c^{3} - 32 \, {\left(7 \, B a^{4} + 6 \, A a^{3} b\right)} c^{5} + 16 \, {\left(27 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{4}\right)} e^{5}\right)} x^{3} + 5 \, {\left(8 \, {\left(B b^{4} c^{5} - 24 \, A a b c^{7} + 2 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{6}\right)} d^{5} - 5 \, {\left(3 \, B b^{5} c^{4} + 48 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} c^{6} + 8 \, {\left(5 \, B a b^{3} - A b^{4}\right)} c^{5}\right)} d^{4} e + 10 \, {\left(16 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{6} + 8 \, {\left(6 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{5} + 3 \, {\left(6 \, B a b^{4} - A b^{5}\right)} c^{4}\right)} d^{3} e^{2} + 20 \, {\left(16 \, A a^{3} c^{6} - 8 \, {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c^{5} - 3 \, {\left(8 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} c^{4}\right)} d^{2} e^{3} + 80 \, {\left(4 \, {\left(2 \, B a^{4} - A a^{3} b\right)} c^{5} + 3 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{4}\right)} d e^{4} - {\left(9 \, B a b^{7} c - 93 \, B a^{2} b^{5} c^{2} + 280 \, B a^{3} b^{3} c^{3} - 128 \, A a^{4} c^{5} + 48 \, {\left(B a^{4} b - 2 \, A a^{3} b^{2}\right)} c^{4}\right)} e^{5}\right)} x^{2} + 5 \, {\left(320 \, {\left(2 \, B a^{4} b - A a^{3} b^{2}\right)} c^{4} d e^{4} - {\left(B b^{5} c^{4} + 96 \, A a^{2} c^{7} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{6} - 2 \, {\left(12 \, B a b^{3} + A b^{4}\right)} c^{5}\right)} d^{5} + 5 \, {\left(48 \, A a^{2} b c^{6} - 24 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c^{5} - {\left(4 \, B a b^{4} + A b^{5}\right)} c^{4}\right)} d^{4} e + 40 \, {\left(4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c^{5} + {\left(6 \, B a^{2} b^{3} - A a b^{4}\right)} c^{4}\right)} d^{3} e^{2} + 80 \, {\left(4 \, A a^{3} b c^{5} - {\left(8 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{4}\right)} d^{2} e^{3} - {\left(9 \, B a^{2} b^{6} c - 98 \, B a^{3} b^{4} c^{2} + 336 \, B a^{4} b^{2} c^{3} - 32 \, {\left(3 \, B a^{5} + 4 \, A a^{4} b\right)} c^{4}\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30 \, {\left(a^{3} b^{6} c^{4} - 12 \, a^{4} b^{4} c^{5} + 48 \, a^{5} b^{2} c^{6} - 64 \, a^{6} c^{7} + {\left(b^{6} c^{7} - 12 \, a b^{4} c^{8} + 48 \, a^{2} b^{2} c^{9} - 64 \, a^{3} c^{10}\right)} x^{6} + 3 \, {\left(b^{7} c^{6} - 12 \, a b^{5} c^{7} + 48 \, a^{2} b^{3} c^{8} - 64 \, a^{3} b c^{9}\right)} x^{5} + 3 \, {\left(b^{8} c^{5} - 11 \, a b^{6} c^{6} + 36 \, a^{2} b^{4} c^{7} - 16 \, a^{3} b^{2} c^{8} - 64 \, a^{4} c^{9}\right)} x^{4} + {\left(b^{9} c^{4} - 6 \, a b^{7} c^{5} - 24 \, a^{2} b^{5} c^{6} + 224 \, a^{3} b^{3} c^{7} - 384 \, a^{4} b c^{8}\right)} x^{3} + 3 \, {\left(a b^{8} c^{4} - 11 \, a^{2} b^{6} c^{5} + 36 \, a^{3} b^{4} c^{6} - 16 \, a^{4} b^{2} c^{7} - 64 \, a^{5} c^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} c^{4} - 12 \, a^{3} b^{5} c^{5} + 48 \, a^{4} b^{3} c^{6} - 64 \, a^{5} b c^{7}\right)} x\right)}}, -\frac{15 \, {\left({\left(B b^{6} c^{3} - 12 \, B a b^{4} c^{4} + 48 \, B a^{2} b^{2} c^{5} - 64 \, B a^{3} c^{6}\right)} e^{5} x^{6} + 3 \, {\left(B b^{7} c^{2} - 12 \, B a b^{5} c^{3} + 48 \, B a^{2} b^{3} c^{4} - 64 \, B a^{3} b c^{5}\right)} e^{5} x^{5} + 3 \, {\left(B b^{8} c - 11 \, B a b^{6} c^{2} + 36 \, B a^{2} b^{4} c^{3} - 16 \, B a^{3} b^{2} c^{4} - 64 \, B a^{4} c^{5}\right)} e^{5} x^{4} + {\left(B b^{9} - 6 \, B a b^{7} c - 24 \, B a^{2} b^{5} c^{2} + 224 \, B a^{3} b^{3} c^{3} - 384 \, B a^{4} b c^{4}\right)} e^{5} x^{3} + 3 \, {\left(B a b^{8} - 11 \, B a^{2} b^{6} c + 36 \, B a^{3} b^{4} c^{2} - 16 \, B a^{4} b^{2} c^{3} - 64 \, B a^{5} c^{4}\right)} e^{5} x^{2} + 3 \, {\left(B a^{2} b^{7} - 12 \, B a^{3} b^{5} c + 48 \, B a^{4} b^{3} c^{2} - 64 \, B a^{5} b c^{3}\right)} e^{5} x + {\left(B a^{3} b^{6} - 12 \, B a^{4} b^{4} c + 48 \, B a^{5} b^{2} c^{2} - 64 \, B a^{6} c^{3}\right)} e^{5}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(640 \, {\left(2 \, B a^{5} - A a^{4} b\right)} c^{4} d e^{4} + {\left(48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{6} + 8 \, {\left(6 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{5} - {\left(2 \, B a b^{4} + 3 \, A b^{5}\right)} c^{4}\right)} d^{5} + 10 \, {\left(48 \, A a^{3} c^{6} - 24 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c^{5} - {\left(4 \, B a^{2} b^{3} + A a b^{4}\right)} c^{4}\right)} d^{4} e + 80 \, {\left(4 \, {\left(2 \, B a^{4} - 3 \, A a^{3} b\right)} c^{5} + {\left(6 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{4}\right)} d^{3} e^{2} + 160 \, {\left(4 \, A a^{4} c^{5} - {\left(8 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} c^{4}\right)} d^{2} e^{3} - {\left(15 \, B a^{3} b^{5} c - 160 \, B a^{4} b^{3} c^{2} + 528 \, B a^{5} b c^{3} - 256 \, A a^{5} c^{4}\right)} e^{5} + {\left(128 \, {\left(B b c^{8} - 2 \, A c^{9}\right)} d^{5} - 80 \, {\left(3 \, B b^{2} c^{7} + 4 \, {\left(B a - 2 \, A b\right)} c^{8}\right)} d^{4} e + 80 \, {\left(B b^{3} c^{6} - 8 \, A a c^{8} + 6 \, {\left(2 \, B a b - A b^{2}\right)} c^{7}\right)} d^{3} e^{2} + 20 \, {\left(B b^{4} c^{5} - 48 \, {\left(B a^{2} - A a b\right)} c^{7} - 4 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{6}\right)} d^{2} e^{3} + 5 \, {\left(3 \, B b^{5} c^{4} - 96 \, A a^{2} c^{7} + 48 \, {\left(5 \, B a^{2} b - A a b^{2}\right)} c^{6} - 2 \, {\left(20 \, B a b^{3} - A b^{4}\right)} c^{5}\right)} d e^{4} - {\left(23 \, B b^{6} c^{3} - 16 \, {\left(46 \, B a^{3} + 15 \, A a^{2} b\right)} c^{6} + 8 \, {\left(114 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{5} - 3 \, {\left(86 \, B a b^{4} + A b^{5}\right)} c^{4}\right)} e^{5}\right)} x^{5} + 5 \, {\left(64 \, {\left(B b^{2} c^{7} - 2 \, A b c^{8}\right)} d^{5} - 40 \, {\left(3 \, B b^{3} c^{6} + 4 \, {\left(B a b - 2 \, A b^{2}\right)} c^{7}\right)} d^{4} e + 40 \, {\left(B b^{4} c^{5} - 8 \, A a b c^{7} + 6 \, {\left(2 \, B a b^{2} - A b^{3}\right)} c^{6}\right)} d^{3} e^{2} + 10 \, {\left(B b^{5} c^{4} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{6} - 4 \, {\left(6 \, B a b^{3} - A b^{4}\right)} c^{5}\right)} d^{2} e^{3} + 5 \, {\left(48 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{6} + 24 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c^{5} - {\left(2 \, B a b^{4} - A b^{5}\right)} c^{4}\right)} d e^{4} - {\left(7 \, B b^{7} c^{2} - 75 \, B a b^{5} c^{3} - 96 \, A a^{3} c^{6} - 16 \, {\left(5 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{5} + 2 \, {\left(120 \, B a^{2} b^{3} + A a b^{4}\right)} c^{4}\right)} e^{5}\right)} x^{4} + 5 \, {\left(16 \, {\left(3 \, B b^{3} c^{6} - 8 \, A a c^{8} + 2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{7}\right)} d^{5} - 10 \, {\left(9 \, B b^{4} c^{5} + 16 \, {\left(B a^{2} - 2 \, A a b\right)} c^{7} + 24 \, {\left(B a b^{2} - A b^{3}\right)} c^{6}\right)} d^{4} e + 10 \, {\left(3 \, B b^{5} c^{4} - 32 \, A a^{2} c^{7} + 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{6} + 2 \, {\left(20 \, B a b^{3} - 9 \, A b^{4}\right)} c^{5}\right)} d^{3} e^{2} + 10 \, {\left(48 \, A a^{2} b c^{6} - 8 \, {\left(12 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{5} - {\left(8 \, B a b^{4} - 3 \, A b^{5}\right)} c^{4}\right)} d^{2} e^{3} + 40 \, {\left(12 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c^{5} + {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} c^{4}\right)} d e^{4} - {\left(3 \, B b^{8} c - 20 \, B a b^{6} c^{2} - 30 \, B a^{2} b^{4} c^{3} - 32 \, {\left(7 \, B a^{4} + 6 \, A a^{3} b\right)} c^{5} + 16 \, {\left(27 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{4}\right)} e^{5}\right)} x^{3} + 5 \, {\left(8 \, {\left(B b^{4} c^{5} - 24 \, A a b c^{7} + 2 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{6}\right)} d^{5} - 5 \, {\left(3 \, B b^{5} c^{4} + 48 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} c^{6} + 8 \, {\left(5 \, B a b^{3} - A b^{4}\right)} c^{5}\right)} d^{4} e + 10 \, {\left(16 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{6} + 8 \, {\left(6 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c^{5} + 3 \, {\left(6 \, B a b^{4} - A b^{5}\right)} c^{4}\right)} d^{3} e^{2} + 20 \, {\left(16 \, A a^{3} c^{6} - 8 \, {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c^{5} - 3 \, {\left(8 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} c^{4}\right)} d^{2} e^{3} + 80 \, {\left(4 \, {\left(2 \, B a^{4} - A a^{3} b\right)} c^{5} + 3 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{4}\right)} d e^{4} - {\left(9 \, B a b^{7} c - 93 \, B a^{2} b^{5} c^{2} + 280 \, B a^{3} b^{3} c^{3} - 128 \, A a^{4} c^{5} + 48 \, {\left(B a^{4} b - 2 \, A a^{3} b^{2}\right)} c^{4}\right)} e^{5}\right)} x^{2} + 5 \, {\left(320 \, {\left(2 \, B a^{4} b - A a^{3} b^{2}\right)} c^{4} d e^{4} - {\left(B b^{5} c^{4} + 96 \, A a^{2} c^{7} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{6} - 2 \, {\left(12 \, B a b^{3} + A b^{4}\right)} c^{5}\right)} d^{5} + 5 \, {\left(48 \, A a^{2} b c^{6} - 24 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c^{5} - {\left(4 \, B a b^{4} + A b^{5}\right)} c^{4}\right)} d^{4} e + 40 \, {\left(4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c^{5} + {\left(6 \, B a^{2} b^{3} - A a b^{4}\right)} c^{4}\right)} d^{3} e^{2} + 80 \, {\left(4 \, A a^{3} b c^{5} - {\left(8 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{4}\right)} d^{2} e^{3} - {\left(9 \, B a^{2} b^{6} c - 98 \, B a^{3} b^{4} c^{2} + 336 \, B a^{4} b^{2} c^{3} - 32 \, {\left(3 \, B a^{5} + 4 \, A a^{4} b\right)} c^{4}\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15 \, {\left(a^{3} b^{6} c^{4} - 12 \, a^{4} b^{4} c^{5} + 48 \, a^{5} b^{2} c^{6} - 64 \, a^{6} c^{7} + {\left(b^{6} c^{7} - 12 \, a b^{4} c^{8} + 48 \, a^{2} b^{2} c^{9} - 64 \, a^{3} c^{10}\right)} x^{6} + 3 \, {\left(b^{7} c^{6} - 12 \, a b^{5} c^{7} + 48 \, a^{2} b^{3} c^{8} - 64 \, a^{3} b c^{9}\right)} x^{5} + 3 \, {\left(b^{8} c^{5} - 11 \, a b^{6} c^{6} + 36 \, a^{2} b^{4} c^{7} - 16 \, a^{3} b^{2} c^{8} - 64 \, a^{4} c^{9}\right)} x^{4} + {\left(b^{9} c^{4} - 6 \, a b^{7} c^{5} - 24 \, a^{2} b^{5} c^{6} + 224 \, a^{3} b^{3} c^{7} - 384 \, a^{4} b c^{8}\right)} x^{3} + 3 \, {\left(a b^{8} c^{4} - 11 \, a^{2} b^{6} c^{5} + 36 \, a^{3} b^{4} c^{6} - 16 \, a^{4} b^{2} c^{7} - 64 \, a^{5} c^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} c^{4} - 12 \, a^{3} b^{5} c^{5} + 48 \, a^{4} b^{3} c^{6} - 64 \, a^{5} b c^{7}\right)} x\right)}}\right]"," ",0,"[1/30*(15*((B*b^6*c^3 - 12*B*a*b^4*c^4 + 48*B*a^2*b^2*c^5 - 64*B*a^3*c^6)*e^5*x^6 + 3*(B*b^7*c^2 - 12*B*a*b^5*c^3 + 48*B*a^2*b^3*c^4 - 64*B*a^3*b*c^5)*e^5*x^5 + 3*(B*b^8*c - 11*B*a*b^6*c^2 + 36*B*a^2*b^4*c^3 - 16*B*a^3*b^2*c^4 - 64*B*a^4*c^5)*e^5*x^4 + (B*b^9 - 6*B*a*b^7*c - 24*B*a^2*b^5*c^2 + 224*B*a^3*b^3*c^3 - 384*B*a^4*b*c^4)*e^5*x^3 + 3*(B*a*b^8 - 11*B*a^2*b^6*c + 36*B*a^3*b^4*c^2 - 16*B*a^4*b^2*c^3 - 64*B*a^5*c^4)*e^5*x^2 + 3*(B*a^2*b^7 - 12*B*a^3*b^5*c + 48*B*a^4*b^3*c^2 - 64*B*a^5*b*c^3)*e^5*x + (B*a^3*b^6 - 12*B*a^4*b^4*c + 48*B*a^5*b^2*c^2 - 64*B*a^6*c^3)*e^5)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(640*(2*B*a^5 - A*a^4*b)*c^4*d*e^4 + (48*(2*B*a^3 - 5*A*a^2*b)*c^6 + 8*(6*B*a^2*b^2 + 5*A*a*b^3)*c^5 - (2*B*a*b^4 + 3*A*b^5)*c^4)*d^5 + 10*(48*A*a^3*c^6 - 24*(2*B*a^3*b - A*a^2*b^2)*c^5 - (4*B*a^2*b^3 + A*a*b^4)*c^4)*d^4*e + 80*(4*(2*B*a^4 - 3*A*a^3*b)*c^5 + (6*B*a^3*b^2 - A*a^2*b^3)*c^4)*d^3*e^2 + 160*(4*A*a^4*c^5 - (8*B*a^4*b - 3*A*a^3*b^2)*c^4)*d^2*e^3 - (15*B*a^3*b^5*c - 160*B*a^4*b^3*c^2 + 528*B*a^5*b*c^3 - 256*A*a^5*c^4)*e^5 + (128*(B*b*c^8 - 2*A*c^9)*d^5 - 80*(3*B*b^2*c^7 + 4*(B*a - 2*A*b)*c^8)*d^4*e + 80*(B*b^3*c^6 - 8*A*a*c^8 + 6*(2*B*a*b - A*b^2)*c^7)*d^3*e^2 + 20*(B*b^4*c^5 - 48*(B*a^2 - A*a*b)*c^7 - 4*(6*B*a*b^2 - A*b^3)*c^6)*d^2*e^3 + 5*(3*B*b^5*c^4 - 96*A*a^2*c^7 + 48*(5*B*a^2*b - A*a*b^2)*c^6 - 2*(20*B*a*b^3 - A*b^4)*c^5)*d*e^4 - (23*B*b^6*c^3 - 16*(46*B*a^3 + 15*A*a^2*b)*c^6 + 8*(114*B*a^2*b^2 + 5*A*a*b^3)*c^5 - 3*(86*B*a*b^4 + A*b^5)*c^4)*e^5)*x^5 + 5*(64*(B*b^2*c^7 - 2*A*b*c^8)*d^5 - 40*(3*B*b^3*c^6 + 4*(B*a*b - 2*A*b^2)*c^7)*d^4*e + 40*(B*b^4*c^5 - 8*A*a*b*c^7 + 6*(2*B*a*b^2 - A*b^3)*c^6)*d^3*e^2 + 10*(B*b^5*c^4 - 48*(B*a^2*b - A*a*b^2)*c^6 - 4*(6*B*a*b^3 - A*b^4)*c^5)*d^2*e^3 + 5*(48*(2*B*a^3 - A*a^2*b)*c^6 + 24*(2*B*a^2*b^2 - A*a*b^3)*c^5 - (2*B*a*b^4 - A*b^5)*c^4)*d*e^4 - (7*B*b^7*c^2 - 75*B*a*b^5*c^3 - 96*A*a^3*c^6 - 16*(5*B*a^3*b + 3*A*a^2*b^2)*c^5 + 2*(120*B*a^2*b^3 + A*a*b^4)*c^4)*e^5)*x^4 + 5*(16*(3*B*b^3*c^6 - 8*A*a*c^8 + 2*(2*B*a*b - 3*A*b^2)*c^7)*d^5 - 10*(9*B*b^4*c^5 + 16*(B*a^2 - 2*A*a*b)*c^7 + 24*(B*a*b^2 - A*b^3)*c^6)*d^4*e + 10*(3*B*b^5*c^4 - 32*A*a^2*c^7 + 48*(B*a^2*b - A*a*b^2)*c^6 + 2*(20*B*a*b^3 - 9*A*b^4)*c^5)*d^3*e^2 + 10*(48*A*a^2*b*c^6 - 8*(12*B*a^2*b^2 - 5*A*a*b^3)*c^5 - (8*B*a*b^4 - 3*A*b^5)*c^4)*d^2*e^3 + 40*(12*(2*B*a^3*b - A*a^2*b^2)*c^5 + (2*B*a^2*b^3 - A*a*b^4)*c^4)*d*e^4 - (3*B*b^8*c - 20*B*a*b^6*c^2 - 30*B*a^2*b^4*c^3 - 32*(7*B*a^4 + 6*A*a^3*b)*c^5 + 16*(27*B*a^3*b^2 - A*a^2*b^3)*c^4)*e^5)*x^3 + 5*(8*(B*b^4*c^5 - 24*A*a*b*c^7 + 2*(6*B*a*b^2 - A*b^3)*c^6)*d^5 - 5*(3*B*b^5*c^4 + 48*(B*a^2*b - 2*A*a*b^2)*c^6 + 8*(5*B*a*b^3 - A*b^4)*c^5)*d^4*e + 10*(16*(2*B*a^3 - 3*A*a^2*b)*c^6 + 8*(6*B*a^2*b^2 - 5*A*a*b^3)*c^5 + 3*(6*B*a*b^4 - A*b^5)*c^4)*d^3*e^2 + 20*(16*A*a^3*c^6 - 8*(4*B*a^3*b - 3*A*a^2*b^2)*c^5 - 3*(8*B*a^2*b^3 - 3*A*a*b^4)*c^4)*d^2*e^3 + 80*(4*(2*B*a^4 - A*a^3*b)*c^5 + 3*(2*B*a^3*b^2 - A*a^2*b^3)*c^4)*d*e^4 - (9*B*a*b^7*c - 93*B*a^2*b^5*c^2 + 280*B*a^3*b^3*c^3 - 128*A*a^4*c^5 + 48*(B*a^4*b - 2*A*a^3*b^2)*c^4)*e^5)*x^2 + 5*(320*(2*B*a^4*b - A*a^3*b^2)*c^4*d*e^4 - (B*b^5*c^4 + 96*A*a^2*c^7 - 48*(B*a^2*b - A*a*b^2)*c^6 - 2*(12*B*a*b^3 + A*b^4)*c^5)*d^5 + 5*(48*A*a^2*b*c^6 - 24*(2*B*a^2*b^2 - A*a*b^3)*c^5 - (4*B*a*b^4 + A*b^5)*c^4)*d^4*e + 40*(4*(2*B*a^3*b - 3*A*a^2*b^2)*c^5 + (6*B*a^2*b^3 - A*a*b^4)*c^4)*d^3*e^2 + 80*(4*A*a^3*b*c^5 - (8*B*a^3*b^2 - 3*A*a^2*b^3)*c^4)*d^2*e^3 - (9*B*a^2*b^6*c - 98*B*a^3*b^4*c^2 + 336*B*a^4*b^2*c^3 - 32*(3*B*a^5 + 4*A*a^4*b)*c^4)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(a^3*b^6*c^4 - 12*a^4*b^4*c^5 + 48*a^5*b^2*c^6 - 64*a^6*c^7 + (b^6*c^7 - 12*a*b^4*c^8 + 48*a^2*b^2*c^9 - 64*a^3*c^10)*x^6 + 3*(b^7*c^6 - 12*a*b^5*c^7 + 48*a^2*b^3*c^8 - 64*a^3*b*c^9)*x^5 + 3*(b^8*c^5 - 11*a*b^6*c^6 + 36*a^2*b^4*c^7 - 16*a^3*b^2*c^8 - 64*a^4*c^9)*x^4 + (b^9*c^4 - 6*a*b^7*c^5 - 24*a^2*b^5*c^6 + 224*a^3*b^3*c^7 - 384*a^4*b*c^8)*x^3 + 3*(a*b^8*c^4 - 11*a^2*b^6*c^5 + 36*a^3*b^4*c^6 - 16*a^4*b^2*c^7 - 64*a^5*c^8)*x^2 + 3*(a^2*b^7*c^4 - 12*a^3*b^5*c^5 + 48*a^4*b^3*c^6 - 64*a^5*b*c^7)*x), -1/15*(15*((B*b^6*c^3 - 12*B*a*b^4*c^4 + 48*B*a^2*b^2*c^5 - 64*B*a^3*c^6)*e^5*x^6 + 3*(B*b^7*c^2 - 12*B*a*b^5*c^3 + 48*B*a^2*b^3*c^4 - 64*B*a^3*b*c^5)*e^5*x^5 + 3*(B*b^8*c - 11*B*a*b^6*c^2 + 36*B*a^2*b^4*c^3 - 16*B*a^3*b^2*c^4 - 64*B*a^4*c^5)*e^5*x^4 + (B*b^9 - 6*B*a*b^7*c - 24*B*a^2*b^5*c^2 + 224*B*a^3*b^3*c^3 - 384*B*a^4*b*c^4)*e^5*x^3 + 3*(B*a*b^8 - 11*B*a^2*b^6*c + 36*B*a^3*b^4*c^2 - 16*B*a^4*b^2*c^3 - 64*B*a^5*c^4)*e^5*x^2 + 3*(B*a^2*b^7 - 12*B*a^3*b^5*c + 48*B*a^4*b^3*c^2 - 64*B*a^5*b*c^3)*e^5*x + (B*a^3*b^6 - 12*B*a^4*b^4*c + 48*B*a^5*b^2*c^2 - 64*B*a^6*c^3)*e^5)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(640*(2*B*a^5 - A*a^4*b)*c^4*d*e^4 + (48*(2*B*a^3 - 5*A*a^2*b)*c^6 + 8*(6*B*a^2*b^2 + 5*A*a*b^3)*c^5 - (2*B*a*b^4 + 3*A*b^5)*c^4)*d^5 + 10*(48*A*a^3*c^6 - 24*(2*B*a^3*b - A*a^2*b^2)*c^5 - (4*B*a^2*b^3 + A*a*b^4)*c^4)*d^4*e + 80*(4*(2*B*a^4 - 3*A*a^3*b)*c^5 + (6*B*a^3*b^2 - A*a^2*b^3)*c^4)*d^3*e^2 + 160*(4*A*a^4*c^5 - (8*B*a^4*b - 3*A*a^3*b^2)*c^4)*d^2*e^3 - (15*B*a^3*b^5*c - 160*B*a^4*b^3*c^2 + 528*B*a^5*b*c^3 - 256*A*a^5*c^4)*e^5 + (128*(B*b*c^8 - 2*A*c^9)*d^5 - 80*(3*B*b^2*c^7 + 4*(B*a - 2*A*b)*c^8)*d^4*e + 80*(B*b^3*c^6 - 8*A*a*c^8 + 6*(2*B*a*b - A*b^2)*c^7)*d^3*e^2 + 20*(B*b^4*c^5 - 48*(B*a^2 - A*a*b)*c^7 - 4*(6*B*a*b^2 - A*b^3)*c^6)*d^2*e^3 + 5*(3*B*b^5*c^4 - 96*A*a^2*c^7 + 48*(5*B*a^2*b - A*a*b^2)*c^6 - 2*(20*B*a*b^3 - A*b^4)*c^5)*d*e^4 - (23*B*b^6*c^3 - 16*(46*B*a^3 + 15*A*a^2*b)*c^6 + 8*(114*B*a^2*b^2 + 5*A*a*b^3)*c^5 - 3*(86*B*a*b^4 + A*b^5)*c^4)*e^5)*x^5 + 5*(64*(B*b^2*c^7 - 2*A*b*c^8)*d^5 - 40*(3*B*b^3*c^6 + 4*(B*a*b - 2*A*b^2)*c^7)*d^4*e + 40*(B*b^4*c^5 - 8*A*a*b*c^7 + 6*(2*B*a*b^2 - A*b^3)*c^6)*d^3*e^2 + 10*(B*b^5*c^4 - 48*(B*a^2*b - A*a*b^2)*c^6 - 4*(6*B*a*b^3 - A*b^4)*c^5)*d^2*e^3 + 5*(48*(2*B*a^3 - A*a^2*b)*c^6 + 24*(2*B*a^2*b^2 - A*a*b^3)*c^5 - (2*B*a*b^4 - A*b^5)*c^4)*d*e^4 - (7*B*b^7*c^2 - 75*B*a*b^5*c^3 - 96*A*a^3*c^6 - 16*(5*B*a^3*b + 3*A*a^2*b^2)*c^5 + 2*(120*B*a^2*b^3 + A*a*b^4)*c^4)*e^5)*x^4 + 5*(16*(3*B*b^3*c^6 - 8*A*a*c^8 + 2*(2*B*a*b - 3*A*b^2)*c^7)*d^5 - 10*(9*B*b^4*c^5 + 16*(B*a^2 - 2*A*a*b)*c^7 + 24*(B*a*b^2 - A*b^3)*c^6)*d^4*e + 10*(3*B*b^5*c^4 - 32*A*a^2*c^7 + 48*(B*a^2*b - A*a*b^2)*c^6 + 2*(20*B*a*b^3 - 9*A*b^4)*c^5)*d^3*e^2 + 10*(48*A*a^2*b*c^6 - 8*(12*B*a^2*b^2 - 5*A*a*b^3)*c^5 - (8*B*a*b^4 - 3*A*b^5)*c^4)*d^2*e^3 + 40*(12*(2*B*a^3*b - A*a^2*b^2)*c^5 + (2*B*a^2*b^3 - A*a*b^4)*c^4)*d*e^4 - (3*B*b^8*c - 20*B*a*b^6*c^2 - 30*B*a^2*b^4*c^3 - 32*(7*B*a^4 + 6*A*a^3*b)*c^5 + 16*(27*B*a^3*b^2 - A*a^2*b^3)*c^4)*e^5)*x^3 + 5*(8*(B*b^4*c^5 - 24*A*a*b*c^7 + 2*(6*B*a*b^2 - A*b^3)*c^6)*d^5 - 5*(3*B*b^5*c^4 + 48*(B*a^2*b - 2*A*a*b^2)*c^6 + 8*(5*B*a*b^3 - A*b^4)*c^5)*d^4*e + 10*(16*(2*B*a^3 - 3*A*a^2*b)*c^6 + 8*(6*B*a^2*b^2 - 5*A*a*b^3)*c^5 + 3*(6*B*a*b^4 - A*b^5)*c^4)*d^3*e^2 + 20*(16*A*a^3*c^6 - 8*(4*B*a^3*b - 3*A*a^2*b^2)*c^5 - 3*(8*B*a^2*b^3 - 3*A*a*b^4)*c^4)*d^2*e^3 + 80*(4*(2*B*a^4 - A*a^3*b)*c^5 + 3*(2*B*a^3*b^2 - A*a^2*b^3)*c^4)*d*e^4 - (9*B*a*b^7*c - 93*B*a^2*b^5*c^2 + 280*B*a^3*b^3*c^3 - 128*A*a^4*c^5 + 48*(B*a^4*b - 2*A*a^3*b^2)*c^4)*e^5)*x^2 + 5*(320*(2*B*a^4*b - A*a^3*b^2)*c^4*d*e^4 - (B*b^5*c^4 + 96*A*a^2*c^7 - 48*(B*a^2*b - A*a*b^2)*c^6 - 2*(12*B*a*b^3 + A*b^4)*c^5)*d^5 + 5*(48*A*a^2*b*c^6 - 24*(2*B*a^2*b^2 - A*a*b^3)*c^5 - (4*B*a*b^4 + A*b^5)*c^4)*d^4*e + 40*(4*(2*B*a^3*b - 3*A*a^2*b^2)*c^5 + (6*B*a^2*b^3 - A*a*b^4)*c^4)*d^3*e^2 + 80*(4*A*a^3*b*c^5 - (8*B*a^3*b^2 - 3*A*a^2*b^3)*c^4)*d^2*e^3 - (9*B*a^2*b^6*c - 98*B*a^3*b^4*c^2 + 336*B*a^4*b^2*c^3 - 32*(3*B*a^5 + 4*A*a^4*b)*c^4)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(a^3*b^6*c^4 - 12*a^4*b^4*c^5 + 48*a^5*b^2*c^6 - 64*a^6*c^7 + (b^6*c^7 - 12*a*b^4*c^8 + 48*a^2*b^2*c^9 - 64*a^3*c^10)*x^6 + 3*(b^7*c^6 - 12*a*b^5*c^7 + 48*a^2*b^3*c^8 - 64*a^3*b*c^9)*x^5 + 3*(b^8*c^5 - 11*a*b^6*c^6 + 36*a^2*b^4*c^7 - 16*a^3*b^2*c^8 - 64*a^4*c^9)*x^4 + (b^9*c^4 - 6*a*b^7*c^5 - 24*a^2*b^5*c^6 + 224*a^3*b^3*c^7 - 384*a^4*b*c^8)*x^3 + 3*(a*b^8*c^4 - 11*a^2*b^6*c^5 + 36*a^3*b^4*c^6 - 16*a^4*b^2*c^7 - 64*a^5*c^8)*x^2 + 3*(a^2*b^7*c^4 - 12*a^3*b^5*c^5 + 48*a^4*b^3*c^6 - 64*a^5*b*c^7)*x)]","B",0
2489,1,1628,0,66.926590," ","integrate((B*x+A)*(e*x+d)^4/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(128 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{4} - 64 \, {\left(3 \, B b^{2} c^{3} + 4 \, {\left(B a - 2 \, A b\right)} c^{4}\right)} d^{3} e + 48 \, {\left(B b^{3} c^{2} - 8 \, A a c^{4} + 6 \, {\left(2 \, B a b - A b^{2}\right)} c^{3}\right)} d^{2} e^{2} + 8 \, {\left(B b^{4} c - 48 \, {\left(B a^{2} - A a b\right)} c^{3} - 4 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} d e^{3} + {\left(3 \, B b^{5} - 96 \, A a^{2} c^{3} + 48 \, {\left(5 \, B a^{2} b - A a b^{2}\right)} c^{2} - 2 \, {\left(20 \, B a b^{3} - A b^{4}\right)} c\right)} e^{4}\right)} x^{5} - {\left(2 \, B a b^{4} + 3 \, A b^{5} - 48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} - 8 \, {\left(6 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c\right)} d^{4} - 8 \, {\left(4 \, B a^{2} b^{3} + A a b^{4} - 48 \, A a^{3} c^{2} + 24 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} d^{3} e + 48 \, {\left(6 \, B a^{3} b^{2} - A a^{2} b^{3} + 4 \, {\left(2 \, B a^{4} - 3 \, A a^{3} b\right)} c\right)} d^{2} e^{2} - 64 \, {\left(8 \, B a^{4} b - 3 \, A a^{3} b^{2} - 4 \, A a^{4} c\right)} d e^{3} + 128 \, {\left(2 \, B a^{5} - A a^{4} b\right)} e^{4} + 5 \, {\left(64 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{4} - 32 \, {\left(3 \, B b^{3} c^{2} + 4 \, {\left(B a b - 2 \, A b^{2}\right)} c^{3}\right)} d^{3} e + 24 \, {\left(B b^{4} c - 8 \, A a b c^{3} + 6 \, {\left(2 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{2} e^{2} + 4 \, {\left(B b^{5} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} - 4 \, {\left(6 \, B a b^{3} - A b^{4}\right)} c\right)} d e^{3} - {\left(2 \, B a b^{4} - A b^{5} - 48 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - 24 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} e^{4}\right)} x^{4} + 10 \, {\left(8 \, {\left(3 \, B b^{3} c^{2} - 8 \, A a c^{4} + 2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{3}\right)} d^{4} - 4 \, {\left(9 \, B b^{4} c + 16 \, {\left(B a^{2} - 2 \, A a b\right)} c^{3} + 24 \, {\left(B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{3} e + 3 \, {\left(3 \, B b^{5} - 32 \, A a^{2} c^{3} + 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} + 2 \, {\left(20 \, B a b^{3} - 9 \, A b^{4}\right)} c\right)} d^{2} e^{2} - 2 \, {\left(8 \, B a b^{4} - 3 \, A b^{5} - 48 \, A a^{2} b c^{2} + 8 \, {\left(12 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} d e^{3} + 4 \, {\left(2 \, B a^{2} b^{3} - A a b^{4} + 12 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} e^{4}\right)} x^{3} + 10 \, {\left(4 \, {\left(B b^{4} c - 24 \, A a b c^{3} + 2 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{4} - 2 \, {\left(3 \, B b^{5} + 48 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} c^{2} + 8 \, {\left(5 \, B a b^{3} - A b^{4}\right)} c\right)} d^{3} e + 3 \, {\left(18 \, B a b^{4} - 3 \, A b^{5} + 16 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{2} + 8 \, {\left(6 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} d^{2} e^{2} - 4 \, {\left(24 \, B a^{2} b^{3} - 9 \, A a b^{4} - 16 \, A a^{3} c^{2} + 8 \, {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} d e^{3} + 8 \, {\left(6 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} + 4 \, {\left(2 \, B a^{4} - A a^{3} b\right)} c\right)} e^{4}\right)} x^{2} - 5 \, {\left({\left(B b^{5} + 96 \, A a^{2} c^{3} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} - 2 \, {\left(12 \, B a b^{3} + A b^{4}\right)} c\right)} d^{4} + 4 \, {\left(4 \, B a b^{4} + A b^{5} - 48 \, A a^{2} b c^{2} + 24 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} d^{3} e - 24 \, {\left(6 \, B a^{2} b^{3} - A a b^{4} + 4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} d^{2} e^{2} + 32 \, {\left(8 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - 4 \, A a^{3} b c\right)} d e^{3} - 64 \, {\left(2 \, B a^{4} b - A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{6} + 3 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(b^{8} c - 11 \, a b^{6} c^{2} + 36 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} x^{4} + {\left(b^{9} - 6 \, a b^{7} c - 24 \, a^{2} b^{5} c^{2} + 224 \, a^{3} b^{3} c^{3} - 384 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a b^{8} - 11 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} - 16 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)}}"," ",0,"2/15*((128*(B*b*c^4 - 2*A*c^5)*d^4 - 64*(3*B*b^2*c^3 + 4*(B*a - 2*A*b)*c^4)*d^3*e + 48*(B*b^3*c^2 - 8*A*a*c^4 + 6*(2*B*a*b - A*b^2)*c^3)*d^2*e^2 + 8*(B*b^4*c - 48*(B*a^2 - A*a*b)*c^3 - 4*(6*B*a*b^2 - A*b^3)*c^2)*d*e^3 + (3*B*b^5 - 96*A*a^2*c^3 + 48*(5*B*a^2*b - A*a*b^2)*c^2 - 2*(20*B*a*b^3 - A*b^4)*c)*e^4)*x^5 - (2*B*a*b^4 + 3*A*b^5 - 48*(2*B*a^3 - 5*A*a^2*b)*c^2 - 8*(6*B*a^2*b^2 + 5*A*a*b^3)*c)*d^4 - 8*(4*B*a^2*b^3 + A*a*b^4 - 48*A*a^3*c^2 + 24*(2*B*a^3*b - A*a^2*b^2)*c)*d^3*e + 48*(6*B*a^3*b^2 - A*a^2*b^3 + 4*(2*B*a^4 - 3*A*a^3*b)*c)*d^2*e^2 - 64*(8*B*a^4*b - 3*A*a^3*b^2 - 4*A*a^4*c)*d*e^3 + 128*(2*B*a^5 - A*a^4*b)*e^4 + 5*(64*(B*b^2*c^3 - 2*A*b*c^4)*d^4 - 32*(3*B*b^3*c^2 + 4*(B*a*b - 2*A*b^2)*c^3)*d^3*e + 24*(B*b^4*c - 8*A*a*b*c^3 + 6*(2*B*a*b^2 - A*b^3)*c^2)*d^2*e^2 + 4*(B*b^5 - 48*(B*a^2*b - A*a*b^2)*c^2 - 4*(6*B*a*b^3 - A*b^4)*c)*d*e^3 - (2*B*a*b^4 - A*b^5 - 48*(2*B*a^3 - A*a^2*b)*c^2 - 24*(2*B*a^2*b^2 - A*a*b^3)*c)*e^4)*x^4 + 10*(8*(3*B*b^3*c^2 - 8*A*a*c^4 + 2*(2*B*a*b - 3*A*b^2)*c^3)*d^4 - 4*(9*B*b^4*c + 16*(B*a^2 - 2*A*a*b)*c^3 + 24*(B*a*b^2 - A*b^3)*c^2)*d^3*e + 3*(3*B*b^5 - 32*A*a^2*c^3 + 48*(B*a^2*b - A*a*b^2)*c^2 + 2*(20*B*a*b^3 - 9*A*b^4)*c)*d^2*e^2 - 2*(8*B*a*b^4 - 3*A*b^5 - 48*A*a^2*b*c^2 + 8*(12*B*a^2*b^2 - 5*A*a*b^3)*c)*d*e^3 + 4*(2*B*a^2*b^3 - A*a*b^4 + 12*(2*B*a^3*b - A*a^2*b^2)*c)*e^4)*x^3 + 10*(4*(B*b^4*c - 24*A*a*b*c^3 + 2*(6*B*a*b^2 - A*b^3)*c^2)*d^4 - 2*(3*B*b^5 + 48*(B*a^2*b - 2*A*a*b^2)*c^2 + 8*(5*B*a*b^3 - A*b^4)*c)*d^3*e + 3*(18*B*a*b^4 - 3*A*b^5 + 16*(2*B*a^3 - 3*A*a^2*b)*c^2 + 8*(6*B*a^2*b^2 - 5*A*a*b^3)*c)*d^2*e^2 - 4*(24*B*a^2*b^3 - 9*A*a*b^4 - 16*A*a^3*c^2 + 8*(4*B*a^3*b - 3*A*a^2*b^2)*c)*d*e^3 + 8*(6*B*a^3*b^2 - 3*A*a^2*b^3 + 4*(2*B*a^4 - A*a^3*b)*c)*e^4)*x^2 - 5*((B*b^5 + 96*A*a^2*c^3 - 48*(B*a^2*b - A*a*b^2)*c^2 - 2*(12*B*a*b^3 + A*b^4)*c)*d^4 + 4*(4*B*a*b^4 + A*b^5 - 48*A*a^2*b*c^2 + 24*(2*B*a^2*b^2 - A*a*b^3)*c)*d^3*e - 24*(6*B*a^2*b^3 - A*a*b^4 + 4*(2*B*a^3*b - 3*A*a^2*b^2)*c)*d^2*e^2 + 32*(8*B*a^3*b^2 - 3*A*a^2*b^3 - 4*A*a^3*b*c)*d*e^3 - 64*(2*B*a^4*b - A*a^3*b^2)*e^4)*x)*sqrt(c*x^2 + b*x + a)/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^6 + 3*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 3*(b^8*c - 11*a*b^6*c^2 + 36*a^2*b^4*c^3 - 16*a^3*b^2*c^4 - 64*a^4*c^5)*x^4 + (b^9 - 6*a*b^7*c - 24*a^2*b^5*c^2 + 224*a^3*b^3*c^3 - 384*a^4*b*c^4)*x^3 + 3*(a*b^8 - 11*a^2*b^6*c + 36*a^3*b^4*c^2 - 16*a^4*b^2*c^3 - 64*a^5*c^4)*x^2 + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)","B",0
2490,1,1370,0,128.734473," ","integrate((B*x+A)*(e*x+d)^3/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(64 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{3} - 24 \, {\left(3 \, B b^{2} c^{3} + 4 \, {\left(B a - 2 \, A b\right)} c^{4}\right)} d^{2} e + 12 \, {\left(B b^{3} c^{2} - 8 \, A a c^{4} + 6 \, {\left(2 \, B a b - A b^{2}\right)} c^{3}\right)} d e^{2} + {\left(B b^{4} c - 48 \, {\left(B a^{2} - A a b\right)} c^{3} - 4 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} e^{3}\right)} x^{5} + 5 \, {\left(64 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{3} - 24 \, {\left(3 \, B b^{3} c^{2} + 4 \, {\left(B a b - 2 \, A b^{2}\right)} c^{3}\right)} d^{2} e + 12 \, {\left(B b^{4} c - 8 \, A a b c^{3} + 6 \, {\left(2 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} d e^{2} + {\left(B b^{5} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} - 4 \, {\left(6 \, B a b^{3} - A b^{4}\right)} c\right)} e^{3}\right)} x^{4} - {\left(2 \, B a b^{4} + 3 \, A b^{5} - 48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} - 8 \, {\left(6 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c\right)} d^{3} - 6 \, {\left(4 \, B a^{2} b^{3} + A a b^{4} - 48 \, A a^{3} c^{2} + 24 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} d^{2} e + 24 \, {\left(6 \, B a^{3} b^{2} - A a^{2} b^{3} + 4 \, {\left(2 \, B a^{4} - 3 \, A a^{3} b\right)} c\right)} d e^{2} - 16 \, {\left(8 \, B a^{4} b - 3 \, A a^{3} b^{2} - 4 \, A a^{4} c\right)} e^{3} + 5 \, {\left(16 \, {\left(3 \, B b^{3} c^{2} - 8 \, A a c^{4} + 2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{3}\right)} d^{3} - 6 \, {\left(9 \, B b^{4} c + 16 \, {\left(B a^{2} - 2 \, A a b\right)} c^{3} + 24 \, {\left(B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{2} e + 3 \, {\left(3 \, B b^{5} - 32 \, A a^{2} c^{3} + 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} + 2 \, {\left(20 \, B a b^{3} - 9 \, A b^{4}\right)} c\right)} d e^{2} - {\left(8 \, B a b^{4} - 3 \, A b^{5} - 48 \, A a^{2} b c^{2} + 8 \, {\left(12 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} e^{3}\right)} x^{3} + 5 \, {\left(8 \, {\left(B b^{4} c - 24 \, A a b c^{3} + 2 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{3} - 3 \, {\left(3 \, B b^{5} + 48 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} c^{2} + 8 \, {\left(5 \, B a b^{3} - A b^{4}\right)} c\right)} d^{2} e + 3 \, {\left(18 \, B a b^{4} - 3 \, A b^{5} + 16 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{2} + 8 \, {\left(6 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} d e^{2} - 2 \, {\left(24 \, B a^{2} b^{3} - 9 \, A a b^{4} - 16 \, A a^{3} c^{2} + 8 \, {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} e^{3}\right)} x^{2} - 5 \, {\left({\left(B b^{5} + 96 \, A a^{2} c^{3} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} - 2 \, {\left(12 \, B a b^{3} + A b^{4}\right)} c\right)} d^{3} + 3 \, {\left(4 \, B a b^{4} + A b^{5} - 48 \, A a^{2} b c^{2} + 24 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} d^{2} e - 12 \, {\left(6 \, B a^{2} b^{3} - A a b^{4} + 4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} d e^{2} + 8 \, {\left(8 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - 4 \, A a^{3} b c\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{6} + 3 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(b^{8} c - 11 \, a b^{6} c^{2} + 36 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} x^{4} + {\left(b^{9} - 6 \, a b^{7} c - 24 \, a^{2} b^{5} c^{2} + 224 \, a^{3} b^{3} c^{3} - 384 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a b^{8} - 11 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} - 16 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)}}"," ",0,"2/15*(2*(64*(B*b*c^4 - 2*A*c^5)*d^3 - 24*(3*B*b^2*c^3 + 4*(B*a - 2*A*b)*c^4)*d^2*e + 12*(B*b^3*c^2 - 8*A*a*c^4 + 6*(2*B*a*b - A*b^2)*c^3)*d*e^2 + (B*b^4*c - 48*(B*a^2 - A*a*b)*c^3 - 4*(6*B*a*b^2 - A*b^3)*c^2)*e^3)*x^5 + 5*(64*(B*b^2*c^3 - 2*A*b*c^4)*d^3 - 24*(3*B*b^3*c^2 + 4*(B*a*b - 2*A*b^2)*c^3)*d^2*e + 12*(B*b^4*c - 8*A*a*b*c^3 + 6*(2*B*a*b^2 - A*b^3)*c^2)*d*e^2 + (B*b^5 - 48*(B*a^2*b - A*a*b^2)*c^2 - 4*(6*B*a*b^3 - A*b^4)*c)*e^3)*x^4 - (2*B*a*b^4 + 3*A*b^5 - 48*(2*B*a^3 - 5*A*a^2*b)*c^2 - 8*(6*B*a^2*b^2 + 5*A*a*b^3)*c)*d^3 - 6*(4*B*a^2*b^3 + A*a*b^4 - 48*A*a^3*c^2 + 24*(2*B*a^3*b - A*a^2*b^2)*c)*d^2*e + 24*(6*B*a^3*b^2 - A*a^2*b^3 + 4*(2*B*a^4 - 3*A*a^3*b)*c)*d*e^2 - 16*(8*B*a^4*b - 3*A*a^3*b^2 - 4*A*a^4*c)*e^3 + 5*(16*(3*B*b^3*c^2 - 8*A*a*c^4 + 2*(2*B*a*b - 3*A*b^2)*c^3)*d^3 - 6*(9*B*b^4*c + 16*(B*a^2 - 2*A*a*b)*c^3 + 24*(B*a*b^2 - A*b^3)*c^2)*d^2*e + 3*(3*B*b^5 - 32*A*a^2*c^3 + 48*(B*a^2*b - A*a*b^2)*c^2 + 2*(20*B*a*b^3 - 9*A*b^4)*c)*d*e^2 - (8*B*a*b^4 - 3*A*b^5 - 48*A*a^2*b*c^2 + 8*(12*B*a^2*b^2 - 5*A*a*b^3)*c)*e^3)*x^3 + 5*(8*(B*b^4*c - 24*A*a*b*c^3 + 2*(6*B*a*b^2 - A*b^3)*c^2)*d^3 - 3*(3*B*b^5 + 48*(B*a^2*b - 2*A*a*b^2)*c^2 + 8*(5*B*a*b^3 - A*b^4)*c)*d^2*e + 3*(18*B*a*b^4 - 3*A*b^5 + 16*(2*B*a^3 - 3*A*a^2*b)*c^2 + 8*(6*B*a^2*b^2 - 5*A*a*b^3)*c)*d*e^2 - 2*(24*B*a^2*b^3 - 9*A*a*b^4 - 16*A*a^3*c^2 + 8*(4*B*a^3*b - 3*A*a^2*b^2)*c)*e^3)*x^2 - 5*((B*b^5 + 96*A*a^2*c^3 - 48*(B*a^2*b - A*a*b^2)*c^2 - 2*(12*B*a*b^3 + A*b^4)*c)*d^3 + 3*(4*B*a*b^4 + A*b^5 - 48*A*a^2*b*c^2 + 24*(2*B*a^2*b^2 - A*a*b^3)*c)*d^2*e - 12*(6*B*a^2*b^3 - A*a*b^4 + 4*(2*B*a^3*b - 3*A*a^2*b^2)*c)*d*e^2 + 8*(8*B*a^3*b^2 - 3*A*a^2*b^3 - 4*A*a^3*b*c)*e^3)*x)*sqrt(c*x^2 + b*x + a)/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^6 + 3*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 3*(b^8*c - 11*a*b^6*c^2 + 36*a^2*b^4*c^3 - 16*a^3*b^2*c^4 - 64*a^4*c^5)*x^4 + (b^9 - 6*a*b^7*c - 24*a^2*b^5*c^2 + 224*a^3*b^3*c^3 - 384*a^4*b*c^4)*x^3 + 3*(a*b^8 - 11*a^2*b^6*c + 36*a^3*b^4*c^2 - 16*a^4*b^2*c^3 - 64*a^5*c^4)*x^2 + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)","B",0
2491,1,1095,0,130.731964," ","integrate((B*x+A)*(e*x+d)^2/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(16 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d^{2} - 4 \, {\left(3 \, B b^{2} c^{3} + 4 \, {\left(B a - 2 \, A b\right)} c^{4}\right)} d e + {\left(B b^{3} c^{2} - 8 \, A a c^{4} + 6 \, {\left(2 \, B a b - A b^{2}\right)} c^{3}\right)} e^{2}\right)} x^{5} + 20 \, {\left(16 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d^{2} - 4 \, {\left(3 \, B b^{3} c^{2} + 4 \, {\left(B a b - 2 \, A b^{2}\right)} c^{3}\right)} d e + {\left(B b^{4} c - 8 \, A a b c^{3} + 6 \, {\left(2 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} e^{2}\right)} x^{4} + 5 \, {\left(16 \, {\left(3 \, B b^{3} c^{2} - 8 \, A a c^{4} + 2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{3}\right)} d^{2} - 4 \, {\left(9 \, B b^{4} c + 16 \, {\left(B a^{2} - 2 \, A a b\right)} c^{3} + 24 \, {\left(B a b^{2} - A b^{3}\right)} c^{2}\right)} d e + {\left(3 \, B b^{5} - 32 \, A a^{2} c^{3} + 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} + 2 \, {\left(20 \, B a b^{3} - 9 \, A b^{4}\right)} c\right)} e^{2}\right)} x^{3} - {\left(2 \, B a b^{4} + 3 \, A b^{5} - 48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} - 8 \, {\left(6 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c\right)} d^{2} - 4 \, {\left(4 \, B a^{2} b^{3} + A a b^{4} - 48 \, A a^{3} c^{2} + 24 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} d e + 8 \, {\left(6 \, B a^{3} b^{2} - A a^{2} b^{3} + 4 \, {\left(2 \, B a^{4} - 3 \, A a^{3} b\right)} c\right)} e^{2} + 5 \, {\left(8 \, {\left(B b^{4} c - 24 \, A a b c^{3} + 2 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} d^{2} - 2 \, {\left(3 \, B b^{5} + 48 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} c^{2} + 8 \, {\left(5 \, B a b^{3} - A b^{4}\right)} c\right)} d e + {\left(18 \, B a b^{4} - 3 \, A b^{5} + 16 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c^{2} + 8 \, {\left(6 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c\right)} e^{2}\right)} x^{2} - 5 \, {\left({\left(B b^{5} + 96 \, A a^{2} c^{3} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} - 2 \, {\left(12 \, B a b^{3} + A b^{4}\right)} c\right)} d^{2} + 2 \, {\left(4 \, B a b^{4} + A b^{5} - 48 \, A a^{2} b c^{2} + 24 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} d e - 4 \, {\left(6 \, B a^{2} b^{3} - A a b^{4} + 4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{6} + 3 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(b^{8} c - 11 \, a b^{6} c^{2} + 36 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} x^{4} + {\left(b^{9} - 6 \, a b^{7} c - 24 \, a^{2} b^{5} c^{2} + 224 \, a^{3} b^{3} c^{3} - 384 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a b^{8} - 11 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} - 16 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)}}"," ",0,"2/15*(8*(16*(B*b*c^4 - 2*A*c^5)*d^2 - 4*(3*B*b^2*c^3 + 4*(B*a - 2*A*b)*c^4)*d*e + (B*b^3*c^2 - 8*A*a*c^4 + 6*(2*B*a*b - A*b^2)*c^3)*e^2)*x^5 + 20*(16*(B*b^2*c^3 - 2*A*b*c^4)*d^2 - 4*(3*B*b^3*c^2 + 4*(B*a*b - 2*A*b^2)*c^3)*d*e + (B*b^4*c - 8*A*a*b*c^3 + 6*(2*B*a*b^2 - A*b^3)*c^2)*e^2)*x^4 + 5*(16*(3*B*b^3*c^2 - 8*A*a*c^4 + 2*(2*B*a*b - 3*A*b^2)*c^3)*d^2 - 4*(9*B*b^4*c + 16*(B*a^2 - 2*A*a*b)*c^3 + 24*(B*a*b^2 - A*b^3)*c^2)*d*e + (3*B*b^5 - 32*A*a^2*c^3 + 48*(B*a^2*b - A*a*b^2)*c^2 + 2*(20*B*a*b^3 - 9*A*b^4)*c)*e^2)*x^3 - (2*B*a*b^4 + 3*A*b^5 - 48*(2*B*a^3 - 5*A*a^2*b)*c^2 - 8*(6*B*a^2*b^2 + 5*A*a*b^3)*c)*d^2 - 4*(4*B*a^2*b^3 + A*a*b^4 - 48*A*a^3*c^2 + 24*(2*B*a^3*b - A*a^2*b^2)*c)*d*e + 8*(6*B*a^3*b^2 - A*a^2*b^3 + 4*(2*B*a^4 - 3*A*a^3*b)*c)*e^2 + 5*(8*(B*b^4*c - 24*A*a*b*c^3 + 2*(6*B*a*b^2 - A*b^3)*c^2)*d^2 - 2*(3*B*b^5 + 48*(B*a^2*b - 2*A*a*b^2)*c^2 + 8*(5*B*a*b^3 - A*b^4)*c)*d*e + (18*B*a*b^4 - 3*A*b^5 + 16*(2*B*a^3 - 3*A*a^2*b)*c^2 + 8*(6*B*a^2*b^2 - 5*A*a*b^3)*c)*e^2)*x^2 - 5*((B*b^5 + 96*A*a^2*c^3 - 48*(B*a^2*b - A*a*b^2)*c^2 - 2*(12*B*a*b^3 + A*b^4)*c)*d^2 + 2*(4*B*a*b^4 + A*b^5 - 48*A*a^2*b*c^2 + 24*(2*B*a^2*b^2 - A*a*b^3)*c)*d*e - 4*(6*B*a^2*b^3 - A*a*b^4 + 4*(2*B*a^3*b - 3*A*a^2*b^2)*c)*e^2)*x)*sqrt(c*x^2 + b*x + a)/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^6 + 3*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 3*(b^8*c - 11*a*b^6*c^2 + 36*a^2*b^4*c^3 - 16*a^3*b^2*c^4 - 64*a^4*c^5)*x^4 + (b^9 - 6*a*b^7*c - 24*a^2*b^5*c^2 + 224*a^3*b^3*c^3 - 384*a^4*b*c^4)*x^3 + 3*(a*b^8 - 11*a^2*b^6*c + 36*a^3*b^4*c^2 - 16*a^4*b^2*c^3 - 64*a^5*c^4)*x^2 + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)","B",0
2492,1,805,0,127.209203," ","integrate((B*x+A)*(e*x+d)/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(8 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} d - {\left(3 \, B b^{2} c^{3} + 4 \, {\left(B a - 2 \, A b\right)} c^{4}\right)} e\right)} x^{5} + 40 \, {\left(8 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} d - {\left(3 \, B b^{3} c^{2} + 4 \, {\left(B a b - 2 \, A b^{2}\right)} c^{3}\right)} e\right)} x^{4} + 10 \, {\left(8 \, {\left(3 \, B b^{3} c^{2} - 8 \, A a c^{4} + 2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{3}\right)} d - {\left(9 \, B b^{4} c + 16 \, {\left(B a^{2} - 2 \, A a b\right)} c^{3} + 24 \, {\left(B a b^{2} - A b^{3}\right)} c^{2}\right)} e\right)} x^{3} + 5 \, {\left(8 \, {\left(B b^{4} c - 24 \, A a b c^{3} + 2 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} d - {\left(3 \, B b^{5} + 48 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} c^{2} + 8 \, {\left(5 \, B a b^{3} - A b^{4}\right)} c\right)} e\right)} x^{2} - {\left(2 \, B a b^{4} + 3 \, A b^{5} - 48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} - 8 \, {\left(6 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c\right)} d - 2 \, {\left(4 \, B a^{2} b^{3} + A a b^{4} - 48 \, A a^{3} c^{2} + 24 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} e - 5 \, {\left({\left(B b^{5} + 96 \, A a^{2} c^{3} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} - 2 \, {\left(12 \, B a b^{3} + A b^{4}\right)} c\right)} d + {\left(4 \, B a b^{4} + A b^{5} - 48 \, A a^{2} b c^{2} + 24 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{6} + 3 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(b^{8} c - 11 \, a b^{6} c^{2} + 36 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} x^{4} + {\left(b^{9} - 6 \, a b^{7} c - 24 \, a^{2} b^{5} c^{2} + 224 \, a^{3} b^{3} c^{3} - 384 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a b^{8} - 11 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} - 16 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)}}"," ",0,"2/15*(16*(8*(B*b*c^4 - 2*A*c^5)*d - (3*B*b^2*c^3 + 4*(B*a - 2*A*b)*c^4)*e)*x^5 + 40*(8*(B*b^2*c^3 - 2*A*b*c^4)*d - (3*B*b^3*c^2 + 4*(B*a*b - 2*A*b^2)*c^3)*e)*x^4 + 10*(8*(3*B*b^3*c^2 - 8*A*a*c^4 + 2*(2*B*a*b - 3*A*b^2)*c^3)*d - (9*B*b^4*c + 16*(B*a^2 - 2*A*a*b)*c^3 + 24*(B*a*b^2 - A*b^3)*c^2)*e)*x^3 + 5*(8*(B*b^4*c - 24*A*a*b*c^3 + 2*(6*B*a*b^2 - A*b^3)*c^2)*d - (3*B*b^5 + 48*(B*a^2*b - 2*A*a*b^2)*c^2 + 8*(5*B*a*b^3 - A*b^4)*c)*e)*x^2 - (2*B*a*b^4 + 3*A*b^5 - 48*(2*B*a^3 - 5*A*a^2*b)*c^2 - 8*(6*B*a^2*b^2 + 5*A*a*b^3)*c)*d - 2*(4*B*a^2*b^3 + A*a*b^4 - 48*A*a^3*c^2 + 24*(2*B*a^3*b - A*a^2*b^2)*c)*e - 5*((B*b^5 + 96*A*a^2*c^3 - 48*(B*a^2*b - A*a*b^2)*c^2 - 2*(12*B*a*b^3 + A*b^4)*c)*d + (4*B*a*b^4 + A*b^5 - 48*A*a^2*b*c^2 + 24*(2*B*a^2*b^2 - A*a*b^3)*c)*e)*x)*sqrt(c*x^2 + b*x + a)/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^6 + 3*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 3*(b^8*c - 11*a*b^6*c^2 + 36*a^2*b^4*c^3 - 16*a^3*b^2*c^4 - 64*a^4*c^5)*x^4 + (b^9 - 6*a*b^7*c - 24*a^2*b^5*c^2 + 224*a^3*b^3*c^3 - 384*a^4*b*c^4)*x^3 + 3*(a*b^8 - 11*a^2*b^6*c + 36*a^3*b^4*c^2 - 16*a^4*b^2*c^3 - 64*a^5*c^4)*x^2 + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)","B",0
2493,1,543,0,5.063035," ","integrate((B*x+A)/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, B a b^{4} + 3 \, A b^{5} - 128 \, {\left(B b c^{4} - 2 \, A c^{5}\right)} x^{5} - 320 \, {\left(B b^{2} c^{3} - 2 \, A b c^{4}\right)} x^{4} - 80 \, {\left(3 \, B b^{3} c^{2} - 8 \, A a c^{4} + 2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{3}\right)} x^{3} - 48 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} - 40 \, {\left(B b^{4} c - 24 \, A a b c^{3} + 2 \, {\left(6 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} x^{2} - 8 \, {\left(6 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c + 5 \, {\left(B b^{5} + 96 \, A a^{2} c^{3} - 48 \, {\left(B a^{2} b - A a b^{2}\right)} c^{2} - 2 \, {\left(12 \, B a b^{3} + A b^{4}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{6} + 3 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(b^{8} c - 11 \, a b^{6} c^{2} + 36 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} x^{4} + {\left(b^{9} - 6 \, a b^{7} c - 24 \, a^{2} b^{5} c^{2} + 224 \, a^{3} b^{3} c^{3} - 384 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a b^{8} - 11 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} - 16 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)}}"," ",0,"-2/15*(2*B*a*b^4 + 3*A*b^5 - 128*(B*b*c^4 - 2*A*c^5)*x^5 - 320*(B*b^2*c^3 - 2*A*b*c^4)*x^4 - 80*(3*B*b^3*c^2 - 8*A*a*c^4 + 2*(2*B*a*b - 3*A*b^2)*c^3)*x^3 - 48*(2*B*a^3 - 5*A*a^2*b)*c^2 - 40*(B*b^4*c - 24*A*a*b*c^3 + 2*(6*B*a*b^2 - A*b^3)*c^2)*x^2 - 8*(6*B*a^2*b^2 + 5*A*a*b^3)*c + 5*(B*b^5 + 96*A*a^2*c^3 - 48*(B*a^2*b - A*a*b^2)*c^2 - 2*(12*B*a*b^3 + A*b^4)*c)*x)*sqrt(c*x^2 + b*x + a)/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^6 + 3*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 3*(b^8*c - 11*a*b^6*c^2 + 36*a^2*b^4*c^3 - 16*a^3*b^2*c^4 - 64*a^4*c^5)*x^4 + (b^9 - 6*a*b^7*c - 24*a^2*b^5*c^2 + 224*a^3*b^3*c^3 - 384*a^4*b*c^4)*x^3 + 3*(a*b^8 - 11*a^2*b^6*c + 36*a^3*b^4*c^2 - 16*a^4*b^2*c^3 - 64*a^5*c^4)*x^2 + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)","B",0
2494,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2495,1,73,0,0.410244," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3240} \, {\left(3456 \, x^{4} - 2160 \, x^{3} - 93912 \, x^{2} - 268750 \, x - 281829\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{28051}{7776} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/3240*(3456*x^4 - 2160*x^3 - 93912*x^2 - 268750*x - 281829)*sqrt(3*x^2 + 5*x + 2) + 28051/7776*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2496,1,68,0,0.397712," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{648} \, {\left(432 \, x^{3} - 1128 \, x^{2} - 11690 \, x - 21759\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{19405}{7776} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/648*(432*x^3 - 1128*x^2 - 11690*x - 21759)*sqrt(3*x^2 + 5*x + 2) + 19405/7776*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2497,1,63,0,0.399905," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{54} \, {\left(24 \, x^{2} - 122 \, x - 645\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} + \frac{1147}{648} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/54*(24*x^2 - 122*x - 645)*sqrt(3*x^2 + 5*x + 2) + 1147/648*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2498,1,58,0,0.398215," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x - 19\right)} + \frac{31}{24} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right)"," ",0,"-1/6*sqrt(3*x^2 + 5*x + 2)*(2*x - 19) + 31/24*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49)","A",0
2499,1,53,0,0.392984," ","integrate((5-x)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{35}{36} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) - \frac{1}{3} \, \sqrt{3 \, x^{2} + 5 \, x + 2}"," ",0,"35/36*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) - 1/3*sqrt(3*x^2 + 5*x + 2)","A",0
2500,1,90,0,0.404085," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + \frac{13}{20} \, \sqrt{5} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right)"," ",0,"1/12*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 13/20*sqrt(5)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9))","A",0
2501,1,80,0,0.398166," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{47 \, \sqrt{5} {\left(2 \, x + 3\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 260 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{100 \, {\left(2 \, x + 3\right)}}"," ",0,"1/100*(47*sqrt(5)*(2*x + 3)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 260*sqrt(3*x^2 + 5*x + 2))/(2*x + 3)","A",0
2502,1,95,0,0.401158," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{389 \, \sqrt{5} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(292 \, x + 503\right)}}{1000 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/1000*(389*sqrt(5)*(4*x^2 + 12*x + 9)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*sqrt(3*x^2 + 5*x + 2)*(292*x + 503))/(4*x^2 + 12*x + 9)","A",0
2503,1,110,0,0.402437," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{993 \, \sqrt{5} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(1728 \, x^{2} + 5674 \, x + 4753\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{3000 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/3000*(993*sqrt(5)*(8*x^3 + 36*x^2 + 54*x + 27)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*(1728*x^2 + 5674*x + 4753)*sqrt(3*x^2 + 5*x + 2))/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
2504,1,125,0,0.403863," ","integrate((5-x)/(3+2*x)^5/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{17313 \, \sqrt{5} {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(65376 \, x^{3} + 314692 \, x^{2} + 509668 \, x + 279039\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{60000 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"1/60000*(17313*sqrt(5)*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*(65376*x^3 + 314692*x^2 + 509668*x + 279039)*sqrt(3*x^2 + 5*x + 2))/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
2505,1,140,0,0.406184," ","integrate((5-x)/(3+2*x)^6/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{385143 \, \sqrt{5} {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(3051072 \, x^{4} + 19313432 \, x^{3} + 46092332 \, x^{2} + 49233702 \, x + 19918587\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{1500000 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"1/1500000*(385143*sqrt(5)*(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*(3051072*x^4 + 19313432*x^3 + 46092332*x^2 + 49233702*x + 19918587)*sqrt(3*x^2 + 5*x + 2))/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
2506,1,97,0,0.419034," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","\frac{6265 \, \sqrt{3} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) - 12 \, {\left(72 \, x^{4} - 102 \, x^{3} - 3331 \, x^{2} + 6920 \, x + 9591\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{486 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/486*(6265*sqrt(3)*(3*x^2 + 5*x + 2)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) - 12*(72*x^4 - 102*x^3 - 3331*x^2 + 6920*x + 9591)*sqrt(3*x^2 + 5*x + 2))/(3*x^2 + 5*x + 2)","A",0
2507,1,92,0,0.397792," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","\frac{247 \, \sqrt{3} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) - 12 \, {\left(6 \, x^{3} - 31 \, x^{2} + 806 \, x + 789\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{54 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/54*(247*sqrt(3)*(3*x^2 + 5*x + 2)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) - 12*(6*x^3 - 31*x^2 + 806*x + 789)*sqrt(3*x^2 + 5*x + 2))/(3*x^2 + 5*x + 2)","A",0
2508,1,87,0,0.414570," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{3} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) - 2 \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x^{2} + 199 \, x + 179\right)}}{3 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/3*(3*sqrt(3)*(3*x^2 + 5*x + 2)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) - 2*sqrt(3*x^2 + 5*x + 2)*(2*x^2 + 199*x + 179))/(3*x^2 + 5*x + 2)","A",0
2509,1,81,0,0.401559," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{3} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) - 6 \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(139 \, x + 121\right)}}{9 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/9*(sqrt(3)*(3*x^2 + 5*x + 2)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) - 6*sqrt(3*x^2 + 5*x + 2)*(139*x + 121))/(3*x^2 + 5*x + 2)","A",0
2510,1,19,0,0.403510," ","integrate((5-x)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, x + 29\right)}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}"," ",0,"-2*(35*x + 29)/sqrt(3*x^2 + 5*x + 2)","A",0
2511,1,95,0,0.409586," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","\frac{13 \, \sqrt{5} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 30 \, \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(47 \, x + 37\right)}}{25 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/25*(13*sqrt(5)*(3*x^2 + 5*x + 2)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 30*sqrt(3*x^2 + 5*x + 2)*(47*x + 37))/(3*x^2 + 5*x + 2)","A",0
2512,1,110,0,0.407784," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","\frac{151 \, \sqrt{5} {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 10 \, {\left(1284 \, x^{2} + 2845 \, x + 1411\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{125 \, {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/125*(151*sqrt(5)*(6*x^3 + 19*x^2 + 19*x + 6)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 10*(1284*x^2 + 2845*x + 1411)*sqrt(3*x^2 + 5*x + 2))/(6*x^3 + 19*x^2 + 19*x + 6)","A",0
2513,1,125,0,0.406543," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","\frac{483 \, \sqrt{5} {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(2592 \, x^{3} + 9453 \, x^{2} + 10988 \, x + 3977\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{250 \, {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)}}"," ",0,"1/250*(483*sqrt(5)*(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*(2592*x^3 + 9453*x^2 + 10988*x + 3977)*sqrt(3*x^2 + 5*x + 2))/(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)","A",0
2514,1,140,0,0.403640," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","\frac{9867 \, \sqrt{5} {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(83376 \, x^{4} + 424938 \, x^{3} + 792065 \, x^{2} + 634312 \, x + 181559\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{3750 \, {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)}}"," ",0,"1/3750*(9867*sqrt(5)*(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*(83376*x^4 + 424938*x^3 + 792065*x^2 + 634312*x + 181559)*sqrt(3*x^2 + 5*x + 2))/(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)","A",0
2515,1,155,0,0.421077," ","integrate((5-x)/(3+2*x)^5/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","\frac{246117 \, \sqrt{5} {\left(48 \, x^{6} + 368 \, x^{5} + 1160 \, x^{4} + 1920 \, x^{3} + 1755 \, x^{2} + 837 \, x + 162\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) - 20 \, {\left(3665952 \, x^{5} + 24066204 \, x^{4} + 62190544 \, x^{3} + 78737669 \, x^{2} + 48537379 \, x + 11545002\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{75000 \, {\left(48 \, x^{6} + 368 \, x^{5} + 1160 \, x^{4} + 1920 \, x^{3} + 1755 \, x^{2} + 837 \, x + 162\right)}}"," ",0,"1/75000*(246117*sqrt(5)*(48*x^6 + 368*x^5 + 1160*x^4 + 1920*x^3 + 1755*x^2 + 837*x + 162)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) - 20*(3665952*x^5 + 24066204*x^4 + 62190544*x^3 + 78737669*x^2 + 48537379*x + 11545002)*sqrt(3*x^2 + 5*x + 2))/(48*x^6 + 368*x^5 + 1160*x^4 + 1920*x^3 + 1755*x^2 + 837*x + 162)","A",0
2516,1,117,0,0.406335," ","integrate((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(38 \, \sqrt{3} {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) - 3 \, {\left(72 \, x^{4} - 58720 \, x^{3} - 146180 \, x^{2} - 118153 \, x - 30819\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{81 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"2/81*(38*sqrt(3)*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) - 3*(72*x^4 - 58720*x^3 - 146180*x^2 - 118153*x - 30819)*sqrt(3*x^2 + 5*x + 2))/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2517,1,112,0,0.396806," ","integrate((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, \sqrt{3} {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + 3 \, {\left(16448 \, x^{3} + 41074 \, x^{2} + 33443 \, x + 8835\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{27 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"2/27*(2*sqrt(3)*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 3*(16448*x^3 + 41074*x^2 + 33443*x + 8835)*sqrt(3*x^2 + 5*x + 2))/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2518,1,51,0,0.398962," ","integrate((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(4372 \, x^{3} + 10932 \, x^{2} + 8925 \, x + 2371\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{3 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"2/3*(4372*x^3 + 10932*x^2 + 8925*x + 2371)*sqrt(3*x^2 + 5*x + 2)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2519,1,51,0,0.391648," ","integrate((5-x)*(3+2*x)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1124 \, x^{3} + 2810 \, x^{2} + 2295 \, x + 611\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}"," ",0,"2*(1124*x^3 + 2810*x^2 + 2295*x + 611)*sqrt(3*x^2 + 5*x + 2)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2520,1,51,0,0.402858," ","integrate((5-x)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(840 \, x^{3} + 2100 \, x^{2} + 1715 \, x + 457\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}"," ",0,"2*(840*x^3 + 2100*x^2 + 1715*x + 457)*sqrt(3*x^2 + 5*x + 2)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2521,1,125,0,0.411923," ","integrate((5-x)/(3+2*x)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(26 \, \sqrt{5} {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 5 \, {\left(15048 \, x^{3} + 37698 \, x^{2} + 30827 \, x + 8227\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{125 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"2/125*(26*sqrt(5)*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 5*(15048*x^3 + 37698*x^2 + 30827*x + 8227)*sqrt(3*x^2 + 5*x + 2))/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2522,1,140,0,0.414213," ","integrate((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(102 \, \sqrt{5} {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 5 \, {\left(19872 \, x^{4} + 80100 \, x^{3} + 116826 \, x^{2} + 73215 \, x + 16667\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{125 \, {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)}}"," ",0,"2/125*(102*sqrt(5)*(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 5*(19872*x^4 + 80100*x^3 + 116826*x^2 + 73215*x + 16667)*sqrt(3*x^2 + 5*x + 2))/(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)","A",0
2523,1,155,0,0.420413," ","integrate((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1221 \, \sqrt{5} {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 5 \, {\left(106272 \, x^{5} + 599148 \, x^{4} + 1316616 \, x^{3} + 1405814 \, x^{2} + 727887 \, x + 146063\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{625 \, {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"2/625*(1221*sqrt(5)*(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 5*(106272*x^5 + 599148*x^4 + 1316616*x^3 + 1405814*x^2 + 727887*x + 146063)*sqrt(3*x^2 + 5*x + 2))/(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)","A",0
2524,1,170,0,0.426737," ","integrate((5-x)/(3+2*x)^4/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(34581 \, \sqrt{5} {\left(72 \, x^{7} + 564 \, x^{6} + 1862 \, x^{5} + 3355 \, x^{4} + 3560 \, x^{3} + 2223 \, x^{2} + 756 \, x + 108\right)} \log\left(\frac{4 \, \sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(8 \, x + 7\right)} + 124 \, x^{2} + 212 \, x + 89}{4 \, x^{2} + 12 \, x + 9}\right) + 5 \, {\left(523584 \, x^{6} + 4495032 \, x^{5} + 15334836 \, x^{4} + 26717636 \, x^{3} + 25105026 \, x^{2} + 12060957 \, x + 2313929\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}\right)}}{9375 \, {\left(72 \, x^{7} + 564 \, x^{6} + 1862 \, x^{5} + 3355 \, x^{4} + 3560 \, x^{3} + 2223 \, x^{2} + 756 \, x + 108\right)}}"," ",0,"2/9375*(34581*sqrt(5)*(72*x^7 + 564*x^6 + 1862*x^5 + 3355*x^4 + 3560*x^3 + 2223*x^2 + 756*x + 108)*log((4*sqrt(5)*sqrt(3*x^2 + 5*x + 2)*(8*x + 7) + 124*x^2 + 212*x + 89)/(4*x^2 + 12*x + 9)) + 5*(523584*x^6 + 4495032*x^5 + 15334836*x^4 + 26717636*x^3 + 25105026*x^2 + 12060957*x + 2313929)*sqrt(3*x^2 + 5*x + 2))/(72*x^7 + 564*x^6 + 1862*x^5 + 3355*x^4 + 3560*x^3 + 2223*x^2 + 756*x + 108)","A",0
2525,1,50,0,0.418084," ","integrate((-1+x)/(1+x)/(x^2+x+1)^(1/2),x, algorithm=""fricas"")","2 \, \log\left(-x + \sqrt{x^{2} + x + 1}\right) - 2 \, \log\left(-x + \sqrt{x^{2} + x + 1} - 2\right) - \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right)"," ",0,"2*log(-x + sqrt(x^2 + x + 1)) - 2*log(-x + sqrt(x^2 + x + 1) - 2) - log(-2*x + 2*sqrt(x^2 + x + 1) - 1)","A",0
2526,1,44,0,0.392504," ","integrate((5-x)*(3+2*x)^(7/2)*(3*x^2+5*x+2),x, algorithm=""fricas"")","-\frac{1}{6435} \, {\left(20592 \, x^{7} + 30096 \, x^{6} - 447048 \, x^{5} - 2029120 \, x^{4} - 3733305 \, x^{3} - 3496257 \, x^{2} - 1636821 \, x - 301887\right)} \sqrt{2 \, x + 3}"," ",0,"-1/6435*(20592*x^7 + 30096*x^6 - 447048*x^5 - 2029120*x^4 - 3733305*x^3 - 3496257*x^2 - 1636821*x - 301887)*sqrt(2*x + 3)","A",0
2527,1,39,0,0.395631," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2),x, algorithm=""fricas"")","-\frac{1}{9009} \, {\left(16632 \, x^{6} - 4284 \, x^{5} - 375242 \, x^{4} - 1116057 \, x^{3} - 1364067 \, x^{2} - 758349 \, x - 157383\right)} \sqrt{2 \, x + 3}"," ",0,"-1/9009*(16632*x^6 - 4284*x^5 - 375242*x^4 - 1116057*x^3 - 1364067*x^2 - 758349*x - 157383)*sqrt(2*x + 3)","A",0
2528,1,34,0,0.375341," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2),x, algorithm=""fricas"")","-\frac{1}{693} \, {\left(756 \, x^{5} - 1568 \, x^{4} - 15627 \, x^{3} - 28143 \, x^{2} - 19251 \, x - 4617\right)} \sqrt{2 \, x + 3}"," ",0,"-1/693*(756*x^5 - 1568*x^4 - 15627*x^3 - 28143*x^2 - 19251*x - 4617)*sqrt(2*x + 3)","A",0
2529,1,29,0,0.377261," ","integrate((5-x)*(3*x^2+5*x+2)*(3+2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{105} \, {\left(70 \, x^{4} - 285 \, x^{3} - 1083 \, x^{2} - 949 \, x - 303\right)} \sqrt{2 \, x + 3}"," ",0,"-1/105*(70*x^4 - 285*x^3 - 1083*x^2 - 949*x - 303)*sqrt(2*x + 3)","A",0
2530,1,24,0,0.408383," ","integrate((5-x)*(3*x^2+5*x+2)/(3+2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{105} \, {\left(45 \, x^{3} - 291 \, x^{2} - 223 \, x - 381\right)} \sqrt{2 \, x + 3}"," ",0,"-1/105*(45*x^3 - 291*x^2 - 223*x - 381)*sqrt(2*x + 3)","A",0
2531,1,24,0,0.378837," ","integrate((5-x)*(3*x^2+5*x+2)/(3+2*x)^(3/2),x, algorithm=""fricas"")","-\frac{9 \, x^{3} - 77 \, x^{2} + 117 \, x + 501}{15 \, \sqrt{2 \, x + 3}}"," ",0,"-1/15*(9*x^3 - 77*x^2 + 117*x + 501)/sqrt(2*x + 3)","A",0
2532,1,36,0,0.382469," ","integrate((5-x)*(3*x^2+5*x+2)/(3+2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, x^{3} - 57 \, x^{2} - 273 \, x - 263\right)} \sqrt{2 \, x + 3}}{3 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"-1/3*(3*x^3 - 57*x^2 - 273*x - 263)*sqrt(2*x + 3)/(4*x^2 + 12*x + 9)","A",0
2533,1,41,0,0.391495," ","integrate((5-x)*(3*x^2+5*x+2)/(3+2*x)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(9 \, x^{3} + 111 \, x^{2} + 245 \, x + 153\right)} \sqrt{2 \, x + 3}}{3 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"-1/3*(9*x^3 + 111*x^2 + 245*x + 153)*sqrt(2*x + 3)/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
2534,1,54,0,0.395186," ","integrate((5-x)*(3+2*x)^(7/2)*(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{1}{2078505} \, {\left(15752880 \, x^{9} + 51274080 \, x^{8} - 262729896 \, x^{7} - 1939330008 \, x^{6} - 5196312621 \, x^{5} - 7690154020 \, x^{4} - 6844462215 \, x^{3} - 3651616134 \, x^{2} - 1077299892 \, x - 135278424\right)} \sqrt{2 \, x + 3}"," ",0,"-1/2078505*(15752880*x^9 + 51274080*x^8 - 262729896*x^7 - 1939330008*x^6 - 5196312621*x^5 - 7690154020*x^4 - 6844462215*x^3 - 3651616134*x^2 - 1077299892*x - 135278424)*sqrt(2*x + 3)","A",0
2535,1,49,0,0.377545," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{1}{51051} \, {\left(216216 \, x^{8} + 348348 \, x^{7} - 4324782 \, x^{6} - 20560239 \, x^{5} - 40692820 \, x^{4} - 43843941 \, x^{3} - 26848368 \, x^{2} - 8789688 \, x - 1198476\right)} \sqrt{2 \, x + 3}"," ",0,"-1/51051*(216216*x^8 + 348348*x^7 - 4324782*x^6 - 20560239*x^5 - 40692820*x^4 - 43843941*x^3 - 26848368*x^2 - 8789688*x - 1198476)*sqrt(2*x + 3)","A",0
2536,1,44,0,0.391158," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","-\frac{1}{15015} \, {\left(36036 \, x^{7} - 2772 \, x^{6} - 747579 \, x^{5} - 2342620 \, x^{4} - 3236325 \, x^{3} - 2333766 \, x^{2} - 857988 \, x - 128736\right)} \sqrt{2 \, x + 3}"," ",0,"-1/15015*(36036*x^7 - 2772*x^6 - 747579*x^5 - 2342620*x^4 - 3236325*x^3 - 2333766*x^2 - 857988*x - 128736)*sqrt(2*x + 3)","A",0
2537,1,39,0,0.385694," ","integrate((5-x)*(3*x^2+5*x+2)^2*(3+2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{117} \, {\left(162 \, x^{6} - 297 \, x^{5} - 3028 \, x^{4} - 5991 \, x^{3} - 5292 \, x^{2} - 2208 \, x - 396\right)} \sqrt{2 \, x + 3}"," ",0,"-1/117*(162*x^6 - 297*x^5 - 3028*x^4 - 5991*x^3 - 5292*x^2 - 2208*x - 396)*sqrt(2*x + 3)","A",0
2538,1,34,0,0.391956," ","integrate((5-x)*(3*x^2+5*x+2)^2/(3+2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{1155} \, {\left(945 \, x^{5} - 3500 \, x^{4} - 12645 \, x^{3} - 15354 \, x^{2} - 6252 \, x - 4344\right)} \sqrt{2 \, x + 3}"," ",0,"-1/1155*(945*x^5 - 3500*x^4 - 12645*x^3 - 15354*x^2 - 6252*x - 4344)*sqrt(2*x + 3)","A",0
2539,1,34,0,0.386597," ","integrate((5-x)*(3*x^2+5*x+2)^2/(3+2*x)^(3/2),x, algorithm=""fricas"")","-\frac{35 \, x^{5} - 150 \, x^{4} - 431 \, x^{3} - 632 \, x^{2} + 432 \, x + 1996}{35 \, \sqrt{2 \, x + 3}}"," ",0,"-1/35*(35*x^5 - 150*x^4 - 431*x^3 - 632*x^2 + 432*x + 1996)/sqrt(2*x + 3)","A",0
2540,1,46,0,0.383149," ","integrate((5-x)*(3*x^2+5*x+2)^2/(3+2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(27 \, x^{5} - 144 \, x^{4} - 215 \, x^{3} - 1530 \, x^{2} - 7164 \, x - 7024\right)} \sqrt{2 \, x + 3}}{21 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"-1/21*(27*x^5 - 144*x^4 - 215*x^3 - 1530*x^2 - 7164*x - 7024)*sqrt(2*x + 3)/(4*x^2 + 12*x + 9)","A",0
2541,1,51,0,0.389602," ","integrate((5-x)*(3*x^2+5*x+2)^2/(3+2*x)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(9 \, x^{5} - 70 \, x^{4} + 275 \, x^{3} + 3300 \, x^{2} + 6760 \, x + 4076\right)} \sqrt{2 \, x + 3}}{5 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"-1/5*(9*x^5 - 70*x^4 + 275*x^3 + 3300*x^2 + 6760*x + 4076)*sqrt(2*x + 3)/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
2542,1,64,0,0.395296," ","integrate((5-x)*(3+2*x)^(7/2)*(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","-\frac{1}{47805615} \, {\left(897914160 \, x^{11} + 4489570800 \, x^{10} - 8356902840 \, x^{9} - 126274674240 \, x^{8} - 465368338149 \, x^{7} - 952484547267 \, x^{6} - 1244240822034 \, x^{5} - 1081998930520 \, x^{4} - 626194644675 \, x^{3} - 232269229971 \, x^{2} - 50041179918 \, x - 4766652846\right)} \sqrt{2 \, x + 3}"," ",0,"-1/47805615*(897914160*x^11 + 4489570800*x^10 - 8356902840*x^9 - 126274674240*x^8 - 465368338149*x^7 - 952484547267*x^6 - 1244240822034*x^5 - 1081998930520*x^4 - 626194644675*x^3 - 232269229971*x^2 - 50041179918*x - 4766652846)*sqrt(2*x + 3)","A",0
2543,1,59,0,0.383821," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","-\frac{1}{15561} \, {\left(160056 \, x^{10} + 543348 \, x^{9} - 2428218 \, x^{8} - 19193889 \, x^{7} - 54383679 \, x^{6} - 87436314 \, x^{5} - 88365578 \, x^{4} - 57400347 \, x^{3} - 23339691 \, x^{2} - 5418846 \, x - 549342\right)} \sqrt{2 \, x + 3}"," ",0,"-1/15561*(160056*x^10 + 543348*x^9 - 2428218*x^8 - 19193889*x^7 - 54383679*x^6 - 87436314*x^5 - 88365578*x^4 - 57400347*x^3 - 23339691*x^2 - 5418846*x - 549342)*sqrt(2*x + 3)","A",0
2544,1,54,0,0.380723," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","-\frac{1}{4849845} \, {\left(27567540 \, x^{9} + 48648600 \, x^{8} - 511413903 \, x^{7} - 2573238129 \, x^{6} - 5488936698 \, x^{5} - 6671966560 \, x^{4} - 4954126305 \, x^{3} - 2231396337 \, x^{2} - 561646746 \, x - 61003962\right)} \sqrt{2 \, x + 3}"," ",0,"-1/4849845*(27567540*x^9 + 48648600*x^8 - 511413903*x^7 - 2573238129*x^6 - 5488936698*x^5 - 6671966560*x^4 - 4954126305*x^3 - 2231396337*x^2 - 561646746*x - 61003962)*sqrt(2*x + 3)","A",0
2545,1,49,0,0.381180," ","integrate((5-x)*(3*x^2+5*x+2)^3*(3+2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{765765} \, {\left(2432430 \, x^{8} + 243243 \, x^{7} - 47045691 \, x^{6} - 157479462 \, x^{5} - 243619810 \, x^{4} - 212153055 \, x^{3} - 107295183 \, x^{2} - 29433414 \, x - 3591558\right)} \sqrt{2 \, x + 3}"," ",0,"-1/765765*(2432430*x^8 + 243243*x^7 - 47045691*x^6 - 157479462*x^5 - 243619810*x^4 - 212153055*x^3 - 107295183*x^2 - 29433414*x - 3591558)*sqrt(2*x + 3)","A",0
2546,1,44,0,0.377207," ","integrate((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{45045} \, {\left(81081 \, x^{7} - 130977 \, x^{6} - 1407294 \, x^{5} - 3109960 \, x^{4} - 3285105 \, x^{3} - 1924641 \, x^{2} - 535098 \, x - 196506\right)} \sqrt{2 \, x + 3}"," ",0,"-1/45045*(81081*x^7 - 130977*x^6 - 1407294*x^5 - 3109960*x^4 - 3285105*x^3 - 1924641*x^2 - 535098*x - 196506)*sqrt(2*x + 3)","A",0
2547,1,44,0,0.378645," ","integrate((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(3/2),x, algorithm=""fricas"")","-\frac{10395 \, x^{7} - 19845 \, x^{6} - 180530 \, x^{5} - 392500 \, x^{4} - 398339 \, x^{3} - 256433 \, x^{2} + 77138 \, x + 431614}{5005 \, \sqrt{2 \, x + 3}}"," ",0,"-1/5005*(10395*x^7 - 19845*x^6 - 180530*x^5 - 392500*x^4 - 398339*x^3 - 256433*x^2 + 77138*x + 431614)/sqrt(2*x + 3)","A",0
2548,1,56,0,0.388268," ","integrate((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(567 \, x^{7} - 1323 \, x^{6} - 9666 \, x^{5} - 21360 \, x^{4} - 17663 \, x^{3} - 42003 \, x^{2} - 184566 \, x - 181486\right)} \sqrt{2 \, x + 3}}{231 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"-1/231*(567*x^7 - 1323*x^6 - 9666*x^5 - 21360*x^4 - 17663*x^3 - 42003*x^2 - 184566*x - 181486)*sqrt(2*x + 3)/(4*x^2 + 12*x + 9)","A",0
2549,1,61,0,0.384834," ","integrate((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(45 \, x^{7} - 135 \, x^{6} - 702 \, x^{5} - 1940 \, x^{4} + 3195 \, x^{3} + 41805 \, x^{2} + 85070 \, x + 51162\right)} \sqrt{2 \, x + 3}}{15 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"-1/15*(45*x^7 - 135*x^6 - 702*x^5 - 1940*x^4 + 3195*x^3 + 41805*x^2 + 85070*x + 51162)*sqrt(2*x + 3)/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
2550,1,86,0,0.397334," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{2125}{243} \, \sqrt{5} \sqrt{3} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) - \frac{8}{2835} \, {\left(270 \, x^{3} - 738 \, x^{2} - 8639 \, x - 24728\right)} \sqrt{2 \, x + 3} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left(\sqrt{2 \, x + 3} - 1\right)"," ",0,"2125/243*sqrt(5)*sqrt(3)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) - 8/2835*(270*x^3 - 738*x^2 - 8639*x - 24728)*sqrt(2*x + 3) + 6*log(sqrt(2*x + 3) + 1) - 6*log(sqrt(2*x + 3) - 1)","A",0
2551,1,81,0,0.401778," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{425}{81} \, \sqrt{5} \sqrt{3} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) - \frac{2}{135} \, {\left(36 \, x^{2} - 202 \, x - 1699\right)} \sqrt{2 \, x + 3} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left(\sqrt{2 \, x + 3} - 1\right)"," ",0,"425/81*sqrt(5)*sqrt(3)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) - 2/135*(36*x^2 - 202*x - 1699)*sqrt(2*x + 3) + 6*log(sqrt(2*x + 3) + 1) - 6*log(sqrt(2*x + 3) - 1)","A",0
2552,1,74,0,0.411055," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{85}{27} \, \sqrt{5} \sqrt{3} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) - \frac{4}{9} \, \sqrt{2 \, x + 3} {\left(x - 14\right)} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left(\sqrt{2 \, x + 3} - 1\right)"," ",0,"85/27*sqrt(5)*sqrt(3)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) - 4/9*sqrt(2*x + 3)*(x - 14) + 6*log(sqrt(2*x + 3) + 1) - 6*log(sqrt(2*x + 3) - 1)","A",0
2553,1,71,0,0.408127," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{17}{9} \, \sqrt{5} \sqrt{3} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) - \frac{2}{3} \, \sqrt{2 \, x + 3} + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left(\sqrt{2 \, x + 3} - 1\right)"," ",0,"17/9*sqrt(5)*sqrt(3)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) - 2/3*sqrt(2*x + 3) + 6*log(sqrt(2*x + 3) + 1) - 6*log(sqrt(2*x + 3) - 1)","A",0
2554,1,56,0,0.401867," ","integrate((5-x)/(3*x^2+5*x+2)/(3+2*x)^(1/2),x, algorithm=""fricas"")","\frac{17}{15} \, \sqrt{15} \log\left(-\frac{\sqrt{15} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 6 \, \log\left(\sqrt{2 \, x + 3} + 1\right) - 6 \, \log\left(\sqrt{2 \, x + 3} - 1\right)"," ",0,"17/15*sqrt(15)*log(-(sqrt(15)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 6*log(sqrt(2*x + 3) + 1) - 6*log(sqrt(2*x + 3) - 1)","A",0
2555,1,95,0,0.411649," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{17 \, \sqrt{5} \sqrt{3} {\left(2 \, x + 3\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 150 \, {\left(2 \, x + 3\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 150 \, {\left(2 \, x + 3\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 130 \, \sqrt{2 \, x + 3}}{25 \, {\left(2 \, x + 3\right)}}"," ",0,"1/25*(17*sqrt(5)*sqrt(3)*(2*x + 3)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 150*(2*x + 3)*log(sqrt(2*x + 3) + 1) - 150*(2*x + 3)*log(sqrt(2*x + 3) - 1) - 130*sqrt(2*x + 3))/(2*x + 3)","B",0
2556,1,120,0,0.418231," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{153 \, \sqrt{5} \sqrt{3} {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 2250 \, {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 2250 \, {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 20 \, {\left(297 \, x + 478\right)} \sqrt{2 \, x + 3}}{375 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/375*(153*sqrt(5)*sqrt(3)*(4*x^2 + 12*x + 9)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 2250*(4*x^2 + 12*x + 9)*log(sqrt(2*x + 3) + 1) - 2250*(4*x^2 + 12*x + 9)*log(sqrt(2*x + 3) - 1) - 20*(297*x + 478)*sqrt(2*x + 3))/(4*x^2 + 12*x + 9)","B",0
2557,1,145,0,0.404118," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2),x, algorithm=""fricas"")","\frac{153 \, \sqrt{5} \sqrt{3} {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 3750 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 3750 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 10 \, {\left(2388 \, x^{2} + 7494 \, x + 5933\right)} \sqrt{2 \, x + 3}}{625 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"1/625*(153*sqrt(5)*sqrt(3)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 3750*(8*x^3 + 36*x^2 + 54*x + 27)*log(sqrt(2*x + 3) + 1) - 3750*(8*x^3 + 36*x^2 + 54*x + 27)*log(sqrt(2*x + 3) - 1) - 10*(2388*x^2 + 7494*x + 5933)*sqrt(2*x + 3))/(8*x^3 + 36*x^2 + 54*x + 27)","B",0
2558,1,129,0,0.399686," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","\frac{1400 \, \sqrt{5} \sqrt{3} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} + 3 \, x + 7}{3 \, x + 2}\right) - 6237 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) + 6237 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 3 \, {\left(48 \, x^{3} - 400 \, x^{2} + 1843 \, x + 2129\right)} \sqrt{2 \, x + 3}}{81 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/81*(1400*sqrt(5)*sqrt(3)*(3*x^2 + 5*x + 2)*log((sqrt(5)*sqrt(3)*sqrt(2*x + 3) + 3*x + 7)/(3*x + 2)) - 6237*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) + 1) + 6237*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) - 1) - 3*(48*x^3 - 400*x^2 + 1843*x + 2129)*sqrt(2*x + 3))/(3*x^2 + 5*x + 2)","A",0
2559,1,124,0,0.403649," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","\frac{50 \, \sqrt{5} \sqrt{3} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} + 3 \, x + 7}{3 \, x + 2}\right) - 195 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) + 195 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - {\left(8 \, x^{2} + 209 \, x + 183\right)} \sqrt{2 \, x + 3}}{3 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/3*(50*sqrt(5)*sqrt(3)*(3*x^2 + 5*x + 2)*log((sqrt(5)*sqrt(3)*sqrt(2*x + 3) + 3*x + 7)/(3*x + 2)) - 195*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) + 1) + 195*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) - 1) - (8*x^2 + 209*x + 183)*sqrt(2*x + 3))/(3*x^2 + 5*x + 2)","A",0
2560,1,119,0,0.408883," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","\frac{124 \, \sqrt{5} \sqrt{3} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} + 3 \, x + 7}{3 \, x + 2}\right) - 477 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) + 477 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 3 \, {\left(139 \, x + 121\right)} \sqrt{2 \, x + 3}}{9 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/9*(124*sqrt(5)*sqrt(3)*(3*x^2 + 5*x + 2)*log((sqrt(5)*sqrt(3)*sqrt(2*x + 3) + 3*x + 7)/(3*x + 2)) - 477*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) + 1) + 477*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) - 1) - 3*(139*x + 121)*sqrt(2*x + 3))/(3*x^2 + 5*x + 2)","B",0
2561,1,113,0,0.406873," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","\frac{158 \, \sqrt{15} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\frac{\sqrt{15} \sqrt{2 \, x + 3} + 3 \, x + 7}{3 \, x + 2}\right) - 615 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) + 615 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 15 \, {\left(35 \, x + 29\right)} \sqrt{2 \, x + 3}}{15 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/15*(158*sqrt(15)*(3*x^2 + 5*x + 2)*log((sqrt(15)*sqrt(2*x + 3) + 3*x + 7)/(3*x + 2)) - 615*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) + 1) + 615*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) - 1) - 15*(35*x + 29)*sqrt(2*x + 3))/(3*x^2 + 5*x + 2)","B",0
2562,1,119,0,0.395028," ","integrate((5-x)/(3*x^2+5*x+2)^2/(3+2*x)^(1/2),x, algorithm=""fricas"")","\frac{192 \, \sqrt{5} \sqrt{3} {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} + 3 \, x + 7}{3 \, x + 2}\right) - 725 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) + 725 \, {\left(3 \, x^{2} + 5 \, x + 2\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 15 \, {\left(47 \, x + 37\right)} \sqrt{2 \, x + 3}}{25 \, {\left(3 \, x^{2} + 5 \, x + 2\right)}}"," ",0,"1/25*(192*sqrt(5)*sqrt(3)*(3*x^2 + 5*x + 2)*log((sqrt(5)*sqrt(3)*sqrt(2*x + 3) + 3*x + 7)/(3*x + 2)) - 725*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) + 1) + 725*(3*x^2 + 5*x + 2)*log(sqrt(2*x + 3) - 1) - 15*(47*x + 37)*sqrt(2*x + 3))/(3*x^2 + 5*x + 2)","B",0
2563,1,144,0,0.405818," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","\frac{678 \, \sqrt{5} \sqrt{3} {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)} \log\left(\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} + 3 \, x + 7}{3 \, x + 2}\right) - 2125 \, {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) + 2125 \, {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 5 \, {\left(1518 \, x^{2} + 3235 \, x + 1567\right)} \sqrt{2 \, x + 3}}{125 \, {\left(6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/125*(678*sqrt(5)*sqrt(3)*(6*x^3 + 19*x^2 + 19*x + 6)*log((sqrt(5)*sqrt(3)*sqrt(2*x + 3) + 3*x + 7)/(3*x + 2)) - 2125*(6*x^3 + 19*x^2 + 19*x + 6)*log(sqrt(2*x + 3) + 1) + 2125*(6*x^3 + 19*x^2 + 19*x + 6)*log(sqrt(2*x + 3) - 1) - 5*(1518*x^2 + 3235*x + 1567)*sqrt(2*x + 3))/(6*x^3 + 19*x^2 + 19*x + 6)","B",0
2564,1,169,0,0.396866," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","\frac{1404 \, \sqrt{5} \sqrt{3} {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)} \log\left(\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} + 3 \, x + 7}{3 \, x + 2}\right) - 1875 \, {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) + 1875 \, {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 5 \, {\left(12348 \, x^{3} + 43032 \, x^{2} + 47767 \, x + 16633\right)} \sqrt{2 \, x + 3}}{375 \, {\left(12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right)}}"," ",0,"1/375*(1404*sqrt(5)*sqrt(3)*(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log((sqrt(5)*sqrt(3)*sqrt(2*x + 3) + 3*x + 7)/(3*x + 2)) - 1875*(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log(sqrt(2*x + 3) + 1) + 1875*(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)*log(sqrt(2*x + 3) - 1) - 5*(12348*x^3 + 43032*x^2 + 47767*x + 16633)*sqrt(2*x + 3))/(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18)","B",0
2565,1,194,0,0.411398," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^2,x, algorithm=""fricas"")","\frac{23814 \, \sqrt{5} \sqrt{3} {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)} \log\left(\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} + 3 \, x + 7}{3 \, x + 2}\right) + 65625 \, {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 65625 \, {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 5 \, {\left(886536 \, x^{4} + 4348428 \, x^{3} + 7782530 \, x^{2} + 5977997 \, x + 1646109\right)} \sqrt{2 \, x + 3}}{9375 \, {\left(24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right)}}"," ",0,"1/9375*(23814*sqrt(5)*sqrt(3)*(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)*log((sqrt(5)*sqrt(3)*sqrt(2*x + 3) + 3*x + 7)/(3*x + 2)) + 65625*(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)*log(sqrt(2*x + 3) + 1) - 65625*(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)*log(sqrt(2*x + 3) - 1) - 5*(886536*x^4 + 4348428*x^3 + 7782530*x^2 + 5977997*x + 1646109)*sqrt(2*x + 3))/(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54)","B",0
2566,1,175,0,0.407026," ","integrate((5-x)*(3+2*x)^(9/2)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{13675 \, \sqrt{5} \sqrt{3} {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 52974 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 52974 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 3 \, {\left(192 \, x^{4} - 45083 \, x^{3} - 112467 \, x^{2} - 90465 \, x - 23327\right)} \sqrt{2 \, x + 3}}{54 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/54*(13675*sqrt(5)*sqrt(3)*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 52974*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) + 1) - 52974*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) - 1) - 3*(192*x^4 - 45083*x^3 - 112467*x^2 - 90465*x - 23327)*sqrt(2*x + 3))/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","A",0
2567,1,169,0,0.403706," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{1225 \, \sqrt{5} \sqrt{3} {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 4746 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 4746 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) + {\left(12443 \, x^{3} + 30979 \, x^{2} + 25073 \, x + 6555\right)} \sqrt{2 \, x + 3}}{6 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/6*(1225*sqrt(5)*sqrt(3)*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 4746*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) + 1) - 4746*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) - 1) + (12443*x^3 + 30979*x^2 + 25073*x + 6555)*sqrt(2*x + 3))/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","B",0
2568,1,170,0,0.398563," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{2905 \, \sqrt{5} \sqrt{3} {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 11250 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 11250 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) + 3 \, {\left(9825 \, x^{3} + 24497 \, x^{2} + 19891 \, x + 5237\right)} \sqrt{2 \, x + 3}}{18 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/18*(2905*sqrt(5)*sqrt(3)*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 11250*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) + 1) - 11250*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) - 1) + 3*(9825*x^3 + 24497*x^2 + 19891*x + 5237)*sqrt(2*x + 3))/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","B",0
2569,1,170,0,0.398237," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{1247 \, \sqrt{5} \sqrt{3} {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 4830 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 4830 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) + 5 \, {\left(2529 \, x^{3} + 6305 \, x^{2} + 5123 \, x + 1353\right)} \sqrt{2 \, x + 3}}{10 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/10*(1247*sqrt(5)*sqrt(3)*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 4830*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) + 1) - 4830*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) - 1) + 5*(2529*x^3 + 6305*x^2 + 5123*x + 1353)*sqrt(2*x + 3))/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","B",0
2570,1,170,0,0.419774," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{4713 \, \sqrt{5} \sqrt{3} {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 18250 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 18250 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) + 5 \, {\left(9567 \, x^{3} + 23847 \, x^{2} + 19373 \, x + 5123\right)} \sqrt{2 \, x + 3}}{50 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/50*(4713*sqrt(5)*sqrt(3)*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 18250*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) + 1) - 18250*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) - 1) + 5*(9567*x^3 + 23847*x^2 + 19373*x + 5123)*sqrt(2*x + 3))/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","B",0
2571,1,170,0,0.410691," ","integrate((5-x)/(3*x^2+5*x+2)^3/(3+2*x)^(1/2),x, algorithm=""fricas"")","\frac{17463 \, \sqrt{5} \sqrt{3} {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 67750 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 67750 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) + 5 \, {\left(35217 \, x^{3} + 87897 \, x^{2} + 71443 \, x + 18913\right)} \sqrt{2 \, x + 3}}{250 \, {\left(9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"1/250*(17463*sqrt(5)*sqrt(3)*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 67750*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) + 1) - 67750*(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)*log(sqrt(2*x + 3) - 1) + 5*(35217*x^3 + 87897*x^2 + 71443*x + 18913)*sqrt(2*x + 3))/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4)","B",0
2572,1,195,0,0.411082," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{12717 \, \sqrt{5} \sqrt{3} {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 50250 \, {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 50250 \, {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) + 5 \, {\left(48006 \, x^{4} + 193455 \, x^{3} + 281403 \, x^{2} + 175465 \, x + 39661\right)} \sqrt{2 \, x + 3}}{250 \, {\left(18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right)}}"," ",0,"1/250*(12717*sqrt(5)*sqrt(3)*(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 50250*(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)*log(sqrt(2*x + 3) + 1) - 50250*(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)*log(sqrt(2*x + 3) - 1) + 5*(48006*x^4 + 193455*x^3 + 281403*x^2 + 175465*x + 39661)*sqrt(2*x + 3))/(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12)","B",0
2573,1,220,0,0.427571," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{136809 \, \sqrt{5} \sqrt{3} {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 581250 \, {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 581250 \, {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) + 5 \, {\left(740124 \, x^{5} + 4247856 \, x^{4} + 9453447 \, x^{3} + 10168583 \, x^{2} + 5278129 \, x + 1057511\right)} \sqrt{2 \, x + 3}}{3750 \, {\left(36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/3750*(136809*sqrt(5)*sqrt(3)*(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 581250*(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)*log(sqrt(2*x + 3) + 1) - 581250*(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)*log(sqrt(2*x + 3) - 1) + 5*(740124*x^5 + 4247856*x^4 + 9453447*x^3 + 10168583*x^2 + 5278129*x + 1057511)*sqrt(2*x + 3))/(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36)","B",0
2574,1,245,0,0.397792," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^3,x, algorithm=""fricas"")","\frac{2420523 \, \sqrt{5} \sqrt{3} {\left(72 \, x^{7} + 564 \, x^{6} + 1862 \, x^{5} + 3355 \, x^{4} + 3560 \, x^{3} + 2223 \, x^{2} + 756 \, x + 108\right)} \log\left(-\frac{\sqrt{5} \sqrt{3} \sqrt{2 \, x + 3} - 3 \, x - 7}{3 \, x + 2}\right) + 12468750 \, {\left(72 \, x^{7} + 564 \, x^{6} + 1862 \, x^{5} + 3355 \, x^{4} + 3560 \, x^{3} + 2223 \, x^{2} + 756 \, x + 108\right)} \log\left(\sqrt{2 \, x + 3} + 1\right) - 12468750 \, {\left(72 \, x^{7} + 564 \, x^{6} + 1862 \, x^{5} + 3355 \, x^{4} + 3560 \, x^{3} + 2223 \, x^{2} + 756 \, x + 108\right)} \log\left(\sqrt{2 \, x + 3} - 1\right) - 5 \, {\left(5272344 \, x^{6} + 14906052 \, x^{5} - 18312714 \, x^{4} - 114099329 \, x^{3} - 160041829 \, x^{2} - 94082723 \, x - 20250051\right)} \sqrt{2 \, x + 3}}{93750 \, {\left(72 \, x^{7} + 564 \, x^{6} + 1862 \, x^{5} + 3355 \, x^{4} + 3560 \, x^{3} + 2223 \, x^{2} + 756 \, x + 108\right)}}"," ",0,"1/93750*(2420523*sqrt(5)*sqrt(3)*(72*x^7 + 564*x^6 + 1862*x^5 + 3355*x^4 + 3560*x^3 + 2223*x^2 + 756*x + 108)*log(-(sqrt(5)*sqrt(3)*sqrt(2*x + 3) - 3*x - 7)/(3*x + 2)) + 12468750*(72*x^7 + 564*x^6 + 1862*x^5 + 3355*x^4 + 3560*x^3 + 2223*x^2 + 756*x + 108)*log(sqrt(2*x + 3) + 1) - 12468750*(72*x^7 + 564*x^6 + 1862*x^5 + 3355*x^4 + 3560*x^3 + 2223*x^2 + 756*x + 108)*log(sqrt(2*x + 3) - 1) - 5*(5272344*x^6 + 14906052*x^5 - 18312714*x^4 - 114099329*x^3 - 160041829*x^2 - 94082723*x - 20250051)*sqrt(2*x + 3))/(72*x^7 + 564*x^6 + 1862*x^5 + 3355*x^4 + 3560*x^3 + 2223*x^2 + 756*x + 108)","B",0
2575,1,52,0,0.418199," ","integrate((5+10*x+35^(1/2))/(5*x^2+3*x+2)/(1+2*x)^(1/2),x, algorithm=""fricas"")","-\frac{2}{31} \, \sqrt{31} \sqrt{10 \, \sqrt{35} + 20} \arctan\left(-\frac{{\left(5 \, \sqrt{31} {\left(2 \, x + 1\right)} - \sqrt{35} \sqrt{31}\right)} \sqrt{10 \, \sqrt{35} + 20}}{310 \, \sqrt{2 \, x + 1}}\right)"," ",0,"-2/31*sqrt(31)*sqrt(10*sqrt(35) + 20)*arctan(-1/310*(5*sqrt(31)*(2*x + 1) - sqrt(35)*sqrt(31))*sqrt(10*sqrt(35) + 20)/sqrt(2*x + 1))","A",0
2576,0,0,0,0.404921," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(4 \, x^{3} - 8 \, x^{2} - 51 \, x - 45\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}, x\right)"," ",0,"integral(-(4*x^3 - 8*x^2 - 51*x - 45)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3), x)","F",0
2577,0,0,0,0.397610," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x^{2} - 7 \, x - 15\right)} \sqrt{2 \, x + 3}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(2*x^2 - 7*x - 15)*sqrt(2*x + 3), x)","F",0
2578,0,0,0,0.408805," ","integrate((5-x)*(3+2*x)^(1/2)*(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5), x)","F",0
2579,0,0,0,0.415426," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(x - 5\right)}}{\sqrt{2 \, x + 3}}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(x - 5)/sqrt(2*x + 3), x)","F",0
2580,0,0,0,0.414169," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{4 \, x^{2} + 12 \, x + 9}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(4*x^2 + 12*x + 9), x)","F",0
2581,0,0,0,0.416592," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(8*x^3 + 36*x^2 + 54*x + 27), x)","F",0
2582,0,0,0,0.406446," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81), x)","F",0
2583,0,0,0,0.405960," ","integrate((5-x)*(3*x^2+5*x+2)^(1/2)/(3+2*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243), x)","F",0
2584,0,0,0,0.405233," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(12 \, x^{5} - 4 \, x^{4} - 185 \, x^{3} - 406 \, x^{2} - 327 \, x - 90\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}, x\right)"," ",0,"integral(-(12*x^5 - 4*x^4 - 185*x^3 - 406*x^2 - 327*x - 90)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3), x)","F",0
2585,0,0,0,0.420916," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(6 \, x^{4} - 11 \, x^{3} - 76 \, x^{2} - 89 \, x - 30\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}, x\right)"," ",0,"integral(-(6*x^4 - 11*x^3 - 76*x^2 - 89*x - 30)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3), x)","F",0
2586,0,0,0,0.415599," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)*(3+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, x^{3} - 10 \, x^{2} - 23 \, x - 10\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}, x\right)"," ",0,"integral(-(3*x^3 - 10*x^2 - 23*x - 10)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3), x)","F",0
2587,0,0,0,0.412690," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x^{3} - 10 \, x^{2} - 23 \, x - 10\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{\sqrt{2 \, x + 3}}, x\right)"," ",0,"integral(-(3*x^3 - 10*x^2 - 23*x - 10)*sqrt(3*x^2 + 5*x + 2)/sqrt(2*x + 3), x)","F",0
2588,0,0,0,0.411330," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x^{3} - 10 \, x^{2} - 23 \, x - 10\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{4 \, x^{2} + 12 \, x + 9}, x\right)"," ",0,"integral(-(3*x^3 - 10*x^2 - 23*x - 10)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(4*x^2 + 12*x + 9), x)","F",0
2589,0,0,0,0.410489," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x^{3} - 10 \, x^{2} - 23 \, x - 10\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27}, x\right)"," ",0,"integral(-(3*x^3 - 10*x^2 - 23*x - 10)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(8*x^3 + 36*x^2 + 54*x + 27), x)","F",0
2590,0,0,0,0.409444," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x^{3} - 10 \, x^{2} - 23 \, x - 10\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81}, x\right)"," ",0,"integral(-(3*x^3 - 10*x^2 - 23*x - 10)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81), x)","F",0
2591,0,0,0,0.400820," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x^{3} - 10 \, x^{2} - 23 \, x - 10\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243}, x\right)"," ",0,"integral(-(3*x^3 - 10*x^2 - 23*x - 10)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243), x)","F",0
2592,0,0,0,0.402316," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x^{3} - 10 \, x^{2} - 23 \, x - 10\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729}, x\right)"," ",0,"integral(-(3*x^3 - 10*x^2 - 23*x - 10)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729), x)","F",0
2593,0,0,0,0.415053," ","integrate((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x^{3} - 10 \, x^{2} - 23 \, x - 10\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187}, x\right)"," ",0,"integral(-(3*x^3 - 10*x^2 - 23*x - 10)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187), x)","F",0
2594,0,0,0,0.411763," ","integrate((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(36 \, x^{7} + 48 \, x^{6} - 551 \, x^{5} - 2151 \, x^{4} - 3381 \, x^{3} - 2717 \, x^{2} - 1104 \, x - 180\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}, x\right)"," ",0,"integral(-(36*x^7 + 48*x^6 - 551*x^5 - 2151*x^4 - 3381*x^3 - 2717*x^2 - 1104*x - 180)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3), x)","F",0
2595,0,0,0,0.409877," ","integrate((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(18 \, x^{6} - 3 \, x^{5} - 271 \, x^{4} - 669 \, x^{3} - 687 \, x^{2} - 328 \, x - 60\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}, x\right)"," ",0,"integral(-(18*x^6 - 3*x^5 - 271*x^4 - 669*x^3 - 687*x^2 - 328*x - 60)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3), x)","F",0
2596,0,0,0,0.400982," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)*(3+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3), x)","F",0
2597,0,0,0,0.402507," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2}}{\sqrt{2 \, x + 3}}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)/sqrt(2*x + 3), x)","F",0
2598,0,0,0,0.407688," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{4 \, x^{2} + 12 \, x + 9}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(4*x^2 + 12*x + 9), x)","F",0
2599,0,0,0,0.412998," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(8*x^3 + 36*x^2 + 54*x + 27), x)","F",0
2600,0,0,0,0.418201," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81), x)","F",0
2601,0,0,0,0.421110," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243), x)","F",0
2602,0,0,0,0.411647," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729), x)","F",0
2603,0,0,0,0.436270," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187), x)","F",0
2604,0,0,0,0.412012," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{256 \, x^{8} + 3072 \, x^{7} + 16128 \, x^{6} + 48384 \, x^{5} + 90720 \, x^{4} + 108864 \, x^{3} + 81648 \, x^{2} + 34992 \, x + 6561}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(256*x^8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561), x)","F",0
2605,0,0,0,0.410105," ","integrate((5-x)*(3*x^2+5*x+2)^(5/2)/(3+2*x)^(17/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{5} - 15 \, x^{4} - 113 \, x^{3} - 165 \, x^{2} - 96 \, x - 20\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683}, x\right)"," ",0,"integral(-(9*x^5 - 15*x^4 - 113*x^3 - 165*x^2 - 96*x - 20)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(512*x^9 + 6912*x^8 + 41472*x^7 + 145152*x^6 + 326592*x^5 + 489888*x^4 + 489888*x^3 + 314928*x^2 + 118098*x + 19683), x)","F",0
2606,0,0,0,0.408850," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(4 \, x^{3} - 8 \, x^{2} - 51 \, x - 45\right)} \sqrt{2 \, x + 3}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}, x\right)"," ",0,"integral(-(4*x^3 - 8*x^2 - 51*x - 45)*sqrt(2*x + 3)/sqrt(3*x^2 + 5*x + 2), x)","F",0
2607,0,0,0,0.410869," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(2 \, x^{2} - 7 \, x - 15\right)} \sqrt{2 \, x + 3}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}, x\right)"," ",0,"integral(-(2*x^2 - 7*x - 15)*sqrt(2*x + 3)/sqrt(3*x^2 + 5*x + 2), x)","F",0
2608,0,0,0,0.398073," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{2 \, x + 3} {\left(x - 5\right)}}{\sqrt{3 \, x^{2} + 5 \, x + 2}}, x\right)"," ",0,"integral(-sqrt(2*x + 3)*(x - 5)/sqrt(3*x^2 + 5*x + 2), x)","F",0
2609,0,0,0,0.412156," ","integrate((5-x)/(3+2*x)^(1/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(6*x^3 + 19*x^2 + 19*x + 6), x)","F",0
2610,0,0,0,0.395159," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(12*x^4 + 56*x^3 + 95*x^2 + 69*x + 18), x)","F",0
2611,0,0,0,0.397600," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(24*x^5 + 148*x^4 + 358*x^3 + 423*x^2 + 243*x + 54), x)","F",0
2612,0,0,0,0.406099," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{48 \, x^{6} + 368 \, x^{5} + 1160 \, x^{4} + 1920 \, x^{3} + 1755 \, x^{2} + 837 \, x + 162}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(48*x^6 + 368*x^5 + 1160*x^4 + 1920*x^3 + 1755*x^2 + 837*x + 162), x)","F",0
2613,0,0,0,0.411194," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(8 \, x^{4} - 4 \, x^{3} - 126 \, x^{2} - 243 \, x - 135\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}, x\right)"," ",0,"integral(-(8*x^4 - 4*x^3 - 126*x^2 - 243*x - 135)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4), x)","F",0
2614,0,0,0,0.410266," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(4 \, x^{3} - 8 \, x^{2} - 51 \, x - 45\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}, x\right)"," ",0,"integral(-(4*x^3 - 8*x^2 - 51*x - 45)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4), x)","F",0
2615,0,0,0,0.422024," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x^{2} - 7 \, x - 15\right)} \sqrt{2 \, x + 3}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(2*x^2 - 7*x - 15)*sqrt(2*x + 3)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4), x)","F",0
2616,0,0,0,0.408702," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(9*x^4 + 30*x^3 + 37*x^2 + 20*x + 4), x)","F",0
2617,0,0,0,0.408240," ","integrate((5-x)/(3*x^2+5*x+2)^(3/2)/(3+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(18*x^5 + 87*x^4 + 164*x^3 + 151*x^2 + 68*x + 12), x)","F",0
2618,0,0,0,0.414304," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(36*x^6 + 228*x^5 + 589*x^4 + 794*x^3 + 589*x^2 + 228*x + 36), x)","F",0
2619,0,0,0,0.416972," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{72 \, x^{7} + 564 \, x^{6} + 1862 \, x^{5} + 3355 \, x^{4} + 3560 \, x^{3} + 2223 \, x^{2} + 756 \, x + 108}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(72*x^7 + 564*x^6 + 1862*x^5 + 3355*x^4 + 3560*x^3 + 2223*x^2 + 756*x + 108), x)","F",0
2620,0,0,0,0.411720," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{144 \, x^{8} + 1344 \, x^{7} + 5416 \, x^{6} + 12296 \, x^{5} + 17185 \, x^{4} + 15126 \, x^{3} + 8181 \, x^{2} + 2484 \, x + 324}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(144*x^8 + 1344*x^7 + 5416*x^6 + 12296*x^5 + 17185*x^4 + 15126*x^3 + 8181*x^2 + 2484*x + 324), x)","F",0
2621,0,0,0,0.412257," ","integrate((5-x)*(3+2*x)^(9/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(16 \, x^{5} + 16 \, x^{4} - 264 \, x^{3} - 864 \, x^{2} - 999 \, x - 405\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-(16*x^5 + 16*x^4 - 264*x^3 - 864*x^2 - 999*x - 405)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
2622,0,0,0,0.401250," ","integrate((5-x)*(3+2*x)^(7/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(8 \, x^{4} - 4 \, x^{3} - 126 \, x^{2} - 243 \, x - 135\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-(8*x^4 - 4*x^3 - 126*x^2 - 243*x - 135)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
2623,0,0,0,0.395643," ","integrate((5-x)*(3+2*x)^(5/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(4 \, x^{3} - 8 \, x^{2} - 51 \, x - 45\right)} \sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-(4*x^3 - 8*x^2 - 51*x - 45)*sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
2624,0,0,0,0.407301," ","integrate((5-x)*(3+2*x)^(3/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} {\left(2 \, x^{2} - 7 \, x - 15\right)} \sqrt{2 \, x + 3}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*(2*x^2 - 7*x - 15)*sqrt(2*x + 3)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
2625,0,0,0,0.406245," ","integrate((5-x)*(3+2*x)^(1/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{27 \, x^{6} + 135 \, x^{5} + 279 \, x^{4} + 305 \, x^{3} + 186 \, x^{2} + 60 \, x + 8}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(27*x^6 + 135*x^5 + 279*x^4 + 305*x^3 + 186*x^2 + 60*x + 8), x)","F",0
2626,0,0,0,0.404928," ","integrate((5-x)/(3*x^2+5*x+2)^(5/2)/(3+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{54 \, x^{7} + 351 \, x^{6} + 963 \, x^{5} + 1447 \, x^{4} + 1287 \, x^{3} + 678 \, x^{2} + 196 \, x + 24}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(54*x^7 + 351*x^6 + 963*x^5 + 1447*x^4 + 1287*x^3 + 678*x^2 + 196*x + 24), x)","F",0
2627,0,0,0,0.403795," ","integrate((5-x)/(3+2*x)^(3/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{108 \, x^{8} + 864 \, x^{7} + 2979 \, x^{6} + 5783 \, x^{5} + 6915 \, x^{4} + 5217 \, x^{3} + 2426 \, x^{2} + 636 \, x + 72}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(108*x^8 + 864*x^7 + 2979*x^6 + 5783*x^5 + 6915*x^4 + 5217*x^3 + 2426*x^2 + 636*x + 72), x)","F",0
2628,0,0,0,0.390215," ","integrate((5-x)/(3+2*x)^(5/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{216 \, x^{9} + 2052 \, x^{8} + 8550 \, x^{7} + 20503 \, x^{6} + 31179 \, x^{5} + 31179 \, x^{4} + 20503 \, x^{3} + 8550 \, x^{2} + 2052 \, x + 216}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(216*x^9 + 2052*x^8 + 8550*x^7 + 20503*x^6 + 31179*x^5 + 31179*x^4 + 20503*x^3 + 8550*x^2 + 2052*x + 216), x)","F",0
2629,0,0,0,0.412740," ","integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 5 \, x + 2} \sqrt{2 \, x + 3} {\left(x - 5\right)}}{432 \, x^{10} + 4752 \, x^{9} + 23256 \, x^{8} + 66656 \, x^{7} + 123867 \, x^{6} + 155895 \, x^{5} + 134543 \, x^{4} + 78609 \, x^{3} + 29754 \, x^{2} + 6588 \, x + 648}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 5*x + 2)*sqrt(2*x + 3)*(x - 5)/(432*x^10 + 4752*x^9 + 23256*x^8 + 66656*x^7 + 123867*x^6 + 155895*x^5 + 134543*x^4 + 78609*x^3 + 29754*x^2 + 6588*x + 648), x)","F",0
2630,0,0,0,0.432849," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A d + {\left(B d + A e\right)} x\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((B*e*x^2 + A*d + (B*d + A*e)*x)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
2631,0,0,0,0.433047," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((B*x + A)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
2632,0,0,0,0.429152," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \sqrt{e x + d}}{c e x^{3} + {\left(c d + b e\right)} x^{2} + a d + {\left(b d + a e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*sqrt(e*x + d)/(c*e*x^3 + (c*d + b*e)*x^2 + a*d + (b*d + a*e)*x), x)","F",0
2633,0,0,0,0.420691," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \sqrt{e x + d}}{c e^{2} x^{4} + {\left(2 \, c d e + b e^{2}\right)} x^{3} + a d^{2} + {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{2} + {\left(b d^{2} + 2 \, a d e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*sqrt(e*x + d)/(c*e^2*x^4 + (2*c*d*e + b*e^2)*x^3 + a*d^2 + (c*d^2 + 2*b*d*e + a*e^2)*x^2 + (b*d^2 + 2*a*d*e)*x), x)","F",0
2634,0,0,0,0.432834," ","integrate((B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \sqrt{e x + d}}{c e^{3} x^{5} + {\left(3 \, c d e^{2} + b e^{3}\right)} x^{4} + a d^{3} + {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} x^{3} + {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} x^{2} + {\left(b d^{3} + 3 \, a d^{2} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*sqrt(e*x + d)/(c*e^3*x^5 + (3*c*d*e^2 + b*e^3)*x^4 + a*d^3 + (3*c*d^2*e + 3*b*d*e^2 + a*e^3)*x^3 + (c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*x^2 + (b*d^3 + 3*a*d^2*e)*x), x)","F",0
2635,0,0,0,0.464259," ","integrate((B*x+A)*(e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{3} + A d^{2} + {\left(2 \, B d e + A e^{2}\right)} x^{2} + {\left(B d^{2} + 2 \, A d e\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e^2*x^3 + A*d^2 + (2*B*d*e + A*e^2)*x^2 + (B*d^2 + 2*A*d*e)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2636,0,0,0,0.449771," ","integrate((B*x+A)*(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{2} + A d + {\left(B d + A e\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e*x^2 + A*d + (B*d + A*e)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2637,0,0,0,0.418313," ","integrate((B*x+A)*(e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2638,0,0,0,0.433037," ","integrate((B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \sqrt{e x + d}}{c^{2} e x^{5} + {\left(c^{2} d + 2 \, b c e\right)} x^{4} + {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} x^{3} + a^{2} d + {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} x^{2} + {\left(2 \, a b d + a^{2} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*sqrt(e*x + d)/(c^2*e*x^5 + (c^2*d + 2*b*c*e)*x^4 + (2*b*c*d + (b^2 + 2*a*c)*e)*x^3 + a^2*d + (2*a*b*e + (b^2 + 2*a*c)*d)*x^2 + (2*a*b*d + a^2*e)*x), x)","F",0
2639,0,0,0,0.462736," ","integrate((B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(B x + A\right)} \sqrt{e x + d}}{c^{2} e^{2} x^{6} + 2 \, {\left(c^{2} d e + b c e^{2}\right)} x^{5} + {\left(c^{2} d^{2} + 4 \, b c d e + {\left(b^{2} + 2 \, a c\right)} e^{2}\right)} x^{4} + a^{2} d^{2} + 2 \, {\left(b c d^{2} + a b e^{2} + {\left(b^{2} + 2 \, a c\right)} d e\right)} x^{3} + {\left(4 \, a b d e + a^{2} e^{2} + {\left(b^{2} + 2 \, a c\right)} d^{2}\right)} x^{2} + 2 \, {\left(a b d^{2} + a^{2} d e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(B*x + A)*sqrt(e*x + d)/(c^2*e^2*x^6 + 2*(c^2*d*e + b*c*e^2)*x^5 + (c^2*d^2 + 4*b*c*d*e + (b^2 + 2*a*c)*e^2)*x^4 + a^2*d^2 + 2*(b*c*d^2 + a*b*e^2 + (b^2 + 2*a*c)*d*e)*x^3 + (4*a*b*d*e + a^2*e^2 + (b^2 + 2*a*c)*d^2)*x^2 + 2*(a*b*d^2 + a^2*d*e)*x), x)","F",0
2640,1,5919,0,0.541349," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left(A a^{3} d e^{7} m^{7} - 5040 \, B c^{3} d^{8} + 40320 \, A a^{3} d e^{7} + 5760 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{7} e - 20160 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{6} e^{2} + 8064 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{5} e^{3} - 10080 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{4} e^{4} + 40320 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{3} e^{5} - 20160 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{6} + {\left(B c^{3} e^{8} m^{7} + 28 \, B c^{3} e^{8} m^{6} + 322 \, B c^{3} e^{8} m^{5} + 1960 \, B c^{3} e^{8} m^{4} + 6769 \, B c^{3} e^{8} m^{3} + 13132 \, B c^{3} e^{8} m^{2} + 13068 \, B c^{3} e^{8} m + 5040 \, B c^{3} e^{8}\right)} x^{8} + {\left(5760 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8} + {\left(B c^{3} d e^{7} + {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{7} + {\left(21 \, B c^{3} d e^{7} + 29 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{6} + 7 \, {\left(25 \, B c^{3} d e^{7} + 49 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{5} + 35 \, {\left(21 \, B c^{3} d e^{7} + 61 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{4} + 56 \, {\left(29 \, B c^{3} d e^{7} + 134 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{3} + 28 \, {\left(63 \, B c^{3} d e^{7} + 527 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m^{2} + 144 \, {\left(5 \, B c^{3} d e^{7} + 103 \, {\left(3 \, B b c^{2} + A c^{3}\right)} e^{8}\right)} m\right)} x^{7} + {\left(35 \, A a^{3} d e^{7} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{6}\right)} m^{6} + {\left(20160 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{8} + {\left({\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} + 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{8}\right)} m^{7} - {\left(7 \, B c^{3} d^{2} e^{6} - 23 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 90 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{8}\right)} m^{6} - {\left(105 \, B c^{3} d^{2} e^{6} - 205 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 1098 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{8}\right)} m^{5} - 5 \, {\left(119 \, B c^{3} d^{2} e^{6} - 181 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 1404 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{8}\right)} m^{4} - {\left(1575 \, B c^{3} d^{2} e^{6} - 2074 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 25227 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{8}\right)} m^{3} - 2 \, {\left(959 \, B c^{3} d^{2} e^{6} - 1156 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 25245 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{8}\right)} m^{2} - 24 \, {\left(35 \, B c^{3} d^{2} e^{6} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d e^{7} - 2143 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} e^{8}\right)} m\right)} x^{6} + {\left(511 \, A a^{3} d e^{7} + 6 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{3} e^{5} - 33 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{6}\right)} m^{5} + {\left(8064 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{8} + {\left(3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{7} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{8}\right)} m^{7} - {\left(6 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} - 75 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{7} - 31 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{8}\right)} m^{6} + {\left(42 \, B c^{3} d^{3} e^{5} - 108 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 723 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{7} + 391 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{8}\right)} m^{5} + {\left(420 \, B c^{3} d^{3} e^{5} - 690 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 3405 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{7} + 2581 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{8}\right)} m^{4} + 2 \, {\left(735 \, B c^{3} d^{3} e^{5} - 990 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 4101 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{7} + 4772 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{8}\right)} m^{3} + 4 \, {\left(525 \, B c^{3} d^{3} e^{5} - 636 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 2370 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{7} + 4891 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{8}\right)} m^{2} + 144 \, {\left(7 \, B c^{3} d^{3} e^{5} - 8 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} e^{6} + 28 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d e^{7} + 141 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} e^{8}\right)} m\right)} x^{5} + {\left(4025 \, A a^{3} d e^{7} - 6 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{4} e^{4} + 180 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{3} e^{5} - 445 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{6}\right)} m^{4} + {\left(10080 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{8} + {\left({\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{7} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{8}\right)} m^{7} - {\left(15 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{6} - 27 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{7} - 32 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{8}\right)} m^{6} + {\left(30 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} - 315 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{6} + 283 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{7} + 418 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{8}\right)} m^{5} - {\left(210 \, B c^{3} d^{4} e^{4} - 420 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} + 2355 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{6} - 1449 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{7} - 2864 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{8}\right)} m^{4} - {\left(1260 \, B c^{3} d^{4} e^{4} - 1770 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} + 7605 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{6} - 3748 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{7} - 10993 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{8}\right)} m^{3} - 2 \, {\left(1155 \, B c^{3} d^{4} e^{4} - 1410 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} + 5295 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{6} - 2286 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{7} - 11656 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{8}\right)} m^{2} - 36 \, {\left(35 \, B c^{3} d^{4} e^{4} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} e^{5} + 140 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} e^{6} - 56 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d e^{7} - 691 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} e^{8}\right)} m\right)} x^{4} + {\left(18424 \, A a^{3} d e^{7} + 24 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{5} e^{3} - 156 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{4} e^{4} + 2130 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{3} e^{5} - 3135 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{6}\right)} m^{3} + {\left(40320 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{8} + {\left({\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{7} + 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{8}\right)} m^{7} - {\left(4 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{6} - 29 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{7} - 99 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{8}\right)} m^{6} + {\left(60 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{5} - 96 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{6} + 331 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{7} + 1341 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{8}\right)} m^{5} - {\left(120 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{4} - 1080 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{5} + 844 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{6} - 1871 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{7} - 9585 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{8}\right)} m^{4} + 4 \, {\left(210 \, B c^{3} d^{5} e^{3} - 330 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{4} + 1545 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{5} - 816 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{6} + 1345 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{7} + 9648 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{8}\right)} m^{3} + 4 \, {\left(630 \, B c^{3} d^{5} e^{3} - 780 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{4} + 2970 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{5} - 1300 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{6} + 1793 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{7} + 21519 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{8}\right)} m^{2} + 48 \, {\left(35 \, B c^{3} d^{5} e^{3} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{4} e^{4} + 140 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} e^{5} - 56 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} e^{6} + 70 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d e^{7} + 2003 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} e^{8}\right)} m\right)} x^{3} + 2 \, {\left(24430 \, A a^{3} d e^{7} - 180 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{6} e^{2} + 252 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{5} e^{3} - 753 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{4} e^{4} + 6210 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{3} e^{5} - 6077 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{6}\right)} m^{2} + {\left(20160 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8} + {\left(3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{7} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8}\right)} m^{7} - {\left(3 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{6} - 93 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{7} - 34 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8}\right)} m^{6} + {\left(12 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{5} - 81 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{6} + 1155 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{7} + 478 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8}\right)} m^{5} - {\left(180 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{4} - 264 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{5} + 831 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{6} - 7275 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{7} - 3580 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8}\right)} m^{4} + {\left(360 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{3} - 2880 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{4} + 2004 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{5} - 3951 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{6} + 24042 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{7} + 15289 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8}\right)} m^{3} - 2 \, {\left(1260 \, B c^{3} d^{6} e^{2} - 1620 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{3} + 6390 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{4} - 2892 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{5} + 4119 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{6} - 18996 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{7} - 18353 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8}\right)} m^{2} - 72 \, {\left(35 \, B c^{3} d^{6} e^{2} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{5} e^{3} + 140 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{4} e^{4} - 56 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{3} e^{5} + 70 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} e^{6} - 280 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d e^{7} - 621 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8}\right)} m\right)} x^{2} + 12 \, {\left(5772 \, A a^{3} d e^{7} + 60 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{7} e - 450 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{6} e^{2} + 292 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{5} e^{3} - 533 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{4} e^{4} + 2972 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{3} e^{5} - 2046 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{6}\right)} m + {\left(40320 \, A a^{3} e^{8} + {\left(A a^{3} e^{8} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{7}\right)} m^{7} + {\left(35 \, A a^{3} e^{8} - 6 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{6} + 33 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{7}\right)} m^{6} + {\left(511 \, A a^{3} e^{8} + 6 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{5} - 180 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{6} + 445 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{7}\right)} m^{5} + {\left(4025 \, A a^{3} e^{8} - 24 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{4} + 156 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{5} - 2130 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{6} + 3135 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{7}\right)} m^{4} + 2 \, {\left(9212 \, A a^{3} e^{8} + 180 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{3} - 252 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{4} + 753 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{5} - 6210 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{6} + 6077 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{7}\right)} m^{3} + 4 \, {\left(12215 \, A a^{3} e^{8} - 180 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e^{2} + 1350 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{3} - 876 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{4} + 1599 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{5} - 8916 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{6} + 6138 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{7}\right)} m^{2} + 144 \, {\left(35 \, B c^{3} d^{7} e + 481 \, A a^{3} e^{8} - 40 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d^{6} e^{2} + 140 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{5} e^{3} - 56 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{4} e^{4} + 70 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{3} e^{5} - 280 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d^{2} e^{6} + 140 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{7}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{8} m^{8} + 36 \, e^{8} m^{7} + 546 \, e^{8} m^{6} + 4536 \, e^{8} m^{5} + 22449 \, e^{8} m^{4} + 67284 \, e^{8} m^{3} + 118124 \, e^{8} m^{2} + 109584 \, e^{8} m + 40320 \, e^{8}}"," ",0,"(A*a^3*d*e^7*m^7 - 5040*B*c^3*d^8 + 40320*A*a^3*d*e^7 + 5760*(3*B*b*c^2 + A*c^3)*d^7*e - 20160*(B*b^2*c + (B*a + A*b)*c^2)*d^6*e^2 + 8064*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^5*e^3 - 10080*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^4*e^4 + 40320*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 20160*(B*a^3 + 3*A*a^2*b)*d^2*e^6 + (B*c^3*e^8*m^7 + 28*B*c^3*e^8*m^6 + 322*B*c^3*e^8*m^5 + 1960*B*c^3*e^8*m^4 + 6769*B*c^3*e^8*m^3 + 13132*B*c^3*e^8*m^2 + 13068*B*c^3*e^8*m + 5040*B*c^3*e^8)*x^8 + (5760*(3*B*b*c^2 + A*c^3)*e^8 + (B*c^3*d*e^7 + (3*B*b*c^2 + A*c^3)*e^8)*m^7 + (21*B*c^3*d*e^7 + 29*(3*B*b*c^2 + A*c^3)*e^8)*m^6 + 7*(25*B*c^3*d*e^7 + 49*(3*B*b*c^2 + A*c^3)*e^8)*m^5 + 35*(21*B*c^3*d*e^7 + 61*(3*B*b*c^2 + A*c^3)*e^8)*m^4 + 56*(29*B*c^3*d*e^7 + 134*(3*B*b*c^2 + A*c^3)*e^8)*m^3 + 28*(63*B*c^3*d*e^7 + 527*(3*B*b*c^2 + A*c^3)*e^8)*m^2 + 144*(5*B*c^3*d*e^7 + 103*(3*B*b*c^2 + A*c^3)*e^8)*m)*x^7 + (35*A*a^3*d*e^7 - (B*a^3 + 3*A*a^2*b)*d^2*e^6)*m^6 + (20160*(B*b^2*c + (B*a + A*b)*c^2)*e^8 + ((3*B*b*c^2 + A*c^3)*d*e^7 + 3*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^7 - (7*B*c^3*d^2*e^6 - 23*(3*B*b*c^2 + A*c^3)*d*e^7 - 90*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^6 - (105*B*c^3*d^2*e^6 - 205*(3*B*b*c^2 + A*c^3)*d*e^7 - 1098*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^5 - 5*(119*B*c^3*d^2*e^6 - 181*(3*B*b*c^2 + A*c^3)*d*e^7 - 1404*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^4 - (1575*B*c^3*d^2*e^6 - 2074*(3*B*b*c^2 + A*c^3)*d*e^7 - 25227*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^3 - 2*(959*B*c^3*d^2*e^6 - 1156*(3*B*b*c^2 + A*c^3)*d*e^7 - 25245*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m^2 - 24*(35*B*c^3*d^2*e^6 - 40*(3*B*b*c^2 + A*c^3)*d*e^7 - 2143*(B*b^2*c + (B*a + A*b)*c^2)*e^8)*m)*x^6 + (511*A*a^3*d*e^7 + 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 33*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*m^5 + (8064*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8 + (3*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^7 - (6*(3*B*b*c^2 + A*c^3)*d^2*e^6 - 75*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 - 31*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^6 + (42*B*c^3*d^3*e^5 - 108*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 723*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + 391*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^5 + (420*B*c^3*d^3*e^5 - 690*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 3405*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + 2581*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^4 + 2*(735*B*c^3*d^3*e^5 - 990*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 4101*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + 4772*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^3 + 4*(525*B*c^3*d^3*e^5 - 636*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 2370*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + 4891*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m^2 + 144*(7*B*c^3*d^3*e^5 - 8*(3*B*b*c^2 + A*c^3)*d^2*e^6 + 28*(B*b^2*c + (B*a + A*b)*c^2)*d*e^7 + 141*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*e^8)*m)*x^5 + (4025*A*a^3*d*e^7 - 6*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^4*e^4 + 180*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 445*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*m^4 + (10080*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8 + ((B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^7 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^7 - (15*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 27*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^7 - 32*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^6 + (30*(3*B*b*c^2 + A*c^3)*d^3*e^5 - 315*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 + 283*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^7 + 418*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^5 - (210*B*c^3*d^4*e^4 - 420*(3*B*b*c^2 + A*c^3)*d^3*e^5 + 2355*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 1449*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^7 - 2864*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^4 - (1260*B*c^3*d^4*e^4 - 1770*(3*B*b*c^2 + A*c^3)*d^3*e^5 + 7605*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 3748*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^7 - 10993*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^3 - 2*(1155*B*c^3*d^4*e^4 - 1410*(3*B*b*c^2 + A*c^3)*d^3*e^5 + 5295*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 2286*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^7 - 11656*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m^2 - 36*(35*B*c^3*d^4*e^4 - 40*(3*B*b*c^2 + A*c^3)*d^3*e^5 + 140*(B*b^2*c + (B*a + A*b)*c^2)*d^2*e^6 - 56*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*e^7 - 691*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*e^8)*m)*x^4 + (18424*A*a^3*d*e^7 + 24*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^5*e^3 - 156*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^4*e^4 + 2130*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 3135*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*m^3 + (40320*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8 + ((3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 + 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m^7 - (4*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 - 29*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 - 99*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m^6 + (60*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^5 - 96*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 + 331*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 + 1341*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m^5 - (120*(3*B*b*c^2 + A*c^3)*d^4*e^4 - 1080*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^5 + 844*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 - 1871*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 - 9585*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m^4 + 4*(210*B*c^3*d^5*e^3 - 330*(3*B*b*c^2 + A*c^3)*d^4*e^4 + 1545*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^5 - 816*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 + 1345*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 + 9648*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m^3 + 4*(630*B*c^3*d^5*e^3 - 780*(3*B*b*c^2 + A*c^3)*d^4*e^4 + 2970*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^5 - 1300*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 + 1793*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 + 21519*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m^2 + 48*(35*B*c^3*d^5*e^3 - 40*(3*B*b*c^2 + A*c^3)*d^4*e^4 + 140*(B*b^2*c + (B*a + A*b)*c^2)*d^3*e^5 - 56*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*e^6 + 70*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*e^7 + 2003*(B*a^2*b + A*a*b^2 + A*a^2*c)*e^8)*m)*x^3 + 2*(24430*A*a^3*d*e^7 - 180*(B*b^2*c + (B*a + A*b)*c^2)*d^6*e^2 + 252*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^5*e^3 - 753*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^4*e^4 + 6210*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 6077*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*m^2 + (20160*(B*a^3 + 3*A*a^2*b)*e^8 + (3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 + (B*a^3 + 3*A*a^2*b)*e^8)*m^7 - (3*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^6 - 93*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 - 34*(B*a^3 + 3*A*a^2*b)*e^8)*m^6 + (12*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^5 - 81*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^6 + 1155*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 + 478*(B*a^3 + 3*A*a^2*b)*e^8)*m^5 - (180*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^4 - 264*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^5 + 831*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^6 - 7275*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 - 3580*(B*a^3 + 3*A*a^2*b)*e^8)*m^4 + (360*(3*B*b*c^2 + A*c^3)*d^5*e^3 - 2880*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^4 + 2004*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^5 - 3951*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^6 + 24042*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 + 15289*(B*a^3 + 3*A*a^2*b)*e^8)*m^3 - 2*(1260*B*c^3*d^6*e^2 - 1620*(3*B*b*c^2 + A*c^3)*d^5*e^3 + 6390*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^4 - 2892*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^5 + 4119*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^6 - 18996*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 - 18353*(B*a^3 + 3*A*a^2*b)*e^8)*m^2 - 72*(35*B*c^3*d^6*e^2 - 40*(3*B*b*c^2 + A*c^3)*d^5*e^3 + 140*(B*b^2*c + (B*a + A*b)*c^2)*d^4*e^4 - 56*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^3*e^5 + 70*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*e^6 - 280*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*e^7 - 621*(B*a^3 + 3*A*a^2*b)*e^8)*m)*x^2 + 12*(5772*A*a^3*d*e^7 + 60*(3*B*b*c^2 + A*c^3)*d^7*e - 450*(B*b^2*c + (B*a + A*b)*c^2)*d^6*e^2 + 292*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^5*e^3 - 533*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^4*e^4 + 2972*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^3*e^5 - 2046*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*m + (40320*A*a^3*e^8 + (A*a^3*e^8 + (B*a^3 + 3*A*a^2*b)*d*e^7)*m^7 + (35*A*a^3*e^8 - 6*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 33*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^6 + (511*A*a^3*e^8 + 6*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 180*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 445*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^5 + (4025*A*a^3*e^8 - 24*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^4 + 156*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 2130*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 3135*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^4 + 2*(9212*A*a^3*e^8 + 180*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^3 - 252*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^4 + 753*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 6210*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 6077*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^3 + 4*(12215*A*a^3*e^8 - 180*(3*B*b*c^2 + A*c^3)*d^6*e^2 + 1350*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^3 - 876*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^4 + 1599*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 8916*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 6138*(B*a^3 + 3*A*a^2*b)*d*e^7)*m^2 + 144*(35*B*c^3*d^7*e + 481*A*a^3*e^8 - 40*(3*B*b*c^2 + A*c^3)*d^6*e^2 + 140*(B*b^2*c + (B*a + A*b)*c^2)*d^5*e^3 - 56*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^4*e^4 + 70*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^3*e^5 - 280*(B*a^2*b + A*a*b^2 + A*a^2*c)*d^2*e^6 + 140*(B*a^3 + 3*A*a^2*b)*d*e^7)*m)*x)*(e*x + d)^m/(e^8*m^8 + 36*e^8*m^7 + 546*e^8*m^6 + 4536*e^8*m^5 + 22449*e^8*m^4 + 67284*e^8*m^3 + 118124*e^8*m^2 + 109584*e^8*m + 40320*e^8)","B",0
2641,1,2156,0,0.449734," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(A a^{2} d e^{5} m^{5} - 120 \, B c^{2} d^{6} + 720 \, A a^{2} d e^{5} + 144 \, {\left(2 \, B b c + A c^{2}\right)} d^{5} e - 180 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{4} e^{2} + 240 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{3} e^{3} - 360 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{4} + {\left(B c^{2} e^{6} m^{5} + 15 \, B c^{2} e^{6} m^{4} + 85 \, B c^{2} e^{6} m^{3} + 225 \, B c^{2} e^{6} m^{2} + 274 \, B c^{2} e^{6} m + 120 \, B c^{2} e^{6}\right)} x^{6} + {\left(144 \, {\left(2 \, B b c + A c^{2}\right)} e^{6} + {\left(B c^{2} d e^{5} + {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m^{5} + 2 \, {\left(5 \, B c^{2} d e^{5} + 8 \, {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m^{4} + 5 \, {\left(7 \, B c^{2} d e^{5} + 19 \, {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m^{3} + 10 \, {\left(5 \, B c^{2} d e^{5} + 26 \, {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m^{2} + 12 \, {\left(2 \, B c^{2} d e^{5} + 27 \, {\left(2 \, B b c + A c^{2}\right)} e^{6}\right)} m\right)} x^{5} + {\left(20 \, A a^{2} d e^{5} - {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{4}\right)} m^{4} + {\left(180 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{6} + {\left({\left(2 \, B b c + A c^{2}\right)} d e^{5} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{6}\right)} m^{5} - {\left(5 \, B c^{2} d^{2} e^{4} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d e^{5} - 17 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{6}\right)} m^{4} - {\left(30 \, B c^{2} d^{2} e^{4} - 47 \, {\left(2 \, B b c + A c^{2}\right)} d e^{5} - 107 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{6}\right)} m^{3} - {\left(55 \, B c^{2} d^{2} e^{4} - 72 \, {\left(2 \, B b c + A c^{2}\right)} d e^{5} - 307 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{6}\right)} m^{2} - 6 \, {\left(5 \, B c^{2} d^{2} e^{4} - 6 \, {\left(2 \, B b c + A c^{2}\right)} d e^{5} - 66 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{6}\right)} m\right)} x^{4} + {\left(155 \, A a^{2} d e^{5} + 2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{3} e^{3} - 18 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{4}\right)} m^{3} + {\left(240 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{6} + {\left({\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{5} + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{6}\right)} m^{5} - 2 \, {\left(2 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{4} - 7 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{5} - 9 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{6}\right)} m^{4} + {\left(20 \, B c^{2} d^{3} e^{3} - 36 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{4} + 65 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{5} + 121 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{6}\right)} m^{3} + 4 \, {\left(15 \, B c^{2} d^{3} e^{3} - 20 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{4} + 28 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{5} + 93 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{6}\right)} m^{2} + 4 \, {\left(10 \, B c^{2} d^{3} e^{3} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e^{4} + 15 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{5} + 127 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{6}\right)} m\right)} x^{3} + {\left(580 \, A a^{2} d e^{5} - 6 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{4} e^{2} + 30 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{3} e^{3} - 119 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{4}\right)} m^{2} + {\left(360 \, {\left(B a^{2} + 2 \, A a b\right)} e^{6} + {\left({\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{5} + {\left(B a^{2} + 2 \, A a b\right)} e^{6}\right)} m^{5} - {\left(3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{4} - 16 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{5} - 19 \, {\left(B a^{2} + 2 \, A a b\right)} e^{6}\right)} m^{4} + {\left(12 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{3} - 36 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{4} + 89 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{5} + 137 \, {\left(B a^{2} + 2 \, A a b\right)} e^{6}\right)} m^{3} - {\left(60 \, B c^{2} d^{4} e^{2} - 84 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{3} + 123 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{4} - 194 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{5} - 461 \, {\left(B a^{2} + 2 \, A a b\right)} e^{6}\right)} m^{2} - 6 \, {\left(10 \, B c^{2} d^{4} e^{2} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{3} e^{3} + 15 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} e^{4} - 20 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e^{5} - 117 \, {\left(B a^{2} + 2 \, A a b\right)} e^{6}\right)} m\right)} x^{2} + 2 \, {\left(522 \, A a^{2} d e^{5} + 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{5} e - 33 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{4} e^{2} + 74 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{3} e^{3} - 171 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{4}\right)} m + {\left(720 \, A a^{2} e^{6} + {\left(A a^{2} e^{6} + {\left(B a^{2} + 2 \, A a b\right)} d e^{5}\right)} m^{5} + 2 \, {\left(10 \, A a^{2} e^{6} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{4} + 9 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{5}\right)} m^{4} + {\left(155 \, A a^{2} e^{6} + 6 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{3} - 30 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{4} + 119 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{5}\right)} m^{3} + 2 \, {\left(290 \, A a^{2} e^{6} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e^{2} + 33 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{3} - 74 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{4} + 171 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{5}\right)} m^{2} + 12 \, {\left(10 \, B c^{2} d^{5} e + 87 \, A a^{2} e^{6} - 12 \, {\left(2 \, B b c + A c^{2}\right)} d^{4} e^{2} + 15 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{3} e^{3} - 20 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d^{2} e^{4} + 30 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{5}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{6} m^{6} + 21 \, e^{6} m^{5} + 175 \, e^{6} m^{4} + 735 \, e^{6} m^{3} + 1624 \, e^{6} m^{2} + 1764 \, e^{6} m + 720 \, e^{6}}"," ",0,"(A*a^2*d*e^5*m^5 - 120*B*c^2*d^6 + 720*A*a^2*d*e^5 + 144*(2*B*b*c + A*c^2)*d^5*e - 180*(B*b^2 + 2*(B*a + A*b)*c)*d^4*e^2 + 240*(2*B*a*b + A*b^2 + 2*A*a*c)*d^3*e^3 - 360*(B*a^2 + 2*A*a*b)*d^2*e^4 + (B*c^2*e^6*m^5 + 15*B*c^2*e^6*m^4 + 85*B*c^2*e^6*m^3 + 225*B*c^2*e^6*m^2 + 274*B*c^2*e^6*m + 120*B*c^2*e^6)*x^6 + (144*(2*B*b*c + A*c^2)*e^6 + (B*c^2*d*e^5 + (2*B*b*c + A*c^2)*e^6)*m^5 + 2*(5*B*c^2*d*e^5 + 8*(2*B*b*c + A*c^2)*e^6)*m^4 + 5*(7*B*c^2*d*e^5 + 19*(2*B*b*c + A*c^2)*e^6)*m^3 + 10*(5*B*c^2*d*e^5 + 26*(2*B*b*c + A*c^2)*e^6)*m^2 + 12*(2*B*c^2*d*e^5 + 27*(2*B*b*c + A*c^2)*e^6)*m)*x^5 + (20*A*a^2*d*e^5 - (B*a^2 + 2*A*a*b)*d^2*e^4)*m^4 + (180*(B*b^2 + 2*(B*a + A*b)*c)*e^6 + ((2*B*b*c + A*c^2)*d*e^5 + (B*b^2 + 2*(B*a + A*b)*c)*e^6)*m^5 - (5*B*c^2*d^2*e^4 - 12*(2*B*b*c + A*c^2)*d*e^5 - 17*(B*b^2 + 2*(B*a + A*b)*c)*e^6)*m^4 - (30*B*c^2*d^2*e^4 - 47*(2*B*b*c + A*c^2)*d*e^5 - 107*(B*b^2 + 2*(B*a + A*b)*c)*e^6)*m^3 - (55*B*c^2*d^2*e^4 - 72*(2*B*b*c + A*c^2)*d*e^5 - 307*(B*b^2 + 2*(B*a + A*b)*c)*e^6)*m^2 - 6*(5*B*c^2*d^2*e^4 - 6*(2*B*b*c + A*c^2)*d*e^5 - 66*(B*b^2 + 2*(B*a + A*b)*c)*e^6)*m)*x^4 + (155*A*a^2*d*e^5 + 2*(2*B*a*b + A*b^2 + 2*A*a*c)*d^3*e^3 - 18*(B*a^2 + 2*A*a*b)*d^2*e^4)*m^3 + (240*(2*B*a*b + A*b^2 + 2*A*a*c)*e^6 + ((B*b^2 + 2*(B*a + A*b)*c)*d*e^5 + (2*B*a*b + A*b^2 + 2*A*a*c)*e^6)*m^5 - 2*(2*(2*B*b*c + A*c^2)*d^2*e^4 - 7*(B*b^2 + 2*(B*a + A*b)*c)*d*e^5 - 9*(2*B*a*b + A*b^2 + 2*A*a*c)*e^6)*m^4 + (20*B*c^2*d^3*e^3 - 36*(2*B*b*c + A*c^2)*d^2*e^4 + 65*(B*b^2 + 2*(B*a + A*b)*c)*d*e^5 + 121*(2*B*a*b + A*b^2 + 2*A*a*c)*e^6)*m^3 + 4*(15*B*c^2*d^3*e^3 - 20*(2*B*b*c + A*c^2)*d^2*e^4 + 28*(B*b^2 + 2*(B*a + A*b)*c)*d*e^5 + 93*(2*B*a*b + A*b^2 + 2*A*a*c)*e^6)*m^2 + 4*(10*B*c^2*d^3*e^3 - 12*(2*B*b*c + A*c^2)*d^2*e^4 + 15*(B*b^2 + 2*(B*a + A*b)*c)*d*e^5 + 127*(2*B*a*b + A*b^2 + 2*A*a*c)*e^6)*m)*x^3 + (580*A*a^2*d*e^5 - 6*(B*b^2 + 2*(B*a + A*b)*c)*d^4*e^2 + 30*(2*B*a*b + A*b^2 + 2*A*a*c)*d^3*e^3 - 119*(B*a^2 + 2*A*a*b)*d^2*e^4)*m^2 + (360*(B*a^2 + 2*A*a*b)*e^6 + ((2*B*a*b + A*b^2 + 2*A*a*c)*d*e^5 + (B*a^2 + 2*A*a*b)*e^6)*m^5 - (3*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^4 - 16*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^5 - 19*(B*a^2 + 2*A*a*b)*e^6)*m^4 + (12*(2*B*b*c + A*c^2)*d^3*e^3 - 36*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^4 + 89*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^5 + 137*(B*a^2 + 2*A*a*b)*e^6)*m^3 - (60*B*c^2*d^4*e^2 - 84*(2*B*b*c + A*c^2)*d^3*e^3 + 123*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^4 - 194*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^5 - 461*(B*a^2 + 2*A*a*b)*e^6)*m^2 - 6*(10*B*c^2*d^4*e^2 - 12*(2*B*b*c + A*c^2)*d^3*e^3 + 15*(B*b^2 + 2*(B*a + A*b)*c)*d^2*e^4 - 20*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e^5 - 117*(B*a^2 + 2*A*a*b)*e^6)*m)*x^2 + 2*(522*A*a^2*d*e^5 + 12*(2*B*b*c + A*c^2)*d^5*e - 33*(B*b^2 + 2*(B*a + A*b)*c)*d^4*e^2 + 74*(2*B*a*b + A*b^2 + 2*A*a*c)*d^3*e^3 - 171*(B*a^2 + 2*A*a*b)*d^2*e^4)*m + (720*A*a^2*e^6 + (A*a^2*e^6 + (B*a^2 + 2*A*a*b)*d*e^5)*m^5 + 2*(10*A*a^2*e^6 - (2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^4 + 9*(B*a^2 + 2*A*a*b)*d*e^5)*m^4 + (155*A*a^2*e^6 + 6*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^3 - 30*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^4 + 119*(B*a^2 + 2*A*a*b)*d*e^5)*m^3 + 2*(290*A*a^2*e^6 - 12*(2*B*b*c + A*c^2)*d^4*e^2 + 33*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^3 - 74*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^4 + 171*(B*a^2 + 2*A*a*b)*d*e^5)*m^2 + 12*(10*B*c^2*d^5*e + 87*A*a^2*e^6 - 12*(2*B*b*c + A*c^2)*d^4*e^2 + 15*(B*b^2 + 2*(B*a + A*b)*c)*d^3*e^3 - 20*(2*B*a*b + A*b^2 + 2*A*a*c)*d^2*e^4 + 30*(B*a^2 + 2*A*a*b)*d*e^5)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)","B",0
2642,1,538,0,0.405455," ","integrate((B*x+A)*(e*x+d)^m*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left(A a d e^{3} m^{3} - 6 \, B c d^{4} + 24 \, A a d e^{3} + 8 \, {\left(B b + A c\right)} d^{3} e - 12 \, {\left(B a + A b\right)} d^{2} e^{2} + {\left(B c e^{4} m^{3} + 6 \, B c e^{4} m^{2} + 11 \, B c e^{4} m + 6 \, B c e^{4}\right)} x^{4} + {\left(8 \, {\left(B b + A c\right)} e^{4} + {\left(B c d e^{3} + {\left(B b + A c\right)} e^{4}\right)} m^{3} + {\left(3 \, B c d e^{3} + 7 \, {\left(B b + A c\right)} e^{4}\right)} m^{2} + 2 \, {\left(B c d e^{3} + 7 \, {\left(B b + A c\right)} e^{4}\right)} m\right)} x^{3} + {\left(9 \, A a d e^{3} - {\left(B a + A b\right)} d^{2} e^{2}\right)} m^{2} + {\left(12 \, {\left(B a + A b\right)} e^{4} + {\left({\left(B b + A c\right)} d e^{3} + {\left(B a + A b\right)} e^{4}\right)} m^{3} - {\left(3 \, B c d^{2} e^{2} - 5 \, {\left(B b + A c\right)} d e^{3} - 8 \, {\left(B a + A b\right)} e^{4}\right)} m^{2} - {\left(3 \, B c d^{2} e^{2} - 4 \, {\left(B b + A c\right)} d e^{3} - 19 \, {\left(B a + A b\right)} e^{4}\right)} m\right)} x^{2} + {\left(26 \, A a d e^{3} + 2 \, {\left(B b + A c\right)} d^{3} e - 7 \, {\left(B a + A b\right)} d^{2} e^{2}\right)} m + {\left(24 \, A a e^{4} + {\left(A a e^{4} + {\left(B a + A b\right)} d e^{3}\right)} m^{3} + {\left(9 \, A a e^{4} - 2 \, {\left(B b + A c\right)} d^{2} e^{2} + 7 \, {\left(B a + A b\right)} d e^{3}\right)} m^{2} + 2 \, {\left(3 \, B c d^{3} e + 13 \, A a e^{4} - 4 \, {\left(B b + A c\right)} d^{2} e^{2} + 6 \, {\left(B a + A b\right)} d e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"(A*a*d*e^3*m^3 - 6*B*c*d^4 + 24*A*a*d*e^3 + 8*(B*b + A*c)*d^3*e - 12*(B*a + A*b)*d^2*e^2 + (B*c*e^4*m^3 + 6*B*c*e^4*m^2 + 11*B*c*e^4*m + 6*B*c*e^4)*x^4 + (8*(B*b + A*c)*e^4 + (B*c*d*e^3 + (B*b + A*c)*e^4)*m^3 + (3*B*c*d*e^3 + 7*(B*b + A*c)*e^4)*m^2 + 2*(B*c*d*e^3 + 7*(B*b + A*c)*e^4)*m)*x^3 + (9*A*a*d*e^3 - (B*a + A*b)*d^2*e^2)*m^2 + (12*(B*a + A*b)*e^4 + ((B*b + A*c)*d*e^3 + (B*a + A*b)*e^4)*m^3 - (3*B*c*d^2*e^2 - 5*(B*b + A*c)*d*e^3 - 8*(B*a + A*b)*e^4)*m^2 - (3*B*c*d^2*e^2 - 4*(B*b + A*c)*d*e^3 - 19*(B*a + A*b)*e^4)*m)*x^2 + (26*A*a*d*e^3 + 2*(B*b + A*c)*d^3*e - 7*(B*a + A*b)*d^2*e^2)*m + (24*A*a*e^4 + (A*a*e^4 + (B*a + A*b)*d*e^3)*m^3 + (9*A*a*e^4 - 2*(B*b + A*c)*d^2*e^2 + 7*(B*a + A*b)*d*e^3)*m^2 + 2*(3*B*c*d^3*e + 13*A*a*e^4 - 4*(B*b + A*c)*d^2*e^2 + 6*(B*a + A*b)*d*e^3)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
2643,0,0,0,0.406398," ","integrate((B*x+A)*(e*x+d)^m/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^m/(c*x^2 + b*x + a), x)","F",0
2644,0,0,0,0.428532," ","integrate((B*x+A)*(e*x+d)^m/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^m/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2645,0,0,0,0.401980," ","integrate((B*x+A)*(e*x+d)^(1+m)/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m + 1}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^(m + 1)/(c*x^2 + b*x + a), x)","F",0
2646,0,0,0,0.480758," ","integrate((B*x+A)*(e*x+d)^(-3-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}, x\right)"," ",0,"integral((B*x + A)*(c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 3), x)","F",0
